A Sub-Synchronous Oscillation Suppression Strategy Based on Active Disturbance Rejection Control for Renewable Energy Integration System via MMC-HVDC

Abstract

To realize the consumption of renewable energy such as wind power and photovoltaics in the power system, renewable energy integration system via modular multilevel converter (MMC)-based high voltage direct current (MMC-HVDC) has been widely applied. However, with the large-scale grid connection of renewable energy units, sub-synchronous oscillation (SSO) is prone to occur. Aiming at the problem, this paper proposes an SSO suppression strategy for renewable energy integration system via MMC-HVDC based on active disturbance rejection control (ADRC) theory. Using the direct drive permanent magnet synchronous generators (PMSG)-based wind farm integration system via MMC-HVDC as an example, firstly the topology and control system principles of the system are described, and a simulation model is built in PSCAD/EMTDC. Moreover, the SSO mechanism of the system is revealed by Nyquist stability criterion, and the major factors affecting the SSO of the system are simulated and analyzed. Subsequently, an additional sub-synchronous damping controller (ASSDC) is proposed based on ADRC theory. Compared to traditional additional damping controllers, the proposed controller considers disturbances of the system during the designing process and has stronger robustness. In addition, when faults happen, the speed of the system with ASSDC reaching a steady-state operating point rises by 33.7% as compared to the system without ASSDC. Finally, the effectiveness of the proposed suppression strategy is verified through simulation analysis.

1. Introduction

Modular multilevel converter (MMC)-based high voltage direct current (MMC-HVDC) has been demonstrated to be an efficient way for integrating renewable energy due to low harmonic content, flexible control, and low switching frequency [1,2]. In addition, it has been widely utilized in many practical projects to realize the consumption of renewable energy. However, with the large-scale grid connection of renewable energy, sub-synchronous oscillation (SSO) accidents have occurred many times in practical projects such as Nanao MMC-HVDC project [3] and Zhangbei flexible DC power grid [4,5], which leads to wind turbine disconnection, power quality issues, and so on [6].

Currently, the SSO suppression methods for renewable energy integration system can be divided into three categories: parameter optimization, adding SSO suppression devices, and adding additional damping control. Among them, the parameter optimization method is simple to use and inexpensive to implement. Reference [7] analyzed the influence of grid-side converter’s parameters on the equivalent damping and suggested a parameter optimization method based on particle swarm optimization algorithm (PSO), whose validity was verified by simulation. Reference [8] optimized the parameters of the grid connected inverter and the wind farm side MMC (WFMMC), respectively, to suppress SSO occurred in wind farm integration system via MMC-HVDC. On this basis, the damping coupling of SSO/super-synchronous oscillation (SupSO) caused by wind power delivery systems was considered in [9] and a coordinated optimization method which selected maximizing the damping ratios of the oscillation modes as optimization object was proposed to suppress the SSO/SupSO. However, when the control system is complicated and control parameters are numerous, there may be coupling between the control parameters [10]. The damping of different oscillation modes may become worse due to improper parameters, and parameter optimization will become more challenging [11]. As for adding SSO suppression devices, references [12,13,14] proposed to add flexible AC transmission systems (FACTS) such as STATCOM to system to restrain the SSO. In addition, it was proved that a renewable energy hydrogen production system (HPS) can mitigate SSO in [15]. Although adding SSO suppression devices has a good suppression impact and a quick response time, it has poor economics [16]. In terms of additional damping control, reference [3] added an SSO suppression controller to the control system of the WFMMC to suppress the SSO of the output current of the wind farm. Although the approach can significantly increase sub-synchronous damping, it pays little attention to the suppression ability of wind turbine converter. Regarding this issue, an SSO damping controller was proposed for double-fed induction generator (DFIG)-based wind farms and the optimum parameters of the controller were obtained by improved PSO in [17], which not only suppressed SSO effectively but also improved the dynamic performance of the system. In [18], it was found that phase-locked loop parameters were key factors affecting the stability of the wind farm integrated system and an additional damping controller was added to PLL to suppress SSO. Reference [19] proposed a damping control strategy for DFIG-based wind farm integrated system to damp SSO, whose performance was proven on a simulation model of a real-world wind power system. Moreover, the effectiveness of additional damping control in both converter stations of an MMC-HVDC and wind turbines was analyzed in [20], and it was proven that additional damping control can dampen SSO under different operating conditions. However, the aforementioned references rarely consider disturbances of the system when designing controllers. The performance of additional damping controllers will be significantly impacted and their robustness will be poor in the presence of disturbances in the system or when the operating point of the system is far from the initial operating point.

