Assessment of a Laguerre Polynomial Based Sphere Decoding Algorithm for Direct MPC of Inverters

In the last years, model predictive control (MPC) has become a significant competitor to conventional control strategies for power electronic applications. In particular, direct MPC using sphere decoding algorithms (SDAs) as optimizers have gained popularity in this context. Besides such specialized optimization algorithms, it is possible to improve the MPC performance by dimensional reduction of the optimization problem using Laguerre polynomials (LaPs). LaP based MPC has already been proven advantageous for example in robotic and marine applications. This paper presents an approach to link the SDA and LaPs by formulating a Laguerre polynomial based sphere decoding algorithm (LaP-SDA) for the control of inverters on the modulation-level. Following some introductions to the SDA and LaPs, the optimization problem and its particular structure for the SDA is transformed using sets of LaPs. This modification of the SDA results in a new admissible set and an additional optimization problem to find the optimal configuration of the LaPs. Moreover, it changes the shape of the search tree tailoring it wider but more shallow. Finally, the LaP-SDA is verified in a simulation using an example system. There, it is shown that, with a suitable configuration, the results of the SDA and LaP-SDA are identical. However, the simulation does not indicate a performance benefit of the LaP-SDA mainly because of the size of the admissible set. Nevertheless, prospective modifications to improve its performance and further applications of the LaP-SDA are presented.