Research on the Fault-Transient Characteristics of a DC Power System Considering the Cooperative Action of a Flexible Current-Limiting Device and a Circuit Breaker

Abstract

As an effective carrier of a new energy collection, the DC power grid has low inertia and weak damping characteristics, making it essential to limit fault current and isolate the DC system. To quickly and effectively suppress fault current, a flexible current-limiting device (FCLD) is proposed, which can realize transient fault self-recovery without circuit breaker action and permanent and quick isolation of a fault. It improves the operational ability of the DC system under an asymmetric condition. First, a rectifier provides a set-slope current to each cascade inductor, so the voltage of the inductor can be clamped. Second, a controlled current source (CCS) is applied to generate inverse flux to prevent the inductor from magnetic saturation. The protection action time of the DC circuit breaker is reformulated. Finally, by considering the synergistic action of the current-limiting device, the circuit breaker, and the transient characteristics of the DC grid fault, the protection scheme of the multi-terminal flexible DC system can be formulated. To verify the validity of the proposed flexible current-limiting device, a multi-terminal flexible DC simulation platform is established, and the faults of DC lines are simulated and analyzed.

1. Introduction

A Flexible DC power grid has the advantages of large transmission capacity, low loss, and excellent safety performance. It can collect energy from the DC supply-and-demand equipment, such as the distributed energy resource, the DC load, and the energy storage device, attracting wide attention from scholars at home and abroad [1,2]. However, some of the active equipment will be off the network quickly and release energy rapidly through the small damping path when a fault occurs in the DC line. It will generate a large fault current and pose a serious threat to the safe operation of the power network [3,4,5].

To improve the toughness of the active DC power grid in response to line faults, current research focuses on joint cooperation among the DC circuit breaker, the converter, and the current-limiting device. Such cooperation can reduce the mechanical stress and the thermal stress of the disconnected functional equipment during the fault removal process and extend the protection action time of the disconnected equipment and the fault-removal capacity margin, thereby realizing the rapid isolation of the faulty line [6,7,8,9,10,11,12]. A previous study [6] integrated the resistance-inductive current-limiting device with the DC circuit breaker, which can limit the current to a certain extent and improve the dynamic recovery performance of the DC power grid. Another study [7] used modular multi-level converters to avoid the capacitors outputting DC voltage to the grid side, reducing the outlet voltage of the converter station to zero and effectively clearing the DC fault current. In [8], the flexible input of current-limiting components and self-bypass design were used to reduce the difficulty of breaking the circuit breaker. In [9,10], a hybrid DC circuit breaker with a current limiting function was used to reduce the fault-current rise rate and the impact damage of the fault current to the equipment. In [11,12], a pre-charged capacitor was used to access the fault circuit to increase the line-side voltage of the mechanical switch so that the mechanical switch could be turned off without arc and the fault could be cleared.

Although the abovementioned methods can play the roles of limiting current and isolating auxiliary fault to a certain extent, they are accompanied by a certain energy loss during the whole operation process, and they cannot quickly and completely eliminate the negative impact of the fault on the non-fault area. There has been no in-depth discussion on whether the circuit breaker can quickly perform the reclosing action again in response to a transient fault after the mechanical switch is broken without arc. To achieve quick reclosing, Refs. [13,14] proposed an adaptive reclosing scheme, which analyzed the characters of capacitive-coupling voltage; then, a fault identification criterion was constructed. However, reducing the converter output fault current by this method will inevitably weaken the DC dynamic recovery performance of the system. One study [15] presented an adaptive reclosing scheme based on pulse injection from a parallel energy-absorption module, but it applied only with a transmission line. Another study [16] proposed an adaptive reclosing scheme based on the phase characteristics, but it only worked in scenarios where the DC circuit breaker was not available.

Therefore, it is necessary to design a control method that is characterized by simple control, arc-free shutdown, and fast execution of the reclosing operation. The advantages of this method are that it can eliminate the negative impact of the fault area on the non-fault area in the DC grid, ensure the reliable operation of the DC circuit breaker in the non-fault area, minimize the impact of transient faults, and, ultimately, improve the resilience of the DC system to cope with different types of faults.

