Disturbance-Suppression Method of Direct-Driven PMSG-Based Wind Power System in Microgrids

: In order to solve the current ﬂuctuation problem in microgrids, a suppression method called the Direct-driven Permanent Magnet Synchronous Generator (DPMSG)-based Wind Power System (WPS) based on an adaptive enhanced moving average ﬁlter algorithm is proposed. Firstly, the mathematical model of the WPS is established. On this basis, the suppression method under unbalanced conditions is derived by the instantaneous power equation to ensure the stable operation of the microgrid. In order to improve the dynamic compensation capability of the DPMSG-based WPS, an enhanced moving average ﬁltering algorithm with frequency adaptability is proposed. The positive and negative sequence components are obtained in the dq frame by this ﬁltering algorithm. Subsequently, the angular frequency of the microgrid is obtained according to the changing phase, which realizes the high-performance control of the WPS and avoids the complicated parameter adjustment of traditional methods. The correctness of this method is veriﬁed by the simulation results. The DPMSG-based WPS with the proposed method can improve the stability of the microgrid.


Introduction
With the development of wind power technology, the proportion of DPMSG-based WPS in the power system is gradually increasing [1,2].However, the DPMSG-based WPS has the characteristics of dispersion, randomness and volatility, which makes the microgrid prone to three-phase asymmetry of the voltage and current, resulting in a decline in the power quality of the microgrid [3][4][5].Therefore, a strong ability to suppress unbalanced disturbances is required in the DPMSG-based WPS connected to the microgrid [6,7].To this end, it is necessary to accurately detect the state information in the transient process and quickly suppress disturbances by the control technology, so as to improve microgrid stability.
Many studies have been performed on the detection technology and control methods of renewable energy systems in unbalanced environments [8][9][10].Based on the DPMSGbased WPS model, the key parameters affecting the stability of the power system are studied [11].A model predictive controller design method is proposed for Maximum Power Point Tracking (MPPT) systems based on the DPMSG [12].The adaptive overall control in the whole wind speed range increases the robustness of the DPMSG-based WPS [13].The modeling and control methods of the DPMSG-based WPS are compared and analyzed, and the direction of future research is demonstrated in [14].
For the problem of synchronous information detection, the detection technology is mainly divided into the closed-loop and open-loop detection algorithms [15][16][17].The closed-loop detection algorithms usually include the Decoupled Double Synchronous Reference Frame Phase-Locked Loop (DDSRF-PLL), the single synchronous reference frame phase-locked loop, and the second-order generalized integrator frequency-locked loop algorithms [18,19].When the microgrid environment is harsh, the dynamic response time of these algorithms is generally longer.To solve this problem, the open-loop detection algorithm is developed in [20,21].The open-loop detection algorithm realizes the accurate acquisition of the synchronous phase of the single-phase signal by the virtual quadrature voltage [22].Three traditional synchronous detection algorithms are analyzed and compared [23].Subsequently, a benchmark model is proposed to study the dynamic performance of the open-loop detection algorithm in unbalanced environments.In an unbalanced environment, phase-locked loop-free control of renewable energy systems is implemented, but this algorithm is only used for power grids with small frequency fluctuations [24].In Table 1, a comparative analysis of state-of-the-art research is presented.From the literature in Table 1, it can be found that in the existing research it is difficult to quickly detect synchronization information with frequency changes.problem in the unbalanced environment [31].In addition, this strategy can also deal with harmonic problems.In [32], the control method can suppress the negative-sequence current in the unbalanced environment by the instantaneous symmetrical component method.A current-compensation method for photovoltaic power systems is proposed, which optimizes the control parameters by the particle swarm optimization algorithm to achieve multi-objective control [33].The compensation method based on the flexible harmonic loop with the fundamental current control solves the unbalance problem [34].In the harsh environment, the unbalanced voltage is compensated by an improved enhanced phase-locked loop [35].A model predictive current controller based on Kalman filter estimator is proposed to improve the power quality of the microgrid in [36].However, the structures of these control methods are relatively complex.
In order to achieve a compensation method with a simpler structure and faster response, this paper proposes a disturbance-suppression method for the WPS based on the adaptive enhanced moving average filter algorithm.The main work of this paper is as follows: (1) The mathematical model of the DPMSG-based WPS is carried out based on the circuit topology and the control strategy.(2) The angular frequency is calculated from the changing phase, and the accurate control of WPS is realized.Then, the command current value under unbalanced conditions is derived by the instantaneous power equation.(3) This method can significantly improve the compensation capabilities, avoids the parameter design problem of the phase-locked loop, and has a faster response speed.
The mathematical model of the DPMSG-based WPS is introduced in Section 2. A synchronization information detection algorithm is proposed, which can realize fast and accurate detection of the synchronization phase and angular frequency in Section 3.For Section 4, the compensation method of current fluctuation is presented.The effectiveness of the proposed method is verified in Section 5.

