On-line Load Test for Induction Machine Stator Inter-turn Fault Detection under Stator Electrical Asymmetries

Transcription

1 On-line Load Test for Induction Machine Stator Inter-turn Fault Detection under Stator Electrical Asymmetries Dhaval C. Patel and Mukul C. Chandorkar Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai 476, INDIA. Abstract The stator inter-turn faults and stator electrical asymmetries such as stator resistance and inductance unbalance generate similar negative sequence current signatures in the induction machine. Hence the stator inter-turn fault is one of the most difficult faults to discriminate and detect in an induction machine. Discrimination of the stator inter-turn fault from stator electrical asymmetry essentially helps to arrange maintenance in a proper schedule. In this paper, a simple on-line load test is proposed to detect the presence of stator inter-turn fault under stator electric asymmetrical condition of the machine. The proposed test is based on the observation of steady-state stator current locus with change in load. The test procedure does not require additional sensors, training and database, past history of the machine and speed measurement. It is also applicable to any unknown machine. This paper presents analytical studies and experiments on a faulted and electrically asymmetrical motors to confirm the simplicity and effectiveness of the proposed load test. I. INTRODUCTION Stator inter-turn faults constitute a large percentage of all the electrical faults in the induction machine [], []. In a stator inter-turn fault, a short circuit of stator winding turns results in a large current through the shorted turns. Ultimately, the large current results in an irreversible damage to the stator winding and core [] [4]. Hence, detection of stator inter-turn fault at its incipient stage saves the machine from its catastrophic failure. Many techniques have been proposed to detect the stator inter-turn faults over the last three decades. Techniques based on the time domain analysis of induction motor currents and voltages basically analyze their sequence components [5]. However, unbalanced supply voltage and machine inherent asymmetries can affect the accuracy of these techniques. Some techniques use the sequence component impedance as a signature of the stator inter-turn faults [6]. These techniques avoid the errors due to unbalanced voltage and machine electrical asymmetries but require the data of induction machine before the occurrence of the fault. The techniques proposed in [7] [9] use the negative as well as the positive sequence components to detect the stator inter-turn faults. The current vector pattern of the induction motor is used to detect the stator inter-turn fault in [7], [8]. These techniques are also affected by the supply unbalance and machine electrical asymmetries. i as i bs i cs B (a) N A N f i f R f C i as i bs i cs R b B R a N s (b) N A Fig.. Different stator asymmetrical conditions (a) Stator inter-turn fault (b) Stator resistance unbalance Several efforts have been made to overcome the effects of supply unbalance, machine inherent asymmetries and load variation [9] [3]. Artificial intelligence (AI) and neural network (NN) based techniques are proposed in [], []. These automatic detection techniques require a training period. Hence they cannot be used easily if the machine is replaced. Stator fault detection based on pendulous oscillation phenomena is proposed in []. This technique discriminates the stator fault from supply unbalance and machine electrical asymmetries but requires precise observation of the fault signature. A discrimination technique of stator inter-turn fault from stator unbalanced resistance proposed in [3], is based on the observation of the phase differences between voltages and currents. The schematics of stator inter-turn fault and stator electrical asymmetry in the form of unbalanced stator resistance are shown in Fig. (a) and (b) respectively. The resistances R a, R b and R c shown in Fig. (b) represent the amount by which the actual stator winding resistances differ from the nominal value. The growth of inter-turn fault to catastrophic failure in the machine is much faster than that due to other stator electrical asymmetries [9]. Hence a technique to discriminate a stator inter-turn fault from other stator electrical asymmetries is crucial for mitigation and maintenance. In this paper, an on-line load test is proposed, which can discriminate stator inter-turn faults from stator electrical asymmetries. The test is based on the observation of the R c C //$6. IEEE 933

