Download GE WTG Modeling-v4 2..

Modeling of GE Wind
Turbine-Generators for
Grid Studies
Prepared by:
Kara Clark
Nicholas W. Miller
Juan J. Sanchez-Gasca
Version 4.2
June 24, 2008
General Electric International, Inc.
One River Road
Schenectady, NY 12345
USA
Legal Notice
This report was prepared by General Electric International, Inc. (GEII) as an account of
work sponsored by GE’s Wind Energy business. Neither Wind Energy nor GEII, nor any
person acting on behalf of either:
1. Makes any warranty or representation, expressed or implied, with respect to the use of
any information contained in this report, or that the use of any information, apparatus,
method, or process disclosed in the report may not infringe privately owned rights.
2. Assumes any liabilities with respect to the use of or for damage resulting from the use
of any information, apparatus, method, or process disclosed in this report.
ii
Foreword
This document was prepared by GE Energy in Schenectady, NY. Technical and
commercial questions and any correspondence concerning this document should be
referred to:
Nicholas W. Miller
GE Energy
Building 2, Room 605
Schenectady, New York 12345
Phone: (518) 385-9865
Fax: (518) 385-5703
E-mail: [email protected]
iii
Summary of Changes in Version 4.2
• Revised generator/converter model source current calculation and interface with network
solution
• Moved low voltage power logic from electrical control models to generator/converter model
• Updated text, figures, and data as appropriate to reflect the above changes
• Reran all DFAG and full converter test simulations for Sections 6, 7 and 8.
Summary of Changes in Version 4.1
• Simplified PLL in generator model, added low voltage active current regulation and reactive
current limits to prevent excessive voltage to generator model
• Modified converter current limiter in control model, and XIQmax/XIQmin limits
• Removed LVRT voltage support function from control model
• Updated official names – i.e., WindVAR became WindCONTROL
• Updated example simulations in Sections 6 and 7. Added comparison to Windtrap.
Summary of Changes in Version 4.0
• Added full converter model block diagrams, discussion, simulation results, etc
• Moved generator voltage protection discussion to generator model section
• Folded “Other Technical Issues” section into other parts of the report
• Modified PLL in generator model.
• Modified turbine control to include Active Power Control.
• Added figure showing details of improved pitch compensation in turbine model
Summary of Changes in Versions 3.4, 3.4a, 3.4b
• Corrections regarding Kqi and Kvi in Section 4.2.2 and Table 4-5 (version 3.4b)
• Adjustment of values of per unit Qmax and unit transformer MVA and impedance for 1.5 MW
WTG (version 3.4a)
• Phase-locked loop added to converter/generator model (version 3.4)
• WindVar emulator model changed to be closer to real control logic (version 3.4)
• Phase angle regulation option added to electrical control (version 3.4)
• Generator protection tripping model description updated and moved to Section 4.4 (version
3.4)
• Recommended parameter values updated based on latest validation testing (version 3.4)
Revision History
Version 1.0 – December 4, 2002
Version 2.0 – March 14, 2003
Version 3.0 – October 27, 2003
Version 3.1 – December 22, 2003
Version 3.2 – May 4, 2004
Version 3.3 – June 7, 2004
Version 3.4 – December 21, 2004
Version 4.0 – September 22, 2006
Version 4.1 – March 2008
Version 4.2 – June 24, 2008
iv
Table of Contents
1
INTRODUCTION.....................................................................................................................1.1
2
MODEL OVERVIEW AND PHILOSOPHY .............................................................................2.1
2.1
2.2
2.3
3
ANALYTICAL APPROACH....................................................................................................3.1
3.1
3.2
4
DOUBLY-FED ASYNCHRONOUS GENERATOR (DFAG) FUNDAMENTALS ................................2.1
FULL CONVERTER WTG FUNDAMENTALS ..........................................................................2.3
OVERALL MODEL STRUCTURE ...........................................................................................2.4
LOAD FLOW MODEL ..........................................................................................................3.1
INITIAL CONDITIONS FOR DYNAMIC SIMULATION ..................................................................3.3
DOUBLY FED ASYNCHRONOUS GENERATOR (DFAG) DYNAMIC MODELS ................4.1
4.1
GENERATOR/CONVERTER MODEL .....................................................................................4.1
4.2
ELECTRICAL (CONVERTER) CONTROL MODEL ....................................................................4.4
4.2.1 WindCONTROL Emulator ..........................................................................................4.6
4.2.2 Electrical Control ........................................................................................................4.7
4.2.3 Open Loop Control Logic ...........................................................................................4.8
4.3
WIND TURBINE AND TURBINE CONTROL MODEL .................................................................4.9
4.3.1 Turbine Control Model..............................................................................................4.11
4.3.2 Rotor Mechanical Model ..........................................................................................4.13
4.3.3 Wind Power Model ...................................................................................................4.15
4.3.4 Active Power Control Model & Rate Limit Function .................................................4.17
5
FULL CONVERTER WTG DYNAMIC MODELS....................................................................5.1
5.1
5.2
5.3
6
GENERATOR/CONVERTER MODEL .....................................................................................5.1
ELECTRICAL (CONVERTER) CONTROL MODEL ....................................................................5.2
WIND TURBINE AND TURBINE CONTROL MODEL .................................................................5.6
DFAG WTG BENCHMARK SIMULATIONS ..........................................................................6.1
6.1
TEST SYSTEM ...................................................................................................................6.1
6.2
DFAG WTG BENCHMARK SIMULATION RESULTS ...............................................................6.2
6.2.1 Fault Response with WindCONTROL Emulator ........................................................6.3
6.2.2 Active Power Control and Power Response Rate Limit Performance .......................6.6
6.2.3 Wind Speed Ramp Simulation ...................................................................................6.8
6.3
DFAG WTG BENCHMARK SIMULATION DYNAMIC DATA....................................................6.10
7
FULL CONVERTER WTG BENCHMARK SIMULATIONS ...................................................7.1
7.1
TEST SYSTEM ...................................................................................................................7.1
7.2
FULL CONVERTER WTG BENCHMARK SIMULATION RESULTS ..............................................7.1
7.2.1 Fault Response with WindCONTROL Emulator ........................................................7.3
7.2.2 Zero-Power Operation................................................................................................7.6
7.2.3 Converter Current Limit Performance ......................................................................7.10
7.2.4 Low Voltage Power Logic Performance...................................................................7.13
7.2.5 Dynamic Braking Resistor Performance ..................................................................7.13
7.3
FULL CONVERTER WTG BENCHMARK SIMULATION DYNAMIC DATA ...................................7.15
8
COMPARISON OF PSLF RESULTS TO WINDTRAP RESULTS.........................................8.1
8.1
8.2
9
1.5 MW DFAG COMPARISON ...........................................................................................8.1
2.5 MW FULL CONVERTER COMPARISON ..........................................................................8.4
CONCLUSIONS......................................................................................................................9.1
v
Table of Figures
Figure 2-1.
Figure 2-2.
Figure 2-3.
Figure 3-1.
Figure 4-1.
Figure 4-2.
Figure 4-3.
Figure 4-4.
Figure 4-5.
Figure 4-6.
Figure 4-7.
Figure 4-8.
Figure 4-9.
Figure 5-1.
Figure 5-2.
Figure 5-3.
Figure 6-1.
Figure 6-2.
Figure 6-3.
Figure 6-4.
Figure 6-5.
Figure 7-1.
Figure 7-2.
Figure 7-3.
Figure 7-4.
Figure 7-5.
Figure 7-6.
Figure 7-7.
Figure 7-8.
Figure 8-1.
Figure 8-2.
Figure 8-3.
Figure 8-4.
Figure 8-5.
Figure 8-6.
Figure 8-7.
GE 1.5 MW and 3.6 MW WTG Major Components. ....................................2.1
GE Full Converter WTG Major Components. ................................................2.3
GE WTG Dynamic Model Connectivity.........................................................2.5
Simplified Wind Plant Power Flow Model. ....................................................3.2
DFAG Generator/Converter Model.................................................................4.2
Overall DFAG Reactive Power and Electrical Control Model. ......................4.5
Reactive Power Control Model. ......................................................................4.5
DFAG Electrical Control Model. ....................................................................4.6
Wind Turbine Model Block Diagram. ..........................................................4.10
Pitch Control and Pitch Compensation Block Diagram................................4.11
Two-Mass Rotor Model. ...............................................................................4.14
Wind Power Cp Curves.................................................................................4.16
Example Frequency Response Curve............................................................4.18
Full Converter WTG Generator/Converter Model..........................................5.1
Full Converter WTG Electrical Control Model. .............................................5.4
Converter Current Limit Model. .....................................................................5.5
DFAG Test System. ........................................................................................6.1
Series of Bus Faults with Various Fault Impedances......................................6.4
3-phase Fault to Ground, Cleared by Tripping 230 kV Line. .........................6.5
Active Power Control Response to Loss of Load. ..........................................6.7
Response to Wind Speed Ramp Up and Down...............................................6.9
Series of Bus Faults with Various Fault Impedances......................................7.4
3-phase Fault to Ground, Cleared by Tripping 230 kV Line. .........................7.5
Increasing Wind Speed Results in Zero-Power Operation..............................7.7
Decreasing Wind Speed Results in Zero-Power Operation. ...........................7.8
Voltage Regulation in Continuous Zero-Power Operation. ............................7.9
Step Reduction in Converter Current Limit with P Priority..........................7.11
Step Reduction in Converter Current Limit with Q Priority. ........................7.12
Low Voltage Power Logic Response to Fault on POI Bus. ..........................7.14
Test System for PSLF and Windtrap Comparison. .........................................8.1
1.5 MW DFAG PSLF and Windtrap Terminal Voltage Response. ................8.2
1.5 MW DFAG PSLF and Windtrap Real Power Response...........................8.3
1.5 MW DFAG PSLF and Windtrap Reactive Power Response. ...................8.3
2.5 MW Full Converter PSLF and Windtrap Terminal Voltage Response.....8.5
2.5 MW Full Converter PSLF and Windtrap Real Power Response. .............8.5
2.5 MW Full Converter PSLF and Windtrap Reactive Power Response........8.6
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Table of Tables
Table 3-1. Individual WTG Power Flow Data...................................................................3.2
Table 4-1. Typical Low-Voltage Ride Through Voltage Thresholds and Durations. .......4.3
Table 4-2. DFAG Generator/Converter Parameters...........................................................4.4
Table 4-3. WindCONTROL Emulator Parameters (on Generator MVA Base). ...............4.7
Table 4-4. DFAG Electrical Control Parameters. ..............................................................4.8
Table 4-5. Open Loop Reactive Power Control Logic. .....................................................4.9
Table 4-6. Open Loop Reactive Power Control Parameters. .............................................4.9
Table 4-7. DFAG WTG Turbine Control Parameters (on Turbine MW Base). ..............4.13
Table 4-8. DFAG WTG Rotor Mechanical Model Parameters (on Turbine MW Base).4.14
Table 4-9. DFAG WTG Wind Power Coefficients..........................................................4.15
Table 4-10. Cp Coefficients αi,j ........................................................................................4.17
Table 4-11. Active Power Control and Rate Limit Function Parameters. .......................4.19
Table 5-1. Full Converter Generator/Converter Parameters. .............................................5.1
Table 5-2. Full Converter WTG Electrical Model. ............................................................5.5
Table 5-3. Full Converter WTG WindCONTROL Emulator Parameters. ........................5.5
Table 5-4. Full Converter WTG Turbine Control Parameters (on Turbine MW Base).....5.7
Table 5-5. Full Converter WTG Rotor Model Parameters (on Turbine MW Base). .........5.7
Table 5-6. Full Converter WTG Wind Power Coefficients. ..............................................5.7
Table 6-1. DFAG Generator Model (gewtg) Data for Simulations. ................................6.10
Table 6-2. DFAG Electrical Control Model (exwtge) Data for Simulations...................6.11
Table 6-3. DFAG Turbine Control Model (wndtge) Data for Simulations. ....................6.12
Table 7-1. Full Converter WTG Generator Model Data for Simulations. .......................7.15
Table 7-2. Full Converter WTG Electrical Control Model Data for Simulations. ..........7.16
Table 7-3. Full Converter WTG Turbine Control Model Data for Simulations. .............7.17
vii
1
Introduction
GE Energy has an ongoing effort dedicated to the development of models of GE wind
turbine generators (WTG) suitable for use in system impact studies. This report
documents the present recommendations for dynamic modeling of wind plants with either
doubly fed asynchronous WTGs (GE 1.5 and 3.6 MW) or WTGs with a full converter (GE
Multi-Megawatt 2.5 MW). The modeling recommendations for the full converter
machines are for the first generation of these machines. This report includes recommended
model structure and data, as well as the assumptions, capabilities and limitations of the
resulting model.
