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This paper compares risk-averse optimization methods to address the self-scheduling and market involvement of a virtual power plant (VPP). The decision-making problem of the VPP involves uncertainty in the wind speed and electricity price forecast. We focus on two methods: risk-averse two-stage stochastic programming (SP) and two-stage adaptive robust optimization (ARO). We investigate both methods concerning formulations, uncertainty and risk, decomposition algorithms, and their computational performance. To quantify the risk in SP, we use the conditional value at risk (CVaR) because it can resemble a worst-case measure, which naturally links to ARO. We use two efficient implementations of the decomposition algorithms for SP and ARO; we assess (1) the operational results regarding first-stage decision variables, estimate of expected profit, and estimate of the CVaR of the profit and (2) their performance taking into consideration different sample sizes and risk management parameters. The results show that similar first-stage solutions are obtained depending on the risk parameterizations used in each formulation. Computationally, we identified three cases: (1) SP with a sample of 500 elements is competitive with ARO; (2) SP performance degrades comparing to the first case and ARO fails to converge in four out of five risk parameters; (3) SP fails to converge, whereas ARO converges in three out of five risk parameters. Overall, these performance cases depend on the combined effect of deterministic and uncertain data and risk parameters. Summary of Contribution: The work presented in this manuscript is at the intersection of operations research and computer science, which are intrinsically related with the scope and mission of IJOC. From the operations research perspective, two methodologies for optimization under uncertainty are studied: risk-averse stochastic programming and adaptive robust optimization. These methodologies are illustrated using an energy scheduling problem. The study includes a comparison from the point of view of uncertainty modeling, formulations, decomposition methods, and analysis of solutions. From the computer science perspective, a careful implementation of decomposition methods using parallelization techniques and a sample average approximation methodology was done. A detailed comparison of the computational performance of both methods is performed. Finally, the conclusions allow establishing links between two alternative methodologies in operations research: stochastic programming and robust optimization. [ABSTRACT FROM AUTHOR]

We propose an approach to solving the AC network-constrained unit commitment problem (AC-NCUC) of large-scale power systems. This approach relies on solving convex (continuous and mixed-integer) optimization problems. First, we formulate a second-order conic relaxation of the original optimization problem, which renders a mixed-integer second-order conic optimization problem. To solve this problem, we use Benders’ decomposition, which decomposes it into a master problem, which is mixed-integer linear, and a subproblem, which is continuous and second-order conic. To improve the convergence of the Benders’ algorithm, we add several linear feasibility constraints to the master problem. Since the second-order relaxation of the original problem cannot guarantee AC feasibility of the solution found, we ensure such feasibility by solving a sequence of continuous convex optimization problems. We numerically validate the proposed approach using a Texas 2000-bus system. [ABSTRACT FROM AUTHOR]

Due to the increasing penetration of large-scale renewable energy generation at transmission level, hybrid AC/DC transmission expansion is becoming more relevant by the day, especially if the considered renewable generation is far away from existing AC grid infrastructure. This paper presents a multi-period hybrid AC/DC network expansion planning model that incorporates node voltages, reactive power and network losses. Since the operation of a high voltage DC link is influenced considerably by the converter stations, converter transformer, filter, and phase reactor are modeled in each converter station. Since the AC power flow equations render a non-convex problem whose solution algorithms do not always guarantee convergence or optimality, a second-order conic relaxation is utilized. The resulting model is a mixed-integer convex problem with a convergence guarantee that embodies a better approximation of system operation than its DC linear counterpart. Three case studies are considered to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

