Design And Implementation Of PI And PR

Current Controllers For Smart Inverter

Applications. Sowmya A.T. , Student at MEPCO SCHLENK Engineering college.

Mr.M.Muhaidheen, Senior Grade (Asst. Prof .EEE) at MEPCO SCHLENK Engineering College.

Abstract-To Regulate the output power of smart inverter in all operating conditions of the grid. Two common

methods for power regulation of the smart inverter are: 1) Proportional-resonant (PR) controllers in

stationary reference frame or equally αβ frame. 2) Transforming the variables to synchronous reference

frame (SRF) or equally DQ frame. To do a comparative study on the performance of these current

controllers.

I. INTRODUCTION

The growing penetration of distributed generation

(DG) units into the power grid, requiring DGs to

provide advanced grid functionality (AGF) such as

improved fault detection and allow self-healing of the

network Flexibility in network topology Load

adjustment/Load balancing Sustainability. These

functionalities aim to support the grid during faults

and fluctuations. Low-/high-voltage ride through

(L/HVRT), low-/high-frequency ride through

(L/HFRT), and reactive power generation are

examples of the AGFs expected by the revised

standards. Realization of such functionalities in the

DG needs an advanced control structure. Since the

inverter plays the key role in control of the DG, its

controller is expected to be designed adequately to

help the DG comply with the new standards.

Accordingly, as the basic requirement, an advanced

and smart inverter needs fast and robust dynamics

with flexible control structure that is able to regulate

its output power in all operating conditions of the

grid. Two common methods for power regulation of

the smart inverter are:

1) Using proportional-resonant (PR)

controllers in stationary reference frame or equally

αβ frame, and

2) Transforming the variables to

synchronous reference frame (SRF) or equally DQ

frame.

Using proportional-integral (PI) controllers,

PR controllers in stationary frame are simple, and

they can control either the instantaneous power of the

inverter directly, or the average value of the output

power by means of the conventional current control

schemes. The PI controller in SRF is also a well-

known structure, providing power regulation based

on the instantaneous power theory. PR controllers in

αβ frame are basically equivalent (in view of the

fundamental frequency) to PI controllers in DQ

frame. Depending on the application, either of these

methods is used. In this study, a DQ frame controller

is applied to the smart inverter to provide a fast and

robust power regulation scheme. DQ frame

controllers were originally introduced for three phase

systems, and then, extended to single-phase

applications. In these controllers, αβ/DQ

transformation turns ac variables into equivalent dc

quantities, thus they can be controlled by PI

controllers. The design process of PI controllers is

simple and they exhibit satisfactory dynamic and

steady-state performance.

∗

Also, as the system variables are converted

to dc quantities, the control loop has no dependence

on the system frequency. In addition, this scheme can

regulate active and reactive power independently by

simple adjustment of the D and Q-axis currents,

respectively. DQ current control of single-phase

inverters requires an orthogonal signal generation

(OSG) block to provide the orthogonal component of

the grid current in αβ frame. Conventionally, OSG is

implemented using phase shift methods such as

Hilbert transform, time delay, all pass filter, and

second-order generalized integrator (SOGI).

Although the steady-state performances of these

methods are acceptable for most part, the delay to

create 90ºphase shift slows down the system dynamic

response that can be problematic in smart inverters.

Moreover, frequency drifts result in an inaccurate

phase shift, which could lead to unacceptable errors

in active and reactive power control.

Stationary reference frame proportional-

resonant (PR) controllers or equally αβ have the

ability of achieving zero steady state error without

the need for computational-intensive reference frame

transformations. Transforming the variables to

synchronous reference frame (SRF) or equally DQ

current controller generates the grid current

orthogonal component without introducing any

additional dynamics or distortions to the control loop.

Proportional-resonant (PR) controllers are equivalent

to conventional PI controllers implemented in the -

reference frame, separately for the positive and

negative sequences. Therefore, the PR controller is

capable of simultaneously tracking the reference for

the positive and negative sequence with zero steady

state error. For example, a sixth harmonic PR

compensator is effective for the fifth and seventh

harmonics of both sequences; hence, four harmonics

are filtered with one PR filter implemented in the

SRF Simulation and experimental results show the

feasibility and performance of this control structure.

II. CURRENT CONTROL

A. PI CONTROL

A general block diagram of a single-phase grid-

connected inverter controlled in DQ frame is shown

in Fig. 2, where the inverter is interfaced with the

grid through a passive filter. Grid voltage and the

current are fed back to the controller. The controller

is responsible for injecting a sinusoidal current

meeting the grids’ requirements on power quality

and dynamic performance. As it can be seen in this

figure, current controller needs an OSG block to

generate the β-axis component of the grid current

(igβ ).

Fig.2 General block diagram for current

control using PI controller.

In addition, a phase-locked loop (PLL) is used in

this scheme to synchronize the inverter to the grid.

Details of the DQ frame current controller is shown

in Fig. 3. This controller consists of PI controllers,

decoupling terms, and feed-forward terms in both D-

and Q-axes.

