DECOUPLED CONTROL STRATEGY OF GRID INTERACTIVE …

DECOUPLED CONTROL STRATEGY OF GRID

INTERACTIVE INVERTER SYSTEM WITH

OPTIMAL LCL FILTER DESIGN

ANUP ANURAG (109EE0250)

Department of Electrical Engineering,

National Institute of Technology, Rourkela

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DECOUPLED CONTROL STRATEGY OF GRID

INTERACTIVE INVERTER SYSTEM WITH OPTIMAL

LCL FILTER DESIGN

A Thesis submitted in partial fulfillment of the requirements for the degree of

Bachelor of Technology in “Electrical Engineering”

By

ANUP ANURAG (109EE0250)

Under the guidance of

Prof. B.CHITTI BABU

Department of Electrical Engineering

National Institute of Technology

Rourkela-769008 (ODISHA)

May-2013

- 3 - | P a g e

DEPARTMENT OF ELECTRICAL ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA

ODISHA, INDIA-769008

CERTIFICATE

This is to certify that the thesis titled “Decoupled Control Strategy of Grid

Interactive Inverter System with Optimal LCL Filter Design”, submitted to the

National Institute of Technology, Rourkela by Mr. Anup Anurag, Roll No:

109EE0250 for the award of Bachelor of Technology in Electrical Engineering is a

bonafide record of research work carried out by him under my supervision and

guidance.

The candidate has fulfilled all the prescribed requirements.

The thesis which is based on candidate’s own work, has not submitted elsewhere

for a degree/diploma.

In my opinion, the thesis is of standard required for the award of a Bachelor of

Technology in Electrical Engineering.

Prof. B. Chitti Babu

Supervisor

Department of Electrical Engineering

National Institute of Technology

Rourkela – 769 008 (ODISHA)

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ACKNOWLEDGEMENTS

I have been highly indebted in the preparation of this report to my supervisor, Prof. B.

Chitti Babu, whose patience and kindness, as well as his academic experience, has been

invaluable to me. I could not have asked for a better role model, inspirational, supportive, and

patient guide. I could not be prouder of my academic roots and hope that I can in turn pass on

the research values and the dreams that he has given to me.

The informal support and encouragement of many friends has been indispensable, and

I would like particularly to acknowledge the contribution of all the students working under

Prof. B. Chitti Babu.

I would not have contemplated this road if not for my parents, who instilled within me

a love of creative pursuits, science and language, all of which finds a place in this report.

AnupAnurag

109EE0250

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Dedicated to

My Parents and My Brother

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ABSTRACT

This thesis presents a control strategy for a three-phase grid interactive voltage source

inverter (VSI) that links a renewable energy source to the utility grid through a LCL-type

filter. An optimized LCL-type filter has been designed and implemented so as to reduce the

current harmonics in the grid considering the conduction and switching losses at constant

modulation index (Ma). The control strategy adopted here decouples the active and reactive

power loops, thus achieving desirable performance with independent control of active and

reactive power injected to the grid. The startup transients are also controlled by the

implementation of this particular control method. Another control technique has also been

studied so as to overcome the hitches faced by the conventional controllers. It

counterbalances the distortions in grid voltage by injecting sinusoidal current into the grid.

The filter has been designed considering the conduction and switching copper losses as well

as core losses. A tradeoff has been made between the total losses due to the inductor and the

THD% of the grid current, and the filter inductor has been designed accordingly. In order to

study the dynamic performance of the system and to confirm the analytical results, the

models are simulated in the MATLAB/Simulink environment and the results are analyzed.

iv | P a g e

CONTENTS

Abstract i

Contents ii

List of Figures iv

List of Tables vi

Abbreviations and Acronyms vii

CHAPTER 1

INTRODUCTION

1.1 Motivation 3

1.2 Background and Literature Review 4

1.3 Thesis Objectives 5

1.4 Organization of Thesis 5

CHAPTER 2

CONTROL OF GRID CONNECTED INVERTER FOR SINUSOIDAL CURRENT

INJECTION WITH IMPROVED PERFORMANCE

2.1 Introduction 8

2.2 Mathematical Modeling of Grid Connected Inverter System 8

2.3 Control Algorithm of Grid Connected Inverter 10

2.3.1 Analysis of Current Controller 10

2.3.2 Filter Design 12

2.3.3 Active and Reactive Power Control 12

2.4 Results and Discussions 15

2.4.1 Active and Reactive Power Control 16

2.4.2 Current Control Strategy 18

A. Under Voltage Sag 18

B. Under line to ground fault 20

C. Under presence of harmonics using conventional controller 21

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D. Under presence of harmonics using MRF PI controller 23

2.5 Conclusions 24

CHAPTER-3

DECOUPLED CONTROL STRATEGY OF GRID INTERACTIVE INVERTER

SYSTEM

3.1 Introduction 26

3.2 Mathematical Modeling of Three Phase Grid Connected Inverter 26

3.3 Control Strategy of the Three Phase Grid Connected Inverter 27


3.5 Conclusions 33

CHAPTER-4

FILTER DESIGN USING POWER LOSS CALCULATIONS

4.1 Introduction 35

4.2 Filter Design 35

4.2.1 Inductor Power Loss 36

4.2.2 Damping Circuit and Capacitor 37

A. Fundamental Frequency Power Loss 37

B. Switching Frequency Power Loss 37


4.4 Conclusions 41

CHAPTER-5

CONCLUSIONS AND FUTURE WORK

5.1 Conclusions 44

References 45

Publications 49

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LIST OF FIGURES

Fig. No Name of the Figure Page No.

2.1 Schematic diagram of Grid Connected PWM Inverter 8

2.2 MRF PI Current Controller structure 12

2.3 Schematic diagram for the Grid Connected Inverter with its control 14

2.4 (a) Distorted grid voltages 17

(b) dq components of distorted grid voltages. 17

(c) Converter current to the grid 17

(d) q-current component converter response 18

(e) Harmonic spectrum of the grid current 18


(b) Converter current to the grid 19

(c) d-current component converter response 19












vii | P a g e

(e) Harmonic spectrum of the grid current. 22






3.1 Schematic Diagram of Three Phase GCI with LCL-type Filter 26

3.2 Control System block diagram of the LCL -type converter 31

3.3 (a) dc-link voltage across the capacitor 32

(b) d and q axis current 32

(c) Grid current waveforms 32

4.1 LCL-type filter with passive damping scheme 35

4.2 Total Power loss vs Inductance value 39

4.3 Plot between THD% and Power Losses vspu value of inductance 39

4.4 Harmonic waveform of the grid current at optimum inductor values 40

viii | P a g e

LIST OF TABLES

Table. No. Name of the Table Page No.

