Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 116.
Performance Enhancement of Grid Connected Wind
Energy Conversion Systems
J. Ravishankar and M.F. Rahman
School of Electrical Engineering & Telecommunications
University of New South Wales
Sydney, NSW 2052, Australia
{jayashri.ravishankar & f.rahman}@unsw.edu.au
compensation results in a very good voltage profile at PCC
and a significant reduction in transmission line current due to
the reduction of reactive power flow through the line. This
also allows more turbines to be connected at the PCC.
When fault occurs, the voltage at the WECS terminals
drops. Thus the generated active power falls, while the
mechanical power does not change and so the induction
generator accelerates. After fault clearance, the reactive power
consumption increases, resulting in reduced voltages near the
generating unit. Thus the induction generator voltage does not
recover immediately after fault, but a transient period follows.
As a consequence, the generator continues to accelerate, and
this may lead to rotor speed instability [2]. Thus, it is clear
that the dynamic controller used should not only provide the
needed reactive power support for voltage regulation but
should also help to damp out the rotor speed oscillations.
Abstract - The aim of this paper is to enhance the steady state
and dynamic performance of grid connected Wind Energy
Conversion Systems (WECSs) in India. The WECS considered is
a fixed-speed system that is equipped with a squirrel-cage
induction generator. The drive-train is represented as a two-mass
model. A wind farm consisting of ten wind turbines is considered
for analysis. The total capacity of the wind farm is 7.5 MW. In
this paper, the steady state performance of the WECS is analyzed
using a simultaneous method of power flow algorithm.
Simulation results using various types of compensation reveal
that a combination of series and shunt compensation improves
the overall steady state performance of the system. The dynamic
performance of grid connected WECS is analyzed in terms of
rotor speed stability. The enhancement of dynamic performance
is explored with a Unified Power Flow Controller (UPFC)
connected at the Point of Common Coupling (PCC). The gains of
the UPFC are tuned using a simple Genetic Algorithm (GA). It is
observed that the UPFC, which is a series-shunt controller, helps
not only in regulating the voltage, but also in mitigating the rotor
speed instability.
II. MODELLING OF WECS
Fig. 1 shows the schematic diagram of a typical WECS. A
description of sub-models (or components) is presented in the
following sections.
Index Terms - Wind energy; reactive power compensation;
power flow; rotor speed stability; UPFC;
I. INTRODUCTION
One of the most critical issues for the development of
wind energy in India has been the transmission capacity of the
grid in the areas where the wind farms exist. Wind farms are
concentrated in the rural areas where the existing transmission
grids are very weak. Most of the electric machines used with
the wind turbines in India, are of fixed-speed type equipped
with squirrel-cage induction generators. In addition, the wind
farms were developed during a comparatively short period of
time in a few areas, and the reinforcement of the transmission
systems in these areas has lagged behind the fast development
of wind energy [1].
In case of fixed-speed wind turbines, reactive power
support is needed at wind energy conversion system (WECS)
terminals for voltage regulation and improvement of low
voltage ride-through capabilities. As the wind speed
continuously changes, the voltage at the point of common
coupling (PCC) fluctuates. A possible way to improve this
situation is by incorporating reactive power compensation.
In this paper, the power flow of a radial system with
WECS is simulated, using a simultaneous method of power
flow. Simulation results show that the series-shunt
Fig. 1 Schematic diagram of a typical WECS
A. Wind Turbine Model
The simple aerodynamic model commonly used to
represent the turbine is based on power performance versus
tip-speed ratio. The power extracted from the wind turbine is
given by [3],
1
Pw = ρaCPυ 3 ,
(1)
2
where ρ is the density of dry air, a is the swept area of the
blades in m2, CP is the power coefficient and υ is the velocity
of the wind in m/s. A general expression for CP is given in [4].
55
B. Drive-Train Model
In case of conventional WECS models, accurate results are
obtained by increasing the number of masses, springs and
damper which are used to represent the physical characteristics
of the actual system. It has been proved that the two-mass
model for WECS representation is fairly accurate [5]. Thus this
approach is adopted here and is shown in Fig. 2, where the
wind turbine and the generator rotor are modelled as two
masses and the wind mill shafts as spring element.
dVq'
[
]
1 '
Vq + ( X s − X s' ) I ds + sVd' ,
(5)
dt
T0'
where V’ is the voltage behind transient reactance, Is is the
stator current, T0’ is the open circuit time constant, Xs is the
stator reactance and Xs’ is the transient reactance of the
machine. The subscripts d and q stand for the direct and
quadrature axis values, respectively. The swing equations have
been included in the mechanical model given by (2). The
electromagnetic torque, Te, is computed as,
Te = Vd' I ds + Vq' I qs .
