電力系統(tǒng)及其自動化外文翻譯--實時檢測諧波和單相電路無功功率的方法

1、<p>　　Real-Time Method for Detecting Harmonic and</p><p>　　Reactive Currents of Single-Phase Circuits</p><p><b>　　Abstract</b></p><p>　　According to the characteris

2、tics of single-phase circuits and demand of using active filter for real-time detecting harmonic and reactive currents, a detecting method based on Fryze's power definition is proposed. The results of theoretic alana

3、lysis and simulation show that the proposed method is effective in real-time detecting of instantaneous harmonic and reactive currents in single-phase circuits. When only detecting the total reactive currents，this method

4、 does not need a phase-locked loop c</p><p>　　Keywords Active filter; Harmonic; Reactive current; Real-time detection; Single-phase circuit; Electric-network</p><p>　　0、Introduction</p>&

5、lt;p>　　At present it is a major tendency to limit harmonics with active filters，which can not only limit harmonics dynamically and compensate reactive power but also can achieve a continuous and dynamic tracking of th

6、e compensation for time-varying harmonic and reactive currents and are not apt to be affected by the resistance of electric network. The key technology of active filter is the real-time detecting of harmonics and reactiv

7、e currents from load currents to receive reference to meet the need of</p><p>　　On the basis of the theory of instantaneous reactive power in three-phase circuit，many relatively mature detecting algorithms f

8、or harmonics and reactive currents of three-phase circuits have been proposed，such as the methods of p, q, ip and </p><p>　　However, in single-phase circuits，these methods can not be directly used and an ext

9、ra two-phase voltage and current need to be constructed，which lowers the real-time ability and makes the algorithm more complicated.</p><p>　　Refs. [1 ,5] presented a method that is construeted on the basis

10、of Fryze's power definition, but it needs one integral cycle before educing the detection results. Since 1980s， many researchers, e.g .Czarnecki, have analyzed the non-sinusoidal currents with new methods, but one in

11、tegral cycle is alsoneeded and the real-time ability is still poor.</p><p>　　In this paper, an in-depth research is made on Fryze's power definition，which is applied to detect harmonic and reactive curre

12、nts in single-phase circuits successfully，and a real-time detecting method for harmonic and reactive currents in single-phase circuits is brought forward. Analysis and simulation reveal that the proposed method can reali

13、ze real-time detection of the instantaneous harmonic and reactive currents in single-phase circuits. This method does not need a phase-locked loop circuit</p><p>　　1、 Fundamentals</p><p>　　Accor

14、ding to Fryze's power definition，instaneous active currents is a component of the total currents and its waveform is the same as that of voltage Moreover, the average power absorbed by active currents in one cycle is

15、 equal to that by total currents，and substraction of the instantaneous active currents from the total currents yields the instantaneous reactive currents.Thus，we have the following expression:</p><p><b&g

16、t;　　(1)</b></p><p><b>　　(2)</b></p><p><b>　　(3)</b></p><p>　　where and are instantaneous active and reactive currents，respectively; and are instan

17、taneous voltage and instantaneous current of electric network, respectively;G is real constant ratio，and P is average active power (if U is the effective value of voltage，then );T is cycle and t is time.</p><p

18、>　　As indicated by Eqs.(1)，(2)and( 3)，G can be calculated if the average active power and the square of voltage virtual value are available.Then from Eqs.(I)and (3)，the instantaneous active current and instantaneous r

19、eactive current can be calculated.</p><p>　　In general，assume the detected voltage and current respectively are</p><p>　　= (4)</p><p>　　=

20、 (5)</p><p>　　where and are the virtual values of the nth harmonic voltage and current, respectively; w is angle frequency; ，and are the phases of the nth harmonic</p>

21、;<p>　　voltage and current, respectively; and n=1, 2, </p><p><b>　　Then</b></p><p>　　+， (6)</p><p><b>　　where，</b>

22、</p><p><b>　　(7)</b></p><p>　　and denotes the sum of the integers whose subscripts n and m are from 1 to </p><p>　　In Eq. (6) ，except that isDC component, the other item

23、s are all AC components. So the lowpass filter (LPF) whose cut-off frequency is lower than the lowest frequency of alternating signals must be used to filter ，and then is obtained. Similarly，the product of instantaneous

