Abstract--In this paper, a stator turn fault detection strategy is developed for a permanent magnet (PM) generator system. Unlike conventional power generation systems, the output of the PM generator is directly rectified by an uncontrolled diode bridge. The only accessible signal is the DC link current/voltage. As a result, most existing detection techniques based on the phase current/voltage signals are not applicable. Instead, the 2nd and 6th harmonics of the DC link current are exploited for turn fault detection and they are extracted by a Kalman filter. It is shown that the phase unbalance caused by a turn fault gives rise to significant increase in the 2nd harmonic DC link current. Consequently, the dominant harmonic under healthy and fault conditions are of the 6th and 2nd orders, respectively. Hence, the turn fault can be detected by comparing the magnitudes of the two harmonics. The detection method is assessed by extensive simulation under various fault scenarios. It is shown that the developed Kalman filter method exhibits significant advantages in response time and computation effort than online fast Fourier transform (FFT) based techniques.

Index Terms--Fault detection, Turn fault, Kalman filter,

DC link current, PM generator.

I. INTRODUCTION ENEFITING from the features of high efficiency and high power/torque density, PM machines are being

favored in electric traction [1, 2] and aerospace applications [3]. Various PM machines including both surface mounted- and interior- PM machines, have been reported in the hybrid electric vehicles, flight control actuators [4, 5] and on-board power generations[6]. In these safety critical applications, it is essential to ensure uninterrupted operation and functionality in the event of a single point failure.

The stator winding insulation degrades gradually due to combined electrical, thermal and mechanical stresses [7, 8]. The gradual insulation degradation may lead to inter-turn short circuit fault, also known as turn fault [9], and large circulating current in the short-circuited turns. The fault current which may be an order of magnitude higher than the rated current will produce excessive heat and create local hotspot. This may lead to a catastrophe failure of the machine if without proper mitigation strategies. Insulation failure between the winding and the stator core can also cause large ground current which would result in irreversible damage to the machine. Therefore, it is

essential to analyze the behavior of the inter-turn fault and detect the fault promptly [10-12] to activate remedial actions.

Turn fault detection techniques have been widely studied in the literatures. Majority of them are based on the motor current signature analysis (MCSA) which does not require additional sensors for the drive systems. Spectral and wavelet analysis have been employed to perform the signal processing [7, 13] for extracting fault signature. Other techniques, such as monitoring parameter variation, positive and negative sequence analysis, PWM ripple current measurement and search coils all have been investigated for the fault detection [14-18].

However, in power generation systems with a passive diode rectifier, active control is not applied, and hence phase voltage and current measurements are usually not available [19]. Consequently, the existing detection techniques based on phase current or voltage analysis cannot be applied directly. Nevertheless, phase unbalance as a result of a turn fault will cause a large increase in the 2nd harmonic DC link current. In [20], a simple detection technique was developed by performing interpolated FFT analysis on the DC link current only. The FFT requires intensive computation efforts and data storage for the online monitoring and detection. It may result in slow detection response. Alternatively, the feature harmonics may be extracted by a Kalman filter that employs an optimal recursive algorithm capable of state estimation in the presence of the measurement noise and model uncertainties [21, 22]. It performs the estimation based on the measurements at the present and previous time steps [23, 24]. Thus, the requirement on the computation efforts and data storage is much less and the response time is also improved [25].

To assess the merits of turn fault detection techniques, it is essential that the dynamic behaviors of the system under study in healthy and fault conditions are accurately represented. For this purpose, a high fidelity, computationally efficient model for the PM generator system with a diode rectifier is first established. A real-time turn fault detection method is developed using a Kalman filter for tracking the 2nd and 6th harmonic in DC link current. The fault is detected by comparing the ratio of the two harmonics. The detection method is evaluated by simulations in various operation scenarios and its performance is compared with the FFT based technique in terms of computation effort and detection response time.

