ICSET 2008

Modeling and Power Quality Analysis of STATCOM using Phasor Dynamics

M A Hannan, A Mohamed, Senior Member IEEE, and A Hussain, Member IEEE

Abstract—This paper deals with the modeling of synchronous static compensator (STATCOM) of a power system based on dynamic phasor model to investigate the performance of STATCOM for power quality analysis and compared with EMTP like simulation. The dynamic phasor model and EMT model of the STATCOM including the system is implemented in Matlab/Simulink toolbox and PSCAD/EMTDC, respectively. Details dynamic phasor model of STATCOM switching function and its control system has been presented. A credible solution to the power quality problems on the distribution network has been analyzed using dynamic phasor model and EMTP like PSCAD/EMTDC simulation techniques. The simulation results demonstrated that the dynamic phasor model of STATCOM including the system makes an excellent agreement with the detailed time-domain EMT model of PSCAD/EMTDC simulation. It is found that the dynamic behavior of STATCOM phasor model have very good potential application in analyzing power quality issues, faster in speed and higher accuracy as compared with PSCAD/EMTDC simulation.

I. INTRODUCTION

ITH the development of power electronic technology, the custom power devices play an important role in

bringing unprecedented efficiency increaseness and cost effectiveness in electrical power systems [1]. The custom power is relatively new concept based on application of power electronic devices aimed at achieving high power quality, operational flexibility and controllable of the electrical power system [2]. The synchronous static compensator (STATCOM) is one of the custom power devices that received much attention on improving the power system performance in steady-state and dynamic stability, voltage regulation and power quality improvement [3]. So as to enhancing system stability for better utilization of existing power system, it is necessary to model STATCOM accurately and efficiently.

Modeling and simulation of electrical power system with custom power device are generally developed using electromagnetic transient (EMT) simulation and quasi-steady-state (QSS) approximations [4]. The electromagnetic

This work was supported in part by the Ministry of Science, Technology and Innovation (MOSTI) under grant IRPA: 03-02-02-0017-SR003/07-03.

M A Hannan is with the Dept. of Electrical, Electronic and Systems Engineering, National University of Malaysia, 43600 Bangi, Selangor, Malaysia (e-mail: eehannan@vlsi.eng.ukm.my)

A Mohamed is with the Dept. of Electrical, Electronic and Systems Engineering, National University of Malaysia, 43600 Bangi, Selangor, Malaysia (e-mail: azah@vlsi.eng.ukm.my)

A Hussain is with the Dept. of Electrical, Electronic and Systems Engineering, National University of Malaysia, 43600 Bangi, Selangor, Malaysia (e-mail: aini@vlsi.eng.ukm.my) .

transient program (EMTP) concept is universally accepted for simulation of complex power system containing non-linearities, power electronic components and their controllers. However, due to limitation of computer storage and computational time, the implementation of a large power system in an EMTP is difficult, time tedious in simulation with extremely small step-length and do not suitable for transient stability study [5]. On the other hand, the QSS approximations models are commonly used in electro-mechanical transient simulation, which is not adequate enough to catch the dynamic behavior of the switching [6]. Moreover, the time domain simulations of QSS are not only a significant computational burden, but also offer little insight into problem sensitive to design quantities and no basis for design for protection scheme [7]. Hence the QSS is impractical for simulation of STATCOM in large-scale power system.

Power electronic elements of STATCOM controller are difficult to model accurately due to their switching behavior. As the EMTP and QSS approximations are not adequate enough to model the dynamic behavior of the switching, a simplified model of STATCOM with sufficient engineering accuracy is required that allow fast and accurate modeling, simulation and control design for improve power quality and dynamic stability analysis.

In order to overcome above problems, dynamic phasor method has been developed using generalized averaging procedure [8] to study the effects of power electronic devices such as FACTS controller, custom power devices and HVDC transmission system [9]. Dynamic phasor theory has a great potential and its offer a number of advantages over conventional methods. Firstly, dynamic phasor can be used to compute the fast electromagnetic transient with larger step size, so that it makes simulation potentially faster than conventional time domain EMTP like simulation. Secondly, it has wider band width in the frequency domain that traditional QSS approximation. Thirdly, by keeping the dominant components in Fourier coefficient series, it can catch significant impact on switching of the power electronic devices

The generalized averaging theory is applied to obtain the dynamic phasor model of STATCOM including a simple test system and evaluated power quality analysis. Dynamic phasor model of STATCOM switching function and its control system are also described in this paper. A comparison of dynamic phasor model and PSCAD/EMTDC simulation is studied to see the close agreement between the techniques. The dynamic phasor model has potential advantages to enhance the power system stability as well as

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power quality solution in term of faster in speed and higher in accuracy.

