Mechanism and suppression of breaking overvoltage of DC circuit breakers

Abstract

The occurrence of breaking overvoltage in a DC circuit breaker (DCCB) poses a potential threat to the safe operation of a DC grid. Based on the structure of the ±10 kV three‐terminal DC distribution network, this paper sets up the medium‐voltage DCCB and formulates a fault protection strategy. Additionally, a simulation model of the system is developed to analyse the overvoltage characteristics within the DC distribution network across different nodes and fault conditions. By examining the factors that influence breaking overvoltage, this paper unravels the fundamental mechanisms associated with DCCB‐related overvoltage generation. Furthermore, the paper suggests measures to alleviate DCCB overvoltage. These insights provide a theoretical and technical basis for the design and operation of DCCBs within DC distribution networks.

INTRODUCTION

The study of overvoltage and insulation coordination is of significant importance in the field of DC grid technology. The research findings in this area serve as crucial guidelines for the design and operation of DC grids. Both domestic and international scholars have conducted initial studies addressing overvoltage concerns in DC grids. He et al. [1] target at the structure of the ±10 kV DC distribution system in Shenzhen. Based on the research results of traditional DC grids and flexible DC grids, and combined with the characteristics of the DC distribution system, two overvoltage protection schemes suitable for this system are proposed. Utilising a simulation model of the DC distribution system, the calculated overvoltage at the critical position of the system under both schemes during a typical fault scenario is presented. Ultimately, the insulation level for key equipment under the two schemes are proposed. Li et al. [2] analyse the DC overvoltage caused by faults in the DC line in the converter station near the transmitting converter station and receiving converter station within the Zhangbei flexible DC grid. The analysis provides a detailed exploration of the mechanism and dynamic processes underlying overvoltage, and proposes the mitigation of DC overvoltage through adjustments to the operational strategy of the DC circuit breaker (DCCB). The authors in refs. [3, 4] study the DC overvoltage caused by DC side faults, particularly focusing on non-fault pole overvoltage induced by a monopole to earth faults in DC lines. Su et al. [5] take the ±10 kV medium-voltage flexible DC distribution network as an example to study the characteristics of various earth faults or short circuits in converter stations and DC lines, and discusse the generation mechanism of breaking overvoltage. Zhao et al. [6] conduct simulations to assess the bus overvoltage level at each converter station when a monopole to earth fault occurs at different positions in the DC grid, and discovers a special phenomenon where the sound pole overvoltage surpasses the fault pole overvoltage. However, there is limited research on the overvoltage caused by DCCB action during faults on the DC side in the DC grid. Sun et al. [7] investigate the key factors influencing the switching overvoltage level in flexible DC grids. Han et al. [8] explore the influence of fault protection on the operating overvoltage of DC grids under five categories and seven types of faults. For the most severe faults, the dynamic process of DC overvoltage before and after the operation of DCCB are analysed in detail, and the influence law of fault protection on the overvoltage level is extracted. Ahmed et al. [9] perform research on the level and mechanism of DC grid overvoltage subsequent to the operation of the DCCB. Yin and Li [10] introduce a quantification method of overvoltage risk, providing an analytical expression for the peak value of overvoltage, laying a foundation for overvoltage suppression. Zheng et al. [11] demonstrate that overvoltage can be mitigated by installing reactive power compensation equipment with a faster response on the sending side. Xue et al. [12] accelerate the recovery speed of DC current, so that the converter station consumes more reactive power, thereby reducing the surplus reactive power fed into the AC system, and achieving the goal of suppressing overvoltage. Teng et al. [13] propose an algorithm to increase the turn-off angle according to the control objective, so as to enhance the reactive power absorbed by rectifier stations and suppress overvoltage. Zhaowei et al. [14] advocate the coordination of synchronous condensers at multiple DC converter stations to diminish the likelihood of DC faults and reduce overvoltage post-fault occurrence. Fang et al. [15] suggest incorporating an energy absorption branch composed of metal oxide varistor (MOV) in rectifier stations to curtail the reactive power transmitted to the AC power grid in the event of a failure to suppress overvoltage. Chen et al. [16] propose a novel fast energy storage DC fault current limiter (EFCL) topology, which can reduce the overvoltage peak of DCCB by 22.9% in coordination with MOV. Chen et al. [16] improved EFCL and proposed a secondary active limiting fault current limiter, which can cope with the secondary impact of DCCB.

However, there is still insufficient knowledge about the DCCB's breaking overvoltage characteristics, and further research is needed to understand the influence of DC breaking on the overvoltage of flexible DC grids. This paper focuses on the mechanism and suppression of breaking overvoltage in DC circuit breakers. In Section 2, the simulation model of the ±10 kV three-terminal DC distribution network is developed. In Section 3, the overvoltage characteristics of the DC distribution network at different nodes and under various fault conditions are analysed. By examining the factors that influence breaking overvoltage, the underlying mechanisms behind its generation in relation to the DCCB are uncovered in Section 4. In Section 5, measures to mitigate the overvoltage of the DCCB are also proposed.

SIMULATION MODEL OF DC BREAKING OVERVOLTAGE

This section, based on the structure of the three-terminal DC distribution network, configures the medium-voltage DCCB and fault protection strategy and establishes the system simulation model after analysing the fault types according to the operation mode of the DC distribution network and the fault location. Then, this section analyses the overvoltage characteristics and dynamic processes of different fault types.

Structure and parameters of the system

This section takes the three-terminal flexible DC distribution network as the study object [17], and the structure and parameters of the system are shown in Figure 1 and Table 1. In order to realise power conversion and improve the power supply reliability of the distribution network, the system adopts a ‘star’ network topology with three independent AC power supplies; the main wiring form adopts a symmetrical monopole form, and the converter station A, converter station B, and converter station C all adopt a modular multilevel converters (MMC) structure and are connected to external wind energy, photovoltaic, storage, charging, and multiple DC loads to form a ±10 kV flexible DC distribution network.

