Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 1977–1988 | Cite as

Exact Cross-Term Decomposition Method for Loss Allocation in Contemporary Distribution Systems

  • Pankaj Kumar
  • Nikhil GuptaEmail author
  • K. R. Niazi
  • Anil Swarnkar
Research Article - Electrical Engineering


High penetration of distributed generation (DG) units in contemporary distribution systems can contribute significantly towards loss reduction in distribution feeders. The loss allocation method should reward the benefit of loss reduction to DG owners (DGOs), instead of diverting the same to the load points which actually never contribute towards loss reduction. This paper presents an exact cross-term decomposition method that decomposes each crossed term of power loss/remuneration among contributing network users while independently addressing their active and reactive power transactions. Separate allocation factors are proposed to decompose each individual crossed term involved. The allocation factors are not based upon heuristic, as in several existing methods, but are derived analytically. The method employs superposition principle to evaluate contributing currents of DGs. Thereafter, the losses/remunerations are allocated fairly among network users by suggesting a suitable remuneration strategy for DGOs. The proposed method is investigated on standard test distribution system. The application results are promising compared with other established methods.


Active distribution systems Circuit theory-based method Distributed generations Loss allocation Superposition 

List of symbols

\(\hbox {CDG}(ij)\)

Set of contributing DG currents in branch ij

\(\hbox {CN}(ij)\)

Set of contributing node currents in branch ij

\(\hbox {CT}^{\mathrm{a}}(ij)/\hbox {CT}^{\mathrm{r}}(ij)\)

Crossed term for active/reactive component of contributing currents in branch ij

\(\hbox {CT}^{\mathrm{a}}(ij, k))/\hbox {CT}^{\mathrm{r}}(ij, k)\)

Crossed term related to active/reactive component of contributing node current I(n(ij,k)) in branch ij

\(\hbox {CT}_{\mathrm{DG}}^\mathrm{a} \left( {ij,p} \right) /\hbox {CT}_{\mathrm{DG}}^\mathrm{r} \left( {ij,p} \right) \)

Crossed term for active/reactive component of contributing pth DG currents in branch ij


Phasor current of branch ij


Contributing phasor current of \(k\hbox {th}\) node in branch ij


Phasor current of branch ij with DGs


Phasor sum of contributing DG currents in branch ij

\(L^{\mathrm{a}}(ij, k)/L^{\mathrm{r}}(ij, k)\)

Loss allocation factor to bifurcate CT\(^{\mathrm{a}}\)(ij, k)/CT\(^{\mathrm{r}}\)(ij, k)

\({\hbox {MT}}_{\mathrm{DG}}(ij, p)\)

Mixed term related to pth contributing DG current in branch ij

\({N}/{\hbox {NB}}/{\hbox {NDG}}\)

Total nodes/branches/DGs in the distribution system


Total real power loss in the system

\(\hbox {Ploss}(ij)\)

Power loss of branch ij

\(\hbox {ploss}(ij, k)\)

Power loss of branch ij allocated to \(k\hbox {th}\) contributing node

\(\hbox {ploss}(k)\)

Power loss allocated to \(k\hbox {th}\) contributing node


Resistance of branch ij

\(R^{\mathrm{a}}(ij, p)/R^{\mathrm{r}}(ij, p)\)

Remuneration allocation factor to bifurcate \(\hbox {CT}_{\mathrm{DG}}^\mathrm{a} \left( {ij,p} \right) /\hbox {CT}_{\mathrm{DG}}^r \left( {ij,p} \right) \)

\(R_{\hbox {DG}}(ij)\)

Remuneration of DG through the branch ij

\(R_{\hbox {DG}}(ij, p)\)

Remuneration of pth DG through the branch ij

\(\mathfrak {R}\{x\}/\hbox {Im}\{{{\varvec{x}}}\}\)

Real/imaginary part of complex quantity x


Sum of squared term of contributing node currents in branch ij

\(\hbox {ST}_{\mathrm{DG}}(ij, p)\)

