JP2940603B2 - Power system harmonic measurement method - Google Patents

Power system harmonic measurement method

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Publication number
JP2940603B2
JP2940603B2 JP9180570A JP18057097A JP2940603B2 JP 2940603 B2 JP2940603 B2 JP 2940603B2 JP 9180570 A JP9180570 A JP 9180570A JP 18057097 A JP18057097 A JP 18057097A JP 2940603 B2 JP2940603 B2 JP 2940603B2
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JP
Japan
Prior art keywords
harmonic
measurement
frequency
power system
current
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
JP9180570A
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Japanese (ja)
Other versions
JPH1114676A (en
Inventor
勲 香田
政和 塚本
荘治 西村
育千 夏田
俊彦 志方
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chubu Electric Power Co Inc
Nissin Electric Co Ltd
Original Assignee
Chubu Electric Power Co Inc
Nissin Electric Co Ltd
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Filing date
Publication date
Application filed by Chubu Electric Power Co Inc, Nissin Electric Co Ltd filed Critical Chubu Electric Power Co Inc
Priority to JP9180570A priority Critical patent/JP2940603B2/en
Priority to US09/099,381 priority patent/US6208945B1/en
Publication of JPH1114676A publication Critical patent/JPH1114676A/en
Application granted granted Critical
Publication of JP2940603B2 publication Critical patent/JP2940603B2/en
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

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Classifications

    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

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  • Measurement Of Resistance Or Impedance (AREA)
  • Testing Electric Properties And Detecting Electric Faults (AREA)
  • Supply And Distribution Of Alternating Current (AREA)

Description

【発明の詳細な説明】DETAILED DESCRIPTION OF THE INVENTION

【０００１】[0001]

【発明の属する技術分野】本発明は、電力系統の高調波
（測定調波）についてのアドミタンス（インピーダン
ス）又は等価回路を求める電力系統の高調波測定方法に
関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring admittance (impedance) or an equivalent circuit of a harmonic (measured harmonic) of a power system, and a method of measuring the harmonics of the power system.

【０００２】[0002]

【従来の技術】電力系統の送，配電系統等の高調波抑制
技術においては、高調波ロスを利用したいわゆる系統切
り換え技術により高調波を低減することが、重要視され
てきた。2. Description of the Related Art In a technique for suppressing harmonics in power transmission and distribution systems of a power system, it has been regarded as important to reduce harmonics by a so-called system switching technique utilizing harmonic loss.

【０００３】そして、系統切り換え等によって生じる高
調波の周波数は、系統電源の基本波の周波数ｆｓの整数
倍であり、代表的な第５調波の周波数は５×ｆｓであ
る。The frequency of a harmonic generated by system switching or the like is an integral multiple of the frequency fs of the fundamental wave of the system power supply, and the typical frequency of the fifth harmonic is 5 × fs.

【０００４】また、高調波の低減はコンデンサ設備に付
属するフィルタ設備により、高調波の電圧レベルの予測
等に基づき、そのフィルタを設置して行われる。[0004] The reduction of harmonics is performed by installing a filter based on prediction of the voltage level of the harmonics by a filter facility attached to the capacitor facility.

【０００５】このとき、高調波の電圧レベルの予測等を
行うには、電力系統のフィルタ設備の接続点より上位
（上流），下位（下流）の高調波に対する特性を把握し
てその等価回路を求める必要がある。At this time, in order to predict the voltage level of the harmonic, for example, the characteristics of the higher (upstream) and lower (downstream) harmonics from the connection point of the filter equipment of the power system are grasped, and the equivalent circuit thereof is determined. Need to ask.

【０００６】この等価回路は、アドミタンスと電流源と
の並列回路又はインピーダンスと電圧源との直列回路と
みなすことができ、そのうちのアドミタンス又はインピ
ーダンスが特性の把握の上からは最も重要である。This equivalent circuit can be regarded as a parallel circuit of admittance and a current source or a series circuit of impedance and a voltage source, of which the admittance or impedance is the most important from the viewpoint of understanding the characteristics.

【０００７】そして、電気学会論文誌Ｂ，１０１巻８
号，ｐ．４５１−４５８，（昭５６−８）には、配電線
の第５調波についての等価回路を求める際、系統の基本
波の電圧，電流を計測し、その結果から高調波に対する
等価回路のアドミタンス（インピーダンス），電流源
（電圧源）の大きさ、位相等を算出して推定することが
記載されている。[0007] The Transactions of the Institute of Electrical Engineers of Japan, B, 101, 8
No., p. 451-458, (Showa 56-8) discloses that when obtaining an equivalent circuit for the fifth harmonic of a distribution line, the voltage and current of the fundamental wave of the system are measured, and the admittance of the equivalent circuit with respect to harmonics is obtained from the results. It describes calculating and estimating (impedance), the size and phase of a current source (voltage source), and the like.

【０００８】[0008]

【発明が解決しようとする課題】前記文献等に記載のよ
うに電力系統の高調波についての等価回路をその基本波
についての電圧，電流の計測結果で求める場合、精度よ
く求めることができない問題点がある。As described in the above-mentioned documents and the like, when an equivalent circuit for harmonics of a power system is obtained from the measurement results of the voltage and current of the fundamental wave, it cannot be obtained with high accuracy. There is.

【０００９】なお、例えば前記フィルタ装置の接続点に
基本波（周波数ｆｓ）の整数倍周波数ｍ×ｆｓ（ｍは
１，２，…の整数）の高調波の電流（電圧）を注入（印
加）し、そのときの系統各所の電流，電圧等の計測結果
からその高調波についての等価回路を求めようとして
も、電力系統にその高調波が存在するため、注入した高
調波変化に基づく電流，電圧等変化を明確に計測するこ
とができず、その高調波についての電力系統のアドミタ
ンス（インピーダンス）や等価回路を正確に求めること
ができなかった。For example, a current (voltage) of a harmonic of an integral multiple of the fundamental wave (frequency fs) m × fs (m is an integer of 1, 2,...) Is injected (applied) to a connection point of the filter device. However, even if an attempt is made to obtain an equivalent circuit for the higher harmonics from the measurement results of the current and voltage at various points in the system at that time, since the higher harmonics exist in the power system, the current and voltage based on the injected harmonic changes Equal changes could not be clearly measured, and the admittance (impedance) and equivalent circuit of the power system could not be accurately obtained for the harmonics.

【００１０】したがって、従来は電力系統の前記フィル
タ装置の接続点等の上位，下位の高調波についてのアド
ミタンス（インピーダンス）や等価回路を個別に精度よ
く求めることができず、この結果、系統切り換え等の際
の高調波の電圧レベルの精度の高い予測ができなかっ
た。Therefore, conventionally, it is not possible to individually and accurately obtain the admittance (impedance) and the equivalent circuit for the higher and lower harmonics such as the connection point of the filter device in the power system. In this case, it was not possible to accurately predict the voltage level of the harmonic.

【００１１】ところで、ｍ次高調波を測定調波とする
と、電力系統（実系統）には、本来、測定調波の上，下
両側の基本波の非整数倍周波数の電流や電圧が存在しな
いため、これらの電流や電圧の注入又は印加に基づく測
定結果から、つぎのようにして電力系統の測定調波につ
いてのアドミタンス（インピーダンス）や等価回路を求
めることが考えられる。By the way, assuming that the m-th harmonic is the measurement harmonic, the electric power system (real system) does not originally have a current or voltage of a non-integer multiple frequency of the fundamental wave above and below the measurement harmonic. Therefore, it is conceivable to obtain an admittance (impedance) and an equivalent circuit for the measured harmonics of the power system from the measurement results based on the injection or application of these currents and voltages in the following manner.

【００１２】すなわち、測定調波の上，下両側の基本波
の非整数倍周波数の電流（電圧）を電力系統に注入又は
印加し、その測定の結果から電力系統の測定調波の上，
下両側でのアドミタンス（インピーダンス）を求める。That is, a current (voltage) having a non-integer multiple frequency of the fundamental wave on both upper and lower sides of the measurement harmonic is injected or applied to the power system.
Find the admittance (impedance) on both lower sides.

【００１３】そして、この測定調波の上，下両側でのア
ドミタンス（インピーダンス）に平均等の補間処理を施
し、その中間の測定調波についての電力系統のアドミタ
ンス（インピーダンス）を求める。Then, the admittance (impedance) on the upper and lower sides of the measured harmonic is subjected to interpolation processing such as averaging, and the admittance (impedance) of the power system for the intermediate measured harmonic is obtained.

