Download reactive power control of isolated wind

SVC BASED REACTIVE POWER CONTROL OF ISOLATED WIND-DIESEL
HYBRID POWER SYSTEMS
R.C. BANSAL1, T.S. BHATTI2, D.P. KOTHARI3
1
Electrical & Electronics Engg. Department, Birla Institute of Technology & Science,
Pilani, (India)
2, 3
Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas,
New Delhi - 110016 (India)
3
E-mail of Corresponding Author: [email protected]
power requirement of the induction generator and of the
load. In the absence of proper reactive device and controls
the system may be subjected to large voltage fluctuations,
which is not desirable. The device used for this function
in conventional power systems is known as static var
compensator (SVC) [11-16] can also be employed for the
hybrid system.
Abstract:
In this paper automatic reactive power control of
isolated wind-diesel hybrid power system having an
induction generator as a power conversion device for
wind power generation is presented. The mathematical
model of the system using reactive power flow equations
is developed. The dynamic voltage stability evaluation is
based on small signal analysis considering a typical Static
VAR Compensator (SVC) and IEEE type -I excitation
system. It is shown that a variable reactive power source
like SVC is a must to meet the varying demand of reactive
power by induction generator and load and to obtain a
very good voltage regulation of the system with minimum
fluctuations. Integral square error (ISE) criterion is used
to evaluate the optimum setting of gain parameters.
Finally the dynamic responses of the power systems
considered with optimum gain setting are also presented.
In conventional power system the power is exported on
transmission lines to load centres. The reactive power
devices are employed in such a way to have minimum
reactive power flow on the transmission lines so that
maximum power can be exported with minimum
transmission loses.
In hybrid systems the load is directly connected to the
generator terminals itself. Therefore the objective of the
reactive power device in this case is to supply the reactive
power required by the load and the induction machine
under varying load conditions. An isolated wind-diesel
hybrid power system has been considered for study
having induction generator for wind power conversion
and synchronous alternator with automatic voltage
regulator (AVR) for diesel unit. The devices AVR and
SVC have different functions but both operate on the
voltage error signal caused by any disturbance in the
system. The main function of the AVR is to maintain the
voltage profile constant at the terminals. The alternator
also provides partial reactive power to the load. Similarly
the main function of SVC is to eliminate the mismatch of
reactive power in the system. The SVC also partially
helps in voltage maintenance at the terminals. A new
innovative scheme, namely, automatic reactive power
control, similar to automatic generation control [17,18]
has been evolved. The scheme is applicable to isolated
hybrid power systems. The system state equations have
been derived with transfer function block diagram
representation of the control system. The voltage
deviation signal is used as area reactive power control
error to eliminate the reactive power mismatch in the
system. The integral square error (ISE) criterion is used to
evaluate the optimum setting of gain parameters of the
Keywords: reactive power control, hybrid power
system, induction generator, static var compensator
Introduction
In recent years, much emphasis has been placed on the
squirrel cage induction machine as the electromechanical
energy converter in generation schemes involving
renewable energy sources [1-4]. The advantages of the
induction generator over the synchronous generator are
low cost, robustness, no moving contacts, i.e., slip- rings,
no synchronization required and no need for d.c.
excitation. But the induction machine requires a reactive
power support for its operation [5-10]. A large number of
papers have appeared in the literature on the subject and a
few papers investigate the capacitance requirement of
self-excited induction generator under steady state
conditions only [1-10]. It has practical significance as it
enables the design and operation engineers to select the
proper value of excitation capacitance for a specific
machine. In a stand-alone hybrid power system, the
reactive power device has to fulfil the variable reactive
1
QL = C1Vq
controller. Finally transient responses are shown for
different disturbance conditions.
where C1 is the constant of the load and the exponent q
depends upon the type of load. For small perturbations
equation (6) can be written as
Incremental Reactive Power Balance
Analysis
QL /V = q (QLo / Vo)
QSG + QSVC - QL - QIG = 2 EMo / (Vo QR) d/dt (V)
+ DV V
(8)
In equation (8) QR divides only one term as all the
other terms are already in pu kVAR. The term E Mo / QR
can be written as
where QSG = reactive power generated by diesel
generator set,
QSVC = reactive power generated by SVC,
EMo / QR = 1/ (4 π f kR) = HR
= reactive power load demand, and
For the incremental reactive power balance analysis of
the hybrid system, let the hybrid system experience a
reactive power load change of magnitude QL. Due to the
action of the AVR and SVC controllers the system
reactive power generation increases by an amount
QSG+QSVC. The reactive power required by the system
will also change due to change in voltage by V. The net
reactive power surplus in the system, therefore, equals
QSG + QSVC - QL - QIG and this power will increase
the system voltage in two ways:
 by increasing the electromagnetic energy absorption
EM of the induction generator at the rate d/dt (EM),
 by an increased reactive load consumption of the
QSG + QSVC – QL - QIG = 2 HR / Vo d/dt (V) +
DV V
(10)
In Laplace form the state differential equation, from
equation (10), can be written as
V(s) = KV /(1 + s TV) [QSG(s) + QSVC(s) - QL(s) QIG(s)]
(11)
Under transient condition QSG is given by
system due to increase in voltage.
