Solving two-stage robust optimization problems using a column-and-constraint generation method

http://www.optimization-online.org/DB_FILE/2012/07/3537.pdf

Recent advances in robust optimization: An overview☆

Due to its reduced communication overhead and robustness to failures, distributed energy management is of paramount importance in smart grids, especially in microgrids, which feature distributed generation (DG) and distributed storage (DS). Distributed economic dispatch for a microgrid with high renewable energy penetration and demand-side management operating in grid-connected mode is considered in this paper. To address the intrinsically stochastic availability of renewable energy sources (RES), a novel power scheduling approach is introduced. The approach involves the actual renewable energy as well as the energy traded with the main grid, so that the supply-demand balance is maintained. The optimal scheduling strategy minimizes the microgrid net cost, which includes DG and DS costs, utility of dispatchable loads, and worst-case transaction cost stemming from the uncertainty in RES. Leveraging the dual decomposition, the optimization problem formulated is solved in a distributed fashion by the local controllers of DG, DS, and dispatchable loads. Numerical results are reported to corroborate the effectiveness of the novel approach.

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Robust Energy Management for Microgrids With High-Penetration Renewables

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.

Stochastic Optimization for Unit Commitment—A Review

Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. It is therefore remarkable that real-life applications of robust optimization are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to understand robust optimization and to successfully apply it in practice. We provide a brief introduction to robust optimization, and also describe important do׳s and don׳ts for using it in practice. We use many small examples to illustrate our discussions.

A practical guide to robust optimization

Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.

/pdf/adaptive-robust-optimization-for-the-security-constrained-vx9kggvs4i.pdf

Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

Flexibility is a widely used term in planning process and real-time operation. The existing research on flexibility uses different techniques to study flexibility property from different aspects. While studying a property from various viewpoints increases the understanding on the subject, we need a consistent theoretical framework to consolidate the ideas generated in the field, compare and contrast results, and build on for future analysis. Based on the insights of the nature of flexibility, this paper proposes a unified framework for defining and measuring flexibility in power system. Under the proposed framework, we propose a flexibility metric which evaluates the largest variation range of uncertainty that the system can accommodate. Such a metric takes into account transmission network and system operations constraints, which are critical to assessing flexibility, but are often ignored in literature. A robust optimization technique is used to calculate the proposed metrics. While the illustrative example presented in this paper focuses on the flexibility in real-time system operation in the presence of wind and load uncertainty, this framework can generally be applicable to long-term studies such as system planning.

A Unified Framework for Defining and Measuring Flexibility in Power System

When participating in electricity markets, owners of battery energy storage systems must bid in such a way that their revenues will at least cover their true cost of operation. Since cycle aging of battery cells represents a substantial part of this operating cost, the cost of battery degradation must be factored in these bids. However, existing models of battery degradation either do not fit market clearing software or do not reflect the actual battery aging mechanism. In this paper we model battery cycle aging using a piecewise linear cost function, an approach that provides a close approximation of the cycle aging mechanism of electrochemical batteries and can be incorporated easily into existing market dispatch programs. By defining the marginal aging cost of each battery cycle, we can assess the actual operating profitability of batteries. A case study demonstrates the effectiveness of the proposed model in maximizing the operating profit of a battery energy storage system taking part in the ISO New England energy and reserve markets.

Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

Due to the variability of renewable resources, the ISO tries to identify do-not-exceed (DNE) limits, which are the maximum renewable generation ranges that the power system can accommodate without sacrificing system reliability. The problem is formulated as an optimization problem whose objective is to find the largest operating ranges of variable resources such that the system remains feasible under any generation realizations within the range. Computing the DNE limits can be conceptually translated into finding the largest uncertain set of a robust optimization problem. Depending on the assumptions on how the system responds to the uncertainty of renewable resources, three alternative approaches are developed to convert the nonstandard robust optimization problem into linear programming, bilinear programming and two-stage robust optimization problems, respectively. Although the linear programming problem is easier to solve as compared to the other two alternatives, its resulting DNE limits are the most conservative. Therefore, the trade-off needs to be considered when deciding which approach is the most appropriate in real-time operation. A 5-bus system and the ISO New England power system are used to test the proposed approaches.

Variable Resource Dispatch Through Do-Not-Exceed Limit

Although the unique characteristics of intermittent wind generation have been acknowledged and drastic impacts of sudden wind drops have been experienced, no effective integration approach has been developed. In this paper, without considering transmission capacity constraints for simplicity, aggregated wind generation is modeled as a discrete Markov process with state transition matrices established based on historical data. Wind generation is then integrated into system demand with multiple net demand levels at each hour. To accommodate the uncertain net demand, a stochastic unit commitment problem is formulated based on states instead of scenarios. The objective is to minimize the total commitment cost of conventional generators and their total expected dispatch cost while satisfying all possible net demand levels. The advantage of this formulation is that the state at a time instant summarizes the information of all previous instants in a probabilistic sense for reduced complexity. With state transition probabilities given, state probabilities calculated before optimization, and the objective function and constraints formulated in a linear manner, the problem is effectively solved by using branch-and-cut. Numerical testing shows that the new Markovian approach is effective and robust through the examined cases, resembling the sudden wind drop in Texas in February 2008.

Jinye Zhao

Papers

Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem

A Unified Framework for Defining and Measuring Flexibility in Power System

Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

Variable Resource Dispatch Through Do-Not-Exceed Limit

Grid Integration of Intermittent Wind Generation: A Markovian Approach