Reinforcement Learning and Adaptive Optimisation of Complex Dynamic Systems and Industrial Applications
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Jiening Li, Hanqi Huang, Xiaoning Chen, Lingxi Peng, Liang Wang, Ping Luo, "The SmallSignal Stability of Offshore Wind Power Transmission Inspired by Particle Swarm Optimization", Complexity, vol. 2020, Article ID 9438285, 13 pages, 2020. https://doi.org/10.1155/2020/9438285
The SmallSignal Stability of Offshore Wind Power Transmission Inspired by Particle Swarm Optimization
Abstract
Voltage source converterhighvoltage direct current (VSCHVDC) is the mainstream technology of the offshore wind power transmission, which has been rapidly developed in recent years. The smallsignal stability problem is closely related to offshore wind power gridconnected safety, but the present study is relatively small. This paper established a mathematical model of the doubly fed induction generator (DFIG) integrated into the IEEE9 system via VSCHVDC in detail, and smallsignal stability analysis of offshore wind farm (OWF) grid connection is specially studied under different positions and capacities. By selecting two load nodes and two generator nodes in the system for experiments, the optimal location and capacity of offshore wind power connection are obtained by comparing the four schemes. In order to improve the weak damping of the power system, this paper presents a method to determine the parameters of the power system stabilizer (PSS) based on the particle swarm optimization (PSO) algorithm combined with different inertia weight functions. The optimal position of the controller connected to the grid is obtained from the analysis of modal control theory. The results show that, after joining the PSS control, the system damping ratio significantly increases. Finally, the proposed measures are verified by MATLAB/Simulink simulation. The results show that the system oscillation can be significantly reduced by adding PSS, and the smallsignal stability of offshore wind power grid connection can be improved.
1. Introduction
Offshore wind power, as a clean and sustainable technology, has been developed rapidly in recent years [1]. At present, the total installed capacity in Europe is increasing every year, among which the UK and Germany dominate the offshore wind power industry [2]. According to Wind Europe’s High Scenario, it is estimated that the offshore wind energy capacity in Europe will reach 99 GW by 2030 [3]. Nowadays, the mainstream transmission technology is VSCHVDC [4–6]. Compared to other traditional transmission modes, it has the advantages of independent control of the active and reactive power output, smaller power loss, and lower voltage drop [7–10].
Smallsignal stability analysis is to study the dynamic response characteristics of the power system after small disturbances (including random fluctuations in power generation or consumption) and to evaluate their ability to suppress oscillations [11]. It is of great significance to promote the development of wind power and improve the safe stability of the system, which needs urgent attention [12]. However, there are few studies on the smallsignal stability analysis of the offshore wind power grid connected by VSCHVDC transmission at present. Based on the smallsignal stability problem of the offshore wind power system transmitted by VSCHVDC, the damping control of the system is increased by introducing PID regulation at the converter station. The modeling method does not consider the aerodynamic model, and the selection of PID parameters based on eigenvalues has limitations [13]. Smallsignal stability analysis method from the perspective of voltage and frequency is discussed in [14, 15]. In [14], the variability of wind power was considered as the interference source of the system and used Prony analysis and swingbased frequency response metric to study the influence of the small signal on the large offshore wind power system. However, the whole system modeling process has not been described in detail but is focused on analysis. In [15], the model of the offshore AC network for pointtopoint VSCHVDC transmission is deduced in detail, and the droop gain boundary under the stable operation is determined by eigenvalue analysis. A lowpass filter was introduced to improve the system damping, but the effect of different gridconnected positions and capacity on the small signal of the system was not considered. At present, neural networks [16, 17], deep learning, and machine learning methods have been widely used in various fields, and remarkable results have been achieved [18, 19].
To improve the stability of the system under the small signal and large signal, the PSO algorithm is used to optimize the parameters of the DFIG controller. However, the PSO algorithm will fall into local optimum, and more controller equations increase the dimension of the state matrix, which will slow down the fast operation of the system [20]. In these studies, although scholars have studied the smallsignal stability of offshore wind power grid connection in different fields, it is still in the exploratory stage to change the gridconnected position and capacity of offshore wind farms for smallsignal stability analysis and to apply damping control.
