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Examples | Doubly-Fed Induction Generator based Wind Turbine with Average and Switching Function Converters
(a)
(b)
Figure 1: HYPERSIM model of Doubly-Fed Induction Generator based Wind Turbine Generation System (WTGS)
(a) average converter based model in Page-1 (b) switching function converter based model in Page-2
Location
This example model can be found in the software under the category "Renewable Energy" with the file name "DFIG_Wind_Turbine_System.ecf".
Description
This example shows the control and operation of a Doubly Fed Induction Generator (DFIG) based Type-III wind turbine generator (WTG) connected to a typical distribution system [1] [2]. The example model shows the simulation of an 8.5 MW, 575 V, 60 Hz wind park connected to a 25 kV distribution system through a 20 km feeder. It is noted that a single 1.7 MW DFIG is scaled-up (by a factor of 'number of wind turbines = 5') to meet 8.5 MW power rating of wind park. Further, the rating of wind park can be changed by varying the 'number of wind turbine' and/or 'rating of wind turbine' in the mask. Each wind turbine operates in the maximum power point mode. Since, the control design is performed in per unit; the model can be simulated for any number of wind turbine and power rating. A single-line diagram of type-III WTG system example model simulated in HYPERSIM is shown in Figure 1. The details of system and controller parameters used in the simulation are given in Table 1.
Electrical model:
This type-III WTGS example model consists of a wound rotor induction generator, and a back-to-back voltage source converter (VSC) placed between the generator rotor and the grid. The WTGS is connected to the grid through a 25kV/575V transformer and a 20km line PI section line. The typical rating of the converter is 30% of its machine rating.
This example demonstrates the control dynamics of the WTGS using both the average (Figure 1(a), Page-1) and switching function (Figure 1(b), Page-2) converter models, and illustrates the comparison between the two. On each page, the grid side converter (GSC) and rotor side converter (RSC) are made using the average converter (AvgC) or the switching function (SWF) converter blocks from the HYPERSIM native library. The average converter model of HYPERSIM library is developed based on the equivalent voltage and current source concept. The AC side of the converter is made using a three-phase voltage source, and the DC side of the converter is made using a DC current source. The voltage reference from the controller and the DC voltage of the converter decides the magnitude of this three-phase voltage, while the value for DC current source is calculated from active power passing through the converter. In the switching function model, the switches are replaced by two voltage sources and two diodes per phase on the AC side and a current source on the DC side. The converter is controlled by firing pulses produced by a PMW generator or by firing pulses averaged over a time step of the simulation (1/Ts). The SWF model presents a good compromise between the real-time performance of an average model and the accuracy of using detailed switches. It can be used for power quality analysis which is not possible with the average converter model. In the SWF model, the switching frequency in RSC-GSC is taken as 3060 Hz; the pu voltage at the point of connection (POC) remains within ± 0.05 pu of 1 pu value, and THD of POC voltage remains within 5 % as per the IEEE std. 1547-2003 [3].
Control mechanism:
Both RSC and GSC adopt a two-level decoupled control approach where outer loops estimate the current references, and inner loops set references for the converter’s AC voltage. The controllers operate in voltage reference frame where d-axis current (active current) components get priority over q-axis currents (reactive current) when controllers reach to their maximum current limits. RSC’s d- and q- axis current regulate the active and reactive power dispatch from the DFIG, respectively. RSC estimates its d-axis current reference using the torque reference, set by the speed and pitch controller. With varying wind speed, speed and pitch controller measures the wind turbine’s rotational speed and convert it into the reference torque through a predefined power-speed tracking curve. On the other hand, GSC’s d- and q-axis current regulate the DC link voltage and reactive power dispatch from GSC, respectively. GSC operates in unity power-factor, hence, it contributes no additional reactive power to the system. To reduce the computational complexities, inner control loops are designed based on the Internal Model Control (IMC) method considering the Г representation of the induction generator. However, to ensure accurate tracking, feed-forward compensating terms have been added. In addition, the multi-mass turbine drive train operates in such a way that the WT operates in maximum power point mode.
