INVERTER CONTROLLER

The inverter control device addresses voltage errors and torque shocks by using a dead time compensation unit that adjusts switching operations based on phase angle differences, effectively improving motor stability.

DE112022007608T5Pending Publication Date: 2025-05-22ASTEMO LTD
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Patent Information

Application Number
DE112022007608
Authority / Receiving Office
DE · DE
Patent Type
Applications
Current Assignee / Owner
Filing Date
2022-09-12
Publication Date
2025-05-22

AI Technical Summary

Technical Problem

Existing inverter control devices face challenges in reducing voltage errors caused by dead time, which leads to torque shocks during mode switching.

Method used

The inverter control device incorporates a dead time compensation unit that adjusts the switching operation based on the difference between the current phase angle and the voltage phase angle, effectively reducing voltage errors and torque shocks.

Benefits of technology

This solution allows for easy reduction of voltage errors caused by dead time, thereby suppressing torque shocks and stabilizing motor operation.

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Abstract

The objective is to easily reduce a voltage error caused by dead time and suppress torque shocks. An inverter control device 100 controls the switching operation of an inverter 10, which converts a DC voltage into an AC voltage and applies the AC voltage to a motor 3, by pulse width modulation. The inverter control device 100 according to Embodiment 1 is provided with a dead time compensation unit 183 that performs dead time compensation to compensate for an error in the output voltage of the inverter 10 caused by the dead time of the inverter 10. The dead time compensation unit 183 performs dead time compensation based on the difference θvi between the current phase angle θi, which indicates the phase angle for outputting a current of the motor 3, and the voltage phase angle θv, which outputs a voltage corresponding to the current.
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Description

Technical area

[0001] The present invention relates to an inverter control device. Technical background

[0002] Inverter controllers are widely used to control the switching operation of an inverter that converts DC voltage into AC voltage and applies the AC voltage to an AC motor through pulse width modulation (hereinafter also referred to as "PWM"). In this type of inverter controller, in order to increase the speed of the AC motor, a technique for operating the inverter in an over-modulation region where the setpoint of the inverter output voltage exceeds the maximum output level of a sine wave is known. In this case, the inverter controller can be operated by a one-pulse control mode or a three-pulse control mode, in which one pulse or three pulses are generated per cycle of the fundamental wave of the inverter output voltage.The inverter control device can switch the control modes according to the operating range of the AC motor.

[0003] An inverter provides a dead time, which is an interval during which both the upper and lower arms are turned off to prevent short circuits during switching. This causes an error (hereinafter referred to as a "voltage error") between the inverter's output voltage and its setpoint. The voltage error caused by the dead time can lead to torque shock, in which the motor fails to output the designed torque when the inverter controller switches control modes. Therefore, it is important to reduce the voltage error caused by the dead time to prevent torque shock.

[0004] Patent Literature 1 discloses a technique for performing dead time compensation by which, in a phase reference synchronization control mode, the phase threshold used for generating a switching command that controls the turning on / off of the switching elements of the inverter is corrected with a dead time compensation phase. Citation listPatent literature

[0005] Patent Literature 1: JP 2011-15566 A Summary of the inventionTechnical problem

[0006] In the technique disclosed in Patent Literature 1, the dead-time compensation phase is calculated based on a detection signal of the current supplied to the motor from the inverter and the fundamental frequency of the voltage command. Therefore, current polarity calculation is required at the switching time. In other words, the technique disclosed in Patent Literature 1 requires rapid current detection to perform dead-time compensation, making it difficult to reduce the voltage error caused by the dead time.

[0007] The present invention has been made in view of the above, and its object is to simply reduce the voltage error caused by the dead time and suppress torque shocks. Solution to the problem

[0008] To solve the problem, an inverter control device according to the present invention controls a switching operation of an inverter that converts a DC voltage into an AC voltage and applies the AC voltage to an AC motor through pulse width modulation. The inverter control device includes a dead-time compensation unit for performing dead-time compensation to compensate for an error in the output voltage of the inverter caused by a dead time of the inverter. The dead-time compensation unit performs the dead-time compensation based on the difference between a current phase angle indicating a phase angle for outputting a current of the AC motor and a voltage phase angle outputting a voltage corresponding to the current. Advantageous effects of the invention

[0009] According to the present invention, the voltage error caused by the dead time can be easily reduced and torque shocks can be suppressed.

[0010] Other problems, configurations and effects will be understood from the following description of the embodiments. Brief description of the drawings

[0011] They show: Fig. 1 is a configuration diagram of a motor drive system provided with the inverter control device according to Embodiment 1, Fig. 2 a configuration diagram of a three-pulse / one-pulse calculation unit when a current phase angle and a voltage phase angle are used as inputs, Fig. 3 a configuration diagram of a three-pulse / one-pulse calculation unit when a current setpoint and a voltage setpoint are used as inputs, Fig. 4 a diagram to explain the voltage waveform when no voltage error caused by the dead time occurs, Fig. 5 a diagram to explain the calculations of a dead time compensation unit when (1) Δα < θvi < α is satisfied, Fig. 6 a diagram to explain the calculations of the dead time compensation unit when (2) α + Δα < θvi < π - α is satisfied, Fig. 7 a diagram to explain the calculations of the dead time compensation unit when (3) π - α + Δα < θvi < π is satisfied, Fig. 8 a diagram to explain the calculations of the dead time compensation unit when (4) π + Δα < θvi < π + α is satisfied, Fig. 9 a diagram to explain the calculations of the dead time compensation unit 183 when (5) π + α + Δα < θvi < 2π - α is satisfied, Fig. 10 a diagram to explain the calculations of the dead time compensation unit 183 when (6) 2π - α + Δα < θvi < 2π is satisfied, Fig. 11 a table showing the relationship between the difference between the voltage phase angle and the current phase angle, the amplitude error and the phase angle error, Fig. 12 a diagram to explain the functioning of the Fig. 1 shown inverter control device, Fig. 13 is a configuration diagram of the three-pulse / one-pulse calculation unit included in the inverter control device according to Embodiment 2; Fig. 14 is a table showing the relationship between the difference between the voltage phase angle and the current phase angle and the phase angle error, and Fig. 15 is a configuration diagram of the inverter control device according to Embodiment 3. Description of embodiments

[0012] Embodiments of the present invention will be described below with reference to the drawings. Note that in the respective embodiments, configurations designated by the same reference numerals have the same functions throughout unless specifically stated otherwise, and redundant descriptions will be omitted. [Embodiment 1]

[0013] An inverter control device 100 according to Embodiment 1 will be described with reference to Fig. 1 to 12 described. Fig. 1 is a configuration diagram of a motor drive system 1 provided with the inverter control device 100 according to Embodiment 1.