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 consider a significant problem that arises in the planning of many projects. Project companies often use outsourced providers that require capacity reservations that must be contracted before task durations are realized. We model these decisions for a company that, given partially characterized distributional information, assumes the worst-case distribution for task durations. Once task durations are realized, the project company makes decisions about fast tracking and outsourced crashing, to minimize the total capacity reservation, fast tracking, crashing, and makespan penalty costs. We model the company's objective using the target-based measure of minimizing an underperformance riskiness index. We allow for correlation in task performance, and for piecewise linear costs of crashing and makespan penalties. An optimal solution of the discrete, nonlinear model is possible for small to medium size projects. We compare the performance of our model against the best available benchmarks from the robust optimization literature, and show that it provides lower risk and greater robustness to distributional information. Our work thus enables more effective risk minimization in projects, and provides insights about how to make more robust capacity reservation decisions. Summary of Contribution: This work studies a financially significant planning problem that arises in project management. Companies that face uncertainties in project execution may need to reserve capacity with outsourced providers. Given that decision, they further need to plan their operational decisions to protect against a bad outcome. We model and solve this problem via adjustable distributionally robust optimization. While this problem involves two-stage decision making, which is computationally challenging in general, we develop a computationally efficient algorithm to find the exact optimal solution for instances of practical size. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology to identify the best locations to install battery energy storage systems (BESS) in radial distribution networks. Such batteries are mainly intended for improving the reliability of the distribution network. The methodology uses utility historical load, outage and project-cost data, and relies on a mixed-integer linear programming optimization tool. The power and energy capacities of any of the BESS considered can be pre-specified based on the system's load and outage data. On the other hand, such parameters can be optimally determined, which generally results in a large number of small BESSs distributed throughout the distribution system. We analyze both alternatives. The optimal siting of BESSs is illustrated and discussed via sensitivity analysis using a small distribution system. In addition, a case study based on a real-worlddistribution network is analyzed. Outcomes show the validity and efficacy of the proposed methodology. [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]

We consider the operation of a power system with high renewable penetration and minimal network bottlenecks and provide a technique to determine the appropriate level of reserve to enforce. Within a daily scheduling framework, we model the production uncertainty of renewable units via scenarios and include security constraints per scenario to ensure an uneventful operation in case of failure of key thermal units. The rarely constraining network is modeled via areas with limited capacity at their interfaces. The considered decision-making framework results in a two-stage stochastic programming problem whose first stage decides on the commitment of thermal units and whose second stage reproduces, per scenario, the operation of the system with and without the failure of key thermal units. The optimal unit scheduling obtained from the proposed model implicitly identifies a generating reserve pattern that we compare with common rules used in industry for reserve identification, such as 20% or 30% of the demand. We use the Illinois 200-bus system to illustrate and computationally characterize the methodology proposed. • An economically efficient yet secure reserve determination procedure. • Renewable uncertainty is modeled via scenarios. • Security regarding unit failures is ensured via security constraints. • The resulting optimization model is tractable and does not need decomposition. • The reserve determined is superior to setting a percentage of the load as reserve. [ABSTRACT FROM AUTHOR]

We study investment equilibria in electricity and gas markets wherein electricity producers and natural gas suppliers behave strategically. We consider also hybrid producers that own both generating units and gas sources. Each strategic producer determines its investment decisions in gas-fired units, and its offering and bidding strategies to maximize its own profit, anticipating electricity and gas market-clearing outcomes. Producers owning gas-fired units submit bids to the gas market to procure fuel and offers to the electricity market to sell electricity. The resulting model is recast as an equilibrium problem with equilibrium constraints that we solve using a direct approach. Numerical results from two test systems illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

