Handbook of Networks in Power Systems I pp 505-522 | Cite as

# Power System Reliability Considerations in Energy Planning

## Abstract

We discuss how to incorporate reliability considerations into power system expansion planning problem. Power system reliability indexes can be broadly categorized as probabilistic and deterministic. Increasingly, the probabilistic criteria have received more attention from the utilities since these can more effectively deal with the uncertainty in system parameters. We propose a stochastic programming framework to effectively incorporate random uncertainties in generation, transmission line capacity and system load for the expansion problem. Favourable system reliability and cost trade off is achieved by the optimal solution. The problem is formulated as a two-stage recourse model where random uncertainties in area generation, transmission lines, and area loads are considered. Power system network is modelled using DC flow analysis. Reliability index used in this problem is the expected cost of load loss as it incorporates duration and magnitude of load loss. Due to exponentially large number of system states (scenarios) in large power systems, we apply sample-average approximation (SAA) concept to make the problem computationally tractable. The method is implemented on the 24-bus IEEE reliability test system.

## Keywords

Energy planning power system reliability sample average approximation stochastic programming## References

- 1.Zhu J, Chow M (1997) A review of emerging techniques on generation expansion planning. IEEE Trans Power Syst 12(4):1722–1728CrossRefGoogle Scholar
- 2.Infanger G (1993) Planning under uncertainty: solving large-scale stochastic linear programs. Boyd & Fraser, DanversGoogle Scholar
- 3.Jirutitijaroen P, Singh C (2008) Reliability constrained multi-area adequacy planning using stochastic programming with sample-average approximations. IEEE Trans Power Syst 23(2):504–513CrossRefGoogle Scholar
- 4.Jirutitijaroen P, Singh C (2008) Composite-system generation adequacy planning using stochastic programming with sample-average approximation. In: Proceedings of the 16th power systems computation conference, Glasgow, 2008Google Scholar
- 5.Jirutitijaroen P, Singh C (2008) Unit availability considerations in composite-system generation planning. In: Proceedings of the 10th international conference on probabilistic methods applied to power systems, Rincon, 2008Google Scholar
- 6.Birge JR, Louveaux F (1997) Introduction to stochastic programming. Duxbury, BelmontzbMATHGoogle Scholar
- 7.Higle JL, Sen S (1996) Stochastic decomposition: a statistical method for large scale stochastic linear programming. Kluwer Academic, The NetherlandsCrossRefzbMATHGoogle Scholar
- 8.Jirutitijaroen P, Singh C (2008) Comparative study of system-wide reliability-constrained generation expansion problem. In: Proceedings of the 3th international conference on electric utility deregulation and restructuring and power technologies, Nanjing, 2008Google Scholar
- 9.IEEE APM Subcommittee (1999) The IEEE Reliability Test System-1996. IEEE Trans Power Syst 14(3):1010–1020CrossRefGoogle Scholar
- 10.Lawton L, Sullivan M, Liere KV, Katz A, Eto J (2003) A framework and review of customer outage costs: integration and analysis of electric utility outage cost surveys. Lawrence Berkeley National Laboratory. Paper LBNL-54365. http://repositories.cdlib.org/lbnl/LBNL-54365. Accessed 1 Nov 2003
- 11.Mak WK, Morton DP, Wood RK (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper Res Lett 24:47–56MathSciNetCrossRefzbMATHGoogle Scholar
- 12.Linderoth JT, Shapiro A, Wright SJ (2006) The empirical behavior of sampling methods for stochastic programming. Ann Oper Res 142(1):215–241MathSciNetCrossRefzbMATHGoogle Scholar
- 13.Verweij B, Ahmed S, Kleywegt AJ, Nemhauser G, Shapiro A (2003) The sample average approximation method applied to stochastic routing problems: a computational study. Comput Optim Appl 24:289–333MathSciNetCrossRefzbMATHGoogle Scholar