A doubly-fed induction generator (DFIG) mainly consists of blades, a gearbox, the doubly-fed induction generator itself, and a PWM converter. The power flow diagram of a DFIG under generator mode is shown in Figure 2.

The PWM converter includes the Grid Side Converter (GSC) and the Rotor Side Converter (RSC). The rotor windings are connected to the grid through a bidirectional frequency converter formed by the GSC and RSC. Therefore, by controlling the GSC and RSC, the rotor amplitude, phase, and frequency can be adjusted to regulate the active and reactive power output of the wind turbine. The main function of the GSC is to maintain the stability of the DC bus voltage, while the RSC can provide more reactive support. Hence, the mechanism by which the control parameters of the RSC affect transient overvoltage can be explored based on its control characteristics.

The Rotor Side Converter (RSC) adopts a dual-loop control based on stator voltage orientation vectors, including inner-loop current control and outer-loop power control, to achieve the decoupling of stator active and reactive power (Zhang et al., 2013). The dual-loop control diagram of the RSC is shown in Figure 3.

In the figure, P s _ r e f and Q s _ r e f are the reference values for stator-side active and reactive power respectively; i q r _ r e f and i d r _ r e f are the reference values for rotor current q-axis and d-axis components respectively; i q r and i d r are the measured values of rotor output current q-axis and d-axis components; u q r and u d r are the q-axis and d-axis components of rotor output voltage; k p 1 and k i 1 are the proportional and integral coefficients of the power outer-loop PI controller, k p 2 and k i 2 are the proportional and integral coefficients of the current inner-loop PI controller; k d is the cross-coupling term between the d-axis and q-axis.

By taking the first-order partial derivatives of the PI controller parameters in the power outer loop and current inner loop of the Rotor Side Converter (RSC), it can be derived that the stator output reactive power and rotor impedance are negatively correlated. Consequently, based on the correlation between rotor impedance and the parameters of the inner and outer loops, an approximation of the relationship between the total output reactive power of the wind turbine and the control parameters can be obtained. Specifically, reducing the proportional coefficients ( k p 1 , k p 2 ) or increasing the integral coefficients ( k i 1 , k i 2 ) of the inner and outer loops will increase Q w , whereas increasing the proportional coefficients ( k p 1 , k p 2 ) or decreasing the integral coefficients ( k i 1 , k i 2 ) will decrease Q w . The severity ranking of the impact of PI parameters on Q w is as follows: k p 2 > k i 2 > k i 1 > k p 1 . Considering the numerous parameters involved in Doubly Fed Induction Generator (DFIG), to simplify the optimization model, priority is given for optimizing the proportional coefficient ( k p 2 ) and integral coefficient ( k i 2 ) of the current inner loop, thus achieving optimal control of wind turbine voltage response.

The high-voltage direct current transmission control system includes constant current control (CCA), constant voltage control, and voltage dependent current limit control (VDCOL). Additionally, the inverter side also has constant extinction angle control to prevent phase-shifting failure caused by excessive overshoot of the controller resulting in an excessively small extinction angle. The CCA and VDCOL sections on the rectifier side are the main factors affecting the control performance of the DC system. The following explores the mechanism of how the control parameters of these two sections affect transient overvoltage.

(1) Rectifier-side constant current control (CCA)

The proportional coefficient and integral coefficient of the CCA control loop are important parameters that affect the transient overvoltage of the sending-end system. By adjusting these two parameters, the magnitude of overcurrent during phase-shifting failure can be quickly suppressed, thereby suppressing overvoltage. Additionally, it affects the subsequent recovery process, shortening the duration of overvoltage and reducing damage to the equipment. The expression for the triggering angle α of the rectifier-side converter station output by the CCA is as follows: α = α 0 − K p 1 I ord − I dmeas − K i 1 ∫ I ord − I dmeas d t (6)

In the equation, α 0 represents the initial value of the triggering angle, I ord represents the reference value of the DC current, and I dmeas represents the measured value of the DC current.

The expression describing the relationship between the DC current and the triggering angle is as follows: I d = 1.35 N p U L cos ⁡ α − cos ⁡ β π 12 X C (7)

In the equation, I d represents the DC current, α represents the triggering angle, N p denotes the number of six-pulse converters per stage, U L signifies the rectifier-side converter bus voltage, X C stands for the commutation reactance, and β denotes the converter lag angle.

From Equations 6, 7, it can be observed that the proportional coefficient and integral coefficient of the CCA control loop, as well as the DC current, are all negatively correlated. That is, as K p 1 and K i 1 increase, α decreases, leading to an increase in the DC current ( I d ). Consequently, the reactive power consumed by the converter station increases, while the exchange of reactive power between the rectifier station and the AC system decreases, thereby serving to suppress overvoltage.

