Research on Opening Reignition Characteristics and Suppression Measures of 750 kV AC Filter Circuit Breakers

Abstract

The operation of converter valves in converter stations often results in high reactive power consumption and harmonic generation, necessitating measures to maintain reactive power balance and ensure power quality. To achieve this, the filter bank circuit breaker is frequently switched on and off during daily operation. In recent years, multiple incidents of circuit breaker breakdown during the opening process have been reported. In this study, power systems computer-aided design (PSCAD)/electromagnetic transients including DC (EMTDC) V5.0 electromagnetic transient simulation software is used to simulate and calculate the overvoltage and inrush current under different configurations of circuit breaker operating mechanism dispersion, opening phase angle, and operating speed. Additionally, the suppression effects of two measures are compared: “phase selection opening” and “phase selection opening combined with controlled opening speed” to mitigate overvoltage and inrush current. The results demonstrate that for BP11/13 filters, HP24/36 filters, and HP3 filters, the combined strategy of “phase-selective opening with controlled opening speed” is more effective in suppressing inrush current and overvoltage. However, for SC filters, the suppression effect of this combined strategy is not significant. Considering economic and practical factors, it is more reasonable to adopt the phase-selective opening measure for SC filters. These findings provide guidance for ensuring the safe operation of AC filter circuit breakers.

1. Introduction

In high-voltage direct current (HVDC) transmission systems, non-linear components such as converter valves in converter stations consume a significant amount of reactive power during operation, accounting for 40% to 60% of the transmitted DC power [1,2,3]. Furthermore, converter stations generate a series of harmonics while consuming power, leading to voltage and current waveform distortions in the AC system [4,5,6,7]. Therefore, a large number of AC filter banks are required within converter stations for harmonic filtering and reactive power compensation. Filter bank circuit breakers are frequently operated to connect or disconnect filter banks based on the operating conditions of the system. However, during breaker switching operations, severe transient inrush currents and ovevoltages often occur. The frequent operations of filter bank circuit breakers also exacerbate insulation degradation [8,9]. According to reported cases, there have been several failures of circuit breakers during the switching of filter banks in the State Grid Corporation of China [10,11]. Hence, it is imperative to investigate the inrush currents and overvoltages generated during the switching operations of filter bank circuit breakers.

Most existing studies on filter bank circuit breakers focus on breaker closing operations. Ni et al. [12] have analyzed the inrush current characteristics and suppression measures for 750 kV filter banks in converter stations. Chen et al. [13] proposed a combination breaker with a pre-insertion resistor (PIR) and a phase-selective closing device, which demonstrated superior inrush current suppression capabilities. However, for breaker opening operations, the accurate modeling of dynamic arc burning and the number of arc reignition–extinction events is critical. Wang et al. [10] proposed an improved three-stage arc model for AC filter banks, which can accurately represent the first two arc events during breaker opening. However, their study lacks clarity on the timing of arc reignition–extinction events. Ahmethodži et al. [14] proposed an improved double-exponential high-frequency arc resistance model, but their research focused on disconnector opening operations. Currently, there is limited research on the arc reignition phenomenon during the opening operations of ±800 kV AC filter bank circuit breakers.

Although the highest voltage level for HVDC transmission in China has reached ±1100 kV, ±800 kV is expected to become the primary voltage level for future HVDC projects in China, considering factors such as technology, cost, and safety [15]. If frequent grid failures are caused by repeated arc reignition in AC filter bank circuit breakers, significant economic losses will result. Therefore, studying the arc reignition characteristics of filter bank circuit breakers is of great significance for ensuring the safe and stable operation of both the filter bank circuit breakers and the entire converter station.

