Dealing with Suboptimality in Multistep Model Predictive Control for Transient Operations

Recently, a computational issue of sphere decoding algorithm (SDA) during transient operation of multistep model predictive control has been addressed in [1] and achieved its real-time implementation in [2] for a medium-voltage electrical drive system. This is achieved by projecting the unconstrained solution onto the convex-hull of the finite control set during transient operation. Therefore, a new initial sphere that guarantees feasibility and includes a significant smaller number of candidate solutions is obtained. This reduces the computation time required to solve the optimization problem. However, the reduction of the computational burden comes at the expense of (mild) suboptimal results [3]. This paper analyses the possibility to obtain a suboptimal solution by the SDA based optimization during transient operation. To deal with this suboptimality issue, this work explores the possibility to enlarge the convex-hull, whose size is by definition tied to the original finite control set. Therefore, in this work, the convex-hull is treated as a SDA initialization parameter during transient operation. As will be demonstrated, enlarging the convex-hull size reduces the possibility to obtain a suboptimal solution during the transient operation retaining, thus, the optimality during the whole converter operation.