The model provided is as detailed as is appropriate for bulk power system studies. It is
valuable to put the model limitations in the context of what analysis is required. Most
important, this model is for positive sequence phasor time-domain simulations – e.g. PSLF
or PSS/e. Second, this assumes that the analysis is mainly focused on how the WTGs react
to grid disturbances, e.g. faults, on the transmission system. Third, the model provides for
calculation of the effect of wind speed fluctuation on the electrical output of the WTG.
Details of the device dynamics have been substantially simplified. Specifically, the very
fast dynamics associated with the control of the generator converter have been modeled as
algebraic (i.e. instantaneous) approximations of their response. Representation of the
turbine mechanical controls has been simplified as well. The model is not intended for use
in short circuit studies or electromagnetic transient studies.
The models, as implemented in GE’s PSLF dynamic simulation program, have been
validated against more detailed design models. Selected validation comparisons are
documented in Section 8. Additional PSLF simulation examples showing doubly-fed
asynchronous generator (DFAG) and full converter WTG performance are included in
Sections 6 and 7.
These models were developed specifically for the latest GE WTGs. The model is
applicable, with care, to other recent vintage GE WTGs and other WTGs, as long as the
basic principles of power conversion and control are the same. However, this model is not
designed for, nor intended to be used as, a general purpose WTG model. There are
substantial variations between models and manufacturers.
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GE WTG Modeling-v4.2.doc, 6/24/08
2 Model Overview and Philosophy
2.1 Doubly-Fed Asynchronous Generator (DFAG) Fundamentals
A simple schematic of an individual GE 1.5 or 3.6 wind turbine-generator (WTG) is
shown in Figure 2-1. The GE WTG generators are unusual from a system simulation
perspective. Physically, the 1.5 or 3.6 MW machine is a relatively conventional wound
rotor induction (WRI) machine. However, the key distinction is that this machine is
equipped with a solid-state voltage-source converter AC excitation system. The AC
excitation is supplied through an ac-dc-ac converter. For the GE 3.6 MW machine the
converter will be connected as shown or to a third winding on the main unit step-up
transformer. For the GE 1.5 MW machine it is connected directly at the stator winding
voltage. Machines of this structure are termed ‘doubly-fed asynchronous generators’
(DFAG), and have significantly different dynamic behavior than either conventional
synchronous or induction machines.
Modeling of any of the GE machines with conventional dynamic models for either
synchronous or induction machines will not give correct results.
P net
Q net
3 φ AC Windings
fnet
Collector
System
(e.g.
34.5kV
bus)
P stator
frotor
P rotor
P rotor
F rotor
P conv
F network
Wind Turbine
Wound-Rotor
Induction Generator
Converter
Figure 2-1. GE 1.5 MW and 3.6 MW WTG Major Components.
The fundamental frequency electrical dynamic performance of the DFAG is completely
dominated by the converter. Conventional aspects of generator performance related to
internal angle, excitation voltage, and synchronism are largely irrelevant. In practice, the
electrical behavior of the generator and converter is that of a current-regulated voltagesource inverter. Like other voltage-source inverters (e.g., a BESS or a STATCOM), the
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WTG converter synthesizes an internal voltage behind a transformer reactance, which
results in the desired active and reactive current being delivered to the device terminals.
In the case of the doubly-fed machines, the machine rotor and stator windings are
primary and secondary windings of the transformer. The rotation of the machine means
that the ac frequency on the rotor winding corresponds to the difference between the stator
frequency (50 or 60 Hz) and the rotor speed. This is the slip frequency of the machine. In
the vicinity of rated power, the GE 1.5 and 3.6 MW machines will normally operate at
120% speed, or -20% slip. Control of the excitation frequency allows the rotor speed to be
controlled over a wide range, ±30%. The rotation also means that the active power is
divided between the stator and rotor circuits, roughly in proportion to the slip frequency.
For rotor speeds above synchronous, the rotor active power is injected into the network
through the converter. The active power on the rotor is converted to terminal frequency
(50 or 60 Hz), as shown in Figure 2-1.
In addition to controlling the rotor speed, the reactive power output of the generator
can be controlled by varying the magnitude of the rotor currents. This gives the doublyfed machine the voltage regulation capability of a synchronous generator but with greater
speed of response.
For all GE machines, the control of active and reactive power is handled by fast, high
bandwidth regulators within the converter controls. The time responses of the converter
regulators are sub-cycle, and as such can be greatly simplified for simulation of bulk power
system dynamic performance.
Broadly stated, the objectives of the turbine control are to maximize power production
while maintaining the desired rotor speed and avoiding equipment overloads. There are
two controls (actuators) available to achieve these objectives: blade pitch control and
torque order to the electrical controls (the converter). The turbine model includes all of the
relevant mechanical states and the speed controls. The implementation of the turbine
model, while relatively complex, is still considerably simpler than the actual equipment.
Losses are not considered throughout the model, since “fuel” efficiency is not presently a
consideration. These simplifications are examined in the detailed model discussion in
Section 4.
The model presented in Section 4 describes the relevant dynamics of a single doubly
fed GE WTG. However, the primary objective of this model is to allow for analysis of the
performance of groups of WTGs and how they interact with the bulk power system. Wind
plants with GE WTGs normally include a wind farm management system
(WindCONTROL). Two components of this system are currently incorporated - the VoltAmpere-Reactive or Var control system and the Active Power Control (APC). The Var
control interacts with the individual WTGs through the electrical controls, the APC is
incorporated in the turbine model. Representation of all the individual machines in a large
wind plant is inappropriate for most grid stability studies. Hence, there is provision within
the model structure to allow a single equivalent WTG machine model to represent multiple
WTGs. The model implementation allows the user access to parameters that might
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reasonably be customized to meet the particular requirements of a system application.
These parameters are discussed in more detail in Section 4.
2.2 Full Converter WTG Fundamentals
The GE Multi-Megawatt WTG product line uses full conversion technology. Unlike
the generators for the 1.5 and 3.6 MW WTGs, the full converter machine is a relatively
conventional permanent magnet synchronous generator. The generator is connected to the
power grid through a full converter. This configuration decouples the generator speed
from the power system frequency and allows for a wide range of variable speed operation.
Figure 2-2 shows the configuration of the full converter WTG.
Converter
f stator
P stator
3φ AC Winding
Wind Turbine
Q
stator
Pnet= Pstator
Q net
fnet
f stator
net
P stator
Collector System
(e.g. 34.5kV bus)
Permanent
frotor
Magnet
P rotor
Rotor
Figure 2-2. GE Full Converter WTG Major Components.
Like the GE 1.5 and 3.6 MW machines, the fundamental frequency electrical dynamic
performance of the GE Multi-Megawatt WTG is completely dominated by the converter.
For the full converter machines, the line-side of the converter corresponds to the WTG
terminals. The electrical behavior on the variable frequency machine side of the converter
is of no interest to the AC system. Further, operation (i.e., rotation) of the turbine is not
required for the converter to continue reactive operation on the line-side. In the vicinity of
rated power, the GE full converter machines will normally operate at a speed selected to
give optimum turbine performance. Control of the frequency converter allows the rotor
speed to be completely decoupled from the grid frequency, and to be controlled over a
wide range.
Similar to the DFAG WTGs, the control of active and reactive power is handled by
fast, high bandwidth regulators within the converter controls, and can be greatly simplified
for simulation of bulk power system dynamic performance.
The turbine control is also similar to that used for a DFAG WTG.
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The model presented in Section 5 describes the relevant dynamics of a single full
converter WTG. As noted above in the DFAG discussion, the primary objective of this
model is to allow for analysis of the performance of groups of WTGs and how they
interact with the bulk power system. Hence, the Var control system and the APC are both
incorporated in the models. Representation of all the individual machines in a large wind
plant is inappropriate for most grid stability studies. Hence, there is provision within the
model structure to allow a single equivalent WTG machine model to represent multiple
WTGS. The model implementation allows the user access to parameters that might
reasonably be customized to meet the particular requirements of a system application.
These parameters are discussed in more detail in Section 5.
2.3 Overall Model Structure
From a load flow perspective, standard generator and transformer models are required
for initialization of the dynamic simulation program. These two devices are represented by
conventional load flow models. Details are presented in Section 3.
The dynamic models presented here are specific to GE WTGs. The implementation is
structured in a fashion that is similar to conventional generators. To construct a complete
WTG model, three device models are used, as shown in Figure 2-3:
•
•
•
Generator/converter model
Electrical control model
Turbine and turbine control model
The generator/converter model injects real and reactive current into the network in
response to control commands, and represents low and high voltage protective functions
(e.g., low voltage ride through capability). The same generator/converter model, with
different data, is used to represent both DFAG WTGs (e.g., GE’s 1.5 and 3.6 MW) and full
converter WTGs (e.g., GE’s Multi-Megawatt 2.5 MW).
The electrical control model includes both closed and open loop reactive power
controls, and voltage regulation with either a simplified emulator of GE’s
WindCONTROL system or a separate, detailed model. This model sends real and reactive
commands to the generator/converter model. Different electrical control models are used
to represent DFAG WTGs and full converter WTGs
The turbine and turbine control model represents the mechanical controls, including
blade pitch control and power order (torque order in the actual equipment) to the converter;
under speed trip; rotor inertia equation; wind power as a function of wind speed, blade
pitch, rotor speed; and active power control. One model is used to represent both DFAG
and full converter WTGs. However, more functions (e.g., dynamic braking resistor) are
enabled for a full converter WTG than for a DFAG machine.
In addition, user-written models can be developed to represent wind gusts or other
profiles by varying input wind speed to the turbine model, or to represent additional
protective functions (e.g., over/under frequency).
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GE WTG Modeling-v4.2.doc, 6/24/08
Vreg bus
Vterm
Trip Signal
Ip (P)
Command
Electrical
Control
Model
Generator/
Converter
Model
E" or IQ (Q)
Command
Pgen , Qgen
Power
Order
Wind Profile
Model
(User-written)
Wind
Speed
Pelec
Turbine &
Turbine Control
Model
Fterm
Figure 2-3. GE WTG Dynamic Model Connectivity.
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3 Analytical Approach
In practice, a wind plant has a local grid collecting the output from the machines into a
single point of interconnection to the grid. Since the wind plant is made up of many
identical machines, it is a reasonable approximation to parallel all the machines into a
single equivalent large machine behind a single equivalent reactance. This approach is
consistent with the models presented in this report. However, there are limitations.
Disturbances within the local collector grid cannot be analyzed, and there is some
potentially significant variation in the equivalent impedance for the connection to each
machine. A single machine equivalent requires the approximation that the power output of
all the machines will be the same at a given instant of time. For grid system impact
studies, simulations are typically performed with the initial wind of sufficient speed to
produce rated output on all machines. Under this condition, the assumption that all
machines are initially at the same (rated) output is not an approximation. Otherwise, this
assumption presumes that the geographic dispersion is small enough that the wind over the
plant is uniform. Simulations of bulk system dynamics using a single machine equivalent
is adequate for most planning studies.
Detailed modeling of the WTG collector system is possible. The inclusion of the
WindCONTROL in each WTG’s electrical control model provides an emulation of the
action of a single centralized control. An intermediate level of modeling detail can also be
used in which groups of WTGs, e.g. those on a single collector feeder, are represented by a
single equivalent model.
3.1 Load Flow Model
The modeling of a GE WTG or wind plant for load flow analysis is generally simple.
As noted above, wind plants normally consist of a large number of individual WTGs.
While the wind plant model may consist of a detailed representation of each WTG and the
collector system, a simpler model is appropriate for most bulk system studies.