(2) Rectifier-Side Voltage Dependent Current Limit Control (VDCOL)

When a DC fault leads to a decrease in the system’s DC voltage, VDCOL will activate to limit the DC current command, thereby reducing the reactive power consumption of the converter station and regulating the AC voltage.

The characteristic equation of the VDCOL control loop is: I = I o r d = I d h − I d l U d h − U d l U − U d l + I d l (8)

In the equation, I d h and I d l represent the maximum and minimum current commands of VDCOL, respectively, while U d h and U d l represent the dropout voltage and startup voltage of VDCOL, respectively.

From Equation 8, it can be observed that the DC current command value ( I o r d ) is dependent on the control parameters of VDCOL. Considering I d h as the rated DC current, taking partial derivatives with respect to I d l , U d h , and U d l , the following relationships can be obtained: the DC current command value ( I o r d ) is positively correlated with the minimum current command ( I d l ), while negatively correlated with U d h and U d l . Therefore, reducing I o r d can be achieved by increasing I d l and decreasing U d h and U d l , thereby suppressing transient overvoltage. While U d h , U d l , and I d l have relatively minor effects on the magnitude of overvoltage and undervoltage, I d l significantly shortens the duration of overvoltage. Hence, it is preferable to prioritize optimizing the CCA control parameters K p 1 and K i 1 , which have a higher impact on overvoltage, and the VDCOL control parameter I d l to reduce the reactive power sent back to the AC system at the sending end, achieving voltage response control (Ji, 2017).

The control modes of SVC mainly include fixed voltage control and fixed reactive power control. In order for SVC to perform reactive power adjustment promptly when overvoltage occurs in the system, achieve coordinated control with DFIG and the DC system, and suppress overvoltage, the fixed voltage control mode can be adopted. The expression for the reference value of reactive power provided by SVC is (Bao et al., 2021): Q S V C − r e f = K p − S V C V m − r e f − V m + K i − S V C V m − r e f − V m s (9)

In Equation 9, Q S V C − r e f represents the reference value of reactive power provided by SVC, where K p − S V C and K i − S V C are the proportional and integral coefficients of the PI loop in the SVC control system, respectively, and V m − r e f is the reference value of the SVC branch terminal voltage.

From the above equation, it can be observed that the reactive power emitted by SVC is directly proportional to K p − S V C and K i − S V C . When K p − S V C and K i − S V C are increased, SVC outputs more reactive power; conversely, when K p − S V C and K i − S V C are decreased, the reactive power transmitted by SVC also decreases. This is because the reactive power Q S V C emitted by SVC depends on the firing angle ( α S V C ) of the internal thyristors and the variation of the branch terminal voltage, and α S V C is determined by the control loop of SVC. Therefore, K p − S V C and K i − S V C can be considered as optimization targets for SVC control parameters in order to obtain the best response control performance.

Based on the analysis in Chapter 2, it is clear that the most critical solution to the overvoltage issue in the wind power DC transmission system after a DC fault is to leverage the system’s own reactive power regulation characteristics or utilize the fast response characteristics of reactive power compensation devices to absorb the excess reactive power from the sending-end grid. In order to quickly respond to fault conditions and effectively mitigate the low voltage caused by the delay effects of equipment after fault clearance, it is necessary to understand the action timing at each level.

Based on the dynamic reactive control response characteristics of DFIG and SVC, as indicated in reference (Ma et al., 2017), it is known that SVC is a circuit composed of TSC and TCR, while DFIG can be considered a circuit formed by GSC and RSC. The action delay of SVC is 20 ms, and the action delay of DFIG is 30 ms. Therefore, SVC acts before DFIG to participate in reactive response and determines the voltage ( U w ) range at the wind turbine grid connection point after a DC fault, using U w ≤ 1.1 p . u . , 1.1 p . u . < U w < 1.2 p . u . and U w ≥ 1.2 p . u . as the voltage control action ranges. This establishes a hierarchical time-sequence control strategy based on DFIG and SVC. Taking DC blocking as an example, the control mode is as follows:

(1) When the system is operating normally or experiences a sudden voltage increase at the wind turbine grid connection point after a fault, but the voltage does not exceed 1.1 p. u. (i.e., U w ≤ 1.1 p . u . ), neither DFIG nor SVC participates in reactive power regulation. In this case, it is sufficient to disconnect some filter banks of the rectifier station to restore the voltage.

The flowchart of the hierarchical time-sequence control strategy based on DFIG and SVC is shown in Figure 4.

Genetic Algorithm (GA) is a stochastic global search optimization algorithm that simulates the process of natural selection and evolution in biological systems. The basic idea of GA is to select individuals with specific structural forms from the population for crossover and mutation, thereby generating a new population. The fitness of individuals is then evaluated, and individuals with strong fitness are retained for further reproduction, while those with poor fitness are eliminated. This process gradually converges towards the optimal solution.

