Research ArticleModel Predictive Voltage Control with Optimal Duty Cycle forThree-Phase Grid-Connected Inverter

Shahrouz Ebrahimpanah Qihong Chen Liyan Zhang andMisbawu Adam

School of Automation Wuhan University of Technology Wuhan 430070 China

Correspondence should be addressed to Qihong Chen chenqhwhuteducn

Received 22 January 2019 Revised 13 April 2019 Accepted 22 April 2019 Published 12 May 2019

Academic Editor Carlos-Andres Garcıa

Copyright copy 2019 Shahrouz Ebrahimpanah et alThis is an open access article distributed under theCreativeCommons AttributionLicensewhichpermits unrestricteduse distribution and reproduction in anymedium provided the original work is properly cited

This paper proposes a model predictive voltage control (MPVC) strategy with duty cycle control for grid-connected three-phaseinverters with output LCL filter The model of the system is used to predict the capacitor filter voltage according to the futureoutput current for each possible switching state at each sampling period Then the cost function for each prediction is determinedand the switching state is selected In the proposed method two voltage vectors are applied during one sampling interval to achievebetter steady-state performance Finally the optimal duration of the nonzero voltage vector is defined based on the duty cycleoptimization which is vital to the control system The proposed strategy offers a better reference tracking error with less THDin linear and nonlinear load situations The effectiveness of the proposed method has been verified by MATLABSimulink andexperimental results exhibit a better steady-state performance with less sampling frequency

1 Introduction

Renewable energy generation systems such as photovoltaicand wind turbine connected to power grid are drawingmore and more attention in recent years The grid-connectedinverters play an important role in the distributed generationsystems [1 2] For this reasons inverter control plays asignificant role in the performance of the grid-tied inverterssystem Therefore selecting a better power converter andbetter control method can lead to efficient system operationand better performance with less total harmonic distortionsto achieve better grid current quality [3 4] Three-phaseinverter with output LCL filter connected to the grid is oneof the most popular applications in the power systems totransfer DC voltage source to a symmetrical three-phase ACsinusoidal voltageThus it can supply symmetrical sinusoidalvoltages to the consumers in the standalone power systemswithout using of a magnetic transformer [5]

The applications with LC or LCL filter the output voltageis selected to regulate the inverter while the output current ischosen for inverter control in L-filter based applications Forcontrolling voltage many classical control techniques such aslinear proportional integral derivative (PID) controllers hys-teresis regulators based on pulse width modulation (PWM)

variable structure control open-loop feed forward con-trollers pole placement controllers and sliding mode controlhave been previously studied Most of these complex controlmethods require 3D-space vector modulation [6 7] which isquite complex in nature time consuming and complicatedsoftware and digital implementation But recently the finitecontrol set model predictive control (FCS-MPC) has beenfound as a new control scheme in power electronics anddrives systems [5] This method has been applied in widerange of power converters applications compared to the clas-sical controlmethods at lower switching frequency operationThis is due to its simple nature fast dynamic responseand nonlinearities in the control design Thus during suchconditions the FCS-MPC strategy provides better steady-state performance [8 9] However the conventional finitecontrol set model predictive voltage control (FCS-MPVC)employs one voltage vector during one sampling period andoptimization of duty cycle is not involved in the controlmethod therefore it needs a high sampling frequency toachieve a better performance Due to these reasons researchon new strategies to obtain better steady-state performancein lower sampling frequency is important [10ndash13]

This paper presents a new proposed method (MPVCwith duty cycle optimization) to control the grid-connected

HindawiJournal of Control Science and EngineeringVolume 2019 Article ID 8951794 13 pageshttpsdoiorg10115520198951794

2 Journal of Control Science and Engineering

GND

Grid

3-Phase

inverter

i Ｃ＝ ＣＡ

６＞＝

２＝

Figure 1 Block diagram of a two-level three-phase inverter withoutput LCL filter connected to the grid

three-phase inverter with output LCL filter In this proposedstrategy predictive voltage is determined by predicted out-put current which means there are two prediction stepsfirst output current prediction and then voltage predictionIt can compensate for the effects of uncertainties in theload Therefore it is suitable for any type of load such asbalanced unbalanced and nonlinear loads In addition ithas better dynamic response However in the conventionalstrategy output voltage is predicted directly which needs highsampling time to get better performance From the otherpoint of view the proposed method uses a nonzero voltagevector and a zero voltage vector during one sampling periodThen the duration of the nonzero and zero voltage vectorsare determined according to the duty cycle optimizationwhich is key in the control system to avoid any effects on thedynamic response and obtain better steady-state performanceat lower sampling time [14ndash18] This paper is organized asfollows Section 2 introduces inverter analysis Principle ofMPVC is surveyed in Section 3 Then Section 4 presentssimulation and experimental results Finally conclusions aresummed up in Section 5

2 Inverter Analysis

This paper connected the three-phase inverter with outputLCL filter to the grid which is shown in Figure 1

The switching state of 6 power switches is represented bygating signals 119878119886 119878119887 and 119878119888 found as follows [18]

119878119886 = 1 119894119891 1198781 119900119899 119886119899119889 1198784 1199001198911198910 119894119891 1198781 119900119891119891 119886119899119889 1198784 119900119899 (1)

119878119887 = 1 119894119891 1198782 119900119899 119886119899119889 1198785 1199001198911198910 119894119891 1198782 119900119891119891 119886119899119889 1198785 119900119899 (2)

119878119888 = 1 119894119891 1198783 119900119899 119886119899119889 1198786 1199001198911198910 119894119891 1198783 119900119891119891 119886119899119889 1198786 119900119899 (3)

And the switching state vector can be determined in vectorialform

119878 = 23 (119878119886 + 119886119878119887 + 1198862119878119888) (4)

where a=119890119895(2Π3)= - (12) + j(radic32)

V1 (100)

V2 (110)V3 (010)

V4 (011)

V5 (001) V6 (101)

V0 (000)V7 (111)

Im

Re

Figure 2 Possible voltage vectors generated by the inverter

The output voltage space vectors are expressed by

119881 = 23 (119881119886119873 + 119886119881119887119873 + 1198862119881119888119873) (5)

where 119881119886119873 119881119887119873 and 119881119888119873 are the phase-to-neutral (N)voltages of the inverter where N is the negative terminalof the DC-link Therefore output voltage vector V can beexpress based on the switching state vector S and dc-linkvoltage as the following

119881 = 119881119889119888119878 (6)

where 119881119889119888 is the DC source voltageAccording to Figure 2 there are seven different possible

combinations of the switching states [18]Using the vectorial format the output current 119894 the

capacitor filter voltage 119881119888 and the grid current 119894119892 can beexpressed as space vectors and are expressed as

119894 = 23 (119894119886 + 119886119894119887 + 1198862119894119888) (7)

119881119888 = 23 (119881119888119886 + 119886119881119888119887 + 1198862119881119888119888) (8)

119894119892 = 23 (119894119892119886 + 119886119894119892119887 + 1198862119894119892119888) (9)

As shown in Figure 1 the LCL filter is modelled in the blockdiagram This model can be expressed by two equations ofinductance dynamics and the capacitor dynamics [19]

The dynamic behaviour of the output current can bedefined by the following

1198711198911 119889119894119889119905 = 119881 minus 119881119888 minus 119877119888 (119894 minus 119894119892) (10)

where 1198711198911 is the first filter inductance and 119877119888 is the dampingresistance

The equation of the filter capacitor is defined as

119862119889119881119888119889119905 = 119894 minus 119894119892 (11)

where C is the filter capacitance

Journal of Control Science and Engineering 3

L1

DC

L1

L1

L2

L2

L2

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6Rc Rc Rc

i

MPCMinimization

of Cost Function

Voltage Reference

S1 S2S3 S4S5 S6

Vc_ref Vc(k+1)

i(k)