(6)
=
III. STEADY STATE ANALYSIS
The power flow analysis with the WECS is quite
complicated, unlike the analysis with conventional sources,
because,
• The power injected into the grid by WECS depends on
the instantaneous wind speed, which varies
unpredictably.
• With the use of squirrel-cage induction generators, the
operating slip of the machine has to be determined. The
machine operates at a slip for which the mechanical
power developed by the turbine is equal to the
electrical power developed by the induction generator.
In this paper, the power flow analysis is carried out using
a simultaneous method [8]. This method determines
simultaneously the state variables corresponding to nodal
voltage magnitudes and angles of the network and slip of
induction generators. In this method, the WECS is modelled
as a variable PQ bus. Assuming adequate initial conditions,
the method retains Newton’s quadratic convergence. Here, the
Newton-Raphson power flow algorithm is reformulated to
include the mismatch equation ΔPm (difference between the
power extracted from the turbine and electrical power
developed in the machine). The unified power flow
formulation is,
⎡ ⎡ ∂P ⎤
⎡ ∂P ⎤
⎡ ∂P ⎤ ⎤ ⎡ [Δθ ] ⎤
V
⎢
⎢
⎥
⎢ ∂s ⎥ ⎥ ⎢
⎥
⎡ [ΔP ] ⎤ ⎢ ⎢⎣ ∂θ ⎥⎦
⎣ ⎦ ⎥
⎢⎣ ∂ V ⎥⎦
⎢
⎥
⎢
⎥ ⎢
⎥
⎡ ∂Q ⎤
⎢
⎥ ⎢ ⎡ ∂Q ⎤
⎡ ∂Q ⎤ ⎥ ⎢ ⎡ Δ V ⎤ ⎥
⎢V
⎥
⎢ [ΔQ ] ⎥ = ⎢ ⎢ ⎥
⎢ ∂s ⎥ ⎥ x ⎢ ⎢ V ⎥ ⎥, (7)
⎣ ⎦
⎢⎣ ∂ V ⎥⎦
⎢
⎥⎦ ⎥
⎢
⎥ ⎢ ⎣ ∂θ ⎦
⎥ ⎢⎣
⎢
⎥
⎢[ΔP ]⎥ ⎢ ⎡ ∂ΔP ⎤ ⎡
⎤
∂ΔPm
⎡ ∂ΔPm ⎤ ⎥
m
⎣ m ⎦
⎢ ⎢− ∂θ ⎥ ⎢− V ∂ V ⎥ ⎢− ∂s ⎥ ⎥ ⎢⎣ [Δs ] ⎥⎦
⎦ ⎢⎣
⎦ ⎥⎦
⎥⎦ ⎣
⎢⎣ ⎣
Fig. 2 The simplified two-mass model
The dynamic equations of the two-mass representation
are given by [6],
dωt Tt − Kδ
dt
=
2Ht
,
dωe Kδ − Te
=
,
dt
2H e
(2)
dδ
= 2πf (ωt − ωe ),
dt
where T is the torque, δ is the angular displacement between
the two ends of the shaft, ω is the angular speed, H is the
inertia constant and K is shaft stiffness. The subscripts t and e
stand for wind turbine and generator parameters, respectively.
C. Electric Generator
The generator model considered here is a squirrel-cage
induction generator driven by a wind turbine with fixed blades,
i.e. a stall-regulated fixed-speed turbine. The induction
generator is directly connected to the grid. In the operating
region, the rotor speed varies within a very small range of slip
(around 1 to 5% of the synchronous speed). This has negligible
aerodynamic effect and hence, these are considered fixed speed
generators.
The steady state model of such an induction machine is
represented by the well known equivalent circuit [7]. The
equation for the air gap power is,
1− s
2
,
Pg = − I 2 R2
(3)
s
where I2 is the rotor current, R2 is the rotor resistance and s is
the slip.
For the dynamic analysis, the differential equations of the
induction generator contains only fundamental frequency
components and the stator flux linkage transients are
neglected. The equations are then given by [7],
[
]
dVd'
1
= ' Vd' + ( X s − X s' ) I qs + sVq' ,
dt
T0
⎡ ∂ΔPm ⎤
⎥
⎣ ∂s ⎦
where ⎢
is a diagonal matrix whose order is equal to the
number of wind farms in the network. Their elements are
given by,
∂ΔPm 1
ω r / υ C6 Λ
A
= ρaυ 3[C2 − EC1 ]C1
e
+ 2 ( B − C ), (8)
∂s
2
D
sC
where the expressions for A to E, and Λ are given in the
Appendix and C1, C2 and C6 are constants in the power
coefficient equation [4].
