A Novel Protection and Location Scheme for Pole-to-Pole Fault in MMC-MVDC Distribution Grid

Nowadays, the efficient and reliable protection and location schemes for MMC-MVDC (Modular Multilevel Converter-Medium Voltage Direct Current) grid are few. This paper is the first to propose a scheme to not only protect the feeders and the busbar, but locate the segments in MMC-MVDC grid. To improve the reliability, this paper analyzes the transient characteristics of the pole-to-pole fault and then obtains the characteristic frequency band. Based on S-transform, STCFB (S-transform characteristic frequency band) Phase of fault component is utilized to construct the identification criterion for faulty feeder and faulty segment. The whole scheme can be divided into three steps, namely, protection starting criterion, faulty feeder and busbar protection criterion, and faulty segment location criterion. Firstly, the current gradient method is utilized to quickly detect the fault and start the protection device. Secondly, the non-unit protection criterion on busbar and feeders is proposed according to STCFB Phase of the voltage and current fault component. Thirdly, according to the STCFB Phase on both sides of the feeder segment, the faulty segment can be located. A radial MMC-MVDC distribution network model was built in PSCAD/EMTDC software to evaluate the performance of the protection and location method. Simulation results for different cases demonstrate that the proposed scheme has high accuracy, good adaptability and reliability.


Introduction
With the development of modern power electronics technology and the increase of new energy power generation systems, the Medium Voltage Direct Current (MVDC) distribution grid will have a good prospect [1][2][3][4]. A Modular Multilevel Converter (MMC) usually has a large number of sub-modules [5]. To improve the quality of converter output waveform, nearest level modulation (NLM) method has been widely adopted [6]. Compared with two-level and three-level voltage source converters (VSCs), MMC has higher reliability and lower switching frequency [7,8]. Thus, MMC-MVDC has been favored in flexible DC projects such as ±10 kV hand-in-hand China Southern Power Grid [9].
As one of the key technologies of flexible DC distribution grid, the protection schemes of MMC-MVDC are still not mature [10]. Due to the huge differences of operation modes and fault characteristics, the protection methods of the AC system cannot be directly implemented to the MMC-MVDC distribution grid [11]. On the other hand, due to the relatively small values of resistance and inductance in DC cables, the rise rate of fault current is very high and DC circuit breakers are yet to be commercially available [12]. In order to prevent the Insulated Gate Bipolar Transistors (IGBTs)

Radial MMC-MVDC Distribution Grid Topology
Compared with hand-in-hand and ring topologies, the radial DC distribution grid is widely adopted due to low investment. As shown in Figure 1, the system is composed by single MMC station which works in DC voltage control. 0.25 MW PV plant is boosted via a DC/DC converter into a ±10 kV DC busbar. The system parameters are shown in Table 1 and the parameters of DC cable are shown in Table 2.

Transient Analysis of DC Feeders
As a MMC-MVDC grid mostly utilizes the small current grounding modes [24], the voltage between two poles remains normal; thus, the system can still operate normally for a period of time. However, when a pole-to-pole fault occurs, the fault current rises rapidly and will bring the most serious hazard to the system. Therefore, this paper proposes the protection scheme mainly focusing on pole-to-pole fault. For a pole-to-pole fault occurring at f1 in Figure 1, the frequency-domain fault superposition circuit schematic of the faulty feeder F1 is shown in Figure 2.

