Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering


Dr. Mohamed A. El-Kady


Professor Raymond D. Findlay


The Transient Energy Function (TEF) method represents a powerful technique to analyze the transient stability of large-scale power systems. Currently, in the applications of the TEF method, the power network is reduced by eliminating all buses and retaining only the internal nodes of the generators. This Reduced Network Formulation (RNF) yields dense (non-sparse) matrices in the computations and consumes significant computational time. This represents a serious drawback of the RNF, especially in applications to large power networks. Also, all system loads are modeled as constant impedance loads in order to use conventional techniques to reduce the network to the internal nodes of the generators. Many loads in practical power systems can be represented as constant power loads. Such loads are conventionally approximated as constant impedance type based on the pre-fault conditions. Consequently, accurate results may not be obtained. Moreover, the TEF is not applicable to very large-scale power systems due to the computer storage related problems (e.g, file paging) and excessive computational time.

A novel formulation of the TEF method, retaining the original structure of the system network, is presented and the associated computerized algorithm is described. All the above mentioned problems are solved using the proposed Sparse Formulation (SF).

The sparse formulation avoids network reduction completely. All matrices used in the calculation of both the Stable Equilibrium Point (SEP) and the Unstable Equilibrium Point (UEP), for which the computational times are dominant in the calculation process of the energy margin (the stability index), are very sparse. This leads to a significant saving in computational time, i.e. the sparse formulation is more efficient as compared with the RNF approach.

The sparse formulation is applied to different (realistic) utility systems of up to 300 generators and 1724 buses. The results prove the superiority of the sparse formulation in contrast with other current methods.

In addition, either constant impedance or constant power load models, or any combination thereof, can be handled explicitly. Considering these actual load models, the stability indices (the critical clearing time and the calculated more accurately.

The proposed technique can handle very large scale power systems which are beyond the scope of RNF approach. Consquently, it enables an improved design methodology of transmission networks by including provision for modeling the network in more detail. Using the sparse formulation, it is possible to perform a transient stability analysis on a microcomputer. This will render coat-effective the use of such analysis throughout the world. Also, a very powerful and robust numerical technique to deal with ill-conditioned power systems is described. Therefore, practical (stressed) power systems can be handled, i.e. the sparse formulation is more reliable than other techniques such as RNF.

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