Fast single‐end line protection method for the meshed multi‐terminal HVDC grid

In view of the short-circuit fault characteristics, the protection technique of the dc lines limits the development of the modular multi-level converter (MMC)-based HVDC grid in a large extent. This study derives the calculation formulas of the transient voltages of internal and external faults and proposes a single-end protection scheme based on the transition period (TP) from the abrupt changing point to the first extreme point of the fault voltage. Due to the current-limiting reactors, the TP of the internal fault is much shorter than that of the external fault, which is used to discriminate internal fault from external fault. A four-terminal symmetrical bipolar HVDC grid based on MMC is modelled using PSCAD/EMTDC, and simulation results demonstrate the validity of the new proposed dc transmission line protection method.


Introduction
Half-bridge-based modular multi-level converters (HB-MMCs) are becoming widely used in the flexible HVDC systems because of their huge advantages [1][2][3], and these will have a great chance in the near future to show their superiority in large-scale meshed multi-terminal flexible HVDC grids [4]. However, the protection system limits the development of the meshed HVDC grids based on HB-MMCs in a large extent [5][6][7].
For a large-scale meshed multi-terminal HVDC grid, in the event of a dc fault, it is the best protection choice to isolate the faulty branches by opening the dc circuit breakers (CBs) that are connected to the faulty branches. However, the fault current rises with a high speed, and the peak value is quite large, which endangers the converter equipment and leads to high stresses on dc CBs. The development of the single-end fast protection principle is essential, which do not need signal transmission from one end to the other and saves much time.
Nowadays, the protection technology of the meshed HVDC system develops fast, and many protection principles have been proposed. The protection method proposed in [7] is based on the change rate of the dc reactor voltage, while the voltage change rate measured at the line side of the current limiting reactor is used in [8] to discriminate internal fault from external fault. However, a voltage-derivative-based protection method is much affected by large fault resistance.
A single-end line protection algorithm based on the detection of the incident traveling wave is presented in [9], with the advantage that the incident wave is independent of the boundary conditions at the line terminal, while in [10] a complex method based on the first current wave on both poles of each link is used to provide fault identification for the symmetrical monopole system. However, these protection schemes may not be so reliable when the transmission line is very short, and the reliability of travellingwave-based protection is much affected by the fault resistance [11].
From the above analysis, it could be seen that the existing protection methods based on the detection of voltage and travelling wave are highly affected by large fault resistance. Besides, the operation of external dc CBs and the reversal of power flow could also influence the reliability of the protection. Also, most of the current protection methods are only applicable for monopole HVDC systems, while a perfect protection method for meshed symmetrical bipolar HVDC systems has not been proposed.
This paper presents a novel single-end transmission line protection scheme based on the transition period from the abrupt changing point to the first extreme point of the fault voltage in the meshed symmetrical bipolar HVDC grid, and takes the positive-toground faults as examples to introduce the method and prove the effectiveness of it.

Analytical solution for the dc fault voltage
Take the Zhangbei four-terminal HVDC grid that will be built in China as an example to illustrate the calculation process of the fault voltage. Fig. 1 shows the one-line-diagram of the project, in which converters 1, 2, 3 and 4 refer to converter stations Zhangbei, Fengning, Kangbao and Beijing, respectively. F 1 , F 2 and F 3 are all metallic positive-pole-to-ground short-circuit faults, and they occur at the right end of the Line 1, the busbars of converter station 2 and converter station 1, respectively. T 12 , T 21 , T 13 etc. are the terminals of transmission lines and are the connection points of the dc PTs and CTs.
Due to the discharging characteristic of the meshed HVDC grid as a short-circuit fault occurs, the total time of fault detection and fault location discrimination should be within several milliseconds. For the HB-MMC-based HVDC grid, in the first several milliseconds, the main discharging elements are the sub-module capacitors as a short-circuit fault occurs [5]; hence, the ac side discharging effect could be neglected when analysing the dc fault voltage in the first few milliseconds.
The positive-pole-to-ground voltage of the point of T 12 is illustrated here to analyse the fault voltage. When F 1 and F 2 occur, the discharging current of all of the converter stations would flow through T 12 , but through the discharging circuit analysis, what could be found is that the main discharging converter station is station 1, because there are less current-limiting reactors and shorter transmission lines between the fault point and the converter station 1 compared with the other stations. Thus, only converter station 1 is considered in the discharging circuit to simplify the calculation process. With the same analysis method, only converter station 2 is considered as F 3 occurs.
In this paper, Laplace transform is used in the calculation process of the fault voltage. For the simplification of the calculation, superposition principle is used, in which the calculation process of non-zero initial state is replaced with the zero initial state. That is, the initial current and voltage of the reactor and capacitor of the additional equivalent circuit are set to be zero. Expressing the voltage of the additional equivalent circuit, taking the inverse Laplace transform, and then adding the initial voltage value, and the fault voltage could be obtained.