(4)
56
The power flow is carried out on a 9-bus radial system
given in Fig. 3 [3]. Ten wind turbines are assumed to be
connected at the PCC (bus 9).
where, V- voltage at WECS terminals at rated speed, P - Real
power generated at rated speed, Q - Reactive power demand at
rated speed and I - Transmission line current.
From the results of Table 1 it is seen that higher value of
combined series and shunt compensation, produces lower
reactive power demand and lesser line current, but the voltage
profile becomes too high (>5%). Therefore, it is clear that the
combination of series compensation equal to 50% of line
reactance and shunt compensation of 150 kVAR, shows better
performance for the 9-bus radial system considered.
IV. DYNAMIC ISSUES
Fig. 3 Single line diagram of 9-bus radial system
The dynamic analysis is necessary (i) to ascertain the
wind farm behaviour against various disturbances occurring in
the WECS or the grid and (ii) to check whether the induction
generators will pick back the load after the fault is isolated.
This analysis becomes particularly relevant in cases where the
wind energy production has become a significant part of the
system production, and consequently the loss of a large part of
the wind production in the event of grid faults can have severe
consequences for the system stability. Moreover, wind turbine
production is often voluntarily reduced at certain times by
automatic grid disconnection especially during low
consumption periods and when there are strong winds [9]. The
purpose is to maintain the stability and reliability of power
systems with high wind power penetration. In fact, today wind
farms are required to actively participate in power system
operation in the same way as conventional power plants.
Therefore, power system operators have revised the grid
connection requirements for wind farms [10] and now demand
that these installations be able to carry out more or less the
same control tasks as conventional power plants.
A three-phase fault near the PCC will reduce the terminal
voltage at the WECS and increase its speed of rotation. After
voltage recovery (fault isolation), the rotor speed of the
induction generator may be so high that it does not return to the
pre-fault value. The mechanical torque of the turbine will
decrease when the turbine speed increases and the turbine may
reach the steady state at elevated speed. This state is not
desirable since it is accompanied by reduced active power,
increased reactive power consumption and reduced voltages
near the generating unit. Existing stability concepts used in
power system analysis do not include this phenomenon. The
phenomenon is however, similar to the motor stalling concept
for induction machines in motor operation mode and is termed
as rotor speed stability [2].
For the purpose of analysis, the 10 wind turbines at the
PCC (bus 9 in Fig. 3) are connected in two groups; Group 1
consisting of 3 turbines aggregated together as one single
turbine of capacity 2.25 MW (750 kW x 3) at bus 10 and
Group 2 consisting of 7 turbines aggregated together as one
single turbine with a capacity of 5.25 MW (750 kW x 7) at bus
11, as shown in Fig. 4. The line between buses 5 and 9 is a
double circuit line. Thus the system considered becomes a 11bus radial system.
The reactive power compensation for WECS is
traditionally done with capacitor banks, which is an economic
and relatively simple solution. In shunt compensation, the
capacitor is used to compensate the individual induction
generators. In series compensation, the capacitor is used to
compensate the line impedance. Thus the advantage of both
shunt and series compensation of an AC capacitor can be
made use of. The overall result will be an improvement in the
voltage and lower losses on the transmission line.
For the system shown in Fig. 3, the series capacitor is
connected in the transmission line between the infinite bus
and the PCC i.e., in the line between buses 4 and 5. Shunt
capacitor is assumed to be connected at the terminals of
WECS. Simulations are carried out with shunt compensation
alone, series compensation alone and for different
combinations of series-shunt compensation.
The results are summarized in Table 1. The results show
that,
1) With shunt compensation, there is improvement in
voltage profile and decrease in the reactive power demand. The
line current reduces thereby reducing transmission losses. The
net effect is an improvement in power factor.
2) With series compensation, there is improvement in
voltage profile, although there is increase in the reactive power
demand. The line current drawn is comparatively large, yet
more turbines can be connected on-line. The net effect is an
improvement in real power penetration.
3) With series-shunt compensation there is a considerable
improvement in voltage profile. At the same time, the reactive
power demand and the line current drawn are both reduced
compared to series compensation alone and are comparable
with shunt compensation.