QSG = (E'q V cos - V2)/ X'd
This can be expressed mathematically as
Taking Laplace transform of both sides we get
(3)
where XM is the magnetizing reactance of the induction
generator. Equation (3) can be further written as
EM = V2 / (4πf XM)
and
(4)
QSG(s) = K3  E'q(s) + K4 V(s)
(14)
where K3 = V cos  / X'd
(15)
K4 = (E'q cos  - 2V ) / X'd
(16)
The reactive power supplied by the SVC is given by
From equation (4), EM can be written as
EM = EM – EMo = 2 (EMo / Vo) V
(12)
where E'q = change in the internal armature emf
proportional to the change in the direct axis field flux
under transient condition. For small perturbation equation
(12) can be written as
QSG = V cos  / X'd E'q + (E'q cos  - 2V)/ X'd V (13)
(2)
The electromagnetic energy stored in the winding of
the induction generator is given by
EM = ½ LM IM2 = ½ LM(V / XM)2
(9)
where HR is a constant of the system and its units are
sec. and kR is the ratio of system reactive power rating to
rated magnetizing reactive power of induction generator.
Substituting the value of EMo / QR from equation (9) in
equation (8) we get
QIG = reactive power required by generator.
QSG + QSVC - QL - QIG = d/dt (EM) + DV V
(7)
In equation (2), DV can be calculated empirically
using equation (7). Let QR be the system reactive power
rating. Using equation (5), equation (3) can be written as
A wind-diesel system is considered for mathematical
modeling, where diesel generator (DG) set acts as a local
grid for the wind energy conversion system connected to
it. The system also has a SVC to provide the required
reactive power in addition to the reactive power generated
by the synchronous generator. The reactive power balance
equation of the system under steady state condition is
Q SG+ QSVC = Q L+ QIG
(1)
QL
(6)
QSVC = V2 BSVC
(5)
(17)
For small perturbation equation (17), taking Laplace
transform, can be written as
QSVC(s)= K6 V(s) + K7 BSVC(s)
(18)
With increase in voltage all the connected loads
experience an increase by DV = QL / V pu kVAR /pu
kV. The parameter DV can be found empirically. The
composite loads are expressed in the exponential voltage
form as
where
2
K6 = 2 V BSVC and K7 = V2
(19)
The optimum value of the parameters corresponds to
the minimum value of the performance index. In the
studies carried out in this paper  is evaluated over a time
period of 2 seconds. The performance index curve for 1 %
step increase in reactive load demand is shown Fig.2. The
minimum value of the gain parameter obtained is KR =
337.
The Flux Linkage Equation
The flux linkage equation of the round rotor
synchronous machine for small perturbation is
d/dt (Eq) = (Efd - Eq)/T'do
(20)
where Eq = change in the internal armature emf
proportional to the change in the direct axis field flux
under steady state condition.
T'do = direct axis open circuit transient time constant
The transient response curves of the system for 1%
step increase in reactive load for optimum gain settings
are shown in Fig. 3. It is observed that the deviation in the
system voltage and firing angle vanishes in 150 msec. The
deviation in voltage behind transient reactance Δ E'q takes
maximum time of 3 sec. to vanish as shown in Fig. 3 (b).
It is clear from the Fig. 3 that the reactive demand by load
and induction generator ΔQL + ΔQIG is met by reactive
power ΔQSVC supplied by the SVC with negligible
reactive power ΔQSG supplied by the synchronous
generator. The system returns to steady state conditions in
7½ cycles of the supply frequency following a step load
disturbance of 1 %.
In equation (20) Eq is given by
Eq = (Xd / X'd) E'q - (Xd - X'd)/ X'd V cos 
(21)
For small changes equation (20), using equation (21)
and taking Laplace transform can be written as
(1+ sTg)  E'q (s) = K1 Efd(s) + K2 V(s)
(22)
where Tg = X'd T'do /Xd
(23)
K1 = X'd/ Xd
(24)
K2 = (Xd – X'd) cos  / Xd
(25)
Mathematical
system
Modelling
of
It indicates that AVR controls the voltage of the
system and the SVC controls the reactive power of the
system.
