Real-Time Optimization-Based Reference Calculation Integrated Control for MMCs Considering Converter Limitations

Abstract

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.

Optimization-Based Methodology to Design the MMC's Sub-Module Capacitors

“…• Step 2 -In this step, the optimal MMC steady-state values are obtained through an optimization method which is formulated to maximize either the voltage or frequency support that the converter must provide during AC network voltage sags. The prioritization between the two types of support is defined in the objective function (OF) of this optimization problem according to the value of the weights λ +− Ip,q given by the user, as shown in ( 1) and further explained presented in [23].…”

“…Based on that, the inequality (2q) can be replaced by two other inequalities, one for the HB SMs and another for FB SMs. Finally, the inequality constrains are imposed as time-domain equations in the optimization algorithm as done in [23].…”

On the Roles and Interactions of the MMC Internal Energy Balancing Degrees of Freedom for Three-Wire Three-Phase Connections

“…it should be noted that unlike the positive-and negative-sequence differential components, this DOF cannot be correlated with the AC network currents. To obtain this DOF, authors in [24] calculated it based on the maximum and minimum SM capacitor voltage levels, whereas [25] used an optimization-based calculation approach. Similarly to the procedures developed for the differential terms, (7) can be rewritten in terms of the symmetric components, leading to…”

Fault Ride-through Hybrid Controller for MMC-HVDC Transmission System via Switching Control Units Based on Bang-bang Funnel Controller

“…By the input-output linearization, the output power of MMC is decoupled without a phase-locked loop (PLL). A real-time optimization-based current reference calculation algorithm is designed in [18] for the MMC operation under the balanced and unbalanced conditions in AC and DC networks. The mathematical optimization-based nonlinear optimal controllers are designed in [19], and the robust control of an MMC is realized with optimized operational costs.…”