We study market equilibria that are achieved by strategic firms that participate in electricity and natural gas markets. Strategic firms submit their offers and bids to both markets with the aim of maximizing profit or utility and we consider firms that can include a combination of electricity and natural gas supply and demand. The strategic actions of these firms are represented by upper-level problems that are optimized subject to shared lower-level problems that represent the clearing of electricity and natural gas markets. This market structure and our modeling approach yields a multiple-leader/two-follower complementarity problem. We develop a modeling approach that can find equilibria with different characteristics, e.g., maximized social welfare, producer profits, or consumer welfare. We demonstrate numerically that producers aim typically to increase market prices while consumers seek to decrease them. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing an algorithm for system operators to solve a robust security-constrained AC optimal power flow (R-SC-ACOPF) problem, which also optimizes the settings of discrete controllers including load tap changers (LTCs) and shunt capacitor banks (SCBs). An iterative algorithm involving a master problem and a number of sub-problems is proposed. The master problem selects the optimal discrete controllers’ settings by taking into account primal SC-ACOPF constraints based on the single-component worst contingencies identified by the sub-problems. Each sub-problem is a bi-level max-min problem used to find the current worst contingency. The overall objective is to minimize the total cost, including generation and load shedding cost, while satisfying all relevant constraints. The master problem and sub-problems allow representing LTC tap positions, SCB status, and contingencies using binary variables. Two case studies are presented as applications of this novel technique. [ABSTRACT FROM AUTHOR]

Electric power and natural gas systems typically are operated independently. However, their operations are interrelated due to the proliferation of natural gas-fired generating units. We analyze the independent but interrelated day-ahead operation of the two systems. We use a direct approach to identify operational equilibria involving these two systems, in which the Karush-Kuhn-Tucker conditions of both electric power and natural gas operational models are gathered and solved jointly. We characterize the equilibria that are obtained under different levels of temporal and spatial granularity in conveying information between the two system operators. Numerical results from the Belgian system are used to examine the impacts of different levels of information interchange on prices, operational costs, and decisions in the two systems. [ABSTRACT FROM AUTHOR]

Pursuing resilience enhancement, we propose a hierarchical decision-making framework for proactive consumers and the supplying utility interacting through an electricity distribution system. Such decision framework enables identifying solutions that are optimal for both the leading partner, the electric utility, and the other agents, proactive consumers and non-proactive consumers, that react to the decisions of the leading agent. Resilience improvement interventions include installing batteries and undergrounding distribution lines. The proposed technique can be helpful to distribution system planners, who can use it to optimally coordinate the resilience enhancement investments by the electric utility and proactive consumers. We analyze cases pertaining to realistic distribution systems. • Resilience enhancement using batteries and undergrounding feeders. • Hierarchical optimization including the electric utility and proactive consumers. • Enhancement outcomes depend significantly on cost and available options. • Hybrid solutions involving both the utility and proactive consumers are common. [ABSTRACT FROM AUTHOR]

The interdependency of electric power and natural gas systems requires co-ordinated operational planning. We propose a unit commitment model that integrates a second-order-cone relaxation of a non-convex nonlinear natural-gas flow model that considers pipeline line pack. The model is enhanced by using convex envelopes of bilinear terms, which tighten the relaxation. By fixing the binary variables at their optimal values and linearizing the natural gas-flow-balance equations around the solution that is obtained, we obtain electricity and natural gas locational marginal prices as the dual variables of electricity- and natural gas-flow-balance equations, respectively. The interdependence between these sets of prices is discussed. Numerical results from two test systems validate the solution-quality and computational-efficiency benefits of the proposed modeling methodology. [ABSTRACT FROM AUTHOR]

The recent leak of the Aliso Canyon natural gas storage facility calls for coordinated planning of natural gas and electric power systems with specific consideration of electrical energy storage. This paper proposes a coordinated planning model that fills this need. The model is formulated as a two-stage stochastic optimization problem, in which electricity- and natural gas-demand growth and natural gas-supply uncertainties are represented. We analyze the tradeoff between building electrical, natural gas, and electrical energy storage infrastructure. The sensitivity of electrical energy storage investment to the modeling of the operating conditions is also studied. The model is tested using a California-based case study. [ABSTRACT FROM AUTHOR]

