Simulation and Characteristics Analysis of Multiple Wind Generators in Large-Scale Wind Farms Based on Simplified Model

In the view of the high complexity and a large amount of data of the electromagnetic transient model for the single wind generator, it is difficult to realize the multi-unit simulation modeling of large-scale wind farms by power system simulation software. In this paper, the simplified models of single direct drive and doubly-fed wind generator system are proposed, respectively. In order to study the output characteristics of the wind generator system, the components with small inertia constant in the electromagnetic transient model are neglected, and the shafting model, the converter model, and the control loops are simplified and reduced, respectively. Based on the study of the single electromagnetic transient model of wind generators, the simplified simulation models are built by the PSCAD (Power Systems Computer Aided Design) simulation platform, which are carried out under the conditions of constant wind speed, step wind speed, and fault. The output characteristics of the simplified models under different working conditions are compared in detail models. The simulation results show that, within the allowable calculation accuracy range, the dynamic response curves of the single simplified model and the electromagnetic transient model are consistent. The simulation speed can be significantly improved, the time consumption can be reduced, and the simulation speed can be increased more obviously when the number of simulation models increases. Therefore, it can be applied to the simulation research of multi-wind generators in large-scale wind farms.


Introduction
As energy and environmental issues become more severe, wind energy has been widely used in power systems due to its technological and cost advantages. Electromagnetic transient simulation is an important tool for studying the operation of the grid power system [1]. At present, electromagnetic transient models are the main research objects for wind power generation systems, including wind turbines, drive shafts, generators, converters, and control systems [2,3]. For the research of a single wind generator, one detailed electromagnetic transient simulation model can be easily established to comprehensively observe its response characteristics [4]. However, a wind farm usually includes a dozen to hundreds of wind generators, with smaller simulation step size (microsecond level) of traditional electromagnetic transient simulation calculations, the calculation speed of simulation is greatly reduced, and even becomes unacceptable. A large number of electromagnetic transient models will make the power system simulation model extremely complicated, which is not suitable for large-scale wind farm research. Therefore, it is urgent to find a new and more efficient method to solve this problem.

Simplification of Drive Shaft Model
For wind power generation systems of different grid-connected types, the shafting model has a unified structure, including three masses: wind turbine mass, gearbox mass, and generator mass (direct drive wind power generation system has no gearbox mass) [20]. The inertia of the gearbox is smaller compared with that of the fan and generator, which can be ignored. With neglection of the damping coefficient and rigidity coefficient of the transmission shaft, the rotation equation of the traditional simple mass model is obtained: where ω is the motor mechanical speed, T m is the mechanical torque, T e is the electromagnetic torque, J is the moment of inertia.

Simplification of Converter Model
With the very high switching frequency of the power electronic devices in the detailed model, the model simulation time-consumption is lengthened. If only the external characteristics of the wind turbine are studied, there is no need to pay attention to the on-off process inside of the converter. Therefore, the equivalent processing of this part can simplify the model greatly.
The simplified electromagnetic transient model usually replaces the converter with a controllable voltage source, ignoring the dynamic process inside the converters. The actual value of the control signal is considered as equal to the reference value, and the input signal of the controllable voltage source is considered as the PWM (Pulse Width Modulation) space vector modulation reference to the voltage command [20]. The simplified electromagnetic transient model not only guarantees the model simulation accuracy, it improves the model simulation speed. However, it still retains most of the remaining structures of the wind generation system, which still has shortcomings to the simulation of large-scale multi-unit wind farms, so it can be further simplified. The replacement of the converter model by a controllable current source, which is an electromechanical transient model, will improve the simplification of the model more significantly.

