Spot Pricing of Electricity

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

The paper focuses on the day-ahead operational planning of a grid-connected local energy community (LEC) consisting of an internal low-voltage network and several prosumers including generation units, battery storage systems, and local loads. In order to preserve, as much as possible, the confidentiality of the features of prosumers’ equipment and the production and load forecasts, the problem is addressed by designing a specific distributed procedure based on the alternating direction method of multipliers (ADMM). The distributed procedure calculates the scheduling of the available energy resources to limit the balancing action of the external grid and allocates the internal network losses to the various power transactions. Results obtained for various case studies are compared with those obtained by a centralized optimization approach. The results confirm that, in the considered LEC framework, each of the prosumers achieves a reduction in costs or increases revenues in case it participates to the LEC with respect to the case in which it can only transact with an external energy provider.

/pdf/day-ahead-scheduling-of-a-local-energy-community-an-12elg5awvo.pdf

Day-Ahead Scheduling of a Local Energy Community: An Alternating Direction Method of Multipliers Approach

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.

After defining a pure-action profile in a nonatomic aggregative game, where players have specific compact convex pure-action sets and nonsmooth convex cost functions, as a square-integrable function, we characterize a Wardrop equilibrium as a solution to an infinite-dimensional generalized variational inequality. We show the existence of Wardrop equilibrium and variational Wardrop equilibrium, a concept of equilibrium adapted to the presence of coupling constraints, in monotone nonatomic aggregative games. The uniqueness of (variational) Wardrop equilibrium is proved for strictly or aggregatively strictly monotone nonatomic aggregative games. We then show that, for a sequence of finite-player aggregative games with aggregative constraints, if the players' pure-action sets converge to those of a strongly (resp. aggregatively strongly) monotone nonatomic aggregative game, and the aggregative constraints in the finite-player games converge to the aggregative constraint of the nonatomic game, then a sequence of so-called variational Nash equilibria in these finite-player games converge to the variational Wardrop equilibrium in pure-action profile (resp. aggregate-action profile). In particular, it allows the construction of an auxiliary sequence of games with finite-dimensional equilibria to approximate the infinite-dimensional equilibrium in such a nonatomic game. Finally, we show how to construct auxiliary finite-player games for two general classes of nonatomic games.

Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players

We consider an instance of a nonatomic routing game. We assume that the network is parallel, that is, constituted of only two nodes, an origin and a destination. We consider infinitesimal players that have a symmetric network cost, but are heterogeneous through their set of feasible strategies and their individual utilities. We show that if an atomic routing game instance is correctly defined to approximate the nonatomic instance, then an atomic Nash Equilibrium will approximate the nonatomic Wardrop Equilibrium. We give explicit bounds on the distance between the equilibria according to the parameters of the atomic instance. This approximation gives a method to compute the Wardrop equilibrium at an arbitrary precision.

https://hal.archives-ouvertes.fr/hal-01762547/document

Routing Game on Parallel Networks: The Convergence of Atomic to Nonatomic

We define and analyze the notion of variational Wardrop equilibrium for nonatomic aggregative games with an infinity of players types. These equilibria are characterized through an infinite-dimensional variational inequality. We show, under monotonicity conditions, a convergence theorem enables to approximate such an equilibrium with arbitrary precision. To this end, we introduce a sequence of nonatomic games with a finite number of players types, which approximates the initial game. We show the existence of a symmetric Wardrop equilibrium in each of these games. We prove that those symmetric equilibria converge to an equilibrium of the infinite game, and that they can be computed as solutions of finite-dimensional variational inequalities. The model is illustrated through an example from smart grids: the description of a large population of electricity consumers by a parametric distribution gives a nonatomic game with an infinity of different players types, with actions subject to coupling constraints.

Cheng Wan

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

Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players

Routing Game on Parallel Networks: The Convergence of Atomic to Nonatomic

Nonatomic Aggregative Games with Infinitely Many Types