Modeling and Control of DSTATCOM for Three-Phase, Four-Wire Distribution Systems

Bhim Singh Department of Electrical Engineering Indian Institute of Technology Hauz Khas, New Delhi-110016, India bsingh@ee.iitd.in

A.Adya, A.P.mittal and J.R.P Gupta Department of Instrumentation and Control Netaji Subhas Institute of Technology New Delhi-110045, India alka106@rediffmail.com, alok@nsit.ac.in , jrpg83@yahoo.com

Abstract— This paper deals with a DSTATCOM (Distribution Static Compensator) for load balancing, neutral current elimination, power factor correction and voltage regulation in three-phase, four-wire distribution system feeding commercial and domestic consumers. A four leg voltage source inverter (VSI) configuration with a dc bus capacitor is employed as DSTATCOM. The modified instantaneous reactive power theory (IRPT) is used in the control of DSTATCOM. The capability of the DSTATCOM is demonstrated through results obtained using MATLAB based developed model of the system at different types of loads.

Keywords-DSTATCOM; load balancing; voltage regulation; IRPT theory; power factor correction; neutral current elimination.

I. INTRODUCTION Three-phase, four-wire systems are widely used in distributing electric energy to commercial and domestic users. Under normal conditions, the loads are assumed to be reasonably balanced and the neutral current is quite small in magnitude. However, due to advances in solid state power conversion technology, there is a tremendous increase in linear and non-linear loads. The situation worsens when three-phase unbalanced nonlinear loads are also existing in three phase, four wire system along with linear loads and ideal operating conditions do not exist. In practice, three-phase, four-wire systems are employed in distributing electric energy to several office buildings, lighting systems and small manufacturing plants. In such systems, under abnormal operating conditions and un-balanced loads, the current in neutral conductor exceeds the normal phase current. The excessive harmonic current in neutral conductor causes problems such as wiring failure, transformer overheating and malfunctioning of electronic equipments. Unbalance and distortion in the voltage affect the performance of other loads. In the past, attempts have been made on electric power quality problems and many solutions have been suggested to improve the power quality in electric distribution systems [1-3]. A number of compensators have been reported for power factor correction, voltage regulation and load balancing using lossless passive elements (L and C) [1] and active elements (solid state CSI and VSI) [2,3]. Development of STATCOM for three-wire system is reported in literature in recent years [1-3] but very little work is available on three-phase, four-wire

systems using DSTATCOM. Many control techniques have been incorporated such as instantaneous reactive power theory [4], power balance theory, indirect current control technique [5-6] etc. In this paper, a modified version of instantaneous reactive power theory is used for control of DSTATCOM. A four leg voltage source inverter (VSI) configuration with a dc bus capacitor is employed as DSTATCOM. This configuration offers use of less complex and more reliable control as compared to three single-phase voltage source converters. A fourth leg is added to control the current in the neutral wire and to reduce it to acceptable levels. Three-phase reference supply currents are derived using sensed ac voltages at point of common coupling (PCC) and dc bus voltage of the DSTATCOM as feedback signals. Two proportional plus integral (PI) controllers are used. One PI controller is used for regulating the DC bus voltage of DSTATCOM and the second PI controller is for regulating the ac terminal voltage at PCC. A dynamic model of DSTATCOM is developed in MATLAB environment to simulate its behaviour. Simulation results during steady state and transient operating conditions of the DSTATCOM are presented and discussed in detail to demonstrate voltage regulation, power-factor correction and load balancing capabilities of the DSTATCOM system.

II. SYSTEM CONFIGURATION Fig.1a and Fig.1b show the basic diagrams of DSTATCOM system connected as a shunt compensator. DSTATCOM system consists of a standard three-phase Insulated Gate Bipolar Transistor (IGBT) based four leg VSI bridge with the input ac inductors and a dc bus capacitor to obtain a self-supporting dc bus. An additional leg is added to control the current in neutral wire. A three-phase ac source with line impedance feeds power to balanced / unbalanced linear and non-linear load. One PI controller is used over the sensed and reference values of dc bus voltage of the DSTATCOM for power factor correction. A second PI controller is used over the reference and sensed values of ac terminal voltage at PCC for voltage regulation. A dynamic model of DSTATCOM is developed in MATLAB environment to simulate its behavior.

III. CONTROL SCHEME The control algorithm used is a modified version of the basic

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IRPT scheme given by Akagi et al [4]. The scheme is illustrated for power factor correction and voltage regulation.