DPMSG-Based WPS
The circuit topology of the DPMSG-based WPS is shown in Figure 1.This WPS is mainly composed of the synchronous generator, the inverter, the rectifier, the equivalent inductance, the equivalent resistance, the transformer and the microgrid.In the figure, ω is the real-time angular frequency of the microgrid, ω r is the wind turbine speed, i sabc is the stator current, u dc is the capacitor voltage, i gabc is the output current of the grid-side converter, L g and R g are the equivalent inductance and resistance, P and Q are the active and reactive power of the DPMSG-based WPS, and P L is the power consumed by the load.
(1) The mathematical model of the DPMSG-based WPS is carried out based on the circuit topology and the control strategy.(2) The angular frequency is calculated from the changing phase, and the accurate control of WPS is realized.Then, the command current value under unbalanced conditions is derived by the instantaneous power equation.(3) This method can significantly improve the compensation capabilities, avoids the parameter design problem of the phase-locked loop, and has a faster response speed.
The mathematical model of the DPMSG-based WPS is introduced in Section 2. A synchronization information detection algorithm is proposed, which can realize fast and accurate detection of the synchronization phase and angular frequency in Section 3.For Section 4, the compensation method of current fluctuation is presented.The effectiveness of the proposed method is verified in Section 5.

DPMSG-Based WPS
The circuit topology of the DPMSG-based WPS is shown in Figure 1.This WPS is mainly composed of the synchronous generator, the inverter, the rectifier, the equivalent inductance, the equivalent resistance, the transformer and the microgrid.In the figure, ω is the real-time angular frequency of the microgrid, ωr is the wind turbine speed, isabc is the stator current, udc is the capacitor voltage, igabc is the output current of the grid-side converter, Lg and Rg are the equivalent inductance and resistance, P and Q are the active and reactive power of the DPMSG-based WPS, and PL is the power consumed by the load.

Mathematical Models of Wind Turbine and DPMSG
The wind turbine is the prime mover in the DPMSG-based WPS, which drives the DPMSG by the fan blades.The main function of the wind turbine is to realize the maximum utilization of wind energy.According to Bates theory [12], the output mechanical power can be expressed as where S is the area of the fan blade, ρ and v are the air density and wind speed, δ and λ are the pitch angle and tip speed ratio, Cp(δ, λ) is the utilization coefficient of wind energy.The pitch angle of the wind turbine is given by where R is the impeller radius of wind turbine.The output torque of the wind turbine is

Mathematical Models of Wind Turbine and DPMSG
The wind turbine is the prime mover in the DPMSG-based WPS, which drives the DPMSG by the fan blades.The main function of the wind turbine is to realize the maximum utilization of wind energy.According to Bates theory [12], the output mechanical power can be expressed as where S is the area of the fan blade, ρ and v are the air density and wind speed, δ and λ are the pitch angle and tip speed ratio, C p (δ, λ) is the utilization coefficient of wind energy.The pitch angle of the wind turbine is given by where R is the impeller radius of wind turbine.The output torque of the wind turbine is Considering the maximum economic benefit of the DPMSG-based WPS, C p (δ, λ) has a corresponding relationship with λ.
The assumptions adopted in this paper are consistent with those in [6].From the stator flux and the stator voltage equations, the mathematical model of the DPMSG in the dq frame can be obtained as follows where Ψ f is the rotor flux linkage of the DPMSG, e sd and e sq are the stator terminal voltage in the dq frame, R s is the stator winding resistance, L sd and L sq are the inductances of the direct and quadrature axis.

