research article reactive power control of single-stage three...

Research ArticleReactive Power Control of Single-Stage Three-PhasePhotovoltaic System during Grid Faults Using Recurrent FuzzyCerebellar Model Articulation Neural Network

Faa-Jeng Lin Kuang-Chin Lu and Hsuan-Yu Lee

Department of Electrical Engineering National Central University Chungli 320 Taiwan

Correspondence should be addressed to Faa-Jeng Lin linfjeencuedutw

Received 15 June 2014 Accepted 27 July 2014 Published 24 August 2014

Academic Editor Franca Morazzoni

Copyright copy 2014 Faa-Jeng Lin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study presents a new active and reactive power control scheme for a single-stage three-phase grid-connected photovoltaic (PV)system during grid faultsThe presented PV system utilizes a single-stage three-phase current-controlled voltage-source inverter toachieve the maximum power point tracking (MPPT) control of the PV panel with the function of low voltage ride through (LVRT)Moreover a formula based on positive sequence voltage for evaluating the percentage of voltage sag is derived to determine the ratioof the injected reactive current to satisfy the LVRT regulations To reduce the risk of overcurrent during LVRT operation a currentlimit is predefined for the injection of reactive current Furthermore the control of active and reactive power is designed using a two-dimensional recurrent fuzzy cerebellar model articulation neural network (2D-RFCMANN) In addition the online learning lawsof 2D-RFCMANN are derived according to gradient descent method with varied learning-rate coefficients for network parametersto assure the convergence of the tracking error Finally some experimental tests are realized to validate the effectiveness of theproposed control scheme

1 Introduction

The cerebellar model articulation neural network (CMANN)is a lookup-table based neural network which can be thoughtof as a learning mechanism that simulates mammalian cere-bellum Basically the input space of the CMANN is dividedinto discrete states which are called elements Moreoverseveral elements construct a block and an overlapped areaformed by quantized blocks is called hypercube Differenthypercubes can be obtained by shifting each block a smallinterval Furthermore the CMANN assigns each hypercubeto a memory cell for storing learning information To obtainthe output of the CMANN for given input data onlythe hypercubes covering the input data will be activatedand effectively contribute to the corresponding output Thebasic concept of the CMANN is to store learned data intohypercubes and the data can easily be recalled with lessoccupied storage space Consequently the behavior of storingthe learned information in the CMANN is similar to the

action of the cerebellar in mammalian Advantages of theCMANN include fast learning good localization capabilityand simplicity of computation [1] However in the generalCMANN there are only two kinds of states in the mappedarea of the state space that is 1 and 0 This directly affectsthe generalization capability of CMANN and may result indiscontinuous output [2 3] In order to acquire the derivativeinformation of input and output variables a CMANN with adifferentiable Gaussian receptive field basis function has beenproposed in [4] Due to the lack of time-delayed feedbackin its inherent feedforward neural network structure theapplication domain of CMANN is limited to static mappingproblems In addition a recurrent fuzzy CMANN (RFC-MANN)withGaussian receptive field basis functionwas pro-posed in [5] to overcome the aforementioned disadvantage ofCMANN In this study a two-dimensional RFCMANN (2D-RFCMANN) with Gaussian basis function control schemeis proposed for the active and reactive power control of thesingle-stage three-phase grid-connected photovoltaic (PV)

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 760743 13 pageshttpdxdoiorg1011552014760743

2 International Journal of Photoenergy

system The first dimension of the 2D-RFCMANN is for thetracking error input and the second dimension of the 2D-RFCMANN is for the derivative of the tracking error input

The penetration of renewable energy sources hasincreased significantly because of raising awareness of theenvironmental issues and the deregulation of the electricpower distribution industry Among these renewable energysources PV system is one of the main candidates to playan important role in the future of power distributionHowever the connection of a large number of distributedenergy sources (DESs) to the electrical power grid can causeinstability when electrical disturbances appear in the gridOne of the most challenging disturbances is the voltagesags [6 7] The sources of the voltage sags are various suchas short circuits between phases or phases and groundlightning and overloads To minimize the negative effectsof a large number of DESs on the reliability of the powergrids different countries have defined various low voltageride through (LVRT) regulations for DESs EON has definedthe voltage profile of the low voltage ride through (LVRT)at the grid connection for type-2 generating plants [8] Gridregulations require that the DESs have to inject reactivecurrent to support grid stability during grid faults [8] inwhich 1 pu of reactive current is required as the depth of thesag reaches 50 In this study the EON LVRT regulationis adopted to determine the ratio of the required reactivecurrent during grid faults

The asymmetrical grid voltage sags will worsen the per-formance of the grid-connected inverter (GCI) especially thedegradation of the power quality caused by the power rippleand the increase of current harmonic distortion In orderto overcome these disadvantages some control methodsbased on symmetric components have been proposed todeal with unbalanced grid faults [9ndash13] A control schemewhich can adjust the characteristics of power quality byusing two adjustable control parameters was developed in[9] In [10] a selective active power quality control based onvarious current reference generating methods was proposedReference [11] has proposed a control method to minimizethe peak value of the injection current during the voltagesag In [12] a positive and negative sequences currentinjection method was proposed to provide the active powerand reactive current without exceeding the current limitof inverter The flexible reactive current injection schemeintroduced in [13] provides voltage support during voltage sagby injecting reactive current via both positive and negativesequences However the aforementioned control methodsprincipally focus on the power control of grid-connectedinverter whereas the fulfillment of the LVRT requirementand the control of the power flow between the dc-link bus andac grid during grid faults are not well explored In this studythe 2D-RFCMANN control scheme is proposed to controlnot only the output voltage of the PV panel via the maximumpower point tracking (MPPT) in normal condition butalso the reactive power based on LVRT requirement withconsidering the power balance between dc-link bus and acgrid during grid faults

In this study the analysis of the instantaneousactivereactive output power of the three-phase GCI during

grid faults is carried out by using symmetric componentmethod The MPPT control of PV system is also consideredto ensure the power balance during grid faults Subsequentlythe dual second-order generalized integrator phase-lockedloop (DSOGI-PLL) method [10 14 15] is adopted forsynchronizing the GCI to the grid Moreover a new formulawhich is based on the positive sequence voltage is derivedto evaluate the percentage of voltage sag and to determinethe injected currents during the grid faults Furthermorethe network structure and online training algorithms ofnetwork parameters of the proposed 2D-RFCMANN for theactive and reactive power control are discussed in detailFurthermore two types of grid faults are tested and discussedto evaluate the performance of the proposed control schemeThe paper is organized as follows In Section 2 the grid-connected PV system is introduced In Section 3 theinstantaneous activereactive power formulation DSOGI-PLL synchronization mechanism and the control strategyof the grid-connected PV system during grid faults arediscussed The 2D-RFCMANN is presented in Section 4 InSection 5 the features of the proposed control scheme areexamined by some experimental results Finally Section 6draws the conclusions

2 System Description

Figure 1 shows the block diagrams of the proposed single-stage three-phase grid-connected PV system The behaviorof the PV panel is emulated by a Chroma 62100H-600S PVpanel simulator operating at 203Vdc output voltage withmaximum output power 1 kW The power grid was emu-lated by three programmable 2 kVA single-phase KIKUSUIPCR2000LE AC power supplies feeding a Y-connected100Ωphase resistive load and connected to the GCI witha 3 kVA Y-998779 transformer The 2 kVA three-phase GCI withoutput 110Vrms line to line voltage is connected to the PVpanel simulator through a dc-link capacitor and connectedto the Y-998779 transformer with three 10mHphase couplinginductorsThe switching frequency119891sw GCI of the three-phaseGCI is set at 10 kHz Table 1 shows the parameters of theexperimental setup Moreover the control system is installedon a desktop personal computer (PC) which includes an ADconverter card (PCI-1716) a PC-based control system anda DA converter card (MRC-6810) In the PC-based controlsystem the SIMULINK control package is adopted for theimplementation of the proposed algorithms of theMPPT andLVRTcontrolThe analog input signals include output voltage119881pv and current 119868pv of the PV panel simulator the outputline voltages V

119886119887 V119887119888 and V

119888119886 and line currents 119894

119886 119894119887 and

119894119888of the GCI The control output of the PC-based control

system is the three-phase reference currents of GCI 119894lowast

119886 119894lowast

119887

and 119894lowast

119888 Furthermore the emulated faults occur at the point

of common coupling (PCC)In Figure 1 the output currents of the GCI are controlled

by the maximum power point (MPP) voltage 119881lowast

pv in the nor-mal conditionThe adoptedMPPTmethod is the incrementalconductance (IC) method with a fixed incremental step sizeset for the voltage [16] Moreover if a grid fault occurs at the

International Journal of Photoenergy 3

DC

AC

Three-phase GCI

Current controlled

PWM

L

110220

LoadPCC

Emulatedfault

PC

AD converter

MPPT and LVRT control

PC-based control system

PV panel Grid

DA converter

Vpv+

minus

Ipv

Cpv

Vpv

ia ib ic

ia ib ic

ilowasta ilowastb i

lowastc

Y Δ

100ΩY-connected

= 3120601ab bc ca

ab bc caVpv Ipv

radic31 2

Figure 1 Block diagrams of experimental single-stage three-phase grid-connected PV system

