Distributed Stochastic Market Clearing with High-Penetration Wind Power

Integrating renewable energy into the modern power grid requires risk-cognizant dispatch of resources to account for the stochastic availability of renewables. Toward this goal, day-ahead stochastic market clearing with high-penetration wind energy is pursued in this paper based on the DC optimal power flow (OPF). The objective is to minimize the social cost which consists of conventional generation costs, end-user disutility, as well as a risk measure of the system re-dispatching cost. Capitalizing on the conditional value-at-risk (CVaR), the novel model is able to mitigate the potentially high risk of the recourse actions to compensate wind forecast errors. The resulting convex optimization task is tackled via a distribution-free sample average based approximation to bypass the prohibitively complex high-dimensional integration. Furthermore, to cope with possibly large-scale dispatchable loads, a fast distributed solver is developed with guaranteed convergence using the alternating direction method of multipliers (ADMM). Numerical results tested on a modified benchmark system are reported to corroborate the merits of the novel framework and proposed approaches.Comment: To appear in IEEE Transactions on Power Systems; 12 pages and 9 figure

An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination in terms of system integration and time coupling of trading floors. We propose an integrated operational model for electricity and natural gas systems under uncertain power supply by applying two-stage stochastic programming. This formulation co-optimizes day-ahead and real-time dispatch of both energy systems and aims at minimizing the total expected cost. Additionally, two deterministic models, one of an integrated energy system and one that treats the two systems independently, are presented. We utilize a formulation that considers the linepack of the natural gas system, while it results in a tractable mixed-integer linear programming (MILP) model. Our analysis demonstrates the effectiveness of the proposed model in accommodating high shares of renewables and the importance of proper natural gas system modeling in short-term operations to reveal valuable flexibility of the natural gas system. Moreover, we identify the coordination parameters between the two markets and show their impact on the system's operation and dispatch

Study Of Stochastic Market Clearing Problems In Power Systems With High Renewable Integration

Integrating large-scale renewable energy resources into the power grid poses several operational and economic problems due to their inherently stochastic nature. The lack of predictability of renewable outputs deteriorates the power grid’s reliability. The power system operators have recognized this need to account for uncertainty in making operational decisions and forming electricity pricing. In this regard, this dissertation studies three aspects that aid large-scale renewable integration into power systems. 1. We develop a nonparametric change point-based statistical model to generate scenarios that accurately capture the renewable generation stochastic processes; 2. We design new pricing mechanisms derived from alternative stochastic programming formulations of the electricity market clearing problem under uncertainty; 3. We devise a novel approach to coordinate strategic operations of multiple noncooperative system operators. The current industry practices are based on deterministic models that do not account for the stochasticity of renewable energy. Therefore, the solutions obtained from these deterministic models will not provide accurate measurements. Stochastic programming (SP) can accommodate the stochasticity of renewable energy by considering a set of possible scenarios. However, the reliability of the SP model solution depends on the accuracy of the scenarios. We develop a nonparametric statistical simulation method to develop scenarios for wind generation using wind speed data. In this method, we address the nonstationarity issues that come with wind-speed time-series data using a nonparametric change point detection method. Using this approach, we retain the covariance structure of the original wind-speed time series in all the simulated series. With an accurate set of scenarios, we develop alternative two-stage SP models for the two-settlement electricity market clearing problem using different representations of the non-anticipativity constraints. Different forms of non-anticipativity constraints reveal different hidden dual information inside the canonical two-stage SP model, which we use to develop new pricing mechanisms. The new pricing mechanisms preserve properties of previously proposed pricing mechanisms, such as revenue adequacy in expectation and cost recovery in expectation. More importantly, our pricing mechanisms can guarantee cost recovery for every scenario. Furthermore, we develop bounds for the price distortion under every scenario instead of the expected distortion bounds. We demonstrate the differences in prices obtained from the alternative mechanisms through numerical experiments. Finally, we discuss the importance of distributed smart grid operations inside the power grid. We develop an information and electricity exchange system among multiple distribution systems. These distribution systems participate/compete in common markets cohere electricity is exchanged. We develop a standard Nash game treating each distribution system (DS) as an individual player who optimizes their strategies separately. We develop proximal best response (BR) schemes to solve this problem. We present results from numerical experiments conducted on three and six DS settings

Pricing Schemes in Electric Energy Markets

abstract: Two thirds of the U.S. power systems are operated under market structures. A good market design should maximize social welfare and give market participants proper incentives to follow market solutions. Pricing schemes play very important roles in market design. Locational marginal pricing scheme is the core pricing scheme in energy markets. Locational marginal prices are good pricing signals for dispatch marginal costs. However, the locational marginal prices alone are not incentive compatible since energy markets are non-convex markets. Locational marginal prices capture dispatch costs but fail to capture commitment costs such as startup cost, no-load cost, and shutdown cost. As a result, uplift payments are paid to generators in markets in order to provide incentives for generators to follow market solutions. The uplift payments distort pricing signals. In this thesis, pricing schemes in electric energy markets are studied. In the first part, convex hull pricing scheme is studied and the pricing model is extended with network constraints. The subgradient algorithm is applied to solve the pricing model. In the second part, a stochastic dispatchable pricing model is proposed to better address the non-convexity and uncertainty issues in day-ahead energy markets. In the third part, an energy storage arbitrage model with the current locational marginal price scheme is studied. Numerical test cases are studied to show the arguments in this thesis. The overall market and pricing scheme design is a very complex problem. This thesis gives a thorough overview of pricing schemes in day-ahead energy markets and addressed several key issues in the markets. New pricing schemes are proposed to improve market efficiency.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Stochastic Electricity Dispatch: A challenge for market design

We consider an electricity market with two sequential market clearings, for instance representing a day-ahead and a real-time market. When the first market is cleared, there is uncertainty with respect to generation and/or load, while this uncertainty is resolved when the second market is cleared. We compare the outcomes of a stochastic market clearing model, i.e. a market clearing model taking into account both markets and the uncertainty, to a myopic market model where the first market is cleared based only on given bids, and not taking into account neither the uncertainty nor the bids in the second market. While the stochastic market clearing gives a solution with a higher total social welfare, it poses several challenges for market design. The stochastic dispatch may lead to a dispatch where the prices deviate from the bid curves in the first market. This can lead to incentives for selfscheduling, require producers to produce above marginal cost and consumers to pay above their marginal value in the first market. Our analysis show that the wind producer has an incentive to deviate from the system optimal plan in both the myopic and stochastic model, and this incentive is particularly strong under the myopic model. We also discuss how the total social welfare of the market outcome under stochastic market clearing depends on the quality of the information that the system operator will base the market clearing on. In particular, we show that the wind producer has an incentive to misreport the probability distribution for wind