Analysis and control of unified active power filter

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A nalysis and Control o f Unified A ctive Power F ilter

by

SUBRAMANÎAN MUTHU

M.Tech., Indian Institute of Techn*-«îogy, Madras, 1092 B.Engg., Bharathiyar University, Coimbatore, 1989

A Dissertation Subm itted in Partial Fulfillment of the Requirements for the Degree of

Do c t o r o f Ph il o s o p h y

in the Department of Electrical and Computer Engineering

We accept this dissertation as conforming to the required standard

Dr. J.M.-S. Kim, Supervisor, Dept, of Elect. & Comp. Eng.

DptnA.K.S. Bhat, Member, Dept, of Elect. & Comp. Eng.

Dr. H.H.L. Kwok, Member, Dept, of Elect. & Comp. Eng.

Dr. G. Shoja, Outside M ^ b e r , Dept, of Computer Science

Dr. Reza M. Iravani, External Examiner, The University of Toronto

© SUBRAMANIAN MUTHU, 1998

University of Victoria

A ll rights reserved. This dissertation may not be reproduced in whole or in part by photocopy or other means, without the permission of the author.

Supervisor: Dr. J.M.-S Kim

A B ST R A C T

The combined series and shunt active filters have been proposed to alleviate the power quality problems at the demand-side power systems. They provide compensation for load reactive power, load harmonics, unbalanced loads, utility harmonics, utility dis­ turbances and utility imbalance. However, the conventional approach for the control of the combined active filter systems have resulted in large operating capacity of the shunt active filter because reactive power compensation involves only the shunt active filter. Furthermore, the harmonic mitigation problems are handled mainly by indirect harmonic compensation schemes rather than direct harmonic isolation schemes.

This thesis presents the analysis and control of Unified Active Power Filter(U A PF) and proposes a novel concept of load reactive power compensation involving both the series active filter and the shunt active filter. This new control strategy of the com­ bined active filter is to achieve the reduction in KVA rating of the shunt active filter and the optim al operation with increased efficiency. The thesis also applies discrete­ time sliding-mode control technique to enhance the performance of the combined active filter system in terms of fast dynamic response and effective solution to har­ monic mitigation problems. The thesis also presents simulation and experimental results to provide verification of the proposed UAPF concept.

In this thesis, the involvement of series active filter for reactive power compen­ sation is achieved by controlling the phase difference between the load voltage and the utility voltage. The complete steady-state operating characteristics of UAPF are analyzed with the identification of the different operating modes of UAPF and the analysis of active and reactive power handled by the active filter components. The results of the analysis are shown to provide an insight about the load reactive power compensation by the series and shunt active filter. The reduction in ratings of the shunt active filter is demonstrated by an apparent power analysis of active filter com­ ponents. The results of the analysis are also useful to design and select the optim al operating point for UAPF.

The performance of UAPF to meet the stringent power quality standards are realized by applying discrete-time sliding-mode control schemes for the load voltage

I l l

regulation and the active power factor correction. Various voltage and current control techniques used for three-phase voltage-source inverters are surveyed to identify the discrete-time sliding mode control technique as the suitable one. A generalized design procedure is derived for the control of power converter systems and the control scheme is extended to the load voltage control of shunt active filter and the line current control of series active filter. The control algorithms are developed to track a given load voltage and line current reference signals respectively. The effect of com putational delay in DSP implementation is studied extensively and the control law is designed with the consideration for the computational delay. The systematic approach for the design of DC link voltage regulation is also presented in this thesis.

A prototype experimental setup including the power circuit for UAPF and DSP based control circuit is built to implement the control and to verify the performance characteristics of UAPF. A real-time control algorithm is developed and is imple­ mented on a DSP TMS320C40 system with PWM implementation by DMA w ithout the intervention of CPU.

The steady-state operating characteristics of UAPF is investigated by experi­ ments. The operation of UAPF at the optimal operating point is shown to reduce the ratings of the shunt active filter and to improve the efficiency. The steady-state op­ eration and the dynamic response of discrete-time sliding mode load voltage control and utility line current control are examined by simulation and experiments. The invariance property and the robustness property of the discrete-time sliding mode control are also dem onstrated by the experimental results. W ith the discrete-time sliding mode control, the compensation characteristics of UAPF are shown to meet the stringent power quality standards.

Examiners:

Dr. J.M.-S. Kim, Supervisor, Dept, of Elect. &: Comp. Eng.

Dr.wV.K.S. Blmt, Member, Dept, of Elect. & Comp. Eng.

Dr. H.H.L. Kwok, Member, Dept, of Elect. & Comp. Eng.

Dr. G. Shoja, Q u t ^ e MertAer, Dept, of Computer Science

Table o f C ontents

Abstract ii

Table of Contents v

List o f Figures x

List o f Tables x v

List of Symbols xvii

Acknowledgement xxvi

D edication xxvii

1 Introduction 1

1.1 Power Q u a l i t y ... 2

1.1.1 Power Quality Problem Identification ... 3

1.1.2 S ta n d a rd s... 5

1.2 Compensators and Active F i l t e r s ... 5

1.2.1 Tuned L-C Filters for Harmonic C o m p e n sa tio n ... 7

1.2.2 VAR C o m p e n s a to rs ... 7

1.2.3 Static Compensators for Transmission S y s te m s ... 8

1.2.4 Active F ilte rs ... 9

1.2.5 Combined Series and Shunt Active F i l t e r s ... 11

1.3 Motivation for the T h e s i s ... 17

1.4 Unified Active Power Filter(UAPF) ... 18

1.5 Realization Stages of U A P F ... 23

1.5.1 Description of Power Circuit for U A P F ... 25

1.6 Organization of the Thesis ... 30

2 Steady S tate O perating Characteristics o f Unified A ctive Power Fil­ ter 33 2.1 Equivalent Circuit Models at Steady-state Operating Conditions . . 34

2.2 Steady-state Analysis at the Fundamental F re q u e n c y ... 38

2.2.1 Power Flow Equations for Utility and L o a d ... 38

2.2.2 Equations for Active Filter C o m p o n e n ts... 40

2.2.3 Power Flow A nalysis... 45

2.3 Critical Modes of O p e ra tio n ... 55

2.3.1 Series Active Filter as a Purely Resistive C o m p o n en t... 55

2.3.2 Series Active Filter as a Purely Capacitive Component and Shunt Active Filter as a Reactive C o m p o n e n t... 56

