Exponential Modulation Integral Observer for Online Detection of the Fundamental and Harmonics in Grid-Connected Power Electronics Equipment

Abstract

𝑇 Δ , 𝑇 𝑟 temporal window length and resetting period of the modulation integral observer 𝑡 time variable 𝑡 𝑘 time instant of the k th resetting sequence 𝑑 process disturbance 𝜙 ℎ general modulation functions, h = 1, 2, 3 𝜙 𝑝,ℎ , 𝜙 𝑒,ℎ polynomial and exponential modulating functions, h = 1, 2, 3 𝑤 ℎ weighting parameters of the modulating functions, h = 1, 2, 3 Γ, Γ ) , Γ * general modulating function matrix and the variants formed by 𝜙 𝑝,ℎ and 𝜙 𝑒,ℎ 𝑣 ϕ,h auxiliary modulated signals Subscripts, superscripts and accents 𝑥 ! estimated signal 𝑥 " estimation error 𝑥 𝑖 𝑖th component of the vector 𝑥 (𝑖) 𝑖th order time-derivative of the signal 𝑥 ⊤ transpose

Firefly Optimization Heuristics for Sustainable Estimation in Power System Harmonics

“…The research community proposed various schemes for powers signals estimation [7][8][9]] and a number of papers have been presented in the literature that pivots the estimation of harmonics contamination [10]. These techniques include fast harmonics estimation using EA-AWNN by Sachin K. Jain et al [11], exponential modulation integral observer by Hin Say Lam et al [12], compressive sensing by Palczynska [13], Bayesian approach used by Gabriele D Antona et al [14], ESPIRIT associated filter bank scheme by Santos [15], Kalman filter [16,17], least mean square based algorithms [18,19], and recursive least square strategy [20].…”