Alternative steady state voltage determination methods for linear time-invariant networks.

摘要

Steady state voltage solutions, derived from a Y-bus network model and unbalanced current injections, are used in a variety of multi-phase power system network analysis applications, such as Z-bus power flow, short circuit and outage studies. When phase coordinate analysis is used to solve these problems, existing techniques can result in "divide by zero" errors. This type of error always occurs when a network contains at least one island of busbars potentially isolated from the ground. In this case, the act of dividing by zero needs to be avoided. Additionally, "divide by zero" errors may be encountered if one or more transformers are defined as requiring no exciting current. Here, the limit process of calculus needs to be employed to determine the correct quotient when zero is a divisor.;The first part of this thesis is devoted to deriving various algorithms for finding all steady state voltage solutions for general linear time-invariant networks. The method of Gauss elimination with partial pivoting, followed by back substitution, is used as the basis for these algorithms. Various modifications are introduced to eliminate all "divide by zero" errors. Additionally, these algorithms can detect when certain network models cannot be physically constructed.;Typical power system networks are sparsely constructed. Therefore, sparse matrix techniques are frequently employed when developing steady state voltage solution algorithms for such networks. This thesis provides for a LDU factorization with back substitution algorithm which incorporates these techniques and still eliminates all "divide by zero" errors. This algorithm requires lhe redefinition of all power system transformer models which are defined as requiring no exciting current. In this thesis, most of the second part describes this algorithm and a technique for determining the new transformer models.