In this paper, the coordinated investment in transmission and storage systems under uncertainty is addressed from the perspective of a central planner. The problem is formulated with the objective of achieving an effective expansion of both transmission and storage that minimizes the investment cost, while achieving an effective operation of a power system with high penetration of renewable power. The problem is stated within an adaptive robust optimization framework that incorporates stochastic modeling. Future available generation capacity and peak load in the target year (long-term uncertainty) are modeled using a robust set, while daily operating conditions (short-term uncertainty) are represented with a scenario set. The expansion tradeoff between transmission and storage systems is analyzed using the IEEE RTS 24-bus and IEEE 118-bus networks. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing an algorithm for identifying the worst contingencies to be used in a security-constrained optimal power flow problem. A bilevel max-min optimization model is proposed to find the worst contingency scenario while solving an ac optimal power flow problem and considering corrective actions. The objective is to minimize the total cost including generation and load shedding cost while satisfying all relevant constraints. The upper-level problem allows representing contingencies using binary variables. We formulate a second-order cone problem in the lower-level to represent the ac power flow equations. Duality is used to merge the upper- and lower-level problems into a single-level one. The resulting mixed-integer second-order conic problem can be efficiently solved. Three case studies are presented as applications of this novel technique. [ABSTRACT FROM AUTHOR]

Many principles underlying the design of restructured electricity markets that are in-use today were developed over three decades ago when power systems were considerably different than today’s and tomorrow’s systems are. Systems of the past typically relied on large dispatchable thermal generators to supply energy. This can be contrasted with power systems today, which are experiencing rising penetrations of weather-dependent renewable energy sources that have limited dispatchability. Moreover, many power systems are experiencing growing adoption of distributed energy resources and novel uses of electric energy by end customers, which adds to demand uncertainty and variability. However, these technologies also provide opportunities for more active participation of the demand-side in maintaining system reliability and service quality. Given these marked changes in the architecture of electric power systems, we are at a unique point at which the tenets of restructured electricity market design can be re-evaluated. While this re-examination is largely driven by changes in power system designs, we can also rely on lessons learned from the past three decades of market-restructuring experience. In this paper, we highlight some of the challenges in designing electricity markets brought about by changes in system designs. We also discuss a number of lessons learned from market designs that have been implemented. We then suggest some important principles that should underlie future reforms of electricity market designs and raise design questions that require further research and examination. [ABSTRACT FROM AUTHOR]

The interdependence between natural gas and electric power systems is becoming increasingly tight, as the share of natural gas-fired units increases. Within this context, this paper addresses the coordinated expansion planning of natural gas and power systems. We analyze the tradeoff of building natural gas-related facilities (e.g., natural gas pipelines and natural gas-fired generation units) versus electric-power-related facilities (e.g., transmission lines and other generation units). We use a two-stage stochastic optimization model that provides an appropriate balance between accuracy and computational tractability and represents uncertainty pertaining to electricity and natural gas demands. We show the importance of representing uncertainty by computing the value of stochastic solution, which is significant. We analyze the functioning of the model through a small example and a case study based on the IEEE 118-bus system. Computational results confirm the need for detailed representation of both the natural gas and power systems to achieve investment decisions that are well coordinated and optimal. [ABSTRACT FROM PUBLISHER]

This paper addresses the transmission expansion planning problem under long- and short-term uncertainty. Long-term uncertainty pertains to changes across years (demand growth and future increase in production capacity), whereas short-term uncertainty pertains to changes within a year (demand and wind/solar power production variability, and equipment availability). This expansion problem is formulated as an adaptive robust optimization problem that provides protection against long-term uncertainty while carefully representing short-term uncertainty via scenarios. The problem is solved via a tailored implementation of the primal Benders’ decomposition algorithm that focuses on an efficient solution of the subproblem. The effectiveness of the proposed algorithm to identify robust expansion plans and its computational efficiency are illustrated through a realistic case study. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing a practical and efficient tool for utility transmission planners to protect critical transmission assets from potential physical attacks. A trilevel min–max–min optimization model is proposed to represent actions of a planner, an attacker, and an operator. These three agents share a common objective function, which is the system load shedding. The strong duality theorem is used to merge the middle- and lower-level problems into a single-level one. The resulting mixed-integer bilevel model is solved by a Benders decomposition technique using primal cuts. Two case studies are presented as applications of this novel technique. Additionally, the proposed technique is compared with an implicit enumeration algorithm. [ABSTRACT FROM AUTHOR]

