2.4.1 Optimization criteria and Objective function:
A multi-objective optimization problem is formulated to meet these requirements. The implicit function F(ts, td) is used to describe the relationship between the objective and decision variables, whose value can be calculated by stochastic short-term simulation. F(•) can be Levelized Cost of Energy (LCOE) and Net present Cost (NPC), corresponding to reliability, economic, and environmental objectives. To make a compromise among conflicting requirements, a weighted-sum approach is introduced to integrate all these objectives into a single objective function
where S[•] denotes the normalized form of objective function, as shown in Equation 15 and 16. H is defined as the set of candidate islanding schemes. Normalization is performed to avoid scaling effect, where the objectives with larger values will outweigh those with smaller values. \(\omega_{O}\) and \(\omega_{e}\) are weight factors of voltage fluctuation, frequency instability, economics, and environmental objectives, which should satisfy the following constraints:
The weight factors are utilized to reflect the decision preference of users, which are typically expressed in linguistic form.