Simplification of a Single Direct Drive Fan Model
The permanent magnet synchronous wind power system installs a full-power converter between the stator winding and the grid to convert the variable-frequency and variable-voltage alternating current output by the generator into a DC voltage, and then it is inverted into an alternating current whose frequency, amplitude, and phase are consistent with the grid and merges it into the grid to achieve variable speed and constant frequency.
The direct drive wind generator unit is mainly composed of a wind turbine, a drive shaft, a permanent magnet synchronous generator (PMSG), a converter and a control system [21,22], whose structure is shown in Figure 1. In the two-phase synchronous rotating coordinate system, the mathematical model of PMSG is obtained: Electronics 2020, 9, 1994 4 of 16 where i d , i q , u d , u q are stator d, q axis current and voltage, respectively; R s is stator resistance; p is the number of generator rotor pole pairs; ψ f is the rotor permanent magnet flux linkage; ω is the generator rotor speed.
where id, iq, ud, uq are stator d, q axis current and voltage, respectively; Rs is stator resistance; p is the number of generator rotor pole pairs; ψf is the rotor permanent magnet flux linkage; ω is the generator rotor speed. Since the direct drive wind generator does not have a gearbox, ω = ωg (ωg is the generator rotor speed). The following equations can be obtained: Additionally, the generator side power is: where Pm is the mechanical power output by the wind turbine; P is the electromagnetic active power output by the generator; Q is the electromagnetic reactive power output by the generator. The generator-side converter uses the generator rotor flux vector control method, which is usually isd = 0 control [23], to control the electromagnetic torque output by the generator and then control the generator speed to achieve the purpose of maximum power point tracking (MPPT). The grid-side converter inverts DC power into AC power. The converter adopts double closed loop control, the outer loop is the power loop, and the inner loop is the current loop.
The electromagnetic time constant of the inner current loop is much smaller than the electromechanical time constant of the outer loop, and the response speed of the inner loop is faster than that of the outer loop. Therefore, in the simplified model, the dynamic process of the current inner loop of the converter is ignored, and the input value of the inner loop is considered equal to  Since the direct drive wind generator does not have a gearbox, ω = ω g (ω g is the generator rotor speed). The following equations can be obtained: ( Additionally, the generator side power is: where P m is the mechanical power output by the wind turbine; P is the electromagnetic active power output by the generator; Q is the electromagnetic reactive power output by the generator. The generator-side converter uses the generator rotor flux vector control method, which is usually i sd = 0 control [23], to control the electromagnetic torque output by the generator and then control the generator speed to achieve the purpose of maximum power point tracking (MPPT). The grid-side converter inverts DC power into AC power. The converter adopts double closed loop control, the outer loop is the power loop, and the inner loop is the current loop.
The electromagnetic time constant of the inner current loop is much smaller than the electromechanical time constant of the outer loop, and the response speed of the inner loop is faster than that of the outer loop. Therefore, in the simplified model, the dynamic process of the current inner loop of the converter is ignored, and the input value of the inner loop is considered equal to output value. The generator output power value P is compared with the reference signal P ref , and the control command i sqref of the current inner loop is obtained by the PI regulator, which is considered equivalent to the current inner loop output value i sq , and i sd = 0 is brought into the control system. The following equations can be obtained: The simplified model of the direct drive wind generator is shown in Figure 2. The fan module calculates the mechanical torque T m through the wind speed V w and the rotor speed ω, and then it Electronics 2020, 9, 1994 5 of 16 is brought into the rotor motion equation. The MPPT model calculates the power reference value P ref through the wind speed V w and the rotor speed ω. After the reference value P ref is compared with the actual value P, the inner loop current reference value i sqref is obtained through the PI controller. Since the inner loop is simplified, its output is equal to its input. After the current value i sq , i sd brought into the stator voltage equations, the stator voltages U sabc are obtained through coordinate transformation. With the active power value P and grid voltage U gabc , the grid current value i gd , i gq are calculated. Then, the reference command value of the controlled current source is obtained through coordinate transformation.
The simplified model of the direct drive wind generator is shown in Figure 2. The fan module calculates the mechanical torque Tm through the wind speed Vw and the rotor speed ω, and then it is brought into the rotor motion equation. The MPPT model calculates the power reference value Pref through the wind speed Vw and the rotor speed ω. After the reference value Pref is compared with the actual value P, the inner loop current reference value isqref is obtained through the PI controller. Since the inner loop is simplified, its output is equal to its input. After the current value isq, isd brought into the stator voltage equations, the stator voltages Usabc are obtained through coordinate transformation. With the active power value P and grid voltage Ugabc, the grid current value igd, igq are calculated. Then, the reference command value of the controlled current source is obtained through coordinate transformation.

Simplification of a Single Doubly-Fed Wind Generator Model
The doubly-fed wind generator unit is mainly composed of doubly-fed induction generator (DFIG), machine-side converter, grid-side converter and its control system [24]. The wind turbine is connected to the generator after speed-increasing by gears, and a converter is used to realize the twoway flow of power with the grid. The structure of the doubly-fed wind generator is shown in Figure  3.

Simplification of a Single Doubly-Fed Wind Generator Model
The doubly-fed wind generator unit is mainly composed of doubly-fed induction generator (DFIG), machine-side converter, grid-side converter and its control system [24]. The wind turbine is connected to the generator after speed-increasing by gears, and a converter is used to realize the two-way flow of power with the grid. The structure of the doubly-fed wind generator is shown in Figure 3.
The simplified model of the direct drive wind generator is shown in Figure 2. The fan module calculates the mechanical torque Tm through the wind speed Vw and the rotor speed ω, and then it is brought into the rotor motion equation. The MPPT model calculates the power reference value Pref through the wind speed Vw and the rotor speed ω. After the reference value Pref is compared with the actual value P, the inner loop current reference value isqref is obtained through the PI controller. Since the inner loop is simplified, its output is equal to its input. After the current value isq, isd brought into the stator voltage equations, the stator voltages Usabc are obtained through coordinate transformation. With the active power value P and grid voltage Ugabc, the grid current value igd, igq are calculated. Then, the reference command value of the controlled current source is obtained through coordinate transformation.