【００１４】さらに、等価回路を求めるときは、求めた
アドミタンス（インピーダンス）と電力系統の測定調波
についての電流，電圧の測定結果とにより、電力系統の
測定調波についての電流源（電圧源）を求め、アドミタ
ンスと電流源との並列回路又はインピーダンスと電圧源
との直列回路からなる等価回路を求める。Further, when an equivalent circuit is obtained, a current source (voltage source) for the measured harmonics of the power system is obtained based on the obtained admittance (impedance) and the current and voltage measurement results for the measured harmonics of the power system. And an equivalent circuit composed of a parallel circuit of the admittance and the current source or a series circuit of the impedance and the voltage source is obtained.

【００１５】この場合、基本波の非整数倍周波数の電流
（電圧）に基づく電力系統のアドミタンス（インピーダ
ンス）が測定結果から正確に求まるため、測定調波のア
ドミタンス（インピーダンス）や等価回路を正確に求め
ることができる。In this case, since the admittance (impedance) of the power system based on the current (voltage) of a non-integer multiple frequency of the fundamental wave is accurately obtained from the measurement result, the admittance (impedance) of the measured harmonic and the equivalent circuit can be accurately determined. You can ask.

【００１６】しかし、基本波の非整数倍周波数の電流
（電圧）の注入又は印加に基づく電力系統の電圧，電流
の計測を、そのサンプリング結果をデジタルフーリエ解
析（ＤＦＴ）等の周波数分析により処理して行うため、
測定精度の要求やいわゆるサンプリングエッジによる分
析誤差の抑制等を考慮して前記非整数倍周波数の電流
（電圧）の周波数を適切に定めることは容易ではない。However, the measurement of the voltage and current of the power system based on the injection or application of a current (voltage) having a non-integer multiple frequency of the fundamental wave is performed by processing the sampling result by frequency analysis such as digital Fourier analysis (DFT). To do
It is not easy to appropriately determine the frequency of the current (voltage) of the non-integer multiple frequency in consideration of a demand for measurement accuracy and suppression of an analysis error due to a so-called sampling edge.

【００１７】そして、とくに、測定調波の上，下両側そ
れぞれの前記非整数倍周波数の電流（電圧）を複数と
し、測定調波の上，下両側それぞれのアドミタンス（イ
ンピーダンス）を複数の測定結果の平均等からより一層
精度よく求めようとするときには、各非整数倍周波数の
電流（電圧）の周波数を定めることは極めて困難であ
る。In particular, a plurality of currents (voltages) of the non-integer multiple frequency on each of the upper and lower sides of the measurement harmonic are set as a plurality, and the respective admittances (impedances) of the upper and lower sides of the measurement harmonic are set as a plurality of measurement results. It is extremely difficult to determine the frequency of the current (voltage) of each non-integer multiple frequency when trying to obtain the current with higher accuracy from the average or the like.

【００１８】なお、サンプリングエッジによる分析誤差
とは、サンプリングの開始と終了の不連続により生じる
周波数分析の誤差のことであり、この誤差を防止するた
め、サンプリングの周波数を基本波の周波数より十分に
高くすると、測定装置が高価かつ複雑になる。The analysis error due to the sampling edge is an error in the frequency analysis caused by the discontinuity of the start and end of the sampling. To prevent this error, the sampling frequency is set to be sufficiently higher than the frequency of the fundamental wave. Higher makes the measuring device expensive and complicated.

【００１９】本発明は、電力系統に測定調波の上，下両
側の基本波の非整数倍周波数の電流（電圧）を注入（印
加）し、その測定結果から電力系統の測定調波について
のアドミタンス（インピーダンス）又は等価回路を求め
る際に、前記基本波の非整数倍周波数の電流（電圧）の
周波数を測定精度等を考慮した簡単な計算式から求めて
決定し、決定した周波数の電流（電圧）を測定時の周波
数分析の誤差等を防止して電力系統に注入し得るように
することを課題とする。According to the present invention, a current (voltage) having a non-integer multiple of the fundamental wave above and below the measurement harmonic is injected (applied) into the power system, and the measured harmonics of the power system are measured based on the measurement results. When obtaining an admittance (impedance) or an equivalent circuit, the frequency of a current (voltage) having a non-integer multiple of the fundamental wave is determined from a simple calculation formula in consideration of measurement accuracy and the like, and the current ( It is an object of the present invention to prevent an error in the frequency analysis at the time of measurement and to inject the voltage into the power system.

【００２０】[0020]

【課題を解決するための手段】前記の課題を解決するた
めに、この出願の請求項１の電力系統の高調波測定方法
においては、電力系統の周波数ｆｓの基本波のｍ倍（ｍ
は整数）を周波数のｍ次高調波測定調波とし、電力系統
の測定波についてのアドミタンス又は該アドミタンスと
電流源との並列回路からなる等価回路を求める際に、測
定調波の上，下両側の基本波の非整数倍周波数の基本波
に同期した電流を、中間次数調波の電流とし、測定調波
（ｍ次高調波）とｍ±１次高調波との間の中間次数調波
の電流の周波数ｆｘを、ｆｘ＝（ｆｓ×ｍ）±｛（ｆｓ
／ｎ）×ｋ｝の式（但し、ｎは測定精度１／ｎ（０＜１
／ｎ＜１）に応じた１，２，…，ｎの整数、ｋは周波数
設定用の１，２，…，ｎの整数）から求めて決定し、電
力系統の高調波注入点に、測定調波の上，下両側の周波
数ｆｘの中間次数調波の電流を基本波のｎ周期注入し、
この注入に基づく高調波注入点の電圧及び電力系統の高
調波注入点より上位，下位の少なくとも一方の電流を計
測し、前記上位，前記下位の少なくとも一方を注目側と
して前記計測の結果から注目側の測定調波の上，下両側
それぞれの中間次数調波についてのアドミタンスを算出
し、この算出の結果に基づく補間処理により、注目側の
測定調波についてのアドミタンスを求めて決定する。In order to solve the above-mentioned problems, a method of measuring harmonics of a power system according to claim 1 of the present application is directed to a method of measuring a harmonic (m times (m) times a fundamental frequency of a frequency fs of a power system).
) Is the m-th harmonic measurement harmonic of the frequency, and when calculating the admittance of the measurement wave of the power system or the equivalent circuit composed of the parallel circuit of the admittance and the current source, the upper and lower sides of the measurement harmonic The current synchronized with the fundamental wave of a non-integer multiple of the fundamental wave is defined as the current of the intermediate harmonic, and the current of the intermediate harmonic between the measured harmonic (mth harmonic) and the m ± 1st harmonic is calculated. The frequency fx of the current is given by fx = (fs × m) ± ｛(fs
/ N) × k} (where n is the measurement accuracy 1 / n (0 <1
/ N <1), and k is an integer of 1, 2,..., N for frequency setting) and determined at the harmonic injection point of the power system. A current of an intermediate order harmonic having a frequency fx on both upper and lower sides of the harmonic is injected for n periods of a fundamental wave,
The voltage at the harmonic injection point based on this injection and at least one of the currents higher and lower than the harmonic injection point of the power system are measured, and at least one of the upper and lower levels is set as the target side, and the result of the measurement is used as the target side. The admittance is calculated for the intermediate order harmonics on both the upper and lower sides of the measured harmonic, and the admittance of the measured harmonic on the side of interest is determined by interpolation processing based on the calculation result.

