Generalized Proportional Model of Relay Protection Based on Adaptive Homotopy Algorithm Transient Stability

Relay protection equipment is important to ensure the safe and stable operation of power systems. The risks should be evaluated, which are caused by the failure of relay protection. At present, the fault data and the fault status monitoring information are used to evaluate the failure risks of relay protection. However, there is a lack of attention to the information value of monitoring information in the normal operation condition. In order to comprehensively improve monitoring information accuracy and reduce, a generalized proportional hazard model (GPHM) is established to fully exploit the whole monitoring condition information during the whole operation process, not just the monitoring fault condition data, with the maximum likelihood estimation (MLE) used to estimate the parameters of the GPHM. For solving the nonlinear equation in the process of parameter estimations, the adaptive homotopy algorithm is adopted, which could ensure the reversibility of the Jacobi matrix. Three testing cases have been reviewed, to demonstrate that the adaptive homotopy algorithm is better than traditional algorithms, such as the Newton homotopy algorithm, regarding the calculation speed and convergence. Therefore, GPHM could not only reflect the real time state of the equipment, but also provide a sound theoretical basis for the selection of equipment maintenance types.

Globally convergent method for designing twice spline contractual function

To design a quadratic spline contractual function in the case of discretely unknown nodes, a modified constraint shifting homotopy algorithm for solving principal–agent problems is constructed in the paper. Then the existence of globally convergent solution to KKT systems for the principal–agent problem with spline contractual function is proved under a much weaker condition. The proposed algorithm only requires that any initial point is in the shifted feasible set but not necessarily in the original feasible set.

A comparative study of the PL homotopy and BFGS methods for some nonsmooth optimization problems

We consider some non-smooth functions and investigate the numerical behavior of the Piecewise Linear Hompotopy (PLH) method ([Bozântan, A., An implementation of the piecewise-linear homotopy algorithm for the computation of fixed points, Creat. Math. Inform., 19 (2010), No.~2, 140–148] and [Bozântan, A. and Berinde, V., Applications of the PL homotopy algorithm for the computation of fixed points to unconstrained optimization problems, Creat. Math. Inform., 22 (2013), No. 1, 41–46]). We compare the PLH method with the BFGS with inexact line search, a quasi-Newton method, having some results reported in [Lewis, A. S. and Overton, M. L., Nonsmooth optimization via BFGS, submitted to SIAM J. Optimiz, (2009)]. For most of the considered cases, the characteristics of the PLH method are quite similar to the BFGS method, that is, the PLH method converges to local minimum values and the convergence rate seems to be linear with respect to the number of function evaluations, but we also identify some issues with the PLH method.

A Tactile Sensor Decoupling Process

An improved hybrid homotopy method is proposed to decouple the multi-input model of tactile sensors. The time-embedded homotopy algorithm is proved to be very suitable for solving the problem. Three tracking factors that control the efficiency of the algorithm are studied: tracking operator, stepsize, and accuracy. Trust region methods are applied to track the zero paths instead of the traditional differential algorithm, and a periodic sampling method is proposed to improve the efficiency of the algorithm. Numerical experiments show that both the robustness and accuracy have received a huge boost after the hybrid algorithm is applied.