We consider a smart-grid connecting several agents, modeled as stochastic dynamical systems, who may be electricity consumers producers. At each discrete time instant, which may represent a 15 minute interval, each agent may consume generate some quantity of electrical energy. The Independent System Operator (ISO) is given the task of assigning consumptions generations to the agents so as to maximize the sum of the utilities accrued to the agents, subject to the constraint that energy generation equals consumption at each time. This task of coordinating generation and demand has to be accomplished by the ISO without the agents revealing their system states, dynamics, or utility cost functions. We show how and when a simple iterative procedure converges to the optimal solution. The ISO iteratively obtains electricity bids by the agents, and declares the tentative market clearing prices. In response to these prices, the agents submit new bids. On the demand side, the solution yields an optimal demand response for dynamic and stochastic loads. On the generation side, it provides the optimal utilization of stochastically varying renewables such as solar wind, and generation with fossil fuel based generation with dynamic constraints such as ramping rates. Thereby we solve a decentralized stochastic control problem, without agents sharing any information about their system models, states or utility functions.
In the setting of the energy market, @cite_0 @cite_8 discuss a general framework for the operation of an electicity grid via the establishment of a marketplace in which the electricity purchases are done on the basis of spot prices. Thus, electrical energy is treated as a commodity which can be bought, sold, and traded, taking into account its time-and space-varying values and costs, and a framework is presented for the establishment of an energy marketplace. Our results can be viewed as providing guidelines for the operation of this marketplace via simple bidding schemes when the agents are nonlinear stochastic dynamical systems. Our scheme maximize the net social utlity.
@cite_0 @cite_8
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This paper proposes a decentralised and privacy-preserving local electricity trading market. The market employs a bidding protocol based on secure multiparty computation and allows users to trade their excess electricity among themselves. The bid selection and trading price calculation are performed in a decentralised and privacy-preserving manner. We implemented the market in C++ and tested its performance with realistic data sets. Our simulation results show that the market tasks can be performed for 2500 bids in less than four minutes in the “online” phase, showing its feasibility for a typical electricity trading period. Integration of distributed generation based on renewable energy sources into the power system has gained popularity in recent years. Many small-scale electricity suppliers (SESs) have recently entered the electricity market, which has been traditionally dominated by a few large-scale electricity suppliers. The emergence of SESs enables direct trading (DT) of electricity between SESs and end-users (EUs), without going through retailers, and promotes the possibility of improving the benefits to both parties. In this paper, the cooperation between SESs and EUs in DT is analyzed based on coalitional game theory. In particular, an electricity pricing scheme that achieves a fair division of revenue between SESs and EUs is analytically derived by using the asymptotic Shapley value. The asymptotic Shapley value is shown to be in the core of the coalitional game such that no group of SESs and EUs has an incentive to abandon the coalition, which implies the stable operation of DT for the proposed pricing scheme. Unlike the existing pricing schemes that typically require multiple stages of calculations and real time information about each participant, the electricity price for the proposed scheme can be determined instantaneously based on the number of participants in DT and statistical information about electricity supply and demand. Therefore, the proposed pricing scheme is suitable for practical implementation. Using computer simulations, the price of electricity for the proposed DT scheme is examined in various environments, and the numerical results validate the asymptotic analysis. Moreover, the revenues of the SESs and EUs are evaluated for various types of SESs and different numbers of participants in DT. The optimal ratio of different types of SESs is also investigated. The trading is a well known, easy and efficient method of distributing goods. Energy cannot be stored efficiently, which implies that supply and demand of power has to be balanced at all times; this adds complexity to the trading of electric power. Introduction of microgrids, with internal balancing of power and trading with external power grid, brings many questions about power distribution, sharing of costs and revenues. Using market mechanism for such purpose seems appropriate. In this article we present an example of balancing a microgrid with its own energy production sources and connected to a higher voltage distribution grid, by introduction of the continuous double auction market with agents following the Adaptive-Aggressive Strategy. A smart grid connects several electricity consumers producers, e.g., wind solar storage farms, fossil-fuel plants, industrial commercial loads, or load-serving aggregators, all modeled as stochastic dynamical systems. In each time period, each consumes supplies some electrical energy. Each such agent's utility is the benefit accrued from its consumption or the negative of its generation cost. The social welfare, the sum of all these utilities, is the total benefit accrued from all consumption minus the total cost of generation. The independent system operator is charged with maximizing the social welfare subject to total generation equalling consumption in each time period, but without the agents revealing their system states, dynamic models, utility functions, or uncertainties. It has to announce prices after interacting with agents via bid-price interactions. This paper examines the case where the agents respond in a compliant price-taking manner. It is shown that there is an iterative bid-price interaction, where agents respond to price announcements by complying to the requirement to announce their optimal responses according to their true stochastic model, or, in the case where the agents are linear quadratic Gaussian (LQG) systems, according to deterministic versions of their true stochastic models, that leads to the same global maximum value of social welfare attainable if all agents had pooled their information. In the important LQG case, the bid-price iteration is dramatically simple, exchanging only real-valued vectors of future prices and consumptions generations at each time step. Agents need not even know of the existence of other agents. DC power flow equations can also be incorporated. The results may be of broader interest vis-a-vis general equilibrium theory of economics for stochastic dynamic agents.