【００２１】また、請求項２の電力系統の高調波測定方
法においては、電力系統の周波数ｆｓの基本波のｍ倍
（ｍは整数）周波数のｍ次高調波を測定調波とし、電力
系統の測定波についてのインピーダンス又は該インピー
ダンスと電圧源との直列回路からなる等価回路を求める
際に、 測定調波の上，下両側の基本波の非整数倍周波
数の基本波に同期した電圧を、中間次数調波の電圧と
し、測定調波（ｍ次高調波）とｍ±１次高調波との間の
中間次数調波の電圧の周波数ｆｘを、ｆｘ＝（ｆｓ×
ｍ）±｛（ｆｓ／ｎ）×ｋ｝の式（但し、ｎは測定精度
１／ｎ（０＜１／ｎ＜１）に応じた１，２，…の整数、
ｋは周波数設定用の１，２，…，ｎの整数）から求めて
決定し、電力系統の高調波注入点に、測定調波の上，下
両側の前記周波数ｆｘの中間次数調波の電圧を基本波の
ｎ周期印加し、この印加に基づく高調波注入点の電圧及
び電力系統の高調波注入点より上位，下位の少なくとも
一方の電流を計測し、前記上位，前記下位の少なくとも
一方を注目側として前記計測の結果から注目側の測定調
波の上，下両側それぞれの中間次数調波についてのイン
ピーダンスを算出し、この算出の結果に基づく補間処理
により、注目側の測定調波についてのインピーダンスを
求めて決定する。In the method for measuring harmonics of a power system according to a second aspect of the present invention, an m-th harmonic having a frequency m times (m is an integer) of a fundamental wave of a frequency fs of the power system is set as a measurement harmonic, and When obtaining the impedance of the measurement wave or an equivalent circuit consisting of a series circuit of the impedance and the voltage source, the voltage synchronized with the fundamental wave of a non-integer multiple of the fundamental wave on the upper and lower sides of the measurement harmonic is calculated as an intermediate value. The frequency of the voltage of the intermediate order harmonic between the measured harmonic (m order harmonic) and the m ± 1 order harmonic is fx = (fs ×
m) ± {(fs / n) × k} (where n is an integer of 1, 2,... depending on the measurement accuracy 1 / n (0 <1 / n <1),
k is an integer of 1, 2,..., n for frequency setting) and determined at the harmonic injection point of the power system, the voltage of the intermediate order harmonic of the frequency fx above and below the measured harmonic. Is applied for n cycles of the fundamental wave, and the voltage at the harmonic injection point based on this application and at least one of the currents higher and lower than the harmonic injection point of the power system are measured, and at least one of the upper and lower levels is noted. As the side, the impedance for the intermediate order harmonics on the upper and lower sides of the measurement harmonic on the attention side is calculated from the measurement result on the attention side, and the impedance for the measurement harmonic on the attention side is calculated by interpolation based on the calculation result. To determine.

【００２２】したがって、前記両請求項の高調波測定方
法の場合、測定波の上，下両側の基本波の非整数倍周波
数の電流（電圧）が、測定精度を考慮した簡単な式の計
算から基本波に同期した中間次数調波の電流（電圧）と
して求まる。Therefore, in the case of the harmonic measuring method according to the above claims, the current (voltage) of a non-integer multiple frequency of the fundamental wave on the upper and lower sides of the measured wave can be calculated from a simple formula in consideration of the measurement accuracy. It is obtained as the current (voltage) of the intermediate order harmonic synchronized with the fundamental wave.

【００２３】さらに、この中間次数調波の電流（電圧）
が基本波のｎ周期にわたって注入又は印加されるため、
中間次数調波の電流（電圧）の注入期間は必ず整数周期
（ｍ×ｎ±ｋ）になる。Further, the current (voltage) of the intermediate order harmonics
Is injected or applied over n periods of the fundamental wave,
The injection period of the current (voltage) of the intermediate order harmonic is always an integer period (m × n ± k).

【００２４】そして、この整数周期の中間次数調波の電
流注入（電圧印加）に基づく電力系統の電圧，電流を計
測し、電力系統の前記整数周期の中間次数調波の電流，
電圧をサンプリングして周波数分析等すれば、基本波に
同期したサンプリングにより、サンプリング周波数を高
くすることなく、サンプリングエッジによる周波数分析
誤差を防止して、所望の測定精度で測定調波についての
アドミタンス（インピーダンス）が求まり、この結果か
ら等価回路も求まる。Then, the voltage and current of the power system are measured based on the current injection (voltage application) of the intermediate order harmonic of the integer period, and the current and the current of the intermediate order harmonic of the integer period of the power system are measured.
If the voltage is sampled and subjected to frequency analysis or the like, the sampling synchronized with the fundamental wave prevents the frequency analysis error due to the sampling edge without increasing the sampling frequency, and the admittance of the measured harmonic wave with the desired measurement accuracy ( Impedance) is obtained, and from this result, an equivalent circuit is also obtained.

【００２５】[0025]

【発明の実施の形態】本発明の実施の形態につき、図
１，図２を参照して説明する。 （実施の１形態）電力系統の高調波を測定する際は、図
１に示すように、電力系統１の系統電源２と負荷３との
間の適当な位置，例えば高調波電流低減用のフィルタ装
置が接続される位置を、高調波注入点４とし、この注入
点４に計測装置５から電流（電圧）を注入又は印加す
る。DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described with reference to FIGS. (First Embodiment) When measuring harmonics of a power system, as shown in FIG. 1, an appropriate position between a system power supply 2 and a load 3 of the power system 1, for example, a filter for reducing a harmonic current. The position where the device is connected is defined as a harmonic injection point 4, and a current (voltage) is injected or applied from the measuring device 5 to the injection point 4.

【００２６】ところで、電力系統１には周波数ｆｓの基
本波のほかに、基本波の整数倍の周波数ｎ×ｆｓの高調
波が存在し、これらの整数倍周波数の高調波に対して、
高調波注入点４からみた系統１の下位（負荷側）はほぼ
負荷３が接続された状態にあり、上位（電源側）は例え
ば線路インピーダンス６を介して系統電源２が接続され
た状態にある。Incidentally, in addition to the fundamental wave having the frequency fs, the power system 1 has harmonics having a frequency n × fs which is an integral multiple of the fundamental wave.
The lower side (load side) of the system 1 viewed from the harmonic injection point 4 is in a state where the load 3 is almost connected, and the upper side (power supply side) is in a state where the system power supply 2 is connected via the line impedance 6, for example. .

【００２７】このとき、上位，下位をノートンの定理で
表現した高調波等価回路は、それぞれアドミタンスと電
流源との並列回路とみなせる。At this time, the harmonic equivalent circuit in which the upper and lower parts are expressed by Norton's theorem can be regarded as a parallel circuit of the admittance and the current source, respectively.

【００２８】なお、下位の電流源は実際に存在するので
はなく、負荷による電流歪み等で等価的に形成されるも
のである。Note that the lower current source does not actually exist but is formed equivalently due to current distortion caused by a load.

【００２９】また、上位の線路インピーダンス６等は電
力系統１の線路特性から予め把握されており、既知であ
る。The upper line impedance 6 and the like are known in advance from the line characteristics of the power system 1 and are known.

【００３０】そして、第５調波（ｍ＝５）等のｍ次高調
波を測定調波とし、この測定調波についての高調波注入
点４の上位，下位の時々刻々変化するアドミタンス（回
路定数）を求める場合、高調波注入点４の電圧（系統電
圧）を変圧器７により計測し、高調波注入点４の上位，
下位の少なくとも一方，例えば上位の電流を変流器８に
より計測する。The m-th harmonic, such as the fifth harmonic (m = 5), is used as a measurement harmonic, and the admittance (circuit constant) of the upper and lower harmonic injection points 4 for this measurement harmonic that changes every moment. ), The voltage (system voltage) at the harmonic injection point 4 is measured by the transformer 7, and
At least one of the lower order, for example, the upper order current is measured by the current transformer 8.

【００３１】さらに、変圧器７の検出電圧の信号をＰＬ
Ｌ回路構成の同期信号作成部９に供給し、この作成部９
により、制御部１０の制御信号に基づき、系統電源２の
例えば６０Ｈｚの基本波に同期した基本波の非整数倍周
波数（周波数ｆｘ）の同期制御信号を形成する。Further, the signal of the detection voltage of the transformer 7 is
The signal is supplied to a synchronizing signal generator 9 having an L circuit configuration.
Thus, based on the control signal of the control unit 10, a synchronization control signal of a non-integer multiple frequency (frequency fx) of the fundamental wave synchronized with the fundamental wave of, for example, 60 Hz of the system power supply 2 is formed.

【００３２】そして、この同期制御信号に基づき、注入
源信号作成部１１により基本波に同期した周波数ｆｘの
信号を、中間次数調波の注入信号として作成し、この注
入信号を増幅器１２により増幅して周波数ｆｘの中間次
数調波の電流を形成し、この電流を注入回路１３，開閉
器１４を介して高調波注入点４に注入する。Then, based on the synchronization control signal, a signal of the frequency fx synchronized with the fundamental wave is created as an injection signal of the intermediate order harmonic by the injection source signal creation section 11, and the injection signal is amplified by the amplifier 12. To form a current of an intermediate order harmonic having the frequency fx, and inject the current into the harmonic injection point 4 via the injection circuit 13 and the switch 14.

【００３３】このとき、中間次数調波の電流は、制御部
１０のつぎの処理により周波数ｆｘ等が設定される。At this time, for the current of the intermediate order harmonic, the frequency fx and the like are set by the following processing of the control unit 10.

