  This paper describes the application of a Progressive Hedging (PH) algorithm
to the least-cost var planning under uncertainty. The method PH is a
scenario-based decomposition technique for solving stochastic programs, i.e.,
it decomposes a large scale stochastic problem into s deterministic subproblems
and couples the decision from the s subproblems to form a solution for the
original stochastic problem. The effectiveness and computational performance of
the proposed methodology will be illustrated with var planning studies for the
IEEE 24-bus system (5 operating scenarios), the 200-bus Bolivian system (1,152
operating scenarios) and the 1,600-bus Colombian system (180 scenarios).

Optimization and Control;Computational Engineering, Finance, and Science;Systems and Control;Systems and Control