Aiming at the problem of smallsignal stability of the offshore wind power gridconnected system, this paper firstly establishes a complete VSCHVDC transmission offshore wind power gridconnected mathematical model and then analyzes the impact of OWFs on the smallsignal stability of the system under different positions and capacities. Secondly, PSS is introduced for damping control. The optimal position of the PSS connected to the power grid is determined by modal control theory, and the parameters of the controller are determined by the PSO algorithm combined with different inertia weight functions. Finally, the correctness of the established model and the effectiveness of the proposed control measures are verified by MATLAB/Simulink simulation.
2. Modeling of Offshore Wind Power Transmitted by VSCHVDC
This paper uses the typical offshore wind power grid connection system [21] for reference, and the designed system topology is shown in Figure 1. The OWFs are composed of 10 2MW DFIGs, and they are equivalent to a DFIG representation according to the aggregated model [22]. The wind turbine (WT) runs on the lowspeed (LS) shaft, the generator runs on the highspeed (HS) shaft, and the gearbox connects the two to act as the booster. Each 690 V DFIG is connected to 10 kV bus through the boost transformer X_{T0} and then sent to 110 kV bus through the boost transformer X_{T1} and the transmission line X_{T1}. VSC1 and VSC2 are converter stations, which play the roles of the rectifier and the inverter, respectively. The HVDC plays the role of power transmission. In addition, there are resistancecapacitance (RC) filters and phase reactors, whose influence on the system is ignored in this paper. The VSCHVDC outlet u_{s2} is connected to the 230 kV 3machine, 9bus test system [23] via the boost transformer X_{T2} and the transmission line X_{L2}, which is represented by IEEE9.
2.1. Aerodynamic Model
WT is driven by the wind, which is converted into mechanical energy through three blades. The equations of the aerodynamic model [24] are given bywhere C_{p} is the coefficient of wind energy utilization; β is the pitch angle; λ is the tip speed ratio (λ = ω_{t}r/ν); ω_{t} is the mechanical angular velocity of the WT; r is the radius of the wind wheel; ν is the wind speed; P_{t} is the mechanical power output by the WT; T_{t} is the mechanical torque; and ρ is the air density.
2.2. Shafting Model
In order to ensure the accuracy of calculation, this paper selects the twomass block shafting model. The mathematical model of the shafting model [25] is as follows:where H_{t} and H_{g} are the inherent inertial time constants of the WT and the generator; T_{t} and T_{e} are the mechanical torque of the WT and the electromagnetic torque of the generator; K and D are the stiffness and damping coefficients of the shaft; θ is the shaft torsional angle; ω_{t} and ω_{r} are the speeds of the rotor of the WT and the generator; ω_{s} is the stator speed of the generator; and ω_{b} is the base value of rotational speed.
2.3. Pitch Angle Control Model
To ensure the smooth power output of the OWFs, the pitch angle [26] needs to be controlled. The equations are given bywhere T_{β} is the inertial time constant of the pitch angle control model; β_{ref} and ω_{t_ref} are the reference values of the pitch angle and the WT speed; and K_{p0} and K_{I0} are the proportional and integral coefficients of the controller.
2.4. DFIG Model
Currently, DFIG is the most widely used WT. Ignoring the electromagnetic transient process of stator winding, the mathematical model of the DFIG [27] is as follows:where = L_{rr}/R_{r}; = L_{m}/L_{ss}; = L_{rr} − L_{m}/L_{ss}; X_{s} = ω_{s}L_{ss}; L_{ss} = L_{s} + L_{m}; and L_{rr} = L_{r} + L_{m} are the sum of selfinductance of the stator and the rotor; R_{s} and R_{r} are the resistances of the stator and the rotor; L_{m} is the mutual inductance between the stator and the rotor; X_{s} is the reactance of the stator; = −(ω_{s}L_{m}/L_{rr})ψ_{qr}; = (ω_{s}L_{m}/L_{rr})ψ_{dr}; = ω_{s}/L_{rr} (L_{ss}L_{rr}−L_{m}); and are the d and qaxis components of the transient voltages; is the transient resistance of the stator; and ψ_{dr} and ψ_{qr} are the d and qaxis components of the rotor flux, respectively. i_{ds}, i_{qs}, i_{dr}, and i_{qr} are the d and qaxis components of the stator and rotor currents, respectively. Let the stator flux ψ_{s} always reunite with the daxis; then, u_{ds} = 0 and u_{qs} = ψ_{s}. u_{ds}, u_{qs}, u_{dr}, and u_{qr} are the voltages of the stator and the rotor.
