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A Novel Control Method for Unified Power Quality Conditioner (UPQC) Under Non-Ideal Mains Voltage and Unbalanced Load Conditions Metin Kesler Kocaeli University Technical Education Faculty, 41380 Umuttepe Kocaeli Turkey [email protected] Engin Ozdemir Kocaeli University Technical Education Faculty, 41380 Umuttepe Kocaeli Turkey [email protected] Abstract--This paper presents a new control method to compensate the power quality problems through a three-phase unified power quality conditioner (UPQC) under non-ideal mains voltage and unbalanced load conditions. The performance of proposed control system was analyzed using simulations with Matlab/Simulink program, and experimental results with the hardware prototype. The proposed UPQC system can improve the power quality at the point of common coupling (PCC) on power distribution system under non-ideal mains voltage and unbalanced load conditions. I. INTRODUCTION Unified power quality control was widely studied by many researchers as an eventual method to improve power quality of electrical distribution system [1-3]. The function of unified power quality conditioner is to compensate supply voltage flicker/imbalance, reactive power, negative-sequence current, and harmonics. In other words, the UPQC has the capability of improving power quality at the point of installation on power distribution systems or industrial power systems. Therefore, the UPQC is expected to be one of the most powerful solutions to large capacity loads sensitive to supply voltage flicker/imbalance [2]. The UPQC consisting of the combination of a series active power filter (APF) and shunt APF can also compensate the voltage interruption if it has some energy storage or battery in the dc link [3]. The shunt APF is usually connected across the loads to compensate for all current-related problems such as the reactive power compensation, power factor improvement, current harmonic compensation, and load unbalance compensation [1-2], whereas the series APF is connected in a series with the line through series transformers. It acts as controlled voltage source and can compensate all voltage- related problems, such as voltage harmonics, voltage sag, voltage swell, flicker, etc. In this paper a new control algorithm for the UPQC system is optimized without measuring transformer voltage, load and filter current, so that system performance is improved. The proposed control technique has been evaluated and tested under non-ideal mains voltage and unbalanced load conditions using Matlab/Simulink software. The proposed method is also validated through experimental study. II. UPQC CONTROL ALGORITHM The UPQC consists of two voltage source inverters connected back to back with each other sharing a common dc link. One inverter is controlled as a variable voltage source in the series APF, and the other as a variable current source in the shunt APF. Fig. 1 shows a basic system configuration of a general UPQC consisting of the combination of a series APF and shunt APF. The main aim of the series APF is harmonic isolation between load and supply; it has the capability of voltage flicker/ imbalance compensation as well as voltage regulation and harmonic compensation at the utility-consumer PCC. The shunt APF is used to absorb current harmonics, compensate for reactive power and negative-sequence current, and regulate the dc- link voltage between both APFs. The proposed UPQC control algorithm block diagram in Matlab/Simulink simulation software is shown in Fig. 2. + = = + 3RT LT Nonlinear Load iLabc RL LL vTabc Mains Voltage vSabc C DC iTabc vLabc iSabc RC LC RS L S Zload iCabc Shunt APF Series APF vSa vTa vLa iSa iCa iLa PCC Fig. 1. Unified power quality conditioner configuration. A. Reference Voltage Signal Generation for Series APF The function of the series APF is to compensate the voltage disturbance in the source side, which is due to the fault in the distribution line at the PCC. The series APF control algorithm calculates the reference value to be injected by the series APF transformers, comparing the positive-sequence component with the load side line voltages. The proposed series APF reference voltage signal generation algorithm is shown in Fig. 3. In equation (1), supply voltages v Sabc are transformed to d-q-0 coordinates. 978-1-4244-4783-1/10/$25.00 ©2010 IEEE 374
Transcript

A Novel Control Method for Unified Power Quality Conditioner (UPQC) Under Non-Ideal Mains

Voltage and Unbalanced Load Conditions

Metin Kesler

Kocaeli University Technical Education Faculty, 41380 Umuttepe Kocaeli Turkey [email protected]

Engin Ozdemir Kocaeli University Technical Education Faculty, 41380

Umuttepe Kocaeli Turkey [email protected]

Abstract--This paper presents a new control method to compensate the power quality problems through a three-phase unified power quality conditioner (UPQC) under non-ideal mains voltage and unbalanced load conditions. The performance of proposed control system was analyzed using simulations with Matlab/Simulink program, and experimental results with the hardware prototype. The proposed UPQC system can improve the power quality at the point of common coupling (PCC) on power distribution system under non-ideal mains voltage and unbalanced load conditions.