Internal fault
As F 1 occurs, the additional equivalent operational circuit is shown in Fig. 2, where p is the complex arithmetic symbol and L T is the summation of L B and L S . L B is the value of the current limiting reactor, while the calculation formulas of L S and C S are shown as follows: where L A and C SM are the values of arm reactor and sub-module capacitor, respectively, and N is the number of sub-modules in each bridge arm. The transmission line makes use of the distributed parameter model, and U 1 , I 1 and U 2 , I 2 are the complex frequencydomain voltages and currents of T 12 and the fault point, respectively, satisfying the following equation: where l is the length of Line 1. The expression formulas of γ and Z c are shown as where R 0 , L 0 , G 0 and C 0 are the resistance, inductance, conductance and capacitance of dc transmission lines per kilometre From Fig. 2, it could be found that U 1 and I 1 also satisfy (5). From (2) and (5), (6) could be obtained, which is the voltage expression of T 12 of the additional equivalent circuit in a complex frequency domain. Taking the inverse Laplace transform of U 1 and then adding the initial voltage, the voltage of u 1 as F 1 occurs could be obtained.

Forward external fault
As F 2 occurs, the additional equivalent operational circuit is shown in Fig. 3,and the voltages and currents of the two side of the transmission line is still satisfy (1), and U 1 , I 1 and U 2 , I 2 satisfy (5) and (7), respectively: and the expression of U 1 is shown as The expressions of Z 1 and Z 2 in (8) are given in (9) and (10), respectively: Taking the inverse Laplace transform of (8) and then adding the initial voltage u 0 , the voltage u 1 as F 2 occurs could be obtained.

Backward external fault
As F 3 occurs, the main discharging converter is converter station 2, and the additional equivalent operational circuit is shown in Fig. 4, in which U 1 , I 1 and U 2 , I 2 satisfy (11) and (12), respectively: From (2), (11) and (12), (13) could be obtained as Also, in (13), the expressions of Z 3 and Z 4 are given in the form of (14) and (15), respectively: Taking the inverse Laplace transform of (13) and then adding the initial voltage of T 12 , the voltage u 1 as F 3 occurs could be obtained.

Fault discrimination criterion
The parameter values of converter stations and transmission lines of the MMC-based Zhangbei four-terminal HVDC grid are shown in Table 1. Substituting the parameters with real numbers and taking the reverse Laplace transform of (6), (8) and (13), then adding the initial voltage of 500 kV of u 0 , the voltages of T 12 in the time domain could be obtained, whose waveforms are shown in Fig. 5 as the solid lines show. From the expression of u 1 of internal and external faults, it could be found that the waveforms of u 1 are composed of many frequency components. In all of the frequency components, the frequency of the lowest frequency waveform is very low. As F 1 occurs, the lowest frequency is 14 Hz, while the lowest frequencies are 12 Hz as F 2 and F 3 occur. No matter the fault is internal or external, the lowest frequency is much lower than other components. Considering the total time of fault detection and discrimination of the Zhangbei four-terminal HVDC grid is limited to 3 ms, the lowest frequency wave could be considered as the attenuating direct component.
The dashed lines in Fig. 5 are the superposition of the lowest frequency part and the second lowest frequency part; compared with the total waveform, it is easy to find that they are the main parts. From Table 2, it could be found that the frequency of the main part of the internal fault is much lower than that of the external faults.
Comparing the numerical expression of u 1 of internal and external faults, it could be found that the amplitude of the high frequency parts of internal fault is much higher than that of the external fault, because the high frequency parts of the external fault voltage are largely filtered out by the current limiting reactors, while for the internal fault, the filtering effect of the transmission line is not so obvious. Also, the large amplitudes of high frequency parts lead to the quickly decrease of the terminal voltage.
From Fig. 5 and Table 3, the significant difference of the transition time (TP) from the abrupt changing point to the first extreme point of internal faults and external faults could be seen. Also, the TP of the internal fault is significant shorter than that of the external fault, based on which the fault location could be extinguished.