TABLE I
SIMULATION RESULTS AT RATED WIND SPEED (17 M/S)
Type of
V
P
Q
Capacity
compensation
(PU)
(MW) (MVAR)
Shunt
150 kVAR 0.9788
3.89
1.49
200 kVAR 0.9912
3.89
1.25
250 kVAR 1.0031
3.89
1.01
0.9580
7.77
4.43
Series
0.5Xline
1.0090
7.77
4.68
0.75Xline
Combined
0.5Xline &
series-shunt
150kVAR
1.0014
7.77
2.27
0.75Xline &
200kVAR
1.0619
7.77
1.91
I
(PU)
0.1807
0.1771
0.1729
0.3604
0.3443
0.1782
0.1253
57
V. DYNAMIC REACTIVE POWER COMPENSATION
Many authors have discussed the application of flexible
AC transmission system (FACTS) controllers like static var
compensator (SVC) and static synchronous compensator
(STATCOM) to improve the voltage ride-through of induction
generators [12–19]. It can be understood that these devices do
not provide damping of speed oscillations. Hence, in this
paper, the effect of unified power flow controller (UPFC) to
enhance the rotor speed stability of fixed speed wind turbines
is analyzed.
UPFC is a shunt-series connected FACTS controller that
can control the various electrical parameters (voltage, real
power and reactive power) either individually or
simultaneously. For the 11-bus system shown in Fig. 4,
simulation is carried out with UPFC connected at the PCC
along with 150 kVAR fixed capacitor at each of the generator
terminals. A transient model is considered for UPFC [20]. In
this paper, fixed capacitor equal to the no-load (operation at
cut-in speed) compensation of 150 kVAR is assumed to be
connected at the terminals of each generator. Then, the
dynamic VAR requirement at the PCC that has to be supplied
by UPFC is selected as the difference between full-load
(operation at rated speed) and no-load compensation. Thus the
UPFC rating is set to ±1.5 MVA (150 kVAR x 10).
The gains of the UPFC are tuned using a simple GA. The
objective is minimising the oscillations in PCC voltage and
rotor speed. Thus the Sum Squared Deviation Index (SSDI) for
UPFC tuning may be written as,
SSDI = ∑ [(Vref − Vk ) 2 + (ωref − ωk ) 2 ].
(9)
Fig. 4 Single line diagram of 11-bus radial system
The rotor speed stability analysis is carried out by
evaluating the transient stability of the system [11]. The time
response of rotor speed of induction generators and PCC
voltage is obtained. One particular case, as described below, is
analysed here as it leads to rotor speed instability:
A solid three-phase to ground fault on one of the
interconnecting lines between the wind farm PCC (bus 9) and
the grid (bus 5) near bus 9 at one second followed by tripping
of faulted line between buses 9 and 5 after a delay of 6 cycles
when the WECS is operating at rated speed (17 m/s).
Fig. 5 and Fig. 6 show the voltage at the PCC and the rotor
speed of WECS respectively. It is seen that the PCC voltage
drops to a very low value of 0.1 p.u. initially and does not
recover. It settles down at a low value of 0.6 p.u. From Fig. 6,
it is seen that the speed of the induction generators
monotonically increases which indicates clear instability.
PCC VOLTAGE (PU)
1.0
k
Ignoring the gains in the measurement circuits, there are
eight other gains in series and shunt elements of UPFC that are
tuned using GA. The assumed gains and the various time
constants in the transient model of UPFC [20] are given in
Appendix.
It is observed that after tuning, the SSDI is reduced from
0.1124 to 0.0347. The initial values of the gains that are tuned
and their optimum values are given in Table 2. With these
gains, the same fault simulated in section 4 is considered in this
section with UPFC and comparative results with and without
UPFC are presented.
0.8
0.6
0.4
0.2
0.0
0
1
2
TIME (SEC)
3
4
5
Fig. 5 PCC voltage for a solid three-phase to ground fault
TABLE II
UNTUNED AND TUNED GAINS OF UPFC
Gain
Untuned
Tuned
parameters Gains
Gains
K
10
7.6932
KD
10
9.7652
KPdc
10
6.4625
KIdc
1
0.4369
KPP
10
2.6936
KIP
1
0.0498
KPQ
10
5.2894
KIQ
1
0.3836
1.30
ROTOR SPEED (PU)
1.25
1.20
1.15
1.10
1.05
1.00
0.95
0.90
0
1
2
3
4
5
Fig. 7–9 show the voltage, real power generated and
reactive power demand at the PCC, respectively, with and
without UPFC. Fig. 10 shows the rotor speed of induction
TIME (SEC)
Fig. 6 Rotor speed oscillations of WECS for a solid three-phase to ground
fault
58
generators with and without UPFC. It is observed that the
induction generators get stabilized and regain their original
speed after fault clearance.
