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

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

Abstract

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.

Keywords

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

\({{\varvec{I}}}(ij)\)

Phasor current of branch ij

\({{\varvec{I}}}(ij,k)\)

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

\({\varvec{I}}_{\mathrm{c}}(ij)\)

Phasor current of branch ij with DGs

\({\varvec{I}}_{\mathrm{DG}}(ij)\)

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

PLoss

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

R(ij)

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

ST(ij)

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

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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

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

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