SIMULATION MODELS FOR WIND PARKS WITH

VARIABLE SPEED WIND TURBINES

IN EMTP

March 2017

Prepared by:
Ulas Karaagac,
Jean Mahseredjian,
Henry Gras,
Hani Saad,
Jaime Peralta,
Luis Daniel Bellomo
TABLE OF CONTENTS
1 INTRODUCTION ................................................................................................ 7
2 WIND PARKS WITH VARIABLE SPEED WIND TURBINES ............................ 8
2.1 VARIABLE SPEED W IND TURBINES ................................................................... 8
2.1.1 Wind Turbine Aerodynamics .............................................................................. 8
2.1.2 Mechanical System .......................................................................................... 10
2.1.3 Control of Variable Speed Wind Turbines ........................................................ 10
2.2 REACTIVE POWER CONTROL IN W IND PARKS WITH VARIABLE SPEED W IND
TURBINES .............................................................................................................. 11
2.3 FULL SIZE CONVERTER (FSC) W IND TURBINES.............................................. 12
2.4 DOUBLY-FED INDUCTION GENERATOR (DFIG) W IND TURBINES ....................... 14
3 EMTP IMPLEMENTATION............................................................................... 16
3.1 DETAILED AND AVERAGE VALUE MODELS ...................................................... 17
3.2 FSC BASED W IND PARK MODEL IN EMTP-RV ............................................... 19
3.2.1 Wind Park Control System Block ..................................................................... 20
3.2.2 FSC Wind Turbine Electrical System Block ...................................................... 20
3.2.3 FSC Wind Turbine Control System Block ......................................................... 22
3.2.3.1 FSC Machine Side Converter Control .................................................................... 24
3.2.3.2 FSC Grid Side Converter Control........................................................................... 25
3.2.4 FSC Protection System Block .......................................................................... 30
3.2.4.1 Over/Under Voltage Relay and Deep Voltage Sag Detector ................................. 30
3.2.4.2 dc Overvoltage Protection Block ............................................................................ 32
3.2.4.3 Overcurrent Protection Block ................................................................................. 32
3.3 DFIG BASED W IND PARK MODEL IN EMTP-RV.............................................. 32
3.3.1 DFIG Wind Turbine Electrical System Block .................................................... 33
3.3.2 DFIG Wind Turbine Control System Block ....................................................... 34
3.3.2.1 DFIG Rotor Side Converter Control ....................................................................... 35
3.3.2.2 GSC Grid Side Converter Control .......................................................................... 37
4 WIND PARK RESPONSE TO UNBALANCED FAULTS ................................. 40
4.1 FSC BASED W IND PARK RESPONSE TO UNBALANCED FAULTS ........................ 41
4.1.1 Simulation Scenarios M1 and M2 with FSC based Wind Park.......................... 41
4.1.2 Simulation Scenarios N1 and N2 with FSC based Wind Park .......................... 42
4.2 DFIG BASED W IND PARK RESPONSE TO UNBALANCED FAULTS ....................... 43
4.2.1 Simulation Scenarios M1 and M2 with DFIG based Wind Park ........................ 43
4.2.2 Simulation Scenarios N1 and N2 with DFIG based Wind Park ......................... 45
5 AVERAGE VALUE MODEL PRECISION AND EFFICIENY ............................ 47
5.1 120 KV TEST SYSTEM SIMULATIONS .............................................................. 47
5.1.1 Simulation Scenarios M2 - M4 with FSC based Wind Park .............................. 47
5.1.2 Simulation Scenarios M2 - M4 with DFIG based Wind Park ............................. 48
5.2 IEEE 39 BUS SYSTEM SIMULATIONS ............................................................. 49
6 DETAILED WIND PARK MODELS AND AGGREGATED MODEL PRECISION
53
7 REFERENCES ................................................................................................. 57
 Table of Figures
Figure 1 Simplified single-line diagram of a typical wind park ........................................................ 8
Figure 2 Wind power Cp curves ..................................................................................................... 9
Figure 3 Wind turbine model for aerodynamics .............................................................................. 9
Figure 4 Schematic diagram of pitch control ................................................................................. 11
Figure 5 Reactive power control at POI (Q-control function) ........................................................ 12
Figure 6 FSC wind turbine configuration ....................................................................................... 12
Figure 7 Simplified diagram of FSC WT control and protection system ....................................... 13
Figure 8 Schematic diagram of FSC WT control .......................................................................... 13
Figure 9 DFIG wind turbine configuration ..................................................................................... 14
Figure 10 Schematic diagram of DFIG WT control ......................................................................... 15
Figure 11 FSC based wind park device, mask parameters shown in Figure 12 ............................ 16
Figure 12 FSC based wind park device mask ................................................................................ 17
Figure 13 ac-dc-ac converter system block in WT models (detailed model version) ..................... 18
Figure 14 (a) Two-level Converter, (b) IGBT valve ......................................................................... 18
Figure 15 PWM control block .......................................................................................................... 18
Figure 16 ac-dc-ac converter system block in WT models (average value model version) ........... 19
Figure 17 AVM Representation of the VSC .................................................................................... 19
Figure 18 EMTP diagram of the FSC based Wind Park ................................................................. 20
Figure 19 EMTP diagram of “WP Control System” block ............................................................... 21
Figure 20 EMTP diagram of FSC “WT Electrical System” block .................................................... 21
Figure 21 “shunt ac harmonic filter” block ....................................................................................... 22
Figure 22 EMTP-RV diagram of FSC “WT Control System” block ................................................. 23
Figure 23 EMTP-RV diagram of DSRF PLL ................................................................................... 24
Figure 24 EMTP diagram of FSC “PMSG Control” block ............................................................... 24
Figure 25 EMTP diagram of FSC “Grid Control” block ................................................................... 26
Figure 26 GSC arrangement ........................................................................................................... 27
Figure 27 Wind turbine reactive output current during voltage disturbances [13]. ......................... 28
Figure 28 EMTP diagram of “Idq reference limiter” block ............................................................... 28
Figure 29 EMTP diagram of “FRT decision logic” block ................................................................. 29
Figure 30 Sequence extraction using decoupling method. ............................................................. 30
Figure 31 LVRT and HVRT requirements [16] ................................................................................ 31
Figure 32 Over/under-voltage relay and deep voltage sag protection ............................................ 31
Figure 33 dc overvoltage protection block ...................................................................................... 32
Figure 34 Overcurrent protection block ........................................................................................... 32
Figure 35 EMTP diagram of the DFIG based Wind Park ................................................................ 33
Figure 36 EMTP diagram of DFIG “WT Electrical System” block ................................................... 33
Figure 37 EMTP diagram of DFIG “WT Control System” block ...................................................... 34
Figure 38 Flux angle calculation ..................................................................................................... 35
Figure 39 EMTP diagram of DFIG “Rotor Control” block ................................................................ 35
Figure 40 Г representation of induction machine ............................................................................ 36
Figure 41 Conversion at RSC input and output variables ............................................................... 37
Figure 42 EMTP diagram of DFIG “Grid Control” block .................................................................. 37
Figure 43 EMTP diagram of “LVRT boost” block ............................................................................ 38
Figure 44 EMTP diagram of “HVRT boost” block ........................................................................... 38
Figure 45 Negative sequence compensation through GSC ........................................................... 39
Figure 46 120 kV, 60 Hz test system .............................................................................................. 40
Figure 47 PC2 and PS2 of aggregated FSC WT in scenarios M1 and M2 ........................................ 41
Figure 48 P0 and P0 of aggregated FSC WT in scenarios M1 and M2 ........................................... 41
Figure 49 In and Ip of FSC WT based WP in scenarios M1 and M2 ............................................... 42
Figure 50 PC2 and PS2 of aggregated FSC WT in scenarios N1 and N2 ........................................ 42
Figure 51 P0 and Q0 of aggregated FSC WT in scenarios N1 and N2 ........................................... 43
Figure 52 In and Ip of FSC WT based WP in scenarios N1 and N2 ................................................ 43
Figure 53 IG electromagnetic torque in scenarios M1 and M2 ....................................................... 44
Figure 54 IG electromagnetic torque in scenarios M1 and M2 (with larger size GSC) ................... 44
Figure 55 P and Q of aggregated DFIG WT in scenarios M1 and M2 ............................................ 44
Figure 56 In and Ip of DFIG WT based WP in scenarios M1 and M2 .............................................. 45
Figure 57 IG electromagnetic torque in scenarios N1 and N2 ........................................................ 45
Figure 58 P and Q of aggregated DFIG WT in scenarios N1 and N2............................................. 46
Figure 59 In and Ip of DFIG WT based WP in scenarios N1 and N2 ............................................... 46
Figure 60 PC2 and PS2 of aggregated FSC WT in scenarios M2 - M4 ............................................ 47
Figure 61 P0 and Q0 of aggregated FSC WT in scenarios M2 - M4 ............................................... 47
Figure 62 In and Ip of FSC WT based WP in scenarios M2 - M4 .................................................... 48
Figure 63 IG electromagnetic torque in scenarios in scenarios M2 - M4 ....................................... 48
Figure 64 P0 and Q0 of aggregated DFIG WT in scenarios M2 - M4 .............................................. 48
Figure 65 In and Ip of DFIG WT based WP in scenarios M2 - M4 ................................................... 49
Figure 66 IEEE 39 Bus System with Wind Parks............................................................................ 50
Figure 67 PC2 and PS2 of aggregated FSC WT in IEEE 39 bus system simulation ........................ 51
Figure 68 P0 and Q0 of aggregated FSC WT in IEEE 39 bus system simulation ........................... 51
Figure 69 In and Ip of FSC WT based WP in IEEE 39 bus system simulation ................................ 51
Figure 70 IG electromagnetic torque in IEEE 39 bus system simulation ........................................ 52
Figure 71 P0 and Q0 of aggregated DFIG WT in IEEE 39 bus system simulation .......................... 52
Figure 72 In and Ip of DFIG WT based WP in IEEE 39 bus system simulation ............................... 52
Figure 73 EMTP diagram of the 45 x 1.5 MW wind park detailed model given in Figure 46. ......... 53
Figure 74 EMTP diagram of the HV/MV Wind Park Substation ...................................................... 53
Figure 75 EMTP diagram of MV Feeder-1 ...................................................................................... 54
Figure 76 Aggregated FSC based wind turbine device mask ......................................................... 55
Figure 77 Active and reactive power at POI, Wind Park with FSC WTs......................................... 55
Figure 78 Positive and negative sequence currents at POI, Wind Park with FSC WTs ................. 56
Figure 79 Active and reactive power at POI, Wind Park with DFIG WTs ....................................... 56
Figure 80 Positive and negative sequence currents at POI, Wind Park with DFIG WTs ............... 56
 Objective

This document presents generic EMT-type models for full size converter (FSC) and Doubly-fed
induction generator (DFIG) based wind parks (WPs) that can be used for stability analysis and
interconnection studies. These models are developed in EMTP Version 3.4 and above. This document
is also intended to be used for educative purposes at Polytechnique Montréal.

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1 INTRODUCTION
The large scale wind parks (WPs) employ variable speed wind turbines (WTs) in order to increase
energy capture, reduce drive train stresses and comply with grid code requirements. Doubly-fed
induction generator (DFIG) and full size converter (FSC) WTs fall into this category.

Interconnecting a large-scale WP into the bulk power system has become a more important issue
due to its significant impact on power system transient behavior. Failure to perform proper
interconnection studies could lead to not only non-optimal designs and operations of WPs, but also
severe power system operation and even stability problems. Manufacturer-specific models of WPs are
typically favored for the interconnection studies due to their accuracy. However, these WP models have
been typically delivered as black box models and their usage is limited to the terms of nondisclosure
agreements. Utilities and project developers require accurate generic WP models to perform the
preliminary grid integration studies before the actual design of the WP is decided. Accurate generic WP
models will also enable the researchers to identify the potential WP grid integration issues and propose
necessary countermeasures.

This document presents EMT-type models for FSC and DFIG based WPs that can be used for
stability analysis and interconnection studies. In the aggregated WP model, the collector grid and the
WTs are represented with their aggregated models. However, the model includes the wind park
controller to preserve the overall control structure in the WP. The WT and the WP control systems
include the necessary nonlinearities, transient and protection functions to simulate the accurate
transient behavior of the WP to the external power system disturbances.
The first part of this document briefly presents the FSC and DFIG based WPs. The developed
EMTP models are presented in the second part. The last part presents the illustrative simulation
examples.

