Measurement based on the "group linear regression method" of harmonic impedance

Size: px

Start display at page:

Download "Measurement based on the "group linear regression method" of harmonic impedance"

Nora Harris
5 years ago
Views:

1 Measuremet based o the "group liear regressio method" of harmoic impedace Wag lei u bo Shaghai uiversity of electric power 203, Pigliag Rd, Shaghai Shaghai extra voltage power trasmissio compay.smepc, wuig Rd,shaghai Abstrat Harmoic pollutio moitorig ad cotrol is the key to a accurate estimate of harmoic impedace, ad thus a accurate assessmet of public coectio poits of the harmoic emissio level. This paper aalyzes the lik uder the star-shaped ad triagular three-phase asymmetrical power systems derived established a three-phase ubalaced power system harmoic impedace matrix estimatio model. Model is based o a large umber of systems ad load the public coectio poit of the simulatio data, the real ad imagiary part of the harmoic impedace by opeig ad usig groupig multiple liear regressio method, o the system side harmoic impedace matrix to estimate the value of each elemet. Simulatio ad error aalysis shows that the model obtaied is more accurate ad effective. dex Terms Three-phase asymmetry; harmoic impedace; harmoic admittace; multiple liear regressios Supported by Leadig Academic Disciplie Preject of Shaghai Muicipal Educatio Commisiio Project Number J530. NTRODUCTON order to estimate the level of harmoics sed by harmoic source better, you eed to kow the harmoic impedace of the system side or the user s side i a poit of commo couplig (PCC); for harmoic currets reflected the o - liear load characteristic, which is usually expressed i curret rather tha voltage. order to tur harmoic currets ito harmoic voltage, we also eed to kow the system harmoic impedace. Nowadays, i the iteratioal ad domestic we ve also produced a cosiderable umber of measuremets, calculatio methods with the ew equipmet. The direct measuremet usually ca be divided ito "itervetio-type" ad "o-itervetio-type" way. The itervetio-type way is to measure the harmoic impedace through the ijectio of harmoic currets to the system or discoect the system; the mai drawback is that the operatio of power system may be brought about a umber of adverse effects. "No-itervetio-type" method is to use the system's ow harmoic source, as well as measurable parameters to estimate the harmoic impedace ad harmoic voltage, but such methods for measurig requires high accuracy of measuremet data such as the "volatility Method or demads for a stable system eviromet such as " bi-liear regressio method. recet years, research refers to both the possibility of the system harmoic features, how to determie the harmoic impedace or the harmoic admittace of the statistical properties, especially for asymmetric three-phase system. Because there are may o-liear loads i the system, such as the electrified railway tractio systems, electric arc furaces, etc., these loads have a radom asymmetry, there are white o-symmetrical couplig, usig the sigle-phase model which is the most popular way for estimatio is difficult to obtai satisfactory results. view of this, G. Carpielli Professor [] [2] suggested i the three-phase ubalaced distributio etwork system to take ito accout the ucertaity to estimate the

2 probability of system harmoic impedace method, but the disadvatage of the method is that a complete system topology ad compoet parameters must be kow. Because of the lack of etwork kowledge as well as the harmoic impedace of the etwork compoets ad systems alog with the chages i operatig coditios are costatly chagig, the estimated harmoic impedace is gettig more ad more difficult. The existig measuremets all have their ow limitatios, ad the estimatio results are affected by may factors. view of this situatio, this paper's mai job is through the star coectio (icludig the eutral poit directly to groud ad eutral-poit-to-groud isulatio both cases), ad triagles coectio to establish the various sub - Uder the asymmetric power system harmoic impedace matrix model. Model draws o the literature metioed i the measuremet method based o measured data, by samplig with asymmetric load power system ad load poit of the measured public coectio voltage ad curret, harmoic impedace by the real ad imagiary part of the ope, usig " Groupig multiple liear regressio, "side of the system harmoic impedace matrix to estimate the value of each elemet, which has bee harmoic impedace matrix. Through simulatio experimets ad results of the estimatio error aalysis, the model error falls i a acceptable rage. Errors caused by chages i the fial aalysis of the causes ad draw the relevat coclusios.. A MATHEMATCAL MODEL TO STRKE THRD HARMONC MPEDANCE Whe study how to estimate the harmoic impedace, regardless of "itervetio-style" method or "o-itervetio-style" method, the public iterface of harmoic curret ad voltage parameters for the observatio data is itroduced. Accordig to the system ad user s equivalet circuit derivatio, combied with the appropriate algorithm to strike system side harmoic impedace. But these are built o the assumptio that the system is symmetry, did ot cosider the asymmetry of power system harmoic source operatig characteristics. This paper, through the right star coectio (icludig the eutral poit directly to groud ad eutral-poit-to-groud isulatio both cases) ad the triagles coectio modes, aalyze three-phase system model is derived uder the establishmet of the various harmoics are ot symmetric power system harmoic impedace matrix model. A. Star Coectio Figure star wirig simulatio model Overlook the iteractio betwee harmoics, h harmoic, ad the star coectio three-phase asymmetric model as show i Figure above. is the eutral groudig admittace (if the eutral poit directly to groud, the the = ; if ot grouded, the the = 0 ) the establishmet of the equivalet model of the ode voltage equatio for figure (take the eutral poit as a referece ode, sice the resistace is positive, mutual resistace is egative, the curret source flows is +, the curret origis out of the -) are: ( ) = ( + + ) OA

