GB2341690A

GB2341690A - Method for automatic measurement of the ohmic rotor impedance of an asynchronous machine

Info

Publication number: GB2341690A
Application number: GB9921956A
Authority: GB
Inventors: Jens Godbersen
Original assignee: Danfoss AS
Current assignee: Danfoss AS
Priority date: 1998-09-17
Filing date: 1999-09-16
Publication date: 2000-03-22
Anticipated expiration: 2019-09-16
Also published as: DE19842540C2; CN1247988A; GB2341690B; FI19991966L; DE19842540A1; GB9921956D0; CN1125347C; FI115860B

Abstract

A method for automatic measurement of the ohmic rotor impedance of an asynchronous machine (1) controlled by means of an inverter (8) while the machine is acted upon by a non-rotating field, in which method: <SL> <LI>i) the ohmic stator impedance, the leakage inductances and the main inductance of the asynchronous machine are measured, <LI>ii) a test signal (U<SB>sa</SB>) formed by a predetermined dc signal with a superimposed ac signal is supplied to a phase winding (a) of the asynchronous machine, the frequency of the ac signal corresponding approximately to the nominal slip frequency of the asynchronous machine, <LI>iii) the amplitude and the phase of the phase signal (<O>I</O><SB>sa</SB>) resulting from the test signal are measured, and <LI>iv) the ohmic rotor impedance is calculated from the measured values according to i) and iii). </SL> Measuring the ohmic rotor impedance in accordance with this method can be performed in a very short time, when the inductances and the ohmic stator impedance are known. Further, because of the low frequency of the ac signal, current displacement does not take place.

Description

2341690 Method for automatic measurement of the ohmic rotor impedance of

an asynchronous machine This invention relates to a method for the automatic measurement of the ohmic rotor impedance of an asynchronous machine controlled by means of an inverter

while the machine is acted upon by a non-ro-Lating field.

In an asynchronous motor, whose speed and torque are controlled, part-Lcularly according to a field oriented control method, knowledge of all impedances, that is the ohmic and inductive impedances, is requ-4--ed to make the control as accurate as possible. They can be estimated and/or measured.

Measurements are made either with rotatable, unloaded rotor or with blocked (braked) rotor. When a test current for measuring the impedances is passed through the stator with the rotor free of load, the largest share of the current will flow through the main reactance, which is determined by the main inductance (the c-ounterinductance), thus allowing measurement of the main inductance, but not of the ohmic rotor impedance. When the measurement is made with a blocked rotor, however, the test current flows through the rotor as well, so that also its ohmic impedance can be measured. Both methods, however, involve disadvantages. Measurement with rotating unloaded rotor is often not possible, for example, when the motor is fixedly incorporated in a finished product and its axis is permanently loaded. on the other hand, blocking of the motor, particularly when full torque is applied, places heavy demands on the mechanical braking device, so that this method is substantially more expensive. Another difficulty in connection with measurements on a blocked rotor is the current displacement in the rotor bars occurring at relatively high frequencies in the range from 30 to 60 Hz, causing too high a measurement value of the ohmic rotor impedance.

Further, on measuring the ohmic impedance, its variation in dependence on the operating temperature is often not considered. Depending on the operating temperature, it can increase or decrease by 20% to 30%. This means that an equivalent circuit diagram of the asynchronous machine forming the basis of the measurement is not applicable to normal operation.

US 5,689,169 discloses a method in which the stator and rotor leakage inductances and the ohmic rotor impedance with the rotor stationary are measured by controlling the q-components and the d- components in a "field oriented" control process. Thus, one phase winding

1S of the stator receives a test signal with a frequency approximately equal to the operating frequency, and, for example, amounts to 30 Hz. The current component Iq is set to zero to avoid generation of torque, and at the same time the actual voltages Vq and Vd fed back to the control device are measured. With a known test signal frequency and previously measured ohmic stator impedance, the approximate value of the rotor impedance can be calculated. This approximation is based on a relatively high test signal frequency so that relatively simple mathematical formulae can be used for the calculation, thus requiring only little computing power from a microprocessor used in the control device. However, the relatively high test signal frequency of approximately 30 Hz has the disadvantage that current displacement takes place in the rotor bars, which results in a too high measurement value of the ohmic rotor impedance. In extreme cases, the measurement value can be 100% to 150% too high. This method, compared with a converter with an inverter having only current sensors, has the additional disadvantage that also voltage sensors must be used.