Transient Analysis of DC Feeders
As a MMC-MVDC grid mostly utilizes the small current grounding modes [24], the voltage between two poles remains normal; thus, the system can still operate normally for a period of time. However, when a pole-to-pole fault occurs, the fault current rises rapidly and will bring the most serious hazard to the system. Therefore, this paper proposes the protection scheme mainly focusing on pole-to-pole fault. For a pole-to-pole fault occurring at f 1 in Figure 1, the frequency-domain fault superposition circuit schematic of the faulty feeder F 1 is shown in Figure 2.
As a MMC-MVDC grid mostly utilizes the small current grounding modes [24], the voltage between two poles remains normal; thus, the system can still operate normally for a period of time. However, when a pole-to-pole fault occurs, the fault current rises rapidly and will bring the most serious hazard to the system. Therefore, this paper proposes the protection scheme mainly focusing on pole-to-pole fault. For a pole-to-pole fault occurring at f1 in Figure 1, the frequency-domain fault superposition circuit schematic of the faulty feeder F1 is shown in Figure 2.  Where, U F represents the fault superimposed voltage source; Z S represents the equivalent impedance of MMC; {∆U 1 , ∆I 1 } represent the voltage fault component and the current fault component of the faulty feeder (F 1 ) at frequency ω; R load is the equivalent load impedance; L is the current-limiting reactor installed at the beginning of the feeder; R A1 , L A1 , R C1 , and L C1 are the equivalent resistances and inductances on both A 1 and C 1 sides, respectively. According to Figure 2, for a faulty feeder, when a pole-to-pole fault occurs on F 1 , the voltage fault component and current fault component of faulty feeder meet the following relationship: While for the normal feeders, the frequency-domain fault superposition circuit can be obtained according to the superposition principle as shown in Figure 3.
While for the normal feeders, the frequency-domain fault superposition circuit can be obtained according to the superposition principle as shown in Figure 3. From Figure 3, it can be seen that the voltage fault component and current fault component of the normal feeders at the protection installation satisfy the following relationship: where, k = 2, 3, 4, represents the feeder F2, F3, F4; {ΔUk, ΔIk} represent the voltage fault component and the current fault component of the normal feeder (Fk) at frequency ω; RAkCk, LAkCk are equivalent resistances and inductances of the feeder AkCk, respectively. According to Equation (2), the phase difference of the voltage fault component and current fault component of the normal feeder should be between 0~90°.
However, the phase of ZS cannot be directly determined. To solve this problem, the equivalent circuit of ZS is constructed as shown in Figure 4. At this time, MMC is only paralleled by three phase units.
where, k = 2, 3, 4, represents the feeder F 2 , F 3 , F 4 ; {∆U k , ∆I k } represent the voltage fault component and the current fault component of the normal feeder (F k ) at frequency ω; R AkCk , L AkCk are equivalent resistances and inductances of the feeder A k C k , respectively. According to Equation (2), the phase difference of the voltage fault component and current fault component of the normal feeder should be between 0~90 • . However, the phase of Z S cannot be directly determined. To solve this problem, the equivalent circuit of Z S is constructed as shown in Figure 4. At this time, MMC is only paralleled by three phase units. However, the phase of ZS cannot be directly determined. To solve this problem, the equivalent circuit of ZS is constructed as shown in Figure 4. At this time, MMC is only paralleled by three phase units.  Where, L 0 , C 0 represent the bridge reactance and submodule capacitors of MMC; R 0 is the equivalent resistance of the bridge arm; N is the number of submodules of bridge arm. To analyze the phase of Z S , defining the equivalent impedance Z C of the equivalent inductor and the equivalent capacitor as follows: Thus, the resonant frequency of the circuit is: According to Equation (4), when f > f res , Z C > 0, Z S is inductive. According to Table 1, f > f res = 71.2 Hz. That is, when f > 71.2 Hz, the phase difference of voltage fault component and the current fault component of faulty feeder is between 180 •~2 70 • .

Transient Analysis of Feeder Segment
(1) Internal fault of feeder segment: Take the fault at f 1 in Figure 1 as an example, when the internal fault occurs at f 1 for the segment B 1 C 1 , the superimposed circuit is illustrated as Figure 5. Assume the positive current direction is from busbar to the line for convenience. According to superposition principle, a negative voltage source ∆U F is equivalent to be added at the fault point. Thus, the resonant frequency of the circuit is: According to Equation (4)

Transient Analysis of Feeder Segment
(1) Internal fault of feeder segment: Take the fault at f1 in Figure 1 as an example, when the internal fault occurs at f1 for the segment B1C1, the superimposed circuit is illustrated as Figure 5. Assume the positive current direction is from busbar to the line for convenience. According to superposition principle, a negative voltage source ΔUF is equivalent to be added at the fault point.
- where, ΔIB1C1, ΔIC1B1 respectively represent current fault components on both sides of segment B1C1. The load is generally connected to the DC busbar via a charging capacitor in the converters. Therefore, when the fault occurs at f1, both sides feed current to the fault point. According to the specified positive direction, the current fault component detected by R13 and R14 should have the same polarity.
(2) External fault of feeder segment: As there is no boundary between the segments of the same feeder, the current is almost not blocked from propagating between segment A1B1 and segment B1C1. Therefore, the polarities of the current fault component of the normal feeder detected by R11 and R12 are opposite.

