In this paper, an application of the recently developed Grasshopper Optimization Algorithm (GOA) for calculation of switching angles for Selective Harmonic Elimination (SHE) PWM in low-frequency voltage source inverter is proposed. The algorithm is based on insect behavior in the food foraging swarm of grasshoppers. The characteristic feature of GOA is the movement of agents is based on the position of all agents in the swarm. This method represents a higher probability of convergence than Particle Swarm Optimization (PSO) Modifications of GOA have been examined regarding their effect on the algorithm’s convergence. The proposed modifications were based on the following techniques: Grey Wolf Optimizer (GWO), Natural Selection (NS), Adaptive Grasshopper Optimization Algorithm (AGOA), and Opposite Based Learning (OBL). The performance of GOA and its modifications were compared with well-known PSO. Areas, where GOA is superior to PSO in terms of probability of convergence, have been shown. The efficiency of the GOA algorithm applied for solving the SHE problem was confirmed by measurements in the laboratory.
The paper is dedicated to the estimation of instantaneous reactive power in a DC traction power system. Currently, the integral and frequency methods are mostly used to define reactive power and do not give high accuracy in the calculations of power balance or cannot describe the essence of physical processes. The problem is complicated in DC electric transport systems due to random impulse character of voltages and currents. As a comparison, the calculation of reactive power according to various approaches was performed for the DE1 electric locomotive. It is suggested that the instantaneous reactive power should be used for the analysis of electromagnetic exchange processes in DC power systems. The paper shows the definition and main formulas for defining the instantaneous reactive power taking into consideration the random character of voltage and current. Numerical calculations together with statistical analysis were performed for two variants of experimentally recorded voltages and currents: the first oneon the bus-bar of traction substation, which supplies the section with the Pendolino trains in Poland and the second oneon the current collector of the VL8 electric locomotive in Ukraine. They confirm the validity of the aforementioned method.
The paper presents the results of economic study of energy storage system (ESS) implemented in 3 kV DC power supply system. Two conceptions of ESS have been investigated: ESS with supercapacitor (SC) and hybrid ESS (HESS) with SC and LFP battery. The investigated locations of energy storage systems are considered among existing traction substations in two railway lines with different density of train operation. The considered aims of energy storage system implementation are decreasing of energy consumption by maximum regenerative energy utilization and reduction of peak 15min power demand of traction substation. The paper presents a method of regenerative power estimation depending on the location of the considered ESS implementation point. Also the method of optimal location selection of ESS in terms of minimization of Simple Payback Time (SPBT) of investment is presented. Besides the influence of initial cost value as well as energy price on the SPBT value are investigated. The results are compared between two railway lines with different number of trains operating.
A spectral analysis of traction voltages and currents is a basis for estimation of electromagnetic compatibility level and quality of consumed power in electric transport systems. However, such an analysis is usually performed for steady-state modes and only under the condition that the time realization of voltages and currents, being deterministic for continuous quantities, have infinite length. De facto, the electric transport devices operate in non-stationary dynamic modes (starting up, coasting, acceleration, regenerative braking, stopping, wheel spin, voltage surges, etc.). As a result, the voltage across the traction motors and the current flowing through them are noncontinuous pulsed stochastic processes. It is necessary to add that in emergency modes the voltage and current are short-term single pulses. The paper presents the spectral analysis of such random sequences of pulses as well as their fronts and decays, the concepts of actual and instantaneous spectra. The analytical expressions for amplitudes and the initial phases of k-th harmonics are obtained using the discrete Fourier transformation. The numerical calculations of the spectral composition of stochastic pulse processes of voltage and current were performed for the DE1 and VL8 electric locomotives (Ukraine) as well as for trams operating on the routes of the city of Dnipro. The actual and instantaneous spectra, as well as the spectra of the full correlation functions and their "tails", were determined for the electric traction voltages and currents.
This article presents investigations performed on a 25 kV AC system with a Scott transformer simulation model. The model includes an energy quality parameter calculation algorithm with consideration to the train timetable. The simulation results enable an analysis of the energy quality parameters at the point of connection of the traction substation to the supplying grid. The presented tool enables the simultaneous calculation of voltage unbalance and harmonic content. The article presents the results of the energy quality analysis at the substation connection point for the specific location. The simulation results of the energy quality parameters are appraised on the basis of standard EN 50160:2010. The tool may prove helpful in the process of designing electrification systems, especially in the choice of traction transformer and power electronics device mitigating an imbalance and harmonic impact.
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