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The power and natural-gas industries have narrowed the time differences between daily power market clearing and natural-gas market clearing. This facilitates the gas-power coordination in day-ahead scheduling. However, using natural-gas-fired power units to balance the variability of renewable energy production may cause fluctuations in natural-gas demand, which result in risks to the natural-gas system in actual operation. As such, gas-power coordination at all time is highly desirable. We analyze the coordinated operation of power and natural-gas systems at the scheduling stage and in actual operation. We assume that the two systems are operated independently, but with information interchange. We use a Lagrangian decomposition approach to identify an operational equilibrium involving the two systems. Numerical results on two test systems verify the value of gas-power coordination in actual operation. [ABSTRACT FROM AUTHOR]

We study the equilibria reached in electricity, natural-gas, and carbon-emission markets, where power producers simultaneously participate in these three markets. We use a conjectural-variations equilibrium model to represent both electricity and natural-gas markets, in which power/natural gas-producers play a quantity game and adjust their production decisions in reaction to the production levels of their rivals. We use a cap-and-trade mechanism to model the carbon-emission market. We develop a direct approach to identify equilibria involving the three markets, in which the optimality conditions of all players and market clearing conditions are gathered and solved jointly. Numerical results from two test systems illustrate the impact of carbon-emission trading and transmission constraints on the equilibria reached. Additionally, we compare equilibrium results under different types of competition. [ABSTRACT FROM AUTHOR]

A supply-function equilibrium model fits well current electricity market practice, but entails the solution of an equilibrium problem composed of bi-level problems, which is computationally very demanding. To ease such computational burden, we propose a computationally efficient single-level equilibrium model that identifies equilibria similar to those obtained by equilibrium models of bi-level problem. In our model, producers/consumers offer/bid both energy and prices. We use a simple example and a case study to illustrate and characterize the performance of the proposed single-level equilibrium model. [ABSTRACT FROM AUTHOR]

This two-paper series introduces a new multistage robust approach for solving the transmission expansion planning (TEP) problem under the uncertainty of loads and wind power productions. The proposed multistage robust TEP model is formulated using mixed binary and linear decision rules, which aims at finding a solution withstanding any realization of the uncertain parameters belonging to a set-based uncertainty model. The robustness of the optimal expansion plan can be adjusted by the budget of uncertainty. The first part of this two-paper series presents the extended and compact formulations for a deterministic TEP problem. Then, the compact formulation of the TEP problem under the uncertainty of loads and wind power productions is introduced as a multistage robust optimization problem, which is reformulated using mixed binary and linear decision rules. The extended formulation of these decision rules, as functions of uncertain parameters, is presented in this part as well. [ABSTRACT FROM AUTHOR]

This paper presents a novel model for two-stage adaptive robust transmission expansion planning (AR-TEP) problem considering the uncertainty of future load demand and future wind power production. Linear decision rules (LDRs) are utilized to reformulate the AR-TEP model as a tractable mixed-integer linear programming problem, which can be directly solved by off-the-shelf optimization packages. The proposed LDR-based AR-TEP model is illustrated using the Garver 6-bus test system, the IEEE 24-bus reliability test system, and a 236-bus test system under different conditions and compared with a decomposition-based AR-TEP model that uses primal cutting planes. Also, the robustness of the expansion plans obtained from these two AR-TEP models is evaluated by carrying out an ex-post out-of-sample analysis for different values of the budget of uncertainty. Simulation results demonstrate the effectiveness of the proposed LDR-based AR-TEP model. [ABSTRACT FROM PUBLISHER]

As the power industry considers moving from a deterministic paradigm to a stochastic one to clear the day-ahead market in systems with significant stochastic production, the following question arises: how should a stochastic clearing algorithm be formulated? Our analyses indicate that a three-stage stochastic approach is clearly superior to a two-stage one. To show this, we propose a model that includes three stages: the first one represents the day-ahead market, the second stage, the intraday market, and the third one, the real-time operation. The objective is to clear the day-ahead market, but with a prognosis of the future: the intraday market and the real-time operation. To assess the impact of the intraday market on the day-ahead outcomes, we compare the results obtained from the proposed model with those of a simpler but more common two-stage model, which represents the day-ahead market and the real-time operation. [ABSTRACT FROM AUTHOR]

