AckermannTh. (ed) Wind Power in Power Systems
Подождите немного. Документ загружается.
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 29_CHA28 .3D – 651 – [629–652/24]
17.12.2004 10:51PM
References
[1] Akhmatov, V., Knudsen, H. (2002) ‘An Aggregate Model of a Grid-connected, Large-scale, Offshore
Wind Farm for Power Stability Investigations – Importance of Windmill Mechanical System’, Inter-
national Journal of Electrical Power and Energy Systems 24(9) 709–717.
[2] Akhmatov, V., Knudsen, H., Nielsen, A. H., Pedersen, J. K., Poulsen, N. J. (2003) ‘Modelling and
Transient Stability of Large Wind Farms’, International Journal of Electrical Power and Energy Systems,
25(2) 123–144.
[3] Bauer, P., De Haan, S. W. H., Meyl, C. R. and Pierik, J. T. G. (2000) ‘Evaluation of Electrical Systems for
Offshore Windfarms’, presented at IAS Annual Meeting and World Conference on Industry Applications
of Electrical Energy, Rome, Italy.
[4] E.On Netz (2001) ‘Erga
¨
nzende Netzanschlussregeln fu
¨
r Windenergieanlagen’, E.ON Netz. Bayreuth,
Germany.
[5] Kundur, P. (1994) Power System Stability and Control, McGraw-Hill Inc., New York.
[6] Pai, M. A. (1989) Energy Function Analysis for Power System Stability, Kluwer Academic Publishers,
Boston, MA.
[7] Petterson, A. (2003) ‘Analysis, Modeling and Control of Doubly-fed Induction Generators for Wind
Turbines’, licentiate thesis, Department of Electric Power Engineering, Chalmers University of Technol-
ogy, Go
¨
teborg, Sweden.
[8] Rogers, G. (1996) ‘Demystifying Power System Oscillations’, IEEE Computer Applications in Power 9(3)
30–35.
[9] Saccomando, G., Svensson, J., Sannino, A. (2002) ‘Improving Voltage Disturbance Rejection for
Variable-speed Wind Turbines’, IEEE Transactions on Energy Conversion 17(3) p. 422–428.
[10] Slootweg J. G., de Haan S. W. H., Polinder H., Kling W. L. (2003a) ‘Aggregated modeling of Wind
Farms with Variable Speed Wind Turbines in Power System Dynamics Simulations’, in Proceedings of the
14th Power Systems Computation Conference, Sevilla, Spain.
[11] Slootweg, J. G., de Haan, S. W. H., Polinder, H., Kling, W. L. (2003b) ‘General Model for Representing
Variable Speed Wind Turbines in Power System Dynamics Simulations’, IEEE Transactions on Power
Systems 18(1) 144–151.
[12] Van Custem, T., Vournas, C. (1998) Voltage Stability of Electric Power Systems, Kluwer Academic
Publishers, Boston, MA.
Wind Power in Power Systems 651
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 29_CHA28 .3D – 652 – [629–652/24]
17.12.2004 10:51PM
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 653 – [653–676/24]
17.12.2004 10:52PM
29
Aggregated Modelling and
Short-term Voltage Stability of
Large Wind Farms
Vladislav Akhmatov
Dedicated to my true friend C. E. Andersen
29.1 Introduction
In aggregated modelling of large wind farms, a distinction is made between two broad
issues. The first issue is concerned with the detailed representation of the electricity-
producing wind turbines, the internal network of the farm and its grid connection to the
entire power system. The individual responses of many wind turbines and their possible
mutual interaction are studied. Therefore, an aggregated model represents a large
number of grid-connected wind turbines within a large wind farm (Akhmatov et al.,
2003a). In this chapter, we will look mainly at this issue.
The transmission power ne twork on the opposite side of the connection point can be
given by a simplified equivalen t. The equivalent may consist of one or a small number of
transmission lines between the connection point of the wind farm and the swing bus
generator. The impedance of the transmission lines is related to the short-circuit cap-
acity, S
K
, of the transmission network at the connection point of the wind farm. The
generator equivalent is based on the lumped power capacity and the lumped inertia,
corresponding to the power generation units of the exter nal power system. According to
Edstro
¨
m (1985), this simplified representation is valid for a group of coherent synchron-
ous generators of conventional power plant units.
Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 654 – [653–676/24]
17.12.2004 10:52PM
The second issue relates to reduced models of large wind farms that are implemented
in detailed models of large power systems and are used to analyse power system
stability. In this case, the focus is on the collective impact of a large wind farm on a
large power system (Slootweg et al., 2002). This implies that a wind farm can be
represented by the single machine equivalent (Akhmatov and Knudsen, 2002). This
means that the wind farm is given by one model of the wind turbi ne of the given concept
with rescaled power capacity, power supp ly and reactive power exchanged between the
wind farm and the entire transmission ne twork at the conn ection point.
A power system may even include a number of small and large wind farms. In this
case, the wind farms are represented by their respective single machine equivalents.
Knudsen and I give examples of flicker investigations in a power system with more than
60 wind farms (in many decentralised sites; see Knudsen and Akhmatov, 2001) and in
Akhmatov (2002) I report the results of a voltage stability a nalysis with 60 decentralised
wind turbine sites and two large offshore wind farms.
29.1.1 Main outline
At the beginning of this chapter, I wish to discuss the application of aggregated models
of wind farms to the analysis of voltage stability. Section 29.2 describes the model of a
large offs hore wind farm consisting of 80 2 MW wind turbines. I will discuss the
simulation results based on the wind turbine types according to the classification in
Chapter 4 (see Section 4.2.3):
.
Type A2 wind turbines (i.e. fixed-speed, active-stall-controlled wind turbines
equipped with no-load compensated induction generators; see Section 29.3), among
the largest manufacturers that produce this type of wind turbi ne are Vestas Wind
Systems, Bonus Energy and Nordex.
.
Type B1 wind turbines (i.e. pitch-controlled wind turbines equipped with induction
generators with variable rotor resistance (VRR); see Section 29.4). The Danish manu-
facturer Vestas Wind Systems produces OptiSlip
TM
wind turbines.
(1)
.
Type C1 wind turbines (i.e. variable-speed, pitch-controlled wind turbines with doubly fed
induction generators (DFIGs) and partial-load frequency converters; see Section 29.5),
largest manufacturers are Vestas Wind Systems, GE Energy, Nordex and Gamesa Eo
´
lica.
.
Type D1 wind turbines (i.e. variable-speed, pitch-controlled wind turbines with full-
load converters and synchronous generat ors excited by permanent magnets; see
Section 29.6). The Dutch manufacturer Lagerwey the Windmaster produced 2 MW
wind turbines eq uipped with permanent magnet generators (PMGs). The German
manufacturer Enercon produces wind turbines with multipole, synchronous gener-
ators with electrical excitation and frequency converters.
Finally, I will discuss the use of single machine equivalents of large wind farms in the
analysis of voltage stability (Section 29.7) and present some conclusions (Section 29.8).
(1)
OptiSlip
TM
is a registered trademark of Vestas Wind Systems.
654 Aggregated Modelling and Short-term Voltage Stability
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 655 – [653–676/24]
17.12.2004 10:52PM
29.1.2 Area of application
Many wonder why and where to use aggregated models of large wind farms in the
analysis of short-term voltage stability and under what conditions the wind farm
representation can be reduced to a single machine equivalent.
Aggregated models of large wind farms are needed to answer another common ques-
tion – whether there is a risk of mutual interaction between the electricity-producing wind
turbines when clustered together in a large wind farm (Akhmatov et al., 2003a). Such
interaction between many wind turbines could be triggered by a grid disturbance in the
external network. This is likely to lead to self-excitation and, subsequently, a group of
wind turbines would be disconnected. This question is most frequently asked in the case of
wind turbines equipped with converter-controlled generators regarding the risk of mutual
interaction between the converter control systems of various wind turbines. There is also
concern in the case of wind turbines equipped with induction generators and blade-angle
control regarding a possible risk of mutual interaction.
Another broad area where aggregated modelling of wind farms is applied is the design
of the farm’s internal network and its (static) reactive compensation (Jenkins, 1993). In
the case of Type A wind turbines, the focus is on the use of power factor correction
capacitors in order to reduce reactive power demands and prevent dangerous over-
voltages during the isolated operation of a section of the wind farm.
Aggregated models can also be used for development and validation of the control
coordination between a large number of wind turbines with similar or different control
systems (Kristoffersen and Christiansen, 2003). An analysis of the robustness of the
control principles can be included in such a study. The robustness of the control
principles can be evaluated from simulations where the control system fails in a number
of wind turbines of a large wind farm (Akhmatov et al., 2003a). Such an evaluation will
look at the maximum number of individual wind turbines that may have a control
system failure wi thout jeopardising the desired outcome of the study (i.e. maintaining
short-term voltage stability during a grid disturbance; see Akhmatov et al., 2003a).