This paper, based on a ±800 kV HVDC converter station, employs PSCAD/EMTDC V5.0 electromagnetic transient simulation software to construct a breaker opening reignition simulation model using the classical Mayr arc model. The influence of breaker operating mechanism dispersion, opening phase angle, and operating speed on the characteristics of breaker reignition is analyzed. Finally, the effectiveness of two mitigation measures—“phase-selective opening” and “phase-selective opening combined with controlled opening speed”—in suppressing overvoltage and inrush currents is compared, providing a reliable basis for breaker insulation configuration.

2. Simulation Initial Conditions

The Lingzhou–Shaoxing ±800 kV HVDC transmission line is the world’s first HVDC project directly connected to a 750 kV AC system. The Lingzhou converter station is also the world’s first ±800 kV DC/750 kV AC converter station [16]. This transmission project adopts a bipolar operation mode, with a rated transmission power of 8000 MW, a ±800 kV DC voltage, and a 5 kA DC current. Since its commissioning, the Lingzhou–Shaoxing HV project has delivered a total of 190 billion kWh of electricity to Zhejiang Province, equivalent to reducing approximately 18.9 million tons of carbon dioxide emissions.

Unlike previous studies that replaced the entire converter station with an idealized 750 kV power source [17], this study establishes a complete PSCAD/EMTDC simulation model based on the Lingzhou–Shaoxing ±800 kV HVDC transmission project to investigate the electromagnetic transient effects of filter bank circuit breaker opening under actual converter station operating conditions. The actual circuit configuration of the Lingzhou–Shaoxing ±800 kV HVDC transmission project is shown in Figure 1 [13,16,18].

The converter station employs 12-pulse converter units, which generate characteristic harmonics of 12k ± 1 and 12k on the AC side. Therefore, the AC filter configuration in the simulation model includes four types of filters: BP11/BP13, HP24/36, HP3, and SC. Every four groups of filters form a large filter group, resulting in a total of four large filter groups. The filter configuration is shown in Figure 2. The detailed structures of the four types of filters are depicted in Figure 3, and the parameters of the AC filter components are listed in Table 1.

3. Simulation Model

3.1. Arc Reignition Module Modeling

The mainstream breakdown theories for circuit breakers currently include the gas dielectric theory and the energy recovery theory [8]. According to the gas dielectric theory, breakdown occurs when the voltage difference across the breaker contacts exceeds the dielectric recovery voltage. The arc extinguishes when the power frequency arc current crosses zero and the gap voltage is less than the minimum arc recovery voltage. On the other hand, the energy recovery theory considers the arc as a process of energy input and output. The arc burns when the energy input exceeds the energy output, and the arc extinguishes when the energy output exceeds the energy input. In this study, these two arc theories are integrated. The gas dielectric breakdown theory is used as the criterion for arc burning, while the energy recovery theory is used as the criterion for arc extinction.

3.1.1. Critical Breakdown Field

During the operation of circuit breaker contacts, the critical breakdown field strength of SF₆ gas can be determined using the Pedersen and streamer theories [19]:

(1)$(E/N)>{(E/N)}^{*}$

In (1), E represents the electric field strength, N represents the gas molecular number density, and * represents the critical breakdown field strength.

According to the streamer theory, the breakdown field strength of the gap between the moving and static contacts of the circuit breaker is calculated based on the weakest point of the air gap, while also considering the density of the gas medium, as follows:

(2)$\rho ={\displaystyle \frac{N{R}_{S{F}_6}}{R_0}}$

In (2), R_SF6 represents the molar mass, and R₀ represents the Avogadro’s constant.

By combining the above two equations and substituting the relevant data, the critical breakdown field strength can be obtained as:

(3)$E_{cirt}=1.467\rho (\mathrm{kV}/\mathrm{mm})$

In this study, the critical breakdown field strength of SF₆ is considered to be a constant. During the operation of the circuit breaker, the density of SF₆ gas inside the chamber may vary. However, according to the findings in [20], the density variation of SF₆ gas in the chamber is negligible. Therefore, the influence of SF₆ gas density changes on the critical breakdown field strength during the breaker opening process is not considered in this study.