2.3.3 Series Active Filter as a Purely Inductive Component and Shunt Active Filter as a Reactive C o m p o n e n t... 58

2.4 kVA Rating ... 59

2.5 Experimental V erificatio n ... 64

2.5.1 Operating Characteristics under Nominal Utility Voltage Con­ dition Vi = 120 V ... 65

2.5.2 Operating Characteristics under 30% Voltage Sag Condition 1C = 84 V ... 80

2.5.3 Steady-state Operating Characteristics with R, L and Diode Rectifier L o a d ... 92

2.6 C onclusions... 96

3 Dynam ic Control o f Shunt A ctive F ilter 98 3.1 Survey of Existing Voltage Control Methods for Three-Phase VSI S y s t e m s ... 99

3.2 Discrete-Time Sliding Mode Control with Reaching Law Approach . 102 3.2.1 Selection of Switching F u n c tio n ... 105

3.2.2 Derivation of Control L a w ... 107

Table o f C ontents vii

3.3 Discrete-time Sliding Mode Voltage Control Scheme for VSI in the

Shunt Active F i l t e r ... 108

3.3.1 System M odeling... 109

3.3.2 Selection of Switching F u n c tio n ... 122

3.3.3 Derivation of Control I n p u t ... 128

3.4 Performance V erification... 130

3.5 Conclusions and Summary... ... 141

4 Dynam ic Control o f Series A ctive Filter 143 4.1 Survey of Existing Current Control Methods for Three-Phase VSI S y s te m s ... 144

4.2 Discrete-time Sliding Mode Line Current Control of VSI System in Series Active F i l t e r ... 146

4.2.1 System M odeling... 146

4.2.2 Selection of Switching F u n c tio n ... 153

4.2.3 Derivation of Expression for Pulse W id th s ... 156

4.3 Performance V erification... 158

4.4 Conclusions and Summary... ... 169

5 R egulation o f DC Link 171 5.1 Regulation of DC Link Voltage for the Control of Utility Active Power F l o w ... 172

5.2 Low Frequency Modelling of...UAPF ... 175

5.2.1 System Equations of UAPF in a — 6 — c C o o rd in a te s ... 175

5.2.2 d — q R otating Reference Frame Transformation ... 182

5.3 Small-Signal Modelling ... 185

5.3.1 Steady-State S o lu tio n s... 185

5.3.2 Small Signal A n a ly s is ... 188

5.4 Closed-Loop DC Link Voltage Regulation D e s ig n ... 191

5.5 Performance V erification... 194

5.5.1 Steady-state P e rfo rm a n c e... 195

5.5.2 Transient P erform ance... 196

6 Control Im plem entation in D SP 201 6.1 Overview of Implementation of Control in D S P ... 202 6.2 Description of DSP-to-Power Circuit In terface...

6.3 Development of Real-time Control A lg o r ith m ... 6.3.1 Various Tasks in DSP Control of U A P F ... 6.3.2 Description of DSP TMS320C40 Multi-board system . . . . 6.3.3 Flow of Control P r o g r a m ... 6.3.4 PWM Generation by D M A ... 6.4 C onclusions... 203 206 206 207 210 217 220 7 Conclusions 222

7.1 Summary of the Thesis ... 222 7.2 Contributions of the T h e s i s ... 224 7.3 Recommended Future W o rk ... 226

Bibliography 228

Bibliography 228

A ppendix A D esign of Laboratory P rototyp e 238

A ppendix B Selection o f P W M Technique 246

B .l Space Vector PWM ... 247

A ppendix C Saber Sim ulation 252

C .l C Program for the Control of Shunt Active F i l t e r ... 259 C.2 C Program for the Control of Series Active F i l t e r ... 263 C.3 Saber N e t l i s t ... 268

A ppendix D A uxiliary Experim ental Circuits 275

A ppendix E D SP Control Program 277

E .l Main P r o g r a m ... 277 E.2 Link Array Initializatio n ... 309 E.3 Power F u n ctio n ... 318

Table of Contents ix

Figure 1.1 Different topologies for combined series and shunt active filter

systems... 14

Figure 1.2 Unified Active Power Filter connected at P C C ... 19

Figure 1.3 Single-phase equivalent representation for U A P F ... 21

Figure 1.4 Realization stages of U A P F ... 24

Figure 1.5 Power circuit diagram for the proposed U A P F ... 26

Figure 1.6 Block diagram for the dynamic control of U A P F ... 28

Figure 2.1 Single-phase equivalent circuit for UAPF at fundamental and harmonic freq u e n c ie s... 37

Figure 2.2 Phasor diagram for steady-state operating characteristics of UAPF (Operating condition; |<^| > |^d, V, > Vi, and lagging pf load). 39 Figure 2.3 Variation of l^r as a function of <Jc... 41

Figure 2.4 Variation of as a function of âc with /{ = 1.0 p.u and —60 < (j) < 60"... 44

Figure 2.5 Possible modes of active power flow for U A P F ... 47

Figure 2.6 Possible modes of reactive power flow for U A P F ... 48

Figure 2.7 Variation of P„ = Pah. as a function of 5 c ... 51

Figure 2.8 Variation of Qar ajid Q,/, as a function of 5cWith % = l.Op.u. . 52

Figure 2.9 Variation of Qsr and Q,/i as a function of 5c with voltage sag V, = 0.7p.u... 53

Figure 2.10 Variation of Qar and Qah as a function of 5c with voltage surge Va = 1.3p.u... 54

Figure 2.11 Phasor diagram for the series active filter operating as a purely resistive component... 56

Figure 2.12 Phasor diagram for the series active filter operating as a purely capacitive component... 57

List o f Figures xi

Figure 2.1^ Phasor diagram for the series active filter operating as a purely inductive component and shunt active filter as purely reactive component 58 Figure 2.14 Variation of kVA ratings of series active filter (or coupling trans­

former) as a function of J c ... 60 Figure 2.15 Variation of kVA rating for shunt active filter as a function of <Jc 61 Figure 2.16 Variation of the total kVA rating as a function of 5c ... 62 Figure 2.17 Load voltage, load current, utility voltage cind utility line cur­

rent for 5c = 0° and Sc = 40°, with = 120 V ... 67 Figure 2.18 The line-to-line voltage across series active filter and the utility

line current for difierent values of Sc with Vj = 120 V ... 72 Figure 2.19 The current and the line-to-line voltage v i ^ { t ) supplied

by the shunt active filter for different values of Sc with Vj = 120 V . . 74 Figure 2.20 Active power flow in UAPF for different values of Sc with =

