1
Direct Output Voltage Control of a Static
Synchronous Compensator Using Current Sensorless
d-q Vector-Based Power Balancing Scheme
Woei-Luen Chen, Student Member
Yuan-Yih Hsu, Senior Member
Department of Electronic Engineering
Hwa Hsia College of Technology and Commerce and
Department of Electrical Engineering
National Taiwan University
Department of Electronic Engineering
Abstract—A new current sensorless method based on power
balancing algorithm is proposed for direct output voltage control
of a static synchronous compensator (STATCOM). The principal
advantage of the proposed control scheme is that the STATCOM
output voltage command is directly achieved via a simple
algebraic algorithm using only the error signals of the AC and
DC voltage regulators. As a result, complicated computations
involved in the d-q current loop can be avoided. In addition, the
implementation cost can be reduced to a great extent since there
is no need for the current sensors. A mathematical formulation
for the proposed control scheme is first described. Then the
dynamic responses of the STATCOM under disturbance
conditions are simulated on the Matlab/Simulink platform. It is
concluded from the simulation results that AC bus voltage can be
effectively regulated by the STATCOM with the proposed
control scheme.
Department of Electrical Engineering
National Taiwan University
Taipei, Taiwan
sensors and current sensors are required since there is a
current control loop in addition to a voltage control loop. In
the present work, a new control method which uses only
voltage control loop is developed for the STATCOM. The
STATCOM output voltage can be directly computed via a
simple algebraic algorithm based on power balance equation.
Complicated computations involved in the decoupled d-q
current control loop can be avoided. The implementation
costs can be reduced since there is no need for the current
sensors. The effectiveness of the proposed controller is
demonstrated by dynamic response simulations.
II. THE PROPOSED DIRECT OUTPUT VOLTAGE CONTROL
STRATEGY
Index Terms—Static Synchronous Compensator (STATCOM),
voltage regulation, PWM inverter, reactive power compensation.
I. INTRODUCTION
N
UMEROUS TYPES of control strategies have been
proposed for the static synchronous compensator
(STATCOM) which can be used for bus voltage regulation,
reactive power compensation, and power factor correction
[1]-[6]. The most essential part of a STATCOM is a threephase pulse-width modulated voltage-sourced inverter with a
voltage-controlled DC bus. The output voltage control
strategies for the voltage-sourced inverter are generally
classified into two types [1]: phase angle control and hybrid
control including modulation index control and phase angle
control. Only one control input is required in the phase angle
control strategy and the modulation index is kept constant.
For this reason, the modulation index must be properly
designed based on the consideration of minimal output
harmonic voltages [3]. To increase the controllability of a
STATCOM, the DC link voltage is kept sufficiently high in
the hybrid control scheme which may result in higher output
harmonic voltages and poorer utilization of the inverter [1].
With these minor disadvantages, the hybrid control scheme
has been examined in many papers due to its flexibility of the
decoupled d-q voltage control of the inverter [1,3,4]. In the
hybrid control scheme developed so far [1,3,4], both voltage
0-7803-8110-6/03/$17.00(C)2003 IEEE
Fig. 1 shows the single line diagram of a STATCOM
connected to a distribution system which is represented by its
Thevenin equivalent circuit. As shown in Fig. 1, the
STATCOM is composed of a voltage-sourced inverter and a
coupling transformer and filter which are represented by the
resistance Rf and inductance Lf. The main objective of the
STATCOM is to maintain constant voltage at the PCC (point
of common coupling) bus. The proposed direct output voltage
control strategy is described below.
STATCOM
Voltage-Sourced Inverter
Coupling transformer
and filter
Rf
v ( vd , vq )
Distribution system
vs
Rs
Ls
Lf
C dc
iL
( e d , e q ) i (i d , i q )
(S1 … S6)
DC Voltage
Feedback
Direct Output
Voltage Controller
AC Voltage
Feedback
PCC
Bus
RL + jX L
(Load)
Fig. 1 Proposed direct output voltage controller
For a balanced three phase system, the three phase voltages
va ,vb ,and vc or currents ia ,ib ,and ic can be described as
2
f a = f cos( ωt + θ f )
(1)
2π
)
(2)
3
2π
f c = f cos( ωt + θ f +
)
(3)
3
, where fa , fb , and fc can be the three phase voltages or
currents. The three phase quantities fa , fb , and fc in a-b-c
coordinates can be transformed into the quantities fq , fd , and
f0 in q-d-0 coordinates using the well-known Park
transformation
f b = f cos( ωt + θ f −
fqd0=P
where
P=
2
3

cos(ωt + θ)


 sin(ωt + θ)