Aggregated models of large wind farms can also be used to evaluate relay settings
during short-circuit faults or other disturbances in the internal network of a wind farm.
To my knowledge, wind farm owners and power system controllers have asked wind
turbine manufacturers to present aggregated models of large wind farms with a repre-
sentation of more than 200 wind turbines. This illustrates that the development of
aggregated models of large wind farms can be of both practical and commercial interest.
It is, however, important to know that aggregated models of large wind farms can
require relatively large computational resources. This is especially true for those cases
where the detailed representation of advanced control systems of wind turbines is
required for reaching accurate simulation results (Akhmatov, 2002). One should also
take into account that there are concerns regarding the computational resources and
time that the setting up of aggregated models may take.
29.1.3 Additional requirements
If the required computational resources become too large there will be restrictions
regarding the practical application of aggregated models of large wind farms. It is only
Wind Power in Power Systems 655
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 656 – [653–676/24]
17.12.2004 10:52PM
reasonable that users require the computational time [i.e. the time during which the user
has (passively) to wait for the results of a single simulation] to be as short as possible.
And a whole analysis may include a significant number of simulations.
The analysis of short-term voltage stability usually takes a few seconds. In this case,
the computational time will be expected not to exceed a few seconds. Therefore, the
wind turbine models and the entire power grid model need to have very efficient codes
and numerical algorithms. This means that an app ropriate simulation tool has to be
chosen that is able to treat models of large power systems with many generation units.
To reach the results presented in this chapter I have applied user-written models of
electricity-producing wind turbines implemented in the simulation tool Power System
Simulator for Engineering (PSS/E
TM
) from the manufacturer Shaw Power Technologies
Inc. (PTI), New York, USA.
(2)
The computational time lies wi thin an acceptable range.
For other simulation tools that also could have been applied for the same purpose, see
Chapter 24.
29.2 Large Wind Farm Model
An aggregated model of a large offshore wind farm consisting of 80 2 MW wind turbines
was set up. Figure 29.2 represents the wind farm model schematically.
In this large wind farm model, single wind turbines are represented by the simulation
models that correspond to their wind turbine concepts. Through the 0.7 kV/30 kV
transformers the wind turbines are connected to the internal network of the large wind
farm. The internal network is organised into 8 30 kV sea-cable sections (8 rows) with 10
electricity-producing wind turbines per section. Within the individual sections, the wind
turbines are connected through the 30 kV sea-cables. The dist ance between two neigh-
bouring wind turbines in the same section is 500 m, and the distance between two
neighbouring sections is 850 m. The electrical connection between the wind turbines is
organised in a way that the disconnection of a single wind turbine in a section does not
cause isolation of the other wind turbines in the same section.
The 8 sea-cable sections are connected through the 30 kV sea-cables to the offshore
platform with a 30 kV/30 kV/132 kV tertiary transformer and then through the 132 kV,
20 km sea-cable/underground-cable to the connection point at the transmission power
network onshore.
The aggregated model allows simulations of the wind farm assuming an irregular
wind distribution. This assumption is realistic because the wind turbine rotors shadow
each other from the incoming wind. Further, the area of the wind farm is 4.5 6km
2
,
and it is reasonable to expect an irregular wind distribution over such a large area.
Figure 29.1 shows the direction of the incoming wind and the power production
pattern of the wind farm. The efficiency of the wind farm at the given wind distribu-
tion is 93%, and the wind farm supplies appr oximately 150 MW to the transmission
power network.
(2)
PSS/E
TM
is a registered trademark of PTI.
656 Aggregated Modelling and Short-term Voltage Stability
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 657 – [653–676/24]
17.12.2004 10:52PM
29.2.1 Reactive power conditions
Type A and B wind turbines are equipped with no-load compensated induction gen-
erators. For excit ation, the induction generators absorb reactive power from the wind
farm’s internal network and from the capacitors (Saad-Saoud and Jenkins, 1995). The
reactive power absorbed by the induction generators depends on the generator para-
meters and its operational point (i.e. the generated electric power, the terminal voltage
magnitude and the slip). The reactive power of all the generators in the wind farm has to
be adjusted before the transient simulations are started (Feijo
´
o and Cidra
´
s, 2000).