It is noted that the control of the grid and rotor side converters helps to feed the power in either direction from the rotor to the grid or vice-versa. It usually depends upon the wind velocity or rotor speed. The control of the Type-III DFIG WTG is shown below in Figure 2.
(a)
(b)
Figure 2: (a) Single line diagram of Type-III WTGS (b)Control Block Diagram of Type-III WTGS.
Mechanical model:
Further, the detailed discussion on the modelling and control of wind turbine/power system are discussed in [4]. The speed-power relationship of the given wind turbine generator system is given as
The reference speed is normally 1.2 pu but is reduced for power levels below 75%. This behaviour is included in the model by using the equation – (1) for speed reference when the power is below 0.75 pu.
The mechanical power extracted from the wind is given as
P_{wind} is the mechanical power extracted from the wind, ρ is the air density in kg/m^{3}, Ar is the area swept by the rotor blades in m^{2}, v_{w} is the wind speed in m/sec, and C_{p} is the power coefficient, which is a function of λ and β. λ is the ratio of the rotor blade tip speed and the wind speed (Vtip/v_{w}), β is the blade pitch angle in degrees. For the rigid shaft representation used in this model, the relationship between blade tip speed and generator rotor speed, ω, is a fixed constant, K_{b}. The calculation of λ becomes:
C_{p} is a characteristic of the wind turbine and is usually provided as a set of curves relating C_{p} to λ, with β as a parameter.
The Cp function used in the model is characterized by the coefficients obtained from the curve fitting are given in Table 2.
Model parameters
Table 1: System and controller Parameters
Name of parameter | Description | Unit | Value |
---|---|---|---|
Nb_wt | Number of wind turbines | 5 | |
Turbine (for a wind turbine) | |||
Pmec1 | Rated mechanical power | W | 1.7E6 |
Generator (for a wind turbine) | |||
Pn | Generator Rated Power | VA | 1.7E6 |
Vpmsg_nom | Stator nominal voltage, VLLrms | V | 575 |
fn | Rated frequency | Hz | 60 |
Rs_pu | Stator Resistance | pu | 0.01028 |
Lls_pu | Stator leakage inductance | pu | 0.1543 |
Lm_pu | Mutual inductance | pu | 3.085 |
Rr_pu | Rotor resistance | pu | 0.006684 |
Llr_pu | Rotor leakage inductance | Pu | 0.1543 |
H | Inertia constant | s | 0.56347 |
F | Friction factor | pu | 0.01 |
np | Number of poles | --- | 6 |
Converter (for a wind turbine) | |||
Vgrid_nom | Nominal voltage on the Grid-side, VLLRMS | V | 575 |
Imax_grid_conv | Maximum current limit, Grid-side | pu | 1.1 |
L_RL | Coupling inductor inductance | pu | 0.3 |
R_RL | Coupling inductor resistance | pu | 0.03 |
Vdc_nom | Rated voltage on DC side | V | 1100 |
C_DClink | Smoothing capacitor capacitance | F | 0.018 |
C_var_filter | Capacitive vars of filtering | Var | 55E3 |
Q_filter | Capacitor quality factor Q | --- | 50 |
Transmission shaft (for a wind turbine) | |||
H_WT | Inertia constant | s | 4.33 |
Ksh | Elasticity constant | pu (couple/rad) | 1.11 |
D_mutual | Mutual damping coefficient | pu (couple/rad/s) | 1.5 |
w_wt0 | Turbine initial speed | pu | 1.2 |
torque0 | Initial torque | pu | 0.83 |
Control system (for a wind turbine) | |||
Kp_dc | Proportional gain of DC voltage regulator | --- | 4 |
Ki_dc | Integral gain of DC voltage regulator | s | 400 |
Kp_grid_side_cur_reg | Proportional gain of the current controller, Grid-side | --- | 1.2 |
Ki_grid_side_cur_reg | Integral gain of current controller, grid side | s | 10 |
Kp_speed | Proportional gain of Speed controller | --- | 3 |
Ki_speed | Integral gain of Speed controller | s | 0.6 |
Kp_rotor_side_cur_reg | Proportional gain of current controller, rotor side | --- | 0.9 |
Ki_rotor_side_cur_reg | Integral gain of current regulator, rotor side | s | 12 |
Ki_var | Integral gain of reactive power regulator | s | 0.1 |
