Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 151.
.
Steady-state and transient analyses of wind farm
connected to an electric grid with varying stiffness
Mazen Abdel-Salam*, Adel Ahmed, and Mahmoud Mahrous
Electric Engineering Department, Assiut University, Assiut, Egypt
* Corresponding author: mazen2000as@yahoo.com
requirements for the connection of wind farms to electrical
network are defined by the new connection code [2].
Abstract- This paper is aimed at investigating the steady
state and transient analysis behaviour of a squirrel cage
induction generator of wind farm connected to a variable
stiffness grid using MATLAB/SIMULINK. Different types
of faults including three-phase-to-ground, double-line-toground, line-line and single-line-to-ground are studied. The
calculated temporal variations of speed, voltage, active
power and reactive power of the generator agreed
reasonably with those obtained using PSCAD for threephase and single-line-to-ground faults. The three-phase-toground is the most severe fault as expressed by the time
required for the voltage to recover to its pre-fault value and
the maximum current drawn by the faulted bus.
The analysis of a configuration consisting wind farm based
on conventional fixed speed induction generator has been
reported before [3] using EMTDC/PSCAD digital
simulator. It was reported that the transient stability
conditions of generator was increased and the short-term
voltage and rotor stability performance were improved for
three-phase to ground and single-phase to ground faults
because of the use of STATCOM as an active voltage/var
supporter.
This paper is aimed at investigating the effect of the
short circuit ratio (SCR) on the steady- state and transient
performance (symmetrical and unsymmetrical faults) of
the same wind farm whose details are reported before
[3].
The
well
known
software
package
MATLAB/SIMULINK was used. This makes it possible
to compare between the MATLAB simulator and the
PSCAD simulator for three-phase to ground fault and
single-line to ground fault for a strong (stiff) grid of SCR
=16. Other faults including line-to-line and double
line to ground faults are also investigated using
MATLAB/SIMULINK package.
Keywords: Wind energy; Fixed speed wind turbine;
Induction generator; Short circuit ratio (SCR).
I. INTRODUCTION
Wind turbine technology has undergone a dramatic
transformation during the last 15 years, developing from a
fringe science in the 1970s to the wind turbines of the
2000s utilizing the latest technology in power electronics,
aerodynamics and mechanical drive train designs.
Induction generators are more attractive than synchronous
generators for wind turbines due to their robust
construction, low cost, low maintenance, long life (more
than 50 years) and low power to weight ratio [1]. However
the reactive power management is a major concern, not
only to compensate for the reactive power requirements of
the wind generator itself but also to support the system
voltage in particular for wind farms based on fixed speed
induction generators.
II. NETWORK
There are a number of possible interconnection structures
for wind farms and thus it is not possible to cover every
type of network configuration, load, and interconnection
point of the wind farm. Frequently wind parks are
connected to weak systems, as they are typically located far
from major load centers and central generation. This
reflects itself in the short circuit ratio (SCR) of the
interconnection, given by:
In the past, there was no requirement by the grid code
for a wind farm to remain connected to the grid during
a fault or a voltage disturbance. The protection of the
wind farms has mainly been focused on turbine
protection without considering the impact it might have
on the power system. This implies that the wind turbine is
disconnected from the grid as soon as a violation of
voltage or frequency operating limits is exceeded.
SCR =
SCC
Sbase
(1)
Where S base is the rated power of wind farm and SCC
or short circuit capacity is the short circuit power
delivered from the grid for a three-phase fault at the
wind park:
However, increasing wind power penetration means that
wind power plants have to behave more like conventional
power plants and hence have to take over many of the
control tasks that hold the power system stable. The
2
Vbase
SCC =
Z line
203
(2)
When the short circuit fault is cleared, the electrical torque
has to be re-established and has to be larger than the
mechanical torque for decelerating the generator to its
original speed. However, the dependence of the terminal
voltage influences the behavior of the generator after the
fault as well. When the fault is cleared, the terminal
voltage Vs is a decreasing function of the generator speed
where Z line is the impedance of the line connecting the
grid with wind farm and Vbase is the rated voltage of
the grid. For weak systems the SCR will usually be
less than 6 [4].The wind generator system have
matched capacities in terms of real and reactive power,
whereby reactive power is supplied from the generator
itself and from the STATCOM for the fixed speed
machines [4].
and stator current, resulting that, in a weak connected grid
system, the electrical torque may not exceed the
mechanical torque, the over speeding may continue and
generator runs away. Hence, the behavior of the induction
generator depends also on the value of short circuit
impedance viewed from the generator terminal into the
electric power grid [3].
III. THE STABILITY OF INDUCTION GENERATORS
The dynamic stability of induction generators
connected to a grid depends on the characteristic of
the generator, the grid configuration and the
characteristic of the disturbance.