In this article, an additional sub-synchronous damping controller (ASSDC) is proposed based on the theory of active disturbance rejection control (ADRC) for renewable energy integration system via MMC-HVDC. Compared to traditional additional damping controllers, the proposed controller considers system disturbances during the designing process and has stronger robustness. Taking direct drive permanent magnet synchronous generators (PMSG)-based wind farm integration system via MMC-HVDC as an example, the main contributions of this article are summarized as follows:

(1) Based on the topology and control principles of the PMSG-based wind farm integration system via MMC-HVDC, a simulation model in PSCAD/EMTDC is established and the impedance characteristics of the wind farm and MMC subsystems are obtained by frequency scanning. Using Nyquist stability criterion, the mechanism of SSO in system is revealed.

(2) An additional sub-synchronous damping controller based on ADRC is proposed, which takes system disturbances as a new state variable of the controller, so it can adapt to different operating conditions and has stronger robustness under various disturbances.

The rest of the article is organized as follows: Section 2 introduces the topology and control system of the PMSG-based wind farm integration system via MMC-HVDC and establishes a simulation model in PSCAD/EMTDC. Then, the stability of the system is analyzed using Nyquist stability criterion and main factors influencing SSO are acquired by simulation analysis in Section 3. Section 4 suggests an additional sub-synchronous damping controller and describes how to tune its control parameters. The effectiveness of the proposed SSO suppression method is verified in Section 5 through simulation analysis. Finally, Section 6 draws the conclusion.

2. Modeling of PMSG-Based Wind Farm Integration System via MMC-HVDC

Establishing a model of the PMSG-based wind farm integration system via MMC-HVDC is one of the vital parts that analyzing the stability of the system. In this section, the topological structure and control principles of the system are initially introduced. On the basis of it, a simulation model in PSCAD/EMTDC is built and its accuracy is investigated.

2.1. Topology and Control Principles of the System

Figure 1 shows the topological structure of the PMSG-based wind farm integration system via MMC-HVDC, which includes a PMSG-based wind farm (WF), a transformer station, high-voltage AC cables, a WFMMC station, high-voltage DC cables, and a grid side MMC (GSMMC) station. The wind farm is composed of 200 identical wind turbines with a total installed capacity of 500 MW. Then, the voltage level is stepped up from 35 kV to 220 kV, and the 220 kV bus as the point of common coupling (PCC) is connected to the WFMMC station for conversion into ±320 kV DC. In addition, the rated capacity of MMC-HVDC is 600 MVA, and the length of DC cables is 200 km.

The configuration and control system of a PMSG-based wind energy conversion system (WECS) are displayed in Figure 2, mainly including wind turbine, permanent magnet synchronous generator, machine side converter (MSC) and corresponding control system, grid side converter (GSC), and its control system [21,22]. Both MSC and GSC adopt dq decoupling control, where the outer loop of MSC controls active power P_MS and AC voltage u_mabc, the outer loop of GSC controls DC voltage U_dc and output reactive power Q_GS. The inner loops are current control loops. In addition, proportional-integral controllers are adopted in outer and inner loops.