2 steady-state stator current locus as the load on the induction motor is changed. In this paper, a mapping of the stator current locus on the X-Y plane to a point on the polar plot is defined. The movement of this point with change in load indicates the presence of a stator inter-turn fault even in the presence of stator electrical asymmetries. The load test is proposed based on the detailed steady-state analysis of stator inter-turn faulted machines and machines with stator electrical asymmetries, which is validated by experiments on a faulted and also otherwise stator electrically asymmetrical induction motor. This test is simple to implement, does not require speed measurements, does not require past data of the machine and is free from training and database requirements. This test can also be used in conjunction with other techniques to make the diagnosis more effective. II. STEADY-STATE ANALYSIS OF INDUCTION MOTOR WITH DIFFERENT STATOR ASYMMETRIES In this section, a detailed analysis of two different stator asymmetrical conditions viz. stator inter-turn fault and stator circuit unbalance is presented. The simplified models of the stator inter-turn fault are derived in [4] [5]. The models of the induction machine with stator circuit unbalance are reported in [6] [8]. The analysis presented here is based on these models. A. Steady-state Equations ) Stator Inter-turn Fault: The three-phase star connected stator circuit of a stator inter-turn faulted induction motor is shown in Fig. (a). In this figure, a short-circuit of a few turns on the balanced three-phase stator winding shows the inter-turn fault. A short-circuit in the stator effectively introduces an extra winding in the motor s winding structure. For simplification of analysis, the fault is assumed to be present only in Phase-A. The fault path is resistive, and the value of the resistance is denoted by R f. The steadystate sequence component phasor equations of stator inter-turn faulted motor [5] are listed as follows: V sp =( + jx s) I sp+jx m Irp ( β 3 Rs + j (X ) qsf jx dsf ) I f () V sn =( + jx s) I sn+jx m Irn ( β 3 Rs + j (X ) qsf + jx dsf ) I f () =jx m Isp + S + jxr =jx m Isn + S + jxr I rp j (X qrf jx drf ) I f (3) I rn j (X qrf + jx drf ) I f (4) (R f + β + jx ff ) I f = ( β + j 3 (X qsf + jx dsf ) ) Isp +j 3 (X qrf + jx drf ) I rp + ( β + j 3 (X qsf jx dsf ) ) Isn +j 3 (X qrf jx drf ) I rn (5) These equations follow the complex notation, where j =. Here, V and I are voltage and current phasors respectively. Suffixes p and n denote positive and negative sequence phasor components. Suffixes s, r and f denote quantities pertaining to the stator, the rotor and the fault circuit respectively. The resistance, R r and R f correspond to the stator, the rotor and the faulted windings respectively. Here, β is the ratio of the number of faulted turns (N f ) to the total number of turns of the phase winding (. In ( equations () (5), X s = ω s Lls + 3 L ms), Xr = ω s Llr + 3 L ms) and 3 Xm = ω s L ms, where L ls and L lr are the leakage inductances of the stator and the rotor respectively, L ms is the magnetizing inductance of the machine, and ω s is the supply frequency. These inductances correspond to the balanced part of the machine windings, as given in [6]. In (3) and (4), S indicates the slip of the rotor, which is given by S = ω ωr ω, where ω r is the rotor angular speed. The impedances denoted by X ff, X qsf, X dsf, X qrf and X drf correspond to the fault loop circuit. The values of these impedances depend on the amount and the location of the fault. Winding functions are used to incorporate the positional effect of the fault in these impedances [5]. ) Stator Circuit Electrical Asymmetries: In a practical induction machine, the stator circuit electrical asymmetries are random in nature and hence difficult to model. They are generally present in the form of unbalanced resistance and inductance in the three-phase stator circuit. The stator circuit asymmetry is assumed to be present in the form of unbalanced stator resistance, the stator inductance being balanced. The extent of unbalance in stator resistance is modeled by including R a, R b and R c in the stator circuit in addition to the nominal balanced stator resistance,as shown in Fig. (b). Hence the resistance of Phase-A is + R a, resistance of Phase-B is +R b and resistance of Phase-C is + R c. The steady-state equations of the induction motor with unbalanced stator resistance are listed as follows: V sp = ( + R qs + jx s ) I sp + R ds Isn + jx m Irp (6) V sn = R ds I sn +( + R qs + jx s ) I sn + jx m Irn (7) = jx m Isp + S + jx r I rp (8) = jx m Isn + S + jx r I rn (9) Here, R qs and R ds are the resistances associated with the unbalanced part, and are given by, R qs = 3 (R a + R b + R c ), R ds = ( R a 3 R b ) R c j 3 (R b R c ), Rds = ( R a 3 R b ) R c + j 3 (R b R c ) 934

