JP4596251B2 - Phase loss detection device and AC-AC direct conversion device - Google Patents

Phase loss detection device and AC-AC direct conversion device Download PDF

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JP4596251B2
JP4596251B2 JP2005114721A JP2005114721A JP4596251B2 JP 4596251 B2 JP4596251 B2 JP 4596251B2 JP 2005114721 A JP2005114721 A JP 2005114721A JP 2005114721 A JP2005114721 A JP 2005114721A JP 4596251 B2 JP4596251 B2 JP 4596251B2
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英樹 大口
以久也 佐藤
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Fuji Electric Co Ltd
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Description

本発明は、多相交流の欠相を検出する欠相検出装置、及び、この欠相検出装置を備えたマトリクスコンバータ等の交流−交流直接変換装置に関するものである。   The present invention relates to a phase loss detection device that detects a phase loss of a polyphase AC, and an AC-AC direct conversion device such as a matrix converter including the phase loss detection device.

図6は、特許文献1に開示されている従来のインバータ装置及びその欠相検出回路の構成であり、入出力は一般的な三相の場合を示している。図6では、入力側をR,S,T相、出力側をU,V,W相としてある。   FIG. 6 shows a configuration of a conventional inverter device and its phase loss detection circuit disclosed in Patent Document 1, and shows an input / output in a general three-phase case. In FIG. 6, the input side is R, S, T phase, and the output side is U, V, W phase.

図6において、整流器301は三相交流電圧を直流電圧に変換し、この直流電圧は直流リンク部のコンデンサ303によって平滑され、インバータ302に供給される。
直流電圧検出手段401は直流電圧の瞬時値を取り込み、電圧比較手段402は直流電圧の瞬時値と設定値とを常時比較している。この電圧比較手段402は直流電圧の比較結果に基づいて入力電圧の欠相を検出する。以下に、その動作を述べる。
In FIG. 6, the rectifier 301 converts a three-phase AC voltage into a DC voltage, and this DC voltage is smoothed by a capacitor 303 in the DC link unit and supplied to the inverter 302.
The DC voltage detection means 401 takes in the instantaneous value of the DC voltage, and the voltage comparison means 402 constantly compares the instantaneous value of the DC voltage with the set value. The voltage comparison means 402 detects an open phase of the input voltage based on the comparison result of the DC voltage. The operation will be described below.

図7は、図6のコンデンサ303による平滑化前後の直流電圧の波形図であり、点線は平滑化前の直流電圧edc0を、実線は平滑化後の直流電圧edcを示している。図7に示すように、平滑化後の直流電圧edcの下限値(正常下限電圧enl1)は、平滑化前の直流電圧edc0の下限値enm1までは低下せず、その分、リプルが低減されている。 FIG. 7 is a waveform diagram of the DC voltage before and after smoothing by the capacitor 303 in FIG. 6, the dotted line indicates the DC voltage e dc0 before smoothing, and the solid line indicates the DC voltage e dc after smoothing. As shown in FIG. 7, the lower limit value (normal lower limit voltage e nl1 ) of the DC voltage e dc after smoothing does not decrease to the lower limit value e nm1 of the DC voltage e dc0 before smoothing. Has been reduced.

一方、図8は入力電圧の欠相時における平滑化前後の直流電圧を示す波形図である。例えば、S相電圧が欠相した場合、整流器301はR相,T相の各単相電圧を整流するため、直流電圧は電源周波数の2倍で脈動する。このため、平滑化後の直流電圧edcの下限値は正常下限電圧enl1よりも低下するので、この値が欠相検出下限電圧eに達することにより欠相を検出することができる。 On the other hand, FIG. 8 is a waveform diagram showing the DC voltage before and after smoothing when the input voltage is lost. For example, when the S phase voltage is lost, the rectifier 301 rectifies each single phase voltage of the R phase and the T phase, so that the DC voltage pulsates at twice the power supply frequency. Therefore, since the lower limit value of the DC voltage e dc after smoothing is lower than the normal lower limit voltage e nl1, it is possible to detect the loss of phase by this value reaches the open phase detection lower limit voltage e s.

