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Experimental Identification of the Magnetic Model of Synchronous Politecnico di Torino Porto Institutional Repository [Article] Experimental Identification of the Magnetic Model of Synchronous Machines Original Citation: Armando, Eric; Bojoi, Iustin Radu; Guglielmi, Paolo; Pellegrino, Gian-Mario Luigi; Pastorelli, Michele (2013). Experimental Identification of the Magnetic Model of Synchronous Machines. In: IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, vol. 49 n. 5, pp. 2116-2125. - ISSN 0093-9994 Availability: This version is available at : http://porto.polito.it/2507496/ since: May 2013 Publisher: IEEE Published version: DOI:10.1109/TIA.2013.2258876 Terms of use: This article is made available under terms and conditions applicable to Open Access Policy Article ("Public - All rights reserved") , as described at http://porto.polito.it/terms_and_conditions. html Porto, the institutional repository of the Politecnico di Torino, is provided by the University Library and the IT-Services. The aim is to enable open access to all the world. Please share with us how this access benefits you. Your story matters. (Article begins on next page) 1 Experimental Identification of the Magnetic Model of Synchronous Machines E. Armando, R. Bojoi, P. Guglielmi, G. Pellegrino and M. Pastorelli Dipartimento Energia - Politecnico di Torino Corso Duca degli Abruzzi, 24 - Torino, 10129 ITALY Abstract—The paper proposes and formalizes a comprehensive 1) the motor performance (torque, power versus speed experimental approach for the identification of the magnetic profile with limited voltage and current) can be off-line model of synchronous electrical machines of all kinds. The calculated with precision. identification procedure is based on controlling the current of the machine under test while this is driven at constant 2) In particular, the determination of the Maximum Torque speed by another, regenerative electric drive. Compensation of per Ampere (MTPA) and the Maximum Torque per Volt stator resistance and inverter voltage drops, iron loss, operating (MTPV) control trajectories is mandatory for the full temperature issues are all taken into account. A road map for exploitation of the motor torque and speed ranges. implementation is given, on different types of hardware setups. 3) The performance comparison of motors provided by dif- Experimental results are presented, referring to two test motors of small size, and references of larger motors identified with the ferent manufacturers is made possible, without the need same technique are given from the literature. of insights about design, materials and manufacturing. The latter point can be important for choosing between different motor suppliers. It results that the magnetic model I. INTRODUCTION is crucial for a proper machine evaluation and also for an optimal control strategy, including sensorless operation [10], Over the last years, the research work regarding the elec- [11]. trical synchronous machines and their control has focused on The literature reports several methods for magnetic model the machine design optimization and also on optimal control identification, divided into analytical/simulation methods and techniques able to fully exploit the machines characteristics. methods based on experimental measurements. The first meth- That was induced and supported by a continuous penetration ods are usually based on Finite Element Analysis (FEA) of synchronous machines in many industrial applications, as [6] and/or analytical computations [7] based on equivalent well as in traction and automotive applications, home appli- magnetic circuits. These methods can be used only by the ances and power generation for renewable systems. The most machine designers since they need all information regarding employed synchronous machine solutions include Surface the motor design. The experimental methods are useful when Mounted Permanent Magnet (SPM) machines, Synchronous only machine rated data are available. Reluctance (SyR) machines and Interior Permanent Magnet The experimental methods can be divided into standstill (IPM) machines. All mentioned machines need accurate mod- methods and constant-speed methods. The standstill methods eling of their magnetic model, both for design and control are well known for wound-field synchronous machines [12], purposes. [13], without taking into account the saturation and cross- The magnetic model is the relationship between the machine saturation. A locked rotor method that takes into account all currents and the machine flux linkages in a specific reference saturation effects is presented in [1], where voltage pulses frame. As known from the literature, the most convenient are applied to one axis (e.g. d), while a constant current reference frame that should be used for the magnetic model is controlled along the other axis (e.g. q). This method is identification is the rotor synchronous (d; q) frame [1]–[9]. very effective, but requires integration of the applied voltage, Even with the proper axes choice, the magnetic model repre- that is critical and prone to drift due to offsets. Moreover, sentation and experimental