JP4857747B2 - AC motor inverter device - Google Patents

Description

  The present invention relates to an inverter device for an AC motor.

Conventionally, speed control using a variable voltage and variable frequency is known as a technique for controlling an AC motor. In order to control the AC motor with higher accuracy, current information and voltage information of the AC motor are required. Normally, an inverter device is provided with a current detector, and current information can be obtained with sufficient accuracy. However, with an inverter device without a voltage detector, voltage information cannot be obtained with sufficient accuracy.
For this reason, in general, the value of the on-state voltage of the power semiconductor element that supplies power to the AC motor is compensated as a constant value or can be approximated by a straight line with respect to the inverter output current, or a voltage error using a disturbance observer As a disturbance, the voltage information of the AC motor is obtained with high accuracy. FIG. 10 shows an example of an on-voltage drop characteristic diagram of a power semiconductor element used in a conventional apparatus. A method for obtaining and compensating for a voltage error as a disturbance using a disturbance observer is known (see, for example, Patent Document 1).
In the inverter device, the P-side and N-side power elements are alternately conducted to control the output voltage. However, since the power semiconductor element has a switching delay due to the turn-off time, both P-side and N-side are not turned on at the same time. It is necessary to provide a period during which both elements are turned off (so-called on-delay).
A method of compensating for an insufficient voltage due to the influence of the on delay according to the polarity of the inverter output current is conventionally known (for example, see Patent Document 2).
JP 2004-64948 A Japanese Patent Laid-Open No. 10-304675

However, since the on-state voltage drop characteristic of the power semiconductor element is actually a non-linear function with respect to the inverter output current, it can be compensated as a constant value or linearly approximated with respect to the inverter output current as shown in FIG. When the compensation is performed with the above values, the on-voltage drop amount cannot be compensated with sufficient accuracy at various operating points. Moreover, when using a disturbance observer, accurate electrical characteristics of the AC motor are required, and cannot be used when the electrical characteristics are unknown.
On the other hand, on-delay compensation cannot be performed with sufficient accuracy due to variations in the on-delay time due to the characteristics of the hardware such as power elements and control circuits. Therefore, it was necessary to individually adjust the compensation amount for each inverter device.
Therefore, the present invention compensates for the on-voltage drop characteristics of the power semiconductor element with high accuracy without using the electrical characteristics of the AC motor, and further automatically adjusts the appropriate on-delay compensation amount to provide very high accuracy. It aims at providing the inverter apparatus which can obtain voltage information.

In order to solve the above problem, an invention according to claim 1 relates to an inverter device for an AC motor, an inverter including a power semiconductor element for converting a DC voltage into AC and supplying the AC to the AC motor ; An inverter device for an AC electric motor comprising a control unit for controlling the magnitude and frequency of the output voltage of the inverter , wherein the control unit represents an on-voltage drop characteristic equation of the power semiconductor element of an output current of the inverter. Built-in logarithmic function, the voltage command value when the AC motor is driven, the current detection value or current command value at that time, and the on-voltage drop characteristic equation, the on-voltage drop amount of the power semiconductor element And an adder for compensating the on-voltage drop amount of the power semiconductor element with the voltage command value .
According to a second aspect of the present invention, in the inverter apparatus for an AC motor according to the first aspect, a voltage command value when the control unit drives the AC motor, and a current detection value or a current command value at that time An on-delay compensation amount calculation unit that calculates an on-delay compensation amount due to a switching delay of the power semiconductor element based on a resistance value of the AC motor, and an addition unit that compensates the on-delay compensation amount to the voltage command value Is further provided .
According to a third aspect of the present invention, in the inverter apparatus for an AC motor according to the second aspect, the control unit sets the switching frequency of the power semiconductor element to at least two of the first switching frequency and the second switching frequency. A switching frequency setter that can be set to two different switching frequencies, and driving the AC motor at the first switching frequency, wherein either the current detection value or the current command value and the voltage command value are Is used to determine the coefficient of the on-voltage drop characteristic equation, and the AC motor is driven at the second switching frequency. At that time, either the current detection value or the current command value, the voltage command value, and the AC motor The on-delay compensation amount is obtained based on the resistance value .
According to a fourth aspect of the present invention, in the inverter apparatus for an AC motor according to the first aspect, the on-voltage drop characteristic equation is a natural logarithm or a common logarithm .
According to a fifth aspect of the present invention, in the inverter apparatus for an AC motor according to the third aspect, the first switching frequency is smaller than the second switching frequency .