また、他の従来技術として、特許文献2に記載された電力変換装置における欠相検出技術が存在する。
この従来技術は、インバータの出力側に接続されたΔ−Y変圧器の出力線間電圧を電圧測定器を介して欠相検出回路に入力し、前記線間電圧の絶対値をローパスフィルタに通して閾値と比較することにより欠相を検出するものである。
As another conventional technique, there is a phase loss detection technique in the power conversion device described in Patent Document 2.
In this prior art, the output line voltage of the Δ-Y transformer connected to the output side of the inverter is input to a phase loss detection circuit via a voltage measuring device, and the absolute value of the line voltage is passed through a low-pass filter. The phase loss is detected by comparing with a threshold value.

特開2004−56893号公報([0007]〜[0010]、図1〜図3等)JP-A-2004-56893 ([0007] to [0010], FIGS. 1 to 3 etc.) 特開2004−88861号公報([0005]〜[0009]、図1〜図3等)Japanese Unexamined Patent Publication No. 2004-88661 ([0005] to [0009], FIGS. 1 to 3 and the like)

特許文献1の従来技術をそのまま交流−交流直接変換器に適用して欠相を検出する場合には、交流入力電圧を直流電圧に変換するための整流器やコンデンサ等の平滑手段、直流電圧検出手段、電圧比較手段等のハードウェアを新たに追加する必要がある。しかし、これらの回路部品を追加すると装置が大形化し、また、コスト上昇の原因ともなる。
更に、特許文献2の従来技術においても、各線間電圧に対して個別に絶対値演算回路、ローパスフィルタ、比較回路等を設けなくてはならず、回路構成が複雑化するという問題がある。また、実際の欠相発生から欠相検出までにローパスフィルタの時定数に応じた時間を要するため、欠相発生時にインバータの運転を直ちに停止する必要がある場合には、停止措置が遅れて運転が継続される結果、負荷に悪影響を及ぼすおそれがある。
そこで本発明の解決課題は、回路部品の増加や構成の複雑化を伴うことなく低コストにて確実かつ迅速に欠相を検出可能とした欠相検出装置、及び、この欠相検出装置を備えた交流−交流直接変換装置を提供することにある。
When the prior art of Patent Document 1 is applied to an AC / AC direct converter as it is to detect an open phase, smoothing means such as a rectifier and a capacitor for converting an AC input voltage into a DC voltage, DC voltage detecting means It is necessary to newly add hardware such as voltage comparison means. However, the addition of these circuit components increases the size of the device and increases costs.
Furthermore, the prior art of Patent Document 2 also has a problem that the circuit configuration becomes complicated because an absolute value calculation circuit, a low-pass filter, a comparison circuit, and the like must be provided for each line voltage. Also, since a time corresponding to the time constant of the low-pass filter is required from the actual occurrence of phase loss to the detection of phase loss, if it is necessary to immediately stop the inverter operation at the time of phase loss, the stop action is delayed. As a result, the load may be adversely affected.
Accordingly, a problem to be solved by the present invention is to provide an open phase detection device capable of detecting a phase loss reliably and quickly at a low cost without increasing the number of circuit components and complication of the configuration, and the open phase detection device. Another object is to provide an AC-AC direct conversion device.

上記課題を解決するため、請求項1に記載した欠相検出装置は、多相交流電源の各相電圧を検出する電源電圧検出手段と、
この電源電圧検出手段により検出した各相電圧から電源電圧ベクトルの大きさを演算する演算手段と、
この演算手段により演算した電源電圧ベクトルの大きさが設定値より低下したことを検出する電圧低下検出手段と、
この電圧低下検出手段の出力に基づいて、前記電源電圧ベクトルの大きさが前記設定値より低下した回数、及び、最初に前記設定値より低下してからの経過時間を検出する手段と、
前記経過時間内に前記回数が所定値になったことにより前記多相交流電源の欠相を検出する手段と、を備えたものである。
In order to solve the above-described problem, the phase loss detection device according to claim 1 includes power supply voltage detection means for detecting each phase voltage of the multiphase AC power supply,
Calculation means for calculating the magnitude of the power supply voltage vector from each phase voltage detected by the power supply voltage detection means,
Voltage drop detection means for detecting that the magnitude of the power supply voltage vector calculated by the calculation means has decreased below a set value;
Based on the output of the voltage drop detection means, the number of times the magnitude of the power supply voltage vector becomes lower than the set value, and means for detecting the elapsed time from the first lower than the set value,
The number of times within the elapsed time is obtained and a means for detecting the open phase of the multiphase AC power supply by having reached a predetermined value.

