A novel AC line distance protection scheme for AC/DC hybrid system based on fault likeness factor

Concerning the mal-operation of distance protection in AC/DC hybrid system due to commutation failure in DC system caused by AC-side fault, a novel AC line distance protection scheme based on fault likeness factor is proposed. First, by analysing the conducting state of converter in different time intervals, the expression of feed-in current from DC system to AC system is derived. On this basis, combining AC-side fault component network, the fault location equation considering the impact of feed-in current from DC system is estab-lished. Thus, by solving the equation consisting of information at multiple time sections, the fault location is calculated. And then, according to the consistency between the calculated fault location and actual fault location, the fault likeness factor is constructed to distinguish between in-zone and out-of-zone faults. Finally, simulation tests in RT-LAB verify that, the proposed scheme can identify in-zone and out-of-zone faults fast and accurately in the case of commutation failure caused by different types of fault, strongly immune to fault resistance.

based on power-frequency variables uses the power-frequency voltage at the beginning end of the protected line and the line power-frequency current information to form the protection criterion [11,12]. Compared to current protection and voltage protection, the protection range and sensitivity of distance protection based on power-frequency variables is less affected by the variation of operation mode of AC system. However, when DC system is integrated to AC system, AC-side fault may cause commutation failure in DC system, which will cause the equivalent feed-in current from DC system to AC system to change suddenly [13][14][15], thus the measured impedance will fluctuate, resulting in narrowed protection range or over-reach operation [16][17][18]. Time-domain distance protection is usually based on the assumption that the current distribution coefficients are constant, and uses parameter estimation method to calculate the fault distance [19]. This method is not affected by overload of line and system oscillation. However, when commutation failure occurs in DC system, due to non-linear time-varying fault characteristic of converter station and fast response of DC system controller, the equivalent impedance of DC system will keep changing, and the above assumption will not be true. Currently, research on AC line protection in the case of commutation failure is rare. Reference [17] uses the ratio of power-frequency current amplitude to current amplitude in normal operation state to construct the protection criterion. This method is applicable to commutation failure cases caused by AC-side fault. However, since the current amplitude ratio in fault state and current amplitude ratio in normal operation state are both close to 1, the reliability of this protection scheme is not adequate.
Concerning the inadaptability of distance protection based on power-frequency variables and time-domain distance protection to the integration of DC system to AC system, a novel AC line distance protection scheme based on fault likeness factor is proposed. First, by analysing the operating conditions of converter in different time intervals, the expression of feed-in current from DC system to AC system is derived. Second, according to AC-side fault component network, the fault location equation considering the impact of feed-in current from DC system is established. Thus, by solving the equation consisting of information at multiple time sections, the fault location is calculated. And then, the consistency between the calculated fault location and actual fault location is quantified as the fault likeness factor, based on which the protection criterion to identify in-zone and out-of-zone faults is constructed. Finally, simulation tests in RT-LAB verify the correctness and effectiveness of the proposed scheme. Compared with traditional methods, this paper builds the detailed model of AC/DC system that can reflect the conducting state of converter valves. Thus, the proposed scheme can identify in-zone and out-of-zone faults fast and accurately when commutation failure occurs in different fault cases (including fault at the outlet of AC line backside system). Besides, the proposed method is strongly immune to fault resistance, and is not affected by the variation of zero-sequence network of receiving-end AC system.