This paper analyzes the impacts of flexible demands on day-ahead market outcomes in a system with significant wind power production. We use a two-stage stochastic market-clearing model, where the first stage represents the day-ahead market and the second stage represents the real-time operation. On one hand, flexibility of demands is beneficial to the system as a whole since such flexibility reduces the operation cost, but on the other hand, shifts in demands from peak periods to off-peak periods may influence prices in such a way that demands may not be willing to provide flexibility. Specifically, we investigate the impacts of different degree of demand flexibility on day-ahead prices. A number of scenarios modeling the uncertainty associated with wind production at the operation stage, and nonconvexities due to start-up costs of generators and their minimum power outputs are taken into account. [ABSTRACT FROM AUTHOR]

This paper proposes a pricing scheme for the day-ahead market in power systems with a large percentage of renewable stochastic production. To clear the day-ahead market, instead of a simplistic deterministic model, we use a two-stage stochastic programming model that embodies a prognosis of future operating conditions. Non-convexities due to start-up costs and the on/off status of generators and their minimum power outputs are properly taken into account. Our goal is to obtain uniform day-ahead clearing prices that deviate in the least possible manner from marginal prices and that allow producers to recover their costs without uplifts. The proposed methodology is illustrated using a simple example and a realistic case study. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive robust network-constrained AC unit commitment (AC-UC) model. This model is formulated as a min–max–min optimization problem, which allows representing the uncertain nature of wind power productions in terms of bounded intervals. A tri-level decomposition algorithm using primal and dual cutting planes is introduced to solve this AC-UC problem and to find a robust commitment schedule withstanding the worst realizations of uncertain wind power. To reduce the computation burden and to obtain a tractable formulation, the AC power flow equations are convexified using a Signomial transformation. The proposed AC-UC model is illustrated using the IEEE 24-bus reliability test system. Simulation results demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Given the significant amount of installed generation-capacity based on wind power, and also due to current economic downturn, the subsidies and incentives that have been widely used by wind-power producers to recover their investment costs have decreased and are even expected to disappear in the near future. In these conditions, wind-power producers need to develop offering strategies to make their investments profitable counting solely on the market. This paper proposes a multi-stage risk-constrained stochastic complementarity model to derive the optimal offering strategy of a wind-power producer that participates in both the day-ahead and the balancing markets. Uncertainties concerning wind-power productions, market prices, demands' bids, and rivals' offers are efficiently modeled using a set of scenarios. The conditional-value-at-risk metric is used to model the profit risk associated with the offering decisions. The proposed model is recast as a tractable mixed-integer linear programming program solvable using available branch-and-cut algorithms. Results of a case study are reported and discussed to show the effectiveness and applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper proposes an efficient solution approach based on Benders’ decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage refers to the day-ahead market, and whose second-stage represents real-time operation. The proposed Benders’ approach allows decomposing the original problem, which is mixed-integer nonlinear and generally intractable, into a mixed-integer linear master problem and a set of nonlinear, but continuous subproblems, one per scenario. In addition, to temporally decompose the proposed ac unit commitment problem, a heuristic technique is used to relax the inter-temporal ramping constraints of the generating units. Numerical results from a case study based on the IEEE one-area reliability test system (RTS) demonstrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

The smart grid technology enables an increasing level of responsiveness on the demand side, facilitating demand serving entities—large consumers and retailers—to procure their electricity needs under the best conditions. Such entities generally exhibit a proactive role in the pool, seeking to procure their energy needs at minimum cost. Within this framework, we propose a mathematical model to help large consumers to derive bidding strategies to alter pool prices to their own benefit. Representing the uncertainty involved, we develop a stochastic complementarity model to derive bidding curves, and show the advantages of such bidding scheme with respect to non-strategic ones. [ABSTRACT FROM PUBLISHER]