Ｃ＝

ＣＡ

+minus

Figure 3 Control diagram of a three-phase inverter connected to the grid

3 Principle of MPVC

Model predictive capacitor filter voltage control design andimplement consist as the following steps

(1) Using a discrete-time model to predict the behaviourof current and voltage for the next time step

(2) Minimizing the cost function to find the best voltagevector 119881(119896)

(3) Determining the duration for the nonzero and zerovoltage vector

The controller design and controller parametersrsquo adjustmentwill be more difficult whereas an LCL filter is involved at theoutput of the inverter So in the applications that include anLCL filter the capacitor filter voltage is regulated while thegrid current is controlled in L-filter based applications As theproposed model predictive voltage control scheme is shownin Figure 3 this method uses the discrete-time model for thethree-leg inverter and LCL filter to predict the capacitor filtervoltage based on prediction of the output current and thenselects a switching state based on the minimization of costfunction for each sampling time [20 21]

Predictions of the future output current and capacitorfilter voltage at the moment of (k + 1) for different valuesof voltage vector 119881119896 will be acquired based on discrete-timeequation respectively as follows [7 18 22]

119894 (119896 + 1)= 119894 (119896) + 119879119904119901

119871 [119881 (119896) minus 119881119888 (119896) minus 119877119888 (119894 (119896) minus 119894119892 (119896))](12)

119881119888 (119896 + 1) = 119881119888 ((119896) + 119879119904119901119862 (119894 (119896 + 1) minus 119894119892 (119896)) (13)

And now by substituting (12) into (13) the following expres-sion is obtained for the future capacitor filter voltage at (119896 +1)119905ℎ instant

119881119888 (119896 + 1) = 119881119888 ((119896) + 119879119904119901119862 119894 (119896)

+ 119879119904119901119871 [119881 (119896) minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))]

minus 119894119892 (119896)

(14)

31 Minimization of Cost Function By considering an outputLCL filter in this method a different analysis and moreaccurate mathematical model is given for controlling theoutput voltage and consequently a better output voltagequality defined as the control objectives in the cost functionHence to select the optimal voltage vector 119881(119896) applied bythe inverter the seven 119881119888((119896 + 1) are compared using acost function 119892 to find the best voltage vector 119881(119896) whichminimizes this function for selecting and applying at the nextsampling instant [20 21]

Therefore a cost function 119892 will be expressed by mea-suring the error between the references and the predictedcapacitor filter voltage

119892 = 10038161003816100381610038161003816119877119890 [119881119888 119903119890119891 minus 119881119888 (119896 + 1)]10038161003816100381610038161003816+ 10038161003816100381610038161003816119868119898 [119881119888 119903119890119891 minus 119881119888 (119896 + 1)]10038161003816100381610038161003816

(15)

where 119881119888(119896 + 1) is predicted from (14) and 119881119888 119903119890119891 is obtainedfrom

119881119888 119903119890119891 = 23 (119881119888119886 119903119890119891 + 119886119881119888119887 119903119890119891 + 1198862119881119888119888 119903119890119891) (16)

4 Journal of Control Science and Engineering

where 119881119888119886 119903119890119891 119881119888119887 119903119890119891 and 119881119888119888 119903119890119891 are the reference capacitorfilter voltage for phases a b and c which are generated bysine wave creator with the 120∘ phase displacement

The capacitor filter voltage equals its reference when 119892 =0 Therefore the goal of the cost function is considered toachieve 119892 value close to zero In other words this paper islooking for less capacitor filter voltage error to choose thevoltage vector and then applied to the next sampling instant[5 19]

32 Duty Cycle Determination In the proposed MPVCdetermination of the duration for the nonzero voltage vectoris the key to control system Hence slopes of the capacitor

filter voltage for the nonzero voltage 1198781 vector and the zerovoltage vector 1198780 will be calculated easily from (11) [14 15 23]

1199041= 119894 (119896) + (119879119904119901119871) [119881119899minus119911 minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)

119862(17)

1199040 = 119894 (119896) + (119879119904119901119871) [minus119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)119862 (18)

where 119881119899minus119911 is the best voltage vector which minimizes thecost function

Thus capacitor filter voltage at the end of the next controlcycle will be written as follows

119881119888 (119896 + 1) = 119881119888 ((119896)+ 119879119900119901119905 119894 (119896) + (119879119904119901119871) [119881119899minus119911 minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896) + 119879119911 119894 (119896) + (119879119904119901119871) [minus119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)

119862(19)

119879119900119901119905 + 119879119911 = 119879119904119901 (20)

119881119899minus119911 + 119881119911 = 119881 (119896) (21)

where 119879119900119901119905 119886119899119889 119879119911 are the optimal duration of the nonzeroand zero voltage vectors respectively

Now by replacing (17) and (18) into (19) the capacitorfilter voltage at the end of the next control period can beobtained by

119881119888 (119896 + 1) = 119881119888 + 1199041 times 119879119900119901119905 + 1199040 times (119879119904119901 minus 119879119900119901119905) (22)

The optimal duration of119879119900119901119905 that minimizes the cost functionduring a control period satisfies the following condition [8]

120597119892120597119879119900119901119905 = 0 (23)

By replacing (22) into (15) and solving (23) the duration ofthe nonzero vector can be expressed as

119879119900119901119905 =10038161003816100381610038161003816119881119888 119903119890119891 minus 119881119888 (119896) minus 1199040 times 1198791199041199011003816100381610038161003816100381610038161003816100381610038161199041 minus 11990401003816100381610038161003816 (24)

It is necessary to consider that the value of119879119900119901119905 can be equaledto zero only if 119879119900119901119905 is less than zero and 119879119900119901119905 is more than 119879119904119901then it will be equaled to 119879119904119901[16]33 Implemented Control Flowchart Flowchart of the pro-posed MPVC with duty cycle optimization for obtaining theoptimal output voltage vector and their optimal durations isillustrated in Figure 4

4 Simulation and Experimental Results

41 Simulation Results To validate the proposed MPVC asimulation model of a two-level three-phase inverter with

output LCL filter connected to the grid has been devel-oped with the parameters as shown in Table 1 by usingMATLABSimulink under various conditions The simulatedmodel is built based on the system shown in Figure 5The simulation analysis is mainly about robustness of theproposed MPVC strategy Hence for this purpose the per-formance of the proposed strategy will be compared with theconventional scheme

First of all by comparison of grid current waveforms forthe proposed and conventional methods it is clear that theproposed MPVC has much less distortion in output currentthan conventional MPVC and the proposedMPCCmethodsand even conventional MPVC has better results as comparedto the conventional MPCC Therefore it is going to presentless current ripples and lower current harmonics as seen inFigure 6

Then to proof this stability for the proposed method thecapacitor filter voltage will be explored in simulation As it isshown in Figure 7 there is a good tracking of capacitor filtervoltage to its reference in the proposed method and even bychanging the voltage level the proposed method tracking thevoltage reference is still more accurate and has lower ripplesthan the conventional Hence it could be a reason to havelower current harmonics

Figures 8 and 9 show a harmonic spectrum analysis atthe sampling times 119879119904119901 =50120583s for the grid current and thecapacitor filter voltage respectively From one point of viewit can be clearly seen the current THDs in the proposedmethods which are 191 and 254 for MPVC and MPCCrespectively much better than the conventional strategiesresults which are 295 for MPVC and 429 for MPCCMoreover the conventional MPVC gets better results as