Table 1 Parameters of experimental setup

Dc-link capacitor 119862pv 3360mFGrid connection inductor 119871 10mHInverter output voltage V

119886119887 V119887119888 V119888119886

110Vrms line to line 60HzInverter maximum current 119868max 5Arms (71 A peak current)Emulated PV panel 119881oc 236V 119868sc 60 A 1 kWSwitching frequency 119891sw GCI 10 kHz

PCC the fault voltages at theGCI terminals appear differentlyfrom the fault voltages at the PCC [6 7] Furthermore in thenormal condition of the grid the GCI regulates the activepower injecting into the grid and maintains the 119881pv voltageso as to track the MPP for maximizing the energy extractionOn the other hand in the fault conditions of the grid thereactive power control can mitigate the effects of voltagesag by injecting additional reactive current to the grid toride through the perturbation and support the grid voltageIn addition the injecting current has to meet the LVRTregulations without going beyond the GCI current limit 119868maxsimultaneously

3 Reactive Power Control Strategyduring Grid Faults

31 Instantaneous Power Formulation under Grid Fault Con-ditions For a three-phase GCI the instantaneous active andreactive power outputs at the grid connection point aredescribed as follows [17]

119875 = k sdot i = V119886119894119886+ V119887119894119887+ V119888119894119888 (1)

119876 = k times i = kperp

sdot i

=1

radic3[(V119886minus V119887) 119894119888+ (V119887minus V119888) 119894119886+ (V119888minus V119886) 119894119887]

(2)

where kperp

= (1radic3) [0 1 minus1

minus1 0 1

1 minus1 0

] k k = [V119886

V119887V119888]119879and i =

[119894119886

119894119887

119894119888]119879 represent the three phase voltages and currents of

the GCI respectively 119875 and 119876 represent the instantaneousactive and reactive power outputs of the GCI respectivelyIn (1) and (2) k

perpand k are orthogonal only when the

three voltages of k are balancedThe asymmetric three-phasevoltage and current vector are represented as

k = k+ + kminus

i = i+ + iminus(3)

where k+ = [V+119886

V+119887

V+119888]119879 and kminus = [Vminus

119886Vminus119887

Vminus119888]119879 represent

the positive and negative sequences of v respectively i+ =

[119894+

119886119894+

119887119894+

119888]119879 and iminus = [119894

minus

119886119894minus

119887119894minus

119888]119879 represent the positive

and negative sequences of i respectively Note that the zerosequence of v and i does not exist due to the three-phasethree-wire AC system configuration of the GCI As a result119875 and 119876 in (1) and (2) can be rewritten as

119875 = k sdot i = (k+ + kminus) sdot (i+ + iminus)

= k+ sdot i+ + kminus sdot iminus + k+ sdot iminus + kminus sdot i+(4)

119876 = kperp

sdot i = (k+perp

+ kminusperp) sdot (i+ + iminus)

= k+perp

sdot i+ + kminusperp

sdot iminus + k+perp

sdot iminus + kminusperp

sdot i+(5)

where the corresponding orthogonal vectors in (5) can bederived by using the matrix transformation in (2) Thus the


abc ++

+

dq

VCOPI

Low pass filter

SOGIBP filter

SOGIBP filter

v+d

v+q

120579e

120579e

SRF-PLL

1

sminus

120572120573

120572120573998400120572

q998400120572

q998400120573

998400120573

+120572

+120573

120572

120573

e

ea

b

c

05

05

Figure 2 Schematic diagram of DSOGI-PLL

instantaneous active and reactive output power of the GCIcan be obtained by using (4) and (5) under both normal andabnormal conditions of the grid

32 Grid Synchronization of GCI The active and reactivepower control of the GCI is based on a synchronous ref-erence frame (SRF) with proportional-integral (PI) or 2D-RFCMANN controllers Moreover it is important to detectthe phase angle of the voltage at PCC in order to synchronizewith the grid during grid faults At present the most popularPLL structure is the synchronous reference frame PLL (SRF-PLL) [14]The input three-phase voltages of the SRF-PLL canbe given by

[

[

V119886

V119887

V119888

]

]

=1003816100381610038161003816119881+1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890minus

2

3120587)

sin(120579119890+

2

3120587)

]]]]]]

]

+1003816100381610038161003816119881minus1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890+

2

3120587)

sin(120579119890minus

2

3120587)

]]]]]]

]

(6)

where |119881+

| and |119881minus

| are the amplitude of the positive andnegative sequence of the three-phase voltage 120579

119890= 120596119890119905 and

120596119890is the utility angular frequency In the SRF-PLL first

the Clarke transformation is applied to transfer the three-phase voltages from the 119886119887119888 natural reference frame to the 120572120573

stationary reference frame [14 15] V120572and V120573are the voltages

of 120572 120573 axis which can be expressed as

[V120572

V120573

] = radic2

3

[[[

[

3

20

radic3

2radic3

]]]

]

[V119886

V119887

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890)

minus cos (120579119890)] + radic

3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890)

cos (120579119890)]

(7)

Then (7) can be expressed in the synchronous referenceframe by using Park transformation in the following [15]

[V119889

V119902

] = [

[

cos (120579119890) sin (120579

119890)

minus sin (120579119890) cos (120579

119890)

]

]

[V120572

V120573

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890minus 120579119890)

minus cos (120579119890minus 120579119890)]

+ radic3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890minus 120579119890)

cos (120579119890minus 120579119890)] (8)

where V119889 V119902are the voltages of the 119889119902 axis 120579

119890= 119890119905 and

119890is the angular frequency of the 119889119902 synchronous reference

frame Suppose that 120579119890is close to 120579

119890 then sin(120579

119890minus 120579119890) is

approximately equal to 120579119890minus 120579119890 and V

119889is approximately equal

to (radic62)[|119881+

|(120579119890minus120579119890)+|119881minus

| sin(2120579119890)]The negative sequence

component voltage of V119889can be filtered by using a properly

designed low pass filterThe difference between 120579119890and 120579119890will

approach zero due to the closed-loop control of 120579119890that makes

V119889approach zero Therefore with 120579

119890asymp 120579119890in steady state the

phase angle detected by the SRF-PLL will be in phase withthe input voltage vector However the dynamic behavior ofthe SRF-PLL will become poor under asymmetric grid faults[15] In order to overcome this disadvantage of SRF-PLL adual second-order generalized integrator PLL (DSOGI-PLL)based on the extraction of the positive sequence has beenproposed in [10 14 15] Define k+

120572120573= [V+120572

V+120573]119879

as the positivesequence voltage vector on the 120572120573 reference frame and it canbe calculated as [10]

k+120572120573

=1

2[1 minus119902

119902 1][

[

V1015840120572

V1015840120573

]

]

(9)

where 119902 = 119890minus1198951205872 is a phase-shift operator in the time domain

V1015840120572and V1015840120573are the filtered voltages of V

120572and V120573 respectively

The schematic diagram of DSOGI-PLL is shown in Figure 2where the dual second-order generalized integrator (SOGI)in Figure 2 is used to generate V1015840

120572 V1015840120573 and in-quadrature

voltages 119902V1015840120572and 119902V1015840

120573of V1015840120572and V1015840

120573 Furthermore V+

119889and V+

119902

which are depicted in Figure 2 are the positive sequencevoltages on the 119889119902 synchronous reference frame In additiona voltage-controlled oscillator (VCO) is employed to convertthe input voltage into

119890 Finally 120579

119890is successfully obtained

by DSOGI-PLL by using the positive sequence voltagesAccording to [15] the instantaneous active and reactive

power outputs of the GCI can be calculated by using the


voltage and current in the 119889119902 synchronous reference frameas follows

119876 =3

2(V119902119894119889minus V119889119894119902) 119875 =

3

2(V119889119894119889+ V119902119894119902) (10)

where 119894119889and 119894119902are the currents of the 119889 119902 axis As mentioned

above an adequate tracking of the grid angular position ofthe SRF-PLL will make V

119889approach zeroThus the active and

reactive power outputs of the GCI can be represented as

119876 =3

2V119902119894119889 119875 =

3

2V119902119894119902 (11)

Accordingly 119875 and 119876 can be regulated by controlling 119894119902and

119894119889

33 Reactive and Active Power Control during Grid FaultsThe positive sequence voltages of the three-phase line volt-ages V+

119886119887 V+119887119888 and V+

119888119886can be expressed as follows

[[[[

[

V+119886119887

V+119887119888

V+119888119886

]]]]

]

=1

3

[

[

1 119886 1198862

1198862

1 119886

119886 1198862

1

]

]

[

[

V119886119887

V119887119888

V119888119886

]

]

= radic21003816100381610038161003816119881+

119897

1003816100381610038161003816

[[[[[[

[

sin 120579119890

sin(120579119890minus

2120587

3)

sin(120579119890+

2120587

3)

]]]]]]

]

(12)

where |119881+

119897| is the rms value of the magnitude of the positive

sequence voltage of the three-phase line voltages and theoperator 119886 is equal to 119890