In Figure 2, P_MS* is the reference value of active power, which is provided by the maximum wind energy tracking module of the wind turbine; P_MS is the actual active power generated by the PMSG; U_mRMS and U_mRMS* are the root mean square (RMS) value of the AC voltage u_mabc and its reference value at the output port of the generator, and U_mRMS* = 1.0 p.u; i_md, i_mq, are dq components of output current i_mabc of the generator; θ_r is the result of rotor angle multiplying by the number of pole pairs; ω_s is the angular speed; L_s is the stator inductance of the generator. U_dc and U_dc* refer to the DC bus voltage and reference value; Q_GS and Q_GS* represents reactive power of the GSC and its reference value; i_gd and i_gq are dq components of output current i_gabc of the GSC; u_gd and u_gq are the dq components of the output voltage u_gabc, respectively; ω_g is the synchronous angular velocity of the AC grid; θ_g is the phase angle of u_gabc output by phase-locked loop (PLL); C_dc is DC capacitor; L_g is the equivalent inductance of the incoming reactor of the GSC; P_GS represents active power of the GSC; P_WECS, i_Gabc, and u_Gabc are output active power, currents, and voltages of the aggregated PMSG-based WECS. The blue arrow represents the reference direction of the system currents.

Figure 3a presents the topology of MMC used for WFMMC and GSMMC. One upper arm and one lower arm are connected in series between the DC terminals to form each phase leg of the MMC. N identical series-connected submodules (SMs) make up each arm, along with an inductor L₀ and an arm-equivalent series resistor R₀. Each SM contains a capacitor C_SM and a half bridge as the switching element. In this paper, WFMMC adopts island droop control, whose control diagram is shown in Figure 3b. GSMMC adopts constant DC voltage control and constant reactive power control, and the control diagrams is displayed in Figure 3c.

In Figure 3b,c, D_f and D_ac are droop control coefficients; f_max and f_min are the limits of frequency; f is the frequency of PCC1; u_ac1* is the reference value of the AC voltage u_abc1 at PCC1 and U_RMS1 is the RMS value of u_abc1; U_DC and U_DC* are the DC voltage and its reference value; L is the equivalent inductance of the AC grid; P_MMC1 and Q_MMC1 are active and reactive power of WFMMC; Q_MMC2 and Q_MMC2* are reactive power of GSMMC and its reference value; u_d1 and u_q1 are dq components of u_abc1; u_d2 and u_q2 are dq components of the AC voltage u_abc2 at PCC2; i_d2 and i_q2 are dq components of the AC current i_abc2 at PCC2.

2.2. Simulation Model of the System

Based on the topological structure and control diagram of the aforementioned system, a model of the PMSG-based wind farm integration system via MMC-HVDC is constructed in PSCAD/EMTDC. In this simulation model, the wind farm is modeled by an aggregated PMSG-based WECS using equivalent processing to simplify the analysis. In addition, the original IGBT switch is replaced with a variable resistor switched between milliohm on resistance and megohm off resistance and the C_SM of SMs are discretized to overcome the issue of enormous computation caused by too many switching elements [23]. The equivalent Thevenin models of each discrete SM and arm are shown in Figure 4, respectively. Some parameters in the simulation model are shown in

Table 1. Some parameters of the simulation model.

Type	Parameters	Values
Parameters of the PMSG-based wind farm	wind speed	7 m/s
	DC bus capacitance	15 mF
	Rated capacity of a wind turbine	2.5 MVA
	Equivalent number of wind turbines	200
	Rated DC voltage	1.45 kV
	Output voltage of a wind turbine	0.62 kV
	Output voltage of the wind farm	35 kV
	Ratio of T	35 kV/220 kV
Parameters of MMC-HVDC	DC voltage	±320 kV
	Number of unipolar SMs	100
	Inductance of an arm	5 mH
	Length of DC cables	200 km
	Rated capacity	600 MVA
Parameters of AC grid	Voltage of the AC grid	220 kV
	Rated frequency	50 Hz

.