120 V ... 77 Figure 2.21 Reactive power flow in UAPF for different values of Sc with

% = 120 V ... 79 Figure 2.22 Line-to-line voltage across the series active filter and the utility

line current for different values of Sc with = 84 V... 84 Figure 2.23 Current supplied by the shunt active filter and the line-to-line

load voltage for different values of Sc with = 84 V ... 86 Figure 2.24 Active power flow for different values of Sc with Vj = 84 V . . 89 Figure 2.25 Reactive power flow for different values of Sc with % = 84 V . 91 Figure 2.26 Current supplied by the shunt active filter and the line-to-line

load voltage for different values of Sc with Vg = 120 V ... 94 Figure 2.27 Current supplied by the shunt active filter and the line-to-line

load voltage for different values of Sc with = 84 V ... 95

Figure 3.1 Switching plane for sliding-mode c o n t r o l ... 104 Figure 3.2 Three-phase PWM VSI system with L C filter for the shunt

active filter... 109 Figure 3.3 SVPWM for control im p le m e n ta tio n ... 118 Figure 3.4 Implementation of control under com putational time delay in

Figure 3.5 Movement of the closed loop poles under time-delay for Kc =

1.04., fs = lO M H z ... 125

Figure 3.6 Allocation of closed loop poles with Kc for To = 0.42],. Increase

in Kc returns the poles to unit-circle... 126 Figure 3.7 Sensitivity of closed-loop poles with To = 0.42], fj.sec and Kc =

15 under variation in filter c o m p o n e n ts ... 127 Figure 3.8 Experimental results: No-load line-to-line voltages v i ^ { t ) and

vijbc{i)- V’-axis: 100 V fD iv., X-axis: 5 m s e c .f D i v ... 131

Figure 3.9 Load line-to-line voltages vi_ab{t), and vijbc{t) and load current

î/-o(0 under the combined full load co ndition... 134 Figure 3.10 Harmonic Spectra and THD measurement for load voltage un­

der R, L and diode-rectifier load. Upper half: vi_ab{t). Lower half:

Harmonic spectra... 136 Figure 3.11 Switching plane for the system in d coordinates: X-axis: de­

viation in capacitor current, Y-axis: deviation in load voltage. The dotted line represents the ideal-switching plane S{k)a = 0 ... 137 Figure 3.12 Load line-to-line voltage vi_ab{t) 100 V /D iv., and current

(10 A /D iv .) supplied by the shunt active filter with 5c = 0®. X-axis:

5 m sec./D iv... 139

Figure 3.13 Demonstration of invariance property: Load line-to-line voltage Ufui6((), and Vi_tc{t). Y-axis: (100 V /D iv.), X-axis: 5 m sec./D iv. . . . 140 Figure 3.14 Performance under unbalanced load condition: Load line-to-

line voltage vi,jabit) (100 V /D iv .), and load current ii_a{t) (20 A /D iv .). X-axis: 5 m sec./D iv... 140

Figure 4.1 Circuit diagram of the series active f i l t e r ... 146 Figure 4.2 Root locus of the closed-loop dynamics under control imple­

mentation d e la y ... 156 Figure 4.3 Utility line-to-line Voltages V3_ab{t), and Uj_6c(i), and utility line

currents ii_a(Oi and i s j , { t ) ... 160 Figure 4.4 Harmonic Spectrum and THD measurement from experiment

for utility line current. Upper-half; Utility line current. Lower-half: Harmonic spectra ... 162

List of Figures x iii

Figure 4.5 Utility line-to-line voltage and line current is_a{t) under 30% utility voltage sag (100 V f Div., 10 A /D iv .). X-axis: om sec.f D iv. 164 Figure 4.6 Performance under 30% utility voltage unbalance: Utility volt­

age Vj^bit) and V3_bc{t) (Upper half: 200 V /D iv.), and line currents

is-a(O) a-nd %,_&(() (Lower half: 10 v4/Dzu.),X-axis: bmsec./ D iv . . . . 166 Figure 4.7 Utility line-to-line voltage V3_ab{t) (100 V /D iv.), and line cur­

rents is^{t) and ijj,(t) (5 A /D iv .) with 50% reduction in filter induc­ tors. X-axis: b m s e c ./D iv .) ... 167 Figure 4.8 V3_ab{t) (100 V /D iv.), and line current ia ^it) (5 A /D iv .) under

10% load condition, X-axis: f>msec./Div... 168 Figure 4.9 Vj^bit) (100 V /D iv .), and line current i3_a{t) (5 A /D iv .) under

50% load condition, X-axis: 5 m sec./D iv... 169

Figure 5.1 Illustration of dynamic control of utility active power flow in UAPF with DC link voltage control scheme ... 174 Figure 5.2 Block diagram of the DC link voltage control s y s t e m 193 Figure 5.3 DC link voltage Vdc{t) under steady-state with = 120 V,

Vi = 120 V, 5c = 0", and R L and diode rectifier load : (20 V /D iv ),

X-axis: (200msec/Dfu.) ... 196 Figure 5.4 Transient performance of UAPF for 0 to 100% step change in

l o a d ... 197 Figure 5.5 Transient performance of UAPF for 100% to 0% step change in

l o a d ... 199

Figure 6.1 Control implementation in D S P ... 203 Figure 6.2 Illustration of DSP-to-power circuit in te rfa c e ... 205 Figure 6.3 Various tasks in DSP control of UAPF and their scheduling . 207 Figure 6.4 DSP TMS320C40 multi-board system with m aster board and

carrier b o a r d s ... 208 Figure 6.5 Flow chart for Real-time Control of U A P F ... 214 Figure 6.6 Timing diagram for the real-time control in each sampling in­

tervals ... 215 Figure 6.7 Illustration for PWM generation by DMA and T im e rs ...218

Figure B .l SVPWM te c h n iq u e ... 249

Figure C .l Saber simulation circuit ... 254 Figure C.2 Power circuit with back-to-back connected VSI’s and DC link 255 Figure C.3 Circuit for power semiconductor sw itc h e s... 256 Figure C.4 LC filters in shunt active f il t e r ... 256 Figure C.5 Coupling transformer and filter inductors in series active filter 257 Figure C.6 Line current sensing ... 257 Figure C.7 Utility voltage sensing with low-pass f i l t e r ... 258 Figure C.8 Non-linear block for DSP e m u la tio n ... 258

Figure D .l Gate-delay logic for dead-time between upper and lower switches275 Figure D.2 Input interface c i r c u i t s ... 276

X V

List o f Tables

Table 1.1 Disturbance limits for and below voltage levels from IEEE standard 519-1992 [8] ... 5

Table 2.1 Measurement of load and utility condition... 66 Table 2.2 Calculated values of steady-state operating conditions of UAPF

at fundamental frequency with = 120 V ... 69 Table 2.3 Measurement of steady-state operating conditions of UAPF with

v , = m v ... 69 Table 2.4 Measurement of utility conditions with Vi = 84 V ... 81 Table 2.5 Calculated values of steady-state operating conditions of UAPF

at fundamental frequency with Vi = 84 K ... 82 Table 2.6 Measurement of steady-state operating conditions of UAP with