The active and the reactive power output of OWFs are
2.5. VSCHVDC Model
According to the relationship between the threephase stationary coordinate system and the d and q synchronous rotating coordinate system, after the Park transformation, the 7order mathematical model [13, 21] can be obtained as follows:where the physical quantities corresponding to the rectifier and the inverter station are denoted by subscripts “1” and “2,” respectively. i_{1d}, i_{1q}, i_{2d}, and i_{2q} represent the current components of the AC network; u_{sd1}, u_{sq1}, u_{sd}, and u_{sq2} represent the voltage components of the AC network; u_{d1}, u_{q1}, u_{d2}, and u_{q2} represent the voltage components between buses of the DC system; and K_{1} and K_{2} are the voltage utilization coefficients of the DC system. δ_{1} and δ_{2} are the deviation angles between the voltage of the converter station and the bus voltage of the AC system; ω_{1} and ω_{2} are the fundamental angular frequencies of the AC system. i_{d} is the DC current transmitted by the highvoltage transmission line.
2.6. System Interface Model
Position the stator voltage u_{s} on the daxis, and the voltage vector between the DFIG and the rectifier station is shown in Figure 2.
Its mathematical relationship iswhere X_{TL1} is the total impedance of line 1; X_{T0} is the equivalent transformer impedance of OWFs; and X_{T1} and X_{L1} are the transformer and the circuit impedance of line 1.
Position the terminal voltage u of the power system on the xaxis, and the vector between the inverter station and the power system is shown in Figure 3.
Its mathematical relationship is
2.7. Complete Model
All the equations of DFIG and VSCHVDC are combined and linearized near the stable value:where and .
The offshore wind power transmitted by VSCHVDC is integrated into the IEEE9 system, as shown in Figure 4. The smallsignal equation of the system iswhere ; ; ; and .
After deducing the complete smallsignal stability model of offshore wind power transmitted by VSCHVDC, it is necessary to do further research on the influence of smallsignal stability on the system of offshore wind power in different positions and capacities.
3. SmallSignal Stability Analyses
This section will combine with the concrete example of the offshore wind power gridconnected position and capacity for smallsignal stability analysis. Firstly, the parameters of each subsystem are initialized, which are detailed in Appendix and then the state of OWFs is found before incorporation into the system. Finally, two load nodes and two generator nodes are chosen, and the influence of the offshore wind power grid connection is analyzed in detail.
3.1. Eigenvalue Analysis
When the OWFs are added at node 6 and the active power output is 0.5 pu, the eigenvalues of the system are shown in Table 1. It can be seen from Table 1 that the real part of the eigenvalues is all negative, which are on the left side of the imaginary axis, indicating that the original power system is running in a stable state.

λ_{7,8}, λ_{10,11}, λ_{12,13}, and λ_{16,17} are related to the generator rotational speed (Δω_{1}, Δω_{2}, and Δω_{3}) and the rotational speed difference Δs of wind generator 10, respectively, belonging to the electromechanical oscillation mode.
3.2. Damping Ratio Analysis
Damping ratio [28] can reflect the speed and the characteristics of oscillation attenuation. The expression is given bywhere σ and ω are the real and the imaginary part of the eigenvalue, respectively.
In the actual power system, it is generally required that the damping ratio of the electromechanical oscillation mode should be above 0.05, and then the operating state of the system could be accepted. However, this principle is not unchanged. If the mode of fluctuation is not large when the system operation mode changes, it is acceptable to have such a low damping ratio (for example, 0.03) [28].
By changing different active power outputs and gridconnected positions of OWFs, the damping ratio curve in various cases can be obtained as shown in Figure 5.
(a)
(b)
(c)
(d)
4. Control Measures
In order to improve the weak damping instability of the system, it is necessary to add a controller to the system for auxiliary regulation. Firstly, PSS needs to be modeled, and the speed difference is used as the feedback signal to be added to the system voltage equation. Secondly, the optimal position of the PSS is determined by the detailed analysis of modal control theory.
