Dynamics of electricity markets with unknown utility functions: An extremum seeking control approach

This paper studies the dynamics of electricity markets with unknown utility functions (i.e, the profit functions of consumers and the cost functions of suppliers). The market clearing procedure is formulated as a social welfare optimization problem, and the dynamics of electricity markets is modeled as primal-dual dynamics based on gradient estimation. The gradients of the unknown utility functions are estimated by adding and multiplying periodic signals at the measurable input and output, respectively. We prove the semi-globally practically asymptotically (SPA) stability of the market dynamics. Numerical results demonstrate the SPA stability and the balance between supply and demand.