【正文】 ， and the real waveform (solid line) of the total active currents and the waveform from the detected circuit (broken line) are in (f). The actual values of the total active and reactive currents can be calculated from Eqs.(10) and(11).It is seen that the detected values of the total active and reactive currents are the same as the actual values， showing that this method is effective. The waveform of the total active currents is the same as that of the power grid voltage. It is the merit of this method. The simulation result of is in .The current which is added to the detected circuit is the same as that in (c) .The voltage which is added to the detected circuit is the unit sinusoidal signal which not only has the same phase as the voltage signal in (a) but also is 2 times the value of the voltage. The actual and detected waveforms of the fundamental active current are shown in (a) where the actual waveform of the fundamental active current is calculated from the Eq.(14).The actual waveform of the harmonic and fundamental reactive current (solid line) and the detected waveform (brocken line) are shown in (b)， where the actual waveform is the difference between the detected current and the fundamental active ponent in it. It is seen that the detected results agree with the actual ones for both active currents and harmonic and fundamental reactive currents. The simulation result of is in .Assume that the detected current is a square wave current which lags voltage by 1/10 cycle， and that the voltage input to the circuit to be tested， which has the same phase as the detected voltage and leads it by 900 ， is 2 times the unit wave From , it is seen that the spectrum of the detected 外文原文 8 harmonic current is the same as that of the detected current except the fundamental current。這種理論分析和仿真的結(jié)果顯示，這種被提出的方法在檢測(cè)瞬時(shí)諧波和在單相電力中的無功電流是有效的。 參考資料 15 呈現(xiàn)了一種建立在 Fryze 功率定義的方法，但在檢測(cè)結(jié)果出來前需要一個(gè)積分周期，從 19 世紀(jì) 80 年代以來，許多研究者包括 已經(jīng)用新方法分析了非正弦電流，但一個(gè)積分的時(shí)間被需要并且實(shí)時(shí)能力仍然較差。 正如等式（ 1）、（ 2）、（ 3）說明的那樣，如果平均有功功率和電壓有效值的平方知道的話， G 被算出是可能的。 圖 1，實(shí)時(shí)檢測(cè)諧波和無功電流 這種檢測(cè)方法的一些特殊應(yīng)用 在圖 1 中，輸出 ??tip 和 ??tiq 隨輸入 ??tus 改變，因此，這個(gè)電路圖在電網(wǎng)的外文原文 15 不 同要求的層面上提供相關(guān)的補(bǔ)償，以下三種應(yīng)用情況被分析。因此，這個(gè)單相電路諧波檢測(cè)方法被認(rèn)為是基于 Fryze 功率定義方法的諧波檢測(cè)的特例。從圖 6 中，可以看出：檢測(cè)諧波電流的頻譜和檢測(cè)電流的頻譜除去基波之后的頻譜相同，這就是說，檢測(cè)出來的諧波分布和頻譜和檢測(cè)電流中的諧波相同。 1931(8):225234。因此，時(shí)間落后 10ms，時(shí)間落后是由濾波器引起的，事實(shí)上，要濾除的諧波的最低 的 階數(shù)是 2，用數(shù)字濾波方法得到最低諧波的一個(gè)周期的平均值，穩(wěn)定的、正確的結(jié)果在半個(gè)功率周期后出現(xiàn)， .， 10ms.很明顯，這個(gè)方法的動(dòng)態(tài)響應(yīng)的顯示出來是好的?？梢钥吹?，檢測(cè)的總的有功和無功電流值和實(shí)際值相同，顯示出 這種方法的有效性，總的有功電流波形和電網(wǎng)電壓的波形相同，這是這種 方法的優(yōu)點(diǎn)。 、實(shí)時(shí)檢測(cè)諧波和基波無功電流 如果 ??tus = ? ?1cos2 ??wt ，然后， nU = ?????? ??,1,1 ,1,nno （ 12） 把等式（ 12）代入等式（ 9），我們得到 P= 11cos?I （ 13） 然后，通過等式（ 1）， ? ?ti p 被表達(dá)為： ??tip = ? ?111 c o sc o s2 ?? ?wtI （ 14） 很明顯， ??tip 是被檢測(cè)電流的基波有功電流部分， ??tiq 是諧波和基波無功電流之和，因此， ??tiq 在限制諧波和補(bǔ)償無功電流方面有參考價(jià)值。跟其它基于瞬時(shí)無功功率的方法相比，這種方法簡(jiǎn)單并且容易實(shí)現(xiàn)。 實(shí)時(shí)檢測(cè) 。 IEEE International Symposium on Industrial Electronics (ISIE) [C]. Pusan, Kore a, . [3] Jiang M C. Aanlysis and design of a novel threephase active power filter [J] .IEEE Transactions on Aerospace and Electronic Systems, 37(3) ， 2022: 824831. [4] Ren Y F, Li H S， He G, et al. Two kinds of realtime detecting method for harmonic and reactive current in signal Circuit [J]. Automation of Electrical Power Society, 2022,15(1):9598(in Chinese). [5] Fryze S. Active, reactive and apparent power in circuits with nonsinusoidal voltage and current [J]. Elektortech, 1931( 7 ):193203。 w is angle frequency。 Singlephase circuit。 Harmonic。 外文原文 3 ??tus and ??tis are instantaneous voltage and instantaneous current of electric work, respectively。 that is， the distribution and magnitude of the detected harmonic is the same as that of the harmonic in the detected current. Fig .7 shows the simulated performance of the dynamic response of the proposed method. Assume that the electricwork current is 1800 square wave， which lags voltage by 360 . For ease of observation， suppose the amplitude of the current increases from 100 A to 200 A between 2030 ms， and the waveform of current is shown in (a). (b)(d) are respectively the outputs of the lowpass filter, the detected results of the fundamental current and the harmonic current. It is found that both the outputs of the lowpass filter and the detected results of the fundamental and harmonic currents begin to change at about 30 ms, and then stabilize at 40 ms. Therefore， the t