V, = 84 y ... 82 Table 2.7 Measured performance characteristics of UAPF with the com­

bined R, L and non-linear load for different values of dc... 93

Table 3.1 Numerical values of the constants in the expression for pulse

w i d t h s ... 129 Table 3.2 Measurement of three-phase load voltages under no-load condi­

tion (Utility condition: Vi = 120 V, P , = 310 W, and = 0.94 A) . . 131 Table 3.3 Experimental Results: Load voltage regulation of UAPF with

P , L and Diode rectifier load with 5c = 0" and Vi = 120 V ... 133 Table 3.4 Measurement of load voltage regulation under unbalanced load

condition: Single phase condition... 141

Table 4.1 Experimental Results: Steady-state performance of UAPF with P , L and Diode rectifier load under nominal utility voltage condition with 5c = 0° and Vi = 120 V ... 159

Table 4.2 Experimental results: Steady-state performance of UAPF under 30% utility voltage sag condition with R, L, and diode rectifier load . 164 Table 4.3 Performance of UAPF under 31% unbalance in utility voltage . 165

Table 4.4 Performance of UAPF under No-load c o n d itio n ... 168

Table 4.5 Performance of UAPF with 10% load c o n d itio n ... 168

Table 4.6 Performance of UAPF with 50% load c o n d itio n ... 168

Table B .l Switching sequence for S V P W M ... 249

X V I I

List o f Sym bols

Circuit Param eters and N otations

X tr ja , XtrJb, X tr .b Cdc Z fs St'q, Stq Stq, Stq L>3tuoli ^3rJ)i L,r_c L3T /2sr S h t , Sh-^ S h g SfiQi Sh.Q ^shjdi ^3hJ)> ^3h-c Lsh ^^3h ^a/i_a6) C>3hJjc> C3h Coupling transformers DC link capacitor Sampling time Sampling frequency

Upper and lower switches in phase a Upper and lower switches in phase b Upper and lower switches in phase c Filter inductors

Impedance of filter inductors Value of filter Inductor

Winding resistance in filter inductor Upper and lower switches in phase a Upper and lower switches in phase b Upper and lower switches in phase c Filter inductors

Value of filter inductor

Winding resistance in filter inductor Filter capacitors

I n s ta n ta n e o u s V aria b le s u se d in S in g le -p h ase R e p r e s e n ta tio n U tility voltage

U5l(t) Fundamental component in utility voltage

V,n{t) n th harmonic component in utility voltage

Vi{t) Load voltage

n th harmonic component in load voltage

is{t) Utility line current

n th harmonic component in utility line current

V3r{t) Voltage across the series active filter

^arnif) n th harmonic component in voltage across the

series active filter

ish{t) Current supplied by shunt active filter

hhn{t) n th harmonic component in current supplied

by shunt active filter

iid{t) Active power component in load current Reactive power component in load current

Unit) n th harmonic component in load current In s ta n ta n e o u s V a ria b le s u se d in T h re e -p h a s e S y ste m s

^s_a(^)t Utility line-to-neutral voltages

^s-co(^) Utility line-to-line voltages

*s_a(^)) *a-c(0 Utility line currents

Vi^{t) Load line-to-neutral voltages

'^luabifyi '^lJbc{P')^ ^f_ca(() Load line-to-line voltages

il A i ) Load line currents

^ar_o6(t), ^ar_6c(0) ^arjxi(^) Line-to-line voltage across series active filter

i3h-a{i)i ishAi)^ ish A i) Currents supplied by shunt active filter

icsh^ip)} iLshJbif) 1 iù3hAj') Currents supplied by VSI in shunt active filter

List of Symbols x ix ^ar^bifyi Esr^a{t) ^ahjoJbify') EjahJ>cif’)i ^ a h j c a i f y Vdc{t ) PÀi) Pi{i) Pan{i) P lnit) Pc{t) G \. G i, Line-to-line output

voltages of VSI in series active filter Line-to-line output

voltages of VSI in shunt active filter DC link voltage

Real power supplied by the utility Real power a t load end

Utility harmonic power Load Harmonic power

Real power absorbed by the DC link capacitor G ating signals to upper switches

RM S values V, ^ a J ic i I ^ _ c a ^ a ji: ^a-C Vi ^IJoci ^ l- c a h Il-at ^IJbi E a r hd h , h n lah ^Lah ^Lar

Utility line-to-neutral voltage

Three-phase utility line-to-line voltages Utility line current

Utility line currents in phase a, b, and c Load line-to-neutral voltage

Three-phase load line-to-line voltages Load current

Load currents in phase a, b, and c

O utput voltage of VSI in series active filter Active component in load current

Reactive component in load current n th harmonic component in load current

Line-to-neutral voltage across the series active filter Current supplied by shunt active filter

Current supplied by the VSI in shunt active filter Current supplied by the VSI in series active filter Utility harmonic voltage of n th order

fan Utility harmonic current of nth order

Vin Load harmonic voltage of nth order

fin Load harmonic current of n th order

Vsrn Harmonic voltage across the series active filter

Ij/in Harmonic current supplied the shunt active filter Phasor N otation s at fundamental frequency

Vi Load voltage

Vs Utility voltage

Is Utility line current

Vsr Voltage across series active filter

îsh Current supplied by shunt active filter

Sah Apparent power a t series active filter

Ssh Apparent power a t series active filter

Sc Phase difference between the utility voltage and load voltage

^cuopt Optim um value of control angle ^c_mai Maximum value of control angle

<j) Load angle/Phase difference between the load voltage and load current at the fundamental frequency

dar Phase angle of Vsr with respect to VJ

Oah Phase angle of /,/, with respect to Vi A ctive, R eactive powers and kVA

Psj Qa Power supplied by utility interface Pi, Qi Load power

Qar Power absorbed by the series active filter Pah, Qah Power Supplied by the shunt active filter

Q„ai Reactive power supplied by the VSI in shunt active filter P r, Qt Power supplied after coupling transformer by

List of Symbols x x i

Q c Reactive power supplied by the filter capacitors

Pan Utility active power at nth order

Sar Apparent power for series active filter

Sah Apparent shunt active filter

kVAxir Combined kVA for the three-phase coupling transformers

k V Ayai kVA for the VSI in shunt active filter Variables \n d — q coordinates

Vs{t)d, Va(t)g Utility voltage h ( t ) d , h{t)q Utility line current

vi{t)q Load voltage i i { t ) q Load current

Var{t)d, Var{t)q Voltage across series active filter

ish{t)d, ish{t)q Current supplied by shunt active filter

iLsh{t)d, iLsh{t)q Current supplied by VSI in shunt active filter

EaT{t)d, Ear{t)q O utput of VSI in series active filter

Eah{t)d, Eah(t)q O utput of VSI in shunt active filter Average values in a sam pling interval

dsr^a, dar^a, dar^a Average duty-ratio for 5r]J, and 5 r J

davjna, t^5r_no Average duty-ratio for S r ^ and

dah^a, dah^a, dah^a Average duty-ratio for 5 /ia + , Sh% and 5 /iJ

dahjia, dah^a, dahjna Average duty-ratio for S h ^ , S h g and S h e Vajic, ^suca Utility Une-to-line voltages

ia_a, iajb, *5-c Utility line currents

vij}c, vi_ca Load liue-to-Iine voltage îj-fl, kj), î’i-c Utility line currents

Varjba Line-to-line voltage across series active filter

hhua, iahj)^ ishuc Currents supplied by shunt active filter

iùshua, iishj), *£,j/i_c Currents supplied by VSI in shunt active filter V „h, icjbci î'c-co Filter capacitor currents in shunt active filter