Such a model is shown in Figure 3-1. This model consists of a single WTG and unit
transformer with MVA ratings equal to N times the individual device ratings, where N is
the number of WTGs in the wind plant (or those considered on-line for study purposes).
An equivalent impedance to reflect the aggregate impact of the collector system can be
included together with the substation step-up transformer(s). The total charging
capacitance of the collector system should also be included. The charging capacitance can
be significant since underground cables are often used for the collector system.
The aggregate WTG is modeled as a conventional generator connected to a (PV) bus.
The generator real power output (Pgen), maximum reactive power output (Qmax), and
minimum reactive power output (Qmin) are input as N times the unit capabilities shown in
Table 3-1. The nominal voltage at the generator terminals depends on the WTG size and
system frequency. Typical unit transformer ratings and impedances are also shown.
Typical collector system voltages are at distribution levels - 12.5 kV or 34.5 kV are
common in 60 Hz applications, 33 kV in 50 Hz applications. The substation transformer
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would be suitably rated for the number of WTGs, with an impedance typically around
10%.
Project Substation
High Side Bus
(collector, e.g. 34.5kV)
Point of
Interconnection
(POI) Bus
Vreg bus
Terminal Bus
P gen
Substation
Transformer
Collector
Equivalent
Impedance
and Charging
Capacitance
Q gen
Unit
Transformer
Vterm
Figure 3-1. Simplified Wind Plant Power Flow Model.
Table 3-1. Individual WTG Power Flow Data.
Generator Rating
Pmax
Pmin
Qmax
Qmin
Terminal Voltage (60 Hz)
Terminal Voltage (50 Hz)
Unit Transformer Rating
Unit Transformer Z
Unit Transformer X/R
GE 1.5
GE 3.6
GE 2.5
1.67 MVA
1.5 MW
0.07 MW
0.726 MVAr
-0.726 MVAr
575 V
690 V
1.75 MVA
5.75%
7.5
4 MVA
3.6 MW
0.16 MW
2.08 MVAr
-1.55 MVAr
4160 V
3300 V
4 MVA
7%
7.5
3 MVA
2.5 MW
0 MW
1.20 MVAr
-1.20 MVAr
690 V
690 V
2.8 MVA
6.0%
7.5
The WindCONTROL system is structured to measure the voltage at a particular bus,
often the point of interconnection (POI) with the transmission system, and regulate this
voltage by sending a reactive power command to all of the WTGs. Line drop
compensation may be used to regulate the voltage at a point some distance from the
voltage measurement bus. For load flow modeling of the WindCONTROL, the aggregate
WTG (or each WTG) should be set to regulate the remote bus at the desired voltage
regulation point. Depending upon the applicable grid requirements for voltage and
reactive power range, the substation transformer may be an automatic load-tap-change
(LTC) transformer. Operation of the LTC controls may be autonomous, or coordinated
with the WindCONTROL.
GE Energy
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3.2 Initial Conditions for Dynamic Simulation
The load flow provides initial conditions for dynamic simulations. The conditions
outlined above are generally applicable to the dynamic model presented below. The
maximum and minimum active and reactive power limits must be respected in order to
achieve a successful initialization.
If the WTG electrical control or additional substation controls are customized to meet a
particular set of desired performance objectives, then the load flow must be initialized in
accordance with those customized rules. For example, if the active power controls are set
to curtail power to 95% of that available in the wind, then the real power at the load flow
generator must be set accordingly. Similarly, it is possible to inject or absorb reactive
power (e.g., regulate voltage) at zero real power with a full converter WTG. Therefore, the
real power at the generator in the power flow must be zero for this type of simulation.
Inconsistencies between the power flow and the dynamic model will result in an
unacceptable initialization.
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4 Doubly Fed Asynchronous Generator (DFAG) Dynamic
Models
This section presents the engineering assumptions, detailed structure, and data for each
of the component models necessary to represent a GE 1.5 or 3.6 MW WTG.
4.1 Generator/Converter Model
This model (gewtg in PSLF) is the equivalent of the generator and field converter, and
provides the interface between the WTG and the network. Unlike a conventional generator
model, it contains no mechanical state variables for the machine rotor – these are included
in the turbine model. Further, unlike conventional generator models, all of the flux
dynamics have been eliminated to reflect the rapid response of the converter to the higher
level commands from the electrical controls. The net result is an algebraic, controlledcurrent source that computes the required injected current into the network in response to
the flux and active current commands from the electrical control model. This controlledcurrent source also incorporates the low voltage power logic and the fast-acting converter
controls that mitigate over-voltages by reducing reactive current output.
The model is shown in Figure 4-1. It holds constant both the active power (X-axis)
component of current and the X-axis voltage (Y-axis flux) behind the generator effective
reactance, X”. The real and reactive command signals are developed in the electrical
control model described in Section 4.2. The low-pass filters on the incoming command
signals are simple approximations to the complex, fast electronic control system. This
small lag (0.02 seconds) provides a reasonable representation in the time frame of interest.
As with all positive sequence fundamental frequency analysis, sub-cycle behavior is not
meaningful.
The Low Voltage Power Logic (LVPL) reduces system stress during and immediately
following sustained faults by limiting the real current command with both a cap (upper
limit) and a ramp rate limit. Under normal operating conditions, the filtered terminal
voltage is above a user-specified breakpoint (brkpt) and there is no cap. When the voltage
falls below the breakpoint during a fault, a cap is calculated and applied. When the voltage
is below a user-specified zero-crossing point (zerox), the cap becomes zero. The userspecified ramp rate limit (rrpwr) is key to the post-fault power recovery. During this
recovery period, the voltage will exceed the breakpoint and the cap is removed. However,
the real current command rate of increase will be restricted by the ramp rate limit.
Comparison with more detailed models of the generator and controls has shown that
this is an accurate model of the combined behavior of the doubly-fed generator and its
rotor converter when the value of X” is set to 0.80 pu (on the generator MVA rating) for
both the 1.5 MW and 3.6 MW WTGs. X” represents an effective equivalent reactance and
is not the actual subtransient reactance of the doubly-fed induction generator.
The actual converter controls include a phase-locked loop (PLL) to synchronize the
generator rotor currents with the stator currents. However, the PLL dynamics are
extremely fast relative to the PSLF time frame, and under normal grid operating conditions
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result in effectively perfect tracking. Under transient conditions of severe voltage
depression and relatively high system impedance, delivery of active current becomes
limited. The control actions of the PLL and current regulator effectively result in reduced
active current delivery. This fast regulator and PLL action is captured in the model by a
low voltage active current management function. This is a linear reduction of active
current injection for terminal voltages below 0.8 pu. This effect is modeled within the
network solution (i.e. without state variables), which is consistent with the overall
algebraic modeling of current injection by the generator/converter model. The reactive
current delivery remains high under these transient conditions, providing voltage support
and short circuit strength.
The fast regulator and PLL dynamics of the converter will also act to limit excess
voltage on the terminals of the generator by suppressing reactive current injection when the
terminal voltage rises excessively. This effect is modeled by a high voltage reactive
current management function in the network solution, which drives reactive current
injection down to limit terminal voltage to 120%. Reactive current injection is limited to
the machine rating.
Eq"cmd
1
1+ 0.02s
(efd)
From
exwtge
-1
High Voltage
X"
Reactive Current
s0
Management
LVPL & rrpwr
IPcmd
Low Voltage
Active Current
IPlv
1
1+ 0.02s
(ladifd)
From
exwtge
Isorc
Management
s1
LVPL
Vterm
1.11
LVPL
V
1
1+ 0.02s
s2
V
zerox
(0.50)
jX"
brkpt
(0.90)
Low Voltage Power Logic
Figure 4-1. DFAG Generator/Converter Model.
The generator model also includes over/under voltage protective functions. In
particular, the low voltage tripping can be set to meet so-called “low-voltage ride through”
or “zero-voltage ride through” requirements. These requirements are explicitly defined
such that wind plants must not trip for events that are less severe than the defined
thresholds and time durations. Wind plants may tolerate more severe events without
tripping. Use of the model therefore does not ensure that the plant will trip, only that it is
allowed to do so. The thresholds and time durations for this protection will vary
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significantly from one project to another as equipment designs are modified to meet
specific grid codes or interconnection agreements. Recommendations for modeling the
generator protection functions are as follows:
•
For feasibility and reliability impact studies of future wind projects: Do not
include the generator protection model or else set the trip levels consistent with
applicable grid codes for the project. An objective of the study should be to
establish the voltage and frequency excursions that may occur. These results
should then be reflected in the equipment specifications. The mechanism for
communicating this is the interconnect agreement. Prior to establishing the
interconnect agreement, the product capability should be understood via
communication with the GE representative.
•
For facility studies for projects in the design phase: Use trip settings consistent
with performance commitments. The results of the study should indicate
acceptable settings for the actual protective devices to satisfy system requirements
while providing adequate protection for the WTG equipment.
•
For studies involving in-service projects: Use the actual trip settings of the
protective equipment.
Table 4-1 gives seven trip levels and durations based on specifications for a 60 Hz,
1.5 MW unit with a typical protection option. The PSLF model provides six levels of
voltage tripping. The short term high voltage threshold can be ignored as sub-cycle
behavior in stability simulations is not meaningful. It is important to note that the low
voltage thresholds are a stepwise fit to a curve which is at zero voltage for 200 msec then
slopes up to 75% voltage at 2.85 seconds. The step-wise curve is conservative, in that it is
always inside the specification. As noted above, low voltage ride through requirements
vary from application to application. The tripping thresholds and durations should be
chosen to appropriately represent the application under study.
Any other desired protective functions (e.g., over/under frequency) would need to be
implemented with additional protective device models.
Table 4-1. Typical Low-Voltage Ride Through Voltage Thresholds and Durations.
V (%)
75
50
30
15
110
115
130
GE Energy
ΔV (pu)
-0.25
-0.50
-0.70
-0.85
0.10
0.15
0.30
4.3
Time (sec)
1.9
1.2
0.7
0.2
1.0
0.1
0.02
GE WTG Modeling-v4.2.doc, 6/24/08
Table 4-2 includes recommended settings for the DFAG generator/converter model.
The maximum allowed ramp rate limit, rrpwr, is 10. The LVPL breakpoint, brkpt, must be
greater than 0.5, less than 1.0, and greater than the zero-crossing, zerox.
Table 4-2. DFAG Generator/Converter Parameters.
Parameter Name
lpp
dvtrp1
dvtrp2
dvtrp3
dvtrp4
dvtrp5
dvtrp6
dttrp1
dttrp2
dttrp3
dttrp4
dttrp5
dttrp6
fcflg
rrpwr
brkpt
zerox
Recommended Value
0.8
-0.25
-0.50
-0.70
-0.85
0.10
0.15
1.9
1.2
0.7
0.2
1.0
0.1
0
5.
0.9
0.5
4.2 Electrical (Converter) Control Model
This model (exwtge in PSLF) dictates the active and reactive power to be delivered to
the system based on inputs from the turbine model (Pord) and from the supervisory VAr
controller (Qord). Qord can either come from a separate model or from the WindCONTROL
voltage and reactive control emulator function included in the electrical control model.
Qord can also be held constant or determined by a power factor regulator. The model
consists of the following control functions:
WindCONTROL Emulator
Power Factor Regulator
Electrical (Volt/VAr) Control
Open Loop Control Logic (used only on some older systems)
The overall block diagram for the Reactive Power Control and the Electrical Control is
shown in Figure 4-2. Figure 4-3 and Figure 4-4 show more detailed representations.
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Vrfq
Vreg
WindCONTROL
Emulator
From
separate
WindCONTROL
model
Open
Loop
Control
Logic
Qord
Qcmd
Eq"cmd
Qref
PFAref
Pelec
Power
Factor
Regulator
To Generator
Model
Electrical
Control
Reactive Power Control
IPcmd
Qgen
Vterm
From
Wind Turbine
Model
Pord
Figure 4-2. Overall DFAG Reactive Power and Electrical Control Model.