Wind/diesel
Conclusions
The block diagram of the system using the Laplace
transfer function equations (11), (14), (18) and (22) with
typical SVC scheme and IEEE type I excitation system is
shown in Fig 1. The state equations in a standard form can
be written as
x =Ax+Bu+Cp
(26)
•
where x, u and p are state, control and disturbance
vectors and A, B and C are system, control and
disturbances matrices, respectively. The vectors are given
by
x =[ Efd Va Vf  E'q  B'SVC BSVC V]T
A dynamic voltage stability study has been presented
in this paper for the hybrid wind-diesel isolated power
system considering transfer function model based on
small signal analysis. The automatic reactive power
control model using reactive power flow equations have
been developed for the first time for hybrid systems. The
integral square error criterion has been used to evaluate
the optimum gain settings. It has been shown that SVC is
essential for an isolated hybrid system to meet the varying
demand of reactive power by induction generator and load
and to have minimum voltage fluctuations. Finally some
of the system transient responses have been shown for
optimum gain settings.
(27)
u = [Vref ]
(28)
p = [QL ]
(29)
The elements of the associated matrices are given in
Appendix I.
References
[1]
B.T.
Ooi,
R.A.David,
"Induction
Generator/Synchronous Condenser System for Power
Systems", IEE Proceedings, Vol. 126, No.1, Jan. 1979,
pp. 69 -74.
[2] S.S. Murthy, O.P. Malik and A.K. Tandon, "Analysis
of Self Excited Induction Generator", IEE Proceedings
129, Pt. C, No. 6, Nov. 1982, pp. 260-265.
[3] M.A. Elsharkawi, J.T. Williams and J. N. Butlar, "An
Adaptive Power Factor Controller for Three-Phase
Induction Generators", IEEE Trans. on PAS, Vol.
PAS-104, No. 7, July 1985, pp. 1825-1831.
Computer Simulation and Results
The data of the wind-diesel power system considered
for simulation is given in Appendix -II. The gains are
optimized using the Liapunov technique for continuous
linear systems with the performance index based upon the
integral square error criterion (ISE) and is given by
 =  [V(t)]2 dt
(30)
3
[4] A.H. Al-Bahrani, N.H.Malik, "Steady-State Analysis
and Performance Characteristic of a 3-Phase Induction
Generator Self-Excited with a single capacitor", IEEE
Transactions on Energy Conversion, Vol.5, No. 4, 1990,
pp. 725-732.
[5] T.F.Chan, "Capacitive Requirements of Self-Excited
Induction Generators", IEEE Trans. on Energy
Conversion, Vol. 08, No. 2, June 1993, pp. 304-311.
[6] N.H. Malik and A.A. Mazi, "Capacitive Requirements
for Isolated Self-Excited Induction Generators", IEEE
Trans. on Energy Conversion, Vol. EC-2, No. 1, March
1987, pp. 62-69.
[7] L. Shridhar, B.Singh, C.S.Jha, 1995, "Transient
Performance of the Self-Regulated Short-Shunt Self
Excited Induction Generator", IEEE Trans. on Energy
Conversion, Vol.10, No. 2, 1995, pp. 261-267.
[8] S.M. Alghuwainem, "Steady State Analysis of an
Induction Generator Self-Excited by a Capacitor in
Parallel with a Saturable Reactor", Electric Machines and
Power Systems, Vol. 26, 1998, pp. 617-625.
[9] Bhim Singh, L. B. Shilpakar, "Analysis of a Novel
Solid State Voltage Regulator for a Self-Excited Induction
Generator", IEE Proceedings- Generation Transmission
Distribution, Vol. 145, No. 6, Nov. 1998.
[10] A. A. Shaltout, M.A. Abdel-Halim, "Solid-State
Control of Wind Driven Self-Excited Induction
Generator", Electric Machines and Power Systems, Vol.
23, 1995, pp. 571-582.
[11] S.E. Haque, N.H. Malik, W. Shepherd, "Operation of
a Fixed Capacitor-Thyristor Controlled Reactor
(FC-TCR) Power Factor Compensator", IEEE Trans. on
PAS, Vol. PAS-104, No. 6, June 1985, pp. 1385-1390.
[12] P. V. Balasubramanyam, A.S.R. Murthy and P.
Parameswaran," Design of Variable Structure Controller
for Static VAR Compensator," Electric Machines and
Power Systems, Vol. 26, 1998, pp. 431-450.
[13] A.E. Hammad, "Analysis of Power System Stability
Enhancement by Static VAR Compensators", IEEE
Transactions on Power Systems, Vol. PWRS-1, No. 4,
November 1986, pp. 222-227.
[14] K.R. Padiyar, R.K. Verma, "Static VAR System
Auxiliary Controllers for Improvement of Dynamic
Stability", Electrical Power and Energy Systems, Vol. 12,
No. 4, Oct. 1990, pp. 287-297.
