Reducing Power Losses in Smart Grids with Cooperative Game Theory

Abstract

In a theoretical framework of game theory, one can distinguish between the noncooperative and the cooperative game theory. While the theory of noncooperative games is about modeling competitive behavior, cooperative game theory is dedicated to the study of cooperation among a number of players. The cooperative game theory includes mostly two branches: the Nash negotiation and the coalitional game theory. In this chapter, we restrict our attention to the latter. In recent years, the concept of efficient management of electric power has become more complex as a result of the high integration of distributed energy resources in the scenarios to be considered, mainly distributed generation, energy storage distributed, and demand management. This situation has been accentuated with the appearance of new consumption elements, such as electric vehicles, which could cause a high impact on distribution gridworks if they are not managed properly. This chapter presents an innovative approach toward an efficient energy model through the application of the theory of cooperative games with transferable utility in which the management, capacity, and control of distributed energy resources are integrated to provide optimal energy solutions that allow achieving significant savings in associated costs. This chapter presents a general description of the potential of the application of the theory to address Smart Grid, providing a systematic treatment.

Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach

“…From (6), it is evident that the second row contains the demand nodal voltages (i.e., V s3ϕ,t ), which are the variables of interest in power flow studies; for simplicity, this equation can be rewritten as follows:…”

“…The following interpretations can be drawn from the optimization model described in (1) to (6). Equation ( 1) corresponds to the objective function of the phase-balancing problem, which is formulated as the minimization of the daily costs of energy loss in all branches of the network.…”

“…Equations ( 4) and ( 5) guarantee that the loads are connected to the phases in a unique form by using a matrix connection at each node (i.e., bus k), formed by the variables x k f g , in which each row and each column must be equal to 1. Finally, the box-type constraint (6) defines the upper and lower voltage regulation bounds of the network, which are typically ±10% for medium-voltage levels [2].…”

“…To illustrate this stage, suppose that a test feeder is composed of 11 nodes (1 slack and 10 demands), in which the individuals x s i and x s j take the following form: 6,6,4,4,4,1,5,5,2].…”

“…The regulatory entity of the electrical distribution service in Colombia, that is, the Energy and Gas Regulation Commission (CREG, based on its acronym in Spanish) allows transferring part of the energy losses to the end-users through the final billing for the electricity service; however, this value cannot exceed 8% of the total energy costs. This implies that, if the distribution company reduces the amount of energy losses to less than 8%, the following benefits can be achieved: (i) an improvement in the potential of the network to supply additional users with the same distribution grid and minimum investment costs (expansion in coverage capacity); (ii) additional economic reedits because lower energy input is needed for supplying the same group of users; and (iii) the possibility to win by billing the difference between the upper regulation bound (i.e., 8%) and the current power losses [6].…”