According to the present invention, the on-state voltage drop characteristic of the power semiconductor element is built in as a characteristic equation approximated using a logarithmic function of the current detection value or current command value of the AC motor, and the on-state voltage drop amount of the power semiconductor element is accurately determined. Since it is calculated and corrected, it is possible to obtain voltage information with very high accuracy, and there is an effect that the AC motor can be controlled with higher accuracy, particularly with less ripple in torque and speed.
Moreover, since the coefficient of the on-voltage drop characteristic equation of the power semiconductor element can be obtained from the voltage command value and the current detection value or the current command value, it is not necessary to use the catalog characteristic of the power semiconductor, and the on-delay compensation value Therefore, it is possible to obtain a very good voltage accuracy.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing the overall configuration of an inverter device for an AC motor according to Embodiment 1 of the present invention.
FIG. 2 is a diagram showing an EXP table in the PWM control unit shown in FIG.
FIG. 3 is a diagram showing an example of characteristic approximation of the on-voltage drop amount of the power semiconductor element shown in FIG.
FIG. 4 is a diagram showing an example of an on-voltage drop characteristic diagram of the power semiconductor element shown in FIG.
First, an on-voltage drop characteristic of a power semiconductor element approximated by a logarithmic function of a current detection value or a current command value of a built-in AC motor will be described.

FIG. 4 shows the on-voltage drop characteristic (catalog value) of the power semiconductor element. As shown in FIG. 4, when the current flowing through the power semiconductor element is very small, the on-voltage drop amount changes abruptly.
Based on the preliminary test and the characteristic data described in the catalog, an approximate expression is obtained by a quadratic expression such as Expression (1) using a logarithmic function for the inverter output current value I. Since the on-voltage drop characteristic indicates the characteristic of the power semiconductor element, the inverter output current value I used for the logarithmic function is indicated by the current value [%] based on the rated current of the power semiconductor element.

この式（１）内のａ、ｂ、ｃは、式（１）がパワー半導体素子のトランジスタ特性とダイオード特性の平均値となるように求めた際の係数である。

“A”, “b”, and “c” in the equation (1) are coefficients obtained when the equation (1) is determined to be an average value of the transistor characteristics and the diode characteristics of the power semiconductor element.

FIG. 3 shows the characteristics of the on-state voltage drop of the power semiconductor element approximated by equation (1) on the horizontal axis in FIG. 3 (a) as the inverter output current value I and in FIG. 3 (b) as LN (I). It is shown. For comparison, the catalog characteristics shown in FIG. 4 are also shown by dotted lines, and it can be seen that they can be approximated very well.
Next, an example in which the on-state voltage drop characteristic of the power semiconductor element is approximated by a linear expression is shown in Expression (2).

式（２）のうち、Ｒｏｎは、インバータ出力電流値Ｉが１００％と２００％のときのＶｏｎ（Ｉ）の傾きで求め、Ｖｏｎ０は、Ｖｏｎ’（１００％）を用いて求める。また、ａ１、ａ２、ｂ１，ｂ２は式（３）に従って求める。

In Expression (2), Ron is obtained from the slope of Von (I) when the inverter output current value I is 100% and 200%, and Von0 is obtained using Von ′ (100%). Moreover, a1, a2, b1, and b2 are calculated | required according to Formula (3).

このようにして式（２）、（３）により求めたパワー半導体素子のオン電圧降下量特性は、図３の式（１）での近似と同様に精度よく近似される。

Thus, the on-voltage drop amount characteristic of the power semiconductor element obtained by the equations (2) and (3) is approximated with high accuracy in the same manner as the approximation in the equation (1) of FIG.