Transient Analysis of Fault on the Bus
Specify the positive current direction is from the busbar to the line. When a pole-to-pole fault occurs on the DC busbar, the transient current characteristics can be illustrated as Figure 6. According to the analysis above, the voltage fault component and current fault component detected by the protection installation of feeder i and the converter satisfy the following relation: Where, ∆ IB1C1 , ∆ IC1B1 respectively represent current fault components on both sides of segment B 1 C 1 . The load is generally connected to the DC busbar via a charging capacitor in the converters. Therefore, when the fault occurs at f 1 , both sides feed current to the fault point. According to the specified positive direction, the current fault component detected by R 13 and R 14 should have the same polarity.
(2) External fault of feeder segment: As there is no boundary between the segments of the same feeder, the current is almost not blocked from propagating between segment A 1 B 1 and segment B 1 C 1 . Therefore, the polarities of the current fault component of the normal feeder detected by R 11 and R 12 are opposite.

Transient Analysis of Fault on the Bus
Specify the positive current direction is from the busbar to the line. When a pole-to-pole fault occurs on the DC busbar, the transient current characteristics can be illustrated as Figure 6. According to the analysis above, the voltage fault component and current fault component detected by the protection installation of feeder i and the converter satisfy the following relation: where, I = 1, 2, 3, 4, represents the feeder F 1 - Energies 2018, 11, x 6 of 16

Analysis of Current Fault Component Characteristic Frequency Band
It can be seen from the analysis above that the faulty feeder and faulty segment can be identified by the characteristics of the current fault component. However, the current fault component of DC feeder is a continuous spectrum signal. The low-frequency band of the signal is susceptible to DC load currents, while the high-frequency signal will be rapidly attenuated due to the fast rise of impedance of feeder in the case of high-frequency band. Therefore, in order to extract the characteristic frequency band of current fault component effectively and improve the sensitivity of the criteria, the amplitude-frequency characteristics of the current fault component will be analyzed. As shown in Figure 7, DC feeder F1 in Figure 1 is modelled by a π-type equivalent circuit, and the frequency characteristics of MMC-MVDC distribution grid are analyzed as follows.
According to the two-port network equation, the current-voltage relation in Figure 7 can be expressed as: Figure 6. Frequency-domain fault superposition circuit for a pole-to-pole fault on the busbar.

Analysis of Current Fault Component Characteristic Frequency Band
It can be seen from the analysis above that the faulty feeder and faulty segment can be identified by the characteristics of the current fault component. However, the current fault component of DC feeder is a continuous spectrum signal. The low-frequency band of the signal is susceptible to DC load currents, while the high-frequency signal will be rapidly attenuated due to the fast rise of impedance of feeder in the case of high-frequency band. Therefore, in order to extract the characteristic frequency band of current fault component effectively and improve the sensitivity of the criteria, the amplitude-frequency characteristics of the current fault component will be analyzed. As shown in Figure 7, DC feeder F 1 in Figure 1 is modelled by a π-type equivalent circuit, and the frequency characteristics of MMC-MVDC distribution grid are analyzed as follows.
load currents, while the high-frequency signal will be rapidly attenuated due to the fast rise of impedance of feeder in the case of high-frequency band. Therefore, in order to extract the characteristic frequency band of current fault component effectively and improve the sensitivity of the criteria, the amplitude-frequency characteristics of the current fault component will be analyzed. As shown in Figure 7, DC feeder F1 in Figure 1 is modelled by a π-type equivalent circuit, and the frequency characteristics of MMC-MVDC distribution grid are analyzed as follows.
According to the two-port network equation, the current-voltage relation in Figure 7 can be expressed as: where, I p 1 and U p 1 denote the current and voltage at the beginning of F1. I L 1 and U L 1 represent the current and voltage at the end of F1. Y1 and Y2 are the admittance parameters of two-port network. The transfer function between the current of beginning and end of the DC feeder is defined as follows: Substituting feeder parameters into Equation (8) and it can be given by: According to the two-port network equation, the current-voltage relation in Figure 7 can be expressed as: where, . I p 1 and . U p 1 denote the current and voltage at the beginning of F 1 . .