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2 WIND PARKS WITH VARIABLE SPEED WIND TURBINES
A simplified single line diagram of a typical wind park is shown in Figure 1. In wind parks, WTs are
connected through a step-up transformer (WT transformer) to the medium voltage (MV) collector bus
by means of subterranean cables. The collector bus voltage is stepped up to the high voltage (HV) level
by means of wind park transformer. Depending on the selection of the function, either the reactive power
or voltage or power factor at the point of interconnection (POI in Figure 1) is controlled by a central wind
park controller (WPC) located at wind park substation. The wind park transformer usually contains an
on load tap changer (OLTC) to maintain nominal voltage at MV collector bus.
The available reactive power at the point of interconnection (POI) is usually much less than the
specified WT capacity due to the reactive power losses at the WT transformers, the medium voltage
(MV) collector grid and the wind park transformer. Therefore, reactive power compensation may be
required to fulfill the grid code requirements regarding power factor control [1].

The EMT model presented in this document does not include the wind park transformer OLTC and
any reactive power compensation device (such as Static VAR Compensator).

MV
Feeder F1 WT
Collector Bus

POI HV /MV X
Wind Park
Transformer
HV Grid
+30
X X
Other MV feeders
X

Figure 1 Simplified single-line diagram of a typical wind park

2.1 Variable Speed Wind Turbines

As the size of the WTs increase, the WT technology has switched from fixed speed to variable
speed. The drivers behind these developments are mainly increasing the energy capture, reducing the
drive train stresses and ability to comply with the grid code requirements. Most common configurations
are FSC and DFIG WTs [2].

2.1.1 Wind Turbine Aerodynamics

The wind turbine extracts kinetic energy from the swept area of the blades. The mechanical power
extracted from the wind is given by [2]:
1
Pt   A3 Cp  ,   (1)
2
where  is the air density (approximately 1.225 kg/m 3), A is the swept area of the rotor (m 2),  is
upwind free wind speed (m/s) and Cp is the power coefficient.

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Cp is a characteristic of the WT and is usually provided as a set of curves ( Cp curves) relating Cp to
tip-speed-ratio  with the blade pitch angle  as a parameter, as shown in Figure 2 [3]. The tip-speed-
ratio is defined as
   tR   (2)
where t is the WT rotational speed (rad/s) and R is the blade radius (m).

CPmax Curve

Figure 2 Wind power Cp curves

At a specific wind speed and pitch angle, there is a unique WT rotational speed that achieves the
maximum power coefficient Cp max , hence the maximum mechanical power as shown in Figure 2.

The mathematical model of the WT aerodynamics is shown in Figure 3. In this modeling approach,
the Cp curves of the WT are fitted with high order polynomials on  and  , as follows

n n
Cp  ,     iji j (3)
i1 j1

n n
 Cp  ,     ij i j
i1 j 1

t
tR 
  Cp

Pt
P t  A3Cp  , 
1
2
Figure 3 Wind turbine model for aerodynamics

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2.1.2 Mechanical System
The mechanical system is constituted by the blades linked to the hub, coupled to the slow shaft,
which is linked to the gearbox which multiplies the rotational speed of the fast shaft connected to the
generator. Although the mechanical representation of the entire WT is complex, representing the
fundamental resonance frequency of the drive train using its two mass model is sufficient as the other
resonance frequencies are much higher and their magnitudes are lower [4]. By referring all magnitudes
in the fast shaft (generator side), the state space equations of the two mass system can be written as

   
t  1 Jt  Tt  Dtg t  g  Dt t  K tg t  g  (4)
t  t (5)
     
g  1 Jg K tg t  g  Dtg g  t  Dg g  Tg  (6)
g  g (7)

where t , t , Tt are the rotor speed (rad/s), angular position of the rotor (rad) and the aerodynamic
torque (Nm) of the WT referred to the fast shaft, respectively. g , g , Tg are the speed, angular
position and electromagnetic torque of the generator, respectively. Jt and Dt are the moment of inertia
(kgm2) and absolute speed self-damping coefficient (Nms/rad) of the WT referred to the fast shaft,
respectively. Jg and Dg are the moment of inertia and absolute speed self-damping coefficient of the
generator, respectively. K tg and Dtg are the equivalent spring constant (Nm/rad) and mutual damping
coefficient (Nms/rad), between the WT and the generator, respectively.

2.1.3 Control of Variable Speed Wind Turbines

The control of variable speed WT calculates the generator power output and the pitch angle in
order to achieve extracting the maximum energy from the wind and keeping the WT in safe operating
mode. The WT remains shut down when the wind speed is too low for energy production (i.e. below
cut-in speed cut in ). When the wind speed is above cut in and below rated speed rated , the pitch
angle is kept at zero (   00 ) and the power reference of the WT generator is produced by the MPPT
(maximum power point tracking) function to achieve optimal operation. The conventional method is
calculating the power reference using a cubic function of the turbine angular speed.

Pref  K opt 3t (8)

where


K opt  1 2  Cp max  A R opt 
3
(9)
When the wind speed is above rated , the pitch angle is increased by the pitch controller (see
Figure 4) in order to limit the mechanical power extracted from the wind and reduce the mechanical
loads on the drive train. The pitch controller should ensure zero pitch angle (   00 ) for the wind speeds
below rated [5]. When the wind speed is above cut-off speed cut off , the WT is shut down.

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 g + + K d dt 
+ PI +
+ 1  sT
-
ref
Pg +
+ PI
-
Pset
Figure 4 Schematic diagram of pitch control

2.2 Reactive Power Control in Wind Parks with Variable Speed Wind
Turbines
The active power at the point of interconnection (POI in Figure 1) depends on the wind conditions
at each WT inside the WP and determined by MPPT function (see (8)) when the wind speed is between
cut in and rated . However, according to customary grid code requirements, the WP should have a
central wind park controller (WPC) to control the reactive power at POI.

The WP reactive power control is based on the secondary voltage control concept [6]. At primary

level, the WT controller (WTC) monitors and controls its own positive sequence terminal voltage ( Vwt )
with a proportional voltage regulator. At secondary level, the WPC monitors the reactive power at POI
( QPOI ) and control it by modifying the WTC reference voltage values ( V  ) via a proportional-integral
(PI) reactive power regulator as shown in Figure 5. In Figure 5 and hereafter, all variables are in pu
(unless otherwise stated) and the apostrophe sign is used to indicate the reference values coming from
the controllers.
Although not shown in Figure 5, the WPC may also contain voltage control (V-control) and power
factor control (PF-control) functions. When the WPC is working under V-control function, the reactive
 ) is calculated by an outer proportional voltage control, i.e.
power reference in Figure 5 ( QPOI

 
  VPOI
QPOI  K Vpoi VPOI  (10)

where VPOI is the positive sequence voltage at POI and K Vpoi is the WPC voltage regulator gain.

 is calculated using the active power at POI

When WPC is working under PF-control function, QPOI
( PPOI ) and the desired power factor at POI ( pfPOI ).

When a severe voltage sag occurs at POI (due to a fault), the PI regulator output ( U ) is kept
  QPOI ) to avoid overvoltage following the fault removal.
constant by blocking the input ( QPOI

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Figure 5 Reactive power control at POI (Q-control function)

2.3 Full Size Converter (FSC) Wind Turbines

FSC WT may or may not have a gearbox and a wide range of electrical generators such as
asynchronous, conventional synchronous and permanent magnet can be employed. As all the WT
power is transferred through an ac-dc-ac converter system, the specific characteristics and dynamics
of the electrical generator are effectively isolated from the grid [7].

The considered topology in this paper is shown in Figure 6. It uses a permanent magnet
synchronous generator (PMSG) and the ac-dc-ac converter system consists of two voltage source
converters (VSCs): machine side converter (MSC) and grid side converter (GSC). The dc resistive
chopper is used for the dc bus overvoltage protection. Although not shown in Figure 6, a line inductor
(choke filter) and an ac harmonic filter are used at the GSC to improve the power quality.

Figure 6 FSC wind turbine configuration

The simplified diagram of FSC WT control and protection system is shown in Figure 7. The
sampled signals are converted to per unit and filtered at “Measurements & Filters” block. The input
measuring filters are low-pass (LP) type. “Compute Variables” block computes the variables used by
the FSC WT control and protection system. “Pitch Control” block (see Figure 4) limits the mechanical
power extracted from the wind by increasing the pitch angle when the wind speed is above its rated.
“Protection System” block contains cut-in and cut-off speed relays, low voltage and overvoltage relays,
MSC and GSC overcurrent protections and dc resistive chopper control.

The control of the FSC WT is achieved by controlling the MSC and GSC utilizing vector control
techniques. Vector control allows decoupled control of real and reactive powers. The currents are
projected on a rotating reference frame based on either ac flux or voltage. Those projections are
referred to d- and q- components of their respective currents. In flux-based rotating frame, the q-
component corresponds to real power and the d-component to reactive power. In voltage-based rotating
frame (900 ahead of flux-based frame), the d and q components represent the opposite.

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 The control scheme is illustrated in Figure 8. In this figure, iqm and idm are the q- and d-axis currents
of the MSC, iqg and idg are the q- and d-axis currents of the GSC, Vdc is the dc bus voltage, T is the

electromagnetic torque of the PMSM, and Vwt is the positive sequence voltage at FSC transformer MV
terminal.

In the control scheme presented in Figure 8, the MSC operates in the stator flux reference (SFR)
frame and the GSC operates in the stator voltage reference (SVR) frame. iqm is used to control T , idg

is used to maintain Vdc and iqg is used to control Vwt .

Both MSC and GSC are controlled by a two-level controller. The slow outer control calculates the
reference dq-frame currents ( idm , iqm , idg and iqg ) and the fast inner control allows controlling the
converter ac voltage reference that will be used to generate the modulated switching pattern.

The reference for PMSM electromagnetic torque is given by MPPT control ( T  K opt 2t ) and the
reference for the positive sequence voltage at FSC transformer MV terminal ( V  ) is calculated by the
WPC (see Figure 5).

WT Measurements Compute
& Filters Variables MSC MSC
Variables
Control Command
GSC GSC
Control Command
Pitch Pitch
Control Command
Protection
Chopper ON/OFF
System
WT Breaker Open/Close

Figure 7 Simplified diagram of FSC WT control and protection system

Figure 8 Schematic diagram of FSC WT control

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2.4 Doubly-Fed Induction Generator (DFIG) Wind Turbines
In WTs with DFIG, the stator of the induction generator (IG) is directly connected to the grid and
the wound rotor is connected to the grid through an ac-dc-ac converter system as shown in Figure 9.
The ac-dc-ac converter system consists of two voltage source converters (VSCs): rotor side converter
(RSC) and grid side converter (GSC). A line inductor and shunt harmonic ac filters are used at the GSC
to improve power quality (not shown in Figure 9). A crowbar is used to protect the RSC against
overcurrent and the dc capacitor against overvoltage. During crowbar ignition, the RSC is blocked and
the IG consumes reactive power. To avoid the crowbar ignition during faults, the dc resistive chopper
is widely used to limit the dc voltage. DFIG WT also includes the protection functions presented in
Section 2.3.

Figure 9 DFIG wind turbine configuration

The overall control and protection scheme in DFIG WT is similar to the one in FSC WT shown in
Figure 7. The sampled signals are converted to per unit and filtered at the “Measurements & Filters”
block. The input measuring filters are low-pass (LP) type. The “Compute Variables” block computes the
variables used by the DFIG WT control and protection system. The “Pitch Control” block (see Figure 4)
limits the mechanical power extracted from the wind by increasing the pitch angle when the wind speed
is above its rated. However, the “Protection System” block contains crowbar protection in addition to
the cut-in and cut-off speed relays, low voltage and overvoltage relays, RSC and GSC overcurrent
protections and dc resistive chopper control. It should be noted that, the crowbar protection is not
expected to operate unless the dc resistive chopper protection is deactivated.
The DFIG converter control scheme is illustrated in Figure 10. In this figure, iqr and idr are the q-
and d-axis currents of the RSC, iqg and idg are the q- and d-axis currents of the GSC, Vdc is the dc

bus voltage, P is the active power output of the DFIG, and Vwt is the positive sequence voltage at
DFIG transformer MV terminal. The RSC operates in SFR frame and the GSC operates in SVR frame.

iqr and idr are used to control P and Vwt , respectively. On the other hand, idg is used to maintain the
dc bus voltage ( Vdc ) and iqg is used to support the grid with reactive power during faults.

Both RSC and GSC are controlled by a two-level controller. The slow outer control calculates the
reference dq-frame currents ( idr , iqr , idg and iqg ) and the fast inner control allows controlling the
converter ac voltage reference.

The reference for DFIG active power output ( P ) is given by MPPT control (see (8)). The reference
for DFIG positive sequence voltage ( V  ) is calculated by the WPC (see Figure 5).