3.1.2. Calculation of Dynamic Breakdown Voltage of SF₆ Gas

A multi-physics simulation model and electric field iterative simulation were used to determine the breakdown voltages of SF₆ gas at different movement distances. First, we established a three-dimensional electric field simulation model for the circuit breaker during the opening process, as shown in Figure 4.

Secondly, using the starting time of the circuit breaker as the zero point in the three-dimensional model, the breakdown voltage U of the circuit breaker at different contact spacings d was simulated and calculated. The specific calculation method is as follows: first set the contact spacing and the voltage at both ends of the circuit breaker, and then simulate and calculate the maximum electric field strength inside the circuit breaker. If the maximum electric field strength is equal to the critical breakdown electric field strength, it is considered that the circuit breaker has broken down under the contact spacing and the applied voltage. The field strength distribution of the circuit breaker under three different distances is shown in Figure 5.

The results were then fitted to derive the voltage–distance function of the circuit breaker under breakdown field strength, as shown in Equation (4).

(4)$U=f(d)$

In (4), U represents the breakdown voltage, and d represents the movement distance.

Subsequently, the distance–time function was obtained based on the circuit breaker’s operating speed, as shown in Equation (5).

(5)$d=v\times t$

In (5), v represents the operating speed, and t represents the time.

Finally, the two curves were combined to derive the voltage–time function, as shown in Equation (6), representing the dynamic breakdown voltage curve of SF₆ gas.

(6)$U=f(v\times t)$

3.1.3. Fitting of SF₆ Gas Dynamic Breakdown Voltage Curve

Considering that the circuit breaker contacts move at a constant speed, the breakdown voltages obtained from the previous simulation under different contact gaps are fitted into a function of contact motion time t. At the initial moment of contact motion (t = 0), the breakdown voltage is zero.

To simulate the statistical nature of arc breakdown during the breaker opening process, Gaussian noise is added to the breakdown voltages obtained from the previous simulations. In this study, the dynamic breakdown voltage curve of SF₆ gas is fitted using a first-order polynomial, second-order polynomial, third-order polynomial, exponential function, and power function [21]. The resulting breakdown voltage curves described by these different expressions are shown in Figure 6.

To evaluate the fitting performance of the above functions, F-tests and calculations were conducted on the fitted functions, as shown in Table 2.

Analysis of Table 2 shows that the cubic function provides the best fitting performance, while the exponential function performs the worst. Therefore, this study selects the cubic function to fit the dynamic breakdown voltage curve of SF₆ gas.

According to the energy recovery theory, the arc extinction process depends on the relationship between energy input and output. Additionally, there is a phenomenon wherein the arc does not extinguish during the current zero-crossing at the initial moment of arc reignition. Hence, the extinction of the arc must simultaneously satisfy the following two equations.

(7)$\left\{\begin{array}{l}{I}_{arc}\ast I_{arc\_last}<0\\ \left|{\displaystyle \frac{d(I_{arc}-I_{arc\_last})}{dt}}\right|<K\end{array}\right.$

In (7), I_arc represents the arc current, I_{arc_last} represents arc current at the last moment in the simulation process, and K represents the arc current change rate.

3.2. Dynamic Arc Model

Currently, the arc models used for very fast transient overvoltage (VFTO) simulation calculations mainly include the static constant resistance model, time-varying arc models, and black-box models [22,23,24]. The static constant resistance model replaces the arc conduction process with a fixed low resistance. However, this model is overly simplistic, resulting in significant simulation errors. The time-varying arc models, such as exponential and hyperbolic models, do not consider the arc extinction process, making them inconsistent with actual operating conditions. The black-box models, including the Mayr arc model and Cassie arc model, can effectively describe the three phases of arc behavior: arc ignition, steady-state burning, and arc extinction. These models offer better fitting performance.

