AckermannTh. (ed) Wind Power in Power Systems
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bridges up to the voltage value that is equal to the value of the line-to-line voltage
magnitude of the PMG at no-load, which is 966 V. This takes only a few milliseconds
and, during this time, the machine current is reduced to zero. That the DC link capacitor
is charged means that the machine current going through the generator reactance cannot
be disrupted instantly. The magnetic energy accumulated in the generator reactance at the
given machine current, before the converter blocking is started, is transformed into the
electric energy of the charged DC link capacitor (Akhmatov, 2002).
The grid-side converter does not supply electric power to the network, but controls
reactive power and voltage. This is similar to the operation of a Statcom. There are restric-
tions on this controllability because of the limited power capacity of the grid-side converter.
At time t ¼T
3
, the fault is cleared. Shortly after, at t ¼T
4
, the generator converter is
synchronised and restarted. After a short while, the wind turbine operation will be
reestablished. In our example, this takes less than one second, when t is between T
5
and
T
6
. However, there are no general requirements regarding how fast the wind turbines
1.6 2.5
2.0
1.5
1.0
0.5
0.0
–0.5
1.4
1.2
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
1.0
0.8
0.6
0.4
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0.2
0.0
Time (s)
Time (s)
Time (s)
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
2.5
2.0
1.5
1.0
0.5
0.0
–0.5
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Voltage (p.u.)Voltage (p.u.)
Electric power (MW)Electric power (MW)
WT 01: DC link voltage
WT 01: terminal voltage
WT 01: Generator power
WT 01: Reference power
WT 10
WT 50
WT 60
WT 70
WT 80
WT 10
WT 50
WT 60
WT 70
WT 80
T
1
T
2
T
3
T
4
T
6
T
1
T
2
T
3
T
4
T
6
T
5
(a) (b)
(c) (d)
Figure 29.8 Response of a large wind farm with permanent magnet generators (PMGs) and full-
load converters to a short-circuit fault: (a) terminal voltage of grid-side converter and DC link
voltage, (b) generator power and its reference, (c) terminal voltage of grid-side converters, and
(d) electric power supplied by grid-side converters of selected wind turbines; voltage is reestablished
without use of dynamic reactive compensation. Note: For the Layout of wind turbines WT 01–
WT 80, see Figure 29.2. Reprinted from Akhmatov. V., Analysis of Dynamic Behaviour of
Electric Power Systems with Large Amount of Wind Power, Ph.D dissertation, Technical
University of Denmark, Kgs. Lyngby, Denmark, copyright 2003, with permission from the
copyright holder
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have to reestablish operation after the restart of the converter. In general, it may take up
to several seconds to reestablish ope ration of a large wind farm.
Voltage is reestablished without using dynamic reactive compensation units. One of
the reasons for this is that the reactive controllability of the frequency converters is used
during the transient event. Figure 29.8 shows the sim ulated behaviour of the terminal
voltage and the generator power of the selected wind turbines operating at different
operational points. The simulation results do not indicate that there is any risk of
mutual interaction between the frequency converters of the different wind turbines.
The variable-speed wind turbines equipped with PMGs and full-load converters show a
coherent response during the grid fault.
29.7 A Single Machine Equivalent
The simulated behaviour of a wind turbine operating at the rated operational point will be
representative of the collective response of the large wind farm at rated operation. The
reason is that the wind turbines in the large wind farm show a coherent response when
subjected to a transient event in the power system. Also, the rated operation corresponds
to the worst case with respect to maintaining voltage stability of Type A and B wind
turbines. During rated operation, Type A and B wind turbines are closest to the level of
excessive overspeeding, and the induction generators absorb most reactive power.
The rated operation will also be the worst case regarding the risk of a converter
blocking in the case of Type C and D wind turbines. This is because the machine current
and the grid-side converter current are both closest to their respective relay settings
during rated operation (Akhmatov, 2003a). It is likely that there is no risk of mutual
interaction between the converter control systems of variable-speed wind turbines. This
is what is commonly expected regarding properly tuned control systems of converters.
