This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2017-141554, filed on Jul. 21, 2017; the entire contents of which are incorporated herein by reference.
Embodiments described herein relate generally to an evaluation apparatus for evaluating an inverter circuit for an electric motor and an evaluation method therefor.
An electric motor (for example, an induction motor and a synchronous motor) moves heavy objects such as trains, electric vehicles, and elevators. An inverter circuit (main circuit) is used for driving the electric motor at a high voltage and a large current. The inverter circuit applies a PWM-controlled voltage to the electric motor using a power module (a switching device such as MOSEFT and IGBT).
The inverter circuit may fail because of, for example, degradation of its component (such as electrolytic capacitors and power modules). Thus, the degradation of its component is desirably detected before its failure.
The power module switches very fast and this disturbs accurate measurement of its characteristics. For example, a controller with a general microcomputer is used for the measurement, but it has a low sampling frequency due to restrictions on processing speed of the microcomputer.
Moreover, the electric motor has a large back electromotive force with its rotation and a large disturbance on its load during its normal driving, and this disturbs accurate detection of characteristic change in the power module.
However, demounting, inspecting, and remounting the power module take large time and effort, and this causes difficulties in periodic inspection of all power modules in an inverter circuit.
An evaluation apparatus of an embodiment for evaluating an inverter circuit for an electric motor includes a three-phase-to-two-phase converter, a current controller, gate signals generator, and a storage. The three-phase-to-two-phase converter converts primary three-phase currents i1u, i1v, and i1w of the electric motor connected to the inverter circuit into a d-axis current i1d and a q-axis current i1q. The current controller generates d-axis and q-axis voltage command values v1d* and v1q* for adjusting the q-axis current i1q to a command value i1q* being substantially zero and the d-axis current i1d to a command value i1d* with feedback control of the electric motor through the inverter circuit. The gate signals generator generates gate signals gs based on the command values v1d* and v1q* and applies the gate signals gs to the inverter circuit. The storage stores the command value v1d*.
Embodiments will be described in detail with reference to the drawings.
The electric motor 10 is an AC motor operated by a three-phase AC voltage v (v1u, v1v, v1w) from the inverter circuit 20, and examples of the electric motor 10 include an induction motor and a synchronous motor.
Each of the induction motor and the synchronous motor rotates the rotor with the rotating magnetic flux formed by three-phase alternating current. In a synchronous motor, its rotor is a magnet (permanent magnet or electromagnet). On the other hand, in an induction motor, its rotor is a simple conductor (or a coil).
The electric motor 10 measures and outputs its rotor angular velocity ωr and its current values i1u, i1v, and i1w of the three phases (u, v, and w phases) on its primary side. The rotor angular velocity ωr and the current values i1u, i1v, and i1w are input to the inverter evaluation apparatus 30. For example, the rotor angular velocity ωr can be determined by detecting the rotational angle θr of the rotor of the electric motor 10 using a position sensor (for example, encoder) and differentiating the determined the rotational angle θr. The rotor angular velocity ωr may be directly determined using the velocity sensor.
Note, the rotor angular velocity ωr may be estimated without using the position sensor or the velocity sensor. For example, in the synchronous motor, its rotor angular velocity ωr can be estimated from the induced voltage (which is proportional to the rotor angular velocity ωr).
The current values i1u, i1v, and i1w can be determined using a sense resistor or a current sensor installed in the inverter circuit 20. Note, any two of the current values i1u, i1v, and i1w may be determined and the remaining one may be obtained from the relationship “i1u+i1v+i1w=0” where the sum is zero.
The MOSFETs 21 are power devices (switching devices). Six MOSFETs 21 (arms 25ul to 25wh) are arranged corresponding to three phases (u, v, and w phases) and high and low (high side, and low side) of voltage (current). Instead of a MOSFET, an IGBT may be used as a power device. The symbols “u”, “v”, and “w” of the arms 25ul to 25wh correspond respectively to the u, v, and w phases, and the symbols “h” and “l” correspond respectively to the high side and the low side of the voltages.
The freewheeling diodes 22 protect the MOSFETs 21 from the reverse current.
Here, one of the MOSFETs 21 and one of the freewheeling diodes 22 constitute one power device unit (arm 25). One arm 25 may include a plurality of MOSFETs 21 and a plurality of freewheeling diodes 22 arranged in parallel to the MOSFETs 21.
