From Turbine to Wind Farms - Technical Requirements and Spin-Off Products

34 Fig. 20. Voltage evolution during the field test and the simulation in phase A. Fig. 21. Comparison of the active power during field test and simulation. Fig. 22. Comparison of the reactive power during field test and simulation.
Wind Farms and Grid Codes

35
¿Is the model validated? Yes
P samples with error < 0.1 p.u. 97.50
Q samples with error < 0.1 p.u. 100.00
Table 10. Validation results for the example.
7. Wind farm verification
As it has been shown in section 4.1, if the General Verification Process of the PVVC is
followed, a simulation study must be performed. The simulation tool used to verify wind
installation according to PVVC must permit to model the electrical system components per
phase, because balanced and unbalanced perturbances must be analyzed.
The simulated model to verify the installation must take into account the different
components of the real system, that is: the wind farm, FACTS and reactive compensating
systems, the step-up transformer, the connection line and a equivalent network defined in
PVVC. Fig. 23 shows the one line diagram of the network to be simulated.

Fig. 23. One line diagram of the wind installation network.
The PVVC establishes the external network model equivalent. This equivalent network

Fig. 25. Wind farm modeling.
Considering identical machines the equivalent generator rating is obtained adding all the
machine ratings (García-Gracia et al, 2008):

1
n
e
q
i
i
SS
=
=
∑

1
n
e
q
i
i
PP
=
=
∑
(11)
where S
i
is the i-th generator apparent power and P
i

and the size of the equivalent compensating capacitors is given by:

1
n
e
q
i
i
CC
=
=
∑
(13)
When the aggregated model is used, the difference between the results obtained by the two
models must be negligible. Fig. 26 and Fig. 27 show the results obtained in a example wind
farm. Fig. 26 shows a comparison between the real power obtained by the simulation of a
Circuit n
a) Detailed model
PCC
Transformer
HV/MV
Equivalent
MV/LV
transformer
Equivalent
generator
Equivalent
circuit
b) Aggregated model
PCC

For squirrel cage induction generator, a fifth order model must be used. If there are
manufacturer data available, the behaviour in rated conditions must be checked with a
tolerance of 10% for real and reactive power.
From Turbine to Wind Farms - Technical Requirements and Spin-Off Products

38
If there are not available data, PVVC establishes the data from Table 11, and the rest of
the parameters must be calculated to obtain the rated characteristics of the modelled
machine.

Stator resistance (p.u.) 0.005 – 0.007
Rotor resistance (p.u.) 0.005 – 0.007
Stator leakage reactance (p.u.) 0.1 – 0.15
Rotor leakage reactance (p.u.) 0.04 – 0.06
Magnetizing reactance (p.u.) 4 – 5
Table 11. Squirrel cage induction generator characteristic parameters.
If there are no manufacturer data for the wind turbine inertia, the value to model the wind
turbine is H = 4 s.
For the doubly fed induction generator, the simplyfied model must take into account the
rotor dynamics, to determine the overcurrent tripping of the wind turbine during voltage
dips.
Finally, the simplified model of the full converter generator consists of a constant current
source.
7.3 Evaluation of the wind installation response
Once the system has been modelled, the evaluation simulations must be performed. The test
categories and the operation point prior the voltage dip in the verification process are the
same of the in-field test, shown in Table 3 and Table 6 (section 5.2), but, in the simulation,
the reactive power before the voltage dip must be zero.
In the simulation results, the next requirements must be checked:
1.

Net consumption P < 10% Pn (20 ms) -0.1 p.u.
Average I
r
/I
tot
0.9 p.u.
ZONE C
Net consumption E
r
< 60% Pn * 150 ms -90 ms*p.u.
Net consumption I
r
< 1.5 I
n
(20 ms) -1.5 p.u.
Table 12. Power and energy requirements for three phase voltage dips in the General
Verification Process.

Two phase faults OP 12.3 requirements
ZONE B
Net consumption E
r
< 40% Pn * 100 ms -40 ms*p.u.
Net consumption Q < 40% Pn (20 ms) -0.4 p.u.
Net consumption E
a
< 45% Pn * 100 ms -45 ms*p.u.
Net consumption P < 30% Pn (20 ms) -0.3 p.u.
Table 13. Power and energy requirements for isolated two phase voltage dips in the General
Verification Process.

