KR102477114B1 - Method and apparatus for predicting bearing volatage characteristic of three phase squirrel-cage induction motor - Google Patents

Abstract

The present invention provides a method for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor reflecting frequency-dependent characteristics. A method for predicting bearing voltage characteristics of a three-phase cage-type induction motor according to an embodiment of the present invention measures between a common mode voltage applied to windings of the three-phase cage-type induction motor and a bearing voltage generated in the bearing of the three-phase cage-type induction motor. obtaining bearing voltage ratio (BVR) measurement data for each frequency and impedance measurement data for each frequency measured between the winding, frame, and shaft end of the three-phase squirrel cage induction motor, respectively, and the BVR measurement data for each frequency and modeling an equivalent circuit corresponding to the three-phase cage-type induction motor based on the impedance measurement data for each frequency; bearings generated in the bearing according to frequency in the three-phase cage-type induction motor using the equivalent circuit; It includes predicting the voltage. According to the present invention, bearing voltage characteristics of a three-phase cage-type induction motor can be more practically and accurately predicted by reflecting frequency-dependent characteristics.

Description

Method and apparatus for predicting bearing voltage characteristics of three-phase squirrel cage induction motor

The present invention relates to a method for predicting bearing voltage characteristics of a three-phase cage-type induction motor.

Recently, a pulse width modulation (PWM) inverter is mainly used in a variable speed motor drive system that is frequently used, and in this case, a high common mode voltage is applied to the windings of the motor. Common mode noise voltage/current, shaft voltage, bearing voltage, etc. are problems caused by high voltage applied to the winding, where the bearing voltage induces partial discharge current inside the bearing connected to the motor shaft. . The partial discharge current serves as an electric discharge machining (EDM) current inside the bearing, which can cause wear inside the bearing and significantly reduce its life.

Recently, various studies have been conducted on a method for modeling an equivalent circuit of such a bearing voltage and a method for reducing it. Examples of conventional reduction methods include methods such as adding a common mode voltage reduction filter between a PWM voltage output terminal and a motor input terminal, or inserting an electrostatic shield to reduce voltage coupling inside the motor. These methods are commonly designed by assuming a bearing voltage ratio (BVR) as a constant. However, the actual BVR has characteristics dependent on the common mode voltage frequency, and for this reason, existing research methods may have problems in predicting the bearing voltage when controlling PWM using a high frequency switching frequency.

Republic of Korea Patent Registration No. 10-1945463 (published on January 29, 2019)

The present invention provides a method and apparatus for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor reflecting frequency-dependent characteristics.

A method for predicting bearing voltage characteristics of a three-phase cage-type induction motor according to an embodiment includes a frequency measured between a common mode voltage applied to windings of the three-phase cage-type induction motor and a bearing voltage generated in a bearing of the three-phase cage-type induction motor. Obtaining bearing voltage ratio (BVR) measurement data and impedance measurement data for each frequency measured between windings, a frame, and a shaft end of the three-phase squirrel cage induction motor, respectively, the BVR measurement data for each frequency and the Modeling an equivalent circuit corresponding to the three-phase cage-type induction motor based on impedance measurement data for each frequency; and calculating a bearing voltage generated in the bearing according to frequency in the three-phase cage-type induction motor using the equivalent circuit. involves predicting.

The equivalent circuit includes lead inductances respectively connected between the three-phase inputs of the three-phase cage-type induction motor and the windings, single-phase impedances respectively connected to the three-phase inputs and the lead inductances, and the windings and the three-phase cage-type induction motor. Winding-rotor capacitance respectively connected between the rotors of the motor, winding-stator capacitance connected between the windings and the stator of the three-phase cage type induction motor, respectively, and rotor-stator capacitance connected between the stator and the rotor and a shaft inductance connected between the rotor and the shaft end, and a frame inductance and frame resistance connected between the stator and the frame.

The single-phase impedance may include parallel resistance between conductors, capacitance between conductors connected in parallel with the parallel resistance between conductors, and series resistance between conductors.

The impedance measurement data includes a common mode impedance measured between the winding and the frame, a winding-shaft impedance measured between the winding and the shaft end, and a shaft-frame impedance measured between the shaft end and the frame. can include

The winding-stator capacitance may be determined based on the common mode impedance at a low frequency band frequency.

The inter-conductor capacitance may be determined based on a resonant frequency in an intermediate frequency band, a leakage inductance of the stator, and a leakage inductance of the rotor.

The lead inductance and the frame inductance may be determined based on the common mode impedance measured in a high frequency band and the BVR data for each frequency in the high frequency band.

The shaft inductance may be determined based on the shaft-frame impedance and the frame inductance measured in the high frequency band.