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Figure 10 Schematic diagram of DFIG WT control

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3 EMTP IMPLEMENTATION
The developed wind park model setup in EMTP is encapsulated using a subcircuit with a
programmed mask as illustrated in Figure 11 and Figure 12. The model consists of a wind turbine, a
LV/MV wind turbine transformer, equivalent PI circuit of the collector grid and a MV/HV wind park
transformer.
The first tab of the wind park mask enables the user to modify the general wind park parameters
(number of WTs in the WP, POI and collector grid voltage levels, collector grid equivalent and zig-zag
transformer parameters (if it exists)), the general wind turbine parameters (WT rated power, voltage
and frequency), and wind park operating conditions (number of WTs in service, wind speed WPC
operating mode and reactive power (or power factor) at POI).

The second and the third tab is used for MV/HV WP transformer and LV/MV WT transformer
parameters, respectively.

The forth tab is used to modify the parameters of converter control system given below:

- Sampling rate and PWM frequency at WT converters

- WT input measuring filter parameters,

- MSC (or RSC) control parameters,

- GSC control parameters,

- Coupled / Decoupled sequence control option for GSC

The fifth tab is used to modify the parameters of voltage sag, chopper, crowbar (for DFIG only)
and overcurrent protections. The sixth tab is used to modify the WPC parameters.

The associated JavaScript file (DFIG_WP_Parameters.dwj and FC_WP_Parameters.dwj, for

DFIG and FSC based WP, respectively) computes the internal model parameters. It also contains the
data that is not accessible from the mask, such as the data for WT aerodynamics, mechanical system
and pitch control.

The wind farm transformer connection is wye-grounded on the HV side and Delta on the MV side.
The WT transformer connection is wye-grounded on the LV side and Delta on the MV side. In both
transformers the magnetizing branch is located at the Delta connection side.

FFC_WP1

FC AVM
75.015MVA
120kV
Control = Q - control

Figure 11 FSC based wind park device, mask parameters shown in Figure 12

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Figure 12 FSC based wind park device mask

3.1 Detailed and Average Value Models

The EMTP diagram of the wind turbine ac-dc-ac converter system detailed model (DM) is shown
in Figure 13. A detailed two-level topology (Figure 14.a) is used for the VSCs in which the valve is
composed by one IGBT switch, two non-ideal (series and anti-parallel) diodes and a snubber circuit as
shown in Figure 14.b. The non-ideal diodes are modeled as non-linear resistances. The DC resistive
chopper limits the DC bus voltage and is controlled by the protection system block.

The PWM block in the ac-dc-ac converter system EMTP diagram receives the three-phase
reference voltages from converter control and generates the pulse pattern for the six IGBT switches by
comparing the voltage reference with a triangular carrier wave. In a two-level converter, if the reference
voltage is higher than the carrier wave then the phase terminal is connected to the positive DC terminal,
and if it is lower, the phase terminal is connected to the negative DC terminal. The EMTP diagram of
the PWM block is presented in Figure 15.

Polytechnique Montréal Page 17 of 58

 VSC_DM1 VSC_DM2

AC_GSC ac pos pos ac AC_MSC

Rchopper
VSC VSC
PWM 2-Level 2-Level PWM

+
+

+
Cdc V Vdc
#CdcPark_F# !v -
Vref_GSC Vref IGBT_chopper Vref Vref_MSC
block_GSC Conv_Active gate_signal S S gate_signal Conv_Active block_MSC
Chopper
PWM2 neg neg PWM1

Figure 13 ac-dc-ac converter system block in WT models (detailed model version)

S1 S3 S5 + p
va

+
vb Vdc g1

RLC +
vc
S2 S4 S6
- n

(a) (b)

Figure 14 (a) Two-level Converter, (b) IGBT valve

PWMsource Triang
f(u) 1 f(u)
Conv_Active
(2*pi*(#CarrierSignal_Freq#)*t) (2/pi)*ASIN(SIN(u[1]))
gate_signal
Vref
1 S1
a PROD
1 2
Compare
2
1 S4
PROD
2

1 S2
b PROD
1 2
Compare
2
1 S5
PROD
2

1 S3
c PROD
1 2
Compare
2
1 S6
PROD
2

Figure 15 PWM control block

The DM mimics the converter behavior accurately. However, the simulation of such switching
circuits with variable topology requires many time consuming mathematical operations and the high
frequency PWM signals force small simulation time step usage. These computational inefficiencies can
be eliminated by using the average value model (AVM) which replicates the average response of
switching devices, converters and controls through simplified functions and controlled sources [8].
AVMs have been successfully developed for wind generation technologies [9], [10]. The AVM obtained
by replacing the DM of converters with voltage-controlled sources on the ac side and current-controlled
sources on the dc side, as shown in Figure 16 and Figure 17.
The forth (converter control) tab of the wind park device mask (see Figure 12) enables used AVM-
DM selection.

Polytechnique Montréal Page 18 of 58

 VSC_AVM1 VSC_AVM2
P P

Rchopper
AC_GSC AC AC AC_MSC
VSC-AVM VSC-AVM
+

+
Vref_GSC Vref_MSC

+
a Cdc V Vdc a
varef - varef
b vbref + IGBT_chopper #CdcPark_F# !v + vbref b
c vcref vcref c
Chopper

block_GSC Blocked N N Blocked block_MSC

Figure 16 ac-dc-ac converter system block in WT models (average value model version)
Page Ia
Page Ib
Page Ic

c
i(t) Iabc
P
AC b

DCside1
Blocked DC_side

Block_conv1

Block_conv2
Block_conv
+

+
1e15

1e15

1e15
Varef Page Vref_phA

+
Vbref Page Vref_phB +
I_dc cI1 V Page Vdc
Vcref Page Vref_phC -
0/1e15
Ia Page Iac_phA
AC_side_phA AC_side_phB
AC_side_phC Ib Page Iac_phB
AC_side AC_side AC_side
Ic Page Iac_phC
+

Vdc Page Vdc Vdc Page Vdc

+
Vac Vac Vdc Page Vdc
Varef Page Vref Vbref Page Vref Vac
0/1e15 0/1e15 Vcref Page Vref
0/1e15

Figure 17 AVM Representation of the VSC

3.2 FSC based Wind Park Model in EMTP-RV

The EMTP-RV diagram of the FSC based Wind Park is shown in Figure 18. It is composed of

- “Wind Turbine” block,

- “WT Electrical System” block,

- “WT Control System” block,

- “WP Control System” block,

- PI circuit that represents equivalent collector grid,

- Wind park transformer,

- Initialization Source with load flow (LF) constraint.

The “Wind Turbine” block contains wind turbine aerodynamics given in Figure 3 and the
mechanical system model given by (4) - (7).

The initialization source contains the load flow constraint. It also prevents large transients at
external network during initialization of WT electrical and control systems.

Polytechnique Montréal Page 19 of 58

 Wind Turbine WT Electrical System WP Control System
WPC
MV_meas
WIND TURBINE MV WPC
Wind_Turbine
Measurement dUref Page dUref

Vpoi
FFC HARDWARE scope

Ipoi
Vmv
FFC_Hardware1

Imv
scp1
FC
transformer WindParkTransfo1

v
#Mean_wind_speed#

i
EqCollectorGrid1
PM-SM PCC
c RL 2 1
VIabc_mv VIabc_POI

tap

c
beta #T_wp_tr#

AC2 SW1
WP Transformer
+

+
-1|0.2|0

Ipmsg_A

Vdc_V

Igsc_A
chopper

Igrid_A

Vgrid_V
Vref_pmsg
Pitch_angle_deg

block_pmsg
wgen_rad
Agen_rad

block_grid

Vref_grid

switch_on
118.9536kVRMSLL /_0.1641
118.9536kVRMSLL /_-119.8359
118.9536kVRMSLL /_120.1641
PQbus:LF2 Equivalent
dVref Page dUref
P=#Plf#
Q=#Qlf#
collector grid
LF
FFC_CONTROL1
FFC CONTROL LF2
Phase:0

WT Control System Initialization Source

& LF constraint
Figure 18 EMTP diagram of the FSC based Wind Park

3.2.1 Wind Park Control System Block

The function of WPC is to adjust the WT controller voltage reference in order to achieve desired
reactive power at POI (see Figure 5). The “WP Control System” block consists a measuring block, an
outer voltage (or power factor) control and a slow inner proportional-integral reactive power control as
shown in Figure 19. The measuring block receives the voltages and the currents at POI (i.e. HV terminal
of wind farm transformer) and calculates the voltage magnitude, active power and reactive power. The
reactive power reference for the inner proportional-integral reactive power control is produced either by
the outer proportional voltage control (V-control) or by the outer power factor control (pf-control) unless
Q-control is selected.
Similar to the “Wind Turbine” block, the “WP Control System” block is identical in both FSC and
DFIG based WPs.

3.2.2 FSC Wind Turbine Electrical System Block

The EMTP diagram of the “WT Electrical System” block is composed of PMSM, ac-dc-ac converter
system, choke filter, shunt ac harmonic filters and WT transformer, as shown in Figure 20.

The measurement blocks are used for monitoring and control purposes. The monitored variables
are MSC, GSC and total FC currents, and FC terminal voltages. The dc voltage is also monitored (in
ac-dc-ac converter system block) as well as the PMSM electromagnetic torque. All variables are
monitored as instantaneous values and meter locations and directions are shown in Figure 20.
The ac-dc-ac converter system block details have been presented in Section 3.1.

Polytechnique Montréal Page 20 of 58

 Fast WPC initialization
Initialize
S_meas Page Spoi Qref Page Qref
Q_meas Page Qpoi Vref Page Vref
P_meas Page Vpoi PFref Page PFref

RC Page RC
RV Page RV

WPC_PQV
PQV Measurement
V Page Vpos_meas S_meas Page scope Spoi
Vpoi Vpoi P Page P_meas P_meas Page scope Ppoi
Ipoi Ipoi Q Page Q_meas Q_meas Page scope Qpoi
S Page S_meas Vpos_meas Page scope Vpoi

SIGN(u[1])
1 f(u)

u[1] / #WPC_Kv#
SQRT(1-u[1]^2) 1
Vref Page + + 1 f(u) Page Qref_VC
PFref Page 1 f(u) 2 PROD Page Qref_RF
- 3
[PROD]
S_meas Page

Vpos_meas Page

Outer V-Control Outer PF-Control

PI_control1

max
c
#dUmax#
min
c
#dUmin#
Outer Q-Control
RC Page RC step
RV Page 1
2
f(u) RV

c
PI
Kp
#C_select# c
#WPC_Kp_Q#
#WPC_Ki_Q# Ki
Qref Page 1
select c sc rc rv
direct
out Sampler 2
Qref_VC Page 2 dUref
Qref_RF Page 3
+ + 1
PROD u
RV Page 1
select
- 2

f(u)

Q_meas Page 1 + (t > 0.75)

Vpos_meas Page Vpoi_pos Block_Input

BLOCK_INPUT

Figure 19 EMTP diagram of “WP Control System” block

choke filter
SW_ON

ac-dc-ac SM_mech_init
Igsc
Vgrid

Imsc
Igrid

w_sm_filt Tsh
converter system w_sm
Tsh = Te
while
Tm t < 0.3s
B_to_B_converter1 PMSM
FC_transformer Ifsc
v

RLchoke
grid + + + PM-SM
2 1 VIabc_grid Iabc_gsc #Rchoke_Ohm#,#Lchoke_H# Iabc_msc

?m Teg
+

100M #Vgen_kVRMSLL# Omega_1

dummyR #Spark_VA# Teta_1 Teta_1

WT Transformer
filter
Vref_msc
Vref_gsc

Vdc

block_msc
block_gsc

chopper

shunt ac
harmonic filters
Figure 20 EMTP diagram of FSC “WT Electrical System” block

Polytechnique Montréal Page 21 of 58

 The “shunt ac harmonic filters” block includes two band-pass filters as shown in Figure 21. These
filters are tuned at switching frequencies harmonics n1 and n2. The filter parameters are computed as
Qfilter Nwt
Cf1  (11)
U2 (2f )
Nwt
L f1  (12)
Cf1(2f n1 )2
(2f )n1 L f1 Q
Rf1  (13)
Nwt
Cf 2  Cf1 (14)
Nwt
Lf 2  (15)
Cf 2 (2f n2 )2
(2f )n2 L f 2 Q
Rf 2  (16)
Nwt

where U is the rated LV grid voltage, Q filter is the reactive power of the filter and Q is the quality factor
with a value of 1000.

