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.