11989521205873 Since V+119886119887 V+119887119888 and V+

119888119886are

symmetric and balanced |119881+119897| can be expressed as

1003816100381610038161003816119881+

119897

1003816100381610038161003816 = radic1

3(V+119886119887

2

+ V+119887119888

2

+ V+119888119886

2

) (13)

Note that V+119886119887 V+119887119888 and V+

119888119886are equal to the magnitude of the

three-phase line voltages when the line voltages are balancedAccording to (12) if the line voltages are unbalanced V+

119886119887

V+119887119888 and V+

119888119886will be changed with the degree of unbalance

Therefore |119881+

119897| is adopted to evaluate the depth of voltage sag

119881sag during grid faults in this study The required percentageof compensation reactive current 119868

lowast

119903during grid faults for

LVRT can be expressed as a function of 119881sag [8]

119868lowast

119903=

0 where 119881sag lt 01

200119881sag where 01 lt 119881sag le 05

100 where 119881sag gt 05

(14)

and 119881sag is defined as follows

119881sag equiv 1 minus

1003816100381610038161003816119881+

119897

1003816100381610038161003816

119881basepu (15)

where119881base is the base value of voltage which equals 110 Vrmsin this study The grid regulation by EON demands reactivecurrent injection during fault condition to support the gridstability when 119881sag is greater than 01 pu Moreover theapparent output power of GCI will be changed due to thevoltage sag at PCC under grid faultsTherefore it is necessaryto calculate the maximum allowable apparent power in orderto decide the maximum injection reactive and active powerThe maximum apparent power 119878 can be expressed as

119878 = (1003816100381610038161003816V119886

1003816100381610038161003816rms +1003816100381610038161003816V119887

1003816100381610038161003816rms +1003816100381610038161003816V119888

1003816100381610038161003816rms) 119868max (16)

where 119868max is the rms value of the GCI current limit and|V119886|rms |V119887|rms and |V

119888|rms are the rms values of V

119886 V119887 and V

119888

respectively Thus the required injection reactive power 119876lowast

and the allowable maximum output active power 119875lowast of GCI

as follows can be derived from (14) and (16)

119876lowast

= 119878119868lowast

119903 119875

lowast

= 119878radic1 minus 119868lowast2119903

(17)

A PV system should inject a certain reactive power inorder to support the voltage sag at the PCC according to theLVRT requirements during grid faults If 119875lowast is greater than 119875then the active power reference 119875ref is set to equal the valueof 119875 before the grid faults Therefore all the power generatedby the PV panel can be totally delivered into the grid duringgrid faults and the MPPT control can be operated to keeptracking the MPP On the other hand if 119875

lowast is smaller than119875 then 119875ref is set to 119875

lowast Thus the output active power will becontrolled to follow 119875ref and the GCI gives up tracking theMPPConsequently the power balance between119875pv and119875 canbe held during grid faults

4 D-RFCMANN Control Scheme

41 Description of 2D-RFCMANN The structure of 2D-RFCMANN with 2 inputs and 1 output is depicted inFigure 3(a) which consists of five spaces input space fuzzi-fication space receptive-field space weight space and outspace Moreover one of the fuzzy if-then rules of the pro-posed 2D-RFCMANN is realized as follows

119877119894

11989511198952

If 1199091is 11989111198941198951

and 1199092is 11989121198941198952

then

11991011989411989511198952

= 11990811989411989511198952

for 119894 = 1 2 119899119894

1198951 1198952= 1 2 119899

119895

(18)

where 119899119894

= 3 is the number of the layers for each inputdimension 119899

119895= 4 is the number of blocks for each layer

11989111198941198951

is the fuzzy set for the first input 119894th layer and 1198951th

block 11989121198941198952

is the fuzzy set for the second input 119894th layerand 1198952th block 119908

11989411989511198952

is the corresponding output weight inthe consequent part Furthermore the signal propagation andthe basic function in each space of the 2D-RFCMANN areintroduced as follows

Space 1 (input space) In this space the input variables 1199091

and 1199092are both divided into 119899

119890regions (which are called

ldquoelementsrdquo)Thenumber of 119899119890represents the input resolution


Input space

Fuzzification space

Receptive-fieldSpace

Recurrent unit

x1

x2

f1ij1

f2ij2

fpijp

rpijp

sum

xp

zminus1

y2pijp

Output space

y5o

h111

h121

w111

w121

hij1j2

hn119894n119895n119895

wij1j2

wn119894n119895n119895

Weight space

(a) Structure of 2D-RFCMANN

S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

S8

S8

S9

S9

S10

S10

f111

f111

f211f221

f231

f121

f131

f212

f112

f212

f222

f232

f122

f132

f113

f123

f213

f223

f233

f133

f114

f214f224

f234

f124

f134

H1

H2

H3

Layer 1 Layer 1

Layer 2

Layer 2

Layer 3

Layer 3

x2

x1

(3 5)

(b) 2D-RFCMANN with 119901 = 2 119899119894= 3 and 119899

119895= 4 and its configuration of receptive-field space

activated by state (3 5)

Figure 3 Two-dimensional RFCMANN

For example a 2D-RFMANN with 119899119890

= 10 is shown as inFigure 3(b)

Space 2 (fuzzification space) According to the concept ofCMANN several elements can be accumulated as a block

In this space each block performs a Gaussian receptive-field basis function The fuzzification of the correspondingmembership function in the 2D-RFCMANN is realizedby the Gaussian basis function which can be expressedas


DC

AC

Current controlled

PWMPC-based control system

L SSR

Instantaneous active and

reactive power calculation

dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation

Active and reactive power

references calculation

P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ

Figure 4 Schematic diagram of PC-based control system

119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901

(119873) is the output of the 119895119901th block of the 119894th layer

of the 119901th input variable 119898119901119894119895119901

and 120590119901119894119895119901

are the mean andstandard deviation of the Gaussian function respectively119903119901119894119895119901

represents the recurrent weight of the 119895119901th block of the

119894th layer for the 119901th input variable internal feedback unit 119873denotes the time step and 119891

119901119894119895119901

(119873 minus 1) represents the valueof 119891119901119894119895119901

(119873) through time delay Note that the memory term119891119901119894119895119901

(119873minus1) stores the past information of the 2D-RFCMANNnetwork and performs the dynamic property Consideringthe example shown in Figure 4(b) the 2D-RFCMANN hastwo input variables with three layers in the 2D-RFCMANNand four blocks in each layer

Space 3 (receptive-field space) In this space each blockhas three adjustable parameters 119903

119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901

Themultidimensional receptive-field function is defined as

ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952

(119873) is associated with the ith layer and the 1198951th

block for input 1199091and the 119895

2th block for input 119909

2according

to the fuzzy rules in (12) The product is computed by usingt-norm product in the antecedent part An organizationdiagram of the 2D-RFCMANN is depicted in Figure 4(b)Areas formed by blocks referred to as 119891

111119891211

119891112

119891211

and so forth are called receptive fields (or hypercube)


Moreover the number of receptive fields is equal to 1198992

119895in each

layer

Space 4 (weight space) Each receptive-field area correspondsto a particular adjustable value in the weight space Theoutput of the weight memory can be described as

1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952

(119873) is the output of the weight memory corre-sponding to ℎ

11989411989511198952

(119873) and 11990811989411989511198952

(119873) denotes the connectingweight value of the output associated with the 119895

1th block of

1199091and the 119895

2th block of 119909

1in the ith layer

Space 5 (output space) The output of the 2D-RFCMANN isthe summation of the entire activated weighted field

1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952

(119873) is the product of the output of the weightmemory and the output of receptive-field Moreover 1199105

119900= 119894lowast

119902

for the active power control and1199105

119900= 119894lowast

119889for the reactive power

control in the GCIAn example is demonstrated to show the relation between

2D-RFCMANN and its fuzzy inference system As shown inFigure 3(b) if the inputs of 2D-RFCMANN fall within thestate (3 5) three reception fields are activated which are119867

1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233

Each hypercubeof the reception-field space is subject to the respectiveweights119908112

119908222

and 119908323

in the weight space

42 Online Learning Algorithm of 2D-RFCMANN Since theonline learning algorithms of the active and reactive powercontrols are the same only the detailed derivation of thereactive power control is discussed in this study To describethe online learning algorithm of the 2D-RFCMANN for theinput command tracking using supervised gradient decentmethod first the energy function 119864 is defined as

119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)

where 119890(119873) represents the tracking error in the learningprocess of the 2D-RFCMANN for each discrete time 119873119910lowast

(119873) and 119910(119873) represent the desired output and the currentoutput of the system Then the backpropagation learningalgorithm is described as follows

Space 5The error term to be propagated is given by

1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)

The weights are updated by the amount

Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)

where the factor 1205781is the learning rate of memory weights

11990811989411989511198952

is updated according to the following equation

11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)

Space 2 Applying the chain rule the update laws for 119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)

where the factors 1205782 1205783 and 120578

4are the learning rates

119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901

are updated according to the followingequation

119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)

Moreover the exact calculation of the Jacobian of the system120597119910120597119910

5

119900(119873) is difficult to be determined due to the unknown

dynamics of the single-stage three-phase grid-connected PVsystem To overcome this problem a delta adaptation law isadopted as follows [18]

