Multi-Objective stochastic model predictive control for MTDC systems with uncertain wind energy

• An Itô SDE – based stochastic state-space model is embedded to capture the effect of wind stochasticity on system dynamics. • A multi-objective MPC scheme for VSC-MTDC considering power tracking, allocation, and stochastic stability is proposed. • Moment stability is incorporated into the probabilistic constraints and undergoes solvable reconstruction. Flexible DC transmission has become one of the ideal solutions for integrating high proportions of wind power into the grid. However, the inherent randomness of wind power and the nonlinearity of power electronic devices pose significant challenges to system stability. As a result, traditional control methods often fail to ensure robustness and system stability under these conditions. To address these issues, this paper proposes a stochastic multi-objective model predictive control strategy. The strategy ensures the system’s stochastic stability and achieves real-time power tracking and cooperative control among multi-converter stations, enabling flexible balancing among multiple objectives. Specifically, stochastic differential equations are adopted for gray-box modeling of stochasticity, and the system equations under the Lamperti transformation are derived. On this basis, the optimization problem of multi-converter station cooperative control considering stochasticity is formulated, simultaneously achieving tracking control, voltage stability and optimal power allocation. Subsequently, the stochastic stability constraint is defined in terms of moment stability, and the probabilistic constraints are reformulated into deterministic constraints to improve the solution efficiency of real-time predictive control. A wind-integrated MTDC system is constructed in Matlab/Simulink to validate the robustness and multi-objective control performance of the proposed strategy.