In this case, a large wind farm can simply be represented in the analysis of voltage
stability by a single machine equivalent. A single machine equivalent means that a single
wind turbine model represents a large wind farm. The following assumptions apply here:
.
The power ca pacity of the single machine equivalent is the sum of the power capacities
of the wind turbines in the wind farm (Akhmatov and Knudsen, 2002).
.
The power supplied by the single machine equivalent is the sum of the power of the
wind turbines in the wind farm (Akhmatov and Knudsen, 2002).
.
The reactive power of the single machine equivalent at the connection point is zero
according to Danish specifications (Eltra, 2000).
.
The mechanism of accumulation of potential energy by the shaft systems of the wind
turbines and the shaft relaxation process at the grid fault have to be taken into account
in the case of Type A and B wind turbines (Akhmatov and Knudsen, 2002). This has an
effect on the behaviour of the generator rotor speed. Voltage instability relates to
excessive overspeeding of fixed-speed wind turbines (Akhmatov et al., 2003).
.
The mechanism relating to shaft twisting and relaxing mentioned in the item above is
not relevant in the case of Type C wind turbines. Electric and reactive power are
controlled independent of each other. Therefore, dynamic behaviour of the generator
speed and the voltage are decoupled in this type (Akhmatov, 2002).
672 Aggregated Modelling and Short-term Voltage Stability
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.
The risk of mutual interaction between the converter control systems of Type C and D
wind turbines is eliminated by efficient tuning of the converter control (Slootweg and
Kling, 2002).
.
Similar arguments also apply to Type D wind turbines, except in special situations
(Westlake, Bumby and Spooner, 1996).
Using single machine equivalents instead of detailed models of wind farms with
representations of a large number of wind turbines can reduce the complexity of the
analysis of voltage stability. The focus is on the incorporation of large wind farms into
large power systems. This simplification is also reasonable because conventional power
plant units are commonly represented in the analysis of voltage stability by their
lumped, single machine equivalents. It is also an advantage if the power system model
is already sufficiently complex and contains a number of power plants, including their
control, consumption centres, parts of the transmission and distribution networks, their
static and dynamic reactive compensation units and so on (Akhmatov, 2002, 2003a).
29.8 Conclusions
It is possible to implement aggregated models of large wind farms with a large number
of electricity-producing wind turbines and their control systems into simulation tools
for the analysis of (short-term) voltage stability. In this chapter this has been illu-
strated with an example that includes a detailed representation of an offshore wind
farm consisting of 80 wind turbines. The analysis of voltage stability has included the
representations of the four main concepts of modern wind turbines: Type A2 fixed-
speed, active-stall wind turbines equipped with induction generators, Type B1 pitch-
controlled wind turbines equipped with induction generators with VRR, Type C1
variable-speed, pitch-controlled w ind turbines equipped with DFIG and partial-load
frequency converters, and Type D1 variable-speed wind turbines equipped with PMG
and frequency converters.
It has been demonstrated that there is practically no risk of mutual interaction
between the wind turbines and their control systems (the converters) in large wind
farms. The wind turbines do not oscillate against each other. The wind turbines show
a coherent response when the power system is subjected to a transient short-circuit fault.
For the analysis of short-term voltage stability in connection with the incorporation
of large wind farms into large power systems the wind farms can be rep resented by single
machine equivalents. This means that the wind farm is represented by a single wind
turbine model of the chosen concept and with rescaled rated power capacity. Com-
monly, the worst case will arise when the wind farm is at rated operation.
References
[1] Akhmatov, V. (2001) ‘Note Concerning the Mutual Effects of Grid and Wind Turbine Voltage Stability
Control’, Wind Engineering 25(6) 367–371.
[2] Akhmatov, V. (2002) ‘Modelling of Variable-speed Wind Turbines with Doubly-fed Induction Generators
in Short-term Stability Investigations’, presented at 3rd International Workshop on Transmission Net-
works for Offshore Wind Farms, Stockholm, Sweden.