2.1 Parameters used in Simulation 16

3.1 Design Parameters for Control Algorithm 31

5.2 Losses at different inductance values 38

4.2 Design Parameter of LCL type filter 40

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ABBREVIATIONS AND ACRONYMS

GCI - Grid Connected Inverter

DG - Distributed Generation

MRF - Multiple Reference Frame

PI - Proportional Integral

AC - Alternating Current

DC - Direct Current

MATLAB - MATrix LABoratory

VSI - Voltage Source Inverter

PID - Proportional, Integral and Derivative

IGBT - Insulated Gate Bipolar Transistor

SRF - Synchronous Reference Frame

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CHAPTER 1

Introduction

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1.1 MOTIVATION

With the impending deregulated environment, it is imperative that the new technologies

provide acceptable power quality and reliability. It has been prophesized that Distribution

Generation (DG) System would play a very vital role in the coming years for meeting the

future energy demand with clean and green environment. Various DG technologies are

present including the photovoltaic systems, wind turbines, gas turbines, diesel engines and

fuel cell systems [1]. At present, wind energy and photovoltaic have become the most

competitive among all. The advent of power electronic devices has also ushered a new era for

the maintenance of power quality as they efficiently interface these renewable energy systems

to the grid. The integration of these renewable energy to the grid can result is several benefits

including line loss reduction, increased overall energy efficiency, reduced environmental

impacts, relieved transmission and distribution congestion etc. However, the asynchronous

interface provided by the power electronic converter raises issues regarding power quality

[1].The power conversion unit basically consists of the source side and the grid side

converters. Due to the persistent narrowing of the standards in the grid code compliances, the

grid connected inverter control has taken the centre stage whenever we consider the

improvement of DGS. The grid code compliances include control of active and reactive

power between the DGS and the grid, balancing the power flow between the input side

converter and the grid, providing high output power quality and maintaining synchronization

with the grid [2].The main functions of the controllers are to maintain the power quality and

to control the active and the reactive power of the grid independently. Optimal filter design is

necessary so as to reduce the current harmonics in the grid considering the conduction and

switching losses at constant modulation index (Ma) leading to better power quality.

12 | P a g e

1.2 BACKGROUND AND LITREATURE REVIEW

A number of control strategies have been proposed and are extensively studied in the

available literature [3-5]. Proper power flow regulation using vector control principle has also

been proposed in [6]. Dual Vector Current control which was first proposed in [7] uses two

VCC’s for positive and negative sequence components along with DC link voltage control.

Synchronous PI current control has also been proposed in [8] which convert the three phase

grid voltages to synchronously rotating (dq) frame for proper decoupling. The grid currents

become DC variables and thus no steady state-state error adjustment is required. A method

for active and reactive power control has been mentioned in [9]. It controls the DC link

voltage by designing a Voltage Control Loop. However, the transient time has not been taken

into consideration. Harmonics mitigation techniques have also been proposed using high-pass

and low-pass filters in [6] which don’t take into account the effect of the filters on the control

loop. The MRF PI controller developed in [2] doesn’t need dq current signal high pass and

low pass filtering. However, it also doesn’t take the filters into consideration while deriving

the control strategy for independent active and reactive power control.

For study purposes, the L-type decoupling terms have been applied to LCL -type filters for

designing the controllers [3,10]. This is just an approximate solution which causes

performance and stability problems for higher values of switching frequencies [3]. However,

this problem has been mitigated in [3] by further addition of second-order transfer functions

in the control loops but they do not guarantee the damping of the resonance mode. An

alternative approach to tackle the problem has been introduced in [11] which is based on a

linear full state feedback and deadbeat control. However, this doesn’t consider the nonlinear

dynamics of the dc link voltage.

13 | P a g e

Also, for the reduction of the current harmonics in the grid an optimal LCL- type filter

design is imperative. LCL-type filters installed at converter outputs offer higher harmonic

mitigation, but careful design is required to damp LCL resonance. Out of the two damping

processes available we prefer passive damping for grid connected applications [8].

1.3 THESIS OBJECTIVES

The following objectives are hopefully achieved at the end of the project.

1. To control the three phase grid connected inverter system for sinusoidal current

injection with improved performance

2. To analyse a control strategy for the three-phase grid connected inverter

3. To provide an optimal filter design which includes the power loss calculations

4. To analyse the results obtained through simulation in the MATLAB/Simulink

environment.

1.4 ORGANISATION OF THESIS

The thesis has been organised into six chapters including the introduction. Each chapter is

different from the other and is described along with the necessary theory required to

comprehend it.

Chapter 2 deals with a control strategy for a three-phase Grid Connected Inverter (GCI)

under abnormal conditions of the grid like voltage sag, line to ground fault and presence of

harmonics. This strategy intends to overcome the hitches faced by the conventional controller

working under abnormal conditions of the grid. The control strategy adopted here

counterbalances the distortions in grid voltage by injecting sinusoidal current into the grid. In

addition to this, active and reactive power control during the step changes of the load has also

been studied. In order to study the dynamic performance of the system, the models are

simulated and the results are analysed.

14 | P a g e

Chapter 3 presents a control strategy for a three-phase grid interactive voltage source

inverter (VSI) that links a renewable energy source to the utility grid through a LCL-type

filter. The control strategy adopted here decouples the active and reactive power loops, thus

achieving desirable performance with independent control of active and reactive power

injected to the grid. The start-up transients are also controlled by the implementation of this

particular control method. In order to study the dynamic performance of the system and to

confirm the analytical results, the models are simulated in the MATLAB/Simulink

environment and the results are analysed.

Chapter 4 presents the optimal design of the LCL-type filter which links a renewable

energy source to the utility grid through a LCL-type filter. The optimal design has been made

so as to reduce the current harmonics in the grid considering the conduction and switching

losses at constant modulation index (Ma). It takes into effect the conduction and switching

copper losses as well as core losses. A trade-off has been made between the total losses due to

the inductor and the THD% of the grid current, and the filter inductor has been made

accordingly. In order to study the dynamic performance of the system and to confirm the

analytical results, the models have been simulated in the MATLAB/Simulink environment

and the results are analysed.

Chapter 5 concludes the work and describes the future scope of the same. Some possible

limitations in the work have also been provided. The future work that can be done in

improving the current scenario is mentioned.

15 | P a g e

CHAPTER 2

Control of Grid Connected

Inverter System for Sinusoidal

Current Injection with Improved

Performance

16 | P a g e

2.1 INTRODUCTION

A design of a current controller along with active and reactive power control in order to

ameliorate the power quality in the grid is shown. This technique intends to overcome the

hitches faced by the conventional controller working under unbalanced conditions of the grid.