Simplification of a Single Doubly-Fed Wind Generator Model
The doubly-fed wind generator unit is mainly composed of doubly-fed induction generator (DFIG), machine-side converter, grid-side converter and its control system [24]. The wind turbine is connected to the generator after speed-increasing by gears, and a converter is used to realize the twoway flow of power with the grid. The structure of the doubly-fed wind generator is shown in Figure  3.   Figure 3. Doubly-fed wind generator structure and its control.
When the stator flux directional control is adopted [25], the stator flux ψ sd is equal to ψ s , and ψ sq = 0. Since the stator of the doubly-fed generator is directly connected to the grid, the stator voltage amplitude U s is a constant, that is, the grid voltage, and the equation pωψ s = U s can be obtained. The electromagnetic torque and the stator flux equation of the generator are as follows: Electronics 2020, 9,1994 6 of 16 where L s and L m are the self-inductance of the stator and the mutual inductance between the stator and rotor, respectively. The value of electromagnetic torque T e can be obtained, T e = L m U s L s pω i rq . The converter adopts double closed-loop control, the outer ring is the rotating speed loop, and the inner ring is the current loop. Similarly, in this simplified model, the dynamic process of the current inner loop of the converter is ignored, and the input of the inner loop is considered equal to the output. The speed ω is compared with the reference signal ω ref , and the control command i qref of the current inner loop is obtained by the PI regulator, which is considered equivalent to the output value of the current inner loop. Then, the electromagnetic torque T e is calculated, which is brought into the motion equation of the drive shaft system to obtain the speed ω to feedback. The simplified model of the doubly-fed wind generator is shown in Figure 4.
where Ls and Lm are the self-inductance of the stator and the mutual inductance between the stator and rotor, respectively. The value of electromagnetic torque Te can be obtained, The converter adopts double closed-loop control, the outer ring is the rotating speed loop, and the inner ring is the current loop. Similarly, in this simplified model, the dynamic process of the current inner loop of the converter is ignored, and the input of the inner loop is considered equal to the output. The speed ω is compared with the reference signal ωref, and the control command iqref of the current inner loop is obtained by the PI regulator, which is considered equivalent to the output value of the current inner loop. Then, the electromagnetic torque Te is calculated, which is brought into the motion equation of the drive shaft system to obtain the speed ω to feedback. The simplified model of the doubly-fed wind generator is shown in Figure 4. The fan module calculates the mechanical torque Tm through the wind speed Vw and the rotor speed ω, and then it is brought into the rotor motion equation. The MPPT model calculates the rotor speed reference value ωref through the wind speed Vw and the rotor speed ω. After the reference value ωref is compared with the actual value ω, the inner loop current reference value irqref is obtained through the PI controller. Since the inner loop is simplified, its output is equal to its input. After current value irq, ird brought into the stator current equations, the stator currents isabc are obtained through coordinate transformation. After current value irq, ird brought into the power equations, the stator active and reactive power P, Q are obtained through coordinate transformation. With the active and reactive power P, Q, and grid voltage Vterm, and then the reference command value of the controlled current source is obtained. The fan module calculates the mechanical torque T m through the wind speed V w and the rotor speed ω, and then it is brought into the rotor motion equation. The MPPT model calculates the rotor speed reference value ω ref through the wind speed V w and the rotor speed ω. After the reference value ω ref is compared with the actual value ω, the inner loop current reference value i rqref is obtained through the PI controller. Since the inner loop is simplified, its output is equal to its input. After current value i rq , i rd brought into the stator current equations, the stator currents i sabc are obtained through coordinate transformation. After current value i rq , i rd brought into the power equations, the stator active and reactive power P, Q are obtained through coordinate transformation. With the active and reactive power P, Q, and grid voltage V term , and then the reference command value of the controlled current source is obtained.

Simplified Model Parameters of Direct-Drive, Doubly-Fed Wind Generator
In order to verify the correctness of the simplified model of a single direct-drive and doubly-fed wind generator based on PSCAD, simulation analysis was carried out under three conditions of constant wind speed, step wind speed, and fault. The model parameters are as shown in Table 1.