請求項2に記載した交流−交流直接変換装置は、請求項1に記載した欠相検出装置を備えたものである。
According to a second aspect of the present invention, there is provided an AC-AC direct conversion device including the open phase detection device according to the first aspect.

請求項3に記載した交流−交流直接変換装置は、請求項2に記載した交流−交流直接変換装置において、前記欠相検出装置から出力される欠相検出信号を用いて直接変換器の運転を停止する手段を備えたものである
The AC-AC direct conversion device according to claim 3 is the AC-AC direct conversion device according to claim 2 , wherein the direct converter is operated using the phase loss detection signal output from the phase loss detection device. those having a means for stopping.

本発明によれば、電源電圧ベクトルの大きさに基づく演算により欠相を検出するため、各相電圧を個別に閾値と比較して欠相が発生した相を特定する方法に比べて回路構成を簡略化することができ、欠相検出装置を低コストにて実現することができる。
このため、例えば交流−交流直接変換装置に適用する場合には、整流器や平滑手段等を付加しなくても既存の制御装置のソフトウェアを追加、改良するだけで、欠相の迅速な検出及び保護動作が可能になる。
According to the present invention, in order to detect an open phase by calculation based on the magnitude of the power supply voltage vector, the circuit configuration is compared with the method of identifying the phase in which the open phase has occurred by individually comparing each phase voltage with a threshold value. This can be simplified, and the phase loss detection device can be realized at low cost.
For this reason, for example, when applied to an AC-AC direct conversion device, it is possible to quickly detect and protect open phases by simply adding or improving software of an existing control device without adding a rectifier or smoothing means. Operation becomes possible.

以下、図に沿って本発明の実施形態を説明する。
図1は本発明の第1実施形態を示すブロック図であり、請求項1に記載した欠相検出装置の実施形態に相当する。この実施形態は、本発明にかかる欠相検出装置を交流−交流直接変換装置に適用した場合のものである。
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a block diagram showing a first embodiment of the present invention, which corresponds to the embodiment of the phase loss detection device described in claim 1. In this embodiment, the phase loss detection device according to the present invention is applied to an AC-AC direct conversion device.

図1において、1は三相交流電源、4はリアクトル41及びコンデンサ42からなる入力フィルタ、3はマトリクスコンバータ等の交流−交流直接変換器、2は交流電動機等の負荷である。なお、本明細書では、電源1、入力フィルタ4、直接変換器3と、以下に述べる各手段とを含めた全体を交流−交流直接変換装置と呼ぶものとする。   In FIG. 1, 1 is a three-phase AC power source, 4 is an input filter comprising a reactor 41 and a capacitor 42, 3 is an AC-AC direct converter such as a matrix converter, and 2 is a load such as an AC motor. In the present specification, the whole including the power source 1, the input filter 4, the direct converter 3, and each means described below is referred to as an AC-AC direct conversion device.

次に、前記直接変換器3の制御装置において、200は電源電圧検出手段であり、201は三相各相の電源電圧v,v,vを数式1に基づいて二相量vα,vβに変換し、数式2によって二相量vα,vβから電源電圧ベクトルの大きさVを演算する大きさ演算手段である。 Next, in the control device for the direct converter 3, reference numeral 200 denotes power supply voltage detection means, and 201 denotes the power supply voltages v R , v S , and v T of the three-phase each phase based on Equation 1 based on the two-phase amount v α. , V β , and a magnitude calculation means for calculating the magnitude V i of the power supply voltage vector from the two-phase quantities v α , v β by Equation 2.

Figure 0004596251
Figure 0004596251

Figure 0004596251
Figure 0004596251

ここで、交流入力電圧の欠相時における電源電圧ベクトルの振る舞いについて述べる。
例えば、R相で欠相が起きると、R相電源電圧検出値はv=0となる。また、零相分が検出できない、すなわち三相電圧検出値の和がゼロであることを考慮すると、v=−vとなる。これらの条件を数式1に代入すると、電源電圧の二相量vα,vβは数式3によって表される。
Here, the behavior of the power supply voltage vector when the AC input voltage is lost is described.
For example, when an open phase occurs in the R phase, the R phase power supply voltage detection value is v R = 0. Considering that the zero-phase component cannot be detected, that is, the sum of the three-phase voltage detection values is zero, v S = −v T. When these conditions are substituted into Equation 1, the two-phase amounts v α and v β of the power supply voltage are expressed by Equation 3.

