Challenge A: A more and more energy efficient railway

A Model and Approaches for Synchronized Energy Saving in Timetabling

K.M. Kim1, K.T Kim1, M.S Han1 Korea Railroad Research Institute, Uiwang-City, Korea1

Abstract This paper proposes a mathematical approach that can increase energy saving in timetables. The energy-efficient timetabling method, we use, maintains the planned traveling time between stations, but coordinates the train departure times at the starting station from current timetable.We formulate this problem as a multi-criteria mixed integer programming to minimize the peak energy and simultaneously to maximize the re-usage of regenerative energy.We also apply our model to the instance obtained from the real-world data of the Korea Metropolitan Subway. From the experiments, we can see an improvement of not only approximately 40% in peak energy, but also 5% in re-usage of regenerative energy.

1.Introduction In these days, railways are being reevaluated as an environmentally friendly mode of transportation. The researchers develop the energy efficient railway technologies, such as energy storage system, energy efficient driving. Mass rapid transit (MRT) railways, which are an important means of public transportation in urban areas, have operational characteristics, short headways, frequent departures and arrivals. Therefore, when multiple trains are operating in the same power supply system, it is important to synchronize the traction energy and regenerative energy which may be exported on deceleration. However, the regenerative energy is used mainly for the vehicle cooling- heating system and has a low reuse rate. Therefore, it is necessary to increase the reuse rate by synchronized energy saving.

Fig. 1 Electric Power Consumption Fig. 2 Electric Charge

Figure 1 and 2 show the annually change of electric power consumption and electric charge of Seoul Metro,operating subway lines 1 to 4 provides mass transportation to the citizens of the Seoul metropolitan area.The cost of energy rise about 2% every year even though the continued effort of reduce energy consumption in vehicle.In Europe, the European International Union of Railways(UIC) and 27 institutes began the Railenergy Project inorder to respond to the rising cost of energy. The goalof the project is to reduce the total energy consumptionof the railroad system by 6% by 2020. Of that goal, 2%will be saved in railway operations as a result of energyefficient driving and timetabling. This paper is organized as follows. Section 2 reviews therelated previous researches. Section 3 defines the timetabling problem.Section 4 formulates the mathematical model. Section 5presents theresults of an experiment examining the current timetable,and Section 6 presents the conclusion and direction offurther study.

Challenge A: A more and more energy efficient railway

2. Literature review Many researchers have addressed ways to reduce energy consumption by railroads. In a study of the energy savings with train operations, Albrecht et al. [1]studied a way to reduce the peak energy consumptionand maximize the regenerative energy by synchronizingbraking and powering using the reserve time when running between stations. They proposed a genetic algorithm to do this. Gordon et al. [2] presented severalstrategies for train operation with reduced energy consumption, especially a method that coordinates coasting and the stop and start times of trains.There are few research articles on saving the traction power of MRT railways. The articles on train scheduling can be classified into two categories, based on methodology: timetabling and the control of train operations based on real-time control. In this paper, we focus on reviewing timetabling methods and adjusting prearranged train schedules including the departure times in an existing timetable to reduce the power consumption. Chen et al. [3] proposed a method of minimizing the maximum traction power by adjusting the dwell times of MRT railways in each station. To solve the problem, they developed a genetic algorithm (GA) and showed that their method saved up to about 29% of the maximum traction power. Kim et al. [4]developed a mathematical model with the objective of minimizing the number of trains running simultaneously in the traction phase. They showed that the number of trains running under power could be reduced by up to 25% at peak times. However, the amount of energy saved could not be estimated. Kim et al. [5] suggested an integer programming model with the aim of reducing the peak traction energy of MRT railways and developed a heuristic algorithm. The basic idea embedded in the algorithm was to adjust the departure times of trains based on an existing timetable. However, the model does not consider the use of the regenerated brake power produced in the deceleration phase. Kim et al. [6] extend that previous model by incorporating both the use of regenerated brake power produced by other trains and measuring the amount of the energy lost. This paper considers the problem of using regenerated brake power as regenerative energy to lessen power consumption of mass rapid transit (MRT) railways. The efficient use of regenerative energy is currently a major issue for the railway industry. The goal of this research is to minimize the peak power consumption and to maximize the use of regenerative energy reduce power consumptionsimultaneously.