Finally, the PSO algorithm is introduced, and the objective function is established according to the research content of this paper. The parameters of PSS controllers are determined with different inertia weight functions.
4.1. PSS Model
The main function of the PSS is to increase damping or suppress lowfrequency oscillation of the power system [29]. The mathematical expression of the PSS iswhere the generator speed difference V_{IS} = ωω_{t} is selected as the input signal. V_{S} is the output signal, which serves as the auxiliary input signal of the stator voltage equation Δu_{qi} (i = 1,2,3) of the IEEE9 system. K_{gain} is the gain of the amplification link; T_{6} is the time constant of the measurement link. T_{5} is the time constant of the filtering link. T_{1}, T_{3}, T_{2}, and T_{4} are the lead and lag time constants of two phase compensation links, respectively.
If the PSS is added to IEEE9 system generator 2, the voltage equation needs to be
4.2. PSS GridConnected Position Selection
When OWFs integrate into load node 6 and in normal operation, the changes of the electromechanical oscillation mode are shown in Table 2.

As can be seen from Table 2, in the eigenvectors of the first and fourth modes, the modulus value of Δs is the largest, but the directions of each component are basically the same, indicating that the influence of each generator on the mode is similar. In the second mode, the modulus value of Δω_{3} and Δs is larger and opposite to the direction of other components (the average argument is about −154.57°), indicating that the oscillation mainly exists in generators 3, 10 and generators 1, 2. The oscillation frequency f = 8.65/(2π) = 1.3767 Hz, belonging to the local oscillation mode. In the third mode, the modulus values of Δω_{2} and Δs are larger and are basically opposite to Δω_{1} in the direction (the argument is −108.95°), indicating that the oscillation mainly exists in generators 2, 10 and generator 1. The oscillation frequency f = 12.89/(2π) = 2.0515 Hz, belonging to the local oscillation mode.
In the participation vector, if the generator speed component is positive and the value is large, it indicates that the generator is the best candidate position for installing the PSS, which can significantly increase the damping of the mode. For increasing system damping, it is better to apply control on a larger capacity generator [30].
The local oscillation modes λ_{10,11} and λ_{12,13} are specifically analyzed. The components of the participation vector corresponding to the rotation speed of each generator are shown in Table 3.

As can be seen from Table 3, for the participation vector of local mode λ_{10,11}, the value of generator 3 is the largest and that of generator 10 is the smallest, indicating that the control is mainly applied in generator 3, and the damping of the system can be significantly increased. Similarly, for the participation vector of local mode λ_{12,13}, the value of generator 2 is the largest and that of generator 10 is the smallest, indicating that fine effects can be achieved by applying control on generator 2.
Furthermore, compared with the capacity of generators 2 and 3, the active power of generator 2 (1.63 pu) is larger than that of generator 3 (0.85 pu), so the damping control of generator 2 can achieve better suppression of the oscillation effect.
4.3. PSO Algorithm Based on Different Inertia Weight Functions
The updating formulas of particle velocity and position are as follows:where k represents the number of iterations; and represent the velocity and position of the ith particle in the Ddimensional space, and the value range is [ν_{lb}, ν_{ub}] and [x_{lb}, x_{ub}]; and c_{1} and c_{2} refer to the individual learning factors and the group learning factors, and c_{1} = c_{2} = 2 is taken in this paper. r_{1} and r_{2} are random numbers between 0 and 1; and represent the individual optimal position and the global optimal position of the ith and th particle in the Ddimensional space; and ω represents the inertia weight.