The control strategy adopted counterbalances the distortions in grid voltage by injecting

sinusoidal current to the grid through a MRF PI controller strategy [19]. For the active and

reactive power control, cross coupling is done in order to decouple the d-q components and

thus helping in effective control of the active and reactive power independently.

2.2 MATHEMATICAL MODELING OF GRID CONNECTED INVERTER

SYSTEM

The schematic diagram of three phase grid-connected PWM inverter is shown in Fig. 2.1,

which consists of dc link capacitor, IGBT switches and filter circuit in the grid side.

PHOTO-VOLTAIC

(PV) PANEL

Va

Vb

Vc

L1

C1

Pin

v

+

- L1

L1

RENEWABLE ENERGY

SOURCE2- LEVEL PWM VSI

L FILTERUTILITY GRID

DC LINK

Fig. 2.1. Schematic diagram of Grid Connected PWM Inverter

Assume that the three phase loop resistance R and L are of the same value, affection of

distribution parameters are negligible and switching loss and on state voltage drop is

negligible.

17 | P a g e

Based on the topology, the dynamic equation of the output side of the grid connected

inverter can be deduced as follows:

)()(

)()( tRidt

tdiLtvte abc

abc

abcabc

(2.1)

We can write the dynamic equation for the input side of the grid connected inverter as:

dt

tdvCtititi dc

Ldcc

)()()()(

(2.2)

The line voltages and the phase currents can be transformed into synchronous reference

frame (dq coordinates) by the use of the transformation matrix

)(.)( tvTtv abcdq

(2.3)

where

1)3/2sin()3/2cos(

1)3/2sin()3/2cos(

1)sin()cos(

T

is the transformation matrix and is the rotating angle of transformation

Now we can transform the dynamic equation directly into synchronous reference frame (dq

coordinates)

)()(

)()()( tMiLdt

tdiLtRitvte dq

dq

dqdqdq

(2.4)

000

001

010

M

By assuming that the three phase voltage source is balanced without the zero sequence

components we can write

)()()(

)()( tiLtRidt

tdiLtetv qd

ddd

(2.5)

18 | P a g e

)()()(

)()( tiLtRidt

tdiLtetv dq

q

qq

(2.6)

The s-domain representation can be shown as follows:

)]()()([1

)( sLisvseRLs

si qddd

(2.7)

)]()()([1

)( sLisvseRLs

si dqqq

(2.8)

For the input side of the converter

dc

L

Ldc i

sCR

Rv

1

(2.9)

Now for the instantaneous power equations we can write

)()(*.)( tjQtPIEtS (2.10)

where * represents the complex conjugate

)(tP represents the instantaneous active power and

)(tQ represents the instantaneous reactive power

)]()()()([2

3)(

)*])(Re[(2

3

titetitetP

jIIjEEP

qqdd

qdqd

(2.11)

)]()()()([2

3)(

)*])(Im[(2

3

titetitetQ

jIIjEEQ

qddq

qdqd

(2.12)

2.3 CONTROL ALGORITHM OF GRID CONNECTED INVERTER

2.3.1 Analysis of Current Controller

Conventional current controllers use only cross coupling and feedforward terms. It has

been seen that even with certain modifications in the PLL structure, there is little

improvement in the power quality, the main culprit being the lower order harmonics.

19 | P a g e

It is seen that the distribution grid voltage is considerably distorted due to the presence of

nonlinear loads. This leads to the presence of significant lower order harmonic content

especially of 5th

, 7th

, 11th

and 13th

order.

)7cos()5cos()cos( 751 VVVva

)3

2(7cos)

3

2(5cos)

3

2cos( 751

VVVvb (2.13)

)3

2(7cos)

3

2(5cos)

3

2cos( 751

VVVvc

,...,, 751 VVV denotes the magnitude of the harmonics.

Transforming these into synchronously rotating reference frame we get

.....)12sin()()6sin().(

.....)12cos()()6cos().(

131175

1311751

VVVVv

VVVVVv

d

d

(2.14)

In addition to these, there are other higher order harmonics present. However, we do not

take them into consideration due to their low magnitudes in the system. Here it is seen that

the d-q grid voltage components have basically frequency components which are multiples of

six of the frequency of the grid. During unbalance conditions such as voltage sags, presence

of harmonics and fault conditions the conventional controller fails to provide the required

sinusoidal grid current and voltage which degrades the power quality of the system.

In order to mitigate lower order harmonics in the grid current, we require a modified

current controller to ensure proper operation of the grid under distorted conditions. The use of

multiple reference frame (MRF) PI controller is used here as shown in Fig. 2.2. The MRF PI

controller doesn’t extract harmonics from the current by the application of high-pass and low

pass filter but injects a component antagonistic to the harmonics present in the same [16]:

20 | P a g e

Fig. 2.2. MRF PI Current Controller structure

2.3.2 Filter Design

It is seen that the converter current is mostly plagued by the lower order harmonics, the

major ones being the lower order harmonics. Appropriate L filters are designed in order to

filter out the harmonic components from the current and thus making them sinusoidal. The

design of the L filters can be done according to the formula [17]:

aa

SWripplerated

dc mmfI

VL )1(

.4

(2.15)

where ratedI is the rated utility current, ripple is the maximum ripple magnitude percentage (5

% - 25 %), dcV is the DC link voltage, L is the total filter inductance, fsw

is the switching

frequency (in Hz) and am is the modulation index.

2.3.3 Active and Reactive Power Control

Moreover the active and reactive power control isn’t possible in case of the conventional

controller. We use the feedback from the grid in order to generate the current reference which

in turn controls the active and reactive power independently. The advantage of dynamic VAR

21 | P a g e

systems is that they detect and instantaneously compensate for voltage disturbances by

injecting leading or lagging reactive power at crucial junctures to the power transmission

grids. Through the dynamic VAR control system, reactive power is supplied in the grid with

fast dynamics. Thus it helps in regulating the system voltage and stabilizing the grid [18].

The instantaneous power flowing into the grid can be written as

)()()( tjQtPtS (2.16)

The instantaneous active and reactive power equations are given by:

)]().()().([2

3)(

)]().()().([2

3)(

titetitetQ

titetitetP

qddq

qqdd

(2.17)

The dc- link power is known by:

dt

dVCtVtItVtP dc

dcdcdcdc ).()().()(

(2.18)

Assuming that the inverter losses are neglected i.e. the switching losses are zero we can

equate the input power with the output power and the power balance can be given by

)]().()().([2

3titutitu

dt

dVCV qqdd

dcdc

(2.19)

Assuming balanced case and taking the q-components to be zero we get

)()(2

3)( titetP dd

(2.20)

From (2.5) and (2.6) it can be seen that the d-component and the q-component are highly

coupled which leads to the degradation of the dynamic performance. The vector controller

decouples these terms and thus providing the ability to control each current component.