1205755

119900cong (119910lowast

minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)

where 119910lowast and 119910 represent the first derivatives of 119910

lowast and 119910respectively Furthermore the selection of the values of the


0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A

Figure 5 Experimental results of irradiance abrupt change using 2D-RFCMANN controller

learning rate parameters of the 2D-RFCMANN has a signif-icant effect on the network performance Therefore in orderto train the 2D-RFCMANN effectively the varied learningrates which guarantee the convergence of the tracking errorsbased on the analysis of a discrete-type Lyapunov functionare derived as follows

1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)

where 120576 is a positive constant The derivation is similar to theone in [18] and is omitted in this study

5 Experimental Results

The schematic diagram of the PC-based control system isdepicted in Figure 4The 120579

119890is obtained byDSOGI-PLL block

The 119875and 119876 are obtained by the instantaneous active andreactive power calculation block shown in (4) and (5) The119881sag calculation block determines the value of 119881sag and thegrid fault signal is activated while 119881sag is greater than 01The 119875ref and119876

lowast are obtained by the active and reactive powerreferences calculation block The first PI controller (PI1) orthe first 2D-RFCMANN(2D-RFCMANN1) is adopted for thecontrol loop of 119881pv or 119875 to regulate the control output 119894lowast

119902 The

control loop of 119876introduces the second PI controller (PI2)or the second 2D-RFCMANN controller (2D-RFCMANN2)to regulate the control output 119894

lowast

119889 Moreover since the single-

stage three-phase grid-connected PV system is a nonlinearsystem with uncertainties the plant model is difficult toobtain by mathematical analysis or experimentation There-fore the parameters of PI controllers are tuned by trial anderror in this study to achieve the best control performanceconsidering the stability requirement The transfer functionsof these PI controllers which are adopted in this paper canbe generally expressed as 119896

119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is

the proportional gain and 119896119894119899is the integral gain The gains

of these PI controllers 1198961199011 1198961198941 1198961199012 and 119896

1198942are tuned to be

12 1 1 and 12 Furthermore both PI and 2D-RFCMANN


0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)

Figure 6 Experimental results of Case 1 (a) using PI controllers and (b) using 2D-RFCMANN controllers

controllers are implemented in the experimentation for thecomparison of the control performance In order to measurethe control performance of the mentioned controllers theaverage tracking error 119879avg the maximum tracking error119879MAX and the standard deviation of the tracking error 119879

120590for

the reference tracking are defined as follows [18]

119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast

(119873) is the 119873th value of the reference (119876lowast(119873)) and119879(119873) is the 119873th value of the response (119876(119873)) The compar-ison of the control performance can be demonstrated usingthe maximum tracking error and the average tracking errorThe oscillation of the reference tracking can be measured bythe standard deviation of the tracking error

The emulated irradiance varying from 600Wm2 to300Wm2 has been programmed in the PV panel simulatorto evaluate the MPPT performance at normal state Themeasured 119875 119875pv 119881pv 119868pv and one of the line currents ofGCI 119894

119886are shown in Figure 5 In the beginning 119875pv 119875 119881pv

and 119868pv are 610W 546W 2038 V and 306A respectivelyand the amplitude of 119894

119886is 41 A At 119905 = 02 s the irradiance

changes abruptly to 300Wm2 and 119875pv drops to 311WThen 119875 drops to 267W 119881pv drops to 2016V 119868pv decreasesto 16 A the amplitude of 119894

119886reduces to 23 A From the

experimental results when the 2D-RFCMANN1 controller is


Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)


used the settling time of 119875 is about 03 s Meanwhile the totalharmonic distortion (THD) of the current of the GSI is about45TheTHDof theGCI is smaller than theTHDregulationof IEEE 1547 standard Therefore the performances of theIC MPPT method satisfy the requirements of fast responseand low THD for the proposed single-stage three-phase grid-connected PV system operating under normal condition

Two cases of emulated grid faults with different voltagesags have been programmed in the ac power supplies toevaluate the behavior of the proposed PV system Thefollowing grid faults at PCC are selected in this study Case1 two-phase ground fault with 02 pu voltage sag (sag typeE) and Case 2 two-phase ground fault with 08 pu voltagesag (sag type E) In the experimentation first the grid linevoltages are balanced and set at 10 puThen at time 119905 = 02 sthe sag happens and the reactive and active power controlsare enabled

Case 1 In this case the measured 119875 119876 119876lowast 119881pv and 119868pv andthe measured three-phase currents are shown in Figure 6(a)for the PI controller and Figure 6(b) for the 2D-RFCMANNcontroller respectively In the beginning 119875pv is 608W and119875 is 538W due to the power losses in GCI Moreover theamplitude of the inverter output currents is 4 A At 119905 = 02 sa two-phase ground fault occurs with 02 pu voltage sag ongrid side and |119881

+

119897| is 0864 pu (95Vrms) according to (13)

where 10 pu is equal to 110Vrms 119881sag and 119868lowast

119903are equal to

0136 pu and 272 according to (15) and (14) respectively Byusing (16) and (17) 119875lowast and 119876

lowast are determined to be 794Wand 2246 var respectively Since 119875

lowast is greater than 119875 119875refis set to 119875 and eventually both 119875pv and 119875 are unchangedThus 119876 rises to 224 var during the grid faults Furthermorethe injection currents are approximately balanced and limitedunder 71 A peak value From the experimental results whenthe PI controllers are used the settling time ofQ is about 12 s


1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN

measuring of Q at Case1Performance

(a)

Maximum Maximum

AverageAverage

Standard deviationStandard deviation

500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)

Figure 8 Performance measuring (a) Performance measuring at Case 1 (b) Performance measuring at Case 2

On the other hand the settling time of 119876 is reduced to 03 sby using the 2D-RFCMANN controllers

Case 2 In this case the measured 119875 119876 119875ref 119876lowast 119881pv and

119868pv and the measured three-phase currents are shown inFigure 7(a) for the PI controllers and Figure 7(b) for the2D-RFCMANN controllers respectively At 119905 = 02 s two-phase ground fault occurs with 08 pu voltage sag on gridside Thus |119881

+

119897| and 119868

lowast

119903are equal to 0462 pu and 100

respectively and 119875ref is set to zero and the GCI gives uptracking theMPPAs a result119875pv and119875 drop to 92Wand 2WrespectivelyMoreover theGCI injects 493 var reactive powerinto the grid due to the 100 reactive current compensationWhen either PI controller or 2D-RFCMANN controller isused 119881pv rises from 202V to 230V and 119868pv drops from31 A to 037A due to the injected active power being set tozero From the experimental results when the PI controllersare used the settling time of 119876 and 119875 is about 10 s and06 s respectively On the other hand the settling time of 119876

and 119875 is about 04s and 01 s by using the 2D-RFCMANNcontrollers Furthermore the maximum injection currentsare still limited within the maximum current limit

From the experimental results of the previous twocases it can be stated that the proposed single-stage three-phase grid-connected PV system has clearly demonstrated

its capabilities These include the ability of dealing withvoltage sags with satisfying the LVRT regulation and theability of avoiding over current of the GCI The perfor-mance measuring of the PI controller and 2D-RFCMANNcontroller for the command tracking is shown in Figure 8using (31) From the resulted performance measuring of PIand 2D-RFCMANN controllers the performances of 2D-RFCMANN controllers are superior to PI controllers

6 Conclusions

This study has proposed an intelligent active and reactivepower control scheme using 2D-RFCMANN for single-stagethree-phase grid-connected PV system operating during gridfaults The mathematical analysis of the injected reactivepower during the grid faults has been introduced A newformula for evaluating the percentage of voltage sag has beenproposed The proposed formula which is based on positivesequence voltage is used to determine the ratio of the injectedreactive current during grid faults for committing to theLVRT regulation Moreover the network structure onlinelearning algorithms and learning rates of the proposed 2D-RFCMANN have been discussed in detail The analyses ofthe experimental results indicate that the proposed scheme


is capable of providing reactive current support for a grid-connected PV system during grid faults Furthermore thecontrol performance of the intelligent control scheme using2D-RFCMANN is better than traditional control schemeusing PI due to its online training of network parameters andthe capability of parallel processing

The contributions of this study are (1) the developmentof a single-stage three-phase grid-connected PV system withthe compensation of reactive current during grid faults (2)the design of the 2D-RFCMANN control scheme and itsonline learning algorithms with convergence analysis and(3) the development of the 2D-RFCMANN controller in thereactive power and PV panel voltage control of a single-stage three-phase grid-connected PV system according to theLVRT regulation with the limitation of themaximum currentoutput of GCI during grid faults

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to acknowledge the financial supportof the National Science Council of Taiwan throughGrant noNSC 103-3113-P-008-001

References

[1] S-Y Wang C-L Tseng and S-C Chien ldquoAdaptive fuzzycerebellar model articulation control for switched reluctancemotor driverdquo IET Electric Power Applications vol 6 no 3 pp190ndash202 2012

[2] Y N Wang T Q Ngo T L Mai and C Z Wu ldquoAdaptiverecurrent wavelet fuzzy CMAC tracking control for de-icingrobot manipulatorrdquo in Proceedings of the World Congress onEngineering and Computer Science vol 1 pp 372ndash379 2012