Wind Power in Power Systems 673
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[3] Akhmatov, V. (2003a) Analysis of Dynamic Behaviour of Electric Power Systems with Large Amount of
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[5] Akhmatov, V. (2004) ‘An Aggregated Model of a Large Wind Farm with Variable-speed Wind Turbines
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[6] Akhmatov, V., Knudsen, H. (2002) ‘An Aggregated Model of a Grid-connected, Large-scale, Offshore
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[7] Akhmatov, V., Knudsen, H., Nielsen, A. H., Poulsen, N. K., Pedersen, J. K. (2001) ‘Short-term Stability
of Large Wind Farms’, presented at European Wind Energy Conference EWEC-2001, Copenhagen,
Denmark, paper PG3.56, 1182-6.
[8] Akhmatov, V., Knudsen, H., Nielsen, A. H., Pedersen, J. K. Poulsen, N. K. (2003) ‘Modelling and
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[9] Akhmatov, V., Nielsen, A. H., Pedersen, J. K., Nymann, O. (2003b) ‘Variable-speed Wind Turbines with
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[10] Edstro
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[12] Feijo
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[13] Grauers, A. (1996) ‘Design of Direct-driven Permanent-magnet Generators for Wind Turbines’, Tech-
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[14] Hinrichsen, E. N. (1984) ‘Controls of Variable Pitch Wind Turbine Generators’, IEEE Transactions on
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[15] Jenkins, N. (1993) ‘Engineering Wind Farms’, Power Engineering Journal 4 (April) 53–60.
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Netherlands, Paper 226.
[17] Kristoffersen, J. R., Christiansen, P. (2003) ‘Horns Rev Offshore Wind Farm: Its Main Controller and
Remote Control System’, Wind Engineering 27(5) 351–360.
[18] Noroozian, M., Knudsen, H., Bruntt, M. (1999) ‘Improving a Wind Farm Performance by Reactive
Power Compensation’, presented at IEEE PES Summer Meeting, Singapore.
[19] Pena, R. S., Cardenas, R. J., Asher, G. M., Clare, J. C. (2000) ‘Vector Controlled Induction Machines for
Stand-alone Wind Energy Applications’, in Conference Record of the 2000 IEEE Industry Applications
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[20] Røstøen, H. Ø., Undeland, T. M., Gjengedal, T. (2002) ‘Doubly-fed Induction Generator in a Wind Turbine’,
presented at the IEEE/CIGRE Workshop on Wind Power and the Impacts on Power Systems, Oslo, Norway.
[21] Saad-Saoud, Z., Jenkins, N. (1995) ‘Simple Wind Farm Model’, IEE Proceedings on Generation, Trans-
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[22] Schauder, C., Mehta, H. (1999) ‘Vector Analysis and Control of Advanced Static VAR Compensators’,
IEE Proceedings-C 140(4) 299–306.
[23] Slootweg, J. G., Kling, W. (2002) ‘Modelling of Large Wind Farms in Power System Simulations’, in
IEEE Power Engineering Society Summer Meeting, Chicago, U.S.A., Volume 1, Institute of Electrical and
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[24] Slootweg J. G., de Haan, S. W. H., Polinder, H., Kling W. (2002) ‘Aggregated Modelling of Wind Parks
with Variable Speed Wind Turbines in Power System Dynamics Simulations’, presented at the 14th Power
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[25] Spooner, E., Williamson, A. C. (1996) ‘Direct Coupled, Permanent Magnet Generators for Wind Turbine
Applications’, IEE Proceedings on Electrical Power Applications 143(1) 1–8.