EXPRESSION OF FEED-IN CURRENT FROM DC SYSTEM TO AC SYSTEM
Take the AC/DC hybrid system in Figure 1, for example. The wiring diagram of inverter-side 12-pulse converter is shown in Figure 2. When fault occurs on AC line, commutation failure may occur in inverter-side converter station due to AC-side fault, and inverter-side 12-pulse converter may operate in the following five conducting states.
a. Four valve arms of 12-pulse converter are conducted. For example, VTD 1 and VTD 2 of D-bridge converter are conducted; VTY 1 and VTY 2 of Y-bridge converter are conducted. b. Five valve arms of 12-pulse converter are conducted. For example, VTD 1 and VTD 2 of D-bridge converter are con-ducted; VTY 1 , VTY 2 and VTY 3 of Y-bridge converter are conducted. c. Six valve arms of 12-pulse converter are conducted. For example, VTD 1 , VTD 4 and VTD 5 of D-bridge converter are conducted; VTY 1 , VTY 4 and VTY 5 of Y-bridge converter are conducted. d. Seven valve arms of 12-pulse converter are conducted. For example, VTD 1 , VTD 4 and VTD 5 of D-bridge converter are conducted; VTY 1 , VTY 4 , VTY 5 and VTY 6 of Y-bridge converter are conducted. e. Eight valve arms of 12-pulse converter are conducted. For example, VTD 1 , VTD 4 , VTD 5 and VTD 6 of D-bridge converter are conducted; VTY 1 , VTY 4 , VTY 5 and VTY 6 of Ybridge converter are conducted.
When VTD 1 and VTD 2 of D-bridge converter, and VTY 1 and VTY 2 of Y-bridge converter are conducted, the following relationships can be obtained according to Figure 2: where u ma , u mb and u mc are three-phase voltages at inverter-side converter bus. u d , u d1 , u d2 , u drec and u drec2 are, respectively, the voltages at d 1 , d 2 , d 3 , d 4 and d 5 in Figure 2. i Ad , i Bd , i Cd , i Ay , i By and i Cy are the currents on the corresponding windings. i d is DC current. k y and k d are the transformation ratios of Y/Y converter transformer and Y/△ converter transformer. L r is the inductance of converter transformer converted to the valve side. L d is the inductance of smoothing reactor. According to (1)-(4), the following equations can be obtained: Combining (2), (3), (4) and (7) yields: According to (8)- (11), the difference between voltages at d 4 and d 5 has the following relationships with the current on valveside winding of Y/△ converter transformer: (12) And according to (5), (6), (10) and (12), the difference between voltages at d 4 and d 5 has the following relationships with the current on valve-side winding of Y/Y converter transformer: Equations (12) and (13) can be written in the form of matrices, as shown in (14) and (15): where I d , I y , U, D d4 , D y4 , A d4 and A y4 are, respectively, Combine (14) and (15), so that the feed-in current from DC system to AC system can be calculated: where f icom (U) is the current that flows through AC filter and reactive power compensation device. When the parameters of AC filter and reactive power compensation device are fixed, f icom (U) is the function of converter bus voltage U. Matrices I, K y and K d are, respectively, When another four valve arms of 12-pulse converter are conducted, or five/six/seven/eight valve arms of 12-pulse converter are conducted, similar derivation process can be applied. By combining the conducting states of converter valves and the wiring diagram in Figure 2, relationships similar to (1)- (7) can be established, and the expression of feed-in current from DC system to AC system in the same form as (16) can be obtained.

EQUATIONS OF FAULT LOCATION CORRESPONDING TO DIFFERENT TYPES OF FAULT ON AC LINE
The protection criterion of traditional distance protection is composed of AC-side fault information and does not consider the impact of feed-in current from DC system on the measured impedance, thus when AC-side fault results in commutation failure, distance protection may mal-operate or refuse to operate. To solve this problem, the feed-in current from DC system is

