Mathematical model of optimum power control of dc electric locomotive in traction mode and the method of its solution

Rational way to improve the operational efficiency of the locomotive is adjustable power.The implementation of this method possible with the use of automatic power regulation implementing the optimal load,the operation mode of the traction and energy unit (TEU) of the locomotive. The aim of this work is to obtain mathematical relationships,establishing the optimal ratio between the number of employees of TD given thrust and speed. Determination of the optimal ratio being in the traction motors is based on finding the minimum power losses at the nodes of the TEU. Search the minimum of complex functions is an optimization problem,which from a mathematical point of view is to determine the minimum of function of several variables with a number of constraints,and relationships. To solve the problem of finding the minimum of a complex function,we used the method of indeterminate Lagrange multipliers. The optimization process is considered at a constant value of the voltage supplied to the TD and sold power.Variables - the force of traction,speed of movement,the ratio of incremental losses,the resistance of the circuit of the armature of TD was assumed constant,which allowed to simplify the solution of the problem,reducing it to find three unknown quantities - current,the number of TD and magnetic flux. The solution to this system of equations for the number TD,participating in the work were obtained analytical dependences the optimum values of the TD depending on the speed,the thrust force on the rim of the driving wheels of the locomotive and tension. Analytical expressions for determining optimal parameters of power regulation of electric DC,allow to obtain the optimal values of the number of workers so and the load depending on the given values of thrust and speed in the entire range of load modes of EPS. The analytical expressions can be used when drawing up regime maps and energy performance certificates EPS,and also in the most important automatic devices of power control of the rolling stock to set the optimal ratio of number of employees and so on.