24、current and instantaneous voltage，P，is</p><p><b>　　p==</b></p><p><b>　　=</b></p><p>　　+ (8)</p><p><b>　　

25、where</b></p><p>　　P= (9)</p><p>　　and =is called the power factor angle of the nth harmonic.Similarly，in Eq.(8 )all the items are AC compone

26、nts except for P. Thus the low-pass filter whose cut-off frequency is lower than the lowest frequency of alternating signals must be used to filter p，and then P is obtained.</p><p>　　After working out P and，

27、the functional block diagram is constructed as shown in Fig. 1，where the real-time detection of harmonics and instantaneous reactive currents are performed on the basis of Fryze's power definition in single-phase cir

28、cuit. Although there is a division unit, it is not difficult to realize.</p><p>　　Fig.1 Real-time detection of harmonic and reactive current</p><p>　　2、 Some Special Applications of the Detectin

29、g Method</p><p>　　In Fig .l， the outputs and vary with the input ，so this circuit can provide different reference compensations on the ground of different requirements of electric network. Three cases of a

30、pplication are analyzed as follows.</p><p>　　2.1 Real-time detection of total reactive currents</p><p>　　If the compensation is only for the reactive power, then the reactive currents need to be

31、 detected.</p><p>　　Assume and are the current and voltage of the detected objects；then from Eqs. (1)，(2)，(4) and(9)，the outputs and in Fig.1 are obtained</p><p>　　(the derivation process is

32、 omitted here):</p><p>　　= (10)</p><p>　　= (11)</p><p>　　Obviously， is the sum of the harmonic active currents, calle

33、d the total active currents. is the sum of the harmonic reactive currents and the fundamental active currents, called the total reactive currents.Therefore, ,the output in Fig. 1，is used as a reference to compensate the

34、reactive power.</p><p>　　When only detecting the total reactive currents，there is no need to detect the unit sinusoidal signal with the same phase as the detected voltage，and hence no need to use the phase-l

35、ocked loop circuit too. This is one of the merits of this method.</p><p>　　2.2 Real-time detection of harmonic and fundamental reactive currents</p><p>　　If =, then,</p><p>　　=

36、 (12)</p><p>　　Substituting Eq. (12) into Eq.(9)，we obtain</p><p>　　P= (13)</p><p>　　Th

37、en by Eq. (1) ， is expressed as</p><p>　　= (14)</p><p>　　Obviously, is the fundamental active part of the detected current, and then is the sum of harmonic an

38、d fundamental reactive currents. Therefore，the output is used as a reference value to limit harmonics and compensate reactive currents.</p><p>　　Since =1，F(xiàn)ig.2 is obtained by simplification of Fig.1. In Fig

39、.2, is an unit sinusoidal signal which has the same phase as the detected voltage and can be obtained from the phase-locked loop circuit.</p><p>　　Fig.2 Real-time detection of harmonic and fundamental reacti

40、ve current</p><p>　　2.3 Real-time detection of harmonic currents</p><p>　　When only harmonics need to be limited, harmonic currents should be detected. We first detect the fundamental currents，a

41、nd then subtract the fundamental currents from the total currents，to obtain the harmonic currents.</p><p><b>　　If</b></p><p><b>　　=</b></p><p>　　by Eq. (8) w

42、e obtain</p><p>　　P= (15)</p><p>　　= (16)</p><p>　　where has the same value as the fundamen

43、tal reactive current. 2.1，the circuit of detecting harmonic currents can be constructed, as shown in Fig.3 .</p><p>　　Fig.3 Real-time detection of harmonic currents</p><p>　　In Fig.3, is harmon

44、ic current. Fig.3 is the same as the detecting block diagram of Ref.[7]，so the method for detecting harmonics in single-phase circuits can be regarded as a special case of the proposed detecting method based on the Fryze

45、's power definition.</p><p>　　3、 Simulation Analysis</p><p>　　The above three kinds of detecting circuits are simulated on Matlab/Simulink. The results of simulation are summarized as follow

46、s.</p><p>　　The simulation result of Fig.1 is in Fig.4 .The spectra and waveforms of the voltage and current are in Fig.4( a)-(d).The real waveform of the total reactive currents(solid line)and the waveform

47、from the detected circuit (broken line) are in Fig.4 (e)，and the real waveform (solid line) of the total active currents and the waveform from the detected circuit (broken line) are in Fig.4(f). The actual values of the

48、total active and reactive currents can be calculated from Eqs.(10) and(11).It is seen</p><p>　　The simulation result of Fig.2 is in Fig.5 .The current which is added to the detected circuit is the same as th

49、at in Fig.4 (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 Fig.4 (a) but also is times the value of the voltage. The actu

50、al and detected waveforms of the fundamental active current are shown in Fig.5 (a) where the actual waveform of the fundamental active current is calculated from the Eq</p><p>　　The simulation result of Fig.