I. INTRODUCTION Unified power quality control was widely studied by

many researchers as an eventual method to improve power quality of electrical distribution system [1-3]. The function of unified power quality conditioner is to compensate supply voltage flicker/imbalance, reactive power, negative-sequence current, and harmonics. In other words, the UPQC has the capability of improving power quality at the point of installation on power distribution systems or industrial power systems. Therefore, the UPQC is expected to be one of the most powerful solutions to large capacity loads sensitive to supply voltage flicker/imbalance [2]. The UPQC consisting of the combination of a series active power filter (APF) and shunt APF can also compensate the voltage interruption if it has some energy storage or battery in the dc link [3].

The shunt APF is usually connected across the loads to compensate for all current-related problems such as the reactive power compensation, power factor improvement, current harmonic compensation, and load unbalance compensation [1-2], whereas the series APF is connected in a series with the line through series transformers. It acts as controlled voltage source and can compensate all voltage-related problems, such as voltage harmonics, voltage sag, voltage swell, flicker, etc.

In this paper a new control algorithm for the UPQC system is optimized without measuring transformer voltage, load and filter current, so that system performance is improved. The proposed control technique has been evaluated and tested under non-ideal mains voltage and unbalanced load conditions using Matlab/Simulink software. The proposed method is also validated through experimental study.

II. UPQC CONTROL ALGORITHM The UPQC consists of two voltage source inverters

connected back to back with each other sharing a common dc link. One inverter is controlled as a variable voltage source in the series APF, and the other as a variable current source in the shunt APF. Fig. 1 shows a basic system configuration of a general UPQC consisting of the combination of a series APF and shunt APF. The main aim of the series APF is harmonic isolation between load and supply; it has the capability of voltage flicker/ imbalance compensation as well as voltage regulation and harmonic compensation at the utility-consumer PCC. The shunt APF is used to absorb current harmonics, compensate for reactive power and negative-sequence current, and regulate the dc-link voltage between both APFs. The proposed UPQC control algorithm block diagram in Matlab/Simulink simulation software is shown in Fig. 2.

+ = = +

3∼

RT LT

Nonlinear Load

iLabc

RL LL

vTabc

Mains Voltage

vSabc

CDC iTabc

vLabciSabc

RC LC

RS LS

Zload

iCabc

ShuntAPF

SeriesAPF

vSa vTa vLa iSa iCa iLa

PCC

Fig. 1. Unified power quality conditioner configuration.

A. Reference Voltage Signal Generation for Series APF The function of the series APF is to compensate the

voltage disturbance in the source side, which is due to the fault in the distribution line at the PCC. The series APF control algorithm calculates the reference value to be injected by the series APF transformers, comparing the positive-sequence component with the load side line voltages. The proposed series APF reference voltage signal generation algorithm is shown in Fig. 3. In equation (1), supply voltages vSabc are transformed to d-q-0 coordinates.

978-1-4244-4783-1/10/$25.00 ©2010 IEEE 374

VDC

C1

C2

vSabc vLabc iLabc

iCabc

RTabc

CTabc

RCabc

CCabc

LTabc LCabc

vTabc

iSabc

iTabc

(Shunt Active Power Filter)

Ldc3

Rdc3

Cdc1

Rdc1

1-Phase Non-Linear Load

LLa1

LLabc3-Phase Source1-Phase Seies Transformers

(Series Active Power Filter)

3-Phase Non-Linear Load

Discrete,Ts = 5e-006 s.

pow ergui

i+ -iSn

i+ -

iLn

h5

dq0

sin_cosabc

abc

sin_cos dq0

A

B

C

a

b

c

A B C

a b c

A

B

C

a

b

c

A B C

a b c

A

B

C

a

b

c

v Sabc PLL

v 'Tabc

v TabcPWM

Vabc

Iabc

p

Valf aEbeta

Vo

Io

I'0

i'Sbeta

i'Salf a

i'Sabc

iSabc

i'SabcPWM

p

Valf aVbetaVo

IoVdc

I'Salf a

I'Sbeta

I'0

Pulse

12

12

12

g

A

B

C

+

-

iSn iLn

g

A

B

C

+

-

iSabc

iSabc

vLabc

vSabc

vDA

vSabcem

g

A

B

C

+

-N

A

B

C

A

B

+

-

Fig. 2. The proposed UPQC control algorithm block diagram in MATLAB Simulink.