Fault location equation in the case of single-phase-to-ground fault
When phase-A-to-ground fault occurs at location x on AC line M-N with the fault resistance being R g , the fault system is shown in Figure 3, where i na , i nb and i nc are N-side three-phase currents. The AC-side zero-sequence fault component network is shown in Figure 4, where d = 1. R W0 and L W0 are zero-sequence resistance and inductance of AC system S 1 . R 0 and L 0 are zerosequence resistance and inductance of AC line M-N. i f0 is the zero-sequence current that flows through the fault resistance. u m0 and i n0 are, respectively, zero-sequence voltage at bus M and zero-sequence current at bus N. According to Figure 3, the voltage of phase A at the fault point can be written as where R l and L l are, respectively, positive-sequence resistance and positive-sequence inductance of AC line M-N.
In (17), the expressions of i m0 , k R and k L are, respectively, According to Figure 3, the following relationships exist between M-side three-phase currents and N-side three-phase currents: where i f is the current that flows through the fault resistance. According to (18) and (21), the voltage of phase A at the fault point is Apply (22) to (17) so that According to Figure 4, the voltage calculated from bus M towards the fault point is equal to the voltage calculated from bus N towards the fault point, thus Combine (23) and (24) so that where the expressions of p 1 , p 2 , p 3 and p 4 are

Fault location equation in the case of phase-to-phase fault
When phase-A-to-phase-B fault occurs at location x on AC line M-N with the fault resistance being R g , the fault system is shown in Figure 5, where i fab is the current that flows through the fault resistance.
According to Figure 5, the voltages of phase A and phase B at the fault point are, respectively, Thus, the voltage difference between phase A and phase B at the fault point is where u mab and i mab are, respectively, the voltage difference and current difference between phase A and phase B at bus M. According to Figure 5, Thus, where i nab is the current difference between phase A and phase B at bus N. Apply (30) to (28) so that According to (31), the fault state network of phase-to-phase short circuit fault can be obtained, as shown in Figure 6(a), while the fault component network of phase-to-phase short circuit fault is shown in Figure 6(b).
In Figure 6(a), E ab is the voltage difference between phase A and phase B of AC system S 1 . In Figure 6(b), △u mab and △i mab are, respectively, the fault components of voltage difference and current difference between phase A and phase B at bus M. △i nab is the fault component of current difference between phase A and phase B at bus N. R W and L W are the equivalent resistance and inductance of AC system S 1 .
According to Figure 6(b), the voltage calculated from bus M towards the fault point is equal to the voltage calculated from bus N towards the fault point, thus, (32) According to the superposition theorem, where i mabn and i nabn are, respectively, the current difference between phase A and phase B at bus M and the current difference between phase A and phase B at bus N in normal operation state. According to (33), Apply (34) to (31) so that Combining (32) and (35) yields  where the expressions of p 5 , p 6 , p 7 and p 8 are

Phase-to-phase grounding fault
When phase-AB-to-ground fault occurs at location x on AC line M-N, the fault system is shown in Figure 7, where the voltage difference between phase A and phase B at the fault point is shown in (28). According to Figure 7, According to (38), Combine (28) and (39) so that Comparing (35) and (40), it can be seen that the circuit of phase-to-phase grounding fault can be decomposed into fault networks similar to those in Figure 6, and by applying the derivation process similar to that of phase-to-phase fault, the fault location equation in the case of phase-to-phase grounding fault can be obtained:

Three-phase short circuit fault
When three-phase short circuit fault occurs at location x on AC line M-N, the fault system is shown in Figure 8. According to Figure 8, where u n is the voltage at the corresponding point in Figure 8. According to (42), Comparing (39) and (43), it can be seen that, when threephase short circuit fault occurs, the expression of voltage difference between any two phases at the fault point is the same as that in the case of phase-to-phase grounding fault. Therefore, by applying the data of any two phases to the fault location equation of phase-to-phase grounding fault, the fault location of three-phase short circuit fault can be calculated.
It can be seen from (25), (36) and (41) that, when different types of fault occur on AC line, the unified expression of fault location equation is In (44), when single phase grounding fault occurs, p c = p 1, p rg = p 2 , p x = p 3 , p x2 = p 4 ; when phase-to-phase fault occurs, p c = p 5, p rg = p 6 , p x = p 7 , p x2 = p 8 ; when phase-to-phase grounding fault or three-phase short circuit fault occurs, p c = p 5, p rg = 2p 6 , p x = p 7 , p x2 = p 8 .
According to the above analysis, only the fault location and fault resistance are unknown in fault location equation. After fault occurs, with the fault instant as the starting point, fault data in the time window of 10 ms are collected. For any two sampling points in the 10 ms, two binary quadratic equations are constructed according to (44). Then Newton iteration method is used to calculate the fault location. Since there are more than two sampling points, the redundant information is used for nonlinear least square optimisation of fault location, so that the calculation error of fault location can be reduced. The optimisation process applies Gauss-Newton method, the detailed steps of which are shown below.
Step 1: Set initial values of fault resistance and fault location Rg(0) and x(0). The initial value of fault resistance can be set as 300Ω in the case of single phase grounding fault, and 100Ω in the case of other fault types. The initial value of fault location can be set as the whole line length.
Step 2: For the kth iteration, calculate Jacobian matrix J.
Step 3: For the kth iteration, calculate matrix H = J T J.
Step 4: For the kth iteration, calculate matrix Step 5: For the kth iteration, calculate △X k = H -1 B.
Step 6: If △X k is small enough or the number of iterations reaches the maximum value, stop iteration; otherwise, update X k+1 = △X k + X k .
Step 7: According to the premise of derivation process in Section 3, fault distance x satisfies 0 ≤ x ≤ d. Thus if the calculated fault distance x exceeds the whole line length d, the fault distance is taken as the whole line length; if the calculated fault distance x is below 0, the fault distance is taken as 0.

AC line distance protection scheme based on fault likeness factor
Suppose four valve arms of inverter-side converter are conducted, currents i ma , i mb and i mc in such conducting state are calculated according to (16).
When fault occurs in the DC system on the backside of bus M, according to the fault location, it may be fault in D-bridge converter, Y-bridge converter or AC filter. For D-bridge converter fault, (1) and (2) are not satisfied; for Y-bridge converter fault, (5) and (6) are not satisfied; for AC filter fault, the currents calculated according to the normal model of AC filter are inconsistent with the actual currents that flow through AC filter. Since (16) is derived according to (1), (2), (5), (6) and the normal model of AC filter, in the above fault cases, currents i ma , i mb and i mc calculated according to (16) will deviate from the actual values. Consider that (44) is based on the actual values of currents i ma , i mb and i mc , in the above fault cases (44) is not satisfied, that is,  (44) is not satisfied, that is, where n is the number of sampling points in 10 ms. p c (i), p rg (i), p x (i) and p x2 (i) are, respectively, the values of p c , p rg , p x and p x2 calculated according to the fault data of the ith sampling point. According to the above analysis, the proposed AC line distance protection scheme based on fault likeness factor can be realised in the following steps.
Step 1: Use differential current transformer to monitor the turn-on and turn-off states of converter valves and determine the conducting state of converter, and calculate the feed-in current from DC system to AC system. Consider that in calculation process, the fault likeness factor will be affected by measuring errors, the threshold value is set to be 5.

3.5
The effect of changes in the R W0 and L W0 parameters in the performance of the proposed method R W0 and L W0 are zero-sequence impedance parameters of receiving-end AC system, which are mainly determined by zero-sequence impedances of transmission line and neutral grounding transformer. Thus only when the transmission line or transformer is switched on/off, system zero-sequence impedance will change. Consider that the time interval between two switchings of line or transformer is much longer than the operation time of protection, during the identification of fault location, R W0 and L W0 can be approximated as constants.
Combining (25) and (26) yields: (50) After fault occurs, with the fault instant as the starting point, fault data in the time window of 10 ms are collected. For any two sampling points in the 10 ms, combining (49) and (50) yields: In (51), eliminating R W0 and L W0 yields: where a 1 , a 2 , a 3 , b 1 , b 2 and b 3 are, respectively, In the equation of fault location shown in (52), fault resistance and fault location are the only unknown numbers. Then, another two sampling points are taken to establish two binary quadratic equations similar to (52), and Newton iteration method is used to calculate the fault location. Since the equations do not contain R W0 or L W0 , the impact of R W0 and L W0 on the calculated fault location can be neglected.

