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# Optimal Parameter Estimation of Transmission Line Using Chaotic Initialized Time-Varying PSO Algorithm

Abdullah Shoukat1, Muhammad Ali Mughal1,*, Saifullah Younus Gondal1, Farhana Umer2, Tahir Ejaz3, Ashiq Hussain1
1 Department of Electrical Engineering, HITEC University, Taxila, 47080, Pakistan
2 Department of Electrical Engineering, Islamia University, Bahawalpur, 63100, Pakistan
3 Department of Electrical Engineering, Iqra University, Islamabad, 44000, Pakistan
* Corresponding Author: Muhammad Ali Mughal. Email:

Computers, Materials & Continua 2022, 71(1), 269-285. https://doi.org/10.32604/cmc.2022.021575

Received 07 July 2021; Accepted 26 August 2021; Issue published 03 November 2021

### Abstract

Transmission line is a vital part of the power system that connects two major points, the generation, and the distribution. For an efficient design, stable control, and steady operation of the power system, adequate knowledge of the transmission line parameters resistance, inductance, capacitance, and conductance is of great importance. These parameters are essential for transmission network expansion planning in which a new parallel line is needed to be installed due to increased load demand or the overhead line is replaced with an underground cable. This paper presents a method to optimally estimate the parameters using the input-output quantities i.e., voltages, currents, and power factor of the transmission line. The equivalent π-network model is used and the terminal data i.e., sending-end and receiving-end quantities are assumed as available measured data. The parameter estimation problem is converted to an optimization problem by formulating an error-minimizing objective function. An improved particle swarm optimization (PSO) in terms of time-varying control parameters and chaos-based initialization is used to optimally estimate the line parameters. Two cases are considered for parameter estimation, the first case is when the line conductance is neglected and in the second case, the conductance is considered into account. The results obtained by the improved algorithm are compared with the standard version of the algorithm, firefly algorithm and artificial bee colony algorithm for 30 number of trials. It is concluded that the improved algorithm is tremendously sufficient in estimating the line parameters in both cases validated by low error values and statistical analysis, comparatively.

### Keywords

Chaos; parameter estimation; transmission line; time-varying particle swarm optimization; pi-network

A. Shoukat, M. Ali Mughal, S. Younus Gondal, F. Umer, T. Ejaz et al., "Optimal parameter estimation of transmission line using chaotic initialized time-varying pso algorithm," Computers, Materials & Continua, vol. 71, no.1, pp. 269–285, 2022.

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