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Allocation of active power losses to generators in electric power networks

  • Adedayo A. Yusuff , Thapelo C. Mosetlhe and Temitope Raphael Ayodele ORCID logo EMAIL logo
Published/Copyright: April 27, 2021
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International Journal of Emerging Electric Power Systems
From the journal International Journal of Emerging Electric Power Systems Volume 23 Issue 1

Abstract

This paper presents a method for allocating active power losses in electric power networks to generators. A technique that uses current distribution factor is used to allocate losses to generator nodes. The core of the allocation scheme is based on graph theory and flows distribution in a network. Losses are only allocated based on the segment of a network that is used for power evacuation. Models of IEEE 14, 39, 57 and 118 test systems in PYPOWER 5.12 were used to test the scheme. It was observed that although the total network losses is minimised when optimal power flow is used for scheduling generation, however that does not translate to minimisation of loss allocation to some generators. The results obtained show that, the scheme can be used to allocate transmission network losses to generation nodes in electric power networks in a fair manner.

Keywords: allocating active power losses; current distribution factor; generator nodes; graph theory; PYPOWER
Corresponding author: Temitope Raphael Ayodele, Electrical and Mining Engineering Department, College of Science and Technology, University of South Africa, Cnr Christiaan de Wet and Pioneer Roads, Pretoria, Florida, South Africa; and Power Energy Machine and Drive Research Group (PEMD), Department of Electrical and Electronic Engineering, Faculty of Technology, University of Ibadan, Ibadan, Nigeria, E-mail:

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix

Consider a node nα that has inflow edges ei, ej and outflow edges ek, el and em. Let the currents that flow in the outflow edges, when only edge ei is supplying current Ii to node nα, be Iki, Ili and Imi. Similarly, the currents that flow in outflow edges when only edge ej is supplying current to node nα are Ikj, Ilj and Imj.

(23)Ii=Iki+Ili+Imi=∑q∈outflowIqi
(24)Ij=Ikj+Ilj+Imj=∑q∈outflowIqj
(25)Ik=Iki+Ikj=∑p∈inflowIkp
(26)Il=Ili+Ilj=∑p∈inflowIlp
(27)Im=Imi+Imj=∑p∈inflowImp
(28)∑q∈outflowIq=∑p∈outflowIp
(29)1=Iki∑q∈outflowIqi+Ili∑q∈outflowIqi+Imi∑q∈outflowIqi=drki+drli+drmiDo
(30)1=Ikj∑q∈outflowIqj+Ilj∑q∈outflowIqj+Imj∑q∈outflowIqj=drkj+drlj+drmj
(31)1=Iki∑p∈inflowIkp+Ikj∑p∈inflowIkp=crki+crkj
(32)1=Ili∑p∈inflowIlp+Ilj∑p∈inflowIlp=crli+crlj
(33)1=Imi∑p∈inflowImp+Imj∑p∈inflowImp=crmi+crmj

A Current inflow and outflow to a node

Let the set of inflow edges be I such that if i is an inflow edge, then i∈I, similarly, let the set of outflow edges be O, such that if l is an outflow edge, then l∈O Current flow in any inflow branch

Ij=∑i∈Ii≠j((Vj−Vi)∏l∈Om∈Im≠i≠jRmRl)+∑n∈O((Vj−Vn)∏i∈Il∈Oi≠j,l≠nRiRl)∑j∈I(∏i∈Il∈Oi≠jRiRj)+∑n∈O(∏l∈Oi∈Il≠nRlRi)

Current flow in any outflow branch

Ik=∑j∈I((Vj−Vk)∏i∈Il∈Ol≠k,i≠jRiRl)+∑n∈O((Vn−Vk)∏i∈Il∈Ol≠k≠nRiRl)∑j∈I(∏i∈Il∈Oi≠jRiRj)+∑n∈O(∏l∈Oi∈Il≠nRlRi)

Inflow current contribution

crj=∑i∈Ii≠j((Vj−Vi)∏l∈Om∈Im≠i≠jRmRl)+∑n∈O((Vj−Vn)∏i∈Il∈Oi≠j,l≠nRiRl)∑j∈I(∑i∈Ii≠j((Vj−Vi)∏l∈Om∈Im≠i≠jRmRl)+∑n∈O((Vj−Vn)∏i∈Il∈Oi≠j,l≠nRiRl))

Outflow current distribution

drk=∑j∈I((Vj−Vk)∏i∈Il∈Ol≠k,i≠jRiRl)+∑n∈O((Vn−Vk)∏i∈Il∈Ol≠k≠nRiRl)∑k∈O(∑j∈I((Vj−Vk)∏i∈Il∈Ol≠k,i≠jRiRl)+∑n∈O((Vn−Vk)∏i∈Il∈Ol≠k≠nRiRl))

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Received: 2021-01-26
Accepted: 2021-04-19
Published Online: 2021-04-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Pre-diagnosis technology for short-circuit withstand capability of distribution transformer based on big data
  4. Residual flux impact in controlled switching of HVDC converter transformer
  5. A novel transient search optimization for optimal allocation of multiple distributed generator in the radial electrical distribution network
  6. Characterization of nano-additive filled epoxy resin composites (ERC) for high voltage gas insulated switchgear (GIS) applications
  7. An intelligent approach towards very short-term load forecasting
  8. Allocation of active power losses to generators in electric power networks
  9. Optimization of controller gains to enhance power quality of standalone wind energy conversion system
  10. A flexible power management strategy for PV-battery based interconnected DC microgrid
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https://doi.org/10.1515/ijeeps-2021-0014
Keywords for this article
allocating active power losses; current distribution factor; generator nodes; graph theory; PYPOWER

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Pre-diagnosis technology for short-circuit withstand capability of distribution transformer based on big data
  4. Residual flux impact in controlled switching of HVDC converter transformer
  5. A novel transient search optimization for optimal allocation of multiple distributed generator in the radial electrical distribution network
  6. Characterization of nano-additive filled epoxy resin composites (ERC) for high voltage gas insulated switchgear (GIS) applications
  7. An intelligent approach towards very short-term load forecasting
  8. Allocation of active power losses to generators in electric power networks
  9. Optimization of controller gains to enhance power quality of standalone wind energy conversion system
  10. A flexible power management strategy for PV-battery based interconnected DC microgrid
  11. Slow flow solutions and stability analysis of single machine to infinite bus power systems
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