vvv

vvv

Sc

Sb

Sa

Sq

Sd

S0

)3π2cos(wt)

3π2-cos(wtcos(wt)

)3π2sin(wt)

3π2-sin(wtsin(wt)

21

21

21

32

⎥⎥⎥

⎢⎢⎢

⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢

=⎥⎥⎥

⎢⎢⎢

+

+ (1)

The voltage in d axes ( Sdv ) given in (2) consists of

average and oscillating components of source voltages ( Sdv and Sdv~ ). The average voltage Sdv is calculated by using second order LPF (low pass filter).

SdSdSd v~vv += (2)

The load side reference voltages ∗

Labcv are calculated as given in equation (3). The switching signals are assessed by comparing reference voltages ( ∗

Labcv ) and the load voltages ( Labcv ) and via sinusoidal PWM controller.

00Sdv

1)3π

2cos(wt)3π

2sin(wt

1)3π

2cos(wt)3π

2-sin(wt

1cos(wt)sin(wt)

32

Lcv

Lbv

Lav

⎥⎥⎥

⎢⎢⎢

⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢

⎥⎥⎥⎥

⎢⎢⎢⎢

++

+=∗

∗ (3)

These produced three-phase load reference voltages are

compared with load line voltages and errors are then processed by sinusoidal PWM controller to generate the required switching signals for series APF IGBT switches.

B. Reference Current Signal Generation for Shunt APF The shunt APF described in this paper used to compensate

the current harmonics and reactive power generated by the nonlinear load. The shunt APF reference current signal generation block diagram is shown in Fig. 3. The instantaneous reactive power (p-q) theory is used to control of shunt APF in real time. In this theory, the instantaneous three-phase currents and voltages are transformed to α-β-0 coordinates as shown in equation (4) and (5).

α-β Reference

current calc.

α-β Inv.

Trans.

α-β conv.

α-βconv.

vαvβ Instantaneous

Power calculate

iαiβ

LPF∗Sβi

∗Sαi

lossp

GAH

GAL

GBH

GBL

GCH

GCL

Shunt APF

HysteresisBand PWM

DC VDC1 PI

-

+

*DCV

Σ

p p

q

∗Sai

∗Sbi

∗Sciio

vo

VDC2

+

d-q Inv.

transform

PLL

d-qtransform.

LPF

GAH

GAL

GBH

GBL GCH

GCL

Series APF

Sinusoidal PWM

vLa vLb vLc

∗Lαv

∗Lbv

∗Lcv

iSa iSb iSc

vSa vSb vSc

vS0

vSq

vSd

vS0

vSq

Sdv0

0

∗S0i

q

p0

0

-1p0

Fig. 3. Series APF reference voltage and shunt APF reference current signal generation block diagram.

375

ScvSbvSav

/23-/2301/2-1/2-1

21/21/21/

3

2

βv

αv

0v

⎥⎥

⎢⎢

⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

= (4)

SciSbiSai

/23-/2301/2-1/2-1

21/21/21/

3

2

βi

αi

0i

⎥⎥

⎢⎢

⎥⎥

⎢⎢

⎥⎥⎥

⎢⎢⎢

= (5)

The source side instantaneous real and imaginary power

components are calculated by using source currents and phase-neutral voltages as given in (6). The instantaneous real and imaginary powers include both oscillating and average components as shown in (7). Average components of p and q consist of positive sequence components ( p and q ) of source current. The oscillating components ( p~ and q~ ) of p and q include harmonic and negative sequence components of source currents [4]. In order to reduce neutral current, 0p is calculated by using average and oscillating components of imaginary power and oscillating component of the real power; as given in (8) if both harmonic and reactive power compensation is required. isα

* , isβ* and is0

* are the reference currents of shunt APF in α-β-0 coordinates. These currents are transformed to three-phase system as shown in (9).