Based on the above principle analysis, actual processing will be described with reference to FIG.
The inverter device that drives the AC motor includes a PWM inverter 1, an AC motor 2, and an inverter control unit 10. A speed detector 9 is connected to the AC motor 2.
The PWM inverter 1 includes a converter 3, a smoothing capacitor 4, an inverse conversion circuit 5, current detectors 6A, 6B, and 6C, and a PWM control unit 7. The inverter control unit 10 includes an excitation current control unit 8A and a torque current control unit. 8B, coordinate converters 11A and 11B, adders 12A to 12D, speed controller 13, exciting current setter 14, slip frequency command calculator 15, integrator 16, and on-voltage characteristic calculators 20A, 20B, and 20C are included. ing.
The converter 3 is connected to a three-phase AC power source (R, S, T) and rectifies its output. The smoothing capacitor 4 is connected to the converter 3 and smoothes its output. The inverse conversion circuit 5 is configured by, for example, a power semiconductor element whose base current is controlled by the output of the PWM control unit 7. As a result, the DC voltage across the smoothing capacitor 4 is converted into a three-phase AC voltage controlled by the output of the PWM controller 7 and supplied to the AC motor 2. The current detector 6A detects a U-phase current Iu, the current detector 6B detects a V-phase current Iv, and the current detector 6C detects a W-phase current Iw.

The detected currents Iu, Iv, Iw of each phase detected by the current detectors 6A, 6B, 6C are supplied to the coordinate converter 11A. The coordinate converter 11A converts the three-phase detection currents Iu, Iv, and Iw into Ia and Ib on the coordinate system (ab axis), and further, the excitation current feedback signal Id and the torque current feedback signal Iq in the rotating coordinate system. And sent to the excitation current control unit 8A and the torque current control unit 8B, respectively.
The excitation current setting unit 14 is set with a predetermined excitation current value, and the set value is set as an excitation current command signal Id * to the excitation current control unit 8A and the speed command value ωr input from the outside of the inverter control unit 10. * And the detected speed value ωr obtained from the speed information from the speed detector 9 connected to the AC motor 2 are sent to the speed controller 13, and the speed controller 13 sets the torque current so that ωr * and ωr coincide with each other. The command signal Iq * is obtained and sent to the torque current control unit 8B.

  The excitation current control unit 8A and the torque current control unit 8B obtain the voltage command signals Vd * and Vq * so that Id * and Id, and Iq * and Iq match, and the coordinate converter 11B receives the voltage command signal Vd *. , Vq * is converted into Vref and Vbref on the phase θ (ab axis), and further converted into three-phase AC output voltage command signals Vu *, Vv *, and Vw * in the fixed coordinate system of the AC motor 2, The data is sent to adders 12A, 12B, and 12C, respectively. The adders 12A, 12B, and 12C add the three-phase AC output voltage command signals Vu *, Vv *, and Vw * and output voltages Vonu, Vonv, and Vonw, which will be described later, on-voltage characteristic calculation units 20A, 20B, and 20C, respectively. Then, the three-phase AC output voltage command signals Vu *, Vv *, and Vw * are corrected again and sent to the PWM controller 7. Although not shown, it is provided to prevent a short circuit due to the simultaneous firing of the power semiconductor elements based on the polarities of the detected currents Iu, Iv, Iw of each phase detected by the current detectors 6A, 6B, 6C. On-delay voltage compensation is also applied to the three-phase AC output voltage command signals Vu *, Vv *, and Vw *.

The slip frequency command calculator 15 obtains a slip frequency command ωs * from the excitation current command Id *, the torque current command Iq *, and the secondary resistance R2 (not shown). The adder 12D adds the speed detection value ωr obtained from the speed information from the speed detector 9 and the slip frequency command ωs * to obtain the primary frequency command signal ω1 *. The integrator 16 integrates the primary frequency command signal ω1 * to obtain the phase θ and sends it to the coordinate converters 11A and 11B.
The PWM controller 7 compares these three-phase AC output voltage commands Vu *, Vv *, and Vw * with a carrier wave signal having a switching frequency fc, and converts them into a pulse width modulation signal. This pulse width modulation signal becomes an ignition signal through a pulse amplifier (not shown), and performs switching control of the inverse conversion circuit 5 as a base current of the transistor. As a result, the DC voltage across the smoothing capacitor 4 is converted into a three-phase AC voltage.
As can be seen from FIG. 1, the “current detection value of the AC motor” described above is the same value as the “inverter output current value”.