Test system
Hardware-in-loop tests are conducted to verify the effectiveness of the proposed method. The hardware-in-loop platform consists of RT-LAB and CPU controller based on PXI protocol, as shown in Figure 9, where the main circuit is AC/DC hybrid system shown in Figure 1 operating in RT-LAB, and the control algorithm operates in CPU controller. The main parameters of AC/DC hybrid system are shown in Table 1. The fault is set to occur at t = 0.

Simulation results of in-zone fault on AC line via different fault resistances
When there is no fault in AC/DC hybrid system, Y-bridge and D-bridge converters can commutate normally. Suppose at t = 0 ms, VTY 1 and VTY 2 of Y-bridge converter and VTD 1 and VTD 2 of D-bridge converter are conducted. After firing signals are issued to VTY 3 of Y-bridge converter and VTD 3 of D-bridge converter, commutation will take place in Y-bridge converter and D-bridge converter. When the voltage that VTD 1 of D-bridge converter bears first turns from negative to positive and the blocking capability of VTD 1 is restored, the commutation in Y-bridge converter and D-bridge converter is finished. In the new conducting state, VTY 2 and VTY 3 of Y-bridge converter and VTD 2 and VTD 3 of D-bridge converter are conducted.
Phase-A-to-ground fault and phase-AB-to-ground fault are set at 50% line length from bus M on AC line M-N with the fault resistance ranging between 0Ω and 300Ω. At t = 0 ms, VTY 1 and VTY 2 of Y-bridge converter and VTD 1 and VTD 2 of Dbridge converter are conducted. After firing signals are issued to VTY 3 of Y-bridge converter and VTD 3 of D-bridge converter, commutation will take place in Y-bridge converter and D-bridge converter. When the voltage that VTD 1 of D-bridge converter bears first turns from negative to positive, the conducting states of Y-bridge converter and D-bridge converter are shown in Table 2.
It can be seen from Table 2 that, when phase-A-to-ground fault occurs on AC line with the fault resistance being 50Ω, VTD 2 and VTD 3 of D-bridge converter are conducted, while VTY 1 and VTY 2 of Y-bridge converter are conducted, which is abnormal, that is, commutation failure occurs in Y-bridge converter. When the fault resistance of phase-A-to-ground fault varies between 150Ω and 300Ω, the conducting states of converters are the same as in normal operation state, that is, both Y-bridge converter and D-bridge converter commutate normally. When phase-AB-to-ground fault occurs, similar analysis procedure is applied, and it can be seen from Table 2 that, when the fault resistance varies between 0Ω and 50Ω, commutation failure occurs; when the fault resistance varies between 100Ω and 300Ω, both Y-bridge converter and D-bridge converter commutate normally. Concerning the above two fault types, whether commutation failure occurs in inverter-side converter station or not, this paper constructs the topology of inverter-side network that can reflect the actual conducting states of converter valves. Thus the fault location calculated according to (44) is the actual fault location, and the fault likeness factor calculated according to (48) is bigger than the threshold value. The signals of voltage and current are shown in Figure 10, and the fault resistances are 300Ω. The calculated fault location and fault likeness factor corresponding to the above two fault types are shown in Figure 10.
It can be seen from Figure 10(c) and (g) that the calculation results of fault location in different fault cases are all close to 50%. The relative locating error slightly fluctuates as the fault resistance increases, but remains below 0.18%, thus the locating result is accurate. The locating error mainly comes from substituting the differential method with difference method.
It can be seen from Figure 10(d) and (h) that, in different fault cases, as the fault resistance increases, the values of fault likeness factors at the same time section all decrease. When phase-A-toground fault occurs with the fault resistance being 300Ω, the fault likeness factor first increases and then decreases as the time window slides, as shown in Figure 10(d). The minimum value of fault likeness factor 38.21 appears at t = 3.85 ms, which is much larger than the threshold value. When phase-AB-to-ground fault occurs with the fault resistance being 300Ω, the minimum value of fault likeness factor 44.51 appears at t = 4 ms, as shown in Figure 10(h).
According to Figure 10, concerning the above two fault types, the calculated fault location is consistent with the actual fault location, and the fault likeness factor is bigger than the threshold value. Thus the fault is identified to be at 50% line length from bus M on AC line M-N, and distance protection will operate correctly. Based on the above analysis, when in-zone fault occurs on AC line via different fault resistances, the proposed