⎥⎥⎦

⎢⎢⎣

⎥⎥⎦

⎢⎢⎣

⎡⎥⎦⎤

⎢⎣⎡

−=

βiα

i

αv

βv

βv

αv

qp

(6)

000 ivp ∗= ; p~pp += (7)

⎥⎦⎤

⎢⎣⎡

⎥⎥⎦

⎢⎢⎣

⎥⎥⎦

⎢⎢⎣

⎡ ++

+=∗

0lossppp

αvβvβ-vαv

2βv2

αv

1

SβiSαi 0 (8)

S*iS*iS0*i

Sc*iSb*iSa*i

/23-1/2-21//231/2-21/

0121/

32

⎥⎥⎥

⎢⎢⎢

⎥⎥⎥

⎢⎢⎢

=⎥⎥⎥

⎢⎢⎢

β

α (9)

The reference currents are calculated in order to compensate neutral, harmonic and reactive currents in the load. These reference source current signals are then compared with sensed three-phase source currents, and the errors are processed by hysteresis band PWM controller to generate the required switching signals for the shunt APF switches [6].

III. SIMULATOIN RESULTS In this study, a new control algorithm for the UPQC is

evaluated by using simulation results given in Matlab/Simulink software under non-ideal mains voltage and

unbalanced load current conditions. The simulated UPQC system parameters are given in Table I. In simulation studies, the results are specified before and after UPQC system are operated. In addition, when the UPQC system is operated, the load has changed and dynamic response of the system is tested. The proposed control method has been examined under non-ideal mains voltage and unbalanced load current conditions. Before harmonic compensation, the THD of the supply current is 26.23%. The obtained results show that the proposed control technique allows the 3.4% mitigation of all harmonic components.

TABLE I. UPQC SYSTEM PARAMETERS

Parameters Value

Source Voltage vSabc 380 Vrms

Frequency f 50 Hz

Load

3-Phase ac Line Inductance LLabc 2 mH 1-Phase ac Line Inductance LLa1 1 mHΩ

3-Phase dc Inductance Ldc3 10 mH 3-Phase dc Resistor Rdc3 30 Ω 1-Phase dc Resistor Rdc1 87,5 Ω

1-Phase dc Capacitor Cdc1 240 μF

dc-link Voltage VDC 700 V

Capacitor 1/2 C1 C2 2200 μF

Shunt APF

ac Line Inductance LCabc 3.5 mH Filter Resistor RCabc 5 Ω

Filter Capacitor CCabc 10 μF Switching Frequency fpwm ~15 kHz

Series APF

ac Line Inductance LTabc 1.5 mH Filter Resistor RTabc 5 Ω

Filter Capacitor CTabc 20 μF Switching Frequency fpwm 12 kHz

Simulation results for the load and source voltages under unbalanced-distorted mains voltage conditions are shown in Fig. 4. Load current compensation simulation results under non-ideal (unbalanced-distorted) mains voltage conditions are given in Fig. 5.

0.15 0.2 0.25 0.3

-2000

200

vSab

c(V

)

0.15 0.2 0.25 0.3

-2000

200

vTab

c(V

)

0.15 0.2 0.25 0.3

-2000

200

vLab

c(V

)

Fig. 4. Simulation results for unbalanced and distorted mains voltage condition.

The neutral current compensation results are given in Fig. 6. The proposed UPQC control algorithm has ability to compensate both harmonics and reactive power of the load

Source Voltages

t(s)

Filter Voltages

Load Voltages

376

and neutral current is also eliminated. The proposed control technique has been evaluated and tested under dynamical and steady-state load conditions. Simulation results for under load changing are shown in Fig. 7.

0.25 0.3 0.35 0.4-40-20

02040

iLab

c(A

)

0.25 0.3 0.35 0.4

-200

20

iCab

c(A

)

0.25 0.3 0.35 0.4

-200

20

iSab

c(A

)

Fig. 5. Simulation results for unbalanced and non-linear load current condition.

0.25 0.3 0.35 0.4

-200

20

iLn(

A)

0.25 0.3 0.35 0.4

-200

20

iCn(

A)

0.25 0.3 0.35 0.4

-200

20

iSn(

A)

Fig. 6. Simulation results for neutral current compensation.

0.1 0.15 0.2 0.25 0.3

-2000

200

vLab

c(V

)

0.1 0.15 0.2 0.25 0.3-40-20

02040

iLab

c(V

)

0.1 0.15 0.2 0.25 0.3-40-20

02040

iSab

c(A

)

0.1 0.15 0.2 0.25 0.3-40-20

02040

iSn(

A)

0.1 0.15 0.2 0.25 0.3600

700

800

VD

C(V

)

Fig. 7. Simulation results for operational performance of the UPQC system.

