Adjusted Electrical Equivalent Circuit Model of Induction Motor with Broken Rotor Bars and Eccentricity Faults А. Petrov, I. Plokhov
Department of Electrical Drives and Automation Systems Pskov State University Pskov, Russia
[email protected]
A. Rassõlkin, T. Vaimann, A. Kallaste
Department of Electrical Engineering and Automation Aalto University Espoo, Finland
Department of Electrical Power Engineering and Mechatronics Tallinn University of Technology Tallinn, Estonia
Abstract— Due to the importance of squirrel cage induction motors in the industry, the fault detection on that type of motors has become a highly developed area of interest for researchers. The electrical machine is designed for stable operation with minimum noise and vibrations under normal conditions. When the fault emerges, some additional distortions appear. The necessity to detect the fault in an early stage, to prevent further damage of the equipment due to fault propagation, is one of the most important features of any condition monitoring or diagnostic technique for electrical machines nowadays. In this paper, possible induction motor faults are classified and basic algorithm for rotor faults pre-determination is presented. Keywords— Electric machines, equivalent circuits, fault diagnosis, modelling, rotors
I.
A. Belahcen
INTRODUCTION
The induction motor (IM) is a simple, cheap, and efficient electrical machine. Full-load IM efficiency can reach beyond 90%, depending on machine rated power and design. Squirrel cage (SC) IM is more rugged and works more efficiently compared to the wound rotor (WR) IM. Hence, it is a popular choice in industrial drive applications. Fault diagnostic and detection on that type of motors become a highly developed area of interest for researchers for many years [1]–[5]. The reasons behind failures in rotating electrical machines have their origin in design, manufacturing tolerance, assembly, installation, working environment, nature of load and schedule of maintenance [6], [7]. Usually, the reason of failures is a combination of one or more of the abovementioned causes. The sources of electrical machine faults may be internal, external or environmental. Environmental faults in the electrical machine are identified as temperature, humidity and cleanliness faults. External mechanical faults are pulsating load, overload and poor mounting. External electrical faults are mainly caused by voltage phenomena, such as transient voltage, unbalanced voltage and voltage fluctuations. Internal mechanical faults mostly refer to bearing faults but also coil This work was supported by the Estonian Research Council grant PUTJD (PUTJD134) and European Regional Development Fund under Mobilitas Pluss programme returning researcher grant (MOBTP13).
and lamination movement, rotor strikes and eccentricity. Eccentricity of the machine air-gap is usually caused by bearing faults, which is the most common mechanical fault in rotating machines. Internal electrical faults refer to dielectric failure, magnetic circuit faults and broken or cracked rotor bars. There has been a number of separate surveys to identify the weakest component in IM [8]–[12]. The fault statistics according to IEEE IAS and EPRI is shown on Fig.1. EPRI
Rotor fault 9%
IEEE
Others 14% Bearing fault 41%
Stator fault 36%
Bearing fault
Others 22% Rotor fault 8%
Bearing fault 42%
Stator fault 28%
Stator fault
Rotor fault
Fig. 1. Induction machine fault statistics [11].
Others
IM, the same as other electric motors, is a device that converts electric energy into mechanical energy, which means the faults can occur on the both sides of machine - mechanical and electrical. As mentioned previously, the most common fault for IM is the bearing fault, which causes the majority of failures. Stator faults are mostly winding faults due to different short circuits (phase-to-phase, turn-to-turn, and winding-to-earth). Electric current, which is induced by the stator field, flows through the rotor bars. It is producing magnetic force that will create necessary torque in the machine. Rotor bars that might crack, break or separate from the end rings prevent current to flow, which in hand limits the motor performance. As a result, there is a thermal difference in the rotor, a lack of induced magnetic field, an unbalanced radial force and vibration
components [13]. The worst case of such fault is when the broken rotor bars are situated closely one after another [14], which is also most probable in practice as broken rotor bars are usually not detected at an early stage. Air-gap eccentricity fault is related to a condition of unequal air-gap that exists between the stator and rotor. Investigation of eccentricity fault has been presented by researches [15]–[19]. Air-gap eccentricity can be caused by different inaccuracies during the production of the machine, such as construction strength, manufacturing tolerances, bending of the shaft and bearings etc. [20]. Eccentricity can be found to some extent in all electrical machines and it has been thoroughly investigated. In fact, up to 10% of eccentricity is usually permissible for any electrical machine [13]. a)
STATOR
b) SHAFT
c)
STATOR
STATOR SHAFT
d) SHAFT
STATOR SHAFT
II.