1


2

ƍf
(4)
abc
2π
2π 
) cos(ωt + θ +
)
3
3 
2π 
2π
)
sin(ωt + θ −
) sin(ωt + θ +
3 
3
1
1


2
2

cos(ωt + θ −
Substituting (1)-(3) into (4), we have
f q = f cos(θ − θ f )
(5)
f d = f sin(θ − θ f )
(6)
Distribution
System and
load
STATCOM
i ∠θ i
v ∠θ v
(vd , vq )
(id* , iq* )
Rf
Lf
C dc
Pe* , Qe*
Po* , Qo*
PCC Bus
Pf* , Q*f
Fig. 2. Power-flow diagram of the STATCOM and power system
Under steady-state balanced three phase conditions, the
total three phase real power and reactive power may be
expressed in terms of d-q quantities as (7) and (8), where the
v and i are the peak values of phase voltage and phase
Pe* = P*f + Po*
(9)
Qe* = Q*f + Q*o
(10)
Using (7) and (8), the inverter output real power and reactive
power in d-q axis are given by
3
(11)
Pe* = (e d* i d* + e *q i q* )
2
3
(12)
Qe* = (e *q i d* − e d* i q* )
2
For the sake of simplicity, a new synchronous reference
frame is defined where the d-axis is always coincident with
the instantaneous PCC bus voltage v and the q-axis is in
quadrature with it. To do this, let = f + /2
Then, from (5) and (6), we have
vd = v
(13)
and fqd0=[fq fd f0]T, and fabc=[fa fb fc]T
3 Phase
( e* , e* )
PWM Inverter d q
Fig. 2 depicts the real power flow and reactive power flow
from the STATCOM to the distribution system through the
PCC bus. It is obvious that the inverter output power
(Pe*+jQe*) must be equal to the sum of the power consumed
by the coupling transformer and the filter (Pf*+jQf*) and the
power delivered to the distribution system and load (Po*+jQo*)
which is defined as STATCOM output power. In other words,
we have the following power balance equations
current, respectively, and v and i are the phase angles for
phase voltage va and phase current ia , respectively.
3
P = v i cos(θv − θi )
2
3
= (v q i q + v d i d )
(7)
2
3
Q = v i sin(θ v − θ i )
2
3
(8)
= (vq id − vd iq )
2
vq = 0
(14)
Substitution of (13) and (14) into (7) and (8) yields
3
3
(15)
Po* = vd i*d = v i*d
2
2
3
3
(16)
Qo* = − vd i*q = − v i*q
2
2
The power consumed by coupling transformer and filter is
given by
3
3
Pf* = i* 2 R f = (id* 2 + iq* 2 ) R f
(17)
2
2
3
3
Q*f = i * 2ωL f = (id* 2 + iq* 2 )ωL f
(18)
2
2
Substitution of (11), (12), and (15)-(18) into (9) and (10)
yields
e *d = R *f i d* − ωL*f i q* + v
(19)
e *q = R *f i q* + ωL*f i d*
(20)
It is obvious from (19) and (20) that the output voltage
commands of inverter, ed* and eq*, can be directly obtained
from the current commands, id* and iq*, the PCC bus voltage,
|v|, and the coupling transformer and filter parameters, Rf and
Lf. It is worth noting that the current feedback loop is not
needed in this control scheme. The way how the d-q current
commands, id* and iq*, generated by the AC and DC voltage
regulator has been discussed in [1] and [4].
Fig. 3 shows the block diagram of the proposed direct
output voltage control scheme in which the AC and DC
voltage regulator are realized by PI controllers. The upper and
lower limiter is included in the PI controller in order to avoid
overload operation.
3
The phase angle of the PCC bus voltage can be obtained by
a phase locked loop (PLL) circuit. The angle is important
when transforming the d-q voltage commands to abc voltage
commands.
AC Voltage Regulator
v
v
*
∑
Current to Voltage Transducer
*
q
i
PI Controller
phase voltage.
Table I gives the nominal power consumed by the load at
nominal voltage. Since constant impedance load model is
employed in the present work, the power consumed by the
load will be proportional to the square of the applied voltage.
Rf
ωL f
∑
eq*
IV. SIMULATION RESULTS
To verify the validity of the proposed control strategy,
three simulated events were investigated as follows:
θv
θv
1. Load Voltage Compensation with Load Reactive Power
Varying from Leading to Lagging
vdc
ωL f
The dynamic response for a step change from 4kVar
∑ PI Controller id*
*
∑
ed*
Rf
vdc
capacitive load to 4kVar inductive load are shown in Fig. 4