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]

The cost of a generating unit as a function of its power output is generally non‐linear and discontinuous. Therefore, the objective function of a unit commitment (UC) problem is generally non‐linear and discontinuous as well. The authors describe two efficient piecewise‐linear formulations of the objective function of an UC problem that are not found in the power literature. These formulations allow representing non‐convexities and discontinuities. They compare these formulations with a common one in the power literature. They show the advantage of the proposed formulations for both deterministic and stochastic UC problems. [ABSTRACT FROM AUTHOR]

In highly polluted regions, it might be necessary to operate power plants enforcing appropriate emission limits to help ensuring air quality. If the air quality is low and pollutants are difficult to diffuse, few additional emissions should be allowed to avoid further deteriorating the air quality. Wind power helps reducing pollution levels as it substitutes polluting thermal production. However, wind and air pollution are generally anti‐correlated. Storage can be used to shift wind power production from hours when higher pollution levels are allowed to hours when lower pollution levels are allowed to help meeting emission constraints at critical hours. Storage availability also achieves a comparatively lower production cost for the system as a whole. To represent the stochastic nature of wind power production and weather‐dependent emission limits, the authors propose a two‐stage stochastic programming model to analyse the trade‐off emission versus cost in an electric energy system with storage facilities. The first stage represents the day‐ahead scheduling, while the second one represents the real‐time operation under different scenarios. The authors analyse the impact of emission limits and/or storage on generation scheduling by comparing different models using an illustrative example and a case study based on the IEEE 118‐node system. [ABSTRACT FROM AUTHOR]

Some areas in China are facing pressing air pollution problems. Measures from the power sector can be taken to cope with air pollution issues, including reducing emission levels of thermal units and integrating wind and solar power. Social welfare, emission, and renewable integration are three major concerns in modern power system operations. This paper describes three stochastic scheduling models aiming at maximizing social welfare (SW), minimizing emission (EM) and maximizing renewable production (RE). A multi-objective scheduling model (MT) is also proposed that properly balances the above objectives. Wind power uncertainty and dispatchable loads are considered in the model. The outcomes of the three models are compared through an illustrative example and a 57-node case study. Results show that model EM results in 36% of the social welfare of model SW, 27% of its emissions, and 43% of its wind spillage, while model RE results in 55% of the social welfare of model SW, 56% of its emissions and 28% of its wind spillage. Additionally, we analyze how the optimal generation scheduling is affected by the weights in model MT. This work provides insight to policy makers on how to balance social welfare, emissions and renewable production. [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]

We propose a two-stage mixed-integer linear stochastic optimization model to analyze the scheduling of electricity-production units under natural gas-supply uncertainty due to pipeline congestion and natural gas-price variability. The first stage of this stochastic optimization model represents the day-ahead scheduling (i .e., unit commitment) stage, while the second stage represents actual real-time operations through a number of scenarios. We use this model to analyze the effect on unit commitment and dispatch of two types of natural gas-supply conditions. First, we analyze a case involving low-cost natural gas supply with natural gas-transmission issues related to potential gas-pipeline congestion. We then examine a case involving higher-cost natural gas, which is used solely to attain feasibility with fast-ramping events. The first case mimics situations in the ISO New England system, in which relatively low-cost natural gas supply is uncertain in cold-weather conditions due to natural gas-transmission bottlenecks. The second case is reminiscent of situations in the California ISO system, in which relatively expensive but flexible natural gas-fired units need to be used to handle rapid changes in net demand in the early mornings and late afternoons. [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]