IV. SYSTEM UNDER STUDY
The over speed of the induction generator resulted from
a transient short circuit in the electrical power system
can exceed the stability limit resulting in collapse of the
system.
The one line diagram of the test system employed in this
study is shown in Fig. 1.
The wind farm consists of 75 units of 1.6 MVA wind
turbines. Each of these wind turbine units consists of rotor,
gear box, squirrel-cage induction generator, shunt capacitors
for the reactive power compensation of the generator
(connected to the 0.69 kV network) and a 0.69/10.5 kV
transformer. The representation of the power plant has
been made by aggregating all wind turbines in one
coherent lumped equivalent model.
Assuming generator operating condition, the generator
will accelerate during fault in the power system according
to the following movement equation
2H
dω (t )
= Tmech − Telec
dt
(3)
The wind farm includes a power station transformer, rated
to 10.5/115 kV, 150 MVA. The large wind farm is
connected to a 115-kV line, which is then connected to the
electric grid. The short circuit power of this grid is
dependent on the SCR. The reactive power required for the
wind farm is 44 MVAr, being fed by both the fixed
capacitor (34 MVAr) installed at bus # 1 as well as the grid
itself. The reactive power required for the transmission line
and transformers is 11 MVAr being fed by the grid. For
weak grids, a 21 MVAr switched capacitor is connected at
bus # 4 to cover the deficiency of the generated reactive
power. The wind turbine induction generator (WTIG)
model is used in phasor model [5]. All the relevant data are
given in appendix.
Where H = the inertia constant, ω = the angular speed of
generator, Tmech = the mechanical torque of generator and
Telec = the electrical torque of generator.
During the failure event in the power system the
mechanical torque Tmech is practically unchanged; on the
other hand the electrical torque will be reduced since the
electrical torque is proportional to the square of terminal
voltage ( Telec
∝ Vs2 ) (where the voltage Vs , the voltage
level at the terminal of the generator during the fault). This
means that the resulted over speed is a function of the
inertia constant H of the generator, the duration of the fault
and severity of the fault.
Fig. 1: Network model
204
connection to grid (bus B5). This corresponds to SCC
values in the range 250 MVA to 500 MVA. Fig. 2
shows the temporal variation of the generator speed for
different SCR values. As shown in Fig. 2, the grid
cannot feed the reactive power requirement of the
transmission lines and transformers for SCR less than 4
and overspeed of the machine is expected. The speed, the
voltage, the active power and the reactive power of the
induction generator at SCR ≥ 4 assume constant values as
given in Table I.
V. SIMULATION STUDIES
In the simulation studies, the reactive power requirements
of the wind farm under both steady state and transient
conditions were investigated. The strength of the electric
grid, to which the wind farm is connected, influences the
reactive power requirements. Therefore, different values of
the SCR of the wind farm to grid connection are attempted
and the steady state and the transient analysis of the wind
farm are studied. The strength of the electric grid
reflects itself on injecting the reactive power required
by the 115-kV transmission line and transformers with
no need for the switched capacitor at bus 4. All p.u data
have base MVA=100.
TABLE I
SPEED, VOLTAGE, ACTIVE POWER AND REACTIVE POWER OF
THE INDUCTION GENRATOR AT SCR ≥ 4.
A. The steady state behaviour
The circuit shown in Fig. 1 was simulated without
considering the 21 MVAr switched capacitor bank for
different SCR values in the range 2 to 4 at the point of
The speed
(p.u)
The voltage
(p.u)
The active
power (p.u)
The reactive
power (p.u)
1.015
0.915
-0.8
0.33
1.8
SCR=2
SCR=3
SCR=4
Speed (p.u)
1.6
1.4
1.2
1
0
2
4
6
8
10
Time (sec)
12
14
16
18
20
Fig. 2: Temporal variation of the generator speed of different values of SCR.
B. Fault analysis
values of SCR in the range 2-6. Fig. 3 shows the temporal
variation of the generator speed as influenced by the value
of SCR.
1) Three-phase to ground fault
A three phase to ground fault is applied to the connection
point between the wind farm and the 115-kV transmission
line at t =3 s for a duration of 140ms (detection time and
operation time of the breakers is 140 ms) [3] with different
As shown in Fig. 3, the grid cannot feed the reactive
power requirement of the transmission lines and
transformers for SCR less than 6 and overspeed of the
machine is expected
1.7
Speed (p.u)
1.5
1.4
Speed (p.u)
SCR=2
SCR=3
SCR=4
SCR=5
SCR=6
1.6
1.3
1.2
1.06
1.04
1.02
2
1.1
1
0
2
4
6
8
10
Time (sec)
12
14
Fig. 3: Temporal variation of the generator speed of different values of SCR.