[3] C Wen and M Cheng ldquoDevelopment of a recurrent fuzzyCMACwith adjustable input space quantization and self-tuninglearning rate for control of a dual-axis piezoelectric actuatedmicromotion stagerdquo IEEETransactions on Industrial Electronicsvol 60 no 11 pp 5105ndash5115 2013

[4] C T Chiang and C S Lin ldquoIntegration of CMAC and radialbasis function techniquesrdquo in Proceedings of the IEEE Interna-tional Conference on Intelligent Systems for the 21st Century vol4 pp 3263ndash3268 1995

[5] C Lin H Chen and C Lee ldquoA self-organizing recurrent fuzzyCMACmodel for dynamic system identificationrdquo in Proceedingof the IEEE International Conference on Fuzzy Systems vol 2pp 697ndash702 July 2004

[6] M H J Bollen ldquoCharacterisation of voltage sags experiencedby three-phase adjustable-speed drivesrdquo IEEE Transactions onPower Delivery vol 12 no 4 pp 1666ndash1671 1997

[7] V Ignatova P Granjon and S Bacha ldquoSpace vector method forvoltage dips and swells analysisrdquo IEEE Transactions on PowerDelivery vol 24 no 4 pp 2054ndash2061 2009

[8] EON Netz GmbH Grid Code-High and Extra High VoltageEON Netz GmbH Bayreuth Germany 2006

[9] M Castilla J Miret J L Sosa J Matas and L G de VicunaldquoGrid-fault control scheme for three-phase photovoltaic invert-ers with adjustable power quality characteristicsrdquo IEEETransac-tions on Power Electronics vol 25 no 12 pp 2930ndash2940 2010

[10] P Rodriguez A V Timbus R Teodorescu M Liserre and FBlaabjerg ldquoFlexible active power control of distributed powergeneration systems during grid faultsrdquo IEEE Transactions onIndustrial Electronics vol 54 no 5 pp 2583ndash2592 2007

[11] J Miret M Castilla A Camacho L G De Vicuna and JMatas ldquoControl scheme for photovoltaic three-phase invertersto minimize peak currents during unbalanced grid-voltagesagsrdquo IEEE Transactions on Power Electronics vol 27 no 10 pp4262ndash4271 2012

[12] C T Lee C W Hsu and P T Cheng ldquoA low-voltage ride-through technique for grid-connected converters of distributedenergy resourcesrdquo IEEE Transactions on Industry Applicationsvol 47 no 4 pp 1821ndash1832 2011

[13] A Camacho M Castilla J Miret J C Vasquez and EAlarcon-Gallo ldquoFlexible voltage support control for three-phase distributed generation inverters under grid faultrdquo IEEETransactions on Industrial Electronics vol 60 no 4 pp 1429ndash1441 2013

[14] A Nicastri and A Nagliero ldquoComparison and evaluation of thePLL techniques for the design of the grid-connected invertersystemsrdquo in Proceedings of the IEEE International Symposium onIndustrial Electronics (ISIE rsquo10) pp 3865ndash3870 July 2010

[15] R TeodorescuM Liserre and P RodriguezGrid Converters forPhotovoltaic andWind Power Systems JohnWiley amp Sons NewYork NY USA 2011

[16] R A Mastromauro M Liserre and A DellrsquoAquila ldquoControlissues in single-stage photovoltaic systems MPPT current andvoltage controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 2 pp 241ndash254 2012

[17] F Wang J L Duarte and M A M Hendrix ldquoPliant activeand reactive power control for grid-interactive converters underunbalanced voltage dipsrdquo IEEE Transactions on Power Electron-ics vol 26 no 5 pp 1511ndash1521 2011

[18] F J Lin M S Huang P Y Yeh H C Tsai and C H KuanldquoDSP-based probabilistic fuzzy neural network control for li-ionbattery chargerrdquo IEEE Transactions on Power Electronics vol 27no 8 pp 3782ndash3794 2012

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system The first dimension of the 2D-RFCMANN is for thetracking error input and the second dimension of the 2D-RFCMANN is for the derivative of the tracking error input

The penetration of renewable energy sources hasincreased significantly because of raising awareness of theenvironmental issues and the deregulation of the electricpower distribution industry Among these renewable energysources PV system is one of the main candidates to playan important role in the future of power distributionHowever the connection of a large number of distributedenergy sources (DESs) to the electrical power grid can causeinstability when electrical disturbances appear in the gridOne of the most challenging disturbances is the voltagesags [6 7] The sources of the voltage sags are various suchas short circuits between phases or phases and groundlightning and overloads To minimize the negative effectsof a large number of DESs on the reliability of the powergrids different countries have defined various low voltageride through (LVRT) regulations for DESs EON has definedthe voltage profile of the low voltage ride through (LVRT)at the grid connection for type-2 generating plants [8] Gridregulations require that the DESs have to inject reactivecurrent to support grid stability during grid faults [8] inwhich 1 pu of reactive current is required as the depth of thesag reaches 50 In this study the EON LVRT regulationis adopted to determine the ratio of the required reactivecurrent during grid faults

The asymmetrical grid voltage sags will worsen the per-formance of the grid-connected inverter (GCI) especially thedegradation of the power quality caused by the power rippleand the increase of current harmonic distortion In orderto overcome these disadvantages some control methodsbased on symmetric components have been proposed todeal with unbalanced grid faults [9ndash13] A control schemewhich can adjust the characteristics of power quality byusing two adjustable control parameters was developed in[9] In [10] a selective active power quality control based onvarious current reference generating methods was proposedReference [11] has proposed a control method to minimizethe peak value of the injection current during the voltagesag In [12] a positive and negative sequences currentinjection method was proposed to provide the active powerand reactive current without exceeding the current limitof inverter The flexible reactive current injection schemeintroduced in [13] provides voltage support during voltage sagby injecting reactive current via both positive and negativesequences However the aforementioned control methodsprincipally focus on the power control of grid-connectedinverter whereas the fulfillment of the LVRT requirementand the control of the power flow between the dc-link bus andac grid during grid faults are not well explored In this studythe 2D-RFCMANN control scheme is proposed to controlnot only the output voltage of the PV panel via the maximumpower point tracking (MPPT) in normal condition butalso the reactive power based on LVRT requirement withconsidering the power balance between dc-link bus and acgrid during grid faults

In this study the analysis of the instantaneousactivereactive output power of the three-phase GCI during

grid faults is carried out by using symmetric componentmethod The MPPT control of PV system is also consideredto ensure the power balance during grid faults Subsequentlythe dual second-order generalized integrator phase-lockedloop (DSOGI-PLL) method [10 14 15] is adopted forsynchronizing the GCI to the grid Moreover a new formulawhich is based on the positive sequence voltage is derivedto evaluate the percentage of voltage sag and to determinethe injected currents during the grid faults Furthermorethe network structure and online training algorithms ofnetwork parameters of the proposed 2D-RFCMANN for theactive and reactive power control are discussed in detailFurthermore two types of grid faults are tested and discussedto evaluate the performance of the proposed control schemeThe paper is organized as follows In Section 2 the grid-connected PV system is introduced In Section 3 theinstantaneous activereactive power formulation DSOGI-PLL synchronization mechanism and the control strategyof the grid-connected PV system during grid faults arediscussed The 2D-RFCMANN is presented in Section 4 InSection 5 the features of the proposed control scheme areexamined by some experimental results Finally Section 6draws the conclusions

2 System Description

Figure 1 shows the block diagrams of the proposed single-stage three-phase grid-connected PV system The behaviorof the PV panel is emulated by a Chroma 62100H-600S PVpanel simulator operating at 203Vdc output voltage withmaximum output power 1 kW The power grid was emu-lated by three programmable 2 kVA single-phase KIKUSUIPCR2000LE AC power supplies feeding a Y-connected100Ωphase resistive load and connected to the GCI witha 3 kVA Y-998779 transformer The 2 kVA three-phase GCI withoutput 110Vrms line to line voltage is connected to the PVpanel simulator through a dc-link capacitor and connectedto the Y-998779 transformer with three 10mHphase couplinginductorsThe switching frequency119891sw GCI of the three-phaseGCI is set at 10 kHz Table 1 shows the parameters of theexperimental setup Moreover the control system is installedon a desktop personal computer (PC) which includes an ADconverter card (PCI-1716) a PC-based control system anda DA converter card (MRC-6810) In the PC-based controlsystem the SIMULINK control package is adopted for theimplementation of the proposed algorithms of theMPPT andLVRTcontrolThe analog input signals include output voltage119881pv and current 119868pv of the PV panel simulator the outputline voltages V

119886119887 V119887119888 and V

119888119886 and line currents 119894

119886 119894119887 and

119894119888of the GCI The control output of the PC-based control

system is the three-phase reference currents of GCI 119894lowast

119886 119894lowast

119887

and 119894lowast

119888 Furthermore the emulated faults occur at the point

of common coupling (PCC)In Figure 1 the output currents of the GCI are controlled

by the maximum power point (MPP) voltage 119881lowast

pv in the nor-mal conditionThe adoptedMPPTmethod is the incrementalconductance (IC) method with a fixed incremental step sizeset for the voltage [16] Moreover if a grid fault occurs at the