Table 1 Summary of Previous Studies

Power Control Model Regenerative Study Objective Supply /Adjust /Algorithm Energy System Gordeon et Min. Power Consumption O X al. (1998) Albercht Max. Re-usage of Running Time GA O O (2004) Regenerative Power Chen et al. Min. Peak Power Dwell Time GA X X (2005) Min. Num. of Kim et al. Departure Heuristic Simultaneous Accelerating X X (2009) State IP Model Trains Kim et al. Departure Min. Peak Power IP Model X X (2010) State Kim et al. Departure MIP Min. Peak Power O O (2010) State Model Min. Peak Power + Min. Departure MIP Our Study O O Power Consumption State Model

3. Problem Description In this section, to describe a reduction in the peak and total energy consumption when timetabling, time slotisdefined. The time slotdivides continuous time into discrete 15-second intervals. Time is expressed indiscrete units because the existing timetable in Korea is based on a 30-second unit scale and the electric energyconsumption over time need not be calculated continuously. Since an analysis of the train speed profile showedthat there are sections where the powering time is less

Challenge A: A more and more energy efficient railway

than 30 seconds, the unit time interval was set to 15 seconds.Next,assumptions made in this paper can be summarized as follows: (a) departure times of trains are given and deterministic; (b) amount of traction energy of forward and backward trains are the same; (c) the travel times between stations and dwell times are constant.

3.1Railwaysoperationsandelectricfeatures

If a train running between two stations consumes electric energy, the energyconsumption of a train can be divided into three phases:the traction phase requires high power(traction energy); thecoast phase requires low or no power;and the deceleration phase may export regenerated brakepower(regenerative energy).Generally, regenerative energy are equal to approximately 30~40% of the total traction energy. This principle is explained by the conversion of kinetic energy into electrical energy. That is, the kinetic energy that originates in the braking phase can be converted into electrical energy and transferred to the power supply system for use by other trains running within same power supply system. Note that if the regenerative energy is not used for other trains, it is lost. The use of regenerative energy is closely related to a group of stations within a specific range of the power supply system.Before explaining the concept of a group of stations, let us consider the power supply system. The power supply system covers adjacent stations. In the power supply system, electricity flows from high to low voltage to operate trains at adjacent stations within a specific range of the power supply system. The group of stations also represents a zone within which regenerative energy can be interchanged. That is, trains with regenerative energy can provide it to other trains running within the group of stations. In figure 3, the regenerative energy produced by train B running in the deceleration phase can be used by trains C, D, and E in the traction phase because the trains are running in adjacent stations within a specific range of the power supply system.

Fig. 3A Group of Stations

Table 1 shows the electricity billingof an MRT railway. We see the main factors determining electric charge are peak and total power consumption.Therefore, we consider how to reduce them at the same time.

Table 2Monthly Electric Charges of an MRT Railway

Num Type Details Ratio = Peak Power Consumption[kW] × Basic 1 Basic Fee 15.3% Rate[KRW/kW] = Total Power Consumption[kWh] × Usage 2 Usage Fee 72.6% Rate[KRW/kWh] 3 Allotment =(Basic Fee + Usage Fee) × Allotment Rate 3.3% 4 VAT =(Basic Fee + Usage Fee) × VAT Rate 8.8% 5 Total = 1 + 2 + 3 + 4 100%

Challenge A: A more and more energy efficient railway

3.2 Peak Energy

The basic fee is about 15% ofthe monthly electric charges, and is related to the maximumpower consumption, which is dealt with here. The greaterthe deviation in the peak power affects to operations at theconcentrated power consumption, the greater the chargefor electricity. If numerous trains are accelerating simultaneously in some adjacent stations as a specific range of power supply system, high traction power is incurred. Figure 4 describes change energy consumption based on situation that the number of trains is simultaneous running in traction phase. Power dissipation of simultaneous departure is higher than that of departure in another time. In this example, case 1 consumes twice as high traction energy as case 2. This research makes power consumption like case 2.

Fig.4 Power Dissipation in Traction Phase

3.3 Synchronized Energy

Total power consumption affects the usagefeeabout 72% ofthe monthly electric charges. When trains are operating simultaneously at adjacent stations within a specific range of the power supply system, power consumption can be considerably reduced by increasing use of regenerative power. Figure 5 describes the change of power consumption in the situation when two trains are running simultaneously in other driving phase; the train A is on the accelerating phase and the train B is on the braking phase. Through matching, traction power consumed by train A decrease as using regenerative energy produced by train B. In this example, more traction powers of the case 1 are consumed than that of the case 2. The goal of this research is to result in power consumption like that in the case 2.