205
16
4 6 8 10 12
Time (sec)
18
20
line at t =3 s for a duration of 140ms (detection time and
operation time of the breakers is 140 ms) [3].
Therefore, the system is in need for the 21 MVAr switched
capacitor at SCR=5. For SCR equal or greater than 6, the
system is not in need for the 21 MVAr switched capacitor.
For SCR equal or greater than 6, the system is not in need
for the 21 MVAr switched capacitor.
Figure 4 shows the temporal variations of the speed, the
voltage, the active power and the reactive power of the
induction generator at SCR value of 16 before, during and
after the fault in comparison with those obtained using
PSCAD simulator [3].
Figure 5 shows the temporal variations of the speed as well
as the voltage, the active power and the reactive power of
the induction generator at SCR value of 16 before, during
and after the fault in comparison with those obtained using
PSCAD simulator [3].
As shown in Fig. 4, the present calculated pre-fault and the
post-fault values of the speed are 1.015 p.u, which are
almost of the same values as obtained previously using
PSCAD simulator calculation [3]. During the fault, the
speed reaches to 1.03 p.u against 1.06 p.u in the previous
calculation [3]. The voltage, the active power and the
reactive power have the same trend during the fault as that
reported before [3]. Generally, the mismatch between the
previous and present calculation of the active and reactive
power is nearly negligible and doesn't exceed 0.1%.
As shown in Fig. 5, the present calculated pre-fault value
of the speed is 1.015 p.u against 1.014 p.u using PSCAD
simulator [3]. During the fault, the speed reaches to 1.018
p.u against 1.03 p.u in the previous calculation [3]. After
the fault, the speed is 1.015 p.u against 1.02 p.u in the
previous calculation [3]. The present calculated pre-fault
value of the voltage is 1.0 p.u which is almost of the same
value and obtained previously using PSCAD simulator [3].
After the fault, the voltage decreased to 0.87 p.u [3] against
the constant voltage value of 1.0 p.u in the present
calculation. The pre-fault and the post-fault values of the
active power and the reactive power have the same and
trend as that reported before [3] during the fault. Generally,
the mismatch between the previous and present calculation
of the active and reactive power is nearly negligible and
doesn't exceed 0.1%.
The temporal-variation trends of the speed, the voltage,
the active power and the reactive power of the induction
generator at SCR values less than 16 are the same as those
of SCR=16.
2) Single line to ground fault
A single line to ground fault is applied at the connection
point between the wind farm and the 115-kV transmission
1.5
1.04
V (p.u)
Speed (p.u)
1.06
1.02
1
2
3
4
5
Time (sec)
6
0
2
3
4
5
Time (sec)
6
7
1
0
Q (p.u)
1
P (p.u)
0.5
7
2
0
-1
-2
1
-1
-2
-3
2
3
4
5
Time (sec)
6
-4
7
2
3
4
5
Time (sec)
6
7
Present calculation
Previous calculation [3]
Fig. 4: Present and previous [3] calculated temporal variations of the speed as well as voltage, active power and reactive power of the induction generator.
206
1.04
1.4
1.03
1.2
1.02
1
1.01
1
0.8
2
3
4
5
Time (sec)
6
7
0
1
-0.5
0.5
Q (p.u)
P (p.u)
the point of connection between the wind farm and the
115-kV transmission line before and during the fault and
the time required to recover pre-fault values for different
types of fault.
V (p.u)
Speed (p.u)
The same as for three-phase-to-ground fault, the
temporal-variation trends of the speed, the voltage, the
active power and the reactive power of the induction
generator at SCR values less than of 16 are the same as
those of SCR=16. Table II shows voltage and current at
-1
-1.5
-2
2
3
4
5
Time (sec)
6
7
2
3
4
5
Time (sec)
6
7
0
-0.5
2
3
4
5
Time (sec)
6
-1
7
Present calculation
Previous calculation [3]
Fig. 5: Present and previous [3] calculated temporal variations of the speed as well as voltage, active power and reactive power of the induction generator
TABLE II
VOLTAGE AND CURRENT AT THE POINT OF CONNECTION BETWEEN THE WIND FARM AND THE 115-kV TRANSMISSION LINE
BEFORE AND DURING THE FAULT AND THE TIME REQUIRED TO RECOVER PRE-FAULT VALUES.