Dispatcher Training Simulator", IEEE Transactions on
Power Systems, Vol. 10, No. 3, August 1994, pp. 12341242.
[17] O.I. Elgerd, "Electric Energy System Theory An
Introduction", a book, Tata McGraw Hill, New Delhi,
1982, pp. 299-361.
[18] A.A.F. Al-ademi, "Load-Frequency Control of
Stand-Alone Hybrid Power Systems Based on Renewable
Energy Sources", Ph. D. Thesis, IIT Delhi, India, July
1996.
Appendix - I
The elements of the system, control and disturbance
matrices are given below:
A (1,1) = -KE/TE
A (1,2) = 1/TE
A (2,1) = -KF KA/(TF TA)
A (2,2) = -1/TA
A (2,3) = KA/TA
A (2,8) = -KA/TA
A (3,1) = KF/(TF TF)
A (3,3) = -1/TF
A (4,1) = K1/TG
A (4,4) = -1/TgA
(4,8) = K2/Tg
A (5,5) = -1/Td
A (5,6) = 1/Td
A (6,6) = -1/T
A (6,7) = K/T
A (7,7) = -1/TR
A (7,8) = -KR/TR
A (8,4) = K3 KV/TV
A (8,5) = KV K9/TV
A (8,8) = -1/TV + KVK4/TV + KVK8/TV-KVK5/TV
B (2,1) = KA/TA
B (5,1) = KR/TR
C (8,1) = -KV/TV
where
K5 = 2 V Xeq/(R2y + X 2eq)
K = 2(1.0-cos (2 ))/(πXR)
Appendix-II
Table I. Ratings and data of the typical example of the
isolated power system studied.
Generation
Capacity (kW)
Load (kW)
Wind
150.0
150.0
Diesel
150.0
100.0
Total
300.0
250.0
System Parameters
Eq = 1.1136 pu
X'd = 0.15 pu
TE = 0.55 sec.
KF = 0.5
TA= 0.05 sec.
QL = 0.75 pu
 = 2.443985
T= 0.02/4 sec
[15] R. Raghunatha, R. Ramanujam, K. Parthasarthy, and
D. Thakuram, " Incorporation of Static VAR
Compensators and Power System Stabilizers for Dynamic
Stability Evaluation", 6th NPSC Conference at IIT
Bombay, June 4-7, 1990, pp. 435-4439.
[16] Ning Zhu, Subramanian Vadari, Davis Hawang,
"Analysis of Static VAR Compensator Using the
4
 = 21.05
E'q = 0.9603 pu
KA = 40.0
KE = 1.0
TR = 0.05 sec.
RY = 4.06415 pu
q = 2.0
Td = 0.02/12 sec.
Xd = 1.0 pu
T'do = 5.0sec.
TF = 0.715 sec.
KR = 337.0
Xeq = 1.12 pu
BSVC = 0.73 pu
XR = 1.0/0.85 pu
SVC Model
(s)
Vref(s)
+
o +   
B'SVC(s)
1 + s1Td
KR
K
1 + s TR
1 + s T
QSVC (s)
1 + s TV
QIG (s)
+
K5
+
E'q (s)
1
K7
QL (s)
KV
((((V9s0
1 + s Td
B SVC(s)
/2  o + 
V(s)
1
K3
+
+
QSG(s)
+
+
K6
K4
1 + s Tg
+
K2
+
K1
s KF
SF
1 + s TF
V
Vref
(s)
ref(s)
+
KA
Va(s)
+
1 + s TA
1
Efd(s)
KE + s TE
Fig. 1 Transfer function block diagram for reactive power control of wind/diesel
hybrid power system.
5
0.0005
0.00024
0
V
Performance Index, 
0.001
0.000245
0.000235
-0.0005
0
50
100
150
200
Time ( msec.)
0.00023
-0.001
0.000225
300
325
350
375
-0.0015
400
KR
(a)
Fig. 2 Optimization of SVC amplifier
gain .
2.5
-0.000005
0
Time (msec.)
0.5
1
1.5
2
Time (sec.)
-0.00001
Time (msec.)
2.49
2.48
2.47

Eq'
0
2.46
-0.000015
2.45
-0.00002
2.44
0
50
100
150
200
-0.000025
0.02
b
0.015
QSVC
Time
) (msec.)
0.005
0
-0.005
Time c(msec.)
0
50
100
150
0.005
200
0
-0.005
(d)
50
100
150
200
(
Fig. 3 Transient responsese of the system
for 1 % step disturbance in
)
reactive power load.
0.00015
0.0001
0.00005
50
100
150
200
-0.0001
-0.00015
0
(e)
(d)
0
-0.00005 0
)
0.01
-0.01
QIG
(
0.015
0.01
QSG
(c)
(
(b)
Time (msec.)
-0.0002
(f)
(
f
)
6