Simulation Results of a Single Wind Generator under Constant Wind Speed Conditions
The simulation step sizes are set to 20,100 µs, respectively. The simulation duration is 20 s, and the constant wind speed is set to 9 m/s. The simulation time-consuming and accuracy comparison results of the detailed model and simplified model built on the PSCAD are shown in Tables 2 and 3, respectively. It shows in Table 2 that under the same simulation step size, since the simplified model does not take the on-off process of power electronic devices in the converter into account, the simulation time-consumption is reduced greatly than the detailed model. When the number of wind generators increases, the simulation efficiency increases more significantly. Therefore, when studying large-scale multi-unit wind farms, the simplified models proposed in this paper have a significant effect in shortening the simulation time-consumption and improving the simulation efficiency.
It shows in Table 3 that with the simplified models proposed in this paper, the error does not exceed 10%. The grid current errors of models are relatively large, mainly due to the switching loss of converters in the detailed model, which is ignored in the simplified models. Therefore, the models proposed in this paper obviously keep good consistency with the detailed models within the reasonable accuracy range.

Simulation Results of a Single Wind Generator under Step Wind Speed Condition
In order to verify the effectiveness of the simplified model in analyzing the dynamic process, the two types of wind generator models are run under step wind speed condition. The wind speed is set to step from 8 m/s to 10 m/s at t = 10 s.

Simulation Results of a Single Direct Drive Wind Generator
Since the permanent magnet synchronous wind power generation system adopts the variable-speed constant-frequency control method, the speed of the wind turbine can be adjusted according to the change of wind speed, so will the speed of the PMSG accordingly. When the rotation speed of the Electronics 2020, 9, 1994 8 of 16 PMSG changes, the voltage and frequency generated at the stator will also change, so will the output power of the generator accordingly. As shown in the Figure 5, when the wind speed stepped from 8 to 10 m/s at t = 10 s.
to step from 8 m/s to 10 m/s at t = 10 s.

Simulation Results of a Single Direct Drive Wind Generator
Since the permanent magnet synchronous wind power generation system adopts the variablespeed constant-frequency control method, the speed of the wind turbine can be adjusted according to the change of wind speed, so will the speed of the PMSG accordingly. When the rotation speed of the PMSG changes, the voltage and frequency generated at the stator will also change, so will the output power of the generator accordingly. As shown in the Figure 5, when the wind speed stepped from 8 to 10 m/s at t = 10 s. In the detailed model, the PMSG speed n gradually increased from 81.2 r/min, and stabilized to 109.0 r/min at t = 11.5 s; in the simplified model, the PMSG speed n_sim increased from 81.1 r/min (error: 0.1%), gradually increased and stabilized to 109.5 r/min (error: 0.5%) at t = 11.5 s.
In the detailed model, the output power Ps of the PMSG gradually increased from 0.333 MW, and stabilized to 0.415 MW at t = 10.5 s; in the simplified model, the output power Ps_sim of the PMSG increased from 0.333 MW (error: 0.0%), gradually increased and stabilized to 0.415 MW (error: 0.0%) at t = 10.5 s.  In the detailed model, the PMSG speed n gradually increased from 81.2 r/min, and stabilized to 109.0 r/min at t = 11.5 s; in the simplified model, the PMSG speed n _sim increased from 81.1 r/min (error: 0.1%), gradually increased and stabilized to 109.5 r/min (error: 0.5%) at t = 11.5 s.
In the detailed model, the output power P s of the PMSG gradually increased from 0.333 MW, and stabilized to 0.415 MW at t = 10.5 s; in the simplified model, the output power P s_sim of the PMSG increased from 0.333 MW (error: 0.0%), gradually increased and stabilized to 0.415 MW (error: 0.0%) at t = 10.5 s.
In the detailed model, the value of the grid-connected current I gRMS of the direct drive wind generator gradually increased from 0.255 kA, and stabilized to 0.317 kA at t = 10.5 s; in the simplified model, the value of the grid-connected current I gRMS_sim of the direct drive wind generator increased from 0.270 kA (error: 5.9%), gradually increased and stabilized to 0.333 kA (error: 5.0%) at t = 10.5 s.
In the detailed model, the amplitude of the PMSG stator voltage U sabc gradually increased from 0.40 kV and stabilized to 0.49 kV at t = 11.0 s, the voltage frequency f gradually increased from 14.1 Hz, and stabilized to 17.5 Hz at t = 11.0 s; In the simplified model, the amplitude of the PMSG stator voltage U sabc_sim gradually increased from 0.40 kV (error: 0.0%), and stabilized to 0.49 kV (error: 0.0%) at t = 11.0 s, and the voltage frequency f _sim increased from 14.0 Hz (error: 0.7%) gradually increased, and stabilized to 17.5 Hz at t = 11.0 s (error: 0.0%).
The relatively large error between grid-connected current I gRMS and I gRMS_sim is mainly due to the installation of a full-power converter between the PMSG and the grid, so there is switching loss in the detailed model, which is ignored in the simplified model. The error is within 10%.
In conclusion, when the wind speed changes, the simplified direct-drive wind generator model can achieve the purpose of maximum power point tracking, while also maintaining good consistency with the dynamic and steady state characteristics of the detailed model.

