Research on Power Quality Evaluation Based on Radar Chart Method and Fuzzy Membership Degree

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Eergy ad Power Egieerig, 207, 9, 725-734 http://www.scirp.

1 Eergy ad Power Egieerig, 207, 9, ISSN Olie: ISSN Prit: X Research o Power Quality Evaluatio Based o Radar Chart Method ad Fuzzy Membership Degree Aiqiag Pa, Jia Zhou, Peg Zhag, Roghui Liu 2, Yichao Wag 2 Electric Power Research Istitute State Grid Shaghai Muicipal Electric Power Compay, Shaghai, Chia 2 College of Electrical Egieerig, Shaghai Uiversity of Electric Power, Shaghai, Chia How to cite this paper: Pa, A.Q., Zhou, J., Zhag, P., Liu, R.H. ad Wag, Y.C. (207) Research o Power Quality Evaluatio Based o Radar Chart Method ad Fuzzy Membership Degree. Eergy ad Power Egieerig, 9, Received: March 0, 207 Accepted: March 30, 207 Published: April 6, 207 Abstract Aimig at the curret limit value of six steady-state eergy idexes, the curret radar method is used for referece. A method of comprehesive evaluatio of power quality based o improved radar method is proposed, which improves the power quality idex Type radar patter to represet the steady-state idicator. Each of the mai idicators correspods to a partial rig, ad the agle of the aular portio is maily affected by the size of the weight. Compared with the previous radar map method to maitai the idepedece of the idicators ad a sigle idicator of the bidig data assessmet. The method has the advatages of good feasibility. Keywords Power Quality, Steady-State Idex, Sub-Idex, Radar Map. Itroductio Electricity as a commoly used eergy, ot oly ecoomical ad easy to cotrol ad coversio. The applicatio of eergy has become a importat idicator of the level of atioal developmet. I recet years, with the cotiuous developmet of idustrializatio ad atioal ecoomic level, the whole society is more ad more practical to the power, the power quality requiremets are gradually improved, the quality of power quality is directly related to the etire power market ecoomic beefits. With the adustmet of eergy structure ad the rapid developmet of atioal ecoomy, log-distace DC trasmissio ad large power grid itercoectio to the fudametal chages i the structure of the grid, the resultig AC ad DC hybrid operatio of the power system ad the icreasigly variable power grid egative characteristics, As well as the o-li- DOI: /epe B078 April 6, 207

2 ear load ad time-varyig load i the power grid, brought about such problems as harmoics, voltage fluctuatio ad flicker, three-phase imbalace [] [2], which deteriorated the power quality idex of the grid. Therefore, it is importat to develop a suitable power quality assessmet method to evaluate the power quality idex sythetically ad to improve the power quality to optimize the electricity market. Chia has proposed ie atioal stadards for power quality to aalyze the power quality problem, which is divided ito six steady-state idicators ad three trasiet idicators, because the trasiet idex is ot clear data limits are ot easy to assess, so the curret power quality, the comprehesive evaluatio maily starts from the steady state idex. This paper combies the cotets of atioal stadard of power quality i Chia [3] [4] [5] [6], ad selects 6 of them as steady-state power quality idicators, which are the allowable deviatio of supply voltage, voltage fluctuatio, voltage flicker, harmoic distortio rate, three-phase voltage Balace, power system frequecy tolerace. The existig methods of comprehesive evaluatio of power quality maily iclude three categories [7] [8] [9] based o fuzzy mathematics theory, probability statistics theory ad itelliget algorithm. These methods solve the problem of comprehesive evaluatio to a certai extet, but the traditioal mathematical algorithm is The evaluatio of power quality idicators ca oly stay i the writte text, ad the radar chart method as the represetative of the graphics aalysis ca be more clearly to show the specific idicators of the specific situatio, this paper refers to the radar map i the assessmet of idicators Simple ad clear, clear the characteristics of the combiatio of fuzzy membership fuctio to carry out the power quality idicators, so that it ca more obectively show the advatages ad disadvatages of the idicators. 2. Idicator Normalizatio ad Selectio The primary obective of the evaluatio of the power quality idicators is to select the appropriate idicators. First, the idicators should be ormalized. () Frequecy deviatio 5 fz fn K f = 00 () 2 f f z is the real-time frequecy value, f N is the rated frequecy value, K f is the ormal value of the frequecy deviatio. (2) Voltage deviatio 00 uz un Ku = (2) U u q u z is the real-time voltage value, u N is the rated voltage value, U q is the voltage deviatio GB allowable limit, K u is the voltage deviatio ormalized value. (3) Voltage fluctuatio ad flicker pstz K p = (3) pst N q N 726