The inertia weight ω indicates the ability to retain existing velocity. The larger the value is, the stronger the global optimization is. On the contrary, the smaller the value is, the better the local optimization is. In order to weigh the global optimization and local optimization, Shi. Y summarized a new method of calculating weights, linear decreasing inertia weights (LDIW) [31], which is specifically expressed aswhere ω_{start} is the inertia weight in the initial state; ω_{end} is the inertia weight at the end of the iteration; k is the number of iterations; and T_{max} is the maximum number of iterations. It is generally believed that ω_{start} = 0.9 and ω_{end} = 0.4 in which the algorithm performs best. In addition to LDIW, the common inertia weight functions [32] are as follows:
4.4. Determination of Optimization Objective Function
In order to improve the weak damping of the system, it is very important to determine the optimal target. As can be seen from Figure 5, when OWFs first join the system, the damping ratio is relatively large. With the increase of the active power output, most damping ratios show a downward trend, and some electromechanical oscillation modes even have weakly damped unstable states. In order to improve the lowfrequency oscillation, when generator 10 active output is 1.0 pu, the minimum damping ratio of each generator is selected as the optimal target, and then the maximum value of this target in the iterative process can be obtained by the PSO algorithm. If the optimization target is larger than 0.03, the variation curve of damping ratio can be ensured to be in a stable running state. The mathematical expressions of fitness function are as follows:where ξ_{ni} (i = 1,2,3,4) is the damping ratio of the component related to the rotation speed of generators 1, 2, 3, and 10 during the nth iteration process.
According to the research of this topic, the steps of the PSO algorithm are as follows:(1)Initialize particle swarm size, velocity, and position. Particle specifically refers to PSS parameters.(2)Take the smallsignal stability program as a subfunction, and then optimize the designed objective function to obtain the individual and the global optimal fitness value of the particle.(3)Compare the fitness value of each generation particle. If the current fitness value is better, update the previously recorded optimal fitness value with the current fitness value, and update the previously recorded optimal position with the current position. If not, leave the value unchanged.(4)Update the position and velocity of each particle.(5)Determine whether the current fitness value reaches the given standard or reaches the upper limit of the number of iterations. If yes, the program ends. If not, return to (2) and continue to execute the loop body.
4.5. Effect of Applying PSS Control
According to the analysis of Section 4.3, PSS installed in generator 2 works well. Under different inertial weights, the fitness curve can be obtained by solving the function for many times and taking the mean value, as shown in Figure 6.
It can be seen from Figure 6 that the deviation of the optimal fitness obtained under the four inertia weights is small. The optimal fitness of the inertia weight ω2 is 0.034232, the effect of ω1 and ω3 is similar, and the worst is ω4. Based on ω2, the control parameters are deeply optimized, and the optimized parameters of each controller are K_{gain} = 10, T_{1} = 0.66, T_{2} = 0.25, T_{3} = 0.45, T_{4} = 0.15, T_{5} = 4.5, and T_{6} = 1.25. By substituting the PSS parameters into the original state matrix and changing the position and capacity of the offshore wind power into the power system, the effect can be obtained, as shown in Figure 7.
(a)
(b)
(c)
(d)
As can be seen from Figure 7, after adding the PSS to generator 2, each damping ratio is improved correspondingly, and the curves are all above 0.03, indicating that the system works stably. The variation trend of each damping ratio is basically the same as that without the PSS, and the damping ratio of generator 2 rotation speed is significantly increased. Furthermore, it can be verified that the theoretical analysis is reasonable, and generator 2 is the best place to add the PSS.
5. Simulink Simulation
Through theoretical analysis and programming experiments, the control measures of offshore wind power grid connection have been obtained. However, how the actual power system operates and whether the controller PSS achieves the desired effect need to be verified by simulation. The circuit in Figure 1 was built on MATLAB/Simulink. By applying the small signal (wind speed disturbance and system fault), the proposed control measures are verified and analyzed.
5.1. Wind Speed Disturbance
Assuming the initial wind speed of the OWFs is 10 m/s, a step signal generator disturbs the wind speed to 12 m/s at 1.8 s. The dynamic response effect of the system before and after adding PSS control to generator 2 is shown in Figure 8.
(a)
(b)
(c)
(d)
(e)
(f)
From the PSS2 control in Figures 8(a) and 8(c), it can be clearly seen that the power of the system fluctuates within a small range after applying the wind speed disturbance, and the system runs stably again at 3.3 s. The process has gone through 1.5 s; it can be seen from Figure 8(a) that, after the addition of PSS2, the electromagnetic torque of synchronous generator 1 is stabilized more quickly, and the oscillation amplitude is effectively suppressed. Figure 8(b) is the voltage curve of synchronous generator 1, and the effect of adding PSS2 is small. It can be seen from Figure 8(c) that the amplitude of the synchronous generator 1 active power is significantly reduced after the addition of PSS2. Figure 8(d) shows the DC curve of HVDC. By comparison, the amplitude of the oscillation is reduced when PSS2 is applied. The amplitude of the voltage stability will drop slightly without PSS2 control, which is also the adverse effect of wind speed disturbance. Figures 8(e) and 8(f) show the active and reactive power of VSC1. It can be seen that, after the addition of the damping controller, the oscillation of the system is better improved. In summary, when the OWFs are disturbed by wind speed, adding PSS2 will improve the smallsignal stability of the whole system.