Fig. 7 shows that the PCC voltage settles down at 1 p.u. in
contrast to 0.6 p.u. without UPFC. The initial transient voltage
drop increases to 0.93 p.u. with UPFC. Fig. 8 shows that the
real power reduces to zero without UPFC, but with UPFC the
power generation by WECS is restored. Similarly, Fig. 9 shows
that without UPFC the reactive power demand is very high due
to the fault, which reduces substantially once the UPFC is
connected.
VI. CONCLUSION
A methodology to investigate the influence of wind power
on the operation of power system is presented in this paper.
Simulation studies are done on a radial system using C++
programming language.
A simultaneous method of power flow technique is used
for analyzing the steady state performance of the WECS. The
effect of different types of compensation, namely, shunt,
series and series-shunt is studied. It is concluded that with a
combined series-shunt compensation there is a considerable
improvement in voltage profile. At the same time, the reactive
power demand and the line current drawn are both reduced
compared to operation only with series compensation and are
comparable with shunt compensation. A combination of series
compensation equal to 50% of line reactance and shunt
compensation of 150 kVAR shows better performance as
compared to either series or shunt compensation alone, for the
analysed 9-bus radial system. Thus with the correct choice of
capacitor sizes, a combination of series and shunt
compensation can be used to improve the steady state
performance.
The dynamic performance of the system is explored using
rotor speed stability analysis. The effect of UPFC, which is a
series-shunt controller, in improving the dynamic performance
is examined. It is seen that a dynamic compensation with
±1.5MVA UPFC at the PCC along with a 150 kVAR fixed
capacitor at the generator terminals provides the best solution
for the analysed 11-bus radial system.
In summary, it is recommended that for improving both the
steady state and dynamic performances, it is better to go in for
series-shunt compensation, rather than the usual practice of
using shunt compensation alone.
The study also reveals that in certain cases, adequate
VAR compensation can be achieved by using the existing
capacitor banks along with the FACTS controllers. This way
the rating of the FACTS controllers can be reduced. This will
lead to a considerable reduction in cost, as the FACTS
controllers are very expensive. Moreover, total dispensing of
the existing capacitor banks can be avoided.
Fig. 7 PCC voltage with and without UPFC for a three-phase fault
Fig. 8 Real power at PCC with and without UPFC for a three phase fault
Fig. 9 Reactive power demand at PCC with and without UPFC for a three
phase fault
APPENDIX
Constants in Simultaneous power flow equation
V 2 X m2 Rr / s
R ⎞
2R ⎛
B = r ⎜ Rx + r ⎟
A= 2
s ⎝
s ⎠
Rs + ( X s + X m )
Fig. 10 Rotor speed of Group 2 with and without UPFC for a three phase fault
2
R ⎞
⎛
C = ⎜ Rx + r ⎟ + ( X x + X r )2
s ⎠
⎝
59
D = (λ + 0.08θ ) 2
E = C2 Λ − C3θ − C5
1
1
0.035
=
−
Λ λ + 0.008θ 1 − θ 3
[15]
where,
jX m ( Rs + jX r )
Rs + j ( X s + X x )
and V-terminal voltage, Rs-stator resistance, Rr-rotor
resistance, Xs-stator leakage reactance, Xr-rotor leakage
reactance, Xm-magnetizing reactance of the induction machine,
λ-tip speed ratio, θ-pitch angle and C2, C3, and C5 are
constants in power coefficient equation [4].
UPFC data
All data are in p.u on a 25 MVA and 15 kV base.
Rsh : 0; Xsh : 0.025; Rse: 0; Xse : 0.0025; RC : 0.077; KPP : 10;
KIP : 1; K : 10; KMP : 1; T1 : 1; TMP : 0.01; KD : 10; KPQ : 10;
T2 : 0.01; KIQ : 1; KMac : 1 ; KMQ : 1; TMac : 0.01 ; TMQ : 0.01;
KP : 10 ; KI : 1; KMdc : 10; TMdc : 0.01
Rx + jX x =
[16]
[17]
[18]
[19]
ACKNOWLEDGMENT
The authors wish to acknowledge the support provided by Anna University,
India for carrying out this research.
[20]
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