The inverter evaluation apparatus 30 (gate signals generator 35) inputs the gate signals gs to a gate driver circuit (not shown) in the inverter circuit 20. The gate driver circuit drives each power device according to the gate signals gs. That is, the gate driver circuit applies a voltage Vgs corresponding to the gate signals gs to between the gate and the source. As a result, the MOSFET 21 is brought into the ON state (reduction in drain-source resistance Rds). In this manner, the MOSFETs 21 are driven according to the gate signals gs to change DC voltage supplied from the DC power supply 23 into voltage pulses having varied pulse width (PWM control). At this time, the electric motor 10 is driven by the generated voltage pulse corresponds to three-phase alternating current.
The inverter evaluation apparatus 30 calculates command values (command values v1u*, v1v*, and v1w* of the primary voltage input to the gate signals generator 35) in accordance with the primary current values i1u, i1v, and i1w of the electric motor 10, the rotor angular velocity ωr, the command value ωr* of the rotor angular velocity, and the command value i1d* of the d-axis current output from the command value generator 31, and feedback controls the electric motor 10 (the current values i1u, i1v, and i1w and the rotor angular velocity ωr).
The inverter evaluation apparatus 30 controls the electric motor 10 using a d-q coordinate system (vector control). The d-axis is the rotation axis of the magnetic flux, and the q-axis is orthogonal to the d-axis. Three-phase currents i1u, i1v, and i1w are expressed as two-phase currents i1d, and i1q in the d-q coordinate system rotating together with the magnetic flux of the electric motor 10. As a result, the currents i1d and i1q and the voltages v1d and v1q can be treated as if they are direct current quantities.
The circuit equation of the d-q coordinate system of the electric motor 10 is expressed in the equation (1).
s: Laplace operator (derivative)
v1d: primary d-axis voltage
v1q: primary q-axis voltage
v2d: secondary d-axis voltage
v2q: secondary q-axis voltage
i1d: primary d-axis current
i1q: primary q-axis current
i2d: secondary d-axis current
i2q: secondary q-axis current
R1: primary resistance
R2: secondary resistance
M: mutual inductance
L1: primary self-inductance (L1=l1+M)
L2: secondary self-inductance (L2=l2+M)
l1: primary leakage inductance
l2: secondary leakage inductance
Ω: electrical angular velocity
ωs: slip angular velocity of induction motor (0 for synchronous motor)
As shown in the equation (1), the voltages v1d, v1q, v2d, and v2q and the currents i1d, i1q, i2d, and i2q in the d-q coordinate system are affected by the electric angular velocity ω (back electromotive force). Therefore, inaccurate electrical angular velocity ω causes difficulty of distinguishing between the characteristic change of the inverter circuit 20 and the influence of the back electromotive force. During normal driving, the influence due to load fluctuations is difficult to be estimated.
However, as described below, the influence due to the back electromotive force and the load fluctuation can be reduced by controlling the electric motor 10 so that the rotational angular velocity ωr of the rotor becomes 0 to adjust the primary q-axis current i1q to 0 (zero)
The torque r applied to the rotor of the electric motor 10 can be expressed by equation (2).
τ=(PnM/L2)(i1qφ2d−i1dφ2q) (2)
Pn: pole pair number
φ2d: secondary d-axis interlinkage magnetic flux
φ2q: secondary q-axis interlinkage magnetic flux
In the d-q coordinate system, since the d-axis is generally set to the same direction as the secondary magnetic flux, equations (3) and (4) hold.
Φ2d=φ2 (3)
Φ2q=0 (4)
By applying the equations (3) and (4) to the equation (1), the secondary flux linkage φ2 is expressed by the following equation (5).
Φ2=[(R2M)/(L2s+R2)]i1d (5)
Also, the torque r of the rotor is expressed by the equation (6).
τ=(PnM/L2)i1qφ2 (6)
If the primary q-axis current i1q is zero the torque r becomes substantially zero according to the equation (6) and the electric motor 10 does not rotate, even if a secondary interlinkage flux φ2 exists (i1d≠0).
As described above, by controlling the speed so that the rotational angular velocity ωr of the rotor becomes 0 to adjust the primary q-axis current i1q to 0, the command value v1d* of the d-axis voltage can be obtained without being influenced by the back electromotive force or the load variation.