3 θ n = θ n θ f I sn θ p I sn I sp θ p Isp θ f I f If V sp a 3Φ b Supply c R ext R ext R ext Induction Motor DC Generator I sn θ n I sn θ n (a) V sp Data Aquisitation & Processing a Taps R f + θ p θ p b c Stator Winding I sp Isp Fig. 3. Experimental setup (b) Fig.. Phasor diagrams for different stator asymmetrical conditions (a) Stator inter-turn fault and (b) Stator resistance unbalance B. Phasor Diagrams with Balanced Supply Voltage In this subsection, the steady-state current phasor diagrams are used to analyze and differentiate between the behavior of induction motor under the stator inter-turn fault and stator resistance unbalance conditions. Parameters of the induction machine used for the analysis are given in Table I. The stator current phasor diagrams, shown in Fig. (a) and (b) correspond to a machine with stator inter-turn fault and a machine with stator resistance unbalance respectively. The supply voltage is assumed to be balance and hence the negative sequence voltage is zero. The voltage vectors are scaled down to fit in the diagrams. In these diagrams, positive sequence ( I sp ), negative sequence ( I sn ) and fault current ( I f ) phasors are drawn with the positive sequence voltage phasor ( V sp )as a reference. Suffixes and are used for two different values of the rotor slip. ) Stator Inter-turn Fault: The phasor diagram of Fig. (a) is drawn using the steady-state equations () (5). The fault path resistance and number of faulted turns are set such that the fault current remains higher than the rated currents of the machine in no-load condition. Curved arrows show the movement of phasors with the increment in slip. From this phasor diagram the following observations can be made ) The phase angle deviation for the positive sequence stator current phasor (θ p θ p ) is much larger than that for the negative sequence stator current phasor (θ n θ n ) with the given increment in slip. ) The magnitude of the positive sequence phasor ( I sp )increases, whereas the magnitude of the negative sequence phasor ( I sn ) remains almost unchanged with the given increment in slip. 3) The phase angle of the fault current phasor (θ f ) changes with the increment in the rotor slip, whereas the magnitude ( I f ) remains unchanged. ) Stator Electrical Asymmetries: Fig. (b) shows the phasor diagram for the induction motor with stator resistance unbalance and is drawn using the steady-state equations (6) (9). Here, R a, R b and R c, as shown in Fig. (b), are taken 3Ω, Ωand Ωrespectively to produce stator resistance unbalance. The following observations are made from this phasor diagram. ) The phase angle deviation for the positive (θ p θ p ) and the negative sequence (θ n θ n ) stator current phasors are of the same amount with a given increment in slip. ) The magnitude for the positive ( I sp ) and the negative ( I sn ) sequence stator current phasors change approximately of the same proportion with a given increment in slip. 3) The angular movement of the positive and the negative sequence phasors are in the same direction. Remark : For the stator inter-turn faulted motor, the phase angle between the positive and the negative sequence current phasors varies with the change in slip, whereas it remains unchanged for the induction motor with stator resistance unbalance. III. EXPERIMENTATION A. Experimental Setup To validate the analysis given in the previous section, experimental studies were done on a 45 V, 3.8 kw, 4 pole squirrel cage induction motor. The schematic of the experimental setup is shown in Fig. 3. The parameters of the induction motor are obtained by the laboratory tests and are given in Table I. The induction motor used for experiments has a 4 pole, 36 coils, 36 slots and double layer winding arrangement short-pitched by one slot with total 64 turns in each phase. The load can be changed by loading the dc generator coupled to the induction motor. The currents and voltages are sensed using the sensing circuit and processed further using signal conditioning circuits, analog to digital converters and 3-bit floating point digital signal processor TMS3VC33. The induction motor stator winding has several taps on each phase to create inter-turn faults of different amounts 935

4 TABLE I INDUCTION MOTOR PARAMETERS Line voltage 45 V Rated power 3.8 kw Stator winding resistance 4.9 Ω Rotor winding resistance (referred to stator) R r 8. Ω Stator leakage inductance L ls 3.5 mh Rotor leakage inductance (referred to stator) L lr 3.5 mh Magnetizing inductance L ms mh Number of stator poles P 4 Rotor inertia J.3 Nm Rated speed at 5 Hz 5.8 rad/s No-load current.87 A and at different locations. These taps are also illustrated in Fig. 3. The taps are provided such that, 8, 6 or 4% of the stator turns can be shorted to create the fault at any phase. The severity of the fault can be changed by varying an external resistance R f between the two taps. Similarly the stator resistance unbalance can be created by connecting extra series resistances R ext in one or more phases as shown in Fig. 3. It is also possible to create both stator inter-turn fault and stator resistance unbalance simultaneously in this experimental setup. B. Extraction of Fundamental Component In the laboratory setup, supply voltage distortions cause the motor to draw currents which are also distorted. For a proper comparison between the experimental and the simulation results, it is necessary to extract the fundamental component of measured motor currents. To extract the fundamental component of the currents, the