the steady state analysis and the controller design of statcom

The steady state analysis and the controller design of STATCOM

LING-LING XI, QIAN AI, CHEN CHEN

Department of Electrical Engineering Shanghai Jiao Tong University

1954, HuaShan, Road, Shanghai, 200030 CHINA

[email protected] [email protected] Abstract: This paper presents a new approach for the dynamic control of VSC STATCOM. Based on d-q transform, the mathematical model is established, and the steady-state characteristic is proposed as a basis for control design. The new approach of control design includes choosing proper model, which avoids linearizing the model around a steady-state operating point, and applying the state-feedback control. The simulation results based on EMTP have proved the correctness and the feasibility of the mathematical model and the proposed control method. Keywords: FACTS, STATCOM, steady-state, state-feedback, dynamic model, V-I characteristic

1 Introduction The concept of Flexible AC Transmission Systems (FACTS) was proposed in the middle and late 1980s. It has been at the center of attention and the subject of active research for many years. FACTS controllers are used to control the power flow in the transmission system and enhance the transmission capacity. Static Var Compensator (SVC) is the first generation of the FACTS controllers. After that, more new devices were developed. Static Synchronous Compensator (STATCOM), which is also called Advanced Static Var Generator (ASVG), is a new controller based on the technology of power electronic.

STATCOM is a kind of shunt-connected reactive power generators, which can supply inductive or capacitive power compensation, and control the particular parameter (voltage, phase, resistance) in the power system. STATCOM can enhance the capability in the following area: dynamic voltage control in the transmission and distribution system, power oscillation damping in

the transmission system, transient stability, voltage flicker and so on.

STATCOM basically has the same function as SVC, but has larger operational range and faster rate of regulation. STATCOM uses Gate Turn-off Thyristors (GTO) for utilities applications, the principle of the converter using GTO is presented in reference [3][4]. The dynamic model of the output voltage while the converter applies the technique of Sinusoid Pulse Width Modulation (SPWM) is proposed in reference [5], and reference [6] analyzes the operating principle and the steady-state model of STATCOM. The control method of STATCOM is one of the most important researches. Generally speaking, its control method can be divided into current direct and indirect control. The current direct control is using the feedback of the instantaneous current waveform, in which STATCOM can be treated as a controlled current source [7]-[8]; and the current indirect control is controlling the amplitude and phase of the output voltage generated by the converter, in which STATCOM can be treated as an ac electrical source.

Proc. of the 5th WSEAS/IASME Int. Conf. on Electric Power Systems, High Voltages, Electric Machines, Tenerife, Spain, December 16-18, 2005 (pp235-240)

In this paper, the current indirect control is applied. In the modeling of STATCOM, it’s a complex problem to linearize the nonlinear model, many papers deal with the nonlinearity by linearizing the model around a steady-state point [9], but the method has drawbacks, the model and the controller are depended on the chosen operating point.

This paper is to establish the dynamic mathematical model of the STATCOM, deduce the steady-state model and analyze the V-I characteristic. By properly modeling the STATCOM, the nonlinearity is avoided. A robust controller design is developed by dealing with the model as a state-feedback control system, and applying the state-feedback control. The simulation on EMTP is used to verify the accuracy of the developed model.

2 The Mathematical Model of

STATCOM The schematic diagram of a VSC-based STATCOM is shown Fig.1.The STATCOM is connected to the transmission line through a shunt transformer, and the DC voltage is provided by the capacitor.

+

+

12

+

+

+

+

+

Fig.1. VSC-Based STATCOM In Fig.1, the turns ratio of the transformer is :1n ,

sL is the leakage reactance of the transformer, sR is the make-break loss of the transformer and the converter, dcR represents the loss resistance of the converter, dcC is the capacitance of the capacitor,

dcV is the capacitive voltage, sE , sθ are the amplitude and phase of the ac-side output voltage,

tE , tθ are the amplitude and phase of the

transmission line voltage, and sai , sbi , sci

are the three-phase current of the ac-side. The control objectives of the STATCOM are to regulate the output voltage of the converter and give the required reactive power compensation to the transmission line, while keeping the capacitive voltage in a constant.

