Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Optimal Adaptive Linearizations of the AC Power Flow Equations

Abstract: The power flow equations are at the heart of many optimization and control problems relevant to power systems. The non-linearity of these equations leads to computational challenges in solving power flow and optimal power flow problems (non-convergence, local optima, etc.), Accordingly, various linearization techniques, such as the DC power flow, are often used to approximate the power flow equations. In contrast to a wide variety of general linearization techniques in the power systems literature, this paper computes a linear approximation that is specific to a given power system and operating range of interest. An “adaptive linearization” developed using this approach minimizes the worst-case error between the output of the approximation and the actual non-linear power flow equations over the operating range of interest. To compute an adaptive linearization, this paper proposes a constraint generation algorithm that iterates between 1) using an optimization algorithm to identify a point that maximizes the error of the linearization at that iteration and 2) updating the linearization to minimize the worst-case error among all points identified thus far. This approach is tested on several IEEE test cases, with the results demonstrating up to a factor of four improvement in approximation error over linearizations based on a first-order Taylor approximation.

On the Ludwig integration algorithm for triangular subregions

Abstract: By using area coordinates one obtains algebraic expressions for the computation of two-dimensional integrals with oscillatory integrands over triangular subregions that are simpler than those published recently [1]. All the advantages of previous methods [1], [2] are retained. Moreover, the new equation is evaluated only once for each triangular subregion.

Nonlinear distortions and multisine signals. I. Measuring the best linear approximation

Abstract: This paper examines the effects of nonlinearities on periodic multifrequency signals. A class of broadband pilot test signals is proposed, termed sparse odd multisines, which can be used to establish the system bandwidth and detect nonlinearities. Signals are then defined within this class which allow the measurement of the best linear approximation to a nonlinear system. A comparison is made with related work in this area.

Slip at the surface of a general axi-symmetric body rotating in a viscous fluid

Abstract: The rotational motion of an arbitrary axi-symmetric body in a viscous fluid is discussed using a combined analytical-numerical technique. A singularity method based on a continuous distribution of a set of Sampson spherical singularities, namely Sampsonlets, along the axis of symmetry within the body, is applied to find the general solution for the fluid velocity that satisfies the general slip boundary condition. Employing a constant and linear approximation for the density functions and applying the collocation technique to satisfy the slip boundary condition on the surface of the body, a system of linear algebraic equations is obtained to be solved numerically. The couple exerted on a prolate and oblate spheroid and on a prolate and oblate Cassini ovals is evaluated for various values of the aspect ratio a / b and for different values of the slip parameter, where a and b are the major and minor semi-axes of the particle respectively. The CPU time elapsed during numerical calculations is measured and tabulated. Numerical work shows that convergence to at least six decimal places is achieved.