[0014] The motor drive system 1 is connected to a battery 2 and provided with an inverter 10 (an inverter power unit), the inverter control device 100 and an AC motor 3 (hereinafter also referred to as “motor 3”).

[0015] The battery 2 is a DC voltage source for the inverter 10. The DC voltage Vdc (hereinafter also referred to as "supply voltage Vdc") of the battery 2 is converted into a three-phase AC voltage with variable voltage and variable frequency by the inverter 10 and applied to the motor 3. The motor 3 is a synchronous motor that is rotated by applying the three-phase AC voltage. A rotational position sensor 4 is attached to the motor 3 for controlling the phase of the three-phase AC voltage applied from the inverter 10 according to the phase of the induced voltage of the motor 3. The rotational position sensor 4 is formed, for example, using a resolver or the like consisting of a core and windings. Alternatively, the rotational position sensor 4 may be formed using a GMR sensor or a Hall element.

[0016] The inverter control device 100 is used to control the inverter 10. The inverter control device 100 is configured, for example, using a microcomputer. The inverter control device 100 can implement various functions of the inverter control device 100 by executing a predetermined program in the microcomputer. Alternatively, the inverter control device 100 can implement some or all of the various functions of the inverter control device 100 using hardware circuits such as a logic IC or FPGA.

[0017] The inverter control device 100 is provided with various functional units, namely a current command unit 110, a current control unit 120, a current detection unit 130, a rotational position detection unit 140, a PWM pulse generation unit 150, a gate circuit 160, an SVPWM calculation unit 170, and a three-pulse / one-pulse calculation unit 180.

[0018] The rotational position detecting unit 140 detects the rotational position θp, which is the position of the rotor of the motor 3, based on the output signal of the rotational position sensor 4.

[0019] The current detection unit 130 obtains the measured values ​​Iuvw (Iu, Iv, Iw) of the three-phase current flowing through the motor 3 from a current sensor Ict. The current detection unit 130 acquires the measured values ​​Idq (Id, Iq) of the dq-axis current by performing three-phase to two-phase conversion on these current measured values ​​based on the rotational position θp detected by the rotational position detection unit 140.

[0020] The inverter control device 100 has a current control function for controlling the output of the motor 3. The current command unit 110 calculates the dq-axis current command values ​​Idq* (Id*, Iq*) based on the torque command value T* output from a higher-level control device (not shown). The current command unit 110 outputs the calculated dq-axis current command values ​​Idq* to the current control unit 120, the SVPWM calculation unit 170, and the three-pulse / one-pulse calculation unit 180. The current command unit 110 can also calculate the current phase angle θi, which indicates the phase angle of the dq-axis current command values ​​Idq*, from the dq-axis current command values ​​Idq*. The current command unit 110 can output the calculated current phase angle θi to the current control unit 120, the SVPWM calculation unit 170, and the three-pulse / one-pulse calculation unit 180.

[0021] The current control unit 120 calculates the dq-axis voltage command values ​​Vdq* (Vd*, Vq*) as the output voltage command value of the inverter 10 according to the dq-axis current command values ​​Idq* output from the current command value unit 110. Specifically, the current control unit 120 calculates the dq-axis voltage command values ​​Vdq* so that the dq-axis current command values ​​Idq* output from the current command value unit 110 match the dq-axis current command values ​​Idq detected by the current detection unit 130. The current control unit 120 outputs the calculated dq-axis voltage command values ​​Vdq* to the SVPWM calculation unit 170 and the three-pulse / one-pulse calculation unit 180. The current control unit 120 may also calculate the voltage phase angle θv, which indicates the phase angle of the dq-axis voltage command values ​​Vdq*, from the dq-axis voltage command values ​​Vdq*.The current control unit 120 may output the calculated voltage phase angle θv to the SVPWM calculation unit 170 and the three-pulse / one-pulse calculation unit 180.

[0022] The three-pulse / one-pulse calculation unit 180 calculates a modulation wave based on the command value of the output voltage of the inverter 10. That is, the three-pulse / one-pulse calculation unit 180 is a modulation wave calculation unit that calculates a modulation wave corresponding to the output voltage of the inverter 10. Specifically, the three-pulse / one-pulse calculation unit 180 calculates the three-phase voltage command values ​​Vuvw* (Vu*, Vv*, Vw*) by performing two-phase to three-phase conversion on the dq-axis voltage command values ​​Vdq* output from the current control unit 120 using the rotation position θp. Among the three-phase voltage setpoints Vuvw*, Vu* is the U-phase voltage setpoint, Vv* is the V-phase voltage setpoint, and Vw* is the W-phase voltage setpoint.Then, the three-pulse / one-pulse calculation unit 180 generates the modulation wave signal duvw indicating the modulation wave represented by the three-phase voltage command values ​​Vuvw* and outputs it to the PWM pulse generation unit 150. At this time, the three-pulse / one-pulse calculation unit 180 may select a modulation scheme other than sine modulation and represent the three-phase voltage command values ​​Vuvw* using a sine waveform of various waveforms such as a trapezoidal wave or a waveform in which harmonics of a predetermined order are superimposed on a sine wave.

[0023] In addition, the three-pulse / one-pulse calculation unit 180 may calculate the modulation factor MF of the output voltage of the inverter 10 based on the power supply voltage Vdc and the dq-axis voltage command values ​​Vdq* output from the current control unit 120, and then output the modulation factor MF to the PWM pulse generation unit 150 instead of the modulation wave signal duvw. Further, the three-pulse / one-pulse calculation unit 180 may calculate the modulation wave signal duvw and the modulation factor MF and output both to the PWM pulse generation unit 150. That is, the three-pulse / one-pulse calculation unit 180 may calculate at least one of the modulation wave signal duvw and the modulation factor MF.