Earuab, E^_6c, Line-to-line output voltages of VSI in series active filter

E a h ^ , Eahjic, E a h ^ Line-to-line output voltages of VSI in shunt active filter

Average values in d — ç rotating reference frame

dsrua, Average duty-ratio for series active filter

d.3h ^ Average duty-ratio for shunt active filter

Ua_d, Vs_q Utility voltage Utility line current

vi_q Load voltage Load current

Uar_j, Voltage across series active filter

ishud, ish^ Current supplied by shunt active filter

iiahud^ h a h ^ Current supplied by VSI in shunt active filter EarJL, E sr^ O utput voltage of the VSI in series active filter

Esh^ O utput voltage of the VSI in shunt active filter Perturbed variables in d — g rotating reference frame

dar^, darjq Dutv-ratio for series active filter

dsh^, dah^ Duty-ratio for shunt active filter

Va^ Utility voltage Utility line current û(_q Load voltage

îi-fl Load current

ûar_d, Varjj Voltage across series active filter

iahuq Current supplied by shunt active filter

tLah^^ h a h ^ Current supplied by VSI in shunt active filter Êaruj O utput voltage for the VSI in series active filter êah^, Êahjj O utput voltage of the VSI in shunt active filter

List o f Symbols x x iii

S y m b o ls U se d in C o n tro l S y ste m D esig n

K , a Constants for power-rate reaching law 0, r , A Coefficients in discrete-time state equation

^max Quasi-sliding mode band

Coefficients of switching function

G Feedback gain

ocsT Constants for power-rate reaching law in line current control

Kst, Osr Constants for power-rate reaching law in load voltage control 05r, F,r, Aar Coefficients in discrete-time state equation

Ksr, Oar Constants for power-rate reaching law in line current control Faro, Far I Coefficients for ZOH model

Aar_mai Quasi-sUding mode band

Ac, Be, Dc Coefficients for state-equation in o — 6 — c coordinates A, B, D Coefficients for state-equation \n d — q coordinates

Ksh, ocsh Constants for power-rate reaching law in load voltage control 0s/i, FaA, Aa/i Coefficients in discrete-time state equation

Fa/,0, F a/ll Coefficients for ZOH model

Aa/i_max Quasi-sUding mode band

Coefficients for switching functions

Kp Proportional constant

Ti Integral constant

Bandwidth of the closed-Ioop system

G(s) Small-signal transfer function

GH{s) Loop transfer function

K i Constant in G(s)

Er(s) Error in DC link voltage

2c, Tc Zero and pole of the small-signal transfer function

Ppi{s) O utput of PI controller

/a(s) RMS value of line current

Variables in D iscrete-tim e k 3 ( t ) X I, X2 n m P X(&) U(fc)

P(&)

Number of state variables Number of control inputs Number of disturbance inputs State variables

Control inputs Disturbance inputs Equivalent control inputs

Pulse widths for the VSI in shunt active filter

Pulse widths for the VSI in series active filter Switching function for load voltage control Switching function for line current control Utility voltage

Utility line current Load voltage Load current

Voltage across series active filter Current supplied by shunt active filter Filter capacitors currents

Pulse widths for the VSI in series active filter

Pulse widths for the VSI in shunt active filter Utility line current

Load voltage

Switching functions for line current control Switching functions for load voltage control

L ist of Symbols X X V

Abbreviations

UAPF Unified Active Power Filter

AC Aiternating Current

DC Direct Current

pf Power Factor

PFC Power Factor Correction

SVC Static VAR Compensator

ASVC Advanced Static VAR Compensator

STATCON Static Condenser

SSSC Static Synchronous Series Compensator FACTS Fiexibie AC Transmission System

PCC Point of Common Coupiing

PWM Puise W idth Moduiation

SVPWM Space Vector PWM

SISO Singie Input, Singie O utput MIMO Muiti Input, Muiti O utput

VSI Voltage Source Inverter

CSI Current Source Inverter

IGBT Insuiated-Gate Bipolar Transistors

ESR Equivalent Series Resistance

KVL Kirchoff’s Voltage Law

KCL Kirchoff’s Current Law

DSP Digital Signal Processor

ZOH Zero-Order-Hold

RMS Root Mean Square

ADC Anaiog-to-Digital Conversion

DIO Digital Input O utput

MOPS Millions Operations per Second

DMA Direct Memory Access

A c k n o w le d g e m e n t

I am greatly indebted to my supervisor Dr. J.M.S Kim for his encouragement and guidance during my study at the university of Victoria. I would like to thank him for his continued help and advice during the course of this thesis work and for providing me a research assistantship.

I also wish to thank my supervisory committee members for their suggestion during the course of this research work.

I gratefully acknowledge the help received from the technical staff of the D epart­ ment of Electrical Engineering. Special acknowledgement goes to Kevin Jones for his technical support while doing the experiment in the power electronics research lab. The help received from Roger Kelly and John Dorocicz for setting up the SABER simulator and the work station is also acknowledged.

x x v u

D e d ic a tio n

In trod u ction

This thesis presents the analysis and control of Unified Active Power Filter (UAPF) and its potential use to alleviate power quality problems for the demand-side power systems. Unified Active Power filter (UAPF) is a combination of a series-type active filter and a shunt-type active filter. It can be connected at the point of common coupling between the utility distribution line and the customer loads and provides complete compensation and isolation for load reactive power, load harmonics, unbal­ anced loads, utility harmonics, utility disturbances and utility imbalance.

The circuit configuration of UAPF has been proposed in the literature [1] and

other combined active filters are also available [2, 3]. The existing combined active

filter systems have requirements for large operating capacity of the shunt active filter because reactive power compensation involves only the shunt active filter. Further­ more, the harmonic mitigation problems are handled mainly by indirect harmonic compensation schemes rather th an direct harmonic isolation schemes.

