301075

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Abstract The static synchronous compensator (STATCOM) is increasingly popular in power system application. In general, power factor and stability of the utility system can be improved by STATCOM. Specifically, STATCOM can regulate the voltage of connection point and compensate the power factors of equipment serviced by that node. STATCOM is a FACTS controller that is used in power systems to regulate the line voltage, enhance the power transmission capacity and extend the transient stability margin. STATCOM is conventionally realized by a voltage-source converter; however, being a current injection device, its performance can be improved when realized by a current-source converter (CSC) that can generate a controllable current directly at its output terminals. In this paper, a STATCOM based on the current-source converter topology is proposed. This model acts as the basis for the design of a decoupled state-feedback controller. The proposed STATCOM has been simulated using the MATLAB-SIMULINK package. The simulation results show that a CSC-based STATCOM can result in excellent current and voltage waveforms as well as very short response time while operating at a low switching frequency. This makes the proposed scheme suitable for high power applications.

Key words: CSC, state-feedback control, FACTS, linear model, STATCOM, VSC.

1Sanjay N.Patel is pursuing M.E. in EPS from BVM Engg. College, V.V. Nagar (e-mail: [email protected]). 2Chintan R. Patel is pursuing M.E. in EPS from BVM Engg. College, V.V. Nagar (e-mail: [email protected]). 3Dr. Axay J. Mehta is with G.H.Patel College of Engg & Tech., V.V.Nagar (e-mail: [email protected]).

I. INTRODUCTION

AS an important member of the FACTS controllersfamily, Static Synchronous Compensator (STATCOM) has been at the center of attention and the subject of active research for many years. STATCOM is a shunt-connected device that is used to provide reactive power compensation to a transmission line. Through regulation of the line voltage at the point of connection, STATCOM can enhance the power transmission capability and thus extend the steady-state stability limit. STATCOM can also be used to introduce damping during power system transients and thus extend the transient stability margin. Theoretically, FACTS controllers can be realized by either a voltage-source converter (VSC) or a current-source converter (CSC) [1]. The reasons behind the choice of VSC over CSC are as follows:

(1) A CSC is more complex than a VSC in both power and control circuits. Filter capacitors are used at the ac terminals of a CSC to improve the quality of the output ac current waveforms. This adds to the overall cost of the converter.

Furthermore, filter capacitors resonate with the ac side inductances. As a result, some of the harmonic components present in the output current might be amplified, causing high harmonic distortion in the ac-side current. Besides, conventional bi-level switching scheme cannot be used in CSC.

(2) Unless a switch of sufficient reverse voltage withstanding capability such as Gate-Turn-Off Thyristor (GTO) is used, a diode has to be placed in series with each of the switches in CSC. This almost doubles the conduction losses compared with the case of VSC.

(3) Fast start-up, where no additional start-up rectifier is needed. In addition, unlike the VSC

Sanjay N. Patel1, Chintan R. Patel2, Dr. Axay J. Mehta3

Modeling and Control of Current Source

Converter (CSC) Based STATCOM

13-14 May 2011 B.V.M. Engineering College, V.V.Nagar,Gujarat,India

National Conference on Recent Trends in Engineering & Technology

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STATCOM, the CSC STATCOM injects no harmonic into the A.C. network when it is operating at zero.

(4) The dc-side energy-storage element in CSC topology is an inductor, whereas that in VSC topology is a capacitor. The power loss of an inductor is expected to be larger than that of a capacitor. Thus, the efficiency of a CSC is expected to be lower than that of a VSC.

II. CSC BASED SYSTEM MODELING

The schematic diagram of a CSC-based STATCOM is shown in Fig. 1 .The control objectives of the STATCOM are to regulate the dc-side current and give the required reactive power compensation to the transmission line. In Fig. 1, the transformer T is modeled as a combination of an ideal transformer and a series R-L impedance.

Fig.-1 CSC based STATCOM. Where:

C Is the capacitance of the filter Ldc Is the smoothing inductor Rdc d.c. side resistor for Conduction losses Idc Is the dc-side current

V Converter phase voltage i i Currents at the terminals of the CSC i Secondary-side currents of the transformer e The vectors of line voltages

[ e ] = [ ea eb ec ]T , [ i ] = [ ia ib ic ]T ,

[ v ] = [ va vb vc ]T , and [ ii ] = [ iia iib iic ]T

Denote the vectors of line voltages , secondary-side currents of the transformer, voltages across the filter capacitors, and currents at the terminals of the CSC, respectively. After applying Parks transformation, with [e] chosen as the reference voltage vector, the above current and voltage vectors become, [E] = [ Ed 0 ]T, [ I ] = [ Id Iq ]T, [V] = [ Vd Vq ]T and [ Ii ] = [ Iid Iiq]T.

CSC is controlled using tri-level SPWM technique. In this way, it behaves as a 3-phase linear power amplifier. CSC under tri-level SPWM control can be modeled as under,

iia = ma Idc iib= mb Idc iic = mc Idc

Where, ma , mb and mc are the modulating signals of the 3phases normalized to the peak of the triangular carrier signal. The modulating signals can be transformed into d-q axis, as well. Thus, Equ. (1) can be re-written as,

Iid = Md Idc

Iiq = Mq Idc

The dynamic equations from the converter to the secondary-side of the transformer are,



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The input variables are Md and Mq .The output variables are Idc and Iq , which are chosen according to the control objectives of the STATCOM. The above system is nonlinear. A common method to deal with the nonlinearity is to linearize the system of equations around a steady-state operating point. The drawback of this approach is that the model and thus the controller design are dependent on the operating point. But, in this particular case, the nonlinearity can be avoided by properly modeling the CSC.