Figure 0004596251
Figure 0004596251

数式3を数式2に代入すると、数式4となる。   Substituting Equation 3 into Equation 2 yields Equation 4.

Figure 0004596251
Figure 0004596251

いま、各相の電源電圧が正弦波であるとすると、S相電圧vは数式5によって表される。 Now, assuming that the power supply voltage of each phase is a sine wave, the S-phase voltage v S is expressed by Equation 5.

Figure 0004596251
Figure 0004596251

数式5を数式4に代入すると、電源電圧ベクトルの大きさVは、図2に示すように電源周波数の2倍で脈動することがわかる。
第1実施形態は上記の点に着目したものであり、図1における電圧低下検出手段202は、電源電圧ベクトルの大きさVが所定の設定値よりも低下した際に“H(High)”レベルの信号を出力し、設定値以上の時は、“L(Low)”レベルの信号を出力する。欠相が発生すると、電源電圧ベクトルの大きさVは前述のように電源周波数の2倍で脈動するので、電圧低下検出手段202の出力信号のレベルは“H”と“L”を繰り返し、“L”から“H”または“H”から“L”へのレベルの切り替わり周期は電源周期の半分となる。このため、図2における電圧低下フラグの周期T1vは、電源周波数が50〔Hz〕であれば10〔ms〕となり、60〔Hz〕であれば約8.3〔ms〕となる。
Substituting Equation 5 into Equation 4, the magnitude V i of the power supply voltage vector, it can be seen that pulsates at twice the power supply frequency as illustrated in FIG.
The first embodiment pays attention to the above points, and the voltage drop detection means 202 in FIG. 1 is “H (High)” when the magnitude V i of the power supply voltage vector falls below a predetermined set value. A level signal is output, and if it is above the set value, an "L (Low)" level signal is output. When phase failure occurs, the magnitude V i of the power supply voltage vector so pulsates at twice the power supply frequency as described above, the level of the output signal of the voltage drop detection means 202 repeats the "H" and "L", The switching cycle of the level from “L” to “H” or “H” to “L” is half the power cycle. For this reason, the period T1v of the voltage drop flag in FIG. 2 is 10 [ms] when the power supply frequency is 50 [Hz], and is approximately 8.3 [ms] when 60 [Hz].

図1の電圧低下検出手段202の出力側に設けられた電圧低下回数検出手段203は、電圧低下検出手段202の出力信号の立上がり(“L”から“H”)または立下がり(“H”から“L”)の回数を計算する。また、時間計測手段204は電圧低下検出手段202の出力信号のレベルが“H”となって最初に電圧低下が検出されてからの経過時間を、ある設定時間の範囲内で計測する。   The voltage drop frequency detection means 203 provided on the output side of the voltage drop detection means 202 of FIG. "L") is calculated. In addition, the time measuring unit 204 measures the elapsed time after the level of the output signal of the voltage drop detecting unit 202 becomes “H” and the voltage drop is first detected within a certain set time.

図3は、本実施形態における欠相発生時のシミュレーション波形を示している。
図示するようにR相に欠相が発生してR相電圧vが消失すると、上述のごとく規則的に電源電圧ベクトルの大きさの低下が検出されるようになる。このため、例えば、電源周波数が50〔Hz〕の場合、時間計測手段204により計測した2周期(40〔ms〕)以内に、電圧低下回数検出手段203によって電圧低下回数が4または5回(すなわち電圧低下フラグの周期が10〔ms〕以下)検出されたら、図1の欠相検出手段205は欠相と判断して欠相検出信号(欠相検出フラグ)を出力する。なお、図3の例は、電圧低下回数を5回検出した時点で欠相を検出している。
FIG. 3 shows a simulation waveform when an open phase occurs in the present embodiment.
As shown in the drawing, when an open phase occurs in the R phase and the R phase voltage v R disappears, a decrease in the magnitude of the power supply voltage vector is regularly detected as described above. For this reason, for example, when the power supply frequency is 50 [Hz], the number of times of voltage drop is 4 or 5 times (ie, by the voltage drop number detection means 203 within two cycles (40 [ms]) measured by the time measuring means 204 (that is, If the period of the voltage drop flag is 10 [ms] or less), the phase loss detection means 205 in FIG. 1 determines that there is a phase loss and outputs a phase loss detection signal (phase loss detection flag). In the example of FIG. 3, the phase loss is detected when the number of voltage drops is detected five times.