Simulation Results of a Single Doubly-Fed Wind Generator
Since the doubly-fed wind generation system adopts the variable-speed constant-frequency control method, the speed of the wind turbine can be adjusted according to the change of wind speed, so will the speed of the DFIG will also change accordingly. When the rotor speed of the DFIG changes, the stator current frequency is kept consistent with the grid frequency by adjusting the rotor current frequency, that is, 50 Hz. Further, the output power of the generator will change accordingly. As shown in the Figure 6, when the wind speed stepped from 8 to 10 m/s at t = 10 s.
The relatively large error between grid-connected current IgRMS and IgRMS_sim is mainly due to the installation of a full-power converter between the PMSG and the grid, so there is switching loss in the detailed model, which is ignored in the simplified model. The error is within 10%.
In conclusion, when the wind speed changes, the simplified direct-drive wind generator model can achieve the purpose of maximum power point tracking, while also maintaining good consistency with the dynamic and steady state characteristics of the detailed model.

Simulation Results of a Single Doubly-Fed Wind Generator
Since the doubly-fed wind generation system adopts the variable-speed constant-frequency control method, the speed of the wind turbine can be adjusted according to the change of wind speed, so will the speed of the DFIG will also change accordingly. When the rotor speed of the DFIG changes, the stator current frequency is kept consistent with the grid frequency by adjusting the rotor current frequency, that is, 50 Hz. Further, the output power of the generator will change accordingly. As shown in the Figure 6, when the wind speed stepped from 8 to 10 m/s at t = 10 s.  In the detailed model, the DFIG rotor speed n gradually increased from 1099 r/min, and stabilized to 1375 r/min at t = 14 s; in the simplified model, the DFIG rotor speed n _sim increased from 1100 r/min (error: 0.1%), gradually increased and stabilized to 1375 r/min (error: 0.5%) at t = 14 s. In the detailed model, the output power P s of the DFIG gradually increased from 0.340 MW, and stabilized to 0.420 MW at t = 14 s; in the simplified model, the output power P s_sim of the DFIG increased from 0.341 MW (error: 0.3%), gradually increased, and stabilized to 0.421 MW at t = 14 s (error: 0.2%).
In the detailed model, the value of the grid-connected current I gRMS of the doubly-fed wind generator gradually increased from 0.262 kA and stabilized to 0.325 kA at t = 14 s; in the simplified model, the value of grid-connected current I gRMS_sim of the doubly-fed wind generator increased from 0.275 kA (error: 5.0%), gradually increased, and stabilized to 0.336 kA (error: 3.4%) at t = 14 s. In the detailed model, the amplitude of the stator current I sabc of the DFIG gradually increased from 0.389 kA and stabilized to 0.475 kV at t = 14.0 s. The current frequency f is 50 Hz at steady state, and fluctuated at t = 10.0 s (∆f = 0.5 Hz). In the simplified model, the amplitude of the stator current I sabc_sim of the DFIG gradually increased from 0.390 kV (error: 0.3%) and stabilized to 0.476 kV (error: 0.2%) at t = 14.0 s, the current frequency f _sim is always maintained at 50.0 Hz (error: 0.0%).
The relatively large error between the grid-connected current I gRMS and I gRMS_sim is mainly due to the installation of a converter between the rotor of the DFIG and the grid, so there is a small amount of slip power, and the error is within 10%.
In conclusion, when the wind speed changes, the doubly-fed wind power generation model can achieve the purpose of maximum power point tracking, while also maintaining good consistency with the characteristics of the detailed model.

Simulation Results of a Single Wind Generator under Fault Condition
In order to verify the effectiveness of the simplified model of the two types of single wind generator under fault condition, both types of wind power generation units are operated under single-phase ground fault condition on the grid-connected side. The constant wind speed is set to 9 m/s. The rated voltage of the grid is 0.69 kV.

Simulation Results of a Single Direct Drive Wind Generator
As shown in the Figure 7, when a phase A grounding fault occurs at the grid-connected end via a 0.1 Ω resistance at t = 10 s. and fluctuated at t = 10.0 s (Δf = 0.5 Hz). In the simplified model, the amplitude of the stator current Isabc_sim of the DFIG gradually increased from 0.390 kV (error: 0.3%) and stabilized to 0.476 kV (error: 0.2%) at t = 14.0 s, the current frequency f_sim is always maintained at 50.0 Hz (error: 0.0%).
The relatively large error between the grid-connected current IgRMS and IgRMS_sim is mainly due to the installation of a converter between the rotor of the DFIG and the grid, so there is a small amount of slip power, and the error is within 10%.
In conclusion, when the wind speed changes, the doubly-fed wind power generation model can achieve the purpose of maximum power point tracking, while also maintaining good consistency with the characteristics of the detailed model.

