Contingency-Constrained Unit Commitment With $n - K$ Security Criterion: A Robust Optimization Approach
TL;DR: This paper presents a new approach for the contingency-constrained single-bus unit commitment problem that incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units.
Abstract: This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions.
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TL;DR: In this paper, the authors proposed a robust optimization approach to accommodate wind output uncertainty, with the objective of providing a robust unit commitment schedule for the thermal generators in the day-ahead market that minimizes the total cost under the worst wind power output scenario.
Abstract: As renewable energy increasingly penetrates into power grid systems, new challenges arise for system operators to keep the systems reliable under uncertain circumstances, while ensuring high utilization of renewable energy. With the naturally intermittent renewable energy, such as wind energy, playing more important roles, system robustness becomes a must. In this paper, we propose a robust optimization approach to accommodate wind output uncertainty, with the objective of providing a robust unit commitment schedule for the thermal generators in the day-ahead market that minimizes the total cost under the worst wind power output scenario. Robust optimization models the randomness using an uncertainty set which includes the worst-case scenario, and protects this scenario under the minimal increment of costs. In our approach, the power system will be more reliable because the worst-case scenario has been considered. In addition, we introduce a variable to control the conservatism of our model, by which we can avoid over-protection. By considering pumped-storage units, the total cost is reduced significantly.
885 citations
Cites background from "Contingency-Constrained Unit Commit..."
...problems [13], portfolio management problems [14], and contingency-constrained unit commitment problems [15], among others....
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TL;DR: The numerical results show attributes of the two approaches for solving the real-time optimal DR management problem for residential appliances via stochastic optimization and robust optimization approaches.
Abstract: This paper evaluates the real-time price-based demand response (DR) management for residential appliances via stochastic optimization and robust optimization approaches. The proposed real-time price-based DR management application can be imbedded into smart meters and automatically executed on-line for determining the optimal operation of residential appliances within 5-minute time slots while considering uncertainties in real-time electricity prices. Operation tasks of residential appliances are categorized into deferrable/non-deferrable and interruptible/non-interruptible ones based on appliances' DR preferences as well as their distinct spatial and temporal operation characteristics. The stochastic optimization adopts the scenario-based approach via Monte Carlo (MC) simulation for minimizing the expected electricity payment for the entire day, while controlling the financial risks associated with real-time electricity price uncertainties via the expected downside risks formulation. Price uncertainty intervals are considered in the robust optimization for minimizing the worst-case electricity payment while flexibly adjusting the solution robustness. Both approaches are formulated as mixed-integer linear programming (MILP) problems and solved by state-of-the-art MILP solvers. The numerical results show attributes of the two approaches for solving the real-time optimal DR management problem for residential appliances.
700 citations
Cites background from "Contingency-Constrained Unit Commit..."
...Without acknowledging differences on electricity prices, they do not have incentives to adjust their electricity consumption patterns....
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TL;DR: The works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC are reviewed to help transform research advances into real-world applications.
Abstract: Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC’s birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.
519 citations
Cites background or methods from "Contingency-Constrained Unit Commit..."
...contingency models [32]–[34], knapsack constraints are used to define ....
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...contingency models [32]–[34] and in models with discrete worst-case wind output scenarios [28], [35], [89]....
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...define the scope of uncertainty [32]–[34]....
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...In the power system literature, RUCmodels have been used to address uncertainties mainly from nodal net electricity injection [29], wind power availability [28], [35], power systems component contingencies [32]–[34], and demand-side management [87]....
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...contingency models [32], [33]; the total allowed number of wind output cases can be varied [35]; the linear coefficients of the polyhedral sets also can be varied, such as in [28] and [29]....
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TL;DR: In this article, a robust optimization approach was developed to derive an optimal unit commitment decision for the reliability unit commitment runs by ISOs/RTOs, with the objective of maximizing total social welfare under the joint worst-case wind power output and demand response scenario.