Next, the operation of the on-voltage characteristic calculation unit 20 will be described.
When the U-phase current Iu is input, the on-voltage characteristic calculation unit 20A calculates what [%] is based on the power semiconductor element rated current for each phase, and the above equation (1) or ( 2) The on-state voltage drop amount Vonu for each phase is obtained based on (3). Similarly, when the V-phase current Iv and the W-phase current Iw are input to the on-voltage characteristic calculation units 20B and 20C, as in 20A, what is the power semiconductor element rated current reference for each? Is calculated, and on-voltage drop amounts Vonv and Vonw for each phase are obtained based on the above formula (1) or (2) and (3).
As described above, the first embodiment of the present invention is implemented.

In the above description, the natural logarithm LN has been described. However, even if the common logarithm LOG is used, it can be similarly realized by appropriately selecting the coefficient in the above formula (1), (2), or (3). .
Further, when the CPU to be used is not prepared for the LN function used for calculating the on-voltage drop characteristic, the EXP table shown in FIG. 2 is stored, and the LN function is calculated by linearly approximating the EXP table. can do.
A method for calculating the LN function will be described by taking an example in which the inverter output current value I is 8.5% of the rated power semiconductor element current. Since 8.5 is between 7.39 and 9.03 from FIG. 2, a straight line approximation is performed using these two points in accordance with Equation (4) to obtain 2.1354. The LN (8.5) calculated by the calculator is 2.140.

なお、ＬＯＧ関数を用いても上記動作は同様にして実現できる。
以上のようにして、本発明は実施でき、パワー半導体素子のオン電圧降下特性を精度よく補償し、非常に精度よい電圧情報を得ることのできるインバータ装置を得ることができる。

Note that the above operation can be realized in the same manner even when a LOG function is used.
As described above, the present invention can be implemented, and an inverter device that can accurately compensate the on-voltage drop characteristic of the power semiconductor element and obtain very accurate voltage information can be obtained.

  In the above description, the induction motor is used as an example of the inverter control unit. However, the present invention can be similarly implemented using a synchronous motor. Needless to say, the present invention can also be applied to speed sensorless vector control without a speed detector and a constant V / f control method.

Next, a second embodiment of the present invention will be described with reference to the drawings.
FIG. 5 is a block diagram of an inverter device for an AC motor according to Embodiment 2 of the present invention.
6 is a block diagram of a tuning selection unit of the inverter device shown in FIG.
FIG. 7 is a block diagram of an on-voltage and on-delay compensation function calculation unit of the inverter device shown in FIG.
FIG. 8 is a flowchart when the on-voltage compensation process is selected by the tuning selection unit shown in FIG.
FIG. 9 is a flowchart when the on-delay compensation process is selected by the tuning selection unit shown in FIG.
In FIG. 5, the same components as those in FIG. 1 are denoted by the same reference numerals, overlapping description will be omitted, and a configuration different from that in FIG. 1 will be described.

  The configuration of FIG. 5 is the same as the configuration of FIG. 1 except that a switching frequency setting unit 27 for setting the switching frequency fc to the inverse conversion circuit 5 and an on-delay compensation amount calculation unit 24 are added to the on-voltage characteristic calculation unit 20. Function calculation unit 28, a tuning selection unit 29 that outputs a switching signal CSW and a switching frequency setting signal Set at the time of tuning, and performs tuning switching of the on-voltage compensation amount and the on-delay compensation amount, and switching from the tuning selection unit 29 Switch circuits 21A to 21G for switching circuits by the signal CSW are newly added.

Further, for details of the tuning selection unit 29, referring to FIG. 6, it is determined which of the on-voltage compensation function tuning processing unit 22 and the on-delay compensation amount tuning processing unit 23 works by switching the switch circuits 26A to 26B. The on-voltage compensation function coefficient tuning processing unit 22 and the on-delay compensation amount tuning processing unit 23 are selected to output the switching signal CSW of the switch circuits 21A to 21G, the excitation current command Id *, the phase θ, and the inverse conversion circuit 5 respectively. Set (Set) the switching frequency fc of the power elements constituting the.
In tuning, the torque current command value Iq * is set to 0 by the switch circuit 21A shown in FIG. 5, and the excitation current command value Id *, the phase θ, and the switching frequency fc are respectively set by the tuning processing unit 22 by the switch circuits 21B, 21C, and 21D. And the indicated value from 23.

  For details of the compensation function calculation unit 28, referring to FIG. 7, on-delay compensation circuits 24A to 24C and adders 25A to 25C are added, and the terminals of the adder 25 are switched by the switches 21E to 21G according to the switching signal CSW. a, b, and c are switched, and the compensation output is switched.