The simulation model is validated when wind speed is 7 m/s and the waveforms of output active power P_WECS, three-phase voltages u_Gabc, and three-phase currents i_Gabc represented by lines with different colors of the aggregated PMSG-based WECS are shown in Figure 5. Figure 6 displays the voltage U_DC and current I_DC waveforms of the DC cables, where the red lines represent the voltage and current of the positive DC cables and the green lines represent the voltage and current of the negtive DC cables [24,25,26].

Figure 5 and Figure 6 show that the simulation model can operate near the given values and soon reach a stable state. As a result, the simulation results confirm the viability of equivalent processing of the wind farm and MMC-HVDC models, as well as the correctness of the control strategies of the system.

3. Stability Analysis and Key Influencing Parameters Analysis of the System

Based on the simulation model established in Section 2, the impedance characteristics of the wind farm and MMC subsystems are obtained by frequency scanning and the stability of the system is analyzed using Nyquist stability criterion in this section. Additionally, the main factors affecting the SSO of the PMSG-based wind farm integration system via MMC-HVDC are analyzed by simulation.

3.1. Stability Analysis of the System

The PMSG-based wind farm integration system via MMC-HVDC can be seen as a cascade of the wind farm and MMC subsystems as shown in Figure 1. According to [27], the cascade system can be equivalent to the small signal model shown in Figure 7. The aggregated PMSG-based WECS can be equivalent to an ideal current source I_WF(s) and an impedance Z_WF(s) in parallel since the inverter employ current control method. WFMMC is equivalent to an ideal voltage source V_s(s) and an impedance Z_MMC(s) in series because of the AC voltage control strategy. The equivalent impedance of the system can be calculated without taking into account the AC cable’s impedance because the distance between the wind farm and the WFMMC station is often short.

The output current I₁(s) and voltage V_PCC1(s) at PCC1 can be expressed as follows:

$$I_1(s)=\left[I_{\mathrm{WF}}(s)-\frac{V_{\mathrm{s}}(s)}{Z_{\mathrm{WF}}(s)}\right]\frac{1}{1+Z_{\mathrm{MMC}}(s)/Z_{\mathrm{WF}}(s)}$$

(1)

$$V_{\mathrm{PCC}1}(s)=\left[Z_{\mathrm{MMC}}(s)I_{\mathrm{WF}}(s)+V_{\mathrm{s}}(s)\right]\frac{1}{1+Z_{\mathrm{MMC}}(s)/Z_{\mathrm{WF}}(s)}$$

(2)

The stability of the system depends on whether the impedance ratio Z_MMC(s)/Z_WF(s) of the two cascaded subsystems meets the Nyquist stability criterion when the subsystems are stable under the ideal voltage source, respectively. When the amplitude-frequency characteristics of Z_WF(s) and Z_MMC(s) have an intersection point and the phase difference at the intersection point is close to or greater than 180°, there is a risk of oscillation in the system.

The curves of Z_WF(s) and Z_MMC(s) are obtained by adding a frequency scanning module to the PCC1 of the simulation model, which is shown in Figure 8. Because this paper mainly focuses on the stability of the sub-synchronous frequency band, Figure 8 only shows the impedance characteristic curves of the sub-synchronous frequency band.

According to Figure 8, the amplitude-frequency characteristic curves of Z_WF(s) and Z_MMC(s) have an intersection point at 29.2 Hz, and the phase difference at the intersection point is 174.73°, which is obviously insufficient. Therefore, the system has the risk of SSO.

3.2. Analysis of Key Influencing Parameters

The stability of the PMSG-based wind farm integration system via MMC-HVDC is easily affected by external factors and control parameters of control loops. In this subsection, it is studied that the influence of wind speed and controller parameters of the MSC and GSC on system stability.