TP < TP th
(16) Equation (16) is the discrimination criterion of internal and external faults, and TP th is the threshold whose computational formula is (17), where TP cal is the analytical value of TP of F 1 , and K 2 is the reliability coefficient. Considering the significant difference of TP between internal and external faults, K 2 could be set as 1.5.

Simulation model
To verify the validity of the new proposed protection method, a model of the Zhangbei four-terminal HVDC grid is built in PSCAD/EMTDC. The model is in the symmetrical bipolar mode, with the central points connected to the ground directly.   The values of the main parameters of the converter stations are shown in Table 1, and the active powers of the four converter stations are shown in Table 4. The converter stations of Zhangbei, Fengning and Kangbao imply the constant active and reactive power control modes, while the station of Beijing implies the control mode of constant voltage and reactive power. The four converter stations are all connected to the 500 kV ac system through the ac side transformers.

Simulation results of internal and external faults
The simulation waveforms of fault voltages are shown in Fig. 6, where (a), (b) and (c) are the corresponding waveforms of voltages as F 1 , F 2 and F 3 occurs, respectively, and the occurring time of the faults is set as 1.5 s. The time of the abrupt changing points and the first extreme points are all labelled in the figure and the TPs of the simulation outcomes are shown in Table 5. Comparing Figs. 5 and 6, and Tables 3 and 5, it could be found that the analytical results could explain the transient voltages up to some extent.
From the simulation waveforms of the internal and external faults and the simulation results of TPs in Table 5, it is easy to see that the method proposed in this paper could easily extinguish internal and external faults.

Influence of transition resistance
From the above analysis and simulation, the new proposed protection method could identify internal fault quickly and reliably when the fault resistance is 0. This sectionwill verify the effectiveness of the protection method when the fault resistance is not 0.
As the positive-to-ground faults occur in the middle of Line 1 with the fault resistances of 0, 50 and 500 Ω, the terminal voltages are shown in Fig. 7. It could be seen that with the increase of the fault resistance, the magnitude of the fault voltage is getting smaller, but the TPs are the same. So, the protection method is not sensitive to the fault resistance.

Consideration of different DC terminal inductances
To test whether the protection method is sensitive to the value of the current limiting reactor, whose value is reduced from 0.2 to 0.1 H, while all of the other parameters are the same as that presented in Section 4. The fault point is set at the middle of Line 1, and the outputs are shown in Table 6. For T 12 and T 21 , the fault is internal, while for other terminals is external. Considering the threshold is 300 μs, the fault location could be easily distinguished.
It could be seen that the protection method could judge whether the fault is inside of the protection region quite easily when the reactor changes to 0.1 H. What needs to be paid attention to is that the value of reactor needs to be properly chosen to ensure that the internal fault could be discriminated from the external fault, and at the same time to limit the fault current in a certain extent to guarantee that the dc CBs could cut off the fault current.

Results
This paper introduces the analytical process of the fault voltage under internal and external faults, and proposes a novel single-end protection method for the transmission lines of HB-MMC-based meshed HVDC grid. The protection method employs the TP of the fault transient voltage to discriminate the internal fault from the external fault. Extensive simulations are conducted to verify the effectiveness of the protection method with a four-terminal HVDC grid simulation model in PSCAD/EMTDC. Also, the simulation results prove that the protection method could work well even with high fault resistance and is not sensitive to the change of the current-limiting reactor values.

Acknowledgments
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (51677109) and the