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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 vi 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. GE Energy 1.1 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 GE Energy 2.1 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 2.2 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 2.3 GE WTG Modeling-v4.2.doc, 6/24/08 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). GE Energy 2.4 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. GE Energy 2.5 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 3.1 GE WTG Modeling-v4.2.doc, 6/24/08 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 3.2 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 3.3 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 4.1 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 4.2 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.4 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.5 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.6 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 4.7 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.8 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.9 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.10 + Σ GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.11 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.12 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.13 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 4.14 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.15 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.16 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 4.18 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 5.2 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 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. GE Energy 5.4 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 5.6 GE WTG Modeling-v4.2.doc, 6/24/08 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). GE Energy 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. GE Energy 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. GE Energy 6.3 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 6.6 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 6-4. Active Power Control Response to Loss of Load. GE Energy 6.7 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 6.8 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 6-5. Response to Wind Speed Ramp Up and Down. GE Energy 6.9 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 6.10 1.5 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 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 GE Energy 6.11 1.5 MW WTG 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 GE Energy 6.12 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 7.1 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 7.2 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 7.3 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-1. Series of Bus Faults with Various Fault Impedances. GE Energy 7.4 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-2. 3-phase Fault to Ground, Cleared by Tripping 230 kV Line. GE Energy 7.5 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 7.6 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-3. Increasing Wind Speed Results in Zero-Power Operation. GE Energy 7.7 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-4. Decreasing Wind Speed Results in Zero-Power Operation. GE Energy 7.8 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-5. Voltage Regulation in Continuous Zero-Power Operation. GE Energy 7.9 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 7.10 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-6. Step Reduction in Converter Current Limit with P Priority. GE Energy 7.11 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-7. Step Reduction in Converter Current Limit with Q Priority. GE Energy 7.12 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 7.13 GE WTG Modeling-v4.2.doc, 6/24/08 Figure 7-8. Low Voltage Power Logic Response to Fault on POI Bus. GE Energy 7.14 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 7.16 GE WTG Modeling-v4.2.doc, 6/24/08 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 GE Energy 7.17 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 GE Energy 8.1 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 8.2 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 8.3 GE WTG Modeling-v4.2.doc, 6/24/08 2 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. GE Energy 8.4 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 8.5 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 8.6 GE WTG Modeling-v4.2.doc, 6/24/08 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. GE Energy 9.1 GE WTG Modeling-v4.2.doc, 6/24/08