The mathematical model of the classic Mayr arc model is expressed as follows:

(8)${\displaystyle \frac{1}{g}}{\displaystyle \frac{dg}{dt}}={\displaystyle \frac{1}{\tau }}({\displaystyle \frac{ui}{P}}-1)$

In (8), g represents the arc conductance, i represents the arc current, P represents the arc dissipated power, and τ represents the time constant.

Using the aforementioned arc model, the transient opening process of the main capacitor voltage, arc current, and arc state is analyzed using the HP24/36 filter as an example. At the initial moment, the contact motion distance is very short, making breakdown phenomena highly likely. Therefore, this study assumes that although the moving and stationary contacts of the circuit breaker have separated at the initial moment, they remain electrically connected, implying that breakdown has already occurred. In the simulation model, the moving contact of the circuit breaker begins to separate at t = 0.11 s. From Figure 7, a total of six breakdown events can be observed. Compared to the hundreds of reignition breakdowns during a single opening operation of an isolating switch, the number of breakdowns in circuit breakers is significantly lower. This is attributed to the shorter contact motion distance and the higher speed of the moving contact in circuit breakers. Observing the transient opening process of the HP24/36 filter in Figure 7, the main capacitor voltage exhibits a step-like waveform. It is evident that at each arc extinction moment, the load-side main capacitor voltage retains a residual voltage, with a magnitude equal to the source voltage at the extinction moment. Additionally, the arc current waveform during the transient opening process exhibits a pulse-like shape. It is observed that as the number of breakdowns increases, the amplitude of each breakdown current pulse progressively grows.

Figure 8 illustrates the transient variation of the source-side bus voltage during the breaker opening process. It can be observed that during each reignition breakdown, the source-side bus voltage exhibits sharp pulse-like spikes. The amplitude of these spikes also increases with the number of breakdowns, and the source-side bus voltage waveform becomes significantly distorted. The maximum spike amplitude reaches 380 kV, which could potentially impact the safe operation of related equipment. Examining the transient variation of the load-side bus voltage during the breaker opening process in Figure 8, it is evident that the load-side bus voltage also displays a step-like waveform. However, the waveform is not smooth and exhibits a sinusoidal variation trend. This is attributed to the fact that the HP24/36 filter consists of capacitors, which discharge at the moment of arc extinction. Therefore, the load-side bus voltage is composed of the residual voltage superimposed with the capacitor discharge voltage.

4. Influence of Mechanical Dispersion in the Operating Mechanism on the Breaker Opening Reignition Process

For a double-fracture circuit breaker, the two fractures are symmetrically connected via a central operating mechanism. During the breaker operation, the moving contacts of both fractures move simultaneously, and the breaker voltage is evenly distributed between the two fractures. However, in practice, the mechanical operating mechanisms of the two fractures cannot guarantee perfectly synchronized operation, resulting in a certain degree of mechanical dispersion. To simulate this condition, this study considers mechanical dispersions of ±0.5 ms, ±1 ms, and ±2 ms to observe their effects on the filter bank, as shown in Figure 9.

From Figure 9, it can be observed that the early operation of any one fracture has no impact on the filter bank’s opening inrush current or the main capacitor overvoltage. When fracture 1 operates early to begin opening, it can be equivalently modeled as a switch, while fracture 2 lags and remains in the closed state. Consequently, the early operation of one fracture can be equivalently represented in the external circuit as a switch and a conductor, meaning that there is no effect on the external circuit’s operating characteristics, including the filter bank’s opening inrush current and main capacitor overvoltage.

However, Figure 9 also shows that different levels of mechanical time dispersion do have a slight impact on the filter bank. As the mechanical time dispersion increases, both the opening inrush current and the main capacitor overvoltage of the filter bank increase accordingly, though the magnitude of the increase is relatively small. The electromagnetic transient process under this condition can be divided into three stages: the early opening stage, the synchronization tendency stage, and the synchronization stage. Figure 10 illustrates the distribution of switch states during these three stages. In an ideal condition where the circuit breaker operates simultaneously, each break handles half of the source voltage. However, for circuit breakers with mechanical dispersion, the early-operating fracture bears the entire source voltage during the early opening stage. This condition increases the number of arc reignition events. When the lagging fracture begins to open, the breaker enters the towards-synchronous stage. At this point, the two fractures jointly bear the source voltage upon the next arc extinction. Finally, when the reignition and extinction moments of the arcs in both fractures become synchronized, the breaker enters the synchronization stage.