Type C wind turbines with DFIGs are exited from the rotor circuits by the rotor
converters (Akhmatov, 2002). That means that it is not necessary to excite the DFIG
from the power grid. Type D wind turbines with PMGs are excited by permanent magnets
Dynamic reactive
compensation unit
Static reactive
compensation
Four 30 kV cable sections
Transmission power nertwork
Faulted bus
Connection point
150 MW 0 MVAR
132 kV cable
30/132 kV
Four 30 kV cable sections
Inside of wind farm:
30 kV Sea-cables
Offshore platform
0.7/30 kV
WT generator
2 MW rated power
WT 10 WT 20 WT 30 WT 40 WT 50 WT 60 WT 70 WT 80
WT 09
WT 08
WT 07
WT 06
WT 05
WT 04
WT 03
WT 02
WT 01
1.5 MW
1.6 MW
1.7 MW
1.8 MW
1.9 MW
2.0 MW
2.0 MW
2.0 MW
Incomin
g
wind
Figure 29.1 Aggregated model of large offshore wind farm with 80 wind turbines (WTs)
Reprinted from Electrical Power and Energy Systems, volume 25, issue 1, V. Akhmatov,
H. Knudsen, A. H. Nielsen, J. K. Pederson and N. K. Poulsen, ‘Modelling and Transient Stability
of Large Wind Farms’, pp. 123–144, copyright 2003, with permission from Elsevier
Wind Power in Power Systems 657
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 658 – [653–676/24]
17.12.2004 10:52PM
and can additionally be excited by generator-side converters. The PMGs are grid-con-
nected through the frequency converters. This means that the PMGs and the power grid
are separated by the DC link. This is the reason why there is no reactive power exchange
between the PMG and the power grid. The power system regards wind turbines of this
concept as grid-side converters supplying electric power. During normal operation, Type
C and D wind turbines can be set not to exchange reactive power with the power grid.
According to the Danish specifications for connecting wind farms to transmission
networks (Eltra, 2000), large wind farms have to be reactive-neutral towards the
transmission power network at the connection point. This means that the reactive power
exchanged between the wind farm and the transmission system must be around zero,
independent of the operational point of the wind farm. This may require the incorpor-
ation of a bank of capacitors and reactors to impose static control of the reactive power
of the large wind farm. These capacitor and reactor banks can be incorporated either at
the connection point onshore or on the offshore platform (with the tertiary trans-
former). In this study, the static compensation units are placed offshore. In the case of
Type A and B wind turbines, it will be necessary to incorporate capacitors for covering
reactive absorption of the induction generators. Type C and D wind turbines will,
rather, require reactors to absorb reactive power produced by the sea-cables (charging).
29.2.2 Faulting conditions
The short-circuit capacity, S
K
, of the transmission power network at the connection
point of the wind farm is 1800 MVA. In all simulations, the distu rbance is a three-
phased, short-circuit fault applied to the faulted node of the transmission power system.
The fault lasts 150 ms. The fault is cleared by tripping the lines that are connected to the
faulted node. When the fault is cleared, S
K
is reduced to 1000 MVA. The line tripping
itself does not lead to voltage instability. This ensures that the short-circuit fault can be
the reason for a possible voltage instability.
The large wind farm is designed according to Danish specifications (Eltra, 2000),
which require the voltage to reestablish after the short-circuit fault in the transmission
power network without any subsequent disconnection of the wind turbines.
29.3 Fixed-speed Wind Turbines
In this analysis, the wind farm consists of 80 wind turbi nes of Type A2. Table 27.1
(page 608) gives the main generator data of the wind turbines and Table 29.1 includes
the shaft system data. The shaft system data have been estimated from the validating
experiment described in Section 27.2.2.
Table 29.1 Shaft system of a 2 MW Type A wind turbine
Parameter Value Parameter Value
Rated power (MW) 2 Turbine rotor inertia (s) 2.5
Generator rotor inertia (s) 0.5 Shaft stiffness (p.u./el.rad) 0.3
658 Aggregated Modelling and Short-term Voltage Stability
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 659 – [653–676/24]
17.12.2004 10:52PM
A regular control system of active stall is applied in order to optimise the power output
in moderate winds and in order to keep the wind turbines at rated operation during wind
speeds that are above the rated wind speed. The active-stall control system compares the
electric power of the generator with its reference value, which is defined in accordance with
the incoming wind, and sets the blade angle to minimise the error signal (Hinrichsen, 1984).
During a short-circuit fault there will be a voltage drop, and the electric power is
reduced as a consequence of this voltage drop. The regular control system of active stall
will interpret this as a lack of power output and keep the optimised value of the blade
angle. That means that active-stall wind turbines will operate with fixed blade angles
during the grid fault (i.e. as stall-controlled wind turbines; see Akhmatov, 2001). For the
analysis of voltage stability under such operational conditions active-stall wind turbines
can therefore be represented as fixed-pitch wi nd turbines.