[0024] The PWM pulse generation unit 150 performs three-phase pulse width modulation (PWM) based on the modulation wave signal duvw or modulation factor MF calculated by the three-pulse / one-pulse calculation unit 180, and generates a PWM pulse signal P for controlling the switching operation of the inverter 10. For example, the PWM pulse generation unit 150 compares the carrier, which periodically varies with the carrier frequency fc, with the modulation wave signal duvw. The PWM pulse generation unit 150 can then generate the PWM pulse signal P by determining the positions (phases) of the rising and falling edges (hereinafter also referred to as "pulse edges") of each pulse based on the comparison result using a well-known scheme. In this case, the PWM pulse generation unit 150 can keep the carrier frequency fc constant or vary it according to the speed of the motor 3.Alternatively, the PWM pulse generation unit 150 may generate the PWM pulse signal P by directly determining the position of each pulse edge by calculation based on the modulation factor MF, without using the carrier and modulation wave signals duvw. Alternatively, the PWM pulse generation unit 150 may generate the PWM pulse signal P by another method. In any case, the PWM pulse generation unit 150 only needs to generate the PWM pulse signal P for controlling the inverter 10 every predetermined control cycle according to the target value of the output voltage of the inverter 10, and any method may be employed.

[0025] The gate circuit 160 outputs a drive signal DR corresponding to the PWM pulse signal P to the inverter 10. The inverter 10 includes a plurality of semiconductor switching elements, each corresponding to the phase of the three-phase AC voltage, and the switching on and off of each semiconductor switching element is controlled by the drive signal DR. In this way, the output voltage of the inverter 10 is adjusted according to the control of the inverter control device 100.

[0026] The SVPWM calculation unit 170 calculates the modulation wave when the space vector pulse width modulation (SVPWM) control mode is used. That is, the SVPWM calculation unit 170 is a modulation wave calculation unit that calculates a modulation wave according to the output voltage of the inverter 10. Specifically, the SVPWM calculation unit 170 calculates the three-phase voltage command values ​​Vuvw* by performing two-phase to three-phase conversion on the dq-axis voltage command values ​​Vdq* output from the current control unit 120 using the rotational position θp. Then, the SVPWM calculation unit 170 performs dead time compensation on the three-phase voltage command values ​​Vuvw* using the dq-axis current command value Idq*. Then, the SVPWM calculation unit 170 calculates the duty cycle duvw by dividing the dead time compensated three-phase voltage command values ​​Vuvw* by the supply voltage Vdc.Then, the SVPWM calculation unit 170 outputs the calculated duty cycle duvw to the PWM pulse generation unit 150.

[0027] The above was made with reference to Fig. 1 describes a configuration example of the motor drive system 1 when the current of the motor 3 is controlled according to the dq-axis current command values ​​Idq* by the current command unit 110. The configuration from Fig. However, 1 can also be applied when other control methods are used. For example, when controlling the speed of the motor 3, the inverter control device 100 can calculate the motor speed ωr based on the temporal variation of the rotational position θp and generate a voltage command or current command that matches the speed command from a higher-level control device. Further, when controlling the output torque of the motor 3, the inverter control device 100 can generate the current command (Idq*) using a relational expression or map between the motor current (Idq) and the motor torque.

[0028] Fig. 2 is a configuration diagram of the three-pulse / one-pulse calculation unit 180 when the current phase angle θi and the voltage phase angle θv are used as inputs. Fig. 3 is a configuration diagram of the three-pulse / one-pulse calculation unit 180 when the current command values ​​Idq* and the voltage command values ​​Vdq* are used as inputs.

[0029] The Fig. 2 and Fig. The three-pulse / one-pulse calculation unit 180 shown in Figure 3 is provided with a dead time compensation unit 183, a firing angle calculation unit 184, a phase angle calculation unit 185, and a duty cycle calculation unit 186. The Fig. The three-pulse / one-pulse calculation unit 180 shown in Fig. 3 is further provided with a modulation factor / voltage phase angle calculation unit 181 and a current phase angle calculation unit 182.

[0030] Fig. 2 shows an example in which the current phase angle θi obtained by calculating the amplitude and phase angle with respect to a target torque through a table is directly input to the three-pulse / one-pulse calculation unit 180, and the voltage phase angle θv obtained using voltage phase control is directly input to the three-pulse / one-pulse calculation unit 180. Fig. 3 shows an example in which the dq-axis current command values ​​Idq* output from the current command value unit 110 are input to the three-pulse / one-pulse calculation unit 180, and the dq-axis voltage command values ​​Vdq* output from the current control unit 120 are input to the three-pulse / one-pulse calculation unit 180. The inverter control device 100 can use either the Fig. 2 shown three-pulse / one-pulse calculation unit 180 or the one shown in Fig. 3 illustrated three-pulse / one-pulse calculation unit 180.

[0031] An example is described below in which the inverter control device 100 uses the Fig. 3 and controls the switching operation in a three-pulse control mode.

[0032] The modulation factor / voltage phase angle calculation unit 181 calculates the modulation factor MF and the voltage phase angle θv based on the dq-axis voltage command values ​​Vdq* of the output voltage of the inverter 10. Specifically, the modulation factor / voltage phase angle calculation unit 181 calculates the root of the sum of the squares of the d-axis voltage command value Vd* and the q-axis voltage command value Vq* output from the current control unit 120. Then, the modulation factor / voltage phase angle calculation unit 181 calculates the modulation factor MF by dividing the calculated root of the sum of the squares by the power supply voltage Vdc.

[0033] The modulation factor / voltage phase angle calculation unit 181 calculates the voltage phase angle θv from the dq-axis voltage command values ​​Vdq* using Formula 1. θv=Atan(Vq*Vd*)

[0034] The current phase angle calculation unit 182 calculates the current phase angle θi based on the dq-axis current command values ​​Idq* of the current flowing through the motor 3. Specifically, the current phase angle calculation unit 182 calculates the current phase angle θi from the dq-axis current command values ​​Idq* using Formula 2. θi=Atan(Iq*Id*)

[0035] Note that the current phase angle calculation unit 182 can calculate the current phase angle θi based on the dq-axis current measurement values ​​Idq, which are the measured values ​​of the current flowing through the motor 3. Similarly, the modulation factor / voltage phase angle calculation unit 181 can calculate the modulation factor MF and the voltage phase angle θv based on the measured values ​​of the output voltage of the inverter 10.