3.2.1. Impact of Wind Speed

The output power of the wind farm is unpredictable and uncontrollable because of the impact of wind speed, which causes it to fluctuate widely. In order to simplify the analysis, it is assumed that the wind speed is equal and changes synchronously of each wind field. The initial wind speed is set as 7 m/s, and the wind speed is changed when t = 1.0 s. As the wind speed increases, the output active power P_WECS and currents i_Gabc of the aggregated PMSG-based WECS are observed, as shown in Figure 9 and Figure 10, respectively.

As seen from Figure 9 and Figure 10, the system oscillates in a tiny amplitude and rapidly converges, reaching a new stable state without visible oscillation when the wind speed reaches 8 m/s; when the wind speed is changed to 9 m/s, the system oscillates; when the wind speed is changed to 10 m/s, the output active power of the wind farm maintains constant amplitude oscillation; when the wind speed is changed to 11 m/s, the oscillation becomes more intense and exhibits a divergent trend, which eventually causes the system to become unstable. The corresponding Fourier analysis results of the output current can be obtained, shown in Figure 11.

As demonstrated in Figure 11, the oscillation frequency of the output current is 25.2 Hz when the wind speed is set to 9 m/s. When the wind speed is increased to 10 m/s, the SSO intensifies and the oscillation frequency at the moment is 28 Hz. The SSO of the system is amplified and a new oscillation frequency emerges when the wind speed is changed to 11 m/s. The oscillation frequencies are 12.67 Hz and 31.33 Hz, respectively.

The analysis presented above leads to the conclusion that the output active power of the aggregated PMSG-based WECS increases and the SSO worsens when wind speed increases. Additionally, as the wind speed increases, the oscillation frequency changes, and a new oscillation frequency even appears in the sub/super-synchronous frequency band.

3.2.2. Impact of Control Parameters

In this subsection, the influence of control parameters of the aggregated PMSG-based WECS on SSO is analyzed, mainly considering the controller parameters of inner loops of the MSC and GSC [28].

(1) Parameters of MSC inner loop controller

Change the proportional coefficient K_p1 of MSC inner loop controller and set it as: (a) K_p1 = 2; (b) K_p1 = 3; (c) K_p1 = 5. The waveforms of the active power and current of the aggregated PMSG-based WECS are shown in Figure 12. Fourier analysis results of the current are shown in Figure 13.

As can be seen from Figure 12 and Figure 13, the oscillation frequency 27.84 Hz appears in the system when K_p1 = 3. When K_p1 = 5, the system oscillates at 17.67 Hz and 23.84 Hz. Compared with the former, the oscillation frequency of the system decreases, and the oscillation frequency points are increased. It can be concluded that with the increase in K_p1, the system oscillates at other frequencies except the fundamental frequency and the oscillation frequency decreases gradually. However, it can be seen from Figure 13 that the system will not become unstable through the above adjustment of K_p1.

Change the integral coefficient K_i1 of MSC inner loop controller and set it as: (a) K_i1 = 30; (b) K_i1 = 100; (c) K_i1 = 200. The waveforms of the active power and current are shown in Figure 14. As can be seen from Figure 14, changing K_i1 has no significant effect on the oscillation of the system.

(2) Parameters of GSC inner loop controller

Change the proportional coefficient K_p2 of GSC inner loop controller as follows: (a) K_p2 = 1; (b) K_p2 = 2; (c) K_p2 = 3. The waveforms of the active power and current are shown in Figure 15.

As demonstrated in Figure 15, the oscillation of the system converges when K_p2 = 1 and K_p2 = 2, and the oscillation amplitude grows as K_p2 increases. The oscillation diverges and the system becomes unstable when K_p2 = 3. FFT analysis is performed on the current, and the outcomes are displayed in Figure 16.

As shown Figure 16, the fundamental frequency is the only frequency in the system that oscillates visibly when K_p2 = 1 and K_p2 = 2. Sub-synchronous and super-synchronous oscillations happen concurrently when K_p2 = 3 and their frequencies are 32.67 Hz and 67.18 Hz, respectively. Therefore, the following conclusions can be drawn: as K_p2 increases, the oscillation amplitude of the system increases, and the oscillation will diverge when K_p2 increases to a certain value.