A. Power Factor Correction and Load Balancing Fig. 2 shows the schematic layout of the control scheme used for DSTATCOM system. For obtaining power factor correction, it is assumed that the source supplies load active power (pl) and power loss (posc). The reactive power

Fig.1a Schematic diagram of DSTATCOM connected to a distribution system

Fig.1b Schematic diagram of DSTATCOM requirement of the load is fed locally from DSTATCOM. The pl is filtered and its DC component (Pl) is extracted. Consider isα, isβ to be the α-β components of the supply currents and vsα and vsβ be the components of the supply voltages (vs). One PI controller is employed for the regulation of DC link voltage (Vdc). The output of this PI controller is considered as power loss (posc) in DSTATCOM. Reference supply currents (isαr ,isβr ) are calculated as: isαr={vsα(Pl+posc)}/(vsα

2+vsβ2) (1)

isβr={vsα(Pl+posc)}/(vsα2+vsβ

2) (2) where vsα, vsβ are obtained by transformation of voltages from a-b-c frame to α-β-o frame as: vsα = (2/3)1/2 (vsa –vsb/2 –vsc/2) (3) vsβ = 1/2(1/2) (vsb-vsc) (4) vso=1/3(1/2)(vsa +vsb +vsc) (5) and the active power requirement of the load (pl) is calculated as:

pl = (vsaila + vsbilb + vscilc) (6) The quantity pl is filtered and its DC component (Pl) is used. The active power loss component (posc) is calculated as: posc(n) = posc(n-1) + Kpd{vde(n)- vde(n-1)} + Kid vde(n) (7) where vde(n) = Vdcr – Vdca(n) denotes error between sensed DC bus voltage Vdc calculated and reference DC voltage (Vdcr). Kpd and Kid are proportional and integral gains of the dc bus voltage PI controller. A reverse transformation of α-β-o frame to a-b-c frame gives three phase reference supply currents (isar ,isbr ,iscr ) as: isar = (2/3)(1/2){ isor/2(1/2) + isαr} (8) isbr= (2/3)(1/2){-( isor /2(1/2) )– (isαr /2) + (3(1/2) isβr /2) } (9) iscr= (2/3)(1/2){- (isor /2(1/2) ) – (isαr /2) + (3(1/2) isβr /2)} (10) where (isαr , isβr , isor ) are obtained from (1)-(2). B. Voltage Regulation and Load Balancing For voltage regulation, a second PI controller is employed over the amplitude of ac terminal voltage at the point of common coupling. The amplitude of ac terminal voltage is calculated as: vtm =(2/3 )1/2(vsa

2 + vsb2 + vsc

2)1/2 (11) This quantity is again filtered to obtain DC component. The output of the second PI controller over vtm and vtmr is considered as Ql. The equations for calculation of reference supply currents are calculated as: isαr= {vsα(Pl+posc)+(vsβQl)}/(vsα

2+vsβ2) (12)

isβr = {-vsβ(Pl+posc) + (vsαQl)} / (vsα2 + vsβ

2) (13) where Ql is calculated as: Ql(n) = Ql(n-1) + Kpq{vae(n)- vae(n-1)} + Kiq vae(n) (14) where vae(n)= vtmr – vtm(n) denotes the error between vtm and reference voltage vtmr and vtm at the nth sampling instant. Kpq and Kiq are the proportional and integral gains of the second PI controller. A reverse transformation of α-β-o frame to a-b-c frame using equations (8)-(10) gives reference supply currents (isar ,isbr,iscr ) are obtained from equations (15)- (17): isar = (2/3)(1/2){ isor/2(1/2) + isαr} (15) isbr= (2/3)(1/2){-( isor /2(1/2) )– (isαr /2) + (3(1/2) isβr /2)} (16) iscr= (2/3)(1/2){- (isor /2(1/2) ) – (isαr /2) + (3(1/2) isβr /2)} (17) C. Hysteresis Current Controller The DSTATCOM consists of 4 legs; each leg having two IGBT devices as shown in Fig.1b. The switching logic for the upper switch and lower switch for ‘phase-a’ is formulated as: if isa< (isar –hb) upper switch is OFF and lower switch is ON. if isa > (isar +hb) upper switch is ON and lower switch is OFF. Similarly, the switching logic of two other phases (b and c) are formulated, using hb the width of hysteresis band. The neutral supply current (ins) and reference (insr) are calculated as: ins = -(isa + isb + isc) (18) insr = 0 (19) The error between ins and insr gives appropriate gating signals for the fourth leg of VSI.

