Maximum Loading Problems Using Stochastic Nonlinear Programming and Confidence Intervals

This paper presents a stochastic non-linear program (S-NLP) with a confidence interval constraint. The problem extends the conventional maximum loading problem to include randomness and uncertainty in system loading levels. The problem restricts the 99% confidence interval of the loading level to be within a pre-specified amount of the mean. The paper presents solutions when the confidence interval is restricted to be within 15, 20, and 25% of the mean. The proposed solution methodology is tested using the IEEE 30 bus system and results are compared against solutions found using Monte Carlo simulations. Each of the Monte Carlo simulations consist of 10,000 samples.