Published in IET Electric Power Applications Received on 11th August 2010 Revised on 12th February 2011 doi: 10.1049/iet-epa.2010.0192 ISSN 1751-8660 Edge optimisation for parameter identification of induction motors D.U. Campos-Delgado 1 E.R. Arce-Santana 1 D.R. Espinoza-Trejo 2 1 Facultad de Ciencias, UASLP, Avenue Salvador Nava s/n, Zona Universitaria, Mexico 2 Coordinacio ´ n Acade ´ mica Regio ´ n Altiplano, UASLP, Mexico E-mail: ducd@fciencias.uaslp.mx Abstract: In this work, a simple off-line identification algorithm for an induction motor (IM) is presented, which is based on an optimisation scheme without derivatives, called edge optimisation. The main idea of this identification scheme is to convert the problem of parameters characterisation to a finite-dimensional optimisation problem over a bounded set. The proposed approach relies on the information of a hard or soft startup of the motor, in order to identify all seven IM parameters: stator and rotor leakage inductances, stator and rotor resistances, mutual inductance, mechanical inertia and friction coefficient. Thus, the edge optimisation considers an iterative approximation in order to obtain a convergent sequence to the optimal parameters. This strategy is compared with an stochastic search algorithm and particle filter optimisation. Experimental results on a 1 and 3 HP IM test-rigs show an accurate characterisation with the proposed identification scheme, and validate the approach illustrated in this work. Nomenclature (i ds , i qs ) stator currents in dq-frame F friction coefficient J moment of inertia IM induction motor L lr rotor leakage inductance L ls stator leakage inductance L m magnetising inductance N number of discrete measurements used for identification n p number of pole pairs PWM pulse width modulation R r rotor resistance R s stator resistance T o observation window for identification (continuous time) T L load torque (u d , u q ) stator voltages in dq-frame VSD variable speed drive (l dr , l qr ) rotor fluxes in dq-frame v m mechanical velocity Q vector of unknown parameters u j jth component of parameter vector Q 1 Introduction In variable speed drives, an accurate representation of the motor dynamics is crucial for either speed regulation, torque estimation, or more recently proposed, fault diagnosis [1]. In this sense, the first step for control, estimation or diagnosis purposes is to run an identification scheme to quantify the motor parameters. In fact, the main challenge in the parameter identification problem is related to the dynamic model of the induction motor (IM), which is non-linear and over-parameterised. Moreover, there are some states that cannot be measured in practice. Owing to the importance of the identification stage, different identification schemes have been proposed in the literature trying to overcome these issues: off-line mechanical tests [2, 3], Kalman filters and observers [4, 5], algebraic methods [6], dynamic optimisation [7], least-squares approximations [8–10], stochastic search [11–13], neural networks [14, 15] and sinusoidal steady-state responses [16]. Overall, the approaches related to Kalman filters and observers look to extend the states in the non-linear IM model by the unknown parameters, where a random walk characteristic is assigned to them. In this way, if error convergence is guaranteed for the observer using the extended model, then a continuous update (on-line method) for the estimated parameters is achieved. However, owing to the over-parameterised property of the model, the performance depends largely on the initialisation procedure. Meanwhile, the approaches related to optimisation and soft- computing are based on recorded input – output data (off-line method). Hence, the parameters of the IM model are selected in order to maximise the likelihood (cost function) between the measurements data and the predicted outputs. Nonetheless, the optimisation problem is non-linear with multiple local minima. As a result, standard optimisation schemes could not give meaningful results, and more complex schemes are needed. For this reason, naturally inspired optimisation algorithms has been proposed to solve 668 IET Electr. Power Appl., 2011, Vol. 5, Iss. 8, pp. 668–675 & The Institution of Engineering and Technology 2011 doi: 10.1049/iet-epa.2010.0192 www.ietdl.org