Spot Pricing of Electricity

We consider a bilevel model where the leader wants to maximize revenues from a taxation scheme, while the follower rationally reacts to those tax levels. We focus our attention on the special case of a toll-setting problem defined on a multicommodity transportation network. We show that the general problem is NP-complete, while particular instances are polynomially solvable. Numerical examples are given.

A Bilevel Model of Taxation and its Application to Optimal Highway Pricing

Power System Economics

This paper reviews approaches for facilitating the integration of small-scale distributed energy resources (DER) into low- and medium-voltage networks, in the context of the emerging transactive energy (TE) concept. We focus on three general categories: (i) uncoordinated approaches that only consider energy management of an individual user; (ii) coordinated approaches that orchestrate the response of several users by casting the energy management problem as an optimization problem; and (iii) peer-to-peer energy trading that aims to better utilize the DER by establishing decentralized energy markets. A second separate, but important, consideration is that DER integration methods can be implemented with diverse levels of network awareness, given their capability to address system or consumer interests. This paper systematically classifies the existing literature on DER integration approaches according to these categories. In doing so, a review of the methods in each category is presented, and differences between the categories are identified and explained through a comparative analysis. In addition, case studies examine technical implementation considerations but leave market aspects aside. The analysis contained in this paper gives researchers and practitioners in DER integration the information needed to select a tailored approach to their specific power network and system integration problems.

Towards a transactive energy system for integration of distributed energy resources: Home energy management, distributed optimal power flow, and peer-to-peer energy trading

A coalition formation game framework for peer-to-peer energy trading

https://hal.archives-ouvertes.fr/hal-01944644/document

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

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.

Game theory has proven to be a valuable tool to study strategic electricity consumers enrolled in a demand response (DR) program. Among the different billing mechanisms proposed, the hourly billing model is of special interest as an intuitive and fair mechanism. We focus on this model and answer to several theoretical and practical questions. First, we prove the uniqueness of the consumption profile corresponding to the Nash equilibrium and we analyze its efficiency by providing a bound on the price of anarchy. Next, we address the computational issue of this equilibrium profile by providing results on the convergence rates of two decentralized algorithms to compute the equilibrium: the cycling best response dynamics and a projected gradient descent method. Last, we simulate this DR framework in a stochastic environment where the parameters depend on forecasts. Numerically, we show the relevance of an online DR procedure which reduces the impact of inaccurate forecasts in comparison to a standard offline procedure.

Analysis and Implementation of an Hourly Billing Mechanism for Demand Response Management

In Demand Response programs, price incentives might not be sufficient to modify residential consumers load profile. Here, we consider that each consumer has a preferred profile and a discomfort cost when deviating from it. Consumers can value this discomfort at a varying level that we take as a parameter. This work analyses Demand Response as a game theoretic environment. We study the equilibria of the game between consumers with preferences within two different dynamic pricing mechanisms, respectively the daily proportional mechanism introduced by Mohsenian-Rad et al, and an hourly proportional mechanism. We give new results about equilibria as functions of the preference level in the case of quadratic system costs and prove that, whatever the preference level, system costs are smaller with the hourly mechanism. We simulate the Demand Response environment using real consumption data from PecanStreet database. While the Price of Anarchy remains always close to one up to 10−3 with the hourly mechanism, it can be more than 10% bigger with the daily mechanism.

https://hal.archives-ouvertes.fr/hal-01651263/document

Demand response in the smart grid: The impact of consumers temporal preferences

We compare two Demand Side Management (DSM) mechanisms, introduced respectively by Mohsenian-Rad et al (2010) and Baharlouei et al (2012), in terms of efficiency and fairness. Each mechanism defines a game where the consumers optimize their flexible consumption to reduce their electricity bills. Mohsenian-Rad et al propose a daily mechanism for which they prove the social optimality. Baharlouei et al propose a hourly billing mechanism for which we give theoretical results: we prove the uniqueness of an equilibrium in the associated game and give an upper bound on its price of anarchy. We evaluate numerically the two mechanisms, using real consumption data from Pecan Street Inc. The simulations show that the equilibrium reached with the hourly mechanism is socially optimal up to 0.1%, and that it achieves an important fairness property according to a quantitative indicator we define. We observe that the two DSM mechanisms avoid the synchronization effect induced by non-game theoretic mechanisms, e.g. Peak/OffPeak hours contracts.

Paulin Jacquot

Papers

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

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

Analysis and Implementation of an Hourly Billing Mechanism for Demand Response Management

Demand response in the smart grid: The impact of consumers temporal preferences

Demand side management in the smart grid: An efficiency and fairness tradeoff