Skip to main content
SpringerLink
Log in

A novel method for transmission system cost allocation with better accuracy and fairness

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

This paper proposes an integrated method for the accurate and fair cost allocation of the transmission system among the users (generators and loads) of the network. It mitigates the existing research gaps and implementation issues in the marginal participation approach for network cost allocation. Major challenges in the marginal participation approach are 1) fair selection of economic slack busses 2) inaccuracy due to use of DC power flow 3) treatment of the counter flows and 4) enforcement of cost-causality. While the prior art has addressed the sub-problems individually, an integrated approach has been missing. This work fills this research gap. Besides, it for the first time introduces the use of linearized AC power flow for calculating the marginal flows. This provides a major improvement over the DC power flow model as nominal voltage and reactive power variables can be modeled without compromising linearity. Economic slack bus selection by min-max fairness approach, modelling of counter flows without resulting in negative cost-shares (payoffs), enhancement of cost-causality by segregating usage cost, reliability cost, and residual costs are other salient contributions of the proposed work. These features result in a rigorously fair, accurate, and yet tractable method computationally. Case-studies on many systems including the IEEE-118 bus system demonstrate the claims made.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

Abbreviations

\(\Delta V_{l}\) :

Deviation in voltage magnitude from 1 p.u. at bus l

\(\Delta V_{m}\) :

Deviation in voltage magnitude from 1 p.u. at bus m

\(\delta _{l}\) :

Phase angle of voltage at bus l

\(\delta _{m}\) :

Phase angle of voltage at bus m

\(\mathbf {P_G}\) :

Vector of active power injection at buses

\(\mathbf {P_L}\) :

Vector of active power withdrawal at buses

\(\mathbf {P_{line}}\) :

Active line-power flow vector

\(\mathbf {Q_L}\) :

Vector of reactive power withdrawal at load buses

\(\mathbf {Q_{line}}\) :

Reactive line-power flow vector

\(\mathbf {S_P}\) :

Sensitivity matrix for active line-power flows

\(\mathbf {S_p}\) :

Sensitivity matrix for active line-power flows for change in active power injection at all buses

\(\mathbf {S_Q}\) :

Sensitivity matrix for reactive line-power flows

\(\mathbf {S_q}\) :

Sensitivity matrix for active line-power flows for change in reactive power injection at (P-Q) buses

\(\mathbf {S}\) :

Sensitivity matrix for active and reactive line-power flows

\(\Omega _i\) :

The set of buses adjacent to bus i

\(\phi _L\) :

The angle between the voltage and current at the load busses

\(b_{lm0}\) :

Shunt susceptance (as per \(\pi \) model) - half of total shunt susceptance of line lm, a positive value

\(b_{lm}\) :

Series susceptance of line lm, a negative value

\(b_{sh_i}\) :

Net shunt susceptance at bus i, a positive value for shunt capacitor and a negative value for shunt reactor

\(c_{lm}\) :

Capacity based cost-rate for line lm

\(g_{lm}\) :

Series conductance of line lm, a positive value

\(M_k\) :

Set of entities whose price have been fixed in \(k^{th}\) LP \(M_0=\{\phi \}\)

n :

Number of buses

n :

Number of the busses in the system

\(n_D\) :

(\(2\times n_G \times n_L +1\))

\(n_E\) :

Total number of entities (\(n_L+n_G\))

\(n_G\) :

Number of the generator busses in the system

\(n_L\) :

Number of the load busses in the system

\(n_l\) :

Number of lines

\(NetCombCost_{LAC}\) :

Network combined cost for ‘extent of use’ and reliability capacity using LAC framework

\(NetEOUCost_{LAC}\) :

‘Extent of use’ cost of the network using LAC framework

\(NetRelCapCost_{LAC}\) :

Network reliability capacity cost obtained using LAC framework

\(P_i^{inj}\) :

Active power injected at bus i

\(P_{lm_{LAC}}\) :

Active power flow in line lm using LAC framework

\(P_{lm}\) :

Active power flow on line from bus l to bus m using DC power flow

\(P_{{REL}_{lm_{LAC}}}\) :

Reliability capacity in line lm using LAC framework

\(Q_i^{inj}\) :

Reactive power injected at bus i

\(Q_{lm_{LAC}}\) :

Reactive power flow on line from bus l to bus m using LAC framework

\(RC_{INT}\) :

Residual capacity cost with reliability is in LAC framework

\(RC_{LAC}\) :

Residual capacity cost in LAC framework

\(S_k\) :

\(S_k = S_{k-1} \setminus M_k\) (\(S_0=\{N\}\))

TotNetCost :

Total network cost to be recovered

TotNetMW :

Total network MW capacity of generator injection and load withdrawals of all participating entities

\(V_{l}\) :

Bus voltage magnitude in p.u. at bus l

\(V_{m}\) :

Bus voltage magnitude in p.u. at bus m

\(z_k^*\) :

Optimal value of \(z_k\)

\(z_{k}\) :

Dummy variable in \(k^{th}\) LP problem

\({\mathbf {d}}\) :