In summary, the impact of different levels of mechanical time dispersion on the filter bank is primarily concentrated in the early opening stage. The fracture that bears the entire source voltage is more likely to experience an increased number of arc reignition events. Furthermore, as the duration of mechanical time dispersion increases—meaning that the fracture endures the entire source voltage for a longer period—the number of arc reignition events also increases.

5. Influence of Opening Phase Angles on the Breaker Opening Reignition Process

At the initial moment of filter bank breaker opening, the opening phase angle determines the voltage difference across the breaker contacts. The magnitude of this voltage difference significantly impacts the number of arc reignition events, as shown in Figure 11.

In Figure 11, the blue, green, and red curves represent the relationship between the contact voltage difference and breakdown voltage for opening phase angles of 0°, 45°, and 90°, respectively. It can be observed that the arc reignition moments differ significantly under the three opening phase angles. Therefore, it is necessary to study the influence of opening phase angles on the breaker opening reignition process. For the four types of filters—BP11/BP13 filters, HP24/36 filters, HP3 filters, and SC capacitors—360 points were selected across the range of 0° to 360°, and the inrush currents and overvoltages of the four filters were simulated. The results are shown in Figure 12 and Figure 13, as well as Table 3.

Overall, the maximum inrush currents and overvoltages of the four filter groups vary significantly with respect to the opening phase angles. For inrush currents, the HP3 filter exhibits relatively small inrush currents under different opening phase angles, with a maximum of 2.65 kA. In contrast, the SC filter shows significant variations in inrush current with the opening phase angles, reaching a maximum of 23.82 kA. For overvoltages, the SC filter consistently exhibits small overvoltages under different opening phase angles, with a maximum of 635.61 kV. However, the overvoltages of the HP3 and BP11/BP13 filters vary significantly with the opening phase angles, reaching maximum overvoltages of 1248.40 kV and 1347.47 kV, respectively.

6. Influence of Operating Mechanism Speed on the Breaker Opening Reignition Process

As discussed earlier, different opening speeds of AC filter circuit breakers result in distinct dynamic breakdown voltage curves for SF₆ gas, as shown in Figure 14.

In Figure 14, the blue, green, and red curves represent the relationship between the contact voltage difference and breakdown voltage for operating mechanism speeds of 5 m/s, 8 m/s, and 10 m/s, respectively. It can be observed that the arc reignition moments differ significantly under the three operating speeds. Therefore, it is necessary to study the impact of different opening speeds on the inrush current and voltage during breaker opening. This study calculated the inrush currents and voltages of four filter groups when the opening speed varied from 5 m/s to 10 m/s, with the results shown in Figure 15.

Analysis of Figure 15 reveals significant differences in the maximum inrush currents and overvoltages of the filter groups under different circuit breaker opening speeds. For the BP11/BP13 filter group, at an opening speed of 6 m/s, the overvoltage and inrush current are relatively high, reaching a maximum of 1171 kV and 8.75 kA, respectively. For the HP3 filter group, the inrush current and overvoltage are relatively small at high opening speeds. However, at an opening speed of 5 m/s, the maximum overvoltage and inrush current can reach 1563 kV and 2.91 kA, respectively. For the HP24/36 filter group and the SC filter group, the inrush current varies significantly with the opening speed, with maximum values of 14.9 kA and 27.5 kA, respectively. These differences are due to the variations in the SF6 gas dielectric recovery curve during the reignition process under different opening speeds. The SF6 dielectric recovery curve further affects the number of arc reignition events during the opening process. Therefore, it is crucial to configure the optimal opening speed for circuit breakers in the converter station’s filter groups.