5.2. System Fault
In order to simulate the actual system fault, a threephase short circuit was applied to the transmission line incorporated into node 8 at 1.5 s, and the fault duration is 0.12 s. The dynamic response of the system controlled by PSS2 is shown in Figure 9.
(a)
(b)
(c)
(d)
(e)
(f)
It can be seen from Figures 9(a) and 9(f) that, after applying a threephase shortcircuit fault, the state of the system changes obviously. The system recovers at 2.8 s, and the adjustment process goes through 1.3 s; Figure 9(a) is the electromagnetic torque curve of synchronous generator 1, and the oscillation of the system is significantly reduced after the addition of PSS2. Figure 9(b) shows the voltage curve of synchronous generator 1, and the effect of adding or not adding PSS2 is small. It can be seen from Figure 9(c) that the amplitude of the synchronous generator 1 active power is remarkably suppressed after the addition of PSS2. Figure 9(d)shows the DC curve of HVDC. It can be seen that the DC voltage fluctuation amplitude is reduced, and the system reaches stability more quickly. Figures 9(e) and 9(f) show the active and reactive power of VSC1. It can be seen that, after the damping controller is added, the oscillation of the system is better improved. In summary, when the onshore power system is disturbed by the fault, adding PSS2 improves the smallsignal stability of the whole system.
6. Conclusions
Based on the establishment of a complete mathematical model, the influence of offshore wind power on the system at different positions and capacities is analyzed in detail according to the damping characteristics. The experimental results show that most of the damping ratios are decreasing, and some of the electromechanical oscillation modes will show weak damping instability. By comparing the experimental results of two load nodes and two generator nodes, the optimal location and capacity of offshore wind farms are obtained. In order to improve the weak damping of the power system, the optimal positions of the PSS in the power grid are obtained through the modal control. PSO algorithm combining with different inertia weight functions is presented to determine the parameters of the PSS. Finally, the whole system model is built on MATLAB/Simulink platform, and the influence of PSS control on the system is compared and analyzed by applying wind speed disturbance and system fault. The simulation results show that the dynamic response of the system is obviously improved, the oscillation amplitude is significantly reduced, and the accuracy of the proposed control strategy is verified.
Appendix
DFIG parameters of offshore wind farms: r = 40 m; ρ = 1.242 kg m^{3}; = 10.45 m s^{−1}; R_{r} = 0.0073 pu; R_{s} = 0.0076 pu; L_{r} = 0.0884 pu; L_{s} = 0.1248 pu; L_{m} = 1.8365 pu; ω_{t0} = 1.1055 rad s^{−1}; s_{0} = −0.003; β_{0} = 0 rad; K_{p0} = 0.1 pu; K_{I0} = 20 s^{−1}; T_{β} = 10 s; H_{t} = 3 s; H_{g} = 0.05 s; K = 10 pu^{.}rad^{−1}; and D = 0.5 pu^{.}rad^{−1}.
VSCHVDC parameters: R_{1} = R_{2} = 0.075 pu; L_{1} = L_{2} = 0.016 pu; ω_{1} = ω_{2} = 1 pu; δ_{1} = δ_{2} = 10°; K_{1} = K_{2} = 0.1; R_{d} = 1.0425 pu; L_{d} = 0.0119 pu; and C = 0.1733 pu.
System interface parameters: X_{T0} = 0.015 pu; X_{T1} = 0.016 pu; X_{L1} = 0.02 pu; X_{T2} = 0.061 pu; and X_{L2} = 0.014 pu.
Data Availability
All data generated or analyzed during this study are included in this article.
Conflicts of Interest
The authors declare no conflicts of interest.