Bo Wang, Jiabin Wang, Antonio Griffo, Vipulkumar I. Patel, Zhigang Sun, Ellis Chong and Riona Smitham

B

Permanent Magnet Generator Turn Fault Detection Using Kalman Filter Technique

Bo Wang, J. Wang, A. Griffo, V. I. Patel are with the Department of Electronic and Electrical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom (e-mail: b.wang@sheffield.ac.uk, j.b.wang@sheffield.ac.uk).

Zhiguang Sun, Ellis Chong and Riona Smitham are with Rolls-Royce plc, PO Box 31, Derby, DE24 8BJ, United Kingdom

978-1-5090-0737-0/16/$31.00 ©2016 IEEE

II. MODELLING OF PM GENERATOR SYSTEM UNDER HEALTHY AND FAULT CONDITIONS

The system under consideration is a 50kW PM generator for aerospace application as schematically shown in Fig. 1. The machine is mounted near the low pressure end of the engine by a stepdown gearbox system. The 3-phase terminals are directly connected to a full bridge diode rectifier. The rectified DC voltage is regulated by an interleaved boost converter to 270V. Finally it feeds the various loads on board. The speed range of the generator operation is 10195~17000rpm.

Fig. 1 Diagram of a 50kW generator system for an aerospace application.

Fig. 2 Cross-section of a 50kW SPM generator with turn modelling.

Fig. 3 Winding connection of the PM generator.

Fig. 2 shows the cross-section of a 50kW SPM generator

having 15-slot, 10-poles configuration. Each phase has five coils connected in parallel branches whilst each coil has 8 turns in series as shown in Fig. 3. A turn fault may occur in any of the parallel coil and causes not only large short-circuit current in the faulted turns but also circulating current between the paralleled coils. The interaction of these currents together with the rotor PM field and the diode rectifier is quite complex but needs to be accurately represented.

To this end, each coil is treated as a separate branch and finite element analyses (FEA) are performed to extract their PM flux linkage, inductance and their mutual inductance. Without loss of generality, a turn fault is assumed to occur in A1 coil and this coil is discretely modelled in 2-D FEA to represent 8 turns in the slots it occupies, whereas other coils are modelled as lumped. Out of 8, 7 and 8 possibilities of 1-turn, 2-turns, and 7-turns faults, respectively, only the combinations having highest probability of faults have been analyzed. For example, two turns that are not next to each other or to the stator tooth is unlikely to be shorted for 2-turns short-circuit case. The FE model is first validated for no-load back electro-motive force (EMF) waveforms and output power at the nominal condition against experimental results on the prototype PM generator.

In healthy condition, the currents in the 5 branches are identical due to the periodicity. However, if a turn short circuit fault occurred in phase A indicated as A1(f) in Fig. 3, large fault current will be induced in the shorted path. This results into unbalanced voltages in the faulted phase leading to circulating currents in the 5 branches (A1, A2… A5). As the faulted turns share the same slot with healthy coils of Phase B and Phase C, the currents in other branches are also influenced due to the mutual coupling between the coils.

The back EMF (or flux linkage) of 15-slot, 10-poles, SPM generator contains 5th and 7th harmonics, which is considered in the machine model. In addition, self-inductance and mutual inductances of various coils derived by FE model, which exhibits variation with the rotor position, is also considered in the machine model. As observed, the variation is well captured by sin 2θ curve-fit function and is embedded in the Simulink model as shown in Fig. 4.

Fig. 4 Variation of self-inductance.

The inductance matrix for 1-turn, 2-turns, and 7-turns faults in the generator under consideration are derived from FEA considering the 15 coils and 1 additional fault turn. Fig. 5 shows inductance matrix for 1-turn fault. However, due to surface-mounted rotor topology and relatively large electromagnetic air-gap, the inductance variation with current is very small and neglected.

Fig. 5 Inductance matrix for 1-turn fault.

The analytical machine model derived using 2-D FEA is summarized as below:

(1)

where λ is resultant flux linkage matrix, L is inductance matrix, and λm is permanent magnet flux linkage matrix for the 16 branches, respectively.

Fig. 6 Simulink-Simscape model with boost converter.

In order to capture the actual fault behavior and provide the accurate signal for the detection method, the generator system was represented by a Simulink-Simscape model, as shown in Fig. 6, which is based on the circuit equations according to [26-28] and analytical machine model derived from 2-D FEA described above.