I L1 and
.
U L1 represent the current and voltage at the end of F 1 . Y 1 and Y 2 are the admittance parameters of two-port network.
The transfer function between the current of beginning and end of the DC feeder is defined as follows: Substituting feeder parameters into Equation (8) and it can be given by: where R, L and C denote the resistance, inductance and capacitance per unit length, respectively; l represents the length of the feeder. The standard form of oscillation links of transfer function can be expressed as: The resonant angle frequency ω * r is given by: Substitute Equation (9) into the form of Equation (10), G(s) will be expressed as: Therefore, the resonant frequency f r can be calculated as: Energies 2018, 11, 2076 8 of 17 According to the line parameters shown in Table 1, the amplitude-frequency curves of the transfer function G(s) can be obtained by substituting the different feeder lengths l = 20 km, 15 km and 10 km into Equation (12), respectively. The curves are shown in Figure 8.
Therefore, the resonant frequency fr can be calculated as: According to the line parameters shown in Table 1, the amplitude-frequency curves of the transfer function G(s) can be obtained by substituting the different feeder lengths l = 20 km, 15 km and 10 km into Equation (12), respectively. The curves are shown in Figure 8. According to Equation (14), the resonance frequencies fr1 = 6054 Hz, fr2 = 8072 Hz and fr3 = 12,107 Hz are obtained respectively. It can be seen from Figure 8 that for the same line length, the amplitude A(ω) of the transfer function G(s) is gradually increased from 1 in the low frequency band range (0 < f < fr); When f = fr, the amplitude reaches the resonance peak and the line has the least attenuation effect on the current fault component. For the high frequency band (f > fr), |A(ω)| decays rapidly from the resonant peak. When the length of the feeder reaches maximum length of 20km, ωr reaches a minimum value of 6054 Hz. As the frequency increases from 6054 Hz, the attenuation effect on the current fault component will become stronger. In order to reduce the attenuation of the circuit, the frequency should not be greater than 6054 Hz. Meanwhile, as most of AC distributed power works According to Equation (14), the resonance frequencies f r1 = 6054 Hz, f r2 = 8072 Hz and f r3 = 12,107 Hz are obtained respectively. It can be seen from Figure 8 that for the same line length, the amplitude A(ω) of the transfer function G(s) is gradually increased from 1 in the low frequency band range (0 < f < f r ); When f = f r , the amplitude reaches the resonance peak and the line has the least attenuation effect on the current fault component. For the high frequency band (f > f r ), |A(ω)| decays rapidly from the resonant peak. When the length of the feeder reaches maximum length of 20km, ω r reaches a minimum value of 6054 Hz. As the frequency increases from 6054 Hz, the attenuation effect on the current fault component will become stronger. In order to reduce the attenuation of the circuit, the frequency should not be greater than 6054 Hz. Meanwhile, as most of AC distributed power works in 50 Hz and most of DC distributed power works in low-frequency band, the low-frequency band of the fault component is easily affected by the load current and distributed power. Therefore, this paper selects characteristic frequency band between 500 Hz and 4000 Hz for analysis.

Application of S-Transform
S-transform has excellent time-frequency resolution characteristics. The height and width of Gaussian window changes with the variation of frequency. Based on good frequency resolution in the low frequency part and good time resolution in the high frequency part [25], it is very easy to extract the characteristic frequency band of current fault component using S-transform.

The S-Transform Theory
S transform is the development of wavelet transform and short-time Fourier transform [26], the S transform of a signal x(t) can be expressed as: where, f and τ are the frequency-shift factor and time-shift factor; ω(τ − t, f ) is Gaussian window function which can be defined as: The S transform of a discrete signal x[kT] can be realized by the fast Fourier transform (letting f → n/NT and τ → jT ): where k, j, m and n∈(0, M − 1). T is the sampling interval and M is the sampling number. X[n/NT] denotes the discrete Fourier transform of x[jT] and e −2π 2 m 2 /n 2 represents the Fourier spectrum of Gaussian window function.

S transform Characteristic Frequency Band (STCFB)
The S matrix obtained by S transform can be defined as S a [p, q], where q is a column vector representing the amplitude-frequency characteristics of the signal at a sampling point, p is a row vector representing the time-domain characteristics of the signal at a certain frequency. Then STCFB of a signal at a certain time q can be defined as: where q = 1, 2 . . . M. STCFB waveform can be drawn by calculating S[q] at each sampling point.

Analysis of STCFB Phase
In the matrix S A [p, q], each element represents both of amplitude information and phase information of the signal at a particular frequency at a particular sampling point. The phase information extracted by single frequency has insufficient reliability and is also susceptible to interference signals. According to the analysis of the characteristic frequency band in the previous section, the STCFB Phase transformed from the signal S can be extracted as: where, S A [q] is the phase of S[q], utilized to identify the faulty feeders and locate the faulty segments.