Vector of unknown variables in \(\mathbf {LP}\) \({\mathbf {d}}\in R_+^{n_D}\)

EOU :

Extent of use

LAC :

Linearized AC power flow

LP :

Linear programming

References

  1. I J Perez-Arriaga 2013 Regulation of the Power Sector. Power Systems. Springer London

    Book  Google Scholar 

  2. Richard Green 1997 Electricity transmission pricing: an international comparison. Utilities Policy, 6(3): 177–184

    Article  Google Scholar 

  3. Jean-Michel Glachant 2003 Features of Transmission Tariffs in Europe. In: Transport Pricing of Electricity Networks, Francois Leveque, editor, chapter 8, pages 205–224. Kluwer Academic Publishers

  4. Dariush Shirmohammadi, Paul R Gribik, Eric T K Law, James H Malinowski and Richard E O’Donnell 1989 Evaluation of transmission network capacity use for wheeling transactions.IEEE Transactions on Power Systems, 4(4): 1405–1413

    Article  Google Scholar 

  5. F D Galiana, A J Conejo and H A Gil 2003 Transmission network cost allocation based on equivalent bilateral exchanges. IEEE Transactions on Power Systems, 18(4): 1425–1431

    Article  Google Scholar 

  6. S Nojeng, M Y Hassan, D M Said, M P Abdullah and F Hussin 2014 Improving the mw-mile method using the power factor-based approach for pricing the transmission services. IEEE Transactions on Power Systems, 29(5): 2042–2048

    Article  Google Scholar 

  7. A J Conejo, J Contreras, D A Lima and A Padilha-Feltrin 2007 Z\(_{\rm bus}\) transmission network cost allocation. IEEE Transactions on Power Systems, 22(1): 342–349

  8. S Pouyafar, M T Hagh and K Zare 2019 Development of a circuit-theory based transmission cost allocation method by orthogonal projection and equal-sharing principle. CSEE Journal of Power and Energy Systems, 5(2): 159–170

  9. Ignacio J Perez-Arriaga, F J Rubio, J F Puerta, J Arceluz and J  Marin 1995 Marginal pricing of transmission services: An analysis of cost recovery. IEEE Transactions on Power Systems, 10(1): 546–553

    Article  Google Scholar 

  10. H  Rudnick, R Palma and J E Fernandez 1995 Marginal pricing and supplement cost allocation in transmission open access. IEEE Transactions on Power Systems, 10(2): 1125–1132

    Article  Google Scholar 

  11. Carlos Vazquez, Luis Olmos and Igancio J Perez-Arriaga 2002 On the selection of the slack bus in mechanisms for transmission network cost allocation that are based on network utilization. 15\(^{th}\)Power System Computing Conference, PSCC, Seville

  12. Z  Yang, H  Zhong, Q  Xia, C  Kang, T  Chen and Y Li 2016 A structural transmission cost allocation scheme based on capacity usage identification. IEEE Transactions on Power Systems, 31(4): 2876–2884

    Article  Google Scholar 

  13. K L Lo, M Y Hassan and S Jovanovic 2007 Assessment of mw-mile method for pricing transmission services: a negative flow-sharing approach. Generation, Transmission Distribution, IET, 1(6): 904–911

    Article  Google Scholar 

  14. A M L da Silva, J G de Carvalho Costa and L H Lopes Lima 2013 A new methodology for cost allocation of transmission systems in interconnected energy markets. IEEE Transactions on Power Systems, 28(2): 740–748

    Article  Google Scholar 

  15. G  A Orfanos, P  S Georgilakis and N  D Hatziargyriou 2013 A more fair power flow based transmission cost allocation scheme considering maximum line loading for n-1 security. IEEE Transactions on Power Systems, 28(3): 3344–3352

    Article  Google Scholar 

  16. M S S Rao and S A Soman 2015 Marginal pricing of transmission services using min-max fairness policy.IEEE Transactions on Power Systems, 30(2): 573–584

    Article  Google Scholar 

  17. R  Mehta and S  A Soman 2016 Efficient cost allocation for transmission system. In: 2016 IEEE International Conference on Power System Technology (POWERCON), pages 1–6

  18. Telles D  A Lima, J  Contreras and N  Alguacil 2017 A new transmission tariff allocation model based on bilevel programming. IEEE Transactions on Power Systems, 32(3): 2204–2213

  19. A M Leite da Silva, J G d C Costa, L H L Lima, C R R Dornellas, Z S Machado and J C O Mello 2017 Transmission network cost allocation via nodal methodology considering different dispatching scenarios and tariff zones. In: 2017 IEEE Manchester PowerTech, pages 1–6

  20. Rashesh P Mehta, M S S Rao and S A Soman 2020 A cost-causal marginal participation method using min-max fairness for transmission services cost allocation. Sadhana, 45(1): 183

  21. Ignacio J Perez-Arriaga and Yves Smeers 2003 Guidelines on Tariff Setting. In: Transport Pricing of Electricity Networks, Francois Leveque, editor, chapter 7, pages 175–203. Kluwer Academic Publishers