3 A method of the kind mentioned in the introduction is known from the publication EPE'97 by Danfoss Drives A/S, Denmark, pages 3.370 to 3.374. With this method, the following measurements and calculations are made, reference being made in the following to the conventional equivalent circuit diagrams of one phase of an asynchronous motor as shown in Figs. 1 and 2 Of the accompanying drawings, Fig. I showing a relatively detailed steady-state equivalent circuit, and Fig. 2 a simplified equivalent circuit diagram referred (transformed) to the stator side by means of an effective turns ratio:

1. A test voltage U,,, in the form of a predetermined dc voltage is applied to the stator, more precisely to the phase winding of the stator, and the associated stator current I,, is measured. As the inductive reactances (inductances) of the stator-side leakage inductance Lc,, and the main inductance Lm (counter- inductance) also represent a short-circuiting of the direct current, the ohmic stator impedance R, can be calculated from the values Usa and I,a.

2. Then the sum of the leakage inductances L,, and L,, transformed to the stator, the "transient" inductance L, is calculated as follows, according to Fig. 2: A short rectangular voltage pulse, consisting of high-frequency components, with a duration of a few milliseconds and an amplitude Usa is applied to the stator, so that the inductance of the main inductance L'm according to Fig. 2 at these high frequencies is so large that the current flowing through L'm is negligibly small. Then, the rear flank of the waveform of the current I,,, produced by this pulse is sampled. The time constant L's/(R,+ R'r) and the differential quotient dI, ,/dt are calculated on the basis of the sampled values. L', is then calculated by means of the equation Usa = R,Isa + L', (dIsa/dt).

3. Then a voltage is applied to the stator with such a low frequency that the current I,y flowing through the rotor is negligibly small and the stator current I,,, is practically equal to the magnetizing current Im flowing through the main inductance. Knowing the ohmic stator impedance R, and the current Isa means that the stator inductance L, (= Lm + L,,,) can be determined. Further, the dynamic main inductance L'D,, (also called differential main inductance) transformed to the stator side can be determined, and its value LDM can be calculated. The dynamic main inductance is determined in that a test voltage, consisting of a dc voltage with a superimposed ac voltage, is applied to the stator, and the resulting alternating current (at the working point determined by the direct current) is measured. This measurement is carried out for different pre-magnetizing direct currents (working points).

4. Since all values, except the ohmic rotor impedance Rr, are known in the equivalent circuit diagrams according to Figs. 1 and 2, the ohmic rotor impedance R, can, in principle, be calculated. The way of doing this, however, is not described in detail in the paper mentioned.

The invention is based on the problem of determining the rotor impedance of an asynchronous machine faster than hitherto, and at the same time preventing errors of measurement caused by current displacement.

The present invention provides a method for the automatic measurement of the ohmic rotor impedance of an asynchronous machine controlled by means of an inverter while the machine is acted upon by a non-rotating field, in which method:

a. the ohmic stator impedance, the leakage inductances and the main inductance of the asynchronous machine are measured, b. a test signal consisting of a predetermined dc signal with a superimposed ac signal is supplied to a phase winding of the asynchronous machine, the frequency of the ac signal corresponding approximately to the nominal slip frequency of the asynchronous machine, c. the amplitude and the phase of the phase signal resulting from the test signal are measured, and d. the ohmic rotor impedance is calculated from the measured values according to a) and c).

With this solution to the above-mentioned problem, one measurement of the resulting phase signal in dependence on the test signal is sufficient. The duration of measuring is correspondingly reduced. As the frequency of the ac signal corresponds approximately to the very low nominal slip frequency of the asynchronous machine, at which the asynchronous machine runs during operation and which results from the known frequency of the rotating field and the nominal speed of the asynchronous machine and is relatively low, measurement inaccuracies caused by current displacement also disappear.

Preferably, the ohmic rotor impedance transformed to the stator side is determined first, and the actual ohmic rotor impedance is calculated by means of the measurement values according to a) and c). Preferably, the frequency of the ac signal is in the range from 1 to 8 Hz inclusive. 30 Advantageously, the dc. signal is a dc voltage, which is chosen so that the resulting direct current is less than half the nominal magnetizing current of the asynchronous machine. Advantageously, the magnitude of the direct current is chosen so that the dynamic main inductance is 6 approximately equal to the static main inductance of the asynchronous machine.