In this paper, a type of flexible DC current-limiting device that consists of a voltage-source converter and current-limiting inductors is proposed. This paper proposes a cascaded current-limiting inductor. The mechanism of magnetic saturation elimination by inverse flux is analyzed. The collaborative-action process of a current-limiting device and a circuit breaker is analyzed. The operational process of a current-limiting device under the permanent fault of a three-terminal DC system is analyzed by simulation.

2. New Type of Flexible DC Current Limiting

2.1. Topology

The proposed new FCLD topology, based on a series inductor with a clamp-voltage function, is shown in Figure 1. It can be seen from Figure 1 that the FCLD has a simple topology and is mainly composed of N inductors coupled in a series. Each series inductor is connected to the DC system after being connected in parallel with the corresponding rectifier.

In order to avoid the insufficient clamping voltage of the current-limiting inductor, the positive and negative lines at the outlet of each converter station are equipped with two current limiters that are powered by two converter stations. When one current-limiting inductor fails, the standby current-limiting device is put into service, which solves the problem of the current-limiting device being unable to provide sufficient clamp voltage due to the fault of the current-limiting inductor.

When the system is in normal operation, the FCLD realizes the no-voltage operation mode of the series inductor through its rectifier control. It can eliminate the voltage fluctuation of the current-limiting inductor that is caused by load fluctuation. When a fault occurs, the rectifier provides a set-slope linear current to the current-limiting inductor, which causes the current-limiting inductor to produce a stable DC voltage. However, due to the magnetic saturation of the current-limiting inductor, a controlled current source is added to the secondary side of the current-limiting inductor. It suppresses the magnetic flux saturation of the primary side by generating inverse magnetic flux to ensure the stable voltage of the primary current-limiting inductor.

2.2. Design of Application Layer Based on Hybrid Algorithm

According to the operational requirements of the FCLD, Figure 2 shows the block diagram of the control system of a single FCLD. Since the current-limiting device is connected in a series with the line, the voltage of the current-limiting inductor is controlled at 0 V when there is no fault, and the voltage of the current-limiting inductor is set to the default value when a fault occurs. Compared with the existing methods, this paper considers the combination of voltage differential and undervoltage detection methods to improve detection speed and accuracy [17].

According to Figure 2, when the DC system is operating normally, the external output voltage of the FCLD is 0 V. Therefore, the application layer output reference voltage u_{c_ref} is set to 0. When a fault occurs, the DC-side voltage changes instantaneously, and the voltage differential component presents a maximum value. According to the parameters of the DC system, different fault types, fault locations, transition resistances, and the influencing factors of the voltage differential component are determined. The minimum value T in the regular interval is used to set the control criterion [17,18]. If the voltage differential component is greater than the minimum value T, the trigger signal appears and it is kept for t* seconds (t* is greater than the whole process time of the circuit breaker operation). Fault type cannot be accurately identified according to an extreme value criterion, so it is necessary to carry out a secondary undervoltage judgment for the control input [17].

Because the fault circuit of the DC system can be equivalent to a second-order circuit, if the FCLD is not put into the converter station (as shown in Figure 1—f is the fault location), the discharge voltage of the outlet capacitor can be expressed as follows:

$$\{\begin{array}{l}{u}_{\mathrm{c}}=e^{-\frac{R_{line\_1}}{2L_{line\_1}}t}\sqrt{{\left(\frac{U_0{R}_{line\_1}}{2\omega L_{line\_1}}-\frac{I_0}{\omega C}\right)}^2+U_0^2}\sin \left(\omega t+\phi \right)\\ \phi =\arctan U_0/\left(\frac{U_0{R}_{line\_1}}{2\omega L_{line\_1}}-\frac{I_0}{\omega C}\right)\\ \omega =\sqrt{1-(C{L}_{line\_1})-R_{line\_1}/2L_{line\_1}}\end{array}$$

(1)

U₀ and I₀ are the initial values of the fault voltage and current at the output port of the DC converter station, and u_c is the discharge capacitor voltage at the output port of the converter station. (R_{line_1}/2L_{line_1}) is the voltage attenuation coefficient.

