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.