Characteristics of the power devices (MOSFETs 21) of the inverter circuit 20 can be evaluated by using the command value v1d* of the d-axis voltage. That is, when the characteristics of the power devices (MOSFETs 21) changes, the command value v1d* of the d-axis voltage is considered to change. When the current control system 33 is working, the currents i1u, i1v, and i1w in the electric motor 10 do not change even if the characteristics of the power devices (inverter circuit 20) change. The command value v1d* is considered to change so as to cancel the characteristic change of the power devices.
When the control is performed as in the embodiment, the electrical angular velocity ω is close to zero, and does not affect the state of the d-axis. Further, the command value i1q* of the q-axis current becomes close to zero, and does not directly relate to the characteristics of the power devices (MOSFETs 21).
The inverter evaluation apparatus 30 includes a command value generator 31, a speed control system 32, a current control system 33, a two-phase-to-three-phase converter 34, gate signals generator 35, a diagnostic unit 36, a phase estimator 41, a phase storage 42, a three-phase-to-two-phase converter 43, and a switch 44.
The command value generator 31 outputs the command value ωr* of the rotor angular velocity and the command value i1d* of the primary d-axis current of the electric motor 10. The command value generator 31 can switch between the normal operation mode and the diagnosis mode. In the normal operation mode, the electric motor 10 is controlled to rotate. On the other hand, in the diagnosis mode, the electric motor 10 is controlled not to rotate. That is, the command value ωr* of the rotor angular velocity is adapted to 0 (zero), and the command value i1d* of the primary d-axis current is set to a predetermined value.
Here, the command value ωr* may be in its vicinity (near zero) even if it is not 0. If the absolute value of the command value ωr* is within a range in which the angular velocity of the rotor can be ignored, it can be said to be near zero. Within this range, it can be said that the electric motor 10 is substantially non-rotating. The command value i1d* can be appropriately changed with time. The details will be described later.
The speed control system 32 feedback controls to generate a command value i1q* for adapting the rotational angular velocity ωr of the electric motor 10 to a command value ωr* in the vicinity of zero. The speed control system 32 receives the rotor angular velocity ωr from the electric motor 10, and the command value ωr* of the rotor angular velocity from the command value generator 31, and outputs the command value i1q* of the primary q-axis current.
As described above, by setting the command value ωr* to 0, the command value i1q* basically converges to 0. However, the command value i1q* may be in its vicinity (near zero) even if it is not 0. If the absolute value of the command value i1q* is within a range in which the angular velocity of the rotor can be ignored, it can be said to be near zero. Within this range, the electric motor 10 can be substantially non-rotated.
The speed control system 32 outputs the command value i1q* of the primary q-axis current according to the difference Δ (=ωr*−ωr) between the rotor angular velocity ωr and the command value ωr*. The speed control system 32 feedback-controls so that the difference Δ approaches zero. For example, the command value i1q* of the primary q-axis current is calculated from the difference Δ using the PI control. That is, the command value i1q* is calculated based on the difference Δ and its integral.
The current control system 33 feedback controls to generate the command values v1d*, and v1q* of the d-axis and q-axis voltages for adjusting the q-axis current i1q to the command value i1q* in the vicinity of zero and the d-axis current i1d to the predetermined command value i1d*. The current control system 33 receives the primary d-axis current value i1d and the primary q-axis current value i1q from the three-phase-to-two-phase converter 43, the command value i1d* of the primary d-axis current from the command value generator 31, and the command value i1q* of the primary q-axis current from the speed control system 32, and outputs the command values v1d* and v1q* of the primary d-axis voltage and the primary q-axis voltage. The current control system 33 can work in non-interference control for suppressing interference between the d-axis and the q-axis.
The currents i1d, and i1q are obtained by converting the three-phase currents i1u, i1v, and i1w into two-phase currents by the three-phase-to-two-phase converter 43. This details will be described later.
The current control system 33 calculates the command values v1d* and v1q* of the primary d-axis voltage and the primary q-axis voltage in accordance with the difference Δ1 (=i1d*−i1d) between the primary d-axis current i1d and its command value i1d*, and the difference Δ2 (=i1q*−i1q) between the primary q-axis current i1q and the command value i1q*). The current control system 33 feedback controls so that the differences Δ1 and Δ2 both approach zero. For example, the command values v1d* and v1q* are calculated from the differences Δ1 and Δ2 respectively using the PI control. At this time, in addition to the differences Δ1 and Δ2 and their integrals, non-interference control for independently controlling the d-axis and q-axis components can be used.