According to the simulation results, changing the integral coefficient K_i2 of GSC inner loop controller has no impact on the oscillation of the system. Therefore, it is not thoroughly examined here.

The above analysis shows that changing K_i1 and K_i2 has no obvious impact on system oscillation. Changing K_p1 and K_p2 has some impact on the system oscillation. The system will oscillate at other frequencies except the fundamental frequency but will not become unstable when K_p1 changes, while changing K_p2 can cause the system to become unstable. Therefore, it may be said that K_p2 is the key factor affecting the sub/super-synchronous oscillation of the system.

4. Design of An Additional Sub-Synchronous Damping Controller Based on ADRC

The proportional coefficient K_p2 of the GSC inner current control, which was examined in the previous section, is a crucial factor in the SSO. Therefore, the parameter design of the current loop controller in GSC plays a vital role in the system stability. The existing PI controller, however, suffers from control lag and there is coupling among the control parameters, making it challenging to suppress oscillations through parameter tuning. This section suggests an additional sub-synchronous damping controller (ASSDC) based on ADRC for the PMSG-based wind farm integration system via MMC-HVDC.

4.1. Active Disturbance Rejection Control Theory

ADRC does not depend on an accurate model of the system and estimates the disturbance in real-time, making it adaptable to various operating conditions and highly robust [29,30]. The control diagram, as shown in Figure 17, includes four parts: tracking differentiator, extended state observer, nonlinear state error feedback, and control signal generation loop.

(1) Tracking differentiator (TD)

The function of TD is to achieve fast tracking of the input signal and synchronous output differential signal, which can solve the conflict between overshoot and rapidity in traditional PID control. The mathematical expression of TD is expressed as follows:

$$\left\{\begin{array}{l}\mathrm{fh}=\mathrm{fhan}(v_1-v,v_2,r_0,h_0)\hfill \\ {\dot{v}}_1=v_1+h{v}_2\hfill \\ {\dot{v}}_2=v_2+h\mathrm{fh}\hfill \end{array}\right.$$

(3)

where v₁ can track the control input v without overshoot and v₂ is the approximate differentiation of v. h is the sampling period, r₀ is the tracking speed factor, h₀ is the filtering factor, and fhan is the comprehensive function, which has a specific mathematical expression in [31].

(2) Extended state observer (ESO)

The ESO expands the total disturbance into a new state variable of the system, and uses feedback compensation to track the signal and eliminate the influence of the total disturbance in the system. Its mathematical expression is:

$$\left\{\begin{array}{l}\begin{array}{l}{\epsilon }_1=z_1-y\hfill \\ {\dot{z}}_1=z_2-{\beta }_{01}{\epsilon }_1\hfill \end{array}\hfill \\ {\dot{z}}_2=z_3-{\beta }_{02}\mathrm{fal}({\epsilon }_1,a_1,{\delta }_1)+b_{0}u\hfill \\ {\dot{z}}_3=-{\beta }_{03}\mathrm{fal}({\epsilon }_1,a_2,{\delta }_1)\hfill \end{array}\right.$$

(4)

where y is the output of the controlled object; z₁, z₂, and z₃ are state variables provided by ESO; u is control variable; β₀₁, β₀₂, β₀₃, a₁, and a₂ are adjustable parameters of the ADRC; b₀ is compensation factor; δ₁ is filtering factor; the nonlinear function fal(x, a, δ) is expressed in (5), and δ > 0; sign(x) denotes the sign function.

$$\mathrm{fal}(x,a,\delta )=\left\{\begin{array}{ll}\frac{x}{{\delta }^{1-a}}\hfill & \left|e\right|\le \delta \hfill \\ \mathrm{sign}(x){\left|x\right|}^a\hfill & \left|e\right|>\delta \hfill \end{array}\right.$$

(5)

(3) Nonlinear State Error Feedback (NLSEF)

NLSEF obtains the error signal e₁ = v₁ − z₁ and the error differential signal e₂ = v₂ − z₂ based on the tracking signal output by TD and the signal observed by ESO, and compensates for disturbances by nonlinear combination to control the corresponding object, whose purpose is to suppress and eliminate disturbances.