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TABLE 1 System parameter configuration of the three-terminal flexible DC distribution network.

Parameter	Converter station A	Converter station B	Converter station C
Rated capacity (MVA)	20	10	10
Reactive output range (Mvar)	−10 to 10	−5 to 5	−5 to 5
Rated DC voltage (kV)	±10	±10	±10
Maximum continuous DC voltage (kV)	±11	±11	±11
Minimum continuous DC voltage (kV)	±9	±9	±9
Rated DC current (A)	1000	500	500
Rated AC on the converter (valve) side (kV)	10.5	10.5	10.5
Maximum AC on the converter (valve) side (kV)	12	12	12
Rated AC current (A)	1155	577	577
Rated arm current (A)	666	333	333

Configuration of the DCCB

To clear and isolate faults in the 10 kV DC line, minimise the damage caused by fault currents to converter valves and other equipment and expedite the restoration of normal operations on the non-failure side; the outlet side of the 10 kV DC line at converter station A, converter station B and converter station C is respectively equipped with a hybrid DCCB [18] and a three-terminal hybrid DCCB at the junction of three DC lines [19]; the topology is shown in Figure 2.

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Overvoltage simulation model

According to the engineering parameters of the three-terminal DC distribution network, the actual engineering structure and control strategy, the overvoltage simulation model for the three-terminal DC distribution network is established. The ideal voltage source of 110 kV is used to simulate the AC power supply at both ends, and the 10 kV AC bus is extracted through the 110/10 kV power transformer. The three-terminal converter adopts the structure of MMC. DC cables with a total length of approximately 10.4 km is adopted for the DC line. The voltage is ±10 kV, setting value of reactive power is 0 Mvar, and the maximum active power can be transmitted is 20 MW.

Fault type

The DC distribution network exhibits complexity with a broad spectrum of potential faults and lacks a standardised classification system. Despite variations in main wiring and grounding methods, the types of faults to be considered remain consistent. Therefore, based on the composition of the DC distribution network and considering the system's protection partition, the following types of faults can be classified based on their location within the system: fault in the AC electric field of the converter station, fault in the valve hall and the DC electric field of the converter station, DC line fault, and access load area fault.

The faults analysed in this section are set in converter station A, converter station B, and converter station C, respectively. Focusing on the three regional faults, fault in the AC electric field of the converter station, fault in the DC electric field of the converter station, and DC line fault, this section analyses the overvoltage characteristics and dynamic process of DC distribution network under different fault types and at different nodes. The fault locations and fault types are shown in Table 2 and Figure 3.

TABLE 2 Fault location and type.

Fault name	Fault description	Fault location
AC1	Single-phase to ground short circuit on the AC valve side	Fault in the AC electric field of the converter station
AC20	Two-phase phase-to-phase short circuit on the AC valve side	Fault in the AC electric field of the converter station
AC21	Two-phase to ground short circuit on the AC valve side	Fault in the AC electric field of the converter station
AC3	Three-phase to ground short circuit on the AC valve side	Fault in the AC electric field of the converter station
V	Short circuit of converter valve	Fault in the DC electric field of the converter station
DCv1	Monopole to earth fault at the outlet of converter valve	Fault in the DC electric field of the converter station
DCv2	Interpole short circuit at the outlet of the converter valve	Fault in the DC electric field of the converter station
DCl1	Monopole to earth fault at the outlet of current limiting reactor	DC line fault
DCl2	Interpole short circuit at the outlet of current limiting reactor	DC line fault
DCb1	Monopole to earth fault at the outlet of DCCB	DC line fault
DCb2	Interpole short circuit at the outlet of DCCB	DC line fault

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Overvoltage observation point

The key equipment in the DC distribution network includes the equipment in the converter area and DC cable lines. Particular attention should be given to the steady state voltage and transient voltage of the DC line and the critical position inside the converter, with a focus on the DC line's monopole to earth voltage and interpole voltage. The key overvoltage observation points in the converter and DC cable line are shown in 1–13 of Figure 3, and the information about the observation points is shown in Table 3.

TABLE 3 Information about overvoltage observation points.

Observation point	Observation point name	Type	Name
1	Grid side of the converter transformer	Phase-to-ground voltage	V1
2	Valve side of the converter transformer	Phase-to-ground voltage	V2
3	Arm reactor	Terminal-to-terminal voltage	V3
4	Bottom of the converter valve	Voltage to ground	V4
5	Converter valve	Terminal-to-terminal voltage	V5
6	Roof of the converter valve	Voltage to ground	V6
7	Outlet of the converter valve	Terminal-to-terminal voltage	V7
8	Current limiting reactor	Terminal-to-terminal voltage	V8
9	Valve side of DCCB	Voltage to ground	V9
10	Outlet of the current limiting reactor	Terminal-to-terminal voltage	V10
11	DCCB	Terminal-to-terminal voltage	V11
12	Line side of DCCB	Voltage to ground	V12
13	Outlet of DCCB	Terminal-to-terminal voltage	V13

Configuration of protection

In order to analyse the influence of DC breaking and protection strategies, as well as MOV configuration on the overvoltage characteristics of DC distribution network, three types of protection strategies for overvoltage simulation configuration are proposed as follows: OV1: The system is not equipped with protection, the DCCB remains inactive, and the system is not equipped with MOV. OV2: The system is equipped with protection, the DCCB activates, and the system is not equipped with MOV. OV3: The system is equipped with protection, the DCCB activates, and the system is equipped with MOV. The specific instructions are shown in Table 4.

