Methodology of Ampacity Calculation for Overhead Line - Technical ...

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Page 1 of 8IEEE PES Transactions on Power Systems> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960Abstract— This paper presents a new methodology forcalculating the steady-state thermal rating of a given overheadline, which uses the wind speed data obtained from numericalanalysis of the atmospheric boundary layer - ABL. Themotivation behind this work is based on the difficulty and thehigh cost for monitoring the main weather parameters along theoverhead line, especially the variation of wind speed. In the newmethodology proposed in this paper, the spans with lower windspeed and lower clearance are defined as critical spans and,naturally, the thermal capacity of the overhead line is limited bythem. The results obtained in applying this methodology in a 138kV overhead line, with 133 spans, demonstrate the consistency ofthe proposed methodology and its applicability. Therefore it willbe discussed how this new methodology can be applied both atdesign and at operation of overhead lines. In this case, theoperation team will improve security with possible maximizationof electric energy transmission.Index Terms — Overhead Line, Weather Parameter, Steady-State Thermal Rating, Ampacity, Atmospheric Boundary Layer.AAmpABL - Methodology of AmpacityCalculation for Overhead Line Considering theEffect of Atmospheric Boundary LayerI. INTRODUCTIONn important point in improving the process of calculatingsteady-state rating is the need to establish the mainweather parameters such as wind speed, temperature and solarradiation [1] throughout all spans of the overhead line. Themonitoring of weather conditions throughout the overhead lineby weather remote stations has a high cost [2], especially forlong lines. Thus, a plausible starting point to work indetermining the wind speed, which is the parameter of majorweather influence in the calculation of thermal rating, is thenumerical study of atmospheric boundary layer - ABL [3], [4]around the overhead line.In order to validate the model of the ABL, it is necessary tohave the digital maps of topography and measurements ofwind speed at some points on the boundary of the region andinside the ABL. Once the model is validated, the next step isto generate a database by simulations with different boundaryconditions and then to apply it in the determination of theworst weather spans, i.e. spans with the lowest values of windManuscript received May 25, 2009. This work was supported in part byCemig and Evolutionary Computation Laboratory from the ElectricalEngineering Department of UFMG.C. A. M. do Nascimento is with the Cemig in the EngineeringManagement of Overhead Lines (caxandre@cemig.com.br).J. A. Vasconcelos is with the Electrical Engineering Department fromUFMG and is the head of the Evolutionary Computation Laboratory(jvasconcelos@ufmg.br).C.A.M. do Nascimento and J.A. Vasconcelosspeed. It is important to mention that there is still nomethodology proposed in the literature for finding criticalspans in Overhead Lines [5]–[7].In this context, the main goal of this work is to present anew methodology for calculating the steady-state rating -AmpABL, which is more realistic than the traditional methodsof calculation [7], [9]. In the presentation that follows, arebriefly presented the method for calculating the steady-statethermal rating, the proposed criterion for determining thecritical span, an introduction of the ABL model, a detaileddescription of the methodology AmpABL and finally itsapplication that was originally proposed in this work.II. STEADY-STATE THERMAL RATING CALCULATIONThe IEEE Std 738 -2006 defines the term “steady-statethermal rating” as "the constant electrical current that wouldyield the maximum allowable conductor temperature forspecified weather conditions and conductor characteristicsunder the assumption that the conductor is in thermalequilibrium (steady state)". Considering only the mostsignificant terms in the thermal equilibrium as in (1),P + P = P + PJSRCit is possible to determine what is the maximum current thatcan flow in a conductor when considering the rate of loss byJoule effect. That is,2R (T )I P = P +CS RThen,I =C(1)+ P(2)PR+ PC− PSR(T )CThrough (1)-(3), P J , P S , P R and P C are respectively the rateof heat gain by Joule effect, the rate of heat gain by solarradiation, the rate of heat loss by radiation and the rate ofconvective heat loss (W/m). The parameters R and T C are theresistance per unit length (Ω/m) and the conductortemperature (°C).The steady-state thermal rating calculation of overhead lineis usually done for a maximum allowable conductortemperature specified in the design stage (T C < 100°C) andconservative weather conditions, that is, bounds of both windspeed of [0.6,1.2] (m/s) and summer temperature [30,45] (°C).(3)
IEEE PES Transactions on Power SystemsPage 2 of 8> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960III. STEADY-STATE CONDUCTOR TEMPERATURECALCULATIONThe rates of heat loss by convection and radiation are notlinearly dependent on the temperature of the conductor, thusthe equation of thermal balance (1) can be solved to determinethe temperature of the conductor in terms of the current andthe weather variables through an iterative process [10], i.e.according to the following steps:a) Take an initial conductor temperature T R , the current I C forwhich the conductor temperature is expected and a smalltolerance number ε.b) Calculate the corresponding heat losses P R and P C , the heatgain by solar radiation P S and the conductor resistanceR(T R ).c) Calculate the conductor current (I R ) for the referencetemperature (T R ) using (3).d) Compare the values of I C and I R .• If |I C -I R | ≤ ε, stop the iteration and consider the T R valueas the solution, i.e., T C = T R .• If |I C -I R | > ε, increase T R , otherwise T R is decreased.e) Return to step “b”.IV. CRITERIA FOR DETERMINING CRITICAL SPANSThe determination of critical spans is an important taskbecause if an electrical failure occurs, the major probability isthat it will take place in one of these spans. The definitions ofcritical spans, with the factors that influence them, are in arefined manner discussed in [2]. The critical spans arebasically those with slowest values of wind speed andconcurrently lowest clearance between conductor and nearestgrounded object.In the proposed AmpABL methodology, the determinationof critical spans is carried out in an original and low cost wayif compared to the cost of instrumenting every span, which isnecessary for monitoring the whole transmission line, asmentioned in [2]. Basically, the difference is that the values ofwind speed considered in the proposed methodology isobtained from simulations of atmospheric boundary layer,with prescribed boundary conditions (wind speed = 1 m/s atdifferent directions of incidence). The spans that havenumerical results of wind speed less than 1 m/s are consideredworst weather spans. The reference value of 1m/s for the windspeed at the boundary surfaces is a technical criterion based onthe region of the world considered. Of course, this valueshould be different for other region in the world.Mathematically, let S we be the set of critical spans withrespect to electrical clearance [11], i.e., the set composed byspans with clearance less than a certain clearance value ofreference, which is dependent of the transmission line design.Let S ww be the set of worst weather spans, i.e., the setcomposed by spans with numerical results of wind speednormal to the axis of the conductor lower than the referencevalue of 1 m/s.Note that a span belonging to S we has a higher probabilityof violating the minimum safety clearance compared toanother not belonging to S we . Therefore, one span of S we willhave a greater probability of electrical failure. Furthermore,the spans that belong to S ww have less cooling capacity of theconductor and therefore greater thermal risk.Now, let S ∩be the set of spans obtained by thewintersection of S ww and S we as in (4).S= S∩ Sew∩ e ww we(4)Eliminating from theS ∩the dominated spans bywapplying a non-dominance criterion, the result is a set of nondominated1 spans with small clearance and wind speed. Letthis set of non-dominated spans be S c .Note that the spans belonging to S c form a non-dominatedfrontier in the space “wind speed versus clearance”. They arethose with simultaneously smallest clearances and lowest windspeeds, among all spans of the overhead line. That is, they arestrong candidates to be the critical critical spans in terms ofrisk of failure and thermal risk. Once determined the set S c , itis necessary to determine the critical spans, by calculating theconductor temperature of each span and their newcorresponding clearance. The critical span is the one thatwould always be hottest and/or nearest to clearance limits fora given current loading.V. ATMOSPHERIC BOUNDARY LAYER - ABLThe region of ABL is defined as a thin layer of theatmosphere, adjacent to the surface (up to 2 km in height),where wind speed show a high Reynolds number. This flow ofwind occurs at different scales, each scale is described interms of computational domain with a different model. Thesemodels use the same governing equations [3], showingdifferences only in terms of simplifications of source, whichdepends mainly on the computational domain and the thermalstratification. The equations governing these flows are thegeophysical equations of continuity, conservation ofmomentum, conservation of energy and conservation ofchemical species. The wind speed simulation models areclassified into four categories: global circulation, weatherforecast, meso-scale and micro-scale. The global circulationmodel is used in domains between 200 and 500 km along theearth’s surface and is used to analyse the vector of wind speed.The models for weather forecast are used for domains between50 and 100 km to solve problems of weather fronts. The mesoscalemodels are used typically for domains from 2 to 50 kmand employed in the wind speed studies influenced by thetopography, and finally the micro-scale models are used forsmall specific domains and employed in studies where thewind is influenced by the regionalization of the earth's surface.The numerical study of the ABL in complex topography foruse in climatological studies was introduced in [4]. The detailsof modelling the boundary layer are presented in Appendix A.e1 One vector u = (u 1, . . . , u k) dominate another vector v = (v 1, . . . , v k)(represented by u v) if and only if u is partially less than v. i.e.,∀ i ∈{1,...,k },ui ≤ vi and ∃ i ∈{1,...,k }| ui < vi} . If the vector u isnot-dominated by any other vector in the space, the vector u is a nondominatedvector.
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