Vrfq
WindCONTROL
Emulator
Vreg
(vref)
+
1
1+ sTr
+
s4
1/fN
-
Qmax
Kiv/s
+
Kpv
1+ sTv
s3
Qwv
1
1+ sTc
Qord
s5
Qmin
s2
PFAref
Pelec
Qref
tan
(vref)
1
1+ sTp
(vref)
x
s6
Qord from separate model
0
(vref)
1
pfaflg
Qord
0
1
-1
Qmax
Open
Loop
Control
varflg
Qcmd
Qmin
Figure 4-3. Reactive Power Control Model.
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Qgen
Qcmd
Vterm
Vmax
+
KQi / s
Vref
s0
XIQmax
-
KVi / s
+
s1
XIQmin
Vmin
Pord
.
.
(vsig)
From
Wind Turbine
Model
Eq"cmd
(efd)
To Generator
Model
IPmax
IPcmd
(ladifd)
Vterm
Figure 4-4. DFAG Electrical Control Model.
4.2.1 WindCONTROL Emulator
The WindCONTROL emulator function represents a simplified equivalent of the
supervisory VAr controller portion of the entire wind farm management system
(WindCONTROL). The function monitors a specified bus voltage and compares it against
the reference voltage. The regulator itself is a PI controller. The time constant, Tc, reflects
the delays associated with cycle time, communication delay to the individual WTGs, and
additional filtering in the WTG controls. The voltage measurement lag is represented by
the time constant Tr. Table 4-3 gives suggested settings for the WindCONTROL emulator
model. The gains are field adjustable to improve performance and may be adjusted in the
model, if necessary. The given values should be suitable for systems with a short circuit
capacity of 5 or more times the wind plant MW rating. For weaker systems, some
reduction in the gains may be desirable.
The parameter, fN, is the fraction of wind turbines in the wind plant that are on-line.
For example, if a case represents a condition with half of the wind turbines on-line, fN
should be set to 0.5. In this case the MVA base of the generator should also be set to onehalf of its full value, and the MW capability of the turbine should be set to one-half of its
full value. If a wind plant is represented by more than one WTG model, the fN values of
each should be set to the same value.
The other reactive power control method available is power factor control. It is
enabled by setting pfaflg to 1. The data associated with this mode are also shown in Table
4-3. The appropriate flag and gain settings to represent various control strategies are
described in the next section.
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Table 4-3. WindCONTROL Emulator Parameters (on Generator MVA Base).
Parameter Name
Unit Size
Tr (sec)
Tv(sec)
fN
Tc(sec)
Kpv**
Kiv**
Qmax (pu)
Qmin (pu)
Tpwr (sec)
Recommended Value
1.5
3.6
0.02
0.05
1.0
0.15
18.
5.
0.436*
0.52
-0.436
-0.39
0.05
* 0.296 on some older GE 1.5 WTGs
** Subject to field tuning to meet system performance objectives
4.2.2 Electrical Control
The electrical controller model is a simplified representation of the converter control
system. This model monitors the generator reactive power, Qgen, terminal voltage, Vterm,
and regulated bus voltage, Vregbus, to compute the voltage and current commands Eq”cmd and
IPcmd.
Several options are available by setting the varflg, pfaflg, and Kqi parameters as
follows:
•
Operation with WindCONTROL and with North American “volt/VAr”
control (varflg = 1, pfaflg = 0, Kqi = 0.1) This represents the normal
configuration for recent and future North American wind plants, using the
WindCONTROL emulator in the model to represent the wind farm management
system.
•
Operation without WindCONTROL and with North American “volt/VAr”
control (varflg = 0, pfaflg = 0, Kqi = 0.001) With the WindCONTROL turned
off, Kvi is reduced so there is a slow reset to desired reactive power and WTG
terminal voltage control is rapid. (This combination of flags and Kqi = 0.1 can be
used to emulate WindCONTROL at a fixed plant reactive power control.)
•
Operation without WindCONTROL and with European fast power factor
control (varflg = 0, pfaflg = 1, Kqi = 0.5) This represents the common
configuration for European wind parks, where a set power factor angle is rapidly
regulated by the converter control. Closed loop voltage control is not used on these
systems, but is left in the model to approximately represent other means that are
used to limit voltage excursions that would otherwise cause unit tripping.
•
Operation with WindCONTROL and with European fast power factor control
(varflg = 1, pfaflg = 0, Kqi = 0.5) This represents the another configuration for
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European wind parks when WindCONTROL is employed. Similar to the North
American model except the regulator gain is at the higher value. The power factor
control flag, pfaflg, is set to zero because the signal from the WindCONTROL is a
reactive power order, rather than power factor angle.
The voltage error, Verr, is multiplied by a gain and integrated to compute the voltage
command Eq”cmd. The magnitude of the gain determines the effective time constant
associated with the voltage control loop. The voltage command, Eq”cmd, is limited to reflect
hardware constraints.
Table 4-4 includes recommended settings for the electrical control model. All settings
are given in terms of rated MVA.
Table 4-4. DFAG Electrical Control Parameters.
Parameter Name
KQi
KVi
XIQmax
XIQmin
Vmax
Vmin
Ipmax
Recommended Value
0.1*
40**
1.45
0.50
1.10
0.90
1.1
* North American WindCONTROL, see text for other configurations.
** Subject to field tuning
4.2.3 Open Loop Control Logic
This feature was used in some wind plants with GE WTGs before the implementation
of the local closed-loop terminal voltage control described above. The open loop control
logic is responsive to large variations in system voltage, and is inactive whenever the
terminal voltage is within its normal range. It is described by Table 4-5. The functions in
this table represent an optional open loop control that was implemented to improve system
performance for large voltage deviations resulting from system events. The open loop
control logic forces the reactive power to pre-specified levels as voltage deviations persist.
This feature has not been offered for several years, and will not be offered for future
projects with GE WTGs. However, representative values from earlier projects for the open
loop control parameters are given in Table 4-6.
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Table 4-5. Open Loop Reactive Power Control Logic.
Voltage Condition
Vterm < VL1
Vterm > VH1
Time Duration
t < TL1
TL1 < t < TL2
t > TL2
t < TH1
TH1< t < TH2
t > TH2
Open Loop Reactive Power Command
QL1
QL2
QL3
QH1
QH2
QH3
Table 4-6. Open Loop Reactive Power Control Parameters.
Parameter Name
VL1 (pu)
VH1 (pu)
TL1 (sec.)
TL2 (sec.)
TH1 (sec.)
TH2 (sec.)
QL1 (pu)
QL2 (pu)
QL3 (pu)
QH1 (pu)
QH2 (pu)
QH3 (pu)
Recommended Value
Open Loop Control**
No Open Loop Control
0.9
-9999.
1.1
9999.
0.1
0.
0.5
0.
0.1
0.
1.0
0.
0*
0.
0.45
0.
0*
0.
0*
0.
-0.245
0.
0*
0.
*
The closed-loop Q command, Qord, is passed without modification by setting this to 0.
** Only for some projects before mid-2003, check with owner.
4.3 Wind Turbine and Turbine Control Model
The wind turbine model (wndtge in PSLF) provides a simplified representation of a
very complex electro-mechanical system. The block diagram for the model is shown in
Figure 4-5. In simple terms, the function of the wind turbine is to extract as much power
from the available wind as possible without exceeding the rating of the equipment. The
wind turbine model represents the relevant controls and mechanical dynamics of the wind
turbine. This model is used for both the DFAG and full converter WTG models.
However, some of the features (e.g., dynamic braking resistor) are not applicable to the
DFAG machines. The differences will be discussed in detail in the following subsections,
as well as in Section 5.3.
Details of the turbine control model (torque control, pitch control, pitch compensation)
are described in Section 4.3.1. The rotor mechanical model is described in Section 4.3.2.
The Wind Power Model is a moderately complex algebraic relationship governing the
mechanical shaft power that is dependent on wind velocity, rotor speed and blade pitch.
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This model is described in Section 4.3.3.
emulator are described in Section 4.3.4.
From
ewtgfc
(elimt)
+
Pdbr
The details of the Active Power Control
+
Σ
From
Pelec getwg
(pelec)
Wind
Speed
(glimv)
Wind
Power
Model
Pmech
s6
ωrotor
Blade
Pitch
θ
θ
d θ /dt max
max &
θ cmd
1
1+ sT p
Σ
+
Kpp+ Kip/s
To
getwg
(glimt )
ω
+
Σ
ω err
s1
+
θ
min & d /dt min
Trip
Signal
Under
Speed
Trip
s9
Anti-windup on
Pitch Limits
s0
θ
ω
Rotor
Model
1
ω ref 1 + 5.0s
- 0.67P2elec+ 1.42Pelec+ 0.51
s5
Pitch Control
Torque Control
Anti-windup on
Power Limits
K ptrq + Kitrq / s
ω
P
wmax
& d P /dt
max
1
1+ sTpc
X
s2
s4
Pwmin& d P /dtmin
Anti-windup on
Pitch
Pitch Limits
Compensation
Σ
K pc+ K ic / s
+
pinp
s3
Wind
Power
Model
Active Power Control
(optional)
Power Response
Rate Limit
pstl
PsetAPC
pavl
1
1+sTpav
WTG Terminal
Bus Frequency
+
Σ
P
0
fbus
+
Auxiliary
Signal
(psig)
plim
1.
s11
pavf
Frequency
Response
Curve
pset
max
perr
1
sTw
1 + sTw
+
Pmin
To gewtg
Trip Signal
(glimt)
if( fbus < fb OR
fbus > fc )
1
s10
Σ
apcflg
fflg
+
wsho
Pord
Release
Pmax
if fflg set
To extwge
or ewtgfc
(vsig)
Figure 4-5. Wind Turbine Model Block Diagram.
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Σ
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4.3.1 Turbine Control Model
The central part of Figure 4-5 is the model of the turbine controls. The practical
implication of the turbine control is that when the available wind power is above the
equipment rating, the blades are pitched to limit the mechanical power (Pmech) delivered to
the shaft to the equipment rating (1.0 pu). When the available wind power is less than
rated, the blades are set at minimum pitch to maximize the mechanical power. The
dynamics of the pitch control are moderately fast, and can have significant impact on
dynamic simulation results. A detailed diagram of that portion of the model is shown in
Figure 4-6.
Kpp
From
Turbine
Model
ω
+
Σ
+
ωerr
Ki p
ωref
From
Converter
Control
Model
*
Σ
+
s
+
Σ
+
θ cmd
rate limit
(PIrate )
PI max
1
1 + sT PI
Blade
Pitch
θ
PImin
Pitch Control
Kpc
+
P or d
Σ
+
Pset
From
Converter
Control
Model
Kic
s
*
Σ
+
0
Non-windup
limit
Pitch
Compensation
* The Pitch Control and Pitch Compensation integrators are non-windup integrators as a function of the pitch,
i.e., the inputs of these integrators are set to zero when the pitch is in limits (Pimax or Pimin) and the integrator
input tends to force the pitch command further against its limit. The outputs of these integrators are not limited
except by the lower (zero) limit on the Pitch Compensation integrator.
Figure 4-6. Pitch Control and Pitch Compensation Block Diagram.
The turbine control model sends a power order to the electrical control, requesting that
the converter deliver this power to the grid. The electrical control, as described in Section
4.2, may or may not be successful in implementing this power order. The control of
turbine speed is quite complex. For modeling purposes, this is approximated by closed
loop control with a speed reference that is proportional to electric power output. For power
levels above rated, the rotor speed will be controlled primarily by the pitch control, with
the speed being allowed to rise above the reference transiently. The actual control does
not use a speed reference or a feedback of power.
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In this model, the blade position actuators are rate limited and there is a time constant
associated with the translation of blade angle to mechanical output. The pitch control does
not differentiate between shaft acceleration due to increase in wind speed or due to system
faults. In either case, the response is appropriate and relatively slow compared to the
electrical control.
The model reference speed is normally 1.2 pu, but is reduced for power levels below
75%. This behavior is represented in the model by using the following equation for speed
reference when the power is below 0.75 pu:
ωref = − 0.67 P 2 + 1.42 P + 0.51
The speed reference slowly tracks changes in power with a low pass filter time constant
of approximately 5 seconds. Note: In the actual controller, the speed reference is not
directly a function of power, but the overall effect on the speed/power relationship is
similar.
The turbine control acts to smooth out electrical power fluctuations due to variations in
shaft power. By allowing the machine speed to vary around reference speed, the inertia of
the machine functions as a buffer to mechanical power variations.