3 Pst z is the real-time flicker value, pst q is the voltage flicker GB allowable limit, K p is the flicker deviatio ormalized value. (4) Harmoic distortio rate A K A = (4) 2 A is the real-time harmoic value, K A is the harmoic distortio rate ormalized value. (5) Odd harmoic voltage cotet K 00 H Ha = q ( H ) a ( H ) H a is the first harmoic value, H is the fudametal harmoic value, H q is the odd harmoics atioal stadard allowable limit, K Ha is the frequecy deviatio ormalizatio value. (6) Voltage three-phase imbalace uc K uc = (6) 2 u c is the voltage three-phase compoet, K uc is the voltage three-phase imbalace ormalized value. After ormalizatio, the idicators are kept at the same level, roughly as the limit, the closer to 0 idicators of the better performace. Excellet idicators i the evaluatio of power quality idicators caot play a correspodig role, ad will require the eed for composite sigle idex umber too much, causig iterferece to the calculatio, should be excluded. Such as odd harmoic voltage from the third harmoic to twety-fifth harmoic, a total of more tha a doze idicators, if all are evaluated, the idex is too large ad meaigless, so from the odd harmoic, Ad for the rest of the idicators, the ormalized idicator with a target value less tha 0. should be excluded ad the remaiig idicators should be retaied. It should be oted that short-term flicker idicators should ot be part of a comprehesive idicator. As show i Figure 2, short-term flicker assessmet results i the vast maority of time is quite good, but the occasioal ump, which is differet from the other idicators of chage, if ad other idicators together, it will affect the comprehesive Idex value, but also caot observe the origial idicators appear i the trasitio time period. 3. Empowermet Algorithm After selectig the appropriate metric, you should calculate the weight. I this paper, subective aalytic hierarchy process ad obective etropy weight method combied with the subective ad obective complex weights. Aalytic Hierarchy Process (AHP) as a way to determie the subective weight, divided ito four steps: the establishmet of the hierarchical hierarchical structure of the problem, determie the compariso matrix, the calculatio of weight [0]. 2 2 (5) 727

4 Hierarchical hierarchical structures ca usually be divided ito target layer, criterio layer ad scheme layer. The compariso udgmet matrix represets the compariso of the relative importace betwee the preset level ad its associated uits for the previous hierarchy, ad the scale of the importace is show i the followig Table ad Table 2. Each colum of the udgmet matrix is ormalized: A α = (7) i i A i= i The ormalized udgmet matrix is added i rows: Make Ai ormalized, seekig weight: i α = α (8) i = i α ω = (9) i α i= i Let the weight values be sorted by weight vectors: ω = ( ω, ω,, ω ) T (0) 2 Etropy method is a kid of typical obective weightig method. May obects ca be evaluated by multiple idexes. Accordig to the weight obtaied by etropy method, a certai value is ofte large (more tha 0.3, sometimes eve up to 0.6 pheomeo, which is seriously icosistet with the importace of idicators. Although the importace of the idicators are ot the same, but there should ot be a large idicator of the weight of the situatio, or by this idicator ca reflect the pros ad cos of the obect, Without regard to other idicators Table. Matrix elemet scale table. Scalig meaig Two factors compared to the same importace 3 Two factors, oe factor is slightly more importat tha the other 5 Two factors compared to oe factor are more importat tha the other 7 Two factors compared to oe factor are more importat tha the other 9 Two factors compared to oe factor are the most importat 2, 4, 6, 8 The media of the two adacet udgmets reciprocal Factor i ad compared to b i, the the factor ad i compared b i = /b i Table 2. Judgmet matrix. Idex weight A A2 A3 A q w A2 /q z A3 /w /z 728

