2021/12/10 by Pengcheng You, Yan Jiang, You, Pengcheng +7
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #General Economics (econ.GN) #Optimization and Control (math.OC) #econ.GN #math.OC #q-fin.EC
paper · pdf · doi:10.48550/arxiv.2112.05811
arxiv created 2021/12/10 · arxiv updated 2021/12/14
This paper focuses on the operation of an electricity market that accounts for participants that bid at a sub-minute timescale. To that end, we model the market-clearing process as a dynamical system, called market dynamics, which is temporally coupled with the grid frequency dynamics and is thus required to guarantee system-wide stability while meeting the system operational constraints. We characterize participants as price-takers who rationally update their bids to maximize their utility in response to real-time schedules of prices and dispatch. For two common bidding mechanisms, based on quantity and price, we identify a notion of alignment between participants' behavior and planners' goals that leads to a saddle-based design of the market that guarantees convergence to a point meeting all operational constraints. We further explore cases where this alignment property does not hold and observe that misaligned participants' bidding can destabilize the closed-loop system. We thus design a regularized version of the market dynamics that recovers all the desirable stability and steady-state performance guarantees. Numerical tests validate our results on the IEEE 39-bus system.