Renewable energy sources are here to stay for a number of important reasons, including global warming and the depletion of fossil fuels. We explore in this paper how a thermal-dominated electric energy system can be transformed into a renewable-dominated one. This study relies on a stochastic programming model that allows representing the uncertain parameters plaguing such long-term planning exercise. Being the final year of our analysis 2050, we represent the transition from today to 2050 by allowing investment in both production and transmission facilities, with the target of achieving a renewable-dominated minimum-cost system. The methodology developed is illustrated using a realistic large-scale case study. Finally, policy conclusions are drawn. [ABSTRACT FROM PUBLISHER]

This paper proposes an optimal power flow (OPF) model with flexible AC transmission system (FACTS) devices to minimize wind power spillage. The uncertain wind power production is modeled through a set of scenarios. Once the balancing market is cleared, and the final values of active power productions and consumptions are assigned, the proposed model is used by the system operator to determine optimal reactive power outputs of generating units, voltage magnitude and angles of buses, deployed reserves, and optimal setting of FACTS devices. This system operator tool is formulated as a two-stage stochastic programming model, whose first-stage describes decisions prior to uncertainty realization, and whose second-stage represents the operating conditions involving wind scenarios. Numerical results from a case study based on the IEEE RTS demonstrate the usefulness of the proposed tool. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of identifying the optimal investment of a strategic wind power investor that participates in both the day-ahead (DA) and the balancing markets. This investor owns a number of wind power units that jointly with the newly built ones allow it to have a dominant position and to exercise market power in the DA market, behaving as a deviator in the balancing market in which the investor buys/sells its production deviations. The model is formulated as a stochastic complementarity model that can be recast as a mixed-integer linear programming (MILP) model. A static approach is proposed focusing on a future target year, whose uncertainties pertaining to demands, wind power productions, and balancing market prices are precisely described. The proposed model is illustrated using a simple example and two case studies. [ABSTRACT FROM PUBLISHER]

We consider a cluster of interconnected price-responsive demands (e.g., an industrial compound or a university campus) that can be supplied through the main grid and a stochastic distributed energy resource (DER), e.g., a wind plant. Additionally, the cluster of demands owns an energy storage facility. An energy management system (EMS) coordinates the price-responsive demands within the cluster and provides the interface for energy trading between the demands and the suppliers, main grid and DER. The DER and the cluster of demands have a contractual agreement based on a take-or-pay contract. Within this context, we propose an energy management algorithm that allows the cluster of demands to buy, store, and sell energy at suitable times. This algorithm results in maximum utility for the demands. The uncertainty related to both the production level of the DER and the price of the energy obtained from/sold to the main grid is modeled using robust optimization (RO) techniques. Smart grid (SG) technology is used to realize 2-way communication between the EMS and the main grid, and between the EMS and the DER. Communication takes place on an hourly basis. A realistic case study is used to demonstrate the advantages of both the coordination provided by the EMS through the proposed algorithm and the use of SG technology. [ABSTRACT FROM AUTHOR]

As a result of subsidies and technological maturity, renewable electricity producers have grown in some jurisdictions to clearly dominant positions in the market. Under this context, we propose an offering strategy for a wind power producer with market power that participates in the day-ahead market as a price-maker, and in the balancing market as a deviator. Uncertainty pertaining to wind power production and balancing market price is represented through a set of correlated scenarios. The proposed model is a stochastic mathematical program with equilibrium constraints (MPEC) that can be recast as a tractable mixed-integer linear programming (MILP) problem, which is solvable using available optimization software. Results from an illustrative example and two case studies show the effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

