516 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 32, NO. 2, JUNE 2017 Parameter Estimation for Deep-Bar Induction Machines Using Instantaneous Stator Measurements From a Direct Startup Joseph Benzaquen, Student Member, IEEE, Johnny Rengifo, Eduardo Alb´ anez, and Jos´ e M. Aller Abstract—A parameter estimation method for deep-bar induc- tion machines is presented. The parameters are estimated using two instantaneous voltage and current waveforms during a direct startup. The instantaneous input impedance is used as a stator in- dicator to solve a constrained nonlinear optimization problem that outputs the model’s parameters. For such purposes, a novel analyti- cal expression for the instantaneous input impedance is introduced. The method is validated in two distinct National Electrical Man- ufacturers Association (NEMA) design type induction machines (designs A and B), and the accuracy of the obtained parameters is determined by comparing the instantaneous input impedance magnitude and angle errors between the deep-bar and single-cage models with experimental data. The two tested motors showed an improvement when implementing the deep-bar model with the estimated parameters. The error decrease is more significant for the NEMA design B motor which corresponds to a deep-bar rotor construction. Finally, the single-cage and deep-bar models are sim- ulated and their outputs are compared to experimental waveforms. The deep-bar model with the estimated parameters outperforms the single-cage model, showing excellent agreement between the ex- perimental and simulated mechanical speed, stator currents, and electromagnetic torque. The results endorse the accuracy of the method and its applicability for transient studies. Index Terms—Deep-bar model, induction machine, parameter estimation, transient measurements. NOMENCLATURE i s , i r Stator and rotor current space-vectors. i r 1 Inner-cage rotor current space-vector. i r 2 Outer-cage rotor current space-vector. v s Stator voltage space-vector. λ s Stator flux linkage space-vector. L s , L r Stator and rotor self inductances. Manuscript received May 1, 2016; revised September 8, 2016 and December 5, 2016; accepted January 7, 2017. Date of publication January 24, 2017; date of current version May 18, 2017. This work was supported by the FONACIT- Venezuela Research Projects #2011000970 and #201400195. Paper no. TEC- 00380-2016. J. Benzaquen was with the Department of Energy Conversion and Delivery, Universidad Sim´ on Bol´ıvar, Caracas 89000, Venezuela. He is now with the Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506 USA (e-mail: jbenzaquen@ksu.edu). J. Rengifo and E. Alb´ anez are with the Department of Energy Conversion and Delivery, Universidad Sim´ on Bol´ıvar, Caracas 89000, Venezuela (e-mail: jwrengifo@usb.ve; ealbanez@usb.ve). J. M. Aller is with the Universidad Polit´ ecnica Salesiana, Cuenca 180107, Ecuador, and also with the Department of Energy Conversion and Delivery, Uni- versidad Sim´ on Bol´ıvar, Caracas 89000, Venezuela (e-mail: jaller@ups.edu.ec). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEC.2017.2657647 L r 1 Inner-cage rotor self inductance. L r 2 Outer-cage rotor self inductance. M Stator-rotor mutual inductance. L σs , L σr Stator and rotor leakage inductances. L σr 1 Inner-cage rotor leakage inductance. L σr 2 Outer-cage rotor leakage inductance. R s , R r Stator and rotor resistances. R r 1 Inner-cage rotor resistance. R r 2 Outer-cage rotor resistance. n p Number of pole pairs. T e , T m Electromagnetic and mechanical torques. ω m Mechanical angular speed. J Moment of inertia. k fr Friction coefficient. I. INTRODUCTION I NDUCTION machine dynamic modeling dates back to the first decades of the 20th century [1]. Since then, these models have become an essential part of: power systems transient anal- ysis, fault detection, protections settings, design and calibration of controllers, among others [2]–[4]. Each induction machine transient model is constituted by a specific set of electrical and mechanical parameters. The accuracy of these parameters is of vital importance for the correct simulation of the induction ma- chine in the aforementioned studies. In this sense, reliable and robust parameter estimation methods are required to fulfill this need. Parameter estimation methods for single-cage induction ma- chine models is a sounded topic in the literature. The simplest and most frequently used technique is described in the IEEE Std. 112 [5] using steady-state sinusoidal measurements from the no- load and locked-rotor tests performed at different frequencies. The remaining majority of the methods can be categorized as follows [6]: steady-state, variable frequency, and transient mea- surements. A comprehensive review of the main offline and online parameter estimation techniques for induction machines is presented in [7]. Specifically, transient measurement based methods can be classified into the following subcategories [6]: Kalman filter methods [4], [8], [9]; linear least-square methods [10]–[13]; nonlinear least-square methods [14]–[17]; instantaneous rms methods [3], [18]; and instantaneous input impedance/power nonlinear constrained optimization methods [19]–[21]. Most of 0885-8969 © 2017 IEEE. 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