The fault
During the fault
Voltage (p.u)
pre-fault value
Current (p.u)
Voltage
(p.u)
Pre-fault recovery after fault
Voltage recovered
Current
(p.u)
Value
(p.u)
Time to
recovery
(sec)
Current recovered
Value
(p.u)
Time
to
recovery
(sec)
Va
Vb
Vc
Ia
Ib
Ic
0
0
0
5.5
5.5
5.5
1
1.05
1
1.5
1.05
1.5
Single-phase
0
1.4
1.4
0.5
1.2
1.2
1
1.05
1
1
1.05
1.5
Line to line
0.5
0.5
0.8
5
5
1
1
1.05
1
1
1.05
1
Double line
0
0
1.4
5
5
1
1
1.05
1
1
1.05
1
Three-phase
207
One can conclude from Table 2 that the three-phase-toground fault is the most severe fault where the time taken
for the voltage to recover to its pre-fault value is
approximately 1.5 sec which is greater than that for the
other faults. The time required for the voltage to recover to
its pre-fault is approximately 1 sec for the other faults;
namely, double-line-to-ground, line-to-line and single-lineto ground faults. For the three-phase-to-ground fault, the
current of faulted bus reaches 5.5 p.u against 5 p.u and 1.2
p.u for double-line and single-line-to-ground faults,
respectively
Rotor unsaturated mutual reactance: 0.0374
Frequency: 50
No. of poles pair: 2
Reactive power compensation in the wind farm: 34 MVAr.
Each Wind farm transformer:
Rating: 1.6 MVA
Winding voltages: 10.5/0.69
Leakage reactance: 0.0626
No-load losses and cooper losses: 0.0017 17 and 0.0002
Magnetizing current: 0.3 68
Step-up transformer:
Rating: 150 MVA
Winding voltages: 10.5/115 kV
Leakage reactance: 0.06
No-load losses and cooper losses: 0.0017 and 0.0002
Magnetizing current: 0.3 68
Load connected at the end terminal of the line: 100 MW
System connected at the end terminal of the line:
Short Circuit Power: 2000 MVA, impedance angle 80°
VI. CONCLUSIONS
1) The simulation results show that the dynamic
model of wind farm using MATLAB
simulator agrees with that using PSCAD
simulator. The mismatch between the present
calculation using MATLAB and the previous
calculation using PSCAD is negligibly small
(about 0.1%).
2)
REFERENCES
Three-phase-to-ground fault is the most
severe fault regarding over speeding and
voltage drop. The current of the faulted bus
reaches 5.5 p.u against 5 p.u and 1.2 p.u for
double-line and single-line-to-ground faults,
respectively.
[1] Bhadra SN, Kastha D, Banerjee S. Wind electrical systems. Oxford:
Oxford University, U.K., 2005.
[2] Jauch C, Sorensen P, Bak-Jensen B. International review of grid
connection requirements for wind turbines.In: Proceedings of the
Nordic wind power conference, Sweden, 2004.
[3] Paulo Fischer de Toledo, Hailian Xie KTH, Kungl Tekniska
Högskolan, EME department Teknikringen 33-35, Stockholm, Sweden
"WIND FARM IN WEAK GRIDS COMPENSATED WITH
STATCOM". Proceedings of the Nordic wind power conference, Topic
7, Sweden, 2005.
[4] C. Abbey, Student Member, B. Khodabakhchian, Member, F. Zhou, Nonmember, S. Dennetière, Member J. Mahseredjian, Member, and G. Joos, Senior
Member “Transient Modeling and Comparison of Wind Generator Topologies”,
Paper No. IPST05, Presented at the International Conference on Power Systems
Transients, Montreal, Canada on June 19-23, 2005.
[5] H.M.EL-Helw and Sarath B. Tennakoon, “Evaluation of the suitability of a
fixed speed wind turbine for large scale wind farms considering the new UK grid
code”, Renewable Energy 33, pp.1-12, 2008.
3) For the three-phase fault, the time taken for
the voltage to recover to its pre-fault value is
approximately 1.5 sec against 1 sec for the
other faults.
4) The single-line-to-ground fault is the less
severe fault when compared with the other
faults.
APPENDIX
Detailed description of input data to model the system
in MATLAB/SIMULINK
115 kV Transmission line data:
Length of line = 70 km
Positive- and zero-sequence resistances:R1 =0.0739 ohm/km, R0 =0.388 ohm/km
Positive- and zero-sequence inductances:X L1 =0.449 ohm/km, X L 0 =1.522 ohm/km
Positive- and zero-sequence capacitances:X C1 =0.272 Mega ohm-km, X C 0 =0.427 Mega ohm-km
The squirrel-cage induction generator:
Generator rating: 1.62 MVA (75 units)
Rated RMS line voltage: 690V
Stator resistance: 0.00408 1
Cage resistance: 0.0165
Stator unsaturated leakage reactance: 0.06 1
Mutual unsaturated reactance: 3.434
208