The winding-rotor capacitance and the winding-stator capacitance may be determined based on the BVR measurement data measured in a low frequency band and the winding-shaft impedance measured in a low frequency band.

In a low frequency band, BVR may be determined based on the winding-rotor capacitance and the rotor-stator capacitance.

In the middle band, BVR can be determined based on the winding-rotor capacitance, the rotor-stator capacitance, the winding-stator capacitance, and the conductor-to-conductor capacitance.

An apparatus for predicting bearing voltage characteristics of a three-phase cage-type induction motor according to an embodiment is a computing device having one or more processors and a memory storing one or more programs executed by the one or more processors, wherein the one or more processors include: , Bearing Voltage Ratio (BVR) measurement data measured between the common mode voltage applied to the windings of the three-phase cage-type induction motor and the bearing voltage generated in the bearing of the three-phase cage-type induction motor, and the three-phase cage-type induction motor Acquiring impedance measurement data for each frequency measured between the winding, frame, and shaft end of each, and based on the BVR measurement data for each frequency and the impedance measurement data for each frequency, an equivalent circuit corresponding to the three-phase squirrel cage induction motor modeling, and predict the bearing voltage generated in the bearing according to the frequency in the three-phase cage-type induction motor using the equivalent circuit.

The equivalent circuit includes lead inductances respectively connected between the three-phase inputs of the three-phase cage-type induction motor and the windings, single-phase impedances respectively connected to the three-phase inputs and the lead inductances, and the windings and the three-phase cage-type induction motor. Winding-rotor capacitance respectively connected between the rotors of the motor, winding-stator capacitance connected between the windings and the stator of the three-phase cage type induction motor, respectively, and rotor-stator capacitance connected between the stator and the rotor and a shaft inductance connected between the rotor and the shaft end, and a frame inductance and frame resistance connected between the stator and the frame.

The single-phase impedance may include parallel resistance between conductors, capacitance between conductors connected in parallel with the parallel resistance between conductors, and series resistance between conductors.

The impedance measurement data includes a common mode impedance measured between the winding and the frame, a winding-shaft impedance measured between the winding and the shaft end, and a shaft-frame impedance measured between the shaft end and the frame. can include

The winding-stator capacitance may be determined based on the common mode impedance at a low frequency band frequency.

The inter-conductor capacitance may be determined based on a resonant frequency in an intermediate frequency band, a leakage inductance of the stator, and a leakage inductance of the rotor.

The lead inductance and the frame inductance may be determined based on the common mode impedance measured in a high frequency band and the BVR data for each frequency in the high frequency band.

The shaft inductance may be determined based on the shaft-frame impedance and the frame inductance measured in the high frequency band.

The winding-rotor capacitance and the winding-stator capacitance may be determined based on the BVR measurement data measured in a low frequency band and the winding-shaft impedance measured in a low frequency band.

In a low frequency band, BVR may be determined based on the winding-rotor capacitance and the rotor-stator capacitance.

In the middle band, BVR can be determined based on the winding-rotor capacitance, the rotor-stator capacitance, the winding-stator capacitance, and the conductor-to-conductor capacitance.

According to the present invention, bearing voltage characteristics of a three-phase cage-type induction motor can be more practically and accurately predicted by reflecting frequency-dependent characteristics.

1 is an exemplary diagram of bearing voltage and current paths in a three-phase cage-type induction motor according to an embodiment;
2 is an exemplary diagram of settings for measuring bearing voltage ratio (BVR) data for each frequency and impedance data for each frequency in a three-phase squirrel cage induction motor according to an embodiment.
3 is an exemplary diagram of BVR measurement data for each frequency according to an embodiment;
4 to 6 are examples of impedance measurement data for each frequency according to an embodiment. FIG. 4 is a common mode impedance for each frequency, FIG. 5 is a winding-shaft impedance for each frequency, and FIG. 6 is an example of shaft-frame impedance for each frequency. do
7 is an equivalent circuit diagram of a three-phase squirrel cage induction motor reflecting frequency dependent characteristics according to an embodiment.
8 is a single-phase impedance equivalent circuit diagram according to an embodiment
9 is an exemplary diagram of a BVR characteristic prediction circuit model using only motor design dimensions according to an embodiment
10 is a flowchart illustrating a method for predicting bearing voltage characteristics of a three-phase cage-type induction motor according to the present invention according to an embodiment.
11 is a result of comparing common mode impedance derived by simulation and actually measured impedance according to an embodiment.
12 is a result of comparing BVR derived by simulation and actually measured BVR according to an embodiment.
13 is a result of comparing a bearing voltage waveform derived by simulation according to an embodiment with a bearing voltage waveform actually measured
14 to 17 are comparison results of bearing voltage time axis waveform measurements and simulations according to an embodiment.
18 is an exemplary view of a FEM model for calculating BVR characteristic prediction circuit model element values according to an embodiment.
19 is a comparison result between predicted BVR characteristics and measured data according to an embodiment.
20 is a block diagram for illustrating and describing a computing environment 10 including a computing device according to an exemplary embodiment.