このようにして欠相検出信号が出力されると、図1のPWM信号作成手段100が交流−交流直接変換器3を全ゲート遮断してその動作を停止させる。なお、制御信号作成手段101はPWM信号作成手段100に対する電圧指令等を作成して出力するものであり、欠相検出信号をこの制御信号作成手段101に入力して動作を停止させてもよい。
また、時間計測手段204における設定時間内に電圧低下回数が設定値に満たない場合には、欠相ではないと判断して通常動作を継続する。
なお、図1の実施形態では電源電圧を入力フィルタ4の一次側から検出しているが、入力フィルタ4の二次側から検出してもよい。
When the phase loss detection signal is output in this way, the PWM signal generating means 100 in FIG. 1 shuts off all the AC-AC direct converters 3 and stops its operation. The control signal creation means 101 creates and outputs a voltage command or the like for the PWM signal creation means 100, and the operation may be stopped by inputting an open phase detection signal to the control signal creation means 101.
If the number of voltage drops does not reach the set value within the set time in the time measuring means 204, it is determined that there is no phase loss and the normal operation is continued.
In the embodiment of FIG. 1, the power supply voltage is detected from the primary side of the input filter 4, but may be detected from the secondary side of the input filter 4.

次に、図4は本発明の第2実施形態を示すブロック図である
第1実施形態と異なる部分を中心に説明すると、この実施形態では、電源電圧ベクトルの大きさVの時間平均値Viavを平均値演算手段206により演算する。この演算は、例えばローパスフィルタを用いたり移動平均を求めることで実現可能である。欠相によって電源電圧ベクトルの大きさVが脈動するとその時間平均値Viavは低下するので、欠相検出手段205は上記時間平均値Viavが設定値より低下したことをもって欠相を検出する。以後の動作は第1実施形態と同様である。
Next, FIG. 4 is a block diagram showing a second embodiment of the present invention.
The description will focus on the differences from the first embodiment. In this embodiment, the average value calculation means 206 calculates the time average value V iav of the magnitude V i of the power supply voltage vector. This calculation can be realized by using, for example, a low-pass filter or obtaining a moving average. Since the magnitude V i of the power supply voltage vectors by phase loss pulsates its time average value V iav lowered, open phase detection means 205 for detecting the open phase with that the time average value V iav are slower than the preset value . Subsequent operations are the same as those in the first embodiment.

図5は、電源電圧ベクトルの大きさVとその平均値Viavの計算結果を示す波形図であり、本実施形態では、平均値Viavが設定値よりも低下した場合に欠相と判断して欠相検出信号(欠相検出フラグ)を発生させる。
なお、この実施形態においても、電源電圧を入力フィルタ4の二次側から検出してもよい。
FIG. 5 is a waveform diagram showing the calculation result of the magnitude V i of the power supply voltage vector and the average value V iav thereof. In this embodiment, it is determined that the phase is missing when the average value V iav is lower than the set value. Then, a phase loss detection signal (phase loss detection flag) is generated.
In this embodiment as well, the power supply voltage may be detected from the secondary side of the input filter 4.

上述したように、各実施形態にかかる欠相検出装置によれば、電源電圧ベクトルの大きさに基づいて簡単な演算によって欠相を検出することが可能であり、交流−交流直接変換装置を保護するためのみならず、多相交流電源全般を対象として確実に欠相を検出することができる。
また、電力変換器の直流リンク電圧に基づいて欠相を検出する方式ではないため、整流器や平滑手段等のハードウェアを付加しなくても交流−交流直接変換装置に適用可能であり、その制御装置にソフトウェアを追加するだけで、欠相時における直接変換器の迅速な保護を図ることができる。
As described above, according to the phase loss detection device according to each embodiment, phase loss can be detected by a simple calculation based on the magnitude of the power supply voltage vector, and the AC-AC direct conversion device is protected. Therefore, it is possible to reliably detect the phase loss not only for the multi-phase AC power supply but also for all.
In addition, since it is not a method of detecting an open phase based on the DC link voltage of the power converter, it can be applied to an AC-AC direct conversion device without adding hardware such as a rectifier and smoothing means, and its control By simply adding software to the device, the direct converter can be protected quickly in the event of a phase failure.