51、3 is in Fig.6 .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

52、it by 90，is times the unit wave From Fig.6, it is seen that the spectrum of the detected harmonic current is the same as that of the detected current except the fundamental current; that is，the distribution and magnitude

53、 of the detected harmonic is th</p><p>　　Fig .7 shows the simulated performance of the dynamic response of the proposed method. Assume that the electric-network current is 180 square wave，which lags voltage

54、by 36. For ease of observation，suppose the amplitude of the current increases from 100 A to 200 A between 20-30 ms，and the waveform of current is shown in Fig.7 (a).Fig.7 (b)-(d) are respectively the outputs of the low-p

55、ass filter, the detected results of the fundamental current and the harmonic current. It is found that both the ou</p><p>　　(a) The voltage of electric network (b) The spectrum of voltage</p>

56、<p>　　(c) The current of electric network (d) The spectrum of current</p><p>　　(e) The total reactive current (f) The total active current</p><p>　　Fig.4 The de

57、tected total active and reactive current</p><p>　　(a) The active current component (b) Harmonic and fundamental reactive current</p><p>　　Fig.5 The detected active current and harmonic and fun

58、damental reactive current</p><p>　　(a) The current of electric network (b) The spectrum of current</p><p>　　(c) The detected harmonic current (d) The spectrum of harmonic curr

59、ent</p><p>　　Fig.6 Dynamically detected harmonic current</p><p>　　(a) The current of electric network (b) The output current of LPF</p><p>　　(c)The fundamental current

60、 (d)The harmonic current</p><p>　　Fig.7 The simulation of performance of dynamic response</p><p>　　4 、Conclusion</p><p>　　In this paper, a real-time detecting method

61、 for harmonics and reactive currents on the basis of the Fryze's power definition is constructed. Analysis and simulation reveal that this method is simple and easy to realize and can detect harmonic currents fundame

62、ntal reactive(active)currents and total reactive (active) currents dynamically and accurately. When only detecting the total reactive currents，this method does not need a phase-locked loop circuit.</p><p>　　

63、References</p><p>　　[1] Wang Z A, Yang J, Liu J J. Harmonic limitation and reactive power compensation[M], Beijing; Machine Press ,1998(in Chinese).</p><p>　　[2 ] Lin B R ,Yang B R .Current harm

64、onics elimination with a series hybrid active filter[ A ] .In; IEEE International Symposium on Industrial Electronics (ISIE) [C]. Pusan, Kore a, 2001.566-570.</p><p>　　[3] Jiang M C. Aanlysis and design of a

65、 novel three-phase active power filter [J] .IEEE Transactions on Aerospace and Electronic Systems, 37(3) ，2001: 824831.</p><p>　　[4] Ren Y F, Li H S，He G, et al. Two kinds of real-time detecting method for h

66、armonic and reactive current in signal Circuit [J]. Automation of Electrical Power Society, 2003,15(1):95-98(in Chinese).</p><p>　　[5] Fryze S. Active, reactive and apparent power in circuits with nonsinusoi

67、dal voltage and current [J]. Elektortech, 1931( 7 ):193-203;1931(8):225-234; 1932(22):673-676 .</p><p>　　[6] Czarnecki L S. Scattered and reactive current, voltage and power in circuits with nonsinusoidal wa

68、veforms and their compensation [J]. IEEE Trans Instrum Meas, 1991, 40 (3); 563-567.</p><p>　　[7] Li T B，Sun Y H, Liao Z L. Study of a real-time detecting method for reactive current in single circuit [J]. El

69、ectrical Measurement and Instrument, 2003 40(451):8-11 (in Chinese).</p><p>　　實時檢測諧波和單相電路無功功率的方法</p><p><b>　　摘要</b></p><p>　　根據(jù)單相電路的特點和為了實時檢測諧波和無功功率而使用有源濾波器，一種檢測基于Fryze功

