An Analytical Method to Determine the Optimal Switching of Modular Multilevel Converter in HVDC System

The lifetime of the submodules (SMs) in a modular multilevel converter (MMC) is significantly impacted by its switching frequency. In this work, the determination of the switching frequency, to be applied to the nearest level modulation (NLM) method used in the SMs, is formulated as a linear integer optimization problem (LIOP). It is shown that there is an ideal minimum switching frequency under which all voltage constraints on the SMs are satisfied. As the loading level on the converter increases, additional switching events are generated and the solution of the LIOP is to yield the gating signals to ensure the voltage constraints are still met and the switching loss is reduced. The LIOP is approximated as a series of Lagrangian relaxation linear programming sub-problems. Each of the sub-problems is then shown to have integrality property and can be solved using the subgradient technique. The solution time is a polynomial function of the number of SMs and the number of voltage constraints in each arm of the converter. The quality of the solution is
$\varepsilon $
-optimal and the corresponding gating signals for each SM are generated by a proposed two-level coordinated control scheme. The feasibility of the proposed optimization method is demonstrated through simulation study performed on a practical 201-level ±200kV/400MW MMC-HVDC system model constructed in a real-time digital simulator (RTDS) platform. Results of the simulation indicate that the tolerance on the voltage difference between any pair of SMs has to be adjusted when the MMC operates at the determined optimum switching.