Squared term of contributing pth DG current in branch ij


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atanasovski, M.; Taleski, R.: Power summation method for loss allocation in radial distribution networks with DG. IEEE Trans. Power Syst. 26(4), 2491–2499 (2011)Google Scholar
  2. 2.
    Atanasovski, M.; Taleski, R.: Energy summation method for loss allocation in radial distribution networks with DG. IEEE Trans. Power Syst. 27(3), 1433–1440 (2012)Google Scholar
  3. 3.
    Gonzalez, J.J., Basagoiti, P.: Spanish power exchange market and information system. Design concepts, and operating experience In: Proceedings of 1999 IEEE Power Industry Computer Applications ConferenceGoogle Scholar
  4. 4.
    Bialek, J.W., Ziemianek, S., Abi-Samra, N.: Tracking-based loss allocation and economic dispatch. In: Proceedings of 13th Power Systems Computation Conference, Trondheim, Norway, July 1999, pp. 375–381Google Scholar
  5. 5.
    Bialek, J.W.: Topological generation and load distribution factors for supplement charge allocation in transmission open access. IEEE Trans. Power Syst. 12(3), 1185–1193 (1997)Google Scholar
  6. 6.
    Kirschen, D.; Allan, R.; Strbac, G.: Contributions of individual generators to loads and flows. IEEE Trans. Power Syst. 12(1), 52–60 (1997)Google Scholar
  7. 7.
    Kashyap, S.S.; De, M.: Loss allocation and loss minimisation for radial distribution system including DGs. IET Renew. Power Gener. 11(6), 806–818 (2017)Google Scholar
  8. 8.
    Elgerd, O.I.: Electric Energy Systems Theory: An Introduction. McGraw-Hill, New York (1982)Google Scholar
  9. 9.
    Galiana, F.D.; Conejo, A.J.; Kockar, I.: Incremental transmission loss allocation under pool dispatch. IEEE Trans. Power Syst. 17(1), 26–33 (2002)Google Scholar
  10. 10.
    Expósito, A.G.; Santos, J.M.R.; Garćia, T.G.; Velasco, E.A.R.: Fair allocation of transmission power losses. IEEE Trans. Power Syst. 15(1), 184–188 (2000)Google Scholar
  11. 11.
    Costa, P.M.; Matos, M.A.: Loss allocation in distribution networks with embedded generation’. IEEE Trans. Power Syst. 19(1), 384–389 (2004)Google Scholar
  12. 12.
    Mutale, J.; Strbac, G.; Curcic, S.; Jenkins, N.: Allocation of losses in distribution systems with embedded generation. IEE Proc. Gener. Transm. Distrib. 147(1), 7–14 (2000)Google Scholar
  13. 13.
    Conejo, A.J.; Galiana, F.D.; Kochar, I.: \(Z\)-bus loss allocation. IEEE Trans. Power Syst. 16(1), 105–110 (2001)Google Scholar
  14. 14.
    Fang, W.L.; Ngan, H.W.: Succinct method for allocation of network losses. IEE Proc. Gener. Transm. Distrib. 149(2), 171–174 (2002)Google Scholar
  15. 15.
    Carpaneto, E.; Chicco, G.; Akilimali, J.S.: Branch current decomposition method for loss allocation in radial distribution systems with distributed generation. IEEE Trans. Power Syst. 21(3), 1170–1179 (2006)Google Scholar
  16. 16.
    Savier, J.S.; Das, D.: Energy loss allocation in radial distribution systems: a comparison of practical algorithms. IEEE Trans. Power Deliv. 24(1), 260–267 (2009)Google Scholar
  17. 17.
    Kumar, P.; Gupta, N.; Niazi, K.R.; Swarnkar, A.: Current decomposition method for loss allocation in distribution systems. IET Gener. Transm. Distrib. (2017). Google Scholar
  18. 18.
    Peng, J.C.; Jiang, H.; Song, Y.H.: A weakly conditioned imputation of an impedance-branch dissipation power. IEEE Trans. Power Syst. 22(4), 2124–2133 (2007)Google Scholar
  19. 19.
    Ghofrani-Jahromi, Z.; Mahmoodzadeh, Z.; Ehsan, M.: Distribution loss allocation for radial systems including DGs. IEEE Trans. Power Del. 29(1), 72–80 (2014)Google Scholar
  20. 20.
    Sharma, S.; Abhyankar, A.R.: Loss allocation for weakly meshed distribution system using analytical formulation of shapley value. IEEE Trans. Power Syst. 32(2), 1369–1377 (2016)Google Scholar
  21. 21.
    Molina, Y.P.; Prada, R.B.; Saavedra, O.R.: Complex losses allocation to generators and loads based on circuit theory and aumann-shapley method. IEEE Trans. Power Syst. 25(4), 1928–1936 (2010)Google Scholar
  22. 22.
    Jagtap, K.M.; Khatod, D.K.: Loss allocation in radial distribution networks with different load models and distributed generations. IET Gener. Transm. Distrib. 9(12), 1275–1291 (2015)Google Scholar
  23. 23.
    Jagtap, K.M.; Khatod, D.K.: Novel approach for loss allocation of distribution networks with DGs. Electr. Power Syst. Res. 143, 303–311 (2017)Google Scholar
  24. 24.
    Lim, V.S.C.; McDonald, J.D.F.; Saha, T.K.: Development of a new loss allocation method for a hybrid electricity market using graph theory. Electr. Power Syst. Res. 79(2), 301–310 (2009)Google Scholar
  25. 25.
    Baran, M.E.; Wu, F.F.: Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Del. 4(2), 1401–07 (1989)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Pankaj Kumar
    • 1
  • Nikhil Gupta
    • 1
    Email author
  • K. R. Niazi
    • 1
  • Anil Swarnkar
    • 1
  1. 1.Department of Electrical EngineeringMalaviya National Institute of Technology JaipurJaipurIndia

Personalised recommendations