Acknowledgments
This paper was carefully guided by Professor Ru Yang of Guangzhou University and was supported by the National Natural Science Foundation of China under Grant nos. 61772147 and 61100150, the University Innovation Team Construction Project of Guangdong Province under Grant no. 2015KCXTD014, Guangdong Province Philosophy and Social Science Foundation under Grant no. GD19CSH03, the key Project of Science and Technology Plan of Guangdong Province under Grant No. 2020b1010010014 and Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province. Here, the authors express their sincere gratitude.
References
 I. Pineda, K. Ruby, A. Ho, A. Mbistrova, and G. Corbetta, “The European Offshore Wind Industry—Key Trends and Statistics 2015, European Wind Energy Association, Brussels, Belgium, 2016.
 C. Walsh, L. Miró, F. Selot, D. Fraile, and G. Brindley, “Offshore Wind in Europe – Key Trends and Statistics 2018, Wind Europe, Brussels, Belgium, 2019.
 P. Tardieu, L. Velde, A. Nghiem, and I. Pineda, Wind Energy in Europe: Scenarios for 2030, Wind Europe, Brussels, Belgium, 2017.
 L. Shen, M. Barnes, R. Preece, and J. Milanović, “Frequency stabilisation using VSCHVDC,” in Proceedings of the 2016 IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5, Boston, MA, USA, 2016. View at: Google Scholar
 L. Yan, S. Wei, C. YongNing, W. LinJun, and L. Wei, “Research on offshore wind farm VSCHVDC transmission system fault ride through issue,” in Proceedings of the 2014 International Conference on Power System Technology, pp. 2190–2195, Chengdu, China, 2014. View at: Google Scholar
 K. Asimenia, Q. Wu, and H. Zhao, “Review of VSC HVDC connection for offshore wind power integration,” Renewable and Sustainable Energy Reviews, vol. 59, pp. 1405–1414, 2016. View at: Publisher Site  Google Scholar
 M. Edrah, K. L. Lo, O. AnayaLara, and A. Elansari, “Impact of DFIG based offshore wind farms connected through VSCHVDC link on power system stability,” in Proceedings of the 11th IET International Conference on AC and DC Power Transmission, pp. 1–7, Birmingham, UK, 2015. View at: Google Scholar
 Q. Fu, W. Du, J. Cao, and H. F. Wang, ““VSCbased HVDC power transmission for the largescale offshore wind power—a survey,” in Proceedings of the International Conference on Renewable Power Generation (RPG 2015), pp. 1–6, Beijing, China, 2015. View at: Google Scholar
 S. Lu and Z. Xu, “A novel control strategy of VSCHVDC for offshore platforms,” in Proceedings of the 12th IET International Conference on AC and DC Power Transmission (ACDC 2016), pp. 1–6, Beijing China, 2016. View at: Google Scholar
 Y. Guo, H. Gao, Q. Wu, H. Zhao, J. Ostergaard, and M. Shahidehpour, “Enhanced voltage control of VSCHVDCConnected offshore wind farms based on model predictive control,” IEEE Transactions on Sustainable Energy, vol. 9, no. 1, pp. 474–487, 2018. View at: Publisher Site  Google Scholar
 J. Machowski, J. Bialek, and J. Bumby, Power System Dynamics: Stability and Control, Wiley, New York, NY, USA, 2nd edition, 2008.
