1330 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 36, NO. 5, SEPTEMBER/OCTOBER 2000 Determination of and Reactances of Permanent-Magnet Synchronous Motors Without Measurements of the Rotor Position Hans-Peter Nee, Member, IEEE, Louis Lefevre, Member, IEEE, Peter Thelin, Student Member, IEEE, and Juliette Soulard, Member, IEEE Abstract—The interest in permanent-magnet synchronous mo- tors (PMSMs) is increasing in a wide area of applications. Since most PMSMs will operate without a shaft sensor in the future, valu- able information for experimental determination of machine pa- rameters will be lost. In this paper, therefore, a method is presented where the induced EMF and the -axis reactance are determined in a no-load test and the -axis reactance is determined in a load test. The load angle is determined from the load test by means of a new analytical method. In this way, no separate measurement of the load angle is required. The method is especially suitable for line-start PMSMs which normally operate with negative -axis current and, therefore, are not saturated in the -axis flux paths. Moreover, the method is very simple to carry out for any laboratory technician, since the only tests that have to be made are standard tests which are made on standard induction motors on a regular basis. Index Terms— model, permanent-magnet machine, power factor, synchronous reactances. I. INTRODUCTION T HE interest for permanent-magnet synchronous motors (PMSMs) is currently increasing in a wide area of appli- cations [1], [2] ranging from high-performance servo drives to line-start applications such as fans and pumps. There are mainly two reasons for this trend: first, the high efficiency and low rotor losses of the PMSM, and second, the falling prices of high-energy magnets. Most three-phase PMSMs in operation today are high-perfor- mance drives with shaft sensors. In the future, however, it is the opinion of the authors that most PMSMs will operate position sensorless. This will be achieved by employing sensorless con- trol algorithms [3] for variable-speed drives and, in the case of line-start applications [4], there is naturally no need for shaft sensors due to the synchronous operation with the mains. As the shaft sensor is removed, valuable information for ex- perimental determination of machine parameters is lost. It will be Paper IPCSD 00–004, presented at the 1999 Industry Applications Society Annual Meeting, Phoenix, AZ, October 3–7, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. Manuscript submitted for review June 15, 1999 and released for publication April 4, 2000. The authors are with Electrical Machines and Power Electronics, Depart- ment of Electric Power Engineering, KTH, Royal Institute of Technology, SE-10044 Stockholm, Sweden (e-mail: hansi@ekc.kth.se; louis@ekc.kth.se; peterthe@ekc.kth.se; juliette@ekc.kth.se). Publisher Item Identifier S 0093-9994(00)07627-1. shown below that the expressions for the - and -axes reactances obtained from load tests are functions of the load angle , which can only be determined by means of some type of shaft sensor or another synchronous machine coupled to the shaft of the ma- chine under investigation. In this paper, therefore, a method is presented where the induced EMF and the -axis reactance are determined in a no-load test and the -axis reactance is deter- mined in a load test. It is the opinion of the authors that this simple test procedure, which requires no additional knowledge or equip- ment compared to standard induction motor tests, is easy to use for laboratory technicians who are used to induction motors. This makes the method especially interesting although it cannot guar- antee high accuracy for highly saturated machines. In Section II, an overview of methods to determine reactances experimentally is given. In Section III, the phasor diagram of the PMSM is presented and some basic relations are derived. In Section IV, it is shown how the load angle can be determined. In Section V, the test procedure is described and, finally, in Sec- tion VI, some conclusions are made. II. EXPERIMENTS TO DETERMINE REACTANCES The test procedure described in Section V is basically a com- bination of a no-load test and a load test. These tests as such are not new, but the interpretation is new. In the literature, sev- eral other methods are described for the determination of the - and -axes reactances without the need for information of the rotor position in relation to the imposed quantities. One impor- tant distinction must, however, be made concerning the applica- bility of the methods. Reactances of, for instance, machines with surface-mounted magnets, i.e., without a damper winding char- acteristic, can easily be determined by means of various methods. A locked-rotor test with either a single-phase alternating voltage or a voltage step applied to the stator winding can be repeated for different rotor positions. A simple analysis of the results will then give comparably accurate results. It should also be noted that the choice of frequency, for the alternating voltage case, is not critical (50 or 60 Hz is good) and, in the voltage-step case, the magnitude of the voltage is not critical since only the initial slope is inter- esting. Methods to take saturation effects into account for these tests have also been presented; see, for instance, [5]. Machines with a damper winding characteristic, for instance, line-start permanent magnet synchronous motors (LSPMs), 0093–9994/00$10.00 © 2000 IEEE