Simulation Results of a Single Wind Generator under Fault Condition
In order to verify the effectiveness of the simplified model of the two types of single wind generator under fault condition, both types of wind power generation units are operated under single-phase ground fault condition on the grid-connected side. The constant wind speed is set to 9 m/s. The rated voltage of the grid is 0.69 kV.

Simulation Results of a Single Direct Drive Wind Generator
As shown in the Figure 7, when a phase A grounding fault occurs at the grid-connected end via a 0.1 Ω resistance at t = 10 s. In the detailed model, the amplitude of phase A voltage U a of the power grid dropped from 0.584 to 0.392 kV, and the amplitude of phase B, C voltage U b , U c remained 0.584 kV without significant change; in the simplified model, the amplitude of phase A voltage U a of the power grid dropped from 0.585 kV (error: 0.2%) to 0.392 kV (error: 0%), and the B, C phase voltage U b , U c amplitude remained 0.585 kV (error: 0.2%) without significant changes.
In the detailed model, the average value of the generator output active power P s was 0.386 MW without significant change; in the simplified model, the average value of the generator output active power P s_sim was 0.387 MW (error: 0.3%) without significant change.
In the detailed model, the reactive power Q s of the generator output was 0.014 MVar, whose average value did not change significantly; in the simplified model, the reactive power Q s_sim of the generator output was 0.014 MVar (error: 0.0%), whose average value did not change significantly.
In the detailed model, the rotor speed n of the PMSG maintained at 99.0 r/min all the time, whose average value did not change significantly with only a slight disturbance after 10 s; in the simplified model, the rotor speed of the PMSG n _sim also maintained 99.0 r/min (error: 0.0%), whose average value did not change significantly. In the detailed model, the value of the grid-connected current I gRMS of the direct drive wind power generation gradually increased from 0.295 kA, and stabilized to 0.330 kA at t = 10.4 s, containing second-harmonic disturbance; in the simplified model, the value of grid-connected current I gRMS_sim of the direct drive wind power generation gradually increased from 0.310 kA (error: 5.1%), and stabilized to 0.345 kA (error: 4.5%) at t = 10.2 s, containing second-harmonic disturbance.
In conclusion, when a single-phase ground fault occurs on the grid-connected side, the simplified direct-drive wind power model can maintain good consistency with the characteristics of the detailed model.

Simulation Results of a Single Doubly-Fed Wind Generator
As shown in the Figure 8, when a phase A grounding fault occurs at the grid-connected end via a 0.1Ω resistance at t = 10 s. average value did not change significantly; in the simplified model, the reactive power Qs_sim of the generator output was 0.014 MVar (error: 0.0%), whose average value did not change significantly.
In the detailed model, the rotor speed n of the PMSG maintained at 99.0 r/min all the time, whose average value did not change significantly with only a slight disturbance after 10 s; in the simplified model, the rotor speed of the PMSG n_sim also maintained 99.0 r/min (error: 0.0%), whose average value did not change significantly.
In the detailed model, the value of the grid-connected current IgRMS of the direct drive wind power generation gradually increased from 0.295 kA, and stabilized to 0.330 kA at t = 10.4 s, containing second-harmonic disturbance; in the simplified model, the value of grid-connected current IgRMS_sim of the direct drive wind power generation gradually increased from 0.310 kA (error: 5.1%), and stabilized to 0.345 kA (error: 4.5%) at t = 10.2 s, containing second-harmonic disturbance.
In conclusion, when a single-phase ground fault occurs on the grid-connected side, the simplified direct-drive wind power model can maintain good consistency with the characteristics of the detailed model.