DC

AC

Three-phase GCI

Current controlled

PWM

L

110220

LoadPCC

Emulatedfault

PC

AD converter



PV panel Grid

DA converter

Vpv+

minus

Ipv

Cpv

Vpv

ia ib ic

ia ib ic

ilowasta ilowastb i

lowastc

Y Δ

100ΩY-connected

= 3120601ab bc ca

ab bc caVpv Ipv

radic31 2




119886119887 V119887119888 V119888119886





119875 = k sdot i = V119886119894119886+ V119887119894119887+ V119888119894119888 (1)


sdot i

=1


(2)

where kperp


minus1 0 1

1 minus1 0

] k k = [V119886

V119887V119888]119879and i =

[119894119886

119894119887





k = k+ + kminus

i = i+ + iminus(3)

where k+ = [V+119886

V+119887


119886Vminus119887



[119894+

119886119894+

119887119894+

119888]119879 and iminus = [119894

minus

119886119894minus

119887119894minus





119876 = kperp

sdot i = (k+perp


= k+perp




sdot i+(5)



abc ++

+

dq

VCOPI

Low pass filter

SOGIBP filter

SOGIBP filter

v+d

v+q

120579e

120579e

SRF-PLL

1

sminus

120572120573

120572120573998400120572

q998400120572

q998400120573

998400120573

+120572

+120573

120572

120573

e

ea

b

c

05

05




[

[

V119886

V119887

V119888

]

]

=1003816100381610038161003816119881+1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890minus

2

3120587)

sin(120579119890+

2

3120587)

]]]]]]

]

+1003816100381610038161003816119881minus1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890+

2

3120587)

sin(120579119890minus

2

3120587)

]]]]]]

]

(6)

where |119881+

| and |119881minus


119890= 120596119890119905 and





[V120572

V120573

] = radic2

3

[[[

[

3

20

radic3

2radic3

]]]

]

[V119886

V119887

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890)

minus cos (120579119890)] + radic

3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890)

cos (120579119890)]

(7)


[V119889

V119902

] = [

[

cos (120579119890) sin (120579

119890)

minus sin (120579119890) cos (120579

119890)

]

]

[V120572

V120573

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890minus 120579119890)

minus cos (120579119890minus 120579119890)]

+ radic3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890minus 120579119890)

cos (120579119890minus 120579119890)] (8)


119890= 119890119905 and



119890 then sin(120579

119890minus 120579119890) is



to (radic62)[|119881+

|(120579119890minus120579119890)+|119881minus








120572120573= [V+120572

V+120573]119879


k+120572120573

=1

2[1 minus119902

119902 1][

[

V1015840120572

V1015840120573

]

]

(9)






voltages 119902V1015840120572and 119902V1015840

120573of V1015840120572and V1015840


119889and V+

119902


119890 Finally 120579






119876 =3

2(V119902119894119889minus V119889119894119902) 119875 =

3

2(V119889119894119889+ V119902119894119902) (10)





119876 =3

2V119902119894119889 119875 =

3

2V119902119894119902 (11)


119894119889


119886119887 V+119887119888 and V+


[[[[

[

V+119886119887

V+119887119888

V+119888119886

]]]]

]

=1

3

[

[

1 119886 1198862

1198862

1 119886

119886 1198862

1

]

]

[

[

V119886119887

V119887119888

V119888119886

]

]

= radic21003816100381610038161003816119881+

119897

1003816100381610038161003816

[[[[[[

[

sin 120579119890

sin(120579119890minus

2120587

3)

sin(120579119890+

2120587

3)

]]]]]]

]

(12)

where |119881+



11989521205873 Since V+119886119887 V+119887119888 and V+

119888119886are


1003816100381610038161003816119881+

119897

1003816100381610038161003816 = radic1

3(V+119886119887

2

+ V+119887119888

2

+ V+119888119886

2

) (13)

Note that V+119886119887 V+119887119888 and V+



119886119887

V+119887119888 and V+


Therefore |119881+



lowast



119868lowast

119903=




(14)



1003816100381610038161003816119881+

119897

1003816100381610038161003816

119881basepu (15)


119878 = (1003816100381610038161003816V119886

1003816100381610038161003816rms +1003816100381610038161003816V119887

1003816100381610038161003816rms +1003816100381610038161003816V119888

1003816100381610038161003816rms) 119868max (16)



119886 V119887 and V

119888




119876lowast

= 119878119868lowast

119903 119875

lowast


(17)






119877119894

11989511198952

If 1199091is 11989111198941198951

and 1199092is 11989121198941198952

then

11991011989411989511198952

= 11990811989411989511198952

for 119894 = 1 2 119899119894

1198951 1198952= 1 2 119899

119895

(18)

where 119899119894



11989111198941198951


block 11989121198941198952


11989411989511198952







Input space

Fuzzification space


Recurrent unit

x1

x2

f1ij1

f2ij2

fpijp

rpijp

sum

xp

zminus1

y2pijp

Output space

y5o

h111

h121

w111

w121

hij1j2

hn119894n119895n119895

wij1j2

wn119894n119895n119895

Weight space


S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

S8

S8

S9

S9

S10

S10

f111

f111

f211f221

f231

f121

f131

f212

f112

f212

f222

f232

f122

f132

f113

f123

f213

f223

f233

f133

f114

f214f224

f234

f124

f134

H1

H2

H3

Layer 1 Layer 1

Layer 2

Layer 2

Layer 3

Layer 3

x2

x1

(3 5)










DC

AC

Current controlled


L SSR



dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation



P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ


119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901



and 120590119901119894119895119901




119901119894119895119901





119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901


ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952




2according


111119891211

119891112

119891211




119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


DC

AC

Three-phase GCI

Current controlled

PWM

L

110220

LoadPCC

Emulatedfault

PC

AD converter



PV panel Grid

DA converter

Vpv+

minus

Ipv

Cpv

Vpv

ia ib ic

ia ib ic

ilowasta ilowastb i

lowastc

Y Δ

100ΩY-connected

= 3120601ab bc ca

ab bc caVpv Ipv

radic31 2




119886119887 V119887119888 V119888119886





119875 = k sdot i = V119886119894119886+ V119887119894119887+ V119888119894119888 (1)


sdot i

=1


(2)

where kperp


minus1 0 1

1 minus1 0

] k k = [V119886

V119887V119888]119879and i =

[119894119886

119894119887





k = k+ + kminus

i = i+ + iminus(3)

where k+ = [V+119886

V+119887


119886Vminus119887



[119894+

119886119894+

119887119894+

119888]119879 and iminus = [119894

minus

119886119894minus

119887119894minus





119876 = kperp

sdot i = (k+perp


= k+perp




sdot i+(5)



abc ++

+

dq

VCOPI

Low pass filter

SOGIBP filter

SOGIBP filter

v+d

v+q

120579e

120579e

SRF-PLL

1

sminus

120572120573

120572120573998400120572

q998400120572

q998400120573

998400120573

+120572

+120573

120572

120573

e

ea

b

c

05

05




[

[

V119886

V119887

V119888

]

]

=1003816100381610038161003816119881+1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890minus

2

3120587)

sin(120579119890+

2

3120587)

]]]]]]

]

+1003816100381610038161003816119881minus1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890+

2

3120587)

sin(120579119890minus

2

3120587)

]]]]]]

]

(6)

where |119881+

| and |119881minus


119890= 120596119890119905 and





[V120572

V120573

] = radic2

3

[[[

[

3

20

radic3

2radic3

]]]

]

[V119886

V119887

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890)

minus cos (120579119890)] + radic

3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890)

cos (120579119890)]

(7)


[V119889

V119902

] = [

[

cos (120579119890) sin (120579

119890)

minus sin (120579119890) cos (120579

119890)

]

]

[V120572

V120573

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890minus 120579119890)

minus cos (120579119890minus 120579119890)]

+ radic3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890minus 120579119890)

cos (120579119890minus 120579119890)] (8)


119890= 119890119905 and



119890 then sin(120579

119890minus 120579119890) is



to (radic62)[|119881+

|(120579119890minus120579119890)+|119881minus








120572120573= [V+120572

V+120573]119879


k+120572120573

=1

2[1 minus119902

119902 1][

[

V1015840120572

V1015840120573

]

]

(9)






voltages 119902V1015840120572and 119902V1015840

120573of V1015840120572and V1015840


119889and V+

119902


119890 Finally 120579






119876 =3

2(V119902119894119889minus V119889119894119902) 119875 =

3

2(V119889119894119889+ V119902119894119902) (10)





119876 =3

2V119902119894119889 119875 =

3

2V119902119894119902 (11)


119894119889


119886119887 V+119887119888 and V+


[[[[

[

V+119886119887

V+119887119888

V+119888119886

]]]]

]

=1

3

[

[

1 119886 1198862

1198862

1 119886

119886 1198862

1

]

]

[

[

V119886119887

V119887119888

V119888119886

]

]

= radic21003816100381610038161003816119881+

119897

1003816100381610038161003816

[[[[[[

[

sin 120579119890

sin(120579119890minus

2120587

3)

sin(120579119890+

2120587

3)

]]]]]]

]

(12)

where |119881+



11989521205873 Since V+119886119887 V+119887119888 and V+

119888119886are


1003816100381610038161003816119881+

119897

1003816100381610038161003816 = radic1

3(V+119886119887

2

+ V+119887119888

2

+ V+119888119886

2

) (13)

