Publications

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As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program. Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Finally, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

In this paper, we derive a strengthened MILP formulation for certain gas turbine unit commitment problems, in which the ramping rates are no smaller than the minimum generation amounts. This type of gas turbines can usually start-up faster and have a larger ramping rate, as compared to the traditional coal-fired power plants. Recently, the number of this type of gas turbines increases significantly due to affordable gas prices and their scheduling flexibilities to accommodate intermittent renewable energy generation. In this study, several new families of strong valid inequalities are developed to help reduce the computational time to solve these types of problems. Meanwhile, the validity and facet-defining proofs are provided for certain inequalities. Finally, numerical experiments on a modified IEEE 118-bus system and the power system data based on recent studies verify the effectiveness of applying our formulation to model and solve this type of gas turbine unit commitment problems, including reducing the computational time to obtain an optimal solution or obtaining a much smaller optimality gap, as compared to the default CPLEX, when the time limit is reached with no optimal solutions obtained.

We describe new capabilities for modeling bilevel programs within the Pyomo modeling software. These capabilities include new modeling components that represent subproblems, modeling transformations for re-expressing models with bilevel structure in other forms, and optimize bilevel programs with meta-solvers that apply transformations and then perform op- timization on the resulting model. We illustrate the breadth of Pyomo's modeling capabilities for bilevel programs, and we describe how Pyomo's meta-solvers can perform local and global optimization of bilevel programs.

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We propose a mathematical programming-based approach to optimize the security-constrained unit commitment problem with a full AC transmission network representation. Our approach is based on our previously introduced successive linear programming (SLP) approach to solving the non-linear, nonconvex AC optimal power flow (ACOPF) problem. By linearizing the ACOPF, we are able to leverage powerful commercial mixed-integer solvers to iteratively optimize the combined unit commitment plus ACOPF model. We demonstrate our approach on six-bus, IEEE RTS-96, and IEEE 118-bus test systems. We perform a comparative analysis of the relative impacts of singlebus, DC, and AC transmission network models on the unit commitment and dispatch solutions and their associated costs.