energy loss estimation in distribution feeders(1)

1092 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 3, JULY 2006

Energy Loss Estimation in Distribution FeedersP. S. Nagendra Rao and Ravishankar Deekshit

AbstractEnergy losses in distribution systems are generally es-timated rather than measured, because of inadequate metering inthese systems and also due to the high cost of data collection. Theseestimations are generally based on some rules of thumb. This paperpresents the results of a joint investigation undertaken in collabo-ration with a local utility to study this issue. Based on data collectedfrom feeders specially instrumented for this purpose, true lossesin some primary and secondary feeders are obtained. These lossesare compared with the estimated losses obtained by the methodspresently in use. In view of the large discrepancies observed be-tween measured and estimated values, two new schemes for esti-mating losses in primary and secondary distribution networks havebeen developed. The measured values are used to highlight the re-liability of the new estimation methods.

Index TermsDistribution systems, loss estimation, primaryand secondary distribution networks, radial feeders.

I. INTRODUCTION

TRADITIONALLY, distribution system loss estimation hasnot received the importance due to it, in Indian utilities.The situation seems to be the same in many other developingcountries. Till very recently utilities were generally governmentcontrolled and the emphasis was on expanding electrification.Concerns regarding social benefits took precedence over profitand efficiency. However, now the impact of economic restruc-turing is being felt in the electricity sector also. There are movestoward divesting government control and operating the utili-ties as private enterprises. Regulatory mechanisms are beingput in place. There is a concerted effort toward improving effi-ciency and profitability. The hitherto neglected distribution sys-tems known for their poor efficiency have started attracting theattention of utilities seeking to improve their operational effi-ciencies.

The local power company KPTCL and its subsidiaries thatoperate in the State of Karnataka (India) are also going throughthis phase. These companies together cater to a geographicalarea of 191 791 square km. The peak demand is about 5400MW and annual energy produced is about 31 billion units. Theyown more than 2000 primary distribution feeders which supplyabout 30% of energy to the vast rural areas of the state. The highvoltage (HV) primary distribution is a 3-wire, 11-kV system.The low voltage (LV) secondary distribution is a 4-wire, 440-Vsystem . Except for a small fraction that is used for lighting, this

Manuscript received June 27, 2005; revised August 11, 2005. Paper no.TPWRD-00366-2005.

P. S. N. Rao is with the Department of Electrical Engineering, Indian Instituteof Science, Bangalore, Karnataka 560012, India.

R. Deekshit is with the Department of Electrical and Electronics Engineering,B.M.S College of Engineering, Bangalore, Karnataka 560012, India.

Digital Object Identifier 10.1109/TPWRD.2005.861240

entire energy in rural areas is used by irrigation pumps drivenby three phase induction motors.

The companies have become corporations and the tariff fixa-tion is now under the jurisdiction of an independent regulatorycommission. The regulatory commission is demanding that thelosses in the system must be quantified and investments madeon system improvement be justified by verifiable loss reduction.The present practice of loss estimation is very inaccurate. Only30% of the total energy consumed is metered. Metering is gen-erally limited to urban areas. Loads in rural areas are rarely me-tered. The consumption of the un-metered categories of con-sumer is guessed based on some rules of thumb. The differencebetween the known generation and the estimated consumptionis considered to be loss. Even though it is well known that thereare many unauthorized consumers, no mechanism is available toseparate out the technical ( loss) and the commercial losses(various forms of theft). These companies need to evolve lossestimation methods which are reliable enough to convince theregulatory commission.

The importance of accurate loss estimation schemes has beenwidely recognized. The near quadratic relationship that existsbetween load and loss has been used to develop empirical re-lations for estimation of loss. These relationships relate eitherthe loss and load factors ([1][3]) or the loss and load ([4], [5]).In these methods, using simplified feeder models for compu-tation of the loss, and then adopting a curve fitting approach,the coefficients in the quadratic function are determined. Ide-alized feeder and load models are used to compute loss in [6]and [7]. A comprehensive loss estimation method using detailedfeeder and load models in a load-flow program is presented in[8]. However, as remarked by the authors of [8] themselves, thedifficulty in obtaining accurate load data has a significant im-pact on the accuracy of their results. In [9], a combination ofstatistical and load-flow methods are applied to find the varioustypes of losses in the Columbian Power System. Here, a radialload-flow program is used to compute the distribution feederpeak load loss. The peak loss is multiplied by a suitable factorto determine the energy losses. Formulas for computation ofenergy and peak losses of different distribution system compo-nents such as substation and line transformers, primary and sec-ondary feeders etc., based on their percentage loading (PL) aredeveloped in [10]. Simplified models of distribution feeder com-ponents for use in load-flow calculations are proposed in [11].An approximate loss formula based on the load-flow model isproposed in [12]. Here, approximations are applied to the powerflow equations in order to derive formulas that estimate lossesunder variation of capacitors and transformer taps. Closed-formformulas for computation of losses using a three phase load-flowmodel are proposed in [13]. Simulation of distribution feederswith load data estimated from typical customer load patterns is

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RAO AND DEEKSHIT: ENERGY LOSS ESTIMATION IN DISTRIBUTION FEEDERS 1093

presented in [14]. A simplified loss model is obtained by car-rying out several computer simulations (by varying differentparameters of the feeder) and a regression analysis. Loss for-mulas based on fuzzy-c-number (FCN) clustering of losses andcluster-wise fuzzy regression techniques are presented in [15].A hybrid top/down and bottom/up approach is applied to esti-mate losses in [16]. In the first step (top-down), feature extrac-tion and clustering methods are applied to arrive at a groupingof feeders based on some similarities among them (intensityof consumption and consumption density). Then, feeders thatrepresent each cluster (zone) are selected and then through anumber of load-flow simulations, loss functions for each repre-sentative feeder are obtained. The losses for each feeder are thencalculated based on the load that they carry.

It is seen that the nonavailability of comprehensive distribu-tion system data (corresponding to all the feeders in the system)is a major reason for the difficulty in computation of losses.Though some authors suggest that loss models obtained fromstudies on a few representative feeders be extrapolated to esti-mate losses for the entire system ([4], [14], [16]), it is pointedout in [8] such generalizations should be applied with care be-cause of varying feeder characteristics. This paper, addressesthe issue of estimation of distribution feeder losses. The resultspresented here form a part of a study [17] undertaken in collab-oration with the local utility to understand the various issues inplanning and operation of their distribution system. One compo-nent of the study was intended to assess the validity of the lossestimation methods presently in use and evolve better methods,if the present ones are found wanting. The scheme envisaged forachieving this was as follows.

1) Identify a few feeders representativeof the different climatic regions of thestate.2) Monitor the load parameters of feedersover an extended period of time usingelectronic meters (with data logging fea-tures).3) Compute losses based on these measuredreadings.4) Assess the validity of existing esti-mation schemes by comparing the estimateswith actual measurements.5) Explore the possibility of evolvingand validating a scheme for these feederswhich can be used to estimate losses whenonly limited measurements are available.

The rest of the paper is organized as follows. We first focuson the HV system (11 kV). The details of the study system andthe instrumentation scheme are presented first. The loss compu-tation through measurements and the associated difficulties areconsidered next. The validity of the existing scheme against themeasured losses is assessed. We then describe as to how a modelto facilitate loss estimation, based on limited measurements, isevolved and discuss its features. In Section VIII, we considerthe problem of LV loss computation, highlight problems unique

to this subsystem, present a new estimation method and discusshow we have attempted to validate it.

II. STUDY SYSTEM

For this study, four 11-kV rural distributionfeedersBukkasagara, Sharadagi, Devagiri, and Kalas-apurafrom different regions of Karnataka state were chosen.Though the recommendations are based on observations fromall the feeders, for the discussion here the results correspondingto only one of the feeders- the Bukkasagara feeder is used.

The Bukkasagara feeder is a feeder supplying a predomi-nantly rural agricultural region. The feeder is typical of a heavilyloaded feeder and the load is mainly due to irrigation pump-sets(IP sets). The Bukkasagara feeder has 70 transformers with aninstalled transformer capacity of 5183 kVA. The feeder is madeup of three types of conductors Squirrel, Weasel and Rabbit,having nominal Aluminum areas of 20 , 30 and50 , respectively. The total feeder length including lateralsis about 38 km and the main segment is about 21.5 km. Of this,about 12 km is made up of Rabbit conductor, 4 km is up ofWeasel and the rest is of the Squirrel type. The feeder is sub-jected to regular load shedding and single phasing as is the casewith most rural feeders in India.

A. Measurement SchemeThe measurement scheme evolved for this study is based on

the consideration that the cost of instrumentation must be assmall as possible and the equipment purchased for the projectmust be of use to the utility in their routine operations (sub-sequent to the project). At the time the project was initiated,a 3-phase electronic energy meter with a capability of loggingkWh and kVARh imports and exports every half an hour wasalready in use to measure the feeder input at the substation.

Since one of the main objectives of the study undertaken wasto evolve a feeder model that closely correlated with the actualsystem, it was decided that additional load data be obtained byinstruments installed at the distribution transformer (DT) sec-ondary terminals. A digital meter to record energy (both activeand reactive), voltage, currents, etc., at half hourly intervals ischosen for this purpose. The data logged are the following.

1) At the main substation(feeder input): Half an hour averageof kW and kVAR input to the feeder (The meter keepstrack of the increment in the kWh and kVARh over half anhour, multiplies the increment by 0.5, stores the resultingvalue as power).

2) At each of the distribution transformer secondaries:a) half an hour average of kW and kVAr input to theLV distribution feeders;b) root mean square (rms) values of the voltages ofthe three phases (3-cycle average measured prior to thelogging instant);c) rms values of the currents of the three phases (again,a 3-cycle average).

Each instrument has the capacity to store data over a 35-dayperiod. Every month, the data is downloaded to a portable handheld device and then transferred to a computer. Though this



TABLE IMONTHLY MEASURED LOSS

scheme is not really ideal because of the need for manual inter-vention for collecting and transferring the data to the computer,it was resorted to because it was the only feasible option. Need-less to say, sophisticated communication options are absent inthe remote rural areas supplied by the feeders.

III. ACTUAL LOSS COMPUTATIONThe total HV feeder power loss during any interval is obtained

as the difference between the recorded power at the feeder inputand the sum of the power output of all distribution transformers.The energy losses can be calculated in the above manner toyield the daily, monthly or annual losses depending on the re-quirement. Since, individual output measurements are carriedout on the secondary side of the distribution transformers, thisnet energy loss corresponds to the sum of the HV line lossesand the transformer losses. The measured energy losses for theBukkasagara feeder over a period of nine months in 2001 isshown in Table I.

Though the computation of energy losses from actual mea-surements is an ideal situation, the required extensive instru-mentation is rarely in place. Also, there are many associatedproblems. One main difficulty is that of installing. maintainingand collecting the readings from meters that are placed at re-mote locations and hostile terrains. It is easy to see that loss ofmeasured data even from one of the meters would make the lossestimation process error prone (even if meter errors are ignored).

IV. THE LOSS ESTIMATION METHOD IN USE

The present practice adopted by the electricity utility forcomputing line losses is to use what is generally known as thekm-kVA method. The annual feeder losses are computed usingthe following formula given in (1):

Annual Loss (1)where

;number of segments of feeder;resistance/ unit length of the feeder segment;length of the feeder segment;

;;

;DF (diversity factor) ;LF (load factor) ;

TABLE IIMONTHLY ESTIMATED LOSS (KM-KVA METHOD)

LLF (loss load factor) ;km-kVA ;LDF (load distribution factor) .For feeders with laterals, this formula is used after reducing

the given feeder (with laterals) to a feeder without laterals. Ifthere are some major laterals then the loss in such laterals iscomputed using the same formula by assuming the quantitiesP, peak load, energy sent out, etc. to be in the same ratio asthe capacity of the transformers connected to the branch to thetotal kVA of the given feeder transformer. The computed lossvalue is incremented by a nominal 10% to account for the lossesin the smaller laterals. The above formula has been based onseveral simplifying assumptions such as uniform load distri-bution; constant feeder voltage (at all nodes at all times). Thekm-kVA method has been used to estimate the energy losses inthe Bukkasagara feeder for each of the nine months.

From the measured substation load for nine months, it isfound that the overall LF, LLF, DF, and LDF values are 0.27,0.11, 1.21, and 2.92, respectively. The monthly LF, LLF, and theDF values are computed for each month and the correspondingenergy loss values are shown in Table II.

Comparing the losses obtained by application of the km-kVAmethod (Table II) with the measured values (Table I), it is clearthat the km-kVA method yields a gross underestimate of losses.This is not surprising in view of the various assumptions in-herent in the method. The transformer losses (not included here)are not large enough to account for this difference. It is quite ap-parent that the km-kVA method presently in use for estimatinglosses is inadequate. In view of this, the development of a lossestimation technique that can provide a more realistic estimateof losses would be very useful. The subsequent sections describethe development and application of such a method for estimatinglosses based on limited measurements that are generally avail-able at the sending end substation.

V. LOSS MEASUREMENT AND ESTIMATION: ISSUES

In order to obtain some insight into the actual system lossvariation under various load conditions, the losses during eachhalf hour interval were computed based on the measured values,using the procedure outlined in Section III. These losses for thenine-month period (48 274 points) are plotted in Fig. 1. A pe-rusal of Fig. 1 indicates that (for each load) most of the points areclustered in a small band. However, there are a few points awayfrom this band. Two factors are together responsible for thisscattering; The first is that the feeder switches between 3-phase,



Fig. 1. Measured losses from January 2001 to September 2001.

1-phase, and no-power modes of operation several times in aday. The second factor is that the 71 clocks (one in each of themeters) are not synchronized and in addition they have a sig-nificant drift. Therefore, for the whole feeder the data logging(every half an hour) would be spread over an interval of a fewminutes instead of being at the same instant across the feeder. Ifthe operation of the feeder changes from one mode to anothermode within this interval sometimes outliers are generated inthe plot of Fig. 1. However, it must be noted this phenomenonwill not affect the calculated monthly/yearly losses.

Ignoring the scattered points, Fig. 1 indicates that at everyfeeder input value, the losses vary over a band. This variation isnot completely due to the errors in measurement. Errors wouldcontribute only to a small spread in the measured losses for agiven load. The more significant reason for this feature is the factthat for a given feeder input, the loss component can vary as thespatial distribution of the load along the feeder changes; it canalso vary because of the substation voltage variations. Hence, itmust be noted that the feeder loss value for a given feeder inputpower is not unique and varies over a band of values.

Therefore, the approach to loss estimation (without detailedmeasurements) here, is to first estimate the mean loss corre-sponding to each value of feeder input and use this informationalong with the measured feeder input (at the substation) to es-timate the losses. The basic premise of this scheme is that eventhough the estimated losses (power) for any given feeder inputcould be marginally in error, as several such estimates are ag-gregated to find the energy loss (over a month/year), the errorswould be compensating and the loss estimate would be quitereliable.

The approach adopted to find the mean loss curve is the fol-lowing. Using the measured data a load-flow model of the net-work is developed and validated. This network model, is usedto estimate the average loss corresponding to each of the feederinput values.

VI. FEEDER MODEL DEVELOPMENT

Validating the network model through load-flow studiesturned out to be more involved than anticipated. First, data was

Fig. 2. Measured and computed voltages (Models 14).

Fig. 3. Measured and computed voltages (Models 14).

collected regarding the feeder topology, segment lengths andconductor types used. The first model considered (Model 1)was the standard load-flow model. All the loads measured onthe secondaries of the distribution transformers are referredto the primary side, assuming all transformers to be ideal.Load-flow solutions obtained using this model did not matchwith the measured voltages at the transformer buses and thecomputed losses turned out to be quite low. As a refinement(Model 2), the transformer core loss is included (as a resistoracross the load). Even though this modification helped to reducethe mismatch between the measured and computed values, themismatches continued to be quite significant. Model 3 was thenext refinement where the magnetizing branch was included(in parallel with the load). As this change also turned out to beinadequate, in the next model (Model 4), the transformer seriesimpedance was also included in addition to shunt componentsresulting in a full transformer model.

In order to illustrate the impact of refinements, the results ofthe load-flow solutions obtained for the Bukkasagara feeder,considering each of these models, for two sample cases arepresented here. The measured and computed voltages (fromModels 14), for two intervals have been plotted in Figs. 2 and3. One of the intervals (Fig. 2) corresponds to a moderate load



TABLE IIICOMPUTED FEEDER LOSS WITH MODELS 15

TABLE IVRESISTANCE CORRECTION FACTORS

condition (1.72 MVA) and the other in Fig. 3 corresponds to aheavily loaded condition (2.9 MVA).

The losses corresponding to each load condition computedusing the different models discussed above, are shown inTable III. The measured losses for these intervals are 15.64%(moderate load) and 30.1% (heavy load).

It can be seen that the computed voltage profiles move closerto the measured values as more details are included in thefeeder models. With Model 4, it is also seen that the voltageprofile and losses match reasonably when the load is moderatewhereas there is significant mismatch during the heavily loadedcondition.

The fact that Model 4 turns out to be reasonably good onlyat light loads but is found wanting at higher loads prompted are-examination of our assumptions regarding the network pa-rameters. One of the key assumptions of our model is that the

and parameters of the lines are considered to be constantfor all intervals. A closer examination reveals that whereas thisis justified as far as the reactances are concerned, it is not so forthe line resistances. It is well documented in the literature thatthe ac resistance of a single-layer ACSR conductor increasessignificantly as the current increases [18], [19]. In fact, all theconductors used in this feeder are single-layer ACSR conduc-tors and under heavy load conditions the current in many seg-ments exceed their capacity. The resistance value that is used inModels 1 to 4 is taken from the Indian standards. It is the dcresistance corrected to 32 . Attempts to learn the exact varia-tion of the resistances of these particular conductors with currentturned out to be futile. None of the concerned organizations suchas the utility, conductor manufacturers, standards institutions,power research institutions, etc., had any data on this. Hence,correction factors for feeder resistance had to be found by trialand error. After a large number of simulations, a set of multi-plication factors shown in Table IV were obtained. Recently, ithas been learnt that some technical literature (source unknown)found in the utility has a few approximate formulas for the resis-tance variation of single-layer ACSR conductors and the valuesfound here through simulations compare well with the valuescomputed using these formulas

The feeder model with temperature correction factor for re-sistance in addition to the detailed transformer model is referredto as Model 5. The computed voltage profiles using Model 5 for

Fig. 4. Measured and computed voltages (Model 5).

Fig. 5. Measured and computed voltages (Model 5).

the load-flow solutions are shown in Figs. 4 and 5 for the twocases. The computed loss is shown in the last row of Table III.It is seen that the computed voltages and losses closely matchthe measured values.

It is seen from the voltage profiles in Figs. 4 and 5 that thedifference between the computed and measured voltages is notquite negligible at some transformer locations. This could bedue to one or several of the following reasons.The first is theabsence of time synchronization among the meters. The volt-ages correspond to the three-cycle average rms value of volt-ages at the instant of storing. Therefore, the voltage recorded ateach meter correspond to a slightly different instant of time. Thesecond is that the loads at each node is the average load over a30-min interval, whereas the voltages used to verifying the cor-rectness are the instantaneous values recorded at the recordinginstant. Another source of error is the absence of data regardingtransformer taps.

VII. PROCEDURE FOR ESTIMATION OF LOSSES

A loss table is generated through a sequence of load-flow so-lutions using Model 5. The feeder loads are varied from zero tomore than the peak value in small steps. In this simulation, theload power factor is taken as equal to the average power factor of



Fig. 6. Measured losses and the computed loss curve.TABLE V

MONTHLY ESTIMATED LOSS (PROPOSED METHOD)

the feeder and all the distribution transformers are considered tobe loaded to the same fraction of their capacity. Correspondingto each load, the losses and the power input at the slack bus(substation) are computed. The computed losses plotted againstthe feeder power input is the desired loss curve. The loss curvegenerated for the Bukkasagara feeder is superimposed on themeasured losses and is shown in Fig. 6.

It is seen from Fig. 6 that the computed loss curve can beconsidered to provide the mean of the measured loss at all theloads. However, at lower load levels, the estimated losses seemto be underestimated. This is due to an unusual type of load man-agement (termed as Single Phasing), that is resorted to by theutility during certain periods of the day. This is done by short cir-cuiting two of the three lines of the 11-kV feeder and energizingthis pair and the remaining conductor. Under the above condi-tion, the three phase supply will not be available for driving the3-phase Motors (IP-sets). Only the single-phase lighting load issupplied and the energy consumption is considerably reduced.It can be easily shown that the loss under this conditionis equal to 1.5 times the loss computed by assuming the samekVA load to be a balanced 3-phase load. The above result hasbeen validated by modeling the single phase condition using a3-phase load-flow and simulating this condition as an unbal-anced 3-phase condition. As the single phase mode is also tobe considered in the loss estimation, the losses obtained fromthe loss graph of Fig. 6 are multiplied by 1.5 during the singlephasing periods (which are easily identifiable from the substa-tion recordings). The monthly energy losses estimated based onthe loss curve using the procedure discussed is shown in Table V.

From Table V, it can be observed that, the difference betweenthis loss estimate (for the nine month period) and the measuredloss given in Table I, is quite small considering the several as-sumptions in our estimate scheme as well as the errors in mea-surement.

The HV loss estimation scheme finally recommended by thestudy is the following. For each of the distribution feeders, dothe following.

1) Collect the network data (length ofsegment, type of conductor, etc.) and dis-tribution transformer locations and sizes.2) Compute the loss curve data through asequence of load-flow studies using Model5 (In this context it is also recommendedthat a study must be initiated to findthe exact ac resistance variation of thefew conductor types in use with respect tocurrent variation).3) Since all the feeders are fitted witha data logging type of electronic meterat their input, every month the feederload variation is downloaded onto a com-puter at the substation. A small programis provided which uses the load profileand the computed loss curve to estimatedaily/monthly/yearly losses.4) The loss curve must be updated wheneverthere is a change in the network or trans-former parameters.

VIII. LV SYSTEM LOSSESA. Features of the LV System

The LV distribution system is a 440-V, 3-phase, 4-wiresystem. In rural areas the only significant loads are the irriga-tion pump loads. The distribution transformer capacities aregenerally 25, 63, or 100 kVA, and each DT essentially suppliesa few motor loads. However, the LV feeders could be quite long.Many of the DTs cater to only IP loads but some of the feedersin addition supply the rural domestic loads. Even in suchfeeders, the non-IP load is quite small. The only domestic loadcommon in rural areas is the lighting load for a few hours in theearly night hours. Other types of consumptions are extremelyrare and not at all significant. The IP consumption is either freeor highly subsidized. When it is subsidized, the charges arebased on the hp ratings of the motors and not on their energyconsumption. The income received from the categories whopay is also only a small fraction of the billed amount. The netimpact of these features is that the utilities have no incentives ininstalling meters and monitor individual consumption. More-over, there is a very strong consumer/political opposition forinstallation of meters.

B. LV Loss MeasurementThe loss measurements in the case of LV feeders was not as

straight forward as in the case of the HV feeders. Even thoughthe power fed from each of the distribution transformers was



TABLE VIMEASURED LV FEEDER LOSSES

metered continuously, there was no record of consumption (tostart with). Though there was stiff opposition from many con-sumers, some of them were persuaded to allow meters to be in-stalled at their premises and data on a number of feeders couldbe obtained in this manner (for different periods of time). Insuch cases, the standard 3-phase electro-mechanical energy me-ters were installed at the IP loads to measure the individual con-sumption. These meters were read once in a month. The energyloss in these LV feeders was obtained by subtracting the IP setconsumption from the input energy measured at the transformer.Losses obtained in this way for some LV feeders, supplied fromthe Bukkasagara feeder are tabulated in Table VI. The resultscorrespond to the month of March 2001.

C. Loss Estimation: Present PracticeTill now the utility has not made any serious effort to esti-

mate the LV losses. When some estimates are needed, it is madeusing one of the following approaches. The first approach is toestimate the energy consumption based on some rules of thumbfor the average consumption per consumer and multiplying itby the number of consumers of that category. This is done onlyat the substation level (or sometimes at the feeder level). Theother approach is to use the following formula for LV energyloss (EL):

(2)where

number of conductor segments in the LV feeder;sum of horsepower ratings of IP sets downstream ofthe conductor segment;length in km of the conductor segment;transformer secondary voltage in kV;average power factor;average efficiency of IP sets;feeder resistance ( );time period of interest (hours);

DF diversity factor.The current practice in the utility is to take LLF as

for the LV system.It is easy to see that use of (2) requires that we use assumed

(estimated) values for each of the parameters in (2). It is almostimpossible to make meaningful estimates for parameters suchas voltage, DF, and LLF in (2). Hence, one can have very littleconfidence in the estimated values of losses. For the sake ofcomparison and since these parameter values for these feederswas readily available, the monthly losses were computed usingthe expression given in (2). The computations have been carried

TABLE VIISYSTEM PARAMETERS AND COMPUTED LOSSES

out with , and values assumed to be 0.4, 0.9, and 0.9 kV,respectively. The conductor used for the LV feeders is Squirrel(20 nominal Al. area) and has a resistance/km of 1.476

. The other parameters of the feeders and the losses estimatedusing this formula are given in Table VII.

Comparing the results obtained using the approximate lossformula given in (2) with the measured losses (Table VII withTable VI), it is seen that this formula yields a gross underesti-mate of energy losses.

D. Proposed MethodThe absence of a method to make at least a reasonable es-

timate of LV losses motivated us to explore the possibility ofevolving a new scheme for this purpose. At the outset, it wasclear that the scheme used for the primary feeders could notbe extended for the LV case because it would involve upfrontcost due to extensive instrumentation and also recurring cost fordata collection, data storage, data management and loss compu-tation. It was also clear that the new method must not be basedon large number of assumptions similar to those made in (2). Anew loss estimation scheme is proposed here which we believeserves these requirements admirably.

E. Basis of the MethodConsider a 3-phase LV feeder consisting of segments made

up of conductors of resistance (if conductors of dif-ferent resistances are used, their lengths are normalized). Thetotal LV losses occurring in the feeder is the sum of the lossesin each of the three phases. The loss occurring in phase- , at anytime , is given by

(3)where is the phase- current flowing in the segment atinstant and is the length of the conductor segment.Let be the total current in phase- , measured at the sec-ondary of the distribution transformer at time and bethe proportion of the total current that flows in the segment,i.e., . Substituting for in (3), we get

(4)Simplifying (4) by noting that the total current and resis-tance/km, are independent of the summation, we get

(5)The energy loss occurring in phase- over a time is obtainedby integrating (5)

(6)



Now, the factor is dependent on the load that is presentdownstream of segment and the total load at the secondaryof the distribution transformer. Therefore, it is a time-varyingquantity. Since the load measurements at the nodes are not avail-able, and also considering the fact that the currents are depen-dent predominantly on the total ratings of the IP sets, we cansimplify the loss estimation by assuming a conforming loadvariation; This assumption is not new. It is used in deriving allthe existing loss formulas. With this assumption, can betreated as a constant i.e., . Here,

is the sum of the HP ratings of the connected IP sets down-stream of the segment and is the total connected HP loadon the entire LV feeder. Equation (6) can therefore be written as

(7)

In (7), the term , accounts for the ef-fect of load distribution along the feeder and is represented by

. The energy loss equation for phase- then reduces to

(8)

The total energy loss is the sum of the loss occurring each of thethree phases. Hence, the energy loss formula for the feeder canbe written as

(9)

A careful study of the new loss formula shows that it is basedon very few assumptions. Given the feeder configuration (ba-sically lengths, topology, location, and ratings of the IP sets),the factor can be calculated which remains constant unlessthe configuration of the feeder itself is changed. , being theresistance per km of the feeder, is also constant. If the quantity

is obtained for any interval oftime , the loss corresponding to the interval is readily given bythe new loss formula.

The applicability of this loss formula lies in how effectivelywe can obtain this quantity. In order to measure this quantity ac-curately, a design for a 3-phase meter has been evolvedand a patent is pending for this design [20]. In this patent pro-posal, two alternate implementations have been described. Oneimplementation is an electro-mechanical type of meter and theother is a digital meter. The cost of the electro-mechanical im-plementation is very nominal; even the electronic version isquite affordable. The other advantage of the meter is that it canbe read at irregular intervals because it is an integrating type ofmeter. With such a meter installed at the output of the distribu-tion transformer, the change in the readings of this meter overany interval gives the quantity over that interval. Thequantity for the feeder need be calculated only once andused as a multiplier with the reading. can be up-dated if there is any significant change in load or configurationof the feeder.

F. Loss Estimates by Proposed SchemeWe have seen that this new scheme is quite reliable, by com-

paring the measured losses in several distribution feeders with

TABLE VIIILV LOSS ESTIMATES FOR MARCH 2001 (PROPOSED METHOD)

the value obtained using this formula for a large number ofcases. For verifying the result, even though we did not have thenew meters in place, the , , and values recorded at every30 min at the DTs, provided the required values of phase cur-rents. For the sake of illustration, the losses computed for themonth of March for the four LV feeders listed in Table VI aregiven in Table VIII.

Comparison of the estimated losses in Table VIII with themeasured losses in Table VI gives an idea of the reliability of theproposed method. It must also be pointed out that such estimatesare obtained at a number of feeders. Hence, the possible errorsin each of the estimates, when combined tend to compensate oneanother while calculating the total LV system loss thus makingthe estimate for the total loss of an area very reliable.

IX. REMARKS

1) The promising results seen in the case of the proposed LVmethod, seem to suggest the possibility of using this ap-proach for the HV feeders also. Since the digital meters atthe substation do not have the capability of recording halfan hourly current and voltage information, at this point wehave not been able to verify this hypothesis. Utilities whohave not already invested in procuring and installing theusual types of meters at the substation could incorporatethis feature while procuring meters in the future. Alter-nately, one could also think of installing the new type of

meters at each of the HV feeders2) The proposed loss curve for the HV feeders has been gen-

erated so as to get the average feeder loss for any specifiedfeeder input. The feeder input considered here is the kVAinput, as this measurement is readily available. It is easy tosee that in situations where the feeder input kVA measure-ment is not available but only the input current informa-tion is available, the proposed approach is still applicable.In that case the loss curve could be generated with respectto input current

3) The discussions in the paper are limited to estimating thelosses in a feeder. In order to apply these schemes for com-puting the system wide losses, two possibilities exist. Thefirst is to estimate the losses for all the feeders. The otheralternative is to find some representative feeders (in a waysimilar to [16]) and estimate the system losses based onthe estimates of the chosen sample set. The latter approachrequires further investigation

X. CONCLUSIONSThe results of a joint study conducted in collaboration with

the local utility, pertaining to distribution system loss estima-



tion has been presented. The results highlight the limitationsof the present methods of loss estimation in use and also themajor difficulties in measuring the losses directly. Two loss es-timation schemes are proposed and an assessment of their relia-bility has been provided by comparing the estimates with mea-sured values. One of the schemes is meant for the 11-kV primaryfeeders and makes use of the logged data of the electronic me-ters already installed at the input of these feeders. The secondscheme is meant for use with LV feeders. As no metering existsat these feeders, use of a new meter (which is not expensive)is proposed. It is shown that the use of this integrating type of

meter when multiplied with a constant gives a good es-timate of the LV feeder loss.

It is envisioned that the results of this study would be of greatinterest not only to utilities in the developing world but also tothose in the developed countries.

ACKNOWLEDGMENT

The first author, P. S. N. Rao, acknowledges the contributionsof V. G. Havanagi and H. N. Dattatreya from KPTCL (assis-tance in instrumentation and data collection); P. S. Nandini andK. Prahlad (assistance in data management); and also thanksProf. I. Sen and Prof. D. P. Sengupta for several discussionsduring the project.

REFERENCES[1] F. H. Buller and C. A. Woodrow, Load factor equivalent hours values

compared, Electr. World, Jul. 1928.[2] H. F. Hoebel, Cost of electric distribution losses, Electr. Light and

Power, Mar. 1959.[3] M. W. Gustafson, J. S. Baylor, and S. S. Mulnix, Equivalent hours loss

factor revisited, IEEE Trans. Power Syst., vol. 3, no. 4, pp. 15021507,Nov. 1988.

[4] M. W. Gustafson, Demand, energy and marginal electric systemlosses, IEEE Trans. Power App. Syst., vol. PAS-102, no. 9, pp.31893195, Sep. 1983.

[5] M. W. Gustafson and J. S. Baylor, Approximating the system lossesequation, IEEE Trans. Power Syst., vol. 4, no. 3, pp. 850855, Aug.1989.

[6] N. E. Chang, Determination of primary feeder losses, IEEE Trans.Power App. Syst., vol. PAS-87, no. 12, pp. 19911994, Dec. 1968.

[7] N. R. Schultz, Distribution primary feeder I r losses, IEEE Trans.Power App. Syst., vol. PAS-97, no. 2, pp. 603609, Mar./Apr. 1978.

[8] D. I. H. Sun, S. Abe, R. R. Shoults, M. S. Chen, P. Eichenberger, andD. Ferris, Calculation of energy losses in a distribution system, IEEETrans. Power App. Syst., vol. PAS-99, no. 4, pp. 13471356, Jul./Aug.1980.

[9] R. Cspedes, H. Durn, H. Hernndez, and A. Rodrguez, Assessmentof electrical energy losses in the Colombian power system, IEEE Trans.Power App. Syst., vol. PAS-102, no. 11, pp. 35093515, Nov. 1983.

[10] D. L. Flaten, Distribution system losses calculated by percent loading,IEEE Trans. Power Syst., vol. 3, no. 3, pp. 12631269, Aug. 1988.

[11] N. Vempati, R. R. Shoults, M. S. Chen, and L. Schwobel, Simplifiedfeeder modeling for load flow calculations, IEEE Trans. Power Syst.,vol. PWRS-2, no. 1, pp. 168174, Feb. 1987.

[12] R. Baldick and F. F. Wu, Approximation formulas for the distributionsystem: The loss function and voltage dependence, IEEE Trans. PowerDel., vol. 6, no. 1, pp. 252259, Jan. 1991.

[13] H.-D. Chiang, J.-C. Wang, and K. N. Miu, Explicit loss formula,voltage formula and current flow formula for large scale unbalanceddistribution systems, IEEE Trans. Power Syst., vol. 12, no. 3, pp.10611067, Aug. 1997.

[14] C. S. Chen, M. Y. Cho, and Y. W. Chen, Development of simplified lossmodels for distribution system analysis, IEEE Trans. Power Del., vol.9, no. 3, pp. 15451551, Jul. 1994.

[15] Y.-Y. Hong and Z.-T. Chao, Development of energy loss formula fordistribution systems using FCN algorithm and cluster-wise fuzzy regres-sion, IEEE Trans. Power Del., vol. 17, no. 3, pp. 794799, Jul. 2002.

[16] C. A. Dortolina and R. Nadira, The loss that is unknown is no loss atall: A top-down/bottom-up approach for estimating distribution losses,IEEE Trans. Power Syst., vol. 20, no. 2, pp. 11191125, May 2005.

[17] Energy Accounting and Rationalization of Distribution Systems,Final Report, KPTCL, Dept. Elect. Eng., Indian Inst. Sci., Bangalore,India, 2004, submitted for publication.

[18] IEEE Standard for Calculating the Current- Temperature Relationshipof Bare Overhead Conductors, IEEE standard 7381993.

[19] Aluminum Electrical Conductor Handbook, 2nd ed., The AluminumAssociation, Washington, DC, 1982.

[20] P. S. N. Rao, An I dtMeter for Energy Loss Estimation in Elec-trical Power Networks, Indian Patent Application Number: 520/CHE2004, Jun. 2004.

P. S. Nagendra Rao was born in Periyapatna, Karnataka, India, in 1950. Hereceived the B.E. degree in electrical engineering and the M.E. degree in powersystems engineering from the University of Mysore, Mysore, India, in 1971 and1973, respectively, and the Ph.D. degree from the Indian Institute of Technology,Delhi, India, in 1981.

From 1973 to 1984, he was on the faculty of the Department of Electrical En-gineering, National Institute of Engineering, Mysore. He joined the Departmentof Electrical Engineering, the Indian Institute of Science, Bangalore, in 1984,where he is currently a Professor. His fields of interest cover many aspects ofpower system analysis, design, operation, and control.

Ravishankar Deekshit was born in Bangalore, Karnataka, India, in 1959. Hereceived the B.E. degree in electrical engineering from Bangalore University in1982 and the M.E. degree in power systems engineering from Anna Universityin 1989. He is currently pursuing the Ph.D. degree with the Department of Elec-trical Engineering, Indian Institute of Science, Bangalore.

He has been on the faculty of the Department of Electrical and Electronics,B.M.S, College of Engineering, Bangalore, since 1984 and is presently Head ofthe department. His field of interest is in the area of power systems.


tocEnergy Loss Estimation in Distribution FeedersP. S. Nagendra Rao and Ravishankar DeekshitI. I NTRODUCTION1) Identify a few feeders representative of the different climat2) Monitor the load parameters of feeders over an extended perio3) Compute losses based on these measured readings.4) Assess the validity of existing estimation schemes by compari5) Explore the possibility of evolving and validating a scheme fII. S TUDY S YSTEMA. Measurement Scheme

TABLE I M ONTHLY M EASURED L OSS III. A CTUAL L OSS C OMPUTATIONIV. T HE L OSS E STIMATION M ETHOD IN U SE

TABLE II M ONTHLY E STIMATED L OSS ( K M- K VA M ETHOD ) V. L OSS M EASUREMENT AND E STIMATION: I SSUES

Fig.1. Measured losses from January 2001 to September 2001.VI. F EEDER M ODEL D EVELOPMENT

Fig.2. Measured and computed voltages (Models 1 4).Fig.3. Measured and computed voltages (Models 1 4).TABLE III C OMPUTED F EEDER L OSS W ITH M ODELS 1 5 TABLE IV R ESISTANCE C ORRECTION F ACTORS Fig.4. Measured and computed voltages (Model 5).Fig.5. Measured and computed voltages (Model 5).VII. P ROCEDURE FOR E STIMATION OF L OSSES

Fig.6. Measured losses and the computed loss curve.TABLE V M ONTHLY E STIMATED L OSS (P ROPOSED M ETHOD ) 1) Collect the network data (length of segment, type of conducto2) Compute the loss curve data through a sequence of load-flow s3) Since all the feeders are fitted with a data logging type of 4) The loss curve must be updated whenever there is a change in VIII. LV S YSTEM L OSSESA. Features of the LV SystemB. LV Loss Measurement

TABLE VI M EASURED LV F EEDER L OSSES C. Loss Estimation: Present Practice

TABLE VII S YSTEM P ARAMETERS AND C OMPUTED L OSSES D. Proposed MethodE. Basis of the MethodF. Loss Estimates by Proposed Scheme

TABLE VIII LV L OSS E STIMATES FOR M ARCH 2001 (P ROPOSED M ETHOIX. R EMARKSX. C ONCLUSIONSF. H. Buller and C. A. Woodrow, Load factor equivalent hours valH. F. Hoebel, Cost of electric distribution losses, Electr. LighM. W. Gustafson, J. S. Baylor, and S. S. Mulnix, Equivalent hourM. W. Gustafson, Demand, energy and marginal electric system losM. W. Gustafson and J. S. Baylor, Approximating the system losseN. E. Chang, Determination of primary feeder losses, IEEE Trans.N. R. Schultz, Distribution primary feeder $I^{2}r$ losses, IEEED. I. H. Sun, S. Abe, R. R. Shoults, M. S. Chen, P. EichenbergerR. Cspedes, H. Durn, H. Hernndez, and A. Rodrguez, AssessmenD. L. Flaten, Distribution system losses calculated by percent lN. Vempati, R. R. Shoults, M. S. Chen, and L. Schwobel, SimplifiR. Baldick and F. F. Wu, Approximation formulas for the distribuH.-D. Chiang, J.-C. Wang, and K. N. Miu, Explicit loss formula, C. S. Chen, M. Y. Cho, and Y. W. Chen, Development of simplifiedY.-Y. Hong and Z.-T. Chao, Development of energy loss formula foC. A. Dortolina and R. Nadira, The loss that is unknown is no lo

Energy Accounting and Rationalization of Distribution Systems, FIEEE Standard for Calculating the Current- Temperature RelationsAluminum Electrical Conductor Handbook, 2nd ed., The Aluminum AsP. S. N. Rao, An $\int I^{2} \times dt$ Meter for Energy Loss Es

energy loss estimation in distribution feeders(1)

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