Simulation results of in-zone fault at different locations on AC line
Phase-A-to-ground fault and phase-A-to-phase-B fault are set at different locations on AC line, and the fault resistance of phase-A-to-ground fault is 300Ω. At t = 0 ms, VTY 1 and VTY 2 of Y-bridge converter and VTD 1 and VTD 2 of D-bridge converter are conducted. After firing signals are issued to VTY 3 of Y-bridge converter and VTD 3 of D-bridge converter, commutation will take place in Y-bridge converter and D-bridge converter. When the voltage that VTD 1 of D-bridge converter bears first turns from negative to positive, the conducting states of Y-bridge converter and D-bridge converter are shown in Table 3. It can be seen from Table 3 that, when phase-A-to-phase-B fault occurs at any location on AC line, the blocking capability of VTY 1 in Y-bridge converter cannot be restored when it bears reverse voltage, thus it can be identified that commutation failure occurs in Y-bridge converter. After the commutation from VTD 1 to VTD 3 of D-bridge converter is finished, VTD 2 and VTD 3 of D-bridge converter are conducted, and VTY 1 and VTY 2 of Y-bridge converter are conducted. Similarly, it can be identified that, when phase-A-to-ground fault occurs with the fault location varying between 20% and 40%, commutation failure occurs; when the fault location varies between 60% and 95%, both Y-bridge converter and D-bridge converter commutate normally.
In the above two fault cases, this paper constructs the equivalent circuit of inverter station that can reflect the actual conducting states of converter valves, thus whether commutation failure occurs in inverter-side converter station or not, the fault location calculated according to (44) is the actual fault location, and the fault likeness factor calculated according to (48) is bigger than the threshold value. The signals of voltage and current are shown in Figure 11, and the actual fault locations are at 80% of AC line M-N. The calculated fault location and fault likeness factor in the above two fault cases are shown in Figure 11.
It can be seen from Figure 11(c) and (g) that the simulation results of actual fault distance percentage and the calculated fault location form a 45 • slanted plane, it means the actual fault distance and the calculated fault location at different time sections are consistent, and the locating error increases as the actual fault distance increases. When phase-A-to-ground fault occurs at 90% line length from bus M, the relative locating error reaches the maximum value 0.16%.
It can be seen from Figure 11(d) and (h) that, the fault likeness factors in different fault cases are bigger than the threshold value, which is consistent with the conclusion of Table 3. When fault occurs at any location on AC line, as the actual  Figure 11(d). When phase-A-to-phase-B fault occurs at 90% line length from bus M, the minimum value of fault likeness factor 80.37 appears at t = 0 ms, as shown in Figure 11(h). In the above fault cases, the calculated fault locations are the same as the actual fault locations, and the fault likeness factors are all bigger than the threshold value, thus they are identified as in-zone faults on AC line M-N, and distance protection will operate correctly. According to the above analysis, the proposed protection criterion is not affected by the fault location and commutation failure, and is highly sensitive even to fault at the end of line.