The model includes a low rotor speed tripping function. If the DFAG machine speed
falls below 0.10pu, the WTG is tripped instantaneously.
The model also includes high and low wind speed cut-out for the turbine. For the
DFAG machine, this results in a generator trip. All of the wind speed thresholds and
timers are internal to the model and can not be changed by the user.
The high wind speed threshold is currently set at 25 m/sec. The difference between the
wind speed and the high wind speed threshold is integrated and if that value exceeds
another threshold (8 m-sec/sec), the unit is tripped. The integration represents an inverse
time function. The more excessive the wind speed, the faster the unit is tripped.
The low wind speed threshold is set at 3 m/sec. For this function, the decrease in rotor
speed and power is approximated with a pseudo drag term. The unit is tripped, via the low
rotor speed tripping function described above, when the rotor speed falls below 0.10 pu.
Once a WTG has tripped, it can not be started again. The model is neither applicable
nor appropriate for simulating start-up scenarios.
Parameter values for the DFAG wind turbine control model are shown in Table 4-7.
None of these values should be modified by the user unless advised to so by the
manufacturer.
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Table 4-7. DFAG WTG Turbine Control Parameters (on Turbine MW Base).
Parameter Name
Kpp
Kip
Tp (sec)
θmax (deg)
θmin (deg)
dθ/dt max (deg/sec)
dθ/dt min (deg/sec)
Pwmax (pu)
Pwmin (pu)
dP/dt max (pu/sec)
dP/dt min (pu/sec)
Kpc
Kic
Kptrq
Kitrq
Tpc
Recommended Value
150.
25.
0.30
27.
0.0
10.0
-10.0
1.12
0.04
0.45
-0.45
3.0
30.0
3.0
0.6
0.05
4.3.2 Rotor Mechanical Model
The block labeled “Rotor Model” in the upper part of Figure 4-5 includes the rotor
inertia equation for the WTG rotor. This equation uses the mechanical power from the
wind power model and the electrical power from the generator/converter model to compute
the rotor speed. This part of the model can be extended to include a two-mass rotor model,
with separate masses for the turbine and generator, as shown in Figure 4-7. Note that the
power from the dynamic braking resistor, Pdbr (also shown in Figure 4-5) is only used
with full converter WTGs as discussed in Section 5.3.
The data for the rotor mechanical model are given in Table 4-8. These parameters
result in torsional oscillation frequencies of approximately 1.8 Hz for the 1.5 MW
machine, and 2.6 Hz for the 3.6 MW machine. The torsional damping coefficient, Dtg, is
set to approximate the damping provided by an damping function in the controller, which
is not included in the model.
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ωο
spd0
+
Σ
+
Turbine Speed
ωrotor
Tmech = Pmech
+
Tmech
+
Σ
1
2H
1
s
+
s6
Σ
Σ
+
-
s7
-
Dtg
Telec
s6 + ω0
1
s
ωbase
Σ
1
2Hg
1
s
s8
Tshaft
Ktg
+
1
s
ωbase
Telec = Pelec + Pdbr
s9
s8 + ω0
ωο
Δω
spd0
+
+
ω
Σ
Generator Speed
Figure 4-7. Two-Mass Rotor Model.
Table 4-8. DFAG WTG Rotor Mechanical Model Parameters (on Turbine MW Base).
One-Mass Model
H (pu torque/ pu acceleration)
Two-Mass Model
Ht
Hg
Ktg (pu torque / radian)
Dtg (pu torque / pu speed)
ωbase* (radians/sec)
GE 1.5
60 Hz
GE 1.5
50 Hz
GE 3.6
60 Hz
GE 3.6
50 Hz
4.94
5.29
5.23
5.74
4.33
0.62
1.11
1.5
125.66
4.33
0.96
1.39
2.3
157.08
4.32
0.91
3.16
1.5
125.66
4.32
1.42
3.95
2.3
157.08
* nominal generator speed
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4.3.3 Wind Power Model
For power system simulations involving grid disturbances, it is a reasonable
approximation to assume that wind speed remains uniform for the 5 to 30 seconds typical
of such cases. However, the mechanical power delivered to the shaft is a complex function
of wind speed, blade pitch angle and shaft speed. Further, with wind generation, the
impact of wind power fluctuations on the output of the machines is of interest. The turbine
model uses the wind power model to provide this mapping.
The function of the wind power model is to compute the wind turbine mechanical
power (shaft power) from the energy contained in the wind, using the following formula:
P=
ρ
A r v 3w Cp (λ , θ)
2
P is the mechanical power extracted from the wind, ρ is the air density in kg/m3, Ar is the
area swept by the rotor blades in m2, vw is the wind speed in m/sec, and Cp is the power
coefficient, which is a function of λ and θ. λ is the ratio of the rotor blade tip speed and
the wind speed (vtip/vw), and θ is the blade pitch angle in degrees. The relationship
between blade tip speed and turbine rotor speed, ω, is a fixed constant, Kb. Thus, the
calculation of λ becomes:
λ = Kb (ω/vw)
For GE WTGs, the parameters given in Table 4-9 will result in Pmech in pu on the unit’s
MW base.
Table 4-9. DFAG WTG Wind Power Coefficients.
GE 1.5
0.00159
56.6
½ρ Ar
Kb
GE 3.6
0.00145
69.5
Cp is a characteristic of the wind turbine and is usually provided as a set of curves
relating Cp to λ, with θ as a parameter. Representative Cp curves for the GE wind turbines
are shown in Figure 4-8. Curve fitting was performed to obtain the mathematical
representation of the Cp curves used in the model:
Cp (θ, λ) =
4
4
∑ ∑ αi, j θi λj
i=0 j=0
The coefficients αi,j are given in Table 4-10. The curve fit is a good approximation for
values of 3 < λ < 15, which are suitable for stability simulations for all blade
configurations and models. These curves should not be used for energy production or
other economic evaluation. Values of λ outside this range represent very high and low
wind speeds, respectively, that are outside the continuous rating of the machine.
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0.5
θ=1o
0.4
o
θ=3
θ=5o
0.3
o
C
p
θ=7
o
θ=9
0.2
θ=11o
θ=13o
θ=15o
0.1
0
0
2
4
6
8
10
λ
12
14
16
18
20
Figure 4-8. Wind Power Cp Curves.
Initialization of the wind power model recognizes two distinct states: 1) initial
electrical power (from the load flow) is less than rated, or 2) initial electrical power equal
to rated. In either case, Pmech = Pelec is known from the load flow and ω = ωref is set at the
corresponding value (1.2 pu if P > 0.75 pu). Then, using the Cp curve fit equation, the
wind speed vw required to produce Pmech with θ = θmin is determined. (Notice from Figure
4-8, that two values of λ will generally satisfy the required Cp for a given θ. The wind
speed vw, corresponding to the higher λ is used.) If Pmech is less than rated, this value of
wind speed is used as the initial value. If Pmech is equal to rated and the user-input value of
wind speed is greater than the θ = θmin value, then θ is increased to produce rated P at the
specified value of wind speed.
Large negative values of Cp are not allowed. The minimum is set to –0.05.
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4.16
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Table 4-10. Cp Coefficients αi,j
i
4
4
4
4
4
3
3
3
3
3
2
2
2
2
2
1
1
1
1
1
0
0
0
0
0
j
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0
aij
4.9686e-010
-7.1535e-008
1.6167e-006
-9.4839e-006
1.4787e-005
-8.9194e-008
5.9924e-006
-1.0479e-004
5.7051e-004
-8.6018e-004
2.7937e-006
-1.4855e-004
2.1495e-003
-1.0996e-002
1.5727e-002
-2.3895e-005
1.0683e-003
-1.3934e-002
6.0405e-002
-6.7606e-002
1.1524e-005
-1.3365e-004
-1.2406e-002
2.1808e-001
-4.1909e-001
4.3.4 Active Power Control Model & Rate Limit Function
The Active Power Control (APC) model and rate limiting function are shown in the
lower portions of Figure 4-5. The APC model is a simple representation of the active
power control required by many European grid codes. This function is a portion of the
wind farm management system (WindCONTROL). The primary objectives of the APC are
to:
•
•
•
•
GE Energy
Enforce a maximum wind plant power output
Provide a specified margin by generating less power than is available
Enforce a plant power ramp rate limit
Respond to system frequency excursions
4.17
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By default, the APC model is disabled.
parameter, apcflg, to 1.
It may be enabled by setting the data
Under normal operating conditions with near nominal system frequency, the control is
either enforcing a maximum plant output (i.e., Pmax) or providing a specified margin by
generating less power than is available from the wind (e.g., actual power generated is 95%
of the available power, or Pbc = 0.95).
In response to frequency excursions, the control switches into another mode and
calculates a plant power order as a function of system frequency. This path requests a
higher than usual power order for low frequency events, and lower than usual power order
for high frequency events. Thus, the wind plant will generate additional power in response
to the loss of other generating facilities or less power in response to the loss of load.
An auxiliary frequency signal, normally zero, may be set by a user-written model to
test APC performance in response to other types of frequency deviations. Such deviations
could include frequency steps, ramps, or other functions defined by the host utility’s
interconnection requirements.
An example frequency response curve is shown in Figure 4-9. Points A through D on
this response curve may be set to meet specific performance objectives or requirements of
the host grid. The value of Pd should be greater than or equal to the minimum power,
which is discussed below. The value of Fb must be less than 1, and that of Fc must be
greater than 1. The value of Tpav may be increased to simulate fixed power reference.
1.2
Point A
(Fa,Pa)
Point B
(Fb,Pbc)
Active Power Output (pu)
1
Point C
(Fc,Pbc)
0.8
0.6
0.4
Point D
(Fd,Pd)
0.2
0
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
Frequency (pu)
Figure 4-9. Example Frequency Response Curve.
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The two primary inputs to the frequency response curve are available power
(determined from wind speed, a Cp curve and the constant Kb) and WTG terminal bus
frequency. At nominal frequency, the filtered version of the available power is multiplied
by the factor, Pbc, to generate a power set point, pset. This set point is compared to
specified limits, Pmin and Pmax. The minimum power is nominally 0.20 pu of maximum
plant output. The maximum power represents an operator specified plant output limit. For
example, this may represent a limit that would be imposed on a given wind plant after the
loss of a local transmission line, or under light load conditions.
In response to frequency excursions, the filtered available power is multiplied by the
appropriate interpolated factor to generate a power set point. No operator limit is imposed
for frequency excursions. The plant is still limited to the maximum power rating of the
WTGs, or to the available power from a given wind speed.
Under all frequency conditions, the maximum power set point, PsetAPC, is an input to
both the pitch compensation (described in Section 4.3.1) and the power response rate limit
function. This rate limit is implemented by applying the maximum power set point
(PsetAPC) to the power order (pinp) from the turbine control, calculating the difference
between the original power order and the limited power order, processing that error
through a washout filter, and adding the output of the washout to the limited power order
to generate the final power order (Pord) for the converter control (extwge) model. The time
constant of the washout filter determines the ramp rate limit imposed on changes to the
power order signal. This function is always in service and is not disabled by setting apcflg
to 0. Example data for both the APC and power response rate limit functions are shown in
Table 4-11.
Table 4-11. Active Power Control and Rate Limit Function Parameters.
Parameter Name
Tw (sec)
apcflg
Tpav (sec)
Pa (pu)
Pbc (pu)
Pd (pu)
Fa (pu)
Fb (pu)
Fc (pu)
Fd (pu)
Pmax (pu)
Pmin (pu)
GE Energy
4.19
Recommended Value
1.0
0
0.15
1.0
0.95
0.40
0.96
0.996
1.004
1.04
1.0
0.2
GE WTG Modeling-v4.2.doc, 6/24/08
5 Full Converter WTG Dynamic Models
This section presents the engineering assumptions, detailed structure, and data for each
of the component models necessary to represent a GE full converter WTG. Since the grid
performance of full converter WTGs, like the 1.5 and 3.6 MW DFAG WTGs, is dominated
by the converter controls, the dynamic models described in Section 4 are the basis for the
full converter models. The modifications made to represent the full converter WTGs are
the focus of this section. Therefore, the common model features are not, in general,
discussed in this section.