IV. EXPERIMENTAL TEST RESULTS Fig. 8 shows an experimental system configuration

photograph of the proposed UPQC system. The aim of the UPQC system is not only to compensate for the current

harmonics produced by a diode-bridge rectifier of 10 kVA, but also to eliminate the voltage harmonics contained in the receiving terminal voltage of the load. The UPQC consists of two back to back connected voltage source inverters and three DSP processors for controlling shunt and series APF’s and computer communication for all system control functions. The dc link of both APFs is connected to a common dc capacitor of 1100 microfarad and 700 V dc. All of the circuit parameters and experimental conditions are set up exactly the same as the simulation conditions. Although the proposed control scheme cannot be studied experimentally for unbalanced mains voltage conditions, an optimal control can be designed to eliminate this problem, which will have been discussed as a future work.

Fig. 8. The photograph of the proposed UPQC system.

The source and load voltages are sensed using LEM LV

25P voltage sensors, whereas, all the currents are sensed using LEM LA-55P Hall-Effect current sensors. The series and shunt inverters are built using SEMIX 101GD128Ds six-pack IGBT switches from Semikron. CONCEPT 6SD106EI and Semikron SKHI 61 IGBT drivers are used for series and shunt APF respectively. The IGBT driver modules have short circuit and over current protection functions for every IGBT and provides electrical isolation for all PWM signals applied to the digital signal processor (DSP). The proposed experimental control system consists of three DSP cards from TI (TMS320F28335). Three DSP cards are designed to control shunt and series APF and one of them is responsible for all system operation and power quality analysis. Both inverters use the variable frequency hysteresis band controller.

Fig. 9 shows source voltage and current waveforms before filtering. After compensation, source current becomes sinusoidal and in phase with the source voltage; hence, both harmonics and reactive power are compensated simultaneously. Before harmonic compensation, the THD of the supply current is 29.13% and after the harmonic compensation, it is reduced to 5.3% which complies with the IEEE 519 harmonic standards. Fig. 10 and Fig. 11 show experimental results for source voltage (vSa), filter current (iCa) and source current (iSa) after filter operation respectively.

Load Neutral Current

Filter Neutral Current

Source Neutral Current

t(s) Source Currents

Load Currents

Filter Currents

Load Currents

Load Voltages

Source Currents

Source Neutral Current

DC Link Voltage

Before UPQC After UPQC Operation

Load Variation (Step-up)

t(s)

377

Fig. 9. Experimental results for source voltage (vSa) and source current (iSa)

before filter operation.

Fig. 10. Experimental results for source voltage (vSa) and filter current (iCa)

after filter operation.

Fig. 11. Experimental results for source voltage (vSa) and source current (iSa)

after filter operation.

Fig. 12 shows experimental results for three-phase source currents (iSabc) before and after filter operation. Fig. 13 shows experimental results for the dc link voltage and the source current (iSa) before and after load variation (load step-up), the shunt APF tested under dynamical and steady-state load conditions under load changing. Fig. 14 shows the experimental results for source currents (iSabc) and neutral current (iSn) before and after filter operation. Fig. 15 shows results for load neutral (iLn), filter neutral (iCn) and source neutral current (iSn) before and after filter operation.

Fig. 12. Experimental results for source current (iSabc) before and after filter

operation.

Fig.13. Experimental results for dc link voltage and source current (iSa) before and after load variation (load step-up).

Fig.14. Experimental results for source current (iSabc) and neutral current iSn before and after filter operation

Fig.15. Experimental results for load neutral (iLn), filter neutral (iCn) and source neutral current (iSn).

These experimental results given above shows that the

harmonic compensation features of the UPQC, by appropriate control of the shunt APF can be done effectively. The shunt APF with reduced current measurement based control method can be compensating neutral, harmonic and reactive currents effectively, in the unbalanced and distorted load conditions. The series APF experimental results for mains and load voltages before filter operation is shown in Fig. 16. Fig. 17 shows the experimental results for the load voltages in three-phase form before and after filter operation.

DC-link Voltage

iSa

iSn Source Neutral Current

iSabc Source Currents

iLn

iCn

iSn

iSa vSa

iSa harmonic spectrum

iCa harmonic spectrum

iSa harmonic spectrum

iCa vSa

iSa vSa

iSabc Source Currents

378

Fig. 16. Experimental results for mains and load voltages before filter

operation.

