# Response Surface Method for Optimization of Synchronous Reluctance Motor Rotor

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## Abstract

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## 1. Introduction

_{2}emissions per year. Therefore, the European Union (EU), as well as the United States (US), China, and other countries have adopted legislation that makes it mandatory to apply gradually increasing energy efficiency requirements in relation to new equipment units. The International Electrotechnical Commission (IEC) has introduced energy efficiency classification for electric motors, also known as IE codes, as stipulated in the international standard IEC 60034-30-1 [4]. According to the international standard, there are currently four energy efficiency classes for electric motors, IE1, IE2, IE3, and IE4 (IE—International Energy Efficiency Class). Increasing the energy efficiency requirements encourages researchers to develop alternative technologies for electric machines. One of the options to reach IE3 and IE4 efficiency classes is using rare-earth permanent magnets in electric machines, ultimately causing a relatively larger impact on the environment. Currently, around eight billion electric motors are being used in the EU, consuming about half of the electricity produced in the EU. The sector is very variegated, with a considerable range of technologies, applications, and sizes, ranging from small motors (e.g., motors that run computer cooling fans) to huge motors used in the heavy industry. The directive on the eco design of energy-using products is to be replaced by a regulation laying down eco-design requirements for electric motors and variable speed drives. The new legal framework will include not previously covered asynchronous motors (small motors ranging from 0.12 kW to 0.75 kW; large motors from 375 kW to 1000 kW) [5]. In addition, the requirements will be toughened as three-phase motors with a nominal power between 0.75 kW and 1000 kW or less have to reach IE3 class. Motors with a power range from 75 kW to 200 kW must comply with IE4 class requirements as of July 2023 [6]. The new rules will also regulate the efficiency of variable-speed motors, and both product groups will be subject to requirements such as efficiency at different load points, speed, and torque.

_{2}emissions will be reduced by 40 million tons, and the annual energy bill of EU households and industries will decrease by around 20 billion EUR by 2030. Integrated optimization of the electric motor drive system (including the use of high-efficiency and well-designed components) is the main strategy for increasing the overall efficiency of electric motors [7,8].

## 2. Design Optimization

- Mapping the response surface (display) in a specific interest area. This gives the designer understanding of what is expected as a result of changes in the parameters of the system or process. For this purpose, different graphical displays are applied: 3D surfaces and counter plots. The problem is that in the case of a larger number of input factors, it is only possible to create section graphics, i.e., record some factors with constant values, and view the other two factors graphically.
- Optimization of the response. Optimization using computer programs is usually not difficult for approximated models. If there is more than one optimization criterion, Pareto ideology or method weighted criteria can be applied. However, optimal result validation is always required. In addition, it may appear that the approximated model has a major error, and its optimum is not applicable to the physical model. Then the whole RSM process must be repeated, adding experimental tests and other regression functions.
- Change product or process parameters to adjust to standard specifications or customer requirements. The main problem of the response surface problem is the number of responses that should be analyzed simultaneously. If a client has determined a certain concentration in its project, the designer must reach this level at a minimum cost.
- Today, the Response Surface Methodology has evolved into a Metamodeling Methodology but is often also referred to as the Response Surface Method. The most significant development of RSM began with the onset of numerical experiments. There are mathematical models for numerical experiments often the Finite Elements (FE) model is applied. In this model, it is possible to calculate responses at the given input parameter values. However, the relationship between input factors and responses is not analytically describable. Numerical experiments and approximations are carried out to obtain an understandable mathematical model. These approximations are the exact approximation of the FE model, which is referred to as a metamodel or surrogate model [10].

- Aim and objective;
- Factors and range;
- Plan of numerical experiment;
- Modelling of experiment;
- Synthesis of metamodel;
- Verify prediction.

## 3. Design of the Experiment

_{3}values during modeling were entered as five equal points. Thus, they have given the greatest weight to the method of least squares. Thus, in the last stage, the number of points is 59, of which only 49 are different. Figure 2 is shown the optimum Legendre polynomial items number, which is selected based on cross-validation value. Cross-validation is one of the most widely used data resampling methods to estimate the true prediction error of models and to tune model parameters [21].