TABLE 4 Simulation analysis of protection configuration.

Type	Configuration illustration
OV1	Without protection, without MOV	The system has no protection, the DCCB does not act, and the system is not equipped with MOV
OV2	With protection, without MOV	Fault occurs at AC1, AC20, AC21, AC3, V, DCv1, DCv2, DCl1, and DCl2 of the converter station	The DCCB of converter station A acts 6 ms after the fault (at 8.5 ms the DCCB breaks), the converter of converter station A is locked 6 ms after the fault, and the AC circuit breaker of converter station A breaks 56 ms after the fault
Fault occurs at DCb1 and DCb2 of converter station A	The DCCB of converter station A acts 6 ms after the fault (at 8.5 ms the DCCB breaks), the three-terminal DCCB operates 6 ms after the fault (at 8.5 ms terminal A breaks), the converter of converter station B is switched to the constant voltage mode 6 ms after the fault, the converter of converter station A is locked 11 ms after the fault, and then unlocked 56 ms after the fault
Fault occurs at AC1, AC20, AC21, AC3, V, DCv1, DCv2, DCl1, and DCl2 of converter station B/C	The DCCB of converter station B/C operates 6 ms after the fault (at 8.5 ms the DCCB breaks), the converter of converter station B/C is locked 6 ms after the fault, and the AC circuit breaker of converter station B/C breaks 56 ms after the fault
Fault occurs at DCb1 and DCb2 of converter station B/C	The DCCB of converter station B/C operates 6 ms after the fault (at 8.5 ms the DCCB breaks), the three-terminal DCCB operates 6 ms after the fault (at 8.5 ms terminal C breaks), the converter of converter station B/C is locked 11 ms after the fault, then switched to constant voltage mode for unlocking 56 ms after the fault
OV3	With protection, with MOV	The system is equipped with MOV, converter protection and DCCB operation strategy is the same as OV2

DC BREAKING OVERVOLTAGE CHARACTERISTICS

The overvoltage simulation model of a three terminal flexible DC distribution network is utilised to conduct a fault simulation analysis. This analysis explores various fault types and their responses under different control and protection strategies. The aim is to determine the overvoltage characteristics at different locations within the flexible DC distribution network and examine the breaking overvoltage characteristics during faults in the AC electric field of the converter station.

Breaking overvoltage characteristics under fault in the AC electric field of the converter station

According to Table 2, fault in the AC electric field of the converter station mainly includes four fault conditions: single-phase to ground short circuit on the AC valve side (AC1), two phase phase-to-phase short circuit on the AC valve side (AC20), two-phase to ground short circuit on the AC valve side (AC21), and three-phase to ground short circuit on the AC valve side (AC3). Since the fault characteristics of converter stations A, B and C are similar to that of converter station A, and the overvoltage characteristics of converter station B are similar to that of converter station C, only the peak overvoltage at observation points 1–13 of converter station A and 1–13 of converter station B under fault in the AC electric field of converter station A is shown in Figure 4a–d, respectively.

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As can be seen from Figure 3, in the event of a fault in the AC electric field of converter station A, if fault protection is adopted (i.e. the DCCB acts for fault isolation), the overvoltage at most observation points in the flexible DC distribution network will increase significantly. In particular, the peak overvoltage of observation point 7 of converter station A is up to 36.40 kV under the single-phase to ground short circuit fault (AC1). In addition, the application of fault protection can significantly reduce the maximum overvoltage of some key nodes in the flexible DC distribution network. This is because the three-phase to ground fault occurs on the converter transformer valve side, and the AC power supply is grounded by the converter transformer, making it impossible for the capacitor in the converter to be charged. DCCB is used to cut off the line and preventing other converter stations from charging the capacitor in the failed converter.

Breaking overvoltage characteristics under fault in the DC electric field of the converter station

According to Table 2, fault in the DC electric field of the converter station mainly includes three fault conditions: short circuit of the converter valve (V), monopole to earth fault at the outlet of the converter valve (DCv1), and interpole short circuit at the outlet of the converter valve (DCv2). Under the fault in the DC electric field of converter station A, the peak overvoltage at observation points 1–13 of converter station A and 1–13 of converter station B is shown in Figure 5a–c, respectively.

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As can be seen from Figure 4, in the event of a fault in the DC electric field of converter station A, if fault protection is adopted, the overvoltage at most observation points in the flexible DC distribution network will significantly increase. Especially, the overvoltage of observation point 13 of converter station A under the interpole short circuit fault (DCv2) at the outlet of the converter will reach 50.08 kV, with an increase of 250.4%. Additionally, the breaking overvoltage of interpole short circuit fault is higher than that of monopole to earth fault, with a maximum overvoltage of 50.08 kV. In contrast, the maximum overvoltage of monopole to earth fault is only 39.50 kV. In the event of an interpole short circuit fault, the overvoltage variation is greater under the fault protection.

Breaking overvoltage characteristics under DC line fault

According to Table 4, fault in the DC line mainly includes four fault conditions: monopole to earth fault at the outlet of current limiting reactor (DCl1), interpole short circuit at the outlet of current limiting reactor (DCl2), monopole to earth fault at the outlet of DCCB (DCb1), and interpole short circuit at the outlet of DCCB (DCb2). In the event of a DC line fault, the peak overvoltage at observation points 1–13 of converter station A and 1–13 of converter station B is shown in Figure 6a–d, respectively.

