Thevenin Equivalents, Adjoint Equivalents and Power Flow Equations

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1 Thevenin Equivalents, Adjoint Equivalents and Power Flow Equations Daniel F. C. M. S. Dias Abstract — This work starts by presenting a theoretical study about power flow, voltage stability, Thevenin’s theorem and Tellegen’s theorem applied to adjoint networks where some existing models are also included. ext follows the approach of the methods of analysis used in this dissertation, with special attention to the two models of Thevenin equivalent, where each one represents an operating situation (situation of short circuit and normal operating conditions of an electrical power system), and corresponding calculation of voltage at its terminals. In addition to these, it is also shown how to calculate the power flow (software MATPOWER) and the method chosen to indicate the voltage collapse ( ). As the simulation part, two types of disturbances are carried out: at a load bus and at a branch. The first is tested in three electrical power systems (3, 6 and 39 buses), in order to compare the two operation situations and their respective equivalent Thevenin models with the solution of the chosen power flow and obtain conclusions about them. The second is analyzed only in the 39 bus system, because it is the most complex one. These disturbances occur on the critical buses and branches of each system, in order to obtain more accurate results. Index Terms — Electrical Power Systems, Power Flow, Tellegen’s Theorem, Thevenin’s Theorem, Voltage Stability. I. INTRODUCTION HE electrical power systems (EPS) are normally studied using the power flow equations, knowing that their interest is not usually in the solution of all currents and voltages, but the current and voltage of a small part of the network. So, given the need to improve the speed of calculations of these systems, it is convenient to be able to replace much of the network by a simple equivalent circuit. It is in this

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