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

1 ( )sas sa sa ta

s

di R i e edt L

×= − + −

1 ( )sbs sb sb tcb

s

di R i e edt L

×= − + −

1 ( )scs sc sc tc

s

di R i e edt L

×= − + − (1)

Applying Park’s transformation, with tE chosen as the reference voltage vector, the current and

voltage vectors become [ ]Is = ] Tsd sqI I⎡ ⎤⎣ ⎦ ,

[ ]Es = ] Tsd sqE E⎡ ⎤⎣ ⎦ , and [ ]Et = ]0

TtdE⎡ ⎤⎣ ⎦ ,

respectively. Thus, (1) can be re-written as

01 ( )sd s

sd sq sd tds s

dI R I W I E Edt L L

−= − + +

01sq s

sd sd sqs s

dI RW I I Edt L L

= − − + (2)

The dynamic equation of the dc-side is 1 ( )dc dc

dcdc dc

dV VIdt C R

= − + (3)

The active power delivered by the ac source ( acP ) is equal to the active power absorbed by the dc-side ( dcP ), the resistance sR is always small, so it is practically reasonable to neglect its power loss ( RsP ) without noticeable loss of accuracy. Thus, the dynamic equation can be represented in d-q axis as

ac dcP P= (4) 32

tdac sd

EP In

= − (5)


2 212

dc dcdc dc

dc

dV VP Cdt R

= + (6)

which can be rewritten as 2 22 3dc dc td

sddc dc dc

dV V E Idt C R n C

= − − (7)

In equation (7), 2dcV can be taken as the state variable. The converter is controlled using tri-level SPWM technique. In this way, the converter under tri-level SPWM control can be modeled as

cossd dcE kV β= ssq dcE kV inβ= (8)

(2), (7), (8) compose the model of the STATCOM.

3 Steady-State Characteristics

Fig.2 STATCOM Operating in Steady-State Fig.2 shows the phasor diagram of STATCOM in the steady-state operation. When the system operates in the steady state, no active power exchange between the STATCOM and the system,

hence, the compensation current sI•

is in orthogona-

lization with the output voltage of the converter sE•

.

If the vector sI• advancing the vector sE

•, then the

STATCOM inject the reactive power to the system; contrarily, STATCOM absorb the reactive power from the transmission line.

Combined with equation (2), (7), (8), the steady-state operation point can be derived

2sindsd

s

EtInR

β= −

sin 22

dsq

s

EtInR

β=

sin( )sin

ddc

EtVnk

α βα−

= (9)

Where 1 s

s

RtgX

α −=

Fig.3 V-I Characteristic of STATCOM In steady-state operation, if the voltage of the

transmission line falls, STATCOM increase the injected reactive power by increasing β to keep the line’s voltage invariable; and if the voltage rises, STATCOM decrease the injected reactive power by decreasing β to keep the line’s voltage invariable.

Fig.3 shows that STATCOM can improve capacitive or inductive compensation and control the output current within the maximal rated capacity, which dose not depend on the ac voltage. That is to say, the STATCOM can supply reactive power of full rated capacity under any voltage (even when the voltage is lower than 0.15pu).

4 Controller Design In the controller design of STATCOM, a common

0.25

1.0

0.50

0.75

ILIC I I Cmax

Lmax

Vt

0

Instantaneous rating (t<1s)Instantaneous rating

Inductive

Capacitive


method to deal with the nonlinearity is to linearize equation (2), (3) around a steady-state operating point. The drawback of this approach is that the model and the controller design are dependent on the operating point. In this paper, 2dcV is taken as the state variable, by replacing (3) with (7), the nonlinearity is avoided. The control objectives of the STATCOM are to regulate the dc-side voltage and give the required reactive power compensation,

thus dcV and qI are the control variables.