Hereinafter, specific embodiments will be described with reference to the drawings. The detailed descriptions that follow are provided to provide a comprehensive understanding of the methods, devices and/or systems described herein. However, this is only an example and disclosed embodiments are not limited thereto.

In describing the embodiments, if it is determined that a detailed description of a related known technology may unnecessarily obscure the gist of the disclosed embodiments, the detailed description will be omitted. In addition, terms to be described later are terms defined in consideration of functions in the disclosed embodiments, which may vary according to intentions or customs of users or operators. Therefore, the definition should be made based on the contents throughout this specification. Terminology used in the detailed description is only for describing the embodiments and should in no way be limiting. Unless expressly used otherwise, singular forms of expression include plural forms. In this description, expressions such as "comprising" or "comprising" are intended to indicate any characteristic, number, step, operation, element, portion or combination thereof, one or more other than those described. It should not be construed to exclude the existence or possibility of any other feature, number, step, operation, element, part or combination thereof.

Hereinafter, a method for predicting bearing voltage characteristics of the three-phase cage-type induction motor 1 reflecting frequency-dependent characteristics will be described.

1 is an exemplary view showing bearing voltage and current paths in a three-phase cage-type induction motor 1 according to an embodiment.

The bearing voltage is a potential difference between the shaft end 30 and the motor frame 20. As shown in Figure 1, the cause of the bearing voltage is a non-zero common mode (CM) input, which is positively transmitted through the stator 50, the air gap, and the rotor 40 surface. transmitted to the shaft end. Thus, the bearing voltage can be expressed as a common mode voltage and a bearing voltage ratio (BVR).

In the prior art, BVR was expressed by an equation consisting of some stray capacitance, so that once the capacitance was calculated, a frequency-independent BVR value was calculated.

The method of reducing the bearing voltage using a simple BVR formula was previously valid, but since the transfer impedance between the common mode input and the shaft end has a frequency-dependent characteristic, the increasing driving bandwidth reflects the variation of the bearing voltage due to frequency. ask to do Frequency-domain measurement data of the bearing voltage show that as the frequency increases to tens of kilohertz (kHz), the BVR value differs from that at that low frequency.

Because of this dependence, the conventional BVR formula is no longer accurate in predicting the bearing voltage when a common mode input voltage with a high frequency is applied. Therefore, it is necessary to analyze the BVR in frequency units for more accurate prediction. For this purpose, the present invention provides an equivalent circuit model capable of describing the frequency-dependent bearing voltage.

2 is a diagram illustrating settings for measuring BVR data for each frequency and measuring impedance data for each frequency in a three-phase squirrel cage induction motor according to an embodiment.

In order to reflect the characteristics of the BVR that varies according to the frequency, first, the BVR in the frequency domain is measured. For example, a 1.5 kW three-phase induction motor can be used for measurement. The motor has fully insulated bearings 60 that are always capacitive regardless of operating conditions. A 2-port vector network analyzer (VNA) can be used to derive the S-parameter matrix.

However, the motor is not necessarily limited to an insulated bearing and may be variously changed according to circumstances for measuring characteristics of the motor. For example, it can also be applied to an electric motor equipped with a rotating general bearing.

Then, the S-parameters are converted into a Z-parameter (impedance parameter) matrix. When the motor is operational, port 2 is open and I ₂ = 0. Thus, Equation 1 below is derived.

Equation 2 below can be derived from Equation 1.

By applying Equation 2 to the impedance parameter, BVR data can be obtained as shown in FIG. 3 .

3 is an exemplary diagram of BVR measurement data for each frequency according to an embodiment.

Referring to FIG. 3, the BVR value is constant below 30 kHz. However, around 60 kHz, the reduced BVR value is maintained up to 5 MHz. Above 5 MHz, the BVR increases.

The frequency-dependent characteristic of a BVR as shown in FIG. 3 can be explained in this way. In the low frequency band, BVR has a constant value. However, as the frequency exceeds 60 kHz, leakage inductance and capacitance between conductors, which were not considered due to relatively low impedance, become effective. At this time, a portion of the common mode voltage drops due to inductance, which causes a decrease in bearing voltage. Above 160 kHz, the impedance of the leakage inductance can be neglected by the reduced parallel impedance of the inter-conductor capacitance. The successive combination of inter-conductor capacitance and other parasitic capacitance then maintains a lowered BVR value until the inductance of the winding leads and the frame inductance become dominant. Then, in the region of 5 MHz or higher, the common mode voltage is mainly influenced by winding leads and frame inductance, and BVR changes according to a value determined by the inductance.