22 | P a g e

Fig. 2.3. Schematic diagram for the Grid Connected Inverter with its control

The elementary principle of the vector oriented control method is to control the

instantaneous active and reactive grid power which can be done by controlling the grid

currents, by separate controllers independent of each other. Two current controllers are

employed namely d-current controller and q-current controller. The grid voltages and currents

are first sensed and with the help of Synchronous Reference Frame (SRF) Phase Locked

Loop, the grid phase angle is detected in order to synchronize the GCI output with grid.

The demanded amount of current and voltage are then estimated from the grid at the

desired power factor and the reference currents in a synchronous frame are calculated.

Consequently, the current controllers try to reduce the error and make the load currents follow

the reference current vector. Thus we try to control the current and therefore controlling the

inherent power flow. So by this process, the active and reactive powers are meticulously

controlled.

The converter DC voltage is determined by:

dttItIC

tV ldcdc .)]()([1

)(

(2.21)

23 | P a g e

The DC voltage can be regulated using PI controller by choosing the current reference

dttVVKtVVKtI dcdcrefidcdcref

v

dcref p)].([)]([)(

(2.22)

wheredcrefV is the reference DC link voltage,

pK and iK are the constant gains of the PI

controller.

The reference currents can be given by:

)]().()().([3

2)(

)]().()().([3

2)(

tQtUtPtUti

tQtUtPtUti

refdrefqqref

refqrefddref

(2.23)

where 22

qd uu , )(tPref and )(tQref are the active and reactive power references.

Now,

)()()()(

)()()()(

tiLtRiUtetv

tiLtRiUtetv

dqqqqref

qddddref

(2.24)

Where vdref(t) and vqref(t)are the d and q voltage references. Ud and Uq are the effective voltage

references.

dttitiKtitiKU

dttitiKtitiKU

qqrefiqqrefpq

ddrefiddrefpd

)].()([)]()(.[

)].()([)]()(.[

(2.25)

Where Kp and Ki are the constant gains of the PI controller.

2.4 RESULTS AND DISCUSSIONS

To validate the MRF PI current controller for Grid Connected Inverter (GCI), extensive

computer simulations were performed using MATLAB/Simulink. Under distorted and

undistorted conditions, the detailed switching model of the space vector modulated

(SVPWM) grid connected inverter has been developed.

The system parameters used in the simulations are given in the Table-2.1

24 | P a g e

TABLE 2.1

PARAMETERS USED IN SIMULATION

Parameter Label Value

Coupling inductance L 7.52 [mH]

Coupling resistance R 0.26 [Ω]

Grid voltage V 240 [V]

DC link voltage Vdc 580 [V]

Switching frequency fSW 5000 [Hz]

Base voltage Vb 964 [V]

Base current Ib 7.84 [A]

The values of the gains Kp and Ki are calculated according to the formulae [18]:

dc

SW

pV

fK

.

dc

SW

iV

fK

.2

.2

(2.26)

where

RL / is grid time constant ;

L is the coupling inductance between the GCI and the grid,

R is the coupling resistance

Vdc is the dc-link voltage in p.u.

fSW is the switching frequency.

The values of the gains Kp and Ki of the MRF PI controller are calculated according to the

formulae [19]

dcSW

pVT

K.3

4 and

i

p

i

KK

where

i =0.02 s (2.27)

2.4.1 Active and Reactive Power Control

For the study of dynamic VAR compensation, a single case is considered i.e. a step

change of the load. A lagging reactive load is added at 0.02 sec. as shown in the Fig 4. The

reference currents are generated from the grid side according to the (2.23) and the actual

values are compared with the reference values through PI controllers in order to bring the

currents and thus the power to their respective reference values.

25 | P a g e

In order to estimate the power injection characteristics we carry out the test of increasing

the reactive load component. The step change to the load is made at 0.02 sec .The response of

the controller is shown in Fig 2.4. With the change in load at 0.02 s, the active current

decreases in order to supply the lagging power to the load (Fig. 2.4(d)). The reactive current

first decreases and then increases to go above the reference value to compensate for the

reactive nature of the load. The converter phase current decreases due to the change in the

load as shown in Fig. 2.4(e). The grid d voltages show a change due to the step change in the

load. The harmonic spectrum using Fast Fourier Analysis for the current is realized in Fig.

2.4(f). We analyze the converter current which shows a THD of 0.66 % which is very much

within the permitted distortion levels as per IEEE 519-1992 specifications.

(a)

(b)

(c)

0 0.01 0.02 0.03 0.04 0.05 0.06-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time [sec]

Grid

vol

tage

s va

bc [p

.u.]

Va

Vb

Vc

0 0.01 0.02 0.03 0.04 0.05 0.06-0.5

-0

0.5

0.1

0.15

0.2

0.25

0.3

Time [sec]

Grid

dq

volta

ges

Vdq

[p.u

.]

Vd

Vq

0 0.01 0.02 0.03 0.04 0.05 0.06-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Time [sec]

Grid

pha

se c

urre

nts

Iabc

[p.u

.]

Ia

Ib

Ic

26 | P a g e

(d)

(e)

Fig. 2.4. (a) Distorted grid voltages (b) dq components of distorted grid voltages. (c) Converter current to the

grid (d) q-current component converter response (e) Harmonic spectrum of the grid current

2.4.2 Current Control Strategy

In order to authenticate the MRF PI controller we take three different conditions of the

grid. The first case investigates the operation under voltage sag conditions. Next the grid

voltages and currents under line to ground fault conditions were analysed and finally we

observe the GCI operation under injection of non-sinusoidal grid voltages.

The MRF PI current controller is basically focused on the mitigation of harmonics in the

converter phase currents. However, it also shows considerable improvement in other

unbalanced conditions. The comparative study regarding the presence of harmonics is

analysed in detail here. Thorough comparisons regarding the other cases are avoided for

brevity.

A. Under Voltage Sag

The voltage sag conditions are employed with the help of a three phase programmable AC

source in Simulink environment as shown in Fig. 2.5. The frequency was maintained at 50

0 0.01 0.02 0.03 0.04 0.05 0.06-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time [sec]

q-cu

rrent

act

ual [

p.u.

]

iq current actual

0 0.01 0.02 0.03 0.04 0.05 0.06

-0.01

0

0.01

Selected signal: 3 cycles. FFT window (in red): 2 cycles

Time (s)

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100

Frequency (Hz)

Fundamental (50Hz) = 0.01212 , THD= 0.66%

Mag (

% o

f F

undam

enta

l)

27 | P a g e

Hz. Voltage amplitude was maintained at 0.2468 p.u. The sag is forced at 0.03 sec and

maintained up to 0.05 sec. (Fig 2.5(a)). The reference d-current is taken as a step input and

the reference q current was maintained at zero. SRF PLL is used for the detection of phase

such that the d-component of the grid voltage is maintained at phase voltage and the q

component is maintained at zero.

