GREAH, University of Le Havre, 25 rue Philippe Lebon, BP 540, 76058 LE HAVRE ... Three phase induction machines are the most widely used type of ac ...
PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1550
Modeling and Diagnostic of Stator Faults in Induction Machines Using Permeance Network Method Y. Amara and G. Barakat GREAH, University of Le Havre, 25 rue Philippe Lebon, BP 540, 76058 LE HAVRE Cedex, France
Abstract— This paper presents an accurate and reasonably complicated model to simulate the faulty induction machines. The proposed model is based on a Permeance Network Method (PNM) coupled to the differential equation system governing the induction machine behavior in presence of stator faults. The proposed model allows taking into account the local magnetic saturation due to the relatively high fault current with moderate simulation time compared to the finite element method (FEM). Simulation results illustrating the impact of saturation in the case of some common stator faults such as stator inter-turn short circuits, shorted phase and open phase faults are presented and their comparison with those issued from coupled magnetic circuit based model proof the pertinence of the proposed approach. Experimental results validate the PNM approach in modeling saturated machines. The presented simulation results demonstrate the necessity to survey multiple quantities in order to distinguish between different fault signatures and in so doing to diagnose the type of a stator fault. 1. INTRODUTION
Three phase induction machines are the most widely used type of ac machines in industrial processes and they are frequently integrated in commercially equipment, featuring 80% of the motors in use. So, early faults detection and diagnosis reduces the machine shutdown time and repairing cost. Recent years, the research on the fault diagnosis and prognosis is in increasing. This research involves three domains, the fault modeling, fault extraction (detection) and classification (diagnosis) [1, 2]. Several recent studies have shown that stator winding faults are the second to bearing faults in incidences of occurrences in induction machines. Almost 30%–40% of all reported induction motor faults belong to this class of faults [3, 4]. They result from failure of turn-to turn insulation. So they start as undetected turn-to-turn faults that finally grow and culminate into major ones such as phase to phase or phase to ground faults that cause catastrophic failure of the machine [3–6]. Therefore, early detection of incipient fault detection has received much attention in recent years. The efforts on electrical machines fault diagnosis including, chemical analysis, mechanical and magnetic measurement and motor current signature analysis (MCSA) techniques have been squared [1–10]. The success of the technique depends not only on its ability to distinguish between healthy and faulty states but also on its ability to discriminate between various faults. Many diagnostic techniques for induction machines can be extended easily to other types of electrical machines [8– 11]. Machine modeling under fault conditions is a key to predicting its behavior. The analysis of stator faults can be made by different models. The availability of more powerful computers and the development of new machine models able to manage geometry together with electric and magnetic features, allow us to move on from the first models of faulty machines [4]. For the most faults, the harmonic contents of the stator current can be calculated satisfactory using linear models of the machine such as the Coupled Magnetic Circuit Method [CMCM] [12– 14]. In the case of the stator faults, the fault current reaches several times the rated value of the phase current in the healthy case and generates by the way an important local saturation around the fault zone. This phenomenon impacts strongly the harmonic contents of the stator current and imposes the use of a nonlinear model for the calculation of this fault signature in the phase currents [9, 13, 14]. The FEM is more and more used for this purpose, but the computing time is too long. Then the objective of this paper is to present an accurate and reasonably complicated model which is capable to predicting the performances of induction machines under stator faults. The proposed model is based on a permeance network approach for the magnetic circuit modeling coupled to the differential equation system governing the induction machine behavior for both the healthy case and the faulty case [14]. The proposed method allows the authors to take into account the local saturation in the magnetic circuit due to the strong short circuit currents as well as all the
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1551
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Figure 1: Flux tubes for a half part of an induction machine.
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Figure 2: Permeance network of an induction machine.
space harmonics of the doubly slotted machine with a simulation time relatively weak compared to the finite element method. 2. PNM MODELING OF INDUCTION MACHINE UNDER STATOR FAULTS 2.1. Case of Healthy Machine
An electrical machine can be represented as a set of flux tubes (Fig. 1) characterized by their magnetic permeances.These permeances are expressed as functions of the machine geometry and the instantaneous fluxes flowing in each one of them [13–18]. Exploiting the flux tubes of Fig. 1, one can deduce the magnetic equivalent circuit of the induction machine as shown in Fig. 2 where one can distinguish the stator magnetic circuit region, the air-gap region as well as the rotor magnetic circuit region. The stator slot currents are modeled by magneto-motive force (m.m.f.) sources in series with the tooth permeances. To establish the relation between these m.m.f and the phase currents we consider a closed contour around a slot as shown in Fig. 3 and we associate a magneto-motive force (Fsi ) to the slot i. Using the magnetic and electric laws the following equation are deduced [15, 18]: R ~ · d~l = nsi · Isi = P Fj H Pj j P Fj (1) Pj − Fsi + Fsi+1 = 0 j Fsi − Fsi+1 = nsi · Isi By generalizing the above equations for all the teeth we can obtain the following compact matrix form: [Fs ] = [Mis ] · [Is ] (2) where [Fs ] is the vector of tooth m.m.f., [Is ] is the vector of the phase currents [Mis ] is the matrix that relates the tooth m.m.f. to the phase currents and nsi is the number of the turns inside the slot carrying the current Isi . In the same manner, the rotor bar currents are modeled by m.m.f. sources in series with the rotor tooth permeances. The air-gap region is subdivided into a set of air-gap elements each one of them is modeled by a permeance in order to connect the stator tooth fluxes to the rotor tooth fluxes. The value of this permeance depends on the rotor position. By this manner, one can take into consideration the rotor motion.
PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1552
P yoke
P tooth I si F si
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P leakage Figure 3: Closed contour around a slot. Figure 4:
The different parameters in the air-gap permeances expression are expressed in terms of the stator and rotor slot dimensions and air-gap length and given in [15]. To take into account the magnetic circuit saturation, the B-H curve can be modeled by the Marrocco’s formula [19] or also numerically by the use of Spline functions fitting the measured B-H curve. The system of magnetic equations governing the machine is obtained by treating the permeance network of Fig. 2 in the same manner as an electric circuit. In this paper, node and branch equations are written considering stator phase and rotor loop currents as the entry of the system of equations. These equations are given by the following general form: · ¸ · ¸ · ¸ [Φt ] [Mi ] [
