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Optimal Design Variables to Minimize the Cost of Materials the Stator of Asynchronous Machine

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Abstract

The aim of this paper was the design of a three-phase induction motor stator, optimizing its production cost by formulating and solving geometric variables. The stator is a part of the motor and its main function is to generate a magnetic field, thus an interesting research theme, since it is related to the production cost of electric motors. Optimizing techniques are used when the structure of the problem is complex. This generally happens when there is no straightforward procedure. Therefore, optimization techniques can be used in search of a better solution for the problem. These techniques are applied in minimizing the cost, volume and copper loss of the asynchronous machine stator. To solve these problems, the MODE algorithm is used (multiobjective optimization differential evolution) and the outcome is compared to the NSGA II algorithm (non-dominated sorting genetic algorithm II).

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Abbreviations

ac :

Specific electric charge (A/m)

\(A_\mathrm{c} \) :

Area of the stator’s core \((\hbox {mm}^{2})\)

\(A_\mathrm{s} \) :

Conductor’s section area \((\hbox {mm}^{2})\)

\(B_\mathrm{av}\) :

Air-gap average flux density (T)

\(B_\mathrm{c} \) :

Flux density in the core (T)

\(B_\mathrm{cu}\) :

Copper density \((8{,}900\,\hbox {kg/m}^{3})\)

\(B_\mathrm{fe}\) :

Iron density \((7{,}600\,\hbox {kg/m}^{3})\)

\(b_\mathrm{t}^{\prime }\) :

Width of the teeth (m)

\(b_\mathrm{s} \) :

Width of the stator’s slot (m)

C :

The output coefficient

\(\cos \varphi \) :

Power factor

\(\textit{Cost}_1\) :

Total cost of the weight of copper (\(\hbox {US}\)$)

\(\textit{Cost}_2\) :

Total cost of the weight of iron (\(\hbox {US}\)$)

\(\textit{Cost}_3 \) :

Total cost of the weight of enameled copper (\(\hbox {US}\)$)

\(\textit{Cost}_4 \) :

Total cost of the weight of silicon steel (\(\hbox {US}\)$)

D :

Internal diameter of the stator (m)

\(d_\mathrm{cs}\) :

Depth of the core (m)

\(D_0 \) :

External diameter of the stator (m)

\(h_\mathrm{ss}\) :

Stator slot height (m)

\(I_\mathrm{s} \) :

Phase current of the stator (A)

\(J_\mathrm{s} \) :

Density current on the stator’s winding \((\hbox {A/mm}^{2})\)

\(k_\mathrm{w} \) :

Winding factor of the stator

\(k_1 \) :

Price of copper per kilo \((\hbox {US}\$/\hbox {kg})\)

\(k_2\) :

Price of iron per kilo \((\hbox {US}\$/\hbox {kg})\)

\(k_3 \) :

Price of enameled copper per kilo \((\hbox {US}\$ /\hbox {kg})\)

\(k_4\) :

Price of silicon steel per kilo \((\hbox {US}\$ /\hbox {kg})\)

L :

Length of the machine (m)

\(L_\mathrm{i} \) :

Actual length of the iron (m)

\(L_\mathrm{mt}\) :

Average turn length (m)

N :

Speed (rpm)

\(N_\mathrm{ph}\) :

Number of turns per phase

P :

Poles

\(P_\mathrm{cu}\) :

Copper loss (W)

Q :

Output equation of the motor (kW)

\(r_\mathrm{s} \) :

Winding resistance \((\Omega )\)

\(S_\mathrm{s} \) :

Number of slots in the stator

\(T_\mathrm{ph}\) :

Number of conductors per slot

\(V_\mathrm{c} \) :

Volume of iron in the yoke \((\hbox {m}^{3})\)

\(V_\mathrm{cu}\) :

Copper volume \((\hbox {m}^{3})\)

\(V_\mathrm{d} \) :

Volume of iron in the teeth \((\hbox {m}^{3})\)

\(V_\mathrm{e} \) :

Total volume of the stator \((\hbox {m}^{3})\)

\(V_\mathrm{i} \) :

Isolation volume \((\hbox {m}^{3})\)

\(\textit{Weight}_\mathrm{c} \) :

Iron weight in the yoke (kg)

\(\textit{Weight}_\mathrm{cu}\) :

Copper weight (kg)

\(\textit{Weight}_\mathrm{d} \) :

Iron weight in the teeth (kg)

\(\eta \) :

Efficiency \((\%)\)

\(\tau _\mathrm{p} \) :

Pole step (m)

\(\tau _\mathrm{s}^{\prime }\) :

Slot step in 1/3 of the height (m)

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Acknowledgments

The author Juliana Almansa Malagoli is grateful to CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for the financial support for this research and the Professor Dr. Fran Sérgio Lobato for help with differential evolution algorithms.

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Authors and Affiliations

  1. Faculdade de Engenharia Elétrica, Universidade Federal de Uberlândia (UFU), Av. João Naves de Ávila 2121, Câmpus Santa Mônica, CEP: 38408-100, Uberlândia, MG, Brazil

    Juliana Almansa Malagoli & José Roberto Camacho

  2. Departamento de Engenharia Elétrica, Universidade Federal de Santa Catarina (UFSC), Câmpus Universitário Reitor João David Ferreira Lima, Trindade, CEP: 88040-970, Florianópolis, SC, Brazil

    Mauricio Valencia Ferreira da Luz

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  1. Juliana Almansa Malagoli
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Correspondence to Juliana Almansa Malagoli.

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Malagoli, J.A., Camacho, J.R. & da Luz, M.V.F. Optimal Design Variables to Minimize the Cost of Materials the Stator of Asynchronous Machine. J Control Autom Electr Syst 27, 157–168 (2016). https://doi.org/10.1007/s40313-016-0227-5

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  • DOI: https://doi.org/10.1007/s40313-016-0227-5

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