The switching frequencies harmonics n1 and n2 are as follows

n1  fPWMgsc fs (17)
n2  2n1 (18)
where fPWMgsc is the PWM frequency at GSC and fs is the nominal frequency.
+

#Cf1# #Cf2#
+

+
+

+
#Rf1#

#Rf2#
#Lf1#

#Lf2#

Figure 21 “shunt ac harmonic filter” block

3.2.3 FSC Wind Turbine Control System Block

The EMTP diagram of the FSC WT control system block is shown in Figure 22. The sampled
signals are converted to pu and filtered. The sampling frequencies are set to 12.5 kHz for both MSC
and GSC from device mask as shown in Figure 12. The “sampling” blocks are deactivated in AVM due
to large simulation time step usage. In the generic model, 2nd order Bessel type low pass filters are
used. The cut-off frequencies of the filters are set to 2.5 kHz for both MSC and GSC. However, the
order (up to 8th order), the type (Bessel and Butterworth) and the cut-off frequencies of the low pass
filters can be modified from the device mask as shown in Figure 12. The “MSC Compute Variables” and

Polytechnique Montréal Page 22 of 58

“GSC Compute Variables” blocks do the dq transformation required for the vector control. The MSC
control (“PMSG Control” block) operates in the stator flux reference frame and the GSC (“Grid Control”
block) operates in the stator voltage reference frame. The pitch control is activated when the wind speed
increases above the rated value and given in Figure 4. The protection block includes the over/under
voltage relay, the deep voltage sag detector, the dc chopper control and overcurrent detector.
CompVar_GSC

GSC P Page P
Computing Variables Pc2 Page Pc2
Ps2 Page Ps2
LPF_GSC Q Page Q
GSC_sampler GSC_conv_to_pu Grid_Ctrl
Igsc_A LPF (GSC) Iabc_gsc
Igrid_A GSC GSC Iabc_grid dVref dVref
Vgrid_V
Sampler SI -> pu Vabc_grid Vdc Vdc Grid Control
Vdc_meas
Vmv_pos_pred Vmv
Vmv_neg_pred Page Vmv_pos_pred
Vlv_pos Page Vlv_pos
Vlv_neg
theta_grid_rad theta
w_grid w Vabc_ref Vref_grid
Idq_gsc Idq
Vdq_grid Vdq
Idq_pos_gsc Idq_pos
Idq_neg_gsc Idq_neg
Vdq_pos_grid Vdq_pos
Vdq_neg_grid Vdq_neg

Protection_Sys
Pitch_Control Protection System Vmv_pos_pred scope Page Vmv_pos_pred
Pitch Control switch_on switch_on Vlv_pos scope Page Vlv_pos
Vdc_meas P scope Page P
w_rotor Page w_rotor Vabc_grid chopper_active chopper Ps2 scope Page Ps2
Pitch_deg Pitch_angle_deg
Iabc_line pmsg_conv_block block_grid Pc2 scope Page Pc2
P Page P
Iabc_pmsg grid_conv_block block_pmsg Q scope Page Q

CompVar_MSC

MSC PMSG_Ctrl
LPF_MSC
MSC_Sampler MSC_conv_to_pu Computing Variables PMSG Control
LPF (MSC) Vdc_meas Vdc Vdc
Vdc_V
wgen_rad
MSC MSC wr w_rotor w_rotor
Ipmsg_A Sampler SI -> pu Agen_rad Angle theta_pmsg_rad theta_pmsg_rad Vref_PWM Vref_pmsg
Iabc_pmsg Idq_pmsg Idq_pmsg

Page w_rotor

Figure 22 EMTP-RV diagram of FSC “WT Control System” block

The transformation matrix T in (19) transforms the phase variables into two quadrature axis (d and
q reference frame) components rotating at synchronous speed   d / dt . The phase angle  of the
rotating reference frame is derived by the double synchronous reference frame (DSRF) PLL [11] (see
Figure 23) from the FSC WT terminal voltages allowing the synchronization of the control parameters
with the system voltage. In matrix the following T, the direct axis d is aligned with the stator voltage.
 cos(t) cos(t  2 / 3) cos( t  2 / 3t) 
T    sin(t)  sin(t  2 / 3)  sin(t  2 / 3)
2
(19)
3
 1/ 2 1/ 2 1/ 2 

Polytechnique Montréal Page 23 of 58

 u[1] / (2*pi)
1 f(u) f

(u[1]) MODULO (2*pi)

out_ini out 1 f(u)
c u
#w#
PI controller
Vabc_to_Vdq
Vabc Vabc
abc to dq
Vdq_pos
qpos Vqpos
Va a
dpos Vdpos
Vb b
Vc c
qneg Vqneg Vdq_neg
wt dneg Vdneg

wt

DCp

DC
teta qn_s LPF qpos
qn
a a d dn dn_s LPF dpos

dm
qm
b b q
c c 0
qneg
wt wt
dneg
3-ph to dq0
dm
qm

a d dn dn_s LPF

DC
b q qn
c 0 teta qn_s LPF
wt
-1
3-ph to dq0 DCn

Figure 23 EMTP-RV diagram of DSRF PLL

3.2.3.1 FSC Machine Side Converter Control

The EMTP diagram of the “PMSG Control” block is shown in Figure 24. The function of the MSC is
to control the electromagnetic torque of the PMSM.

Outer Current Control Inner Current Control

MSC_InnerCtrl_daxis
id_ref
Idref
0c MSC
Inner Ctrl Loop Vdref
w_rotor Page w_rotor
Idq_pmsg
(d-axis)
Linearization2
Page w_rotor
Idq_pmsg
MSC_InnerCtrl_qaxis Linearization
Idq_pmsg & dq to abc
MPPT1
w_rotor Page w_rotor
MSC Vd_ref m
MPPT
T to_Iq
Inner Ctrl Loop Vqref Vq_ref
Vabc_ref Vref_PWM
1 (q-axis) Vdc Vdc
theta

w_rotor i o -1 Iqref
w
#Flux_pu#

theta_pmsg_rad

Figure 24 EMTP diagram of FSC “PMSG Control” block

The d-axis current reference is set to zero ( idm  0 ) to achieve unity power factor. The q-axis current
reference is given by
iqm  T m (20)

Polytechnique Montréal Page 24 of 58

where m is the constant flux generated by the permanent magnet and T (  K opt 2t ) is the reference
for PMSM electromagnetic torque given by the MPPT control.

The MSC inner control loop is designed based on internal model control (IMC) method. This
method results dq-frame proportional integral (PI) or PI-type controllers, the parameters (gain and
integration time) of which are expressed directly in certain machine parameters and the desired closed-
loop bandwidth. This simplifies the controller design procedure, eliminating or reducing the need for
trial-and-error [12].
The PMSG stator voltages are found from
v dm  Rsidm  Ld  d idm dt   gL qiqm (21)
 
v qm  Rsiqm  Lq d iqm dt  g Ldidm  m  (22)
where Rs is the armature resistance, Ld and Lq are the d- and q-axis inductances of PMSG.

The idm and iqm errors are processed by the PI controller to give v dm and v qm , respectively. To
ensure good tracking, feed-forward compensating terms gLqiqm in (21) and g Ldidm  m  in (22) are
added. The converter reference voltages become

 
v dm   k pd  k id s idm  idm   gLqiqm (23)
  
v qm   k pq  k iq s iqm  iqm  g L didm  m  (24)

Using IMC [12],

c k pd  k id s 0 
1
Fmsc (s)  Gmsc (s)    (25)
s  0 k q
 k q
s 
 p i 

where Gmsc  s  is the transfer function that describes the link between MSC output current and voltage,
and c is the bandwidth. Gmsc  s  is given by

1
Rs  sLd 0 
Gmsc (s)    (26)
 0 Rs  sL q 

The relationship between the bandwidth and the rise time (10%–90%) is c  ln(9) / trise .

The PI controller parameters are found as

k pd  c L d (27)
k pq  c Lq (28)
k id  k iq  c Rs (29)

The PI controller parameters are calculated for the MSC rise time given in the device mask.

3.2.3.2 FSC Grid Side Converter Control

The function of GSC is maintaining the dc bus voltage Vdc at its nominal value and controlling the

positive sequence voltage at MV side of FSC WT transformer ( Vwt ).The EMTP diagram of the “Grid
Control” block is shown in Figure 25. The GSC control offers both coupled and decoupled sequence

Polytechnique Montréal Page 25 of 58

control options. The user can select the GSC control option from the device mask as shown in Figure
12.

Outer Current Control Inner Current Control

InnerCtrl
Linearization1
Idq_gsc Page Idq Linearization
GSC_Vdc_Ctrl Idref Page Idref dVdq Page dVdq
Iqref Page Iqref c & dq to abc
GSC Idq_ref_limiter #CtrlType#
Ctrl_type
Vdc Page Vdc Outer Ctrl Loop Idref Id_ref_in Id_limit Page Id_limit
InnerCtrl_pos theta Page
w Page
theta
w
(Vdc) Iq_limit Page Iq_limit
Idq_pos
Idref_pos Page
Idq
Idref dVdq Page dVdq_pos
Vdc Page Vdc
Vabc_ref Vabc_ref
Iq_ref_in Id_ref_out Page Idref dVdq
GSC_Vac_Ctrl Iqref_pos Page Iqref Page dVdq_ref
Iq_ref_out Page Iqref dVdq_pos Page dVdq_pos_ref
dVref Page dVref GSC Idq reference limiter dVdq_neg
Vdq_grid
Page dVdq_neg_ref
InnerCtrl_neg Page Vdq_grid
Vmv Page Vmv Outer Ctrl Loop Iqref
FRT Page FRT Idq_gsc Page Idq_gsc

FRT Page FRT (Voltage) Idq_neg

Idref_neg Page
Idq
Idref dVdq Page dVdq_neg
Iqref_neg Page Iqref
Vdq Page Vdq_grid
Idq Page Idq_gsc

Elimination of 2nd Harmonic Pulsations theta

w
Page
Page
theta
w
Vdc Page Vdc
scale_references
dVref Page dVref
Idref Page
Fm2
Id_limit Page id_lim Vmv Page Vmv
Iref_calculation
f(u)
Iq_limit Page iq_lim
FRT_logic
Vdq_pos Vpos_dq iref_dpos Idpos Idpos_rev Page Idref_pos
C2
Vdq_neg Vneg_dq iref_dneg Idneg Idneg_rev Page Idref_neg FRT decision logic
select 1
1 PROD P iref_qpos Iqpos Iqpos_rev Page Iqref_pos
c 2
Vmv Page 2 Iqref Page iq_pos_ref iref_qneg Iqneg Iqneg_rev Page Iqref_neg
1 Vmv FRT Page FRT

Figure 25 EMTP diagram of FSC “Grid Control” block

3.2.3.2.1 FSC GSC Coupled Control

The q-axis reference current is calculated by the proportional outer voltage control, as follows

iqg  K V V   Vwt   (30)

where K V is the voltage regulator gain. The reference for MV side of FSC WT transformer positive
sequence voltage ( V  ) is calculated by the WPC (see Figure 5).

The positive sequence voltage at MV side of FSC WT transformer is not directly measured by the
WT controller and it is approximated by

   V 
2 2
  
Vwt  Vdwt qwt (31)

where
   
Vdwt  Vdwt  Rtr Idwt  Xtr Iqwt (32)
   
Vqwt  Vqwt  Rtr Iqwt  Xtr Idwt (33)
 
In (31) - (33), Vdwt and Vqwt are the d-axis and q-axis positive sequence voltage at MV side of FSC WT
 
transformer, Vdwt and Vqwt are the d-axis and q-axis positive sequence voltage at FSC WT terminals
 
(i.e. the d-axis and q-axis positive sequence voltage at LV side of FSC WT transformer), Idwt and Iqwt
are the d-axis and q-axis positive sequence currents of FSC WT (i.e. the d-axis and q-axis positive
sequence currents at LV side of FSC WT transformer), R tr and Xtr are the resistance and reactance
values FSC WT transformer.

The d-axis reference current is calculated by the proportional outer dc voltage control. It is a PI
controller tuned based on inertia emulation.

k p  02  2HCdc  (34)

k i  20  2HCdc  (35)

Polytechnique Montréal Page 26 of 58

where 0 is the natural frequency of the closed loop system and  is the damping factor.
HCdc  ECdc S wt  is the static moment of inertia, ECdc is the stored energy in dc bus capacitor (in
Joules) and S wt is the wind park rated power (in VA).

The schematic of the GSC connected to the power system is shown in Figure 26. Z  R  jL
represents the grid impedance including the transformers as well as the choke filter of the GSC. The
voltage equation is given by


vabc  R igabc  L d igabc dt  vgabc  (36)

R  j L iag
vag va

Vdc
dc vbg ibg vb Power
System
ac vcg icg vc

Figure 26 GSC arrangement

The link between GSC output current and voltage can be described by the transfer function
Ggsc (s)  1 R  sL  (37)

Using (25), the PI controller parameters of the inner current control loop are found as
k p  cL (38)
k i  cR (39)
The PI controller parameters are calculated for the GSC rise time given in the device mask.
Similar to the MSC, the feed-forward compensating terms Lchokeiqg  v dchoke and

 Lchokeidg  vqchoke  are added to the d- and q-axis voltages calculated by the PI regulators,
respectively. The converter reference voltages are as follows

  
v dg   k p  k i s idg  idg  Lchokeiqg  v dchoke (40)
v qg    k p  k i s  iqg  iqg   Lchokeidg  v qchoke (41)

During normal operation, the controller gives the priority to the active currents, i.e.

idg  Ilim
dg
(42)
I   i 
2 2
iqg  Ilim
qg 
lim
g dg

where Ilim lim lim

dg , Iqg and Ig are the limits for d-axis, q-axis and total GSC currents, respectively.

