The air-conditioning load is large in scale and has flexible controllability. At the same time

the charging and discharging behavior of energy storage is closely related to its life. To address the challenge of achieving a win-win situation in interactive games among multi-agents within the distribution network

a two-stage robust game control method is proposed

considering both air conditioning load and the decay of energy storage life. Firstly

considering the heat exchange between the wall and the external environment

the two-parameter thermal model is used to establish the thermodynamic model of air conditioning load. Secondly

considering the influence of discharge depth

battery cycle times

and temperature on battery life

an energy storage life decay model is established. Then

based on the distribution network operation model

the air conditioning load aggregator model

and the energy storage life decay model

a two-layer interactive game model with the largest profit for each subject is constructed. Then

the (Karush-Kuhn-Tucker

KKT) condition is used to transform it into a single-layer mixed integer second-order cone problem. Aiming at the uncertainty of distributed photovoltaic output

a diamond-shaped cutting convex hull uncertainty set is established

and the (column and constraint generation

C&CG) algorithm is used to solve the two-stage robust game problem. Finally

the simulation analysis is carried out on the actual example of 52 nodes

which verifies the effectiveness of the proposed two-stage robust game control method for the distribution network

considering the attenuation of air conditioning load and energy storage life.