Next, the operation when the tuning processing unit 22 is selected by the tuning selection unit 29 of this embodiment will be described with reference to the flowchart of FIG.
The switch circuit 21B is set to the b side, and Id and the integrator so that the magnitude Id of the direct current flowing during tuning is 0.5% of the rated current of the power semiconductor element constituting the inverse converter 5 on the phase basis. The phase θ, which is 6 outputs, is set to θ1. Specifically, Id = k × 0.5% (k = √3 / 2), and θ1 is a phase where the current for one phase is 0 and the absolute values of the other two-phase currents are equal ( Block 22a).
Next, the switch circuits 21E, 21F, and 21G shown in FIG. 7 are set to the b side so that the on-voltage compensation amount of each phase is not added to the voltage command, and the on-delay compensation amount is added to the voltage command. To. The switch circuit 21D is set to the b side, and fc is set to a frequency as low as possible so that the voltage error due to the influence of the on delay is reduced. (Block 22b).

として記憶する（ブロック２２c）。
さらに、Id=ｋ×5％、ｋ×30％を設定した場合についても、上記ブロック（２２b〜２２c）の処理を実行し、その時の一次電流値I2、I3と一次電圧指令値Vref2、Vref3を記憶する。 Next, the switch circuit 21C is set to the b side, the phase θ is set to a fixed value θ1, and the inverter is driven. At this time, the primary current value I1 and the primary voltage command value V1 ^* are

(Block 22c).
Further, even when Id = k × 5% and k × 30% are set, the processing of the blocks (22b to 22c) is executed, and the primary current values I2, I3 and the primary voltage command values Vref2, Vref3 at that time are obtained. Remember.

（ブロック２２ｄ）。 Next, based on the measured primary current values I1, I2, and I3 and the primary voltage command values Vref1 (V1 in Formula 5), Vref2, and Vref3, the following formulas (6) and (7) are used. The coefficients a1, b1, a2, b2, Von0 of 2) are obtained.

(Block 22d).

Next, the operation of the tuning processing unit 23 of the selection unit 29 will be described using the flowchart of FIG.
The switch circuit 21B is set to the c side, and the magnitude of the direct current that flows during tuning is determined as Id based on the rated currents of the PWM inverter 1 and the alternating current motor 2. (Block 23a).
Next, the switch circuits 21E, 21F, and 21G shown in FIG. 7 are set to the c side so that the ON voltage compensation amount of each phase is added to the voltage command, and the ON delay compensation amount is not added to the voltage command. The switch circuit 21D is set to the c side, and fc is set to a frequency as high as possible so that a voltage error due to the on-delay effect is large. At this time, as the coefficient of the on-voltage compensation function, the coefficient obtained by the coefficient tuning processing unit 22 of the on-voltage function may be used. (Block 23b).
Next, the switch circuit 21C is set to the c side, the phase θ is set to a fixed value θ1, and the inverter is driven. At this time, the primary current value I4 and the primary voltage command value Vref4 are stored. (Block 23c).

電圧誤差分Eから下記式（９）式に基づいて、オンディレイ補償量tdを求める。
パワー素子などの電気的特性がカタログ記載通りであれば、オンディレイ補償量tdはオンディレイ時間と等しくなり、カタログ値からずれた分、両者は異なる値となる。そこで、求められたtdを用いてオンディレイ補償することでパワー素子などの電気的特性のバラツキを考慮した、より正確なオンディレイ補償を行う事が出来る。（ブロック２３d）。
このように、オン電圧とオンディレイの補償が精度良く実施できる。
以上、パワー半導体素子のオン電圧降下特性を求める電流情報を交流電動機の電流検出値を用いるように説明したが、電流制御等のように電流指令値と電流検出値が一致するように制御されていれば、電流検出値の替わりに電流指令値を用いて全く同様に実現できることは言うまでもない。 Next, from the stored primary current value I4, primary voltage command value Vref4, and armature resistance R1 of the AC motor 2, a voltage error E due to the influence of on-delay is obtained based on the following equation (8).

