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.
Viewed from the power system end, there have been many efforts since the deregulation of the electricity sector on a market-based framework to clear the system. @cite_7 have proposed a two-layered approach that internalizes individual constraints of market participants while allowing the ISO to manage the spatial complexity. The approximated MPC algorithm is shown to perform well in many realistic applications. In order to analyze the strategic interactions between the ISO and market participants, game theoretical approaches have been proposed, e.g., @cite_10 uses a Stackelberg game framework for studying economic dispatch with demand response. @cite_1 pose the problem as a noncooperative game, and prove the existence of a Nash equilibrium under some assumtpions.
@cite_1 @cite_10 @cite_7
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In this paper, we study resource allocation for a multicarrier-based cognitive radio (CR) network. More specifically, we investigate the problem of secondary users’ energy-efficiency (EE) maximization problem under secondary total power and primary interference constraints. First, assuming cooperation among the secondary base stations (BSs), a centralized approach is considered to solve the EE optimization problem for the CR network where the primary and secondary users are using either orthogonal frequency-division multiplexing (OFDM) or filter bank based multicarrier (FBMC) modulations. We propose an alternating-based approach to solve the joint power-subcarrier allocation problem. More importantly, in the first place, subcarriers are allocated using a heuristic method for a given feasible power allocation. Then, we conservatively approximate the nonconvex power control problem and propose a joint successive convex approximation-Dinkelbach algorithm (SCADA) to efficiently obtain a solution to the nonconvex power control problem. The proposed algorithm is shown to converge to a solution that coincides with the stationary point of the original nonconvex power control subproblem. Moreover, we propose a dual decomposition-based decentralized version of the SCADA. Second, under the assumption of no cooperation among the secondary BSs, we propose a fully distributed power control algorithm from the perspective of game theory. The proposed algorithm is shown to converge to a Nash-equilibrium (NE) point. Moreover, we propose a sufficient condition that guarantees the uniqueness of the achieved NE. Extensive simulation analyses are further provided to highlight the advantages and demonstrate the efficiency of our proposed schemes. In this paper, the problem of energy trading between smart grid prosumers, who can simultaneously consume and produce energy, and a grid power company is studied. The problem is formulated as a single-leader, multiple-follower Stackelberg game between the power company and multiple prosumers. In this game, the power company acts as a leader who determines the pricing strategy that maximizes its profits, while the prosumers act as followers who react by choosing the amount of energy to buy or sell so as to optimize their current and future profits. The proposed game accounts for each prosumer’s subjective decision when faced with the uncertainty of profits, induced by the random future price. In particular, the framing effect, from the framework of prospect theory (PT), is used to account for each prosumer’s valuation of its gains and losses with respect to an individual utility reference point. The reference point changes between prosumers and stems from their past experience and future aspirations of profits. The followers’ noncooperative game is shown to admit a unique pure-strategy Nash equilibrium (NE) under classical game theory which is obtained using a fully distributed algorithm. The results are extended to account for the case of PT using algorithmic solutions that can achieve an NE under certain conditions. Simulation results show that the total grid load varies significantly with the prosumers’ reference point and their loss-aversion level. In addition, it is shown that the power company’s profits considerably decrease when it fails to account for the prosumers’ subjective perceptions under PT. This paper presents two different approaches to model expansion planning in electricity markets under imperfect competitive conditions. Both approaches consider a market in which firms compete in quantity as in the Nash-Cournot game. However, the two models differ from each other in how each firm makes its expansion-planning decisions. In the first model, the key assumption that permits its formulation as a Mixed Linear Complementarity Problem (LCP) is that firms not only decide their output in a Cournot manner but also their new generating capacity. In contrast, in the second model, there is a leader firm that anticipates the reaction of the follower firms as in the Stackelberg game. The latter model is formulated as a Mathematical Program with Equilibrium Constraints (MPEC), wherein the leader firm decides its optimal new capacity subject to a set of market equilibrium constraints. Both models have been implemented in GAMS. A simple example is also presented to illustrate their comparison and application. This paper describes a Benders decomposition-based framework for solving the large scale energy management problem that was posed for the ROADEF 2010 challenge. The problem was taken from the power industry and entailed scheduling the outage dates for a set of nuclear power plants, which need to be regularly taken down for refueling and maintenance, in such a way that the expected cost of meeting the power demand in a number of potential scenarios is minimized. We show that the problem