This thesis proposes a new control strategy of the combined active filter to achieve the reduction in KVA rating of the shunt active filter by reactive power compensation involving both active filter components. This method results in optim al operation w ith increased efficiency. The thesis also applies modem control techniques to enhance the performance of the combined active filter system in terms of fast dynamic response and effective solution to harmonic mitigation problems.

The scope of the thesis encompasses:

a) A new control strategy to involve the series active filter for reactive power compensation and to reduce the kVA rating of the shunt active filter.

b) The analysis of steady-state operating characteristics of the proposed unified active power filter for optim al operation.

1. Introduction 2

c) The formulation of discrete-time sliding mode control for the dynamic control of load voltage and utility line current.

d) The small-signal modelling of the unified active power filter for the design of the DC link voltage regulation.

e) The development of a real-time control algorithm with the integration of load voltage, utility line current and DC link voltage control schemes, for a single-

DSP system and its implementation with PWM generation by Z?M/l(Direct

Memory Access) in particular.

1.1

Power Q uality

Power quality is a describing term which narrates the aspects of electric utility sup­

ply to customers a t industrial and domestic load sites. A power quality problem is any anomaly occurring in voltage, current or frequency th a t results in failure, mis- operation, and interruption of electrical equipment. A severe power quality problem may lead to shutdown of processes and services, causing economical losses to utility consumers. The recent technical publications manifest th at the power quality prob­ lem is a m ajor issue in electric utilities and its large industrial or commercial clients. The m ajor development for this growing concern on power quality problems can be summarised [4, 5] as follows:

• Microelectronics and VLSI technology have produced modem chips with faster and complex components. These m odem chips are designed to operate in low power levels and require a stable power supply for proper operation. However, the lower voltage levels of the power are easier to be disturbed.

• Power electronics has produced various low-cost supplies and high capacity de­ vices and their applications are ever expanding. Many of these power electronic devices are also responsible for injecting harmonic currents and switching tran­ sients which deteriorate the power quality. It is projected by quality surveys [4] th a t the use and the power processed by this power electronics equipment will increase from the present level of 10% - 20% up to 50% — 60% by the year 2010. • Modem electrical devices are designed for high eflSciency and their design and

components are kept to their limits. This makes the electrical equipment suc­ cumb to any small power quality variations.

• W ith these contemporary changes in progress, more capacitor banks are in­ stalled by electric utilities and industries for power factor correction and loss reductions. These capacitors alter the characteristics of the power system and can improve or worsen the power quality.

• The increase in the power demand owing to the growth in the load is not equally met by an increase in power generation. Consequently, the number of disturbances in the power system has gone up.

W ith the proliferation of electrical loads, and the power-quality-induced down­ time for industrial process and the associated cost, the quality and the reliability of power supplied to utility customers are now increasing concerns. The de-regulation of electric utility and the choice for the consumers to choose and pick the suppliers to buy power above certain level of quality have also an impact on this issue [4].

1.1.1

Power Q uality P roblem Identification

Although the power produced by electric utilities may be of a good quality, the distribution environment is always disturbed and the power oflfered at the customer end may not be of rich in quality. The kind of electric activities th a t contribute to the anomaly in the power quality and its reliability are identified below, in association with 1) the voltage supplied by the electric utility and 2) the current drawn by the

consumers. These electrical disturbances and their source can be summarised as follows [4] -[7]:

• The diode or thyristor rectifier and cyclo-converter loads generate harmonic currents, and the Total Harmonic Distortion(THD) levels in the line current drawn by these loads are normally more than 40%. The Tiigh frequency har­ monic currents can cause electromagnetic interference with the communication networks and the mal-operation of microprocessors and relays.

• The large induction motors used in the steel mills and hoists draw reactive current. Due to this, the RMS value of the line current and the power loss increase. The reactive current also causes the reduction in supply voltage.

I. Introduction 4

• Domestic consumer loads normally represent single-phase loads and present an unbalanced loading to the power system. The unbalanced loading causes the circulation of negative and zero sequence currents in the networks.

• Voltage unbalance [4] describes a state in which the three phase voltages are not equal either in magnitude, or in the phase difference (120°). The unbal­ ance condition is harmful for the motors and other devices th at depend upon a balanced supply voltage.

• The starting of induction motors used in hoists/industrial loads momentarily draws a large amount of reactive current, which produces voltage flicker and fluctuations. The voltage flicker is also caused by the sub-harmonic currents drawn by arc-furnaces. The voltage fluctuations are harmful for the sensitive digital and electronic loads.

• Harmonics are introduced in the system voltage due to the load harmonic cur­ rents flowing into the network. Because of the presence of the voltage harm on­ ics, a resonance network is formed along the installed L-C filters with the line inductance, which again increases the voltage distortion levels.

• Voltage sags are short voltage depressions caused by fault currents and may also appear during the starting of large motors. An industrial survey on voltage sags [5] reports th at voltage sag up to 30%, ranging from 0.6 cycles to 150 cycles exists during sag conditions. These voltage sag related problems are one of the main issues in the power quality problems, because of the process interruptions caused by the voltage sags. Although the frequency of the voltage sags in a year may be less than 2 0 times (from the survey), the disturbance causes the loss of

millions of dollars for industries.

• Voltage swells normally accompany voltage sags. They are also introduced during the light loading conditions. The voltage swells seriously undermine the insulation levels in electric equipment.

• Voltage impulsive or oscillatory transients are caused by lightning or load/capacitor switchings. The notching (voltage waveform may cross zero potential line more than twice in a cycle) are introduced during the transients, are troublesome for the electronic circuits based on zero-crossing detection.

T a b le 1.1. Disturbance limits fo r 6 9 K V and below voltage levels from IE E E standard

Harmonic current Limits in % of fundamental h < n 11 < h < 17 17 < h < 23 23 < /i < 35 35 < h

4.0 2 .0 1 .0 0 . 6 0.3

Total Harmonic Distortion factor. 5% Continuous current unbalance: 10% Harmonic voltage limits in % o f fundamental

Maximum Individual harmonics 3%

Continuous Voltage Unbalance in 120V7208V system 5% Maximum Total Harmonic Distortion factor. 5%

In conclusion, the source of the power quality problems are classified into: 1) disturbance in the utility voltage supplied to the load and 2) disturbance in the load

current th at is drawn from the electric utility.

1.1.2 Standards

IEEE standard 519-1992 [8] and other international standards such as lE C 1000-

2-1 Electromagnetic Compatibility [9], and E N 50160-1994 provides guidelines for

acceptable levels of disturbance on the utility system. The excerpts from IEEE 519- 1992, and lEC 1 0 0 0-2 - 1 standards for acceptable limits of harmonic currents and

voltages in 69fcV and below systems are summarized in Table. 1.1. Any existence of

disturbance above the prescribed levels is considered as a power quality problem and means must be provided to contain them within the allowed limits. The IEEE and other standards are useful when designing such a compensating system.