Ki_volt | Integral gain of AC voltage regulator | s | 165 |
Kp_volt | Proportional gain of AC voltage regulator | --- | 0 |
Kp_pitch | Proportional gain of the pitch regulator | --- | 150 |
Ki_pitch | Integral gain of the pitch regulator | s | 25 |
Kp_compensation | Proportional gain | --- | 3 |
Ki_compensation | Integral gain | s | 30 |
Pitch_max | Maximum pitch angle | degrees | 27 |
Pitch_min | Minimum pitch angle | degrees | 0 |
Pitch_rate | Positive rate of pitch | deg/s | 10 |
Pitch_rate_neg | Negative rate of pitch | deg/s | -10 |
Protection system | |||
crowbar_off | DC voltage low threshold | V | 1.03 |
crowbar_on | DC voltage high threshold | V | 1.15 |
Simulation and Results
To demonstrate the control system dynamics and its interaction with the grid, the DFIG-based WTG is simulated for three event changes within a 95 s time span. The three events are a 3LG fault, a reactive power change, and a wind velocity variation. The model is tested at a time-step of 50 µs, and the results are provided from the ScopeView acquisition. The control sequence displaying different scenarios is summarized in the table below.
Table 3: Example Model Test Scenario Sequence
Operation Points | From | To | Wind Velocity (m / s) | Qref (pu) | Fault Type | Machine Speed (pu) |
1 | 0 | 1 | 12 | 0 | - | Super-Synchronous |
2 | 1 | 1.1 | 12 | 0 | 3LG | Super-Synchronous |
3 | 1.1 | 5 | 12 | 0 | - | Super-Synchronous |
4 | 5 | 15 | 12 | 0.25 | - | Super-Synchronous |
5 | 15 | 20 | 15 | 0.25 | - | Super-Synchronous |
6 | 20 | 25 | 15 | 0 | - | Super-Synchronous |
7 | 25 | 55 | 8 | 0 | - | Sub-Synchronous |
8 | 55 | 95 | 12 | 0 | - | Super-Synchronous |
The simulation results show that the DFIG-based WTG model maintains stable operation before and after any perturbation. The dynamics of pitch angle, active power, reactive power, machine speed, machine torque, DC voltage, and AC voltage at the POC obtained with the average (B1_575V_1) and SwF (B1_575V_2) models are compared in the following figures. The results also show instantaneous stator and rotor currents along with these wind farm parameters.
At the beginning of the simulation, the rated wind velocity of 12 m/s, and Qref of 0 MVAr, are given to average and SWF models to have a stable initialization. The machine torque and speed reach -0.86 pu and 1.19 pu, respectively. A 3LG Fault is applied at bus B1_25kV_1 at 1 s for a duration of 0.1 s. A similar fault situation is applied in the SWF model at bus B1_25kV_2 (Page 2). At 1.1 s, the fault is removed, and the controller of RSC forces the machine's torque and speed to follow its previous steady-state values, as shown in Figure 4. At the moment of fault, the transient is observed in active power and reactive power from WTG in Figure 3. The pitch angle controller takes measured active power (Pmeas) as the input signal. Hence, the transient with respect to fault indirectly influences pitch angle oscillation, as shown in Figure 4. This transient oscillation is also observed in the DC-link voltage in Figure 5, which is controlled using the GSC controller. At the moment of 3LG fault, the POC voltage and current from the average and SWF model show a good match in Figure 6. Similarly, the stator current from both models shows a good match in Figure 7. However, a mismatch is present in the rotor current between average and SWF models in Figure 7. These discrepancies might be attributed to the fact that the RSC controller in the SWF based model behaves slightly different compared to the average model due to the high-frequency response of SWF converter. This difference causes that the machine speed of average and SWF models have a little mismatch between them. The speed mismatch is integrated and transferred to rotor angle calculation creating a phase shift in the rotor current in the SWF model with respect to the rotor current in the average model.