[0036] The dead time compensation unit 183 performs dead time compensation to compensate for an output voltage error caused by the dead time Δα of the inverter 10. Specifically, the dead time compensation unit 183 performs dead time compensation when the switching operation of the inverter 10 is controlled by at least one of the one-pulse control mode and the three-pulse control mode.

[0037] In one-pulse control mode, one pulse is generated per fundamental wave cycle of the output voltage of the inverter 10. The one-pulse control mode is used in a range where the fundamental wave frequency of the output voltage of the inverter 10 is high. In three-pulse control mode, three pulses are generated per fundamental wave cycle of the output voltage of the inverter 10. The three-pulse control mode is used in a range where the fundamental wave frequency of the output voltage of the inverter is intermediate. In SVPWM control mode, one pulse is generated by comparing the carrier and the modulation wave based on their relative magnitudes. The SVPWM control mode is used in a range where the fundamental wave frequency of the output voltage of the inverter 10 is low.

[0038] The dead time compensation unit 183 performs dead time compensation based on the difference θvi (= θv - θi) between the current phase angle θi, which indicates the phase angle for outputting the current of the motor 3, and the voltage phase angle θv, which outputs a voltage corresponding to the current. Specifically, the dead time compensation unit 183 calculates at least one of the amplitude error ΔA and the phase angle error Δθ of the output voltage, which are voltage errors caused by the dead time Δα, as a dead time compensation amount. The three-pulse / one-pulse calculation unit 180 uses the amplitude error ΔA calculated as the dead time compensation amount to correct the modulation factor MF, which is used to calculate the firing angle α of the output voltage.The three-pulse / one-pulse calculation unit 180 also uses the phase angle error Δθ calculated as the dead-time compensation amount to correct the phase angles θ1 and θ2 of the output voltage. In this way, the dead-time compensation unit 183 can perform dead-time compensation.

[0039] The firing angle α refers to the pulse width that must be adjusted when determining the number of pulses per fundamental wave cycle of the output voltage. The relationship between the firing angle α and the modulation factor MF is expressed by Formula 3. MF=4π{∫0π2−α(−1)sin θ dθ+∫π2−απ2sin θ dθ}=4π(2 cos α−1)

[0040] Accordingly, the firing angle α can be expressed as given in Formula 4 using the modulation factor MF. α=cos−1(π4MF+12)

[0041] The dead time compensation unit 183 calculates the amplitude error ΔA and the phase angle error Δθ as the dead time compensation amount according to the relationship between the firing angle α and the difference θvi. The details of the calculations of the amplitude error ΔA and the phase angle error Δθ by the dead time compensation unit 183 will be described with reference to Fig. 4 to 11.

[0042] Fig. Figure 4 is a diagram to explain the voltage waveform when no voltage error is caused due to the dead time.

[0043] If no voltage error is caused due to the dead time, the switching times α1 to α4 in the interval [0, 2π] can be expressed in terms of the firing angle α as given in formula 5. α1=αα2=π−αα3=π+αα4=2π−α

[0044] The Fourier coefficients an and bn obtained by performing a Fourier series expansion of the output voltage of the inverter 10 using the supply voltage Vdc, the firing angle α and the dead time Δα with respect to the switching timings α1 to α4 can be expressed as given in Formula 6. an=2 Vdcπ(2 cos α−1)bn=0

[0045] The amplitude A of the output voltage of the inverter 10 can be expressed as given in Formula 7 using the Fourier coefficients an and bn from Formula 6. A=2Vdcan2+bn2=4π(2 cos α−1)

[0046] The phase angle error Δθ of the output voltage of the inverter 10 when no voltage error is caused due to the dead time can be expressed as given in Formula 8. Δθ=tan−1(bn / an)=0

[0047] The dead time compensation unit 183 calculates the amplitude error ΔA and the phase angle error Δθ by determining the above formulas 5 to 8 according to the relationship between the firing angle α and the difference θvi as the dead time compensation amount.

[0048] Fig. 5 shows diagrams to explain the calculations of the dead time compensation unit 183 when (1) Δα < θvi < α is satisfied.

[0049] The upper part (a) from Fig. Figure 5 shows the voltage waveform before dead time compensation. Regarding the firing angle α, the switching timings α1 to α4 in the interval [0, 2π] of a fundamental wave cycle can be calculated as given in Formula 9 based on Fig. 4 and formula 5. α1=αα2=π−αα3=π+αα4=2π−α

[0050] In fact, there is a phase difference between the output voltage of the inverter 10 and the current flowing through the motor 3. The inventor focused on the fact that the amplitude error ΔA and the phase angle error Δθ depend on the difference θvi between the voltage phase angle θv and the current phase angle θi. Specifically, the amplitude error ΔA and the phase angle error Δθ take different values ​​for each of the cases (1) to (6) shown in Formula 10, according to the ranges of the difference θvi between the voltage phase angle θv and the current phase angle θi. Therefore, the dead time compensation unit 183 calculates the amplitude error ΔA and the phase angle error Δθ for each of the cases (1) to (6) shown in Formula 10. (1)Δα<θvi<α(2)α+Δα<θvi<π−α(3)π−α+Δα<θvi<π(4)π+Δα<θvi<π+α(5)π+α+Δα<θvi<2π−α(6)2π−α+Δα<θvi<2π

[0051] If (1) Δα < θvi < α is satisfied, the relationship between the output voltage of the inverter 10 before the dead time compensation and the current flowing through the motor 3 becomes as in the middle (b) of Fig. 5. The output voltage after dead time compensation, when (1) Δα < θvi < α is satisfied, has the value shown in the lower part (c) of Fig. 5. The waveform shown in the lower part (c) of Fig. The switching times α0 to α5 shown in Figure 5 can be expressed as given in Formula 11 using the ignition angle α and the dead time Δα. α0=Δαα1=α+Δαα2= π−αα5= π+Δαα3= π+α+Δαα4=2π−α

[0052] The dead time compensation unit 183 calculates the amplitude error ΔA and the phase angle error Δθ, which are the correction amounts for the modulation factor and the phase angle, such that at the switching times α0 to α5, the average modulation factor and phase angle in one fundamental wave cycle are the same as those that occur when no voltage error is caused due to the dead time.

