基于量化状态时间离散的城轨牵引供电系统动态仿真方法

A dynamic simulation method of urban rail traction power supply system based on quantized state time discretization

在建立城市轨道交通牵引供电系统动态数学模型时需要求解常微分方程组,而城轨牵引供电系统是典型的刚性系统,具有拓扑复杂、参数时变的特点,使用传统的时间离散算法对其进行动态仿真时,仿真结果与实际情况存在一定偏差。因此提出了一种结合传统时间离散算法与量化状态系统算法的混合仿真求解方法。首先将系统模型按照状态变量变化速度分为大步长求解与小步长求解2个子系统,对变化速度快的小步长子系统的状态变量进行量子化离散,并通过改进量化状态系统算法减小仿真数值的“假性振荡”;而对变化速度相对缓慢的大步长的子系统的状态变量则使用传统的时间离散算法以提高计算效率。其次运用常微分方程组分别建立城轨牵引供电系统多脉波不控整流机组和功率源列车的动态数学模型,在MATLAB中运用量化状态时间离散混合仿真方法实现模型交直流侧的实时潮流解析。然后在Simulink中建立等效模型,将运用此混合算法求解得到的波形与Simulink仿真波形进行对比,验证此方法的准确性。最后在同一仿真条件下对比不同方法的仿真时间与步长。结果表明量化状态时间离散混合求解方法运用在城轨牵引供电动态仿真系统中具有可行性、准确性与高效性。

When establishing the dynamic mathematical model of traction power supply system for urban rail transit, it is necessary to solve the group of ordinary differential equations. However, because the traction power supply system of urban rail transit is a typical rigid system with complex topology and time-varying parameters, deviation between the simulated result and the reality exists in dynamic simulation when the traditional time-discrete algorithm is used to simulate the system. Therefore, a hybrid simulation method combining traditional time discretization and the quantized state system algorithm was proposed. Firstly, according to the varying rates of state variables, the system model was divided into two subsystems: large step solution and small step solution. The state variables of small step subsystem with fast-varying rates were quantized and discretized, and the pseudo-oscillation of simulation value was reduced by improving the quantized state system algorithm, while the traditional time discretization algorithm was used to improve the computational efficiency for the state variables of subsystems with relatively slow changes and large steps. Secondly, the dynamic mathematical models of multi-pulse uncontrolled rectifier unit and the power source train of the urban rail traction power supply system were established by using the ordinary differential equations, and the real-time power flow analysis of AC and DC side of the model was implemented by using the mixed simulation method of quantized state time discretization in MATLAB. Then an equivalent model was established in Simulink,and the waveforms obtained by using this algorithm were compared with the Simulink simulation waveforms to verify the accuracy of this method. Finally, the simulation time and step length of different methods were compared under the same simulation conditions. The results show that the quantized state time discretization hybrid solution method is feasible, accurate and efficient in the dynamic simulation system of urban rail traction power supply.