A Labview based Rotor Fault Diagnostic Tool for Inverter Fed Induction Machines by Means of the Vienna Monitoring Method at Variable Speed C. Kral, F. Pirker, G. Pascoli, W. Berghold
Arsenal Research Faradaygasse 3, Object 221 A{1030 Vienna, Austria email:
[email protected] Abstract | The Vienna Monitoring Method (VMM) is a fault detection technique for squirrel cage induction machines. It is based on the comparison of the calculated torque values of two machine models with di erent model structure. Up till now steady state operation has been investigated only. This contribution deals with an exploitation for variable speed drives under dynamic conditions. The introduced con guration is due to a Labview application, based on a portable personal computer system. I. Introduction
Common rotor fault diagnostic tools are designed for mains supplied induction machines only. They are normally based on Fourier analysis of one machine current [1], [2]. Rotor asymmetry causes fault speci c frequency harmonics components, mainly (fs : : :supply frequency, s : : :slip) f = fs (1 2s) : (1) For sinusoidal voltage supply fault related frequency components (1) occur in all machine currents. Improved diagnostic tools use neural network and arti cial intelligence approaches to sense this e ect [3], [4], [5]. Other fault detection techniques are based on the analysis of the pattern for the current space phasor (park's vector) [6], [7]. Higher sophisticated methods already rely on a simple machine model to overcome in uence of variable load torque [8], [9]. Most of these methods are restricted to steady state conditions and xed supply frequency. Rotor faults cause double slip frequency shaft torque modulations, too. This torque harmonics can be sensed with the help of a simple machine model which estimates torque [10]. Amplitude of the fault speci c second harmonic due to slip frequency depends on load torque and inertia [11], [12]. All these in uences complicate an accurate and reliable fault detection technique. The monitoring task for an inverter drive is complicated by some additional facts. side band
The voltage and current waveforms are nonsinusoidal and the high voltage derivation values vt from fast switching inverters distort measurements Speed can not be assumed to be constant because the drive is designed to operate at variable speed Variable torque (slip) in uences location and extend of side band current components Control structure in uences extend of both signi cant side band frequencies in currents voltages [13]; their participation appears in dependence on the applied model for eld oriented control and the control mode (speed or torque control) If the fault detection algorithm is integrated as a part of the digital signal processor (DSP) program of the inverter drive, required current and voltage samples can be determined synchronous to inverter switch conditions [14], [15]. Applications with independent measurement and evaluation equipment require a low-pass lter to obtained the fundamental and the fault speci c components which appear near the fundamental (1); the introduced Labview based rotor fault diagnostic tool relies on this approach. Rotor fault diagnostic is a challenging task for variable speed drives. In case of steady state conditions a Fourier analysis can be applied, where the sampling interval varies with the speed of the induction machine [16]. Synchronous sampling ensures that a signal is sampled at an integral multiple of its fundamental frequency. Other fault detection approaches are due to park's vector pattern analysis [17] or other suitable transformations of the obtained voltages and currents [18], [19]. Some of these methods are based on a time-frequency transformation even to overcome the dependence of transient speed operation [20], [21].
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II. Vienna Monitoring Method
Originally the Vienna Monitoring Method (VMM) has been developed for an inverter fed induction machine. The whole evaluation technique has been implemented to the DSP program structure. There required measurement values have been obtained on-line from the machine control module. This application has been employed for constant
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Fig. 3. Torque di erence and calculation of the smoothed load torque
B. Current Model
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speed operation only [13], [22]. In this contribution an o -line calculated and Labview based implementation of the VMM will be introduced. In order to enable fault detection at transient conditions, some modi cations due to the further implementation of the VMM have to be performed. The detection of faulty rotor bars will be demonstrated for steady state and transient conditions. The employed VMM is based on a portable personal computer system which is equipped with several analog to digital converters (ADC) and counter inputs. The VMM is based on the comparison of the calculated torque values of a voltage and a current space phasor model. Calculation of the required ux space phasors of these models is due to (normalized) space phasor theory [23], [24]. Therefore measurement of voltages and currents as well as rotor position is required. Current measurement is performed with the help of click shut current transformers or current probes. Rotor position can be acquired by a high resolution or a single pulse per revolution position (e.g. optical) encoder. Hence easy handling and a minimum of intervention is required only.