Circuit Topology and Control Strategy of Wind Turbine Side Converter
The circuit topology and control strategy of the wind turbine side converter of the DPMSG-based WPS are shown in Figure 2. P WT is the output power of the wind turbine, P vic is the virtual inertia power command and P MPPT is the MPPT power command.
tor flux and the stator voltage equations, the mathematical model of the DPMSG in the dq frame can be obtained as follows where Ψf is the rotor flux linkage of the DPMSG, esd and esq are the stator terminal voltage in the dq frame, Rs is the stator winding resistance, Lsd and Lsq are the inductances of the direct and quadrature axis.

Circuit Topology and Control Strategy of Wind Turbine Side Converter
The circuit topology and control strategy of the wind turbine side converter of the DPMSG-based WPS are shown in Figure 2. PWT is the output power of the wind turbine, Pvic is the virtual inertia power command and PMPPT is the MPPT power command.
where ud and uq are the terminal voltage of the wind turbine side converter in the dq frame.
The main goal of power control is to achieve the maximum utilization of wind energy.In order to effectively utilize the kinetic energy on the rotor for the auxiliary support of the microgrid, the control method requires virtual inertia control.This method will affect the rotor speed during this transient to ensure a fast response for the angular frequency.The virtual inertia power command can be expressed as where kd is the virtual inertia control coefficient.(5) where u d and u q are the terminal voltage of the wind turbine side converter in the dq frame.
The main goal of power control is to achieve the maximum utilization of wind energy.In order to effectively utilize the kinetic energy on the rotor for the auxiliary support of the microgrid, the control method requires virtual inertia control.This method will affect the rotor speed during this transient to ensure a fast response for the angular frequency.The virtual inertia power command can be expressed as where k d is the virtual inertia control coefficient.
The output power of MPPT control can be written as where k max is the coefficient maximizing captured wind energy.From Figure 2, the power control command of the wind turbine side converter is It can be seen from ( 8) that when the power control is added with virtual inertia control, the essence is to couple the angular frequency with the wind turbine, so that the kinetic energy of the wind turbine can be used to participate in the adjustment process of the angular frequency.For the case of no disturbance in microgrids, the wind turbine operates at the maximum power point.where kmax is the coefficient maximizing captured wind energy.

Circuit Topology and Control Strategy of Grid Side Converter
From Figure 2, the power control command of the wind turbine side converter is It can be seen from ( 8) that when the power control is added with virtual inertia control, the essence is to couple the angular frequency with the wind turbine, so that the kinetic energy of the wind turbine can be used to participate in the adjustment process of the angular frequency.For the case of no disturbance in microgrids, the wind turbine operates at the maximum power point.

Circuit Topology and Control Strategy of Grid Side Converter
where egd and egq are the output voltage of the grid side converter, Ugd and Ugq are the microgrid voltage in the dq frame.
The purpose of the capacitor voltage control is to maintain the stability of DC voltage, so as to ensure that the DPMSG-based WPS can effectively realize the connection with the microgrid.According to Figure 3, the current command of the capacitor voltage control is where kp and ki are the proportional and integral coefficients of the capacitor voltage control, udcref is the capacitor voltage command.From Figure 3 and Park's transformation, the mathematical model of the converter is (9) where e gd and e gq are the output voltage of the grid side converter, U gd and U gq are the microgrid voltage in the dq frame.
The purpose of the capacitor voltage control is to maintain the stability of DC voltage, so as to ensure that the DPMSG-based WPS can effectively realize the connection with the microgrid.According to Figure 3, the current command of the capacitor voltage control is where k p and k i are the proportional and integral coefficients of the capacitor voltage control, u dcref is the capacitor voltage command.

Synchronous Information Detection Algorithm in Microgrid
Microgrids often suffer from unbalanced three-phase loads, the single-phase-to-ground fault and the two-phase short-circuit, resulting in unbalanced conditions, which lead to the introduction of low-frequency harmonics into the control strategy.
The grid-connected voltage of the DPMSG-based WPS in the unbalanced condition can be expressed as From (11), the positive and negative sequence components of the grid-connected voltage is given by Processes 2023, 11, 2189 where α and β are the initial phases of the positive and negative sequence components, U m + and U m − are the amplitudes of the positive and negative sequence components.( 11) is brought into the transformation matrix, which can be obtained as sin ωt sin(ωt − 2π 3 ) sin(ωt Therefore, ( 14) can be rewritten as When the microgrid voltage is asymmetrical, its components still contain negative sequence components in the dq frame.Therefore, the control strategy of DPMSG-based WPS cannot effectively support the microgrid.