There are generally two forms of nonlinear combinations, shown in Equations (6) and (7), respectively. In (6) and (7), c is the damping factor; r is the control gain; and h₁ is the precision factor; β₁, β₂, a₃, and a₄ are adjustable parameters. In this paper, (6) is selected.

$$u_0={\beta }_1\mathrm{fal}(e_1,a_3,{\delta }_2)+{\beta }_2\mathrm{fal}(e_2,a_4,{\delta }_2)$$

(6)

$$u_0=\mathrm{fhan}(e_1,c{e}_2,r,h_1)$$

(7)

(4) Control signal generation loop

The mathematical expression of the control variable can be obtained from Figure 17, shown as follows:

$$u=\frac{u_0-z_3}{b_0}$$

(8)

where −z₃/b₀ is the compensation for disturbance, and u₀/b₀ is the part that uses nonlinear feedback to control the integral cascade.

4.2. Additional Sub-Synchronous Damping Controller Based on ADRC

The previous subsection describes the control structure of the proposed ASSDC based on ADRC. To effectively suppress the SSO and promote the robustness of the system, it is also necessary to determine the input and output signals of the proposed controller and its parameters. This subsection will introduce the position of the controller within the PMSG-based wind farm integration system and the procedure for adjusting control parameters.

(1) Position of the controller and choice of the control signal

The input signal of the ASSDC needs to accurately reflect the characteristics of the SSO of the system and be easy to measure and control. Based on the analysis of the impact of wind speed on SSO in Section 2 and considering external disturbances in the system, this subsection takes the θ_r of the wind turbine as the input signal and adds the control loop to the inner loop control of the GSC. The specific position of the ASSDC in the system is shown in Figure 18.

(2) Optimization of parameters of the ASSDC based on genetic algorithm

It is clear from Section 4.1 that the following parameters need to be adjusted: r₀, h, h₀, β₀₁, β₀₂, β₀₃, a₁, a₂, δ₁, β₁, β₂, a₃, a₄, and δ₂. Among them, h needs to be consistent with the actual simulation step size in the simulation model; when h is fixed, h₀ is usually an integer multiple of h to achieve the filtering effect; r₀ is typically set to 1000 [32]. In ESO, the values of a₁ and a₂ are usually taken as 0.5 and 0.25, respectively; δ₁ is generally set to h; in NLSEF, 0 < a₃ < 1<a₄, and δ₂ can generally be set between 5h and 10h. Therefore, the parameters that need to be tuned in practice are β₀₁, β₀₂, β₀₃, β₁, and β₂.

In this subsection, genetic algorithm (GA) [33] is used to tune and optimize the above five parameters, and the ITAE criterion is selected as the fitness function for performance evaluation. The expression of the fitness function is shown in (9).

$$J={\displaystyle {\int }_0^{\infty }t\left|P_{\mathrm{WECS}}{}^{*}-P_{\mathrm{WECS}}\right|}\mathrm{d}t+{\displaystyle {\int }_0^{\infty }t\left|Q_{\mathrm{WECS}}{}^{*}-Q_{\mathrm{WECS}}\right|\mathrm{d}}t+{\displaystyle {\int }_0^{\infty }t\left|U_{\mathrm{dc}}{}^{*}-U_{\mathrm{dc}}\right|}\mathrm{d}t$$

(9)

where P_WECS*, P_WECS, Q_WECS*, and Q_WECS represent the reference and actual values of active and reactive power of the aggregated PMSG-based WECS, respectively; U_dc* and U_dc represent the reference and actual values of the DC bus voltage of the wind turbine; t is simulation time.

