ISSN 8756-6990, Optoelectronics, Instrumentation and Data Processing, 2022, Vol. 58, No. 4, pp. 381–390. © Allerton Press, Inc., 2022. Russian Text © The Author(s), 2022, published in Avtometriya, 2022, Vol. 58, No. 4, pp. 76–87. ANALYSIS AND SYNTHESIS OF SIGNALS AND IMAGES Resonant PID Controller Design for a Three-Phase Four-Wire Voltage Inverter with Split DC Buses V. D. Yurkevich * Novosibirsk State Technical University, Novosibirsk, 630073 Russia Received March 21, 2022; revised May 12, 2022; accepted May 31, 2022 Abstract—The problem of improving the synchronization accuracy of three-phase voltages of an autonomous four-wire inverter with the network is considered. Increasing the synchronization accuracy is achieved by applying a proportional-integral-differential (PID) resonant controller. A new structure of the PID resonant controller and a methodology for calculating its parameters are proposed. The peculiarity of the proposed approach consists in the application of the time- scale separation method, which makes it possible to calculate the PID component of the controller regardless of the choice of the parameters of its resonant components. Application of this approach to the calculation of the controller of autonomous voltage inverters makes it possible to improve electromagnetic compatibility and reduce losses in distributed power generation systems. The results of numerical simulation are presented. DOI: 10.3103/S8756699022040148 Keywords: distributed power generation system, grid synchronization, inverter, PID control, time-scale separation method, internal model principle 1. INTRODUCTION One of the current trends in the development of modern energy industry is the increasing use of renewable energy sources. Therefore, much attention is currently paid to the development of solar, wind, tidal, geothermal, and other types of power plants of small capacity [1]. Reliability and economic efficiency of power supply to consumers on the basis of renewable energy sources can be achieved by forming a distributed power generation system, where multiple local sources of electricity of low power are connected to a common three-phase AC network [2, 3]. The solution to the problem of power transmission from the local source to the network is provided by the use of three-phase voltage inverters. In particular, under conditions of significant load asymmetry of phases, the effective formation of three- phase voltages can be achieved through the use of three-phase four-wire voltage inverters with split power buses [4–6]. When connecting local power sources, it is important to ensure synchronization of the generated three-phase voltage with the network voltage to ensure electromagnetic compatibility and reduce losses in the distributed power generation system [7, 8]. One way to improve the accuracy of synchronization of the inverter voltages with the grid is to use resonant controllers [9, 10]. For example, paper [11] considered the method of calculating a two-loop control system with a proportional resonant controller for a three-phase voltage inverter with four racks based on the application of Bode diagrams and the root-locus method. In paper [12] the structure of the proportional resonant controller with compensation of a delay in the control loop is proposed, where the delay is due to the digital implementation of the control algorithm. In paper [13] the calculation method of proportional-integral-differential (PID) controller for a three- phase four-wire voltage inverter with split power buses based on the time-scale separation method [14, 15] was considered. The peculiarity of the proposed work is the joint application of the time-scale separation method and the principle of internal model [16, 17] to calculate the PID resonant controller * E-mail: yurkev@mail.ru 381