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[27] Westlake, A. J. G., Bumby, J. R., Spooner, E. (1996) ‘Damping the Power-angle Oscillations of a
Permanent-magnet Synchronous Generator with Particular Reference to Wind Turbine Applications’,
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[28] Yamamoto, M., Motoyoshi, O. (1991) ‘Active and Reactive Power Control for Doubly-fed Wound Rotor
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Index
Absolute power constraint 136
Active management 462–3
Active management control
strategies 464–5
Active power 45, 48
see also Power, active
Active power control 122
Active power generation
curtailment 464, 465
Active stall 55, 57, 614, 659
Active stall control 55, 58, 346, 532,
618, 662
Advanced wind power prediction
tool 367, 372–6
Aerodynamic
modelling 525, 526–34, 550–1
representation 528, 533–4
system 526, 535
Aeroelastic code 534
Aeroelastic code algebraic
variables 538
Aggregated wind farm model 656–8
Aggregation of wind power
production 36–8, 150
Air density 34, 55, 371, 452, 527, 562
Ancillary services 146, 147, 224, 461,
475, 476, 493, 540
Angle of attack 344, 528–9
ANN, see Artificial neural network
Apparent power 81–4, 86, 87, 103, 106,
416–17, 490, 594, 622
Artificial neural network 367
Asynchronous generator 32, 48, 50, 66,
71, 106, 109–10, 292, 294, 588
see also Induction generator
Average wind speed 80, 82, 87, 98, 103,
324, 365, 560, 564
AWPT, see Advanced wind power
prediction tool
Backup voltage operation 243, 246,
251, 253
Balance control 136, 137, 146, 209
Balancing market 49, 395, 403–5
costs for wind power 222, 387
impact on wind power 165, 403–5
Balancing power 159, 160, 209, 404, 405
Base values 541, 543, 579, 593
BEM, see Blade element momentum
method
Betz’s limit 527
Blade angle 344, 528–9, 533, 535,
538–40, 605, 614, 618, 626, 655,
659, 662–3
Blade element momentum method 534
Bottleneck 156, 161, 236, 238, 239, 254,
447, 448, 449, 450, 453
Braking torque 538
Wind Power in Power Systems Edited by T. Ackermann
Ó 2005 John Wiley & Sons, Ltd ISBN: 0-470-85508-8 (HB)
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Capacitance 264, 343, 361, 414, 416, 438
Capacitor 50, 62, 67, 73, 75, 81, 86, 110,
260, 264–5, 266–7, 268, 269–74,
278–9, 292, 294, 295, 340, 342, 346,
355, 361, 413, 416, 418–19, 423, 426,
444, 621, 623, 637, 655, 657, 670–1
Capacitor bank 54, 57, 58, 60, 67, 72–3,
93, 106, 266, 339, 346, 355, 356, 360,
363, 415, 417, 423, 426, 445, 551
Capacity credit 162, 163–4, 165, 170,
171–4, 181–2
Capacity factor 39–40, 149, 263, 314
Cascading Voltage Collapse 275
CHP, see Combined heat and power
CO
2
Denmark 228–9
emissions 27–8, 162, 231
Coincident Generation 162, 261–4, 282
Combined heat and power (CHP) 149,
201, 227, 380, 385, 396, 419, 510
Congestion management 238, 443
see also bottlenecks
Connection charges 384, 387–90, 409
Connection requirements, see Tec hnical
interconnection requirements
Constant power 435, 532, 541, 549
Constant speed 47, 48, 66, 420, 422,
423, 426, 430, 533, 557, 559, 562–3,
564, 567–8, 576, 582, 583, 592, 631,
632–9, 641, 643, 645, 646
Control area 157, 208, 233, 236, 238, 240,
244, 248–9, 252, 254, 372, 375, 635
Control system 43, 45, 76, 83, 90, 108,
