Skip to main content
Log in

Stochastic and minimum regret formulations for transmission network expansion planning under uncertainties

  • Theoretical Paper
  • Published:
Journal of the Operational Research Society

Abstract

After deregulation of the Power sector, uncertainty has increased considerably. Vertically integrated utilities were unbundled into independent generation, transmission and distribution companies. Transmission network expansion planning (TNEP) is now performed independent from generation planning. In this environment TNEP must include uncertainties of the generation sector as well as its own. Uncertainty in generation costs affecting optimal dispatch and uncertainty in demand loads are captured through composite scenarios. Probabilities are assigned to different scenarios. The effects of these uncertainties are transferred to the objective function in terms of total costs, which include: generation (dispatch), transmission expansion and load curtailment costs. Two formulations are presented: stochastic and minimum regret. The stochastic formulation seeks a design with minimum expected cost. The minimum regret formulation seeks a design with robust performance in terms of variance of the operational costs. Results for a test problem and a potential application to a real system are presented.

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

Access this article

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

Instant access to the full article PDF.

Figure 1

Similar content being viewed by others

References

  • Alguacil N, Motto AL and Conejo AJ (2003). Transmission expansion planning: A mixed-integer LP approach. IEEE Trans Power Syst 18: 1070–1077.

    Article  Google Scholar 

  • Al-Khayyal FA (1992). Generalized bilinear programming: Part I. Eur J Opns Res 60: 306–314.

    Article  Google Scholar 

  • Al-Khayyal FA and Falk JE (1983). Jointly constrained biconvex programming. Math Opns Res 8: 273–286.

    Article  Google Scholar 

  • Bunn DW, Larsen ER and Vlahos K (1993). Complementary modelling approaches for analyzing several effects of privatization on electricity investment. J Opl Res Soc 44: 957–971.

    Article  Google Scholar 

  • Buygi MO, Shanechi HM, Balzer G and Shahidehpour M . (2003). Transmission planning approaches in restructured power systems. Power Tech Conference Proceedings, Vol. 2, 2003, IEEE Bologna.

  • Cagigas C and Madrigal M . (2003). Centralized vs. competitive transmission expansion planning: The need for new tools, Vol. 2. IEEE: Toronto, Ont., Canada, pp. 1012–1017.

  • Cory BJ and Weedy BM (1998). Electric Power Systems. John Wiley & Sons: New York.

    Google Scholar 

  • De J. Silva I, Rider MJ, Romero R and Murari CA . (2005). Transmission network expansion planning considering uncertainness in demand. Power Engineering Society General Meeting, 2005, IEEE: San Francisco, CA, pp. 1051–1056.

  • De la Torre T, Feltes JW, Gomez San Roman T and Merrill HM (1999). Deregulation, privatization, and competition: Transmission planning under uncertainty. IEEE Trans Power Syst 14: 460–465.

    Article  Google Scholar 

  • Dodu JC and Merlin A (1981). Dynamic model for long-term expansion planning studies of power transmission systems: The Ortie Model. Int J Elec Power 3: 2–16.

    Article  Google Scholar 

  • Dyner I (2000). Energy modelling platforms for policy and strategy support. J Opl Res Soc 51: 136–144.

    Article  Google Scholar 

  • Dyner I and Larsen ER (2001). From planning to strategy in the electricity industry. Energy Pol 29: 1145–1154.

    Article  Google Scholar 

  • Fischl R, Guvenis A and Halpin TF (1982). Statistical power transmission network design. IEEE Trans Circuits Syst CAS-29 10: 679–687.

    Article  Google Scholar 

  • Gabriel SA, Garcia-Bertrand R, Sahakij P and Conejo AJ (2006). A practical approach to approximate bilinear functions in mathematical programming problems by using Schur's decomposition and SOS type 2 variables. J Opl Res Soc 57: 995–1004.

    Article  Google Scholar 

  • Gallego RA, Monticelli A and Romero R (1998). Comparative studies on non-convex optimization methods for transmission network expansion planning. IEEE Trans Power Syst 13: 822–828.

    Article  Google Scholar 

  • Haffner S, Monticelli A, Garcia A, Mantovani J and Romero R (2000). Branch and bound algorithm for transmission system expansion planning using a transportation model. IEE Proc Gener Trans Distrib 147: 149–156.

    Article  Google Scholar 

  • Hashimoto SHM, Romero R and Mantovani JRS (2003). Efficient linear programming algorithm for the transmission network expansion planning problem. IEE Proc Gener Trans Distrib 150: 536–542.

    Article  Google Scholar 

  • Horst R, Pardalos PM and Thoai NV (2000). Introduction to Global Optimization. Kluwer Academic Publisher: The Netherlands.

    Book  Google Scholar 

  • Kouvelis P and Yu G (1997). Robust Discrete Optimization and Its Applications. Kluwer Academic Publishers: Boston.

    Book  Google Scholar 

  • Larsen ER and Bunn DW (1999). Deregulation in electricity: Understanding strategic and regulatory risk. J Opl Res Soc 50: 337–344.

    Article  Google Scholar 

  • Malcolm SA and Zenios SA (1994). Robust optimization for power systems capacity expansion under uncertainty. J Opl Res Soc 45: 1040–1049.

    Article  Google Scholar 

  • Miranda V and Proenca LM (1998a). Why risk analysis outperforms probabilistic choice as the effective decision support paradigm for power system planning. IEEE Trans Power Syst 13: 643–648.

    Article  Google Scholar 

  • Miranda V and Proenca LM (1998b). Probabilistic choice vs. risk analysis—Conflicts and synthesis in power system planning. IEEE Trans Power Syst 13: 1038–1043.

    Article  Google Scholar 

  • Roman AJ (2002). Electricity deregulation in Canada: An idea which has yet to be tried? Alberta L Rev 40: 97–128.

    Google Scholar 

  • Sengupta JK (1991). Robust solutions in stochastic linear programming. J Opl Res Soc 42: 857–870.

    Article  Google Scholar 

  • Silver EA (2004). An overview of heuristic solution methods. J Opl Res Soc 55: 936–956.

    Article  Google Scholar 

  • Vajda S (1972). Probabilistic Programming. Academic Press: New York.

    Google Scholar 

  • Wen F and David AK (2001). Transmission planning and investment under competitive electricity market environment. IEEE 3: 1725–1730.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E Bustamante-Cedeño.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bustamante-Cedeño, E., Arora, S. Stochastic and minimum regret formulations for transmission network expansion planning under uncertainties. J Oper Res Soc 59, 1547–1556 (2008). https://doi.org/10.1057/palgrave.jors.2602492

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/palgrave.jors.2602492

Keywords

Navigation