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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.03.037 Byline: Raquel Garci'a-Bertrand (a), Antonio J. Conejo (a), Steven Gabriel (b) Keywords: Quadratic programming; Market equilibrium; Pool-based electric energy market; Linear complementary problem; Minimum profit conditions Abstract: This paper provides a tool to determine the near-equilibrium of an electric energy market. This market works under locational marginal pricing, i.e., generating units and demand loads are paid and pay, respectively, the locational marginal prices corresponding to the nodes they are connected to. The near-equilibrium is defined as the energy transaction levels for which generating companies maximize their respective profits and consumption companies maximize their respective utilities. An independent system operator clears the market maximizing the social welfare. Conditions that ensure minimum profit for generating units can be included. However, these conditions may render a generating unit uncompetitive and expel it from the market. Demands are taken to be non-constant and values are determined as part of the solution. The near-equilibrium is obtained through the solution of a mixed-integer quadratic problem equivalent to a mixed linear complementarity problem that includes the minimum profit conditions. It is important to note that the near-equilibrium concept presented in this paper does not solve a market equilibrium when indivisibilities such as start up costs or the like are present. Lastly, we validate the proposed model on a case study using data from the IEEE Reliability Test System. Author Affiliation: (a) Department of Electrical Engineering, Universidad de Castilla -- La Mancha, Ciudad Real, 13071 Spain (b) Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742, USA Article History: Received 14 October 2003; Accepted 21 March 2005

A dynamic tool for calculating near-equilibrium in electricity markets under minimum profit conditions and marginal pricing is presented.

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]

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]

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]

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]

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]

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]

• 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]

Abstract: This paper provides a technique to derive the bidding strategy in the day-ahead market of a large consumer that procures its electricity demand in both the day-ahead market and a subsequent adjustment market. Price uncertainty is modeled using concepts derived from information gap decision theory, which allows deriving robust decisions with respect to price volatility. Risk aversion is built implicitly within the proposed model. Correlations among prices in the day-ahead and the adjustment markets are properly modeled. The proposed technique is illustrated through a realistic case study. [Copyright &y& Elsevier]

Abstract: The paper investigates the effects of emissions constraints and Emissions Trading Scheme (ETS) on the generation scheduling outcome. ETS is a cap-and-trade market mechanism that has been introduced in European Union in order to facilitate CO2 emissions management. This scheme gives generators certain amount of CO2 allowances which they can use to cover emissions produced during energy generation. In a current setting, most of the allowances are given for free. However, under ETS generators also have an opportunity to buy and sell CO2 allowances on the market. Since generation power outputs are bounded by the amount of CO2 emissions that they are allowed to produce over time, it is becoming increasingly important for generating units to manage their allocations in the most profitable way and decide when and how much of permissions to spent to produce electricity. The method proposed here allows for modeling of this new limitation by including costs of buying and selling of CO2 allowance in the generation scheduling procedure. It also introduces additional emissions constraints in the problem formulation. Although CO2 permissions and energy are traded in separate markets, the proposed formulation permits analysis on how emission caps and emission market prices can influence market outcome. The method is illustrated on a 5-unit system. Given examples compare (i) a base-case when all generators have made a decision to use portions of their total free allocations that do not cause any shortfall during the investigated time period; (ii) two cases when the least expensive generators’ decisions on the amount of free allowances they are willing to use during the considered period are insufficient. In all cases generators also submit prices at which they expect to be able to “top-up” or sell allowances on the market, however, only in the second and third case the “buying” option becomes active and affects generation scheduling and total costs. In addition, the paper investigates how aggregation of emissions allowances of generators belonging to the same company can affect market clearing. [Copyright &y& Elsevier]

Abstract: This paper extends basic economic dispatch analytical results to the reserve-constrained case. For this extended problem, a cost and payment allocation analysis is carried out and a detailed economic interpretation of the results is provided. Sensitivity values (Lagrange multipliers) are also analyzed. A case study is considered to illustrate the proposed analysis. Conclusions are duly drawn. [Copyright &y& Elsevier]

The paper introduces a method for solving the failure probability-safety factor problem for designing engineering works proposed by Castillo et al. that optimizes an objective function subject to the standard geometric and code constraints, and two more sets of constraints that simultaneously guarantee given safety factors and failure probability bounds associated with a given set of failure modes. The method uses the dual variables and is especially convenient to perform a sensitivity analysis, because sensitivities of the objective function and the reliability indices can be obtained with respect to all data values. To this end, the optimization problems are transformed into other equivalent ones, in which the data parameters are converted into artificial variables, and locked to their actual values. In this way, some variables of the associated dual problems become the desired sensitivities. In addition, using the proposed methodology, calibration of codes based on partial safety factors can be done. The method is illustrated by its application to the design of a simple rubble mound breakwater and a bridge crane. [Copyright &y& Elsevier]