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios. • A solution approach for the risk-constrained unit commitment with weekly storage. • Approach uses a column-and-constraint generation algorithm into a Benders framework. • Master problem embeds primal information from the subproblems to enhance convergence. • An active set strategy is used to speed up the solution time of the proposed method. • Numerical experiments are carried out using the South Carolina synthetic system. [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]

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]

Capacity expansion planning (CEP) of power systems determines the optimal future generation mix and/or transmission lines. Due to the increasing penetration of renewables, CEP has to capture the hourly variations of renewable generator outputs and load demand. Since CEP problems typically involve planning horizons of several years, solving the fullspace models where the operating decisions corresponding to all the days is intractable. Therefore, some "representative days" are selected as a surrogate to the fullspace model. We present an input-based and a cost-based approach in combination with the k -means and the k -medoids clustering algorithms for representative day selection. The mathematical properties of the proposed algorithms are analyzed, including an approach to calculate the "optimality gap" of the investment decisions obtained from the representative day model to the fullspace model, and the relationship between the clustering error and the optimality gap. To capture the extreme operating conditions, two novel approaches, i.e., a "load shedding cost" approach and a "highest cost" approach, are proposed to identify the "extreme days". We conclude with a case study based on the Electric Reliability Council of Texas (ERCOT) region, which compares the different approaches and the effects of adding the extreme days. • Representative days are used for capacity expansion planning. • We present an input-based and a cost-based methods for representative day selection. • The theoretical properties of both methods, including the optimality gap, are analyzed. • Computational studies are performed for the Texas region. [ABSTRACT FROM AUTHOR]

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 proposes a decentralized methodology to optimally schedule generating units while simultaneously determining the geographical allocation of the required reserve. We consider an interconnected multi-area power system with cross-border trading in the presence of wind power uncertainty. The multi-area market-clearing model is represented as a two-stage stochastic programming model. The proposed decentralized procedure relies on an augmented Lagrangian algorithm that requires no central operator intervention but just moderate interchanges of information among neighboring regions. The methodology proposed is illustrated using an example and a realistic case study. [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]

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]

The cross-border trading among electricity markets in an interconnected multi-area system (e.g., in central Europe) and the integration of renewable resources (e.g., wind energy) have remarkably increased in recent years. To efficiently operate such system, a proper coordination among different areas is required. Within this context, a decentralized algorithm for market clearing is proposed in this paper to dispatch simultaneously energy and reserve under wind generation uncertainty and equipment failures. The proposed technique does not require a central operator but just a moderate interchange of information among neighboring areas. Additionally, the benefit of cross-border trading is studied. [ABSTRACT FROM PUBLISHER]

• Propose a model to quantitatively assess the consequences of data-integrity cyber attacks in the operation of power systems. • Based on AC models of state estimation and optimal power flow. • The proposed model considers a resource-constrained omniscient attacker. • The attacker pursues to stage an attack while remaining unobservable to the bad data detection algorithm. • Demonstrate the effectiveness of the proposed model using a 6-bus system a and the IEEE 30-bus test system. We propose in this paper a model to quantify the consequences of the vulnerabilities of the AC-based state estimation against data-integrity cyber attacks. We consider attacks whose goals are to corrupt the state estimator and/or the operation of the power grid. By considering AC-based models of the state estimator and the operation of the power system, the proposed model allows quantifying the reliability consequences (i.e., alteration in the active and reactive power), and the economic consequences (e.g., distorting locational marginal prices) of such attacks. We consider a resource-constrained omniscient attacker intending to alter the operation of the power system. We impose a stealthy condition on the attacker so that its malicious action is invisible to the bad-data-detection algorithm. The upper-level problem of the proposed bilevel model represents the attacker's action and pursues disrupting the system operation and it is constrained by two lower-level problems. The first lower-level problem is the state-estimation that calculates the most likely state of the system considering the corrupted measurement. The second lower-level problem is a conic relaxation of the optimal power flow that uses the output of the state estimation problem to minimize operation costs. We illustrate the proposed bilevel model using two test systems. [ABSTRACT FROM AUTHOR]