Thereafter, in order to determine the value of each element in the equivalent circuit, impedance data for each frequency of the 3-phase induction motor is measured.

4 to 6 are examples of impedance measurement data for each frequency according to an embodiment. FIG. 4 is a common mode impedance (Z _CM ) for each frequency, FIG. 5 is a winding-shaft impedance (Z _ew ) for each frequency, and FIG. 6 is It is an exemplary diagram of shaft-frame impedance (Z _fe ) for each frequency.

Values of each element of the equivalent circuit are derived from impedance data for each frequency measured as shown in FIGS. 4 to 6 , and the equivalent circuit can be modeled through these element values.

7 is an equivalent circuit diagram of a three-phase cage-type induction motor 1 reflecting frequency dependent characteristics according to an embodiment.

The equivalent circuit of FIG. 7 is designed based on the T-equivalent circuit, and the node in the dotted line represents the middle position of each winding 5 of the 3-phase motor 1. In addition, lead inductance L _lead is the lead wire inductance of each input terminal of winding 5, C _sw,u , C _sw,v , C _sw,w are winding-stator capacitance for each u, v, w phase, , C _rw,u , C _rw,v , C _rw,w are the winding-rotor capacitances for each u, v, w phase. C _sr is the rotor-stator capacitance, and L _DE is the inductance caused by the conduction distance from the axial center point of the surface of the rotor 40 to the drive end (DE) 32 of the shaft. L _frame and R _frame are inductance and resistance caused by the conduction distance from the axial central point of the inner surface of the stator 50 to the position of the frame 20 closest to the shaft DE 32.

Since the equivalent circuit in this document assumes a balanced three-phase circuit (the impedance components of each phase are the same), the middle positions of each winding 5 in FIG. can be achieved

8 is a single-phase impedance equivalent circuit diagram according to an embodiment.

Half of the impedance of the circuit of FIG. 8 corresponds to 1/2*Z _ph,u , 1/2*Z _ph,v , and 1/2*Z _ph,w of FIG. 7 . The dotted line in this circuit diagram is a single-phase low-frequency equivalent circuit of a widely used three-phase cage-type induction motor, and the components of the circuit are well-known elements, so a description thereof will be omitted. Other elements C _tt , R _tt,s , R _tt,p represent the equivalent inter-conductor capacitance, series resistance, and parallel resistance, respectively.

Element values of each circuit of FIGS. 7 and 8 may be determined from BVR measurement data and impedance measurement data obtained as shown in FIGS. 3 to 6 .

Common mode impedance (Z _cm ) in a low frequency band of 10 kHz or less has a capacitive characteristic. Using this characteristic, the winding-stator capacitance (C _SW ) value can be determined as shown in Equation 4 below.

In Equation 4, f _lf means an arbitrary frequency value in a low frequency band.

When using the resonant frequency (170 kHz of FIG. 4) of the common mode impedance in the middle frequency band (10 kHz to 1 MHz), the inter-conductor capacitance (C _tt ) can be determined as shown in Equation 5 below.

In Equation 5, fsr denotes a resonant frequency in the intermediate frequency band, and L _ls and L _lr are leakage inductances of the stator 50 and the rotor 40. Also, Equation 5 can be derived using parallel LC resonance characteristics of inter-conductor capacitance and winding leakage inductance.

In a high-frequency band of 10 MHz or higher, the common mode impedance (Z _cm ) shows characteristics of an inductor and can be determined as shown in Equation 6 below.

In Equation 6, f _hf means an arbitrary frequency in a high frequency band, and referring to FIG. 7 from the point of view of common mode input impedance, since it is interpreted as a structure in which three identical components are connected in parallel, 1/3 of L _lead It multiplies. In addition, the BVR value in the same frequency band is determined by Equation 7 below.

By combining Equation 6 and Equation 7, the values of L _lead and L _frame can be obtained. The value of L _DE can be obtained as shown in Equation 8 below using the value of L _frame obtained through Equations 6 and 7 and the high-frequency value of the shaft-frame impedance (Z _fe ).

The values of C _sr and C _rw can be calculated by combining Equations 9 and 10 below using the low-frequency band characteristics of BVR and winding-shaft impedance (Zew).

Resistance values of the single-phase equivalent impedance of FIG. 8 may be calculated as shown in Equations 11 to 13 below using each impedance value at the resonant frequency.

In the case of a general three-phase PWM inverter, since the switching frequency is only a few tens of kHz at most, the characteristics of the high frequency band (10 MHz or more) among the BVR frequency characteristics can be ignored in the prediction. Therefore, when predicting the BVR characteristics, the main attention is paid to the BVR value in the low frequency band (BVR _lf ), the BVR value in the middle band (BVR _mf ), and the boundary frequency f _t between the two.

