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The paper addresses a real-time optimization-based reference calculation integrated with a control structure for Modular Multilevel Converters (MMC) operating under normal and constrained situations (where it has reached current and/or voltage limitations, as it may occur during system faults). Firstly, a nonlinear optimization problem has been developed in which it prioritizes to satisfy the AC grid current set-points imposed by the transmission System Operator (TSO). The constrained nonlinear optimization problem is formulated based on the steady-state model of the MMC, whereby the prioritization is achieved through distinct weights defined in the Objective Function’s (OF) terms. The resultant optimization problem, however, is highly nonlinear requiring high computation burden to be solved in real-time. To cope with this issue, this paper applies a Linear Time-Varying (LTV) approximation, which permits to represent the nonlinear dynamics of the system as constant parameters, while a Linear Time-Invariant (LTI) system is used to formulate the optimization constraints. The converter’s current references are determined in real-time by solving a constrained linearized optimization problem at each control time step, which considers the TSO’s demands, the current MMC operating point and its physical limitations. Theoretical analyses comparing the responses of the linear and nonlinear optimization problems are performed to validate the accuracy of the LTV approximation. Finally, the linearized-optimization problem is integrated with the MMC controllers, evaluated under different AC and DC network conditions and compared with conventional control strategies, where it is shown that the presented method can be potentially employed to obtain the MMC current references for distinct network scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-stage model of zonal electricity markets with day-ahead market clearing, and real-time re-dispatch and balancing that accounts for transmission line switching at both stages. We show how the day-ahead problem with switching can be formulated as an adaptive robust optimization problem with mixed integer recourse, and present a new algorithm for solving the adversarial max-min problem that obeys the structure of an interdiction game. We apply the model on a realistic instance of the Central Western European system, and comment on the impacts of both proactive, and reactive transmission switching on the operating costs of the system. Part I presents day-ahead models of a short-term zonal electricity market with switching, and describes our algorithmic approach for solving these models efficiently. Part II describes variants of the real-time model, and presents the results of our case study on the Central Western European market. [ABSTRACT FROM AUTHOR]