The efficient parameter estimation of harmonics is required to effectively design filters to mitigate their adverse effects on the power quality of electrical systems. In this study, a fractional order swarming optimization technique is proposed for the parameter estimation of harmonics normally present in industrial loads. The proposed fractional order particle swarm optimization (FOPSO) effectively estimates the amplitude and phase parameters corresponding to the first, third, fifth, seventh and eleventh harmonics. The performance of the FOPSO was evaluated for ten fractional orders with noiseless and noisy scenarios. The robustness efficiency of the proposed FOPSO was analyzed by considering different levels of additive white Gaussian noise in the harmonic signal. Monte Carlo simulations confirmed the reliability of the FOPSO for a lower fractional order ($\lambda$ = 0.1) with a faster convergence rate and no divergent run compared to other fractional orders as well as to standard PSO ($\lambda$ = 1).

The sustainable power development requires the study of power quality while taking into account of electrical equipment is an important aspect because it highly compromises the overall efficiency including quality, reliability and continuity of power flow. The aim for smooth power flow is only accomplished if compatibility is met between all the instruments connected to the system. The odd harmonics both on amplitude and phase domain must be known in order to exactly cop up with their adverse effects on overall working of the system. In this regard, parameter estimation is performed in detail for diverse generation size (gs) and particle size (ps), besides for altered signal to noise ratio. Firefly optimization technique under different scenarios for both phase and amplitude parameters accurately estimated the power signal harmonics and proved its robustness under different noise levels. The MSE values achieved by FFO are 6.54 × 10⁻³, 1.04 × 10⁻⁵ and 1.35 × 10⁻⁶ for 20 dB, 50 dB and 80 dB respectively for gs = 200 in case study 1. While the respective results in case study 2 are 7.33 × 10⁻³, 6.67 × 10⁻⁶ and 6.59 × 10⁻⁹ for gs = 1000. Whereas no significant effect in performance is seen with the change in ps values.