The predicted turn fault currents are then compared with the FE results as shown in Fig. 7 which exhibited good accuracy for both operating points considered (1) 30kW at 10195 rpm, and (2) 50kW at 17000 rpm. The resultant turn fault currents is around 10 times the rated current, therefore, it should be immediately detected and mitigated before developing to a more serious fault.

Fig. 7 Turn fault currents at rated operating condition.

For this uncontrolled rectifying system, no sensors are implemented to measure the phase current or voltage. The only available signals are the current/voltage of the DC link and output bank. Since the output bank is near the load side which is far away from the machine, it is less affected by the inter-turn fault. Hence, the following analysis will focus on the current and voltage of the DC link.

The current and voltage signals under healthy and single turn fault condition are compared in Fig. 8 and Fig. 9. As for the voltage signal at healthy condition, the main harmonic is the 6th order which is caused by turn-on and turn-off of the 6 diodes. There are also high frequency harmonics which are due to the switching action of the interleaved boost inverter. However, if a single turn fault occurs, the short circuit gives rise to phase unbalance. Consequently, the dc link voltage is further distorted, and the 2nd harmonic emerges and becomes the dominate harmonic. The internal reason is that the back electromotive force and inductance of each phase is no longer symmetrical. The asymmetrical component which is at the fundamental frequency modulated by the diodes becomes a 2nd harmonic. Similar change is also observed in the DC link current. It is apparent that the influence of the turn fault is more notable in the current signal. This is because the voltage signal is more affected by the DC link capacitance and voltage regulation of the interleave converter.

Hence, the current signal has been selected and analyzed by FFT at healthy state and several different turn fault scenarios as shown in Fig. 10. As can be seen, under healthy condition, the main harmonic in the dc link current is the 6th harmonic, and the 2nd harmonic is negligible. Whilst the amplitude of the 2nd harmonic is much higher than the 6th harmonic in case of a turn fault, regardless it is 1-turn, 2-turn or 7-turn fault. As a result, the ratio of the amplitudes between the 2nd and 6th harmonics in the DC link current can be exploited as the indicator of the turn fault. Similar analyses are performed in different speed and load conditions over the generator operating range, and the resultant fault signatures are essentially consistent, with the ratio being virtually zero in healthy condition and greater than one under a turn fault condition.

-4000

-2000

0

2000

4000

0 60 120 180 240 300 360

Cur

rent

(A)

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If1 If1_FEAIf2 If2_FEAIf7 If7_FEA

Fig. 8 DC link voltages under healthy and 1-turn fault conditions.

Fig. 9 DC link currents under healthy and 1-turn fault conditions.

Fig. 10 FFT of DC link currents under healthy and fault conditions.

III. FAULT DETECTION DESIGN The turn fault can be detected by comparing the

amplitudes of the 2nd and the 6th harmonics in the DC link current. Since the PM machine is attached to the engine by the gearbox, the speed of the machine is available. Hence, the primary task is to track the amplitudes of the 2nd and the 6th harmonics. In order to develop a fast and accurate detection method, a Kalman filter is employed to estimate the magnitudes of the two key harmonics.

According to the FFT analysis in Fig. 10, the DC link current mainly consists of a dc component (omitted in the figure), 2nd, 4th and 6th harmonics. Higher order harmonics are assumed to be very small in magnitude

compared to these components and hence neglected. Thus can be written as:

(2)

where , , , and are the magnitudes of the dc component and the 2nd, 4th and 6th harmonics while , ,

represent the phase angle of each harmonic. is the electrical angular speed of the PM machine which is derived from the engine rotating speed. During a short time interval, all the variables listed above can be assumed to be constant. Therefore, these variables at the ( th time step are equal their values at the th time step.