Case 1 Case 2

Fig.5AnExample for Synchronized Driving

Challenge A: A more and more energy efficient railway

3.4Adjust Departure State

In order to reduce power consumption, we suggest a timetabling method that adjusts the departure times of trains in an existing timetable. Timetabling adjusts the departure times of trains based on a discrete planning horizon (i.e., expressed as 15-s unit time intervals). For timetabling, we define criteria of departure time: early, on-time, and late departure. In the early departure, the train departure time is 30-s earlier than that in the current timetable. In the on-time departure, the departure time of a train is unchanged (i.e., the existing timetable is used). In the late departure, the departure time is 30-s late. Table 1 applies the adjusting departure time method to this case. In the table, positive and negative numbers represent traction and regenerative power, respectively. A zero indicates either no power or a 30-s stop at the station. To lessen the traction power consumption, we find an optimal matching in order to reduce the power consumption by providing regenerative energy produced with other trains in the accelerating phase. If the number of trains is n, the possible combination of departure states is 3n. For example, two trains have nine possible combinations. In the table based on the current schedule, the current total power consumption is 62.5 kWh (1O-2O). By adjusting the departure times of trains 1 and 2, it can be reduced to 51.5 kWh with the combination (1O-2E) involving an early departure by train 1 (1O) and a late departure by train 2 (2E). The peak power consumption decreases to 17.3 kWh from 34.5 kWh. The main reason for adjusting the schedule by a few seconds is that it is helpful to retain the current timetable to the extent possible to sustain other operational plans such as vehicle routing and crew scheduling.

Table 3An Example of Timetable Revise Method

Planning MRT Railway 1 MRT Railway 2 All Combination of MRT Railways Time Power Power Power slot Early On- Late Early On- Late E-E E-O E-L O-E O-O O-L L-E L-O L-L time time 06:18:45 17.3 0 0 0 0 0 17.3 17.3 17.3 0 0 0 0 0 0 06:19:00 3.0 0 0 0 0 0 3.0 3.0 3.0 0 0 0 0 0 0 06:19:15 0 17.3 0 0 0 0 0 0 0 17.3 17.3 17.3 0 0 0 06:19:30 0 3.0 0 0 0 0 0 0 0 3.0 3.0 3.0 0 0 0 06:19:45 -1.4 0 17.3 0 0 0 (0) (0) (0) 0 0 0 17.3 17.3 17.3 06:20:00 -9.7 0 3.0 0 0 0 (0) (0) (0) 0 0 0 3.0 3.0 3.0 06:20:15 0 -1.4 0 0 0 0 0 0 0 (0) (0) (0) 0 0 0 06:20:30 0 -9.7 0 17.3 0 0 17.3 0 0 7.6 (0) (0) 17.3 0 0 06:20:45 17.2 0 -1.4 3.0 0 0 20.2 17.2 17.2 3.0 0 0 1.5 (0) (0) 06:21:00 4.7 0 -9.7 0 0 0 4.7 4.7 4.7 0 0 0 (0) (0) (0) 06:21:15 0 17.2 0 0 17.3 0 0 17.3 0 17.2 34.5 17.1 0 17.3 0 06:21:30 0 4.7 0 -1.3 3.0 0 (0) 3.0 0 3.3 3.3 4.4 (0) 3.0 0 06:21:45 -5.4 0 17.2 -9.1 0 17.3 (0) (0) 11.8 (0) 0 17.3 8.0 17.2 34.5 06:22:00 -3.7 0 4.7 0 0 3.0 (0) (0) (0) 0 0 3.2 4.7 4.7 7.7 06:22:15 0 -5.4 0 0 -1.3 0 0 (0) 0 (0) (0) (0) 0 (0) 0 06:22:30 0 -3.7 0 0 -9.1 0 0 (0) 0 (0) (0) (0) 0 (0) 0 06:22:45 0 0 -5.4 0 0 -1.3 0 0 (0) 0 0 (0) (0) (0) (0) 06:23:00 0 0 -3.7 0 0 -9.1 0 0 (0) 0 0 (0) (0) (0) (0) 06:23:15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06:23:30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Power Consumption 62.5 62.5 54.1 51.5* 62.5** 62.5 52.0 62.5 62.5 Peak Power Consumption 20.2 17.3 17.3 17.3* 34.5** 17.3 17.3 17.3 34.5 *Optimal Power Consumption ** CurrentPower Consumption(0) Regenerative Power Lost

4. Mathematical Programming For a more formal description, we formulate the problem as a mixed integer program. Before describing the model, the notation used in this paper is summarized as follows:

1) Sets

-I: the set of trains -J: the set of stations -G: the set of groups of stations -J: the set stations belonging to group g

Challenge A: A more and more energy efficient railway

-S: the set of departure states -T: the set of planning time slots

2) Parameters

- e: > 0, the amount of power consumed at station j in time slott if traini is operated under

departure states.(e = 0, no power, e< 0, the amount of regenerative energy produced) - M: arbitrarily large number - α: weight of total energy consumption (usage rate) - β: weight of peak energy consumption (basic rate)