(a)

(b)

(c)

(d)

0 0.01 0.02 0.03 0.04 0.05 0.06-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Grid

Vol

tage

Vab

c [p

.u.]

Va

Vb

Vc

0 0.01 0.02 0.03 0.04 0.05 0.06-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Conv

erte

r Pha

se C

urre

nt Ia

bc [p

.u.]

Ia

Ib

Ic

0.01 0.02 0.03 0.04 0.05

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time [sec]

d-cu

rrent

act

ual [

p.u.

]

d current actual

0.01 0.02 0.03 0.04 0.05

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

q-cu

rrent

act

ual I

q [p

.u.]

q current actual

28 | P a g e

(e)

Fig. 2.5. (a) Distorted grid voltages (b) Converter current to the grid (c) d-current component converter response

(d) q-current component converter response (e) Harmonic spectrum of the grid current

B. Under line to ground fault

The grid is assumed to be under fault from 0.03 sec to 0.05 sec. which was created with

the help of a programmable AC source in Simulink environment. Reference d current and

reference q current are taken the same as before. SRF PLL is used for detection of the phase

and to transform the abc to dq reference frame in order to maintain proper decoupling

between the d and q voltages of the grid. The grid voltages and grid currents were then

examined.

(a)

(b)

(c)

0 0.01 0.02 0.03 0.04 0.05 0.06-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Grid

Pha

se V

olta

ges

Vabc

[p.u

.]

Va

Vb

Vc

0 0.01 0.02 0.03 0.04 0.05 0.06-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Conv

erter

Phas

e Curr

ent I

abc [

p.u.]

Ia

Ib

Ic

0 0.01 0.02 0.03 0.04 0.05 0.06-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Time [sec]

d-curr

ent a

ctual

Id [p.

u.]

29 | P a g e

(d)

(e)



C. Under presence of harmonics using conventional controller

Due to the presence of huge proportions of non-linear load, the grid voltages generally

deviate from its sinusoidal nature.

A robust controller is required in order to maintain reliability and regulate quality power

flow to the load. Fig. 2.7 gives simulation results for GCI operation connected to the distorted

grid when the conventional controller is used. The response of the current controller was

observed. All the other parameters remained the same as in the previous cases.

(a)

(b)

0 0.01 0.02 0.03 0.04 0.05 0.06-0.2

-0.15

-0.1

-0.05

0

0.05

Time [sec]

q-cu

rrent

act

ual [

p.u.

]

Iq

0 0.01 0.02 0.03 0.04 0.05 0.06-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Grid

Volta

ges V

abc [

p.u.]

Va

Vb

Vc

0 0.01 0.02 0.03 0.04 0.05 0.06-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time [sec]

Conv

erter

curre

nt Iab

c [p.u

.]

Ia

Ib

Ic

30 | P a g e

(c)

(d)

(e)

Fig.2.7. (a) Distorted grid voltages (b) Converter current to the grid (c) d-current component converter response

(d) q-current component converter response (e) Harmonic spectrum of the grid current.

Fig. 2.7 (e) shows that the harmonics compensation capability is very poor considering

the use of the conventional controller. The THD level of 16.23 % expresses it all. From the

Fig. 7(c) and 7(d) it is obvious that the 6th

harmonic and the 12th

harmonic components

present around the reference values aren’t eliminated.

D. Under presence of harmonics using MRF PI controller

In order to satisfy this drawback the MRF PI current controller is used where mitigation

techniques for the 6th

and the 12th

harmonics are employed. Fig. 2.8 shows the simulation

results for the GCI operation connected to distorted grid when the MRF PI controller was

used.

0.01 0.02 0.03 0.04 0.05-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time [sec]

d-cu

rrent

act

ual I

d [p

.u.]

d current

0.01 0.02 0.03 0.04 0.05-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Time [sec]

q-cu

rrent

act

ual I

q [p

.u.]

31 | P a g e

(a)

(b)

(c)

(d)

(e)



It is seen from the Fig. 2.8(e) that, the THD of the grid current is reduced to 2.68 % in

comparison to the THD of 16.23 % of conventional controller with sinusoidal current

0 0.01 0.02 0.03 0.04 0.05 0.06-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Grid

Volta

ges V

abc [

p.u.]

Va

Vb

Vc

0.01 0.02 0.03 0.04 0.05-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

Conv

erte

r Cur

rent

s Ia

bc [p

.u.]

Ia

Ib

Ic

0.01 0.02 0.03 0.04 0.05

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time [sec]

d-cu

rrent

act

ual [

p.u.

]

d current actual

0.01 0.02 0.03 0.04 0.05

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time [sec]

q-cu

rrent

act

ual I

q [p

.u.]

q current actual

32 | P a g e

injection into grid. The d-q current components of grid also show the faster response with

proper decoupling over conventional controller to improve the grid dynamics.

2.5 CONCLUSIONS

This provides an analytical background of the active and reactive power control strategy

for a grid connected inverter system. In this method independent control of the active and

reactive power was realized in an effective way. It also includes an improved current

harmonics compensation capability through the use of MRF PI controller. Comparative

studies made in the text have shown that the MRF PI controller provides better performance

in terms of improvement of grid dynamics as compared to the conventional controller. The

agreement with the simulation results to a prodigious extent with a good sinusoidal grid

current, a lesser harmonic component was also obtained by MRF PI controller.

33 | P a g e

CHAPTER 3

Decoupled Control Strategy of

Grid interactive Inverter System

34 | P a g e

3.1 INTRODUCTION

A control strategy for a three-phase grid connected voltage source inverter that links a

renewable energy source to the grid through an optimized LCL-type filter so as to attenuate

the current harmonics in the grid is shown. This approach uses a modified set of variables that

removes the non-linearity of the original set of equations. This linear system has been

decoupled into two different control loops corresponding to the active and reactive power

control. The active power loop is controlled by the dc link energy rather than dc link voltage

and the reactive power loop is controlled by the reactive component of the grid current.

Perfect decoupling can be obtained by the proper design of the control structure. The major

advantage of having two decoupled loops is the neutralization of undesirable transients of

reactive current caused by changes of active power and vice versa. Also, the start-up

transients are minimized by the use of additional terms in the control structure.

3.2 MATHEMATICAL MODELING OF THE THREE PHASE GRID

CONNECTED INVERTER

The schematic diagram of three phase grid-connected PWM inverter is shown in Fig.3.1,

which consists of dc link capacitor, IGBT switches and filter circuit in the grid side.