Note that V+119886119887 V+119887119888 and V+



119886119887

V+119887119888 and V+


Therefore |119881+



lowast



119868lowast

119903=




(14)



1003816100381610038161003816119881+

119897

1003816100381610038161003816

119881basepu (15)


119878 = (1003816100381610038161003816V119886

1003816100381610038161003816rms +1003816100381610038161003816V119887

1003816100381610038161003816rms +1003816100381610038161003816V119888

1003816100381610038161003816rms) 119868max (16)



119886 V119887 and V

119888




119876lowast

= 119878119868lowast

119903 119875

lowast


(17)






119877119894

11989511198952

If 1199091is 11989111198941198951

and 1199092is 11989121198941198952

then

11991011989411989511198952

= 11990811989411989511198952

for 119894 = 1 2 119899119894

1198951 1198952= 1 2 119899

119895

(18)

where 119899119894



11989111198941198951


block 11989121198941198952


11989411989511198952







Input space

Fuzzification space


Recurrent unit

x1

x2

f1ij1

f2ij2

fpijp

rpijp

sum

xp

zminus1

y2pijp

Output space

y5o

h111

h121

w111

w121

hij1j2

hn119894n119895n119895

wij1j2

wn119894n119895n119895

Weight space


S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

S8

S8

S9

S9

S10

S10

f111

f111

f211f221

f231

f121

f131

f212

f112

f212

f222

f232

f122

f132

f113

f123

f213

f223

f233

f133

f114

f214f224

f234

f124

f134

H1

H2

H3

Layer 1 Layer 1

Layer 2

Layer 2

Layer 3

Layer 3

x2

x1

(3 5)










DC

AC

Current controlled


L SSR



dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation



P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ


119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901



and 120590119901119894119895119901




119901119894119895119901





119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901


ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952




2according


111119891211

119891112

119891211




119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


abc ++

+

dq

VCOPI

Low pass filter

SOGIBP filter

SOGIBP filter

v+d

v+q

120579e

120579e

SRF-PLL

1

sminus

120572120573

120572120573998400120572

q998400120572

q998400120573

998400120573

+120572

+120573

120572

120573

e

ea

b

c

05

05




[

[

V119886

V119887

V119888

]

]

=1003816100381610038161003816119881+1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890minus

2

3120587)

sin(120579119890+

2

3120587)

]]]]]]

]

+1003816100381610038161003816119881minus1003816100381610038161003816

[[[[[[

[

sin (120579119890)

sin(120579119890+

2

3120587)

sin(120579119890minus

2

3120587)

]]]]]]

]

(6)

where |119881+

| and |119881minus


119890= 120596119890119905 and





[V120572

V120573

] = radic2

3

[[[

[

3

20

radic3

2radic3

]]]

]

[V119886

V119887

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890)

minus cos (120579119890)] + radic

3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890)

cos (120579119890)]

(7)


[V119889

V119902

] = [

[

cos (120579119890) sin (120579

119890)

minus sin (120579119890) cos (120579

119890)

]

]

[V120572

V120573

]

= radic3

2

1003816100381610038161003816119881+1003816100381610038161003816 [

sin (120579119890minus 120579119890)

minus cos (120579119890minus 120579119890)]

+ radic3

2

1003816100381610038161003816119881minus1003816100381610038161003816 [

sin (120579119890minus 120579119890)

cos (120579119890minus 120579119890)] (8)


119890= 119890119905 and



119890 then sin(120579

119890minus 120579119890) is



to (radic62)[|119881+

|(120579119890minus120579119890)+|119881minus








120572120573= [V+120572

V+120573]119879


k+120572120573

=1

2[1 minus119902

119902 1][

[

V1015840120572

V1015840120573

]

]

(9)






voltages 119902V1015840120572and 119902V1015840

120573of V1015840120572and V1015840


119889and V+

119902


119890 Finally 120579






119876 =3

2(V119902119894119889minus V119889119894119902) 119875 =

3

2(V119889119894119889+ V119902119894119902) (10)





119876 =3

2V119902119894119889 119875 =

3

2V119902119894119902 (11)


119894119889


119886119887 V+119887119888 and V+


[[[[

[

V+119886119887

V+119887119888

V+119888119886

]]]]

]

=1

3

[

[

1 119886 1198862

1198862

1 119886

119886 1198862

1

]

]

[

[

V119886119887

V119887119888

V119888119886

]

]

= radic21003816100381610038161003816119881+

119897

1003816100381610038161003816

[[[[[[

[

sin 120579119890

sin(120579119890minus

2120587

3)

sin(120579119890+

2120587

3)

]]]]]]

]

(12)

where |119881+



11989521205873 Since V+119886119887 V+119887119888 and V+

119888119886are


1003816100381610038161003816119881+

119897

1003816100381610038161003816 = radic1

3(V+119886119887

2

+ V+119887119888

2

+ V+119888119886

2

) (13)

Note that V+119886119887 V+119887119888 and V+



119886119887

V+119887119888 and V+


Therefore |119881+



lowast



119868lowast

119903=




(14)



1003816100381610038161003816119881+

119897

1003816100381610038161003816

119881basepu (15)


119878 = (1003816100381610038161003816V119886

1003816100381610038161003816rms +1003816100381610038161003816V119887

1003816100381610038161003816rms +1003816100381610038161003816V119888

1003816100381610038161003816rms) 119868max (16)



119886 V119887 and V

119888




119876lowast

= 119878119868lowast

119903 119875

lowast


(17)






119877119894

11989511198952

If 1199091is 11989111198941198951

and 1199092is 11989121198941198952

then

11991011989411989511198952

= 11990811989411989511198952

for 119894 = 1 2 119899119894

1198951 1198952= 1 2 119899

119895

(18)

where 119899119894



11989111198941198951


block 11989121198941198952


11989411989511198952







Input space

Fuzzification space


Recurrent unit

x1

x2

f1ij1

f2ij2

fpijp

rpijp

sum

xp

zminus1

y2pijp

Output space

y5o

h111

h121

w111

w121

hij1j2

hn119894n119895n119895

wij1j2

wn119894n119895n119895

Weight space


S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

S8

S8

S9

S9

S10

S10

f111

f111

f211f221

f231

f121

f131

f212

f112

f212

f222

f232

f122

f132

f113

f123

f213

f223

f233

f133

f114

f214f224

f234

f124

f134

H1

H2

H3

Layer 1 Layer 1

Layer 2

Layer 2

Layer 3

Layer 3

x2

x1

(3 5)










DC

AC

Current controlled


L SSR



dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation



P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ


119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901



and 120590119901119894119895119901




119901119894119895119901





119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901


ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952




2according


111119891211

119891112

119891211




119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119876 =3

2(V119902119894119889minus V119889119894119902) 119875 =

3

2(V119889119894119889+ V119902119894119902) (10)





119876 =3

2V119902119894119889 119875 =

3

2V119902119894119902 (11)


119894119889


119886119887 V+119887119888 and V+


[[[[

[

V+119886119887

V+119887119888

V+119888119886

]]]]

]

=1

3

[

[

1 119886 1198862

1198862

1 119886

119886 1198862

1

]

]

[

[

V119886119887

V119887119888

V119888119886

]

]

= radic21003816100381610038161003816119881+

119897

1003816100381610038161003816

[[[[[[

[

sin 120579119890

sin(120579119890minus

2120587

3)

sin(120579119890+

2120587

3)

]]]]]]

]

(12)

where |119881+



11989521205873 Since V+119886119887 V+119887119888 and V+

119888119886are


1003816100381610038161003816119881+

119897

1003816100381610038161003816 = radic1

3(V+119886119887

2

+ V+119887119888

2

+ V+119888119886

2

) (13)

Note that V+119886119887 V+119887119888 and V+



119886119887

V+119887119888 and V+


Therefore |119881+



lowast



119868lowast

119903=




(14)



1003816100381610038161003816119881+

119897

1003816100381610038161003816

119881basepu (15)


119878 = (1003816100381610038161003816V119886

1003816100381610038161003816rms +1003816100381610038161003816V119887

1003816100381610038161003816rms +1003816100381610038161003816V119888

1003816100381610038161003816rms) 119868max (16)



119886 V119887 and V

119888




119876lowast

= 119878119868lowast

119903 119875

lowast


(17)






119877119894

11989511198952

If 1199091is 11989111198941198951

and 1199092is 11989121198941198952

then

11991011989411989511198952

= 11990811989411989511198952

for 119894 = 1 2 119899119894

1198951 1198952= 1 2 119899

119895

(18)

where 119899119894



11989111198941198951


block 11989121198941198952


11989411989511198952







Input space

Fuzzification space


Recurrent unit

x1

x2

f1ij1

f2ij2

fpijp

rpijp

sum

xp

zminus1

y2pijp

Output space

y5o

h111

h121

w111

w121

hij1j2

hn119894n119895n119895

wij1j2

wn119894n119895n119895

Weight space


S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

S8

S8

S9

S9

S10

S10

f111

f111

f211f221

f231

f121

f131

f212

f112

f212

f222

f232

f122

f132

f113

f123

f213

f223

f233

f133

f114

f214f224

f234

f124

f134

H1

H2

H3

Layer 1 Layer 1

Layer 2

Layer 2

Layer 3

Layer 3

x2

x1

(3 5)










