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1、1 Abstract-This paper provides a concise review on the maindevelopments and conclusions in the area of power systemharmonic analysis. Commonly accepted methods for conductingharmonic studies have been summarized. The area of harmonicanalysis is still a very fertile ground for exploration. With thehe
2、lp of four example research topics, the paper alsodemonstrates possible future directions of power systemharmonic analysis research.Index Terms-Harmonics, Harmonic AnalysisI. INTRODUCTIONower system harmonic analysis is to determine the impactof harmonic producing loads on a power system.Harmonic an
3、alysis has been widely used for system planning,operation criteria development, equipment design,troubleshooting, verification of standard compliance, and soon. Over the past two decades, significant efforts andprogresses have been made in the area of power systemharmonic analysis. Well-accepted com
4、ponent models,simulation methods and analysis procedures for conductingharmonic studies have been established. Harmonic studies arebecoming an important component of power system analysisand design.With the widespread use of digital computers, computersimulation has become the preferred method to co
5、nductharmonic analysis. This has transformed the subject ofharmonic analysis into two main areas: computer modeling ofpower systems for harmonic analysis and computersimulation of harmonic propagation in power systems.Research work in the above two areas has resulted in anumber of software packages
6、for harmonic analysis andsimulation. It is important to note, however, that harmonicanalysis still requires a good knowledge on the subject areaand the skill of analytical thinking.One of the purposes of this paper is to review the status ofcomputer-aided harmonic analysis methods. The mostcommonly
7、accepted techniques for harmonics modeling andsimulation are discussed. The readers will find from thisreview that the research and application of harmonic analysishave entered a relatively mature stage. This naturally leads tothe following question: what are the future directions ofharmonic analysi
8、s? In the second part of this paper, somethoughts to this question are presented using examples ofresearch work conducted at the University of Alberta and W. Xu is with the Department of Electrical and Computer Engineering,University of Alberta, Canada. He is also an adjunct professor of ShandongUni
9、versity, China. (e-mail: wxuee.ualberta.ca).other places. It is hoped that these examples or thoughts willserve as a step stone for continued research efforts in thisarea. For people who are interested in applying harmonicanalysis techniques, this paper could serve as a channel toobtain feedback fro
10、m industry.II. MODELING OF POWER SYSTEM COMPONENTS FOR HARMONICANALYSISHarmonics are a high frequency phenomenon involvingfrequencies from 50/60Hz to about 3000Hz. For harmonicstudies, it is important to take into account the componentresponse characteristics at the harmonic frequency range.Since mo
11、st harmonic analysis tools are based on frequencydomain algorithms, component models for harmonic analysisnormally takes the frequency domain form as well. A detailedsummary on this topic can be found from reference 1 andother papers presented in this panel session. In this section,we will focus on
12、the development status of componentmodeling research.Overhead Lines and Underground Cables: There is aconsensus that lines and cables can be modeled with amultiphase coupled equivalent pi-circuit. For balancedharmonic analysis, the model can be further simplified into asingle-phase pi-circuit determ
13、ined from the positivesequence impedance data of the component. It is important toinclude the shunt element and its associated long-line effectin the model. The shunt admittance of the component, thoughsmall at the fundamental frequency, can become quitesignificant at higher frequencies. This effect
14、 can be easilyrepresented using the exact or equivalent pi-circuit model 1.Transformers: A transformer affects harmonic flowsthrough its series impedance, winding connection, andmagnetizing branch. Many research results in this topic haveconcluded that a transformer can be modeled using its short-ci
15、rcuit impedance for most harmonic studies. It is alsoimportant to include the transformer phase-shift effect. Thisphase-shifting effect could lead to significant harmoniccancellations in a system 2. The magnetizing branch of atransformer is a harmonic source. Inclusion of the saturationcharacteristi
16、c of the branch is important only when theharmonics generated by a transformer are of primaryconcern.Rotating Machines: This component includes synchronousand induction machines. The consensus is that a machine canbe represented using its short-circuit impedance for mostharmonic analysis tasks, alth
17、ough more complex models areavailable for advanced applications.Wilsun Xu, Senior Member, IEEEStatus and Future Directions ofPower System Harmonic AnalysisP2Aggregate Loads: Aggregate loads refer to a group of loadbuses that are treated as one component in harmonic analysis.Typical aggregate loads a
18、re distribution feeders seen from asubstation bus or a customer plant seen at the point ofcommon coupling. Although such loads typically containharmonic sources, the main concern is the frequencyresponse characteristics of its equivalent impedance. If theharmonic sources are of concern, the load sho
19、uld not betreated as an aggregate one.The model for aggregate loads, therefore, has the form ofa frequency-dependent impedance. Research has shown thatthe impedance is not only a function of the individual loadscontained in the component but also dependent on the lines orcables connecting the loads.