Gamesa Eólica, S.A. Patent WO/2006/108890. Voltage sag generator device. Sag-swell and
outage generator for performance test of custom power devices
Gamesa Innovation and Technology, S.L. Patent WO/2006/106163. Low-Voltage dip
generator device.
García-Gracia, M.; Comech, M.P.; Sallán, J. & Llombart, A. (2008) Modelling wind farms for
grid disturbance studies. Renew Energy (2008), doi:10.1016/j.renene.2007.12.007.
García-Gracia. M.; Comech, M.P.; Sallán. J.; Lopez-Andía, D. & Alonso, O. (2009). Voltage
dip generator for wind energy systems up to 5 MW, Applied Energy, 86 (2009) 565–
574, doi:10.1016/j.apenergy.2008.07.006
Jauch, C.; Sørensen, P.; Norhem, I. & Rasmussen, C. (2007). Simulation of the impact of wind
power on the transient fault behaviour of the Nordic power system. Electric Power
Syst Res 2007;77:135-44.
Khadkikar, V. ; Aganval, P.; Chandra, A.; Bany A.O. & Nguyen T.D. (2004). A Simple New
Control Technique For Unified Power Quality Conditioner (UPQC), 11th
International Conference on Harmonics and Quality of Power
López, J.; Gubía, E.; Olea, E.; Ruiz, J. & Luis Marroyo, L. (2009). Ride Through of Wind
Turbines With Doubly Fed Induction Generator Under Symmetrical Voltage Dips.
IEEE Transactions On Industrial Electronics, Vol. 56, No. 10, Oct 2009
Molinas, M.; Suul, J.A. & Undeland, T. (2008). Low Voltage Ride Through of Wind Farms
With Cage Generators: STATCOM Versus SVC. IEEE Transactions On Power
Electronics, Vol. 23, No. 3, May 2008
Morren, J. & de Haan, S.W.H (2005) .Ridethrough of wind turbines with doubly fed
induction generators during a voltage dip. IEEE Trans. Energy Convers. vol. 20, no.
2, pp. 435-441, Jun. 2005
Morren, J. & de Haan, S.W.H. (2007) Short-Circuit current of wind turbines with doubly fed
induction generator. IEEE Trans. On Energy convers, vol. 22, no. 1, march 2007
Muyeen, S.M.; Takahashi, R.; Murata, T.; Tamura, J.; Ali, M.H.; Matsumura, Y.; Kuwayama,
A. & Matsumoto, T. (2009). Low voltage ride through capability enhancement of
wind turbine generator system during network disturbance. IET Renew. Power
Gener., 2009, Vol. 3, No. 1, pp. 65–74, ISSN 1752-1416

fundamental-frequency, positive-sequence voltages and currents; this is because these last
quantities determinate generators working and electromechanical stability. The IEEE
Standard 1459-2010 explicitly holds one of these theories, due to A.E. Emanuel. The p-q-r
theory, developed by Akagi and others, also establishes fundamental-frequency, positive-
sequence active and reactive powers. The Unified Theory described in this Chapter gives
one more step in front of the two above mentioned theories and decomposes fundamental-
frequency, positive-sequence active and reactive powers and currents into two quantities: a)
due to the active and reactive loads and b) caused by the unbalances. According to the
Unified Theory unbalances can originate additional active and reactive powers and currents
which can have the same or different sign of those due to active and reactive loads and,
therefore, total active and reactive powers and currents can be increased or decreased. This
active and reactive powers and currents decomposition can deliver important
complementary information for verifying accomplishment of the grid code requirements
and to regulate wind generators in order to win without disconnection transitory
perturbations, such as voltage dips.
In this Chapter, the two above indicated fundamental-frequency, positive-sequence active
and reactive components of powers and currents are expressed and their properties are
established. Formulations of these quantities are applied on actual wind farms to verify
some European Grid Code requirements, focusing on the Spanish grid code, and their
results are compared with those obtained from other power approaches.
From Turbine to Wind Farms - Technical Requirements and Spin-Off Products

42
Conclusions show that power and current formulations established in this Chapter are
important tools to analyze wind farms working in normal operation and in presence of
transitory disturbances, and these formulations can be proposed for a future grid code
harmonisation.
2. Active and reactive powers and currents formulations applied to wind
farms
Figure 1 schematically shows the equivalent circuit of a wind generator connected to the

by Fourier’s analysis are unbalanced, in general, and their CRMS line to line values
(
,,
A
BBCCA
VVV) can be decomposed into the positive-sequence (
A
B
V
+
) and the negative-
sequence (
A
B
V
−
) components, by Stokvis-Fortescue:

2
2
AB AB AB
BC BC BC AB AB
CA CA CA AB AB
VV V
VV V aV aV
VV V aV aV
+−
+
−+−
+

the load admittances (
,,
A
BBCCA
YYY):

2
2
()
()
()
AB AB AB AB AB AB
BC BC BC BC AB AB
CA CA CA CA AB AB
IYVYV V
IYVYaV aV
IYVYaV aV
+−
+
−
+
−
=⋅=⋅ +
=⋅=⋅ +
=⋅=⋅ +
(3)
These currents are unbalanced, in general, and thus their symmetrical components are, by
Stokvis-Fortescue:

A

−
=++= (5)
-
Basic unbalance admittance for the negative-sequence,

2
1
3
()
i
iABBCCAi
YYaYaYY
α
−
=++= (6)
-
Basic unbalance admittance for the positive-sequence,

2
1
3
()
h
hABBCCAh
YYaYaYY
α
−
=++ = (7)
Positive admittance (
e

+−
+−
−
== (8)
Fundamental positive-sequence line currents (
,,
A
BC
III) supplied by the wind-generator
showed in fig. 1 are unbalanced have the following general expression, from (4) and (8):

