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Implementation of complex-valued sliding mode controllers in three-phase power converters

Arnau Dòria-Cerezo, Pau Boira, Víctor Repecho, Domingo Biel

TL;DR

This work tackles implementing robust, fast-responding complex-valued sliding mode controllers in three-phase power converters via two low-complexity, sampled-time methods that average the discontinuous control action over available switching vectors. It provides a formal framework for complex-valued control on abc variables, including a complex transformation of three-phase signals and two switching-action strategies: SbI and CSA. The methods preserve sliding-mode robustness without requiring decoupling or modulation-based synthesis, and are validated through numerical simulations and hardware-in-the-loop experiments on a microcontroller. The results demonstrate practical, low-burden implementations that leverage sector-based switching while enabling zero-vector utilization in power-converter control.

Abstract

This paper presents two methods for implementing complex-valued sliding mode controllers in three-phase power converters. The paper includes the description of the algorithms and a detailed analysis of the proposed implementations. The methods, that are easy to code and have a low computational burden, retain the sliding mode properties of robustness and fast response and do not require any additional processing often used to decouple the dynamics of the three-phase system. The performance of the methods is compared in numerical simulations, and the algorithms are experimentally tested in a microcontroller using a Hardware-in-the-Loop platform.

Implementation of complex-valued sliding mode controllers in three-phase power converters

TL;DR

This work tackles implementing robust, fast-responding complex-valued sliding mode controllers in three-phase power converters via two low-complexity, sampled-time methods that average the discontinuous control action over available switching vectors. It provides a formal framework for complex-valued control on abc variables, including a complex transformation of three-phase signals and two switching-action strategies: SbI and CSA. The methods preserve sliding-mode robustness without requiring decoupling or modulation-based synthesis, and are validated through numerical simulations and hardware-in-the-loop experiments on a microcontroller. The results demonstrate practical, low-burden implementations that leverage sector-based switching while enabling zero-vector utilization in power-converter control.

Abstract

This paper presents two methods for implementing complex-valued sliding mode controllers in three-phase power converters. The paper includes the description of the algorithms and a detailed analysis of the proposed implementations. The methods, that are easy to code and have a low computational burden, retain the sliding mode properties of robustness and fast response and do not require any additional processing often used to decouple the dynamics of the three-phase system. The performance of the methods is compared in numerical simulations, and the algorithms are experimentally tested in a microcontroller using a Hardware-in-the-Loop platform.
Paper Structure (7 sections, 5 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 7 sections, 5 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Complex-valued Sliding Mode Control
  4. Complex-valued SMC in three-phase power converters
  5. Transformation from three-phase electrical variables to complex variables
  6. Available control actions in three-phase power converters
  7. Complex Sliding Averaging

Figures (2)

  • Figure 4: Sectors defined by the Sector-based Implementation. The example (in red) shows a complex control value with $105^\circ$ that belongs to Sector S3, and the control switching vector, $V_3$, $u_{abc}=(-1,1,-1)$, is applied (in blue).
  • Figure 5: Sectors defined by the Complex Sliding Averaging (CSA). The example (in red) shows a complex control value with $105^\circ$ that belongs to Sector S2, and the averaged equivalent complex vector is applied $\hat{\bm{u}}$ (in blue).