【００３４】すなわち、測定調波をｍ次高調波とし、測
定精度を１／ｎ（ｎは０＜１／ｎ＜１を満足する１，
２，…の整数）とすると、制御部１０はつぎの数１の式
の計算から、ｍ次の測定調波とその上，下両側のｍ±１
次高調波との間の各中間次数調波の周波数ｆｘを求めて
決定する。That is, the measurement harmonic is the m-th harmonic, and the measurement accuracy is 1 / n (where n is 0 <1 / n <1).
2, the control unit 10 calculates the m-order measurement harmonic and m ± 1 on both upper and lower sides from the calculation of the following equation (1).
The frequency fx of each intermediate-order harmonic with the second-order harmonic is obtained and determined.

【００３５】[0035]

【数１】ｆｘ＝（ｆｓ×ｍ）±｛（ｆｓ／ｎ）×ｋ｝Fx = (fs × m) ± {(fs / n) × k}

【００３６】但し、ｋは周波数設定用の１，２，…，ｎ
の整数であり、ｋ＝１，２，…，ｎ−１のときは数１の
式からｆｓ／ｎの間隔の中間次数調波の周波数が求ま
り、ｋ＝ｎのときはｆｘ＝ｆｓ×（ｍ±１）となり、数
１の式の周波数が測定調波の上，下両側のｍ±１次高調
波の周波数に一致する。Here, k is 1, 2,..., N for frequency setting.
When k = 1, 2,..., N−1, the frequency of the intermediate-order harmonic at an interval of fs / n is obtained from Expression 1, and when k = n, fx = fs × ( m ± 1), and the frequency of the equation (1) coincides with the frequencies of the m ± 1 order harmonics on both upper and lower sides of the measured harmonic.

【００３７】なお、ｋ＝０とすれば、数１の式の周波数
は、ｆｘ＝ｆｓ×ｍとなり、測定調波（ｍ次高調波）の
周波数に一致する。If k = 0, the frequency of the equation (1) becomes fx = fs × m, which coincides with the frequency of the measured harmonic (mth harmonic).

【００３８】ところで、数１の式中のｆｓ，ｍ，ｎ，ｋ
の値は操作部１５のキーボード操作等で制御部１０に与
えられ、６０Ｈｚの電力系統の第５調波（５次高調波）
を測定調波とし、そのアドミタンスを１／１０の測定精
度で求める場合は、操作部１５によりｆｓ＝６０（Ｈ
ｚ），ｍ＝５，ｎ＝１０，ｋ＝１，２，…，１０が制御
部１０に与えられる。By the way, fs, m, n, k in the equation (1)
Is given to the control unit 10 by a keyboard operation of the operation unit 15 or the like, and the fifth harmonic (5th harmonic) of the 60 Hz power system is provided.
Is used as a measurement harmonic, and its admittance is obtained with a measurement accuracy of 1/10, fs = 60 (H
z), m = 5, n = 10, k = 1, 2,..., 10 are given to the control unit 10.

【００３９】この場合、ｋ＝１ではｆｘ＝３００±６Ｈ
ｚ，ｋ＝２ではｆｘ＝３００±１２Ｈｚ，ｋ＝３ではｆ
ｘ＝３００±１３Ｈｚ，…，ｋ＝１０ではｆｘ＝３００
±６０Ｈｚとなり、第５調波（３００Ｈｚ）とその上，
下の６次，４次高調波（３００±６０Ｈｚ）との間それ
ぞれを１０等分した６Ｈｚ間隔の中間次数調波の周波数
ｆｘが求まる。In this case, at k = 1, fx = 300 ± 6H
fx = 300 ± 12 Hz for z and k = 2, f for k = 3
When x = 300 ± 13 Hz,..., k = 10, fx = 300
± 60 Hz, the fifth harmonic (300 Hz) and above
The frequency fx of the intermediate-order harmonic at intervals of 6 Hz, which is obtained by equally dividing each of the lower sixth harmonic and the fourth harmonic (300 ± 60 Hz) into ten, is obtained.

【００４０】なお、測定精度を１／２に下げたときは、
ｋ＝１，２になり、ｋ＝１ではｆｘ＝３００±３０Ｈ
ｚ，ｋ＝２ではｋ＝３００±６０Ｈｚ（６次，４次の高
調波の周波数）が計算から求まる。When the measurement accuracy is reduced to half,
k = 1, 2 and fx = 300 ± 30H at k = 1
When z and k = 2, k = 300 ± 60 Hz (the frequency of the sixth and fourth harmonics) can be obtained from the calculation.

【００４１】そして、制御部１０は計算から求めた各周
波数ｆｘの全部又は一部につき、例えば測定調波の周波
数との比のデータからなる逓信制御信号を形成し、同期
信号作成部９からの同期の確立を示す信号の受信に基づ
き、各逓信制御信号を順次に注入源信号作成部１１に供
給する。The control unit 10 forms, for all or a part of each of the frequencies fx obtained from the calculation, a transmission control signal composed of, for example, data of the ratio to the frequency of the measured harmonic. Based on the reception of the signal indicating the establishment of synchronization, each transmission control signal is sequentially supplied to the injection source signal creation unit 11.

【００４２】この供給に基づき、注入源信号作成部１１
は測定調波の上，下両側それぞれの基本波に同期した各
周波数ｆｘの注入信号を、順次に基本波のｎ周期形成す
る。Based on this supply, the injection source signal generator 11
Forms an injection signal of each frequency fx synchronized with each of the fundamental waves on the upper and lower sides of the measurement harmonic in order, and sequentially forms n periods of the fundamental wave.

【００４３】そして、注入波信号作成部１１の各注入信
号が増幅されて測定調波の上，下両側それぞれの基本波
に同期した周波数ｆｘの各中間次数調波の電流が形成さ
れ、これらの電流が順次に基本波のｎ周期発生して高調
波注入点４に注入する。Then, each injection signal of the injection signal generator 11 is amplified to form a current of each intermediate order harmonic having a frequency fx synchronized with the fundamental wave on each of the upper and lower sides of the measurement harmonic. A current is sequentially generated for n periods of the fundamental wave and injected into the harmonic injection point 4.

【００４４】このとき、基本波のｎ周期の注入により、
各中間次数調波の電流は、Ｔｘ＝（ｎ／ｆｓ）／（１／
ｆｘ）周期注入されることになり、この注入周期Ｔｘは
つぎの数２の式に示すように、必ず整数周期になる。At this time, by injecting n periods of the fundamental wave,
The current of each intermediate order harmonic is: Tx = (n / fs) / (1 /
fx) Period injection is performed, and the injection period Tx always becomes an integer period as shown in the following equation (2).

【００４５】[0045]

【数２】Ｔｘ＝（ｎ／ｆｓ）×ｆｘ＝（ｎ×ｍ）±ｋTx = (n / fs) × fx = (n × m) ± k

【００４６】そして、高調波注入点４に注入される各中
間次数調波の電流は、変流器１６により検出される。The current of each intermediate-order harmonic injected into the harmonic injection point 4 is detected by the current transformer 16.

【００４７】また、各中間次数調波の電流の注入に基づ
く高調波注入点４の電圧が変圧器７により検出されると
ともに、高調波注入点４の上位を流れる電流が変流器８
により検出される。The voltage at the harmonic injection point 4 based on the injection of the current of each intermediate harmonic is detected by the transformer 7, and the current flowing above the harmonic injection point 4 is changed by the current transformer 8.
Is detected by

【００４８】そして、変圧器７の電圧の検出信号及び変
流器８，１６の電流の検出信号がＡ／Ｄ変換部１７に供
給され、この変換部１７は同期信号作成部９の同期制御
信号に基づくサンプリングタイミング作成部１８のタイ
ミング制御により、各中間次数調波の電流の注入毎に、
電力系統の基本波に同期して各検出信号を基本波のｎ周
期にわたって位相をずらしながらサンプリングする。The detection signal of the voltage of the transformer 7 and the detection signal of the current of the current transformers 8 and 16 are supplied to an A / D converter 17, which converts the synchronization control signal of the synchronization signal generator 9. By the timing control of the sampling timing creating unit 18 based on the above, each time the current of each intermediate order harmonic is injected,
Each detection signal is sampled while shifting the phase over n periods of the fundamental wave in synchronization with the fundamental wave of the power system.