The two-phase-to-three-phase converter 34 converts the command values v1d*, and v1q* of the two-phase voltage into the command values v1u*, v1v*, and v1w* of the three-phase voltage. The conversion equations from command values v1d*, and v1q* to command values v1u*, v1v*, and v1w* are expressed in the equation (7).
The two-phase-to-three-phase converter 34 receives the electrical angle θ from the phase estimator 41 or the phase storage 42. The details will be described later.
The gate signals generator 35 generates the gate signals gs based on the command values v1d* and v1q*, and applies them to the inverter circuit 20. Specifically, gate signals gs is generated by comparing the command values v1u*, v1v*, and v1w* of the three-phase voltages converted from the command values v1d*, and v1q* of the two-phase voltage with the carrier signal (for example, triangular wave or saw-tooth wave).
As described above, the gate signals gs is input to the gate driver circuit (not shown) of the inverter circuit 20. The gate driver circuit drives each power device (gate terminal 24) according to the gate signals gs to apply the voltage v (v1u, v1v, vw1) to the electric motor 10.
The diagnostic unit 36 stores the command value v1d* of the d-axis voltage and diagnoses the power device (MOSFET 21) of the inverter circuit 20 (evaluates the characteristics) by using the command value v1d*. For example, the command value v1d* of the recorded d-axis voltage is compared with the reference value, and if the absolute value of the difference is larger than the threshold value, the quality of the inverter circuit 20 is determined to degrade. The details will be described later.
The phase estimator 41 estimates the phase (electrical angle θ). As described above, the electrical angle θ is used for conversion in the two-phase-to-three-phase converter 34. The phase estimation method differs depending on the type of the electric motor 10 (induction motor, or synchronous motor).
If the electric motor 10 is an induction motor, the electrical angle θ can be determined using the rotor angular velocity ωr, the primary q-axis current i1q, and the secondary flux linkage φ2.
The secondary flux linkage flux φ2, and the slip frequency ωs are expressed by the following equations (11) and (12).
φ2=[M/(1+(L2/R2)s)]i1d (11)
ωs=(R2M/L2Φ2)i1q (12)
Further, the electrical angular velocity ω of the electric motor 10, the rotor angular velocity ωr, and the slip frequency ωs have the relationship of the equation (13).
ω=ωr+ωs (13)
The electric angular velocity ea is determined using equations (11) to (13). The electrical angle θ is obtained by integrating the electrical angular velocity ω as follows.
θ=∫ωdt=∫(ωr+ωs)dt (14)
If the electric motor 10 is a synchronous electric motor, the electric angle θ can be determined by multiplying the rotational angle θr of the rotor by the pole pair number Pn.
θ=Pnθr (15)
Although an example of a method for estimating the electrical angle θ is described above, other methods may be used.
The phase storage 42 stores a fixed value of the electrical angle θ. The phase storage 42 can store a plurality of fixed values. In the case of an induction motor, the electrical angle θ may be fixed. Setting the electrical angle θ to an appropriate fixed value enables a change in the distribution of the currents (the direction of the current and the ratio of currents in each phase (u, v, and w)) to the arms 25 of the inverter circuit 20. The details will be described later.
The switch 44 switches between the phase estimator 41 and the phase storage.
The three-phase-to-two-phase converter 43 converts the three-phase current i1u, i1v, and i1w (three-phase currents on the primary of the electric motor 10 connected to the inverter circuit 20) into two-phase currents i1d, and i1q (d-axis current i1d, and q-axis current i1q). The conversion equation from the three-phase currents i1u, i1v, and i1w to the two-phase currents i1d, and i1q is expressed in Equation (16).
Hereinafter, the control based on the fixed electrical angle θ will be described. The change in the fixed value varies the direction of the current in the inverter circuit 20 and the ratio of current in each phase. The conversion equation from two-phase current to three-phase current is expressed in equation (17).
As shown in the equation (17), when (the command value of) the currents i1d, and i1q are fixed, the currents i1u, i1v, and i1w change according to the phase (electrical angle θ). As described above, when the current i1q is 0, the electric motor 10 (rotor) does not rotate. At this time, the electrical angle θ is independent of the rotation of the rotor. That is, the electrical angle θ may be set to an arbitrary value, or it may be changed with time.
