Analytical Solution of Optimized Energy Consumption of Induction Motor Operating in Transient Regime

doi:10.3166/ejc.17.397-411

European Journal of Control

Volume 17, Issue 4, 2011, Pages 397-411

https://doi.org/10.3166/ejc.17.397-411 Get rights and content

The problem of energy optimization of induction motor (IM) using the concept of a Rotor Field Oriented Control (RFOC) can be treated by an Optimal Control Strategy (OCS). 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 induction motor. From the Hamilton-Jacobi-Bellman (HJB) 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 minimumenergy rotor flux. Under RFOC, this analytical solution of rotor flux achieved maximum IM's efficiency and was implemented in transient torque. The current study discusses a saturation model with respect to the rotor flux, which has significant influence in the motor's parameters. A comparative study of simulation results given from conventional and optimized RFOC proves the presented strategy's validity and effectiveness.

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Cited by (12)

Optimal control strategy of an induction motor for loss minimization using Pontryaguin principle
2019, European Journal of Control
Citation Excerpt :
The choice of y(x0) in Eq. (58) leads to the same first-order differential equation proposed by the OCP but at initial conditions. The scheme of the optimal RFOVD is presented in Fig. 2 [1]. Based on the flux and torque currents, components are obtained.
This paper presents a new design of loss-minimization optimization control for Induction Machine (IM) drives. It describes a closed-loop optimal control law and exploits the Pontryagin principle to get optimal energy consumption. This proposal is based on the Optimal Control Problem (OCP) which focuses on minimizing a cost function given as an integral of a weighted sum of the mechanical power, copper losses and magnetic power of the IM. In order to minimize the IM energy consumption, we consider a normalized cost function with respect to the optimization finite-interval [0,T]. This functional is subjected to dynamic constraints which are developed from a reduced IM model. The system depends on two state variables: the rotor flux and the motor speed. The proposed method provides an optimal rotor flux that performs the minimal energy consumption of an IM along a given torque and velocity. This OCP conducts to a system of combined nonlinear differential equations of state and co-state variables. Long and hard developments lead to many calculus steps. Finally, an optimal time-varying rotor flux is successfully turned out. This OCP satisfies also abrupt torque conditions and can cover dynamic operations when the proposed solution fulfills some criteria of sub-optimality. The validity of the suggested optimal control design is tested via simulation and then via experimental results by comparing a dynamic control law using the proposed optimal rotor flux trajectory with a conventional control utilizing the rated flux value.
Real time induction motor efficiency optimization
2017, Journal of the Franklin Institute
Citation Excerpt :
The optimization algorithm modulates the energy injected into the induction motor according to the driven load, which can significantly improve their yields. Mainly, there are two Loss Minimization Techniques (LMT) to address this problem viz. the model based LMT [2,12–14] and search algorithm based LMT [1,3,15–17]. The model based optimization strategy uses a mathematical steady-state induction motor model to achieve a minimum loss by controlling the magnitude of the flux reference in a vector control.
The induction machine efficiency optimization issue is the subject of many contributions in the literature. Few solutions, have shown interest in the rapidity-stability dilemma regarding the presence of sudden load torque variations. This paper presents a new useful hybrid approach for efficiency optimization of the direct vector-controlled induction motor drives. The efficiency improvement approach consists of adjusting the rotor flux with respect to the load torque in order to minimize total losses in the induction machine. The optimal rotor flux is defined in two steps. Firstly, the controller defines a suboptimal operating point by a fast analytical algorithm based on the model of induction machine. The suboptimal flux helps to minimize the size of possible solutions space of the optimization issue. The global optimal flux is achieved in the second step using a simulated annealing method. This latter adjusts the flux level in order to reduce the power input at its minimum. This choice overcomes the influence of parameters uncertainty on the controller stability. The proposed controller has been experimentally tested and validated on a 3 kW squirrel age induction motor.
Optimal vector control to a double-star induction motor
2017, Energy
The problem of energy optimization of a Double Star Induction Motor (DSIM) using the concept of a Rotor Field Oriented Control (RFOC) can be treated by an Optimal Control Strategy (OCS). 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 induction motor. From the Euler-Lagrange 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. The current study discusses a saturation model with respect to the rotor flux, which has significant influence in the motor's parameters. A comparative study of simulation results given from conventional and optimized RFOC proves the presented strategy's validity and effectiveness.
Vector Control of Asynchronous Motor of Drive Train Using Speed Controller H<inf>∞</inf>
2022, Emerging Science Journal
Modeling and analysis of energy losses under transient conditions in induction motors
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Analytical Solution of Optimized Energy Consumption of Induction Motor Operating in Transient Regime

Differential equations linear, non linear, ordinary partial

Design of an Adaptative Nonlinear Controller-Based Optimal Control Theory for a Voltage Source Induction Motor Drive System

Handbook of Mathematics for Engineers and Scientist

Chapman & Hall/CRC

Exact solutions For ordinary differential equations

CRC Press Inc

Improved Efficiency Optimization for Vector Controlled Induction Motor

Optimal control

Birkhauser Verlog

Optimal Torque Control for Current-feeded Induction Motors

IEEE Trans Autom Control

Nonlinear H2 and H∞ Optimal controllers for Current-Fed Induction Motors

IEEE Trans Autom Control

Optimal Control with engineering application

Nonlinear systems

Nonlinear Control of Induction Motor with Unknown Rotor Resistance and Load Adaptation

Verification of Enhanced Dynamic Torque per Ampere Capability in Saturated Induction Machines

IEEE Trans Ind Appl

Energy Consumption and Losses Calculation Approach for Different Classes of Induction Motor Drives