20、 For example, the distributionfeeder conductors and shunt capacitors can have a largerimpact on the frequency-dependent impedance seen at thefeeder terminal than those of the loads connected to thefeeder. As a result, it is almost impossible to use a set ofgeneral formulas to construct an adequate i
21、mpedance modelfor aggregate loads. Although a few models for aggregateloads have been proposed in the past, the validity of thesemodels has not been fully verified. Modeling of aggregateloads is one of the weakest areas in the harmonics modelingfield. A lot of research work is still needed. In autho
22、rsopinion, solutions to the following topics would be valuable: Verified techniques to construct aggregate load models. The impact of model inaccuracy on harmonic analysisresults. Measured harmonic impedance data for aggregate loadsand analysis on the correlation of the measured data withthe load co
23、mposition.External System: External system for power quality analysistypically refers to either the utility supply system seen at thepoint of common coupling from a customers perspective orthe neighboring networks of a utility system under study.Reference 1 has more information on this subject.Power
24、 Electronic Devices: Power electronic devices can bea load or a compensator. In terms of harmonic analysis, acommon characteristic of them is that they are harmonicsources. As a result, a number of different models have beenproposed to represent such devices. Among these models,the most commonly acc
25、epted one is the current sourcemodel. The model simply treats a power electronic device asa harmonic current source. The magnitude and phase of thesource can be calculated, for example, from the typicalharmonic current spectrum of the device. A more accurateprocedure to establish the current source
26、model is asfollows:1) The power electronic load device is treated as a PQ loadat the fundamental frequency, and the fundamentalfrequency power flow of the system is determined;2) The current injected from the load to the system is thencalculated and is denoted as I1/?1.3) The magnitude of the harmon
27、ic current sourcerepresenting the load can be determined as follows:( )1 11spectrumspectrumhhIIII=4) The phase angle of the harmonic current source can becalculated using the following formula:( )2 ) spectrum-11spectrum-hh-( h+=where subscript “spectrum” standards for the typicalharmonic current spe
28、ctrum of the load. This data can bemeasured, obtained from manufacturers, or calculatedaccording to formulas. The current source model is the mostcommon one used in commercial power system harmonicanalysis programs. Its main disadvantage is the use of typicalharmonic spectrum and, as such, assessmen
29、t of casesinvolving non-typical operating conditions becomes difficult.This has prompted the development of other modelingtechniques such as detailed time-simulation based models anda hybrid of current source model and the detailed model.It is reasonable to say that power electronic devicemodeling t
30、echniques for harmonic calculations have becomea mature subject. What is needed is to improve ourunderstanding on the harmonic characteristics of the devicesfor other applications. For example, harmonic sources arecommonly treated as current sources for harmonic sourcedetection applications. There i
31、s an urgent need to determinethe degree of validity of this assumption. Another caseinvolves the generation of interharmonics from variablefrequency drives. As will be demonstrated later, thetraditional models are insufficient to analyze some aspects ofthe interharmonic problems.III. NETWORK SOLUTIO
32、N TECHNIQUES FOR HARMONIC ANALYSISOver the past two decades, considerable progress has beenmade in the area of computing harmonic power flows for apower system. Mature techniques are now available forassessing harmonic distortions in a network containingsignificant harmonic sources. In this section,
33、 two mostcommon and useful harmonic analysis techniques arepresented and discussed.A. Frequency Scan AnalysisFrequency scan is the simplest and most commonly usedtechnique for harmonic analysis 3. The input datarequirement is minimal. It calculates the frequency responseof a network seen at a partic
34、ular bus or node. Typically, anone per unit sinusoidal current is injected into the bus ofinterest and the voltage response is calculated. Thiscalculation is repeated using discrete frequency stepsthroughout the range of interest. Mathematically, the processis to solve the following network equation
35、 at frequency f:( )3 IVYfff=where If is the known current vector and Vf is the nodalvoltage vector to be solved. In a typical frequency scananalysis, only one entry of If is nonzero. In other analysis, aset of positive or zero sequence currents may be injected intothree phases of a bus respectively.
