1. Introduction

The electrification of the railroad is continuously accomplished with the opening of the demands of the domestic high speed railway and need for a quality-enhanced means of railroad transportation is increasing dependent on changing transportation demands. In addition, the reliance on electrical power is gradually rising in the railroad field of industry [1-2]. Therefore, the stable supply of electricity power applied to the electric railway vehicle and claims about improvement of power quality are suddenly increasing and the importance of the protective relay acting in the stability maintenance of the power system is increasing. The cause of the failure in the AC electric railway power system is divided into Ground, Short of feeding circuit and faults on the inside of the substation[3-4], because the fault current is high, the real-time current is detected and the failure promptly has to be removed. because of high speed of the railway vehicle powered by the electrical energy and the increase of power load and regenerative power available from the electric railway vehicle, there is not a big difference between fault current and load current. The high performance protection system is necessary in order to prevent malfunction to the protective relay due to the load current. In order to implement the high performance protection system, detailed modelling about the element of the power feeding system has to be preceded. The foreign product is mostly applied to the AC protective relay for the feed system that is the constituent of AC feeding system that is being applied domestically. High cost of the protective relay construction and maintenance is occurred with the independent technical absence of the protective relay. Protection function of every foreign product is already equipped, standardized protection for the AC feeder system is difficult.

In this paper, the short-circuit current is analyzed by numerical analysis and simulation for the correct operation of the protective relay and the formula has been proposed for simple and accurate calculation of the short-circuit current.

Also, in order to confirm the validity of the proposed formula, the simulation error rate was analyzed compared with the conventional numerical methods. And the formula applying the AT leakage impedance was derived and compared with simulation.

2. Impedance Calculation and Simulation

The AT feeding method is widely used, and for power, has good characteristics for high power long-distance feeding and induced obstacle because of the recent surge in load current. AT feeding method is the system for connecting the neutral point of the transformer winding on a rail at about 10 [km] intervals along the track.

In this paper, a short-circuit current was calculated through a short-circuit impedance derived in accordance with the circuit configuration for fault current analysis.

2.1 AC AT feeder system

Typically, the feed circuit applied in Korea for supporting a train which uses electricity as the energy source is shown as in Fig. 1.

Fig. 1.Configuration diagram of AC feeder circuit

This circuit consists of substation, sectioning post which uses closing and opening for division and extension of feeder section, sub sectioning post for restriction from power failure or blackout when working and accident, auto transformer post for voltage drop compensation of overhead trolley wire on catenary terminal and reduction of inductive disturbance [5-7].

Also, TP(Tie-Post) is installed and operated as arc measures for cross over road for short railroad terminal.

Fig. 2 is equivalent circuit of Fig. 1 and shows AT method of electric supply which most of Korea has been using. The AT is installed on the trolley and feeder, and the neutral point is installed on the rail. This method has both ends of ATs connected to trolley and feeder.

Fig. 2.AC Electric railway of AT feeder method

Thus, trolley has higher electric potential than rail and feeder has lower electric potential than rail and earth.

AT applies 55[kV] between trolley and feeder based on scott transformer secondary-side and 27.5[kV] between trolley and rail since neutral point is connected to the trolley and rail.

2.2 Conventional calculation method

Fig. 3 shows power supply circuit impedance characteristic between trolley, rail and feeder, as shown in Fig. 2. There are T-R short circuit, F-R short circuit, T-F short circuit in AC electric railway AT feeding method. Impedance increases with distance increase of fault location from traction substation (SS). However, impedance decreases if it gets closer to the specific location AT such as sectioning post (SP), then sub sectioning post (SSP) is installed [8].

Fig. 3.Impedance characteristic of AT feeder method

Conversely, in the first section of Fig. 3, when AT interval distance is represented by D, the distance to the T-R short circuit point at the substation installed AT is represented by x, circuit excluding the load of the vehicle is the same as Fig. 4. Short circuit impedance as a short circuit occurs in first section impedance is represented by Z and Short circuit impedance, as a short circuit, occurs in a second section represented by Z' [9].