Journal of Control Science and Engineering 5

No

Startup

Measure

In MATLABSimulink

Yes

Wait for next sampling

Apply Optimal Vector and Duty Cycle

Calculate s1 s0

g 1opt = infin i = minus1

i = i + 1

i = 7

(( + ) = (() +

() +

[() minus () minus ( () minus ())] minus ()

( + ) = () +

[ () minus () minus (() minus ())]

=[_ minus ( + )]

+[_ minus ( + )]

If lt = = =

=

_ minus ()minus times

minus

= minus

Figure 4 Flowchart of the proposed MPVC with duty cycle optimization

Table 1 Parameters used for the simulation and experiment

Variable System Parameters Value119881119889119888 DC-Link voltage 700V119890 Grid Voltage (RMS) 220V119891 Line voltage frequency 50HzV119903119890119891 Reference voltage peak amplitude 311 amp 240V1198712 Filter inductance 1mH1198711 Filter Inductance 3mH119862119891 Filter Capacitance 15120583F119877119888 Damping Resistance 10Ω119879119904119901 Sampling time 25 to 100 120583s

6 Journal of Control Science and Engineering

L1

DC

L1

L1

L2

L2

L2

Rc

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6

+- v

-i+

-i+

-i+

iaibicVdcVc_aVc_bVc_cVa_ref

Vb_ref

Vc_ref

MPVCMPV

+ -v

+ -v

+ -v

-i+

-i+

-i+

ig_a

ig_b

ig_c

S1S4S2S5S3S6

Rc

Rc

+minus

(a)

1

gt=

gt=

gt=

Boolean

Boolean

Boolean

NOT

234567

1

2

NOT

3

4

NOT

5

6

ta

tb

tc

iaibic

VdcVc_aVc_bVc_c

Va_ref

Vb_ref

Vc_ref

MPVC

S1

S4

S2

S5

S3

S6

567 Ig_c

Ig_bIg_a

(b)

Figure 5 Simulation diagram in MATLABSimulink (a) Proposed MPVC with duty cycle control for a three-phase inverter connected tothe grid (b) Subsystem of the MPVC

compared to the conventional MPCC which proves thebenefits of controlling the capacitor filter voltage Thereforethe current waveforms are more closed to sinusoidal whichproves the efficiency of proposed MPVC with optimal dutycycle control On the other side comparing the THD ofcapacitor filter voltage for two methods shows that the

proposed MPVC still has a better performance by 405than conventional by 603 So in the conventional strategyto achieve less THD the sampling frequency is neededto increase and increasing the sampling frequency can bea reason for higher hardware expenses However in theproposed MPVC this problem is solved by using duty cycle

Journal of Control Science and Engineering 7

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(a)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(b)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(c)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(d)

Figure 6 Simulation waveform of three phase grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC(c) the conventional MPCC and (d) the proposed MPCC

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(a)

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(b)

Figure 7 Simulation waveform of capacitor filter voltage (phase a) at the sampling time 119879119904119901 =50120583s for two different voltage levels (a) theconventional MPVC (b) the proposed MPVC

optimization then this goal is obtained without increasingthe sampling time

Figure 10 shows a bar chart of THD for the grid currentand the capacitor filter voltage in different methods withvarious sampling times and it can prove that the proposedmethod has significantly lower THD values than the con-ventional one because of the idea of duty cycle optimiza-tion As shown in Figure 10 the proposed method can setmore substantial advantages in systems by a larger samplingfrequency

Figure 11 shows the results for a step change in theamplitude of the reference voltage from 311 V to 240 VTherefore the grid current also will be changed accordingto the reference voltage step change (see Figure 12) It canbe observed that by following the change of the referencevoltage the amplitude of the grid currents will be changedwith extremely rapid dynamics while being not affectedby this step change However as shown in Figure 7 theamplitude of the capacitor filter voltage does not gain itsreference in a short timeOverall by comparing twomethods

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

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Journal of Control Science and Engineering 3

L1

DC

L1

L1

L2

L2

L2

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6Rc Rc Rc

i

MPCMinimization

of Cost Function

Voltage Reference

S1 S2S3 S4S5 S6

Vc_ref Vc(k+1)

i(k)

Ｃ＝

ＣＡ

+minus

Figure 3 Control diagram of a three-phase inverter connected to the grid

3 Principle of MPVC

Model predictive capacitor filter voltage control design andimplement consist as the following steps

(1) Using a discrete-time model to predict the behaviourof current and voltage for the next time step

(2) Minimizing the cost function to find the best voltagevector 119881(119896)

(3) Determining the duration for the nonzero and zerovoltage vector

The controller design and controller parametersrsquo adjustmentwill be more difficult whereas an LCL filter is involved at theoutput of the inverter So in the applications that include anLCL filter the capacitor filter voltage is regulated while thegrid current is controlled in L-filter based applications As theproposed model predictive voltage control scheme is shownin Figure 3 this method uses the discrete-time model for thethree-leg inverter and LCL filter to predict the capacitor filtervoltage based on prediction of the output current and thenselects a switching state based on the minimization of costfunction for each sampling time [20 21]

Predictions of the future output current and capacitorfilter voltage at the moment of (k + 1) for different valuesof voltage vector 119881119896 will be acquired based on discrete-timeequation respectively as follows [7 18 22]

119894 (119896 + 1)= 119894 (119896) + 119879119904119901

119871 [119881 (119896) minus 119881119888 (119896) minus 119877119888 (119894 (119896) minus 119894119892 (119896))](12)

119881119888 (119896 + 1) = 119881119888 ((119896) + 119879119904119901119862 (119894 (119896 + 1) minus 119894119892 (119896)) (13)

And now by substituting (12) into (13) the following expres-sion is obtained for the future capacitor filter voltage at (119896 +1)119905ℎ instant

119881119888 (119896 + 1) = 119881119888 ((119896) + 119879119904119901119862 119894 (119896)

+ 119879119904119901119871 [119881 (119896) minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))]

minus 119894119892 (119896)

(14)

31 Minimization of Cost Function By considering an outputLCL filter in this method a different analysis and moreaccurate mathematical model is given for controlling theoutput voltage and consequently a better output voltagequality defined as the control objectives in the cost functionHence to select the optimal voltage vector 119881(119896) applied bythe inverter the seven 119881119888((119896 + 1) are compared using acost function 119892 to find the best voltage vector 119881(119896) whichminimizes this function for selecting and applying at the nextsampling instant [20 21]

Therefore a cost function 119892 will be expressed by mea-suring the error between the references and the predictedcapacitor filter voltage

119892 = 10038161003816100381610038161003816119877119890 [119881119888 119903119890119891 minus 119881119888 (119896 + 1)]10038161003816100381610038161003816+ 10038161003816100381610038161003816119868119898 [119881119888 119903119890119891 minus 119881119888 (119896 + 1)]10038161003816100381610038161003816

(15)

where 119881119888(119896 + 1) is predicted from (14) and 119881119888 119903119890119891 is obtainedfrom

119881119888 119903119890119891 = 23 (119881119888119886 119903119890119891 + 119886119881119888119887 119903119890119891 + 1198862119881119888119888 119903119890119891) (16)

4 Journal of Control Science and Engineering

where 119881119888119886 119903119890119891 119881119888119887 119903119890119891 and 119881119888119888 119903119890119891 are the reference capacitorfilter voltage for phases a b and c which are generated bysine wave creator with the 120∘ phase displacement

The capacitor filter voltage equals its reference when 119892 =0 Therefore the goal of the cost function is considered toachieve 119892 value close to zero In other words this paper islooking for less capacitor filter voltage error to choose thevoltage vector and then applied to the next sampling instant[5 19]