9 is an exemplary diagram of a circuit model for predicting BVR characteristics using design dimensions of a motor according to the present invention according to an embodiment.

The approximate common mode input impedance is calculated using the circuit of FIG. 9 and the relationship C _sw >> C _rw + C _sr as shown in Equation 14 below.

In Equation 14, Z _ph is approximated as in Equation 15 below, and L _l = L _ls + L _lr .

The magnetizing inductance and other elements of the single-phase impedance (Z _ph ) of FIG. 9 can be ignored since they have a relatively small impedance in approximate calculation. The impedance between the middle position of the winding and the motor frame 20 can be calculated as shown in Equation 16 below.

In addition, the voltage at the middle position of the winding is shown in Equation 17 below.

Equation 17 is derived through the voltage division equation between the input terminal and the winding middle position voltage. If the bearing voltage is obtained using Equation 17, Equation 18 is shown below.

BVR is calculated using Equation 18 as Equation 19 below.

Substituting Equations 14 and 16 into Equation 19 gives Equation 20 below.

When BVR _lf , BVR _mf , and f _t are obtained using Equation 20, the following Equations 21 to 23 are obtained.

However, as described above, the boundary frequency f _t is not limited to the middle of BVR _lf and BVR _mf and may be variously changed according to design and modeling purposes.

10 is a flowchart illustrating a method for predicting bearing voltage characteristics of a three-phase cage-type induction motor 1 according to the present invention according to an embodiment.

A method for predicting bearing voltage characteristics of a three-phase cage-type induction motor (1) according to the present invention relates to a common mode voltage (V _cm ) applied to a winding (5) and a bearing (60) in a three-phase cage-type induction motor (1). BVR measurement data for each frequency measured between the generated bearing voltage (V _b ) and impedance for each frequency measured between the winding (5), frame (20), and shaft end (30) of the three-phase cage-type induction motor (1) Obtaining measurement data (S910), modeling an equivalent circuit corresponding to the three-phase squirrel cage induction motor 1 based on the BVR measurement data for each frequency and the impedance measurement data for each frequency (S920), and and estimating the bearing voltage (V _b ) generated in the bearing 60 according to the frequency in the three-phase squirrel cage induction motor 1 using the method (S930).

According to one embodiment of the present invention, as shown in FIG. 7, the equivalent circuit is between the three-phase inputs (U, V, W-phase inputs) of the three-phase cage-type induction motor (1) and the winding (5). The lead inductance (L _lead ) connected to each, the single-phase impedance (Z _ph ) connected to each of the three-phase input and lead inductance (L _lead ), the winding (5) and the rotor (40) of the three-phase squirrel cage induction motor (1) ), winding-rotor capacitance (C _rw ), winding-stator capacitance (C _sw ), respectively connected between the winding 5 and the stator 50 of the three-phase squirrel cage induction motor (1), and the stator ( 50) and the rotor-stator capacitance (C _sr ) connected between the rotor 40, the shaft inductance (L _DE ) connected between the rotor 40 and the shaft end 30, and the stator 50 and the frame (20) may include a frame inductance (L _frame ) and a frame resistance (R _frame ) connected between them.

According to an embodiment of the present invention, the single-phase impedance (Zph) is, as shown in FIG. 8, a conductor connected in parallel with the parallel resistance between conductors (R tt, _p ) and the parallel resistance between conductors (R _tt,p ) capacitance between conductors (C _tt ) and series resistance between conductors (R _tt,s ).

According to an embodiment of the present invention, the impedance measurement data is the common mode impedance (Z _cm ) measured between the winding 5 and the frame 20, and the winding- It may include a shaft impedance (Z _ew ) and a shaft-frame impedance (Z _fe ) measured between the shaft end 30 and the frame 20 .

According to an embodiment of the present invention, the winding-stator capacitance (C _sw ) may be determined based on the common mode impedance (Z _cm ) in a low frequency band. For example, the winding-stator capacitance (C _sw ) can be determined as in Equation 4.

According to an embodiment of the present invention, the inter-conductor capacitance (C _tt ) is the resonant frequency (f _sr ) in the intermediate frequency band, the leakage inductance (L _ls ) of the stator 50, and the leakage inductance (L ) of the rotor 40 _lr ) can be determined based on. For example, the inter-conductor capacitance (C _tt ) may be determined as in Equation 5.

According to an embodiment of the present invention, the lead inductance (L _lead ) and the frame inductance (L _frame ) are the common mode impedance (Z _cm (f _hf )) measured in the high frequency band and the BVR data (BVR (f _hf ) in the high frequency band). ))). For example, the lead inductance (L _lead ) and the frame inductance (L _frame ) may be determined by Equations 6 and 7.

