Reliability constrained multi-area adequacy planning using stochastic programming with sample-average approximations

This paper proposes a mixed-integer stochastic programming approach to the solution of generation and transmission line expansion planning problem including consideration of system reliability. Favorable 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. Reliability index used in this problem is expected cost of load loss as this index incorporates duration and magnitude of load loss. The objective is to minimize the expansion cost in the first stage and the operation and expected cost of load loss in the second stage. Due to exponentially large number of system states (scenarios) in large power systems, direct application of the L-shaped algorithm seems impractical. The expected cost of load loss is therefore approximated by considering only sampled scenarios and evaluated in the optimization. The estimated objective value is called sample-average approximation (SAA) of the actual expected value. In this paper, Monte Carlo sampling and Latin hypercube sampling techniques are implemented. Confidence intervals of upper and lower bound are discussed. The method is implemented to an actual 12-area power system for generation expansion planning and transmission line expansion planning. Index Terms--Latin hypercube sampling, Monte Carlo sampling, multi-area power system, power system optimization, reliability, sample-average approximation, stochastic programming, two-stage recourse model.