For example, when controlling the q-axis current i1q to 0 (q-axis current command value: i1q*=0), the ratio of the currents i1u, i1v, and i1w changes according to the electrical angle θ (=0, 2π/3, −2π/3 [rad]), as follows.
i
1u=−2i1v=−2i1w (when θ=0 [rad])
−2i1u=i1v=−2i1w (when θ=2π/3 [rad])
−2i1u=−2i1v=i1w (when θ=−2π/3 [rad])
That is, even if the command value i1d* of the d-axis current is constant, the ratio of the currents i1u, i1v, and i1w can be appropriately changed according to the electrical angle θ.
When the currents i1d, i1q, i1u, i1v, and i1w of the equation (17) are replaced with the voltages v1d*, v1q*, v1u*, v1v*, and v1w*, respectively, an equation of the voltage holds. That is, even if the command value v1d* of the d-axis voltage is constant, the ratio of the voltages v1u*, v1v*, and v1w* can be appropriately changed according to the electrical angle θ.
In this way, changing the electrical angle θ can vary where the current flows and the voltage is applied, that is, change the arms 25 (the MOSFET 21) through which the current flows. For example, as described above, setting the electrical angle θ to 0 [rad], 2π/3 [rad], and −2π/3 [rad] increases the contribution of the u-phase high-side arm 25uh, the v-phase high-side arm 25vh, and the w-phase high-side arm 25wh, respectively.
When the electrical angle θ is set to any one of π/6 [rad], π/2 [rad], 7π/6 [rad], −π/6 [rad], −π/2 [rad], and −7π/6 [rad], one of the phase currents i1u, i1v, and i1w becomes 0. That is, an arm 25 (MOSFET 21) without current flow can be achieved. In this case, the three-phase inverter circuit 20 is driven like a single-phase inverter.
As described above, adjusting the electrical angle θ can limit the arm 25 (the MOSFET 21) through which the current flows. This makes it easy to distinguish the arm 25 (MOSFET 21) whose characteristics has changed.
The operation procedure of the inverter evaluation apparatus 30 will be described.
The normal operation mode, or the diagnosis mode are selected. In accordance with the selected mode, the operation of the command value generator 31 is switched. In the normal operation mode, the command value generator 31 outputs normal speed command value (or normal q-axis current command value i1q*) and the d-axis current command value i1d*. In accordance with the gate signals gs outputted from the inverter evaluation apparatus 30, the electric motor 10 rotates (steps S21, and S22).
(2) Outputting the Command Value from the Command Value Generator 31 (Steps S12, and S13)
In the diagnostic mode, the command value generator 31 sets the speed command value ωr* (command value of the rotor angular velocity ωr) to 0 and sets the command value i1d* of the primary d-axis current to a predetermined value.
As the speed command value ωr* is 0, the inverter evaluation apparatus 30 performs feedback control so that the electric motor 10 is in a non-rotating state, and the command value v1d* of the d-axis voltage is recorded when the control state is stabilized.
(4) Change of Command Value i1d* (Steps S16 and S17)
When the measurement is continued, the command value i1d* is changed, and the non-rotation control and recording is repeated. For example, a step value is added to the command value i1d* (step input), and a command value v1d* of the d-axis voltage is obtained. Instead of step input, DC input or AC input may be used. In accordance with the pattern (step, DC, or AC) of the current i1d, the command value i1d* is changed.
Here, the switch 44 may switch the phase estimator 41 and the phase storage 42. In this case, the electrical angle θ is switched between the estimated value in the phase estimator 41 and the fixed value in the phase storage 42. Further, different electric angles θ may be selected from a plurality of fixed values of the phase storage 42.
Upon completion of the measurement, the inverter circuit 20 is diagnosed based on the recorded command value v1d* of the d-axis voltage, and a sign of failure is detected. For example, comparing the command value v1d* of the recorded d-axis voltage with the reference value can determine whether the MOSFET 21 is degraded.
As the reference value, the nominal command value v1dn* and the initial command value v1d0* (initial value) can be used. For example, with respect to a new inverter circuit 20, the command value v1d0* in the initial state is acquired and held, and is compared with the command value v1d* in the inverter circuit 20 after aged degradation. When the current i1d is changed with time, the reference value may be a command value v1d* at a certain time or a value obtained by processing the command values (for example, the average value of the command value v1d*).
