电力系统及其自动化外文翻译实时检测谐波和单相电路无功功率的方法.docx

外文原文real-time method for detecting harmonic andreactive currents of single-phase circuitsabstractaccording 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 definition 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 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.keywords active filter; harmonic; reactive current; real-time detection; single-phase circuit; electric-network0、introductionat 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 the 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 reactive currents from load currents to receive reference to meet the need of the active filter.therefore，the result of the filter will be influenced by the 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 currents of three-phase circuits have been proposed，such as the methods of p, q, ip and however, in single-phase circuits，these methods can not be directly used and an extra two-phase voltage and current need to be constructed，which lowers the real-time ability and makes the algorithm 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, have analyzed the non-sinusoidal currents with new methods, but one integral 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 currents 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 reactive 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 presented in the ref.7 is a special case of application of our method.1、 fundamentalsaccording to fryzes 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 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: (1) (2) (3)where and are instantaneous active and reactive currents，respectively; and 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 );t is cycle and t is time.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 reactive current can be calculated.in general，assume the detected voltage and current respectively are= (4)= (5)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 harmonicvoltage and current, respectively; and n=1, 2, then+， (6)where， (7)and denotes the sum of the integers whose subscripts n and m are from 1 to in eq. (6) ，except that isdc component, the other items 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 current and instantaneous voltage，p，isp=+ (8)wherep= (9)and =is called the power factor angle of the nth harmonic.similarly，in eq.(8 )all the items are ac components 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.after working out p and，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 fryzes power definition in single-phase circuit. although there is a division unit, it is not difficult to realize.fig.1 real-time detection of harmonic and reactive current2、 some special applications of the detecting methodin 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 application are analyzed as follows.2.1 real-time detection of total reactive currentsif the compensation is only for the reactive power, then the reactive currents need to be detected.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(the derivation process is omitted here):= (10)= (11) obviously， is the sum of the harmonic active currents, called 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 reactive power.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-locked loop circuit too. this is one of the merits of this method.2.2 real-time detection of harmonic and fundamental reactive currentsif =, then,= (12)substituting eq. (12) into eq.(9)，we obtainp= (13)then by eq. (1) ， is expressed as= (14)obviously, is the fundamental active part of the detected current, and then is the sum of harmonic and fundamental reactive currents. therefore，the output is used as a reference value to limit harmonics and compensate reactive currents.since =1，fig.2 is obtained by simplification of fig.1. in fig.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.fig.2 real-time detection of harmonic and fundamental reactive current2.3 real-time detection of harmonic currentswhen only harmonics need to be limited, harmonic currents should be detected. we first detect the fundamental currents，and then subtract the fundamental currents from the total currents，to obtain the harmonic currents.if=by eq. (8) we obtainp= (15)= (16)where has the same value as the fundamental reactive current. 2.1，the circuit of detecting harmonic currents can be constructed, as shown in fig.3 .fig.3 real-time detection of harmonic currentsin fig.3, is harmonic 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 fryzes power definition.3、 simulation analysisthe above three kinds of detecting circuits are simulated on matlab/simulink. the results of simulation are summarized as follows.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 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 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 fig.2 is in fig.5 .the current which is added to the detected circuit is the same as that 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 actual 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.(14).the actual waveform of the harmonic and fundamental reactive current (solid line) and the detected waveform (brocken line) are shown in fig.5(b)，where the actual waveform is the difference between the detected current and the fundamental active component 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 fig.