本発明の第1実施形態を示すブロック図である。1 is a block diagram showing a first embodiment of the present invention. 第1実施形態における欠相時の動作を示す波形図である。It is a wave form diagram which shows the operation | movement at the time of a phase loss in 1st Embodiment. 第1実施形態における欠相時のシミュレーション波形を示す図である。It is a figure which shows the simulation waveform at the time of a phase loss in 1st Embodiment. 本発明の第2実施形態を示すブロック図である。It is a block diagram which shows 2nd Embodiment of this invention. 第2実施形態における欠相時の動作を示す波形図である。It is a wave form diagram which shows the operation | movement at the time of a phase loss in 2nd Embodiment. 従来技術の構成図である。It is a block diagram of a prior art. 図6における平滑化前後の直流電圧の波形図である。FIG. 7 is a waveform diagram of a DC voltage before and after smoothing in FIG. 6. 図6における欠相時の直流電圧の波形図である。FIG. 7 is a waveform diagram of a DC voltage at the time of phase loss in FIG. 6.

符号の説明Explanation of symbols

1:三相交流電源
2:負荷
3:交流−交流直接変換器
4:入力フィルタ
41:リアクトル
42:コンデンサ
100:PWM信号作成手段
101:制御信号作成手段
200:電源電圧検出手段
201:電源電圧ベクトルの大きさ演算手段
202:電圧低下検出手段
203:電圧低下回数検出手段
204:時間計測手段
205:欠相検出手段
206:平均値演算手段
1: Three-phase AC power supply 2: Load 3: AC-AC direct converter 4: Input filter 41: Reactor 42: Capacitor 100: PWM signal generating means 101: Control signal generating means 200: Power supply voltage detecting means 201: Power supply voltage vector Magnitude calculation means 202: Voltage drop detection means 203: Voltage drop count detection means 204: Time measurement means 205: Phase loss detection means 206: Average value calculation means

Claims (3)

多相交流電源の各相電圧を検出する電源電圧検出手段と、
この電源電圧検出手段により検出した各相電圧から電源電圧ベクトルの大きさを演算する演算手段と、
この演算手段により演算した電源電圧ベクトルの大きさが設定値より低下したことを検出する電圧低下検出手段と、
この電圧低下検出手段の出力に基づいて、前記電源電圧ベクトルの大きさが前記設定値より低下した回数、及び、最初に前記設定値より低下してからの経過時間を検出する手段と、
前記経過時間内に前記回数が所定値になったことにより前記多相交流電源の欠相を検出する手段と、
備えたことを特徴とする欠相検出装置。
Power supply voltage detection means for detecting each phase voltage of the multiphase AC power supply;
Calculation means for calculating the magnitude of the power supply voltage vector from each phase voltage detected by the power supply voltage detection means,
Voltage drop detection means for detecting that the magnitude of the power supply voltage vector calculated by the calculation means has decreased below a set value;
Based on the output of the voltage drop detection means, the number of times the magnitude of the power supply voltage vector becomes lower than the set value, and means for detecting the elapsed time from the first lower than the set value,
Means for detecting an open phase of the multiphase AC power supply when the number of times has reached a predetermined value within the elapsed time ;
Open-phase detecting apparatus characterized by comprising a.
請求項1に記載した欠相検出装置を備えたことを特徴とする交流−交流直接変換装置。 An AC-AC direct conversion device comprising the phase loss detection device according to claim 1 . 請求項2に記載した交流−交流直接変換装置において、
前記欠相検出装置から出力される欠相検出信号を用いて直接変換器の運転を停止する手段を備えたことを特徴とする交流−交流直接変換装置。
In the AC-AC direct conversion device according to claim 2 ,
An AC-AC direct conversion device comprising means for stopping the operation of the direct converter using the phase loss detection signal output from the phase loss detection device.
JP2005114721A 2005-04-12 2005-04-12 Phase loss detection device and AC-AC direct conversion device Expired - Fee Related JP4596251B2 (en)

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