Probability Distribution Characteristics And Mathematical Models Of Traction Power Load Of Electrified Railways

Power load modeling is one of the key technologies in power system simulations,and the traction load model has important theoretical value and engineering significance to study the influence of electrified railways on power grid.However,the traction load has the features of strong randomness,large fluctuation range and three-phase imbalance,which bring the challenge to the load modeling work.The probabilistic approaches are promising to be used for analyzing the statistical characteristics of traction load.The decisive factors can be then studied as well as their influence in terms of the degree and the way.In this dissertation,the probability distributions of the power load of electrified locomovtives,supply feeders and substations have been discussed on both fundamental and harmonics.The load models and the identification algorithms of their parameters are then presented.Meanwhile,an estimation method of harmonic impedance has been proposed.In the beginning,the probability characteristics of the fundamental load of a single electric train,which is the research foundation of the superimposed load of a feeder or a substation,are fully analyzed.In addition,the statistical law of harmonic currents of an EMU(Electric Multiple Unit)is introduced,then a probabilistic modeling approach based on the field-testing data for electric trains is put forward,and a detailed model of an EMU has been built as well as its effectiveness has been verified.This approach has some advantages over the analytical methods based on the main circuit,such as more real,more reliable,and more practical.Many researchers analyzed the statistical features of a supply feeder current,but it is very difficult to find a regular pattern because the feeder current is related to both active and reactive power.Actually,the active power is dominated by the conditions of railway lines,and this is different from the reactive power which is related to both these conditions and the main circuit types of electrice trains.This dissertation points out that the load of a feeder or a substation can be described with the number and the active power levels of electric trains which are running in the power supply section.A probabilistic load model is then presented.The nonlinear optimization algorithms are then designed in detail to identify the parameters as well as its steps are particularly introduced.Its validity and applicability has been proved by several instances.Based on the above probabilistic load model,the negative sequence current on the primary side of the traction substation can be simulated by the Monte-Carlo procedure,and its statistical features has been obtained.First,the probability distribution of the negative sequence current is discussed for both the single-phase and the balancing traction transformers.Second,the effects of the correlation of two power supply arms on the statistical characteristics of negative sequence current is demonstrated.The simulation results show that the correlation is very weak especially for double-tracking railways,thus the simulation approach for negative sequence current is proposed,which depends on the identified parameters of the power load model of two supply arms.Last,an alternative model with independent parameters for negative sequence current,and the parameter identification steps,are both presented.In the study of harmonic related issues,the harmonic current probability distribution,the harmonic emission level,and the harmonic impedance estimation,are individually mentioned and studied.First,this dissertation points that the harmonic current distribution of a feeder or a substation is decided by the train types and their numbers.By means of the Monte-Carlo simulation,the influences of both DC-drive and AC-drive locmotives on the distribution are analyzed.A mathematical model is then brought forward for the harmonic current,and its parameter identification has been worked out as well as its effectiveness has been tested through the instances.Second,the evaluation of emission level for load harmonics is an important issue in the field of electric power quality.According to the operation features of railways,a combination formula is put forward as the probability density function(PDF)to describe the statistical profiles of the harmonic voltages on the primary side of a transformer in a traction substation,and its parameters can be identified by the non-linear curve fitting method.This approach is very helpful for simplifying the evaluation work.Last,the harmonic impedance estimation is very challenging to control the error and to filter the testing data.Based on the fluctuation method,this dissertation gives a probabilistic method to process measurement data for improving estimate stability,reliability,and precision,and the method has been proved to be effective by simulations and examples.