The test signal may be a phase voltage, whose reference value is derived and set on the basis of a previously measured characteristic, stored in a memory, representing the dependency of the phase current on the reference value.

A method, in accordance with the invention, for the automatic measurement of the ohmic rotor impedance of an asynchronous machine and an asynchronous machine controlled by means of an inverter arranged to carry out the method will now be described, by way of example only, with reference to the accompanying drawings, in which:

Fig. 1 is a traditional, relatively detailed equivalent circuit diagram of an asynchronous machine; Fig. 2 is a simplified equivalent circuit 20 diagram of an asynchronous machine at standstill with values transformed to the stator side; Fig. 3 is a characteristic curve plot showing the dependency of the static main inductance Lm 25 and the dynamic main inductance LDIn on the magnetizing direct current of an asynchronous machine; Fig. 4 shows the waveform of a phase voltage 30 used as test signal, comprising a de voltage with a superimposed triangular ac voltage; Fig. 5 is a block diagram of a converter controlling an asynchronous machine whose impedances are measured automatically by means of the control device; and Fig. 6 is a relatively detailed block diagram of parts of the control device of the converter according to Fig. 5.

Since the determination of the ohmic stator impedance R,, the leakage inductances L,,, and L<,r, and the main inductance L, can normally be effected according to the initially described method steps 1), 2) and 3) known per se, as well as the transformation of the variables, assuming an effective number of turns per phase on the rotor side, into the variables on the stator side written as primed in Fig. 2, the following is a detailed description of the determination of the ohmic rotor impedance Rr Of the asynchronous machine. Besides the three steps mentioned above, a fourth step is required for the determination of the ohmic rotor impedance R With reference to the simplified equivalent circuit diagram according to Fig. 2, the following equations apply:

(1) R,' = I U.' 1 - 1 T", 1 R,- being the ohmic rotor impedance referred to the stator side, Um being the voltage drop across the main inductance determined by the main inductance Lm and Iy being the current flowing through the rotor. A horizontal bar across a variable indicates that a complex value is represented.

Further, in known manner, the ohmic rotor impedance transformed to the stator side is given by:

(2) R,, = L,,,. R, 2 5 In this equation, L. is equal to L, + L,, and s stands for the slip of the asynchronous machine. As, during standstill of the asynchronous machine, the slip s is 1 and the measurements are made by using the dynamic main inductances, it can be shown that = Rr L + L, Dw (3) R, LDin The dynamic inductances LD, and L:,,, are known from the initially described step 3). Rr is unknown. It is assumed that L,,, is approximately equal to half the transient inductance L, In this fourth process step a test signal in the form of a phase voltage Usa consisting of a dc voltage with a superimposed, triangular ac voltage according to Fig. 4 is applied to a phase winding of the stator, and the resulting stator current I.. is measured.

The voltage drop U, ,across the main inductance can be expressed as:

(4) Un'i = U,, - R,. I, - jo). L,. - I,, For the rotor current Iy transformed to the stator side, the following equation then applies:

(5) T13 -cos 0 In this equation 0 is the phase displacement between Um and I,,. The arctangent (arctan) of the ratio of the 9 imaginary part to the real part of equation (4) gives the phase displacement a between U,,, and U,,. Denoting the phase displacement between U,, and Isa as 9, then 0 = (x + (p. The angle T can be determined by means of a discrete Fourier-transformation. For this purpose, the sampled values of the waveform of the current isa are multiplied by a complex e-function, whose exponent comprises the frequency o of the current ISa and whose oscillation is in phase with that of the test voltage. The sampled values are numerically integrated to a complex number, and the angle T results from the formation of the arctangent of the ratio of the real and imaginary parts of this number.

Adding a and (p gives 0 and thus, according to equation (5), the current Iy. As, in the simplified equivalent circuit diagram according to Fig. 2, Uir. and ISY are in phase, Rr is obtained from the quotient Um/!' To prevent current displacement, a low angular frequency co is used. However, too low an angular frequency causes the current to flow through the main inductance, not through the ohmic rotor impedance. It has turned out that a frequency in the range of the nominal slip frequency f,, usually in the range from 1 to 8 Hz, meets both requirements.