30º
33()
A
AB A e u i
II VYY
δ
++ +
−
=
=⋅+⋅ (9)
where

AB
uu
AB
V
V
α
α

(11)
being
cos
ee e
GY
α
=⋅ the load positive conductance, the real part of the positive admittance
(
e
Y ). The above current is 0º dephased with the fundamental positive-sequence phase to
ground voltage (
A
V
+
) and it transfers the useful power (positive-sequence active power, P
+
)
produced by the wind-generator. Active fundamental positive-sequence line current may be
decomposed into two components too, as it is appreciated from (11):

3cos 3
3cos( )
Aaa e e A e A
A
au u i i A
IY VGV
IY V
α
δααα
++

r
I
+
) is the component of
A
I
+
90º
dephased with respect to
A
V
+
, which transfers the positive-sequence reactive power (Q
+
).
General expression of this current is, from (9):
Active and Reactive Power Formulations for Grid Code Requirements Verification

45

3(sin sin( ))
3( sin( ))
Ar A e e u i i
Aeui i
IjVY Y
jV B Y
αδ ααα
δααα
++ −+
+−+

+
−+ +
=− ⋅ ⋅ =
=⋅⋅ −−⋅
∓
(14)
First component,
A
rr
I
+
, transfers the positive-sequence reactive power with balanced
voltages (
r
Q
+
); thus, this current delivers the load reactive power (negative sign of this
quantity in (14) corresponds with inductive loads and positive sign is for capacitive loads).
Second component,
A
ru
I
+
, represents the increasing (positive or negative) of the reactive
power caused by the voltage and load (grid) unbalances (
u
Q
+
).
2.1.2 Unified theory’s active and reactive powers

39
39cos()
A
Aa A e u i i a u
aAAaa eA
uAAauui iA
PVI VG Y PP
PVI GV
PVI Y V
δααα
δααα
++++ +− ++
+++ +
+++ +− +
=⋅=⋅+⋅⋅ −+=+
=⋅=
=⋅=⋅⋅ −+⋅
(16)
a
P
+
is the positive-sequence active power supplied by the wind-generator under positive-
sequence balanced voltages; thus, it may be defined as the positive-sequence active power
due to the load consumptions. This quantity measures the active power which is
transformed under the best efficiency and power quality conditions.
u
P
+
represents the
increasing of the positive-sequence active power produced by the voltage and load

⋅= ⋅⋅ +⋅⋅ −+=
=⋅±+⋅⋅−+=+
(17)
From Turbine to Wind Farms - Technical Requirements and Spin-Off Products

46
Positive-sequence reactive power characterizes the main magnetic field of the wind-
generator and it holds two components, due to the reactive loads (
r
Q
+
) and caused by the
unbalances (
u
Q
+
):

*22
*2
39sin9
39sin()
rAArr eeA eA
uAAru ui iA
QVI jY V jBV
QVI jY V
α
δ ααα
+
++ + +

appreciated in the grid code text, such as will be seen in the next section. Those active and
reactive formulations are obtained from Budeanu´s approach, applied to sinusoidal circuits,
and they are included into the IEEE Standard 1459-2010.
Active and reactive currents supplied by the wind-generator (
az
I
,
rz
I
, z=A,B,C) are the
traditionally known fundamental-frequency line current 0º and ± 90º respectively dephased
with respect to its fundamental phase voltage (
z
V
),

22
zz
az z z z rz z z z
zz
PQ
IGV V IBV
j
V
VV
=⋅= =⋅=∓
(19)

Active current transfers the active power of each phase (
z

+
) described in the before section are
respectively included in the above quantities, but also active and reactive powers expressed
by (20) contain quantities due to the fundamental-frequency negative-sequence voltages and
currents (
P
-
, Q
-
).
Active and Reactive Power Formulations for Grid Code Requirements Verification

47
3. Grid code requirements
Grid codes established by the different countries provides the minimum operation and
security requirements of the wind farms installations connected to the Electric Network in
order to guarantee the supply continuity in presence of voltage dips. The Spanish Operation
Procedure O.P. 12.3, which constitutes the present Spanish Grid Code, establishes wind
farms and all their components must be able to withstand, without disconnection, transient
voltage dips at the grid point of common coupling caused by three-phase, two-phase and
single-phase faults within the area described by the voltage-time characteristic showed in
fig.2a. That characteristic or LVRT (Low Voltage Ride Through) requirements has been
recently modified by the draft of the Spanish Operation Procedure O.P. 12.2 by increasing
the allowed depth of the voltage drop up to zero during the first 150 ms after the beginning
of the disturbance (fig.2b), similar to the LVRT requirements of the German Grid Code from
E.ON Netz, represented in fig.2c. Fig. 2. Low Voltage Ride Through requirements: (a) Spanish O.P. 12.3, (b) Spanish O.P. 12.2
(draft), (c) E.ON Netz

unbalanced voltage dips