Protection Starting Criterion
When MMC-MVDC system is in normal operation, the current fault component at the protection installation of DC distribution grid is almost zero. While the pole-to-pole fault occurs, the short circuit current at the protection installation of the line will rise rapidly. The current gradient is utilized to detect the abnormality since the system abnormality can be characterized by a current change [27], which can be expressed as: where, I(k-i) is the i-th sampling current value prior to the present moment; ∇I(k) is the calculated current gradient. The start criterion of the protection is defined as: where, ∆ 1 is the starting threshold value. The value is greater than the maximum value of the current gradient during normal operation and switching load. According to the analysis and large simulations, ∆ 1 = 5 A is obtained.

Protection Criterion on the Busbar and Feeders
According to the analysis above, it can be seen that in the characteristic frequency band, both the forward and backward impedance of the protection can be considered to be inductive. Therefore  On the other hand, when the feeder i is a normal feeder, the STCFB Phase difference between the two signals should be between 0 •~9 0 • . Considering the sensitivity and selectivity comprehensively, the criteria for identifying the faulty feeder can be constructed as follows: If Equation (24) is satisfied, the feeder i can be determined as faulty feeder. The criterion for identifying the faulty busbar can be constructed as follows: If ∆S Ai and ∆S Ac satisfy the criterion in Equation (25), the pole-to-pole fault can be determined on the DC busbar.

Faulty Segment Location Criterion
On the basis of the characteristic analysis in Section 2.3, when an internal fault occurs on the segment, the STCFB Phase of current fault component on both sides of the segment are approximately the same; while the segment is faulty, the STCFB Phase on both sides of the segment are approximately opposite. Defining ∆S Al as STCFB Phase difference of different feeder segments, then: where, S AIl (q) and S AIr (q) are the STCFB Phase of the current fault component at the q-th sampling point on both sides of the segment. The faulty segment location criterion can be constructed as follows: When Equation (27) is satisfied, the faulty segment is determined. Otherwise, it is judged as a normal segment.

Flow Chart of Protection and Location Scheme
Based on the analysis above, the flow chart of protection and segment location scheme shown in Figure 9 can be designed based on the protection starting criterion, feeders and busbar protection criterion, and segment location criterion.
If ΔSAi and ΔSAc satisfy the criterion in Equation (25), the pole-to-pole fault can be determined on the DC busbar.

Faulty Segment Location Criterion
On the basis of the characteristic analysis in Section 2.3, when an internal fault occurs on the segment, the STCFB Phase of current fault component on both sides of the segment are approximately the same; while the segment is faulty, the STCFB Phase on both sides of the segment are approximately opposite. Defining ΔSAl as STCFB Phase difference of different feeder segments, then: where, SAIl(q) and SAIr(q) are the STCFB Phase of the current fault component at the q-th sampling point on both sides of the segment. The faulty segment location criterion can be constructed as follows: When Equation (27) is satisfied, the faulty segment is determined. Otherwise, it is judged as a normal segment.

Flow Chart of Protection and Location Scheme
Based on the analysis above, the flow chart of protection and segment location scheme shown in Figure 9 can be designed based on the protection starting criterion, feeders and busbar protection criterion, and segment location criterion.

Simulation and Analysis
In order to validate the proposed protection and location criteria, a ±10 kV natural bipolar radial MMC-MVDC simulation model was built in Figure 1. The pole-to-pole faults are set at different fault locations to test the reliability of the method. The protection units (R 11 , R 12 , R 13 , R 14 , R 21 , R 22 , R 23 , R 24 , R 31 , R 32 , R 33 , R 34 , R 41 , R 42 , R 43 , R 44 , and R 1 ) are located as shown in the figure. The entire data window is 2ms in length and the sampling frequency is 25 kHz.

Metallic Pole-to-Pole Fault
Setting a metallic pole-to-pole fault at f 1 in the middle of segment B 1 C 1 , the STCFB Phase of current and voltage fault component of all feeders are shown in Figure 10. The results are indicated in Table 3.
In order to validate the proposed protection and location criteria, a ±10 kV natural bipolar radial MMC-MVDC simulation model was built in Figure 1. The pole-to-pole faults are set at different fault locations to test the reliability of the method. The protection units (R11, R12, R13, R14, R21, R22, R23, R24,  R31, R32, R33, R34, R41, R42, R43, R44, and R1) are located as shown in the figure. The entire data window is 2ms in length and the sampling frequency is 25 kHz.