【００４９】このとき、Ａ／Ｄ変換部１７のサンプリン
グの開始は、同期信号作成部９の同期の確立を示す信号
に基づき、作成部９の同期の確立を検出した後、制御部
１０から注入波信号作成部１１，開閉器１４とともにＡ
／Ｄ変換部１７に開始（閉成）の指示が与えられて設定
される。At this time, the sampling of the A / D converter 17 is started by detecting the establishment of the synchronization of the generator 9 based on the signal indicating the establishment of the synchronization of the synchronization signal generator 9 and then injecting the signal from the controller 10. A together with the wave signal generator 11 and the switch 14
A start (close) instruction is given to the / D converter 17 and set.

【００５０】また、各中間次数調波の電流（電圧）が基
本波に同期し、しかも、そのサンプリング期間が必ず基
本波の整数倍の周期になるため、基本波に同期したサン
プリングにより、サンプリングの開始，終了の連続性を
保つことができ、この場合、サンプリング周波数を極端
に高くすることなくサンプリングエッジによる周波数分
析誤差が防止され、比較的低周波数の安価かつ簡単なサ
ンプリング回路でＡ／Ｄ変換部１７を形成することがで
きる。Further, since the current (voltage) of each intermediate-order harmonic is synchronized with the fundamental wave, and the sampling period is always an integral multiple of the period of the fundamental wave, the sampling in synchronization with the fundamental wave is performed. Continuity of start and end can be maintained. In this case, a frequency analysis error due to a sampling edge can be prevented without extremely increasing the sampling frequency, and A / D conversion can be performed by a relatively low-frequency and inexpensive and simple sampling circuit. The part 17 can be formed.

【００５１】そして、Ａ／Ｄ変換部１７のサンプリング
データ（計測データ）が信号処理部１９に供給され、こ
の信号処理部１９はつぎに説明する演算により、電力系
統１の高調波注入点４より上位，下位の少なくとも一方
を注目側としてこの注目側の測定調波についてのアドミ
タンス等を求める。Then, the sampling data (measurement data) of the A / D converter 17 is supplied to the signal processor 19, and the signal processor 19 performs a calculation described below to place the data higher than the harmonic injection point 4 of the power system 1. , At least one of the lower levels is set as the target side, and the admittance and the like of the measurement harmonic on the target side are obtained.

【００５２】まず、説明を簡単にするため、高調波注入
点４に注入される中間次数調波の電流をＩｘとすると、
この電流Ｉｘは電力系統１に存在しない周波数ｆｘの電
流であり、電力系統１は電流Ｉｘに対してアドミタンス
Ｙｘのみが存在した状態になる。First, for the sake of simplicity, assuming that the current of the intermediate order harmonic injected into the harmonic injection point 4 is Ix,
The current Ix is a current having a frequency fx that does not exist in the power system 1, and the power system 1 is in a state where only the admittance Yx exists with respect to the current Ix.

【００５３】このとき、電流Ｉｘに基づく高調波注入点
４の電圧をＶｘとすれば、アドミタンスＹｘは電力系統
１に存在する高調波の影響を受けることなく、つぎの数
３の式から正確に求まる。At this time, if the voltage at the harmonic injection point 4 based on the current Ix is Vx, the admittance Yx can be accurately obtained from the following equation (3) without being affected by the harmonics existing in the power system 1. I get it.

【００５４】[0054]

【数３】Ｙｘ＝Ｉｘ／Ｖｘ## EQU3 ## Yx = Ix / Vx

【００５５】また、電流Ｉｘの注入に基づき電力系統１
の高調波注入点４より上位，下位それぞれを流れる電流
をＩｘ1 ，Ｉｘ2 とし、この電流Ｉｘ1 ，Ｉｘ2 に基づ
く電力系統の高調波注入点４より上位，下位のアドミタ
ンスをＹｘ1 ，Ｙｘ2 とすると、アドミタンスＹｘ1 ，
Ｙｘ2 は、つぎの数４，数５の２式それぞれから求ま
る。Further, based on the injection of the current Ix, the power system 1
The currents flowing higher and lower than the harmonic injection point 4 are Ix 1 and Ix 2, and the admittances higher and lower than the harmonic injection point 4 of the power system based on the currents Ix 1 and Ix 2 are Yx 1 and Yx. Assuming 2 , admittance Yx 1 ,
Yx 2 is obtained from each of the following two equations (4) and (5).

【００５６】[0056]

【数４】Ｙｘ1 ＝Ｉｘ1 ／Ｖｘ## EQU4 ## Yx 1 = Ix 1 / Vx

【００５７】[0057]

【数５】Ｙｘ2 ＝Ｉｘ2 ／Ｖｘ## EQU5 ## Yx 2 = Ix 2 / Vx

【００５８】そして、電流Ｉｘ1 ，Ｉｘ2 はいずれか一
方を測定すれば、Ｉｘ1 ＝Ｉｘ−Ｉｘ2 ，Ｉｘ2 ＝Ｉｘ
−Ｉｘ1 の演算により他方が求まる。If one of the currents Ix 1 and Ix 2 is measured, Ix 1 = Ix−Ix 2 and Ix 2 = Ix
The other is obtained by calculation of -ix 1.

【００５９】したがって、電力系統１の高調波注入点４
より下位を注目側とする場合、信号処理部１９は、Ａ／
Ｄ変換部１７の計測データのＤＦＴ解析等の周波数分析
により電圧Ｖｘ及び電流Ｉｘ，Ｉｘ1 を求める。Therefore, the harmonic injection point 4 of the power system 1
If the lower side is the attention side, the signal processing unit 19
Voltage Vx and current Ix by frequency analysis of the DFT analysis or the like of the measurement data D converter 17 obtains the Ix 1.

【００６０】このとき、注入電流が電力系統１の基本波
に同期した整数周期の電流であり、基本波に同期したサ
ンプリングにより、サンプリングの開始，終了の連続性
が保たれるため、サンプリングエッジによるＤＦＴ誤差
等の周波数分析の誤差は生じない。At this time, the injection current is an integer period current synchronized with the fundamental wave of the power system 1, and the sampling start and end continuity is maintained by the sampling synchronized with the fundamental wave. No frequency analysis error such as a DFT error occurs.

【００６１】さらに、電流Ｉｘ，Ｉｘ1 に基づき、Ｉｘ
2 ＝Ｉｘ−Ｉｘ1 の演算から注目側の測定調波の上，下
両側の中間次数調波の電流Ｉｘ2 を求める。[0061] Further, the current Ix, on the basis of the Ix 1, Ix
2 = on the calculation of the Ix-Ix 1 attention side of the measuring harmonics, determine the current Ix 2 intermediate degree harmonics below both sides.

【００６２】そして、電流Ｉｘ2 ，電圧Ｖｘに基づき、
数５の式から注目側の測定調波の上，下両側の中間次数
調波についてのアドミタンスＹｘ2 を求める。Then, based on the current Ix 2 and the voltage Vx,
The admittance Yx 2 for the intermediate order harmonics on the upper and lower sides of the measurement harmonic on the side of interest is calculated from the equation (5).

【００６３】なお、数１の式から求められた周波数ｆｘ
の複数の中間次数調波の電流が注入されるときは、測定
調波の上，下両側それぞれにつき、複数の中間次数調波
の電流Ｉｘ2 を求め、各中間次数調波についてのアドミ
タンスＹｘ2 を求める。The frequency fx obtained from the equation (1)
When multiple intermediate degree harmonic current is injected, on the measurement harmonic, per each lower sides, it seeks current Ix 2 of the plurality of intermediate orders harmonics admittance Yx 2 for each intermediate orders harmonic Ask for.

【００６４】このとき、電流Ｉｘが電力系統１に存在し
ない周波数の電流であるため、注入電力量が微小であっ
ても、アドミタンスＹｘ2 は電力系統１の高調波の影響
を受けることなく正確に求まる。At this time, since the current Ix is a current having a frequency that does not exist in the power system 1, the admittance Yx 2 can be accurately obtained without being affected by harmonics of the power system 1 even if the amount of injected power is minute. I get it.

【００６５】なお、電流Ｉｘの代わりに測定調波の高調
波電流を注入しても、この高調波が電力系統１に存在し
ているため、注入した高調波電流に基づくアドミタンス
を求めることはできない。Even if a harmonic current of the measured harmonic is injected instead of the current Ix, the admittance based on the injected harmonic current cannot be obtained because the harmonic exists in the power system 1. .

【００６６】つぎに、注目側の測定調波についてのアド
ミタンスをＹｍ，その上，下両側の電流Ｉｘ2 について
のアドミタンスをＹｘ2 （ｕ），Ｙｘ2 （ｄ）とする
と、測定調波についてのアドミタンスＹｍは、アドミタ
ンスＹｘ2 （ｕ），Ｙｘ2 （ｄ）の中間値として求める
ことができる。Next, assuming that the admittance of the measurement harmonic on the side of interest is Ym, and that the admittance of the current Ix 2 on the upper and lower sides is Yx 2 (u) and Yx 2 (d), The admittance Ym can be obtained as an intermediate value between the admittances Yx 2 (u) and Yx 2 (d).

