Optimal resonance-free third-order high-pass filters based on minimization of the total cost of the filters using Crow Search Algorithm

The most common damped filters (DFs) are the second-order, third-order, C-type, and double-tuned filters. Other DFs such as the first-order and band-pass filters exist, but their high operating losses considerably diminish their usage. In this paper, firstly, for the third-order damped filter with equal and unequal capacitors, the relations among their circuit parameters are derived. Secondly, the optimal design problem of the two third-order high-pass filters is formulated by regarding these expressions to minimize the filter cost taking into account both the investment and operating expenses. The total and individual harmonic distortion indices, power factor and the harmonic voltage amplification ratios which measure the filter's resonance damping capability, are considered as constraints. A recent metaheuristic optimization technique based on the intelligent behavior of crows, known as the Crow Search Algorithm (CSA), is employed for the solution of the formulated design problem. Further, a comparative analysis of the two designs of the third-order high-pass filters and a third-order C-type filter is presented. The results reveal that all the proposed filters guarantee no electrical resonance hazards while maintaining the allowable limits for the various performance indices of the system, load, and filter. Besides, the comparative analysis validates that the C-type filter provides higher power factor, system efficiency and transmission loss improvement than the other two filters, and that the proposed filters achieve almost the same voltage and current harmonic mitigation levels. The solution of the cost minimization problem reveals that the C-type filter and the third-order high-pass filter with equal capacitors have the worst and best resonance damping capabilities respectively, under the worst case conditions. Additionally, the filters with the lowest and highest cost are found as the third-order filter with unequal capacitors and the C-type one, respectively. Besides, the CSA is compared to the genetic algorithm (GA), and particle swarm optimization (PSO) techniques and the results show the fast convergence capability and the effectiveness of the proposed algorithm in solving the problem of optimal design of third-order resonance-free passive filters in distribution networks.