II. CONCEPT OF PHASOR DYNAMICS

The concept of dynamic phasor is based on generalized averaging theory in the form of time-varying Fourier coefficient [8]. A complex periodic waveform x( ) can be represented on the interval ),( tTt using a Fourier series of the form

)1()()( sjk

kk etXx

where s = 2 /T and Xk (t) are the complex time-varying Fourier coefficient, which refers as dynamic phasors. The k th coefficient of dynamic phasor at time t is determined by the following averaging operation,

)2()()(1)( txdeXT

tXk

jkt

Ttks

where <x>k (t) is the complex quantity, used to denote the averaging operation. Dynamic phasor method is the function of frequency decomposition that focused on the dynamics of the Fourier coefficient. There are two key properties of the phasors as follows;

A. K-Phasor Differential Properties A key factor for dynamic phasor development is that the

derivative of k th Fourier coefficient is given by the following expression,

)3()()()( tXjktdtdxt

dtdX

ksk

k

This formula is easily verified using (1) and (2), and integration by parts.

B. Phasor Properties of a Product The kth phasor of a product of two time-domain variables,

x( ) and y( ) equals a discrete time convolution that can be obtained by the following expression,

)4(iik

ik

yxyx

III. STATCOM DYNAMIC PHASOR MODELING

The STATCOM is a shunt reactive power compensating electronic device that generates ac voltage, which intern causes a current injection into the system through a shunt transformer. The basic configuration of STATCOM consists of a voltage source inverter (VSI), injecting transformer, dc capacitor as energy storage device and control system as

shown in Fig. 1. VSI realizes constant voltage control of VSand Vd. The VSI output voltage VE is obtained in term of inverter modulation index of SPWM control mE and the measured dc link capacitor voltage Vd.

Fig. 1. Basic configuration of STATCOM.

The phase angle of output voltage VE is E, which is controlled by the firing angle E. The relations among them are as follows,

ESE

dEE VmV )5(

A. Modeling of STATCOM including Switching Function Let us consider the equivalent circuit of phase a as the

reference phase and its valve switching simulated by the ideal switch-state function SEa and S’

Ea (SEa + S’Ea=1) as

shown in Fig. 2. The small resistance rs is consider as equivalent power loss.

Fig. 2. Equivalent circuit of STATCOM.

The vEa and iEa have the relation at the ac system neutral point as follows,

HnEasEaEadcsEa

nHEaHEa

vSriSvri

vvv

]).().[(

)6('

For a balance ac system, it is easy to drive

)7(31

,, cbajEjdcHn Svv

idc

Cdc vd+-

rs

vEa

rs

G

iEa

SEa

S’Ea

H

E

Control System

.

RV

.

SV

.

SI .

EV

.

EI VSI

Cdc Vd+-

1: n EmE

1014

Substituting (7) into (6), we have,

)8(31.

,, cbajEjdcEadcsEaEa SvSvriv

The dc capacitor dynamics can be described as

)9(,, cbaj

EjEjdcdc

dc Siidt

dVc

According to (8) and (9), keeping fundamental frequency component (k=1) and dc component (k=0), based on phasor product properties, the dynamic phasor of vEa and vdc are,

cbajEjdcEadcsEaEa SVSVrIV

,,101011

)10(31.

cbajEjEa

dc

dc SICdt

Vd

,,11

0 )11()(1

The switch-state function SEA and S’Ea are discrete and

periodic function of time, determined by SPWM control, the fundamental wave component and dc component of the switching function can be represent as [10],

)12(21)(cos

2 jEE

Ej tm

d

Where j = a, b, c and a =0, b=2/3 , c= 4/3For phase a, the dynamic phasors of the dc and fundamental wave components are,

)13(44

,21

110EE jE

EajE

EaEa em

dem

dd

Substituting dynamic phasor dEj in (13) for SEj in (10) and separating real and imaginary parts, we obtain the overall dynamic phasor model of STATCOM are as,

EE

dcsi

Eai

Ea

EE

dcsr

Ear

Ea

mVrIV

mVrIV

sin4

..

)14(cos4

..

011

011

)15(]sincos[23

110

Ei

EaEr

Eadc

Edc IICm

dtVd

Thus, in a steady-state, dynamic phasor model of (14) and (15) interfacing with ac network equations can be solved the overall system.