The WTs are equipped with an FRT function to fulfill the grid code requirement regarding voltage
support shown in Figure 27. The FRT function is activated when

1  Vwt  VFRT ON (43)

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and deactivated when

1  Vwt  VFRT OFF (44)

after a pre-specified release time tFRT .

When the FRT function is active, the GSC controller gives the priority to the reactive current by
reversing the d- and q-axis current limits given in (42), i.e.

iqg  Ilim
qg
(45)
I   i 
2 2
idg  Ilim
dg 
lim
g qg

The EMTP diagram of “Idq reference limiter” and “FRT decision logic” blocks are given in Figure
28 and Figure 29, respectively. The limits for d-axis, q-axis and total GSC currents and FRT function
thresholds can be modified from the device mask.

Figure 27 Wind turbine reactive output current during voltage disturbances [13].
c #Iq_lim_gsc_pu#
2
MIN
1
Iq_limit
(u[2]==1)*#Iq_lim_FRT_pu# + (u[2]==0)*u[1]
Limiter2
1
FRT Page 2
f(u) MAX

Iq_ref_in Iq_ref_out

MIN c #I_lim_gsc_pu#
-1
f(u)

SQRT(u[1]*u[1]-u[2]*u[2])
1
2
2
1

SQRT(u[1]*u[1]-u[2]*u[2])
#I_lim_gsc_pu# c
f(u)

FRT Page FRT

Id_limit
(u[2]==0)*#Id_lim_gsc_pu# + (u[2]==1)*u[1]
Limiter1
1
FRT Page 2
f(u) MAX

Id_ref_in Id_ref_out

-1 MIN

Figure 28 EMTP diagram of “Idq reference limiter” block

Polytechnique Montréal Page 28 of 58

 ABS(u[1]) > #FRT_ON#
Vmv 0.5/+Inf FRT
Vmv + + Timer 1 f(u) S Q FRT
- R notQ
ABS(u[1]) < #FRT_OFF#
1pu S-R flip-flop
1 f(u) ideal
c
1
c
0
+Inf
u[1] > #FRT_time# rv rc
f(u) 1

Figure 29 EMTP diagram of “FRT decision logic” block

3.2.3.2.2 FSC Grid Side Converter Decoupled Sequence Control

Ideally, the GSC control presented in the previous section is not expected to inject any negative
sequence currents to the grid during unbalanced loading conditions or faults. However, the terminal
voltage of FSC WT contains negative sequence components during unbalanced loading conditions or
faults. This causes second harmonic power oscillations in GSC power output. The instantaneous active
and reactive powers such unbalanced grid conditions can be also written as [14]
p  P0  PC2 cos(2t)  PS2 cos(2t)
(46)
q  Q0  QC2 cos(2t)  QS2 cos(2t)

where P0 and Q0 are the average values of the instantaneous active and reactive powers respectively,
whereas PC2 , PS2 , QC2 and QS2 represent the magnitude of the second harmonic oscillating terms in
these instantaneous powers.

With decoupled sequence control usage, four of the six power magnitudes in (46) can be controlled
for a given grid voltage conditions. As the oscillating terms in active power PC2 , PS2 cause oscillations
       
in dc bus voltage Vdc , the GSC current references ( idg , iqg , idg , iqg ) are calculated to cancel out these
terms (i.e. PC2  PS2  0 ).

The outer control and Idq limiter shown in Figure 8 calculates idg , iqg , Ilim lim
dg and Iqg . These values
       
are used to calculate the GSC current references idg , iqg , idg and iqg for the decoupled sequence
current controller. As the positive sequence reactive current injection during faults is defined by the grid
code (see Figure 27), the GSC current reference calculation in [14] is modified as below:
i    1 0 0 0 
1
 qg    iqg 
i    v qg   
  P 
  
v dg v qg v dg
 dg   
  
0
     v
(47)
 PC2 
 
v dg v qg v dg
iqg   qg
    v      P 
idg   dg
v qg v dg v qg   S2 

where P0 is approximated by

P0  Vwt idg (48)

The calculated reference values in (47) is revised considering the converter limits Ilim lim
dg and Iqg . For
 
example when iqg   
 iqg 
 Ilim
qg , the q-axis reference current references are revised as below

Polytechnique Montréal Page 29 of 58

  
iqg    lim
 iqg I
 qg i
 
qg  iqg 
  

(49)
 
iqg    lim
 iqg I i
  
 iqg 
 qg qg 
 
where Iqg " and Iqg " are the revised reference values for q-axis positive and negative currents,
respectively.
 
The revised d-axis positive and negative current references Idg " and Idg " can be obtained with
the same approach using Ilim
dg . It should be emphasized here that, during faults the priority is providing

Idg specified by the grid code. The remaining reserve in GSC is used for eliminating PC2 and PS2 .
Hence, its performance reduces with the decrease in electrical distance between the WP and the
unbalanced fault location.
   
As idg , iqg , idg and iqg are controlled, the decoupled sequence control contains four PI regulator
and requires sequence extraction for GSC currents and voltages. The sequence decoupling method
[15] shown in Figure 30 is used in EMTP implementation. In this method, a combination of a low-pass
filter (LPF) and double line frequency Park transform ( P 2 and P 2 ) is used to produce the oscillating
signal, which is then subtracted. The blocks C and P represent the Clarke and Park transformation
matrices, and the superscripts ±1 and ±2 correspond to direct and inverse transformation at line
frequency and double line frequency, respectively.

In EMTP implementation, the feed-forward compensating terms  Lchokeiqg  v dchoke  and

 Lchokeidg  vqchoke  are kept in coupled form and added to the PI regulator outputs in stationary αβ-
frame.
+
i dq
+
P
+1
-
Σ
-2
LPF P
iabc i αβ
C
+2
LPF P - -
i dq
P
-1
+ Σ
Figure 30 Sequence extraction using decoupling method.

3.2.4 FSC Protection System Block

The “protection system” block includes an over/under voltage relay, deep voltage sag detector, dc
overvoltage protection and an overcurrent detector for each converter to protect IGBT devices when
the system is subjected to overcurrent. For initialization, all protection systems, except for dc chopper
protection, are activated after 300ms of simulation (i.e. init_Prot_delay = 0.3s). The protection system
parameters (except over/under voltage relay) can be modified from the device mask.

3.2.4.1 Over/Under Voltage Relay and Deep Voltage Sag Detector

The over/under protection is designed based on the technical requirements set by Hydro Quebec
for the integration of wind generation. The over/under limits as a function of time is presented in Figure

Polytechnique Montréal Page 30 of 58

31. The voltages below the red line reference and above the black line reference correspond to the ride-
through region where the WT is supposed to remain connected to the grid.
Canada
Hydro Quebec - LV & HV RT
1,5
1,4
1,3
1,2
1,1
1,0 Ride Through Region
0,9
0,8
Voltage (pu)

0,7 Trip Region

0,6
0,5
0,4
0,3
0,2
0,1
0,0
0,0 0,1 1,0 Time (s) 10,0 100,0 1000,0

Figure 31 LVRT and HVRT requirements [16]

This block measures the rms voltages on each phase and sends a trip signal to the FSC circuit
breaker when any of the phase rms voltage violates the limits in Figure 31 (see the upper part of Figure
32). The “Deep Voltage Sag Detector” block (lower part of Figure 32) temporary blocks the GSC and
MSC in order to prevent potential overcurrents and restrict the FRT operation to the faults that occur
outside the wind farm.
Vabc_grid LP_filter_2nd2
Phase_A_Vprot activate_Protection
ph_1 LP Filter f(u)
Va i
2nd Odrer o Vpu out
in mag
#activate_VoltageProt#+1
rad cumul
inst to polar LP_filter_2nd3
OR_Vprot
Phase_B_Vprot Vprot_Initialization_Delay
select
ph_2 LP Filter 1 sc rc rv 0 1
Vb 1 f(u) switch_on
i
2nd Odrer o Vpu out
in mag 2 OR
Sampler 2
rad 3 (u[1]>0)*( t > #init_Prot_delay#)
inst to polar LP_filter_2nd6 VProtectionSampler Voltage_Prot_selector
Phase_C_Vprot
ph_3 LP Filter
Vc i
2nd Odrer o Vpu out
in mag
rad
inst to polar
Va_rms_pu
scope
Vb_rms_pu
scope
Vc_rms_pu
scope
activate_Protect1
f(u)
Deep Voltage Sag Detector
#activate_VoltageProt#+1
Va_rms
Vb_rms
Vc_rms DVS_Initialization_Delay
select
0 1
Deep_Voltage_Sag_Level 1 f(u) Deep_Voltage_Sag
dvs 2
dvs_level (u[1]>0)*( t > #init_Prot_delay #)
c Voltage_Prot_selector1
Deep_Voltage_Sag_Hysteresis
#DVS_level#
dvs_hysteresis
c
#DVS_hysteresis#

Figure 32 Over/under-voltage relay and deep voltage sag protection

Polytechnique Montréal Page 31 of 58

3.2.4.2 dc Overvoltage Protection Block
The function of dc chopper is to limit the dc bus voltage. It is activated when the dc bus voltage
exceeds Uchopper ON and deactivated when dc bus reduces below Uchopper OFF . The EMTP diagram
of the “dc overvoltage protection” is shown in Figure 33.

activate_Protect1
f(u)
#activate_ChopperProt#+1
Vdc_meas
scope
(u[1]>u[3])+((u[1]>=u[2])*(u[1]<=u[3]))*u[4]
Vdc 1 select
0 1
2 chopper_active
Chopper_Low_limit c 3
f(u) 2
#Chopper_OFF# 4 Chopper_activation_selector
Chopper_function
Chopper_High_Limit c
Delay
#Chopper_ON#
1
Chopper_in_Delay

Figure 33 dc overvoltage protection block

3.2.4.3 Overcurrent Protection Block

The overcurrent protection shown in Figure 34 blocks the converter temporarily when the
converter current exceeds the pre-specified limit.

Imax_MSC
scope

Imsc
Imsc_MAX
Ia Overcurrent_limit release_delay1
1
Ib initialization_Delay
2 MAX 1
Ic 3 2
f(u) 1 f(u) i release_delay o OC_msc
(u[1]>0)*( t > #init_Prot_delay #)
(u[1]>u[2])

c
#Iconv_max#
I_MacSideConv_max_pu

Imax_GSC
scope

Igsc
Igsc_MAX
Ia release_delay3
1 Overcurrent_limit
Ib initialization_Delay
2 MAX 1
Ic 3 2
f(u) 1 f(u) i release_delay o OC_gsc
(u[1]>0)*( t > #init_Prot_delay #)
(u[1]>u[2])

c
#Iconv_max#
I_GridSideConv_max_pu

Figure 34 Overcurrent protection block

3.3 DFIG based Wind Park Model in EMTP-RV

The EMTP diagram of the DFIG based Wind Park is shown in Figure 19. It is composed of “Wind
Turbine”, “WT Electrical System”, “WT Control System”, “WP Control System” blocks, PI circuit that
represents equivalent collector grid, wind park transformer and initialization source with load flow
constraint.

Polytechnique Montréal Page 32 of 58

 This model is the same as with the FSC based wind park model except “WT Electrical System”
and “WT Control System” blocks.

Figure 35 EMTP diagram of the DFIG based Wind Park

3.3.1 DFIG Wind Turbine Electrical System Block

The EMTP diagram of the “WT Electrical System” block consists of IG, ac-dc-ac converter system,
GSC choke filter, shunt ac harmonic filters, crowbar and WT transformer as shown in Figure 36.

pu_to_actual
sign_change
wr_pu 1 f(u) wr_rad
u[1] * #wb_gen_mech# -1 Te
SW_ON

WT Transformer
Istator

Irotor
Vgrid

Igrid

Speed ASM Teg

DFIG_transformer
v

GRID
i

SW2
+ + S ASM R
2 1 1e-9|1E15|0 VIabc_grid Iabc_stator Iabc_rotor
N

#Vgen_kVRMSLL#
choke filter #Spark_MVA#
Iconv

crowbar
i

RLchoke
+
filter Iabc_converter GSC RSC
#Rchoke_Ohm#,#Lchoke_H#
abc

shunt ac
harmonic filters connection to CROW_act crowbar

ac-dc-ac converter system Crowbar

Figure 36 EMTP diagram of DFIG “WT Electrical System” block

The measurement blocks are used for monitoring and control purposes. The monitored variables
are IG stator, IG rotor, GSC and total DFIG currents, and DFIG terminal voltages. The dc voltage is also
monitored (in ac-dc-ac converter system block) as well as the IG electromagnetic torque. All variables
are monitored as instantaneous values and meter locations and directions are shown in Figure 36. The
ac-dc-ac converter system block details have been presented in Section 3.1.