Simulation Results of a Single Doubly-Fed Wind Generator
As shown in the Figure 8, when a phase A grounding fault occurs at the grid-connected end via a 0.1Ω resistance at t = 10 s. In the detailed model, the amplitude of phase A voltage U a of the power grid dropped from 0.584 to 0.392 kV, and the amplitude of phase B, C voltage U b , U c remained 0.584 kV without significant change; in the simplified model, the amplitude of phase A voltage U a of the power grid dropped from 0.585 kV (error: 0.2%) to 0.392 kV (error: 0%), the amplitude of phase B, C voltage U b , U c remained 0.585 kV (error: 0.2%) without significant changes.
In the detailed model, the generator output active power P s remained 0.387 MW, whose average value did not change significantly; in the simplified model, the generator output active power P s_sim remained 0.388 MW (error: 0.3%), whose average value did not change significantly.
In the detailed model, the average value the reactive power Q s of the generator output was 0.01 MVar, which did not change significantly; in the simplified model, the reactive power Q s_sim of the generator output was 0.01 MVar (error: 0.0%), which did not change significantly but with disturbance.
In the detailed model, the rotor speed n of the PMSG changed from 1220.5 r/min after t = 10 s, containing a peak value of 1234.0 r/min fluctuation. In addition, it returned to 1220.5 r/min at t = 14 s. In the simplified model, the rotor speed n _sim of the PMSG maintained at 1220.5 r/min (error: 0.0%) all the time.
In the detailed model, the value of the grid-connected current I gRMS of the direct drive wind power generation system decreased slightly from 0.295 kA and then gradually increased, which stabilized to 0.331 kA at t = 14 s, containing second-harmonic disturbance; in the simplified model, the value of grid-connected current I gRMS_sim of the direct drive wind power generation system gradually increased from 0.311 kA (error: 5.4%), and stabilized to 0.346 kA (error: 4.5%) at t = 10.2 s, containing second-harmonic disturbance.
The relatively large error between grid-connected current I gRMS and I gRMS_sim is mainly due to the installation of a converter between the rotor side of the DFIG and the grid, so there is a small amount of slip power, and the error is within 10%.
In conclusion, when a single-phase ground fault occurs on the grid-connected side, the simplified doubly-fed wind power model can maintain good consistency with the characteristics of the detailed model.

Simulation Results of Multi-Unit Hybrid Simplified Model
In order to verify the effectiveness of application of single simplified model to large-scale multi-unit wind farm study, a large-scale multi-unit wind farm was built on the PSCAD software platform. The total installed capacity is 100 units and the total capacity is 50 MW, including 50 direct drive and 50 doubly-fed units. In order to reduce the line loss, every single wind generator is connected to the collector line after being boosted by a 0.69 kv/35 kv transformer. The 100 wind generators are divided into 10 columns, each with 10 units. The unit spacing is 0.15 km, and the row spacing is 0.5 km. The line resistance is 0.2 Ω/km, and the line inductance is 0.002 H/km. Its overall structure is shown in Figure 9. MVar, which did not change significantly; in the simplified model, the reactive power Qs_sim of the generator output was 0.01 MVar (error: 0.0%), which did not change significantly but with disturbance.
In the detailed model, the rotor speed n of the PMSG changed from 1220.5 r/min after t = 10 s, containing a peak value of 1234.0 r/min fluctuation. In addition, it returned to 1220.5 r/min at t = 14 s. In the simplified model, the rotor speed n_sim of the PMSG maintained at 1220.5 r/min (error: 0.0%) all the time.
In the detailed model, the value of the grid-connected current IgRMS of the direct drive wind power generation system decreased slightly from 0.295 kA and then gradually increased, which stabilized to 0.331 kA at t = 14 s, containing second-harmonic disturbance; in the simplified model, the value of grid-connected current IgRMS_sim of the direct drive wind power generation system gradually increased from 0.311 kA (error: 5.4%), and stabilized to 0.346 kA (error: 4.5%) at t = 10.2 s, containing second-harmonic disturbance.
The relatively large error between grid-connected current IgRMS and IgRMS_sim is mainly due to the installation of a converter between the rotor side of the DFIG and the grid, so there is a small amount of slip power, and the error is within 10%.
In conclusion, when a single-phase ground fault occurs on the grid-connected side, the simplified doubly-fed wind power model can maintain good consistency with the characteristics of the detailed model.

Simulation Results of Multi-Unit Hybrid Simplified Model
In order to verify the effectiveness of application of single simplified model to large-scale multiunit wind farm study, a large-scale multi-unit wind farm was built on the PSCAD software platform. The total installed capacity is 100 units and the total capacity is 50 MW, including 50 direct drive and 50 doubly-fed units. In order to reduce the line loss, every single wind generator is connected to the collector line after being boosted by a 0.69 kv/35 kv transformer. The 100 wind generators are divided into 10 columns, each with 10 units. The unit spacing is 0.15 km, and the row spacing is 0.5 km. The line resistance is 0.2 Ω/km, and the line inductance is 0.002 H/km. Its overall structure is shown in Figure 9.

Simulation Results under Constant Wind Speed Condition
Since the same amount of detailed model data is too large to run on the PSCAD platform, the sum of 50 times the output value of a single detailed model under the same working condition is the expected value. The simulation step size is set to 20, 100 µs, respectively. The simulation duration time is 20 s, and the constant wind speed is set to 9 m/s. The simulation time-consuming and accuracy comparison results are shown in Tables 4 and 5.  In Table 4, it shows that the simplified model has a significant effect on shortening the time-consumption. Under the condition that the simulation step size is 20 µs and the simulation duration time is 20 s, the time-consumption (1617 s) of 100 hybrid simplified models is even less than that of the detailed model of 5 doubly-fed wind generators (2256 s). The error between the actual value and the expected value of the simulation results does not exceed 10%. It shows that the single simplified model can still maintain excellent accuracy in large-scale wind farm simulation to study the characteristics of the system.