To prevent the loss of the optimal individual in the current population during evolution and enhance the global convergence capability of traditional genetic algorithms, an elitism retention strategy is introduced. The basic idea of the elitism retention strategy is to construct an elite pool, where the fittest individuals are selected to fill it. Then, during each generation, the weakest individuals in the current population are eliminated during the selection and replenishment process, and new optimal individuals are reintroduced to fill the population.

To ensure that the transient overvoltage requirements are met at the direct current transmission end for bundled wind and thermal power delivery of new energy, this paper adopts an improved genetic algorithm with the introduction of an elitism retention strategy, called Strengthen Elitist Genetic Algorithm (SEGA) (Wang and Liu, 2019; Shao et al., 2010). During the evolution process of the population individuals, the elite individuals’ genes (i.e., the optimal individuals) are directly copied into the chromosomes of the next-generation population without undergoing crossover and mutation operations. This ensures the integrity of the elite individuals. The process aims to solve the coordinated optimization model for suppressing transient overvoltage. The workflow of controlling parameters optimization affecting transient overvoltage is as follows:

1) Setting up the electromagnetic transient simulation model involves specifying the voltage data to be tested and the control parameters to be optimized. The iteration accuracy ( E )is preset to obtain the objective function and primary constraints.

The coordinated optimization solving process based on the improved genetic algorithm SEGA is illustrated in Figure 5.

The paper adopts the model of a doubly-fed wind turbine connected to a high-voltage direct current (HVDC) transmission system as shown in Figure 6. In the model, direct current faults are configured to observe the variations in voltage, current, and power at the sending end of the grid.

After conducting operational tests on the established simulation model according to the bipolar full-voltage operation mode, and simulating the rectifier side voltage and current conditions of the high-voltage direct current transmission system as well as the export voltage and power of the DFIG equivalent wind farm, it demonstrates the correctness and effectiveness of the model established.

The SVC is connected to the rectifier station’s converter bus. A DC lockout fault is applied at 3 s, lasting for 0.2 s. The aim is to verify whether the overvoltage control strategy, after the addition of the SVC, can effectively suppress overvoltage above 1.2p.u. At this point, the DC system is set to bipolar lockout. The simulation observes the wind turbine connection point voltage, DC bus voltage, and the reactive power output of both the DFIG and SVC. The simulation results are shown in Figures 7, 8.

From Figure 9, it can be seen that the reactive power output waveforms of the DFIG and SVC. At 20 ms, the SVC begins to respond and absorbs about 400Mvar of inductive reactive power. After 10 ms, by 30 ms, the DFIG’s reactive power regulation is activated, participating in the absorption of around 100 Mvar of surplus reactive power. Together, the two systems absorb approximately 500Mvar of reactive power, which is 165Mvar more than when the DFIG is solely involved in reactive power regulation. This effectively reduces the wind turbine connection point voltage from 1.22p.u. to 1.08p.u., a 3.3% improvement compared to relying solely on the reactive power support capability of the DFIG converter.

After the fault is cleared, both the SVC and DFIG promptly withdraw from reactive power response, with the SVC returning to normal operation. This helps to mitigate the low voltage phenomenon after fault clearance to some extent. However, since the DFIG itself does not fully utilize its reactive power support capability, the improvement in the DC bus voltage is less noticeable compared to the control strategy that relies solely on the DFIG for reactive power regulation.

To verify the optimization performance of the coordinated transient overvoltage suppression optimization model in the wind power DC transmission system, it is necessary to analyze the sensitivity of transient overvoltage to the control parameters of HVDC, DFIG, and SVC respectively. By using the method of controlling variables, each parameter is adjusted up or down by 30% to obtain the percentage change of U w ⁡ max under different DFIG and SVC control parameters, as shown in Figures 10, 11.

From Figures 10, 11, it can be observed the varying degrees of influence of different control parameters on overvoltage. Therefore, during HVDC control, K p 1 , K i 1 , and I d l can be considered as the primary control parameters. While during DFIG and SVC control, k p 2 , k i 2 , K p − S V C , and K i − S V C can be considered as the parameters for optimization, thus mitigating transient overvoltage.

Using the proposed transient overvoltage suppression coordinated optimization model based on improved genetic algorithm, the control parameters of DC, wind power, and SVC in the wind power DC transmission system are optimized. The parameter ranges are set as follows: K p 1 ∈ 1 , 2 , K i 1 ∈ 0.01 , 0.025 , k p 2 ∈ 0.1 , 3 , k i 2 ∈ 0.01 , 0.05 , K p − S V C ∈ 0.1 , 1 , K i − S V C ∈ 0.001 , 0.01 . A comparison analysis is conducted with the optimization results of the basic genetic algorithm (GA). In the rectification station of the wind power DC transmission system, a DC blocking fault is set, with a simulation duration of 3 s. The fault starts at 2 s and lasts for 0.2 s. The simulation iterations, or the number of iterations, are set to 50 times.