At 5 s, the Qref is increased from 0 MVAr to 0.25 MVAr, and the RSC controller injects reactive power from WTG. After that, the wind velocity is changed from 12 m/s to 15 m/s at 15 s. The pitch angle controller increases the blade angle (Figure 4) to receive 1 pu active power (Figure 3) at 15 m/s wind velocity. Hence, the torque and speed of the machine remain the same at -0.86 pu and 1.19 pu, respectively (Figure 4). From 5 s to 20 s, 0.25 MVAr reactive power injects from WTG operating at super-synchronous speed. At 20 s, the Qref is reduced to 0 MVAr, and the reactive power injection from the WTG gradually decreases to 0 MVAr (Figure 3).
At 25 s, the wind velocity is decreased from 15 m/s to 8 m/s to observe the behavior of the GSC and RSC controller for an abrupt change in the input variable. In this condition, the pitch angle controller reduces the blade angle to 0 degrees as the WTG is operated at less than its rated wind velocity of 12 m/s (Figure 4). The machine torque and speed are reduced with the reduction of wind velocity (Figure 4), and WTG operates at sub-synchronous speed. Additionally, the active power is extracted with respect to 8 m/s wind velocity, as shown in Figure 3.
At 55 s, the wind velocity is increased from 8 m/s to 12 m/s, and the WTG gradually resumes its original stable mode of operation (with respect to wind velocity 12 m/s and Qref = 0 MVAr inputs). It is noted that the pitch angle controller is limited by ±10 deg/s pitch rate. Then, when a step input of wind velocity is applied to the model, the pitch angle cannot increase abruptly. The pitch angle gradually increases to 10 deg angle while the machine torque and speed increase at a slower rate due to inertia. As the time approaches, the difference between machine torque and speed values and their steady-state values (-0.86 pu and 1.19 pu, respectively) are reduced. Hence, the pitch angle falls down to 0 deg angle between 72 s to 78 s. As the simulation continues the machine torque and speed resume to their respective steady-state values, and the pitch angle reach 4.5 deg. angle (original value with respect to 12 m / s). The simulation ends at 95 s.
Figure 3: Wind Velocity, Active Power Generation, and Reactive Power Reference & generated from the Type III Wind Turbine Generation System
Figure 4: Mechanical Parameters of the Type III Wind Turbine Generation System
Figure 5: Magnitude of AC Voltage and DC-link Voltage of the Type III Wind Turbine Generation System
If we look at the instantaneous waveforms at the Point of Connection during the fault, it can be noticed that the SWF model waveforms contains some harmonics which do not present in the AVG Model, but overall the voltages and currents have a good agreement between the two models. These instantaneous waveforms are not included in the provided ScopeView template due to the large amount of data during the long acquisition.
Figure 6: POC Voltage and Current waveforms during the 3LG fault at B1_25kV of the Type III Wind Turbine Generation System
Figure 7: Stator and Rotor Current waveforms during the 3LG fault at B1_25kV of the Type III Wind Turbine Generation System
References
[1] Gagnon, Richard, Gilbert Turmel, Christian Larose, Jacques Brochu, Gilbert Sybille, and Martin Fecteau. "Large-scale real-time simulation of wind power plants into Hydro-Québec power system." In 9th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as on Transmission Networks for Offshore Wind Power Plants, pp. 18-19. 2010.
[2] Karaagac, Ulas, Jean Mahseredjian, Henry Gras, Hani Saad, Jaime Peralta, and Luis Daniel Bellomo. "Simulation models for wind parks with variable speed wind turbines in EMTP." Polytechnique Montréal (2017).
[3] "IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems," in IEEE Std 1547-2003 , vol., no., pp.1-28, 28 July 2003, doi: 10.1109/IEEESTD.2003.94285.
[4] DYNAMIC MODELING OF GE 1.5 AND 3.6 MW WIND TURBINE GENERATORS FOR STABILITY SIMULATIONS, Nicholas W. Miller, Juan J. Sanchez-Gasca, William W. Price Robert W. Delmerico, GE Power Systems GE Research Schenectady, NY Niskayuna, NY.
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