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Switching Frequency Limitation with Finite Control Set Model Predictive Control via Slack Variables

Luca M. Hartmann, Orcun Karaca, Tinus Dorfling, Tobias Geyer

TL;DR

This work tackles the challenge of controlling switching frequency in finite control set MPC for power converters without sacrificing current-tracking performance. It introduces c3, which limits switching frequency by penalizing a slack variable associated with an upper bound on $f_{sw}$ and reformulates the optimization as an integer least-squares problem solvable via a sphere decoder. A key contribution is the modified sphere-decoder framework for c3, augmented with a provable lower-bound-based speed-up that prunes search branches and reduces worst-case computation time. Case studies demonstrate that c3 often yields equal or better current-tracking accuracy while maintaining the switching frequency within the desired limit, with significant computational benefits enabling real-time feasibility. The approach offers a practical pathway to reduce switching losses and device stress in grid-connected converters while preserving performance.

Abstract

Past work proposed an extension to finite control set model predictive control to track both a current reference and a switching frequency reference, simultaneously. Such an objective can jeopardize the current tracking performance, and this can potentially be alleviated by instead limiting the switching frequency. To this end, we propose to limit the switching frequency in finite control set model predictive control. The switching frequency is captured with an infinite impulse response filter and bounded by an inequality constraint; its corresponding slack variable is penalized in the cost function. To solve the resulting problem efficiently, a sphere decoder with a computational speed-up is presented.

Switching Frequency Limitation with Finite Control Set Model Predictive Control via Slack Variables

TL;DR

This work tackles the challenge of controlling switching frequency in finite control set MPC for power converters without sacrificing current-tracking performance. It introduces c3, which limits switching frequency by penalizing a slack variable associated with an upper bound on and reformulates the optimization as an integer least-squares problem solvable via a sphere decoder. A key contribution is the modified sphere-decoder framework for c3, augmented with a provable lower-bound-based speed-up that prunes search branches and reduces worst-case computation time. Case studies demonstrate that c3 often yields equal or better current-tracking accuracy while maintaining the switching frequency within the desired limit, with significant computational benefits enabling real-time feasibility. The approach offers a practical pathway to reduce switching losses and device stress in grid-connected converters while preserving performance.

Abstract

Past work proposed an extension to finite control set model predictive control to track both a current reference and a switching frequency reference, simultaneously. Such an objective can jeopardize the current tracking performance, and this can potentially be alleviated by instead limiting the switching frequency. To this end, we propose to limit the switching frequency in finite control set model predictive control. The switching frequency is captured with an infinite impulse response filter and bounded by an inequality constraint; its corresponding slack variable is penalized in the cost function. To solve the resulting problem efficiently, a sphere decoder with a computational speed-up is presented.
Paper Structure (13 sections, 1 theorem, 31 equations, 5 figures, 5 tables, 2 algorithms)

This paper contains 13 sections, 1 theorem, 31 equations, 5 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Physical system model
  4. Switching frequency estimation
  5. FCS-MPC for $f_\mathrm{sw}$ tracking
  6. FCS-MPC for $f_\mathrm{sw}$ Limiting via Slack Variables
  7. Problem formulation
  8. Sphere decoder
  9. Lower bound for computational speed-up
  10. Case Studies
  11. Conclusion
  12. Sphere decoder for c2
  13. Matrices for c2 and c3

Key Result

Proposition 1

Given $\ell<k+N_\mathrm{p}$, define We have that $\underbar{d}_{\text{bound},\ell}^2\leq J_\mathrm{S}(\ell).$

Figures (5)

  • Figure 1: Grid-connected 3L-NPC converter.
  • Figure 2: Block diagram of FCS-MPC with switching frequency estimation (EST).
  • Figure 3: Steady-state operation.
  • Figure 4: Current transients.
  • Figure 5: Switching frequency step-up.

Theorems & Definitions (1)

  • Proposition 1