3 Order was: OA = + ( OA ) B phase ad C phase respectively, relative to a separate aalysis of empathy available: ad are: OA OA AA AB AC = AB BB BC + AC BC CC Will be o the type lauched i accordace with the Miistry of real ad imagiary parts, formig two ew equatios, This meas: * + * + * + = k = k A B = k OA OA ( ka ) kb kc k A ( kb ) k C = k A k B ( kc ) ka ka ka + kb kb k B kc kc k C C OA OA ( ka ) k B k C = k ( k ) k + k A k B ( kc ) A B C X OA = BBX CCX AAX = AAX BBX CCX X OA AB BB BC AC BC CC AA AB AC + AA AB AC AB BB BC AC BC CC OA + X As ca be see from the above derivatio, the model ca be described as a symmetrical harmoic impedace matrix ad a set of system + harmoic voltage sources together. Ad we assume that the system side s backgroud harmoic source i a smooth radom fluctuatios i the viciity of ε [3] [4], therefore, the use of public coectio poits, the measured voltage ad curret data to opeed i accordace with the real ad imagiary parts, usig groupig multiple liear regressio ij,, ad B. Triagle Coectio ca be estimated. X X X The equatio above ca be tur ito

4 Figure2.triagle coectio Overlooks the iteractio betwee harmoics, h harmoic, the star coectio three-phase asymmetric model as show i Figure 2 above, to poit out A ode voltage equatio, the availability of the followig equatio: ( + ) = + OA OA By the same toke by other two-phase, writte i matrix form, as follows: OA ( + ) = ( + ) ( + ) OA We assume: = A = B = C From the above defiitio, the availability of a matrix as follows, OA OA A AA AB AC = + AB BB BC B AC BC CC C Will be o the style i accordace with the real ad imagiary part of the ope, you ca get the same matrix type with eq.7 X OA = = AAX AAX BBX BBX CCX CCX X OA + AA AB AC AA AB AC AB BB BC AB BB BC AC BC CC AC BC CC OA By equatio (2) ca be see, the model ca be described as a symmetrical harmoic admittace matrix, ad a set of system harmoic curret source together. Similarly, i a short eough samplig time, that i the time period the chages i matrix elemets ca be eglected, ad assumig that the system-side backgroud harmoic source i a smooth radom fluctuatios i the viciity of its mea, so the public ca also joi poits by usig the measured voltage, the curret data will be lauched i lie with its real ad imagiary parts, re-use of the above two matrix usig multiple liear regressio group, which ca be estimated out.. SMULATON AND ANALSS A. The Simulatio order to verify the correctess ad validity of the above model, this article will be as show below i Figure 4-4 of the experimetal circuit for the simulatio model i Simulik usig Matlab software, a simulatio experimet, aalyzed the three times, 5 times uder harmoic samplig poits per uit time ad load a serious asymmetry i differet ru-time, the estimated results of the harmoic impedace matrix ad error causes. + X AX BX CX + A B C