Fig. 17. Experimental results for load voltages in three-phase form before

and after filter operation.

V. CONCLUSION This paper describes a new control strategy used in the

UPQC system, which mainly compensate reactive power and voltage and current harmonics in the load under non-ideal mains voltage and unbalanced load current conditions. The proposed control strategy use only loads and mains voltage measurements for series APF based on the synchronous reference frame theory. The instantaneous reactive power theory is used for shunt APF control algorithm by measuring mains voltage and currents. The conventional methods require measurements of the load, source and filter voltages and currents.

The simulation results show that, when unbalanced and nonlinear load current or unbalanced and distorted mains voltage conditions, the above control algorithms eliminate the impact of distortion and unbalance of load current on the power line, making the power factor unity. Meanwhile, the series APF isolates the loads voltages and source voltage, the shunt APF provides three-phase balanced and rated currents for the loads.

The experimental results obtained from a laboratory model of 10 kVA, along with a theoretical analysis, are shown to verify the viability and effectiveness of the proposed UPQC control method.

ACKNOWLEDGEMENT

This study is supported financially by TUBITAK research fund number 108E083 and Kocaeli University Scientific Research Fund.

This work is also supported by Concept Inc. (Concept IGBT driver), Semikron Inc. (IGBT and IGBT driver), LEM Inc. (voltage and current sensor) and TI Inc. (F28335 eZdsp), which is gratefully acknowledged. The authors gratefully acknowledge the contributions of Halim Ozmen (from Semikron Turkey) and Robert Owen (from TI).

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[2] H. Fujita, and H. Akagi, “The unified power quality conditioner: The integration of series and shunt-active filters,” IEEE Trans. Power Electron., vol. 13, no. 2, pp. 315–322, Mar. 1998.

[3] H. Akagi, E. H. Watanabe and M. Aredes, Instantaneous Power Theory and Applications to Power Conditioning. Wiley-IEEE Press. April 2007.

[4] D. Graovac, A. Katic, and A. Rufer, ‘‘Power Quality Problems Compensation with Universal Power Quality Conditioning System,’’ IEEE Transaction on Power Delivery, vol. 22, no. 2, 2007.

[5] B. Han, B. Bae, H. Kim, and S. Baek, ‘‘Combined Operation of Unified Power-Quality Conditioner with Distributed Generation,’’ IEEE Transaction on Power Delivery, vol. 21, no. 1, pp. 330-338, 2006.

[6] M. Aredes, “A combined series and shunt active power filter,” in Proc. IEEE/KTH Stockholm Power Tech Conf., Stockholm, Sweden, pp. 18–22, June 1995.

[7] Y. Chen, X. Zha, and J. Wang, “Unified power quality conditioner (UPQC): The theory, modeling and application,” Proc. Power System Technology Power Con Int. Conf., vol. 3, pp. 1329–1333, 2000.

[8] F. Z. Peng, J.W. McKeever, and D. J. Adams, “A power line conditioner using cascade multilevel inverters for distribution systems,” IEEE Trans.Ind. Appl., vol. 34, no. 6, pp. 1293–1298, Nov./Dec. 1998.

[9] G. M. Lee, D.C. Lee and J. K. Seok, “Control of series active power filter compensating for source voltage unbalance and current harmonics,” IEEE Transaction on Industrial Electronics, vol. 51, no. 1, pp. l32- 139, Feb. 2004.

[10] V. Khadkikar, A. Chandra, “A New Control Philosophy for a Unified Power Quality Conditioner (UPQC) to Coordinate Load-Reactive Power Demand Between Shunt and Series Inverters,” IEEE Trans. on Power Delivery, vol.23, no.4, pp. 2522-2534, 2008.

[11] M. Aredes, H. Akagi, E.H. Watanabe, E. V. Salgado, L. F. Encarnacao, “Comparisons Between the p-q and p-q-r Theories in Three-Phase Four-Wire Systems,” IEEE Transactions on Power Electronics, vol. 24, no. 4, pp. 924-933, April, 2009.

[12] A. Esfandiari, M. Parniani, A. Emadi, H. Mokhtari, “Application of the Unified Power Quality Conditioner for Mitigating Electric Arc Furnace Disturbances,” International Journal of Power and Energy Systems, vol. 28, no. 4, pp. 363-371, 2008.

vLa Load voltage

vSa Source voltage

vLabc Load voltages

379


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