# Impact of Sequential Model Predictive Control on Induction Motor Performance: Comparison of Converter Topologies

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## Abstract

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## 1. Introduction

- Study of the selection of the control parameter for the application of the SMPC strategy in electric motor control. The domain of the control parameter is established, and a selection criterion based on the THD is defined.
- The study addresses the VSI and 3L-NPC converters, which are common in low and medium-power motor drives. The objective is to highlight that as the power of the motor drive increases, the complexity of the converter increases, as well as the difficulty in adjusting the controller.
- The SMPC strategy is validated not only through simulation but also through HIL using two PLEXIM’s RT Boxes, one as a controller and the other one as a plant.

## 2. Methodological Approach

#### 2.1. Modeling

#### 2.1.1. VSI Converter

#### 2.1.2. 3L-NPC Converter

#### 2.1.3. Induction Motor

#### 2.2. Prediction Equations

#### 2.3. Cost Functions

#### 2.4. Sequential Model Predictive Control

- Step 0: Measure motor variables and estimate flux.
- Step 1: Evaluate the first cost function for all possible switching states (M). M value depends on the converter topology. M value is 8 in the VSI or 27 in the 3L-NPC converter.
- Step 2: Order the results of the first cost function evaluation in ascending order, and select the top N states. It is important to note that $N<M$ must be satisfied.
- Step 3: Evaluate the second cost function for the N states selected in the previous step.
- Step 4: Select the switching state that best minimizes the flux cost function, which will be applied to the converter in the next sampling period.

## 3. Results

#### 3.1. Simulations

#### 3.2. Experimental Results

## 4. Discussion

#### 4.1. Simulation

#### 4.1.1. Cost Functions Evaluation Order

#### 4.1.2. Control Parameter Domain

- VSI converters, $N\in [2,3]$.
- 3L-NPC converters, $N\in [4,12]$.

#### 4.1.3. SMPC Performance According to Selected Parameter

#### 4.2. Experimental Results

#### 4.3. Limitation of the Proposed Approach

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

EH-SMPC | Even Handed Sequential Model Predictive Control. |

EEH-SMPC | Enhanced Even Handed Sequential Model Predictive Control. |

FS-MPC | Finite Set Model Predictive Control. |

G-SMPC | Generalized Sequential Model Predictive Control. |

HIL | Hardware-in-the-Loop. |

IM | Induction Motor. |

MPC | Model Predictive Control. |

MVSCs | Multilevel Voltage Source Converters. |

SMPC | Sequential Model Predictive Control. |

VSI | Voltage Source Inverter. |

3L-NPC | Neutral Point Clamped converter of three levels. |

## Nomenclature

${u}_{s}$ | stator voltage. |

${\psi}_{s}$ | stator flux. |

${\psi}_{r}$ | rotor flux. |

${i}_{s}$ | stator current. |

${i}_{r}$ | rotor current. |

${R}_{s}$ | stator resistance. |

${R}_{r}$ | rotor resistance. |

${L}_{s}$ | stator inductance. |

${L}_{r}$ | rotor inductance. |

${L}_{m}$ | mutual inductance. |

w | electrical speed. |

T | electromagnetic torque. |

p | number of pole pairs. |

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**Figure 3.**General scheme of the proposed sequential model predictive control (SMPC) for motor drive applications.

**Figure 9.**Experimental setup: (

**a**) oscilloscope; (

**b**) analog input board; (

**c**) RT Box 1’ (

**d**) RT Box 2; (

**e**) laptop.

Parameters | Value |
---|---|

${V}_{DC}$ | 1500 V |

${R}_{s}$ | 1.35 $\Omega $ |

${R}_{r}$ | 7.2 $\Omega $ |

${L}_{s}$ | 0.2861 H |

${L}_{r}$ | 0.2861 H |

${L}_{m}$ | 0.2822 H |

Power Converter | VSI | 3L-NPC | ||
---|---|---|---|---|

Parameter | $\mathit{N}=2$ | $\mathit{N}=3$ | $\mathit{N}=4$ | $\mathit{N}=12$ |

Peak current [Ap] | 15.49 | 15.67 | 15.49 | 15.89 |

THD [%] | 9.52 | 5.48 | 6.88 | 4.92 |

Fundamental frequency [Hz] | 67.15 | 66.83 | 67.89 | 66.57 |

Fundamental component [Ap] | 14.76 | 14.69 | 14.83 | 14.75 |

Main harmonics | 470.0 Hz 0.29 Ap | 133.7 Hz 0.19 Ap | 539.4 Hz 0.22 Ap | 466.0 Hz 0.32 Ap |

872.9 Hz 0.14 Ap | 468.0 Hz 0.18 Ap | 746.7 Hz 0.22 Ap | 133.1 Hz 0.30 Ap | |

335.7 Hz 0.13 Ap | 334.3 Hz 0.17 Ap | 882.5 Hz 0.17 Ap | 732.3 Hz 0.30 Ap |

VSI | 3L-NPC | |||
---|---|---|---|---|

Approach | $\mathit{N}=2$ | $\mathit{N}=3$ | $\mathit{N}=4$ | $\mathit{N}=12$ |

Simulation | 0.80 | 0.81 | 0.66 | 0.72 |

HIL | 0.96 | 0.97 | 0.77 | 0.80 |

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**MDPI and ACS Style**

Murillo-Yarce, D.; Araya, B.; Restrepo, C.; Rivera, M.; Wheeler, P.
Impact of Sequential Model Predictive Control on Induction Motor Performance: Comparison of Converter Topologies. *Mathematics* **2023**, *11*, 972.
https://doi.org/10.3390/math11040972

**AMA Style**

Murillo-Yarce D, Araya B, Restrepo C, Rivera M, Wheeler P.
Impact of Sequential Model Predictive Control on Induction Motor Performance: Comparison of Converter Topologies. *Mathematics*. 2023; 11(4):972.
https://doi.org/10.3390/math11040972

**Chicago/Turabian Style**

Murillo-Yarce, Duberney, Baldomero Araya, Carlos Restrepo, Marco Rivera, and Patrick Wheeler.
2023. "Impact of Sequential Model Predictive Control on Induction Motor Performance: Comparison of Converter Topologies" *Mathematics* 11, no. 4: 972.
https://doi.org/10.3390/math11040972