As can be seen from Formula (1), due to the large voltage attenuation coefficient of the general DC line, there is a delay of several milliseconds between the capacitor discharge and the judgment threshold in undervoltage protection, so judgment at this stage can be carried out simultaneously with an extreme value judgment. When the positive and negative voltages are both lower than 0.9 times their own voltage ratings (when the DC system voltage is as low as 90% of its rated value, it is considered that there is a voltage sag problem) and when (∆u/∆t) > T is established at the same time, it is determined that an inter-electrode fault has occurred on the DC side. The positive and negative current-limiting application layer output reference voltage u_{c_ref} is set to u_cn. Then, the positive and negative capacitor voltage of the output of the DC side is raised to the rating value, so that the fault area is completely isolated. The fault current in the whole dynamic process is obviously suppressed. When either the positive or the negative output capacitor voltage is lower than 0.9 times its rated value, it is determined that a positive or negative ground fault has occurred on the DC side. It is necessary to adjust only the output reference voltage of the positive or negative current-limiting the application layer to u_{c_ref} = u_cn. The output reference voltage of the non-fault current-limiting application layer maintains u_{c_ref} = 0.

At the same time, in order to realize the coordination between the FCLD and the circuit breaker, we adopted adaptive adjustment to the output reference voltage u_{c_ref} of the application layer, and its specific control structure is shown in Figure 2. The current limiter adopts model predictive control [19], and its control method is shown in Figure 2.

The adaptive method of this paper takes the line current as the reference value, and outputs the regulated voltage Δu_{c_ref} through the adjustment coefficient K_ad. Because the adaptive adjustment control can correct the clamping voltage of the current-limiting device, the line current during the fault quickly drops to around 0 A. This avoids the tedious process of manual testing and realizes the automatic correction of the clamp voltage and the zero-crossing of the circuit-breaker current.

2.3. Core Saturation Suppression

In order to solve the magnetic saturation problem of the inductor, we eliminated the magnetic saturation of the primary-side inductor by generating reverse flux through the secondary-side controllable current source, based on the primary- and secondary-side magnetic linkage relationship of the closed-loop iron core [20].

Figure 3 shows the magnetic circuit diagram of the closed-loop iron core. It can be seen from Figure 3 that the primary-side flux linkage equation can be expressed as follows:

$$\{\begin{array}{l}{\psi }_1=N_1{\phi }_1=N_1{L}_1{I}_1\\ e_1=\mathrm{d}{\psi }_1/\mathrm{d}t=N_1\mathrm{d}(L_1{I}_1)/\mathrm{d}t\end{array}$$

(2)

where ${\psi }_1$ is the primary-side total magnetic flux, $e_1$ is the primary-side voltage, ${\phi }_1$ is the single-turn coil magnetic flux, N₁ is the number of primary-side winding turns, and I₁ is the primary-side current. When the controlled current source ki₁ is added to the secondary side, the impedance value of the primary-side current-limiting inductor is as follows [20,21]:

$$L_1=\frac{N_1^2{S}_1}{l}\left(\frac{B}{H}-\frac{N_2\lambda i_1-N_1{i}_1}{N_1}\frac{\mathrm{d}(\frac{B}{H})}{\mathrm{d}{i}_1}\right)$$

(3)

where N₂, S₁, l, B, and H are coil windings, cross-sectional area, magnetic circuit length, magnetic field density, and magnetic field strength, respectively. N₂, S₁, and l are the inherent properties of the closed-loop iron core inductor coil.

According to Equation (3), when the secondary winding is affected by a controlled voltage source, the ratio of B and H is changed to ensure that the primary winding is in an unsaturated state.

When the secondary side of the closed-loop iron core generates inverse magnetic flux before the magnetic flux is saturated, the total magnetic flux on the primary side is as follows:

$${\psi }_1^{*}={\psi }_1-{\psi }_2=B\ast S_1$$

(4)

Figure 4 shows the change curves of B-H and μ-H. As can be seen from Figure 4, under the compensation effect of the secondary-side controlled current source, the saturation state of the primary winding is eliminated. The closed-loop iron core has the ability of self-adaptive adjustment. When the primary winding is about to reach the saturation state, the value of the controlled current source of the secondary winding will be increased, and the inverse magnetic flux will be generated to eliminate the saturation state of the primary winding. When the fault time is too long, the saturation state of the current-limiting inductor can be eliminated through multiple compensations, and the process of the compensations can be seen:

(1) If the inverse magnetic flux on the secondary side reduces B* to a small value, the magnetic flux saturation of the closed-loop iron core disappears, and the primary-side current continues to increase linearly. At this time, since the B-H curve (as shown in Figure 4) can be approximately regarded as a linear increase, L₁ is assumed to be constant. In this case, the inductance voltage can be obtained, as follows:

$$\begin{array}{l}{e}_1=\frac{N_1^2{S}_1}{l}\left(\frac{B}{H}-\frac{N_1{i}_1-N_2\lambda i_1}{N_1}\frac{\mathrm{d}(\frac{B}{H})}{\mathrm{d}{i}_1}\right)\frac{d{i}_1}{dt}\\ e_1=\frac{N_1^2{S}_1}{l}\frac{B}{H}\frac{d{i}_1}{dt}\end{array}$$

(5)

It can be seen from Formula (5) that only the linear change of i₁ can make the magnetic flux saturation disappear. Figure 5a,b show the current of the flexible current limiting inductor without and with the addition of the inverse flux at different clamp voltages. Figure 5c shows that when the clamp voltage increases, the change in current slope also increases.

(2) In order to prevent the primary- and secondary-side current from being too large within the set time, the secondary-side inverse magnetic flux eliminates the magnetic flux saturation in the early stage of the fault, and the magnetic flux saturation problem still exists in the later stage of the fault. Then, the primary current at the later stage of the fault remains at a stable value, as shown in Figure 5c. Therefore, at this time, it is only necessary to maintain the set value by adjusting the primary-side current-limiting inductance L₁. The primary-side voltage is as follows:

$$e_1=-\frac{N_1{i}_1-N_2\lambda i_{1}B}{N_1}\frac{\mathrm{d}(\frac{1}{H})}{dt}$$

(6)

In the saturated state, B remains unchanged as H increases, so

$$e_1=\frac{N_1^2{S}_1{i}_{1}B}{l}\frac{d\frac{1}{H}}{dt}$$

(7)

According to Equation (7) and the definition formula of magnetic field strength H = N₂i₂/l, the λ of the secondary-side controlled current source can be obtained as follows:

$$\lambda =\frac{N_1^2{S}_{1}B}{e_1{N}_{2}t}$$

(8)

3. Synergistic Effect of Flexible Current Limiting and DC Circuit Breaker

3.1. Analysis on the Synergistic Process of Current-Limiting Inductor and DC Circuit Breaker

The studies in [5,22] analyzed the transient characteristics of the bipolar fault current of the DC power grid with a current-limiting inductor, and divided the whole operation process into six stages, as shown in Figure 6.

If the synergistic effect of the current-limiting inductor and the circuit breaker is fully considered in this operation process, the transient current equation of a DC power grid system with N converter stations in the case of bipolar fault can be expressed as Formula (9) [22,23,24,25]:

$$\{\begin{array}{l}A·u=\underset{\mathrm{Level}\_\mathrm{IV};\mathrm{V}}{\underbrace{\begin{array}{l}\underset{\mathrm{Level}\_\mathrm{II};\mathrm{III}}{\underbrace{\underset{\mathrm{Level}\_\mathrm{I}}{\underbrace{R·i_F+L_{line}·i_F}}+{\left[u_{MF\_1},u_{MF\_2},0,\cdots \right]}^T}}\\ +{\left[u_{M\mathrm{B}\_1},u_{M\mathrm{B}\_2},0,\cdots \right]}^T\end{array}}}\\ u=C·i_F\\ u_{MF\_1}=L_{F\_1}d(i_{F\_1}-i_{MOA\_1})/dt\\ u_{MF\_2}=L_{F\_2}d(i_{F\_2}-i_{MOA\_2})/dt\end{array}$$

(9)

where u is the node capacitance voltage matrix; A is the association matrix of branches and nodes; i_F is the branch current matrix; R is resistance matrix; L is inductance matrix; C is capacitance matrix; i_{F_1} and i_{F_2} are the current on both sides of the fault line respectively. i_{MOA_1} and i_{MOA_2} are the metal oxide arrester (MOA) current of the current-limiting inductor on both sides, respectively. L_{F_1} and L_{F_2} are the inductances of the current-limiting inductor on both sides, respectively. U_{MF_1} and u_{MF_2} are the voltages of the current-limiting inductor. U_{MB_1} and u_{MB_2} are the voltages of the MOA in the DC circuit breaker. According to Formula (9) and Figure 6, if the above current-limiting and isolation methods are adopted when bipolar faults occur in the N-terminal DC system, the following problems exist in the six stages.