Abstract: With the increasing penetration of wind power into the power grid, maintaining system reliability has been a challenging issue for ISOs/RTOs, due to the intermittent nature of wind power. In addition to the traditional reserves provided by thermal, hydro, and gas generators, demand response (DR) programs have gained much attention recently as another reserve resource to mitigate wind power output uncertainty. However, the price-elastic demand curve is not exactly known in advance, which provides another dimension of uncertainty. To accommodate the combined uncertainties from wind power and DR, we allow the wind power output to vary within a given interval with the price-elastic demand curve also varying in this paper. We develop a robust optimization approach to derive an optimal unit commitment decision for the reliability unit commitment runs by ISOs/RTOs, with the objective of maximizing total social welfare under the joint worst-case wind power output and demand response scenario. The problem is formulated as a multi-stage robust mixed-integer programming problem. An exact solution approach leveraging Benders' decomposition is developed to obtain the optimal robust unit commitment schedule for the problem. Additional variables are introduced to parameterize the conservatism of our model and avoid over-protection. Finally, we test the performance of the proposed approach using a case study based on the IEEE 118-bus system. The results verify that our proposed approach can accommodate both wind power and demand response uncertainties, and demand response can help accommodate wind power output uncertainty by lowering the unit load cost.
457 citations
Cites result from "Contingency-Constrained Unit Commit..."
...As compared to the recent works on robust optimization to solve power system optimization problems [13], [24]–[26], the contributions of this paper can be summarized as follows: 1) Both wind power output and demand response uncertainties are considered in the unit commitment problem....
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TL;DR: Computational studies on the IEEE distribution test systems validate the effectiveness of the RDNP and reveal that distributed generation is critical in increasing the resilience of a distribution system against natural disasters in the form of microgrids.
Abstract: Natural disasters such as Hurricane Sandy can seriously disrupt the power grids. To increase the resilience of an electric distribution system against natural disasters, this paper proposes a resilient distribution network planning problem (RDNP) to coordinate the hardening and distributed generation resource allocation with the objective of minimizing the system damage. The problem is formulated as a two-stage robust optimization model. Hardening and distributed generation resource placement are considered in the distribution network planning. A multi-stage and multi-zone based uncertainty set is designed to capture the spatial and temporal dynamics of an uncertain natural disaster as an extension to the traditional ${N}$ - ${K}$ contingency approach. The optimal solution of the RDNP yields a resilient distribution system against natural disasters. Our computational studies on the IEEE distribution test systems validate the effectiveness of the proposed model and reveal that distributed generation is critical in increasing the resilience of a distribution system against natural disasters in the form of microgrids.
414 citations
Cites background from "Contingency-Constrained Unit Commit..."
...convention in power system research to use an attack set to model system contingency [24], [25], terrorists attacks, and natural disasters [4], [7], [23]....
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References
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TL;DR: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization as mentioned in this paper, which is a standard of graduate-level courses since 1972.
Abstract: The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected and much-cited text, a standard of graduate-level courses since 1972, presents a comprehensive treatment of the first two decades of research on integer programming.
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TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.
Abstract: A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.
3,364 citations
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TL;DR: An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.
Abstract: A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.
3,359 citations
"Contingency-Constrained Unit Commit..." refers background or methods in this paper
...Problem (25)–(39) can be viewed as a particular instance of robust optimization [23], [24] in which the parameters allowed to vary are parameters representing the availability of generation units in each period under each contingency state....
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...Using recent findings from robust optimization [23], [24], the CCUC bilevel program is subsequently transformed into an equivalent single-level mixed-integer programming (MIP) problem....
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...Based on the robust optimization approach presented in [23], an efficient single-level equivalent formulation is provided for the bilevel problem (42)–(59)....
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...Recent theoretical advances by Bertsimas and Sim [23] allow an easy control of the degree of conservatism with moderate computational effort by controlling the number of coefficients that may change in each constraint of the problem....
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...The interested reader is referred to [23] for a de-...
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TL;DR: In this article, a Task Force, set up jointly by the CIGRE Study Committee 38 and the IEEE Power System Dynamic Performance Committee, addresses the issue of stability definition and classification in power systems from a fundamental viewpoint and closely examines the practical ramifications.
Abstract: The problem of defining and classifying power system stability has been addressed by several previous CIGRE and IEEE Task Force reports. These earlier efforts, however, do not completely reflect current industry needs, experiences and understanding. In particular, the definitions are not precise and the classifications do not encompass all practical instability scenarios. This report developed by a Task Force, set up jointly by the CIGRE Study Committee 38 and the IEEE Power System Dynamic Performance Committee, addresses the issue of stability definition and classification in power systems from a fundamental viewpoint and closely examines the practical ramifications. The report aims to define power system stability more precisely, provide a systematic basis for its classification, and discuss linkages to related issues such as power system reliability and security.
3,249 citations
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
Abstract: We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
2,501 citations
"Contingency-Constrained Unit Commit..." refers methods in this paper
...In the late 1990s and early 2000s, robust optimization was further developed by Ben-Tal and Nemirovski’s works [21], [22]....
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