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Abstract The traction power supply network in electric railways is a complicated single-phase unbalanced network with the earth as a part of the current return loop,which is different from the three-phase power system.The nodal analysis is a method in common use to describe the network.With the train regarded as a power consumption model,it needs iterations to solve the nonlinear power flow equations.The Picard iteration is the most popular iteration method.However,if the loads are set to be very heavy in the calculation,it may fail to converge.It has not been discussed whether the failure of the Picard iteration means the nonexistence of the power flow solution or not.In this paper,the converging characteristics of the Picard iteration,the Newton-Raphson method and the Levenberg-Marquardt algorithm are compared with an example.The relation between the convergency of the algorithms and the existence of the power flow solution is discussed.The Picard iteration is also discussed in the aspects of the iteration time,the change of the train voltage during the iteration,and the influence of the initial value.
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Received: 20 May 2015
Published: 24 August 2016
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2016, Vol. 31 