The first stage is from the occurrence of a DC fault to the input stage of the current-limiting inductor. The time for this stage is 3.5 ms [5,17]. In this stage, the fault current and the DC line loss increase.

The second stage is from the time when the current-limiting inductor begins to operate to the time when the MOA on one side of the fault line exits. The time is restricted by the V-I characteristic of the MOA. In this stage, although the MOA is triggered to absorb part of the energy, it will prevent the current-limiting inductor from generating overvoltage. The energy loss is obvious, and there is still a negative impact on the non-fault areas.

The third stage is from the time when the fault current-limiting MOA on the other side is activated until the MOA on both sides of the fault current-limiting inductor is withdrawn. The time is also restricted by the V-I characteristics of the MOA. The negative effects of the fault area and the energy loss still exist in this stage.

The fourth stage is when the current-limiting inductor is fully put into operation. Combined with the time of the second and third stages, the total time is about 0.5 ms to 1 ms. In this stage, the fault current is slightly reduced, but the energy loss and the negative influence of the fault area are similar to those in the second and third stages.

The fifth and sixth stages are when the DC circuit breakers on both sides start to cut off the fault current. The two stages include the MOA action of the circuit breakers on both sides. The time is about 2 ms [25]. In this stage, the fault current is cleared, but there is an MOA energy loss.

According to the above analysis, when the DC system with the traditional current-limiting inductor responds to the DC line two-pole fault, the process takes about 6 ms to 6.5 ms, during which there is an energy loss, and the negative impact of the fault area on the non-fault area cannot be eliminated [5]. If the time of the whole current-limiting operation process is taken as the reference, when dealing with a “transient fault” with a fault duration greater than 4.5 ms, the line protection is bound to act, increasing the number of switching actions and shortening its working life.

3.2. Analysis on the Synergistic Process of Flexible Current Limiting and DC Circuit Breaker

According to Figure 6, there is an obvious power loss in the whole process of cooperative protection between traditional current limiters and circuit breakers [17], and the system self-recovery without the circuit breaker cannot be realized through the auxiliary role of the traditional current-limiting device. The FCLD proposed in this paper uses differential undervoltage [26] and its own secondary undervoltage monitoring to enable it to operate instantaneously. By adjusting the u_{c_ref} control system, the DC output voltage of the converter station can be rapidly increased, the fault current can be suppressed, the fault type can be identified, the permanent fault can be quickly isolated, and the instantaneous fault can be eliminated without circuit breaker action.

After the flexible current limiter is added to the DC system, the transient current equation of a DC power grid system with N converter stations under the bipolar fault can be expressed as follows:

$$\{\begin{array}{l}A·u=\underset{\mathrm{level}\_\mathrm{II}, \mathrm{level}\_\mathrm{III}}{\underbrace{\underset{\mathrm{level}\_\mathrm{I}}{\underbrace{R·i_{\mathrm{F}}+L_{line}·i_{\mathrm{F}}}}+{\left[u_{\mathrm{CLD}\_1},u_{\mathrm{CLD}\_2},0,\cdots \right]}^T}}\\ u=C·i_{\mathrm{F}}\\ u_{\mathrm{CLD}\_1}=L_{\mathrm{F}\_1}\frac{d{i}_{\mathrm{F}\_1}}{dt}\\ u_{\mathrm{CLD}\_2}=L_{\mathrm{F}\_2}\frac{d{i}_{\mathrm{F}\_2}}{dt}\end{array}$$

(10)

U_{CLD_1} and u_{CLD_2} are the voltages of the FCLD. Problems existing in the six stages of traditional current limiting and isolation can be solved by the FCLD. The whole process of synergistic action between the proposed FCLD and the DC circuit breaker is shown in Figure 7.

The first stage is from the occurrence of the DC fault to the full operation of the current-limiting inductor. In this stage, the fault type is identified through undervoltage detection, the reference voltage of the application layer is adjusted, and the FCLD on both sides is operated. In the case of permanent fault, the time length of starting the FCLD is controlled by the attenuation coefficient of the capacitor voltage of the converter station. The FCLD has no energy loss and completely eliminates the negative impact of the fault area on the non-fault area. The time of the current limiting is shortened, compared with the traditional method.

It can be seen from Formula (10) that when the sum of the voltage of the current-limiting device and the impedance voltage of the line is greater than the voltage at the outlet of the converter station, the current of the DC system will continue to decrease until the current passes zero.

