The holomorphic embedding method (HEM) applied to the power-flow problem (HEPF) has been used in the past to obtain the voltages and flows for power systems. The incentives for using this method over the traditional Newton-Raphson based nu-merical methods lie in the claim that the method is theoretically guaranteed to converge to the operable solution, if one exists.

In this report, HEPF will be used for two power system analysis purposes:

a. Estimating the saddle-node bifurcation point (SNBP) of a system

b. Developing reduced-order network equivalents for distribution systems.

Typically, the continuation power flow (CPF) is used to estimate the SNBP of a system, which involves solving multiple power-flow problems. One of the advantages of HEPF is that the solution is obtained as an analytical expression of the embedding parameter, and using this property, three of the proposed HEPF-based methods can es-timate the SNBP of a given power system without solving multiple power-flow prob-lems (if generator VAr limits are ignored). If VAr limits are considered, the mathemat-ical representation of the power-flow problem changes and thus an iterative process would have to be performed in order to estimate the SNBP of the system. This would typically still require fewer power-flow problems to be solved than CPF in order to estimate the SNBP.

Another proposed application is to develop reduced order network equivalents for radial distribution networks that retain the nonlinearities of the eliminated portion of the network and hence remain more accurate than traditional Ward-type reductions (which linearize about the given operating point) when the operating condition changes.

Different ways of accelerating the convergence of the power series obtained as a part of HEPF, are explored and it is shown that the eta method is the most efficient of all methods tested.

The local-measurement-based methods of estimating the SNBP are studied. Non-linear Thévenin-like networks as well as multi-bus networks are built using model data to estimate the SNBP and it is shown that the structure of these networks can be made arbitrary by appropriately modifying the nonlinear current injections, which can sim-plify the process of building such networks from measurements.

t temperature (HST) and top-oil temperature (TOT) are reliable indicators of the insulation temperature. The objective of this project is to use thermal models to estimate the transformer's maximum dynamic loading capacity without violating the HST and TOT thermal limits set by the operator. In order to ensure the optimal loading, the temperature predictions of the thermal models need to be accurate. A number of transformer thermal models are available in the literature. In present practice, the IEEE Clause 7 model is used by the industry to make these predictions. However, a linear regression based thermal model has been observed to be more accurate than the IEEE model. These two models have been studied in this work.

This document presents the research conducted to discriminate between reliable and unreliable models with the help of certain metrics. This was done by first eyeballing the prediction performance and then evaluating a number of mathematical metrics. Efforts were made to recognize the cause behind an unreliable model. Also research was conducted to improve the accuracy of the performance of the existing models.

A new application, described in this document, has been developed to automate the process of building thermal models for multiple transformers. These thermal models can then be used for transformer dynamic loading.