32 Duty Cycle Determination In the proposed MPVCdetermination of the duration for the nonzero voltage vectoris the key to control system Hence slopes of the capacitor

filter voltage for the nonzero voltage 1198781 vector and the zerovoltage vector 1198780 will be calculated easily from (11) [14 15 23]

1199041= 119894 (119896) + (119879119904119901119871) [119881119899minus119911 minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)

119862(17)

1199040 = 119894 (119896) + (119879119904119901119871) [minus119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)119862 (18)

where 119881119899minus119911 is the best voltage vector which minimizes thecost function

Thus capacitor filter voltage at the end of the next controlcycle will be written as follows

119881119888 (119896 + 1) = 119881119888 ((119896)+ 119879119900119901119905 119894 (119896) + (119879119904119901119871) [119881119899minus119911 minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896) + 119879119911 119894 (119896) + (119879119904119901119871) [minus119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)

119862(19)

119879119900119901119905 + 119879119911 = 119879119904119901 (20)

119881119899minus119911 + 119881119911 = 119881 (119896) (21)

where 119879119900119901119905 119886119899119889 119879119911 are the optimal duration of the nonzeroand zero voltage vectors respectively

Now by replacing (17) and (18) into (19) the capacitorfilter voltage at the end of the next control period can beobtained by

119881119888 (119896 + 1) = 119881119888 + 1199041 times 119879119900119901119905 + 1199040 times (119879119904119901 minus 119879119900119901119905) (22)

The optimal duration of119879119900119901119905 that minimizes the cost functionduring a control period satisfies the following condition [8]

120597119892120597119879119900119901119905 = 0 (23)

By replacing (22) into (15) and solving (23) the duration ofthe nonzero vector can be expressed as

119879119900119901119905 =10038161003816100381610038161003816119881119888 119903119890119891 minus 119881119888 (119896) minus 1199040 times 1198791199041199011003816100381610038161003816100381610038161003816100381610038161199041 minus 11990401003816100381610038161003816 (24)

It is necessary to consider that the value of119879119900119901119905 can be equaledto zero only if 119879119900119901119905 is less than zero and 119879119900119901119905 is more than 119879119904119901then it will be equaled to 119879119904119901[16]33 Implemented Control Flowchart Flowchart of the pro-posed MPVC with duty cycle optimization for obtaining theoptimal output voltage vector and their optimal durations isillustrated in Figure 4

4 Simulation and Experimental Results

41 Simulation Results To validate the proposed MPVC asimulation model of a two-level three-phase inverter with

output LCL filter connected to the grid has been devel-oped with the parameters as shown in Table 1 by usingMATLABSimulink under various conditions The simulatedmodel is built based on the system shown in Figure 5The simulation analysis is mainly about robustness of theproposed MPVC strategy Hence for this purpose the per-formance of the proposed strategy will be compared with theconventional scheme

First of all by comparison of grid current waveforms forthe proposed and conventional methods it is clear that theproposed MPVC has much less distortion in output currentthan conventional MPVC and the proposedMPCCmethodsand even conventional MPVC has better results as comparedto the conventional MPCC Therefore it is going to presentless current ripples and lower current harmonics as seen inFigure 6

Then to proof this stability for the proposed method thecapacitor filter voltage will be explored in simulation As it isshown in Figure 7 there is a good tracking of capacitor filtervoltage to its reference in the proposed method and even bychanging the voltage level the proposed method tracking thevoltage reference is still more accurate and has lower ripplesthan the conventional Hence it could be a reason to havelower current harmonics

Figures 8 and 9 show a harmonic spectrum analysis atthe sampling times 119879119904119901 =50120583s for the grid current and thecapacitor filter voltage respectively From one point of viewit can be clearly seen the current THDs in the proposedmethods which are 191 and 254 for MPVC and MPCCrespectively much better than the conventional strategiesresults which are 295 for MPVC and 429 for MPCCMoreover the conventional MPVC gets better results as

Journal of Control Science and Engineering 5

No

Startup

Measure

In MATLABSimulink

Yes

Wait for next sampling

Apply Optimal Vector and Duty Cycle

Calculate s1 s0

g 1opt = infin i = minus1

i = i + 1

i = 7

(( + ) = (() +

() +

[() minus () minus ( () minus ())] minus ()

( + ) = () +

[ () minus () minus (() minus ())]

=[_ minus ( + )]

+[_ minus ( + )]

If lt = = =

=

_ minus ()minus times

minus

= minus

Figure 4 Flowchart of the proposed MPVC with duty cycle optimization

Table 1 Parameters used for the simulation and experiment

Variable System Parameters Value119881119889119888 DC-Link voltage 700V119890 Grid Voltage (RMS) 220V119891 Line voltage frequency 50HzV119903119890119891 Reference voltage peak amplitude 311 amp 240V1198712 Filter inductance 1mH1198711 Filter Inductance 3mH119862119891 Filter Capacitance 15120583F119877119888 Damping Resistance 10Ω119879119904119901 Sampling time 25 to 100 120583s

6 Journal of Control Science and Engineering

L1

DC

L1

L1

L2

L2

L2

Rc

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6

+- v

-i+

-i+

-i+

iaibicVdcVc_aVc_bVc_cVa_ref

Vb_ref

Vc_ref

MPVCMPV

+ -v

+ -v

+ -v

-i+

-i+

-i+

ig_a

ig_b

ig_c

S1S4S2S5S3S6

Rc

Rc

+minus

(a)

1

gt=

gt=

gt=

Boolean

Boolean

Boolean

NOT

234567

1

2

NOT

3

4

NOT

5

6

ta

tb

tc

iaibic

VdcVc_aVc_bVc_c

Va_ref

Vb_ref

Vc_ref

MPVC

S1

S4

S2

S5

S3

S6

567 Ig_c

Ig_bIg_a

(b)

Figure 5 Simulation diagram in MATLABSimulink (a) Proposed MPVC with duty cycle control for a three-phase inverter connected tothe grid (b) Subsystem of the MPVC

compared to the conventional MPCC which proves thebenefits of controlling the capacitor filter voltage Thereforethe current waveforms are more closed to sinusoidal whichproves the efficiency of proposed MPVC with optimal dutycycle control On the other side comparing the THD ofcapacitor filter voltage for two methods shows that the

proposed MPVC still has a better performance by 405than conventional by 603 So in the conventional strategyto achieve less THD the sampling frequency is neededto increase and increasing the sampling frequency can bea reason for higher hardware expenses However in theproposed MPVC this problem is solved by using duty cycle

Journal of Control Science and Engineering 7

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(a)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(b)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(c)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(d)

Figure 6 Simulation waveform of three phase grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC(c) the conventional MPCC and (d) the proposed MPCC

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(a)

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(b)

Figure 7 Simulation waveform of capacitor filter voltage (phase a) at the sampling time 119879119904119901 =50120583s for two different voltage levels (a) theconventional MPVC (b) the proposed MPVC

optimization then this goal is obtained without increasingthe sampling time

Figure 10 shows a bar chart of THD for the grid currentand the capacitor filter voltage in different methods withvarious sampling times and it can prove that the proposedmethod has significantly lower THD values than the con-ventional one because of the idea of duty cycle optimiza-tion As shown in Figure 10 the proposed method can setmore substantial advantages in systems by a larger samplingfrequency

Figure 11 shows the results for a step change in theamplitude of the reference voltage from 311 V to 240 VTherefore the grid current also will be changed accordingto the reference voltage step change (see Figure 12) It canbe observed that by following the change of the referencevoltage the amplitude of the grid currents will be changedwith extremely rapid dynamics while being not affectedby this step change However as shown in Figure 7 theamplitude of the capacitor filter voltage does not gain itsreference in a short timeOverall by comparing twomethods