The second stage: By adjusting the control objectives of FCLD application layer, the permanent and transient faults of the system can be distinguished according to the output current variation characteristics of the DC circuit breaker. In this stage, there is no energy loss and no negative impact on the fault area. At this stage, the voltage of the circuit breaker is expressed as follows:

$$u_{\mathrm{DCCB}}=A·u-\left\{R·i_{\mathrm{F}}+L_{line}·i_{\mathrm{F}}+{\left[u_{\mathrm{CLD}\_1},u_{\mathrm{CLD}\_2},0,\cdots \right]}^T\right\}$$

(11)

The third stage: According to the line current feedback process in Figure 2 and Formula (11), the sum of the voltage of the FCLD and the line impedance voltage is equal to the outlet voltage of the converter station, and the voltage of the DC circuit breaker is zero. Within t* time, if the output current of the current-limiting device has the feature of fault disappearance, the normal working state is restored. Otherwise, the DC circuit breaker is switched off. After that, the FCLD exits the current-limiting state so that the fault line of the DC system can be switched off without arc under the condition of permanent fault.

This stage can improve the flexibility of the original traditional current-limiting device and the circuit breaker. The energy loss and negative impact of the fault area are the same as those in the second and third stages.

The fourth stage: The FCLD on both sides feeds the stored energy into the power grid through its rectifier. The input current of the rectifier is controlled by the energy feedback time. In this stage, the fault is cleared without energy loss.

According to the above four stages, the FCLD can significantly suppress the fault current and ensure that the output voltage of the converter station stays at the rated voltage and there is no voltage-sag problem. The negative impact of the fault area on the non-fault area is completely eliminated. Compared with the traditional six stages, the method proposed in this paper can identify instantaneous faults and greatly reduce the number of circuit breaker reclosing actions. Because the saturation problem of current-limiting inductance is eliminated by the inverse flux of the controllable power supply, the current-limiting operation time t* can be set according to the actual protection requirements of the system.

4. Simulation Analysis

In order to verify whether the new FCLD can assist the DC system to achieve fault current suppression and fault area isolation, Matlab/Simulink simulation software was used to build a simulation platform of a DC ± 5 kV distribution network system with three terminals, as shown in Figure 8. The voltage source converter (VSC1) is the power end, and VSC2 and VSC3 are the load ends.

Table A1. System parameters of three terminal DC distribution network.

	Converter Station 1	Converter Station 2	Converter Station 3
Rated Capacity of Converter Station (MV·A)	20	10	10
DC Voltage/kV	±5	±5	±5
DC Capacitance Value/mF	4	2	2
AC Reactance Value/mH	50	70	70
Smoothing Reactor/mH	20	20	20
R	Constant Voltage	P/Q	P/Q
Parameter	Value	Parameter	Value
R12/R13/R14/R23/R24/R34	0.08/0.08/0.08/0.08/0.08	R1f/R2f	0.02/0.08
L12/L13/L14/L23/L24/L34	5 mH/5 mH/5 mH/5 mH/5 mH/5 mH	L1f/L2f	1 mH/4 mH

and

Table A2. FCLD system parameters.

Parameter	Value	Parameter	Value
ku_P	1	L1I	0.1 mH
ku_I	500	L2I	1 mH
R	0.15	n	5
L	1.5 mH	k	10
Rc	0.5	C	10
a	100 ms	tb	100 ms
t*	400 ms

in Appendix A provide the relevant simulation parameters of the DC system. According to the normal operation standard of the international DC distribution network system, the judgment criteria of whether the line fault area is completely eliminated are set: (1) During the fault, the system voltage must not be lower than 90% of the rated voltage, and the fault line current must not exceed the rated current of the circuit breaker. (2) The fault inrush current does not exceed 10 times the rated current of its circuit breaker. The fault stable current does not exceed 1 time the rated current of its circuit breaker. (3) The DC system runs rapidly and stably after the line fault, and the maximum voltage fluctuation of DC bus satisfies ΔU_N ≤ 10% U_N during the recovery process, and there is no distorted fluctuation current.

4.1. Comparative Analysis of Current-Limiting Effect

In order to analyze the synergistic effect of the new FCLD and the circuit breaker, the current-limiting effects of the superconducting current-limiting device and the FCLD without the coordinated action of the circuit breaker are compared. Taking the interpole fault of the three-terminal DC system as an example, the simulation comparison diagram is shown in Figure 9.

