A study of the power capacity of regenerative inverters in a DC electric railway system

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1 Energy Management in the Train Operation 35 A study of the power capacity of regenerative inverters in a DC electric railway system C. H. Bae, M. S. Han, Y. K. Kim, S. Y. Kwon & H. J. Park Korea Railroad Research Institute, South Korea Abstract This paper presents a method of determining power capacity and installation positions of regenerative inverters installed in DC electric railway system. This method uses the regenerative power data obtained from Train Performance Simulation (TPS) and Power Flow Simulation (PFS). The simulation results of TPS and PFS for Seoul subway lines 5 and 6 were applied, and suitable substations where regenerative inverters should be installed and the suitable power capacity to be installed were decided. Keywords: regenerative inverter, electric railway system, train performance simulation, power flow simulation. 1 Introduction In a DC electric railway system, 22.9kV system voltage is converted into DC 1500V voltage through a 3-phase silicon diode rectifier and supplied to traction energy with railway motor cars. Since the regenerative power generated at the regenerative braking of motor cars cannot be absorbed into the supply grid in the case of diode rectifiers, this power should be used at nearby powering trains or consumed as heat at resistances mounted on the cars. However, if a regenerative inverter is installed in inverse-parallel with the diode rectifier, it can absorb this dump regenerative energy and feed it into an electric high-voltage grid for reuse. Accordingly, the energy can be saved by reusing dump regenerative power wasted away as heat, and the braking and ATO performance of motor cars can be improved through enhancing the regenerative power absorption rate of catenary lines. Despite these advantages, regenerative inverters cannot be installed at all substations for electric railways because the manufacturing and installation cost of regenerative inverters is higher than the benefit from the reuse of regenerative doi: / / 04

2 36 Power Supply, Energy Management and Catenary Problems powers. Thus, they should be installed at sections with a long continuous slope or where regenerative power loss in the resistor bank becomes a problem. In order to determine the appropriate installation positions, number and capacity of the regenerative inverter, it is necessary to calculate the accurate regenerative power generated in a subway line. This paper suggests determination schemes of the capacity and installation positions of regenerative inverters installed in 1500V DC electric railway system. We suggested a method that approximates using parameters related to substations where regenerative inverters are installed, railway lines and operating motor cars, and another that calculates using regenerative power obtained from Train Performance Simulation (TPS) and Power Flow Simulation (PFS) developed by Korea Railroad Research Institute for light rail transit system [1]. We carried out TPS and PFS for Seoul subway lines 5 and 6 and calculated the regenerative power and decided the substations where regenerative inverters should be installed and the suitable power capacity to be installed. 2 Power capacity of the regenerative inverter Fig. 1 shows a diode rectifier and a regenerative inverter at an electric railway substation. The 12-pulse diode rectifier generates 1500V DC voltage and the IGBT regenerative inverter detects the voltage rise of the catenary line caused by the dump regenerative energy, absorbs the regenerative power, and transmit it to a high-voltage grid for reuse. Since many trains can brake simultaneously in a subway line, the peak power rating of the regenerative inverter needs to be higher than that of industrial inverters. Thus, the regenerative inverter allows the output AC current to limit at a certain level in constant current control mode in general. However, since this current cannot increase infinitely due to the limitations of the overhead line voltage, it is inevitable that the intermittent peak power rating of the regenerative inverters increases as much as possible. In order Figure 1: DC electric railway substation equipped with a regenerative inverter.

3 Energy Management in the Train Operation 37 to estimate the correct power capacity of such a regenerative inverter installed at substations for DC electric railways, it is desirable to block the regenerative power loss in the breaking chopper and resistor of all trains on a subway line, make a route for absorbing regenerative energy, and measure this surplus regenerative energy. Although this method can measure the surplus regenerative energy at a substation exactly, it requires regenerative power absorbing equipment, such as a resistor bank, installed at a substation. However, the additional installation of resistor banks at electric railway substations is not easy due to insufficient underground capacity in general. There are other methods, such as approximating based on variables related to the substation, operating line, train condition and regenerative power in other lines and calculating using TPS and PFS. However, because the level of regenerative power varies according to the conditions of the line on which the regenerative inverter is installed, the train condition and the operation condition, it is difficult to determine the accurate capacity through approximation based on these major variables. Accordingly, we need to calculate dump regenerative power in various train operation conditions by conducting TPS and PFS under different conditions of line, train and substation. 3 Approximation method Fig. 2 shows the layout of a substation for a DC electric railway for calculating the power capacity of a regenerative inverter, and table 1 shows the calculation conditions. A regenerative inverter in charge of a 12km-long regeneration section is installed at substation B, and the number of trains running in the section, n, is obtained by eqn. (1). l n 60 [trains/hour] (1) v h s where b means an integer larger than b, distance ( l ), headway ( h ) and commercial speed ( v s ) are represented as units of meters, minutes, and km / h, Figure 2: DC 1500V electric railway power system.