7. Implementing the “Phase-Selective Opening + Opening Speed” Strategy

As shown in Figure 12, different opening phase angles have varying effects on the inrush current and overvoltage when filter banks are opened. Similarly, as shown in Figure 15, different opening speeds result in significant differences in the inrush current and overvoltage during filter bank opening. Therefore, it is essential to determine the appropriate phase-opening moment and opening speed when implementing the “phase-selective opening + opening speed” strategy. The goal is to minimize the inrush current and overvoltage during breaker opening reignition.

This study calculated the inrush current and overvoltage of four filter types at various opening moments when the opening speed varied from 5 m/s to 10 m/s. Figure 16 presents the calculated results for the HP3 filter group’s inrush current and overvoltage, while the results for the other filter groups are shown in Appendix A, Figure A1, Figure A2 and Figure A3.

From Figure 16, it can be observed that for the HP3 filter, the opening inrush current and overvoltage of the AC filter vary significantly under different combinations of opening phase angles and opening speeds. When the breaker opening speed is 7.5 m/s and the opening phase angle is 117°, the minimum inrush current is 0.83 kA, and the minimum overvoltage is 940 kV. For the HP3, under the condition of phase-selective opening alone, the maximum inrush current does not exceed 2.65 kA. Although the “opening speed + phase-selective opening” strategy can provide some suppression of inrush currents, considering the additional costs and potential reliability issues associated with installing additional control devices, adopting phase-selective opening alone is a more reasonable choice.

To compare the results of the “phase-selective opening” strategy with those of the “opening speed + phase-selective opening” strategy, this study calculated the inrush currents and overvoltages during the opening of four types of filters under both strategies. The results are shown in Figure 17.

From Figure 17, it can be observed that for the BP11/13 filter, HP24/36 filter, and HP3 filter, compared to using the phase-selective opening strategy alone, adopting the “opening speed + phase-selective opening” strategy results in smaller inrush currents and overvoltages during filter opening, demonstrating a stronger suppression effect. For the SC filter, the overvoltage remains the same under both strategies. Although the “opening speed + phase-selective opening” strategy provides some suppression of inrush currents, considering economic and practical factors, the phase-selective opening strategy alone is a more reasonable choice.

8. Conclusions

This study conducted detailed modeling of the filter bank circuit breaker opening process for four filter groups, exploring the effects of mechanical time dispersion, opening phase angles, and opening speeds on the arc reignition process. The main conclusions are as follows:

During the initial stage of breaker opening, mechanical dispersion in the operating mechanism causes a single fracture to bear the entire source voltage transiently. As the mechanical time dispersion increases—resulting in a longer duration of the fracture bearing the entire source voltage—the number of arc reignition events also increases.

During the initial stage of breaker opening, mechanical dispersion in the operating mechanism causes a single fracture to bear the entire source voltage transiently. As the mechanical time dispersion increases—resulting in a longer duration of the fracture bearing the entire source voltage—the number of arc reignition events also increases. This highlights the critical role of mechanical dispersion in determining circuit breaker performance during transient processes.

For the four filter groups, both the opening phase angle and the opening speed are found to effectively suppress the inrush currents and overvoltage generated during the arc reignition process. Therefore, in practical engineering applications, configuring the circuit breaker with optimal opening phase angles and opening speeds is crucial for reducing electrical stress and improving system reliability.

For BP11/13 filters, HP24/36 filters, and HP3 filters, the “opening speed + phase-selective opening” strategy is suitable for stronger suppression. For SC filters, the suppression effect is not obvious with the “opening speed + phase-selective opening” strategy, and it is more reasonable to adopt the phase-selective tap measure in consideration of economy and practicality.