Fig. 4.Single-line simplified equivalent circuit

Eqs. (1)~(3) of equivalent circuit of Fig. 4 are satisfied by the Kirchhoff's law in the loop 1~3 single-line simplified equivalent circuit of Fig. 4[10].

I1 , I2 can be derived from equations (1)~(3). And it is possible to determine the line impedance of the case of T-R short circuit at a distance x through following equation.

In the second section, the addition of in Eq. (5) is the same as Eq. (6).

where, G = ZT + ZF + 4ZR, H = ZTZF + ZTZR + ZFZR

2.3 Proposed calculation method

The conventional formula does not include the value of AT transformer. But the proposed method is calculated by the conventional method in addition to AT leakage reactance in section 1. but in this paper, a new calculation method is proposed for a simple and fast calculation in section 2~3

Eqs. (7)~(9) of equivalent circuit of Fig. 5 are satisfied by the Kirchhoff's law in the loop 1~3 single-line simplified equivalent circuit of Fig. 5.

Fig. 5.Simple equivalent circuit in 2nd section

I1 , I2 can be derived from equations (7)~(9). And it is possible to determine the line impedance of the case of T-R short circuit at a distance x through following equation.

In the second section, the addition of ( ZT + ZF) D in Eq. (10) is the same as Eq. (11).

where, ZT is catenary impedance [Ω/km], ZR is rail impedance [Ω/km], ZF is feeder line impedance [Ω/km], Z is impedance of short point[Ω], ZAL is line impedance of T-R short, D is distance between AT[km], Distance to the short circuit point at AT [km], ZAT is leakage reactance of auto transformer[Ω]

Similarly, each time a section is increased, ( ZT + ZF) D is added.

2.4 Impedance for the fault current numerical calculation

When an accident, such as a short circuit and ground fault occurs, EMTDC/PSACD was used to analyze the fault current. A short-circuit accident in a section of 1~20 [km], has been simulated at intervals of 1 [km].

In order to calculate the fault point impedance, applied catenary impedance is shown in Table 1 as the data of the real system between the Wonju ~ Gangneung.

Table 1.Catenary Data for fault impedance calculation

Table 2 shows the calculated impedance values using the conventional numerical calculation of the impedance. The short-circuit impedance of 1[km] is 5.2499 [A], which was the largest current. And it was confirmed that if the distance increases and short-circuit impedance increases.

Table2.Data of short-circuit Impedance according to distance

2.5. Simulation

Simulation was modelled with each one of the auto-transformer of SP, SSP from scott transformer secondary and was modelled to be powered up to 27.5[kV]. The catenary was modelled in detail.

Fig. 6 is configured in the catenary modelling, using PSCAD / EMTDC to apply the resistance and reactance components o f trolley, rail and feeder and it is also possible to short-circuit simulation.

Fig. 6.AT feeder system modeling of AC electric railway (The 1st Section)

The scott transformer secondary voltage is 55 [kV] and modelling is made in the order of SS-SSP-SP. The primary winding is connected to twice times the number of turns of the secondary side in auto-transformer (AT). The voltage on the primary side is 55 [kV], Voltage on the secondary side is 27.5 [kV]. The point connecting both windings is connected to the rail.

The short circuit fault is simulated at each 1[km] interval in a section of 1~30 [km]. Fig. 7 shows an example of short circuit fault, and shows the (a) instantaneous value and the (b) RMS current value. Comparison of numerical analysis and simulation result was done in a steady-state of the RMS values.