Detection Principle
The moving average filter algorithm is an effective algorithm for suppressing periodic harmonics [17], which can be written as where L is the sliding period.
The dynamic response time of this algorithm is proportional to its sliding period.With the increase of sliding period, the dynamic response time of moving average filter algorithm is longer.The transfer function of this algorithm is According to the amplitude-frequency characteristic of ( 17), when ω is 2πn/L, the gain of this algorithm is zero.For other values of ω, the algorithm gain is less than 1, and decreases rapidly as ω increases.The moving average filter algorithm is similar to the lowpass filter algorithm (see Figure 4), which can filter out harmonics of specific frequencies.The dynamic response time of this algorithm is proportional to its sliding period.With the increase of sliding period, the dynamic response time of moving average filter algorithm is longer.The transfer function of this algorithm is According to the amplitude-frequency characteristic of ( 17), when ω is 2πn/L, the gain of this algorithm is zero.For other values of ω, the algorithm gain is less than 1, and decreases rapidly as ω increases.The moving average filter algorithm is similar to the lowpass filter algorithm (see Figure 4), which can filter out harmonics of specific frequencies.In order to further analyze the influence of the moving average filter algorithm that filters out the nth harmonic on the mth harmonic, the specific research is as follows.The nth harmonic can be expressed as n In order to further analyze the influence of the moving average filter algorithm that filters out the nth harmonic on the mth harmonic, the specific research is as follows.The nth harmonic can be expressed as where θ m n and U m n are the initial phase and amplitude of the nth harmonic, respectively.In the transient process of the moving average filter algorithm, it is assumed that the time t is less than the sliding period L. The mth harmonic can be described as where A m is the transient amplitude coefficient.
When the algorithm reaches a steady state, the nth harmonic is completely filtered out.The mth harmonic can be described as where B m is the steady-state amplitude coefficient.The steady-state amplitude coefficient is given by From ( 19) and (20), the attenuation capability of the moving average filter algorithm for the transient and steady state of the harmonic amplitude is shown in Figure 5.With the decrease of n, this algorithm has a stronger ability to attenuate the transient harmonics.In the transient process, this algorithm can usually attenuate the amplitude of the harmonics by 60%.When the steady state is reached, the moving average filter algorithm has a good ability to suppress all harmonics.
Processes 2023, 11, x FOR PEER REVIEW 8 of 21 From ( 19) and (20), the attenuation capability of the moving average filter algorithm for the transient and steady state of the harmonic amplitude is shown in Figure 5.With the decrease of n, this algorithm has a stronger ability to attenuate the transient harmonics.
In the transient process, this algorithm can usually attenuate the amplitude of the harmonics by 60%.When the steady state is reached, the moving average filter algorithm has a good ability to suppress all harmonics.According to (16), the moving average filter algorithm can be discretized as In order to filter out multiple harmonics at the same time, an enhanced moving average filter algorithm is used in this paper, which has better flexibility in design.The en- According to (16), the moving average filter algorithm can be discretized as In order to filter out multiple harmonics at the same time, an enhanced moving average filter algorithm is used in this paper, which has better flexibility in design.The enhanced moving average filter algorithm can be obtained as where N is the magnification of the sliding period.Therefore, by designing an appropriate sliding period, the enhanced moving average filter algorithm can be used to suppress multiple harmonics.In addition, this algorithm averages high-frequency random noise.

