Simulation of nonisothermal, multiphase flow through fractured geothermal reservoirs involves the solution of a system of strongly nonlinear algebraic equations. The Newton-Raphson method used to solve such a nonlinear system of equations requires the evaluation of a Jacobian matrix. In this paper we discuss automatic differentiation (AD) as a method for analytically computing the Jacobian matr...

The score and hessian functions The score vector ∇L(β, x) and hessian matrix ∇ 2 L(β, x) used in the Newton-Raphson

Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load,...

The load flow study in a power system constitutes a study of paramount importance. The study reveals the electrical performance and power flows (real and reactive) for specified condition when the system is operating under steady state. This paper gives an overview of different techniques used for load flow study under different specified conditions. Keywords—Load Flow Studies, Y-matrix and Z-m...

This paper presents an application of the so-called modified quasilinean'zation method to the solution nonlinear, implicite two-point boundary-value problems. Analogously as in the explicit case the resulting algorithm exhibits the descent property in the auxiliary performance index which measures the cumulative error in the differential equations and the boundary conditions. Practical importan...

Two mismatch functions (power or current) and three coordinates (polar, Cartesian and complex form) result in six versions of the Newton–Raphson method for the solution of power flow problems. In this paper, five new versions of the Newton power flow method developed for single-phase problems in our previous paper are extended to three-phase power flow problems. Mathematical models of the load,...

Simulation of nonisothermal, multiphase flow through fractured geothermal reservoirs involves the solution of a system of strongly nonlinear algebraic equations. The Newton-Raphson method used to solve such a nonlinear system of equations requires the evaluation of a Jacobian matrix. In this paper we discuss automatic differentiation (AD) as a method for analytically computing the Jacobian matr...

We introduce a novel method to compute a rank m approximation of the inverse of the Hessian matrix in the distributed regime. By leveraging the differences in gradients and parameters of multiple Workers, we are able to efficiently implement a distributed approximation of the Newton-Raphson method. We also present preliminary results which underline advantages and challenges of secondorder meth...