First order derivative computation of jacobian matrices in load flow algorithms using automatic differentiation

Power flow analysis requires computation of derivatives of Jacobian for the expressions of real and reactive power with Newton-Raphson method for every iteration. Generally sparse Jacobian and Hessian matrices computed by hand calculations and finite-differentiation methods. But these methods gives poor performance because of the complexity involved. With the use of Automatic Differentiation (AD) technique and tools developed using this technique like ADMAT, the tedious and error-prone work of computation of first order derivatives becomes very simple. The load flow problem dealt here is to evaluate the network at state variables and to maintain control variables to meet operating and physical constraints. In this paper Automatic Differentiation method is performed on a five-bus test system and results of this work explains the benefits of the Automatic Differentiation comparing to all other approaches to solve the Jacobian Elements in Power Flow Equations.