Further, the test signal voltage must be kept low with this frequency, as the impedance of the asynchronous machine during standstill is small. Non-linearities and dead times of the switching elements of the inverter mean, however, that its output current and thus also the stator current of the asynchronous machine are not proportional to the control voltage of the inverter, nor to a reference voltage of the control voltage, when the control voltage is controlled through a control device in dependence on a pre-set reference value. Thus, without measuring the output voltage of the inverter and the phase voltage Usa by means of an additional voltage sensor, at the same time, as the stator current and the phase current isa respectively, it is not possible through a mere measurement of the current I,, to deduce the associated phase voltage U,,,. Thus, before starting the measurement of the ohmic impedances and inductances of the asynchronous machine, a characteristic curve of the dependence of the output voltage of the inverter and/or the input voltage of the asynchronous machine on a reference value of the control voltage is determined, and the departure (the error) from a straight-line characteristic, which represents the ideal case, for each stator current I,, is stored. This departure is used for automatic correction of a test signal that determines the reference value of the control voltage.

The amplitude chosen for the direct current in the stator current I, determined by the test sianal U, is derived from a comparison between a characteristic of the dependency of the dynamic main inductance LD,, on the magnetizing current Im and the corresponding characteristic of the static main inductance Lm. These characteristics are shown in Fig. 3, the dash- and-dot line representing the dynamic main inductance LD,, and the solid line representing the static main inductance L, as a function of the magnetizing current 1,. The static inductance Lm is defined as the gradient of a straight line from the origin to the working point on the magnetizing curve, that is, through the relation (1),/Im, (Dm [Vs] being the main flux. The dynamic inductance, also called the differential inductance, corresponds to the gradient of the magnetizing curve at a predetermined point. The dynamic inductance can be expressed in known manner as follows:

dL,, (6) LDin. I,,, + L,, In step 3) of the known measurement process, the transient dynamic inductance LD,, was measured and used for calculating LDm. Based on these values, all other values must also be expressed as dynamic values. However, with regard to equation (3) the problem occurs that Rr must be determined through Um/I' According to equation (4), U' ly M 1 1 depends on, among other things, L,. However, L, is a static inductance, and as it is not known how this static 10 inductance is distributed between the leakage inductances 1 L,, and L,r, the transient dynamic inductance LDs cannot be calculated. For a completely accurate calculation of the ohmic rotor impedance, however, the transient dynamic inductance LDs should be used instead of the static inductance L;. To solve -this problem, the measurement is made at a direct current, at which the static main inductance L, is equal to the dynamic main inductance LDm.

The static transient inductance L., can be expressed in known manner as follows:

L 2 (7) ú, = L,,, + L. - - "' Lm + L, and the dynamic transient inductance LD,in known manner as follows:

2 (8) L = L +L - LDni Ds Din CS LDipi + L, 1 When LL),, and L, are equal, L, is equal to L[),. This means that with a suitable selection of the magnetizing current I, according to Fig. 3, the determined value of the inductance L., can be used as value for the dynamic inductance LDs.

12 - In Fig. 3 the dot-and-dash curve shows the dynamic main inductance LD,, and the solid line curve shows the Static Ma4 Ln inductance L, for different direct current amplitudes in an asynchronous machine with a nominal power output of 7.5 kW, an operating voltage of 380 V and an operating frequency of 50 Hz. The curves cross at a point at approximately 40% of the nominal magnetizing current Imr., which amounts to 14.64 A. At this point the dynamic and the static main inductances are equal. This means that the direct current of I,a should be set at approximately 40% of the nominal magnetizing current Im, for the measuring of the ohmic rotor impedance.

In the following, reference is made to Figs. 5 and 6.

T Lhe converter according to Fig. 5 controls the rotary speed of a three-phase asynchronous machine 1. For this purpose it comprises a bridge-rectifier 3 supplied from a three-phase current supply mains 2, and a direct current intermediate circuit 4, consisting of a choke coil 5 and a smoothing capacitor 6. Parallel to the smoothing capacitor 6 is arranged an ohmic voltage divider 7, from which, as actual value, a relatively low voltage is tapped as measure of the dc voltage 'Led to a three-phase inverter 8 in bridge configuration, having transistors, each with an anti-parallel connected diode, the relatively low voltage being passed to the comparator of a controller 11 by way of an A/D-converter 9 and a control unit 10, the components 9, 10 and 11 together forming a control device for the inverter 8. A current sensor 12 is connected with each of the input lines of the asynchronous machine 1.