Simulation of the SCIM with rotor fault is based on lumped parameter model. MATLAB/Simulink software is used for modelling the machine and faulty conditions of the rotor bars and eccentricity. EEC is based on [23], [24]. The parameters of the simulated machine are presented in Table I. TABLE I.
There are three types of eccentricities that can be present in electrical machines – static (Fig. 2. a), elliptic (Fig. 2. b) and dynamic eccentricity (Fig. 2. c and d). In the case of static eccentricity fault, the rotational axis of the rotor coincides with the rotor symmetry axis, but at the same time, it is displaced from the stator symmetry axis. In case of elliptic eccentricity, the rotor and stator symmetry points are matching, but as the rotor is shaped as an ellipse, there are still deviations in the uniformity of the air-gap. In case of dynamic eccentricity, the rotor symmetry point is shifted from the stator center, but the rotation of rotor is happening around the stator symmetry point. As the rotor center is not at the center of rotation, the position of minimum air-gap rotates with the rotor. Both, broken rotor bars and eccentricity faults, can be included at Electrical Equivalent Circuit (EEC) to simulate the performance of faulty induction machines. The paper is based on previous publication on the topic [21], with specified EEC and extended number of simulated faults.
MAIN PARAMETERS OF THE SIMULATED MACHINE
Parameter Number of poles Number of phases Connection Number of stator slots Number of rotor slots Terminal voltage Rated slip Rated power
Value 4 3 Star 48; non-skewed 40; non-skewed 400V@60 Hz; 333V@50 Hz 0.0667 22 kW@60 Hz; 18 kW@50 Hz
According to the T-shaped EEC of IM (Fig. 3) with stator resistance (r1=0.2167 Ω) and leakage reactance (xσ1= 0.5088 Ω), converted to stator side rotor resistance (r’2=0.3955 Ω, for rated mode r’2/s=4.465 Ω) and reactance (x’σ2=0.2664 Ω), magnetizing reactance (xµ=9.7389 Ω) appears in the vertical branch of the circuit. All values are presented considering the skin effect and core saturation, operation temperature for resistance recalculation is 130 ̊C. r’2 а) jxσ1 jx’σ2 r1 s I1 Iµ=I1 +I’2 I’2 U1
Fig. 2. Static (a), elliptic (b) and dynamic (c, d) rotor eccentricities.
SIMULATION OF THE MACHINE FAULTS
b)
I1 U1
jω1ψ1
r1
jω1ψ1
jxµ
Lσ1 dtd dψ1 dt
jω1ψ2
Lσ2 dtd j(ω1-ω2)ψ1 r2 d
Lµ dt
dψ2 dt
I’2 U2
Fig. 3. One phase T-shaped steady state (a) and transient (b) equivalent electrical circuits of induction motor.
For any ac machine, the rotor side of the T-shaped EEC is converted to the stator part by converting gain that determines by phase ratio, numbers of winding turns, and windings gains. The converting gain v12 is obtained as: v12 4m1
w1 k w1 2
, (1) Z2 where, m1 is the number of stator phases, w1 is the number of stator winding turns, kw1 is the stator winding gain and Z2 is the number of rotor bars in the cage.
By converting rotor resistance r2 to stator side, the equivalent rotor resistance r’2 is obtained as: 2 4m1 w1 k w1 r ' 2 r2 v12 r2 Z2 . (2) Number of rotor phases was taken into account for magnetic conductivity gain (λdc) for differential scattering calculation. This gain calculates the according rotor slots: t ds 2 12k , (3) with 1 p z 2 5 Z 2 1 p / Z2 2
1
, (4) where t2 is the distance between the centers of two neighboring rotor slots of the rotor core, measured along the surface, thereof facing the air-gap; δ is the air-gap; kβ is the gain that takes into account the reduction of MMF of the slot, caused by winding step shortening (kβ =1 if no shortening, kβ