PHOTO-VOLTAIC

(PV) PANEL

Va

Vb

Vc

L1

C2

Rd

C2 C2

C1

Pin

v

Vc2

+

-

+

-

RdRd

L1

L1

L2

L2

L2

RENEWABLE ENERGY

SOURCE2- LEVEL PWM VSI

LCL FILTER

UTILITY GRID

DC LINK

Fig. 3.1. Schematic Diagram of Three Phase Grid Connected Inverter with LCL-type Filter

35 | P a g e

Assume that the three phase loop resistance R and L are of the same value and affection

of distribution parameters are negligible. Based on the topology, the dynamic equation of the

output side of the grid connected inverter in the dq frame can be deduced as follows:

cdcdqd vvuiL

dt

diL 11

cqcqd

qvvuiL

dt

diL 11

gddcq

cd iivCdt

dvC 22

gqqcd

cqiivC

dt

dvC 22

(3.1)

gdcdgq

gdvviL

dt

diL 22

cqgd

gqviL

dt

diL 22

ingdgd

c

c pivdt

dvvC 1

The dqtransformation has been made taking the grid voltage angle as the reference. The

system is a multivariable nonlinear system of order seven.

3.3 CONTROL STRATEGY OF THE THREE PHASE GRID CONNECTED

INVERTER

The main objectives of implementing this control strategy are to control the active and

reactive power injection to the grid independently and to maintain pure sinusoidal form of

grid current.

As seen, the system is a multivariable nonlinear system and the reactive power is

controlled by the reactive part of grid current whereas the active power control is done taking

the dc-link energy. In this paper, the decoupling terms and controller design are accomplished

36 | P a g e

without any approximation. As a result of which the performance of the system is not affected

by the switching frequency. The decoupling is done by the introduction of a new control

variable ηqwhich follows the equation

qL = qv +

diL +qiL (3.2)

From (1) we can find the values of 2

2

,dt

id

dt

di gqgq and 3

3

dt

id gq as

),(2

cqgd

cq

gd

gqviA

L

vi

dt

di (3.3)

)(1

)(2222

2

2

2

gqqcdgdcdgq

gqii

LCv

Lvv

Li

dt

id

),,,(2

)( 2

1

22

2

1

2

gdqcdgqqgdcdgp viviBivL

vL

i

(3.4)

)(

1)(

12).(

1

2

1

222

2

1

2

3

3

cqcqidgddcq

cq

gd

gqvvu

Lii

Cv

LL

vi

dt

id

qcqdcqgd vuL

iviC

1

2

1),,( (3.5)

gqqqqqq iaAaBa 012 (3.6)

where 22

2

1 1 CL and ηqis the input signal. We get that from ηq to the reactive current igqthe

system is decoupled and linearized. The open loop transfer function is given by

qqqq

gq

asasass

sI

01

2

2

3

1

)(

)(

(3.7)

Taking qa2 = 3 , qa1 = 23 and qa0 = 3 the closed loop transfer function results in

q

q

ref

gq

gq

kss

k

sI

sI

3)()(

)(

(3.8)

wherekqis the controller gain.

37 | P a g e

The control law can thus be derived from the above:

gq

gqgq

cq

gq

q

ref

q

c

q idt

di

dt

idvu

Ldt

iddtii

v

Lu 32

2

2

1

2

1

3

3

2

1

1 33)(

(3.9)

Similar equations can be derived for the active power control loop. Basing on feedback

technique we find the values of 3

3

2

2

,,dt

wd

dt

wd

dt

dw ccc and 4

4

dt

wd c from (3.1).

),( ingdingdgdc piDpiv

dt

dw (3.10)

))(1

(2

2

2

gdcdgqgd

c vvL

ivdt

wd

),,(1 2

22

gdcdgqgdcd

gd

gqgd vviEvL

vL

viv (3.11)

))(1

()1

(222

3

3

gddcq

gd

cqgdgd

c iiC

vL

vv

Liv

dt

wd

),,(2

)( 2

1

2

2

1

2

dcqgddgdcq

gd

gdgd iviFivvL

viv

(3.12)

))(1

(2

))(1

()(222

2

1

2

4

4

gqqcd

gd

gdcdgqgd

c iiC

vL

vvv

Liv

dt

wd

))(1

(1

2

1 cddqgd vvL

iv

qgdcd

gdgd

gqgd ivvLL

vLvLiv 2

1

21

2

121

2

1

2

2

1

2 3)3(

)3(

38 | P a g e

cd

gd

gd vuL

vv

L 1

2

12

2

2

1

2 )(

cd

gd

gdqcdgq vuL

vviviG

1

2

1),,,(

cdddddd waDqEaFa 0123 (3.13)

Here it has been assumed that the input power pin remains constant and thus the derivative

of the same has been neglected. The open loop transfer function can thus be given by

ddddd

cd

asasasass

sWsG

01

2

2

3

3

4

1

)(

)()(

(3.14)

With the selection of 4

0

3

1

2

23 ,4,6,4 dddd aaaa this can be simplified to

4)(

1

)(

)()(

ss

sWsG

d

c

d (3.15)

With the help of an integral controller sksC dd )( , the closed loop transfer function results in

d

d

ref

c

C

kss

k

sW

sW

4)()(

)(

(3.16)

The coefficients are selected to place the poles at desired location and thus obtaining

desirable transient response.

The control law can hence be written as:

c

ccc

cd

gdc

c

ref

c

gdc

d wdt

dw

dt

wd

dt

wdvu

L

v

dt

wddtww

vv

Lu 43

2

2

2

3

1

2

1

4

4

2

1

1 464)(

(3.17)

39 | P a g e

The start-up control is done by some modifications to the existing controller which isn’t

shown here for brevity.

The control system block diagram for the LCL-type converter has been shown in Fig. 3. 2.

It can be seen that the terms above are a linear combination of the system state variables and

there are no time derivatives involved.

kq/s

Nβ

4

4Nβ

3

4Nβ N

M

Mβ

3

3Mβ

2

3Mβ

M

6Nβ

2

BLACKBOX OF THE

CONVERTER AS WELL AS THE FILTER

kq/s -N

uq

ud

Ioq

Iod

D E F G

A B C

vc

vc

Igq

wc

wcref

iqref

M=L1/ω2

N=L1/Vgdω12

ηq

ηd

+_

+ + +

_ _ _

++

÷

÷+ + + + + +_ _ _ _ _ +

igq

wc1/2C(.)2+

_

+_

Fig. 3.2. Control System block diagram of the LCL -type converter


A 3 kW solar PV model connected to the three phase grid connected inverter system is

considered for the study and is simulated in MATLAB/Simulink environment.Table 3.1 gives

the design parameters for the control method.

