Topic
Successive linear programming
About: Successive linear programming is a research topic. Over the lifetime, 225 publications have been published within this topic receiving 5624 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, a practical monthly optimization model, called SISOPT, is developed for the management and operations of the Brazilian hydropower system, where the basic model is formulated in nonlinear programming (NLP).
Abstract: A practical monthly optimization model, called SISOPT, is developed for the management and operations of the Brazilian hydropower system. The system, one of the largest in the world, consists of 75 hydropower plants with an installed capacity of 69,375 MW, producing 92% of the nation's electrical power. The system size and nonlinearity pose a real challenge to the modelers. The basic model is formulated in nonlinear programming ~NLP!. The NLP model is the most general formulation and provides a foundation for analysis by other methods. The formulated NLP model was first linearized by two different linearization techniques and solved by linear programming ~LP!. A comparative analysis was made of the results obtained from the linearized and the NLP models. The results show that the simplest linearized model ~referred to as the LP model! without iteration is suitable for planning purposes. For example, the LP model could be used in system capacity expansion studies or to explore various design parameters in connection with feasibility studies, where details in storage variation are not as important as the power production. With a good initial policy provided by the LP model, the successive linear programming ~SLP! model produced excellent results with fast convergence. The NLP model, the most complex and accurate model in the suite, is particularly suited for setting up guidelines for real-time operations using inflow forecast with frequent updating. The performance of the NLP model was checked against the historical operational records, and the comparison yields indica- tions of superior performance.
294 citations
TL;DR: A successive linear programming methodology is presented to treat more effectively those applications where a local structure change is performed to a power system already in operation, and where the modification of the settings of already existent relays is not desirable.
Abstract: A successive linear programming methodology is presented to treat more effectively those applications where a local structure change is performed to a power system already in operation, and where the modification of the settings of already existent relays is not desirable. The dimension of the optimization problems to be solved is substantially reduced, and a sequence of small linear programming problems is stated and solved in terms of the time dial settings, until a feasible solution is reached. With the proposed technique, the number of relays of the original system to be reset is reduced substantially. It is found that there is a trade-off between the number of relays to be reset and the optimality of the settings of the relays.
277 citations
TL;DR: This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza and incorporates a trust-region constraint.
Abstract: This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the l1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program. The EQP incorporates a trust-region constraint and is solved (inexactly) by means of a projected conjugate gradient method. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEr [1, 15] test set.
147 citations
1 Jan 2009
TL;DR: This review illustrates the long-standing symbiosis between the industrial challenge of optimally combining feed stocks into products and the mathematical fleld of global optimization.
Abstract: The pooling problem, an optimization challenge of maximizing proflt subject prod- uct availability, storage capacity, demand, and product speciflcation constraints, has applica- tions to petroleum reflning, wastewater treatment, supply-chain operations, and communica- tions. This review illustrates the long-standing symbiosis between the industrial challenge of optimally combining feed stocks into products and the mathematical fleld of global optimization. We present flve sub-classes of pooling problems: standard pooling, generalized pooling, extended pooling, nonlinear blending, and crude oil operations as representative industrial challenges. We also discuss solution techniques: successive linear programming, the global optimization algo- rithm GOP and other Lagrangian-based approches, the reformulation-linearization technique (RLT), and piecewise-a-ne underestimation in the context of the pooling problem.
135 citations
TL;DR: In this paper, a successive linear programming (SLP) approach is proposed to solve the alternating current optimal power flow (ACOPF) problem, which is mathematically equivalent to the canonical ACOPF formulation.
Abstract: Improved formulations of and solution techniques for the alternating current optimal power flow (ACOPF) problem are critical to improving current market practices in economic dispatch. We introduce the IV-ACOPF formulation that unlike canonical ACOPF formulations–which represent network balancing through nonlinear coupling–is based on a current injections approach that linearly couple the quadratic constraints at each bus; yet, the IV-ACOPF is mathematically equivalent to the canonical ACOPF formulation. We propose a successive linear programming (SLP) approach to solve the IV-ACOPF, which we refer to as the SLP IV-ACOPF algorithm. The SLP IV-ACOPF leverages commercial LP solvers and can be readily extended and integrated into more complex decision processes, e.g., unit commitment and transmission switching. We demonstrate with the standard MATPOWER test suite an acceptable quality of convergence to a best-known solution and linear scaling of computational time in proportion to network size.
135 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 11 |
| 2020 | 7 |
| 2019 | 15 |
| 2018 | 10 |
| 2017 | 8 |
| 2016 | 11 |