Fig. 7.6[km] point short circuit fault current waveform

2.5.1 Simulation of conventional calculation method ( ZAT =0.033j[Ω])

The leakage reactance is applied to confirm the effect of leakage reactance in the simulation. First, the leakage reactance is set to a very small value in order to analyze the values of the condition without leakage reactance of auto-transformer in 2.5.2, and the simulation was carried out. Table 4 shows comparison of simulation results and short-circuit current value using conventional numerical calculation. And the maximum error rate in the section 1 is 2.676 [%] of 1[km] point, and the minimum error rate is 0.008 [%] of 30[km] points. The result is less than 1 [%] excepting at point 1[km] and 2[km]. Because the short-circuit current of 1, 2[km] is larger than the short-circuit current of the other point, the error rate is increased. The short circuit current value and the value of the numerical simulation calculations were almost similar as the average error rate was 0.363[%].

Table 4.Comparison of conventional calculation and simulation value for short-circuit current

2.5.2 Simulation of proposed calculation method ( ZAT = 0.033j[Ω])

Table 5 shows comparison of the simulation results and short-circuit current value using the proposed numerical calculation and the maximum error rate in section 1 is 1.641 [%] of 1[km] point like the conventional calculation method, and minimum error rate is 0[%] over 12[km] point and the result is less than 1 [%] except points 1[km].

Table 5.Comparison of proposed calculation and simulation value for short-circuit current

The proposed formula is simpler but the results were more accurate as the average error rate is 0.281 [%].

2.5.3 Simulation of conventional calculation method ( ZAT =0.45j[Ω])

The leakage impedance of the actual auto-transformer is applied in the simulation. Table 6 is tables comparing the simulation results with short-circuit current value using conventional numerical calculation and the maximum error rate in the section 1 is 25.299 [%] of 1[km] point, and the minimum error rate is 1.23 [%] of 25[km] points. The average error rate was 4.624[%].

Table 6.Comparison of conventional calculation and simulation value for short-circuit current

2.5.4 Simulation of proposed calculation method ( ZAT = 0.45j[Ω])

Table 7 is tables comparing the simulation results with short-circuit current value using the proposed numerical calculation and the maximum error rate in section 1 is 8.787 [%] of 10[km] point and minimum error rate is 0.099 [%] over 16[km] points.

Table 7.Comparison of proposed calculation and simulation value for short-circuit current

The proposed formula is simpler but the results were more accurate as the average error rate is 1.888 [%].

2.6 Comparing the error rate on the basis of simulation

Fig. 8 is a compares the proposed and conventional error rate calculation method. In section 1, error rates are the same. but error rate of the proposed calculation method is lower except after 23[Km] and It can be confirmed that the proposed calculation method is lower by as much as 0.006 [%].

Fig. 8.Comparison of error rate( ZAT =0.033j[Ω])

Fig. 9 shows comparison of the proposed and conventional error rate calculation method when applying the leakage reactance. Error rate of the proposed calculation method is lower and It can be confirmed that the proposed calculation method is lower by as much as 2.836 [%].

Fig. 9.Comparison of error rate( ZAT =0.45j[Ω])

3. Conclusion

In this paper, short-circuit current is analyzed by numerical analysis and simulation for the correct operation of the protective relay and the formula has been proposed for simple and accurate calculation of the short-circuit current.

In order to confirm the validity of the proposed formula, the simulation error rate was analyzed compared with the conventional numerical methods.

The average error rate of comparing the short circuit current value using conventional calculation method and the value of the numerical simulation calculations was 0.363[%]; and the average error rate of comparing the short circuit current value using proposed calculation method with the value of the numerical simulation calculations was 0.357[%]. These results were similar but the error rate of the proposed calculation method is lower than the conventional one.

Compared to simulation applying the leakage reactance of the actual auto-transformer, error rate of the conventional method is 4.624% and error rate of the proposed method is 1.888%. It can be confirmed that the proposed calculation method is lower by as much as 2.836 [%]. It is considered an error because the simulation results are not correct to 100%. Thus, it demonstrated the feasibility of the proposed calculation method.

In future research, the study to increase the accuracy of the protection relays is required taking into consideration the source impedance.