The specific optimization process is shown in Figure 19, and the parameter settings of the GA are shown in

Table 2. Parameters of converter stations.

Parameter	Value
Initial population	100
Population of the surviving generation	90
Population of the mating pool	50
Elite population	10
Percentage of population to be deviated	3
Pairing method	random

.

5. Simulation Verification

This section adds the ASSDC proposed in Section 4 to the model built in Section 1, and uses the optimized control parameters of ASSDC for simulation to verify the oscillation suppression effect of the controller under different wind speed and system faults.

(1) Effectiveness verification when wind speed changes

To verify the effectiveness of ASSDC in suppressing SSO under different wind speeds, the wind speeds are set to 9 m/s, 10 m/s, and 11 m/s. The corresponding output active power of the aggregated PMSG-based WECS and FFT analysis results are shown in Figure 20.

It can be seen from Figure 20 that the system can quickly reach a new stable state after adding the ASSDC, and the frequency components of SSO in the active power are much diminished. As the wind speed increases, the output active power P_WECS of the PMSG-based WECS with ASSDC will also fluctuate slightly, but still accomplish adequate oscillation suppression effect. Therefore, the proposed ASSDC can effectively suppress the SSO of the system under different wind speeds, verifying the robustness of the ASSDC and helping to increase the transmission power of the system.

(2) Effectiveness verification under system fault

A three-phase short circuit to ground fault that lasts for 0.05 s is set in PCC1 when the model runs for 1.0 s. Figure 21 displays the output active power of the PMSG-based WECS with and without ASSDC under the fault and

Table 3. Performance comparison of the PMSG-based WECS with and without ASSDC under a three-phase short circuit to ground fault.

	Minimum Value of PWECS	Time of PWECS to Become Stable after Fault Removal	The Total Harmonic Distortion (THD) of Stable PWECS after Fault Removal
The PMSG-based WECS with ASSDC	23.1 MW	1.65 s	0.14%
The PMSG-based WECS without ASSDC	−100 MW	1.88 s	3.98%

is a table of performance comparison. It can be seen that the P_WECS of the system without ASSDC has a wide fluctuation range and the minimum value is −100 MW at 1.28 s, indicating that the output active power of the PMSG-based WECS is reversed. The P_WECS of the system with ASSDC, however, is always positive and has a narrow range of variation, with a minimum value of 23.1 MW at 1.32 s. The P_WECS with ASSDC stabilizes after 0.6 s of the fault removal, while the P_WECS without ASSDC still shows significant power fluctuations. Therefore, the proposed ASSDC can effectively suppress the fluctuation of the output active power and the system with ASSDC can reach the stable state faster under the three-phase short circuit to ground fault.

6. Conclusions

This paper uses the PMSG-based wind farm integration system via MMC-HVDC as an example of the SSO issue in large-scale renewable energy integration systems via MMC-HVDC. First, based on the system topology and control system principles, a simulation model of the system is constructed in PSCAD/EMTDC and the stability of the system is analyzed using Nyquist stability criterion and impedance characteristic curves of the wind farm and MMC subsystems obtained through frequency scanning. Then the impact of wind speed and the control parameters of MSC and GSC on SSO is analyzed by simulation, which can be concluded that the proportional coefficient K_p2 of the GSC inner current loop is the key factor affecting the SSO. Subsequently, an ASSDC based on ADRC theory is proposed. Considering external disturbances in the system, the ASSDC takes the θ_r of the wind turbine as the input signal and the output signal is added to the inner loop control of the GSC, and GA is utilized to optimize the parameters of the controller. Compared to previous additional damping controllers, this controller does not rely on the precise model of the system and takes into consideration potential disturbances and changes in the system. The ASSDC is able to improve the robustness of the system under disturbances and the recovery speed of system under faults. Finally, the effectiveness and robustness of the proposed ASSDC in suppressing SSO are verified through simulation analysis.