5 of the patet for the traditioal etropy method to improve the obective weight calculatio. The first is to establish the model, with m evaluatio obects recorded as M = ( M, M2,, Mm ), Suppose there are evaluatio idicators recorded as D( D, D2,, D ), The value of the evaluatio obect M i to the idex D is recorded as Xi ( i =, 2,, m; =, 2,, ), The iitial iformatio matrix ca be obtaied: X X X = Xm X m where X i is the value of the i-th evaluated obect uder the th idex. The origial matrix is dimesioless: v i max = max ( x ) xi ( x) mi ( x) () I the case of the th idex, the proportio of the i-th evaluatio obect is p i : vi pi = (2) m v i= i Calculate the etropy e of the th idex: e (l m m = ) ( p i l p i ) (3) It should be oted that the greater the differece i the idex value of each item to be evaluated, idicatig that the greater the amout of iformatio reflected by the idicator, the smaller the etropy. While the etropy is too large, idicatig that the iformatio provided by the idicator is very small, you ca give it appropriate to remove it. The differece coefficiet h of the th idex is: h = e (4) Calculate the etropy weight i= ω of the th idex: h ω = (5) h = The traditioal etropy method is used as the obective weight directly after calculatig the etropy weight accordig to the above process, but the modified etropy method eeds to correct the etropy. Let the maximum etropy weight obtaied by the above formula be ω, ad whe ω > 0.3, it ca be set to 0.3, that is, the modified etropy weight ω, i = 0.3, the excess part ( ω 0.3 ) is scaled by the followig fuctio To the remaiig (m ) idicators., ωi ωi = ωi + m ω ( ω (6) 0.3) = k k ( i, i =, 2,, m) The etropy weight of each idex is obtaied,,,, W = ω ω2 ω m (,,, ) 729

6 If there is a modified etropy weight ω > 0.3 for a idicator i, k, W, it ca, be reordered to 0.3, ad the weight ( ω 0.3 )of the redudat part is assiged k to the rest (m 2) idicators, ad the agai (m 2) idicators of the revised etropy. After obtaiig the subective ad obective weight value, it will be merged ito subective ad obective compoud weight: ωi= uv ( i i= ω, ω2, ω3,..., ω) (7) 4. Improved Radar Map Method Radar graph method due to the differet order of the idicators caused by the evaluatio results are ot uique, the fudametal reaso is that whe drawig the radar map, the order of liear coectio poits o the axis of the formatio of polygos [] [2]. Whe costructig the evaluatio fuctio, the polygo area ad the circumferece are ot equal due to the differet idexes, ad the evaluatio results are icosistet. Therefore, this paper uses the arc istead of the triagular area, ad costructs the evaluatio fuctio accordig to the draw radar map. Trasform the composite weights obtaied above ito the weight agles of the improved radar graphs θi = 2πωi. The ceter of the circle as a startig poit, the horizotal right to make a ray as the first idicator of the referece axis, i which to take p legth, with idicators, the θ i as the ceter agle for the fa radius couterclockwise for a fa, the represets the represetative area of the first idicator. Ad the i order to as a fa radius, as the ceter of the ceter of the couterclockwise directio to make each idicator of the represetative area, Six idicators of the improved radar map show i Figure. Ca be calculated fa area is 2 S ( θ ) ipi = (8) The ormalized value of the composite idex ca be regarded as ormalizig the sector area Figure. Example of six idicators radar. 730

7 2 θipi Z = ( ) (9) 2π p i is the ormalized value for the i-th item. After the ormalized weight of the comprehesive idex is determied, the fuzzy evaluatio method is used to classify the obtaied idex. It is very importat to use fuzzy mathematics to deal with the problem of power quality evaluatio ad the selectio ad establishmet of fuzzy model. The validity of the membership fuctio directly affects the credibility of the fial udgmet [3]. The quality evaluatio ca be described by the five-level fuzzy evaluatio set V {excellet, good, medium, qualified, uqualified}, ad the evaluatio criteria of the comprehesive idex are show i Table 3. The establishmet of a sigle factor evaluatio matrix for each sub-idex of power quality is the most critical step i evaluatig the quality of power. I order to establish the uivariate evaluatio method of the idex to be evaluated, the membership degree of the subordiate idex of a specific power quality should be determied o the basis of establishig the membership fuctio desity fuctio. Sice the idex is ambiguous relative to the two quality levels, the membership fuctio betwee the two levels ca be quatified for the five quality levels of the divisio, where Z ad Z 2 are determied by the actual The situatio is determied, X is the idex limit. The idex correspods to the membership fuctio for the excellet quality level, 0 Z Z + C µ ( Z) = si ϕ, Z + C < Z < Z2 + C 2 2 0, Z Z2 + C π Z2 + Z I this fuctio: ϕ = Z ; C is a costat, ca be take as Z2 Z 2 8 X. Idicators correspod to the membership fuctio of good, medium ad qualified quality ( ) 0, Z Z2 + k + C + si ϕ, Z2 + ( k + C ) < Z < Z + ( k + C ) µ ( Z) = 2 2 si ϕ, Z + ( k + C ) < Z < Z2 + ( k + C ) 2 2 0, Z Z2 + ( k + C) (20) (2) Table 3. Comprehesive idex ratig table. Comprehesive idex excellet good medium qualified uqualified Z > 73

8 I this fuctio: the value of parameter K is determied by the atioal stadard limit, preferably X ; =, 2, 3. 4 The idex correspods to the membership fuctio for the uqualified quality level I this fuctio: = 4., Z Z + ( k + C) µ ( Z) = + si ϕ, Z2 + k + C < Z < Z + ( k + C) 2 2 0, Z Z2 + ( k + C) (22) The above model ca be used to describe the relatioship betwee the two quality levels, rather tha the membership of the overall qualified rage, by describig the membership of the idividual quality evaluatio idex relative to each quality level. 5. Case Study I this paper, three substatios i Shaghai are selected to aalyze the eergy quality idexes of 204, ad the evaluatio idexes ad correspodig statistical data are show i Table 4. Through the cosistecy test, we ca draw a reasoable idex weight. I this paper, we select the priority udgmet, frequecy deviatio > odd harmoics > harmoic distortio> voltage deviatio> imbalace i the evaluatio of power quality i [4]. The subective weight is calculated by aalytic hierarchy process ad the etropy The obective weight of the three sites is obtaied, ad the weight of the subective ad obective weights of the three sites is obtaied. Takig S as a example, the weight values of each idex are = (0.7, 0.4, 0.7, 0.9, 0.22), They represet the odd harmoic voltage cotet, imbalace, frequecy deviatio, harmoic distortio rate, voltage deviatio, S site drawig radar show i Figure 2. After the radar map processig of the composite idex ito the membership fuctio, the resultig three site membership values were: S (0.2, 0.462, 0.56, 0.098, 0.046) S2 (0.08, 0.45, 0.236, 0.347, 0.54) S3 (0.425, 0.30, 0.57, 0.5, 0.023) Accordig to the priciple of maximum membership degree, the fuzzy evaluatio results of three sites are as follows: S is good, S2 is passed ad S3 is excellet. The results of this method are show i Table 5. Table 4. Sample data sets to be evaluated. Substatio Voltage deviatio Harmoic distortio rate Ubalace Frequecy deviatio Odd harmoic S S S

9 Figure 2. S site measuremet data from the radar map. Table 5. Compariso of the results of the comprehesive evaluatio of power quality. Substatio Gray correlatio method Fuzzy Mathematics Improved radar map method The method of this article S excellet good good good S2 Uqualified qualified qualified Uqualified S3 excellet excellet excellet excellet It ca be see from Table 5 that the method is i good agreemet with the results of other evaluatio methods. It ca be see from Table 4 that the harmoic distortio rate of the substatio S2 is excessive, so the power quality should be uqualified, ad oly the gray correlatio method is correctly evaluated with the method, It ca be see that by selectig a reasoable classificatio iterval, this method ca effectively classify the power quality ad prove the effectiveess of the method. 6. Coclusio I this paper, the etropy weight method is used to effectively restrict the excessive weight. Appropriate idicators are selected by meas of the ormalizatio of idividual idicators to esure the accuracy of the assessmet results. Combied with the radar method to deal with the comprehesive idex, ad the fuzzy evaluatio method for classificatio, effectively combied with the advatages of the two methods, by comparig the results of the traditioal algorithms to prove that the evaluatio of this method has bee greatly improved, The assessmet method is reasoable ad feasible. Ackowledgemets The work was supported by Sciece Proect of State Grid Corporatio of Chia ( ). 733

10 Refereces [] Salarvad, A., Mirzaeia, B. ad Moallem, M. (200) Obtaiig a Quatitative Idex for Power Quality Evaluatio i Competitive Electricity Market. IET Geeratio, Trasmissio ad Distributio, 4, [2] Mamo, X. ad Javerzac, J. (200) Power Quality Idicators. 200 IEEE Porto Power Tech Proceedigs, -4. [3] GB/T Powerquality -Deviatio of Supply Voltage. [4] GB/T Power Quality -Frequecy Deviatio for Power System. [5] GB/T Powerquality -Three Phase Voltage Ubalace. [6] GB/T Qualityof Electrical Eergy Supply -Harmoic i Public Supply Network. [7] Farghal, S.A., Kadil, M.S. ad Elmitwally, A. (2002) Quatifyig Electric Power Quality via Fuzzy Modelig ad Aalytic Hierarchy. IEE Proceedigs: Geeratio, Trasmissio ad Distributio, 49, [8] Li, L.J., Yao, J.G., Log, L.B., et al. (2007) Applicatio of Combiatio Weighig Method i Fuzzy Sythetic Evaluatio of Power Quality. (2007) Automatio of Electric Power Systems, 3, [9] Zhag, M., Li, T., Cao, J., et al. (2008) A Comparative Study o two Methods for Sythetic Evaluatio of Power Quality. Automatio of Electric Power Systems, 32, [0] Yag, J.H., Ouyag, S., Shi, Y.L., et al. (204) Combied Membership Fuctio ad Its Applicatio o Fuzzy Evaluatio of Power Quality. Advaced Techology of Electrical Egieerig ad Eergy, 33, [] Wag, Y.Y. (2007) The Existig Problems ad Improved Measures i Sythetic Evaluatio Usig Radar Chart. Statistical Educatio, 4, [2] Li, G.D., Li, G.Y., Yag, X.D., et al. (200) A Comprehesive Power Quality Evaluatio Model Based o Radar Chart Method. Automatio of Electric Power Systems. [3] Liu, H.L., Liu, A.X., Zhag, B., et al. (2008) A Fuzzy Comprehesive Evaluatio Method of Maiteace Quality Based o Improved Radar Chart. ISECS Iteratioal Colloquium o Computig, Commuicatio, Cotrol ad Maagemet, [4] Li, Y.J. ad Wag, Y.L. (202) Applicatio of Improved Radar Chart i Compressive Evaluatio of Power Trasmissio ad Trasformatio Proect. North Chia Electric Power Uiversity, Beiig. 734

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Research and Application of FAHP in Bidding Quotation for Petroleum Geophysical Prospecting Project

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