According to an embodiment of the present invention, the shaft inductance (L _DE ) may be determined based on the shaft-frame impedance (Z _fe (f _hf )) and the frame inductance (L _frame ) measured in a high frequency band. For example, the shaft inductance (L _DE ) may be determined by Equation 8.

According to an embodiment of the present invention, winding-rotor capacitance (C _rw ) and winding-stator capacitance (C _sr ) are BVR measurement data (BVR(f _lf )) for each frequency measured in a low frequency band and measured in a low frequency band It can be determined based on the winding-shaft impedance Z _ew (f _lf ). For example, winding-rotor capacitance (C _rw ) and winding-stator capacitance (C _sr ) can be determined by Equations (9) and (10).

According to an embodiment of the present invention, BVR (BVR _lf ) in a low frequency band may be determined based on winding-rotor capacitance (C _rw ) and rotor-stator capacitance (C _sr ). For example, BVR (BVR _lf ) in a low frequency band may be determined as in Equation 21.

According to an embodiment of the present invention, BVR (BVR _mf ) in the middle band is the winding-rotor capacitance (C _rw ), the rotor-stator capacitance (C _sr ), the winding-stator capacitance (C _sw ), and the inter-conductor capacitance (C _tt ) It can be determined based on. For example, BVR (BVR _mf ) in the middle band may be determined by Equation 22.

11 to 13 are results of comparing data predicted by reflecting frequency-dependent characteristics according to the present invention with actually measured data, and FIG. 11 is a result of comparing common mode impedance derived by simulation with actually measured impedance. 12 is a result of comparing the BVR derived by simulation with the actually measured BVR, and FIG. 13 is a result of comparing the bearing voltage waveform derived by simulation with the actually measured bearing voltage waveform.

Element values derived from modeling of the equivalent circuit described above are as follows.

L _lead = 459.4nH,

_Ctt = 153.7pF,

R _tt,s = 52.77Ω,

R _tt,p = 4.53 kΩ,

C _sw = 4758.6pF,

C _{r w} = 28.1 pF,

Csr = _651pF ,

L _DE = 74.774nH,

_Lframe = 10.9nH,

R _frame = 100 mΩ

Comparison results of frequency-axis common mode input impedance and BVR calculated by applying the above values to the equivalent circuit of FIG. 7 and measurement data are shown in FIGS. 11 and 12 .

Meanwhile, the time-axis waveform comparison result of the bearing voltage is shown in FIG. 13 .

14 to 17 are bearing voltage time-axis waveform measurement and simulation comparison results according to an embodiment.

According to an embodiment, after applying a square wave voltage of 20V peak-to-peak and four basic frequencies (f _f =10kHz, 60kHz, 100kHz, 200kHz) to the motor 1 to verify the BVR frequency-axis characteristics, Bearing voltage time axis waveform measurement and simulation comparison results are shown in FIGS. 14 to 17 .

Figure 14 is a bearing voltage waveform at f _f =10kHz, BVR _meas =0.053, BVR _sim =0.064, Figure 15 is a bearing voltage waveform at f _f =60kHz, BVR _meas =0.066, BVR _sim =0.076, Figure 16 is f Bearing voltage waveforms at _f =100kHz, BVR _meas =0.042, BVR _sim =0.037, Figure 17 shows the bearing voltage waveforms at f _f =200kHz, BVR _meas =0.018, BVR _sim =0.017, and each BVR value is peak Calculated based on -to-peak magnitude.

Element values of FIG. 9 necessary for predicting bearing voltage characteristics (BVR) using Equations 21 to 23 may be calculated using a finite element method (FEM). An example model used for calculation is shown in FIG. 18 .

18 is an exemplary diagram of a FEM model for calculating device values of a BVR characteristic prediction circuit model according to an embodiment.

The example models of FIG. 18 were designed using the design dimensions of example motors used for measurement. The 3D model in (a) of FIG. 18 was used to calculate C _rw , C _sr , and C _sw , and the 2D cross-sectional model in (b) was used to calculate C _tt . The calculated element values are as follows.

_Ctt = 182.2pF,

Csw = 4755.3pF,

Crw = 26.9pF,

Csr = 633pF

19 is a comparison result between predicted BVR characteristics and measured data according to an embodiment.

The comparison result of the bearing voltage characteristic (BVR) predicted according to an embodiment and the measured data is shown in FIG. 19.

20 is a block diagram illustrating and describing a computing environment 10 including a computing device according to an exemplary embodiment.

In the illustrated embodiment, each component may have different functions and capabilities other than those described below, and may include additional components other than those described below.

The illustrated computing environment 10 includes a computing device 12 . In one embodiment, the computing device 12 may be a bearing voltage characteristic predictor.