【００６７】そのため、信号処理部１９は求めたアドミ
タンスＹｘ2 （ｕ），Ｙｘ2 （ｄ）に基づき、単純平均
或いは最小二乗法等により補間演算を実行し、測定調波
についてのアドミタンスＹｍを求めて決定する。For this reason, the signal processing section 19 executes an interpolation operation by a simple average method or a least square method based on the obtained admittances Yx 2 (u) and Yx 2 (d) to obtain the admittance Ym for the measured harmonic. To decide.

【００６８】このとき、アドミタンスＹｘ2 （ｕ），Ｙ
ｘ2 （ｄ）がそれぞれ複数求められていれば、例えば、
アドミタンスＹｘ2 （ｕ），Ｙｘ2 （ｄ）毎に単純平均
や最小二乗法等で平均値（代表値）を求め、この平均値
を用いて前記の補間演算を実行してアドミタンスＹｍを
求める。At this time, the admittance Yx 2 (u), Y
If a plurality of x 2 (d) are determined, for example,
An average value (representative value) is obtained by a simple average, a least squares method, or the like for each of the admittances Yx 2 (u) and Yx 2 (d), and the admittance Ym is obtained by performing the above-described interpolation operation using the average value.

【００６９】このとき、アドミタンスＹｘ2 （ｕ），Ｙ
ｘ2 （ｄ）が電力系統１の高調波の影響を受けることな
く正確に算出されるため、測定調波についてのアドミタ
ンスＹｍが正確に求まる。At this time, the admittance Yx 2 (u), Y
Since x 2 (d) is accurately calculated without being affected by harmonics of the power system 1, the admittance Ym of the measured harmonic can be accurately obtained.

【００７０】なお、高調波注入点４の上位の電流Ｉｘ1
を計測する代わりに、その下位の電流Ｉｘ2 を計測して
もよく、この場合は、計測された電流から直ちに注目側
の電流Ｉｘ2 が求まる。The higher current Ix 1 at the harmonic injection point 4
Instead of measuring may measure the current Ix 2 of the lower, in this case, immediately noticed side current Ix 2 is obtained from the measured current.

【００７１】また、高調波注入点４の上位を注目側とす
る場合にも、計測又はＩｘ−Ｉｘ2の演算から得られた
電流Ｉｘ1 と電流Ｉｘ，電圧Ｖｘとに基づき、前記と同
様にして測定調波についてのアドミタンスを、電力系統
１の高調波の影響を受けることなく正確に求めることが
できる。[0071] In the case of a target-side upper harmonic injection point 4 also based current obtained from the operation of the measurement or Ix-Ix 2 Ix 1 and the current Ix, the voltage Vx, in the same manner as the Thus, the admittance of the measured harmonic can be accurately obtained without being affected by harmonics of the power system 1.

【００７２】なお、高調波注入点４の上位，下位の両方
を注目側とし、それぞれの測定調波についてのアドミタ
ンスを求めることもでき、この場合、上位，下位の両方
に変流器を設け、上位，下位を流れる電流Ｉｘ1 ，Ｉｘ
2 をそれぞれ計測してもよい。It is also possible to determine the admittance of each of the measured harmonics by using both the upper and lower harmonics of the harmonic injection point 4 as the attention side. In this case, current transformers are provided in both the upper and lower harmonics. Currents Ix 1 , Ix flowing in the upper and lower parts
2 may be measured respectively.

【００７３】そして、注目側の測定調波についてのアド
ミタンスが求まれば、注目側の測定調波に対する挙動等
を把握することができる。When the admittance of the measurement harmonic on the target side is obtained, the behavior of the measurement harmonic on the target side can be grasped.

【００７４】ところで、この実施の形態においては、ア
ドミタンスだけでなく、このアドミタンスと電流源との
並列回路からなる測定調波についての等価回路をより完
全に求めるため、信号処理部１９は測定調波についての
注目側のアドミタンスを求めて決定した後、つぎに説明
するように、測定調波についての注目側の電流源を算出
してその等価回路を求める。By the way, in this embodiment, not only the admittance but also an equivalent circuit for a measurement harmonic composed of a parallel circuit of this admittance and a current source is more completely obtained. After determining and determining the admittance of the target side for the target, the current source of the target side for the measured harmonic is calculated and its equivalent circuit is determined, as described below.

【００７５】すなわち、測定調波についての注目側のア
ドミタンスが求まると、中間次数調波の電流注入の終了
後、開閉器１４が開放した状態での変圧器７，変流器８
の検出信号に基づくＡ／Ｄ変換部１７の計測データの周
波数分析により、電力系統１の測定調波の電圧（高調波
電圧），電流（高調波電流）を求める。That is, when the admittance of the attention side of the measured harmonic is determined, the transformer 7 and the current transformer 8 with the switch 14 opened after the completion of the current injection of the intermediate order harmonic.
The voltage (harmonic voltage) and the current (harmonic current) of the measured harmonic of the power system 1 are obtained by frequency analysis of the measurement data of the A / D converter 17 based on the detection signal of the above.

【００７６】そして、求めた測定調波の高調波電圧をＶ
ｍ，高調波電流をＩｍ（上位から下位の向きを正）と
し、高調波注入点４の上位，下位の測定調波の等価回路
のアドミタンスをＹｍ1 ，Ｙｍ2 ，電流源をＩGm1 ，Ｉ
Gm2 （高調波注入点４に流れる方向を正）とすると、図
２の等価回路からも明らかなように、高調波注入点４の
下位，上位につき、つぎの数６，数７の２式それぞれが
成立する。Then, the obtained harmonic voltage of the measured harmonic is V
m, the harmonic current is Im (the direction from the upper to the lower is positive), the admittances of the equivalent circuits of the upper and lower measurement harmonics at the harmonic injection point 4 are Ym 1 and Ym 2 , and the current sources are I Gm1 and I Gm1 .
Assuming that Gm2 (the direction flowing to the harmonic injection point 4 is positive), as can be seen from the equivalent circuit of FIG. Holds.

【００７７】[0077]

【数６】ＩGm1 ＝Ｉｍ＋Ｖｍ・Ｙｍ1 [ Formula 6] I Gm1 = Im + Vm · Ym 1

【００７８】[0078]

【数７】ＩGm2 ＝Ｖｍ・Ｙｍ2 −Ｉｍ[Expression 7] I Gm2 = Vm · Ym 2 -Im

【００７９】そこで、信号処理部１９は数６，数７の２
式のいずれか一方又は両方の演算から注目側の測定調波
の電流源ＩGm1 ，ＩGm2 を求めて決定し、図２に示す測
定調波の等価回路２０，２１を求めて決定する。Therefore, the signal processing section 19 calculates 2
Determining seeking current source I Gm1, I Gm2 measurement harmonics of the target side from either or both of the calculation formulas determined seek equivalent circuits 20 and 21 of the measuring harmonics shown in FIG.

【００８０】この場合、注目側の測定調波についての等
価回路２０，２１が個別にしかも精度よく求められる。In this case, the equivalent circuits 20 and 21 for the measurement harmonic on the side of interest are individually and accurately obtained.

【００８１】そして、注目側の等価回路２０，２１の決
定された各回路定数Ｙｍ1 ，Ｙｍ2，ＩGm1 ，ＩGm2 等
の情報は、計測装置５の記憶部（図示せず）に記憶され
るとともに表示部（図示せず）に例えば等価回路図の形
式で画面表示される。[0081] Then, each circuit constant Ym 1 determined attention side of the equivalent circuit 20,21, Ym 2, I Gm1, I Gm2 such information is stored in the storage unit of the measuring device 5 (not shown) At the same time, a screen is displayed on a display unit (not shown) in the form of, for example, an equivalent circuit diagram.

【００８２】また、系統切換え等による高調波の低減を
行う場合は、前記の各測定がくり返されて注目側の最新
の等価回路２０，２１の状態が把握され、この結果等か
ら系統切り換えに伴う高調波の発生を予測し、高調波注
入点４に接続したフィルタ装置（図示せず）のフィルタ
容量が最適に設定される。When the harmonics are reduced by system switching or the like, the above-described measurements are repeated to grasp the state of the latest equivalent circuits 20 and 21 on the side of interest. The generation of accompanying harmonics is predicted, and the filter capacity of a filter device (not shown) connected to the harmonic injection point 4 is optimally set.