structure naturally lends itself to Benders decomposition; however, not all constraints can be included in the mixed integer programming model. We present a two phase approach that first uses Benders decomposition to solve the linear programming relaxation of a relaxed version of the problem. In the second phase, integer solutions are enumerated and a procedure is applied to make them satisfy constraints not included in the relaxed problem. To cope with the size of the formulations arising in our approach we describe efficient preprocessing techniques to reduce the problem size and show how aggregation can be applied to each of the subproblems. Computational results on the test instances show that the procedure competes well on small instances of the problem, but runs into difficulty on larger ones. Unlike heuristic approaches, however, this methodology can be used to provide lower bounds on solution quality. Microgrid (MG) system with multienergy resources has a wide and dispatchable generation range and shows instant response, therefore, constituting a potentially suitable real-time power balancing resource. In this paper, we introduce the concept of MG aggregator to involve small-scale MGs in real-time balancing market bidding via a hierarchical market framework. At the upper real-time market level, the bidding strategy of aggregator is optimized by a risk-constrained mean-variance model to depress the effects of renewable energy sources (RES) uncertainty; at the lower intramarket level, an event-driven mechanism is presented to reach the cleared quantity of the upper market while realizing maximum economy. Furthermore, the above-centralized self-scheduling problem of MG aggregator is decomposed into individual MG optimization problems to achieve an optimal solution with fast convergence. Simulation results verify that the proposed market framework and the bidding strategy for MG aggregator are of high applicability in real market environment. This paper proposes a decentralized interference control scheme for an OFDMA (Orthogonal Frequency Division Multiple Access) cellular scenario where multiple macrocells and femtocells are deployed. In particular, we model the distributed resource allocation problem by means of a potential game, which is demonstrated to converge to a unique and pure Nash equilibrum. In this game, the femto base stations are the players, their actions are the resource blocks and the corresponding power levels to be allocated for downlink transmission, and the utility is designed to guarantee coexistence with the macro system, guaranteeing a fair tradeoff between femto and macro systems' performances. To do that, the utility function does not only consider the capacity of the femtocells, but also the different sources of inter-system interference: macrocell to femtocell, femtocell to femtocell, and femtocell to macrocell. The game is solved by applying a better response dynamic, which first selects the best resource blocks allocation policy for the femtousers, and then selects the most appropriate power levels for each resource block, through the solution of the corresponding convex optimization problem. Simulation results show that the introduction of femtocells in the scenario increases the total system capacity, and that the considered utility function provides an improvement in macro system performance of up to 40 , while reducing the femto capacity only up to 7 , with respect to the well known iterative waterfilling game. Model Predictive Control (MPC) plays an important role in optimizing operations of complex cyber-physical systems because of its ability to forecast system’s behavior and act under system level constraints. However, MPC requires reasonably accurate underlying models of the system. In many applications, such as building control for energy management, Demand Response, or peak power reduction, obtaining a high-fidelity physics-based model is cost and time prohibitive, thus limiting the widespread adoption of MPC. To this end, we propose a data-driven control algorithm for MPC that relies only on the historical data. We use multi-output regression trees to represent the system’s dynamics over multiple future time steps and formulate a finite receding horizon control problem that can be solved in real-time in closed-loop with the physical plant. We apply this algorithm to peak power reduction in buildings to optimally trade-off peak power reduction against thermal comfort without having to learn white grey box models of the systems dynamics. Due to the stochastic nature of wind power, its large-scale integration into the power grid requires techniques to constantly balance the load with the time-varying supply. This can be done via smart scheduling of energy consumption and storage units among end users. In this paper, we propose a game-theoretic algorithm to be implemented in an aggregator in order to coordinate the operation of demand-side resources via pricing in order to tackle the intermittency and fluctuations in wind power generation. The demand-side resources to be considered are both non-shiftable and shiftable load, in particular, electric vehicles that charge or discharge their batteries to provide extra resource management flexibility. After formulating the interactions in an aggregator-consumer system as a game, we analytically prove the existence and uniqueness of the Nash equilibrium in the formulated game model. Simulation results show that our proposed design scheme can benefit both end users (in terms of reducing energy expenses) and the power grid (in terms of integrating wind power). This paper presents a joint market structure for energy, spinning reserves and VAR support in a multiarea setting. It is based on a cooptimization that can simultaneously optimize all three commodities across the "seams". An auxiliary problem principle based decomposition scheme is applied to the overall optimization for coordinating interchanges of energy and ancillary services between control areas. The proposed decomposition approach preserves independent dispatching for neighboring areas while achieves overall optimum. Nodal prices for energy and opportunity cost payments to forgone energy profit due to providing reserves and VAR support are also addressed. We believe the algorithm is of particular interest in the restructuring electricity industry for resolving seams issues. An illustrative example of a modified IEEE 30-bus system is used to demonstrate the validity of proposed algorithm. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. This paper proposes an innovative game theoretic framework for a next-generation retail electricity market (“Energy Internet”) with high penetration of distributed residential electricity suppliers (“Energy Cells”). The envisioned Energy Internet is developed for plug-and-play of a large number of distributed renewable energy generation and energy storage. The residential customers, referred as Energy Cells, are not only the electricity consumers but can also be the electricity suppliers by locally operating and managing their own distributed generators, distributed energy storage devices, and dispatchable loads. This paper formulates a set of mathematical models of the retail electricity market participants with a number of local and global constraints. A numerical case study is performed to validate the proposed next-generation retail electricity market framework using game-theoretic methodologies. The numerical simulation results demonstrate the effectiveness of the proposed market clearing scheme with high penetration of distributed residential electricity suppliers. Abstract This paper proposes a stochastic and dynamic mixed-integer linear program (SD-MILP) for optimal coordinated bidding of a risk-averse profit-maximizing hydropower producer. The day-ahead, intra-day, and real-time markets are considered. To model and predict day-ahead, intra-day, and real-time prices, the Holt–Winter (HW) and the Generalized Autoregressive Conditional Heteroscedastic (GARCH) predictors are combined using a proposed Markov switch. The discrete behavior of intra-day and real-time prices is modeled as different Markov states. The proposed Markov-based HW–GARCH model with a standard scenario generation-reduction technique is used to capture the uncertainty in day-ahead, intra-day, and real-time prices. The time-dependent conditional value at risk (T-CVaR) is proposed to model the risk of trading in different considered markets. The convex combination of the expected profit and T-CVaR is used as the objective of SD-MILP. The Markov-based HW–GARCH is modeled in Matlab and the SD-MILP is coded in GAMS. The Markov-based HW–GARCH predictor and the SD-MILP are used to develop the bidding curve of a three-reservoir hydropower producer using the electricity prices from the Nordic power market. To further examine the developed models a seven-reservoir hydropower producer is also studied. For these two cases, the coordinated bidding curves are derived and discussed. This paper tackles the problem of joint users’ uplink transmission power and data rate allocation in multi-service two-tier femtocell networks. Each user—either macrocell (MUE) or femtocell user equipment (FUE)—is associated with a two-variable utility function that represents his perceived satisfaction with respect to his allocated resources (i.e., power and rate). User's utility function is differentiated based both on the tier that the user belongs to and the service he requests. The joint resource allocation problem is directly confronted as a two-variable optimization problem and formulated as a non-cooperative game. The theory of supermodular games is utilized towards treating the two-variable optimization problem and the inherent multidimensional competition that arises among the users. The existence of proposed game's Nash Equilibrium (NE) point is analytically shown, while game's convergence to its NE point is proven. A distributed and iterative algorithm for computing the desired NE is introduced, where the optimal values of each user's uplink transmission power and data rate are simultaneously updated at the same step. The performance of the proposed approach is evaluated via modeling and simulation and its superiority compared to other state of the art approaches is illustrated. 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. In this paper, the problem of optimally charging or discharging customer-owned storage units in a smart grid is studied. In particular, a noncooperative game is formulated between customers equipped with distributed storage units who seek to decide on their optimal charging strategy so as to optimize a utility that reflects both the monetary benefit from the charging discharging operation and the associated penalty from power regulation. In contrast to the traditional game-theoretic models that are often based on rational and objective decisions, we introduce the behavioral framework of prospect theory (PT) so as to explicitly incorporate how the customers estimate their utilities with respect to their real-world considerations of gains and losses. The existence of the mixed-strategy Nash equilibrium is shown for the PT case and the properties of the game are analyzed under both PT and classical game theory. Simulation results show how the individual customer perceptions on their utilities can significantly impact the overall charging and discharging operations. This paper investigates the residential energy consumption