There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Theory of Incentives I: The Principal-Agent Model

Spot Pricing of Electricity

The article reviews the book "Information and Learning in Markets: The Impact of Market Microstructure," edited by Xavier Vives.

Information and Learning in Markets: The Impact of Market Microstructure

We consider a network of prosumers involved in peer-to-peer energy exchanges, with differentiation price preferences on the trades with their neighbors, and we analyze two market designs: (i) a centralized market, used as a benchmark, where a global market operator optimizes the flows (trades) between the nodes, local demand and flexibility activation to maximize the system overall social welfare; (ii) a distributed peer-to-peer market design where prosumers in local energy communities optimize selfishly their trades, demand, and flexibility activation. We first characterizethe solution of the peer-to-peer market as a Variational Equilibrium and prove that the set of Variational Equilibria coincides with the set of social welfare optimal solutions of market design (i). We give several results that help understanding the structure of the trades at an equilibriumor at the optimum. We characterize the impact of preferences on the network line congestion and renewable energy waste under both designs. We provide a reduced example for which we give the set of all possible generalized equilibria, which enables to give an approximation of the price ofanarchy. We provide a more realistic example which relies on the IEEE 14-bus network, for which we can simulate the trades under different preference prices. Our analysis shows in particular that the preferences have a large impact on the structure of the trades, but that one equilibrium(variational) is optimal.

Peer-to-Peer Electricity Market Analysis: From Variational to Generalized Nash Equilibrium

With the fast-paced deployment of battery energy storage systems (BESSs), efficiency and safety issues of BESS, caused by the notorious “bucket effect”, have become prominent. Therefore, dynamic reconfigurable battery system (DRB) provides a promising approach to overcome the “bucket effect” by integrating batteries with power electronics switches in a systematic fashion and dynamically changing battery cell topology based on battery status. However, since the battery energy flow is digitized within milliseconds, there is no theoretical study of the transient behavior of DRB. In this paper, we will fill this gap by establishing a hybrid system model with considerations of the dynamic behaviors of battery cell and power electronics switch, and then to study the transient response of the hybrid system at different working frequencies under constant discharging current profile. Both analytical study and simulation analysis are carried out, which providing design insights for such hybrid system design.

Yue Chen

Papers

Transient Analysis in Dynamic Reconfigurable Battery System