The on-delay compensation amount td is obtained from the voltage error E based on the following equation (9).
If the electrical characteristics of the power element and the like are as described in the catalog, the on-delay compensation amount td is equal to the on-delay time, and the two values differ from each other by a deviation from the catalog value. Therefore, by performing on-delay compensation using the obtained td, more accurate on-delay compensation can be performed in consideration of variations in electrical characteristics of the power element and the like. (Block 23d).
Thus, the ON voltage and the ON delay can be compensated with high accuracy.
As described above, the current information for obtaining the on-voltage drop characteristic of the power semiconductor element has been described so as to use the current detection value of the AC motor. However, the current command value and the current detection value are controlled to match each other as in current control or the like. Needless to say, the current command value can be used in place of the current detection value to achieve the same effect.

  As described above, since the on-voltage drop characteristic and the on-delay correction of the power semiconductor element can be accurately compensated by tuning, it is suitable for use in inverter devices such as induction motors and synchronous motors.

It is a block diagram of the inverter apparatus of the alternating current motor concerning Example 1 of the present invention. It is a figure which shows the example of the EXP table in the PWM control part shown in FIG. It is a figure which shows the characteristic approximation example of the amount of on-voltage drops of the power semiconductor element shown in FIG. It is a figure which shows the ON voltage drop characteristic of the power semiconductor element shown in FIG. It is a block diagram of the inverter apparatus of the alternating current motor concerning Example 2 of the present invention. It is a block diagram of the tuning selection part of the inverter apparatus shown in FIG. FIG. 6 is a block diagram of an on-voltage and on-delay compensation function calculation unit of the inverter device shown in FIG. 5. 7 is a flowchart when an on-voltage compensation process is selected by a tuning selection unit shown in FIG. 6. 7 is a flowchart when an on-delay compensation process is selected by a tuning selection unit shown in FIG. 6. It is a figure which shows the on-voltage drop characteristic figure of the conventional power semiconductor element.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 PWM inverter 2 AC motor 3 Converter 4 Smoothing capacitor 5 Inverse conversion circuit 6 Current detector 7 PWM control part 8A Excitation current control part 8B Torque current control part 9 Speed detector 10 Inverter control part 11 Coordinate converter 12 Adder 13 Speed Controller 14 Excitation current setter 15 Slip frequency command calculator 16 Integrator 20 On-voltage calculator 21 Switch circuit 22 On-voltage compensation tuning section 23 On-delay compensation tuning section 24 On-delay compensation circuit 25 Adder circuit 26 Switch circuit 27 Switching frequency Setter 28 On-voltage and on-delay compensation function calculator 29 Tuning selection section

Claims (5)

An inverter for an AC motor comprising: an inverter provided with a power semiconductor element for converting a DC voltage into an AC and supplying the AC to an AC motor ; and a control unit for controlling the magnitude and frequency of the output voltage of the inverter. A device ,
The control unit incorporates an on-voltage drop characteristic formula of the power semiconductor element as a logarithmic function of the output current of the inverter, a voltage command value when the AC motor is driven, a current detection value or a current command at that time An on-voltage calculator that calculates the on-voltage drop amount of the power semiconductor element using the value and the on-voltage drop characteristic equation;
An inverter device for an AC motor , comprising: an adder that compensates an on-voltage drop amount of the power semiconductor element with the voltage command value . The control unit compensates for an on-delay caused by a switching delay of the power semiconductor element based on a voltage command value when the AC motor is driven, a current detection value or a current command value at that time, and a resistance value of the AC motor. An on-delay compensation amount calculation unit for calculating the amount;
An adder for compensating the on-delay compensation amount to the voltage command value;
The inverter device for an AC motor according to claim 1, further comprising: The control unit further includes a switching frequency setting unit capable of setting the switching frequency of the power semiconductor element to at least two different switching frequencies of a first switching frequency and a second switching frequency,
Driving the AC motor at the first switching frequency, using either the current detection value or the current command value and the voltage command value at that time, obtain the coefficient of the on-voltage drop characteristic equation,
The AC motor is driven at the second switching frequency, and the on-delay compensation amount is obtained based on either the current detection value or the current command value, the voltage command value, and the resistance value of the AC motor. The inverter device for an AC motor according to claim 2 . The inverter apparatus for an AC motor according to claim 1, wherein the on-voltage drop characteristic equation is a natural logarithm or a common logarithm . The inverter device for an AC motor according to claim 3, wherein the first switching frequency is lower than the second switching frequency .

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