• An all-solar electricity production mix makes sense in regions with high and stable solar irradiation, such as Saudi Arabia. • An all-solar power system heavily relies on storage to cover nighttime hours. • Simulation results for an all-solar power system in Saudi Arabia throughout one year are reported and discussed. • The best option is generally a combination of CSP plants, PV plants and storage facilities. This paper considers the operation of an all-solar electric energy system in Saudi Arabia, that is, a system which generation mix includes solely solar (PV and/or concentrated solar power (CSP)) and battery energy storage units (used to cover hours with no solar resource and hours beyond the CSP thermal storage capacity). We analyze the operation of this system using realistic data. These data pertain to the actual transmission system and the demand throughout the country in 2015. The Saudi Arabian power system exhibits a rather flat demand during both the summer and winter seasons (there are mostly two season in Saudi Arabia: winter and summer), being the peak demand for 2015 in these seasons 49 and 25 GW, respectively. Solar generation units and storage units are sized and sited using a fully-fledged capacity expansion model (not described in this paper). To comprehend the daily operation of such all-solar power system in Saudi Arabia throughout 2015, we analyze three cases in which the demand is served (i) using PV and storage units, (ii) using CSP and storage units, and (iii) using PV, CSP and storage units. We compare in detail the above three cases. We conclude that using an optimal combination of PV an CSP units results in minimum total (investment and operation) cost, minimum storage needs, and moderate solar energy spillage. [ABSTRACT FROM AUTHOR]

Rising wind penetrations can suppress wholesale energy prices by displacing higher-cost conventional generation from the merit order. Wind suffers disproportionately from this price suppression, because the price is most suppressed when wind availability is high, hindering wind-investment incentives. One way to mitigate this price suppression is by wind exercising market power, which introduces efficiency losses. An alternative is to use energy storage, which allows energy to be stored when wind availability is high. This stored energy is later discharged when wind availability is lower and prices are higher. This paper proposes a bilevel equilibrium model to study market equilibrium interactions between energy storage and wind and conventional generators. We represent the market interaction using an equilibrium problem with equilibrium constraints. An illustrative case study is used to demonstrate the social welfare and profit benefits of using energy storage in this manner. [ABSTRACT FROM AUTHOR]

Rising penetrations of variable renewable generation in electric power systems can raise operational challenges. One is that renewables can increase the need for dispatchable generation with fast-ramping capabilities. This can be costly, because in many instances flexible generators can be more expensive than baseload units that have slower ramping capabilities. If ramping capacity is not available, renewable curtailment may be needed. An alternate solution to this need for ramping is to use energy storage. A question that this raises is how renewable and conventional generators and energy storage would interact in a market environment, and whether certain asset-ownership structures would result in more efficient coordination. To this end, this paper presents a multi-period market-equilibrium model of interactions between these different types of market agents. The impacts on renewable integration of conventional generators having limited ramping capabilities are studied through an illustrative case study. We also examine a variety of structures for the participation of energy storage in the market. We find that co-ownership and co-operation of renewable generators and energy storage brings about the best results from the perspective of alleviating market inefficiencies. Having energy storage directly controlled by the market operator or participating as an independent profit-maximizing firm is less efficient. [ABSTRACT FROM AUTHOR]

This paper proposes a tri-level adaptive robust AC optimal power flow (AR-ACOPF) model incorporating wind units. The uncertain wind power production as well as the system demand are characterized in terms of bounded intervals forming a polyhedral uncertainty set. The proposed model is robust against any realization of uncertain parameters (i.e. wind power production and system demand) within the uncertainty set. Also the robustness of the solutions is controlled through a parameter denominated budget of uncertainty. Since the proposed tri-level model is not solvable via an off-the-shelf optimization package, a decomposition strategy relying on primal and dual cuts is proposed to solve it. To reduce the computation burden of the proposed AR-ACOPF problem, an effective initialization process is also presented. The proposed AR-ACOPF model and solution approach are illustrated using the well-known IEEE 300-bus and Polish 2746-bus test systems. [ABSTRACT FROM AUTHOR]

