Energy-saving optimization strategy of multi-train metro timetable based on dual decision variables: A case study of Shanghai Metro line one
Introduction
Due to air and noise pollution, highway and street traffic congestion, and high energy costs (Watanabe and Koseki, 2015; Khodaparastan et al., 2019; Wang et al., 2018), people are increasingly inclined to use metro instead of ground transportation (Liu et al., 2018a), (Yang et al., 2018a). According to some surveys, although metros are more energy-efficient than ground transportation, there is still a lot of energy loss (Liu et al., 2018b). One of the important reasons for the loss of this energy is the unsatisfactory driving strategy and timetable. The train needs to consume a large amount of electrical energy during acceleration, and a large amount of electrical energy will be regenerated during braking (Liu et al., 2019a). The regenerative braking energy (RBE) can be used by other acceleration trains or stored in storage devices such as flywheels (Suzuki et al., 2015; Tzeng et al., 2006; Liu and Jiang, 2007), super capacitors (Ahmadi et al., 2018; Iannuzzi and Tricoli, 2010; Burke and Miller, 2011) and batteries (Kraytsberg and Ein-Eli, 2011; Czerwiaski et al., 2012). Otherwise, the energy is consumed by resistors (Liu et al., 2019b). Due to the limited capacity and high cost of energy storage equipment, most metro systems are not equipped with energy storage equipment. Therefore, it is necessary to optimize the driving strategy and timetable of the train to reduce the traction energy consumption and make better use of the RBE.
The principle of energy-saving optimization is to reduce the traction energy consumption or make full use of the RBE by formulating a reasonable driving strategy and timetable, thereby reducing the net traction energy consumption of the metro system. There are mainly two types in the existing literature. The first is to arrange the optimal energy-saving driving strategy of each train between stations under the constrained running time (Scheepmaker et al., 2020). Sicre et al. (2010) solved the single-objective optimization problem of minimizing the traction energy consumption. The input variable is the running time of the train. The energy optimization strategy consists of two parts: first, the optimal operation strategy of a single train is obtained by using GA. Then the feasible running time is allocated to the train, and finally the optimal energy consumption is obtained. Ding et al. (2011) established a two-layer iterative optimization model to describe the relationship between train timetables and energy consumption. The first layer is to optimize the control strategy of each car, and the second layer is to optimize the running time of all trains by using GA. The results show that the proposed method can save 19.1% of energy compared to the non-optimized timetable. Yang et al. (2018b) transformed the non-convex train scheduling problem to a strictly quadratic model by using the Taylor approximation and applied the active set method (ASM) to find the approximate optimal solution. The results performed on the Beijing Metro Yizhuang Line in China shows that the developed approach can save 4.52% of energy. Mo et al. (2019a) designed a modified tabu search algorithm (MTS) with prior enumeration methods (PE) is to minimize the energy cost and passenger waiting time.
The second type of energy-saving optimization is to synchronize the acceleration and braking processes of the trains so that the RBE can be fully utilized (Yang et al., 2016). Yang et al. (2015) fully utilized the RBE by synchronizing the acceleration and braking processes of nearby trains. They formulated an integer programming model and used GA to find a good solution. The test results on Beijing Metro Yizhuang Line show that the proposed method can reduce the energy consumption by 6.97% compared with the current timetable. Luo et al. (2019) proposed a sparse optimization model with -norm and the squared -norm as the objective function to improve the utilization of the RBE. The results on the Beijing Metro Yizhuang Line show that the proposed model has a good performance in the energy-saving rate and computation time. He et al. (2019) proposed an energy-saving optimization method based on an improved chicken swarm optimization algorithm for obtaining an operation curve of a train with minimum energy-consumption and improve the utilization of the RBE. The results on Nanning metro line one in China show that the proposed method can save 17.15% of energy. Mo et al. (2019b) proposed an integrated model to simultaneously generate the optimal train schedule and rolling stock circulation plan to maximize the brake-traction overlapping time.
