ISEF 2007 - XIII International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering Prague, Czech Republic, September 13-15, 2007
Simulation and Fault Detection of Short Circuit Winding in a Permanent Magnet Synchronous Machines (PMSM) J. Rosero1
O. Almonacid2
M. Amaya2
L. Romeral1
1. Motor Control and Industrial Applications, Technical University of Catalonia., Calle Colon, 1 TR 2225, 08222 Terrassa, Barcelona - España.
[email protected] 2. Research Group in Energy Conversion, Universidad del Valle, Calle 13 N° 100-00, Colombia, ,
[email protected],
[email protected]
Abstract The permanent magnet synchronous motor – PMSM, are a key piece in development of high precision process. In searching of improving the control systems and diagnose, techniques of analysis like the Finite Element Analysis (FEA) are used, coupled with the control models which could establish the behavior of the Driver – Motor set. This paper presents a two-dimensional (2-D) finite-element analysis (FEA) of the permanent magnet synchronous machine with stator short circuit turns. Relationships between stator-current-induced harmonics and short circuit winding were investigated. The simulation is also compared with experimental results. Shorted Turns Winding Model The state space model describing the motor drive system is as follows [1]:
V = RI +
∂L ∂ψ ∂ψ ∂I ± ωr = RI + L ± ω r I ∂θ (1) ∂t ∂θ ∂t
Where: I are three-phases stator currents and state variables of PMSM, V are three-phases stator terminal voltages, Ψ is linkage flux, L represents self and mutual inductances, R are three-phases phases resistances, θ is the rotor position, and ωr is the rotor speed. Modeling shorted turn faults requires the introduction of an additional differential equation defining the shorted turns. The equation for the shorted turns, coupled to all the other circuits in the machine is:
0 = Rsh I sh +
∂ψ sh ∂ψ sh + ωm ∂t ∂θ
(1)
Where ish , λsh and Rsh are fault current, total flux linking and resistance of the shorted turns. In addition, the equation used t o solve for the rotor speed, ωr, is given as [2]:
∂ω r 1 = (Te − Bω r − TL ) J ∂t
∂θ = ωr ∂t
(3) Where J is the inertia of the rotor, Te is the developed electromechanical torque, B is the coefficient of viscous friction, and TL is the load torque. The short circuit between turns is the most critical fault in the machine, and is quite difficult to detect and almost impossible to remove. These faults are usually short circuits between a phase winding and the ground or between two phases. It is strongly believed that such faults initiate as undetected turn-to-turn faults that develop to a major short circuit. There are a number of techniques to detect turn-to-turn faults, the majority of them based on stator voltages and currents and axial flux analysis. However, the models they used did not include either saturation or controller interactions. The FEA is proposed for the simulation of electrical machines. Because, the coupling between the non-linear magnetic and electric circuits should be accounted for in the analysis when predicting the performance characteristics of a system, especially when the system is under fault conditions.
The numerical simulation was developed with the combination of a finite-element software, Flux2D [3], and of an electronic circuit and control simulation, Matlab - Simulink. The coupling between the circuit, control and the finite-element model in Flux 2D is coupling (see ¡Error! No se encuentra el origen de la referencia..), automatically linking local variations in flux with the circuit voltage [3].
Fig. 1. Scheme of coupled model with short circuit.
Results Some simulation and experiments have been carried out for different motors with short turns. The experiment starts driving the motor to the nominal operation, and then closing the external switch to provoke a short circuiting. The simulations for 4, 8 and 12 turns in short circuit and different operation speeds: 300 and 3000 rpm, are compared with the load test to healthy motor. The results are show in Fig. 2. . 0
0 M M M M
Amplitude (dB)
-20
Healthy 4 Short turns on phase A 8 Short turns on phase A 12 Short turns on phase A
M M M M
w=300 rpm Amplitude (dB)
w=3000 rpm -10
-30 -40
-20
Healthy 4 Short turns on phase A 8 Short turns on phase A 12 Short turns on phase A
-40
-60
-50 -60 0
2
4
6
8
10 12 Harmonics
14
16
18
20
22
-80 0
2
4
6
8
10 12 Harmonics
14
16
18
20
22
a) b) Fig. 2. Results to Short Circuit Turn. a). To 3000 rpm b). To 300 rpm Short circuit fault detection in a PMSM stator winding has been presented in this paper. Experimental and simulated results support the claims made in the paper and they prove that these synchronous harmonics are more adequate to detect short circuit failures, especially those of the lower order. It is concluded that signal processing of stator harmonics can give accurate information about the faulty or healthy state of the machine, and thus it can be used for fault diagnosis and fault tolerance PMSM electrical drives. References [1] [2] [3]
J. F. Gieras and M. Wing, Permanent magnet motor technology : design and applications, 2nd ed. New York: Marcel Dekker, 2002. P. Pillay and R. Krishnan, "Modeling, simulation, and analysis of permanent-magnet motor drives. I. The permanent-magnet synchronous motor drive," Industry Applications, IEEE Transactions on, vol. 25, p. 265, 1989. CEDRAT, CAD package for electromagnetic and thermal analysis using finite elements, User´s guide. Flux 2D. France, 2005, www.cedrat.com