Integration of the rotor ux space phasor with reference to a rotor xed reference frame (index (r)) requires the rotor xed stator current space phasor only ( g. 2). dir r = 1 x i ir r (3) r sr d r Required parameters for the current model (superscript i) are the rotor reactance xr and the rotor time constant r . The simple approach (3) relies on the assumption, that the whole leakage reactance is due to the stator windings. This condition is valid without any restrictions [14]. The required rotor xed stator current space phasor is r must be calculated out of the stator xed phasor is s and the angular displacement of the rotor with reference to the stator. (4) is r = is s e ; ( )
Stator ux space phasor in the stator xed reference frame (index (s)) can be calculated out of the normalized current and voltage space phasor ( g. 1) dvs s = v rs is s ; (2) ss d where is the normalized time and rs is the normalized stator resistance. The open loop integration of the voltage model (superscript v) must be stabilized for practical application. Otherwise errors and disturbances of the input signals will lead to an uncontrolled output quantity. ( )
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C. Evaluation Technique
Torque di erence
t = tv ti (5) is calculated out of the torque values of the voltage and the current model. Each torque value can be calculated with the help of the accessory conjugate complex (superscript ) current and ux space phasor (2), (3). tv = Im is r vs s ti = Im is r ir r (6) In case of an ideal symmetric induction machine and exact estimated machine parameters torque di erence equals zero, anyway. Rotor asymmetries cause the mentioned side band frequencies of currents (and voltages). In addition fault related disturbances cause double slip frequency torque and speed modulation, too. The e ect of torque modulations can be sensed by means of the calculated torque di erence. Occurring shaft torque modulations equal the calculated torque of the voltage model. But the amplitude of these modulations depends on the actual mass moment of inertia and operating conditions. By the way of contrast torque di erence is independent of the in uence of inertia [11], [12] and control structure ( )
A. Voltage Model
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[13] of the inverter drive. The amplitude of this quantity depends on the grade of rotor asymmetry and load torque only. As the amplitude of (5) and the mean value of the actual load torque show a linear progressive coherence [22], a load independent quantity can be de ned { the relative torque deviation t~ = t~vt : (7) Under normal operating conditions the smoothed shaft torque t~v can be calculated out of the torque value of the voltage model with the help of a low-pass lter ( g. 3). For the application of the VMM under speed transient conditions this approach (7) can be seen as suitable. To overcome the dependence of slip frequency, a spatial data evaluation technique is performed. There the torque di erence (7) will be examined versus the actual
ux location of the rotor xed rotor ux space phasor, (8)
= arg ir r ; which mainly rotates with slip frequency. By that double slip frequency components become mapped into a second harmonic component due rotor circumference. This strategy covers the in uence of variable slip (variable load torque). A spatial data clustering algorithm [22] smooths the obtained data and makes the evaluation technique robust against measurement noise and disturbances. For that reason rotor circumferences becomes subdivided into 32 equidistant evaluation segments. The actual segment is selected with the help of rotor ux location (8). The segment value will be computed by means of a recursive averaging algorithm of the accessory relative torque deviation. These technique can be seen as an overlay procedure including the calculation of the average values of the patterns of the discretizated relative torque deviation. After a certain measurement time a discrete Fourier spectrum of the 32 cluster values can be calculated. The amplitude of the second harmonic component f deals as fault indicator for the VMM. The extend of this component depends on the grade of rotor asymmetry only. ( )
III. Operating Conditions
The VMM is usable for steady state and transient operating conditions. Nevertheless there are some restriction due to the evaluated load torque and speed range. For each excluded operating range the spatial evaluation procedure must be interrupted.
Fig. 4. Labview-Window
Under speed transient conditions estimated torque ( g. 3) is not fast enough due to low-pass ltering. Very high values of time derivative of torque have to be excluded from data evaluation, too. B. Speed
Normalized rotor speed values less than approximately 0.3 cause the voltage model to be unreliable. This is due to the integration structure ( g. 1) where measurement errors cause uncontrolled ux values. There, evaluated speed range must be restricted, too. Field weakening range leads to a decrease of the magnetizing and saturation level. If this speed range should be covered, an adequate parameter estimation must be implemented. C. Measurement Time
The discrete Fourier analysis of the clustered torque values can be performed after a certain measurement time. The choice of this length of time rests on experimental knowledge. Accuracy of the fault indicator can be increased according to a an increased measurement time. The given experimental results are based on an evaluation time of approximately 18 seconds, which leads to a medium accuracy range. IV. Labview Based Measurement System
Measured currents and voltages are acquired by means of ADCs. Position encoder signal is processed with the help of a digital counter input. All these values are recorded into a data le according to the selected sampling time. Data measurement and Labview based evaluation are implemented at a portable personal computer system. An Calculation of the relative torque deviation is based on av example of a data set obtained from an inverter fed 10 kW simple division (7). For smoothed load torque values t~ induction machine at steady state operation is depicted in smaller than 0.3 (normalized value) measuring and esti- g. 4. The sampling frequency is 2000 Hz. Voltage and mation errors distort results. There, load torque must be current inputs have been equipped with a 100 Hz low-pass greater than this given threshold. lter to suppress in uence of the fast switching inverter. A. Load Torque
Fig. 4 shows a snapshot of a Labview evaluation at steady state conditions: (a) Spatial shape (polar coordinate plot) of the clustered relative torque deviation including participation of the voltage and current model (b) Linear shape of the clustered relative torque deviation including participation of the voltage and current model (c) Amplitudes of discrete Fourier analysis of the shape (b); second harmonic deals as fault indicator (d) Shape of the stator ux space phasor (or rotor ux space phasor) including transient e ect (model startup) (e) Calculated torque of the voltage model (or current model or torque di erence) including transient e ect After approximately two seconds steady state conditions of the models are reached ((e), 2 s , 4000 samples). There calculated values for time grater than two seconds are evaluated only. Sub gures (d) and (e) demonstrate the convergence of employed models. Obtained shape of the torque di erence consists of a second harmonic essentially. Discrete Fourier analysis shows this property clearly (c). The Labview application allows a fast failure state estimation including the representation of the most significant state variables. In addition to this representations a more detailed investigation is presented in the chapter after next. V. Applications
The introduced measurement system allows a continual or temporary monitoring of inverter fed induction machines under given operating conditions. The Labview based o line application of the VMM can be performed if intervention of the DSP software isn't desired or possible. VI. Measurement Results
The following results rely on measurements at an inverter drive with a 10 kW induction machine with either healthy or three broken rotor bars. Figure 5 shows (a) the evaluated fault indicator f as a function of time for a fault free induction machine. According to steady state operation and the symmetric rotor cage the fault indicator shows noise signals only. Sub gures (b) and (c) show the operating conditions due to estimated shaft torque and speed. In order to exclude model start-up, data evaluation starts two seconds (t = 2 s) after the beginning of data recording. Overall recording time is limited to 20 seconds. Reliable values of the fault indicator can be obtained after a minimum evaluation time of approximately eight second (t = 10 s). A representative fault indicator can be obtained only, if the rotor ux phasor passes the rotor circumference several times. Only then a complete set of cluster values is available. The e ect of start-up of
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