B. Modeling of STATCOM Control The STATCOM control strategies adopted in the paper

are shown in Fig. 3. The constant ac terminal voltage is achieved by controlling mE of the VSI PWM controller shown in Fig. 3 (a). The PI controlled PLL generated synchronizing signal of the system voltage S, in which it is very confident for calculation of the STATCOM output voltage phase angle E. The constant dc capacitor voltage is realized by controlling firing angle E of the VSI. The controller is modeled as a simplified 1st order inertia block. If the phase angle S of VS and STATCOM control output mEand E are known, the dynamic phasor model of STATCOM with interface to ac system can be used to represent transient stability analysis.

Fig. 3. STATCOM control of a) Modulation index b) Synchronizing signal c) Firing angle.

IV. RESULTS AND DISCUSSION

A simplified test distribution system has been chosen for investigating power quality analysis of the STATCOM, in order to verify dynamic phasor model, comparing EMTP like simulation of the system. The dynamic phasor model and EMT model simulation of the STATCOM including the system is implemented in Matlab/Simulink toolbox and PSCAD/EMTDC, respectively. To illustrate the results obtained with the models of the network elements, the STATCOM is connected in shunt between loads and the 22 kV, 10 MVA systems as shown single line diagram in Fig. 4. The detailed load characteristics of various ratings are given in Table 1.

sTK

1

1

1VS

freSV

+- mE

VS EPLL

a) b)

Vd

fredV

+-

sTK

2

2

1E

c)

1015

6(a)

6(b)

Fig. 4. STATCOM test distribution system.

Table 1 Loads in the test distribution system

ParametersLoad

(L)Type Rating

R (ohms) L(Henry)

L1 RL 1.2MVA, 0.90

pf

363.33 0.46

L2 RL 0.5MVA, 0.95

pf

871.21 1.119

L3 IM 1600 H P, 50 Hz

--- ---

L4 IM 1600 H P, 50 Hz

--- ---

L5 RL 1.2MVA, 0.90

pf

363.33 0.46

A. STATCOM Function as Voltage Regulator To illustrate the effectiveness of the STATCOM for

providing continuous voltage regulation, dynamic phasor model and EMT model of PSCAD/EMTDC simulation are carried out of a test distribution system and superimposed to produce accuracy between the waveforms. Two loads condition is considered either fully capacitive or inductive at load L1 and L5 of the existing system keeping same value of 1.2 MVA. Under inductive load condition, Fig. 5 shows that the STATCOM current of phase ‘a’ lagging behind the load voltage by 900, so as to illustrate the operation of the system as an inductive compensator. The black lines are the predictive dynamic phasor model, while the blue and red lines correspond to the time-domain PSCAD/EMTDC simulation. It can be seen that the dynamic phasor models of STATCOM voltage and current are closely hug with the PSCAD/EMTDC simulation.

L1

L2

L3

L4

L5

B1

B2

B3

STATCOM

10 MVA, 22 kV

Fig. 5. Dynamic phasor model and PSCAD/EMTDC simulation of STATCOM output current and load voltage under inductive load condition.

To illustrate further operation of the STATCOM as an inductive compensator, the dc voltage and reactive power responses are measured as shown in Fig. 6. With STATCOM connected and switched at t = 0.1 sec, it can be seen that dc power is reduced and reactive power generated by inductive load is absorbed by the STATCOM, which intern reduced overall system voltage at swell condition. In Fig. 6 (a) and Fig. 6 (b), STATCOM switching at 0.1 sec, it can be seen that simulation results of dynamic phasor models of STATCOM load voltage and current are closely hug with PSCAD/EMTDC simulation.

Fig. 6. Dynamic phasor model and PSCAD/EMTDC simulation of STATCOM dc voltage and reactive power under inductive load condition.

Similarly under capacitive load condition, Fig. 7 shows that the D-STATCOM current leads the load voltage by 900,so as to illustrate the capacitive compensation effect of the STATCOM. With respect to STATCOM switched on, Fig. 8 shows that the dc voltage is increased and reactive power is generated by the STATCOM, which intern increase the load voltage from sag condition to unity. In Fig. 7 and Fig. 8, it can be seen that simulation results of dynamic phasor models have very good accuracy as compared with PSCAD/EMTDC simulations. Also, due to larger integration step, dynamic phasor of STATCOM model has faster simulation speed of 2.57 sec, while PSCAD/EMTDC simulation cost 8.23 sec which is much larger than that of dynamic phasor model. Hence, observation can be made that the results of the system with STATCOM using dynamic phasor and EMT models are consistent. These results thus prove the capability of the STATCOM in regulating the

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system voltage to near its rated value under sag and swell condition.

