No Arabic abstract
The emerging interest in deployment of renewable energy resources (RESs) in smart system represents a great challenge to both system planners and owners of Microgrids (MGs) operators. In this regard, we propose a Tri-level power market models for designing demand side management systems to match power supply and shape renewable power generations. We characterize the resulting equilibria in competitive as well as oligopolistic market, and propose distributed demand response algorithms to achieve the equilibria. The models serve as a starting point to include the appliance-level details and constraints for designing practical demand response schemes for smart power grids. In order to show the usefulness of proposed model, two various case studies are considered in this paper: uncoordinated and coordinated load demand. A novel mathematical model is further developed whereby the behavior of RES, in response to different electricity prices owing to demand response programs, is considered in generating the energy consumption of MGs.
We consider a smart grid with an independent system operator (ISO), and distributed aggregators who have energy storage and purchase energy from the ISO to serve its customers. All the entities in the system are foresighted: each aggregator seeks to minimize its own long-term payments for energy purchase and operational costs of energy storage by deciding how much energy to buy from the ISO, and the ISO seeks to minimize the long-term total cost of the system (e.g. energy generation costs and the aggregators costs) by dispatching the energy production among the generators. The decision making of the entities is complicated for two reasons. First, the information is decentralized: the ISO does not know the aggregators states (i.e. their energy consumption requests from customers and the amount of energy in their storage), and each aggregator does not know the other aggregators states or the ISOs state (i.e. the energy generation costs and the status of the transmission lines). Second, the coupling among the aggregators is unknown to them. Specifically, each aggregators energy purchase affects the price, and hence the payments of the other aggregators. However, none of them knows how its decision influences the price because the price is determined by the ISO based on its state. We propose a design framework in which the ISO provides each aggregator with a conjectured future price, and each aggregator distributively minimizes its own long-term cost based on its conjectured price as well as its local information. The proposed framework can achieve the social optimum despite being decentralized and involving complex coupling among the various entities.
We consider a two-stage electricity market comprising a forward and a real-time settlement. The former pre-dispatches the power system following a least-cost merit order and facing an uncertain net demand, while the latter copes with the plausible deviations with respect to the forward schedule by making use of power regulation during the actual operation of the system. Standard industry practice deals with the uncertain net demand in the forward stage by replacing it with a good estimate of its conditional expectation (usually referred to as a point forecast), so as to minimize the need for power regulation in real time. However, it is well known that the cost structure of a power system is highly asymmetric and dependent on its operating point, with the result that minimizing the amount of power imbalances is not necessarily aligned with minimizing operating costs. In this paper, we propose a mixed-integer program to construct, from the available historical data, an alternative estimate of the net demand that accounts for the power systems cost asymmetry. Furthermore, to accommodate the strong dependence of this cost on the power systems operating point, we use clustering to tailor the proposed estimate to the foreseen net-demand regime. By way of an illustrative example and a more realistic case study based on the European power system, we show that our approach leads to substantial cost savings compared to the customary way of doing.
We develop an optimization model and corresponding algorithm for the management of a demand-side platform (DSP), whereby the DSP aims to maximize its own profit while acquiring valuable impressions for its advertiser clients. We formulate the problem of profit maximization for a DSP interacting with ad exchanges in a real-time bidding environment in a cost-per-click/cost-per-action pricing model. Our proposed formulation leads to a nonconvex optimization problem due to the joint optimization over both impression allocation and bid price decisions. We use Lagrangian relaxation to develop a tractable convex dual problem, which, due to the properties of second-price auctions, may be solved efficiently with subgradient methods. We propose a two-phase solution procedure, whereby in the first phase we solve the convex dual problem using a subgradient algorithm, and in the second phase we use the previously computed dual solution to set bid prices and then solve a linear optimization problem to obtain the allocation probability variables. On several synthetic examples, we demonstrate that our proposed solution approach leads to superior performance over a baseline method that is used in practice.
We consider an energy system with $n$ consumers who are linked by a Demand Side Management (DSM) contract, i.e. they agreed to diminish, at random times, their aggregated power consumption by a predefined volume during a predefined duration. Their failure to deliver the service is penalised via the difference between the sum of the $n$ power consumptions and the contracted target. We are led to analyse a non-zero sum stochastic game with $n$ players, where the interaction takes place through a cost which involves a delay induced by the duration included in the DSM contract. When $n to infty$, we obtain a Mean-Field Game (MFG) with random jump time penalty and interaction on the control. We prove a stochastic maximum principle in this context, which allows to compare the MFG solution to the optimal strategy of a central planner. In a linear quadratic setting we obtain an semi-explicit solution through a system of decoupled forward-backward stochastic differential equations with jumps, involving a Riccati Backward SDE with jumps. We show that it provides an approximate Nash equilibrium for the original $n$-player game for $n$ large. Finally, we propose a numerical algorithm to compute the MFG equilibrium and present several numerical experiments.
We propose a contextual-bandit approach for demand side management by offering price incentives. More precisely, a target mean consumption is set at each round and the mean consumption is modeled as a complex function of the distribution of prices sent and of some contextual variables such as the temperature, weather, and so on. The performance of our strategies is measured in quadratic losses through a regret criterion. We offer $T^{2/3}$ upper bounds on this regret (up to poly-logarithmic terms)---and even faster rates under stronger assumptions---for strategies inspired by standard strategies for contextual bandits (like LinUCB, see Li et al., 2010). Simulations on a real data set gathered by UK Power Networks, in which price incentives were offered, show that our strategies are effective and may indeed manage demand response by suitably picking the price levels.