Simulation results of fault in DC system on the backside of AC line
Phase-A-to-ground fault is set at f 1 in Figure 1 with the fault resistance ranging between 0Ω and 300Ω. At t = 0 ms, VTY 1 and VTY 2 of Y-bridge converter and VTD 1 and VTD 2 of Dbridge converter are conducted. After firing signals are issued to VTY 3 of Y-bridge converter and VTD 3 of D-bridge converter, commutation will take place in Y-bridge converter and D-bridge converter. When the voltage that VTD 1 of D-bridge converter bears first turns from negative to positive, the conducting states of Y-bridge converter and D-bridge converter are shown in Table 4.
It can be seen from Table 4 that, when the fault resistance is 0Ω, the blocking capability of VTY 1 in Y-bridge converter cannot be restored when it bears reverse voltage, thus commutation failure occurs in Y-bridge converter. When the fault resistance varies between 50Ω and 300Ω, the conducting states of Y-bridge converter and D-bridge converter are the same as in normal operation state, thus Y-bridge converter and D-bridge converter both commutate normally.
In the above fault case, since the fault point is at f 1 in DC system, (44) is not satisfied, and the fault likeness factor calculated according to (48) is smaller than the threshold value. The signals of voltage and current are shown in Figure 11, and the fault resistances are 10Ω. The calculated fault likeness factor is shown in Figure 12.
It can be seen from Figure 12(c) that, in this fault case, as the fault resistance increases, the fault likeness factors at different time sections fluctuate slightly but remain below the threshold value. According to Figure 12(d), when the fault resistance is 0 Ω, the maximum value of fault likeness factor 0.11 appears at t = 3.45 ms, which is much smaller than the threshold value, thus no in-zone fault on AC line M-N is identified, and distance

Simulation verification of the proposed method regarding varying fault inception angle, window size and sampling frequency
Phase-A-to-ground fault is set at 50% line length from bus M on AC line M-N, with the fault resistance being 300Ω. When the window size is 10 ms, the sampling frequency is 10 kHz, and the fault inception angle varies from 0 to 90 • , the variation of fault location and fault likeness factor is shown in Figure 13.
It can be seen from Figure 13 that, as the fault inception angle increases, fault likeness factor at the same time section first increases and then decreases, while the relative error of fault When the fault inception angle is 0 • , the sampling frequency is 10 kHz, and the window size varies from 4 to 10 ms, the variation of fault location and fault likeness factor is shown in Figure 14.
It can be seen from Figure 14 that, as the window size increases, the relative error of fault locating at the same time section keeps decreasing, while fault likeness factor keeps increasing. In Figure 14(a), when the window size is 4 ms, the relative error of fault locating reaches the maximum value 0.99% at t = 1.35 ms. In Figure 14(b), when the window size is 5 ms, fault likeness factor reaches the minimum value 20.82 at t = 9.9 ms.
When the fault inception angle is 0 • , the window size is 10 ms, and the sampling frequency varies from 4 to 10 kHz, the variation of fault location and fault likeness factor is shown in Figure 15.
It can be seen from Figure 15(a) and (b) that, as the sampling frequency increases, the relative error of fault locating at the same time section keeps decreasing, while fault likeness factor keeps increasing. According to Figure 15(a), when the sampling frequency is 4 kHz, the relative error of fault locating reaches the maximum value 1.2% at t = 6.8 ms. In Figure 15(b), when the sampling frequency is 4 kHz, the fault likeness factor reaches the minimum value 26.69 at t = 9.9 ms. Based on the above analysis, the proposed protection criterion is not affected by the variation of fault inception angle. Even when the sampling frequency is relatively low and the window size is relatively small, the proposed scheme can still correctly and reliably identify in-zone and out-of-zone faults.