Polytechnique Montréal Page 33 of 58

 Similar to the FSC WT, the “shunt ac harmonic filters” block includes two band-pass filters as
shown in Figure 21. These filters are tuned at switching frequencies harmonics n1 and n2 of the GSC.

3.3.2 DFIG Wind Turbine Control System Block

The EMTP diagram of the DFIG WT control system block is shown in Figure 37. The sampled
signals are converted to pu and filtered. The sampling frequency are set to to 22.5 kHz and 11.25 kHz
(from device mask as shown in Figure 12) for GSC and RSC, respectively. The “sampling” blocks are
deactivated in AVM due to large simulation time step usage. In the generic model, 4th order Bessel type
low pass filters are used. The cut-off frequencies of the filters are set to 4.5 kHz and 2.25 kHz for GSC
and RSC, respectively. However, the order (up to 8th order), the type (Bessel and Butterworth) and the
cut-off frequencies of the low pass filters can be modified from device mask as shown in Figure 12. The
“RSC Compute Variables” and “GSC Compute Variables” blocks do the dq transformation required for
the vector control. The RSC control (“Rotor Control” block) operates in the stator flux reference frame
and the GSC (“Grid Control” block) operates in the stator voltage reference frame. The pitch control is
activated when the wind speed increases above the rated value and given in Figure 4. The protection
block includes the over/under voltage relay, the deep voltage sag detector, the dc chopper control, the
crowbar protection and overcurrent detector.
Rotor_Control
RSC_Comp_Vars
Rotor Control
RSC dVref dVref
Compute Variables Vlv Vlv
predicted_Vmv predicted_Vmv
P P
RSC_conv_to_pu
RSC_sampler RS_LPF
w_rotor w_rotor Vref_PWM Vref_RSC
wgen_rad w_rotor_meas
Udc_V RSC LPF (RSC) Vdc_meas
Idq_stator Idq_stator
Idq_rotor Idq_rotor
Istator_A
Irotor_A
RSC Convert to pu Iabc_stator
w_stator w_stator
Iabc_rotor
Igrid_A Sampler SI -> pu Iabc_grid
Vdc Vdc
Vgrid_V theta_rotor_rad theta_rotor_rad
Vabc_grid
GSC_Comp_Vars1
Grid_Control1
GSC
Compute Variables Grid Control
GSC_conv_to_pu GS_LPF
GSC_sampler Vlv_pos Vlv
GSC LPF (GSC) Vdc_meas
pred_Vmv_pos
w_stator
Vmv
w_stator
GSC Convert to pu Iabc_grid
Vdc Vdc
Vref_PWM Vref_GSC
Vabc_grid
Iconv_A Sampler SI -> pu Iabc_converter Vdq_grid Vdq_grid
Idq_gsc Idq_converter
Idq_pos_gsc Idq_pos_gsc
Idq_neg_gsc Idq_neg_gsc
Idq_neg_grid Idq_neg_grid
theta_grid_rad theta_grid_rad

Pitch_Control

Pitch Control
Protection
w_rotor
Pitch_deg Pitch_deg
Protection System P
switch_on SW_ON
Vdc_meas
crowbar_active Crowbar_ON
Vabc_grid
chopper_active Chopper_ON
Iabc_rotor
RSC_block Block_RSC
Iabc_converter
GSC_block Block_GSC

Figure 37 EMTP diagram of DFIG “WT Control System” block

The direct axis d is aligned with the stator voltage in transformation matrix (see (19)); therefore,
the rotor and stator currents are shifted to align with the stator flux. The shifted-angle flux block used to
achieve a Stator Flux Orientation (SFO) is shown in Figure 38.

The frequency of the rotor voltage is controlled so that under steady conditions, the combined
speed of the rotor plus the rotational speed of the rotor flux vector matches that of the synchronously
rotating stator flux vector fixed by the network frequency. Manipulation of the rotor voltage permits
control of the generator operating conditions.

Polytechnique Montréal Page 34 of 58

 #Lmd_pu#
Idq_rotor
Irotor_d Idm
Irotor_q
+ +
+

x mag
y rad Flux_ang
Idq_stator Iqm xy to polar
Istator_d + +
Istator_q +
#Lmq_pu#

Figure 38 Flux angle calculation

3.3.2.1 DFIG Rotor Side Converter Control

The EMTP diagram of the “Rotor Control” block is shown in Figure 39. The d- and q-axis currents
of RSC ( idr and iqr in Figure 10) are used to control the positive sequence voltage at MV side of DFIG

transformer ( Vwt ) and the active power output of DFIG. The positive sequence voltage at MV side of
DFIG WT transformer is not directly measured by the WT controller and it is approximated using (31) -
(33).
w_rotor Page w_rotor Slip
scope Inner Current Control
w_stator 1
f(u) Page Slip
w_rotor Page 2
u[1]-u[2] Idq_stator Page Idq_stator

Outer Current Control Page FRT

Idq_rotor Page Idq_rotor
RSC_InnerCtrl_daxis
RSC_VoltageCtrl
FRT Idq_stator Page Idq_stator
dVref dVref scope Idq_rotor Page Idq_rotor RSC
RSC Idq_ref_limiter1
FRT FRT Slip Page Slip Inner Ctrl Loop Vdref Linearization1
Vmv Outer Ctrl Loop
(d-axis)
predicted_Vmv
Idq reference limiter Linearization
(Voltage) Idref
Id_ref_in Id_ref_out Id_ref & dq to abc
Vlv Vlv
Vd_ref m
Vq_ref
Vlv Iq_ref_in Iq_ref_out Iq_ref Vabc_ref Vref_PWM
RSC RSC Vdc Vdc

theta
FRT Page FRT
Outer Ctrl Loop Iqref
Slip Page Slip Inner Ctrl Loop Vqref
w_rotor Page w
(Power) Idq_rotor Page Idq_rotor (q-axis)
P P
Idq_stator Page theta_rotor_rad
Idq_stator

RSC_PowerCtrl RSC_InnerCtrl_qaxis

Figure 39 EMTP diagram of DFIG “Rotor Control” block

The d-axis reference current is calculated by the proportional outer voltage control

idr  K V V   Vwt idr m  (50)

In (50) idr m is the compensating term for the reactive current absorbed by the IG and
approximated by

idr m  Vwt  sLm  (51)

where Lm is the IG magnetizing inductance and Vwt is the positive sequence voltage at DFIG WT
terminals.

The q-axis reference current is calculated by the power controller

iqr  KPP  KIP s P  P  (52)

During normal operation, the controller gives the priority to the active currents.

Polytechnique Montréal Page 35 of 58

 iqr  Ilim
qr
(53)
   
2 2
idr  Ilim
dr  Irlim  iqr

lim
where Ilim lim
dr , Iqr and Ir are the limits for d-axis, q-axis and total RSC currents, respectively.

When the FRT function is activate, the RSC controller gives the priority to the reactive current by
reversing the d- and q-axis current limits given in (53).

The RSC inner control loop is designed based on the IMC method [12][17] considering the Г
representation of the IG [17] shown in Figure 40. The Г representation eliminates the complexity of the
well-known T representation without loss of information or accuracy. It is obtained by adjusting the
rotor/stator turn ratio for eliminating the stator leakage inductance. The Г representation parameters are
as follows:
  L s Lm (54)
LM  L s  Lm (55)
L  Lls   2Llr (56)
RR   2Rr (57)
where Lm is the magnetizing inductance, Lls and Llr are the stator and rotor leakage inductances, and
Rs and Rr are the stator and rotor resistances of the machine.

Figure 40 Г representation of induction machine

After transformation, the rotor currents, fluxes and voltages become

iR  ir  (58)
λR   λ r (59)
vR   vr (60)
By neglecting dλ s dt [18], the rotor side voltages can be written as:

d idR
v dR  RR idR  L  r L iqR (61)
dt
d iqR
v qR  RR iqR  L  r LM  L  idR  LMids  (62)
dt
The idR and iqR errors are processed by the PI controller to give v dR and v qR , respectively. To
ensure good tracking, feed-forward compensating terms for r L  iqR in (61) and
r LM  L  idR  LMids  in (62) are added. The converter reference voltages become

Polytechnique Montréal Page 36 of 58

 v dR   kp  ki s   idR
  idR   r L iqR (63)
v qR   kp  ki s   iqR
  iqR   r LM  L  idR  LMids  (64)

Using (25) with

Grsc (s)  1 RR  sL   (65)
the PI controller parameters of the inner current control loop are found as
k p  cL  (66)
k i  c RR (67)
The PI controller parameters are calculated for the RSC rise time given in the device mask as
shown in Figure 12.

The RSC inner current control has variable conversion blocks for the input RSC currents and the
output RSC voltages as shown in Figure 41.

idqr idqR
T  vdqR vdqr
RSC
idqs  T
slip
Control

Figure 41 Conversion at RSC input and output variables

3.3.2.2 GSC Grid Side Converter Control

The function of GSC is maintaining the dc bus voltage Vdc at its nominal value. It operates at
unity power factor except severe fault conditions. The EMTP diagram of the “Grid Control” block is
shown in Figure 42. GSC control offers both coupled and decoupled sequence control options. User
can select the GSC control option from the device mask as shown in Figure 12.

Outer Current Control

GSC_Ctrl_Vdc
Vdc_ref
Vdc_ref GSC MAX w_stator Page w_stator
c
1 Outer Ctrl Loop Idref Page Idref
Vdq_grid Page Vdq_grid
Page Idq_converter
Vdc Vdc (Vdc) -1 MIN
Idq_converter

Vdc
scope
Page Vdc Inner Current Control
Linearization1
LVRT_boost
CCC Ctype Linearization
LVRT Boost
Idq_converter Page Idq c & dq to abc
Vmv Vmv Id_max 1
MIN Idref Page Idref dVdq_ref #Ctrl_type#
2 Ctrl_type
Vlv Vlv Iqref Iqref Page Iqref
theta_grid_rad theta
HVRT_boost w_stator Page w
HVRT Boost DCC_pos Vdc Page Vdc
Vabc_ref Vref_PWM
Id_max
Vmv 1 Idq_pos_gsc Idq dVdq_ref
SUM Page Iqref
Iqref 2 Idref_pos Page Idref dVdq_ref dVdq_pos_ref
Igsc_max
Iqref_pos Page Iqref dVdq_neg_ref
Vdq_grid Page Vdq_grid
scale_references1 Idq_converter Page Idq_gsc
c DCC_neg
#Igsc_max_OV# limit
Idq_neg_gsc Idq
Idq_neg_grid Idref Page Idpos Idpos_rev Page Idref_pos
Id Idref_neg Page Idref dVdq_ref
Idneg Idneg_rev Page Idref_neg
Iq Iqref_neg Page Iqref
Iqref Page Iqpos Iqpos_rev Page Iqref_pos
Iqneg Iqneg_rev Page Iqref_neg

Figure 42 EMTP diagram of DFIG “Grid Control” block

Polytechnique Montréal Page 37 of 58

3.3.2.2.1 DFIG GSC Coupled Control
Except the q-axis reference current calculation, the DFIG WT GSC control is similar to the FSC WT
GSC control. In DFIG WTs, the GSC operates at unity power factor, hence the q-axis reference current
is set to zero (i.e. iqg  0 ). However, GSC starts injecting reactive currents during faults when the RSC
reactive current contribution is not sufficient to satisfy the grid code requirement due to the reactive
current absorbed by the IG. In that condition GSC q-axis reference current becomes

 
iqr  K V V   Vwt  
 Ilim
dr  idr m  (68)

Similar to RSC, the priority is given to the GSC reactive currents when FRT function is activate. In
order to improve the high voltage ride through (HVRT) capability of the DFIG WT, reactive current
contribution of GSC is also used. The GSC reactive current contribution is achieved by “LVRT boost”
and “HVRT boost” blocks (shown in Figure 43 and Figure 44, respectively) during low voltage and high
voltage conditions.