DC

AC

Current controlled


L SSR



dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation



P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ


119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901



and 120590119901119894119895119901




119901119894119895119901





119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901


ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952




2according


111119891211

119891112

119891211




119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Input space

Fuzzification space


Recurrent unit

x1

x2

f1ij1

f2ij2

fpijp

rpijp

sum

xp

zminus1

y2pijp

Output space

y5o

h111

h121

w111

w121

hij1j2

hn119894n119895n119895

wij1j2

wn119894n119895n119895

Weight space


S1

S1

S2

S2

S3

S3

S4

S4

S5

S5

S6

S6

S7

S7

S8

S8

S9

S9

S10

S10

f111

f111

f211f221

f231

f121

f131

f212

f112

f212

f222

f232

f122

f132

f113

f123

f213

f223

f233

f133

f114

f214f224

f234

f124

f134

H1

H2

H3

Layer 1 Layer 1

Layer 2

Layer 2

Layer 3

Layer 3

x2

x1

(3 5)










DC

AC

Current controlled


L SSR



dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation



P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ


119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901



and 120590119901119894119895119901




119901119894119895119901





119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901


ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952




2according


111119891211

119891112

119891211




119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


DC

AC

Current controlled


L SSR



dqabc

LimiterLimiter

3-phase grid

Grid fault signal

Y

110220

PI22D-RFCMANN2

Three-phaseGCI

MPPT

SW1

PI12D-RFCMANN1

+

P

Q

Q

PV panel

DSOGI-PLL

calculation



P

+

SW20

+

ia ib ic

ia

ib

ic

ilowasta

ilowastq

ilowastb ilowastc

ilowastd

ab bc ca

ab

bc ca

radic31 2

Vpv

Vsag

Vsag

Cpv

Vpv

VpvI pv

100Ω

Imax

Δminus

minus

minus

minus

minus

minus

minus

e

Pre fPre f

Qlowast

++

+

+

+ Vlowastpv

Y-Δ


119891119901119894119895119901(119873) = exp(minus

(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205902

119901119894119895119901

)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

1199102

119901119894119895119901

(119873) = 119909119901(119873) + 119903

119901119894119895119901

119891119901119894119895119901(119873 minus 1)

119901 = 1 2 119894 = 1 2 119899119894 119895119901

= 1 2 119899119895

(19)

where 119891119901119894119895119901



and 120590119901119894119895119901




119901119894119895119901





119901119894119895119901

119898119901119894119895119901

and 120590119901119894119895119901


ℎ11989411989511198952(119873) = 119891

11198941198951(119873) 11989121198941198952(119873)

= exp(minus

(1199102

11198941198951

(119873) minus 11989811198941198951

)2

1205902

11198941198951

)

times exp(minus

(1199102

21198941198952

(119873) minus 11989821198941198952

)2

1205902

21198941198952

)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(20)

where ℎ11989411989511198952




2according


111119891211

119891112

119891211




119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119895in each

layer


1199104

11989411989511198952

(119873) = 11990811989411989511198952(119873)

119894 = 1 2 119899119894 1198951 1198952= 1 2 119899

119895

(21)

where 1199104

11989411989511198952


11989411989511198952

(119873) and 11990811989411989511198952


1th block of

1199091and the 119895

2th block of 119909

1in the ith layer


1199105

119900(119873) =

119899119894

sum

119894=1

1199105

11989411989511198952

(119873)

1199105

11989411989511198952

(119873) = 11990811989411989511198952(119873) ℎ11989411989511198952(119873)

(22)

where 1199105

11989411989511198952


119900= 119894lowast

119902


119900= 119894lowast




1=

119891111

119891212

1198672

= 119891122

119891222

and 1198673

= 119891132

119891233


119908222

and 119908323

in the weight space


119864 (119873) =1

2(119910lowast

(119873) minus 119910 (119873))2

=1

21198902

(119873) (23)




1205755

119900= minus

120597119864

1205971199105119900(119873)

= minus120597119864 (119873)

120597119910

120597119910

1205971199105119900(119873)

= 119890 (119873)120597119910

1205971199105119900(119873)

(24)


Δ11990811989411989511198952(119873) = minus120578

1

120597119864

12059711990811989411989511198952(119873)

= minus1205781

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

12059711990811989411989511198952(119873)

= 12057811205755

119900ℎ11989411989511198952(119873)

(25)


11990811989411989511198952


11990811989411989511198952(119873 + 1) = 119908

11989411989511198952(119873) + Δ119908

11989411989511198952(119873) (26)


120590119901119894119895119901

and 119903119901119894119895119901

are

Δ119898119901119894119895119901(119873) = minus120578

2

120597119864

120597119898119901119894119895119901

= minus1205782

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119898119901119894119895119901

= 12057821205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

Δ120590119901119894119895119901(119873) = minus120578

3

120597119864

120597120590119901119894119895119901

= minus1205783

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597120590119901119894119895119901

= 12057831205755

1199001199105

11989411989511198952

(119873)

2(1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

2

1205903

119901119894119895119901

Δ119903119901119894119895119901(119873) = minus120578

4

120597119864

120597119903119901119894119895119901

= minus1205784

120597119864

1205971199105119900(119873)

1205971199105

119900(119873)

120597119903119901119894119895119901

= 12057841205755

1199001199105

11989411989511198952

(119873)

2 (1199102

119901119894119895119901

(119873) minus 119898119901119894119895119901

)

1205902

119901119894119895119901

times 1198911119894119895119901(119873 minus 1)

(27)



119898119901119894119895119901

120590119901119894119895119901

and 119903119901119894119895119901


119898119901119894119895119901(119873 + 1) = 119898

119901119894119895119901(119873) + Δ119898

119901119894119895119901(119873)

120590119901119894119895119901(119873 + 1) = 120590

119901119894119895119901(119873) + Δ120590

119901119894119895119901(119873)

119903119901119894119895119901(119873 + 1) = 119903

119901119894119895119901(119873) + Δ119903

119901119894119895119901(119873)

(28)


5



1205755


minus 119910) + ( 119910lowast

minus 119910) = 119890 + 119890 (29)




0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

Irradiance change

10V1A

0

Irradiance change

Irradiance change

P

Ipv

Ia

Vpv

Ppv

200W

600W

160V0A

01 s

01 s

01 s

190V3A

25A



1205781=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119908

11989411989511198952

))2

+ 120576]

1205782=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119898

119901119894119895119901

))

2

+ 120576]

1205783=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597120590

119901119894119895119901

))

2

+ 120576]

1205784=

119864 (119873)

4 [sum119899119894

119894=1((1205971198641205971199105

119900(119873)) (1205971199105

119900(119873) 120597119903

119901119894119895119901

))

2

+ 120576]

(30)







119902 The


lowast



119901119899+ 119896119894119899119904 119899 = 1 2 where 119896

119901119899is






0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0Fault occurs

0

Fault occurs

4A

0

4A

Fault occurs

600W

02 s

02 s

02 s

Ipv

Vpv

Qlowast

Ppv

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

71A

minus71A

001 s

ia ib ic

|V+l |

(a)

4A

4A 02s

0

0

0

600W

02 s

02 sIpv

Qlowast

ia ib ic

ia ib ic

200V

P

Q

50Vrms2A

200Wvar

0

minus71A

001 s

|V+l |

Fault occurs

Fault occurs

Fault occurs

Vpv

Ppv

71A

(b)



120590for


119879119889(119873) = 119879

lowast

(119873) minus 119879 (119873)

119879MAX = max119873

(1003816100381610038161003816119879119889 (119873)

1003816100381610038161003816) 119879avg =1

119898(

119898

sum

119873=1

119879119889(119873))

119879120590

= radic1

119898(

119898

sum

119873=1

(119879119889(119873) minus 119879avg)

2

)

(31)

where 119879lowast










Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Qlowast

ia ib

ib

ic

ia ic

4A

4A

|V+l |

02 s

02 s

02 s

001 s

Q Ppv

200Wvar

50Vrms2A

Pref

P

Ipv

Vpv

Fault occurs

Fault occurs

Fault occurs

0

0

0

600W

200V

0

71A

minus71A

(a)

0

0

0

600W

200V

0

71A

minus71A

4A

4A

200Wvar PREF

02 s

02 s

02 s

Qlowast

PpvQP

Vpv

50Vrms2A

|V+l |

Ipv

ia i ic

ia i ic

b

b

001 s

Fault occurs

Fault occurs

Fault occurs

(b)





+



119903are equal to





1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


1009080706050403020100 Maximum Average

702

9858

147234

1102 832

Standard deviation

PI2D-RFCMANN


(a)

Maximum Maximum

AverageAverage


500 300

450400350300250

250

200

200

150100500

150

100

50

0

29958

25468

minus1686minus625

47651342

PI2D-RFCMANN

PI2D-RFCMANN

minus50

45843

30091

21911868 5387 482



(b)





+

119897| and 119868

lowast






6 Conclusions







Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






Acknowledgment


References




























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

research article reactive power control of single-stage three...

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