distorted line currents are transformed into the synchronous and anti-synchronous rotating reference frames using transformation matrix given in (). The rotating reference frame currents are then filtered by a low pass filter, which gives positive sequence and negative sequence currents in the form of dc quantities. These currents are then transformed back into the stationary reference frame to get the fundamental positive sequence and the fundamental negative sequence components of the currents. To reconstruct the unbalanced fundamental current space phasor, the q axis component of the space phasor is obtained by adding the q axis currents of the positive and negative sequence components, and the same procedure is followed to obtain the d axis component. The following matrix is used to transform electrical variables from the stationary a b c reference frame to the rotating q d reference frame. K = cos θ cos θ π 3 cos θ + π 3 sin θ sin θ π 3 3 sin θ + π 3 () where, θ = ωt + θ(). Here, ω is the angular speed of the reference frame and θ() is the initial angle of the q d reference frame. C. Experimental Results Fig. 4 shows the experimental and the simulation steadystate stator current vector loci for the stator inter-turn faulted Experimental (a) i s qs(a) (b) i s qs(a) Fig. 4. Stator current vector loci of induction motor with stator inter-turn fault (a) Experimental and (b) Experimental (a) i s qs(a) (b) i s qs(a) Fig. 5. Stator current vector loci of induction motor with stator resistance unblanace (a) Experimental and (b) induction motor under different load conditions. The stator inter-turn fault was created by shorting the taps correspond to 8 % turns on the stator phase A. The experiments and simulations were carried out with a V, 5 Hz balanced three-phase ac supply and a resistance of.9 Ωconnected in the short-circuit path of the fault (denoted by R f in Fig. (a)). As the load increases on the motor, the ellipse formed by the current vector locus expands and the major axis of the ellipse moves towards the q-axis, as shown by the curved arrows in Fig. 4 (a) and (b). A close agreement can be observed between the simulation and experimental results. The movement of the major axis of elliptical stator current locus indicates the change in the phase angle difference of positive and negative sequence stator current components (θ p θ n ), which confirms the remark at the end of the previous section. Similar experiments were also performed for the induction motor with the stator resistance unbalance under the same operating conditions as used for the faulted motor experiments. Fig. 5 shows the corresponding elliptical stator current vector loci, obtained from experiments and simulations, under different load conditions. The stator resistance unbalance is produced by connecting a resistor of 3Ωin series with phase A (shown in Fig. (b) by R a ). With increment in the load, the ellipse expands without the angular movement of its major axis. The mismatch in the results as observed from Fig. 5 is due to the small unbalance present in the supply voltage. Also the fixed position of the major axis confirms the remark at the end of the previous section. 936

5 y Major Axis A I p θ p ω ω I n θ n D Minor Axis C θ B x Experimental.6 Test-.4 Slip Increment. 6 3 Ellipse 8 Fig. 6. Ellipse with positive and negative sequence phasors Test- 33 To represent the changes in the elliptical current locus under different operating as well as load conditions more clearly, a mapping from the X-Y plot to the polar plot is required. This also enables a comparative study of faulted and asymmetrical induction motors. 4 7 (a) 3 IV. GRAPHICAL ANALYSIS OF CURRENT VECTOR LOCUS Due to the presence of a negative sequence component, the stator current vector locus forms an ellipse, whose eccentricity and inclination angle depend on the stator inter-turn faults or the stator circuit asymmetries and the operating conditions of the machine. The eccentricity of current vector elliptical pattern is determined by the magnitude of the negative sequence and positive sequence components of the currents. The inclination of the major axis of the ellipse is determined by the phase angles of the positive and negative sequence components. The inclination angle of ellipse also depends on the initial angle θ() in the transformation equation (). Here the initial angle θ() is taken to be zero; the q axis quantities are thus aligned with the a-phase quantities. Fig. 6 shows an ellipse with inclination angle θ. The major and minor axes of the ellipse are AB and CD respectively. The lengths of AB and CD are a and b respectively [5]. The length of the major and minor axes of the ellipse directly give the positive ( I p ) and the negative ( I n ) sequence component magnitudes, which are Ip = (a + b) and In = (a b). The relationship of the phase angles of the positive sequence phasor (θ p ) and the negative sequence phasor (θ n ), and inclination angle (θ) of ellipse is θ p + θ n = θ + nπ, where n