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Based on the provided figure, it is evident that the implementation of fault protection in the event of a DC line fault will lead to a notable increase in overvoltage at the majority at observation points within the flexible DC distribution network. Notably, observation point 10 at converter station B will experience a substantial overvoltage of 62.79 kV during an interpole short circuit fault (DCl2) at the outlet of the current limiting reactor. Besides, the breaking overvoltage of interpole short circuit fault is higher than that of monopole to earth fault, with a maximum overvoltage of 62.79 kV. By contrast, the maximum overvoltage of monopole to earth fault is only 36.34 kV. In the event of an interpole short circuit fault, the overvoltage variation is greater under the fault protection.

Statistical analysis

According to the 3 areas and 11 types of typical faults of converter station A, the peak values of overvoltage are scanned from the observation points 1–13 of converter stations A and B. The maximum value of overvoltage for each observation point under the two protection strategies of ‘without protection, without MOV’ and ‘with protection, without MOV’ is determined as shown in Table 5. The observation data marked in red are the maximum overvoltage at observation points 1–13 of station A and 1–13 of station B.

TABLE 5 Statistics of the maximum overvoltage of each observation point.

Observation point	Maximum overvoltage (kV)	Corresponding fault type
Without protection, without MOV	With protection, without MOV	Without protection, without MOV	With protection, without MOV
A-1	8.986	13.274	A-DCv2	A-DCb1
A-2	33.168	27.010	C-AC1	C-DCv1
A-3	23.955	21.383	A-AC3	A-DCv2
A-4	33.467	27.931	C-AC1	C-DCv1
A-5	35.410	30.834	A-AC3	A-AC3
A-6	36.174	39.492	C-AC1	A-DCv1
A-7	23.413	39.494	A-AC20	A-DCv1
A-8	9.979	32.569	A-DCv2	A-DCv1
A-9	36.251	47.331	C-AC1	C-DCb2
A-10	27.012	94.516	A-DCb1	C-DCb2
A-11	0.275	23.840	A-DCb2	A-DCl2
A-12	36.278	47.182	C-AC1	C-DCb2
A-13	27.064	94.218	A-DCb1	C-DCb2
B-1	9.753	15.877	B-AC1	B-AC20
B-2	33.892	36.125	C-AC1	A-DCv1
B-3	32.730	20.407	B-AC3	B-AC3
B-4	34.926	38.525	C-AC1	A-DCv1
B-5	46.955	29.149	C-AC3	B-AC3
B-6	36.269	38.018	C-AC1	A-DCv1
B-7	28.815	38.489	B-AC3	B-DCb1
B-8	11.772	23.216	B-AC1	C-DCb2
B-9	36.349	43.387	C-AC1	B-DCl1
B-10	28.301	77.929	B-DCb1	C-DCb2
B-11	0.349	23.866	B-DCl2	B-DCl2
B-12	36.335	38.897	C-AC1	C-DCb2
B-13	28.271	77.649	B-DCb1	C-DCb2

It can be observed from Table 5 that, if fault protection and the MOV are not adopted in the flexible DC distribution net-work, the maximum overvoltage of converter station A appears at the observation point 12 when a single-phase to ground short circuit fault (AC1) occurs in converter station B. The overvoltage is 36.28 kV and the waveform is shown in Figure 7a.

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If fault protection and the MOV are not adopted in the flexible DC distribution network, the maximum overvoltage of converter station B appears at the observation point 5 when the three-phase to ground short circuit on the AC valve side (AC3) occurs in converter station C. The overvoltage is 46.96 kV, and the waveform is shown in Figure 7b.

In the event of a flexible DC distribution network with fault protection and without MOV, the maximum overvoltage of converter station A appears at the observation point 10 when interpole short circuit at the outlet of DCCB (DCb2) occurs in converter station C. The overvoltage is 94.52 kV, and the waveform is shown in Figure 8a.

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In the event of a flexible DC distribution network with fault protection and without MOV, the maximum overvoltage of converter station B appears at the observation point 10 when interpole short circuit at the outlet of DCCB (DCb2) occurs in converter station C. The overvoltage is 77.93 kV, and the waveform is shown in Figure 8b.

Summarily, in the event of a flexible DC distribution network without fault protection and MOV, the fault in the AC electric field of the converter station leads to high overvoltage. While in the event of having protection and without MOV, DC line fault, especially interpole short circuit fault, leads to high overvoltage.

MECHANISM OF DC BREAKING OVERVOLTAGE

The occurrence of a fault in the flexible DC distribution network leads to a considerable increase in overvoltage, primarily due to the DCCB's action. This increase in overvoltage poses a significant threat to the safe operation of the system. Therefore, it is crucial to thoroughly investigate the mechanisms that generate DC breaking overvoltage. Specifically, in the absence of MOV and with fault protection in place, the highest levels of overvoltage are observed when there is an interpole short circuit fault in the DC line. This section focuses on the study of the generation mechanism behind DC breaking overvoltage. In the flexible DC distribution network, when the interpole short circuit fault occurs at 300 ms at the outlet of the DCCB (DCb2), the DCCB of converter station A acts 6 ms after the fault occurs, and the three-terminal DCCB also acts 6 ms after the fault occurs (8.5 ms after the fault occurs, the power electronic switch of the commutation branch of the DCCB is turned off, and the fault current is commutated to the energy absorption branch; 11 ms after the fault occurs, the energy is dissipated through MOV). Converter station B is switched to constant voltage mode 6 ms after the fault, and converter station A is locked 11 ms after the fault then unlocked 60 ms after the fault. The overvoltage waveform at the observation point 7 (at the outlet of the converter valve) of converter station A is shown in Figure 9.

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It can be seen from Figure 9 that the variation of DC voltage at the outlet of the converter valve of converter station A can be divided into three stages: stages a, b and c. Stage a lasts from 300 to 306 ms, stage b lasts from 306 to 311 ms, and stage c lasts from 311 to 360 ms. The variation mechanism of voltage in the three stages is described in detail below.