Fast Detection Algorithm
After the enhanced moving average filter algorithm, the positive sequence component of the voltage in ( 15) can be expressed as The transformation matrix of negative sequence is According to (25) and the enhanced moving average filter algorithm, the negative sequence component can be rewritten as The initial phase of grid-connected voltage in ( 24) is This initial phase in ( 27) is not the initial phase (α ∈ [0, 2π)) of the actual gridconnected voltage, so the compensation phase Z x is introduced in this paper.Therefore, the synchronous phase of the grid-connected voltage of the DPMSG-based WPS can be described as where ω 0 is the constant angular frequency and Z x is the compensation phase.The compensation phase is given by Combining the grid-connected voltage shown in ( 11) with ( 14), ( 23) and ( 28), the synchronous phase of the grid-connected voltage can be quickly and accurately detected.
In order to further obtain the real-time angular frequency, the synchronous phase of the positive sequence is decomposed into the ideal angular frequency ω 0 t and the changing phase θ c .Therefore, when the microgrid reaches a steady state, the difference angular frequency ∆ω between the angular frequency ω and the constant angular frequency ω 0 also remains stable, which can be expressed as The initial phase α is unknown, so ( 30) cannot be directly used to calculate the changing phase θ c .However, the change amount of the changing phase in a steady state is also in a linear relationship with the difference angular frequency ∆ω.Therefore, the change amount of the changing phase can be obtained indirectly by the closed-loop control, namely According to (31), the real-time angular frequency of the microgrid is where K p and K i are the proportional and integral coefficients of the angular frequency control.
The algorithm changes the changing phase θ c into a continuous phase, and then the noise-free angular frequency can be obtained by the closed-loop control.The flow chart of frequency detection is shown in Figure 6.Therefore, the real-time synchronous information of the microgrid can be calculated through (23), (28) and Figure 6.According to (31), the real-time angular frequency of the microgrid is where Kp and Ki are the proportional and integral coefficients of the angular frequency control.
The algorithm changes the changing phase θc into a continuous phase, and then the noise-free angular frequency can be obtained by the closed-loop control.The flow chart of frequency detection is shown in Figure 6.Therefore, the real-time synchronous information of the microgrid can be calculated through (23), (28) and Figure 6.

Disturbance-Suppression Method for Microgrids
Due to the isolation between the DPMSG and the microgrids by the converters, this WPS has certain advantages in assisting the operation of the microgrid compared with the doubly fed induction generator-based WPS.The wind turbine side converter is not directly connected to the microgrid, so the microgrid has little influence on it.However, the grid side converter directly connected to the microgrid is affected by microgrid failures.
From Figure 1, the instantaneous power equation on the grid side can be described as

Disturbance-Suppression Method for Microgrids
Due to the isolation between the DPMSG and the microgrids by the converters, this WPS has certain advantages in assisting the operation of the microgrid compared with the doubly fed induction generator-based WPS.The wind turbine side converter is not directly connected to the microgrid, so the microgrid has little influence on it.However, the grid side converter directly connected to the microgrid is affected by microgrid failures.
From Figure 1, the instantaneous power equation on the grid side can be described as According to (33), the instantaneous power of the DPMSG-based WPS is where P 0 and Q 0 are the constant components of active and reactive power, P 1 and Q 1 are the amplitudes of active and reactive sinusoidal components, P 2 and Q 2 are the amplitudes of active and reactive cosine components, respectively.It can be seen from ( 34) that in unbalanced conditions, the active and reactive output power by the DPMSG-based WPS have not only constant power components, but also double frequency power components.From (34), the constant and double frequency power components can be written as In order to suppress the power fluctuations and the negative sequence current, the commands of the constant and double frequency power components can be expressed as where the subscript ref is the reference value of the physical quantity.
By substituting (36) into (35), the sequence current command in the current control loop can be obtained as For the sequence current problem in the microgrid, the negative sequence current command of the DPMSG-based WPS is Substituting (38) into (37), the positive sequence current command can be described as Therefore, (39) can be rewritten as According to (40), the positive sequence current command of the DPMSG-based WPS can be obtained when the power fluctuation occurs in the microgrid.In order to improve the utilization efficiency of the WPS, the reactive power command is usually zero.The proposed method is shown in Figure 7.The voltage and current of this method are calculated and controlled, which eliminates the complex dynamic adjustment process.Therefore, this method can significantly improve the grid-connected current control speed of the DPMSG-based WPS, suppress the current overload degree, and rapidly improve the power quality of the microgrid.

Verification of Disturbance-Suppression Method
This paper uses the simulation to verify the correctness of the compensation control method.The circuit topology and control method of the DPMSG-based WPS are shown in Figures 1 and 7.