From Equations (3) to (7), it is obvious that Idc is the source of nonlinearity in the model of the CSC-based STATCOM. An alternate method for describing the dynamics of Idc is to use the active power balance equation. The active power delivered by the ac source (Pac ) and the active power absorbed by the dc-side (Pdc ) can be expressed as,

The relationship between (P ac ) and (P dc ) is Pac = Pdc + Ploss , where Ploss is the power loss in the resistor R. The resistance R is always very small; hence, it is practically reasonable to neglect its power loss without noticeable loss of accuracy. From Pac = Pdc , the following dynamic equation results ,

This can be written as,

In equ. (11), I2dc can be taken as the state variable, instead of Idc , to make the dynamic equation linear. Since Idc does not change direction, it does not cause any technical problem to choose I2dc as the state variable. The resulting improved dynamic model of the STATCOM is as follows.

Where, I2dc, Iq , Id , Vd and Vq are the state variables, Iid and Iiq are the input variables, and I2dc and Iiq are the output variables. R, L, C, Rdc , Ldc and are system parameters and considered as constants. In the steady-state, the system voltage Ed is close to 1 p.u. Thus, there is no problem in considering it as a constant value. In order to get a better accuracy, Ed can be considered as the disturbance input in (13). This makes a variable.

The dynamic model in matrix form is,

(17)

y = C. x (18)

Where,

x = [I2dc Id Iq Vd Vq]T

u = [Iid Iiq]T

e = Ed



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y = [I2dc Iq]T

2 3 0 0 0

10 0

10 0

10 0 0

10 0 0

dc d

dc dc

R EL L

RL L

RAL L

C

C

=

0 00 00 01 0

10

B

C

C

=

01

000

LF

=

1 0 0 0 00 0 1 0 0

C =

III. DECOUPLED STATE-FEEDBACK CONTROLLER

For a linear system represented by (17) and (18), it is easy to design a state-feedback controller so that the output variables follow the reference input variables and are not influenced by the disturbance input. The controller (Fig.-2) can be in the form of,

Where,

is the reference input;

K = 2x5 constant state feedback gain matrix for State variables;

T = 2 2 constant diagonal gain matrix for the Reference input;

M = 21 constant gain vector for the disturbance Input;

The closed-loop input-output relationship is,

y = C (sI A +BK)-1[B.T.yref + (B.M +F)e] (20)

In this particular case, it is possible to find a such that the matrix is diagonal matrix, C(sI A +BK)-1B implying a

Fig.-2 Diagram of STATCOM Controller

decoupled closed-loop system, and place the poles at the desired locations.

IV. CONCLUSION

In this paper, a CSC-based STATCOM is proposed. A linear model for the STATCOM is derived from the original nonlinear model by applying the power balance equation and a nonlinear input transformation. The new linear model is independent of the operating point. The decoupled state-feedback control is formulated and applied to the CSC-based STATCOM. The performances of the STATCOM at steady-state and in response to step changes in the reference values of the system voltage and the dc-side current are evaluated using the simulation results from MATLAB package.

V. REFERENCES

[1] N. G. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems. New York: IEEE Press, 2000

[2] Dong Shen, Lehn P.W. Modeling, analysis, and control of a current source inverter-based STATCOM // IEEE Trans on Power Delivery. 2002. Vol. 17, No. 1. P. 248 253.

[3] C. D. Schauder and H. Mehta, Vector analysis and control of advanced static VAR comp., IEE Proc. C, vol. 140, no. 4, July 1993.



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[4] Y. Ye and M. Kazerani, Decoupled state- feedback control of CSI based STATCOM, in Proc. 32nd Annual North American Power Symp., vol. 2, Oct. 2324, 2000, pp. 18.

[5] Current-Source Converter Based STATCOM: Modeling and Control, Yang Ye, Member, IEEE, Mehrdad Kazerani, Senior Member, IEEE, and Victor H. Quintana, Fellow, IEEE.

[6] Modeling and State Feedback Controller for Current Source Inverter Based STATCOM, A. Ajami and M.Younesi, International Conference on Control, Automation and Systems 2008.

[7] State-feedback Control of a Current Source Inverter based STATCOM, Gang Yao , LiXue Tao, LiDan Zhou, Chen Chen, ELECTRONICS AND ELECTRICAL ENGINEERING, ISSN 1392 1215, 2010.

[8] A Nonlinear Fuzzy PID Controller for CSI STATCOM, A.Kazemi, A.Tofighi, and B.MahdianIEEE-2006.

[9] Multivariable Nonlinear Control of Current Source Inverter-based STATCQM for Synchronous Generator Stabilization, , Boniface H. K. Chia, Stella Morris, P.K.Dash,, SICE Annual Conference

[10] A Hybrid, Current-Source/Voltage-Source Power Inverter Circuit,, Andrzej M. Rzynadlowski, , Niculina Patriciu, Frede Blaabjerg, , and John K. Pedersen, IEEE Transactionson Power Electronics, VOL. 16, NO. 6, NOVEMBER 2001.

[11] Current source converter based STATCOM: Operating principles, design and field performance, H.F. Bilgin, M. Ermis,, Electric Power Systems Research 81 (2011) 478487.

[12] System Modeling and Control Design for FastVoltage Regulation Using STATCOMs,, Amit K. Jain, Student Member, IEEE, Aman Behal, and Ned Mohan, Fellow, IEEE..



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