DC voltage variation mechanism at stage a

Stage a lasts from 300 to 306 ms. The DCCB remains closed until the DCCB acts after the interpole short circuit fault occurs. The MMC sub-module (SM) performs switching in accordance with normal modulation mode. The equivalent circuit of MMC is shown in Figure 10. The SM capacitor discharges through T1, the current of the bridge arm increases, the voltage of the capacitor drops, and the DC voltage drops.

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The DC voltage change at the outlet of converter station A is closely related to the current of converter station A's converter bridge arm and the working mode of SM. Taking phase A as an example, the current of the upper and lower bridge arm before and after the fault is <0. At this time, the input SM is in the normal working input state and the capacitor is in the discharging state.

N SMs are put into the upper and lower arms at any time. According to the capacitor voltage balance control principle, all SMs within 4 ms will be put into or removed (in engineering, about 1/5–1/2 SMs are put into or removed within 1 ms), and all SMs in each phase can be divided into two groups (each group contains N SMs). The SMs discharge alternately in turn, and it is approximately considered that the two groups of SMs discharging alternately in each phase are in parallel connection. After the fault occurs, the converter topology can be equivalent to resistance R, inductance L, capacitance C (RLC) second-order discharge circuit as shown in Figure 10b. Besides, the DC voltage U_dc at the outlet of the converter station is equal to the voltage at both ends of the impedance of the discharge circuit.

Thus, the second-order transient process in this stage can be expressed using Equation (1): 1 $${L}_{\mathrm{e}}{C}_{\mathrm{e}}\frac{{\mathrm{d}}^{2}{u}_{\mathrm{c}}}{\mathrm{d}{t}^{2}}+{R}_{\mathrm{e}}{C}_{\mathrm{e}}\frac{\mathrm{d}{u}_{\mathrm{c}}}{\mathrm{d}t}+{u}_{\mathrm{c}}=0$$ where $${L}_{\mathrm{e}}=\frac{2L}{3}+{L}_{0}$$, $${R}_{\mathrm{e}}=\frac{2R}{3}+{R}_{0}$$, $${C}_{\mathrm{e}}=\frac{6C}{N}$$. In the above simulation, L_e, R_e and C_e are the equivalent inductance, equivalent resistance and equivalent capacitance of the bridge arm, respectively, and they are 8 mH, 1 mΩ and 3 mF, respectively, where N is the number of SM, L is the bridge arm reactance, C is the SM capacitance, R is the resistance of the bridge arm, L₀ is the equivalent reactance on the DC side of the discharge circuit, u_c is voltage of equivalent capacitance and R₀ is the equivalent resistance on the DC side of the discharge circuit.

Owing to $${R}_{\mathrm{e}}< 2\sqrt{{L}_{\mathrm{e}}/{C}_{\mathrm{e}}}$$, the capacitor discharge of the SM is an underdamping oscillation process. The characteristic roots of the equation are a pair of conjugate complex numbers: 2 $${\lambda }_{1,2}=-\frac{{R}_{\mathrm{e}}}{2{L}_{\mathrm{e}}}\pm \sqrt{{\left(\frac{{R}_{\mathrm{e}}}{2{L}_{\mathrm{e}}}\right)}^{2}-\frac{1}{{L}_{\mathrm{e}}{C}_{\mathrm{e}}}}=-\sigma \pm \mathrm{j}{\omega }^{\prime }$$ where $$\sigma ={R}_{\mathrm{e}}/2{L}_{\mathrm{e}}$$, $${\omega }^{\prime }=\sqrt{1/{L}_{\mathrm{e}}{C}_{\mathrm{e}}-{\left({R}_{\mathrm{e}}/2{L}_{\mathrm{e}}\right)}^{2}}$$.

At the moment when the fault occurs, the DC voltage is U₀ and the DC current is I₀. Thus, the instantaneous value of the voltage at both ends of the capacitor, the loop current and the DC voltage U_dc can be obtained by the following: 3 $$\left\{\begin{array}{@{}l@{}}{u}_{\mathrm{c}}=A{\mathrm{e}}^{(-\sigma t)}\,\sin \left({\omega }^{\prime }t+\theta \right)\\ {i}_{\mathrm{l}}=A\sqrt{{C}_{\mathrm{e}}/M{L}_{\mathrm{e}}}{\mathrm{e}}^{(-\sigma t)}\,\sin \left({\omega }^{\prime }t+\theta -\beta \right)\\ {U}_{\text{dc}}={u}_{\mathrm{c}}+\frac{2R}{3}{i}_{\mathrm{l}}+\frac{2L}{3}\frac{\mathrm{d}{i}_{\mathrm{l}}}{\mathrm{d}t})\end{array}\right.$$ where $$\left\{\begin{array}{@{}l@{}}A=\sqrt{{U}_{0}^{2}+{\left({U}_{0}\sigma /{\omega }^{\prime }-{I}_{0}/{\omega }^{\prime }{C}_{\mathrm{e}}\right)}^{2}}\\ \theta =\mathrm{arctan}\left(\frac{{U}_{0}}{{U}_{0}\sigma /{\omega }^{\prime }-{I}_{0}/{\omega }^{\prime }{C}_{\mathrm{e}}}\right)\\ \beta =\mathrm{arctan}\left({\omega }^{\prime }/\sigma \right)\end{array}\right.$$

Because the SM capacitor discharging is an underdamping oscillation process, the DC voltage at the outlet of converter station A gradually drops. If the flexible DC distribution network has no fault protection and the DCCB is always in the closing state, the DC voltage at the outlet of the converter station will attenuate to zero.