scheduling problem, which is formulated as a coupled-constraint game by taking the interaction among users and the temporally-coupled constraint into consideration. The proposed solution consists of two parts. Firstly, dual decomposition is applied to transform the original coupled-constraint game into a decoupled one. Then, Nash equilibrium of the decoupled game is proven to be achievable via best response, which is computed by gradient projection. The proposed solution is also extended to an online version, which is able to alleviate the impact of the price prediction error. Numerical results demonstrate that the proposed approach can effectively shift the peak-hour demand to off-peak hours, enhance the welfare of each user, and minimize the peak-to-average ratio. The scalability of the approach and the impact of the user number are also investigated. This paper proposes a model to determine the optimal size of an energy storage facility from a strategic investor's perspective. This investor seeks to maximize its profit through making strategic planning, i.e., storage sizing, and strategic operational, i.e., offering and bidding, decisions. We consider the uncertainties associated with rival generators’ offering strategies and future load levels in the proposed model. The strategic investment decisions include the sizes of charging device, discharging device, and energy reservoir. The proposed model is a stochastic bi-level optimization problem; the planning and operation decisions are made in the upper-level, and market clearing is modeled in the lower-level under different operating scenarios. To make the proposed model computationally tractable, an iterative solution technique based on Benders’ decomposition is implemented. This provides a master problem and a set of subproblems for each scenario. Each subproblem is recast as an mathematical programs with equilibrium constraints. Numerical results based on real-life market data from Alberta's electricity market are provided. Abstract This paper proposes a parallel hurricane optimization algorithm (PHOA) for solving economic emission load dispatch (EELD) problem in modern power systems. In PHOA, several sub-populations moving independently in the search space with the aim of simultaneously optimizing the problem objectives considering the local behavior between sub-populations. By this way, it is intended to search for the Pareto optimal solutions which are contrasting to the single optimal solution. The inherent characteristics of parallelization strategy can enhance the Pareto solutions and increase the convergence to reach the Pareto optimal solutions. Simulations are conducted on three test systems and comparisons with other optimization techniques that reported in the literature are demonstrated. The obtained results demonstrate the superiority of the proposed PHOA compared to other optimization techniques. Additional economic benefits with secure settings are fulfilled, while preserving all system constraints within their permissible limits. Added to that, two security indices are proposed from generation units and transmission lines. The highest security index from generation units reflects that the operating condition achieves more power reserve. In transmission lines, the highest security index means that the transmission lines operated beyond their congestion limits. For justification of the proposed security indices, the proposed solution methodology is employed to assure their benefits in terms of economical and environmental issues. The proposed algorithm improves the economic issue as well as enhances the power system operation in the technical point of view with acceptable levels of emissions. Moreover, design of experiments using the Taguchi approach is employed to calibrate the parameters of the algorithms. So, it can be considered as a promising alternative algorithm for solving problems in practical large-scale power systems. This paper addresses the attraction domain of model-based predictive control (MPC) for nonlinear systems with control input and state constraints. Based on a stability condition of nonlinear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilising control law to maximise the domain of attraction of the nonlinear MPC is proposed. The problem of maximisation of the attraction region is recast as a well-defined optimisation problem. By an LMI based optimisation approach, the terminal weighting item and fictitious terminal stabilising control law axe optimised to enlarge the attraction domain and hence the feasibility domain of the nonlinear MPC method. The proposed method is illustrated by a numerical example and favourably compared with existing results. While electric vehicles (EVs) are expected to provide environmental and economical benefit, judicious coordination of EV charging is necessary to prevent overloading of the distribution grid. Leveraging the smart grid infrastructure, the utility company can adjust the electricity price intelligently for individual customers to elicit desirable load curves. In this context, this paper addresses the problem of predicting the EV charging behavior of the consumers at different prices, which is a prerequisite for optimal price adjustment. The dependencies on price responsiveness among consumers are captured by a conditional random field (CRF) model. To account for temporal dynamics potentially in a strategic setting, the framework of online convex optimization is adopted to develop an efficient online algorithm for tracking the CRF parameters. The proposed model is then used as an input to a stochastic profit maximization module for real-time price setting. Numerical tests using simulated and semi-real data verify the effectiveness of the proposed approach.