The transfer function of PI current

controller HPI(s) is represented by:

OSG TECHNIQUE

Assuming the grid current as (1), the 90º delayed

version of this current will have the form of (2)

igα = A sin(θ + ϕ) (1)

igβ = −A cos(θ + ϕ) (2)

where θ

(3)

In (1)–(3), ω and θ are the angular frequency and

phase angle of the grid voltage, and ϕ is the phase

angle between the grid voltage and current. The

reference value of the D- and Q-axes currents (Id*

and Iq* ) correspond to α-axis reference current

(igα*) in the form of

igα * = B sin(ψ ) (4)

where ψ is angle of the αβ/DQ transformation and

B= (Id*2 +Iq*

2 ) , =

(5)

The objective is to estimate the actual igβ . If

the PLL is operating in steady state, ψ will be equal

to θ. Meanwhile, since PI controllers are chosen and

they eliminate the steady-state error of the current

controller, igα will eventually become equal to

igα∗ Similarly, if the β-axis component of the grid

current actually existed, this current also would have

become equal to igβ* . Therefore, the β-axis

component can be estimated based on the reference

value of the D- and Q-axes currents. In view of that,

the proposed method uses Id* and Iq* values to

generate an estimation of igβ (i.e.,ˆigβ ) in the form

of (6). A block diagram of this method is shown in

Fig. 4

igβ * = - B cos(ψ ) (6)

The proposed method does not introduce any

dynamics in generating the orthogonal signal and

does not introduce any distortion into it. Therefore, it

results in a fast and smooth output current response.

In addition, this method has no dependence on the

systems’ model (such as the inductance), since the β-

axis current is generated solely based on the

reference values of the D- and Q-axis currents.

B. PR CONTROL

A shortcoming with the PI controller

generally is that it is not able to follow a sinusoidal

reference without steady state error due to the

dynamics of the integral term. The inability to track a

sinusoidal reference causes the need to use the grid

voltage as a feed-forward term to obtain a good

dynamic response by helping the controller to try to

reach steady state faster. A current controller which is

more suited to operate with sinusoidal references and

does not suffer from the above mentioned drawback

is the PR controller. The PR controller provides gain

at a certain frequency (resonant frequency) and

almost no gain exists at the other frequencies. Block

diagram of this method is shown in Fig. 5

PR controller transfer function is given by,

The relationship between the DQ-

components and the -components is given by an

anticlockwise rotating Park’s vector;

Thus, the influence of the Park

transformation can be expressed as the frequency

shift of all the frequencies in the frequency

domain. The equivalent transfer function of the

PR controller is in the SRF. can be derived from a PI

controller implemented in positive- and negative-

sequence HRFs, taking into account (6. 2) and (6.3)

For the non-ideal integrators of

, the PR

controller transfer function takes the form. Equation

(6.4) describes an ideal PR controller with infinite

gain at the tuned frequency and no phase shift and

gain at the other frequencies. The disadvantage of

such a controller in practical applications is the

possible stability problem associated with in-finite

gain. The controller gains such as Proportional and

resonant gains are computed at frequency for the

design of the controller.

This method is based on an optimization problem,

which provides the control signal

P*(t) = P*(1 + cos (2θ)) + Q* sin (2θ) (11)

The control signal generation block is shown

in Fig. 6

III. PI AND PR CURRENT CONTROLLER

DESIGN

A. PI Controller Design

The PI controller was designed for a damping

factor in the range of 0.8 and a natural frequency in

the range of 314.2 rad/sec, obtaining a Kp of 4.21 and

KI of 2107. The damping factor ζ obtained was 0.85

and the natural frequency ωn obtained was 3360

rad/sec.

B.PR Controller Design

The PR controller was designed for a resonant

frequency ω0 of 314.2rad/s (50Hz) and ωc was set to

be 0.5rad/s, obtaining a Kp of 5.1 and KI of 2073.15.

IV. SIMULATION RESULTS

MATLAB SIMULATION USING PI CURRENT

CONTROLLER

Parameters Value

Dc link voltage 750V

Grid voltage 230V

Grid frequency 50Hz

Kp 4.21

Ki 2107

Filter inductances

Li

1.2mH

Lg 0.7mH

Filter Capacitances 9μF

Table.1 SYSTEM PARAMETERS FOR

SIMULATION USING PI CONTROL

Fig .7 SIMULATION USING PI CURRENT

CONTROLLER

OUTPUT WAVEFORM

Fig.8 INVERTER OUTPUT VOLTAGE AND

CURRENT

THD ANALYSIS

THD Analysis for Inverter output voltage is shown in

Fig 9

Fig .9 THD ANALYSIS FOR OUTPUT INVERTER

VOLTAGE

THD Analysis for Inverter output current is shown in

Fig.10

Fig .11 THD ANALYSIS FOR OUTPUT

INVERTER CURRENT

MATLAB SIMULATION USING PR CURRENT

CONTROLLER

PARAMETERS VALUE

Dc link voltage 750V

Grid voltage 230V

Grid frequency 50Hz

Kp 5.1

KR 2073.15

Filter inductances

Li

1.2mH

Lg 0.7mH

Filter Capacitances 9μF

Table.2 SYSTEM PARAMETERS FOR

SIMULATION USING PR CONTROL

Fig. 10 SIMULATION USING PI CURRENT

CONTROLLER

OUTPUT WAVEFORM

Fig.12 INVERTER OUTPUT VOLTAGE AND

CURRENT

THD ANALYSIS

THD Analysis for Inverter output voltage is shown in

Fig.13

Fig.13 THD ANALYSIS FOR OUTPUT

INVERTER VOLTAGE

THD Analysis for Inverter output current is shown in

Fig 14

Fig. 14 THD ANALYSIS FOR OUTPUT

INVERTER CURRENT

V. CONCLUSION

This report has presented a comparison

between standard PI and PR current controllers in

Grid-Connected Inverters. Results from simulations

of both current controllers are shown. Simulations

and results shows that a PI controller with voltage

feed-forward suffered from harmonic distortions

when following a sinusoidal reference. These

distortions are reduced to zero when using the PR

controller. These results demonstrate the superiority

of the PR controller for applications requiring

sinusoidal references; additional harmonic

compensation is needed in both cases to conform to

the standard regulations.

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