Game theory and hybrid genetic algorithm for energy management and real-time pricing in smart grid: the Tunisian case

ABSTRACT

Microgrids are the key for integrating renewable energy from different sources into smart grid, that is why power grid evolves into a combination of interconnected microgrids. In fact, future power grids are undergoing this groundbreaking change that will help meet the increasing demand of electric power and reduce carbon emission. In this sense we study in this paper, based on measured data, a real case of energy management in the area of Beja located in Tunisia. Indeed, we propose a model for the power exchange which proves the potential of applying game theory in the development of both real-time pricing and energy management mechanism for an open electricity market. We also introduce a hybrid genetic algorithm to compute the Nash Equilibrium. Results show that the proposed smart energy management can decrease the real cost of power up to 20%, to divide the energy transmission losses by a factor of two and to reduce the carbon emission in the area of Beja.

KEYWORDS:

• Smart grid
• microgrids
• game theory
• genetic algorithm
• energy management
• CO₂ emissions

List of symbols

$N$	=	Set of suppliers
$M_S$	=	Maximum number of suppliers
$R$	=	Set of consumers
$M_C$	=	Maximum number of consumer
$P_n^t$	=	Power generated by supplier n at time t (W)
$P_n^{t,max}$	=	Maximum power available for supplier n at time t (W)
$D_r^t$	=	Demand of consumer r at time t (W)
$N_r$	=	Set of suppliers connected to consumer r
$R_n$	=	Set of consumers connected to supplier n
$P_{n,r}^t$	=	Power received by consumer r from supplier n at time t (W)
$P_{n,r}^{t,loss}$	=	Power loss between a supplier n and consumer r at time t (W)
$\beta$	=	Resistance of the distribution line between supplier n and consumer r (ohm/km)
$L_{n,r}$	=	Length of the electrical line connecting supplier n to consume r (km)
$U_{n,r}$	=	Voltage (V)
$I_{n,r}$	=	Current flow from supplier n to consume r (A)
$C_n^t$	=	Power production cost of supplier n at time t in Tunisian Dinar
$C_n^{t,total}$	=	Total power production cost of supplier n at time t in Tunisian Dinar
$\mathrm{\Gamma }$	=	A normal (strategic) form of the game
$S_n$	=	Set of available strategies for supplier n
$s_n$	=	A strategy of supplier n
$s_{-n}$	=	A strategy of all suppliers except n
$u_n$	=	Utility function of supplier n
$\phi$	=	Potential function