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Fig.2 Control scheme for DSTATCOM system

Fig.3 MATLAB model of DSTATCOM system

vsb

vsα

vsβ

abc –αβ transformation

vsa

vsc

abc –αβ transformation

isa

isb

isc

isα

isβ

Estimate Supply

Reference Currents isαr, isβr

Transform αβ -abc

Reference Supply currents

isar, isbr,iscr

Hysteresis Current

Controller

DSTATCOM

8 gating pulses

PI controller --I

posc

PI controller -II

ql

Vdcr Vdc

Vtmr Vtm

isαr

isβr

isar

isbr

iscr

isa isb isc

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Fig. 4 MATLAB Control scheme based on modified IRPT

IV. MATLAB BASED MODELING OF SYSTEM Model of the DSTATCOM including power distribution system network and its controller is developed in MATLAB environment with Simulink and Power System Block-sets (PSB) toolboxes. Figs. 3 and 4 show the MATLAB diagram representing DSTATCOM and the ac mains as well as load on the distribution system. The source consists of three phase ac voltages with neutral and load. Provision is made for linear / non-linear loads to be balanced and unbalanced using appropriate switches. The DSTATCOM consists of 8-IGBTs each shunted by a reverse parallel connected fast switching free wheeling diode. The output of DSTATCOM is coupled in parallel to the distribution system network through inductances of the coupling transformer.

V. PERFORMANCE OF DSTATCOM SYSTEM Performance of DSTATCOM for power-factor correction, voltage regulation and harmonic rduction along with load balancing is studied. The performance of the model is analyzed under various conditions. A. Performance of DSTATCOM with Linear Loads for Power Factor Correction Fig.5 shows the response of DSTATCOM with lagging power –factor load of 11kW for power-factor correction and load magnitude but the supply currents still remain balanced and in– phase. It is observed that DSTATCOM is able to improve the supply power-factor to unity. The supply currents are balanced, sinusoidal and in-phase with the voltages. At t= 0.06 sec, the three phase balanced load (11kW) is changed to two phase load. It is observed that the load currents are of unequal phase with the supply voltages. The neutral current in supply is also reduced to a small magnitude even though neutral load current and neutral DSTATCOM currents are having large

magnitude. The DC link voltage is regulated to reference value of 700 V before and after disturbance.

Fig.5 Performance of DSTATCOM with linear loads for power factor correction and load balancing for 11kW load. B. Performance of DSTATCOM with Linear Loads for Voltage Regulation Fig.6 shows the response of DSTATCOM with lagging power factor load for voltage regulation and load balancing. It is

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observed that DSTATCOM is able to regulate the voltage (vtm) to reference value of 338V. The supply currents are balanced, sinusoidal and slightly leading with respect to the voltages. At t= 0.06sec, three phase balanced load is changed to two phase and then back to three phase load at t=0.1sec. The neutral current in supply remains negligible in magnitude even when the neutral load current is high from 0.06 to 0.1sec. The load currents are of unequal magnitude as one of the phase is switched off from t=0.06 sec to t=0.1sec, but the supply currents are still balanced and sinusoidal. The voltage at PCC is regulated to its reference value of 338V and DC bus voltage is maintained at nearly its reference value. C. Performance of DSTATCOM with Non-Linear Loads for Power Factor Correction and Load Balancing Fig.7 shows the response of DSTATCOM with nonlinear

Fig.6 Performance of DSTATCOM with linear loads for voltage regulation and load balancing for 11kW load.

Fig.7 Performance of DSTATCOM with nonlinear load (50 kW) for power factor improvement loads for power-factor correction and load balancing. The nonlinear load considered is R=6.75 ohms across a diode rectifier. It is observed that DSTATCOM is able to make the supply currents nearly sinusoidal. The supply currents are balanced, sinusoidal and in-phase with the voltages. At t= 0.14 sec, the three phase balanced load having 50kW power is changed to two phase load. The supply currents are still balanced and sinusoidal even when the load current in one of

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Fig.8 Waveform and Harmonic spectrum for supply current (Is).