[0053] In particular, the dead time compensation unit 183 can calculate the Fourier coefficients an and bn as given in Formula 12 using the supply voltage Vdc, the firing angle α and the dead time Δα. an≒2 Vdcπ(2 cos α−Δα sin α−1)bn≒0

[0054] Accordingly, the dead time compensation unit 183 can calculate the amplitude A of the output voltage of the inverter 10 as given in Formula 13 using the Fourier coefficients an and bn from Formula 12. A=2Vdcan2+bn2=4π(2 cos α−Δα sin α−1)

[0055] Compared to Formula 7 and Formula 8, which were developed using Fig. 4 for the case where no voltage error is caused due to the dead time, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ as given in Formula 14 when (1) Δα < θvi < α is satisfied. ΔA≒4π(−Δα×α)Δθ=0

[0056] Fig. 6 shows diagrams to explain the calculations of the dead time compensation unit 183 when (2) α + Δα < θvi < π - α is satisfied.

[0057] If (2) α + Δα < θvi < π - α is satisfied, the relationship between the output voltage of the inverter 10 before the dead time compensation and the current flowing through the motor 3 becomes as in the middle (b) of Fig. 6. The output voltage after dead time compensation, when (2) α + Δα < θvi < π - α is satisfied, has the value shown in the lower part (c) of Fig. 6. The waveform shown in the lower part (c) of Fig. The switching times α0 to α5 shown in Figure 6 can be expressed as given in Formula 15 using the ignition angle α and the dead time Δα. α0=Δαα1=αα2=π−αα5=π+Δαα3=π+αα4=2π−α

[0058] The dead time compensation unit 183 can calculate the Fourier coefficients an and bn as given in Formula 16. an≒2 Vdcπ(2 cos α−1)bn≒2 Vdcπ(Δα)

[0059] Accordingly, the dead time compensation unit 183 can calculate the amplitude A of the output voltage of the inverter 10 as given in Formula 17 using the Fourier coefficients an and bn from Formula 16. A=4π(2 cos α−1)

[0060] Compared to Formula 7 and Formula 8, which were developed using Fig. 4, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ as given in Formula 18 when (2) α + Δα < θvi < π - α is satisfied. ΔA=0Δθ=Δα

[0061] Fig. Figure 7 shows diagrams to explain the calculations of the dead time compensation unit 183 when (3) π - α + Δα < θvi < π is satisfied.

[0062] If (3) π - α + Δα < θvi < π is satisfied, the relationship between the output voltage of the inverter 10 before the dead time compensation and the current flowing through the motor 3 becomes as in the middle (b) of Fig. 7. The output voltage after the dead time compensation, when (3) π - α + Δα < θvi < π is satisfied, has the value shown in the lower part (c) of Fig. 7. The waveform shown in the lower part (c) of Fig. The switching times α0 to α5 shown in Figure 7 can be expressed as given in Formula 19 using the ignition angle α and the dead time Δα. α0=Δαα1=αα2=π−α+Δαα5=π+Δαα3=π+αα4=2π−α+Δα

[0063] The dead time compensation unit 183 can calculate the Fourier coefficients an and bn as given in Formula 20. an≒2 Vdcπ(2 cos α+Δα sin α−1)bn≒2 Vdcπ{(1−cos α)Δα}

[0064] Accordingly, the dead time compensation unit 183 can calculate the amplitude A of the output voltage of the inverter 10 as given in Formula 21 using the Fourier coefficients an and bn from Formula 20. A=4π(2 cos α+Δα sin α−1)

[0065] Compared to Formula 7 and Formula 8, which were developed using Fig. 4, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ as given in Formula 22 when (3) π - α + Δα < θvi < π is satisfied. ΔA=4π(Δα sin α)≒4π(Δα×α)Δθ≒0

[0066] Fig. 8 shows diagrams to explain the calculations of the dead time compensation unit 183 when (4) π + Δα < θvi < π + α is satisfied.

[0067] If (4) π + Δα < θvi < π + α is satisfied, the relationship between the output voltage of the inverter 10 before the dead time compensation and the current flowing through the motor 3 becomes as in the middle (b) of Fig. 8. The output voltage after dead time compensation, when (4) π + Δα < θvi < π + α is satisfied, is as shown in the lower part (c) of Fig. 8. The lower part (c) of Fig. The switching times α1 to α4 shown in Figure 8 can be expressed as given in Formula 23 using the ignition angle α and the dead time Δα. α1=αα2= π−α+Δαα3= π+αα4=2π−α+Δα

[0068] The dead time compensation unit 183 can calculate the Fourier coefficients an and bn as given in Formula 24. an≒2 Vdcπ(2 cos α+Δα sin α−1)bn≒2 Vdcπ(−Δαcos α)

[0069] Accordingly, the dead time compensation unit 183 can calculate the amplitude A of the output voltage of the inverter 10 as given in Formula 25 using the Fourier coefficients an and bn from Formula 24. A=4π(2 cos α+Δα sin α−1)

[0070] Compared to Formula 7 and Formula 8, which were developed using Fig. 4, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ as given in Formula 26 when (4) π + Δα < θvi < π + α is satisfied. ΔA≒4π(Δα×α)Δθ≒−Δα

[0071] Fig. Figure 9 shows diagrams to explain the calculations of the dead time compensation unit 183 when (5) π + α + Δα < θvi < 2π - α is satisfied.

[0072] If (5) π + α + Δα < θvi < 2π - α is satisfied, the relationship between the output voltage of the inverter 10 before the dead time compensation and the current flowing through the motor 3 is as shown in the middle (b) of Fig. 9. The output voltage after dead time compensation, when (5) π + α + Δα < θvi < 2π - α is satisfied, is as shown in the lower part (c) of Fig. 9. The lower part (c) of Fig. The switching times a1 to α4 shown in Figure 9 can be expressed as given in Formula 27 using the ignition angle α and the dead time Δα. A=4π(2 cos α+Δα sin α−1)

[0073] The dead time compensation unit 183 can calculate the Fourier coefficients an and bn as given in Formula 28. an≒2 Vdcπ(2 cos α−1)bn≒2 Vdcπ(−2Δαcos α)

[0074] Accordingly, the dead time compensation unit 183 can calculate the amplitude A of the output voltage of the inverter 10 as given in Formula 29 using the Fourier coefficients an and bn from Formula 28. A=4π(2 cos α−1)

[0075] Compared to Formula 7 and Formula 8, which were developed using Fig. 4, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ as given in Formula 30 when (5) π + α + Δα < θvi < 2π - α is satisfied. ΔA=0Δθ≒−2Δα

[0076] Fig. 10 shows diagrams to explain the calculations of the dead time compensation unit 183 when (6) 2π - α + Δα < θvi < 2π is satisfied.