It can be seen from Figure 8 that the peak value of the fault current can reach 550 A when an inter-pole fault occurs without a current-limiting inductor. The peak value of the fault current with the superconducting current-limiting inductor is up to 350.6 A, which is 36.25% lower than that without the superconducting current-limiting inductor.

Table A3. Comparison of two kinds of current limiter.

	Superconducting Current-Limiting Inductor	Flexible Current-Limiting Inductor
Cost	USD 2,500,000	USD 250,000
Peak fault current	350.6 A	85.7 A
Time of the whole operation process	>200 ms	35 ms
Device applications	Interpole faults	Interpole faults/pole to ground fault
Arc	Circuit breaker break-off with arc	Arc free

compares the superconducting current limiter and the flexible current limiter in terms of economy and current-limiting effect.

When an FCLD is installed, the peak current of the fault line is suppressed to 85.7 A, which is 84.4% lower than the fault current without the current-limiting inductor and 75.6% lower than that with the superconducting current-limiting inductor. Because the clamping voltage of the FCLD can be flexibly adjusted according to the line current, it can be seen from Figure 9 that without the circuit breaker, the current in the faulty line is held steadily at zero. Compared with the superconducting current-limiting inductor, which only suppresses the faulty line current, the FCLD can provide a new breaking environment for the DC circuit breaker and realize zero-current and arc-free breaking.

4.2. Transient Analysis of Interpole Faults of Transmission Lines

(1)

Permanent failure

When t = 0.5 s is set, a permanent fault occurs between the poles at position f₁ and position f₂ of line_1–2, respectively. As shown in Figure 8, t_a is set to 10 ms and t* is set to 50 ms. The clamping voltage of the positive FCLD on the VSC1 output terminal can be seen in Figure 10.

From the simulation results in Figure 10 and Figure 11(a₁–a₃) and, it can be seen that under an inter-pole fault, the voltage differential component instantly activates the FCLD at each port of the converter station, so the FCLD clamping voltage on both sides of line_1–2 can take effect quickly. Figure 11(a₁–b₃) show the output voltage and the output current curve of the DC system, the VSC1 power supply terminal, and the VSC2 and VSC3 load terminal ports. Figure 11(c₁–c₃) provides the current variation curves of the FCLD on both sides of the fault position. The positive and negative output voltages at each port of the DC system are kept at ±5 kV within 0.506 s, and the voltage fluctuation of each port does not exceed 1 kV. That is, the voltage has no sag problem. Compared with the DC system without the current-limiting inductor, the output voltage of each port drops to 0 V when an inter-pole fault occurs. The installation of the current-limiting inductor effectively solves the problem of the voltage sag of the DC system when an inter-pole fault occurs.

As can be seen from the comparison of the curve changes before and after the installation of the current-limiting inductor in Figure 11(b₁–b₃), the proposed current-limiting technique suppresses the inrush current caused by the line fault in fault position f₁ and position f₂. When a permanent fault occurs at position f₁ and position f₂, due to the action of the current-limiting inductor, the peak fault current of VSC1 is suppressed from 654.3 A and 816.6 A to 147.7 A and 173.2 A, respectively, the peak fault current of VSC2 is suppressed from −130.1 A and −130 A to 54.63 A and 27.58 A, respectively and the peak fault current of VSC3 is suppressed from −107.1 A and −128.1 A to 53.96 A and 26.34 A, respectively. The surge current during the fault is effectively suppressed, and the fault current is quickly suppressed to below 200 A.

As can be seen from the current change curve of the FCLD terminal in Figure 11(c₁–c₃), when the current-limiting inductor starts normally, the line current is made to cross zero at t = 0.533 s and t = 0.538 s at the positions f₁ and f₂, respectively, and the DC circuit breaker is switched off at the moment when the fault current passes zero so as to realize the arc-free shutdown of the DC circuit breaker and the rapid isolation of the fault line. When the power is supplied by the normal line, the current on this line increases.

(2)

Instantaneous failure

When t = 0.5 s is set, a transient fault occurs between the poles at position f₁ and position f₂ of line_1–2, respectively. As shown in Figure 8, t* and t_a are set to 50 ms. Figure 12 (a₁–b₃) show the output voltage and output-current curve of the DC system VSC1 power supply terminal and the VSC2 and VSC3 load terminal ports. Figure 11(c₁–c₃) provides the current variation curves of the FCLD on both sides of the fault position.

