The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is insta...The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is instable.So the prototype relaxation procedure is improved in this paper.Additionally,an immediate test of the existence of a solution following branch_and_bound is proposed,which avoids unwanted computations in those intervals that have no solution.The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality,stability and convergent speed.展开更多
The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtai...The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.展开更多
By considering the static voltage characteristic of the load, we propose a WAMS/SCADA mixed nonlinear method to estimate the voltage of unobservable buses caused by topology change or phasor measurement unit (PMU) mal...By considering the static voltage characteristic of the load, we propose a WAMS/SCADA mixed nonlinear method to estimate the voltage of unobservable buses caused by topology change or phasor measurement unit (PMU) malfunction in a power system. By modeling the load characteristic with data from SCADA, we employed the Gauss-Seidel method to solve the nonlinear equations and estimate the voltage of unobservable buses with the high precision voltages of neighboring buses measured by a PMU. Simulations were carried out on the IEEE 39-bus system, and the results show that this novel method can dynamically and accurately trace the variation of the voltage phasor of the unobservable buses.展开更多
文摘The basic principle of interval arithmetic and the basic algorithm of the interval Newton methods are introduced.The prototype algorithm can not find any zero in an interval that has zero sometimes,that is,it is instable.So the prototype relaxation procedure is improved in this paper.Additionally,an immediate test of the existence of a solution following branch_and_bound is proposed,which avoids unwanted computations in those intervals that have no solution.The numerical results demonstrat that the improved interval Newton method is superior to prototype algorithm in terms of solution quality,stability and convergent speed.
基金supported by the Fujian Provincial Natural Science Foundation of China (No. Z0511048)
文摘The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.
基金Project supported by the National Natural Science Foundation of China (Nos. 50507018, 50595414, 50677062, and 60421002)the National Basic Research Program (973) of China (No. 2004CB217902)+1 种基金the National Key Technologies Supporting Program of Chinaduring the 11th Five-Year Plan Period (No. 2006BAA02A01)theKey Grant Project of MOE of China (No. 305008)
文摘By considering the static voltage characteristic of the load, we propose a WAMS/SCADA mixed nonlinear method to estimate the voltage of unobservable buses caused by topology change or phasor measurement unit (PMU) malfunction in a power system. By modeling the load characteristic with data from SCADA, we employed the Gauss-Seidel method to solve the nonlinear equations and estimate the voltage of unobservable buses with the high precision voltages of neighboring buses measured by a PMU. Simulations were carried out on the IEEE 39-bus system, and the results show that this novel method can dynamically and accurately trace the variation of the voltage phasor of the unobservable buses.