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

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4 Journal of Control Science and Engineering

where 119881119888119886 119903119890119891 119881119888119887 119903119890119891 and 119881119888119888 119903119890119891 are the reference capacitorfilter voltage for phases a b and c which are generated bysine wave creator with the 120∘ phase displacement

The capacitor filter voltage equals its reference when 119892 =0 Therefore the goal of the cost function is considered toachieve 119892 value close to zero In other words this paper islooking for less capacitor filter voltage error to choose thevoltage vector and then applied to the next sampling instant[5 19]

32 Duty Cycle Determination In the proposed MPVCdetermination of the duration for the nonzero voltage vectoris the key to control system Hence slopes of the capacitor

filter voltage for the nonzero voltage 1198781 vector and the zerovoltage vector 1198780 will be calculated easily from (11) [14 15 23]

1199041= 119894 (119896) + (119879119904119901119871) [119881119899minus119911 minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)

119862(17)

1199040 = 119894 (119896) + (119879119904119901119871) [minus119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)119862 (18)

where 119881119899minus119911 is the best voltage vector which minimizes thecost function

Thus capacitor filter voltage at the end of the next controlcycle will be written as follows

119881119888 (119896 + 1) = 119881119888 ((119896)+ 119879119900119901119905 119894 (119896) + (119879119904119901119871) [119881119899minus119911 minus 119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896) + 119879119911 119894 (119896) + (119879119904119901119871) [minus119881119888 (119896) minus 119877 (119894 (119896) minus 119894119892 (119896))] minus 119894119892 (119896)

119862(19)

119879119900119901119905 + 119879119911 = 119879119904119901 (20)

119881119899minus119911 + 119881119911 = 119881 (119896) (21)

where 119879119900119901119905 119886119899119889 119879119911 are the optimal duration of the nonzeroand zero voltage vectors respectively

Now by replacing (17) and (18) into (19) the capacitorfilter voltage at the end of the next control period can beobtained by

119881119888 (119896 + 1) = 119881119888 + 1199041 times 119879119900119901119905 + 1199040 times (119879119904119901 minus 119879119900119901119905) (22)

The optimal duration of119879119900119901119905 that minimizes the cost functionduring a control period satisfies the following condition [8]

120597119892120597119879119900119901119905 = 0 (23)

By replacing (22) into (15) and solving (23) the duration ofthe nonzero vector can be expressed as

119879119900119901119905 =10038161003816100381610038161003816119881119888 119903119890119891 minus 119881119888 (119896) minus 1199040 times 1198791199041199011003816100381610038161003816100381610038161003816100381610038161199041 minus 11990401003816100381610038161003816 (24)

It is necessary to consider that the value of119879119900119901119905 can be equaledto zero only if 119879119900119901119905 is less than zero and 119879119900119901119905 is more than 119879119904119901then it will be equaled to 119879119904119901[16]33 Implemented Control Flowchart Flowchart of the pro-posed MPVC with duty cycle optimization for obtaining theoptimal output voltage vector and their optimal durations isillustrated in Figure 4

4 Simulation and Experimental Results

41 Simulation Results To validate the proposed MPVC asimulation model of a two-level three-phase inverter with

output LCL filter connected to the grid has been devel-oped with the parameters as shown in Table 1 by usingMATLABSimulink under various conditions The simulatedmodel is built based on the system shown in Figure 5The simulation analysis is mainly about robustness of theproposed MPVC strategy Hence for this purpose the per-formance of the proposed strategy will be compared with theconventional scheme

First of all by comparison of grid current waveforms forthe proposed and conventional methods it is clear that theproposed MPVC has much less distortion in output currentthan conventional MPVC and the proposedMPCCmethodsand even conventional MPVC has better results as comparedto the conventional MPCC Therefore it is going to presentless current ripples and lower current harmonics as seen inFigure 6

Then to proof this stability for the proposed method thecapacitor filter voltage will be explored in simulation As it isshown in Figure 7 there is a good tracking of capacitor filtervoltage to its reference in the proposed method and even bychanging the voltage level the proposed method tracking thevoltage reference is still more accurate and has lower ripplesthan the conventional Hence it could be a reason to havelower current harmonics

Figures 8 and 9 show a harmonic spectrum analysis atthe sampling times 119879119904119901 =50120583s for the grid current and thecapacitor filter voltage respectively From one point of viewit can be clearly seen the current THDs in the proposedmethods which are 191 and 254 for MPVC and MPCCrespectively much better than the conventional strategiesresults which are 295 for MPVC and 429 for MPCCMoreover the conventional MPVC gets better results as

Journal of Control Science and Engineering 5

No

Startup

Measure

In MATLABSimulink

Yes

Wait for next sampling

Apply Optimal Vector and Duty Cycle

Calculate s1 s0

g 1opt = infin i = minus1

i = i + 1

i = 7

(( + ) = (() +

() +

[() minus () minus ( () minus ())] minus ()

( + ) = () +

[ () minus () minus (() minus ())]

=[_ minus ( + )]

+[_ minus ( + )]

If lt = = =

=

_ minus ()minus times

minus

= minus

Figure 4 Flowchart of the proposed MPVC with duty cycle optimization

Table 1 Parameters used for the simulation and experiment

Variable System Parameters Value119881119889119888 DC-Link voltage 700V119890 Grid Voltage (RMS) 220V119891 Line voltage frequency 50HzV119903119890119891 Reference voltage peak amplitude 311 amp 240V1198712 Filter inductance 1mH1198711 Filter Inductance 3mH119862119891 Filter Capacitance 15120583F119877119888 Damping Resistance 10Ω119879119904119901 Sampling time 25 to 100 120583s

6 Journal of Control Science and Engineering

L1

DC

L1

L1

L2

L2

L2

Rc

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6

+- v

-i+

-i+

-i+

iaibicVdcVc_aVc_bVc_cVa_ref

Vb_ref

Vc_ref

MPVCMPV

+ -v

+ -v

+ -v

-i+

-i+

-i+

ig_a

ig_b

ig_c

S1S4S2S5S3S6

Rc

Rc

+minus

(a)

1

gt=

gt=

gt=

Boolean

Boolean

Boolean

NOT

234567

1

2

NOT

3

4

NOT

5

6

ta

tb

tc

iaibic

VdcVc_aVc_bVc_c

Va_ref

Vb_ref

Vc_ref

MPVC

S1

S4

S2

S5

S3

S6

567 Ig_c

Ig_bIg_a

(b)

Figure 5 Simulation diagram in MATLABSimulink (a) Proposed MPVC with duty cycle control for a three-phase inverter connected tothe grid (b) Subsystem of the MPVC

compared to the conventional MPCC which proves thebenefits of controlling the capacitor filter voltage Thereforethe current waveforms are more closed to sinusoidal whichproves the efficiency of proposed MPVC with optimal dutycycle control On the other side comparing the THD ofcapacitor filter voltage for two methods shows that the

proposed MPVC still has a better performance by 405than conventional by 603 So in the conventional strategyto achieve less THD the sampling frequency is neededto increase and increasing the sampling frequency can bea reason for higher hardware expenses However in theproposed MPVC this problem is solved by using duty cycle

Journal of Control Science and Engineering 7

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(a)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(b)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(c)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(d)

Figure 6 Simulation waveform of three phase grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC(c) the conventional MPCC and (d) the proposed MPCC

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(a)

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(b)