## 4. Experimental Study

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**View of investigated synchronous reluctance motor (r

_{1}-radial rib; r

_{2}-tangential rib).

**Figure 7.**Cross-section of the rotor with transversally laminated anisotropy: (

**a**) rotor sheet (

**b**) experimental rotor model.

**Figure 9.**(

**a**) Motor current vs. torque and efficiency and (

**b**) SynRM input power values as a function of motor stator current for the case of 1500 rpm.

Parameters | Value | |

Number of slots | 36 | |

Outer diameter | 139 mm | |

Inner diameter | 92.7 mm | |

Stack length | 110 mm | |

Number of turns | 47 | |

Number of parallel paths | 2 | |

Coil pitch | 1–8 | |

Filling factor | 69.48% | |

Wire diameter | 0.56 mm |

Variables | Unit | Limits | |
---|---|---|---|

${x}_{1}$ | Rotor outer radius | mm | 45.25 < $R$ < 46.05 |

${x}_{2}$ | Radial rib | mm | 1 < ${r}_{1}$ < 3 |

${x}_{3}$ | Tangential rib | mm | 1 < ${r}_{2}$ < 3 |

${x}_{4}$ | Insulation ratio | - | 0.2 < ${k}_{w}$ < 1.2 |

${x}_{5}$ | Number of barriers | - | 1 < $b$ < 5 |

Variables | Unit | Aim | |
---|---|---|---|

${y}_{{}_{1}}$ | Torque | Nm | Maximize |

${y}_{2}$ | Specific torque | Nm/kg | Maximize |

${y}_{3}$ | Efficiency | % | Maximize |

${y}_{1}$ | ${y}_{2}$ | ${y}_{3}$ | |

Criterion | −10.443548 | −3.5202343 | −0.95434034 |

${x}_{1}$ | 0.0461 | 0.0461 | 0.0461 |

${x}_{2}$ | 0.001 | 0.001 | 0.001 |

${x}_{3}$ | 0.001 | 0.001 | 0.001 |

${x}_{4}$ | 0.69776964 | 1.2 | 0.33468864 |

${x}_{5}$ | 1 | 1 | 5 |

${y}_{1}$ | 10.443548 | 9.7631095 | 9.4437398 |

${y}_{2}$ | 3.0903761 | 3.5202343 | 2.527117 |

${y}_{3}$ | 0.86956646 | 0.80096256 | 0.95687512 |

Voltage (V) | 220 | 290 | 340 | 385 |

Phase current (A) | 1.33 | 1.33 | 1.33 | 1.33 |

Speed (rpm) | 750 | 1050 | 1347 | 1500 |

Voltage (V) | 380 | 380 | 380 | 380 | 380 | 380 |

Phase current (A) | 1.6 | 2.08 | 2.33 | 2.7 | 3.49 | 5.01 |

Input power (W) | 410 | 814 | 1118 | 1280 | 1650 | 2460 |

Torque (Nm) | 2.5 | 4.5 | 6.5 | 7.5 | 8.5 | 11.5 |

Output power (W) | 368 | 670 | 988 | 1140 | 1319 | 1770 |

Efficiency | 87 | 87 | 88 | 89 | 80 | 72 |

Speed (rpm) | 1500 | 1500 | 1500 | 1500 | 1500 | 1500 |

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**MDPI and ACS Style**

Orlova, S.; Auzins, J.; Pugachov, V.; Rassõlkin, A.; Vaimann, T.
Response Surface Method for Optimization of Synchronous Reluctance Motor Rotor. *Machines* **2022**, *10*, 897.
https://doi.org/10.3390/machines10100897

**AMA Style**

Orlova S, Auzins J, Pugachov V, Rassõlkin A, Vaimann T.
Response Surface Method for Optimization of Synchronous Reluctance Motor Rotor. *Machines*. 2022; 10(10):897.
https://doi.org/10.3390/machines10100897

**Chicago/Turabian Style**

Orlova, Svetlana, Janis Auzins, Vladislav Pugachov, Anton Rassõlkin, and Toomas Vaimann.
2022. "Response Surface Method for Optimization of Synchronous Reluctance Motor Rotor" *Machines* 10, no. 10: 897.
https://doi.org/10.3390/machines10100897