For the Kalman filter design, it is essential to obtain the transition matrix for the estimated states. Firstly, the dc component is written as,

(3)

Whilst for the three harmonic components, they are modelled by decomposing the sinusoidal equation at time step as in [23, 29]. By way of example, the 2nd harmonic at time step can be written as

where,

(4)

(5)

represents the 2nd harmonic component in at the kth time step while is introduced as an intermediate state variable. At time step, , where is the sampling interval. The value of at the th time step can be similarly derived and given by:

(6)

Thus, the state transition matrix for the 2nd harmonic can be written as,

(7)

As can be seen, the state transition matrix is not dependent on the phase angle and this is, indeed, one of the advantages of this decomposing modelling. The above equation can be notationally simplified as,

(8)

where denotes the

transition matrix for the 2nd harmonic as in (7). The state transition matrices for the 4th and 6th harmonics can be similarly derived, and the difference is indeed only in the harmonic orders in the sines and cosines. The overall discretized system equation was written as in (9) and the transition matrix was denoted as A.

0

50

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250

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Vol

tage

(V)

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V_DC_h

V_DC_f

0

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200

300

400

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rent

(A)

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I_DC_h

I_DC_f

(9)

where

denote the transition matrix for the 4th and 6th harmonics respectively. is updated according to the machine speed at each time step. According to equations (2) and (9), the measurement equation for the Kalman filter is obtained in (10), and the estimation matrix is denoted as H.

(10)

Based on the above equations, the Kalman filter is designed according to [30]. The Kalman filter algorithm is typically represented by two-step time update and measurement equations, which are also known as prediction and correction steps, respectively. The time update equation is written in (11) and the measurement equation in (12).

(11)

(12)

where Q and R represent the covariance for the process noise and measurement noise, respectively. Their values are usually obtained through a tuning process and regarded as constant after tuning. For the PM generator system under consideration, the two matrices are given in (13).

(13)

As shown in the previous equations, the Kalman filter is performed based on the data at the th and th time steps, so the requirement on the memory is minimum. While a few matrix multiplications have to be performed in each step, the matrices in (11) and (12) are sparse and the

computation load for the filter is quite low. Therefore, the Kalman filter algorithm can be easily implemented online with modest processing power.

As a result, the magnitudes of the 2nd and 6th harmonics are tracked by the Kalman filter in each time step. A fault is flagged when the magnitude of the 2nd harmonic is greater than that of the 6th harmonic according to Fig. 10. The threshold ratio can be adjusted for a given system, accounting for inherent phase unbalance and measurement noise.

It is worth noting that in case of a 7-turn fault, one phase is almost short-circuited. The resultant DC link voltage becomes very low and the DC link current is significantly increased. Hence the current transducer will be saturated and its output reaches the maximum without any harmonic signature. A short circuit at the DC output stage may also lead to the current transducer saturation. To address this, another fault indicator is introduced in the fault detection algorithm as shown in Fig. 11. If the DC link current exceeds the maximum permissible value, the fault flag will also be triggered. Additionally, in order to prevent false triggering, the estimated values of , , are filtered by a low pass filter before sending to the decision logic.

Fig. 11 Fault flag decision logic

IV. SIMULATION STUDIES The effectiveness of the proposed detection strategy was

evaluated by simulations under various operation conditions. Initially, the generator was operating at 17000rpm with 50kW output. At 0.2s, a single turn fault was injected in the stator winding as shown in Fig. 12. The amplitudes of the 2nd and the 6th harmonics monitored by the Kalman filter are shown in Fig. 13. In healthy condition, the magnitude of the 2nd harmonic is much smaller than that of the 6th harmonic. When the turn fault occurred, the amplitude of the 2nd harmonic is increased rapidly and becomes larger than that of the 6th harmonic. The fault flag is triggered correctly. The time delay of the fault alarm was only 0.7ms. There are visible ripples on the magnitude of the tracked 2nd and 6th harmonics, particularly under the fault conditions. These are caused by high order harmonics which are ignored in the Kalman filter design. However, these ripples are relatively small and do not affect the fault detection.