Each current sensor 12 supplies the measurement value of one of the phase currents Ia, Ib and I, flowing through the phase windings a, b and c of the asynchronous machine 1 to the A/D-converter 9. Together with the control unit 10 and the current sensors 12, the A/D-converter 9 forms a current-measuring device 13, shown in Fig. 6. During 13 - standstill of the asynchronous machine, while the ohmic impedances and the inductivities/inductances of the phase windings a, b and c are measured, the phase currents Ib and I, have the same phase as the current I, and only half the amplitude of the phase current Ia- From the measured values of the three phase currents!a to I., the currentmeasuring device 13 calculates the stator current I,,, which consequently, apart from a proportionat-ity factor, corresponds to the phase current I,. The stator current I,, is supplied to a function unit 14, which, from the stator current I,,, calculates its amplitude and additionally also its phase displacement (p in relation to the voltage U,,, applied to the phase winding a as test signal. For this purpose, the stator current I., is sampled in the function unit 14. The sampled values are multiplied by a complex e-function, whose exponent contains the frequency o) = 2nf, of the current Isa and whose oscillation "I-s in phase with that of the current Isa, U-ref, determining this oscillation and fs being the test or slip frequency of the asynchronous machine 1. The sampled values are numerically integrated to a complex number. The phase displacement T is calculated through the formation of the quotient of the real and imaginary parts and the formation of the arctangent function of the quotient. The ohmic rotor impedance R, is then calculated in a function unit 15 from the amplitude of the stator current I,,, the phase displacement (p, the slip frequency I f, and the previously determined variables R, and L,.

To ensure in advance that the desired stator current Isa equal to Ia is determined by the correct phase voltage forming the test signal, independent of dead times and non-linearities of the inverter 8, which voltage is in turn determined by a corresponding reference voltage Uref, 14 - which is supplied to the controller 11, the departures or correction values, determined previously in connection with the formation of the current-voltage characteristic of the inverter 8, are stored in tabular form in a error correcting function unit 16 in dependence on the stator current I,a. The dc signal component (here about 40% of the nominal magnetizing current) is set in a function unit 17 on the basis of the nominal magnetizing current Im, and in dependence on the previously determined ohmic stator impedance Rs, and in a 'test signal generator 18 the dc signal has superimposed on it a triangular ac voltage, as shown in Fig. 4, whose frequency is equal to the slip IC frequency f, and then corrected in the error correction function unit 16 in dependence on the measured stator current I,,,, so that the result is the correct reference value Uref Of the control voltage of the inverter 8, and thus also the phase voltage Us, , corresponding to the stator current Isa.

After determination of the correct reference value Uret and consequently also the phase voltage Usar the control unit 10 or the function unit 15 contained in the control unit 10 calculates the voltage drop U,,according to equation (4), and, in the function unit 15, after determining the angle 0 by means of the angle (p, the rotor current I, _Y. is calculated according to equation (5), and the ohmic rotor impedance Rr according to (1) is calculated on the basis of equations (4) and (5), and the ohmic rotor impedance Rr is calculated on the basis of the previously determined inductances according to equation (3).

The test signal Us,, shown in Fig. 4 is shown as a triangular signal, but can instead be in the form of a rectangular pulse or a sine wave, and is applied until the resulting stator current has stabilized, that is, until the phase displacement (p and the amplitude of the stator current Isa have stabilized. The duration, for which the h_est signal is applied is about 5 seconds, but depends on the size of the asynchronous machine.

Carrying out L-he measuring process according to the invention on an asynchronous machine of 7.5 kW, an operat;Lng voltage of 380 V and an operating frequency of Hz gave the following values during the three initially described steps: R, = 0.65 Ohm, L, = 8.3 mH and Lr,, = 88.7 mH. Based on this, the dynamic inductance LD, was calculated to be 92.7 mH. To determine the transformed ohmic rotor impedance, the frequency of the test signal U,a was set at the nominal slip frequency f, = 2 Hz. Af ter correction in the error correction function unit 16, the test signal U, had a magnitude of 21 V. The result of the calculation of the phase displacement (p was -0.226 rad and the amplitude of the stator current I,, = 20.4 A. For R, this resulted in a value of 0.39 Ohm, and in accordance with equation (3) for Rr a value of 0.44 Ohm. Compared with the correct value of the ohmic rotor impedance of 0.45 Ohm, the error was approximately 2.3 %, which is a typical value with this method, and which is sufficiently accurate for an inverter with field oriented control, as in the present case.

