Citation: Gerber, I.P.; Mwaniki, F.M.; Vermeulen, H.J. Parameter Estimation of a Grid-Tied Inverter Using In Situ Pseudo-Random Perturbation Sources. Energies 2023, 16, 1414. https://doi.org/10.3390/ en16031414 Academic Editors: Zhanhong Jiang and Chao Liu Received: 29 December 2022 Revised: 20 January 2023 Accepted: 27 January 2023 Published: 31 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Parameter Estimation of a Grid-Tied Inverter Using In Situ Pseudo-Random Perturbation Sources Ian Paul Gerber , Fredrick Mukundi Mwaniki * and Hendrik Johannes Vermeulen Department of Electrical and Electronic Engineering, Stellenbosch University, Stellenbosch 7600, South Africa * Correspondence: fmmwaniki@sun.ac.za Abstract: Inverters are playing an increasingly important role in the electrical utility grid due to the proliferation of renewable energy sources. Obtaining inverter models with accurate parameters is, therefore, essential for grid studies and design. In this paper, a methodology to estimate the output impedance and parameters of a residential grid-tied inverter is proposed. The methodology is first verified through simulation. A sensitivity analysis is conducted to determine the influence of the filter and controller parameters on the output impedance of the inverter. The simulated output impedance, voltage, and current are used in a parameter estimation methodology to obtain filter and controller parameters. It is shown that up to seven parameters can be estimated accurately. The proposed methodology is further investigated through a practical experiment. Two perturbation sources, the pseudo-random binary sequence perturbation and pseudo-random impulse sequence perturbation, are used, in turn, to perturb a residential grid-tied inverter that delivers up to 1.6 kW with the aim of obtaining its output impedance. The output impedances obtained through both pseudo-random sources are compared. It is shown that a pseudo-random binary sequence perturbation source applied in series between the grid and the inverter under test allows for the best estimation of the grid-tied inverter’s output impedance. A black-box modeling approach aimed at estimating an analytical transfer function of the output impedance from experimental data is also discussed. Keywords: inverter; wideband; output impedance; frequency response; parameter estimation; inverter modeling; system identification 1. Introduction Inverter-based generation is vital in the global shift towards renewable energy. Wind and solar power plants use DC–AC inverters to integrate with the electrical utility grid [1,2]. The use of inverters on a residential level has also increased significantly [3]. Inverter-based power plants generally make use of grid-connected three-phase inverters [4]. Single-phase inverters are predominantly used on a residential scale [5]. These residential inverters typi- cally use an outer DC voltage control loop and inner current control loop [6,7]. Residential single-phase, grid-tied inverters also need to adhere to specific standards and regulations, such as their response to a change in frequency and the grid voltage [8]. Relying on inverter- based energy sources instead of fossil-fueled generation comes with challenges regarding power quality [9–12] and grid stability [13–16]. To mitigate these challenges, thorough design and analysis of inverter systems are required, necessitating accurate modeling of inverters and accurate estimation of model parameters [17,18]. This can be done through system identification and parameter estimation studies. Parameter estimation and system identification studies typically excite a target system with a suitable excitation signal, and the input and output signals are then recorded over a time interval [19]. The measured response of the system is then cross-correlated with the measured input signal. Wideband excitation signals, such as the swept-sine signal, impulse signal, and Pseudo-Random Binary Sequence (PRBS), are commonly used to obtain fre- quency response information of power system equipment [20]. A Pseudo-Random Impulse Energies 2023, 16, 1414. https://doi.org/10.3390/en16031414 https://www.mdpi.com/journal/energies