According to Figure 12(a₁–a₃), inter-pole faults occur at position f₁ and position f₂ without the current-limiting inductor, the peak-to-peak values of VSC1’s output voltage are 4209 V and 5914 V, respectively, and the peak-to-peak values of VSC2’s output voltage are 13,069.1 V and 12,939.1 V, respectively. The peak-to-peak output voltages of VSC3 are 12,679 V and 12,999 V, respectively. The positive and negative voltages of each output port of the DC system at the time of inter-pole failure are kept at ±5 kV at 0.506 s through the rapid rise of the clamp voltage of the FCLD, so that the voltage fluctuation of each port does not exceed 1 kV and the voltage-sag problem under the condition of failure is suppressed.

It can be seen from Figure 12(b₁–b₃) that when a unipolar fault occurs at position f₁ and position f₂ of the DC system line_1–2, and the DC system is not equipped with a current-limiting inductor, the peak fault current of the VSC1 output port within 50 ms reaches 506.1 A and 504.7 A, respectively, the peak-to-peak value of fault current of VSC2 output port reaches 283.8 A and 284.3 A, respectively, and the peak-to-peak value of fault current of VSC3 output port reaches 273.9 A and 273.9 A, respectively. The proposed current-limiting technology can rapidly increase the FCLD clamping voltage to suppress the inrush current and suppress the peak current of the VSC1 output port to 153.7 A and 177.2 A, respectively, when the f₁ and f₂ faults occur and suppress the peak current of the VSC2 output port to 29.7 A and 47.8 A, respectively, when the fault occurs. The peak-to-peak values of the VSC3 output port fault current are reduced to 28.3 A and 50.3 A, respectively.

From the current change curve of the FCLD terminal in Figure 12(c₁–c₃), it can be seen that when an inter-pole fault occurs, the current of the faulty line is quickly suppressed, and the current of the faulty line is kept at the normal system level after 34 ms. Therefore, the DC system can smoothly proceed through the inter-pole fault continuous process without the action of the circuit breaker and realize self-recovery.

Under normal operation of the three-terminal DC network, the two load sides are always operating symmetrically, due to the parameter setting of load–source–load. The current of the two source–load transmission lines is almost equal, and the current of the load–load transmission line is almost zero.

It is assumed that a short-circuit fault occurs in one of the source–load transmission lines in the three-terminal network, and the balance of the three-terminal DC network is destroyed and the voltage symmetry of the two load sides is broken. The fault line voltage is raised by a current-limiting device, so that the DC line current of the fault is quickly increased and the voltage on the load side is kept stable.

5. Conclusions

In view of the defects existing in the whole process of the synergistic action between the circuit breaker and the current limiting inductor in the existing DC system, this paper proposed a new FCLD suitable for the DC power grid, and we draw the following conclusions via theoretical analysis and simulation verification:

(1)

By introducing reverse magnetic flux compensation of the controllable current source, the FCLD current-limiting reactance can obtain a stable clamping voltage. It can achieve obvious suppression on the fault current. It can eliminate the negative impact of the fault area on the non-fault area and ensure that distributed power sources in the network will not be disconnected due to voltage sags.

(2)

The cooperation of the FCLD and the DC circuit breaker can realize the circuit-breaker close without arc. The device can eliminate the negative impact of the fault on the non-fault area and realize the arc-free shutdown of the permanent-fault DC circuit breaker. Through the identification of permanent fault and transient fault, the circuit breaker action can be prevented when an instantaneous fault occurs. It can reduce the times of the circuit breaker action, the instantaneous-fault DC circuit breaker action probability, and the user power-loss rate.

(3)

According to the control scheme and the simulation results of the coordinated action of an FCLD and a DC circuit breaker, the FCLD proposed in this paper prolongs the protection action time of the circuit breaker and greatly reduces the interruption requirements of the DC circuit breaker. Furthermore, the validity of the proposed FCLD is verified, and a new protection idea is provided for the practical application of DC-system engineering.

(4)

The FCLDs can adjust the internal voltage of the system to maintain symmetrical operation of the system in the event of asymmetrical operation of the DC system.