DC voltage variation mechanism at stage b

Stage b lasts from 306 to 311 ms, and the DCCB stops action until the converter station locks. This stage can be divided into two processes according to the operating state of DCCB (1) The opening and breaking process of the DCCB is between 306 and 308.5 ms. From 306 ms, the DCCB receives the trip signal and starts to act. At 308.5 ms, the power electronic switch of the DCCB's commutation branch breaks. (2) The energy absorption process of the DCCB is between 308.5 and 311 ms. The DCCB's power electronic switch of the commutation branch opens at 308.5 ms and completes fault energy absorption at 311 ms.

Breaking process of DCCB

During the breaking process of the coupling negative pressure hybrid DCCB, the voltage at both ends of the DCCB is U_cb. The SM is switched according to the normal modulation mode. The SM capacitor is discharged through T1, the current of bridge arm increases, and the voltage of the SM capacitor drops. The equivalent circuit of MMC is shown in Figure 11a.

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The converter topology can be equivalent to the RLC second-order discharging circuit as shown in Figure 11b because the SM of the MMC is switched in accordance with the normal modulation mode in this process. The DC voltage U_dc at the outlet of the converter station is the sum of the voltage at both ends of the impedance of the discharging circuit and the voltage at both ends of the DCCB.

As the voltage U_cb at both ends of the DCCB is negligible when compared with the DC voltage U_dc at the outlet of the converter station A, the DC voltage U_dc at the outlet of the converter station still decreases gradually according to Equation (3).

Energy absorption process of DCCB

During the energy absorption process of the hybrid DCCB, the voltage at both ends of the DCCB is U_mov. The SM is switched according to the normal modulation mode. The SM capacitor is discharged through T1, the current of bridge arm increases, and the voltage of the SM capacitor drops. The equivalent circuit of MMC is shown in Figure 12a. The converter topology can be equivalent to the RLC second-order discharging circuit as shown in Figure 12b, because the SM of the MMC is switched in accordance with the normal modulation mode in this process. The DC voltage U_dc at the outlet of the converter station is the sum of the voltage at both ends of the impedance of the discharging circuit and the voltage at both ends of the MOV. The voltage U_mov at both ends of the MOV is the residual voltage of MOV, and the simulation setting is 17 kV. Considering that in the energy absorption process, the discharging loop current is relatively small, the discharging voltage at both ends of the loop impedance is small as well, which can be ignored when compared with MOV residual voltage. Hence, at the breaking of the power electronic switch of the commutation branch (308.5 ms), the DC voltage U_dc at the outlet of converter station A will increase rapidly, approximately equal to 34 kV, which is equivalent to the extreme value of the overvoltage simulated in Figure 9, verifying the accuracy of the analysis.

[IMAGE OMITTED. SEE PDF]

DC voltage variation mechanism at stage c

During the energy absorption process of the coupling negative pressure hybrid DCCB, the voltage at both ends of the DCCB is $${U}_{\text{mov}}$$. The SM is switched according to the normal modulation mode. The SM capacitor is discharged through T1, the current of bridge arm increases, and the voltage of the SM capacitor drops. The equivalent circuit of MMC is shown in Figure 12a.

Stage c lasts from 311 to 360 ms, and the converter station is locked until its unlocking. The DCCB cuts off the fault line. At 311 ms, converter station A is locked, and the AC power is continuously injected but there is no energy output path, which leads to the imbalance of input and output power of the converter station. Therefore, the SM capacitor of converter station A is in the charging state and the voltage rises.

At this stage, the bridge arm of each phase in the converter station will conduct alternating conduction according to the conduction of diode of each phase. However, because of the arm reactor, when the diode does not meet the conduction condition, the current will not immediately decrease to 0 but shows an attenuation process. When the current decreases to 0, the bridge arm will be turned off. Meanwhile, the bridge arm current gradually increases from 0 in the process of turning off to conducting. All the SMs of the conducting bridge arm work in the locked state. The diode of the non-conducting bridge arm does not meet the conducting condition, and the current of bridge arm is 0. The equivalent circuit of MMC is shown in Figure 13a.

[IMAGE OMITTED. SEE PDF]

Taking one of the conduction modes as an example, at the time of simultaneous conduction between the upper bridge arm of phase A and the lower bridge arm of phase C, the line voltage as shown in Figure 13b is calculated using Kirchhoff’s Voltage Law, and it can be obtained as follows: 4 $${u}_{\mathrm{A}}(t)+{u}_{\text{ap}}(t)-{u}_{\text{dc}}(t)+{u}_{\text{cn}}(t)-{u}_{\mathrm{C}}(t)=0$$

The solution is as follows: 5 $${u}_{\text{dc}}(t)={u}_{\text{AC}}(t)+{u}_{\text{ap}}(t)+{u}_{\text{cn}}(t)$$

In the equation, u_A(t) is the instantaneous voltage of phase A at the outlet of the converter station, u_C(t) is the instantaneous voltage of phase C at the outlet of the converter station, u_AC(t) is the instantaneous phase voltage between phase A and phase C, u_ap(t) is the instantaneous voltage of the upper arm of phase A, u_cn(t) is the equivalent capacitor instantaneous voltage of lower bridge arm of phase C, and u_dc(t) is the instantaneous value of U_dc.