and Fig. 5, respectively, for the uncompensated system and
the compensated system. Note that when the load changes
DC Voltage Regulator
from capacitive to inductive operation, the PCC bus voltage
is decreased from 1.01 to 0.89 p.u. and 1.01 to 0.99 p.u. for
Fig. 3 Block diagram of direct output voltage control scheme
the uncompensated and the compensated system,
respectively. The STATCOM output reactive power is
III. SIMULATION MODEL
increased rapidly (in about one cycle) from 0 to 7000 Var,
The configuration of the simulation model has been
as shown in Fig. 5(c). Besides, the STATCOM DC link
depicted in Fig. 1.
voltage can be kept nearby constant at 360V, as evidenced
The program Matlab/Simulink is used for computer
by the response curve in Fig. 5(b).
simulation to verify the effectiveness of the proposed control
strategy.
2. Load Voltage Compensation with Load Reactive Power
TABLE I
Varying from Lagging to Leading
CIRCUIT AND CONTROL PARAMETERS
The dynamic responses for a step change from 4kVar
Supply nominal voltage
vs
220 V
inductive load to 4kVar capacitive load are shown in Fig. 6
Supply line inductance
Ls
2.25mH
and Fig. 7, respectively, for the uncompensated system and
Rs
0.85
Supply line resistance
the compensated system. It is observed from Fig. 7 that
Inverter series line inductance
Lf
0.265mH
constant PCC bus voltage profile can be achieved by the
Rf
0
Inverter series line resistance
proposed direct output voltage controller. In addition, the
Inverter dc bus voltage
Vdc
360V
STATCOM output reactive power is decreased from 8000
C dc
8600 F
Inverter dc bus capacitance
Var to -650 Var in order to maintain constant PCC bus
fs
1980Hz
Inverter switching frequency
voltage when the reactive power load demand is changed
Load model
from 4kVar inductive load to 4kVar capacitive.
(Parallel constant impedances)
Nominal power at nominal voltage
PL
3kW
QL
4kVar
Control parameters
Kp
9
AC voltage regulator
KI
1
Kp
0.35
DC voltage regulator
KI
0.2
The circuit and control parameters in Fig. 1 are given in
Table I. It is to be noted that a distribution line with an Xs/Rs
ratio of approximately 1 has been selected for computer
simulation. The output harmonic voltages and control ability
of the STATCOM should be taken into consideration while
setting the DC link voltage. A High setting of the DC link
voltage corresponds to an operating point with a low
modulation index, a wide control range but a high level of
harmonic contents. In the present work, the DC link voltage is
set at 360V which is about two times of the supply nominal
Fig. 4 Uncompensated system responses for a step change from 4kVar capacitive
load to 4kVar inductive load (nominal load at nominal voltage). (a) PCC voltage.
(b) Load real power. (c) Load reactive power.
4
Fig. 5 Compensated System responses for a step change from 4kVar capacitive
load to 4kVar inductive load (nominal load at nominal voltage). (a) PCC voltage.
(b) DC link voltage. (c) STATCOM output reactive power.
Fig. 6 Uncompensated system responses for a step change from 4kVar inductive
load to 4kVar capacitive load (nominal load at nominal voltage). (a) PCC
voltage. (b) Load real power. (c) Load reactive power.
Fig. 7 Compensated system responses for a step change from 4kVar inductive
load to 4kVar capacitive load (nominal load at nominal voltage). (a) PCC
voltage. (b) DC link voltage. (c) STATCOM output reactive power.
3. Bus Voltage Sag Compensation
In this simulated event, the source voltage is decreased
from 1 p.u. to 0.8 p.u. at t=0.5s.
This simulated response curves for the system without
the compensator and with the compensator are depicted in
Fig. 8 and Fig. 9, respectively. It is observed from the
response curves in Fig. 8 that, for the system without the
compensator, the PCC bus voltage sags from 0.892 p.u. to
0.714 p.u. due to voltage drop on the supply line. In addition,
the real power Ps and reactive power Qs consumed by the