5.1 Generator/Converter Model
This model (gewtg in PSLF with fcflg = 1) is the equivalent of the generator and the
full converter and provides the interface between the WTG and the network. The GE
1.5 MW DFAG WTG is represented by a flux and active current command. The GE full
converter WTG model differs in that it is represented by both reactive and active current
commands. The model is shown in Figure 5-1. Modified data parameters appropriate for
the full converter model are shown in Table 5-1.
IQcmd
(efd)
From
exwtge
1
1+ 0.02s
High Voltage
-1
Reactive Current
s0
Management
LVPL & rrpwr
IPcmd
(ladifd)
From
exwtge
Isorc
Low Voltage
IPlv
1
1+ 0.02s
Active Current
Management
s1
LVPL
Vterm
1.11
V
LVPL
1
1+ 0.02s
V
zerox
(0.0)
s2
brkpt
(0.70)
Low Voltage Power Logic
Figure 5-1. Full Converter WTG Generator/Converter Model.
Table 5-1. Full Converter Generator/Converter Parameters.
Parameter Name
fcflg
brkpt
zerox
GE Energy
5.1
Recommended Value
1
0.7
0.0
GE WTG Modeling-v4.2.doc, 6/24/08
5.2 Electrical (Converter) Control Model
This model (ewtgfc in PSLF) dictates the active and reactive power to be delivered to
the system based on inputs from the turbine model (Pord) and from the supervisory VAr
controller (Qord). Figure 5-2 shows the electrical control as modified to represent the full
converter WTG. The reactive power control, shown in Figure 4-3, remains unchanged.
Therefore, the WindCONTROL emulator (Section 4.2.1) can be used.
The primary philosophical change to the model was to generate a reactive current
command rather than a flux command. Additional functions include a dynamic braking
resistor and converter current limit. The open loop control logic available in the DFAG
electrical control model for representing old 1.5 MW WTGs is not included in the control
model for the full converter WTGs.
The objective of the dynamic braking resistor (DBR) is to minimize the WTG response
to large system disturbances, such as extended periods of low voltage. This is
accomplished by absorbing energy in the braking resistor when the power order is
significantly greater than the electrical power delivered to the grid. In this model, the
power order is compared to the actual electrical power to determine the power absorbed by
the braking resistor, Pdbr. This power is integrated to determine the resulting energy
absorbed by the braking resistor, Edbr. As long as that energy level is less than the
threshold, EBST, no other action occurs. When the energy level exceeds the threshold, the
resulting error signal is greater than zero and the amount of power absorbed by the
dynamic braking resistor is reduced. This ensures that the energy capability of the resistor
is respected. The model does not include thermal reset, so simulations with multiple
events may result in limited DBR response.
The details of the converter current limit are shown in Figure 5-3. The objective of this
function is to prevent the combination of the real and reactive currents from exceeding
converter capability. Depending upon the value of a user-specified flag, pqflag, either real
or reactive power has priority. This flag is dependent upon the equipment features
selected, and is normally dictated by the host system grid code.
When real power has priority, the real current order, IPcmd, is limited to the minimum
of the maximum temperature dependent converter current, ImaxTD, and a hard active
current limit, Iphl. The calculation of the limit on the reactive current begins by
determining the minimum of a hard reactive current limit, Iqhl, and a voltage dependent
limit, Iqmxv. The voltage dependent limit will be equal to the steady-state rating of the
wind plant (as defined by the input parameter Qmax) at 1.0 pu voltage and will linearly
increase as voltage drops. The maximum voltage dependent reactive current limit is 1.6 pu
at zero voltage. The minimum of Iqhl and Iqmxv is compared to the remaining converter
current capability, SQRT(ImaxTD2 - IPcmd2). That minimum is the maximum (capacitive)
limit, Iqmx, applied to the reactive current order, IQcmd. The minimum (inductive) reactive
current, Iqmn, is the negative of the maximum. No minimum is applied to the real current
order.
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5.2
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When reactive power has priority, the calculation of the limit on the reactive current
begins by determining the minimum of a hard reactive current limit, Iqhl, and the voltage
dependent limit, Iqmxv, as described above. The minimum of Iqhl and Iqmxv is compared to
a maximum temperature dependent converter current, ImaxTD. That minimum is the
maximum limit, Iqmx, applied to the reactive current order, IQcmd. The minimum reactive
current, Iqmn, is the negative of this maximum limit. The remaining converter current
capability, SQRT(ImaxTD2 – IQcmd2), becomes the maximum, Ipmx, applied to the real
current order, IPcmd. No minimum is applied to the real current order. Reactive power
priority is recommended, which is equivalent to the default value of 0 for pqflag.
The preliminary values for the additional data associated with the converter current
limit and dynamic braking resistor are shown in Table 5-2. The converter current limit,
ImaxTD, is a function of time and operation. However, it is constant in this model (1.7 pu)
and not user-specified.
The bulk of the remaining data is unchanged from that used for a DFAG WTG. Data
associated with the reactive power control model that should be modified to correctly
represent a full converter WTG are shown in Table 5-3.
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5.3
GE WTG Modeling-v4.2.doc, 6/24/08
Qgen
Qcmd
+
Iqmx
Vmax
-
+
s0
Vterm
IQcmd
Vref
KQi / s
KVi / s
-
Converter Current Limit
Porx
Pord
to Wind
Generator Model
Iqmn
Vmin
P,Q Priority Flag
(efd)
s1
Ipmx
.
.
(vsig)
IPcmd
(ladifd)
from Wind
Turbine Model
to Wind
Generator Model
Vterm
Pelec
from Wind
Generator
Model
-
1
+
+
Pdlt
Pdbr
(elimt)
-
0
Eerr
Kdbr
0
to Wind
Turbine Model
+
-
1/s
Edbr
s7
EBST
Dynamic Braking Resistor
Figure 5-2. Full Converter WTG Electrical Control Model.
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5.4
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P,Q Priority Flag
(pqflag)
0
Iqmn
1
Iqmx
Iqmx
Vt
Q Priority
Iqmn
P Priority
Iqmxv
1.6
qmax
Vt
1.0
-1
-1
Iqmxv
Iqhl
Minimum
Minimum
Minimum
ImaxTD2 - IPcmd2
ImaxTD
IQcmd
ImaxTD2 - IQcmd2
Iphl
Minimum
Minimum
Ipmx
Ipmx
Figure 5-3. Converter Current Limit Model.
Table 5-2. Full Converter WTG Electrical Model.
Parameter Name
Iphl (pu)
Iqhl (pu)
pqflag
EBST (pu)
Kdbr
Recommended Value
1.11
1.25
0=Q priority
0.2
10.
Table 5-3. Full Converter WTG WindCONTROL Emulator Parameters.
Parameter Name
KVi
Qmax (pu)
Qmin (pu)
GE Energy
5.5
Recommended Value
120.
0.40
-0.40
GE WTG Modeling-v4.2.doc, 6/24/08
IPcmd
5.3 Wind Turbine and Turbine Control Model
Only minor modifications were made to represent the additional functions of the full
converter wind turbine. Therefore, the same model is used in PSLF (wndtge) for both
DFAG and full converter WTGs. The modifications included the following:
•
Incorporation of the dynamic braking resistor power, and
•
Implementation of a no-wind (i.e., zero power) var capability.
The block diagram for the turbine model is unchanged, and is shown in Figure 4-5.
The signal representing the dynamic braking resistor power, Pdbr, is now added to the
electrical power as an input to both the rotor model and the creation of the speed reference.
When this model is used to represent the 1.5 MW or 3.6 MW DFAG WTG, the dynamic
braking resistor power is automatically set to zero.
With a full converter WTG, it is possible to inject or absorb reactive power (e.g.,
regulate voltage) at zero real power. Zero power may be the result of no wind, excessive
wind, or an operator directive to curtail output. All three of these zero power scenarios
may be simulated with this model.
For the first scenario (no wind), a user-written wind profile model is required to drive a
specific WTG’s wind speed below the low wind speed threshold. As the wind speed
drops, so does the machine speed, electrical power and mechanical power. Below the low
wind speed threshold, the decrease in mechanical power is implemented with a pseudo
drag term. Unlike the DFAG machine, no trip signal is generated when the rotor speed
falls below 0.10 pu. Therefore, the generator model will still respond to reactive power
commands from the electrical control model (e.g., WindCONTROL emulator). The low
wind speed threshold is set at 3 m/sec, and cannot be changed by the user.
The second scenario (excessive wind) also requires a user-written wind profile model.
Once the wind speed exceeds the high wind speed threshold, the difference between the
wind speed and the threshold is integrated. If that value exceeds another threshold, the full
converter machine goes into zero-power operation (i.e., electrical power and rotor speed
are zero). The integration represents an inverse time function. The more excessive the
wind speed, the earlier the unit enters zero-power operation. All of the wind speed
thresholds and timers are internal to the model and cannot be changed by the user. The
high wind speed threshold is currently set at 25 m/sec and the inverse-time threshold at
8 m-sec/sec.
For the third scenario (curtailed output), the real power at the generator in the power
flow is zero. The WTG will initialize at zero wind speed, machine speed, electrical and
mechanical power. Again, the generator model will inject or absorb reactive power in
response to reactive power commands from the electrical control model.
The key limitation on zero-power operation is that once in that mode, the WTG stays
there. The model is neither applicable nor appropriate for simulating start-up scenarios.
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5.6
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Three turbine control parameters are different from those used to represent a DFAG
WTG. Those parameters and their recommended values are shown in Table 5-4. The
remaining turbine control parameters can be used for the full converter without change.
Note that they are on the MW rating base of the turbine. The turbine-generator mechanical
model parameters for the full converter WTG are given in Table 5-5. The same Cp curves
are used for the full converter WTG together with the wind power coefficients shown in
Table 5-6.
Table 5-4. Full Converter WTG Turbine Control Parameters (on Turbine MW Base).
Parameter Name
Pwmin (pu)
Kptrq
Kitrq
Recommended Value
0.
0.3
0.1
Table 5-5. Full Converter WTG Rotor Model Parameters (on Turbine MW Base).
Parameter Name
One-mass Model
H
Two-mass Model
Ht
Hg
Ktg
Dtg
ωbase
Recommended Value
4.18
3.36
0.82
3.86
1.5
144
Table 5-6. Full Converter WTG Wind Power Coefficients.
Parameter Name
½ρ Ar
Kb
GE Energy
5.7
Recommended Value
0.00159
56.6
GE WTG Modeling-v4.2.doc, 6/24/08
6 DFAG WTG Benchmark Simulations
The models described in this report have been implemented in GE’s PSLF load flow
and dynamic simulation software. The PSLF models have been validated by comparison
with more detailed simulation models, as described in Section 8. Representative results
using the PSLF models are presented in this section using data for 60 Hz., 1.5 MW WTGs.
Results for other models of the GE WTGs do not differ significantly from these results.
Upon request, GE will provide complete data and results for the PSLF benchmark
simulations to those who wish to implement the models in other simulation programs. The
results can be supplied in ASCII format for cross-plotting in order to validate the model
implementation.
6.1 Test System
One line diagrams of the test system are shown in Figure 6-1. The top diagram shows
real and reactive power flow (MW, MVAr), and the bottom diagram shows impedances
(pu on 100 MVA). The test system represents an aggregate model of a wind plant, suitable
for analyzing the response of the wind plant to grid disturbances. The many WTGs of the
actual wind plant are combined into a single WTG model, a single unit transformer, a
single 34.5 kV feeder representing the collector system, and a substation transformer to the
system point of interconnection. For this test system, the wind plant is rated 100.5 MW,
representing the aggregation of 67 1.5 MW WTGs.
Figure 6-1. DFAG Test System.
The dynamic data used for the benchmark simulations are listed in Section 6.3. Note
that the WindCONTROL emulator was on (varflg = 1) for all cases. The Active Power
Control was only on for the example showing its performance (Section 6.2.2).
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6.1
GE WTG Modeling-v4.2.doc, 6/24/08
6.2 DFAG WTG Benchmark Simulation Results
Plotted simulation results are provided for each example. Traces plotted together
generally share the same scaling, as shown on the y-axis. However, there are exceptions.
Scaling for a particular trace can be confirmed by checking the legend below each plot.