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 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 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 electric-network current is 180 square wave，which lags voltage 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-pass filter, the detected results of the fundamental current and the harmonic current. it is found that both the outputs of the low-pass 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 time lag is 10 ms. the time lag is caused by the filter. in fact, the lowest order of harmonics to be filtered is 2. using the digital filtering method to get the average value in one cycle of the lowest harmonic，the steady and accurate result can be obtained after a half power cycle，i.e. ，10m s.it is obvious that the performance of the dynamic response of this method is good. (a) the voltage of electric network (b) the spectrum of voltage (c) the current of electric network (d) the spectrum of current (e) the total reactive current (f) the total active currentfig.4 the detected total active and reactive current (a) the active current component (b) harmonic and fundamental reactive currentfig.5 the detected active current and harmonic and fundamental reactive current (a) the current of electric network (b) the spectrum of current (c) the detected harmonic current (d) the spectrum of harmonic currentfig.6 dynamically detected harmonic current (a) the current of electric network (b) the output current of lpf (c)the fundamental current (d)the harmonic currentfig.7 the simulation of performance of dynamic response4 、conclusionin this paper, a real-time detecting method for harmonics and reactive currents on the basis of the fryzes power definition is constructed. analysis and simulation reveal that this method is simple and easy to realize and can detect harmonic currents fundamental 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.references1 wang z a, yang j, liu j j. harmonic limitation and reactive power compensationm, beijing; machine press ,1998(in chinese).2 lin b r ,yang b r .current harmonics elimination with a series hybrid active filter a .in; ieee international symposium on industrial electronics (isie) c. pusan, kore a, 2001.566-570.3 jiang m c. aanlysis and design of a novel three-phase active power filter j .ieee transactions on aerospace and electronic systems, 37(3) ，2001: 824831.4 ren y f, li h s，he g, et al. two kinds of real-time detecting method for harmonic and reactive current in signal circuit j. automation of electrical power society, 2003,15(1):95-98(in chinese).5 fryze s. active, reactive and apparent power in circuits with nonsinusoidal voltage and current j. elektortech, 1931( 7 ):193-203;1931(8):225-234; 1932(22):673-676 .6 czarnecki l s. scattered and reactive current, voltage and power in circuits with nonsinusoidal waveforms and their compensation j. ieee trans instrum meas, 1991, 40 (3); 563-567.7 li t b，sun y h, liao z l. study of a real-time detecting method for reactive current in single circuit j. electrical measurement and instrument, 2003 40(451):8-11 (in chinese).21实时检测谐波和单相电路无功功率的方法摘要根据单相电路的特点和为了实时检测谐波和无功功率而使用有源滤波器，一种检测基于fryze功率定义的方法被提出。这种理论分析和仿真的结果显示，这种被提出的方法在检测瞬时谐波和在单相电力中的无功电流是有效的。当只要求检测总的无功电流时，这种方法并不需要一个索相环电路，并且它也能在一些特殊的应用方面提供不同的补偿，这种补偿是在电网的不同要求的层面上。跟其它基于瞬时无功功率的方法相比，这种方法简单并且容易实现。关键词：有源滤波器；谐波；无功电流; 实时检测; 单相电路；电网0、介绍目前，用有源滤波器限制谐波是主要的趋势，有源滤波器不仅能动态的限制谐波和补偿无功功率，而且能取得一个为随时间变化的谐波和无功电流的连续的和动态的补偿轨迹，同时它不受电网阻力的影响，有源滤波器的关键技术是实时检测谐波和无功电流时，负载电流的接收范围要满足有源滤波器的需要。因此，这种滤波器的结果受准确度和实时检测能力的影响。在三相瞬时无功功率的基础上，许多相对成熟的关于三相谐波和无功电流的算法被提出，例如p,q和，法，不管怎样，在单相电路里，这些方法不能直接使用，并且额外的两相电压和电流需要重建，这样可以降低实时性并使算法更复杂。参考资料1-5呈现了一种建立在fryze功率定义的方法，但在检测结果出来前需要一个积分周期，从19世纪80年代以来，许多研究者包括e.g.czamecki 已经用新方法分析了非正弦电流，但一个积分的时间被需要并且实时能力仍然较差。在这里，一种对于基于fryze功率定义方法做了更深的研究，这个研究成功的应用在单相电路里检测谐波和无功电流，并且一种在单相电路里实时检测谐波和无功电流方法被提出。分析和仿真显示，这种被呈现的方法能在单相电路能有效的实时检测瞬时谐波和无功电流。当只要求检测总的无功电流时，这种方法并不需要一个索相环电路，并且它也能在一些特殊的应用方面提供不同的补偿，这种补偿是在电网的不同要求的层面上。跟其它基于瞬时无功功率的方法相比，这种方法简单并且容易实现。这种检测无功功率和谐波电流的方法在ref里被呈现，【7】是我们方法应用的一种特例。1、 原理根据fryze功率定义，瞬时有功电流是总电流的一部分，并且它的波形和电压波形相似，而且，在一个周期里，有功电流吸收的平均功率和总电流吸收的相等，并且，总电流减去瞬时有功电流等于瞬时无功电流。因此，我们有以下的表达式： （1） （2） （3）这里和分别是瞬时有功和无功电流；和分别是瞬时电压和电网的瞬时电流，g是实常数系数，p是平均有功功率（如果u是电压的有效值，那么）t是周期，t是时间。正如等式（1）、（2）、（3）说明的那样，如果平均有功功率和电压有效值的平方知道的话，g被算出是可能的。然后，从等式（1）和（3），瞬时有功电流和无功电流可以被算出。一般来讲，计算被检测的电压和电流公式各自为：= （4）= （5）这里和分别各自是n次谐波电压和电流的有效值；w是角频率；和分别是n次谐波电压和电流的角度，并且n=1、2、3、。然后， +， （6）这里， （7）表示数字的和，n，m是从1到在等式（6）中，除了是直流量外，其余参数都是交流量，因此切断频率比可变信号的最低频率还低的低通滤波器（lpf）必须用来滤除，然后，被包含在内，类似的，瞬时电流和瞬时电压的产品p为：p=+ （8）这里，p= （9）并且，=被叫做n次谐波的功率因子。在等式（8）中，除了p是直流量外，其余参数都是交流量，因此切断频率比可变信号的最低频率还低的低通滤波器（lpf）必须用来滤除p，然后，p被包含在内。在算出p和后，功能方框图构造如图1，在图1中，实时检测谐波和无功电流方法是在单相电路中基于fryze功率定义方法，虽然有一个分解组件，但它不难实现。图1，实时检测谐波和无功电流2、 这种检测方法的一些特殊应用在图1中，输出和随输入改变，因此，这个电路图在电网的不同要求的层面上提供相关的补偿，以下三种应用情况被分析。2.1、 实时检测总无功电流如果只需要补偿无功功率，那么无功电流需要被检测。假设和是被检测物体的电流和电压，然后，从等式（1）、（2）、（4）、（9），图1的输出和被包含（这里计算过程被省略）：= （10）= （11）很明显，是谐波有功电流和基波有功电流之和，叫做总的有功电流，是谐波无功电流和基波无功电流之和，叫做总的无功电流，因此，在图1中的输出作为补偿无功功率是有参考价值的。当只检测总的无功电流时，没有必要检测和被检测电压有相同的相位的单位正弦信号，也没有必要用锁相环，这是这种方法的优点。2.2、实时检测谐波和基波无功电流如果=，然后，= （12）把等式（12）代入等式（9），我们得到p= （13）然后，通过等式（1），被表