1、外文原文 1 Real-Time Method for Detecting Harmonicand Reactive Currents of Single-Phase Circuits Abstract According to the characteristics of single-phase circuits and demand of using active filter for real-time detecting harmonic and reactive currents, a detecting method based on Fryzes power definitio
2、n is proposed. The results of theoretic alanalysis 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 does not need a phase-locked loop
3、 circuit, and it also can be used in some special applications to provide different compensations on the ground of different requirements of electric network. Compared with the other methods based on the theory of instantaneous reactive power, this method is simple and easy to realize. KeywordsActiv
4、e filter； Harmonic； Reactive current； Real-time detection； Single-phase circuit； Electric-network 0、 Introduction At present it is a major tendency to limit harmonics with active filters 31 ， which can not only limit harmonics dynamically and compensate reactive power but also can achieve a continuo
5、us and dynamic tracking of the compensation for time-varyingharmonic 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 ofharmonics and reactive currents from load currents to receive reference to
6、 meet the need of the active filter.Therefore， the result of the filter will be influenced bythe accuracy and real-time ability of the detection. On the basis of the theory of instantaneous reactive power in three-phase circuit，many relatively mature detecting algorithms for harmonics and reactive c
7、urrents of three-phase circuits have been proposed， such as the methods of p, q, ip and 41qi However, in single-phase circuits， these methods can not be directly used and an extra 外文原文 2 two-phase voltage and current need to be constructed， which lowers the real-time ability and makes the algorithm
8、more complicated. Refs. 1 ,5 presented a method that is construeted on the basis of Fryzes power definition, but it needs one integral cycle before educing the detection results. Since 1980s， many researchers, e.g .Czarnecki 6 , have analyzed the non-sinusoidal currents with new methods, but one int
9、egral cycle is alsoneeded and the real-time ability is still poor. In this paper, an in-depth research is made on Fryzes power definition， which is applied to detect harmonic and reactive currents in single-phase circuits successfully，and a real-time detecting method for harmonic and reactive curren
10、ts in single-phase circuits is brought forward. Analysis and simulation reveal that the proposed method can realize real-time detection of the instantaneous harmonic and reactive currents in single-phase circuits. This method does not need a phase-locked loop circuit when only detecting the total re
11、active currents， and can provide different compensations on the ground of different requirements of electric network. Compared with other methods with the theory of instantaneous reactive power, this method is simple and easy to realize. The method of detecting reactive power and harmonic currents p
12、resented in the Ref.7 is a special case of application of our method. 1、 Fundamentals According to Fryzes power definition 5 ， 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 on
13、e cycle is 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: ,tGuti sp (1) tpT sTtsT sT dtitudtitup 0101 (2) ,tititi psq (3) where tip and tiq are instantan
14、eous active and reactive currents， respectively； 外文原文 3 tus and tis are instantaneous 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 2/UPG )；T is cycle and t is time. As indicat
15、ed 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 reactive current can be calculated. In general， assume the detected voltage and current respect
16、ively are tus = nnn nwtU c o s2(4) tis = nnn nwtI c o s2(5) where nU and nI are the virtual values of the nth harmonic voltage and current, respectively； w is angle frequency； n ， and n are the phases of the nth harmonic voltage and current, respectively； and n=1, 2, Then )(2 tus mnnmn mmnnmn m wtmn
17、UUUn w tn w tUU c o sc o sc o s2 ,2, + mnnmn m wtmnUU c o s， (6) where， ,22 n nUU (7) andmn,denotes thesum of the integers whose subscripts n and m are from 1 to In Eq. (6)， exceptthat 2U isDCcomponent,the other items are all AC components. So the lowpassfilter(LPF)whose cut-off frequency is lowerthan the lowest frequency of alternating signals mustbeusedto filter )(2tus ， andthen 2U is obtained.Similarly， the product of instantaneous current and instantaneousvoltage， P， is p= tus tis = mnnmn m n w tn w tUI c o sc o s2 , = mnnmn m wtmnUIP c o s,