The dynamic model composed of (2), (7) can be expressed in the state-space system as

X AX BU De•

= + +

Y CX= (10) Where

0

0

2 3 0

0

0

td

dc dc dc

s

s

s

s

EC R nC

RA wL

RwL

− −⎛ ⎞⎜ ⎟⎜ ⎟

−⎜ ⎟= ⎜ ⎟⎜ ⎟−⎜ ⎟−⎜ ⎟⎝ ⎠

,

0 01 0

10

s

s

BL

L

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

,

1 0 00 0 1

C ⎛ ⎞= ⎜ ⎟⎝ ⎠

，

01

0s

DL

⎛ ⎞⎜ ⎟−⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

;

2 Tdc sd sqX V I I⎡ ⎤= ⎣ ⎦ , 2 T

dc sqY V I⎡ ⎤= ⎣ ⎦ ,

[ ]0 Tsd sqU E E= , and dEte

n= . The state

variable is X , the input variable isU ; the output variable is Y , and tdE can be treated as the disturbance input.

Based on the model (10), add a predicting filter K and a state controller F , the state-feedback control system of STATCOM is formed.

Fig.4. State-Feedback Control System

Where,U KW FX Me= − + K is a 2 2× constant diagonal gain matrix. And

can be chosen when W = 2* *T

dc sqV I⎡ ⎤⎣ ⎦ ;

2* *T

dc sqV I⎡ ⎤⎣ ⎦ means Y in the steady state.

F is a 2 3× constant matrix. And can be chosen by placing the poles at the desired location. From Fig.4, the following equation can be given

( ) ( )Y G s W H s e= + (11)

Where

11 12

21 22

( ) ( )( )

( ) ( )G s G s

G sG s G s⎛ ⎞

= ⎜ ⎟⎝ ⎠

, 1

2

( )( )

( )H s

H sH s

⎛ ⎞= ⎜ ⎟⎝ ⎠

(12)

Since W = 2* *T

dc sqV I⎡ ⎤⎣ ⎦ , and the control objective

is to make Y W= in steady-state and not influenced by the disturbance input variable e , these can be achieved by

1 20lim ( ) ( ) 0s

H s H s→

= = , 12 21( ) ( ) 0G s G s= =

1 11 1( ) ( ) ( )Y s G s W s= , 2 22 2( ) ( ) ( )Y s G s W s=

(13) The control model of STATCOM is a second-order system, hence we can design as

21

11 2 21

( )( )( ) 2

Y sG sW s S S

ωξω ω

= =+ +

(14)

The characteristic equation is 2 22S Sξω ω+ + =0,

and its eigenvalues are 21,2

1S ξω ω ξ= − ± − . when

0 1ξ< < , 21,2

1jS ξω ω ξ= − ± − , the equation

have a pair of negative real part conjugate roots, then the systems is in state of underdamping, by using inverse Laplace transformation, the time

domain response of 1( )Y s can be given

1 1 12

1( ) sin( )1

tdy t w e t wξω ω θ

ξ−= − + ×

− (15)

k

D

A

B C

M

F

⊗ ⊗ ∫

e

W YU+

+

+

++

−

X


Where 21dω ω ξ= − , 2

1 1tg ξθ

ξ− −

= (16)

In (12), 1w is the steady component of the

second-order system, and

12

1 sin( )1

tde t wξω ω θ

ξ− + ×

− is the dynamic

component, which is an exponential attenuation

oscillation wave with the frequency of` dω ; the

oscillation speed depends on ξω , and they are

inverse proportional.

Proper ξ , ω can be chosen to make the system

have good transient characteristic, and get

1 1( )y t w= , which means 2 2*dc dcV V= .

2 2( )y t w= ( *sq sqI I= ) can also be derived by

using the same method.

5 Simulation Results The simulation is based on EMTP, the system parameters are

100BS MVA= , 230BU MVA= , rE =

1.05 0rE = ∠ o , 0.05vL pu= , 0.005vR pu= ,

0.008rR pu= , 0.08rL pu= , 0.006sR pu= ,

0.06sL pu= , 50dcR pu= , 0.07sC pu= .