load decrease significantly as a result of the voltage drop at
the PCC bus. This is as expected since constant impedance
load model is employed in the simulations.
The voltage sag at the PCC bus can be improved as the
STATCOM is installed. As evidenced by the response
curves in Fig. 9, the PCC bus voltage can be maintained at a
level slightly higher than 0.9 p.u. In addition, the DC link
voltage and the STATCOM output reactive power will reach
their steady-state values in 0.3 sec.
Fig. 8 Uncompensated system responses for a step change from 1 p.u. to 0.8 p.u.
in source voltage. (a) PCC voltage. (b) Load real power. (c) Load reactive power.
Fig. 9 Compensated system responses for a step change from 1 p.u. to 0.8 p.u. in
source voltage. (a) PCC voltage. (b) DC link voltage. (c) STATCOM output
reactive power.
5
V. CONCLUSIONS
In this paper, a STATCOM which employs direct output
voltage control strategy has been developed and investigated.
The simulation results showed that fast response for varying
load and good voltage regulation in voltage sag event can be
achieved by the proposed controller. Moreover, the current
sensorless scheme is economic in practical implementation
since current sensors are not needed. Finally, it is significant
to note that the controller gains for the AC voltage regulator
are higher than those for the DC voltage regulator. The
coordination between the controller gains for two voltage
regulators is an important issue and needs further
consideration.
VI. REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
C. Schauder and H. Mehta, “Vector analysis and control of advanced static
var compensators,” IEE Proceedings-C, vol. 140, no. 4, pp. 299-306,
1993.
G. Joos, L. Moran and P.Ziogas, “Performance analysis of a pwm inverter
var compensator,” IEEE Trans. on Power Electronics, vol. 6, no. 3, pp.
380-391, 1991.
L. Moran, P. Ziogas and G. Joos, “Analysis and design of a three-phase
synchronous solid-state var compensator,” IEEE Trans. on Industry
Applications, vol. 25, no. 4, pp. 598-608, 1989.
C.T. Chang and Y.Y. Hsu, “Design of UPFC controllers and
supplementary damping controller for power transmission control and
stability enhancement of a longitudinal power system,” IEE ProceedingsC, vol. 149, no. 4, pp. 463-470, 2002.
P. Giroux, G. Sybille and H. Le-Huy, “Modeling and simulation of a
distribution STATCOM using simulink’s power blockset,” The 27th
Annual Conference of the IEEE Industrial Electronics Society, pp.990994, 2001.
T. J. E. Miller, Reactive Power Control in Electric Systems, New York,
John Wiley & Sons, 1982.
VII. BIOGRAPHIES
Woei-Luen Chen was born in Taiwan on Nov. 29 1971. He received the
B.S.E.E. degree from Chung-Yung Christian University in 1995, the M.S.E.E.
degree from National Taiwan University in 1997. Currently, he is a Ph.D.
candidate at the Department of Electrical Engineering, National Taiwan
University.
His employment experience included the China Engineering Consultants, Inc.
Since October 2001, he has been a lecture at the Department of Electronic
Engineering, Hwa Hsia College of Technology and Commerce. His present
research interests include power electronic applications, reactive power
compensation systems and the wind energy conversion systems. Mr. Chen is a
registered professional engineer in Taiwan R.O.C..
Yuan-Yih Hsu was born in Taiwan on June 19 1955. Since 1977, he has been
with National Taiwan University, where he is now a professor. He worked at the
University of Calgary, Canada, as a postdoctoral fellow and instructor from
1982 to 1983. From 1988 to 1989, he was a visiting scholar at the University of
California, Berkeley. He was elected as one of the Ten Outstanding Young Men
by the Junior Chamber of Republic of China in 1995.
At present, his research interests include power system dynamics and
stability analysis, distribution automation, and the application of artificial
intelligence to power systems.