Under the conduction of the upper arm of phase A and lower arm of phase C, all SM capacitors start charging, u_ap(t) = nu_ap1(t), u_cn(t) = nu_cn1(t), in which n is the number of the SM capacitor, and u_ap1(t) is the instantaneous voltage of the upper arm SM capacitor of phase A. u_cn1(t) is the instantaneous voltage of the lower arm SM capacitor of phase C and it can be known from the equivalent inverter circuit, 0 >> u_AC > −u_dc. Therefore, the following can be obtained through Equation (5): 6 $${u}_{\text{dc}}(t)={u}_{\text{AC}}(t)+n{u}_{\text{ap}1}(t)+n{u}_{\text{cn}1}(t)$$

According to Equation (6), DC overvoltage will occur during the capacitor charging process, and because of the alternating conduction of bridge arm of each phase, the overvoltage's waveform will pulsate.

During the period of 311–360 ms, the three-phase SM capacitor and the bridge arm inductor will be in alternating charging and discharging state. During the charging and discharging process, there will be overvoltage on the DC side of the converter station. When the converter station unlocks at 360 ms, the DC voltage gradually returns to the normal level.

It can be known from the above analysis that the cause of DC breaking overvoltage at the outlet of the converter station is the unbalanced power on both sides of the converter station. Specifically, the input power is greater than the output power, and the unbalanced power charges the SM capacitor of the converter station, leading to the rise of the DC voltage.

SUPPRESSION MEASURES AND VERIFICATION OF DC BREAKING OVERVOLTAGE

To ensure the safety of the equipment in the flexible DC distribution network, one effective measure is to decrease the input power of the converter station on the fault side. By doing so, the unbalanced power can be reduced, which in turn helps to suppress the occurrence of DC breaking overvoltage. This can be achieved by incorporating MOV on the DC side of the converter station and modifying the control strategy of the DCCB. The primary objective of this section is to highlight the role of MOV in mitigating DC breaking overvoltage.

Breaking overvoltage suppression measures

In the flexible DC distribution system under various typical faults, if fault protection is adopted, the overvoltage at the critical position of the system increases significantly. Referring to the overvoltage protection scheme of the traditional high voltage direct current transmission system and the flexible DC transmission grid, the flexible DC distribution grid can also use the metal oxide arrester to suppress DC breaking overvoltage.

MOV configuration scheme

The MOV configuration in flexible DC distribution network primarily considers the MOV configuration in the main converters (converter station A, converter station B, and converter station C), buck converter stations, and other key converter equipment areas.

The main converter adopts MMC structure. The key equipment to be considered in the converter area includes the interface transformer, AC connecting bus, arm reactor, converter valve, DC bus and switching equipment, and DC reactor. See Figure 14 for the MOV configuration scheme.

[IMAGE OMITTED. SEE PDF]

The protection functions of each type of MOV in the figure are as follows:

• The ‘A’ type MOV is used to protect the AC bus equipment in the converter. It should be as close as possible to the side bushing of the interface transformer system to limit the overvoltage of the primary side and the secondary side of the interface transformer;

• The ‘A₂’ type MOV is used to protect the arm reactor and the secondary side of the interface transformer, and also to protect the grounding branch of the valve side of the interface transformer;

• The ‘DB’ type MOV is used to protect the DC bus and its related equipment (such as DC switching equipment) and cooperate with the A₂ type MOV to realise the protection of the converter valve;

• The ‘DL’ type MOV, installed on the side of the DC line, is used to protect the DC bus and related equipment, and plays the role of maintaining the voltage between the two poles.

MOV parameter selection

The MOV parameters are determined using the general design method, calculated based on the charge rate, and the factors, such as the charge rate, lightning impact, operational impact protection level, and the energy of the MOV are considered.

The charge rate of DC MOV is defined as the ratio of continuous operating peak voltage continuous operating voltage to reference voltage U_ref. The selection of the charge rate must consider the stability of the MOV and the magnitude of the leakage current, the peak value of the continuous operating voltage, the component of the DC voltage, the installation position (indoor or outdoor), the influence of temperature on the volt-ampere characteristics, and the influence of pollution on the point distribution of the porcelain or silicone rubber coat of the MOV. For DC MOV, the value of 0.8–1.0 can be set according to its voltage waveform and installation position.

In order to enhance the power supply reliability of the flexible DC distribution network, it is considered that the MOV should not operate during the monopole to earth fault if it can continue to operate for a period of time. Therefore, when determining the MOV's continuous operating voltage, it is necessary to comprehensively consider the voltage at the critical position of the system under the normal operation of the system and the monopole to earth fault. The larger value under the two circumstances will be selected as the MOV's continuous operating voltage.

According to the above selection principles, the selection basis of various types of MOV parameters in the flexible DC distribution network is determined as shown in Table 6.

TABLE 6 MOV parameter selection basis.

MOV category	CCOV (kV)	Charge rate	Uref (kV)
A	8.25	0.8	10.31
A2	18.47	0.85	21.73
DB	20.05	0.85	23.59
DL	20.41	0.85	24.01

The protection level and maximum absorption energy of each MOV are shown in Table 7. Among them, the operating overvoltage protection level is selected as the residual voltage under the operating impulse current of 1 kA, and the lightning overvoltage protection level is selected as the residual voltage under 5 kA.

TABLE 7 MOV protection level and maximum absorption energy.

Parameters	Values
MOV type	A2/DB/DL
Uref (kV)	26
Protection level of operating overvoltage (kV)	40
Protection level of lightning overvoltage (kV)	45
Maximum absorption energy (kJ)	50

Verification of breaking overvoltage suppression

Utilising the overvoltage simulation model of the three-terminal flexible DC distribution network and the MOV configuration scheme above, the overvoltage characteristics of different positions in the flexible DC distribution network under the condition of ‘with protection, with MOV’ were obtained by simulating and analysing the three fault areas and 11 types of typical faults in the converter station A. By scanning the peak overvoltage at observation points 1–13 of converter station A and 1–13 of converter station B, the maximum overvoltage of each observation point under the strategy of ‘with protection, without MOV’ can be determined as shown in appendix Table A1.