Figure 7 Simulation waveform of capacitor filter voltage (phase a) at the sampling time 119879119904119901 =50120583s for two different voltage levels (a) theconventional MPVC (b) the proposed MPVC

optimization then this goal is obtained without increasingthe sampling time

Figure 10 shows a bar chart of THD for the grid currentand the capacitor filter voltage in different methods withvarious sampling times and it can prove that the proposedmethod has significantly lower THD values than the con-ventional one because of the idea of duty cycle optimiza-tion As shown in Figure 10 the proposed method can setmore substantial advantages in systems by a larger samplingfrequency

Figure 11 shows the results for a step change in theamplitude of the reference voltage from 311 V to 240 VTherefore the grid current also will be changed accordingto the reference voltage step change (see Figure 12) It canbe observed that by following the change of the referencevoltage the amplitude of the grid currents will be changedwith extremely rapid dynamics while being not affectedby this step change However as shown in Figure 7 theamplitude of the capacitor filter voltage does not gain itsreference in a short timeOverall by comparing twomethods

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Control Science and Engineering 5

No

Startup

Measure

In MATLABSimulink

Yes

Wait for next sampling

Apply Optimal Vector and Duty Cycle

Calculate s1 s0

g 1opt = infin i = minus1

i = i + 1

i = 7

(( + ) = (() +

() +

[() minus () minus ( () minus ())] minus ()

( + ) = () +

[ () minus () minus (() minus ())]

=[_ minus ( + )]

+[_ minus ( + )]

If lt = = =

=

_ minus ()minus times

minus

= minus

Figure 4 Flowchart of the proposed MPVC with duty cycle optimization

Table 1 Parameters used for the simulation and experiment

Variable System Parameters Value119881119889119888 DC-Link voltage 700V119890 Grid Voltage (RMS) 220V119891 Line voltage frequency 50HzV119903119890119891 Reference voltage peak amplitude 311 amp 240V1198712 Filter inductance 1mH1198711 Filter Inductance 3mH119862119891 Filter Capacitance 15120583F119877119888 Damping Resistance 10Ω119879119904119901 Sampling time 25 to 100 120583s

6 Journal of Control Science and Engineering

L1

DC

L1

L1

L2

L2

L2

Rc

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6

+- v

-i+

-i+

-i+

iaibicVdcVc_aVc_bVc_cVa_ref

Vb_ref

Vc_ref

MPVCMPV

+ -v

+ -v

+ -v

-i+

-i+

-i+

ig_a

ig_b

ig_c

S1S4S2S5S3S6

Rc

Rc

+minus

(a)

1

gt=

gt=

gt=

Boolean

Boolean

Boolean

NOT

234567

1

2

NOT

3

4

NOT

5

6

ta

tb

tc

iaibic

VdcVc_aVc_bVc_c

Va_ref

Vb_ref

Vc_ref

MPVC

S1

S4

S2

S5

S3

S6

567 Ig_c

Ig_bIg_a

(b)

Figure 5 Simulation diagram in MATLABSimulink (a) Proposed MPVC with duty cycle control for a three-phase inverter connected tothe grid (b) Subsystem of the MPVC

compared to the conventional MPCC which proves thebenefits of controlling the capacitor filter voltage Thereforethe current waveforms are more closed to sinusoidal whichproves the efficiency of proposed MPVC with optimal dutycycle control On the other side comparing the THD ofcapacitor filter voltage for two methods shows that the

proposed MPVC still has a better performance by 405than conventional by 603 So in the conventional strategyto achieve less THD the sampling frequency is neededto increase and increasing the sampling frequency can bea reason for higher hardware expenses However in theproposed MPVC this problem is solved by using duty cycle

Journal of Control Science and Engineering 7

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(a)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(b)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(c)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(d)

Figure 6 Simulation waveform of three phase grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC(c) the conventional MPCC and (d) the proposed MPCC

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(a)

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(b)

Figure 7 Simulation waveform of capacitor filter voltage (phase a) at the sampling time 119879119904119901 =50120583s for two different voltage levels (a) theconventional MPVC (b) the proposed MPVC

optimization then this goal is obtained without increasingthe sampling time

Figure 10 shows a bar chart of THD for the grid currentand the capacitor filter voltage in different methods withvarious sampling times and it can prove that the proposedmethod has significantly lower THD values than the con-ventional one because of the idea of duty cycle optimiza-tion As shown in Figure 10 the proposed method can setmore substantial advantages in systems by a larger samplingfrequency

Figure 11 shows the results for a step change in theamplitude of the reference voltage from 311 V to 240 VTherefore the grid current also will be changed accordingto the reference voltage step change (see Figure 12) It canbe observed that by following the change of the referencevoltage the amplitude of the grid currents will be changedwith extremely rapid dynamics while being not affectedby this step change However as shown in Figure 7 theamplitude of the capacitor filter voltage does not gain itsreference in a short timeOverall by comparing twomethods

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

6 Journal of Control Science and Engineering

L1

DC

L1

L1

L2

L2

L2

Rc

Ea

Eb

Ec

C

GND

GND

n

a

b

N

c

S1 S2 S3

S4 S5 S6

+- v

-i+

-i+

-i+

iaibicVdcVc_aVc_bVc_cVa_ref

Vb_ref

Vc_ref

MPVCMPV

+ -v

+ -v

+ -v

-i+

-i+

-i+

ig_a

ig_b

ig_c

S1S4S2S5S3S6

Rc

Rc

+minus

(a)

1

gt=

gt=

gt=

Boolean

Boolean

Boolean

NOT

234567

1

2

NOT

3

4

NOT

5

6

ta

tb

tc

iaibic

VdcVc_aVc_bVc_c

Va_ref

Vb_ref

Vc_ref

MPVC

S1

S4

S2

S5

S3

S6

567 Ig_c

Ig_bIg_a

(b)

Figure 5 Simulation diagram in MATLABSimulink (a) Proposed MPVC with duty cycle control for a three-phase inverter connected tothe grid (b) Subsystem of the MPVC

compared to the conventional MPCC which proves thebenefits of controlling the capacitor filter voltage Thereforethe current waveforms are more closed to sinusoidal whichproves the efficiency of proposed MPVC with optimal dutycycle control On the other side comparing the THD ofcapacitor filter voltage for two methods shows that the

proposed MPVC still has a better performance by 405than conventional by 603 So in the conventional strategyto achieve less THD the sampling frequency is neededto increase and increasing the sampling frequency can bea reason for higher hardware expenses However in theproposed MPVC this problem is solved by using duty cycle

Journal of Control Science and Engineering 7

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(a)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(b)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(c)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(d)

Figure 6 Simulation waveform of three phase grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC(c) the conventional MPCC and (d) the proposed MPCC

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(a)

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(b)

Figure 7 Simulation waveform of capacitor filter voltage (phase a) at the sampling time 119879119904119901 =50120583s for two different voltage levels (a) theconventional MPVC (b) the proposed MPVC

optimization then this goal is obtained without increasingthe sampling time

Figure 10 shows a bar chart of THD for the grid currentand the capacitor filter voltage in different methods withvarious sampling times and it can prove that the proposedmethod has significantly lower THD values than the con-ventional one because of the idea of duty cycle optimiza-tion As shown in Figure 10 the proposed method can setmore substantial advantages in systems by a larger samplingfrequency

Figure 11 shows the results for a step change in theamplitude of the reference voltage from 311 V to 240 VTherefore the grid current also will be changed accordingto the reference voltage step change (see Figure 12) It canbe observed that by following the change of the referencevoltage the amplitude of the grid currents will be changedwith extremely rapid dynamics while being not affectedby this step change However as shown in Figure 7 theamplitude of the capacitor filter voltage does not gain itsreference in a short timeOverall by comparing twomethods