However, the above two types of methods have their own disadvantages. The first type of energy-saving optimization method does not consider the utilization of the RBE between trains. The second type of energy-saving optimization method is only for better use of the RBE, without considering the traction energy consumption. The energy-saving optimization problems of metro line with both reducing of traction energy consumption and increasing the use of regenerative braking energy are rarely mentioned in previous literatures. Yang et al. (2013) proposed an approach to improve the overlapping time of acceleration and braking and designed a GA with binary encoding to solve the optimal timetable. The results show that the proposed approach can improve the overlapping time by 22.06% at peak hours and 15.19% at off-peak hours. Su et al. (2013) proposed a method to calculate the optimal speed curve with a fixed travel time and designed an algorithm to allocate the total travel time between different sections. The simulation results show that the proposed method can reduce 14.5% of energy.
This paper proposes an energy-saving optimization strategy of multi-train metro timetable based on double decision variables, which takes both energy-saving strategy and the use of the RBE (i.e., feedback energy) into account. Various mathematic models of the metro system are established based on the actual situation of the SML1 pilot network (Yang et al., 2019a). By formulating an appropriate driving strategy and timetable, the traction energy consumption and feedback energy of the trains are optimized, thereby reducing the net traction energy consumption of the trains in the multi-train metro system.
The remainder of this paper is organized as follows. In Section 2, based on the actual situation of the Shanghai Metro Line One (SML1) pilot network, metro system models are established, and two optimized driving strategies are proposed. The energy-saving optimization principle of timetable is introduced in Section 3. In Section 4, genetic algorithm (GA) is introduced. In Section 5, three numerical experiments are carried out. Our proposed method is compared with a strategy that takes the utilization of the RBE as the objective function in Section 6. Finally, Section 7 concludes this paper.
Section snippets
Model formulation
In this section, for the multi-train metro model, the objective function and constraints of energy-saving optimization are described. For the single train model, an energy-saving driving strategy is obtained based on the Pontryagin maximum principle (Scheepmaker and Goverde, 2015), (Ross and Primer, 2009), and the switching points are calculated. Then, according to the actual situation of the SML1 pilot network, we propose two driving strategies.
Principle of energy-saving optimization
This section discusses the use of dwell time and cruising speed as the decision variables on the energy-saving optimization.
Solution algorithm
In this paper, GA is applied to solve the optimization problem (Fan et al., 2012). GA is a heuristic algorithm that can simulate the process of natural evolution. The essence of this method is to evolve from generation to generation according to the principle of survival of the fittest, and finally obtains the optimal or local optimal solution.
In this paper, Pontryagin maximum principle is used to obtain the energy-saving driving strategy of the single train model. However, for the multi-train
Experiment
In this section, the SML1 of Xujiahui Station to Xinzha Road Station is used as a pilot network to conduct numerical experiments. And its information is shown in Table 1. The configuration of the numerical experiment is shown in Table 2. The number of trains is set to 2. The departure interval is 120 s. Dwell time includes fixed dwell time and variable dwell time. The fixed dwell time is set to 20 s, and the variable dwell time varies from 0 to 10 s.
Fig. 12 shows the difference between the
Comparison
This section compares the proposed energy-saving optimization strategy based on dual decision variables with a cooperative scheduling approach which aims to maximize the overlapping time with the cruising speed and dwell time control proposed by Yang et al. (2013), and a metro train timetable optimization approach based on energy-efficient operation strategy proposed by Su et al. (2013).
The cruising speed obtained by GA is shown in Fig. 18 by using the cooperative scheduling approach. As can be
Conclusion
This paper proposes an energy-saving optimization strategy of multi-train metro timetable based on dual decision variables. The goal of the proposed method is to minimize the net traction energy consumption of metro trains while meeting the train operation constraints.
In the two-train metro system, instead of the acceleration-coasting-braking (ACOB) driving strategy, each train adopts the acceleration-cruising-braking (ACRB) driving strategy, which can reduce the iteration time when using
Acknowledgments
The authors would like to acknowledge the fund supported by the Shanghai Shentong Metro Group Co., Ltd., which also provides experimental environment and assistance.
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