Computing device 12 includes at least one processor 14 , a computer readable storage medium 16 and a communication bus 18 . Processor 14 may cause computing device 12 to operate according to the above-mentioned example embodiments. For example, processor 14 may execute one or more programs stored on computer readable storage medium 16 . The one or more programs may include one or more computer-executable instructions, which when executed by processor 14 are configured to cause computing device 12 to perform operations in accordance with an illustrative embodiment. It can be.

Computer-readable storage medium 16 is configured to store computer-executable instructions or program code, program data, and/or other suitable form of information. Program 20 stored on computer readable storage medium 16 includes a set of instructions executable by processor 14 . In one embodiment, computer readable storage medium 16 includes memory (volatile memory such as random access memory, non-volatile memory, or a suitable combination thereof), one or more magnetic disk storage devices, optical disk storage devices, flash memory devices, other forms of storage media that can be accessed by computing device 12 and store desired information, or any suitable combination thereof.

Communications bus 18 interconnects various other components of computing device 12, including processor 14 and computer-readable storage medium 16.

Computing device 12 may also include one or more input/output interfaces 22 and one or more network communication interfaces 26 that provide interfaces for one or more input/output devices 24 . An input/output interface 22 and a network communication interface 26 are connected to the communication bus 18 . Input/output device 24 may be coupled to other components of computing device 12 via input/output interface 22 . Exemplary input/output devices 24 include a pointing device (such as a mouse or trackpad), a keyboard, a touch input device (such as a touchpad or touchscreen), a voice or sound input device, various types of sensor devices, and/or a photographing device. input devices, and/or output devices such as display devices, printers, speakers, and/or network cards. The exemplary input/output device 24 may be included inside the computing device 12 as a component constituting the computing device 12, or may be connected to the computing device 12 as a separate device distinct from the computing device 12. may be

Meanwhile, embodiments of the present invention may include a program for performing the methods described in this specification on a computer, and a computer readable recording medium including the program. The computer readable recording medium may include program instructions, local data files, local data structures, etc. alone or in combination. The media may be specially designed and configured for the present invention, or may be commonly available in the field of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and specially configured to store and execute program instructions such as ROM, RAM, and flash memory. Hardware devices are included. Examples of the program may include not only machine language codes generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter.

Although representative embodiments of the present invention have been described in detail above, those skilled in the art will understand that various modifications are possible to the above-described embodiments without departing from the scope of the present invention. . Therefore, the scope of the present invention should not be limited to the described embodiments and should not be defined, and should be defined by not only the claims to be described later, but also those equivalent to these claims.

1: 3-phase squirrel cage induction motor
5: Winding
20: frame
30: shaft end
40: rotor
50: stator
60: bearing

Claims (22)