If no dynamic reactive compensation is applied, the grid fault will result in voltage
instability. Figure 29.2 presents the simulated behaviour of voltage, electric and reactive
power and generator rotor speed of selected wind turbines. When the wind turbi nes are
grid-connected, the generator rotor speed, terminal voltage and other electrical and
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
WT 10
WT 50
WT 60
WT 70
WT 80
3.0
2.5
2.0
1.5
1.0
0.5
0.0
–0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
WT 10
WT 50
WT 60
WT 70
WT 80
Time (s)
1.5
1.0
0.5
0.0
–0.5
–1.0
–0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
WT 10
WT 50
WT 60
WT 70
WT 80
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
WT 10
WT 50
WT 60
WT 70
WT 80
1.25
1.20
0.15
0.10
0.05
–0.05
0.00
Electric power (MW)
Reactive power (MVAR) Speed deviation (p.u.)
Voltage (p.u.)
(a)
(c) (d)
(b)
Figure 29.2 Response of a large wind farm to a short-circuit fault: (a) terminal voltage,
(b) generator rotor speed, (c) electric power and (d) reactive power of selected wind turbines
for the case with no dynamic reactive compensation and the occurrence of voltage instability.
Note: For the layout of wind turbines WT 01–WT 80, see Figure 29.2 Parts (a) and (b) reprinted
from Electrical Power and Energy Systems, volume 25, issue 1, V. Akhmatov, H. Knudsen,
A. H. Nielsen, J. K. Pederson and N. K. Poulsen, ‘Modelling and Transient Stability of Large
Wind Farms’, pp. 123–144, copyright 2003, with permission from Elsevier
Wind Power in Power Systems 659
//INTEGRAS/KCG/P AGIN ATION/ WILEY /WPS /FINALS_1 4-12- 04/0470855088_ 30_CHA29 .3D – 660 – [653–676/24]
17.12.2004 10:52PM
mechanical parameters of the individual wind turbines in the wind farm sho w a coherent
fluctuating behaviour. The wind turbines do not oscillate against each other. The
frequency of the fluctuations is the shaft torsional mode, which is 1.7 Hz in this
particular case.
Note that voltage instability will not necessarily cause a voltage collapse. The reason
is that the wind turbines will be tripped by their protective relays if an uncontrollable
voltage decay is registered (Akhmatov et al., 2001). After this trip, the voltage is
reestablished, but immediate power reserves of approximately 150 MW will be required
for this (Akhmatov et al., 2001). A risk of tripping indicates that the solution does not
comply with the specifications (Eltra, 2000).
If a static VAR compensator (SVC) with a rated capacity of 100 MVAR is applied,
the voltage will be reestablished. Figure 29.3 shows the simulated curves of voltage,
electric power and generator rotor speed. Fluctuations of voltage, electric power, speed
and other parameters are damped quickly and efficiently if an SVC unit is applied.
There is no risk of a self-excitation of the large wind farm.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.2 0.3 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
WT 10
WT 50
WT 60
WT 70
WT 80
3.0
2.5
2.0
1.5
1.0
0.5
0.0
–0.5
0.0 0.2 0.3 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
WT 10
WT 50
WT 60
WT 70
WT 80
Time(s)
1.5
1.0
0.5
0.0
–0.5
–1.0
–1.5
–2.0
0.0 0.2 0.3 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
WT 10
WT 50
WT 60
WT 70
WT 80
0.0 0.2 0.3 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
WT 10
WT 50
WT 60
WT 70
WT 80
0.10
0.08
0.06
0.04
0.02
–0.02
0.00
Electric power (MW)
Reactive power (MVAR) Speed deviation (p.u.)
Voltage (p.u.)
(a)
(c)
(d)
(b)
Figure 29.3 Response of large wind farm to a short-circuit fault: (a) terminal voltage,
(b) generator rotor speed, (c) electric power and (d) reactive power of selected wind turbines for
the case with a 100 MVAR static VAR compensation (SVC) unit and voltage reestablishment.
Note: For the layout of wind turbines WT 01–WT 80, see Figure 29.2 parts (a) and (b) reprinted
from Electrical Power and Energy Systems, volume 25, is sue 1, V. Akhmatov, H. Knudsen,
A. H. Nielsen, J. K. Pederson and N. K. Poulsen, ‘Modelling and Transient Stability of
Large Wind Farms’, pp. 123–144, copyright 2003, with permission from Elsevier
660 Aggregated Modelling and Short-term Voltage Stability