3) Variables

-X: 1 if train i is operated under departure state s; and 0 otherwise - E: the amounts of total power consumption in group g in time slott - K: the amounts of peak powerconsumption

4) Mathematical model

min α × ∑∈ ∑∈ E + β × K (1) subject to

∑∈ X = 1, ∀i ∈ I (2)

∑∈ ∑∈ ∑∈ eX ≤ E , ∀g ∈ G,∀t ∈ T (3)

E ≤ K, ∀g ∈ G,∀t ∈ T (4)

X ∈ {0,1}, ∀i ∈ I,∀s ∈ S (5)

E ≥ 0, ∀g ∈ G,∀t ∈ T (6)

The objective function is to minimize the power consumption to maximize re-usage of regenerative energy. Constraint (2) guarantees that trains must be assigned to one departure criteria among three types of departure criteria. Constraint (3) represents the fact that train departure determines the amount of traction/regenerative energy consumed/produced by trains running between stations belonging to group g in time slott . Constraint (4) calculates the peak power consumption. Constraints (5) and (6) represent the restrictions on decision variables.

5. Numerical Results and Case Study To validate the effectiveness of model and heuristics algorithm suggested in this research, we simulate the experiments based on current situation. The data for this experiment is derived from real data from Seoul Metro line 4 (Figure 6). The experiment instance includes 23 stations and 160 trains (up and down) a day from 05:30:00 to 11:00:00 (peak time). The planning time slotis discrete from 1 to 1333 time slot. For power data, we used the data generated by simulator of Korea Railroad Research Institute (KRRI). The test has been conducted with a Pentium processor operating at 2.67 GHz lock speed with 1.99 GB Ram. In the test, CPLEX 11.2, a commercial software package, was used to solve the mixed integer programming model. This experiment limited the run time of CPLEX to 200,000 seconds because an optimal solution could not be obtained within a reasonable time.

Challenge A: A more and more energy efficient railway

Table 4 shows the experiment results of case study. CPLEX finds a feasible solutionwithin a 12% optimality gap. The peakand total power consumption is 41% and 5% less than with the current timetablerespectively. This confirms that our idea canreduce the energy consumption effectively.

Fig.6Route Map of Seoul Metro Line 4

Table 4Experiment Results of Case Study

Peak Power Total Power Consumption (kW) Consumption (kWh) Current 353,749 66,353 Time Table New Time Table 207,783(↓41%) 63,047(↓5%)

6. Conclusions and Future Study This paper considered a mathematical approach that can increase energy saving in timetables. We developed the multi-criteriamixed integer programming model. To verify the model, we conduct a numerical experiment using real data of Seoul Metro line 4. The model can reduce the peak energy up to more 40% than current maximum traction power. In addition, we improve the re-usage of re-generative energy about 5%. We demonstrated that our methodology can be applied successfully to energy efficient timetabling, particularly for a high-density MRT line. Energy efficient train timetabling can help the company operating MRT reduces power costs, decreasing the investment required in power facilities. For future research direction, heuristic algorithms can be developed in order to obtain good solution within a short amount of computational times.

References

[1] T. Albrecht (2004), Reducing power peaks and energy consumption in rail transit systems by simultaneous train running time control, Computers in Railways IX, WIT Press, Southampton, pp885- 894. [2] S.P. Gordon, D.G. Lehrer (1998) Coordinated train control and energy management control strategies, Proceedings of ASME/IEEE Joint Railroad Conference, pp165-176. [3] J.F. Chen, R.L Lin, Y.C Liu (2005) Optimization of an MRT trains schedule: reducing maximum traction power by using genetic algorithms, IEEE Transactions on Power Systems, 20(3), pp. 1366- 1372. [4] K.M. Kim, S.M. Oh (2009) A model and approaches for smoothing peaks of traction energy in timetabling, Journal of the Korean Society for Railway, 12(6), pp. 1018-1023.

Challenge A: A more and more energy efficient railway

[5] K.M. Kim, S.M. Oh, M.S. Han (2010) A mathematical approach for reducing the maximum traction energy: the case of Korean MRT trains, Proceedings of the International MultiConference of Engineers and Computer Scientists, 3, pp. 2169-2173, Hong Kong, China. [6] K.T. Kim, K.M. Kim (2010) An optimization for reducing maximum traction power of MRT railways: a case study of Seoul Metro line 4, Proceedings of the Conference of the Korean Institute of Industrial Engineers, Donguk University, Seoul.