A Generic Convex Model for a Chance-Constrained Look-Ahead Economic Dispatch Problem Incorporating an Efficient Wind Power Distribution Modeling

Power systems with high penetration of wind resources must cope with significant uncertainties originated from wind power prediction error. This uncertainty might lead to wind power curtailment and load shedding events in the system as a big challenge. Efficient modeling and incorporation of wind power uncertainty in generation and reserve scheduling can prevent these events. This paper presents a new framework for wind power cumulative distribution function (CDF) modeling and its incorporation in a new chance-constrained economic dispatch (CCED) problem. The proposed CDF modeling uses few moments of wind power random samples. To validly capture the actual features of the wind power distribution such as main mass, high skewness, tails, and especially boundaries from the moments, an efficient moment problem is presented and solved using the beta kernel density representation (BKDR) technique. Importantly, a new polynomial cost function for efficient modeling of wind power misestimation costs is proposed for the CCED problem that eliminates the need for an analytical CDF and enables the use of an accurate piecewise linearization technique. Using this technique, the non-linear CCED problem is converted to a mixed-integer linear programming (MILP)-based problem that is convex with respect to the continuous variables of the problem. Therefore, it is solved via off-the-shelf mathematical programming solvers to reach more optimal results. Numerical simulations using the IEEE 118-bus test system show that compared with conventional approaches, the proposed MILP-based model leads to lower power system total cost, and thereby is suggested for practical applications.