In summary, this study provides an in-depth understanding of the transient processes in filter bank circuit breakers under different operating conditions, offering valuable insights into mitigating arc reignition phenomena. The results emphasize the importance of selecting appropriate opening strategies tailored to specific filter groups to ensure safe and reliable operation of high-voltage systems. Furthermore, these findings contribute to the optimization of circuit breaker designs, particularly for HVDC and large-scale AC systems.

Future work could explore the integration of advanced control algorithms or real-time monitoring systems to dynamically adjust breaker operating parameters. Additionally, experimental validation of the proposed strategies under a broader range of operating conditions would further enhance the practical applicability of the conclusions drawn in this study.

Author Contributions

Conceptualization, X.C.; methodology, J.D.; software, P.S.; validation, B.N.; data curation, H.N.; writing—original draft preparation, J.Z.; writing—review and editing, F.M. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.

Acknowledgments

The authors would like to thank all those who provided valuable comments and suggestions to improve the quality of this study.

Conflicts of Interest

J.Z., F.M., B.N. and H.N. were employed by State Grid. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The authors declare that this study received funding from State Grid Corporation of China. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.

Footnotes

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Figures and Tables

Figure 1. Lingzhou–Shaoxing ±800 kV high-voltage direct current transmission system diagram.

Figure 2. Converter AC filter configuration.

Figure 3. Structure of four types of filters.

Figure 3. Structure of four types of filters.

Figure 4. Three-dimensional electric field simulation model.

Figure 5. The field strength distribution of the circuit breaker.

Figure 6. Breakdown voltage fitting curves for different functions.

Figure 7. Main capacitor voltage, arc current, and arc state of the HP24/36 filter for opening.

Figure 8. Bus voltage on the power side and load side of the HP24/36 filter for opening.

Figure 9. The influence of mechanical dispersion of operating mechanisms on four filters: (a) inrush current; (b) main capacitor overvoltage.

Figure 9. The influence of mechanical dispersion of operating mechanisms on four filters: (a) inrush current; (b) main capacitor overvoltage.

Figure 10. Arc reignition extinguishing state under 2 ms mechanical dispersion.

Figure 11. The effect of different opening phase angles on arc reignition.

Figure 12. Relationship between inrush current and opening phase angle of four filters.

Figure 13. The relationship between the overvoltage and the opening phase angle of four types of filters.

Figure 14. The influence of different action speeds on arc reignition.

Figure 15. The influence of the operating speed of four types of filter operating mechanisms on the opening inrush current and overvoltage.

Figure 16. Reignition characteristics under HP3 different phase angles and rapid opening speeds.

Figure 17. Comparison of inhibitory effects under two measures.

Table 1

AC filter element parameters.

Component	BP11/BP13	HP24/36	HP3	SC
C1/μF	1.46	2.77	2.77	3.73
L1/mH	57.31	4.23	456.19	0.94
C2/μF	1.29	16.62	22.21	—
L2/mH	46.28	0.70	—	—
R1/Ω	12,000	300	1146.53	0.0015
R2/Ω	12,000	—	—	—

Table 2

Fit test values.

Fitting Function	${\mathit{R}}^2$	F	P
Linear	0.856122	24.527769	0.004276
Quadratic	0.963644	60.713735	0.001017
Cubic	0.990706	111.299472	0.001423
Power	0.894141	38.950130	0.001547
Exponential	−1.540007	11.755128	0.068664

Table 3

Breaking inrush current and overvoltage under the most severe operating conditions of four types of filters.

Filter Bank	Angle/°	Current/kA	Voltage/kV
BP11/BP13	141°	9.12	1248.40
HP3	114°	2.65	1347.47
HP2426	339°	16.4	878.96
SC	3°	23.82	635.61

Appendix A

Figure A1. Reignition characteristics under BP11/13 different phase angles and rapid opening speeds.

Figure A2. Reignition characteristics under HP24/36 different phase angles and rapid opening speeds.

Figure A3. Reignition characteristics under SC different phase angles and rapid opening speeds.

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