A Unified Approach to Generalized Network Sensitivities with Applications to Power System Analysis and Planning

Abstract

<p>This thesis presents a new methodology for describing adjoint network approaches to sensitivity calculations performed in various power system analysis and planning studies. Difficulties observed by previous workers regarding the exact modelling of some power network elements are overcome by proper techniques employed with special complex notation. A generalized version of the Tellegen's theorem-based approach is developed which provides the required sensitivities based on the exact a.c. load flow model for any chosen set of real and/or complex variables of practical interest. A theoretical consistency study is performed to allow proper modelling of adjoint elements for direct treatment of general complex functions. A simplified version with many desirable features is described for real function sensitivities. It employs a simple adjoint network. General sensitivity expressions common to all relevant power system studies are derived and tabulated. A new method for solving the load flow problem using Tellegen's theorem is described with several advantages claimed. A special elimination technique is used to describe the Newton-Raphson method for load flow solution in a compact complex mode. A complex version of the Lagrange multiplier approach is developed and applied to allow a general number of complex dependent variables to be defined in a particular problem. A generalized version of the class of methods of sensitivity calculations which exploit the Jacobian matrix of the load flow analysis in formulating the adjoint equations is developed. Generalized sensitivity expressions common to different modes of formulating power flow equations, e.g., cartesian and polar, are derived and tabulated for direct programming use. A unified comprehensive comparison between the Lagrange multiplier and Tellegen's theorem approaches to sensitivity calculations in electrical networks is presented.</p>