1.2

C om pensators and A ctive Filters

In order to m aintain the quality and the reliability of the oflfered power, the distur­ bance and distortion in the supplied voltage and the line current must be eliminated or suppressed to tolerable limits. This can be achieved by power electronics devices

1. Introduction 6

such as various compensators and active filters. The objectives of these devices can be defined as follows:

• The voltage a t the load end is regulated such th at a balanced, constant, sinu­ soidal voltage is presented to the consumers, irrespective of the utility condi­ tions. This implies th a t compensation or isolation is achieved for,

a) voltage harmonics or waveform distortion, b) voltage swells, sags and imbalances, c) voltage fluctuations and flicker,

d) voltage impulsive and oscillatory transients.

• The load current is compensated such th at a unity power factor load is presented to the electric utility, which implies a flow of only active power from the electric utility. This enhances the power transmission and the capacity of the existing system can be utilised to the maximum. The compensation or isolation is generally achieved for,

a) reactive load currents, b) harmonics load currents,

c) unbalanced loading.

Power electronics and micro-controller development have made possible to solve the many power system related problems. Over the last decade, the advent of fast switching devices with the Pulse W idth Modulation (PWM) techniques has spurred remarkable development in this area. The advancement in DSP has also made possi­ ble to utilize the modem control techniques for this area and various compensation techniques have been developed for selective applications to generalised ones.

The existing compensation techniques are primarily classifled into passive filters, VAR compensators, static compensators for transmission systems, active filters, and combined active filter systems. The passive filters are basic L —C tuned filters. On the other hand, the VAR compensators and active filters use power converters to achieve the filtering characteristics. The existing compensation techniques are discussed in the following sections.

1.2.1

Tuned L-C Filters for H arm onic C om pensation

k L-C filter tuned to a particular frequency is commonly used for harmonic current

elimination in power systems. The L — C filters are economical and easier to de­ sign with high reliability. However, their performance is influenced by the network impedance and they have serious drawbacks due to resonance. The formation of se­ ries/parallel resonance with the line impedance hinders their application in power systems.

1.2.2

V A R C om pensators

The VAR compensators are primarily for the reactive power compensation, and they can be classifled into 1) Static VAR compensators, and 2) Advanced static VAR

compensators.

(a) S ta tic V A R C o m p e n s a to rs (S V C ): The use of thyristor controlled reactor

(TO R) and thyristor switched capacitor (TSC) is a well established practice in power

system for reactive power compensation [10]. Static VAR compensators overcome the drawbacks faced by the shunt capacitors for reactive power compensation due to the resonance phenomena. When the SVC’s are installed for power transmission appli­ cations, they increase the steady-state power transfer and the voltage profile along the transmission line. Despite their ability to provide variable VAR compensation, SVC’s produce undesirable harmonic currents during the generation of the reactive current, for which L-C filters need to be installed.

(b ) A d v a n c e d S ta tic V A R C o m p e n s a to rs (A S V C ): The advanced static VAR compensators are essentially solid-state synchronous voltage sources (SVS) [11] -[19] and are precursors to the active filters. The solid-state synchronous voltage sources are basic inverters driven to perform the function of static VAR compensator with the additional features for dynamic compensation and real-time control of power flow in transmission systems. The SVS, when operated as a shunt reactive power compensator, exhibits similar operating and performance characteristics of a rotating synchronous condenser and therefore it is also called Static Condenser ov STATCON. The SVS has the significant advantage over the SVC’s in providing fast dynamic

1. Introduction 8

reactive power compensation and control, and hence it finds the application in both the industrial and transmission system for reactive power compensation and voltage regulation.

1.2.3

S ta tic C om pensators for T ransm ission S ystem s

The application of switching converters is also well found for the transmission lines. The static compensators control the power transmission param eters such as voltage, impedance, and transmission angle. The existing static compensators are described as follows:

(a) S ta tic S y n c h ro n o u s S eries C o m p e n s a tio n (S S S C ): In the past, Thyristor-

Controlled Series Capacitors (TCSC) [20] were used for the compensation of transm is­

sion lines. In a nutshell, the effect of adding the series capacitor reduces the effective line impedance and it enhances the maximum transm ittable power. However, the series capacitor causes the phenomenon of sub-synchronous resonance. A solid-state synchronous source by using PWM converters is made to accomplish the objective of a series capacitor [20, 21]. The synchronous voltage source injects a voltage a t the fundamental frequency which is locked in quadrature (lagging) with the line current. The amplitude of this injected voltage is made in proportional to the line current and hence the series compensation is achieved to th at provided by a series capaci­ tor a t the fundamental frequency. In addition, it is immune to the sub-synchronous resonance. The approach to the use of the synchronous voltage source also offers additional advantages. W ith the additional control dynamics equipped, the series source can also be made to develop dampings for the power system’s oscillations and sub-synchronous resonance phenomenon due to any series capacitors th a t are con­ nected in the system. In addition with the series compensation, the SSSC can also compensate for the resistive voltage drop in the transmission line.

(b ) P h a s e S h ifte rs fo r T ra n sm issio n A n g le C o n tro l: Conventional thyristor

controlled tap changing transformer provides the necessary phase shifting by the in­

jection of quadrature voltage with the line to neutral system voltage. The phase shifting changes the effective transmission angle, which controls the real power

trans-fer between the sending and the receiving ends. The use of a solid-state synchronous voltage source offers completely different approach to the transmission angle control, because of its capability to exchange the real power with the AC system, and provides a comprehensive dynamic control of transmission system under transients [2 0, 2 1].

(c) U n ified P o w e r F lo w C o n tro lle r: The concept of unified power flow controller was proposed for real-time control and dynamic compensation of AC transmission system and it is an im portant tool in the implementation of Flexible A C Transmission

Systems (FACTS) [2 2] -[24]. The unified power flow controller consists of two switching

converters which perform the functions of a series synchronous voltage source and a shunt current source. The control of the sources provides the multi-functional flexibilities for power flow control such as 1) voltage regulation, 2) series compensation,

3) phase angle regulation and 4) reactive power compensation. The unified power flow controller configuration has the capability to exchange both the real and reactive powers with the AC system th a t it provides an absolute control over the power th at is negotiated between the sending and the receiving end of the transmission. The unified power flow controller is a powerful tool for concurrent control of voltage, line impedance and transmission angle for the increased effective dam ping of power oscillations and the transients.

