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
1514445503 2075236287
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. There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with an increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to exploit variations in electricity spot prices, is becoming an important way of paying for expensive investments into grid-level storage. Independent system operators such as the New York Independent System Operator NYISO require that battery storage operators place bids into an hour-ahead market although settlements may occur in increments as small as five minutes, which is considered near "real-time". The operator has to place these bids without knowing the energy level in the battery at the beginning of the hour and simultaneously accounting for the value of leftover energy at the end of the hour. The problem is formulated as a dynamic program. We describe and employ a convergent approximate dynamic programming ADP algorithm that exploits monotonicity of the value function to find a revenue-generating bidding policy; using optimal benchmarks, we empirically show the computational benefits of the algorithm. Furthermore, we propose a distribution-free variant of the ADP algorithm that does not require any knowledge of the distribution of the price process and makes no assumptions regarding a specific real-time price model. We demonstrate that a policy trained on historical real-time price data from the NYISO using this distribution-free approach is indeed effective. The classic Vickrey-Clarke-Groves (VCG) mechanism ensures incentive compatibility, i.e., that truth-telling of all agents is a dominant strategy, for a static one-shot game. However, in a dynamic environment that unfolds over time, the agents' intertemporal payoffs depend on the expected future controls and payments, and a direct extension of the VCG mechanism is not sufficient to guarantee incentive compatibility. In fact, it does not appear to be feasible to construct mechanisms that ensure the dominance of dynamic truth-telling for agents comprised of general stochastic dynamic systems. The contribution of this paper is to show that such a dynamic stochastic extension does exist for the special case of Linear-Quadratic-Gaussian (LQG) agents with a careful construction of a sequence of layered payments over time. We propose a layered version of a modified VCG mechanism for payments that decouples the intertemporal effect of current bids on future payoffs, and prove that truth-telling of dynamic states forms a dominant strategy if system parameters are known and agents are rational. An important example of a problem needing such optimal dynamic coordination of stochastic agents arises in power systems where an Independent System Operator (ISO) has to ensure balance of generation and consumption at all time instants, while ensuring social optimality (maximization of the sum of the utilities of all agents). Addressing strategic behavior is critical as the price-taking assumption on market participants may not hold in an electricity market. Agents, can lie or otherwise game the bidding system. The challenge is to determine a bidding scheme between all agents and the ISO that maximizes social welfare, while taking into account the stochastic dynamic models of agents, since renewable energy resources such as solar wind are stochastic and dynamic in nature, as are consumptions by loads which are influenced by factors such as local temperatures and thermal inertias of facilities. During the last years, operators of combined heat and power (CHP) plants are challenged by changing circumstances in the electricity markets. While ensuring a stable heat and power supply for customers, CHP plant operators seek to maximise the profitability of the CHP plant operation. We propose a comprehensive concept and illustrate its potential for increasing the profitability when operating a CHP plant with heat storage by participating in multiple electricity markets. For this purpose, the structure of the decision-making process consisting of bid submission, market clearing and CHP plant operation planning is represented. A multistage stochastic mixed-integer linear programming (MILP) model is developed that simultaneously optimises the operation of the CHP plant with heat storage and bidding in sequential electricity markets. Price uncertainty is captured by means of stochastic processes. The proposed concept is applied to the real case of a municipal energy supply company that participates in the German day-ahead spot and balancing market. Results of the case study illustrate how trading in sequential electricity markets can result in an increased profitability of the CHP plant operation, where additional revenues from trading offset higher generation costs. Furthermore, we exemplify how the optimal operation of the CHP plant and heat storage device are adjusted according to revenue potential in multiple electricity markets.