4.6
The impact of R W0 and L W0 on the performance of the proposed protection scheme Phase-A-to-ground fault is set at 50% line length from bus M on AC line M-N, with the fault resistance being 100Ω and zerosequence impedance varying from 1.0 + j3.19Ω to 2.0 + j6.37Ω. In this case, the variation of fault location and fault likeness factor is shown in Figure 16.
It can be seen from Figure 16(a) that, as zero-sequence impedance varies, the calculated results of fault location remain close to 50%, with the relative error of fault locating fluctuating slightly. When zero-sequence impedance is 1.4 + 3.822Ω, the relative error of fault locating reaches the maximum value 0.18%, thus the locating result is relatively accurate. According to Figure 16(b), as zero-sequence impedance varies, fault likeness factor remains above the operation threshold value. When zero-sequence impedance is 1.4 + 5.096Ω, fault likeness factor reaches the minimum value 873.71, which is much larger than the operation threshold value. Thus it is correctly identified as in-zone fault on AC line M-N, and the protection will operate.
Based on the above analysis, the proposed protection criterion can correctly distinguish between in-zone and out-of-zone faults, and is scarcely affected by the variation of zero-sequence impedance of inverter-side AC system.

4.7
The applicability of the proposed protection scheme in large AC/DC hybrid system To verify the applicability of the proposed protection scheme in large AC/DC hybrid system, simulation tests are conducted on RT-LAB platform. The structure of test system is shown in Figure 17, where the receiving-end AC system uses IEEE 39bus system, and DC system applies CIGRE HVDC standard model. Phase-A-to-ground fault is set at 50% line length from bus M on AC line M-N, with the fault resistance varying between 0Ω and 300Ω. In such fault case, the variation of fault location and fault likeness factor is shown in Figure 18.
According to Figure 18(a), as the fault resistance varies, the calculated results of fault location remain close to 50%, with the relative error of fault locating fluctuating slightly. When the fault resistance is 80Ω, the relative error of fault locating reaches the maximum value 0.5% at t = 1.8 ms. Thus, the locating result is relatively accurate.
It can be seen from Figure 18(b) that, as the fault resistance increases, fault likeness factor at different time sections first increases and then decreases, but it remains above the operation threshold value. When the fault resistance is 0Ω, fault likeness factor reaches the minimum value 40.51 at t = 9.95 ms, which is much larger than the operation threshold value. Thus it is identified as in-zone fault, and protection will operate correctly.
Phase-A-to-ground fault is set at different locations within the protection zone of AC line, with the fault resistance being  Figure 19.
It can be seen from Figure 19(a) that, a 45 • inclined plane is formed by the axes of time, actual fault location and calculated fault location. It means the calculated fault location is consistent with the actual fault location at different time sections, and the relative error of fault locating increases as the actual fault distance increases. When phase-A-to-ground fault occurs at 90% line length from bus M, the relative error of fault locating reaches the maximum value 0.25% at t = 0.8 ms.
According to Figure 19(b), in different fault cases, fault likeness factor remains above the threshold value. As the actual fault distance increases, fault likeness factor at the same time section keeps decreasing. When phase-A-to-ground fault occurs at 90% line length from bus M, fault likeness factor reaches the minimum value 26.18 at t = 9.9 ms.
Based on the above analysis, the proposed protection criterion is applicable to large AC/DC hybrid system, with relatively high sensitivity and fast identification capability.

CONCLUSION
Concerning the mal-operation of distance protection in AC/DC hybrid system due to commutation failure caused by AC-side fault, a novel AC line distance protection scheme based on fault likeness factor is put forward, which can solve problems in traditional distance protection caused by commutation failure, such as narrowed protection range and over-reach operation. The proposed scheme has the following characteristics.
1. The time-varying model of AC/DC hybrid system considering the dynamic process of commutation failure is built, which can simultaneously reflect the current conducting state of inverter valves and AC-side fault state. Thus, the inaccuracy of fault model in traditional method caused using controlled source to represent DC system can be avoided. 3. The proposed scheme can correctly and reliably identify inzone and out-of-zone faults when commutation failure is caused by different types of fault at different locations. 4. When fault occurs at the outlet of AC line backside system, the protection does not operate. Even when the zerosequence network of receiving-end AC system varies, the proposed method can still correctly identify the fault location. 5. The proposed scheme is strongly immune to fault resistance, and is highly sensitive even to high-resistance fault at line end.