Linear State Signal Shaping Explicit Model Predictive Control Using Tensor Decompositions

Due to the increasing use of nonlinear loads in modern power systems, harmonic currents have become a more prominent problem for power quality. Typically, harmonic currents are compensated by using shunt active power filters. Recently, a novel constrained linear state signal shaping model predictive controller has been proposed for shunt active power filter control. However, due to the high computational requirements of online quadratic programming solvers, the real-time implementation of this solution is quite challenging. Therefore, the present work proposes the use of a linear state signal shaping explicit model predictive control formulation, such that the optimizations are done offline. However, the generated offline data introduces a large memory footprint, hindering real-time implementation. To break the curse of dimensionality, a tensor representation is proposed, which can be efficiently compressed via tensor decomposition methods. The proposed approach was tested in simulation and was able to provide good results. Due to the use of efficient tensor decomposition methods, a considerable reduction of the memory requirement could be achieved.