 H. Huang, C. Mao, J. Lu, and D. Wang, “Smallsignal modelling and analysis of wind turbine with direct drive permanent magnet synchronous generator connected to power grid,” IET Renewable Power Generation, vol. 6, no. 1, pp. 48–58, 2012. View at: Publisher Site  Google Scholar
 Y. Yang and G. Li, “The small signal stability control of offshore wind farm based on VSCHVDC,” Transactions of China Elect Rotechnical Society, vol. 31, no. 13, pp. 101–110, 2016. View at: Google Scholar
 A. Sajadi, S. Zhao, K. Clark, and K. A. Loparo, “Smallsignal stability analysis of largescale power systems in response to variability of offshore wind power plants,” IEEE Systems Journal, vol. 13, no. 3, pp. 1–10, 2018. View at: Publisher Site  Google Scholar
 M. Raza, E. PrietoAraujo, and O. GomisBellmunt, “Smallsignal stability analysis of offshore AC network having multiple VSCHVDC systems,” IEEE Transactions on Power Delivery, vol. 33, no. 2, pp. 830–839, 2018. View at: Publisher Site  Google Scholar
 C. Wang, H. Fang, and S. He, “Adaptive optimal controller design for a class of LDIbased neural network systems with input timedelays,” Neurocomputing, vol. 385, pp. 292–299, 2020. View at: Publisher Site  Google Scholar
 S. He, H. Fang, M. Zhang, F. Liu, and Z. Ding, “Adaptive optimal control for a class of nonlinear systems: the online policy iteration approach,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 2, pp. 549–558, 2020. View at: Publisher Site  Google Scholar
 S. He, H. Fang, M. Zhang, F. Liu, X. Luan, and Z. Ding, “Online policy iterativebased H∞ optimization algorithm for a class of nonlinear systems,” Information Sciences, vol. 495, pp. 1–13, 2019. View at: Publisher Site  Google Scholar
 S. He, M. Zhang, H. Fang, F. Liu, X. Luan, and Z. Ding, “Reinforcement learning and adaptive optimization of a class of Markov jump systems with completely unknown dynamic information,” Neural Computing and Applications, 2019. View at: Publisher Site  Google Scholar
 F. Wu, X.P. Zhang, K. Godfrey, and P. Ju, “Small signal stability analysis and optimal control of a wind turbine with doubly fed induction generator,” IET Generation, Transmission & Distribution, vol. 1, no. 5, pp. 751–760, 2007. View at: Publisher Site  Google Scholar
 G. Tang, HVDC Transmission Technology Based on Voltage Source Converter, China Electric Power Press, Beijing, China, 2010.
 C. Qin and Y. Yu, “Small signal stability region of power systems with DFIG in injection space,” Journal of Modern Power Systems and Clean Energy, vol. 1, no. 2, pp. 127–133, 2013. View at: Publisher Site  Google Scholar
 Z. Li, X. Zhang, Y. Deng, and B. He, “Studies of transient stability of wind power acess grid system,” J of China Three Gorges Univ. (Natural Sciences), vol. 38, no. 2, pp. 47–50, 2016. View at: Google Scholar
 B. Mehta, P. Bhatt, and V. Pandya, “Small signal stability analysis of power systems with DFIG based wind power penetration,” International Journal of Electrical Power & Energy Systems, vol. 58, pp. 64–74, 2018. View at: Google Scholar
 E. Prasanthi and K. N. Shubhanga, “Stability analysis of a grid connected DFIG based WECS with twomass shaft modeling,” in Proceedings of the 2016 IEEE Annual India Conference (INDICON), pp. 1–6, Bangalore, India, 2016. View at: Google Scholar
 S. Feng, D. Liu, X. Yang, and X. Xiang, “The impact of wind power inversepeaking characteristics on power system low frequency oscillation,” in Proceedings of the 2012 China International Conference on Electricity Distribution, pp. 1–4, Shanghai, China, 2012. View at: Google Scholar
 H. Huang, Research on SmallSignal Stability of Wind and Photovoltaic Power Generation System, Department Electronical Engineering, HUST University, Wuhan, China, 2012, Ph.D. dissertation.
 X. Wang, W. Fang, and Z. Du, Modern Power System Analysis, Science Press, Beijing, China, 2003.
 K. Thanpisit and I. Ngamroo, “Power oscillation damping control by PSS and DFIG wind turbine under multiple operating conditions,” Turkish Journal of Electrical Engineering & Computer Sciences, vol. 25, pp. 4354–4368, 2017. View at: Publisher Site  Google Scholar
 D. Gautam and V. Vittal, “Impact of DFIG based wind turbine generators on transient and small signal stability of power systems,,” in Proceedings of the 2009 IEEE Power & Energy Society General Meeting, pp. 1–6, Calgary, Canada, 2009. View at: Google Scholar
 J. Xin, G. Chen, and Y. Hai, “A particle swarm optimizer with multistage linearlydecreasing inertia weight,,” in Proceedings of the 2009 International Joint Conference on Computational Sciences and Optimization, pp. 505–508, Sanya, China, 2009. View at: Google Scholar
 L. Yu, F. Shi, H. Wang, and F. Hu, Analysis of 30 Cases of Intelligent Algorithms in MATLAB, Beihang University Press, Beijing, China, 2011.
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