Tuning Successive Linear Programming to Solve AC Optimal Power Flow Problem for Large Networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy's (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. The results show that our proposed algorithm is tractable and can solve more than 80\% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

Tuning Successive Linear Programming to Solve AC Optimal Power Flow Problem for Large Networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy's (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. The results show that our proposed algorithm is tractable and can solve more than 80\% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

Configuration optimization of photogrammetry system based on spectral radius for on-orbit measurement

Non-contact optical measurement is a potential approach to on-orbit vibration measurement for flexible appendages, providing dynamic information for spacecraft control system. Binocular photogrammetry system is a practical configuration to achieve this measurement. In this paper, optimization approach and strategy for configuration parameters of this system are raised. Measurement matrix is specially defined to obtain the objective function for the optimization. Successive linear programming algorithm is used for optimization iteration. Transient responses of flexible appendages calculated by finite element model and corresponding images generated by OpenGL help to achieve this simulation-based optimization. The feasibility and effectiveness of the optimization are verified both by numerical study and experiment. Error analysis of the optimal system reveals great improvement in accuracy and robustness after optimization. This optimization is a promising approach to designing the configuration of binocular photogrammetry system and helping to achieve reliable on-orbit dynamic measurement results.

Sparse Reject Option Classifier Using Successive Linear Programming

In this paper, we propose an approach for learning sparse reject option classifiers using double ramp loss Ldr. We use DC programming to find the risk minimizer. The algorithm solves a sequence of linear programs to learn the reject option classifier. We show that the loss Ldr is Fisher consistent. We also show that the excess risk of loss Ld is upper bounded by excess risk of Ldr. We derive the generalization error bounds for the proposed approach. We show the effectiveness of the proposed approach by experimenting it on several real world datasets. The proposed approach not only performs comparable to the state of the art, it also successfully learns sparse classifiers.

Identification of gas pipelines hydraulic efficiency coefficients

This study investigates the identification of non-measureable parameters of the gas transmission system (gas pipelines hydraulic efficiency coefficients). The problem statement and solution procedure are presented. The original problem is divided into two interrelated components: the nonlinear optimization problem and the temperature calculation. The nonlinear optimization problem is solved using the Successive Linear Programming (SLP) method. The problems of insufficiency of measurements and multiplicity of solutions are described, and appropriate approaches are proposed (introduction of additional subcriteria and uniting gas pipelines into groups). Identification of gas pipelines hydraulic efficiency coefficients for gas transmission systems of various complexity has been performed using the given algorithm.

An Algorithm for Calculating Gas Transmission System Optimal Stationary Mode

In this paper, we consider the problem of calculating the optimal stationary mode of the gas transmission system. The maximum throughput of the gas transmission system was used as optimization criterion. Presented are the problem statement and the solution procedure. The original problem is divided into two interrelated components: the MINLP problem and the temperature calculation. To solve the MINLP problem, the Successive Linear Programming (SLP) method was used in combination with the branch and boundary method applied to integer variables. Modeling of compressor shop operating modes was performed using integer variables. Described are the approaches to improving the convergence of the algorithm: the introduction of an additional optimization subcriterion and additional constraints for gas flows through GTS sections.