[0077] If (6) 2π - α + Δα < θvi < 2π is satisfied, the relationship between the output voltage of the inverter 10 before the dead time compensation and the current flowing through the motor 3 becomes as in the middle (b) of Fig. 10. The output voltage after dead time compensation, when (6) 2π - α + Δα < θvi < 2π is satisfied, is as shown in the lower part (c) of Fig. 10. The lower part (c) of Fig. The switching times α1 to α4 shown in Figure 10 can be expressed as given in Formula 31 using the ignition angle α and the dead time Δα. α1=α+Δαα2= π−αα3= π+α+Δαα4=2π−α

[0078] The dead time compensation unit 183 can calculate the Fourier coefficients an and bn as given in Formula 32. an≒2 Vdcπ(2 cos α−Δα sin α−1)bn≒2 Vdcπ(−Δαcos α)

[0079] Accordingly, the dead time compensation unit 183 can calculate the amplitude A of the output voltage of the inverter 10 as given in Formula 33 using the Fourier coefficients an and bn from Formula 32. A=4π(2 cos α−Δα sin α−1)

[0080] Compared to Formula 7 and Formula 8, which were developed using Fig. 4, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ as given in Formula 34 when (6) 2π - α + Δα < θvi < 2π is satisfied. ΔA≒4π(−Δα×α)Δθ≒−Δα

[0081] Fig. Figure 11 is a table showing the relationship between the difference θvi between the voltage phase angle θv and the current phase angle θi and the amplitude error ΔA and the phase angle error Δθ. The table from Fig. 11 summarizes the amplitude error ΔA and the phase angle error Δθ, which are calculated for each of the Fig. 5 to 10 cases presented were calculated.

[0082] In each of the cases (1) to (6) using the Fig. 5 to 10, the amplitude error ΔA and the phase angle error Δθ had different values, as shown in Fig. 11. The three-pulse / one-pulse calculation unit 180 corrects the modulation factor MF used to calculate the firing angle α of the output voltage by using the amplitude error ΔA according to the Fig. 11. The three-pulse / one-pulse calculation unit 180 also corrects the phase angles θ1 and θ2 of the output voltage using the phase angle error Δθ corresponding to the range of the difference θvi. In this way, the three-pulse / one-pulse calculation unit 180 can cause the inverter 10 to output an output voltage that takes the dead time into account with respect to the required voltage. Note that, as shown in Fig. 11, the three-pulse / one-pulse calculation unit 180 may not need to correct the modulation factor MF when the amplitude error ΔA is zero. Similarly, the three-pulse / one-pulse calculation unit 180 may not need to correct the phase angles θ1 and θ2 of the output voltage when the phase angle error Δθ is zero.

[0083] In addition, the dead time compensation unit 183 can calculate the amplitude error ΔA and the phase angle error Δθ in an intermediate case between (6) 2π - α + Δα < θvi < 2π and (1) Δα < θvi < α, for example, in the interval [0, Δα], by performing linear interpolation between the amplitude error ΔA and the phase angle error Δθ calculated for each respective range. Alternatively, because Δα is very small, the dead time compensation unit 183 can set the amplitude error ΔA and the phase angle error Δθ to zero in an intermediate case between (6) 2π - α + Δα < θvi < 2π and (1) Δα < θvi < α, respectively.

[0084] The firing angle calculation unit 184 calculates the firing angle α of the output voltage of the inverter 10 based on the amplitude error ΔA calculated as the dead time compensation amount and the modulation factor MF. Specifically, the firing angle calculation unit 184 adds the amplitude error ΔA calculated as the dead time compensation amount to the modulation factor MF as an operation amount, and then calculates the firing angle A using the modulation factor MF to which the amplitude error ΔA has been added. Specifically, the firing angle calculation unit 184 can calculate the firing angle A using Formula 35. α=cos−1(π4MF+1+ΔA2)

[0085] The phase angle calculation unit 185 calculates the phase angles θ1 and θ2 of the output voltage of the inverter 10 based on the phase angle error Δθ calculated as the dead time compensation amount and the electrical angle θp of the motor 3. The phase angle θ1 indicates the phase angle of the output voltage at the next control timing. The phase angle θ2 indicates the phase angle of the output voltage at the control timing after the next control timing. Specifically, the phase angle calculation unit 185 considers the electrical angle deviation ωtc per carrier cycle calculated from the electrical angular velocity ω of the motor 3 and the carrier period tc as the one-sample delay of the phase angle. Then, the phase angle calculation unit 185 adds the phase angle error Δθ calculated as the dead time compensation amount as an operating amount to the previous voltage phase angle θv to calculate the phase angles θ1 and θ2.Specifically, the phase angle calculation unit 185 calculates the phase angles θ1 and θ2 using Formula 36 when the speed of the motor 3 is positive. θ1=θp+π2+ωtc+(θv+Δθ)θ2=θp+π2+2ωtc+(θv+Δθ)

[0086] When the rotational speed of the motor 3 is negative, the phase angle calculation unit 185 can calculate the phase angles θ1 and θ2 by changing (+π / 2) on the right side of Formula 36 to (-π / 2). Formula 36 represents the phase angles θ1 and θ2 of one phase (for example, the U phase) of the three-phase voltage. When calculating the phase angles θ1 and θ2 of the other phases of the three-phase voltage (for example, the V phase or the W phase), the phase angle calculation unit 185 can calculate the phase angles θ1 and θ2 of the other phases by shifting the phase angles θ1 and θ2 calculated using Formula 36 by 120 degrees.

[0087] The duty ratio calculation unit 186 calculates the duty ratio duvw in each phase of the three-phase voltage based on the output voltage firing angle α calculated by the firing angle calculation unit 184 and the output voltage phase angles θ1 and θ2 calculated by the phase angle calculation unit 185, and determines the position of each pulse edge (switching timing). The duty ratio calculation unit 186 then inputs the calculated position of each pulse edge to the PWM pulse generation unit 150.

