The electricity distribution network is experiencing a profound transformation with the concept of the smart grid

providing possibilities for selfish consumers to interact with the distribution system operator (DSO) and to maximize their individual energy consumption utilities. However

this profit-seeking behavior among consumers may violate the network constraints

such as line flows

transformer capacity and bus voltage magnitude limits. Therefore

a network-constrained energy consumption (NCEC) game among active load aggregators (ALAs) is proposed to guarantee the safety of the distribution network. The temporal and spatial constraints of an ALA are both considered

which leads the formulated model to a generalized Nash equilibrium problem (GNEP). By resorting to a well-developed variational inequality (VI) theory

we study the existence of solutions to the NCEC game problem. Subsequently

a two-level distributed algorithm is proposed to find the variational equilibrium (VE)

a fair and stable solution to the formulated game model. Finally

the effectiveness of the proposed game model and the efficiency of the distributed algorithm are tested on an IEEE-33 bus system.