Simulation Results under Step Wind Speed Condition
When the wind speed is set to step from 8 to 10 m/s at t = 10 s, the output characteristics of wind farm are shown in Figure 10.
comparison results are shown in Tables 4 and 5.  In Table 4, it shows that the simplified model has a significant effect on shortening the timeconsumption. Under the condition that the simulation step size is 20 μs and the simulation duration time is 20 s, the time-consumption (1617 s) of 100 hybrid simplified models is even less than that of the detailed model of 5 doubly-fed wind generators (2256 s). The error between the actual value and the expected value of the simulation results does not exceed 10%. It shows that the single simplified model can still maintain excellent accuracy in large-scale wind farm simulation to study the characteristics of the system.

Simulation Results under Step Wind Speed Condition
When the wind speed is set to step from 8 to 10 m/s at t = 10 s, the output characteristics of wind farm are shown in Figure 10. Although the line loss is considered, the switching loss of the converter and the slip power are ignored in the simplified models, which lead to the error, but the error is also within 10%. It shows that the simplified multi-unit model can also maintain good consistency with the characteristics of the detailed model under step wind speed condition.

Simulation Results under Fault Condition
Single-phase grounding fault occurs on 35 kV bus at t = 10 s. The constant wind speed is 9 m/s. Under fault condition, the characteristic results of the wind farm model are shown in Figure 11. ignored in the simplified models, which lead to the error, but the error is also within 10%. It shows that the simplified multi-unit model can also maintain good consistency with the characteristics of the detailed model under step wind speed condition.

Simulation Results under Fault Condition
Single-phase grounding fault occurs on 35 kV bus at t = 10 s. The constant wind speed is 9 m/s. Under fault condition, the characteristic results of the wind farm model are shown in Figure 11. In the simplified model, for 35 kV bus, the amplitude of phase A voltage Ua of the power grid dropped from 28.62 to 19.1 kV, the amplitude of phase B, C voltage Ub, Uc remained 28.62 kV without significant changes. For 0.69 kV bus, the amplitude of phase A voltage Ua of the power grid dropped from 0.585 to 0.392 kV, the amplitude of phase B, C voltage Ub, Uc remained 0.585 kV without significant changes. In the simplified model, the steady-state value of wind farm grid-connected power Pg_sim_100 is 37.178 MW, and second-harmonic disturbance began to appear at t = 10 s. In the simplified model, the value of the grid-connected current IgRMS of the wind farm gradually increased from 0.613 kA, and stabilized to 0.690 kA at t = 10.2 s, containing second-harmonic disturbance. It shows that the simplified multi-unit model can also maintain good consistency with the characteristics of the detailed model under single-phase ground fault condition.

Conclusions
In the view of the low simulation efficiency of multiple wind generators in large-scale wind farms, the simplified models of single direct drive and doubly-fed wind generator system are proposed in this paper, respectively. Through the simplified models proposed in this paper and its verification, the following conclusions can be obtained: In the simplified model, for 35 kV bus, the amplitude of phase A voltage U a of the power grid dropped from 28.62 to 19.1 kV, the amplitude of phase B, C voltage U b , U c remained 28.62 kV without significant changes. For 0.69 kV bus, the amplitude of phase A voltage U a of the power grid dropped from 0.585 to 0.392 kV, the amplitude of phase B, C voltage U b , U c remained 0.585 kV without significant changes.
In the simplified model, the steady-state value of wind farm grid-connected power P g_sim_100 is 37.178 MW, and second-harmonic disturbance began to appear at t = 10 s. In the simplified model, the value of the grid-connected current I gRMS of the wind farm gradually increased from 0.613 kA, and stabilized to 0.690 kA at t = 10.2 s, containing second-harmonic disturbance. It shows that the simplified multi-unit model can also maintain good consistency with the characteristics of the detailed model under single-phase ground fault condition.

Conclusions
In the view of the low simulation efficiency of multiple wind generators in large-scale wind farms, the simplified models of single direct drive and doubly-fed wind generator system are proposed in this paper, respectively. Through the simplified models proposed in this paper and its verification, the following conclusions can be obtained:

1.
In the simplified models proposed in this paper, the converter model and control system are simplified. The controllable current source and voltage source models are used to replace detailed model converters. Therefore, a large amount of data in detailed models is reduced, which significantly improves the simulation efficiency.

2.
The simplified models proposed in this paper are built by mathematical method simplification based on the mathematical models, so there is no need to change the simulation software algorithm and it reduces the dependence on computer performance.

3.
The simplified simulation models proposed in this paper not only improve the simulation efficiency, but also maintain good consistency with the simulation results of the detailed model under normal and fault conditions.