【００８３】（実施の他の形態）つぎに、電力系統１の
高調波等価回路をインピーダンスと電圧源との直列回路
とし、注目側の測定調波についてのインピーダンス又は
このインピーダンスと電圧源との等価回路を求める場合
について説明する。(Other Embodiment) Next, the harmonic equivalent circuit of the power system 1 is a series circuit of an impedance and a voltage source, and the impedance for the measurement harmonic on the target side or the equivalent of this impedance and the voltage source. A case where a circuit is obtained will be described.

【００８４】この場合、高調波注入点４に電圧Ｖｘ，周
波数ｆｘの数１の式から求めた中間次数調波の電圧を基
本波のｎ周期印加して測定すると、数３の式の代わり
に、この式のアドミタンスＹｘをインピーダンスＺｘ
（＝１／Ｙｘ）に変えた式が成立し、数４，数５の２式
に相当する式として、つぎの数８，数９の２式が成立す
る。In this case, when the voltage of the intermediate order harmonic obtained from the equation (1) of the voltage Vx and the frequency fx is applied to the harmonic injection point 4 for n periods of the fundamental wave and measured, the equation (3) is obtained instead of the equation (3). , Admittance Yx of this equation is represented by impedance Zx
(= 1 / Yx) holds, and the following two equations (8) and (9) hold as equations corresponding to the two equations (4) and (5).

【００８５】[0085]

【数８】Ｚｘ1 ＝Ｖｘ／Ｉｘ1 [Equation 8] Zx 1 = Vx / Ix 1

【００８６】[0086]

【数９】Ｚｘ2 ＝Ｖｘ／Ｉｘ2 ## EQU9 ## Zx 2 = Vx / Ix 2

【００８７】そこで、信号処理部１９は計測した高調波
注入点４の電圧Ｖｘ及び下位，上位の電流Ｉｘ1 ，Ｉｘ
2 に基づき、数８，数９の式から注目側の基本波の上，
下両側の中間次数調波についてのインピーダンスＺｘ1
（＝Ｚｘ1 （ｕ），Ｚｘ1 （ｄ），Ｚｘ2 （＝Ｚｘ
2 （ｕ），Ｚｘ2 （ｄ））を求める。Therefore, the signal processor 19 measures the measured voltage Vx at the harmonic injection point 4 and the lower and upper currents Ix 1 and Ix.
Based on 2, number 8, on a number 9 expression of the fundamental wave of interest side,
Impedance Zx 1 for lower-order intermediate order harmonics
(= Zx 1 (u), Zx 1 (d), Zx 2 (= Zx
2 (u), Zx 2 (d)).

【００８８】さらに、前記上，下両側のインピーダンス
Ｚｘ1 又はＺｘ2 に前記と同様の補間処理を施し、測定
調波についてのインピーダンスＺｍ（＝１／Ｙｍ）を求
めて決定する。[0088] Further, on the, the same interpolation processing on the impedance Zx 1 or Zx 2 below both sides, determining seeking impedance Zm (= 1 / Ym) for measuring harmonic.

【００８９】また、このインピーダンスＺｍと電圧源と
の等価回路を求める場合は、高調波注入点４の測定調波
の電圧Ｖｍ，電流Ｉｍを計測し、数６，数７の式に相当
する式の演算から図２の電流源ＩGm1 ，ＩGm2 に相当す
る電圧源を求めて決定する。When obtaining an equivalent circuit of the impedance Zm and the voltage source, the voltage Vm and the current Im of the measured harmonic at the harmonic injection point 4 are measured, and the equations corresponding to the equations (6) and (7) are obtained. current source I Gm1 from operation of FIG. 2, is determined to seek a voltage source which corresponds to I Gm2.

【００９０】なお、中間次数調波の電圧を印加する代わ
りに、中間次数調波の電流を注入し、数４，数５の式の
代わりに数８，数９の式からインピーダンスＺｘ1 ，Ｚ
ｘ2を求め、測定調波についてのインピーダンスＺｍ及
び等価回路を求めることも可能である。Instead of applying the voltage of the intermediate order harmonic, the current of the intermediate order harmonic is injected, and the impedances Zx 1 , Zx 1 , Z x
seeking x 2, it is also possible to determine the impedance Zm and an equivalent circuit for measuring harmonic.

【００９１】そして、前記両形態のいずれにおいても、
測定調波の上，下両側の中間次数調波の電流又は電圧の
周波数ｆｘが数１の極めて簡単な式の演算により測定精
度等を考慮して求められ、とくに、中間次数調波の電流
又は電圧を複数注入又は印加する際に極めて有用であ
る。Then, in both of the above embodiments,
The frequency fx of the current or voltage of the intermediate order harmonics on both the upper and lower sides of the measurement harmonic is determined in consideration of the measurement accuracy and the like by calculating a very simple formula of Equation 1, and particularly, the current or voltage of the intermediate order harmonics It is extremely useful when multiple voltages are injected or applied.

【００９２】さらに、各中間次数調波の電流（電圧）が
基本波に同期し、しかも、その注入（印加）期間が基本
波のｎ周期に設定され、このとき、中間次数調波の電流
（電圧）が必ず基本波の整数倍の周期注入されるため、
注入（印加）に基づく所定結果等にＤＦＴ解析等の周波
数分析を施して電力系統の注目側の基本波の上，下両側
の中間次数調波についてのアドミタンス（インピーダン
ス）を求める際、サンプリング周波数を高くして周波数
分解能を極めて高くしたりすることなく、基本波に同期
したサンプリングにより、サンプリングの始端，終端の
連続性を保ってサンプリングエッジによる周波数分析誤
差等を防止することができ、安価かつ簡単に精度の高い
測定が行える。Further, the current (voltage) of each intermediate-order harmonic is synchronized with the fundamental wave, and its injection (application) period is set to n periods of the fundamental wave. Voltage) is always injected as an integral multiple of the fundamental wave,
When frequency analysis such as DFT analysis is performed on a predetermined result based on the injection (applied) to obtain admittance (impedance) for intermediate-order harmonics above and below the fundamental wave on the target side of the power system, the sampling frequency is Sampling synchronized with the fundamental wave without increasing the frequency resolution to a very high level can prevent continuity of sampling start and end points and prevent frequency analysis errors due to sampling edges. Highly accurate measurement can be performed.

【００９３】[0093]

【発明の効果】本発明は、以下に記載する効果を奏す
る。測定調波の上，下両側の基本波の非整数倍周波数の
注入電流（印加電圧）を、測定精度を考慮した簡単な式
の計算から基本波に同期した適切な周波数の中間次数調
波の電流（電圧）として求めることができる。The present invention has the following effects. The injection current (applied voltage) at a frequency that is a non-integer multiple of the fundamental wave on the upper and lower sides of the measurement harmonic is calculated from a simple formula that takes into account the measurement accuracy. It can be obtained as a current (voltage).

【００９４】また、この中間次数調波の電流（電圧）が
基本波のｎ周期にわたって注入又は印加されるため、中
間次数調波の電流（電圧）の注入期間を必ず整数周期
（ｍ×ｎ±ｋ）にすることができる。Further, since the current (voltage) of the intermediate order harmonic is injected or applied over n periods of the fundamental wave, the injection period of the current (voltage) of the intermediate order harmonic must be set to an integer period (m × n ± k).

【００９５】したがって、この整数周期の中間次数調波
の電流注入（電圧印加）に基づく電力系統１の電圧，電
流を計測し、電力系統１の前記整数周期の中間次数調波
の電流（電圧）を基本波に同期してサンプリングし、周
波数分析等すれば、サンプリング周波数を極端に高くし
たりすることなく、サンプリングエッジによる周波数分
析誤差等を防止して電力系統１の注目側の測定調波の
上，下両側の中間次数調波についてのアドミタンス（イ
ンピーダンス）を求めることができる。Therefore, the voltage and current of the power system 1 are measured based on the current injection (voltage application) of the intermediate order harmonic of the integer cycle, and the current (voltage) of the intermediate order harmonic of the integer cycle of the power system 1 is measured. Is sampled in synchronism with the fundamental wave and frequency analysis is performed, thereby preventing a frequency analysis error or the like due to a sampling edge without excessively increasing the sampling frequency and preventing the measurement harmonic of the attention side of the power system 1 from being measured. The admittance (impedance) of the upper and lower intermediate harmonics can be obtained.