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

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AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

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Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Control Science and Engineering 7

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(a)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(b)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(c)

0 001 002 003 004 005 006 007 008 009 01Time (s)

minus20minus15minus10

minus505

101520

Grid

Cur

rent

(A)

iaibic

(d)

Figure 6 Simulation waveform of three phase grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC(c) the conventional MPCC and (d) the proposed MPCC

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(a)

0081 0082 0083 0084 0085 0086 0087 0088Time (s)

150

200

250

300

350

Capa

cito

r Filt

er V

olta

ge (v

)

VcaVca-ref

(b)

Figure 7 Simulation waveform of capacitor filter voltage (phase a) at the sampling time 119879119904119901 =50120583s for two different voltage levels (a) theconventional MPVC (b) the proposed MPVC

optimization then this goal is obtained without increasingthe sampling time

Figure 10 shows a bar chart of THD for the grid currentand the capacitor filter voltage in different methods withvarious sampling times and it can prove that the proposedmethod has significantly lower THD values than the con-ventional one because of the idea of duty cycle optimiza-tion As shown in Figure 10 the proposed method can setmore substantial advantages in systems by a larger samplingfrequency

Figure 11 shows the results for a step change in theamplitude of the reference voltage from 311 V to 240 VTherefore the grid current also will be changed accordingto the reference voltage step change (see Figure 12) It canbe observed that by following the change of the referencevoltage the amplitude of the grid currents will be changedwith extremely rapid dynamics while being not affectedby this step change However as shown in Figure 7 theamplitude of the capacitor filter voltage does not gain itsreference in a short timeOverall by comparing twomethods

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

8 Journal of Control Science and Engineering

Fundamental (50Hz) = 2163 THD= 295

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

04

05M

ag (

of F

unda

men

tal)

(a)

Fundamental (50Hz) = 244 THD= 191

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)

(b)

Fundamental (50Hz) = 2248 THD= 429

0 200 400 600 800 1000Frequency (Hz)

0

05

1

Mag

( o

f Fun

dam

enta

l)

(c)

Fundamental (50Hz) = 2224 THD= 254

0 200 400 600 800 1000Frequency (Hz)

0

02

04

06

Mag

( o

f Fun

dam

enta

l)(d)

Figure 8 Total harmonic distortion of grid current at 50120583s sampling time for (a) the conventional MPVC (b) the proposed MPVC (c) theconventional MPCC and (d) the proposed MPCC

Fundamental (50Hz) = 312 THD= 603

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(a)

Fundamental (50Hz) = 3102 THD= 405

0 200 400 600 800 1000Frequency (Hz)

0

01

02

03

Mag

( o

f Fun

dam

enta

l)

(b)

Figure 9 Total harmonic distortion of capacitor filter voltage at 50120583s sampling time for (a) the conventional MPVC and (b) the proposedMPVC

the proposed MPVC has a better dynamic performance thanconventional method

The absolute error will be defined as differences betweenthe reference current and the measured grid current Toreveal the possibilities of the proposed MPVCmethod com-parison of the absolute reference tracking error for theMPVCand MPCC strategies is presented in Figure 13 Thereforeit is clear that the MPVC strategy is more stable than theproposed MPCC as it has less absolute reference trackingerror compared to the MPCC method

At last the detailed measurements of THD for the capac-itor filter voltage and the grid current are summarized inTable 2 for the MPVC and MPCC methods Hence it isclear that the proposed MPVC with duty cycle optimizationachieves much better steady-state performance and lowerTHD as compared to the proposed MPCC

42 Experimental Tests To verify whether simulation modelcan be realized an experiment was performed and evaluatedas well Therefore the proposed MPVC algorithm has beentested on a laboratory prototype system including a three-phase inverter connected to the grid The main systemparameters are summarizedwith the same systemparametersused for the simulation (see Table 1) The core of the controlhardware is based on A 32-bit floating digital signal processor(DSP) TMS320F28335 where the proposed MPVC algorithmhas been coded And a Fluke 434 power quality analyser isused in the prototype as measuring equipment The three-phase grid-tied inverter prototype was set up according toFigure 14

As shown in Figure 15 the experimental output currentwaveform seems slightly worse than the simulation resultsbut still in the proposed methods the current waveform is

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Control Science and Engineering 9

Capacitor Filter Voltage

25 500

1

2

3

4

5

6

7

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(a)

Grid Current

25 500

05

1

15

2

25

3

THD

()

Conventional MPVCProposed MPVC

Sampling Time (s)

(b)

Figure 10 Comparative simulation results of THD for the conventional and proposed MPVC (a) Capacitor filter voltage (b) Grid current

６＝６＝-Ｌ

６＝６＝-Ｌ

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

(a)

008 0081 0082 0083 0084 0085 0086 0087 0088 0089 009Time (s)

minus400minus300minus200minus100

0100200300400

Capa

cito

r Filt

er V

olta

ge (v

)

６＝６＝-Ｌ

６＝６＝-Ｌ

(b)

Figure 11 Results of capacitor filter voltage for a step in the amplitude of 119881119888120572 119903119890119891 and 119881119888120573 119903119890119891 (a) The conventional MPVC (b) The proposedMPVC

smoother as compared to the conventional methods To con-firm these changes Figure 16 shows the distorted waveformof the inverter output current THD where the conventionaland the proposed MPVC methods are 72 and 31 andthe conventional and proposed MPCC methods are 73and 33 respectively Thus the proposed strategy has muchbetter performance in comparison with the conventional oneand along with the voltage controlling gets better results ascompared to the current controlling

5 Conclusion

In this paper a new and simplified control strategy waspresented for a three-phase inverter with output LCL filterThe capability of the proposed predictive voltage controllerhas been simulated in MATLABSimulink Results show that

the proposed strategy obtains a better voltage regulation withlinear loads as well as nonlinear loads The cost function inthe algorithm of the control strategy checks each of the 7possible switching states to choose a better switching statethat minimizes the errors The proposed MPVC achievesan improved steady-state performance by using nonzeroand zero vector during one control period In additionit improves performance by employing predictive outputcurrent to predict capacitor filter voltage as well Hence thealgorithm defines the duration of the nonzero vector basedon the principle of capacitor voltage error minimizationTherefore this idea (duty ratio optimization) is anotheradvantage to get a better steady-state performance Theproposed MPVC method can decrease steady-state voltageerrors and reduce grid current ripples without increasingthe sampling frequency compared to the Proposed MPCC

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

10 Journal of Control Science and Engineering

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A)

0085 00855 0086 00865 0087Time (s)

89

1011121314

Grid

Cur

rent

(A)

(a)

006 0065 007 0075 008 0085 009 0095 01 0105 011Time (s)

minus20

minus15

minus10

minus5

0

5

10

15

20

Grid

Cur

rent

(A) 0085 00855 0086 00865 0087

Time (s)

89

1011121314

Grid

Cur

rent

(A)

(b)

Figure 12 Grid current of phase A for (a) the conventional MPVC and (b) the proposed MPVC

0 002 004 006 008 01 012 014 016 018 020

5

10

15

20

25

Absolute Error (Conventional MPCC)Absolute Error (Conventional MPVC)Absolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

(a)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

0

2

4

6

Abso

lute

Err

or

Lower ToleranceUpper ToleranceAbsolute Error (Proposed MPCC)Absolute Error (Proposed MPVC)

0098 00985 0099 00995 01 01005 0101 01015 0102 01025Time (s)

01020

Abso

lute

Err

or

Difference of Baseline from Lower Tolerance

Difference of Baseline from Upper ToleranceDifference

(b)