70、率定義的方法被提出。這種理論分析和仿真的結果顯示，這種被提出的方法在檢測瞬時諧波和在單相電力中的無功電流是有效的。當只要求檢測總的無功電流時，這種方法并不需要一個索相環(huán)電路，并且它也能在一些特殊的應用方面提供不同的補償，這種補償是在電網(wǎng)的不同要求的層面上。跟其它基于瞬時無功功率的方法相比，這種方法簡單并且容易實現(xiàn)。</p><p>　　關鍵詞：有源濾波器；諧波；無功電流; 實時檢測; 單相電路；電網(wǎng)</p&

71、gt;<p><b>　　0、介紹</b></p><p>　　目前，用有源濾波器限制諧波是主要的趨勢，有源濾波器不僅能動態(tài)的限制諧波和補償無功功率，而且能取得一個為隨時間變化的諧波和無功電流的連續(xù)的和動態(tài)的補償軌跡，同時它不受電網(wǎng)阻力的影響，有源濾波器的關鍵技術是實時檢測諧波和無功電流時，負載電流的接收范圍要滿足有源濾波器的需要。因此，這種濾波器的結果受準確度和實時檢測能力的

72、影響。</p><p>　　在三相瞬時無功功率的基礎上，許多相對成熟的關于三相諧波和無功電流的算法被提出，例如p,q和，法，不管怎樣，在單相電路里，這些方法不能直接使用，并且額外的兩相電壓和電流需要重建，這樣可以降低實時性并使算法更復雜。</p><p>　　參考資料1-5呈現(xiàn)了一種建立在Fryze功率定義的方法，但在檢測結果出來前需要一個積分周期，從19世紀80年代以來，許多研究者包括e

73、.g.Czamecki 已經用新方法分析了非正弦電流，但一個積分的時間被需要并且實時能力仍然較差。</p><p>　　在這里，一種對于基于Fryze功率定義方法做了更深的研究，這個研究成功的應用在單相電路里檢測諧波和無功電流，并且一種在單相電路里實時檢測諧波和無功電流方法被提出。分析和仿真顯示，這種被呈現(xiàn)的方法能在單相電路能有效的實時檢測瞬時諧波和無功電流。當只要求檢測總的無功電流時，這種方法并不需要一個索相環(huán)

74、電路，并且它也能在一些特殊的應用方面提供不同的補償，這種補償是在電網(wǎng)的不同要求的層面上。跟其它基于瞬時無功功率的方法相比，這種方法簡單并且容易實現(xiàn)。這種檢測無功功率和諧波電流的方法在Ref里被呈現(xiàn)，【7】是我們方法應用的一種特例。</p><p><b>　　1、 原理</b></p><p>　　根據(jù)Fryze功率定義，瞬時有功電流是總電流的一部分，并且它的波形和電

75、壓波形相似，而且，在一個周期里，有功電流吸收的平均功率和總電流吸收的相等，并且，總電流減去瞬時有功電流等于瞬時無功電流。因此，我們有以下的表達式：</p><p><b>　?。?）</b></p><p><b>　?。?）</b></p><p><b>　?。?）</b></p>

76、<p>　　這里和分別是瞬時有功和無功電流；和分別是瞬時電壓和電網(wǎng)的瞬時電流，G是實常數(shù)系數(shù)，P是平均有功功率（如果U是電壓的有效值，那么）T是周期，t是時間。</p><p>　　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。然后，從等式（1）和（3），瞬時有功電流和無功電流可以被算出。</p><p>　　一般來講，計

77、算被檢測的電壓和電流公式各自為：</p><p>　　= （4）</p><p>　　= （5）</p><p>　　這里和分別各自是n次諧波電壓和電流的有效值；w是角頻率；和分別是n次諧波電壓和電流的角度，并且n=1

78、、2、3、···。</p><p><b>　　然后，</b></p><p>　　+， （6）</p><p><b>　　這里，</b></p><p><b>　?。?）</b&g

79、t;</p><p>　　表示數(shù)字的和，n，m是從1到</p><p>　　在等式（6）中，除了是直流量外，其余參數(shù)都是交流量，因此切斷頻率比可變信號的最低頻率還低的低通濾波器（LPF）必須用來濾除，然后，被包含在內，類似的，瞬時電流和瞬時電壓的產品p為：</p><p><b>　　p==</b></p><p>&l