[0088] The PWM pulse generation unit 150 generates a PWM pulse signal P according to the calculated position of each pulse edge and outputs it to the gate circuit 160. The gate circuit 160 outputs the drive signal DR corresponding to the PWM pulse signal P to the inverter 10. The semiconductor switching elements of the inverter 10 are controlled by the drive signal DR. This adjusts the output voltage of the inverter 10.

[0089] Fig. 12 shows the functionality of the Fig. 1 shown inverter control device 100.

[0090] As described above, the inverter control device 100 according to Embodiment 1 controls the switching operation of the inverter 10, which converts a DC voltage into an AC voltage, and applies the AC voltage to the motor 3 through pulse width modulation. The inverter control device 100 according to Embodiment 1 is provided with the dead time compensation unit 183, which performs dead time compensation to compensate for an error in the output voltage of the inverter 10 caused by the dead time of the inverter 10. The dead time compensation unit 183 performs dead time compensation based on the difference θvi between the current phase angle θi, which indicates the phase angle for outputting the current of the motor 3, and the voltage phase angle θv, which outputs a voltage corresponding to the current.

[0091] Consequently, the inverter control device 100 according to Embodiment 1 can perform dead time compensation for the required voltage, thereby enabling the output voltage of the inverter 10 to match the required voltage, as shown in Fig. 12. Accordingly, the inverter control device 100 according to Embodiment 1 can reduce the voltage error caused by the dead time. In addition, the dead time compensation unit 183 according to Embodiment 1 can perform dead time compensation based on the difference θvi between the voltage phase angle θv, which can be calculated from the dq-axis voltage command values ​​Vdq*, and the current phase angle θi, which can be calculated from the dq-axis current command values ​​Idq*. In this way, the inverter control device 100 according to Embodiment 1 does not need to perform high-speed current measurement, unlike conventional systems, and can easily perform the dead time compensation.Accordingly, the inverter control device 100 according to Embodiment 1 can easily reduce the voltage error caused by the dead time during switching from the SVPWM control mode to the three-pulse control mode, thereby suppressing torque shocks.

[0092] Furthermore, the inverter control device 100 according to Embodiment 1 is provided with the modulation factor / voltage phase angle calculation unit 181 for calculating the modulation factor MF and the voltage phase angle θv of the output voltage, and the current phase angle calculation unit 182 for calculating the current phase angle θi. The inverter control device 100 according to Embodiment 1 is provided with the firing angle calculation unit 184 for calculating the firing angle α of the output voltage and the phase angle calculation unit 185 for calculating the phase angles θ1 and θ2 of the output voltage. The dead time compensation unit 183 calculates at least one of the amplitude error ΔA and the phase angle error Δθ of the output voltage caused by the dead time as a dead time compensation amount.The ignition angle calculation unit 184 calculates the ignition angle α based on the amplitude error ΔA calculated as the dead time compensation amount and the modulation factor MF. The phase angle calculation unit 185 calculates the phase angles θ1 and θ2 based on the phase angle error Δθ calculated as the dead time compensation amount.

[0093] Therefore, the inverter control device 100 according to Embodiment 1 can calculate the firing angle α and the phase angles θ1 and θ2 so that the amplitude error ΔA and the phase angle error Δθ can be corrected even when the amplitude error ΔA and the phase angle error Δθ vary due to the range of the difference θvi. Accordingly, the inverter control device 100 according to Embodiment 1 can appropriately compensate for the voltage error even when the voltage error caused by the dead time varies according to the phase difference between the output voltage of the inverter 10 and the current flowing through the motor 3. Accordingly, the inverter control device 100 according to Embodiment 1 can easily and reliably reduce the voltage error caused by the dead time and reliably suppress torque shocks.

[0094] Therefore, in the inverter control device 100 according to Embodiment 1, the dead time compensation unit 183 performs the dead time compensation when the switching operation is controlled by the three-pulse control mode.

[0095] Therefore, when controlled by the three-pulse control mode, the inverter control device 100 according to Embodiment 1 can easily reduce the voltage error caused by the dead time and suppress torque shocks. Specifically, the inverter control device 100 according to Embodiment 1 can suppress torque shocks that conventionally occurred during switching from the SVPWM control mode to the three-pulse control mode. In addition, the inverter control device 100 according to Embodiment 1 can suppress the torque shocks that occurred during switching from the three-pulse control mode to the SVPWM control mode. Accordingly, the inverter control device 100 according to Embodiment 1 can stabilize the operation of the motor 3. [Embodiment 2]

[0096] The inverter control device 100 according to Embodiment 2 will be described with reference to Fig. 13 and Fig. 14. Description of configurations and operations of the inverter control device 100 according to Embodiment 2, which are similar to those according to Embodiment 1, will be omitted. Fig. 13 is a configuration diagram of the three-pulse / one-pulse calculation unit 180 provided in the inverter control device 100 according to Embodiment 2. Fig. Figure 14 is a table showing the relationship between the difference θvi between the voltage phase angle θv and the current phase angle θi and the phase angle error Δθ.

[0097] In Embodiment 2, an example is described in which the inverter control device 100 controls the switching operation in the one-pulse control mode.

[0098] Also in the case of the single-pulse control mode, the relationship between the range of the difference θvi and the phase angle error Δθ is the same as in Fig. 14, when the Fourier coefficients an and bn are calculated in the same way as in the case of the three-pulse control mode described in Embodiment 1. That is, as shown in Fig. 14, in the case of the one-pulse control mode, it is not necessary to calculate the amplitude error ΔA as the dead time compensation amount, and the modulation factor MF does not need to be corrected.

[0099] Accordingly, the dead time compensation unit 183 according to Embodiment 2 calculates only the phase angle error Δθ as the dead time compensation amount based on the difference θvi. The phase angle calculation unit 185 according to Embodiment 2 calculates the phase angles θ1 and θ2 of the output voltage based on the phase angle error Δθ calculated as the dead time compensation amount and the electrical angle θp of the motor 3, as in Embodiment 1. In contrast, the ignition angle calculation unit 184 according to Embodiment 2 calculates the ignition angle α of the output voltage based on the modulation factor MF that has not been corrected.

[0100] Therefore, the inverter control device 100 according to Embodiment 2 can simplify the control logic compared to Embodiment 1 because it does not need to calculate the amplitude error ΔA as the dead time compensation amount and does not need to correct the modulation factor MF. Accordingly, the inverter control device 100 according to Embodiment 2 can further easily reduce the voltage error caused by the dead time and suppress torque shocks.

