aVsIs: An Analytical-Solution-Based Solver for Model-Predictive Control With Hexagonal Constraints in Voltage-Source Inverter Applications

Abstract

The theory of a new analytical-solution-based algorithm for calculating the optimal solution in model-predictive control applications with hexagonal constraints is discussed in this article. Three-phase voltage-source inverters for power electronic and electric motor drive applications are the target of the proposed method. The indirect model-predictive control requires a constrained quadratic programming (QP) solver to calculate the optimal solution. Most of the QP solvers use numerical algorithms, which may result in unbearable computational burdens. However, the optimal constrained solution can be calculated in an analytical way when the control horizon is limited to the first step. A computationally efficient algorithm with a certain maximum number of operations is proposed in this article. A thorough mathematical description of the solver in both the stationary and rotating reference frames is provided. Experimental results on real test rigs featuring either an electric motor or a resistive-inductive load are reported to demonstrate the feasibility of the proposed solver, thus smoothing the way for its implementation in industrial applications. The name of the proposed solver is aVsIs, which is released under Apache License 2.0 in GitHub, and a free example is available in Code Ocean. IndexTerms-Continuous control set (CCS), interior permanent magnet (IPM), model-predictive control (MPC), permanent magnet synchronous motor (PMSM), synchronous reluctance (SynR). I. INTRODUCTION T HE model-predictive control (MPC) paradigm is popular in the scientific research community working in the power electronic and electric drive application fields. Two different MPC technique groups can be found, namely, direct and indirect MPC algorithms [1]-[3]. The former techniques do not require

Continuous Control Set Model Predictive Torque Control With Minimum Current Magnitude Criterion for Synchronous Motor Drives

“…A three-phase voltage inverter is considered. In order to obtain a feasible voltage vector u k+1 dq , the hexagonal constraint in the dq current plane is implemented as linear inequality constraints [26], [31], [32]. Matrices M and m in (8) are defined as…”

Continuous Control Set Model Predictive Torque Control with Minimum Current Magnitude Criterion for Synchronous Electric Motor Drive

“…In order to obtain a feasible voltage vector u k+1 dq , the hexagonal constraint in the dq current plane are implemented as linear inequality constraints [18], [22], [23]. Matrices M and m in (8) are defined as:…”

Recent Achievements in the Control of Interior Permanent-Magnet Synchronous Machine Drives: A Comprehensive Overview of the State of the Art

“…Gradient methods [31,142] and active-set methods [143] are the two most commonly used QP solver techniques for electrical drives. It should be noted that most of the QP solvers apply an iterative numerical method, which can drastically increase the computational load [144]. Paper [31] proposes an iteration scheme with a fixed number of steps for IPMSM drives using a nonlinear dq model, which takes into account the saturation and parasitic effects.…”

“…An MPC scheme for PMSMs using the active-set method and implemented on low-performance hardware is presented in [143]. A computationally efficient method with a maximum number of arithmetic operations is proposed in [144] for VSI applications, like IPMSM drives, with hexagonal voltage constraints.…”

“…A CS-MPCC method for an IPMSM with the capability to work even in the overmodulation region, including the six-step operation mode, is introduced in [78]. The methods presented in [144,147] also have the capability to work in the overmodulation region.…”