115, 136, 232, 266, 277, 290, 301,
314, 318, 386, 390, 428, 526, 535–40,
547–50, 588, 598, 601, 607, 655, 659,
662, 665–8, 670, 672–3
Control value 170, 174–7, 180, 182–8
Converter
capacity 423
protection 75, 665
Coordinate transformation 591, 592
Correlation between load and wind 158
Cos ’ 246, 417, 435–6
Cost
network connection 384–90
network upgrade 384–90
system operation 390–5
Cost–benefit analysis 498
Critical clearing time 634
Crowbar firing 244, 250
Current 29–31, 42
Current-carrying capacity 434–5, 438,
439, 443, 445
Curtail generation 161, 263
Curtailment payments 262, 280
Cut-in wind speed 34, 38–9, 83, 104, 174
Cut-out wind speed 35–6, 38–9, 174
Daily peak 32–3
Damped grid oscillation 265
Damping 240, 549, 596, 623, 625, 631,
643, 646–8, 666
Danish Meteorological Institute 370
DC offset 538, 610, 621–3
DC link 68, 333, 588–589
Deep connection charges 387–8, 390, 409
DEFU 111, 118–19, 121, 128
Delta control 137
Design tip-speed ratio 21–2, 54, 528,
529, 530, 562, 568, 573
Deutscher Wetterdiens t (German weather
service) (DWD) 381
DFIG, see Doubly-fed induction
generator
Diodes 60, 73
Direct component 571, 575, 576, 579
Direct-drive synchronous generator
428, 432, 576, 582
Disconnection, nonselective,
see Nonselective disconnection
Distributed Control 224, 279
Distributed Generation 48, 116, 164,
201, 224, 262, 299, 387, 419–20,
461, 475
Distribution network 116–18, 121, 124,
128, 144, 165, 259, 300, 316, 384–8,
419, 461–8, 472, 474–5, 481, 512,
612, 673
Disturbance reserve 146, 157
Diurnal variation of wind 149, 151,
155, 336–7
678 Index
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DMI, see Danish Meteorological
Institute
Doubly-fed induction generator 28, 65,
67, 68–9, 537, 552, 587–602,
665–7
Drag device 8
Drive train 32, 60, 68, 97, 105, 346, 536,
545, 559, 564, 596
Duration curve 150, 220, 321, 448, 451
DWD, see Deutscher Wetterdienst
Dynamic behaviour 128, 240–1, 243–4,
252, 296, 428, 556, 584, 622, 629,
635, 636, 641, 670
Dynamic stability 287, 526, 538–9,
548–9, 551
Dynamic stability model 538
Economic aspects 383–409, 455–7
Economic efficiency 395
Efficiency 155, 160, 507–10
Eigenvalue 549–50, 630–1, 645–647,
648, 650
Eigenvectors 549–50
Electrical engineering basics 29–32
Electrical torque 566, 570–1, 595, 596,
598, 646
Electricity market 144, 155, 156, 159,
180, 204–7, 231, 365, 393, 395, 515
Electrolysis 506–9, 511
Electromagnetic transients
program 361, 556
simulation 556–7, 630, 587, 588
Electromechanical transient simulation
556, 588, 630
Eltra grid code 104
Eminent Domain 280
EMTP 361, 547, 548
see also Electromagnetic transients,
program
EN 50160 86, 88, 89, 91, 92, 93, 338,
342, 349
Energy payback time 20
Energy storage 62, 73, 160, 260, 263,
282, 303, 305, 307, 308, 309, 322,
458, 505
Environmental issues 20–1
E.ON grid code 120, 244
E.ON Netz 104, 119–20, 175, 233, 234,
236, 238, 239, 240, 242, 244, 249,
254, 372, 373, 635
eWind 370–1
Extra high-voltage system 120
FACTS 241, 251, 259, 260–1, 274,
277–9, 415, 417, 426, 444, 646
Fast reserve 146
Fast valving 541
Fast voltage variations 88–9
Fault
current 290, 292, 294, 547,
552, 572
resistance 599
three-phase 245, 247, 250, 252, 294,
599, 600, 601
