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Analytical solution of optimized energy consumption of Double Star Induction Motor operating in transient regime using a Hamilton–Jacobi–Bellman equation

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  • Kortas, Imen
  • Sakly, Anis
  • Mimouni, Mohamed Faouzi

Abstract

The problem of energy optimization of a DSIM (Double Stator Induction Motor) using the concept of a RFOC (Rotor Field Oriented Control) can be treated by an OCS (Optimal Control Strategy). Using OCS, a cost-to-go function can be minimized and subjected to the motor dynamic equations and boundary constraints in order to find rotor flux optimal trajectories. This cost-to go function consists of a linear combination of magnetic power, copper loss, and mechanical power. The dynamic equations are represented by using a reduced Blondel Park model of the DSIM. From the HJB (Hamilton–Jacobi–Bellman) equation, a system of nonlinear differential equations is obtained, and analytical solutions of these equations are achieved so as to obtain a time-varying expression of a minimum-energy rotor flux. This analytical solution of rotor flux achieved maximum DSIM's efficiency and was implemented in the ORFOC (optimal rotor flux oriented control) and compared to the conventional RFOC at different dynamic regime of the DSIM. Simulation results are given and improved the effectiveness of the proposed strategy.

Suggested Citation

  • Kortas, Imen & Sakly, Anis & Mimouni, Mohamed Faouzi, 2015. "Analytical solution of optimized energy consumption of Double Star Induction Motor operating in transient regime using a Hamilton–Jacobi–Bellman equation," Energy, Elsevier, vol. 89(C), pages 55-64.
    • Handle: RePEc:eee:energy:v:89:y:2015:i:c:p:55-64
    DOI: 10.1016/j.energy.2015.07.035
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    References listed on IDEAS

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    1. Song, Ziyou & Hofmann, Heath & Li, Jianqiu & Han, Xuebing & Ouyang, Minggao, 2015. "Optimization for a hybrid energy storage system in electric vehicles using dynamic programing approach," Applied Energy, Elsevier, vol. 139(C), pages 151-162.
    2. Buoro, Dario & Pinamonti, Piero & Reini, Mauro, 2014. "Optimization of a Distributed Cogeneration System with solar district heating," Applied Energy, Elsevier, vol. 124(C), pages 298-308.
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    Cited by:

    1. Memon, Abdul Jabbar & Shaikh, Muhammad Mujtaba, 2016. "Confidence bounds for energy conservation in electric motors: An economical solution using statistical techniques," Energy, Elsevier, vol. 109(C), pages 592-601.
    2. Behzad Kafash, 2019. "Approximating the Solution of Stochastic Optimal Control Problems and the Merton’s Portfolio Selection Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 763-782, August.
    3. Lei, Fei & Du, Bin & Liu, Xin & Xie, Xiaoping & Chai, Tian, 2016. "Optimization of an implicit constrained multi-physics system for motor wheels of electric vehicle," Energy, Elsevier, vol. 113(C), pages 980-990.
    4. Lei, Fei & Gu, Ke & Du, Bin & Xie, Xiaoping, 2017. "Comprehensive global optimization of an implicit constrained multi-physics system for electric vehicles with in-wheel motors," Energy, Elsevier, vol. 139(C), pages 523-534.

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