Shadow Price Formulation and Decomposition for Economic Emission Dispatch

Evolutionary and scalarization methods are the most common algorithms of solving power system multi-objective problems. However, it is challenging to calculate Lagrangian multipliers for each objective directly by these two methods. The lack of an effective algorithm for performing sensitivity analysis on power system multi-objective problems prevents the collection of important information for market studies. In this paper, a sensitivity matrix formulation method for power system multi-objective problems is proposed and applied to the economic emission dispatch problem (EED). An emission related locational marginal price is first formulated and then decomposed regarding the cost objective and the emission objective. Then, a detailed sensitivity analysis of EED is performed on the IEEE 30-bus system to investigate the influence of resources on operation costs and pollutions.