1.2.4

A ctive F ilters

Active filters with switching devices and their basic compensation principles were proposed in the 1970’s [25]. The development of fast switching devices over the last two decades, has made possible to realize the active filters which have been a popular research topic since then. The active filters are primarily classified into 1) shunt active

filter and 2) series active filter, and are used for the compensation of disturbances

in load current and utility voltage. The research on active filters is now advanced to the development of the combined systems, such as a series active filter w ith a shunt passive filter, and the integration of series and shunt active filters. The active filters are described in the following:

1. Introduction 10

(a ) S h u n t A c tiv e F ilte rs : Shunt active filters are basic PWM converters com­ monly, realised as non-linear current source for the compensation of reactive power, harmonic currents, imbalance, and flicker produced by the industrial loads [26]-[59]. The PWM converter of the shunt active filter is connected in parallel with the load and is made to generate a compensating current with the help of a current control scheme. The popular control techniques such as hysteresis, predictive, and sliding-mode con­ troller have been proposed to use for the line current control scheme. Irrespective of the current control scheme, the shunt active filter generates a compensating current which is equal in magnitude but out of phase by 180® to the unwanted component of the load current. Thus the shunt active filter supplies the reactive power, harmonic currents and unbalance to the load so th a t the utility line current is compensated. A unity power factor condition is ultim ately presented to the utility. The shunt active filters, in general, have the following disadvantages [37]:

• Since the load is directly connected to the utility, it is still subjected to the utility power quality problems such as distortions, sags,transients and imbalance. • The shunt active filters require large ratings for PWM converters when they

are installed for the compensation of reactive and harmonic currents generated by the loads. The accompanying initial costs are high compared to the passive filters.

There have been approaches to reduce the rating of the shunt active filters by the combination of active filters and passive elements such as capacitors and reactors [53].

(b) S erie s A c tiv e F ilte rs : Series active filters are also basic PWM converters commonly realised as non-linear voltage sources and are connected in series with the utility. The series active filter injects a compensating voltage in series with the utility voltage [60]-[63], which is equal in magnitude but out of phase by 180° to the unwanted component in the utility voltage. Thus the unwanted components are compensated, and the voltage supplied to the load is regulated to a constant- magnitude low THD sinusoidal voltage. The series active filters generally provide compensation for voltage harmonics, unbalance, transients and sags. The ratings of the series active filter depends on the nature of the compensation. The compensation for utility voltage is indirect and the series active filter requires protection firom line

faults. Furthermore, the reactive power and harmonic currents injected by the loads are transferred to the utility side without compensation.

(c) C o m b in e d S y s te m o f S erie s A c tiv e a n d S h u n t P a ssiv e F ilte rs : A com­ pensator for harmonic currents generated by large rectifier and arc furnace loads requires a large shunt active filter system. The combined system with a series active filter and a shunt passive filter has been developed as a suitable alternative for this specific purpose [64] - [6 8]. The combined system utilises the collective advantages

both in active filter and passive filter. The passive filter is connected in parallel to the load and the active filter is connected between the utility and the combined passive filter and load. The passive filter provides a shunt path for the harmonic currents, while the active filter isolates the passive filter from the power system network. The active filter exhibits high impedance at harmonic frequencies and effectively prevents any formation of resonance between the utility and the passive filter. The active filter does not involve in the actual filtering of harmonic currents, therefore, the size of the active filter is very small. The combined system is primarily developed for the har­ monic current compensation only. However, the application of the combined systems can also be found for the compensation of utility voltage unbalance in addition to the harmonic current compensation [62].

1.2.5

C om bined Series and Shunt A ctiv e Filters

The combined Series and Shunt Active filter systems are aimed to provide a com­ prehensive isolation of disturbances between the utility and the load [l]-[3]. More specifically, with the combined series and shunt active filters, it is possible to supply a constant magnitude, low-THD, balanced sinusoidal load voltage while sim ultane­ ously presenting a unity-power factor condition to the utility. The application of the combined systems can be of two types: One is a general compensator for power distri­ bution systems and industrial power systems. The other is the specific compensator with low power ratings which can be installed on the premises of an electric power consumer. In any case, the combined system consists of a series active filter amd a shunt active filter and has the capability to improve the power quality at the point of installation on demand-side power systems.

i. Introduction 12

For the compensation, each active filters in the combined system functions as either current source or voltage source. Since there are two active filters, one active filter functions as a current source and the other as a voltage source resulting in the following two possible topologies:

a) Series active filter as a voltage source and shunt active filter as a current source. b) Series active filter as a current source and shunt active filter as a voltage source.

Fig. 1.1 shows the single-phase equivalent representation of diflferent possible topologies. In Fig. 1.1, the utility is represented by a voltage source Vg which supplies the instantaneous voltage Vs{t). The utility voltage «,(<) contains the fundamental component v,\{t), and the disturbances Vsn(t). The disturbance term Vjn(t) includes the voltage sag, harmonics etc. The load is represented by the non-linear load, which draws the active current iid(t), reactive current iig(t), and the harmonic components iin(t). The active filters are inserted between the utility and the load. The series ac­ tive filter is inserted in series with the utility, and the shunt active filter is connected in parallel.

Fig. 1.1(a) and Fig. 1.1(b) show the topologies comprising the series active filter as

a voltage source and the shunt active filter as a current source. In these topologies, the disturbance in the utility voltage Vjn(t) is sensed and the series active filter generates the voltage Vj„(t) such th at the voltage vi(t) supplied to the load is compensated. The disturbance terms in the load current iig(t) and iin(t) are sensed and the shunt active filter is made to supply these disturbances. Therefore, the utility line current is compensated and only the active component iid(t) flows from the utility. The shunt active filter basically supplies the reactive power, harmonic current, and unbalance to the load. Thus a near unity power factor condition is achieved a t the utility interface.

The topologies illustrated by Fig. 1.1(a) and Fig. 1.1(b) are identical, except they are different in the installation point for series and shunt active filters depending upon the application [2]. Fig. 1.1(a) shows the configuration in which the series active filter

is installed a t downstream near the load and the shunt active filter is a t upstream near the utility. This configuration is applicable where the passive filters are already in use with the load, and can share the load reactive and harmonic current compensation. The shunt active filter doesn’t have to be rated for the full reactive and harmonic load currents. The series active filter prevents any interaction between the shunt active

Series Active Filter

V[(t)

- •Shunt Active Filter

Compensator

(a) Series active filter as a v o lta g e source a t d ow n stream and th e sh u n t activ e filter as a current source a t upstream

Series Active Filter

Vg

Shunt Active Filter Compensator

(b) Series activ e filter as a v o lta g e sou rce a t u p stream an d th e sh un t a c tiv e filter a s a cu rren t sou rce at dow nstream

Fig. 1.1. Different topologies fo r œm bined series and shunt active filter systems. (Continued...)

/. Introduction 14 Series: Active Filter Vg V ](t) Shunt Active Filter Compensator

(c) Series a ctiv e filter as a current sou rce a t u pstream an d sh un t activ e filter as a v o lta g e sou rce a t dow nstream