020406080

100

1 4 7 10 13 16 19 22 25 28 31

Harmonic Order

I l(A

)

THD Il =27.2%

Fig.9 Waveform and Harmonic spectrum for supply current (Is). the phases is zero. The THD of load currents is 27.2% which is reduced to THD of 5.2% for supply currents using DSTATCOM. Fig.8 and Fig.9 show the waveforms for load current and supply current. The THD of supply currents is reduced to 3.98% in time interval t=0.14 sec to t=0.18sec when the THD of load currents is 16.1%. The neutral current in supply is also reduced to a small magnitude. The DC link voltage is regulated nearly to reference value of 700V. D. Performance of DSTATCOM with Non-Linear Loads for Voltage Regulation Fig.7 shows the response of DSTATCOM with nonlinear loads for voltage regulation. The nonlinear load considered is R=6.75 ohms across a diode rectifier. Here, two PI controllers are used – one is for the regulation of DC link voltage and the second is for ac terminal voltage regulation. It is observed that DSTATCOM is able to make the supply currents nearly

sinusoidal and slightly leading with respect to the voltage.

Fig.10 Performance of DSTATCOM with nonlinear load (40 kW) for voltage regulation under load change from 40kW to 50 kW at t=0.24sec

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100

1 4 7 10 13 16 19 22 25 28 31

Harmonic Order

Il (A

)

THD : 27.2%

Fig.11 Waveform and Harmonic spectrum for load current (Is).

THD : 5.2%

0 20 40 60 80

100 120

1 4 7 10 13 16 19 22 25 28 31

Harmonic Order

Is(A)

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020406080

100120

1 4 7 10 13 16 19 22 25 28 31

Harmonic Order

Is(A

)

THD: 5.2%

Fig.12 Waveform and Harmonic spectrum for supply current (Is). At t= 0.24 sec, the diode rectifier load is changed from R= 10ohms to R=7.5 ohms. The supply voltage, supply current, load current and compensator current waveforms are shown in Fig.10. It is seen that the terminal voltage is maintained close to the reference value of 338V. Moreover, the DC link voltage is regulated to its reference of 700V. Fig. 11 and Fig.12 show the waveform and harmonic spectrum for load current and supply current respectively. It is observed that DSTATCOM is able to reduce the THD of load current from 27.2% to THD of 5.2% in supply current.

V. CONCLUSIONS The proposed control algorithm of the DSTATCOM has been found suitable for compensation of balanced / unbalanced linear as well as nonlinear loads. The proposed DSTATCOM with modified instantaneous control scheme provides quick and independent control for various power quality features like – power factor correction, voltage regulation along with load balancing. It has reduced neutral current which can become excessive under load unbalancing and nonlinear loads. The control algorithm of the DSTATCOM is flexible and it can be applied to any category of loads. DSTATCOM is likely to replace conventional compensators for improving power quality in near future due to improved performance and reduced cost.

REFERENCES

[1] T. J. E. Miller, Reactive Power Control in Electric Systems. Toronto, Ontario, Canada: Wiley, 1982.

[2] R.M.Mathur (Editor), Static Compensators for Reactive Power Control, Contexts Publications, Winnipeg, Canada, 1984.

[3] A.Ghosh and G. Ledwich,Power Quality Enhancement using Custom Power devices, Kluwer Academic Publishers, London 2002.

[4] H.Akagi, Y.Kanazawa and A.Nabae, “Instantaneous reactive compensators comprising switching devices without energy storage components,” IEEE Transactions on Industry Applications, vol. IA-20, no. 3, May/June 1984, pp. 625-630.

[5] B.N.Singh, K.Al-Haddad, A.Chandra, “DSP based indirect-current controlled STATCOM -I Multifunctional capabilities” IEE Proceedings, vol. 147, no. 2, March 2000, pp. 107-112.

[6] B.N.Singh, K.Al-Haddad, A.Chandra, “DSP based indirect-current controlled STATCOM -II Multifunctional capabilities” IEE Proceedings, vol. 147, no. 2, March 2000, pp. 113-118.

[7] O. Lara and E. Acha, “Modeling and analysis of custom power systems by PSCAD/ EMTDC,” IEEE Transactions on Power Delivery, vol. 17, No.1, Jan. 2002, pp. 266-270.

[8] P.Giroux, G.Sybille and H.LeHully, “Modeling and Simulation of a Distribution STATCOM using Simulink’s Power System Block set,” IECON’01 27th Annual Conference of IEEE Industrial Electronics Society, pp. 990-996.

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