Simulation Verification
When the microgrid voltage is suddenly reduced and unbalanced, Figure 8 shows the suppression process of the DPMSG-based WPS using the DDSRF-SPLL algorithm and the proposed method.The unbalanced voltage of the microgrid leads to the unbalance of the output current of the DPMSG-based WPS, which makes the current amplitude significantly increase.After being disturbed, the microgrid changes from three-phase balance to three-phase unbalance, and the voltage amplitude decreases (see Figure 8a).The positive sequence voltages obtained by the proposed method are shown in Figure 8b.The current suppression process of the WPS with the DDSRF-SPLL algorithm and the proposed method are shown in Figure 8c,d.Figure 8e illustrates the comparison results of the output current value of the DPMSG-based WPS by this method and the DDSPF algorithm.The output current based on the DDSRF-SPLL algorithm does not contain the negative sequence component after the dynamic response time in Figure 8d.However, this dynamic process is too lengthy to achieve the goal of quickly supporting the microgrid.The suppression time of the DPMSG-based WPS using the two methods is 0.06 s and 0.08 s, respectively.The proposed method has fast response speed and small transient current fluctuation, so that the output current reaches the steady-state value faster.The voltage and current of this method are calculated and controlled, which eliminates the complex dynamic adjustment process.Therefore, this method can significantly improve the grid-connected current control speed of the DPMSG-based WPS, suppress the current overload degree, and rapidly improve the power quality of the microgrid.

Verification of Disturbance-Suppression Method
This paper uses the simulation to verify the correctness of the compensation control method.The circuit topology and control method of the DPMSG-based WPS are shown in Figures 1 and 7.

Simulation Verification
When the microgrid voltage is suddenly reduced and unbalanced, Figure 8 shows the suppression process of the DPMSG-based WPS using the DDSRF-SPLL algorithm and the proposed method.The unbalanced voltage of the microgrid leads to the unbalance of the output current of the DPMSG-based WPS, which makes the current amplitude significantly increase.After being disturbed, the microgrid changes from three-phase balance to three-phase unbalance, and the voltage amplitude decreases (see Figure 8a).The positive sequence voltages obtained by the proposed method are shown in Figure 8b.The current suppression process of the WPS with the DDSRF-SPLL algorithm and the proposed method are shown in Figure 8c,d.Figure 8e illustrates the comparison results of the output current value of the DPMSG-based WPS by this method and the DDSPF algorithm.The output current based on the DDSRF-SPLL algorithm does not contain the negative sequence component after the dynamic response time in Figure 8d.However, this dynamic process is too lengthy to achieve the goal of quickly supporting the microgrid.
The suppression time of the DPMSG-based WPS using the two methods is 0.06 s and 0.08 s, respectively.The proposed method has fast response speed and small transient current fluctuation, so that the output current reaches the steady-state value faster.Figure 9 shows the suppression process of the DPMSG-based WPS with the DDSRF-SPLL algorithm and the proposed method in the case of unbalance and phase increase.After the unbalanced disturbance, the phase of the microgrid voltage increases suddenly, as shown in Figure 9a. Figure 9 shows the suppression process of the DPMSG-based WPS with the DDSRF-SPLL algorithm and the proposed method in the case of unbalance and phase increase.After the unbalanced disturbance, the phase of the microgrid voltage increases suddenly, as shown in Figure 9a.
According to Figure 9c,d, the DPMSG-based WPS using the proposed method and the DDSRF-SPLL algorithm can eliminate the unbalance problem and achieve the goal of supporting the microgrid.The response times of the DPMSG-based WPS with the proposed method and DDSRF algorithm to suppress the disturbance are 0.08 s and 0.11 s (see Figure 9e).The dynamic response time of this method is 27.3% faster than that of the DDSRF-SPLL algorithm.Under this working condition, the DPMSG-based WPS with this method can still maintain excellent current control capability.Figure 9 shows the suppression process of the DPMSG-based WPS with the DDSRF-SPLL algorithm and the proposed method in the case of unbalance and phase increase.After the unbalanced disturbance, the phase of the microgrid voltage increases suddenly, as shown in Figure 9a.According to Figure 9c,d, the DPMSG-based WPS using the proposed method and the DDSRF-SPLL algorithm can eliminate the unbalance problem and achieve the goal of supporting the microgrid.The response times of the DPMSG-based WPS with the proposed method and DDSRF algorithm to suppress the disturbance are 0.08 s and 0.11 s (see Figure 9e).The dynamic response time of this method is 27.3% faster than that of the DDSRF-SPLL algorithm.Under this working condition, the DPMSG-based WPS with this method can still maintain excellent current control capability.
When the fundamental frequency of the microgrid changes suddenly and the threephase voltage is unbalanced, the suppression process of the DDSRF-SPLL algorithm and this method is shown in Figure 10.The suppression effect of the proposed method in the wind power system is shown in Figure 10c,e.In Figure 10d,e, the DPMSG-based WPS with the DDSRF-SPLL algorithm can suppress unbalanced conditions to realize compensation current, and its dynamic response time is about 0.08 s.Compared with the DDSRF-SPLL algorithm, the DPMSG-based WPS using the proposed method can compensate the elec- When the fundamental frequency of the microgrid changes suddenly and the threephase voltage is unbalanced, the suppression process of the DDSRF-SPLL algorithm and this method is shown in Figure 10.The suppression effect of the proposed method in the wind power system is shown in Figure 10c,e.In Figure 10d,e, the DPMSG-based WPS with the DDSRF-SPLL algorithm can suppress unbalanced conditions to realize compensation current, and its dynamic response time is about 0.08 s.Compared with the DDSRF-SPLL algorithm, the DPMSG-based WPS using the proposed method can compensate the electric energy required by the microgrid faster, and effectively solve the problem of transient unbalance.In Figures 8-10, the control ability of the DPMSG-based WPS with the proposed method is significantly improved under complex conditions.