TABLE 3.1

DESIGN PARAMETERS FOR CONTROL ALGORITHM

Parameters Value

Rated power P 3 kW

Rated voltage V 230 V

Grid frequency fo 50 Hz

Switching frequency fsw 20 kHz

DC Link Voltage Vdc 500 V

Resonant frequency fr 1 kHz

Modulation Index Ma 0.8

40 | P a g e

The simulation scenario has been defined as follows: the system has been given a full

irradiation of 1 kW at the beginning which drops down to 600 W at t=0.05 sec and the

reactive current step change from 0 A to 20 A is done at t=0.1 sec. Fig. 4 shows the graphs for

the grid current components id and iq, the dc-link capacitor voltage Vdc and the grid current

waveforms, Iabc. It is seen that the dc-link voltage is regulated to 500 V with small transients

at the change instants.

(a)

(b)

(c)

Fig. 3.3. (a) dc-link voltage across the capacitor (b) d and q axis current (c) Grid current waveforms

0 0.025 0.05 0.075 0.1 0.125 0.15 0.175495

496

497

498

499

500

501

502

503

504

505

Time (in sec)

Vca

pa

cito

r (in

V)

0 0.05 0.1 0.15 0.2-5

0

5

10

15

20

25

Time (in sec)

Idq

(in

A)

Id

Iq

0 0.05 0.1 0.15 0.2-15

-12

-9

-6

-3

0

3

6

9

12

15

Time (in sec)

Iab

c(

in A

)

Ia

Ib

Ic

0.05

499

499.5

500

500.5

501

Time (in sec)

Vca

pa

cito

r (

in V

)

0.075 0.1 0.125

497.5

498

498.5

499

499.5

500

500.5

501

501.5

502

Time (in sec)

Vca

pa

cito

r (in

V)

41 | P a g e

It is seen that the controller shows desirable performance with decoupled active and

reactive power flow. The reactive current follows the desired response when a step change is

introduced with fewer transients in the dc-link voltage.

3.5 CONCLUSIONS

Here, a control scheme for a three-phase grid-connected inverter with an LCL-type filter

has been investigated. For the inverter system, the control method has been given to

accurately formulate the decoupling terms for LCL-type filter. The decoupling method

obviates the need for incorporating additional filters to compensate for instabilities which are

caused by approximate decoupling done in high switching frequencies. The agreement with

the simulation results to a prodigious extent with a good sinusoidal grid current, a lesser

harmonic component was also obtained.

42 | P a g e

CHAPTER 4

Filter Design using Power Loss

Calculations

43 | P a g e

4.1 INTRODUCTION

An inverter generally introduces higher order harmonics into the grid system due to

nonlinear characteristics of the inverter switches. In order to attenuate these introduced

harmonics an LCL-type filter is connected in series with the inverter on the grid side. It makes

sure that the harmonic content is below a specified limit. However, in addition to it the filter

causes extra power losses which are undesirable. Here, the LCL-type filter is chosen over L-

type and LC-type due to its better harmonic attenuation properties for the same value of

inductances [15]. However, a resonance problem is present which can be mitigated by using

different damping methods.

Here a passive damping method has been adopted to eliminate the resonance problem in

here, a resistor and a capacitor has been added in parallel to the original capacitor as shown in

fig. 3. It is known that for grid connected applications a passive method is more appropriate,

as when the inverter is switched off while grid is still on the ON condition, the resistor that is

used helps in protecting the system.

UgUi

C1 Cd

L1 L2

i 1 I g

Uc

Id

Rd

Fig. 4.1.LCL-type filter with passive damping scheme

4.2 FILTER DESIGN

Here, the filter has been designed considering the THD% of the current waveform and

losses. It is known that the THD% would be higher for lower values of L and conduction

44 | P a g e

losses would be higher for higher value of filter. Hence, the trade-off between them gives the

optimal value of inductor to be used in the filter design. Power losses are adopted from [13].

The optimal value of inductance obtained is divided into L1 and L2 in such a way that the

capacitance obtained should be minimal and it occurs when L1 is a little higher than L2, since

the harmonics in the current entering L1 is higher than that in L2.

We can say, 21 LLL (4.1)

where2

21

LLL (4.2)

We know, LC

r

42 (4.3)

The resonant frequency (ωr) should be in the range of 10 ωo<ωres< (ωsw/2) in order to reduce

resonance problems and a constant value in this range is selected.

Capacitor value can be obtained by

LC

r

2

4

(4.4)

where dCCC 1 (4.5)

When quality factor and power losses are considered, the effective damping occurs when

C1 and Cd are equal. The resistance (Rd) of damping circuit is obtained as follows

C

LRd (4.6)

4.2.1 Inductor Power Loss:

Power losses in an inductor are divided into core loss and copper loss. There are some

additional losses which are negligible. So both core and copper losses at fundamental and

switching frequencies are calculated using software called Magnetic Design. As input we give

inductor value, peak to peak current and rms current.

45 | P a g e

4.2.2 Damping Circuit and Capacitor:

Power losses of the damping circuit can be calculated as follows:

A. Fundamental frequency power loss:

It is calculated at the fundamental frequency of 50 Hz. At fundamental frequency,

thevoltage across the damping circuit (Uc) is same as that of grid voltage. Therefore, gc UU

Power loss can be calculated from

)50(dP Real ][ *

dc IU (4.7)

where, Id is current flowing through damping circuit and can be derived as follows,

31 RsC

sCUI

d

dcd

(4.8)

2

3

22

50

35050

1

)1(

RC

RCjCjUI

d

ddcd

(4.9)

2

3

22

50

3

22

50

2

)50(1 RC

RCUP

d

dcd

(4.10)

B. Switching frequency power loss:

Grid is considered as a short circuit at the switching frequency but it is an ideal voltage at

fundamental frequency. So at switching frequency Ug=0,

)1

11()1(

5.05.0

2

2

32

2

3

cr

swdsw

r

sw

dswic

aRCj

RCjUU

(4.11)

2

3

22

3

1

)(

RC

jRCCUI

dsw

dswdswcd

(4.12)

)(swdP ][ *

dc IU (4.13)

Representing Ucand Id as complex fractions,

46 | P a g e

jdc

jbaUU ic

(4.14)

)(1 222

jyxRC

CUI

ddsw

dswcd

(4.15)

*

2

3

22

** )(1

)( jyxRC

C

jdc

jbaU

jdc

jbaUIU

dsw

dswiidc

(4.16)

)(swdP Real xRC

C

dc

baUIU

dsw

dswidc 2

3

2222

22*

1][

(4.17)

Here, 5.0a , 35.0 RCb dsw , 2

2

1r

swc

, )

1

11(

2

2

3

cr

swdsw

aRCd

, 3RCx dsw , 1y


The fundamental copper loss, iron loss and the switching core loss and the copper loss were

all calculated and are shown in Table 4.1.