The detection strategy was also evaluated with a 7-turn fault. The sampled DC link current waveform is shown in Fig. 14. The current transducer is saturated due to the

current exceeding its maximum value. The detection results are illustrated in Fig. 15. The fault is also promptly detected and the time delay is ~0.5ms which is even faster than the 1 turn fault scenario. During the fault transient, the variations of the 2nd and 6th harmonics are captured quickly. The fault is subsequently detected due to the increased 2nd harmonic initially. After a short time, the current sensor is saturated. The estimated magnitudes of the two harmonics became 0 but the fault was still triggered by the over current limit

Fig. 12 @17000rpm, 50kW, 1TF.

Fig. 13 Detection results@17000rpm, 50kW, 1TF.

Fig. 14 @17000rpm, 50kW, 7TF.

Operations at different speeds and turn fault scenarios were extensively evaluated to assess the effectiveness of the proposed detection technique. The PM generator system was simulated at the minimum and maximum operation speeds with 1-turn, 2-turn and 7-turn short circuits. The turn

faults were all alarmed correctly, and the time delays were listed in Table I. The maximum time delay is 0.9ms which is sufficiently fast to activate the remedial operation strategy. This verifies that the fault detection is effective over the whole operation region.

Fig. 15 Detection results@17000rpm, 50kW, 7TF.

Fig. 16 Detection results with transient load.

TABLE I TIME DELAY OF DIFFERENT FAULT SCENARIOS Time delay

Speed 1 turn 2 turns 7 turns 10195rpm 0.9ms 0.7ms 0.6ms 17000rpm 0.7ms 0.6ms 0.5ms

The detection method was also examined with transient

load and speed variations as shown in Fig. 16 and Fig. 17. In Fig. 16, a load step from 10kW to 20kW at 10195rpm is applied, and a similar change in the DC link current is seen. However, no false alarm was produced during the transient. In Fig. 17, the speed varies from 15100rpm to 15300rpm over 0.2s when 36kW output is maintained by the converter regulation. The fundamental angular frequency, , of the generator is updated in each step according to equation (7). A 1-turn fault is injected at 0.2s and the magnitudes of the

0.1 0.15 0.2 0.25 0.30

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/A

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/A

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-1

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1fault flag

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idc

2nd and 6th harmonics are tracked by the Kalman filter quite well. As can be seen, when the turn fault occurs at 0.2s it is successfully detected. Therefore, the developed technique is robust to load transient and speed variations.

Fig. 17 Detection results with transient speed.

Fig. 18 FFT detection @17000rpm, 50kW, 1TF.

For the sake of comparison, the online FFT combined

with Goertzel algorithm was also simulated for estimation of the amplitudes of the two harmonics. The same fault scenario as that described in Fig. 12 and Fig. 13 was used to assess the FFT technique as shown in Fig. 18. While the fault is also correctly detected, the time delay of 4.8ms is much longer than that of the Kalman filter. In fact, it can be observed that the response of the estimated 2nd harmonic amplitude is much slower than the Kalman filter compared with that shown Fig. 13. The time delays of the FFT technique under different operating and fault scenarios are listed in Table II. It is evident that the delays associated with the FFT are longer in all scenarios. This is because the FFT requires a quite wide data window to perform the frequency decomposition process while the Kalman filter technique uses the instantaneous values in two sampling intervals. It follows that the Kalman filter not only requires much less computation resources, but also exhibits fast

detection response. Therefore, it is more advantageous for the turn fault detection.

TABLE II

TIME DELAY OF DIFFERENT FAULT SCENARIOS USING FFT Time delay

Speed 1 turn 2 turns 7 turns 10195rpm 4ms 3.2ms 1.6ms 17000rpm 4.8ms 2.4ms 1.6ms

V. CONCLUSION In this paper, a Kalman filter based turn fault detection

technique has been developed for a PM generator system with a diode rectifier. The detection method only requires the DC link current and speed information. The magnitudes of the 2nd and 6th harmonics have been selected as the features tracked by the Kalman filter. A turn fault is detected by comparing the two magnitudes online. Extensive simulations based on a high fidelity, computationally efficient model of the PM generator system have been performed and the performance of the proposed turn fault detection technique has been assessed. Compared with the existing FFT based technique, the Kalman filter based detection technique shows faster response and requires much less computation efforts, therefore being more cost effective in an online monitoring system when speed signal is available.

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