Figure 2 .
Figure 2. Circuit topology and control strategy of wind turbine side converter.According to Figure 2 and Park's transformation, the mathematical model of the wind turbine side converter in the dq frame is

Figure 2 .
Figure 2. Circuit topology and control strategy of wind turbine side converter.According to Figure 2 and Park's transformation, the mathematical model of the wind turbine side converter in the dq frame is

Figure 3
Figure 3 shows the circuit topology and control strategy of the grid-side converter of the DPMSG-based WPS.The stable control of the capacitor voltage is realized by the grid side converter.

Figure 3
Figure 3 shows the circuit topology and control strategy of the grid-side converter of the DPMSG-based WPS.The stable control of the capacitor voltage is realized by the grid side converter.

Figure 3 .
Figure 3. Circuit topology and control strategy of grid side converter.From Figure 3 and Park's transformation, the mathematical model of the converter is

Figure 3 .
Figure 3. Circuit topology and control strategy of grid side converter.

Figure 4 .
Figure 4. Amplitude-frequency characteristic of moving average filter algorithm.

Figure 4 .
Figure 4. Amplitude-frequency characteristic of moving average filter algorithm.

Figure 5 .
Figure 5. Attenuation capability of moving average filter algorithm for harmonics.(a) Transient amplitude of harmonics.(b) Steady-state amplitude of harmonics.

Figure 5 .
Figure 5. Attenuation capability of moving average filter algorithm for harmonics.(a) Transient amplitude of harmonics.(b) Steady-state amplitude of harmonics.

Figure 6 .
Figure 6.Flow chart of frequency detection.

Figure 6 .
Figure 6.Flow chart of frequency detection.

Figure 8 .
Figure 8.Comparison results of amplitude change.(a) Three-phase voltage.(b) Positive sequence voltages of the proposed method.(c) Suppression process of the proposed method.(d) Suppression process of DDSRF algorithm.(e) Output current value.

Figure 8 .
Figure 8.Comparison results of amplitude change.(a) Three-phase voltage.(b) Positive sequence voltages of the proposed method.(c) Suppression process of the proposed method.(d) Suppression process of DDSRF algorithm.(e) Output current value.

Figure 9 .
Figure 9.Comparison results of phase change.(a) Three-phase voltage.(b) Positive sequence voltages of the proposed method.(c) Suppression process of the proposed method.(d) Suppression process of DDSRF algorithm.(e) Output current value.

Figure 9 .
Figure 9.Comparison results of phase change.(a) Three-phase voltage.(b) Positive sequence voltages of the proposed method.(c) Suppression process of the proposed method.(d) Suppression process of DDSRF algorithm.(e) Output current value.
unbalance.In Figures8-10, the control ability of the DPMSG-based WPS with the proposed method is significantly improved under complex conditions.
sq + L sd di sd dt e sq = R s i sq + ω e L sd i sd + L sq