identification are non trivial efforts, the voltage level to be handled by the inverter during the especially for those machines exhibiting significant magnetic tests is very low and then potentially imprecise, in particular saturation and cross-saturation. As a general assumption, the for motors with a low per-unit resistance. Stator resistance (d; q) machine flux linkages are a non linear function of both variations are compensated, but no clue is given about the d− and q−axis current components. PMs temperature and what the effect of core loss on the The synchronous machines that are renowned for being magnetic curves is. In [2], the flux-linkages are evaluated at highly non-linear due to saturation and cross-saturation are the constant speed via the measurement of the d− and q−axis IPM and the SyR ones [1]–[7]. However, the same problem voltages when a couple of constant (d; q) current components has been reported for saturated (i.e. compact and overloaded) is impressed to the machine. The voltage is measured at the SPM machines [8], [9]. machine terminals and then low-pass filtered for pulse-width The benefits of the experimental identification of the mag- modulation (PWM) harmonics elimination. A compensation of netic model of such machines are: the filter attenuation and phase is necessary, as well as a FFT 2 scheme for fundamental components extraction. The solution b and c, for including transient working points either in flux- presented in [2] does not take into account the stator resistance controlled drives or drives adopting a flux-observer [14], [15]. variation during the test. This may be a problem when the magnetic model is evaluated in overload current conditions. The stator resistance variation can be mitigated by increasing the test speed, but this may increase the iron losses, that are not taken into account, either. This paper proposes a comprehensive experimental ap- proach for the identification of the magnetic model of any syn- chronous electrical machine. The machine is running at steady- (a) SyR (b) IPM, SPM (c) PMASR state speed and current, and the flux linkages are obtained Fig. 1. dq current mesh. from the evaluation of the (d; q) voltage components, as in [2]. The stator resistance variation is compensated here, allowing For the sake of flux linkage identification, the steady-state the magnetic model identification for any current level. Three voltage equation of the synchronous machine is considered voltage estimation methods are compared, showing that easier- (3), e.g. with reference one of the points of the identification to-implement rigs can give reasonable accuracy, without the grid (i ; i 0 ): need for analog measurement of the PWM voltages. Voltage d;k q;k harmonics due to spatial harmonics and inverter dead-time vd;kk0 = Rs · id;k − !e · λq;kk0 (3) effects are averaged during the signal acquisition without vq;kk0 = Rs · iq;k0 + !e · λd;kk0 complicate post-processing, such as FFT. Iron loss are taken where !e the electrical speed and Rs is the stator resistance. into account, and it is suggested how to avoid them to interfere From (3), the flux linkages can be evaluated as: with the identification process. The operating temperature ( vq;kk0 −Rs·iq;k0 is monitored, since temperature variations would distort the λd;kk0 = !e magnetic curves of PM-based machines. vd;kk0 −Rs·id;k (4) λq;kk0 = − The identification methodologies have been applied to two !e motors of small size: one SyR machine one IPM machine of For reproducing the steady state conditions properly, the the PM-assisted SyR (PMASR) type. experimental setup is organized as follows: • the machine under test is driven at constant speed by a II. MEASUREMENT PROCEDURE speed controlled servo motor (constant !e) and the speed The goal of the identification procedure is to evaluate is measured; the steady-state machine flux linkages, in dq coordinates, • the machine under test is vector current controlled at synchronous to the rotor, as a function of the corresponding (id;k; iq;k0 ); current components (1): • the PWM voltages are measured or accurately estimated; • the stator resistance voltage drop must be compensated; λ = f (i ; i ) d d q • 0 (1) in case of PM machines, all tests must be at the same λq = f (id; iq) operating temperature; The area of evaluation of the model is a rectangle, in the dq • the effect of iron loss must be negligible. current plane, delimited within the ranges id;min to id;max and In the following, all those aspect are analyzed in detail. iq;min to iq;max, that must include all the operating conditions of interest for the drive under test, i.e. continuous and transient A. Current control sequence for series voltage drop compen- overload points. The risk of demagnetization must be also sation taken into account for machines with PMs. The current area is organized in a regularly spaced grid, defined by the equally As said, the (id; iq) region under analysis includes transient spaced arrays of current values (2): overload conditions. In other words, all tested points at over- load current may produce rapid variations of the operating stator and magnets temperature even in short times.
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