Thus, comparisons of peak overvoltage at observation points 1–13 of converter station A and 1–13 of converter station B under three different protection strategies are shown in Figure 15.

[IMAGE OMITTED. SEE PDF]

The figure above illustrates that in the event of a fault in the AC electric field, DC electric field, and DC line of converter station A, if fault protection is adopted without MOV, the overvoltage at most observation points in the flexible DC distribution network will increase significantly. By comparison, when fault protection is used along with MOV configuration, the breaking overvoltage at most observation points in the flexible DC distribution network can be effectively suppressed.

In particular, in the event of a flexible DC distribution network with fault protection and without MOV, the maximum overvoltage of converter station A appears at the observation point 10 when interpole short circuit at the outlet of DCCB (DCb2) occurs in converter station B, and the overvoltage is as high as 94.52 kV. In the event of with fault protection and without MOV, the overvoltage is suppressed to 57.20 kV and drops by 60.52%. The overvoltage waveform is shown in Figure 16.

[IMAGE OMITTED. SEE PDF]

CONCLUSION

This study centres on the Zhuhai three-terminal DC distribution network as the research context. It analyses the different fault types and their dynamic characteristics while considering the system architecture and parameter configuration. Moreover, this paper explores DC breaking overvoltage characteristics, mechanism, and suppression technology, leading to the following conclusions:

• The configuration of the medium voltage DCCB and fault protection strategy is based on the system structure of a three-terminal DC distribution network. Additionally, a simulation analysis model of DC breaking overvoltage is established. This model allows for the determination of the overvoltage characteristics of the flexible DC distribution network under various protection strategies, fault types, and positions. It is observed that if fault protection is implemented (i.e. DCCB breaks for fault isolation), the overvoltage at most observation points in the flexible DC distribution network increases significantly. Furthermore, the highest DC breaking overvoltage is observed in cases of interpole short circuit faults.

• The equivalent circuit of the DCCB converter fault is established, enabling the determination of the variation of DC voltage at the outlet of the converter station by solving the equation. This aids in understanding the mechanism behind the breaking overvoltage of the DCCB. In other words, the DC breaking overvoltage at the converter station outlet is caused by unbalanced power on both sides of the station. Specifically, the input power exceeds the output power, resulting in an unbalanced power charge on the SM capacitor of the converter station, leading to an increase in DC voltage.

• The overvoltage suppression measures and a configuration scheme to reduce unbalanced power through reducing the input power of the converter station on the fault side are proposed based on MOV in order to suppress the DC breaking overvoltage. The simulation results indicate effective suppression of the breaking overvoltage at most observation points of the flexible DC distribution network. Particularly, the overvoltage at the maximum observation point 10 of converter station A is reduced from 94.52 to 57.20 kV.

These findings provide a theoretical and technical basis for the design and operation of DCCBs within DC distribution networks.

ACKNOWLEDGEMENTS

This work was supported in part by the National Natural Science Foundation of China under grant 51922062 and 52241701.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT

The data that supports the findings of this study are available in the supplementary material of this article.

Appendix

APPENDIX

TABLE A1 Statistics of the maximum overvoltage of each observation point.

Observation point	Maximum overvoltage (kV)	Corresponding fault type
Without protection, without MOV	With protection, without MOV	With protection, with MOV	Without protection, without MOV	With protection, without MOV	With protection, with MOV
A-1	8.986	13.274	11.538	A-DCv2	A-DCb1	A-AC1
A-2	33.168	27.010	23.825	C-AC1	C-DCv1	C-AC1
A-3	23.955	21.383	21.379	A-AC3	A-DCv2	A-DCv2
A-4	33.467	27.931	24.607	C-AC1	C-DCv1	A-AC1
A-5	35.410	30.834	30.836	A-AC3	A-AC3	A-AC3
A-6	36.174	39.492	27.126	C-AC1	A-DCv1	A-DCv1
A-7	23.413	39.494	36.426	A-AC20	A-DCv1	A-AC1
A-8	9.979	32.569	23.322	A-DCv2	A-DCv1	A-DCv2
A-9	36.251	47.331	28.603	C-AC1	C-DCb2	C-DCb2
A-10	27.012	94.516	57.199	A-DCb1	C-DCb2	C-DCb2
A-11	0.275	23.840	23.834	A-DCb2	A-DCl2	A-DCl2
A-12	36.278	47.182	28.452	C-AC1	C-DCb2	C-DCb2
A-13	27.064	94.218	56.896	A-DCb1	C-DCb2	C-DCb2
B-1	9.753	15.877	11.555	B-AC1	B-AC20	B-AC20
B-2	33.892	36.125	23.561	C-AC1	A-DCv1	C-DCb1
B-3	32.730	20.407	20.401	B-AC3	B-AC3	B-AC3
B-4	34.926	38.525	24.692	C-AC1	A-DCv1	A-DCv1
B-5	46.955	29.149	29.150	C-AC3	B-AC3	B-AC3
B-6	36.269	38.018	26.773	C-AC1	A-DCv1	B-DCl1
B-7	28.815	38.489	38.264	B-AC3	B-DCb1	B-AC1
B-8	11.772	23.216	22.675	B-AC1	C-DCb2	B-DCv2
B-9	36.349	43.387	42.680	C-AC1	B-DCl1	B-DCl1
B-10	28.301	77.929	63.535	B-DCb1	C-DCb2	B-DCb1
B-11	0.349	23.866	23.864	B-DCl2	B-DCl2	B-DCl2
B-12	36.335	38.897	27.646	C-AC1	C-DCb2	A-DCb2
B-13	28.271	77.649	55.292	B-DCb1	C-DCb2	A-DCb2

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