Figure 13 Absolute reference current tracking error (a) Comparison of the conventional and proposed strategies (b) Difference betweenproposed MPCC and MPVC

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Control Science and Engineering 11

Table 2 Comparison of THD for MPVC and MPCCmethods

THD ()

Conventional MPVC Proposed MPVC ConventionalMPCC

ProposedMPCC

Sampling Time(120583s) Grid Current Capacitor filter

Voltage Grid Current Capacitor filterVoltage Grid Current Grid Current

25 098 352 07 28 32 19450 295 603 191 405 429 254

DC SourceInverter

LCL Filter

Grid

Controller amp Driver

FLUKE-434 Analyzer

Figure 14 Laboratory setup

(a) (b)

(c) (d)

Figure 15 Waveform of three-phase grid current (a) the Conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and(d) the proposed MPCC

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

12 Journal of Control Science and Engineering

(a) (b)

(c) (d)

Figure 16 THD of the three-phase grid current (a) the conventional MPVC (b) the proposed MPVC (c) the conventional MPCC and (d)the proposed MPCC

strategy The proposed strategy offers a better referencetracking error with less THD values in the capacitor voltageand grid current as well From the other point of view itcan be a reason for better system stability and remarkableimprovement in the dynamic performance of the inverterby the reference voltage step changing Hence the presentedsimulation and experimental results agree on the efficiency ofthe proposed MPVC with duty cycle optimization

Data Availability

The system analysis data achieved from the MATLABSimulink and experimental test used to support the findingsof this study are available from the first author (ShahrouzEbrahimpanah shahrooz6485yahoocom) upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under contract 61374050 6167330561673306 and the National Key Research and DevelopmentProgram of China under contract 2017YFB0103001

References

[1] X Xing C Zhang J He A Chen and Z Zhang ldquoModelpredictive control for parallel threelevel T-type grid-connectedinverters in renewable power generationsrdquo IET RenewablePower Generation vol 11 no 11 pp 1353ndash1363 2017

[2] D Abbes A Martinez and G Champenois ldquoEco-design opti-misation of an autonomous hybrid wind-photovoltaic systemwith battery storagerdquo IET Renewable Power Generation vol 6no 5 pp 358ndash371 2012

[3] C H F Silva H M Henrique and L C Oliveira-LopesldquoExperimental application of predictive controllersrdquo Journal ofControl Science and Engineering vol 2012 Article ID 159072 18pages 2012

[4] M B Shadmand X Li R S Balog and H Abu Rub ldquoCon-strained decoupled power predictive controller for a single-phase grid-tied inverterrdquo IET Renewable Power Generation vol11 no 5 pp 659ndash668 2017

[5] V Yaramasu B Wu M Rivera and J Rodriguez ldquoEnhancedmodel predictive voltage control of four-leg inverters withswitching frequency reduction for standalone power systemsrdquoin Proceedings of the 15th International Power Electronics andMotion Control Conference EPE-PEMC 20 12 ECCE Europe ppDS2c6-1ndashDS2c6-5 Novi Sad Serbia September 2012

[6] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoModel predictive approach for a simple and effective loadvoltage control of four-leg inverter with an output LC filterrdquo

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Journal of Control Science and Engineering 13

IEEE Transactions on Industrial Electronics vol 61 no 10 pp5259ndash5270 2014

[7] J Rodriguez BWuM Rivera et al ldquoPredictive current controlof three-phase two-level four-leg inverterrdquo in Proceedings ofthe 14th International Power Electronics and Motion ControlConference (EPEPEMC 2010) pp 106ndash110 IEEE Press OhridMacedonia September 2010

[8] V Yaramasu M Rivera M Narimani B Wu and J RodriguezldquoHigh performance operation for a four-leg NPC inverter withtwo-sample-ahead predictive control strategyrdquo Electric PowerSystems Research vol 123 pp 31ndash39 2015

[9] W Chen ldquoImproved distributed model predictive control withcontrol planning setrdquo Journal of Control Science and Engineer-ing vol 2016 Article ID 8167931 14 pages 2016

[10] G Du Z Liu F Du and J Li ldquoPerformance improvement ofmodel predictive control using control error compensation forpower electronic converters based on the lyapunov functionrdquoJournal of Power Electronics vol 17 no 4 pp 983ndash990 2017

[11] C Xia T Liu T Shi and Z Song ldquoA simplified finite-control-set model-predictive control for power convertersrdquoIEEE Transactions on Industrial Informatics vol 10 no 2 pp991ndash1002 2014

[12] P Cortes J Rodriguez C Silva and A Flores ldquoDelay com-pensation in model predictive current control of a three-phaseinverterrdquo IEEETransactions on Industrial Electronics vol 59 no2 pp 1323ndash1325 2012

[13] J Rodrıguez J Pont CA Silva et al ldquoPredictive current controlof a voltage source inverterrdquo IEEE Transactions on IndustrialElectronics vol 54 no 1 pp 495ndash503 2007

[14] Y Zhang W Xie Z Li and Y Zhang ldquoModel predictive directpower control of a PWM rectifier with duty cycle optimizationrdquoIEEE Transactions on Power Electronics vol 28 no 11 pp 5343ndash5351 2013

[15] Y Zhang and Y Peng ldquoModel predictive current control withoptimal duty cycle for three-phase grid-connected ACDCconvertersrdquo in Proceedings of the 2014 International PowerElectronics and Application Conference and Exposition (PEAC)IEEE PEAC 2014 pp 837ndash842 IEEE Press China November2014

[16] Y Zhang Y Peng and B Xia ldquoEfficient model predictivecontrol with optimal duty cycle for power convertersrdquo inProceedings of the 8th IEEE International Power Electronics andMotion Control Conference IPEMC-ECCE Asia 2016 pp 1076ndash1083 IEEE Press China May 2016

[17] Y Zhang CQu Z Li Y Zhang and L Cao ldquoDirect power con-trol of PWM rectifier with optimal duty ratio under unbalancednetworkrdquo in Proceedings of the 9th International Conference onPower Electronics - ECCE Asia ICPE 2015-ECCE Asia pp 1116ndash1122 Seoul South Korea June 2010

[18] S Ebrahimpanah Q Chen and L Zhang ldquoModel predictivecurrent controlwith duty cycle optimization for two-level three-phase grid-tied inverter with output LCLfilter based on forwardeuler approximationrdquo in Proceedings of the 3rd InternationalConference on Industrial Informatics - Computing TechnologyIntelligent Technology Industrial Information Integration ICI-ICII 2017 pp 155ndash158 China December 2017

[19] P Cortes G Ortiz J I Yuz et al ldquoModel predictive control ofan inverter with output LC filter for UPS applicationsrdquo IEEETransactions on Industrial Electronics vol 56 no 6 pp 1875ndash1883 2009

[20] E Zangeneh Bighash S M Sadeghzadeh E Ebrahimzadehand F Blaabjerg ldquoHigh quality model predictive control for

single phase grid-connected photovoltaic invertersrdquo ElectricPower Systems Research vol 158 pp 115ndash125 2018

[21] E Z Bighash S M Sadeghzadeh E Ebrahimzadeh and FBlaabjerg ldquoRobust MPC-based current controller against gridimpedance variations for single-phase grid-connected invert-ersrdquo ISA Transactions vol 84 pp 154ndash163 2019

[22] J Rodriguez and P Cortes Predictive Control of Power Convert-ers and Electrical Drives Wiley-IEEE Press 2012

[23] P Mercorelli ldquoA multilevel inverter bridge control structurewith energy storage using model predictive control for flatsystemsrdquo Journal of Engineering vol 2013 Article ID 750190 15pages 2013

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom