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Home / Technical Articles / Total Losses in Power Distribution and Transmission Lines

Introduction

Power generated in power stations pass through large and complex networks like transformers, overhead lines, cables and other equipment and reaches at the end users.

Total Losses in Power Distribution and Transmission Lines // Part 1
Total Losses in Power Distribution and Transmission Lines (photo credit: Total Losses in Power Distribution and Transmission Lines (on photo: A transmission line of constant voltage of 600 kVDC, at 2400 kilometers built in Brazil; credit: IVOLINES via Flickr)

It is fact that the unit of electric energy generated by Power Station does not match with the units distributed to the consumers. Some percentage of the units is lost in the distribution network.

This difference in the generated and distributed units is known as Transmission and Distribution loss. Transmission and Distribution loss are the amounts that are not paid for by users.

T&D Losses = (Energy Input to feeder(Kwh) – Billed Energy to Consumer(Kwh)) / Energy Input kwh x 100

Distribution Sector considered as the weakest link in the entire power sector. Transmission Losses is approximate 17% while Distribution Losses is approximate 50%.

There are two types of Transmission and Distribution Losses:

  1. Technical Losses
  2. Non Technical Losses (Commercial Losses)

1. Technical Losses

The technical losses are due to energy dissipated in the conductors, equipment used for transmission line, transformer, subtransmission line and distribution line and magnetic losses in transformers.

Technical losses are normally 22.5%, and directly depend on the network characteristics and the mode of operation.

The major amount of losses in a power system is in primary and secondary distribution lines. While transmission and sub-transmission lines account for only about 30% of the total losses. Therefore the primary and secondary distribution systems must be properly planned to ensure within limits.

  • The unexpected load increase was reflected in the increase of technical losses above the normal level
  • Losses are inherent to the distribution of electricity and cannot be eliminated.

There are two Type of Technical Losses.


1. Permanent / Fixed Technical losses

  • Fixed losses do not vary according to current. These losses take the form of heat and noise and occur as long as a transformer is energized
  • Between 1/4 and 1/3 of technical losses on distribution networks are fixed losses. Fixed losses on a network can be influenced in the ways set out below
  • Corona Losses
  • Leakage Current Losses
  • Dielectric Losses
  • Open-circuit Losses
  • Losses caused by continuous load of measuring elements
  • Losses caused by continuous load of control elements

2. Variable Technical losses

Variable losses vary with the amount of electricity distributed and are, more precisely, proportional to the square of the current. Consequently, a 1% increase in current leads to an increase in losses of more than 1%.

  • Between 2/3 and 3/4 of technical (or physical) losses on distribution networks are variable Losses.
  • By increasing the cross sectional area of lines and cables for a given load, losses will fall. This leads to a direct trade-off between cost of losses and cost of capital expenditure. It has been suggested that optimal average utilization rate on a distribution network that considers the cost of losses in its design could be as low as 30 per cent.
  • Joule losses in lines in each voltage level
  • Impedance losses
  • Losses caused by contact resistance.

Main Reasons for Technical Losses

1. Lengthy Distribution lines

In practically 11 KV and 415 volts lines, in rural areas are extended over long distances to feed loads scattered over large areas. Thus the primary and secondary distributions lines in rural areas are largely radial laid usually extend over long distances.

This results in high line resistance and therefore high I2R losses in the line.

  • Haphazard growths of sub-transmission and distribution system in to new areas.
  • Large scale rural electrification through long 11kV and LT lines.

2. Inadequate Size of Conductors of Distribution lines

The size of the conductors should be selected on the basis of KVA x KM capacity of standard conductor for a required voltage regulation, but rural loads are usually scattered and generally fed by radial feeders. The conductor size of these feeders should be adequate.

3. Installation of Distribution transformers away from load centers

Distribution Transformers are not located at Load center on the Secondary Distribution System.

In most of case Distribution Transformers are not located centrally with respect to consumers. Consequently, the farthest consumers obtain an extremity low voltage even though a good voltage levels maintained at the transformers secondary.

This again leads to higher line losses. (The reason for the line losses increasing as a result of decreased voltage at the consumers end therefore in order to reduce the voltage drop in the line to the farthest consumers, the distribution transformer should be located at the load center to keep voltage drop within permissible limits.)

4. Low Power Factor of Primary and secondary distribution system

In most LT distribution circuits normally the Power Factor ranges from 0.65 to 0.75. A low Power Factor contributes towards high distribution losses.

For a given load, if the Power Factor is low, the current drawn in high  And  the losses proportional to square of the current will be more. Thus, line losses owing to the poor PF can be reduced by improving the Power Factor.

This can be done by application of shunt capacitors.

  • Shunt capacitors can be connected either in secondary side (11 KV side) of the 33/11 KV power transformers or at various point of Distribution Line.
  • The optimum rating of capacitor banks for a distribution system is 2/3rd of the average KVAR requirement of that distribution system.
  • The vantage point is at 2/3rd the length of the main distributor from the transformer.
  • A more appropriate manner of improving this PF of the distribution system and thereby reduce the line losses is to connect capacitors across the terminals of the consumers having inductive loads.
  • By connecting the capacitors across individual loads, the line loss is reduced from 4 to 9% depending upon the extent of PF improvement.

5. Bad Workmanship

Bad Workmanship contributes significantly role towards increasing distribution losses.

Joints are a source of power loss. Therefore the number of joints should be kept to a minimum. Proper jointing techniques should be used to ensure firm connections.

Connections to the transformer bushing-stem, drop out fuse, isolator, and LT switch etc. should be periodically inspected and proper pressure maintained to avoid sparking and heating of contacts.

Replacement of deteriorated wires and services should also be made timely to avoid any cause of leaking and loss of power.

6. Feeder Phase Current and Load Balancing>

One of the easiest loss savings of the distribution system is balancing current along three-phase circuits.

Feeder phase balancing also tends to balance voltage drop among phases giving three-phase customers less voltage unbalance. Amperage magnitude at the substation doesn’t guarantee load is balanced throughout the feeder length.

Feeder phase unbalance may vary during the day and with different seasons. Feeders are usually considered “balanced” when phase current magnitudes are within 10.Similarly, balancing load among distribution feeders will also lower losses assuming similar conductor resistance. This may require installing additional switches between feeders to allow for appropriate load transfer.

Bifurcation of feeders according to Voltage regulation and Load.

7. Load Factor Effect on Losses

Power consumption of customer varies throughout the day and over seasons.

Residential customers generally draw their highest power demand in the evening hours. Same commercial customer load generally peak in the early afternoon. Because current level (hence, load) is the primary driver in distribution power losses, keeping power consumption more level throughout the day will lower peak power loss and overall energy losses.

Load variation is Called load factor and It varies from 0 to 1.

Load Factor = Average load in a specified time period / peak load during that time period.

For example, for 30 days month (720 hours) peak Load of the feeder is 10 MW. If the feeder supplied a total energy of 5,000 MWH, the load factor for that month is (5,000 MWh)/ (10MW x 720) =0.69.

Lower power and energy losses are reduced by raising the load factor, which, evens out feeder demand variation throughout the feeder.

The load factor has been increase by offering customers “time-of-use” rates. Companies use pricing power to influence consumers to shift electric-intensive activities during off-peak times (such as, electric water and space heating, air conditioning, irrigating, and pool filter pumping).

With financial incentives, some electric customers are also allowing utilities to interrupt large electric loads remotely through radio frequency or power line carrier during periods of peak use. Utilities can try to design in higher load factors by running the same feeders through residential and commercial areas.

8. Transformer Sizing and Selection

Distribution transformers use copper conductor windings to induce a magnetic field into a grain-oriented silicon steel core. Therefore, transformers have both load losses and no-load core losses.

Transformer copper losses vary with load based on the resistive power loss equation (P loss = I2R). For some utilities, economic transformer loading means loading distribution transformers to capacity-or slightly above capacity for a short time-in an effort to minimize capital costs and still maintain long transformer life.

However, since peak generation is usually the most expensive, total cost of ownership (TCO) studies should take into account the cost of peak transformer losses. Increasing distribution transformer capacity during peak by one size will often result in lower total peak power dissipation-more so if it is overloaded.

Transformer no-load excitation loss (iron loss) occurs from a changing magnetic field in the transformer core whenever it is energized. Core loss varies slightly with voltage but is essentially considered constant. Fixed iron loss depends on transformer core design and steel lamination molecular structure. Improved manufacturing of steel cores and introducing amorphous metals (such as metallic glass) have reduced core losses.

9. Balancing 3 phase loads

Balancing 3-phase loads periodically throughout a network can reduce losses significantly. It can be done relatively easily on overhead networks and consequently offers considerable scope for cost effective loss reduction, given suitable incentives.

10. Switching off transformers

One method of reducing fixed losses is to switch off transformers in periods of low demand. If two transformers of a certain size are required at a substation during peak periods, only one might be required during times of low demand so that the other transformer might be switched off in order to reduce fixed losses.

This will produce some offsetting increase in variable losses and might affect security and quality of supply as well as the operational condition of the transformer itself. However, these trade-offs will not be explored and optimized unless the cost of losses are taken into account.

11. Other Reasons for Technical Losses

  • Unequal load distribution among three phases in L.T system causing high neutral currents.
  • leaking and loss of power
  • Over loading of lines.
  • Abnormal operating conditions at which  power and distribution transformers are operated
  • Low voltages at consumer terminals causing higher drawl of currents by inductive loads.
  • Poor quality of equipment used in agricultural pumping in rural areas, cooler air-conditioners and industrial loads in urban areas.

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author-pic

Jignesh Parmar

Electrical Middle management professional having more than 22 years rich and dynamic experience in Project Execution / Project Management / Designing / Maintenance diversifies from Electrical Power Transmission (400KV/220KV/66KV)- Distribution(11KV/220V) to Lifts-HVAC-Ventilation-Fire Fighting-Fire Alarm-Lifts-CCTV-Stack Parking Works (High Rise Buildings, Townships, Shopping Complex, Commercial Complex, School, Temple).

Profile: Jignesh Parmar

60 Comments


  1. Jess Stuart
    Aug 14, 2023

    Please list sources for this article.


  2. A.karunasri
    Nov 26, 2022

    amazing


  3. Christian Pando
    Jul 02, 2022

    What country is that power line on the image located at?


  4. Durga Khatri
    Aug 14, 2021

    what will be the possible non technical loss in power system?


  5. Chris okafor
    Aug 10, 2021

    Please, I would like to see the references,you used in making this claim for percentage losses at distribution, and transmission losses


  6. Malik Imtiaz Ahmad
    Aug 22, 2020

    In the opening part of the above article, it has been explained that technical and distribution (T&D) losses are not chargeable to end-user. would you give reference in this regard and whether this rule would also apply to a consumer having installed independently feeder and the losses goes beyond the permissible limit, moreover what is the standard of T&D permissible limit, both for distribution feeder and dedicated 11kv feeder. thanks


  7. Hye Jin Koh
    Jan 28, 2020

    Hello! I am wondering what it means to have a negative line loss? Thank you so much for your time.

    Hye Jin Koh


  8. Sanjeev kumar
    Nov 06, 2019

    Dear sir, i want to calculate the effect of loss by increasing the size of conductor 0.05 to 0.1 sq. inch also the payback period to recover the investment in 11 kv transmission line


  9. Sakhare Chandrakant
    Nov 16, 2018

    Sir, how calculate station loss, Transformer loss
    We have 2nos of 220kv I/C line and 8nos of 110kv O/G feeder, in day time solar injection from 7nos 110kv line is high that power stepup and given 220 kv grid, in night time it just opposite power drawn from grid consuming 8nos of feeders, here we can export and import energy for individual feeder but how to calculate for entire Receiving Station


  10. sravani
    Apr 04, 2018

    how to calculate the power loss & power backed to power supply or grid from battery charger circuit(LCV or LCN or FTV) while discharging the lead acid battery??


  11. Deepak A
    Mar 13, 2018

    The same article is available in ELECTRICAL INDIA Vol 58 Jan 2018 As a front page article details at Page No 38.

    Further step of your line losses, please take a study/ already done please share….

    We need to highlight 11 Kv effects on single phase line at jumping, as long running as kms in rural areas both lines together in same poles with non maintained distance.
    Many times due to birds lands, wind, tree branches touching the both lines same times, Vehicle accidents to poles, other uncontrolled effects fraction of seconds to some seconds both the HT and LT powers linked each other cause heavy damage in single phase connected loads.

    TC centers also not maintained in all rural areas of the country cause the major burns of house hold single phase load including public street light mainly during rainy season starts.as observed…

    Thank you very much..

    Deepak A
    720 4363 665 Whatsapp
    988 6668 661
    Bangalore
    INDIA


  12. D.K.YADAV
    Jan 20, 2018

    How can we reduce Load Factor.How can we calculate Load Factor.


  13. Mohammad ali Nazeriyan
    Jan 05, 2018

    Dear Sir
    I want calculate the power loss in distribution cable by inductive load.The formula of line power loss is P=RI^2 for each phase.so if it is true how can i calculate the I parameter in lag load.
    thanks


  14. ovie matthew
    Nov 28, 2017

    please kindly educate me on how to reduce electric transmission loses using artificial intelligence


  15. Clemente c. Hermosilla Jr
    Sep 29, 2017

    sir, In our company their were 3 divisions each division has a check meter for individual kwh consumption,as a basis for our individual payment of our bills and a primary meter to sum total consumption for the 3 divisions.1.) their is a current loss or difference between the primary meter reading and the total check meter reading after we add all the meter readings of the 3 division check meter. Example: Total kwh used by Divisions: a. 22,000kwh b. 12,000kwh c. 10,000kwh = 44,000kwh, and the primary meter is=39,000kwh or a 5,000kwh difference. HOw can we distribute the 5,000kwh difference for the 3 divisions? can you give us a mathematical furmula/computation, so that we can fairly distribute this to users?
    Thank you;
    JUn


    • Deepak A
      Mar 13, 2018

      Convert all consumption to % from total of 44000. that is 50%, 27.3% and 22.7. Than … distribute the difference 5000 in to as per % available. That is 2500 Kwh, 1365 and 1135.

      Good Day..


  16. akbar
    Feb 02, 2017

    sir tell me how to calculate transmission losses in different types (short, medium, long) lines.


  17. South East Asia Engineer
    Jan 30, 2017

    Hi,

    You have mentioned “Switching off transformers” is there an effect on the life of transformer if I will de-energize a 78 MVA transformer for 1 month then energize after that period?


    • East South Asia Engineer
      Jun 18, 2020

      No, there is no effect


  18. Christina
    Jan 06, 2017

    Hello,

    I had a couple of questions.

    1. When you say “Distribution Sector considered as the weakest link in the entire power sector. Transmission Losses is approximate 17% while Distribution Losses is approximate 50%.”, you’re referring to 17% of what and 50% of what?

    2. When you say “Technical losses are normally 22.5%”, do you mean technical losses are 22.5% of the total T&D losses?

    Thanks for your help!

    Best,
    Christina


  19. kazem
    Dec 07, 2016

    DEAR Sir
    Thank you for your published
    I have one question about the references of your paper. For example in the first part of your paper you aimed that technical loss is normally near 22%. would you please tell me abut the references of that?
    with best regard
    Kazem


    • Chris okafor
      Aug 10, 2021

      I also would want to see the references


  20. Benwari
    Sep 06, 2016

    Please i intend to do a design for power plant using gas engines (about 5MW capacity) to export power to a customer on overhead lines of about 6KM, please how do i calculate the line power loss if customer requires on about 4MW of power.


  21. Ambrose F Jada
    Jun 06, 2016

    Why the primary distribution voltage is preferred at high ranges


  22. P ANAND
    Apr 20, 2016

    Hello Sir,
    We are looking for a technical losses calculation and comparision between a 11KV ACSR 55 Sq mm Conductor Line compared with a 11KV Covered Conductor Line of higher size.

    Can you please let us know about the procedure for calculations and adoption of various methods in this procedure.

    Thank you
    Regards
    P. Anand


  23. saeed
    Mar 31, 2016

    What’s the mathematics relation (formula) between reactive power (Q) and transformer tap position?(If transformer DY11 and tap of transformer be on high voltage side(Y)).


  24. Aung myo naing
    Mar 30, 2016

    Dear sir…
    How many the lowest percent of technical losses? And which country is the
    best reducing unit losses.?


  25. Ruser
    Aug 22, 2015

    Hello. I was under the understanding that the reason for raising the voltage of electricity prior to transmission was to reduce the loss occurring between source and load by relying on the fact that the power dissipated is (V^2)/R so that current “I” would be low thus (I^2)R would be low even for high “R” and that for high “R” (V^2)/R would be low. In this article it is written that cables and other transmission conductors are made with higher cross section in order to lower resistance and thus lower (I^2)R. From what I gather having read this article, this applies mainly to the higher current more local distribution systems closer to the consumer. Please correct me if I am mistaken as I am not a power distribution engineer.


    • GSM
      Oct 26, 2015

      SIR PLZZ TELL
      How we mitigating the effect of load factor on distribution loses


  26. shashank
    Aug 05, 2015

    sir, i am working in a power distribution company and i found that when the 33/11 kv power transformer was on no load and was only feeding from 132 kv ss to its 33 kv side it was taking 2.2 A to 2.7 A on 33 kv side also it includes the subtransmission loss from 132 / 33 kv sub station, then i calcute its energy consumed or loss for 1 hour as :
    1.732 * 33000 (V) * 2.2 (A) * 1 (hour) = 125743.2 WH = 125.743 KWH
    So does it mean the 125.743 kwh are the loss ?
    Please analyse my analysis ..


  27. IFTIKHAR ALI
    Jul 19, 2015

    Plz sir give your email id ? I want to arrange a conversation with u.plz


  28. istiaque
    Jul 05, 2015

    would u plz give your email id sir? its really an important article to me.I want to arrange a conversation with u.plz


  29. zafar iqbal
    Jun 30, 2015

    Sir ,
    please help me.
    calculate the transmission line losses formoula.
    11kv transmission line 3.5km ospray conductor double circuit maximum load 10MW P.F .92.
    Calculate the line losses.


  30. thokozani
    Jun 13, 2015

    please sign me up


  31. Hazel Brock
    Jun 09, 2015

    Thank You for sharing the article. Transmission and Distribution Losses are great threat for energy solutions. Big Hybrid generators with low budget are a great solution for energy and power. Really an informative thread.


  32. farzana
    Jun 07, 2015

    hai sir,iam having one dought i.e., what are the permitted losses sir?if u dont mind plz send me answer sir


  33. Jose Abraham Landa Palma
    May 31, 2015

    Thanks, I learned more about this subject.


  34. Shewaye gidaye
    May 27, 2015

    Hello, it is very help full articles it helps me
    thank you


  35. Bahubali.B.Kuranagi
    May 10, 2015

    Sir…. NJY feeder (Which are feeding power supply to rural area villages) are having 40% loss ,these feeders are running 30Kms HT LINE and 60Kms LT LINE reasons for such a huge losses..Peak load of these feeders are 30Amps…HT Conductor is rabit and LT Conductor is weasel…


  36. Kent Crosslet
    Mar 29, 2015

    Sir, Very good article explaining distribution loss and ways to correct it. I help industrial companies reduce distribution losses typically by installing shunt capacitors at the load. Often these induction motors can be from 30-150 hp and located over 100 ft from the transformer. how do you recommend calculating the distribution loss and the savings based on capacitor installation? You mentioned a range from 4-9%. Thank you. Kent


  37. Shine
    Mar 23, 2015

    Hi,

    I find your article useful. I am a student working on Simulation and Analysis of Technical Losses on Electric power Transmission Line. Can you please provide me materials on Technical Losses on Transmission Lines for my study?


  38. Jack Durcan
    Mar 05, 2015

    I enjoyed the article and, as mentioned earlier, feel that some of the findings apply to grid operations outside of the US.

    Regards,
    Jack


  39. dilusha nuwan
    Jan 17, 2015

    Thanks for the article!! very useful for distribution losses


  40. Alaina
    Nov 12, 2014

    This is very confusing especially to middle schools. I mean what the heck is shunt capacitors.


  41. Ahmed
    Oct 09, 2014

    what about the non-technical losses??


  42. akshay
    Aug 08, 2014

    respected jignesh ji,
    I want to know that what is duration between electricity generation till it reaches home ???
    ex generated from plant & home in Rajasthan
    please answer via email


  43. Yomi Biyi
    Apr 24, 2014

    I am given a topic to write a research proposal on analysis and reduction Losses on Nigeria 330KV can anyone help me on a new methodology to investigate power losses. Thanks.


  44. Gene Hawkridge
    Mar 05, 2014

    System or technical losses can be estimated by modelling the system. These can be checked against substation feeder measurements. When these losses appear to be excessive, check for “non-technical” losses. I encountered a situation some years ago in which the meter for one of the largest loads in a small community was not wired correctly, with the result that the measured energy use of the cusomer was a tiny fraction of actual use. Re-wiring that meter dropped system losses in half, and considerably improved the balance sheet of the small utility involved. It is unknown whether intentional theft was involved. Of course, meters must be locked securely. Modern data processing methods can be used to identify customer services with suspiciously low energy use.


  45. Ross Baldick
    Mar 01, 2014

    The technical losses quoted in this article seem rather high by North American standards. I recollect that EIA data suggests more like 3% of losses in the transmission system and 5% in the distribution system. Was the 22.5% technical loss figure specifically for, eg, India.


    • Lalit
      Oct 28, 2015

      It depends on calculation….in india i have generated thounsand of feeders in Cymdist..(cyme cooper power) application but while calculating the instantaneous tech loss report…%loss was ranging from 5 to 25% or more…but the same feeder if calculate with monthly load survey data it was below 5%.

      In india I think tech loss will nearly 5% or below.


  46. farouk
    Feb 28, 2014

    nice article , i hope if you can give me the reactive losses “QL ” expressed by tap position of the OLTC , i read an article give Vx and Vm represent the loss equation
    gradient vectors, and Vxx, Vmm are the corresponding Hessian matrixes :
    Vm=(∂QL)/∂m=2m/x_cc * (m * V2 – V1 * cos(θ_12 ) )
    (∂^2 QL)/(∂Vk ∂V_i )=(2V_2^2)/x_cc

    V_mm=(∂^2 Q_L)/(∂V_k ∂V_i )=(2V_2^2)/x_cc
    V_mx=[(∂^2 Q_L)/∂m∂θ , (∂^2 Q_L)/∂m∂V]
    (∂^2 Q_L)/∂m∂θ=[-(2V_2 V_1)/x_cc sin (θ_12 ) 0……..0]
    (∂^2 Q_L)/∂m∂V=[-2 ??/x_cc (V_1 cos (θ_12+2mV_2 ) ) 0 ] … (!!!!!)
    Xcc is the short circuit reactance of the transformer between bus 1 and bus 2 .
    i hope some one corrected this equation (!!!!!)
    thanks you .


  47. Babar
    Jan 06, 2014

    I have built a 50 KW Microhydel Power project. The Total No of house holds is 106. These house holds are to be electrified from the project. I want to transmit the voltage by stepping it up to 415/11000 Volts through step up transformer of 62.5 KVA. There are two other step down Distribution transformers of 25 KVA. I want to transmit the step up voltage by using GNAT ACSR over head conductor of 25 mm^2 an and want to use Rabbit AC of 50mm^2. Now i want to calculate The entire area of transmission net work is nearly 5 KM and distribution area is about 13 Km. I want to calculate the transmission and distribution line losses. Plz help me thanks


  48. Electrocita
    Sep 07, 2013

    hello,,, I study electrical engineering and I can’t understand some terms and the difference between them!!..can I get help???


    • Babar
      Jan 08, 2014

      What terms and differents you do not understand. Plz write them so that it would be easy for me to answer you Thank you


      • Babar
        Jan 08, 2014

        ACSR Stands for Alluminium conductors Steel Reinforced. GNAT(GEENAT) is used for Commercial Name of the overhead Conductors.
        Sorry it is not Rabbit AC it is Rabbit AAC(All alluminium Conductors)
        Pleas please help me to calculate losses in transmission and distribution lines

        Thank you very much


        • Babar
          Jan 08, 2014

          Sorry once again the entire area of Transmission is 5 Km and Distribution area is 13 Km


  49. abhilash dash
    Aug 30, 2013

    Nice article……..
    Post another good article on transmission and distribution netwok to me plz…..
    [email protected]


    • Babar
      Jan 09, 2014

      I have built a 50 KW Microhydel Power project for the community of a small village.The Total No of house holds is 106. These house holds are to be electrified from the project. I want to transmit the voltage by stepping it up to 415/11000 Volts through step up transformer of 62.5 KVA. There are two other step down Distribution transformers of 25 KVA. Total Distance for Transmission line is 4 Kilometer and for Distribution line, it is 12 Kilomenter.
      Plz help me in calculating of

      1- Size of Overhead conductor for Transmission and Distribution Line
      2- Losses in Transmission line
      3- Losses in Distribution line
      I shall be very thankful if some friends may help me
      2-

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