Predictive Converter Control: Hidden Convexity and Real-Time Quadratically Constrained Optimization

This brief considers model predictive control of voltage source converters with $LC$ filter. The converter model describes the nonlinear effect of the switching on the converter state, and the model predictive control (MPC) problem is thus nonlinear and nonconvex. An in-depth analysis reveals a convex structure of the converter model, and a nonlinear variable transformation is introduced, which allows to equivalently reformulate the MPC problem as a convex, quadratically constrained quadratic problem (QCQP). Thus, a problem, which has previously been formulated as a nonconvex problem and solved approximately, can be solved exactly without approximation error. This brief also contains experimental results showing the practical applicability of the approach: The QCQP is solved in real time at a kilohertz sampling rate using the projected gradient and constraint linearization method FalcOpt.