The same plot format was used for all simulations, and a brief description follows.
From top to bottom, the left column shows the infinite bus voltage (dark blue line, pu),
WTG terminal voltage (red line, pu), and point of interconnection voltage (green line, pu)
in the first plot.
The second plot shows WTG real power generated (dark blue line, MW), reactive
power generated (red line, MVAr), and mechanical power (green line, MW).
The third plot shows variables associated with the active power control. Specifically, it
shows the total available power in the wind (Pavf, dark blue line, pu), turbine power order
from the torque control (Pinp, red line, pu), the output of the active power control (Pstl,
green line, pu), the power order after the active power control limit is applied (Plim, light
blue line, pu), the output of the washout in the power response rate limit (Wsho, pink line,
pu), and the final power order from the turbine to the electrical control model (Pord, black
line, pu).
The fourth and final plot in the left column shows the WTG terminal bus frequency
(dark blue line, Hz), and the flag from the active power control indicating a frequency
excursion (red line).
From top to bottom, the right column shows the WindCONTROL emulator voltage
reference (dark blue line, pu) and regulated voltage (red line, pu). In all cases, the
regulated bus was the point of interconnection.
The second plot shows the rotor speed (dark blue line, pu).
The third plot shows the blade pitch (dark blue line, deg) and wind speed (red line,
m/sec).
The fourth and final plot in the right column shows the real power current command
(Ipcmd, dark blue line, pu) and the reactive power voltage behind a reactance command
(E”qcmd, red line, pu).
Note that per unit values of real and reactive power are on the MVA base for variables
associated with the generator and electrical control models. Per unit values of real and
reactive power are on the MW base for variables associated with the turbine model.
Transfer variables between models (e.g., Pord from the turbine to the electrical control) are
on the MVA base of the receiving model.
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6.2
GE WTG Modeling-v4.2.doc, 6/24/08
6.2.1 Fault Response with WindCONTROL Emulator
Two simulations illustrate WTG response to grid disturbances. One disturbance is a
series of 3-phase bus faults with various fault impedances, the other is a 3-phase fault to
ground cleared by tripping one of the 230 kV lines from the POI bus to the Infinite bus.
The results are shown in Figure 6-2 and Figure 6-3, respectively.
In both examples, the reactive power output of the WTG is at or near its maximum
during the fault in an effort to regulate voltage. After each fault is removed, the
WindCONTROL emulator quickly restores the voltage at the POI bus to its initial value.
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6.3
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Figure 6-2. Series of Bus Faults with Various Fault Impedances.
GE Energy
6.4
GE WTG Modeling-v4.2.doc, 6/24/08
Figure 6-3. 3-phase Fault to Ground, Cleared by Tripping 230 kV Line.
GE Energy
6.5
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6.2.2 Active Power Control and Power Response Rate Limit Performance
The Active Power Control (APC) and power response rate limit performance are
presented in this section. This is the only case for which the APC was active, i.e., the input
parameter apcflg was set to 1.
Figure 6-4 shows the APC’s response to a loss of load. Initially, the wind plant is
constrained to 0.95 pu of the power available in the wind. Therefore, the blade pitch is
non-zero.
At 1 second, 100 MW of load is tripped. As a result, system frequency increases.
Shortly thereafter, the frequency exceeds the first high frequency threshold (Fc = 1.004 pu
or 60.24 Hz) in the APC’s frequency response curve. This defines a frequency excursion
event, and the frequency excursion flag is set to 1. The output of the APC function, which
is the upper limit imposed on the power order from the turbine, begins to decrease (Pstl,
left column, third plot, green line). The washout in the power response rate limit (Wsho,
pink line) transiently allows the higher power order from the turbine control (Pinp, red
line) through to the final power order (Pord, black line).
At about 8 seconds, the washout settles to near zero, and the final power order is equal
to the output of the APC. Between about 12 and 14 seconds, the frequency is below the
high frequency threshold for APC operation. However, this is only temporary. The
frequency rises a bit and the wind plant APC continues to operate.
Throughout the simulation, the large machine on the Infinite bus is attempting to
control frequency by reducing its output. By the end of the simulation, the frequency has
settled to about 60.3 Hz and the APC output to about 0.92 pu in accordance with the
frequency response curve characteristic.
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Figure 6-4. Active Power Control Response to Loss of Load.
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6.2.3 Wind Speed Ramp Simulation
Wind plant response to a wind speed ramp function (both up and down) is shown in
Figure 6-5. The initial wind speed of about 9 m/sec results in a power output of about
50 MW, and a blade pitch of 0 degrees.
Starting at 10 seconds, the wind speed increases over the next 40 seconds to a
maximum of 15 m/sec. The power output follows the wind speed up to the maximum
output of 100 MW. The blade pitch increases to shed the excess power available in the
wind. The reactive power output increases to maintain the POI voltage with the higher
power output.
At about 65 seconds, the wind speed starts to fall, with the power output following.
The reactive power also decreases to regulate POI voltage with the lower real power
output.
At about 105 seconds, the wind speed falls below the minimum wind speed threshold,
which is a non-user-specified value of 3 m/sec. The rotor speed continues to fall until it
reaches 0.1 pu, which is another non-user-specified threshold. At this point, the WTG
models are tripped. Real and reactive power output go to zero, and the POI voltage is no
longer regulated.
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Figure 6-5. Response to Wind Speed Ramp Up and Down.
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6.3 DFAG WTG Benchmark Simulation Dynamic Data
The generator, electrical control and turbine control dynamic data used in the
benchmark simulations are shown in Table 6-1, Table 6-2, and Table 6-3, respectively.
Table 6-1. DFAG Generator Model (gewtg) Data for Simulations.
Model Parameter
MVA
lpp
dvtrp1
dvtrp2
dvtrp3
dvtrp4
dvtrp5
dvtrp6
dttrp1
dttrp2
dttrp3
dttrp4
dttrp5
dttrp6
fcflg
rrpwr
brkpt
zerox
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111.
0.80
-0.25
-0.50
-0.70
-0.85
0.10
0.15
1.90
1.20
0.70
0.20
1.00
0.10
0
5.0
0.90
0.50
GE WTG Modeling-v4.2.doc, 6/24/08
Table 6-2. DFAG Electrical Control Model (exwtge) Data for Simulations.
Model Parameter
varflg
kqi
kvi
vmax
vmin
qmax
qmin
xiqmax
xiqmin
tr
tc
kpv
kiv
vl1
vh1
tl1
tl2
th1
th2
ql1
ql2
ql3
qh1
qh2
qh3
pfaflg
fn
tv
tpwr
ipmax
xc
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1
0.10
40.
1.10
0.90
0.436
-0.436
1.45
0.50
0.02
0.15
18.
5.
-9999
9999
0
0
0
0
0
0
0
0
0
0
0
1.0
0.05
0.05
1.10
0
GE WTG Modeling-v4.2.doc, 6/24/08
Table 6-3. DFAG Turbine Control Model (wndtge) Data for Simulations.
Model Parameter
mwcap
usize
spdw1
tp
tpc
kpp
kip
kptrq
kitrq
kpc
kic
pimax
pimin
pirat
pwmax
pwmin
pwrat
ht
nmass
hg
ktg
dtg
wbase
tw
apcflg
tpav
pa
pbc
pd
fa
fb
fc
fd
pmax
pmin
1.5 MW WTG
100.5
1.5
11.0
0.30
0.05
150.
25.
3.0
0.60
3.0
30.
27.
0.
10.
1.12
0.04
0.45
4.94
1
1.0
0 or 1*
0.15
1.0
0.95
0.40
0.96
0.996
1.004
1.04
1.0
0.20
* Different values for different simulations
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7 Full Converter WTG Benchmark Simulations
The models described in this report have been implemented in GE’s PSLF load flow
and dynamic simulation software. The PSLF models have been validated by comparison
with more detailed simulation models, as described in Section 8. Representative results
using the PSLF models are presented in this section using data for 60 Hz., 2.5 MW full
converter WTGs. These simulations focus on the capabilities of this type of machine,
rather than repeating the tests performed for the DFAG benchmark simulations.
Upon request, GE will provide complete data and results for the PSLF benchmark
simulations to those who wish to implement the models in other simulation programs. The
results can be supplied in ASCII format for cross-plotting in order to validate the model
implementation.
7.1 Test System
The test system was similar to that used for the 1.5 MW DFAG simulations, which is
described in Section 6.1. The wind plant was rated at 100 MW, and consisted of 40
2.5 MW full converter WTGs. Minor modifications were made to the wind plant power
output and system voltage profile as necessary to test the various functions.
7.2 Full Converter WTG Benchmark Simulation Results
As noted above, the test simulations described in this section focus on the capabilities
of the full converter machine, rather than repeating the tests performed for the DFAG
benchmark simulations. Specifically, the following subsections will describe simulation
results illustrating the performance of the zero-power operation capability, converter
current limit, low voltage power logic, and dynamic braking resistor. A variety of
disturbances are represented – fault events, wind profiles, and control input changes.
Plotted results are provided for each test simulation. Traces plotted together generally
share the same scaling, as shown on the y-axis. However, there are exceptions. Scaling
for a particular trace can be confirmed by checking the legend below each plot. The same
plot format was used for all simulations, and a brief description follows.
From top to bottom, the left column shows the infinite bus voltage (dark blue line, pu),
WTG terminal voltage (red line, pu), and point of interconnection voltage (green line, pu)
in the first plot.
The second plot shows WTG real power generated (dark blue line, MW), reactive
power generated (red line, MVAr), and mechanical power (green line, MW).
The third plot shows the final power order from the turbine to the electrical control
model (Pord, dark blue line, pu).
The fourth and final plot in the left column shows variables associated with the
dynamic braking resistor. Specifically, this plot shows the difference between electrical
power and the power order (Pdlt, dark blue line, pu), the power absorbed by the dynamic
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braking resistor (Pdbr, red line, pu), the energy absorbed by the dynamic braking resistor
(Edbr, green line, pu), and the difference between the energy absorbed by the dynamic
brake and the energy threshold (Eerr, light blue line, pu).
From top to bottom, the right column shows the WindCONTROL emulator voltage
reference (dark blue line, pu) and regulated voltage (red line, pu). In all cases, the
regulated bus was the point of interconnection.
The second plot shows the rotor speed (dark blue line, pu).
The third plot shows the blade pitch (dark blue line, deg) and wind speed (red line,
m/sec).
The fourth and final plot in the right column shows the real power (Ipcmd, dark blue
line, pu) and reactive power (Iqcmd, red line, pu) current commands from the electrical
control to the generator. Three converter current limits are also plotted: the maximum real
current (Ipmx, green line, pu), the maximum reactive current (Iqmx, light blue, pu), the
voltage dependent reactive current limit (Iqxv, pink line, pu). Finally, the real power
current command after the low voltage power logic (Iplv, black line, pu) is shown.
Note that per unit values of real and reactive power are on the MVA base for variables
associated with the generator and electrical control models. Per unit values of real and
reactive power are on the MW base for variables associated with the turbine model.
Transfer variables between models (e.g., Pord from the turbine to the electrical control) are
on the MVA base of the receiving model.
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7.2.1 Fault Response with WindCONTROL Emulator
Two simulations illustrate WTG response to grid disturbances. One disturbance is a
series of 3-phase bus faults with various fault impedances, the other is a 3-phase fault to
ground cleared by tripping one of the 230 kV lines from the POI bus to the Infinite bus.
The results are shown in Figure 7-1 and Figure 7-2, respectively.
In both examples, the reactive power output of the WTG is at or near its maximum
during the fault in an effort to regulate voltage. After each fault is removed, the
WindCONTROL emulator quickly restores the voltage at the POI bus to its initial value.
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Figure 7-1. Series of Bus Faults with Various Fault Impedances.
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Figure 7-2. 3-phase Fault to Ground, Cleared by Tripping 230 kV Line.
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7.2.2 Zero-Power Operation
Three scenarios involving zero-power operation of the full converter WTG are
illustrated in this section.