【００９６】そして、この結果から所望の測定精度で測
定調波についてのアドミタンス（インピーダンス）又は
等価回路を求めることができ、従来は不可能であった電
力系統１の高調波についてのアドミタンス（インピーダ
ンス）又は等価回路の精度のよい測定を、簡単な信号注
入式の演算に基づいて行うことができる。The admittance (impedance) or the equivalent circuit of the measured harmonic can be obtained with the desired measurement accuracy from the result, and the admittance (impedance) of the higher harmonics of the power system 1 which was conventionally impossible is obtained. Alternatively, accurate measurement of the equivalent circuit can be performed based on a simple signal injection type calculation.

【図面の簡単な説明】[Brief description of the drawings]

【図１】本発明の実施の１形態の回路ブロック図であ
る。FIG. 1 is a circuit block diagram of one embodiment of the present invention.

【図２】図１の電力系統の高調波等価回路である。FIG. 2 is a harmonic equivalent circuit of the power system of FIG.

【符号の説明】[Explanation of symbols]

１ 電力系統 ４ 高調波注入点 ５ 計測装置 ２０，２１ 等価回路 Reference Signs List 1 power system 4 harmonic injection point 5 measuring device 20, 21 equivalent circuit

───────────────────────────────────────────────────── フロントページの続き (72)発明者 西村 荘治 京都市右京区梅津高畝町47番地 日新電 機株式会社内 (72)発明者 夏田 育千 京都市右京区梅津高畝町47番地 日新電 機株式会社内 (72)発明者 志方 俊彦 京都市右京区梅津高畝町47番地 日新電 機株式会社内 (58)調査した分野(Int.Cl.6，ＤＢ名) G01R 23/20 G01R 31/00 H02J 3/01 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Shoji Nishimura, 47, Umezu Takaune-cho, Ukyo-ku, Kyoto-shi Inside Nissin Electric Machinery Co., Ltd. Inside (72) Inventor Toshihiko Shikata 47, Umezu Takaune-cho, Ukyo-ku, Kyoto-shi Nissin Electric Machinery Co., Ltd. (58) Field surveyed (Int.Cl. 6 , DB name) G01R 23/20 G01R 31/00 H02J 3/01

Claims (2)

(57)【特許請求の範囲】(57) [Claims] 【請求項１】 電力系統の周波数ｆｓの基本波のｍ倍
（ｍは整数）周波数のｍ次高調波を測定調波とし、前記
電力系統の前記測定調波についてのアドミタンス又は該
アドミタンスと電流源との並列回路からなる等価回路を
求める際に、 前記測定調波の上，下両側の前記基本波の非整数倍周波
数の前記基本波に同期した電流を、中間次数調波の電流
とし、 前記測定調波（ｍ次高調波）とｍ±１次高調波との間の
中間次数調波の電流の周波数ｆｘを、ｆｘ＝（ｆｓ×
ｍ）±｛（ｆｓ／ｎ）×ｋ）｝の式（但し、ｎは測定精
度１／ｎ（０＜１／ｎ＜１）に応じた１，２，…，ｎの
整数、ｋは周波数設定用の１，２，…，ｎの整数）から
求めて決定し、 前記電力系統の高調波注入点に、前記測定調波の上，下
両側の前記周波数ｆｘの中間次数調波の電流を前記基本
波のｎ周期注入し、 該注入に基づく前記高調波注入点の電圧及び前記電力系
統の前記高調波注入点より上位，下位の少なくとも一方
の電流を計測し、 前記上位，前記下位の少なくとも一方を注目側として前
記計測の結果から前記注目側の前記測定調波の上，下両
側それぞれの中間次数調波についてのアドミタンスを算
出し、 該算出の結果に基づく補間処理により、前記注目側の前
記測定調波についてのアドミタンスを求めて決定するこ
とを特徴とする電力系統の高調波測定方法。1. An m-order harmonic having a frequency that is m times (m is an integer) a fundamental frequency of a frequency fs of a power system is set as a measurement harmonic, and admittance of the measurement harmonic of the power system or the admittance and a current source are measured. When obtaining an equivalent circuit composed of a parallel circuit with the above, a current synchronized with the fundamental wave of a non-integer multiple of the fundamental wave on the upper and lower sides of the measurement harmonic is defined as a current of an intermediate order harmonic, The frequency fx of the current of the intermediate harmonic between the measurement harmonic (mth harmonic) and the m ± 1st harmonic is given by fx = (fs ×
m) ± {(fs / n) × k)} (where n is an integer of 1, 2,..., n according to measurement accuracy 1 / n (0 <1 / n <1), and k is frequency And an integer of 1, 2,..., N for setting), and at the harmonic injection point of the power system, the current of the intermediate-order harmonic of the frequency fx above and below the measurement harmonic. Inject n cycles of the fundamental wave, measure the voltage at the harmonic injection point based on the injection and at least one of the higher and lower currents than the higher harmonic injection point of the power system, The admittance of each of the intermediate order harmonics on the upper and lower sides of the measurement harmonic on the side of interest is calculated from the result of the measurement using the one side as the side of interest, and interpolation processing based on the calculation result is performed. Determining admittance for the measured harmonics and determining Harmonic measurement method that the power system. 【請求項２】 電力系統の周波数ｆｓの基本波のｍ倍
（ｍは整数）周波数のｍ次高調波を測定調波とし、前記
電力系統の前記測定調波についてのインピーダンス又は
該インピーダンスと電圧源との直列回路からなる等価回
路を求める際に、 前記測定調波の上，下両側の前記基本波の非整数倍周波
数の前記基本波に同期した電圧を、中間次数調波の電圧
とし、 前記測定調波（ｍ次高調波）とｍ±１次高調波との間の
中間次数調波の電圧の周波数ｆｘを、ｆｘ＝（ｆｓ×
ｍ）±｛（ｆｓ／ｎ）×ｋ｝の式（但し、ｎは測定精度
１／ｎ（０＜１／ｎ＜１）に応じた１，２，…の整数、
ｋは周波数設定用の１，２，…，ｎの整数）から求めて
決定し、 前記電力系統の高調波注入点に、前記測定調波の上，下
両側の前記周波数ｆｘの中間次数調波の電圧を前記基本
波のｎ周期印加し、 該印加に基づく前記高調波注入点の電圧及び前記電力系
統の前記高調波注入点より上位，下位の少なくとも一方
の電流を計測し、 前記上位，前記下位の少なくとも一方を注目側として前
記計測の結果から前記注目側の前記測定調波の上，下両
側それぞれの中間次数調波についてのインピーダンスを
算出し、 該算出の結果に基づく補間処理により、前記注目側の前
記測定調波についてのインピーダンスを求めて決定する
ことを特徴とする電力系統の高調波測定方法。2. An m-order harmonic having a frequency m times (m is an integer) a fundamental frequency of a frequency fs of a power system as a measurement harmonic, and an impedance or the impedance and a voltage source for the measurement harmonic of the power system. When obtaining an equivalent circuit consisting of a series circuit with the following, a voltage synchronized with the fundamental wave of a non-integer multiple of the fundamental wave on the upper and lower sides of the measurement harmonic is defined as a voltage of an intermediate order harmonic, The frequency fx of the voltage of the intermediate order harmonic between the measurement harmonic (mth harmonic) and the m ± 1st harmonic is given by fx = (fs ×
m) ± {(fs / n) × k} (where n is an integer of 1, 2,... depending on the measurement accuracy 1 / n (0 <1 / n <1),
k is an integer of 1, 2,..., n for frequency setting), and is determined at the harmonic injection point of the power system by intermediate order harmonics of the frequency fx above and below the measured harmonic. Is applied for n periods of the fundamental wave, and the voltage at the harmonic injection point based on the applied voltage and at least one of the currents higher and lower than the harmonic injection point of the power system are measured. At least one of the lower order is set as the attention side, and the impedance of the intermediate order harmonic on each of the upper and lower sides of the measurement harmonic on the attention side is calculated from the measurement result on the attention side, and the interpolation processing based on the calculation result, A method for measuring harmonics in a power system, comprising determining and determining impedance of the measurement harmonic on a target side.
JP9180570A 1997-06-19 1997-06-19 Power system harmonic measurement method Expired - Fee Related JP2940603B2 (en)

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JP9180570A JP2940603B2 (en) 1997-06-19 1997-06-19 Power system harmonic measurement method
US09/099,381 US6208945B1 (en) 1997-06-19 1998-06-18 Harmonic component measuring method for power system

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JP9180570A JP2940603B2 (en) 1997-06-19 1997-06-19 Power system harmonic measurement method

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JP2940603B2 true JP2940603B2 (en) 1999-08-25

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