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Estimation of induction motor parameters using shuffled frog-leaping algorithm

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Abstract

This paper introduces a shuffled frog-leaping algorithm based method to approximate the equivalent circuit parameters of induction machines from the manufacturer data, such as nameplate data and motor performance characteristics. The steady-state equivalent circuit is applied for the simulations. The circuit parameters are found as the result for the error minimization function between the estimated and maker data. The suggested algorithm solves the parameter estimation problem and surpasses the solutions reached by differential evolution, particle swarm optimization and genetic algorithms. Therefore, this algorithm can be employed in motor energy management system for bettering the overall energy savings in industry.

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Abbreviations

\(c_{1}\) and \(c_{2}\) :

Positive constant numbers

DE :

Differential evolution

\(D_\mathrm{max}\) :

Maximum allowed change in a frog’s position

\(D_\mathrm{min}\) :

Minimum allowed change in a frog’s position

\(\mathbf{d}_k^{t}\) :

Change vector of the \(k\) memeplex in iteration \(t\)

\(f\) :

Frequency

\(F\) :

Objective function

\(g\) :

Number of generation for each memeplex before shuffling

GAs :

Genetic algorithms

\(I_{1}\) :

Stator current per phase

\(I_{2}\) :

Rotor current per phase

\(I_{fl}\) :

Full load current

\(I_\mathrm{st}\) :

Starting current

\(m\) :

Number of memeplexes

MSFLA :

Modified shuffled frog-leaping algorithm

\(n\) :

Number of frogs in every memeplex

\(N\) :

Number of variables, which is considered as a frog

\(p\) :

Number of pairs of poles

\(P\) :

Population of frogs

\(P_{e}\) :

Active electric power

\(P_{n}\) :

Motor nominal power

\(pf_\mathrm{fl}\) :

Full load power factor

PSO :

Particle swarm optimization

\(Q_{e}\) :

Reactive electric power

\(R_{1}\) :

Stator resistance

\(R_{2}\) :

Rotor resistance referred to stator side

\(R_\mathrm{th}\) :

Thevenin’s equivalent resistance

\(\text{ rand}, \text{ rand}_{1}\) :

Random number between 0 and 1

\(\text{ rand}_{2},\text{ rand}_{3}\) :

Random numbers between 0 and 1

\(\bar{{S}}\) :

Complex power

SFLA :

Shuffled frog-leaping algorithm

\(s_\mathrm{fl}\) :

Full load slip

\(s_\mathrm{m}\) :

Slip at which the maximum torque is obtained

\(T\) :

Torque

\(T_\mathrm{fl}\) :

Full load torque

\(T_\mathrm{max}\) :

Maximum torque

\(T_\mathrm{st}\) :

Starting torque

\(t\) :

Time or iteration

\(t_\mathrm{max}\) :

Number of shuffling iterations

\(V\) :

Nominal voltage

\(V_\mathrm{ph}\) :

Stator voltage per phase

\(V_\mathrm{th}\) :

Thevenin’s equivalent voltage

\(X_{1}\) :

Stator leakage reactance

\(X_{2}\) :

Rotor reactance referred to stator side.

\(X_{m}\) :

Magnetizing reactance

\(X_\mathrm{th}\) :

Thevenin’s equivalent reactance

\(\mathbf{x}_{i}\) :

Position of the particle or frog \(i\)

\(\mathbf{x}_{\mathrm{best},k}^t \) :

Frog with the best fitness of the memeplex \(k\) in iteration \(t\)

\(\mathbf{x}_{\mathrm{worst},k}^t \) :

Frog with the worst fitness of the memeplex \(k \)in iteration \(t\)

\(\mathbf{x}_\mathrm{gbest}^t \) :

Frog with the global best fitness in iteration \(t\)

\(Z_\mathrm{th}\) :

Thevenin’s equivalent impedance

\(\eta _{fl}\) :

Full load efficiency

\(\omega _{s}\) :

Motor angular velocity

cal:

Calculated value

mf:

Manufacturer value

fl:

Full load value

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Authors and Affiliations

  1. Department of Electrical Engineering, EPS Jaén, University of Jaén, 23071 , Jaén, Spain

    I. Perez

  2. Department of Electrical Engineering, EPS Linares, University of Jaen, 23700 , Jaén, Spain

    M. Gomez-Gonzalez & F. Jurado

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  1. I. Perez
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  3. F. Jurado
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Correspondence to F. Jurado.

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Perez, I., Gomez-Gonzalez, M. & Jurado, F. Estimation of induction motor parameters using shuffled frog-leaping algorithm. Electr Eng 95, 267–275 (2013). https://doi.org/10.1007/s00202-012-0261-7

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