This paper analyzes numerically the approach reported in the companion paper for identifying generation investment equilibria in an electricity market where the producers behave strategically. To this end, a two-node illustrative example and a large-scale case study based on the IEEE reliability test system (RTS) are examined and the results obtained are reported and discussed. [ABSTRACT FROM PUBLISHER]

The first of this two-paper series proposes a methodology to characterize generation investment equilibria in a pool-based network-constrained electricity market, where the producers behave strategically. To this end, the investment problem of each strategic producer is represented using a bilevel model, whose upper-level problem determines the optimal investment and the supply offering curves to maximize its profit, and whose several lower-level problems represent different market clearing scenarios. This model is transformed into a mathematical program with equilibrium constraint (MPEC) through replacing the lower-level problems by their optimality conditions. The joint consideration of all producer MPECs, one per producer, constitutes an equilibrium problem with equilibrium constraints (EPEC). To identify the solutions of this EPEC, each MPEC problem is replaced by its Karush-Kuhn-Tucker (KKT) conditions, which are in turn linearized. The resulting mixed-integer linear system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem. [ABSTRACT FROM PUBLISHER]

We consider a strategic producer that trades its energy in a multi-period network-constrained electricity pool and, for strategic reasons, is interested in identifying its rival producers' offer prices. Considering industry practice, we assume that the strategic producer has knowledge of the daily market outcomes, i.e., energy quantities sold/bought and resulting locational marginal prices (LMPs) for each time period and all nodes of the network. Using this information we formulate an inverse optimization problem that allows estimating the rival producers' offer prices that have been marginal at any of the time periods under study. Such problem is well behaved, effectively identifies rival offer prices and can be efficiently solved. The effectiveness of the proposed technique is illustrated through a simple example and a realistic case study. [ABSTRACT FROM PUBLISHER]

When deciding on wind power investments, three major issues arise: the production variability and uncertainty of wind facilities, the eventual future decline in wind power investment costs, and the significant financial risk involved in such investment decisions. Recognizing the above important issues, this paper proposes a risk-constrained multi-stage stochastic programming model to make optimal investment decisions on wind power facilities along a multi-stage horizon. The proposed model is illustrated using a clarifying example and a case study. [ABSTRACT FROM PUBLISHER]

Investment in wind power facilities involves a high level of uncertainty. To properly model such uncertainty, we consider a large number of scenarios and formulate this investment problem as a mathematical program with equilibrium constraints. The target of this problem is to maximize the profit from wind power investment in a target year, and it is subject to complementarity constraints describing a large number of market clearing conditions. Since the profit as a function of the investment variables has as sufficiently convex envelope, the considered problem can be solved by Benders decomposition. Thus, we propose, describe, and analyze a Benders decomposition algorithm to efficiently tackle the wind power investment problem. [ABSTRACT FROM PUBLISHER]

This paper provides a technique to build hourly offering curves for a price-taker producer participating in a pool. The technique relies on solving a sequence of robust mixed-integer linear programming problems. Instead of using price predictions as input data, price confidence intervals are considered. These intervals are successively divided into a sequence of nested subintervals, which allow formulating a collection of meaningful and easy-to-solve robust mixed-integer linear programming problems. The solutions of these problems provide adequate information to build hourly offering curves. [ABSTRACT FROM PUBLISHER]

This paper provides an overview of market issues related to the economic operation of an electric energy system with a high penetration of distributed energy resources. Models and tools to tackle these issues are discussed. A fully-fledged market structure of the pool type is considered. The analysis focuses on a particular distributed resource, wind power, the most economically successful renewable source. [ABSTRACT FROM AUTHOR]

This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]

This paper analyzes the impact of wind production on the locational marginal prices of a fully competitive pool-based electricity market. Wind productions are modeled as negative loads and characterized by historical data records. The analysis pertains to the structural relationship between wind production and locational marginal prices, and disregards the collateral effect of strategic offering. The study presented allows a statistical characterization of locational marginal prices as a function of the statistical data of the wind plants and the structure of the considered electric energy system. [ABSTRACT FROM PUBLISHER]