TABLE 4.1

LOSSES AT DIFFERENT INDUCTANCE VALUES

L

Switching

Losses

Fundamental

Losses At

fundamental

frequency

At switching

frequency Total losses Copper

Loss

Core

Loss

Copper

Loss

Core

Loss

0.001 0.223 0.055 0.042 0.042 1.5700 628 629.3620

0.003 0.071 0.055 0.118 0.055 0.5200 209 210.1990

0.005 0.041 0.055 0.191 0.055 0.3100 125.60 126.242

0.007 0.029 0.055 0.294 0.055 0.2200 89.7000 90.3330

0.008 0.024 0.055 0.313 0.061 0.1960 78.5000 78.9530

0.009 0.021 0.055 0.351 0.061 0.1740 69.7900 70.2780

0.01 0.019 0.055 0.417 0.061 0.1570 62.8191 63.5282

0.02 0.031 0.040 0.511 0.149 0.0785 31.4096 32.2191

0.03 0.021 0.040 0.777 0.186 0.0523 20.9397 22.0161

0.04 0.016 0.040 0.993 0.215 0.0393 15.7048 17.0080

0.05 0.012 0.040 1.033 0.290 0.0314 12.5638 13.9702

0.06 0.010 0.040 1.016 0.322 0.0262 10.4699 11.8848

0.07 0.007 0.040 1.850 0.275 0.0224 8.97420 11.1686

0.08 0.007 0.040 1.847 0.330 0.0196 7.85240 10.0960

0.09 0.005 0.040 1.814 0.330 0.0174 6.97990 9.1864

0.1 0.005 0.040 1.689 0.479 0.0157 6.28190 8.5106

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The plot between the total losses and the value of inductor is given in Fig. 4.2.

Fig. 4.2.Total Power loss vs Inductance value

It is seen that both the core loss and the copper loss of the inductor at the switching

frequency has a very high value at lower inductance and it decreases with increase in the

inductor values; whereas the losses at fundamental frequency increase with the rise in

inductor value. Hence, the total losses due to the inductor increase with an increase in

inductance value as seen from the Fig. 5.and a lower inductance is to be selected so that the

losses are optimized.

Fig. 4.3. Plot between THD% and Power Losses vs pu value of inductance

When the damping circuit losses are studied, it is observed that at the lower inductor

values, losses are higher than that present, at higher inductor values. Fig. 6 shows the plot of

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

100

200

300

400

500

600

700

L(pu)

Tot

al p

ower

loss

es

(in

wat

t)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

10

20

30

Inductance (in pu)

TH

D %

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

500

1000

THD%

Power Loss

48 | P a g e

total losses and the THD of current waveformvs the inductor value. It is seen that at lower

value of inductance the total losses off whole filter is very high. The point of intersection

provides the optimal value of the inductor where a tradeoff has been made between the losses

and the THD% of current waveform

Fig. 4.4. Harmonic waveform of the grid current at optimum inductor values

The optimized value of inductance can be found from the above figure which comes out to

be 0.0135 p.u. which comes out to be 2.226 mH. Fig. 7 shows the value of THD% of the grid

current. It is seen that the THD% is 1.99% which is well within the limit of 5% from

L1=2.268 mH. L2is chosen to be a bit less than L1 and it comes out to be 0.988 mH. The

optimal values of the capacitor is then calculated from (21) by taking the effect of both the

losses and the capacity of filter and have been shown in table 2. At the same time, the one

with lower THD% is given prime consideration.

TABLE 4.2

DESIGN PARAMETERS OF LCL-TYPE FILTER

Parameters Value

L1 1.28 mH

L2 0.988 mH

C1 22.337 uF

Cd 22.337 uF

Rd 7.1251 ohms

Losses 52.198 W

THD% 1.99 %

0 0.01 0.02 0.03 0.04 0.05 0.06

-50

0

50

Selected signal: 3 cycles. FFT window (in red): 1 cycles

Time (s)

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

Harmonic order

Fundamental (50Hz) = 74.55 , THD= 1.99%

Mag

(%

of

Fu

nd

am

en

tal)

49 | P a g e

4.4 CONCLUSIONS

Here, it is seen that the filter design is done by a trade-off between the THD% and the

total losses, and thus provides the optimal values for the filter design. Simulation results

verify the effectiveness of the system. The agreement with the simulation results to a

prodigious extent with a good sinusoidal grid current, a lesser harmonic component was also

obtained by the optimization done by the filter design.

50 | P a g e

CHAPTER 5

Conclusions

51 | P a g e

5.1. CONCLUSIONS

Here, a control scheme for a three-phase grid-connected inverter with an LCL-type filter

has been investigated. For the inverter system, the control method has been given to

accurately formulate the decoupling terms for LCL-type filter.

An analytical background of the active and reactive power control strategy for a grid

connected inverter system is provided.

In this method independent control of the active and reactive power was realized in an

effective way.

It also includes an improved current harmonics compensation capability through the use

of MRF PI controller.

Comparative studies made in the text have shown that the MRF PI controller provides

better performance in terms of improvement of grid dynamics as compared to the

conventional controller.

The agreement with the simulation results to a prodigious extent with a good sinusoidal

grid current, a lesser harmonic component was also obtained by MRF PI controller.

For the inverter system, the control method has been given to accurately formulate the

decoupling terms for LCL-type filter.

It is also seen that the filter design is done by a trade-off between the THD% of grid

current and the total losses, and thus provides the optimal values for the filter design.

Simulation results verify the effectiveness of the system.

The agreement with the simulation results to a prodigious extent with a good sinusoidal

grid current, a lesser harmonic component was also obtained by the optimization done by

the filter design.

52 | P a g e

References

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54 | P a g e

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55 | P a g e

PAPERS PUBLISHED

1. Anup Anurag, T.Naga Sowmya, Debati Marandi, B.Chitti Babu,” Decoupled

Control Strategy of Grid Interactive Inverter System with Optimal LCL Filter

Design”, International Journal of Emerging Electric Power Systems (IJEEPS), UC

Berkeley Press, (Paper ID: IJEEPS.2013.0015)- Under review

2. Anup Anurag, B.Chitti Babu, ” Control of Grid Connected Inverter System for

Sinusoidal Current Injection with Improved Performance”, In Proc. IEEE Students’

Conference on Engineering & Systems (SCES 2012), MNNIT, Allahabad,

Mar/2012.

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