4 38 Power Supply, Energy Management and Catenary Problems respectively. The total regenerative energy that takes place in a day in section l can be approximated in the following equations. Maximum power consumption per hour, P m, is calculated from the train ton-kilo capacity as follows, P m 2 n s w l (1 a) k [kw] (2) Here, the coefficient 2 means a double track section, and a is the standard deviation of power variation according to the train diagram. The power capacity of the regenerative inverter can be estimated using a power regeneration rate and a regenerative braking efficiency rate obtained from substations equipped with regenerative inverters at different railway substations. The power regeneration rate, 1, means the ratio of absorbed regenerative power to the maximum power consumption of substations with a regenerative inverter, P m. The regenerative braking efficiency rate, 2, means the ratio of absorbed regenerative power to the total regenerative power generated within the section covered by a substation with a regenerative inverter. Here, the total regenerative power includes the regenerative power consumed by nearby accelerating trains and regenerative power loss in the resistor bank. In general, power regeneration rate 1 ranges from 0.23 to 0.20, and regenerative braking efficiency rate 2 from 0.67 to 0.63 [2]. Using these data, the capacity of a regenerative inverter can be calculated as eqn. (3), where W denotes the total regenerative power generated from the section covered by the regenerative inverter. W includes the regenerative power consumed by nearby accelerating trains and power loss in the resistor bank. Accordingly, the capacity of the regenerative inverter should be larger than W considering the operation condition of the line. 1 W P m [kw] (3) Braking force at deceleration rate,, can be obtained as eqn. (4). The braking electric power generated from the regenerative braking performance of a train at speed of v [km/h] is calculated by eqn. (5). F b ( 31 r ) s w [N] (4) Fb v Pb [kw] (5) 367 The regenerative peak current, I b, can be calculated as follows. Pb Ib [ka] (6) V inv On the conditions of table 1, W is obtained as 1480[kW] and I b 3.5[kA]. Thus, the power capacity of the regenerative inverter can be approximated as

5 Energy Management in the Train Operation MVA, 350% 1 minute. However, this approximated calculation method does not consider the railroad and train operation conditions: grade, curvature, and headway duration. It can be used only to review the total system capacity rather than as a specification to install a regenerative inverter. Table 1: Calculation conditions. Item Value Item Value Number of cars, s 8 (4M4T) Running resistance, r 10kg/ton Headway, t h 2.5 min Maximum speed, v m 80km/h Weight, w 48 ton/car Commercial speed, v s Regenerative operation Decelerating rate, 0.97 m/s 2 voltage, V inv 35km/h 1650V Train ton-kilo capacity, k 50kW/1000ton km Power regeneration rate, Regenerative braking Power delivery efficiency, efficiency rate, 2 4 Power flow simulation method This section explains how to determine the capacity of a regenerative inverter using TPS and PFS. PFS is performed by changing the power capacity and the installation number of regenerative inverters, and the regenerative power loss of a railway line is calculated. The loss ratio of regenerative power means the ratio of regenerative power consumed as heat on the train to the whole regenerative power generated as shown in eqn. (7). After the optimal position and the number of regenerative inverters are determined, as a way of reducing the calculated loss ratio of regenerative power to the maximum, the root mean square of regenerative power (RMS power) and peak power are calculated. The effective regenerative power per hour calculated by eqn. (8) determines the continuous rating of the regenerative inverter, and is used to determine the peak power rating based on the maximum regenerative power rate and the braking time of motor cars. P 1 inv R 100 (7) Preg where P reg denotes the 1-hour average value of the regenerative power generated in a subway line and P inv denotes the 1-hour average output power of regenerative inverters in a subway line. In order to decide the continuous and intermittent peak power capacity of the regenerative inverter, the mean square value of the regenerative power generated in a substation is calculated as eqn. (8).

6 40 Power Supply, Energy Management and Catenary Problems 1 t 2 P preg ( t) dt (8) T t s 1 Here, P is the root mean square of regenerative power P reg (t), and T s sets 1 hour from t 1 to t 2. The determination method of the suitable installation location and power capacity of the regenerative inverters to be installed is shown in the block diagram in fig. 3, and the details are as follows. 1. Perform PFS for the case that regenerative inverters are installed in all substations on the line. 2. Calculate the mean square of regenerative power of each substation, and rank the substations according to regenerative power. 3. Perform PFS after removing the regenerative inverters from the two substations with the lowest regenerative power. 4. Again calculate the root mean square of regenerative power of each station with a regenerative inverter, and calculate the loss ratio of regenerative power for the whole line. 5. Perform PFS while removing the regenerative inverters one by one from the substations with the lowest regenerative power. 6. Draw the curve of the loss ratio of regenerative power according to the number of regenerative inverters installed in substations, and select the curve that shows the largest reduction in regenerative power loss. 2 Train Performance Simulation DC Power Simulation Calculate Maximum and Root Mean Square value of Regenerative Power Calculate Loss Rate of Regenerative Power Decrease Installation Number of Regenerative Inverter Decide installation substation Decide Power Rating of Regenerative Inverter Figure 3: Flowchart for substation selection.