• Propose a solution approach for the AC network-constrained unit commitment problem. • The proposed approach relies on convex (continuous and mixed-integer) programming. • An active set strategy is used to speed up the solution time of the proposed approach. • An AC feasible solution is recovered using a sequence of convex optimization problems. • Demonstrate the effectiveness of the proposed approach using the IEEE 24-bus test system and an Illinois 200-bus system. To address the AC network-constrained unit commitment problem, we propose an effective three-step solution approach. We first solve a DC (mixed-integer linear) approximation of the original problem to identify an initial solution and the set of transmission lines likely to be congested. Secondly, with the linear solution as a starting point, we solve a mixed-integer second-order conic relaxation of the original problem using an active set strategy regarding transmission constraints. Finally, using the solution of the relaxed problem as a starting point, we solve a set of increasingly accurate continuous convex optimization problems to ensure full AC feasibility. We show the effectiveness of the proposed approach using the IEEE 24-bus test system and an Illinois 200-bus system with 49 generators and 245 lines. [ABSTRACT FROM AUTHOR]

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]

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]

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]

This paper proposes an alternative formulation for the problem of dispatching generation units in a predominantly hydro system considering a medium-term horizon. Hydro-power dispatch is expressed as a equilibrium problem with equilibrium constraints (EPEC) and its solutions are compared to the solutions of a classical optimal hydro dispatch problem. A stochastic formulation is used to represent uncertainties in water inflows. Results are presented for realistic test systems with interconnected reservoirs. [ABSTRACT FROM PUBLISHER]

This paper considers the yearly maintenance scheduling of generating units within a market environment. Each producer schedules its units' maintenance periods to maximize its revenue using a bilevel approach. The upper-level problem of this bilevel model seeks maximum revenue and contains unit scheduling constraints, while the lower-level problems represent the market clearing process under different operating conditions. This single producer maintenance problem can be recast as a mathematical program with equilibrium constraints (MPEC). Since the MPECs of all producers have to be considered simultaneously and the market clearing process is common to all of them, the proposed formulation for maintenance scheduling is an equilibrium problem with equilibrium constraints (EPEC) corresponding to a multiple-leader-common-follower game. The solution of this EPEC is a set of equilibria, in which none of the producers is able to increase its revenue unilaterally by changing the maintenance periods of its generating units. [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]

Within a yearly horizon, a transmission system operator needs to schedule the maintenance outages of the set of transmission lines due for maintenance. Facing this task, two conflicting objectives arise: on one hand, the transmission system adequacy should be preserved as much as possible, and, on the other hand, market operation should be altered in the least possible manner. To address this scheduling problem, a bilevel model is proposed whose upper-level problem schedules line maintenance outages pursuing maximum transmission capacity margin. This upper-level problem is constrained by a set of lower-level problems that represent the clearing of the market for all the time periods considered within the yearly planning horizon. This bilevel model is conveniently converted into a nonlinear mathematical program with equilibrium constraints (MPEC) that can be recast as a mixed-integer linear programming problem solvable with currently available branch-and-cut techniques. [ABSTRACT FROM PUBLISHER]

We address the generation investment problem faced by a strategic power producer and consider a detailed description of the uncertain parameters involved, namely, rival producer investment and market offering, and demand growth. To identify optimal investment decisions, we consider a target year and propose a bilevel model whose upper-level problem determines investment and offering decisions to maximize expected profit, and whose many lower-level problems represent market clearing conditions per demand block and scenario. Since the producer total expected profit is sufficiently convex with respect to investment decisions, a Benders' decomposition approach is proposed that results in a tractable formulation even if hundred of scenarios are used to describe uncertain parameters. Extensive numerical simulations based on realistic case studies show the good performance of the proposed decomposition approach. [ABSTRACT FROM PUBLISHER]