80、t;b>　　=</b></p><p>　　+ （8）</p><p>　　這里，P= （9）</p><p>　　并且，=被叫做n次諧波的功率因子。</p><p>　　

81、在等式（8）中，除了P是直流量外，其余參數(shù)都是交流量，因此切斷頻率比可變信號的最低頻率還低的低通濾波器（LPF）必須用來濾除p，然后，P被包含在內。</p><p>　　在算出P和后，功能方框圖構造如圖1，在圖1中，實時檢測諧波和無功電流方法是在單相電路中基于Fryze功率定義方法，雖然有一個分解組件，但它不難實現(xiàn)。</p><p>　　圖1，實時檢測諧波和無功電流</p>

82、<p>　　2、 這種檢測方法的一些特殊應用</p><p>　　在圖1中，輸出和隨輸入改變，因此，這個電路圖在電網(wǎng)的不同要求的層面上提供相關的補償，以下三種應用情況被分析。</p><p>　　2.1、 實時檢測總無功電流</p><p>　　如果只需要補償無功功率，那么無功電流需要被檢測。</p><p>　　假設和是被檢測物體

83、的電流和電壓，然后，從等式（1）、（2）、（4）、（9），圖1的輸出和被包含（這里計算過程被省略）：</p><p>　　= （10）</p><p>　　= （11）</p><p>　　很明顯，是諧波有功電流和基波有功電流之和，叫做總的有

84、功電流，是諧波無功電流和基波無功電流之和，叫做總的無功電流，因此，在圖1中的輸出作為補償無功功率是有參考價值的。</p><p>　　當只檢測總的無功電流時，沒有必要檢測和被檢測電壓有相同的相位的單位正弦信號，也沒有必要用鎖相環(huán)，這是這種方法的優(yōu)點。</p><p>　　2.2、實時檢測諧波和基波無功電流</p><p><b>　　如果=，然后，<

85、/b></p><p>　　= （12）</p><p>　　把等式（12）代入等式（9），我們得到</p><p>　　P= （13）</p><

86、p>　　然后，通過等式（1），被表達為：</p><p>　　= （14）</p><p>　　很明顯，是被檢測電流的基波有功電流部分，是諧波和基波無功電流之和，因此，在限制諧波和補償無功電流方面有參考價值。</p><p>　　因為=1，圖2是由圖1簡化而來，在圖2中，是一個和被檢測電壓有

87、相同的相位的單位正弦信號，并且，能被包含在鎖相環(huán)里。</p><p>　　圖2 實時檢測諧波和基波無功電流</p><p>　　2.3、 實時檢測諧波電流</p><p>　　當只需被限制的諧波電流時，諧波電流應該被檢測，我們首先檢測基波電流，然后，從總的電流中減去基波電流，得到諧波電流。</p><p><b>　　如果</

88、b></p><p><b>　　=</b></p><p>　　通過等式（8），我們得到：</p><p>　　P= （15）</p><p>　　=

89、 （16）</p><p>　　這里，是基波無功電流，通過2.1章節(jié)的事情相關介紹，檢測諧波電路圖如圖3</p><p>　　圖3實時檢測諧波電流</p><p>　　在圖3中，是諧波電流，圖3和等式7的方框圖相同。因此，這個單相電路諧波檢測方法被認為是基于Fryze功率定義方法的諧波檢測的特例。</p><p><b&g

90、t;　　3、 仿真分析</b></p><p>　　以上的檢測電路的三種方法被基于Matlab/Simulink仿真。仿真結果總結如下。</p><p>　　圖1的仿真結果在圖4里，電壓和電流的頻譜圖和波形圖如圖4（a）-（d）</p><p>　　總的無功電流的真正波形（實線）和被檢測出來的波形（虛線）在圖4（e），總的真正波形（實線）和被檢測出來的波

91、形（虛線）在圖4（f）. 總的有功電流和總的無功電流的實際值可以通過等式（10）、（11）可以被算出。可以看到，檢測的總的有功和無功電流值和實際值相同，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。</p><p>　　圖2的仿真結果在圖5里，加進檢測電路的電流和圖4相同，加進檢測電路的電壓是單位正弦信號，它不僅和圖4的電壓信號相同，而且是電壓值的倍，實際和檢測的基波有功波形在