  22. Richard Green 2003 Cost recovery and the efficient development of the grid. In: Transport Pricing of Electricity Networks, Francois Leveque, editor, chapter 5, pages 175–203. Kluwer Academic Publishers

  23. CERC Regulations. Central Electricity Regulatory Commission (Sharing of Inter-state Transmission Charges and Losses) Regulations, 2020, May 2020

  24. Zhaoxia Jing, Xianzhong Duan, Fushuan Wen, Yixin Ni and F F Wu 2003 Review of transmission fixed costs allocation methods. In: Power Engineering Society General Meeting, IEEE, volume 4, page 2592

  25. CERC India Central electricity regulatory commission (sharing of inter state transmission charges and losses) regulations, 2010. Technical report, Central Electricity Regulatory Commission, June 2010

  26. R  Romero, A  Monticelli, A Garcia and S  Haffner 2002 Test systems and mathematical models for transmission network expansion planning. Generation, Transmission and Distribution, IEE Proceedings-, 149(1): 27–36

    Article  Google Scholar 

  27. N Alguacil, A L Motto and A J Conejo 2003 Transmission expansion planning: a mixed-integer LP approach. IEEE Transactions on Power Systems, 18(3): 1070–1077

    Article  Google Scholar 

  28. RichardP O’Neill, EricA Krall, Kory W Hedman and Shmuel S Oren 2013 A model and approach to the challenge posed by optimal power systems planning. Mathematical Programming, 140(2): 239–266

    Article  MathSciNet  Google Scholar 

  29. Hui Zhang, G T Heydt, V  Vittal and J  Quintero 2013 An Improved Network Model for Transmission Expansion Planning Considering Reactive Power and Network Losses. IEEE Transactions on Power Systems, 28(3): 3471–3479

    Article  Google Scholar 

  30. Saverio Bolognani and Sandro Zampieri 2016 On the existence and linear approximation of the power flow solution in power distribution networks. IEEE Transactions on Power Systems, 31(1): 163–172

  31. J  W Bialek 1996 Tracing the flow of electricity. Proc. Inst. Elect. Eng. Gen., Transm., Distrib., 143(4): 313–320

  32. J  Bialek 1997 Topological generation and load distribution factors for supplement charge allocation in transmission open access. IEEE Transactions on Power Systems, 12(3): 1185–1193

    Article  Google Scholar 

  33. J  W Bialek and P  A Kattuman 2004 Proportional sharing assumption in tracing methodology. IEE Proceedings-Generation, Transmission and Distribution, 151(4): 526–532

    Article  Google Scholar 

  34. A  Bakirtzis, P  Biskas, A  Maissis, A  Coronides, J  Kabouris and M  Efstathiou 2001 Comparison of two methods for long-run marginal cost-based transmission use-of-system pricing. 2001 Generation, Transmission and Distribution, IEE Proceedings-, 148(5): 477–481

  35. R  Allan Kirschen and G Strbac 2007 Implicit Slack Bus in the Calculation of Transmission Tariffs for the LRMC Methodology, PSR Tech. Rep

    Google Scholar 

  36. M  Junqueira, L C da Costa, L A Barroso, G C Oliveira, L M Thome, and M V Pereira 2007 An aumann-shapley approach to allocate transmission service cost among network users in electricity markets. IEEE Transactions on Power Systems, 22(4): 1532–1546

    Article  Google Scholar 

  37. Y P Molina, O R Saavedra and H  Amaris 2013 Transmission Network Cost Allocation Based on Circuit Theory and the Aumann-Shapley Method. IEEE Transactions on Power Systems, 28(4): 4568–4577

    Article  Google Scholar 

  38. R D Zimmerman, C E Murillo-Sanchez 2020 MATPOWER (Version 7.1) [Software], August 2011

  39. R D Zimmerman, C E Murillo-Sanchez and R J Thomas 2011 MATPOWER: Steady-State Operations, Planning and Analysis Tools for Power Systems Research and Education. IEEE Transactions on Power Systems, 26(1): 12–19

    Article  Google Scholar 

  40. John W Eaton, David Bateman, Søren Hauberg and Rik Wehbring 2020 GNU Octave version 6.1.0 manual: a high-level interactive language for numerical computations

  41. R D Christie, B F Wollenberg and I Wangensteen 2000 Transmission management in the deregulated environment. Proceedings of the IEEE, 88(2): 170–195, Feb 2000

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, Birla Vishvakarma Mahavidyalaya Engineering College, Vallabh Vidyanagar, Gujarat, India

    Rashesh P Mehta

  2. Department of Electrical Engineering, IIT Bombay, Mumbai, India

    S A Soman & M S S Rao

Authors
  1. Rashesh P Mehta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S A Soman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M S S Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rashesh P Mehta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mehta, R.P., Soman, S.A. & Rao, M.S.S. A novel method for transmission system cost allocation with better accuracy and fairness. Sādhanā 47, 62 (2022). https://doi.org/10.1007/s12046-022-01835-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-022-01835-0

Keywords

Search

Navigation