is an integer. The eccentricity of ellipse is ε = b a. For a circle, ε =. V. MAPPING OF CURRENT VECTOR LOCUS ON POLAR PLOT The ellipse formed by the current vector locus is mapped as a point on the polar plot. On this plot, the eccentricity of the ellipse (ε) and the inclination angle of the major axis (θ) decide the polar coordinates of this point [5]. In the proposed on-line load test, for different loads on the machine, the points (ε, θ) are plotted on the polar plot. The precise load variation is not needed to carry out the proposed Experimental 8 Test- Test- 7 (b) Fig. 7. Polar plot representation of current vector loci (a) Stator inter-turn fault and (b) Stator resistance unbalance test. The polar coordinates of these points are calculated from measured steady-state currents, with balanced supply. For a healthy machine, since the current vector locus is always a circle for all values of load, the (ε, θ) points remain on the unit circle in the polar plot. For the machine with electrically asymmetrical stator, these points lie inside the unit circle, and are observed to remain stationary with load changes. These points lie inside the unit circle also for a machine with stator inter-turn faults. However, these points shift with load changes. Fig. 7 (a) and (b) show the polar plot mappings of Fig

6 and 5 respectively, where and indicate experimental and simulation results respectively. In Fig. 7 (a), the points marked as Test- show the polar plot mapping for stator inter-turn fault with different loads on the motor. It is observed that the experimental and the simulation points (ε, θ) on the polar plot shift in the direction as indicated by the arrow. The simulation results are obtained using the steady-state equations () to (5). The simulation and experimental results show good agreement. Similarly, an experiment was also performed with stator interturn fault on phase A along with the stator resistance unbalance created by connecting an external resistance in phase B, which is marked as Test- in Fig.7 (a). Here, the value of the fault current limiting resistance R f is.9 Ωand the value of the external resistance R ext is 3Ω. The shift in the (ε, θ) point indicates the presence of the stator inter-turn fault exclusively even under the stator electric asymmetrical condition of the induction motor. In Fig. 7 (b), the points marked as Test- show the experiments for induction machine with stator resistance unbalance produced by connecting resistor of 3 Ω in Phase-A. It is observed that the simulation points remain stationary, whereas the experimental points (ε, θ) remain almost stationary with small deviations in the angle and magnitude with load change. results are obtained using equations (6) to (9). These deviations are due to the supply unbalance and machine inherent asymmetries, which cannot be modeled. In Fig. 7 (b), the points marked as Test- are for the stator resistance unbalance created by connecting external resistor of Ωin phase B in addition to that in phase A for Test-. The experimental points (ε, θ) on the polar plot remain almost stationary indicating the absence of stator inter-turn fault in the machine. Although the stator resistance unbalance considered for the experimental studies is heavy, the same behavior is also observed for the machine intrinsic electrical asymmetries due to manufacturing issues. The load variation from no-load to % of the rated load is sufficient to get these points. In summary, the shifting of (ε, θ) point on the polar plot mapped from the steady-state current vector locus with load change indicates the presence of the stator inter-turn fault in the induction motor. Whereas the stationary position of the point indicates the presence of only the stator electrical asymmetries in the induction motor. VI. CONCLUSION A simple on-line load test to detect the presence of stator inter-turn faults and discriminate them from stator electrical asymmetrical conditions is proposed in this paper. The test is based on the observation of the steady-state stator current vector locus with load change. The proposed on-line load test is easily implementable, does not require any special installation for the detection, or past history of the machine, training or database and speed measurement. This test is applicable to any unknown machine. The experimental results and the mathematical analysis show the effectiveness in the absolute identification of the presence of stator inter-turn fault even under the stator electric asymmetrical conditions. The discrimination of the stator inter-turn fault from the stator electric asymmetries is advantageous in arranging for scheduled maintenance of the machine more effectively. The test can also be used in conjunction with other methods to effectively detect stator inter-turn faults. REFERENCES [] A. Bellini, F. Filippetti, C. Tassoni, and G.-A. Capolino, Advances in diagnostic techniques for induction machines, IEEE Trans. Ind. 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