Citation: Choeung, C.; Soth, P.; Tang, H.; Ean, S.; Srang, S. A Linear Matrix Inequality Approach to Optimal Voltage Control of a Three-Phase UPS Inverter under Unbalanced Loads. Eng. Proc. 2023, 56, 87. https://doi.org/10.3390/ ASEC2023-15365 Academic Editor: Letizia De Maria Published: 26 October 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/). Proceeding Paper A Linear Matrix Inequality Approach to Optimal Voltage Control of a Three-Phase UPS Inverter under Unbalanced Loads † Chivon Choeung 1, * , Panha Soth 1 , Heng Tang 1 , Sreyleak Ean 2 and Sarot Srang 3 1 Faculty of Electricity, National Polytechnic Institute of Cambodia, Phnom Penh 12409, Cambodia; sothpanha@npic.edu.kh (P.S.); tangheng@npic.edu.kh (H.T.) 2 Lanchang-Mekong Vocational Training Center, National Polytechnic Institute of Cambodia, Phnom Penh 12409, Cambodia; eansreyleak@npic.edu.kh 3 Department of Industrial and Mechanical Engineering, Institute of Technology of Cambodia, Phnom Penh 12409, Cambodia; srangsarot@itc.edu.kh * Correspondence: choeungchivon@npic.edu.kh † Presented at the 4th International Electronic Conference on Applied Sciences, 27 October–10 November 2023; Available online: https://asec2023.sciforum.net/. Abstract: Unbalanced loads are extremely prevalent in real systems, and they create power quality issues for the UPS system. To address this problem, this work provides an optimal voltage control scheme for a three-phase inverter using the linear matrix inequality method. In addition, the pur- pose of this controller is to provide a well-balanced three-phase sinusoidal voltage regardless of the imbalance of the loads. This symmetrical component-based controller features two paralleled voltage controls: a positive sequence to regulate output signals and a negative sequence to elimi- nate unbalanced voltages. Along with that, the optimization problem is formulated such that the convergence rate is maximized to obtain the output voltage as swiftly as possible. PSIM is used to carry out the simulation, and MATLAB is utilized to assist in determining the optimal control gain for the state feedback and integral control of each sequence. The control algorithm is then deployed utilizing an in-house designed control board together with a TMS320F28335 digital signal processor. To determine the efficacy of the proposed control, simulation, and experiment results are compared to those of an optimal controller without a negative sequence. Keywords: three-phase inverter; optimal control; linear matrix inequality; UPS; voltage regulation; all-pass filter; symmetrical component 1. Introduction The purpose of UPS inverters is to safeguard vital equipment and appliances from the negative effects of power outages by maintaining a constant power supply to them. To ensure that the voltage quality is well regulated, a lot of research has been conducted, such as reducing the output voltage distortion [1], improving transient performance [2–4], and increasing robustness [5,6]. However, the above-mentioned methods have not taken the unbalanced load conditions into account. When the voltage levels in each phase of a three-phase system are unequal, unbalanced three-phase voltage issues occur. This imbalance can also be caused by a variety of factors, including unequal loads, defective equipment, and distribution system problems. In such instances, the voltage magnitude and phase angles vary between the phases, which may cause operational issues with electrical devices and equipment. To address this problem, this paper presents a systematic control design with optimal gain computation to provide fast output performance and a well-balanced three-phase voltage even under unequal load conditions. The controller is based on dual-voltage control for positive and negative sequences with the purpose of regulating the output signals and eliminating unbalanced voltage, respectively. The process Eng. Proc. 2023, 56, 87. https://doi.org/10.3390/ASEC2023-15365 https://www.mdpi.com/journal/engproc