Metallic Pole-to-Pole Fault
Setting a metallic pole-to-pole fault at f1 in the middle of segment B1C1, the STCFB Phase of current and voltage fault component of all feeders are shown in Figure 10. The results are indicated in Table 3.  Further analyzing STCFB Phase on both sides of segment A1B1 and B1C1, the waveforms are shown in Figure 11 and the simulation results are indicated in Table 4.   Figure 10 and Table 3 Further analyzing STCFB Phase on both sides of segment A 1 B 1 and B 1 C 1 , the waveforms are shown in Figure 11 and the simulation results are indicated in Table 4.    Where, {S AA1B1 , S AB1A1 }, {S AB1C1 , S AC1B1 } represent the STCFB Phase on both sides of segment A 1 B 1 and B 1 C 1 ; ∆S Al is the STCFB Phase difference on both sides of segment A 1 B 1 and B 1 C 1 . As shown in Figure 11 and Table 4 Table 5.  ΔSAl is the STCFB Phase difference on both sides of segment A1B1 and B1C1. As shown in Figure  11 and Table 4

Metallic Bus Fault
A metallic fault is set at f2 on the busbar as shown in Figure Table 5.  According to Figure 12 and Table 5   According to Figure 12 and

Simulation for Influencing Factors
In order to verify the reliability of the proposed protection and location criterion under different factors, extensive simulations were performed as follows.
(1) Fault on the feeder under different fault resistances: Faults under different resistances are set at f 1 in the middle of segment B 1 C 1 . The simulation results of feeders are indicated in Table 6. The results of segments are indicated in Table 7.  On the basis of Tables 6 and 7, F 1 can be selected as faulty feeder under different resistances. In addition, segment B 1 C 1 can be correctly located.
(2) Simulation of fault on the busbar under different fault resistances: Faults with different transition resistances are set at f 2 on the busbar. The identification results are shown in Table 8. As the results shown in Table 8, the fault on the busbar can be correctly determined under different resistances. The results show that the resistance has little impact on the criteria.
(3) Simulation of different fault locations: Set the pole-to-pole fault at f 3 and take the transition resistance as 20Ω. The simulation results of STCFB Phase difference on both sides of segment A 2 B 2 and B 2 C 2 are shown in Figure 13. The abscissa indicates the distance from the fault point to A 2 .

Simulation for Influencing Factors
In order to verify the reliability of the proposed protection and location criterion under different factors, extensive simulations were performed as follows.
(1) Fault on the feeder under different fault resistances: Faults under different resistances are set at f1 in the middle of segment B1C1. The simulation results of feeders are indicated in Table 6. The results of segments are indicated in Table 7.  On the basis of Tables 6 and 7, F1 can be selected as faulty feeder under different resistances. In addition, segment B1C1 can be correctly located.
(2) Simulation of fault on the busbar under different fault resistances: Faults with different transition resistances are set at f2 on the busbar. The identification results are shown in Table 8. As the results shown in Table 8, the fault on the busbar can be correctly determined under different resistances. The results show that the resistance has little impact on the criteria.  According to Figure 13, when the fault occurs on different locations of the segment, the faulty segment can be correctly located, and the sensitivity is high. According to Figure 13, when the fault occurs on different locations of the segment, the faulty segment can be correctly located, and the sensitivity is high.
(4) Noise: The noise interferences will be doped in the voltage and current fault component, which will easily cause maloperation of protection. Therefore, Gaussian white noise with different decibels is added to the voltage and current fault component signals. The simulation results are shown in Table 9. On the basis of the simulation results above, it can be seen that the scheme is hardly affected by noise.
(5) Fault on AC side: Different types of pole-to-pole faults are set at f 4 on the AC busbar. According to the simulation, during the entire transient process, ∇I(k) < ∆ 1 is always satisfied. Therefore, the protection does not start, and the system can still operate normally.

Conclusions
Due to the existing protection and location scheme mainly focus on HVDC grid and LVDC grid, a novel protection and location method was firstly proposed for MMC-MVDC grid. Considering the transient characteristics of MMC-MVDC distribution grids, the scheme can be divided into three stages, namely: (1) Protection starting criterion; (2) feeders and busbar protection criterion, and (3) segment location criterion. Utilizing PSCAD/EMTDC software, a radial MMC-MVDC distribution grid was constructed and extensive simulations were realized. From the theoretical analysis and simulation results, the following conclusions could be drawn: (1) The simulation results show that influencing factors such as the fault resistance, the noises and fault position, can hardly affect the correct operation of the proposed criteria.
(2) Utilizing the non-unit data and the data window of 2 ms to protect the feeder and the busbar, the protection is fast and reliable. (3) The criteria only utilizes the current and voltage fault component to protect the system and locate the fault, which is adaptable in the intricate topologies.