Figure 7-3 shows the WTG’s response to increasing wind speed. As wind speed
increases, the blade pitch increases in an effort to maintain the desired power output. At
about 19 seconds, the wind speed exceeds the high speed threshold, 25 m/sec, and the
inverse time tripping characteristic starts incrementing. At about 24 seconds, the tripping
threshold is reached and the turbine is tripped. The rotor speed, electrical and mechanical
power are all zero at this point. Note however, that the full converter WTG continues to
generate reactive power in order to regulate voltage at the POI bus.
Figure 7-4 shows the WTG’s response to decreasing wind speed. At about 18 seconds,
the wind speed falls below the minimum wind speed threshold, 3 m/sec. The turbine slows
down and by about 26 seconds, the rotor speed, electrical and mechanical power are all
zero. The full converter WTG, however, continues to generate reactive power in order to
regulate voltage at the POI bus.
The final example of zero-power operation is shown in Figure 7-5. This simulation
used a modified test system with an initial wind plant power output of 0 MW. At 1
second, the POI bus voltage schedule is reduced by 0.03 pu. While real power output
remains zero, reactive power is reduced to regulate the POI bus voltage to the new
reference. At 5 seconds, the voltage schedule is increased by 0.03 pu. Again, the WTG
regulates the voltage with zero real power output.
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Figure 7-3. Increasing Wind Speed Results in Zero-Power Operation.
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Figure 7-4. Decreasing Wind Speed Results in Zero-Power Operation.
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Figure 7-5. Voltage Regulation in Continuous Zero-Power Operation.
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7.2.3 Converter Current Limit Performance
The performance of the converter current limit function is illustrated in this section. In
general, the converter current capability will not be limiting except for severe system
disturbances. Therefore, an arbitrary step was applied to one of the hardwired current
limits, ImaxTD, as a test. Realistic limits and the converter current limit function’s response
to a system fault were shown in Section 7.2.1.
Figure 7-6 shows WTG response to a reduction in the converter current limit, ImaxTD,
with real power or P priority. The WTG was initially operating at about 0.9 pu of
generator MVA base, equivalent to 1.0 pu on the turbine MW base. At 1 second, the
current limit was reduced from 1.7 pu to 0.80 pu. As a result the real power command is
reduced to 0.80 pu. Due to the P priority, the reactive power command is reduced to zero.
The converter current limit was returned to its initial value of 1.7 pu at 5 seconds.
Figure 7-7 shows WTG response to the same reduction in converter current capability
with reactive power or Q priority. Again, the WTG was initially operating at about 0.9 pu.
At 1 second, the current limit was reduced to 0.80 pu. Due to the Q priority, there was no
change in the reactive power command. However, the real power command was reduced
to about 0.78 pu, which constituted the remaining current capability equal to
2
2
2
2
SQRT(ImaxTD -IQcmd ) or SQRT(0.8 -0.18 ). The reduction in real power reduces the
stress on the system such that less reactive power is now required to regulate the POI bus
voltage. Therefore, the real power limit inches up a bit as the reactive power output
decreases. The converter current limit was returned to its initial value of 1.7 pu at 5
seconds.
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Figure 7-6. Step Reduction in Converter Current Limit with P Priority.
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Figure 7-7. Step Reduction in Converter Current Limit with Q Priority.
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7.2.4 Low Voltage Power Logic Performance
The performance of the low voltage power logic (LVPL) is illustrated in this section.
The rate of post-fault power recovery in the LVPL is governed by the value of the
generator input data parameter rrpwr. The recommended value for this parameter is 5.
However, a value of 1 was used in this simulation for a clearer illustration of the LVPL’s
performance.
Figure 7-8 shows WTG response to a long, depressed voltage due to a fault on the POI
bus. The fault is applied at 1 second, reducing POI bus voltage to near 0 pu for the next
0.5 seconds. During this time, the power order sent from the turbine to the electrical
controls increases with rotor speed. The LVPL becomes active shortly after fault
application when the terminal bus voltage falls below 0.70 pu, to about 0.25 pu. As a
result, the real power command to the generator is reduced to about 0.40 pu due to the
voltage dependent cap calculated by the LVPL. After the fault is removed, the terminal
voltage returns to its pre-fault level. However, the recovery of the power order and thus,
the generated power is ramp rate limited. The chosen rrpwr value results in a 0.5 second
recovery time. Thus the generated power reaches its pre-fault level at about 2 seconds, or
0.5 seconds after fault removal.
7.2.5 Dynamic Braking Resistor Performance
The performance of the dynamic braking resistor is also illustrated by the test
simulation shown in Figure 7-8.
As described above, the fault induced voltage depression causes the low voltage power
logic to operate. This, in turn, results in a difference between the power order and the
electrical power delivered to the system which is dissipated in the dynamic braking
resistor. At about 1.3 seconds, the energy absorbed by the resistor exceeds the specified
threshold, EBST, of 0.2 pu. From that point forward, the rate at which energy is absorbed
into the braking resistor is reduced to minimize energy absorption in excess of the
capability. By the end of the simulation, the energy absorbed into the dynamic braking
resistor is about 0.30pu.
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Figure 7-8. Low Voltage Power Logic Response to Fault on POI Bus.
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7.3 Full Converter WTG Benchmark Simulation Dynamic Data
The generator, electrical control and turbine control dynamic data used in the benchmark
simulations are shown in Table 7-1, Table 7-2, and Table 7-3, respectively. Any data
changes required to test specific functions were noted in the simulation descriptions
provided in Section 7.2.
Table 7-1. Full Converter WTG Generator Model Data for Simulations.
Model Parameter
MVA
lpp
dvtrp1
dvtrp2
dvtrp3
dvtrp4
dvtrp5
dvtrp6
dttrp1
dttrp2
dttrp3
dttrp4
dttrp5
dttrp6
fcflg
rrpwr
brkpt
zerox
GE Energy
7.15
2.5 MW WTG
111.
0.80
-0.25
-0.50
-0.70
-0.85
0.10
0.15
1.90
1.20
0.70
0.20
1.00
0.10
1
5.0
0.70
0.00
GE WTG Modeling-v4.2.doc, 6/24/08
Table 7-2. Full Converter WTG Electrical Control Model Data for Simulations.
Model Parameter
varflg
kqi
kvi
vmax
vmin
qmax
qmin
tr
tc
kpv
kiv
pfaflg
fn
tv
tpwr
iphl
iqhl
pqflag
kdbr
ebst
2.5 MW WTG
1
0.10
120.
1.10
0.90
0.40
-0.40
0.02
0.15
18.
5.
0
1.0
0.05
0.05
1.11
1.25
0 or 1*
10.
0.2
* Different values for different simulations
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Table 7-3. Full Converter WTG Turbine Control Model Data for Simulations.
Model Parameter
mwcap
usize
spdw1
tp
tpc
kpp
kip
kptrq
kitrq
kpc
kic
pimax
pimin
pirat
pwmax
pwmin
pwrat
h
nmass
hg
ktg
dtg
wbase
tw
apcflg
tpav
pa
pbc
pd
fa
fb
fc
fd
pmax
pmin
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2.5 MW WTG
100.
2.5
9.0
0.30
0.05
150.
25.
0.30
0.1
3.0
30.
27.
0.
10.
1.12
0.0
0.45
4.18
1
1.0
0
0.15
1.0
0.95
0.40
0.96
0.996
1.004
1.04
1.0
0.2
GE WTG Modeling-v4.2.doc, 6/24/08
8 Comparison of PSLF Results to Windtrap Results
Performance of both the PSLF fundamental frequency 1.5 MW DFAG and 2.5 MW
full converter WTG models is compared to that of the detailed cycle-by-cycle EMTP type
models incorporated in GE’s Windtrap program.
8.1 1.5 MW DFAG Comparison
The performance of GE 1.5 MW WTGs as modeled in PSLF and Windtrap is
compared to provide validation of the PSLF model.
The study system, shown in Figure 8-1, was based on one developed for the WECC
generic WTG modeling project. A single machine equivalent of a 100 MW wind plant is
connected via appropriate transformers and a collector system to a 230 kV equivalent
system. Figure 8-1 shows the weak system with MW and MVAr flows in the upper
diagram and pu impedances in the lower diagram. The point of interconnection (POI) is
defined as bus 2.
Figure 8-1. Test System for PSLF and Windtrap Comparison.
Several test disturbances were applied to this system. However, the results of only one
are described here. This disturbance consisted of a 150 msec, 3-phase fault through an
impedance at bus 2. The fault is cleared by tripping one of the 230 kV lines.
The PSLF 1.5 MW DFAG model, as described in this document, and the Windtrap
1.5 MW WTG model with the most recent GE controller (WCNTRLFLAG = 33) were
used for this comparison.
Cross plots of PSLF (blue line) and Windtrap (pink line) simulation results are shown
in Figure 8-2 through Figure 8-4. The first figure shows terminal voltage (pu), the second
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shows real power output from the WTG (MW), and the third shows reactive power output
(MVAr).
In all figures, the PSLF response matches the Windtrap response in the frequency
range of interest. Thus the PSLF model is an appropriate representation of the GE 1.5 MW
WTG’s behavior for fundamental frequency analysis.
1.50
Terminal Voltage (pu)
Windtrap
PSLF
1.00
0.50
0.00
0
0.5
1
1.5
Time (Seconds)
Figure 8-2. 1.5 MW DFAG PSLF and Windtrap Terminal Voltage Response.
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2
3.0
Windtrap
PSLF
Single WTG Real Power (MW)
2.0
1.0
0.0
-1.0
0
0.5
1
1.5
2
Time (Seconds)
Figure 8-3. 1.5 MW DFAG PSLF and Windtrap Real Power Response.
3.0
Single WTG Reactive Power (MVAr)
Windtrap
PSLF
2.0
1.0
0.0
-1.0
0
0.5
1
1.5
Time (Seconds)
Figure 8-4. 1.5 MW DFAG PSLF and Windtrap Reactive Power Response.
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8.2 2.5 MW Full Converter Comparison
The performance of GE 2.5 MW full converter WTGs as modeled in PSLF and
Windtrap is compared to provide validation of the PSLF model. The same study system
used in the 1.5 MW DFAG comparison and shown in Figure 8-1 was also used for this
comparison.
Several test disturbances were applied to this system. However, the results of only one
are described here. This disturbance consisted of a 150 msec, 3-phase fault to ground at
bus 2.
The PSLF 2.5 MW model, as described in this document, and the Windtrap 2.5 MW
WTG model with the most recent GE controller (WCNTRLFLAG = 4) were used for this
comparison.
Cross plots of PSLF (blue line) and Windtrap (pink line) simulation results are shown
in Figure 8-5 through Figure 8-7. The first figure shows terminal voltage (pu), the second
shows real power output from the WTG (MW), and the third shows reactive power output
(MVAr).
In all figures, the PSLF response matches the Windtrap response in the frequency
range of interest. Thus the PSLF model is an appropriate representation of the GE 2.5 MW
WTG’s behavior for fundamental frequency analysis.
The low frequency oscillations in the Windtrap results are merely the result of
sampling aliasing.
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1.50
Terminal Voltage (pu)
Windtrap
PSLF
1.00
0.50
0.00
0
0.5
1
2
1.5
Time (Seconds)
Figure 8-5. 2.5 MW Full Converter PSLF and Windtrap Terminal Voltage Response.
4.0
Windtrap
PSLF
Single WTG Real Power (MW)
3.0
2.0
1.0
0.0
0
0.5
1
1.5
Time (Seconds)
Figure 8-6. 2.5 MW Full Converter PSLF and Windtrap Real Power Response.
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2
3.0
Single WTG Reactive Power (MVAr)
Windtrap
PSLF
2.0
1.0
0.0
-1.0
0
0.5
1
1.5
Time (Seconds)
Figure 8-7. 2.5 MW Full Converter PSLF and Windtrap Reactive Power Response.
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2
9 Conclusions
The wind turbine model presented in this report is based on presently available design
information, test data and extensive engineering judgment. The modeling of wind turbine
generators for bulk power system performance studies is still in a state of rapid evolution,
and is the focus of intense activity in many parts of the industry. More important, the GE
equipment is being continuously improved, to provide better dynamic performance. These
ongoing improvements necessitate continuing changes and improvements to these models.
This model is expected to give realistic and correct results when used for bulk system
performance studies. It is expected that as experience and additional hard test data is
obtained, these models will continue to evolve, in terms of parameter values and structure.
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