92、圖5（a），實際的基波有功電流波形可以通過等式（14）被計算出來，諧波和基波無功電流的實際波形（實線）和檢測出的波形（虛線）在圖5（b），在圖5（b）中，實際波形不僅和被檢測電流波形不同，也和基波的有功成份不同?？梢钥闯?，檢測結果和有功電流波形和諧波和基波無功電流波形都相同。</p><p>　　圖形3的仿真結果在圖6里，假設被檢測的電流是方波電流，落后電壓1/10周期，輸入到電路中的電壓和被檢測的電壓有相同的波

93、形，并將它移90度，同時是單位波形的倍。從圖6中，可以看出：檢測諧波電流的頻譜和檢測電流的頻譜除去基波之后的頻譜相同，這就是說，檢測出來的諧波分布和頻譜和檢測電流中的諧波相同。</p><p>　　圖7顯示的是被呈現(xiàn)的這種方法的動態(tài)響應的仿真結果。假設電網(wǎng)電流是180度的方波波形，落后電壓36度。由于觀察的原因，我們假設電流的振幅在20-30ms從100A到200A增長，電流的波形顯示在圖7（a）中，圖7（b）-

94、7（b）分別是低通濾波器的輸出，基波電流的檢測結果，諧波電流的檢測結果，我們發(fā)現(xiàn)低通濾波器的輸出，基波電流的檢測結果，諧波電流的檢測結果在大約30ms時發(fā)生變化，然后在40ms時穩(wěn)定。因此，時間落后10ms，時間落后是由濾波器引起的，事實上，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周期的平均值，穩(wěn)定的、正確的結果在半個功率周期后出現(xiàn)，i.e.，10ms.很明顯，這個方法的動態(tài)響應的顯示出來是好的。</p>

95、;<p>　?。╝）電網(wǎng)電壓 (b) 電壓頻譜</p><p>　　(c ) 電網(wǎng)電流 (d) 電流頻譜</p><p>　　(e) 總的無功電流 （f）總的有功電流</p><p>　　圖4 檢測總的有功和無功電流</p>

96、<p>　?。╝）有功電流部分 (b) 諧波和基波無功電流</p><p>　　圖5 檢測有功電流和諧波和基波無功電流</p><p>　?。╝）電網(wǎng)電流 (b) 電流頻譜</p><p>　?。╟）檢測的電流 （d）諧波電流頻譜&

97、lt;/p><p>　　圖6 動態(tài)檢測諧波電流</p><p>　?。╝）電網(wǎng)電流 (b) LPF的輸出電流</p><p>　　(c) 基波電流 （d）諧波電流</p><p>　　圖7 動態(tài)響應的仿真</p><p>&

98、lt;b>　　4、 結論</b></p><p>　　在這篇文章中，一個基于Fryze功率定義的實時檢測諧波和無功電流的方法被提出，分析和仿真顯示這種方法簡單和能夠動態(tài)的、精確的發(fā)現(xiàn)和檢測諧波，基波無功（有功）電流和總的無功（有功）電流。這種方法不需要一個鎖相環(huán)。</p><p><b>　　參考文獻</b></p><p>

99、　　[1] 王 Z A，揚 J J. 諧波限制和無功功率補償 [M]. 北京：機械出版社，1998（中國）.</p><p>　　[2] 林B R，揚B R.用一系列有源濾波器消除電流諧波[A].IEEE.國際研討會工業(yè)電子（ISIE）[C].釜山，韓國，2001.566-570.</p><p>　　[3] 江M C. A 分析和設計一種新型三相電力有源濾波器[J] IEEE航天交易和電

100、子系統(tǒng)，37（3），2001：824-831.</p><p>　　[4] 任Y F，李H S，何G，在信號電路中兩種實時檢測諧波和無功電流的方法[J] 自動化電力協(xié)會，2003，15（1）：95-98（中國）.</p><p>　　[5] Fryze S.非正弦電壓和電流的有功，無功和視在功率[J] Elektortech, 1931(7):193-203; 1931(8):225-23

101、4; 1932(22):673-676</p><p>　　[6] Czarnecki L S.無功電流，非正弦波形的電壓和功率和它們的補償[J]. IEEE Trans Instrum Meas. 1991, 40(3); 563-567</p><p>　　[7] 李TB，孫YH　廖ZL，信號電路中一種實時檢測無功電流的研究[J].電力測量和儀表,2003,40(451): 8-11(