8(a)

8(b)

9(a)

9(b)

Fig. 7. Dynamic phasor model and PSCAD/EMTDC simulation of STATCOM output current and load voltage under capacitive load condition

9(c)

Fig. 8. Dynamic phasor model and PSCAD/EMTDC simulation of STATCOM dc voltage and reactive power under capacitive load condition.

B. STATCOM Function as Voltage Sag Compensation and Harmonic Reduction

To illustrate the use of STATCOM in compensating voltage sag, a voltage sag condition is created by applying a balance three-phase to ground fault on the RL load L1 at time t = 1.5 sec for a fault duration of 0.75 sec. Fig. 9 (a) shows that the phase A voltage at load L1 drops to 0.48 p.u. due to 3-phase fault, where fault impedance X/R ratio equal to 1. For the system with the STATCOM connected, the load voltage increases from 0.48 p.u to its rated value as shown in Fig. 9 (b) and (c). This is due to the voltage sag compensation capability of the D-STATCOM. Dynamic phasor and EMT model of phase ‘a’ is shown here, however the responses are similar for the phase ‘b’ and ‘c’ voltages. It can be seen that a transient under/over voltage appears during staring and ending period of voltage sag mitigation due to the delay of the control system. Fig. 9 (b) and (c) also shows that due to high frequency switching of STATCOM, its generated harmonic distortion.

10(a)

10(b)

Keeping frequency component of k = 1, 2, 3 … and dc component k = 0 in (8) and (9), the dynamic phasor of harmonic distortion is measured using fast Fourier transform (FFT) technique. The results of dynamic phasor and EMT model of PSCAD/EMTDC simulation of phase ‘a’ are shown in Fig. 11 (b) and (c), in which that STATCOM generate almost 6.5% of harmonic distortion at fault period of 1.5 sec to 2.25 sec due to its high frequency switching loss. This value is still higher than the acceptable level of 5% [11].

Fig. 9. Dynamic phasor model and PSCAD/EMTDC simulation of the system a) without STATCOM b) with connected STATCOM at starting mitigation c) with connected STATCOM at ending mitigation.

In order to reduce the harmonics, a passive LC filter is connected at the point of common coupling to the distribution system. Fig 10 shows the dynamic phasor model and EMT model PSCAD/EMTDC simulation of harmonic distortion of the system including STATCOM with connected passive filter. It can be seen that the harmonics are suppressed and the harmonic distortion of the system is reduced to 0.65% from 6.5% measured by FFT, which is far below than the IEEE standard distortion limit of 5%.

Fig. 10. Dynamic phasor model and PSCAD/EMTDC simulation of STATCOM dc voltage and reactive power under capacitive load condition.

Fig. 9 and Fig. 10 show that the dynamic phasor models have good consistency and accuracy as compared with the PSCAD/EMTDC simulation. Dynamic phasor models make an excellent agreement with the time-domain PSCAD/EMTDC simulation as well as faster in computing the simulation. Hence, in both cases, STATCOM with and without filter, the rms values of dynamic phasor model are still able to provide satisfactory agreement of tracking between PSACD/EMTDC and the dynamic phasor model.

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B. STATCOM Capability on Flicker Reduction To illustrate the use of the STATCOM in reducing voltage

flicker, simulations were carried out by first connecting a variable electric load of 5.2 MVA, 22 kV as the source of voltage flicker. The rms value of phase a voltage flicker is shown in Fig. 11 (a). It is found that voltage flicker index is 0.40 measured by FFT technique in which the value exceeds IEEE standard limit of 0.07. However, with the STATCOM connected, it is noted that the calculated voltage flicker index is reduced to 0.02 as shown in Fig. 11 (b). These results prove that the system including STATCOM can be used for reducing voltage flicker. Both, Fig. 11 (a) and Fig. 11 (b) show that test results of dynamic phasor models have very good accuracy as compared with the EMT model of PSCAD/EMTDC simulation.

11(a)

11(b)

Fig. 11. RMS voltage flicker using dynamic phasor model and PSCAD/EMTDC simulation a) without STATCOM b) with STATCOM.

V. CONCLUSION

Dynamic phasor model were used to model STATCOM including a simple test system to analysis the power quality issues using Matlab/Simulink and validated by comparing its results with PSCAD/EMTDC simulation. The test results shows that the dynamic phasor model achieve a very good accuracy and faster in speed compared with standard time-domain PSCAD/EMTDC simulation. Thus, proposed model is well suited for accurate, faster dynamic simulation and power quality analysis by improving performance of the overall system.

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