The ohmic rotor impedance RT, determined at a predetermined temperature T1 can be recalculated to an ohmic rotor impedance RT2 at a different temperature T2 by means of equation (9):

(9) R, = R ' T2 + KT 2 TI T, +KT In this equation, KT is a material constant (in the case of copper, for example, KT = 235, when the operating temperatures T1 and T2 are measured in 'C).

Equation (9), however, assumes that the second temperature T2 is known, which is not always the case. BY means of the method according to the invention, however, the ohmic rotor impedance can be determined during a short standstill of the asynchronous machine, without knowledge of the temperature.

List of the physical variables Usa Test signal, phase voltage, stator voltage Isa Phase current, stator current, phase signal a, Ib, Ic Phase currents in the stator U, Voltage across main inductance 1, Magnetizing current Imr. Nominal magnetizing current Isy Rotor current RS Ohmic stator impedance Rr Ohmic rotor impedance Uref Reference voltage L, Static main inductance LD,, Dynamic main inductance L, Stator inductance (L,+L,,,) L,,, Stator leakage inductance L,,, Rotor leakage inductance Transformed main inductance L:D. Transformed dynamic main inductance 1:[), Transformed dynamic transient inductance f - cd) S' Transformed transient inductance (L,,+L tim Voltage drop across the transformed main inductance I M Current through the transformed main inductance I SY Transformed rotor current R r Transformed rotor impedance 0 Phase displacement between U m and Isa cc Phase displacement between hen Usa and U M (P Phase displacement between Usa and Isa 0) Angular frequency 27rf,, f, Test and nominal slip frequency, S Slip (DM Main flux Ti, T2 Operating temperatures of the asynchronous machine RTI RT2 Ohmic impedances at different operatLng temperatures 5 KT Material constant of the conductor material of the rotor

Claims

C L A I M S:

1. A method for the automatic measurement of the ohmic rotor impedance of an asynchronous machine controlled by means of an inverter while the machine is -ating field, in which method:

acted upon by a non-rot a. the ohmic s.'t--ator impedance, the leakage inductances and the main inductance of the asynchronous machine are measured, b. a test signal consisting of a predetermined dc signal with a superimposed ac signal is supplied to a phase winding of the asynchronous machine, the frequency of the ac signal corresponding approximately to the nominal slip frequency of the asynchronous machine, c. the amplitude and the phase of the phase signal resulting from the test signal are measured, and d. the ohmic rotor impedance is calculated from the measured values according to a) and c).

2. A method according to claim 1, wherein the ohmic rotor impedance transformed to the stator side is determined first, and the actual ohmic rotor impedance is calculated bv means of the measurement values according to a) and c).

3. A method according to claim 1 or 2, wherein the frequency of the ac signal is in the range from 1 to 8 Hz inclusive.

4. A method according to any one of claims 1 to 3, wherein the de signal is a dc voltage, which is chosen so that the direct current driven by it is less than half the nominal magnetizing current of the asynchronous machine.

5. A method according to claim 4, wherein the magnitude of the direct current is chosen so that the dynamic main inductance is approximately equal to the static main inductance of the asynchronous machine.

6. A method according to any one of claims 1 to 5, wherein the test signal is a phase voltage the reference value of which is derived and set on the basis of a previously measured characteristic, stored in a memory, the characteristic representing the relation of the phase current and the reference value.

1. A method for the automatic measurement of the ohmic impedance of an asynchronous machine controlled by means of an inverter while the machine is acted upon by a non-rotating field, the method being substantially as herein described with reference to, and as illustrated by, the accompanying drawings.

8. An asynchronous machine controlled by means of an inverter arranged to carry out a method according to any one of the preceding claims.

9. A machine as claimed in claim 8, substantially as herein described with reference to, and as illustrated by, Figures 5 and 6 of the accompanying drawings.

I 1