A Game Theoretic Horizon Decomposition Approach for Real-Time Demand-Side Management

This article introduces two instances of rolling horizon algorithms, viz, shrinking horizon proximal decomposition algorithm (SHPDA) and distributed horizon proximal decomposition algorithm (DHPDA), to solve the demand-side management problem in real time. Both these algorithms are comprised of "two-step". The number of time-slots to be considered in each iteration is decided in first step. In second step, the solution for considered time-slots is obtained through a non-cooperative game-theoretic approach using the proximal decomposition algorithm (PDA). An investigation is carried out to establish the existence and multiplicity of Nash equilibrium for the formulated game. The convergence of PDA has a strong dependency on system parameters and is unique for a system. Hence an analysis is performed to derive the convergence criteria for the formulated problem. The system model includes distributed energy storage, distributed dispatchable generation, time-shiftable, power-shiftable (PSD), and essential devices. The reduction in power consumption of PSD caused due to the optimization process creates discomfort to users. Therefore, we have incorporated an objective to minimize the discomfort and reduce consumers' energy bills. Simulation is carried out to show the efficacy of developed algorithms in terms of the energy bill, peak reduction, and solution time. Also, eight scenarios have been analyzed to show the impact of adding discomfort cost on the above-mentioned system parameters.