Choose ξ =0.5, ω =300, the only input variables

of STATCOM are k , β , which are the input

variables of the converter.

From equation (8), k , β can be derived

2 2

sq sd

dc

E Ek

V+

= , 1 sd

sq

EtgE

β −= .

Where sdE , sqE , dcV can be measured in the

system. The simulation results are shown as follows

Fig.5 Simulation Results Fig.5 shows how the dc voltage and the

reactive current can be regulated to their reference

values. At first, *sqI is maintained at 4 KA , dcV ∗


is maintained at 30 KV . Then at 0.2t s= the

reference value *sqI is set to be 8 KA . As seen

from Fig.4.(a), sqI responds to the change in the

reference and settles at the new steady-state value

8kv , but in Fig.4(b) and Fig.4(c), sdI and

dcV remain almost constant during the transient period of the line current regulation. And at

0.35t s= , dcV ∗ is set to be 80 KV , as seen from

the Fig.4(b),Fig.4(c) , sdI , dcV follow the change

in the reference and reach the new set point, but

sqI remains almost constant during the transient

period. During the twice change, sdE , sqE always

respond to the change and reach the new steady-state point after a transient period fluctuation. During the simulation, the transient period almost last less than 0.02s, and the dynamic behaviour of the transient period is depended on the system

parameters and ξ ,ω .

6 Conclusion In this paper, a VSC-based STATCOM is proposed. The mathematical model for the STATCOM is derived from the original equation. And linearize the model by applying the power balance equation

and taking 2dcV as the state variable instead of

dcV , and the model is independent of the operating point. Based on the model, the steady-state operation point and the V-I characteristic are proposed. It is founded that the STATCOM can supply reactive power of full rated capacity under any voltage. From the linear model, the controller design is formulated by using the state-feedback control, and the simulation results have verified the

accuracy of the developed model and the proposed control method. Reference: [1] N. G. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems, New York: IEEE Press, 2000 [2] Li Chun, Jiang Qiring, Xu Jianxin, Investigation of Voltage Regulation Stability of Static Synchronous Compensator in Power System, Power Engineering Society Winter Meeting, 2000.IEEE, Vol.4, No.23, 2000, pp.2642-2647. [3] Rizzo, S. C., Bin Wu, Sotudeh, R., Symmetric GTO and Snubber Component Characterization in PWM Current-Source Inverters, Power Electrionics, IEEE Transaction, Vol.13, No.4, 1998, pp.617-625. [4] R. Mohan Mathur, Rajiv K, Varma, Thyristor-Based FACTS Controllers for Electrical Transmission Systems, China Machine Press, 2005 [5] A. Nabavi Niaki, M.R.Iravani, Steady-state and Dynamic Models of Unified Power Flow Controller (UPFC) for Power System Studies, IEEE Transaction, Vol.11, No.4, 1996, pp.1937-1943. [6] C. D. Schauder and H. Mehta, Vector Analysis and Control of Advanced Static Var Compensators, IEEE Proceedings-C, Vol.140, No.4, 1993, pp.299-306. [7] Ke Li, Investigation on Static VAR Generator with a Direct Current Control Strategy, Power Electronics, Vol.37, No.3, 2003, pp.8-11. [8] Tahri A, Draou A, et al, A Fast Current Control Strategy of a PWM Inverter used for static Var Compensator, IEEE Transaction on Industrial Electronics, Vol.45, No.3, 1998, pp.450-455. [9] Mou Yu, Yu He, Nonlinear Control of Static Synchronous Compensator, Natural Science Edition, Vol.32, No.6, 2003, pp.1009-0193. [10] Dong Shen, P. W. Lehn, Modeling, Analysis, and Control of a Current Source Inverter-Based STATCOM, IEEE Transaction on Power Delivery, Vol.17, No.1, 2002, pp.248-233.


the steady state analysis and the controller design of statcom

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