Eilyan Bitar

Bringing Wind Energy to Market

Wind energy is a rapidly growing source of renewable energy generation. However, the current extra-market approach to its assimilation into the electric grid will not scale at deep penetration levels. In this paper, we investigate how an independent wind power producer might optimally offer its variable power into a competitive electricity market for energy. Starting with a stochastic model for wind power production and a model for a perfectly competitive two-settlement market, we derive explicit formulae for optimal contract offerings and the corresponding optimal expected profit. As wind is an inherently variable source of energy, we explore the sensitivity of optimal expected profit to uncertainty in the underlying wind process. We also examine the role of forecast information and recourse markets in this setting. We quantify the role of reserves in increasing reliability of offered contracts and obtain analytical expressions for marginal profits resulting from investments in improved forecasting and local auxiliary generation. The formulae make explicit the relationship between price signals and the value of such firming strategies.

Smart grid data integrity attacks: characterizations and countermeasures π

Coordinated cyberattacks of power meter readings can be arranged to be undetectable by any bad data detection algorithm in the power system state estimation process. These unobservable attacks present a potentially serious threat to grid operations. Of particular interest are sparse attacks that involve the compromise of a modest number of meter readings. An efficient algorithm to find all unobservable attacks [under standard DC load flow approximations] involving the compromise of exactly two power injection meters and an arbitrary number of line power meters is presented. This requires O(n2m) flops for a power system with n buses and m line meters. If all lines are metered, there exist canonical forms that characterize all 3, 4, and 5-sparse unobservable attacks. These can be quickly detected in power systems using standard graph algorithms. Known-secure phasor measurement units [PMUs] can be used as countermeasures against an arbitrary collection of cyberattacks. Finding the minimum number of necessary PMUs is NP-hard. It is shown that p + 1 PMUs at carefully chosen buses are sufficient to neutralize a collection of p cyberattacks.

The role of co-located storage for wind power producers in conventional electricity markets

In this paper we study the problem of optimizing contract offerings for an independent wind power producer (WPP) participating in conventional day-ahead forward electricity markets for energy. As wind power is an inherently variable source of energy and is difficult to predict, we explore the extent to which co-located energy storage can be used to improve expected profit and mitigate the the financial risk associated with shorting on the offered contracts. Using a simple stochastic model for wind power production and a model for the electricity market, we show that the problem of determining optimal contract offerings for a WPP with co-located energy storage can be solved using convex programming.

Wind energy aggregation: A coalitional game approach

In this paper we explore the extent to which a group of N wind power producers can exploit the statistical benefits of aggregation and quantity risk sharing by forming a willing coalition to pool their variable power to jointly offer their aggregate power output as single entity into a forward energy market. We prove that wind power generators will always improve their expected profit when they aggregate their generated power and use tools from coalitional game theory to design fair sharing mechanisms to allocate the payoff among the coalition participants. We show that the corresponding coalitional game is super-additive and has a nonempty core. Hence, there always exists a mechanism for profit-sharing that makes the coalition stable. However, the game is not convex and the celebrated Shapley value may not belong to the core of the game. An allocation mechanism that minimizes the worst-case dissatisfaction is proposed.

Systems and Control Opportunities in the Integration of Renewable Energy into the Smart Grid

Abstract The Smart Grid is among the most important and ambitious endeavors of our time. Deep integration of renewable energy sources is one component of the Smart Grid vision. A fundamental difficulty here is that renewable energy sources are highly variable – they are not dispatchable, are intermittent, and uncertain. The electricity grid must absorb this variability through a portfolio of solutions. These include aggregation of variable generation, curtailment, operating reserves, storage technologies, local generation, and distributed demand response. The various elements in this portfolio must be dynamically coordinated based on available information within the framework of electricity grid operations. This, in turn, will require critical technologies and methods drawn from optimization, modeling, and control, which are the core competencies of Systems and Control. This paper catalogues some of these systems and control research opportunities that arise in the deep integration of renewable energy sources.

Risk limiting dispatch of wind power

Integrating wind and solar power into the grid requires dispatching various types of reserve generation to compensate for the randomness of renewable power. The dispatch is usually determined by a system operator (SO) or an aggregator who `firms variable energy by bundling it with conventional power. The optimal dispatch is formulated as the solution to a stochastic control problem and shown to have a closed form that can be quickly computed. Different objectives and risk constraints can be included in the formulation and trade-offs can be evaluated. In particular one can quantify the influence of sequential forecasts on the total integration cost and the choice of dispatched generation. When the forecast error is Gaussian, the optimal dispatch policy can be precomputed.

Optimal contracts for wind power producers in electricity markets

This paper is focused on optimal contracts for an independent wind power producer in conventional electricity markets. Starting with a simple model of the uncertainty in the production of power from a wind turbine farm and a model for the electric energy market, we derive analytical expressions for optimal contract size and corresponding expected optimal profit. We also address problems involving overproduction penalties, cost of reserves, and utility of additional sensor information. We obtain analytical expressions for marginal profits from investing in local generation and energy storage.

Optimal sharing of quantity risk for a coalition of wind power producers facing nodal prices

It is widely accepted that aggregation of geographically diverse wind energy resources offers compelling potential to mitigate wind power variability, as wind speed at different geographic locations tends to decorrelate with increasing spatial separation. In this paper, we explore the extent to which a coalition of wind power producers can exploit the statistical benefits of aggregation to mitigate the risk of quantity shortfall with respect to forward contract offerings for energy. We propose a simple augmentation of the existing two-settlement market system with nodal pricing to permit quantity risk sharing among wind power producers by affording the group a recourse opportunity to utilize improved forecasts of their ensuing wind energy production to collectively modify their forward contracted positions so as to utilize the projected surplus in generation at certain buses to balance the projected shortfall in generation at complementary buses. Working within this framework, we show that the problem of optimally sizing a set of forward contracts for a group of wind power producers reduces to convex programming and derive closed form expressions for the set of optimal recourse policies. We also asses the willingness of individual wind power producers to form a coalition to cooperatively offer contracts for energy. We first show that the expected profit derived from coalitional contract offerings with recourse is greater than that achievable through independent contract offerings. And, using tools from coalitional game theory, we show that the core for our game is non-empty.

Linear minimax estimation for random vectors with parametric uncertainty

In this paper, we take a minimax approach to the problem of computing a worst-case linear mean squared error (MSE) estimate of X given Y , where X and Y are jointly distributed random vectors with parametric uncertainty in their distribution. We consider two uncertainty models, PA and PB. Model PA represents X and Y as jointly Gaussian whose covariance matrix Λ belongs to the convex hull of a set of m known covariance matrices. Model PB characterizes X and Y as jointly distributed according to a Gaussian mixture model with m known zero-mean components, but unknown component weights. We show: (a) the linear minimax estimator computed under model PA is identical to that computed under model PB when the vertices of the uncertain covariance set in PA are the same as the component covariances in model PB, and (b) the problem of computing the linear minimax estimator under either model reduces to a semidefinite program (SDP). We also consider the dynamic situation where x(t) and y(t) evolve according to a discrete-time LTI state space model driven by white noise, the statistics of which is modeled by PA and PB as before. We derive a recursive linear minimax filter for x(t) given y(t).