5 : amplitude(0.373,0.0)phase(-.4248, LC 0.00). (5) The harmoic impedace of each phase of user s side: /LA is j 282.6( Ω) ; /LB is j 273.4( Ω) ; /LC is j 278.8( Ω) Figure3. MATLAB simulatio circuit B. Set the basic parameters of the circuit simulatio Here i this article to three times the first harmoic, for example, to set the basic parameters of the circuit is as follows: () As the fudametal frequecy is 50Hz, the the three harmoics of the harmoic frequecy of 50Hz. (2) System side of the equal value of harmoic voltage source obeys the uiform distributio, where the amplitude to satisfy N (5, 0.05) (uit ), phase agle to meet the N (0,0.00) (i radias), the amplitude ad phase respectively, to meet the N (5,0.05) ad N (2.039,0.00), respectively, the amplitude ad phase agle to meet the N (5.3,0.05) ad N (-2.,0.00). (3) The system side harmoic impedace of each phase, respectively, j20.0( Ω) for ; j22.0( Ω) for ; j25.0( Ω) for ; = 4 Ω (4) The system side harmoic curret of each phase, respectively, : amplitude LA (0.403,0.0)phase (0.403,0.0), LB : amplitude(0.398,0.0)phase(.4326,0.00), The above parameters of each phase have bee cosidered to some extet the asymmetric characteristics of the system. Through the MATLAB simulatio, we ca be i eed of the sampled data, each simulatio to chage the voltage amplitude to meet the uiform distributio. Accordig to previously obtaied matrix equatio 7, the followig groups accordig to multiple liear regressio ca estimate ad calculate the exact value of the relative error [5] [6] [7]. Because the formula for the two groups of 7 matrix equatio, the average of the various compoets whichever is later. To calculate the error, first of all ivolved to the exact terms, the exact value is calculated with the formula 5 ad 6 arrived at. 准确值 N=50 N=00 估误差估值误差值 AAX % % % % % % BAX % % BBX % -2. 0% % %

6 CAX % % CBX % % CCX % -9..7% X % % X % 4.5 0% X % % From the above three sub-harmoic of the simulatio results ca be cocluded that, with the samplig poits icreases, the impedace matrix elemets ad the system side of each phase harmoic voltage source of estimatio error showig a tred towards smaller ad smaller. Harmoics i each case, whe the poit of takig to the N = 00 system, each elemet has a substatially reduced errors; most errors are dow to 0%. Mai reasos for this error of chage i tred, maily by aalyzig the followig reasos, amely, as the samplig poits icreased, the amout of disturbace to be effective average, thus reducig the error. However, large error occurs the situatio, causes may come from the followig two aspects: First, ot eough sample poits, so for the uiform distributio of this probability distributio is difficult to achieve a more satisfactory level; The other is because of this simulatio i such a radom process simulated by the huma brai, ad the samplig time loger, which also icreases the simulatio results to some degree of error. AA AB AC BA 准 N=50 N=00 确估值误差估值误差 %% % % % BB BC CA CB % % CC. CONCLUSON Harmoic impedace is used to desig harmoic filters to determie the harmoic limits ad the forecast system harmoic resoace eeded for importat data. Based o the measured curret harmoic impedace estimatio method is maily cocetrated i the symmetric system, while for the system related to the asymmetry is almost ot ivolved. For asymmetric systems, the use of symmetric model calculatios is difficult to obtai satisfactory results. This article is derived i detail ad the establishmet of a triagle i the star-shaped wirig ad wirig circumstaces, icludig three-phase harmoic load impedace matrix asymmetric system harmoic admittace matrix estimatio model of harmoy. The model ca be described as symmetrical harmoic impedace matrix ad a set of system harmoic voltage source of commo effects or symmetric harmoic admittace matrix ad a set of system harmoic curret source together. Through the measurig poit i the public obtaied from measurig the measured voltage, curret, usig multiple liear regressio aalysis, we ca estimate the system side of the harmoic impedace, or harmoic admittace, which ca further estimate the joi poit of public Harmoic emissio levels. Based o "multiple

7 liear regressio" estimate harmoic impedace data acquisitio of this method is relatively simple, ad the liear regressio model calculatio speed is faster, it ca be used as real-time estimates. Through the simulatio results of the data ad error aalysis, the samplig poits to the coclusio that the purpose of asymmetry ad how much load a certai extet, will affect the model error. So how serious asymmetry i the load-side ru-time, to cosider o-liear factors ad the impact of load characteristics of the model to improve the accuracy of the model is the eed for further i-depth exploratio ad detailed research. REFERENCES [] Carpielli G, ariloe P, Adreotti A, et al. Probabilistic Evaluatio of Harmoic mpedace i Ubalaced Distributio System[C]. Bologa, taly: EEE Bologa PowerTech Coferece,2003 [2] EC : Assessmet of Emissio Limits for Distortig Loads i M ad H Power Systems[S].996. [3] EN Stardard 5060: oltage Characteristics of Electricity Supplied by Public Distributio Systems[S].Europea Stadard, CLC,BTTF 68-6,994 [4] Domiguez M, Coope D,Arrillaga J,et al.a A-daptive Scheme for the Derivatio of Harmoic mpedace Cotours[J].EEE Trasactioso Power Delivery.994,9 (2):

ELE B7 Power Systems Engineering. Symmetrical Components

ELE B7 Power Systems Engineering. Symmetrical Components ELE B7 Power Systems Egieerig Symmetrical Compoets Aalysis of Ubalaced Systems Except for the balaced three-phase fault, faults result i a ubalaced system. The most commo types of faults are sigle liegroud