Bearing Voltage Ratio (BVR) measurement data for each frequency measured between the common mode voltage applied to the winding of the three-phase cage-type induction motor and the bearing voltage generated in the bearing of the three-phase cage-type induction motor and the three-phase cage-type induction motor Acquiring impedance measurement data for each frequency measured between windings, frames, and shaft ends of the motor;
modeling an equivalent circuit corresponding to the three-phase squirrel cage induction motor based on the BVR measurement data for each frequency and the impedance measurement data for each frequency; and
A method of predicting bearing voltage characteristics of a three-phase cage-type induction motor, comprising predicting a bearing voltage generated in the bearing according to a frequency in the three-phase cage-type induction motor using the equivalent circuit.
According to claim 1,
The equivalent circuit is
lead inductances respectively connected between the three-phase input of the three-phase squirrel cage induction motor and the windings;
single-phase impedances respectively connected to the three-phase input and the lead inductance;
winding-rotor capacitances respectively connected between the windings and the rotor of the three-phase cage-type induction motor;
winding-stator capacitances respectively connected between the windings and the stator of the three-phase cage-type induction motor;
a rotor-stator capacitance coupled between the stator and the rotor;
a shaft inductance connected between the rotor and the shaft end; and
A method for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor, comprising frame inductance and frame resistance connected between the stator and the frame.
According to claim 2,
The single-phase impedance is,
parallel resistance between conductors; and
A method for predicting bearing voltage characteristics of a three-phase cage-type induction motor, including the inter-conductor capacitance and the series resistance between conductors connected in parallel with the parallel resistance between conductors.
According to claim 3,
The impedance measurement data,
common mode impedance measured between the winding and the frame;
winding-shaft impedance measured between the winding and the shaft end; and
A method for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor, comprising a shaft-frame impedance measured between the shaft end and the frame.
According to claim 4,
The method of predicting bearing voltage characteristics of a three-phase squirrel cage induction motor, wherein the winding-stator capacitance is determined based on the common mode impedance at a low frequency band frequency.
According to claim 4,
The inter-conductor capacitance is determined based on a resonant frequency in an intermediate frequency band, a leakage inductance of the stator, and a leakage inductance of the rotor.
According to claim 4,
Wherein the lead inductance and the frame inductance are determined based on the common mode impedance measured in the high frequency band and the BVR data for each frequency in the high frequency band.
According to claim 7,
Wherein the shaft inductance is determined based on the shaft-frame impedance and the frame inductance measured in the high frequency band, a method for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor.
According to claim 7,
The winding-rotor capacitance and the winding-stator capacitance are determined based on the BVR measurement data measured in a low frequency band and the winding-shaft impedance measured in a low frequency band, predicting bearing voltage characteristics of a three-phase squirrel cage induction motor Way.
According to claim 9,
In a low frequency band, BVR is determined based on the winding-rotor capacitance and the rotor-stator capacitance, a method for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor.
According to claim 10,
In the middle band, the BVR is determined based on the winding-rotor capacitance, the rotor-stator capacitance, the winding-stator capacitance, and the inter-conductor capacitance. Method for predicting bearing voltage characteristics of a three-phase cage-type induction motor.
one or more processors; and
An apparatus for predicting bearing voltage characteristics of a three-phase cage-type induction motor having a memory for storing one or more programs executed by the one or more processors,
The one or more processors,
Bearing Voltage Ratio (BVR) measurement data for each frequency measured between the common mode voltage applied to the winding of the three-phase cage-type induction motor and the bearing voltage generated in the bearing of the three-phase cage-type induction motor and the three-phase cage-type induction motor Acquiring impedance measurement data for each frequency measured between windings, frames, and shaft ends of the motor,
modeling an equivalent circuit corresponding to the three-phase squirrel cage induction motor based on the BVR measurement data for each frequency and the impedance measurement data for each frequency;
An apparatus for predicting bearing voltage characteristics of a three-phase cage-type induction motor, which predicts a bearing voltage generated in the bearing according to a frequency in the three-phase cage-type induction motor using the equivalent circuit.
According to claim 12,
The equivalent circuit is
lead inductances respectively connected between the three-phase input of the three-phase squirrel cage induction motor and the windings;
single-phase impedances respectively connected to the three-phase input and the lead inductance;
winding-rotor capacitances respectively connected between the windings and the rotor of the three-phase cage-type induction motor;
winding-stator capacitances respectively connected between the windings and the stator of the three-phase cage-type induction motor;
a rotor-stator capacitance coupled between the stator and the rotor;
a shaft inductance connected between the rotor and the shaft end; and
An apparatus for predicting bearing voltage characteristics of a three-phase cage-type induction motor, including frame inductance and frame resistance connected between the stator and the frame.
According to claim 13,
The single-phase impedance is,
parallel resistance between conductors; and
An apparatus for predicting bearing voltage characteristics of a three-phase cage-type induction motor, including an inter-conductor capacitance and an inter-conductor series resistance connected in parallel with the inter-conductor parallel resistance.
According to claim 14,
The impedance measurement data,
common mode impedance measured between the winding and the frame;
winding-shaft impedance measured between the winding and the shaft end; and
An apparatus for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor, comprising a shaft-frame impedance measured between the shaft end and the frame.
According to claim 15,
The winding-stator capacitance is determined based on the common mode impedance at a low frequency band frequency, a bearing voltage characteristic predictor of a three-phase squirrel cage induction motor.
According to claim 15,
The inter-conductor capacitance is determined based on a resonant frequency in an intermediate frequency band, a leakage inductance of the stator, and a leakage inductance of the rotor.
According to claim 15,
The lead inductance and the frame inductance are determined based on the common mode impedance measured in the high frequency band and the BVR data for each frequency in the high frequency band.
According to claim 18,
The shaft inductance is determined based on the shaft-frame impedance and the frame inductance measured in the high frequency band, the bearing voltage characteristic prediction device of the three-phase squirrel cage induction motor.
According to claim 18,
The winding-rotor capacitance and the winding-stator capacitance are determined based on the BVR measurement data measured in a low frequency band and the winding-shaft impedance measured in a low frequency band, bearing voltage characteristics of a three-phase squirrel cage induction motor. prediction device.
According to claim 20,
In the low frequency band, the BVR is determined based on the winding-rotor capacitance and the rotor-stator capacitance, the apparatus for predicting bearing voltage characteristics of a three-phase squirrel cage induction motor.
According to claim 21,
In the middle band, the BVR is determined based on the winding-rotor capacitance, the rotor-stator capacitance, the winding-stator capacitance, and the inter-conductor capacitance, Bearing voltage of a three-phase cage-type induction motor Predicting device.

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