36、 The results are the positive3or zero sequence driving-point impedance of the network.Frequency scan analysis is the most effective tool to detectharmonic resonance conditions in a system. It has also beenwidely used for filter design.B. Harmonic Power Flow AnalysisIf one needs to find the harmonic
37、distortion levels forcertain operating conditions, a network harmonic power flowanalysis should be conducted. Several harmonic power flowtechniques have been proposed in the past 4, 5. Many yearsof application experiences have shown that a non-iterativetechnique that represents harmonic sources as c
38、urrentsources is sufficient for many common harmonic analysistasks. This technique is summarized as follows:Step 1: Compute the fundamental frequency power flow ofthe network. The results define the operating scenario forharmonic analysis. In this step, the harmonic-producingloads are modeled as con
39、stant power loadsStep 2: Determine the harmonic current source models forthe harmonic-producing loads. The model consists of themagnitudes and phase angles of current source at variousharmonic frequencies. Equations needed to establish themodel are described in Section II, Equations (1) and (2).Step
40、 3: Calculate the network harmonic voltages and currentsby solving the following network nodal equation forharmonic number h of interest:( )4 =hhhIVYwhere Ih is a known vector that has all harmonic currentsources included, and Vh is the nodal voltage vector tobe solved. Equation (4) is solved for al
41、l harmonicsinterested.Step 4: The results of Steps 1 and 3 jointly define theharmonic power flow conditions of the study system.Harmonic indices such as total harmonic distortions andtransformer k factors can be calculated from the results.The main disadvantage of the above method is the use oftypic
42、al harmonic spectra to represent harmonic-producingdevices. It prevents an adequate assessment of cases involvingnon-typical operating conditions. Such conditions include,for example, partial loading of harmonic-producing devices,excessive harmonic voltage distortions and unbalancednetwork condition
43、s. The applications of harmonic power flowanalysis include 1) network harmonic distortion assessment,2) harmonic limit compliance verification, 3) filterperformance evaluation, and 4) equipment de-ratingcalculation.C. Comments on Network Harmonic Analysis TechniquesThe development of harmonic analys
44、is techniquesfollowed mainly two directions over the past many years. Onedirection is to improve solution algorithms for harmonicpower flow calculation. Examples of this direction are theiterative harmonic method 4 and the Newton-Raphson basedsolution method 5. The second direction is to include mor
45、ecomplete network models in the solution. A good example ofthis direction is the three-phase or multiphase harmonicanalysis 6. This direction is needed since certain harmonicproblems such as harmonic-telephone interference, must beanalyzed in three phase.For both directions, the focus has been on th
46、e analysis ofnetworks with dominant harmonic sources. This is a refectionof the industry situation in the past, where harmonic-producing loads are large and are concentrated in a fewlimited locations. With the proliferation of power electronicloads, a power system may contain many harmonic sourceswi
47、th comparable sizes. How to analysis such systems hasbecome one of the challenges in harmonic analysis research.IV. FUTURE DIRECTIONS OF HARMONIC ANALYSISIt is always dangerous to predict research directions forthe future. Taking into account the fact that there is only asingle author for this paper
48、 and the authors knowledge on thesubject is limited, possibilities of error are high. Instead ofpredicting the future, what we attempt to do in this section isto illustrate some interesting research topics in the area ofharmonic analysis. It is hoped that the examples or thoughtspresented will serve
49、 as a step stone for continued researchefforts in the area.A. Distributed Harmonic SourcesA noticeable trend in power systems nowadays is theemergence of distributed harmonic-producing loads. Theseloads typically have comparable sizes and are distributed allover an electric network. Traditional tech
50、niques for harmonicpower flow analysis generally have difficulties in determiningthe collective impact of these sources. Determination ofharmonic distortions for systems with distributed sources is anew and challenging research topic in the area of harmonicanalysis. In order to make the problem mana