Instead of the reference value, the command values v1d* may be compared with each other. For example, the electrical angle θ is adjusted to change phases where current flows through and the command values v1d* between the different phases can be compared with each other. Changes in characteristics between the power devices (arms 25) can be compared.
As described above, feedback controlling the electric motor 10 in a non-rotating state and recording the command value v1d* of the d-axis voltage enable diagnosis of the inverter circuit 20 and detection of a sign of failure.
The command value generator 31 can switch between the normal operation mode and the diagnosis mode. In the normal operation mode, the electric motor 10 is controlled to rotate. On the other hand, in the diagnosis mode, the electric motor 10 is controlled not to rotate. That is, the command value i1q* of the primary q-axis current is 0 (zero), and the command value i1d* of the primary d-axis current is a predetermined value. The command value i1d* can be appropriately changed with time.
As in the first embodiment, the command value i1q* may be in the vicinity (near zero) even if it is not 0. If the absolute value of the command value i1q* is within a negligible range of the angular velocity of the rotor, it can be said to be near zero. Within this range, the electric motor 10 can substantially non-rotate.
As in the first embodiment, the current control system 33 calculates the command values v1d* and v1q* of the primary d-axis voltage and the primary q-axis voltage in accordance with the difference Δ1 (=i1d*−i1d) between the primary d-axis current i1d and its command value i1d*, and the difference Δ2 (=i1q*−i1q) between the primary q-axis current i1q and its command value i1q*. The current control system 33 performs feedback control so that the differences Δ1 and Δ2 both approach zero.
As described above, even in the absence of the speed control system 32, similarly to the first embodiment, feedback controlling the electric motor 10 in a non-rotating state and recording the command value v1d* of the d-axis voltage enable diagnosis of the inverter circuit 20 and detection of a sign of failure.
Hereinafter, the operation result of the inverter evaluation system in the diagnostic mode will be described.
The command value ωr* of the rotor angular velocity is set to 0, the electrical angle θ is set to 0, and the command value i1d* of the current i1d of the d-axis is a value obtained by passing the step input through a low-pass filter.
Since the command value i1q* of the q-axis current is 0, the q-axis current i1q is also controlled to be substantially 0. In addition, the current i1d on the d-axis quickly reached substantially a constant value corresponding to the command value i1d* (see
The line currents i1u, i1u, and i1w has seemingly the relation “i1u=−2i1v=−2i1w” corresponding to the electrical angle θ equal to 0 (see
In addition, since no torque is generated, the rotor angular velocity ωr is seemingly extremely small, and the electric motor 10 is not substantially rotated (see
The input capacitances Ciss of the MOSFETs 21 in the arm 25uh (u-phase high side) are increased from the nominal value Ciss0 to Ciss1, and Ciss2 in two steps, and the command value v1d* of the d-axis voltage is obtained. Note, the command values ωr* and i1d* and the electrical angle θ are the same as in the first embodiment.
The on-resistance Rdson of the MOSFET 21 of the u-phase high side (arm 26) is increased from the nominal value Rdson0 to Rdson1, and Rdson2 to obtain the command value v1d* of the d-axis voltage. Note, the command values ωr* and i1d* and the electrical angle θ are the same as in the first embodiment
The electrical angle θ is changed into three values θ1, θ2, and θ3 (θ1=0 [rad], θ2=2π/3 [rad], and θ3=−2π/3 [rad]). When the electrical angle θ is θ1, θ2, and θ3, the contribution of the u-phase high-side power device (arm 25uh), v-phase high-side power device (arm 25vh), and w-phase high-side power device (arm 25wh), respectively, becomes large.
The input capacitance Ciss of the u-phase high-side (arm 25uh) MOSFET 21 is set to be large from the nominal value Ciss0, the electrical angle θ is changed to θ1, θ2, and θ3, and the d-axis voltage command value v1d* is obtained in these cases. The command values ωr* and i1d* are the same as those in Example 1.
As described above, comparing the control output (the command value v1d* of the d-axis voltage) enables evaluation of the switching characteristics of the power device even with a low sampling frequency.
While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.
Number | Date | Country | Kind |
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2017-141554 | Jul 2017 | JP | national |