Feed-in law 12 –13
Field-oriented control 597
Fifth-order model 538, 607, 609–11,
613, 623, 625, 626
Firm transmission rights 263
Fixed-speed wind turbine 53–4, 57, 64,
67, 72, 81, 83, 84, 93, 101, 105, 106,
108, 112, 355, 356–7, 358, 363, 446,
531, 537, 538, 539, 540, 551, 552,
603, 605, 613, 619, 622, 631, 658–61,
662, 672
Flexible AC transmission syst ems,
see FACTS
Flicker 352–4
coefficient 82–3, 90, 103
continuous operation 90–1
investigation 551
step factor 83, 111
switching operation 80
Fluctuations of wi nd power
production 31, 154, 156
Flux 538, 565–6, 577, 578, 590–6, 599,
600–1, 606, 646
Flux linkage 566, 569, 590, 601
Forecast 44, 146, 155, 158, 159, 204,
209, 211, 212, 213–15, 223, 226, 234,
237, 238, 251, 366, 368, 370, 371,
373, 374, 375, 379, 380, 393
Index 679
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Frequency
control 49, 121, 123–4, 146, 156,
208–9, 217, 224, 243, 286, 288,
291, 305, 445, 511
converter 58–62, 65, 73, 74–5, 76, 81,
246, 497, 531, 537, 654, 658, 665,
666, 669, 670, 672, 673
deviation 86, 146, 248, 249, 251, 391,
572, 635
domain 561, 630–1, 645
fluctuations 241, 317, 361, 363
regulation 204, 241, 246, 288
stability 239, 240, 244, 248–52
tolerance 131
Fuel cells 219, 309, 505–6, 510–12, 517,
518, 519
Full load hours 39, 149
Full-load converter connected generator
drive 552, 672
Fundamental frequency component 556
Fundamental frequency simulation 630
Funen 26, 199
G59/1 119
G75 119
Gate turn-off thyristor (GTO) 61
Gearbox 21, 22, 48, 59, 60, 66, 69–70,
71, 250, 346, 420–1, 498, 536, 542–3,
545, 546, 550, 557, 564, 588, 589,
604, 618, 631, 632, 670
Generator
direct-driven 498
high voltage 66, 70–1
induction
doubly fed 28, 58, 65, 68–9, 76, 116,
135, 250, 339, 420, 423, 425,
428, 431, 432, 537, 552, 557,
558, 567, 568, 569, 570, 571,
573, 575, 576, 578, 580, 582,
583, 587, 588, 599–601, 632
squirrel cage 57, 65, 66–7, 420–3,
426, 557, 565, 568, 569, 570,
572, 629, 632–5, 646, 650,
665–7
variable slip 68
wound rotor 58, 65, 67–9
rotor 58, 535, 538, 541, 543, 544,
587–601, 605, 609, 612, 623–5,
659–60, 672
switched reluctance 71
synchronous
permanent magnet 65, 70
wound rotor 65, 69–70
system 60, 542
transverse flux 71–2
Generic wind turbine model 525, 553
Geographical distribution 37, 38, 44,
149, 150, 154, 513
Germany 9, 10, 11, 13, 22, 2 6, 27, 28,
62, 99, 104, 112, 116, 119, 120, 140,
154, 171, 201, 207, 225, 229, 233, 234,
236, 240, 241, 254, 366, 367, 370, 372,
376, 377, 378, 385–7, 389–91, 393, 396,
453, 479, 480, 492, 497, 499, 509, 517
Gotland 3, 26, 77, 179, 188, 189, 193,
283–97, 435, 453, 486, 488
Green certificates 13, 15
Grid
code, see Technical interconnection
requirements
failure 253
impedance 32, 102–4
interference 97, 105
investment 170
investment value 170
model 103, 104, 257, 321, 559, 568,
577, 656
offshore 499–500
operation 241, 275, 417
short circuit 572
specifications 31
stability 119, 260, 275, 278, 320, 321,
322
voltage 71, 83, 260, 265–6, 270, 276,
417, 418, 425, 426, 428, 430, 432,
572, 610, 633, 666
weak 257–82
Grid-side converter 68, 75, 658, 666–7,
669, 670, 671, 672
GTO, see Gate turn-off thyristor
Gusts 32, 38, 55, 37, 67, 68, 151, 153,
292, 353, 354, 550, 551, 589
680 Index