The PI controller parameters are calculated for the GSC rise time given in the device mask as shown
in Figure 12. The parameters regarding GSC reactive current contribution can be modified from the
device mask as shown in Figure 12.

maximum RSC
Id_rsc
contribution
SQRT(#Igsc_max#*#Igsc_max#-u[1]*u[1])
c
Id_max
#Id_lim_FRT_pu# 1 f(u) Id_max

Vmv
Vmv desired DFIG
reactive current #Iq_gsc_max#
1pu
-
FRT_Gain during LVRT -
c + + + + 1 1
PROD
Iqref
Iqref
+ 2
1 #VoltReg_FRT_Gain# 0

reactive loss gsc_frt

f(u)
@ ASM
Vlv
Vlv 1 f(u)

u[1] / #Lmd_pu#

Figure 43 EMTP diagram of “LVRT boost” block

SQRT(#Igsc_max#*#Igsc_max#-#Iq_gsc_max#*#Iq_gsc_max#*u[1])
1 f(u)
Id_max
Id_max
u[1] > #GSC_OVRT_ON# -u[1]*#Iq_gsc_max#
0.3/+Inf
Vmv + + Timer 1
PROD 1 f(u) S Q 1 f(u)
Iqref
Iqref
- 2
R notQ
u[1] < #GSC_OVRT_OFF#
1pu S-R flip-flop
frt_active
1 f(u) ideal
c f(u)
1

Figure 44 EMTP diagram of “HVRT boost” block

3.3.2.2.2 DFIG Side Converter Decoupled Sequence Control

Unbalanced steady state operation and fault conditions give rise to high frequency components in
rotor currents and torque pulsations [19]. To mitigate the corresponding stress different control methods
has been proposed [20] - [24]. The primary objective in these methods is to reduce the oscillating air
gap torque during periods of asymmetry so that the drive-train of the wind turbine is not subjected to

Polytechnique Montréal Page 38 of 58

the resulting stress. Either RSC or GSC (or both of them) can be used for this purpose. The performance
of these methods depends on the severity of the voltage dip at DFIG terminal as well as the severity of
its asymmetry. The major limiting factor of the performances of these methods is the FRT requirement
specified by the grid code.

The implementation in this document considers the method in which the GSC compensates the
negative sequence current required in the network during any unbalanced operation [23]. As the GSC
will supply the negative sequence components for the currents to the grid, the stator currents will remain
balanced as shown in Figure 45.
       
The reference GSC currents ( idg , iqg , idg , iqg ) will become

 
idg  idg , iqg
 
 iqg , idg
  
 idwt  
, iqg 
 iqwt (69)

The calculated reference values in (69) is revised considering the converter limit Ilim
g . For example

i   i 
2 2
       
when dg  idg qg  iqg  Ilim
g , the q-axis positive sequence current reference is revised as

below

i   i  
 

  lim    
2
   
2 
iqg  iqg Ig dg  idg qg  iqg (70)



I wt  I wt
Is

IG
I g  I g
Ir
RSC GSC
dc dc
ac ac

Figure 45 Negative sequence compensation through GSC

Polytechnique Montréal Page 39 of 58

4 WIND PARK RESPONSE TO UNBALANCED FAULTS
This section provides a comparison between the wind park responses with coupled and decoupled
sequence controls. Although the comparison is conducted for various type unbalanced faults in the 120
kV, 60 Hz test system shown in Figure 46 [25]-[27], only the 250 ms double line to ground (DLG) fault
simulation scenarios are presented. The simulation scenarios are presented in Table I. The WT
converters are represented with their AVMs. The simulation time step is 10 µs.

In the test system, the loads are represented by equivalent impedances connected from bus to
ground on each phase. The transmission lines are represented by constant parameter models and
transformers with saturation. The equivalent parameters for the 34.5 kV equivalent feeders are
calculated on the basis of active and reactive power losses in the feeder for the rated current flow from
each of the WTs [28]. The aggregated model of 1.5 MW, 60 Hz DFIG wind turbines is used for 45 units.
In all simulations, the WT is operating at full load with unity power factor (i.e. QPOI = 0).

Figure 46 120 kV, 60 Hz test system

Table I Simulation Scenarios

Scenario Fault Location GSC Control Scheme
M1 BUS4 Coupled Control
M2 BUS4 Decoupled Sequence Control
N1 BUS6 Coupled Control
N2 BUS6 Decoupled Sequence Control

Polytechnique Montréal Page 40 of 58

4.1 FSC based Wind Park Response to Unbalanced Faults
4.1.1 Simulation Scenarios M1 and M2 with FSC based Wind Park
As shown in Figure 47, the simulated unbalanced fault results second harmonic pulsations in the
active power output of FSC WT in scenario M1. These second harmonic pulsations are eliminated in
the scenario M2 with decoupled sequence control scheme in GSC at the expense of a reduction in the
active power output of FSC WT as shown in Figure 48. On the other hand, the reactive power output of
FSC WT is similar in scenarios M1 and M2. This is due to the strict FRT requirement on positive
sequence reactive currents.
The performance of the GSC decoupled sequence control is limited to the GSC rating as well as
the FRT requirement specified by the grid code. The complete elimination of second harmonic
pulsations cannot be achieved when the required GSC current output exceeds its rating. It should be
noted that, when the electrical distance between the WP and unbalanced fault decreases, larger GSC
currents are required to achieve both FRT requirement and the elimination of second harmonic
pulsations.
The negative and positive sequence fault currents ( In and Ip ) of the WP in scenarios M1 and M2
are also quite different as illustrated in Figure 49. This difference strongly depends on the unbalanced
fault type, its electrical distance to the WP, GSC rating and the FRT requirement specified by the grid
code. It becomes less noticeable especially for the electrical distant faults such as an unbalanced fault
at BUS6 as presented in Section 4.1.2.

Figure 47 PC2 and PS2 of aggregated FSC WT in scenarios M1 and M2

Figure 48 P0 and P0 of aggregated FSC WT in scenarios M1 and M2

Polytechnique Montréal Page 41 of 58

Figure 49 In and Ip of FSC WT based WP in scenarios M1 and M2

4.1.2 Simulation Scenarios N1 and N2 with FSC based Wind Park

As the electrical distance between the WP and the unbalanced fault is much larger in scenario N1
compared to scenario M1, both the voltage sag and the second harmonic pulsations in the active power
output are much smaller in scenario N1 compared to the scenario M1 (see Figure 50 and Figure 47).
As a result, the decupled sequence control of GSC achieves elimination of these pulsations in scenario
N2 without any reduction in the active power output of FSC WT (see Figure 51 and Figure 48). As seen
from Figure 52 and Figure 49, the WP fault current contribution difference between the scenarios N1
and N2 also becomes less noticeable especially for positive sequence fault currents compared to the
difference between scenarios M1 and M2.

Figure 50 PC2 and PS2 of aggregated FSC WT in scenarios N1 and N2

Polytechnique Montréal Page 42 of 58

Figure 51 P0 and Q0 of aggregated FSC WT in scenarios N1 and N2

Figure 52 In and Ip of FSC WT based WP in scenarios N1 and N2

4.2 DFIG based Wind Park Response to Unbalanced Faults

4.2.1 Simulation Scenarios M1 and M2 with DFIG based Wind Park
As shown in Figure 53, the decoupled sequence control reduces the second harmonic pulsations
in IG electromechanical torque. It should be noted that, the performance of decoupled sequence control
is limited with the size of the GSC and the FRT requirement specified by the grid code as well as the
unbalanced fault type, its electrical distance to the WP. With a larger size GSC, these pulsations can
be totally eliminated as shown in Figure 54.

As shown in Figure 55, the active and reactive power outputs of the DFIG WT are similar for both
coupled and decoupled sequence control schemes in GSC. However, the decoupled sequence control
scheme in GSC results much higher negative sequence fault current contribution of the WP as shown
in Figure 56.

Polytechnique Montréal Page 43 of 58

Figure 53 IG electromagnetic torque in scenarios M1 and M2

Figure 54 IG electromagnetic torque in scenarios M1 and M2 (with larger size GSC)

Figure 55 P and Q of aggregated DFIG WT in scenarios M1 and M2

Polytechnique Montréal Page 44 of 58

Figure 56 In and Ip of DFIG WT based WP in scenarios M1 and M2

4.2.2 Simulation Scenarios N1 and N2 with DFIG based Wind Park

As shown in Figure 57, decoupled sequence control totally eliminates the second harmonic
pulsations in IG electromechanical torque. This is due to less severe voltage sag at POI due to large
electrical distance between WP and the fault.

Similar to the BUS4 fault scenario, the active and reactive power output of DFIG WT is similar for
both control schemes in GSC as shown in Figure 58.

Alike BUS4 fault scenario, the decoupled sequence control scheme in GSC results much higher
negative sequence fault current contribution of the WP as shown in Figure 59.

Figure 57 IG electromagnetic torque in scenarios N1 and N2

Polytechnique Montréal Page 45 of 58

Figure 58 P and Q of aggregated DFIG WT in scenarios N1 and N2

Figure 59 In and Ip of DFIG WT based WP in scenarios N1 and N2

Polytechnique Montréal Page 46 of 58

5 AVERAGE VALUE MODEL PRECISION AND EFFICIENY

5.1 120 kV Test System Simulations

This section provides a comparison between average value model (AVM) and detailed model (DM)
of the presented wind park models. The simulation scenario M2 in Table I is repeated for 50 µs
simulation time step (M3) and for DM with 10 µs simulation time step (M4).

5.1.1 Simulation Scenarios M2 - M4 with FSC based Wind Park

As shown in Figure 60 - Figure 62, AVM usage instead of DM provides very accurate results even
for 50 µs time step usage.

Figure 60 PC2 and PS2 of aggregated FSC WT in scenarios M2 - M4

Figure 61 P0 and Q0 of aggregated FSC WT in scenarios M2 - M4

Polytechnique Montréal Page 47 of 58

Figure 62 In and Ip of FSC WT based WP in scenarios M2 - M4

5.1.2 Simulation Scenarios M2 - M4 with DFIG based Wind Park

As shown in Figure 63 - Figure 65, AVM usage instead of DM provides acceptable accuracy even
for 50 µs time step usage. From Figure 60 - Figure 65, it can be said that AVM provides more accurate
results when it is used to represent FSC WT converters.

Figure 63 IG electromagnetic torque in scenarios in scenarios M2 - M4

Figure 64 P0 and Q0 of aggregated DFIG WT in scenarios M2 - M4

Polytechnique Montréal Page 48 of 58

Figure 65 In and Ip of DFIG WT based WP in scenarios M2 - M4

5.2 IEEE 39 Bus System Simulations

A multi wind park system is developed from the IEEE-39 bus system by replacing two of the thermal
power plants (TPPs), as shown in Figure 66. Both WPs have 400 MW (266 x 1.5 MW) installed capacity.
However, the WP at bus B2 is FSC type and the WP at bus B25 is DFIG type. In the presented
simulation the WPs are operating at full load (i.e. under nominal wind speed) with unity power factor
(i.e. QPOI = 0). The transmission lines are modeled with constant parameter models, and the saturation
of transformers are taken into account.
In the simulated scenario, the disturbance is a DLG fault on transmission line that connects busses
B3 and B4 (as bus B3 end). The fault is cleared with the operation of line circuit breakers indicated with
CB1 and CB2 in Figure 66. The fault is applied at t = 1s. The fault clearing time is 200 ms (for testing
purposes). The system is simulated for 3 s. The simulations are performed for the models and simulation
time steps presented in Table II.