Abstract: A virtual power plant aggregates various local production/consumption units that act in the market as a single entity. This paper considers a virtual power plant consisting of an intermittent source, a storage facility, and a dispatchable power plant. The virtual power plant sells and purchases electricity in both the day-ahead and the balancing markets seeking to maximize its expected profit. Such model is mathematically rigorous, yet computationally efficient. The offering problem is cast as a two-stage stochastic mixed-integer linear programming model which maximizes the virtual power plant expected profit. The uncertain parameters, including the power output of the intermittent source and the market prices, are modeled via scenarios based upon historical data. The proposed model is applied to a realistic case study and conclusions are drawn. [Copyright &y& Elsevier]

Abstract: As wind power technology matures and reaches break-even cost, wind producers find it increasingly attractive to participate in pool markets instead of being paid feed-in tariffs. The key issue is then how a wind producer should offer in the pool markets to achieve maximum profit while controlling the variability of such profit. This paper compares two families of offering strategies based, respectively, on a naive use of wind production forecasts and on stochastic programming models. These strategies are compared through a comprehensive out-of-sample chronological analysis based on real-world data. A number of relevant conclusions are then duly drawn. [Copyright &y& Elsevier]

In some highly populated areas of the planet, air quality is an issue. Since power plants in those areas significantly contribute to air pollution due to SO 2 and NO x emissions, it is appropriate to operate such power plants enforcing admissible emission limits. Since emissions directly impact the air quality index, which is highly uncertain 24 h in advance, admissible emission limits should be modeled as stochastic parameters.To represent the stochastic nature of such admissible emission limits, we propose a two-stage stochastic programming model for the commitment of power plants. The first stage represents the day-ahead scheduling, and the second stage represents the real-time power system operation under different weather and thus admissible emission limit conditions. We show the effect of stochastic emission limits on power system operations using a simple example and a 118-node case study. [ABSTRACT FROM AUTHOR]

With a rapid increase in capacity, independently-invested energy storage systems (ESSs) might take up a significant share in the generation mix, and would be required to participate in the electricity market. Considering the arbitrage capability of ESSs, their behaviors would be remarkably different from those of conventional generators, impacting the market equilibrium. These impacts would vary with the type of ESSs and the generation mix. Therefore, this paper formulates a multi-period market equilibrium problem with equilibrium constraints (EPEC) to study the strategic behaviors of different types of ESSs and their impacts on the market outcomes, assuming that ESSs behave as price-makers. The EPEC model is established within a general framework, which considers the individual profit-maximization behaviors of different ESSs and generators, including thermal units, hydro units and renewable units. Interactions between different generators and the market operator are also represented. Finally, numerical studies based on a modified IEEE 57-node system with different wind generation curves are performed for illustration and validation. [ABSTRACT FROM AUTHOR]

Abstract: Electricity market simulators have become a useful tool to train engineers in the power industry. With the maturing of electricity markets throughout the world, there is a need for sophisticated software tools that can replicate the actual behavior of power markets. In most of these markets, power producers/consumers submit production/demand bids and the Market Operator clears the market producing a single price per hour. What makes markets different from each other are the bidding rules and the clearing algorithms to balance the market. This paper presents a realistic simulator of the day-ahead electricity market of mainland Spain. All the rules that govern this market are modeled. This simulator can be used either to train employees by power companies or to teach electricity markets courses in universities. To illustrate the tool, several realistic case studies are presented and discussed. [Copyright &y& Elsevier]

With increasing penetration of renewable energy, multi-energy systems constitute an effective mechanism to optimize energy distribution and improve social welfare. However, a centralized operation of the multi-energy system might not be appropriate under the existing energy markets. Therefore, this paper proposes an equilibrium model for improving the operation of the electricity, gas and district heating subsystems of a district or urban area. The proposed model allows each energy subsystem to pursue its own objective (i.e., maximum social welfare), while considering the interconnection with other subsystems. More specifically, this model represents the behavior of each subsystem and reflects the interactions of the multi-energy system in a practical way. This equilibrium problem is formulated as a nonlinear complementarity problem. An illustrative case study is analyzed to show the relevance of the proposed approach. • A multi-energy market model is proposed for the joint operation of the electricity, gas and district heating systems. • An equilibrium problem is developed to simulate the gaming process of subsystem operators in the multi-energy market. • The proposed equilibrium model is also compared with a centralized optimization model. • Real-time market prices are solved to further explore the interactions among the different energy subsystems. • The effect of different wind power levels on the market behavior and energy exchange is discussed. [ABSTRACT FROM AUTHOR]