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A large number of single-phase loads and sources create unbalanced voltage in microgrids. Voltage unbalance reduces the power quality, which results in misoperation or failure of customer equipment and microgrid. Also, voltage unbalance negatively impacts induction motors, power electronic converters, and adjustable speed drives. Static synchronous compensator (STATCOM), as an influential segment of the Flexible Alternative Current Transmission Systems (FACTS), has been extensively utilized as shunt compensators for controlling reactive power and regulation voltage in transmission and distribution networks. Under unbalanced conditions, an oscillating couple between the positive and negative sequence components of control loops emerge in the d-q frame. This paper suggests an innovative point of common coupling (PCC) voltage controller in Decoupled Double Synchronous Reference Frame (DDSRF) to compensate for an unbalanced PCC voltage and reduce the oscillating couple using STATCOM. Implementation of the proposed DDSRF involves several steps. Firstly, unbalance signals are rotated counterclockwise to split up the positive sequences. Secondly, those signals are rotated clockwise to separate negative sequences. Finally, by utilizing mathematical equations, the proposed DDSRF is introduced, which enables independent control of positive and negative sequence components. This study controls DC capacitor voltage for unbalanced conditions. Furthermore, the regulation voltage at PCC is performed. The control system scheme is also designed under unbalanced conditions, and simulation results guarantee the suggested control strategy. DC-side capacitor. _ qd ref i + Positive sequence d-q components of the reference current. _ dc ref V References of DC voltage.

In recent years, permanent magnet synchronous motors (PMSMs) have received more attention in industries due to their higher efficiency in comparison to induction motors. Moreover, they play a growingly important role in applications where variable speeds are necessary. This paper is concerned with the speed control of PMSMs, and the controller design procedure is developed in two steps. Firstly, a novel robust controller is designed via linear matrix inequalities (LMIs) approach in order to guarantee the robustness of the speed control under the load variation and uncertainty. The design of the main LMI, uncertainty, and disturbance elimination LMI involves several steps which are presented in the paper. For comparison, classic state feedback controller and proportional-integral-derivative controller with parameters optimized by genetic algorithm are implemented in different scenarios. Secondly, a gain-scheduled controller is designed and simulated. The controller design conditions are derived in terms of LMIs, which can be solved via convex optimization in MATLAB using YALMIP toolbox. It is observed that instead of using one robust controller for all operating points, several ones can be used, and by measuring the speed feedbacks, the control system opt for the appropriate controller. The suggested gain-scheduled control method via LMI approach gives excellent performance over the complete operational range, and the results validate the robustness and effectiveness of the proposed method.

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