Optimization methodology for coasting operating point of high-speed train for reducing power consumption
Introduction
Due to the large volume, fast speed and high efficiency, high-speed train plays an important and ir-replaceable role in the transportation system of many countries (Xing et al., 2015; Sharma et al., 2015). However, compared with other public transportation, high-speed train consumes a lot of energy while pro-viding more convenient and efficient services (Hasegawa et al., 2015; Feng, 2011). Therefore, it is very important for high-speed train to reduce power consumption during the operation. At present, coasting is considered to be one of the most effective energy-saving measures for high-speed trains while operating. between stations (Lin et al., 2017; Wong and Ho, 2004a,b). Therefore, it is of great academic significance and engineering application value to optimize the energy-saving control method for high-speed train during coasting.
Aiming at the problem of energy-saving optimization of the coasting for high-speed train, domestic and foreign scholars have done a lot of in-depth research work. Lin established a multi-particle train model driven by asynchronous motor to optimize a energy consumption curve. Multi-population genetic algorithm was adopted to solve this multi-point combinatorial optimization problem and improve global search capability and convergence speed by parallel optimization (Lin et al., 2017). Hwang presented an approach to identify a fuzzy control model for determining an economical running pattern for a high-speed railway through an optimal compromise between trip time and energy consumption, and the impact of different soft speed limits on energy consumption was explored (Hwang, 1998). Bocharnikov designed a fitness function with variable weightings to balance saving energy and trip time. Energy savings were found, both qualitatively and quantitatively, to be affected by acceleration and braking rates, and the fitness function was used to identify optimal train trajectories (Bocharnikov et al., 2007). Albrecht systematically discussed the mathematical modeling of train operation, the typical optimal control mode, the existence of optimal switching points, and the optimal strategy under speed limitation (Albrecht et al., 2015; Albrecht et al., 2016). Chang applied the genetic algorithm to optimise train movements using appropriate coast control that can be integrated within automatic train operation systems. By calculating the most suitable idle position in the train operation process, the energy consumption is minimized on the basis of ensuring that the train runs smoothly and on time (Chang and Sim, 1997; Acikbas and Soylemez, 2008). Wong presented an application of hierarchical genetic algorithms to identify the number of coasting points required according to the traffic conditions. Single and multiple coasting point control with simple genetic algorithms were developed to attain the solutions and their corresponding train movement is examined (Wong and Ho, 2004a,b). Chuang applied a train performance simulation to solve the energy consumption, and created the data set for artificial neural network (ANN) training accordingly. The ANN model was established and the optimal coasting speed was then derived by performing the ANN training (Chuang et al., 2009). At present, many scholars pay more attention to the impact of the optimization of the coasting point on power conservation, with the aim of achieving the destination with the least power consumption. By summarizing the results of the coasting optimization study, most of them are to increase the speed of the coasting point, prolong the coasting time or increase the number of coastin, and less consideration is given to the operation safety of train idling process. In the course of train operation, safety is the most basic requirement. The traction system of high-speed train is a complex electromechanical coupling system (Liu and Zhu, 2013; Chen et al., 2015; Shanmugasundram et al., 2014), and the change of electromechanical parameters may significantly affect its operation stability. The change of the coasting load torque, ie the coasting speed, may cause the high-speed train to generate complex nonlinear dynamic behavior during coasting, which affects the safe operation of the train. Therefore, it is very meaningful to propose an optimization methodology of the coasting point to simultaneously ensure the safety operation and energy saving of the train.
The remainder of this paper is organized as follows. In Section 2, a mathematical model of PMSM for high-speed train during coasting is established. Section 3 derives the local stability condition and bifurcation condition of PMSM based on Routh-Hurwitz criterion. And the influence of load torque variation on bifurcation characteristics of equilibrium point and stable operation domain of the high-speed train is studied. In Section 4, detailed numerical simulations are carried out to analyze the effect of load torque on the coasting point, and an optimization methodology is proposed. Experimental platform is set up to verify the correctness and the effectiveness of the proposed optimization methodology. The research methods and results of this paper are compared with those of previous study on the high-speed train during coasting in Section 6. Section 7 concludes this paper with final remarks. Before ending this introductory section, it is worthwhile pointing out the main contributions of this paper as follows.
- 1.
The mathematical model of the high-speed train during coasting is established, and the influence of the change of load torque on the stable operation domain of the system is studied.
- 2.
Under the premise of ensuring the safety operation of high-speed train, an optimization methodology of the coasting point is proposed to save energy consumption of the train.
Section snippets
Model of PMSM for high-speed train during coasting
As a big power consumer, if the high-speed train are always in the driving state during its operation, it may lead to a large amount of power wasted. Therefore, after reaching a certain speed, the high-speed train coasts by its own inertia to save power. In general, the operating mode of a high-speed train is following: accelerating-cruising-coasting-braking, and the schematic structure of high-speed train at coasting condition is shown in Fig. 1.
The mathematical model of PMSM for high-speed
Stability analysis of equilibrium point for high-speed train
To further reveal the stable operation domain of PMSM during coasting, we firstly analyze the influence of parameters , and on the equilibrium points. The equations of equilibrium points Eq= () can be written as
Thus the equilibrium point can be expressed as Eq = (), where satisfies the following equation
The Jacobian matrix of Eq. (3) can be expressed as
Optimization methodology for coasting point of high-speed train
From the previous analysis, it can be seen that the change of parameters may cause non-smooth bifurcation of the system. Moreover, the variety of load torque may change bifurcation characteristics of equilibrium point and stable operation domain of the system. According to Table .1 and related formulas, the parameter values are calculated as , . From Fig. 2, it can be seen that with increasing, the area where point P (, ) is always changing, from region A to region C,
Experimental facilities
In order to further verify the correctness and effectiveness of the proposed optimization methodology, the 600 kW PMSM test bench is established as shown in Fig. 4, Fig. 5. Fig. 4 shows that the test bench involves two parts, namely the hardware and software. The hardware includes the power battery, PMSM, eddy current dynamometer, current sensor and speed sensor, where the power battery provides high-voltage power for the PMSM, and the PMSM is used to simulates the states of the motor in a real
Discussion
On the premise of guaranteeing the stable operation of high-speed train, this paper studies the influence of the variation of load torque on the stable operation domain of the system, and proposes an optimization methodology of optimal idling point to reduce power consumption. It is found that the change of motor parameters may cause the equilibrium points to generate Fold bifurcation and Hopf bifurcation. These two kinds of bifurcation divide the operation domain of the system into three
Conclusion
In this paper, a mathematical model of PMSM at coasting condition is established, and research work was carried out on the problem of energy-saving optimization of the coasting for high-speed train. The following conclusions are obtained:
- (1)
The change of motor parameters may cause the equilibrium points to generate Fold bifurcation and Hopf bifurcation, dividing the operation domain of the system into three categories: absolutely stable domain, progressively stable domain, and chaotic domain.
- (2)
The
Conflicts of interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgements
This research is supported by the National Natural Science Foundation of China (51705208) and China Postdoctoral Science Foundation (2018M632240).
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