To better compare and analyze the effect of coordinated parameter optimization on overvoltage suppression, the simulation is divided into the following two scenarios:

Scenario 1: Only optimize HVDC control parameters.

Scenario 2: Coordinated optimization of HVDC, DFIG, and SVC control parameters.

(1) Only optimize HVDC control parameters

Using SEGA and traditional GA respectively, the control parameters of CCA and VDCOL on the rectification side of HVDC are optimized. The voltage of the wind turbine grid-connected bus under different optimization schemes is obtained, and the optimization results and simulation images are shown in Table 1 and Figure 12.

Compared with the initial state, applying optimization algorithms to optimize the parameters resulted in varying degrees of suppression in U w ⁡ max . All control parameters increased, consistent with the trend of theoretical analysis. Among them, the voltage U w ⁡ max using the traditional GA algorithm decreased to 1.1106p.u., a reduction of 0.68%, while the voltage U w ⁡ max using the SEGA algorithm decreased to 1.1075p.u., a reduction of 0.96%. The latter achieves a 0.28% better overvoltage suppression effect compared to the former, demonstrating the superior global search capability of the SEGA algorithm. However, neither of the two optimization schemes was able to suppress the overvoltage to below 1.1p.u., indicating that further optimization of the control parameters for both the DFIG and SVC is required.

(2) Coordinated optimization of HVDC, DFIG, and SVC control parameters

Using both SEGA and GA algorithms for coordinated optimization of HVDC, DFIG, and SVC control parameters, the parameter optimization results are shown in Table 2, and the grid-connected bus voltage of the wind turbine under different optimization schemes is shown in Figure 13.

Compared to the initial state, after employing the SEGA algorithm to coordinate and optimize the parameters of HVDC, DFIG, and SVC, U w ⁡ max decreased to 1.0836 p. u., a reduction of 3.2%, which is below 1.1 p. u. This successfully eliminated the transient overvoltage phenomenon. On the other hand, when using the traditional GA algorithm for parameter coordination and optimization, U w ⁡ max decreased to 1.1023 p. u., a reduction of 1.4% compared to optimizing only HVDC parameters. Although this reduction was higher in suppressing overvoltage, it still did not decrease below 1.1 p. u. This further validates the effectiveness and superiority of the coordinated optimization model for transient overvoltage suppression based on the improved genetic algorithm, SEGA.

The above simulation analyses were conducted under a single operating condition of the system. To validate the effectiveness of the transient overvoltage coordinated control strategy based on parameter optimization under multiple operating conditions, two operating scenarios were set: (1) Setting the monopole transmission power of the high-voltage DC transmission system to 1000 MW, with a total power output of 2000 MW in bipolar operation, wind power output of 400 MW, accounting for 20% of the total power output; (2) Setting the monopole transmission power of the high-voltage DC transmission system to 1000 MW, with a total power output of 2000 MW in bipolar operation, wind power output of 800MW, accounting for 40% of the total power output.

Using the SEGA algorithm to coordinate and optimize the control parameters of HVDC, DFIG, and SVC, the parameter optimization results are shown in Tables 3, 4. A comparative analysis is conducted on the peak voltage U w ⁡ max of the wind turbine grid connection point bus before applying the control strategy, with only DFIG and SVC coordinated control, and after simultaneous parameter optimization. The bus voltage of the wind turbine grid connection under different control strategies is illustrated in Figures 14, 15.

(1) Operating condition 1: Low wind power output

When the wind power output is low, the transient overvoltage reaches 1.1733 p. u. after a DC blocking fault occurs. After adopting a coordinated control strategy based on DFIG and SVC, the overvoltage decreases to 1.1021 p. u. Subsequently, after further optimization of the control parameters of HVDC, DFIG, and SVC, the overvoltage decreases to 1.0738 p. u., which is 2.4% lower than before parameter optimization. This indicates that optimizing the parameters can more effectively suppress overvoltage.

(2) Operating condition 2: High wind power output

Under high wind power output conditions, due to the increase in wind power DC output and the rise in the penetration rate of new energy sources, there is more excess reactive power after the DC blocking, leading to a higher severity of transient overvoltage compared to low wind power output, reaching 1.2306 p. u. By adopting coordinated control strategies with DFIG and SVC separately or by conducting parameter optimization based on these control strategies, the transient overvoltage is suppressed to 1.1387 p. u. and 1.0965 p. u. respectively, both higher than the operating conditions with low wind power output. However, after parameter optimization, the overvoltage is suppressed to below 1.1 p. u., confirming the effectiveness of transient overvoltage coordinated control strategies based on parameter optimization in eliminating transient overvoltage phenomena under various operating conditions.