The presented waveforms in Figure 67 - Figure 72 demonstrate that AVM usage instead of DM
provides acceptable accuracy even for 50 µs time step usage while providing a significant computational
gain as illustrated in Table III. The computational gain over DM is more than 9 when the AVM is used
with 50 µs time step.
Table II IEEE 39 Bus System Simulations
Scenario WT Converter Model Simulation Time Step
S1 DM 10 µs
S2 AVM 10 µs
S3 AVM 50 µs

Table III IEEE 39 Bus System Simulations CPU Timings

Scenario CPU time
S1 1368 s
S2 615 s
S3 145 s

Polytechnique Montréal Page 49 of 58

 266 x 1.5 MW DFIG bus26_29
WP_DFIG_AVM1 +

418.90

shB29_75
shB26_75
DFIG WP
(AVM-V5) Load26
B25 bus26_28 bus28_29 Load29
B25 V1:1.07/_-10.3 +
317.70
+
101.20
B26
bus25_26 B28
266 x 1.5 MW FSC +
216.50
V1:1.04/_-12.44
V1:1.05/_-5.9
V1:1.05/_-0.0
FFC_WP_AVM1

bus26_27
Load25 Load28 B29

shB25_50

shB26_50
SM PowerPlant_09

bus02_25

22.9km+

98.50
B38

PI

+
FFC WP
B27 V1:0.99/_-15.9
(AVM - V3)

B2 V1:1.06/_-10.7

bus17_27
116.00
B2 772.9uS
bus01_02
+

bus17_18
109km

Load27 92MVAR@345kV

+
PI

PI
BUS24_shunt
+

+
55km
B18 B17 B24
bus02_03

101.20

B1 V1:0.99/_-15.5 V1:0.99/_-14.7 V1:0.99/_-13.4

V1:1.07/_-13.5
CP

bus16_17
Load24

+
+

Load18
bus03_18

bus16_24
+
+

89.10

PI
60km

PI
40km
B3 V1:0.98/_-13.4
B3 B16
V1:1.00/_-16.0
Load16
CB1 BRKB3B4
+
bus01_39

+
Load3

bus16_21
+
bus15_16

90.50
167.60

63.00
PowerPlant_06
FAULT
Fault
bus03_04

SM
142.80

bus21_22 B35
+
PowerPlant_01
B15 B21 93.80 B22
+

V1:0.95/_-15.7
SM Load21 V1:1.05/_0.5
Load4
CB2 Load15
BRKB4B3
B4 bus14_15
+
V1:0.99/_-8.4
145.40

bus22_23

bus23_24
+
B39 B4

bus16_19

234.60
130.70

64.30
V1:0.96/_-16.3 bus04_14
+
V1:1.03/_-16.5

+
86.50
+

Load39 B14
bus04_05

V1:0.98/_-13.3 Load23
85.80

+
bus13_14

67.70

B5 V1:1.05/_-2.8
B19
V1:0.99/_-12.2 B23
V1:1.05/_0.1
SM SM
bus05_06

17km +

B36
PI

Load12
PowerPlant_04
B33 PowerPlant_07
B6
1

V1:0.99/_-11.3 V1:0.97/_-39.8 B12

Change Scenario
xfo12_11

200MVA
tap=1.006 200MVA xfo19_20
xfo12_13
-30

-30
2

2
+

Ssenario 1 is normal load model

bus05_08

bus06_07

tap=1.006
SM
2

365.7/300/12.5 Scenario 2 is advanced load model

75.10

347.07/25 Load20
61.70

347.07/25 tap=1.06
1

1
bus06_11

1400MVA
+

55km

PowerPlant_02 B20 View Steady-State

+

PI

B31AndLoad 300kV
B7 SLACK V1:0.98/_-3.9
V1:0.95/_-15.9 B13 Show Load-Flow
B11
Load7 V1:1.00/_-9.7 PowerPlant_05
SM
bus07_08

V1:1.00/_-9.7
+

+
bus10_11
+

B34
31km

29km
+

bus10_13

MPLOT
29km
bus09_39

PI

PI
PI
167.60

line345_ACSR26_7_418_9
ON
B8 B10
V1:1.00/_-8.9 Load-Flow
V1:0.95/_-16.4
Load8
+
bus08_09

SM
243.30

LINE DATA
model in: line345_acsr26_7_418_9_rv.csv
PowerPlant_03
B32
B9
V1:1.03/_-17.0

Figure 66 IEEE 39 Bus System with Wind Parks

Polytechnique Montréal Page 50 of 58

Figure 67 PC2 and PS2 of aggregated FSC WT in IEEE 39 bus system simulation

Figure 68 P0 and Q0 of aggregated FSC WT in IEEE 39 bus system simulation

Figure 69 In and Ip of FSC WT based WP in IEEE 39 bus system simulation

Polytechnique Montréal Page 51 of 58

Figure 70 IG electromagnetic torque in IEEE 39 bus system simulation

Figure 71 P0 and Q0 of aggregated DFIG WT in IEEE 39 bus system simulation

Figure 72 In and Ip of DFIG WT based WP in IEEE 39 bus system simulation

Polytechnique Montréal Page 52 of 58

 6 DETAILED WIND PARK MODELS AND AGGREGATED MODEL
PRECISION
Certain grid integration studies, such as analysing collector grid faults and collector grid
overcurrent protection system performance, LVRT and HVRT capability studies [1], ferroresonance
study [29], require EMT type simulations with detailed wind park model. These studies do not only
require detailed MW collector grid model, but also detailed model of HV/MV wind park substation
including overvoltage protection, overcurrent and differential current protections, measuring current and
voltage transformers as shown in Figure 73 - Figure 75.

detailed MV collector grid model detailed HV / MV WP

dUref
Page
substation model
Detailed_Feeder1
dUref
Page WP_Substation

WPC
X
Feeder-1 (Detailed Feeder Model) F1

120 kV / 34.5 kV
Wind Park
Detailed_Feeder2
dUref Transformer
Page

F2
X X X grid PCC
Feeder-2 (Detailed Feeder Model)

Detailed_Feeder3
dUref
Page
X
F3
Feeder-3 (Detailed Feeder Model)

Figure 73 EMTP diagram of the 45 x 1.5 MW wind park detailed model given in Figure 46.
grid
dUref

Can be improved to include measuring transformers

dUref
WPC

VIabc_POI

Ipoi
WPC

i
Vpoi
v

DR_trip Page
CB_TR
X

Page CB_OWF_trip CB_OWF_trip Page

DistR_trip Page

400/5
Simulation Model does not contain
CT_DistR

Star
connected to Ict_DistR Page
Connected Distance Relay & associated Voltage Transformer
distance relay Secondary

DR
400/5
DIFFERENTIAL
CT_TR_DR

connected to
RELAY differential relay Ict_TR_IN_DR Page Star
Connected
Secondary
Ict_f3_DR Page Iabc_F3

Ict_f2_DR Page Iabc_F2 TapRatio

TRIP Page DR_trip
1

Ict_f1_DR Page Iabc_F1 c

WindParkTransfo1
#T_wp_tr#
Ict_TR_IN_DR Page Iabc_TR_IN
2

OCR_IN

I 45kW AUX_TR
15kVAR 2 1
Load1 LF
-30
50m_cable

34.5/0.208
RL

ZZ_TR
+

VBB_20125e115 Page Vabc1 t 3.1741

9.5222Ohm
Ict_IN_OCR Page Iabc TRIP Page OCR_IN_trip
CB_IN

busbar input OCR 10 ohm / phase

X

CB_IN_trip Page
zig-zag transformer
V_34p5kV_bus
DR_trip Page

Page CB_IN_trip 1500/5 Star

V
CT_IN

Connected
OCR_IN_trip Page Ict_IN_OCR Page Secondary

VT_BusBar
Page VBB_20125e115
CB_F3

ZnO +
CB_F2

60000 >e S1
X
X
CB_F1

CB_F3_trip Page P Page VBB_20125e67

X

CB_F2_trip Page
CB_F1_trip Page ZnO_BusBar S2

600/5 600/5 Star

CT_F3_OCR

600/5 Star 20125 / 115 / 67.08

CT_F2_OCR

Star Connected
CT_F1_OCR

Connected connected to OCR

Connected connected to OCR Ict_f3_OCR Page Secondary
connected to OCR Ict_f1_OCR Page Secondary
Ict_f2_OCR Page Secondary

600/5 600/5
600/5 Star Star
CT_F2_DR

CT_F3_DR

Star connected to Connected connected to Connected

CT_F1_DR

connected to Connected Ict_f2_DR Page Secondary differential relay Ict_f3_DR Page Secondary
Ict_f1_DR Page Secondary differential relay
OCR_F1
differential relay OCR_F2 OCR_F3

I VT_F1 I VT_F2 I VT_F3

Page VF1_20125e115 Page VF2_20125e115 Page VF3_20125e115
S1 S1 S1
15m_1250kcmil_cable_F1

15m_1250kcmil_cable_F2

15m_1250kcmil_cable_F3

P Page VF1_20125e67 P Page VF2_20125e67 P Page VF3_20125e67

S2 S2 S2

t 15 m 1250 kcmil cable t 15 m 1250 kcmil cable t 15 m 1250 kcmil cable

RL

RL

RL

VF1_20125e115 Page Vabc1 20125 / 115 / 67.08 VF2_20125e115 Page Vabc1 20125 / 115 / 67.08 VF3_20125e115 Page Vabc1 20125 / 115 / 67.08
+

Ict_f1_OCR Page Iabc TRIP Page OCR_F1_trip Ict_f2_OCR Page Iabc TRIP Page OCR_F2_trip Ict_f3_OCR Page Iabc TRIP Page OCR_F3_trip

Feeder-1 OCR Feeder-2 OCR Feeder-3 OCR

DR_trip Page
DR_trip Page
DR_trip Page
Page CB_F3_trip
Page CB_F1_trip
Page CB_F2_trip
ZZ_F1 ZZ_F2
OCR_F3_trip Page ZZ_F3
OCR_F1_trip Page
ZnO +

OCR_F2_trip Page
ZnO +

60000 >e
ZnO +

60000 >e
42.85 60000 >e 42.85
128.55Ohm 128.55Ohm 42.85
128.55Ohm ZnO_F3
ZnO_F2
ZnO_F1
135.5 ohm / phase 135.5 ohm / phase 135.5 ohm / phase F3
zig-zag transformer zig-zag transformer
F3

F1 F2
zig-zag transformer
F1

F2

Figure 74 EMTP diagram of the HV/MV Wind Park Substation

Polytechnique Montréal Page 53 of 58

Figure 75 EMTP diagram of MV Feeder-1

The WT model in Figure 75 is obtained from the WP model presented in Chapter 3 by excluding
the WPC, WP transformer and collector grid equivalent. The associated device mask is shown in Figure
76. It does not include the tabs used for MV/HV WP transformer and WPC parameters. On the other
hand, the first tab of the aggregated wind turbine mask includes certain wind park parameters (total
number of WTs in the WP, POI and collector grid voltage levels, collector grid equivalent and the MV/HV
WP transformer impedances) in addition to the general wind turbine parameters (WT rated power,
voltage and frequency) and wind speed. It should be noted that, the MV/HV WP transformer and the
collector grid equivalent impedances are used GSC parameter calculation (see section 3.2.3.2).

Scenario M2 in Table I (DLG fault at BUS4 for GSC decoupled sequence control scheme) is
simulated using the detailed wind park model to conclude on accuracy of the aggregated model. As
shown in Figure 77 - Figure 80, the aggregated models of wind parks provide accurate results.

Polytechnique Montréal Page 54 of 58

Figure 76 Aggregated FSC based wind turbine device mask

Figure 77 Active and reactive power at POI, Wind Park with FSC WTs

Polytechnique Montréal Page 55 of 58

Figure 78 Positive and negative sequence currents at POI, Wind Park with FSC WTs

Figure 79 Active and reactive power at POI, Wind Park with DFIG WTs

Figure 80 Positive and negative sequence currents at POI, Wind Park with DFIG WTs

Polytechnique Montréal Page 56 of 58

7 REFERENCES

[1] U. Karaagac, J. Mahseredjian and L. Cai, “High Voltage Ride-Through Capability of DFIG-based
Wind Parks with FACTS,” Proc. of 13th International Workshop on Large-Scale Integration of
Wind Power into Power Systems, Berlin, Germany, Nov. 2014.
[2] O. Anaya-Lara, N. Jenkins, J. Ekanayake, P. Cartwright, and M. Hughes, Wind Energy
Generation: Modelling and control, Wiley, 2009, John Wiley & Sons, Ltd.
[3] N. W. Miller, W. W. Price, and J. J. Sanchez-Gasca, “Dynamic modeling of GE 1.5 and 3.6 wind
turbine-generators,” GE-Power System Energy Consulting, General Electric International, Inc.,
Schenectady, NY, USA, Oct. 2003.
[4] G. Abad, J. Lopez, M. A. Rodriguez, L. Marroyo, G. Iwanski, Doubly Fed Induction Machine:
Modeling and Control for Wind Energy Generation, 2011, Wiley.
[5] M. Singh, S. Santoso, Dynamic Models for Wind Turbines and Wind Power Plants, 2011.
[6] J. M. Garcia, “Voltage control in wind power plants with doubly fed generators,” Ph.D. thesis,
Alaborg Univ., Denmark, Sep. 2010.
[7] V. Akhmatov, A. H. Nielsen, J. K. Pedersen, O. Nymann, "Variable-speed wind turbines with multi-
pole synchronous permanent magnet generators. Part I: Modelling in dynamic simualtion tools",
Wind Eng., vol. 27, no. 6, pp. 531-548, Dec. 2003.
[8] S. R. Sanders, J. M. Noworolski, X. Z. Liu, and G. C. Verghese, “Generalized averaging method
for power conversion circuits,” IEEE Trans. on Power Electron, vol. 6, no. 2, pp. 251–259, Apr.
1991.
[9] J. Morren, S. W. H. de Haan, P. Bauer, J. Pierik, and J. Bozelie, “Comparison of complete and
reduced models of a wind turbine with Doubly-fed Induction Generator,” in Proc. 10th Eur. Conf.
Power Electron. Appl., Toulouse, France, Sep. 2003.
[10] J. G. Slootweg, H. Polinder, and W. L. Kling, “Representing wind turbine electrical generating
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