[0101] In addition, in the inverter control device 100 according to Embodiment 2, the dead time compensation unit 183 performs dead time compensation when the switching operation is controlled by the one-pulse control mode.

[0102] Therefore, when controlled by the one-pulse control mode, the inverter control device 100 according to Embodiment 2 can easily reduce the voltage error caused by the dead time and suppress torque shocks. Specifically, the inverter control device 100 according to Embodiment 2 can suppress the torque shocks that occur during switching from the three-pulse control mode to the one-pulse control mode. In addition, the inverter control device 100 according to Embodiment 2 can suppress the torque shocks that occur during switching from the one-pulse control mode to the three-pulse control mode. Accordingly, the inverter control device 100 according to Embodiment 2 can further stabilize the operation of the motor 3. [Embodiment 3]

[0103] The inverter control device 100 according to Embodiment 3 will be described with reference to Fig. 15. Description of configurations and operations of the inverter control device 100 according to Embodiment 3, which are similar to those according to Embodiment 1, will be omitted. Fig. 15 is a configuration diagram of the inverter control device 100 according to Embodiment 3.

[0104] In Embodiment 3, the reduction of the voltage error caused by the dead time is used not only for torque shock suppression but also for estimating the position of the rotor of the motor 3.

[0105] The inverter control device 100 according to Embodiment 3 is provided with an induced voltage estimation axis misalignment calculation unit 141 and a speed phase estimation unit 142 instead of the rotational position detection unit 140 (or as part of the rotational position detection unit 140). The other configurations of the inverter control device 100 according to Embodiment 3 are the same as those of Embodiment 1.

[0106] The induced voltage estimation axis misalignment calculation unit 141 estimates the induced voltage E0 of the motor 3 based on the dq-axis voltage command values ​​Vdq*, the dq-axis current measurement values ​​Idq, and the speed command value ωr* that prescribes the motor speed. Then, the induced voltage estimation axis misalignment calculation unit 141 calculates the axis misalignment estimate Δθp based on the phase of the estimated induced voltage E0. The speed phase estimation unit 142 estimates the rotational position θp, which is the position of the rotor of the motor 3, based on the magnitude |E0| of the induced voltage E0 and the axis misalignment estimate Δθp.

[0107] The method for estimating the rotational position θp from the induced voltage E0 estimated using the dq-axis voltage command values ​​Vdq* is disclosed in JP 3411878 B. The inverter control device 100 according to Embodiment 3 can use the method disclosed in JP 3411878 B.

[0108] In the above method of estimating the dq-axis voltage command values ​​Vdq* using the rotational position θp, when the voltage error occurs due to the dead time, the error is superimposed on the phase of the induced voltage E0, thereby deteriorating the accuracy of estimating the rotational position θp. Because the inverter control device 100 according to Embodiment 3 can reduce the voltage error caused by the dead time as in Embodiment 1, it can improve the accuracy of estimating the rotational position θp. The same applies to estimating the magnetic flux and torque of the motor 3 using the dq-axis voltage command values ​​Vdq*, thereby enabling the inverter control device 100 according to Embodiment 3 to improve the accuracy of estimating the magnetic flux and torque of the motor 3 using the dq-axis voltage command value Vdq*. [Other]

[0109] It should be noted that the present invention is not limited to the above embodiments and may include various modifications. For example, the above embodiments have been described in detail to facilitate understanding of the present invention, and they are not necessarily limited to having all of the described configurations. In addition, a part of the configuration of one embodiment may be replaced with that of another embodiment, and a configuration of one embodiment may also be added to another embodiment. Furthermore, a part of the configuration of each embodiment may be added to, removed from, or replaced by another configuration.

[0110] Furthermore, the above-described configurations, functions, processing units, processing means, and the like may be implemented in hardware by designing all or part of them as, for example, an integrated circuit. Alternatively, the configurations, functions, and the like may be implemented in software by having a processor interpret and execute a program that realizes the respective functions. The information such as programs, tapes, and files that realize the respective functions may be stored in a memory, a recording device such as a hard disk or SSD (Semiconductor Disk Drive), or a recording medium such as an IC card, an SD card, or a DVD.

[0111] The control and information lines shown are those considered necessary for explanation purposes and do not necessarily represent all control and information lines in an actual product. In practice, it can be assumed that almost all configurations are interconnected. List of reference symbols 3 Motor (AC motor) 10 inverters 100 inverter control device 181 Modulation factor / voltage phase angle calculation unit 182 Current phase angle calculation unit 183 Dead time compensation unit 184 Ignition angle calculation unit 185 Phase angle calculation unit QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] JP 2011-15566 A

[0005] JP 3411878 B

[0107]

Claims

[1] Inverter control device for controlling a switching operation of an inverter which converts a direct current voltage into an alternating current voltage and applies the alternating current voltage to an alternating current motor, by pulse width modulation, wherein the inverter control device comprises a dead time compensation unit for performing dead time compensation to compensate for an error in an output voltage of the inverter caused by a dead time of the inverter, wherein the dead time compensation unit performs the dead time compensation based on the difference between a current phase angle indicating a phase angle for outputting a current of the AC motor and a voltage phase angle for outputting a voltage corresponding to the current. [2] The inverter control device according to claim 1, further comprising: a modulation factor / voltage phase angle calculation unit for calculating a modulation factor of the output voltage and the voltage phase angle, a current phase angle calculation unit for calculating the current phase angle, a firing angle calculation unit for calculating a firing angle of the output voltage and a phase angle calculation unit for calculating the phase angle of the output voltage, where: the dead time compensation unit calculates at least one of an amplitude error and phase angle error of the output voltage caused by the dead time as a dead time compensation amount, the ignition angle calculation unit calculates the ignition angle based on the amplitude error calculated as the dead time compensation amount and the modulation factor, and the phase angle calculation unit calculates the phase angle based on the phase angle error calculated as the dead time compensation amount. [3] The inverter control device according to claim 1, wherein the dead time compensation unit performs the dead time compensation when the switching operation is controlled by at least one of a one-pulse control mode and a three-pulse control mode.

Citation Information

Patent Citations

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    JP2011015566A

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