7 Energy Management in the Train Operation 41 Figure 4: Flowchart for regenerative inverter capacity line voltage[v] comsumed power[kw] Time[min] Figure 5: Seoul line 6 substation 8 without a regenerative inverter. Once the position and number of regenerative inverters to be installed are determined, the rated capacity of the regenerative inverter and the peak power capacity are calculated through the procedure in fig. 4. The rated capacity of a regenerative inverter sets the root mean square value of regenerative power obtained from the substations, and the peak power rating is determined by the ratio of the peak regenerative power to the root mean square value of regenerative power. In addition, because the time for the rise of catenary line voltage caused by the dump regenerative power of the subway substations does not exceed 1 minute, the peak power rating is assumed to continue for 1 minute. We performed TPS and PFS using data on trains and lines of Seoul subway lines 5 and 6. Figs. 5 and 6 show the catenary line voltage and the power consumption waveform of substations according to whether a regenerative inverter is installed or not. In fig. 5, the regenerative power generated by the power braking of motor cars is increasing the catenary line voltage instantaneously. Fig. 6 shows that regenerative power is absorbed by the substation and the variation of catenary line voltage is reduced.

8 42 Power Supply, Energy Management and Catenary Problems Fig. 7 shows absorbed regenerative power according to the number of substations with a regenerative inverter. Fig. 7 (a) shows the case that regenerative inverters are installed in all substations. Regenerative power is different among substations because of the grade differences of line, distance between stations and train operation conditions. Figs. 7(b) (f) show the regenerative power of each substation while removing the regenerative inverters one by one from the substations with the lowest regenerative power. As the number of substations with a regenerative inverter decreases, the regenerative power at nearby substations with a regenerative inverter increases to some degree line voltage[v] comsumed power[kw] Time[min] Figure 6: Seoul line 6 substation 12 with a regenerative inverter. (a) (b) (c) (d) (e) (f) Figure 7: RMS of regenerative power in Seoul line 6.

9 Energy Management in the Train Operation 43 Figure 8: Loss rate of regenerative power in Seoul line 5. Figure 9: Loss rate of regenerative power in Seoul line 6. Table 2: Power simulation results of Seoul subway lines. Line 5 6 Substation RMS of regenerative Peak regenerative Ratio power[kw] power[kw] [%] Euljiro 4-ga Haengdang Majang Eungam Daeheung Samgakji Shinnae Figs. 8 and 9 show the curve of loss ratio of regenerative power changing according to the number of regenerative inverters in Seoul lines 5 and 6. As a large-capacity regenerative inverter makes it possible to transmit more regenerative power to the supply grid, the loss ratio of regenerative power is reduced, and the curve of regenerative power loss goes down with the increase in the number of regenerative inverters installed. However, the reduction rate of regenerative power loss is not constant. This is because regenerative power is different among substations. As shown in figs. 8 and 9, reduction in the loss ratio of regenerative power decreases gradually with the increase in the number of substations with a regenerative inverter. In the case of Seoul line 6, the reduction in the loss ratio of regenerative power is largest when regenerative inverters are installed at four substations. Because a larger reduction in regenerative power loss is not expected from the installation of more regenerative inverters, it is desirable to install four regenerative inverters. As in fig. 7, the adequate capacity of the regenerative inverters for substations 1 and 5 can be selected as 1.5MVA and 1MVA for substations 6 and 12, respectively. However, it is economically more efficient to install a regenerative inverter only at substation 5 than at both, because substations 5 and 6 are neighboring to each other. We performed PFS for Seoul subway lines 5 and 6, and present the results in table 2. The suitable power capacity of the regenerative inverter is determined by

10 44 Power Supply, Energy Management and Catenary Problems estimating the rated capacity as larger than the root mean square of regenerative power from each substation and determining the peak power rating using the ratio of peak regenerative power to the rated capacity. 5 Conclusions This paper presents the methods for determining the installation location and power capacity of regenerative inverters in DC electric railway systems. Using a simple approximated calculation based on the conditions of the substations and train operation and the regeneration rate of other railway lines, the power capacity of the regenerative inverter was calculated. Also, the loss ratio of regenerative power and the root mean square of regenerative power for each substation were obtained using TPS and PFS and the installation location and number of regenerative inverters was decided. Applying TPS and PFS to Seoul subway lines 5 and 6, we obtained the suitable installation location and the power capacity of the regenerative inverters to be installed. References [1] S.K. Jung et al., Right Rail transit system development, Korea Railroad Research Institute, [2] Electric Railway DC Power Supply System Investigation Committee, Phenomena of Power Supply System Including Regenerative Cars and Future Directions, Technological Report No. 296 of Japanese Institute of Electrical Engineers, 1989

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