Optimal electricity load shedding problem for feeders using Knapsack and Game theory

Abstract

A combination of Knapsack and Game Theory to Electricity Load Shedding (KGTLS) in the Kumasi Metropolis is presented. A minimization problem of single constraint 0-1 Knapsack known as Knapsack Load Shedding (KLS) is modeled to selects items (loads/MW) up to a minimum capacity of the knapsack in other to minimize some objective function (lost). The KLS comprise of two objective functions belonging to a Day schedule (DS) and a Night schedule (NS), with both linked to a single constraint equation. The problem again is modeled into a Mixed Strategy Game Theory in which strategic probabilities of two players in the game are computed by the linear programing approach. The game comprise of two players: the row player NS and the column player DS each competing for loads to be shed. The game is played with the probabilities using the minimax theory and loads are selected. The minimum capacity of load to be shed calls the fusion of the game theory and the knapsack, hence the K-GTLS model. A data from a load shedding already done by the Electricity Company of Ghana, ECG at the catchment area is fitted onto the models, the K-GTLS in a cyclic mode of load shedding obtained a lost of GH¢9607.30 up against GH¢9621.50 by the KLS and GH¢9667.70 by the ECG. In a proposed Revenue bias mode, the K-GTLS obtained a lost of GH¢9302.25 up against GH¢9326.20 by the KLS and GH¢9429.85 by the ECG. In conclusion, the fusion of Knapsack and game theory in a combinational optimization is a good approach to solving resource constraint project scheduling problem.