abstract: 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. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

It is specifically important to focus on voltage stability analysis of the power system to avoid worst case scenarios such as voltage collapse. The purpose of this thesis is to identify methods for enhancing the steady-state voltage stability using FACTS devices and determining their impact on real and reactive power losses, improvement of bus voltage magnitude, and transmission line loadability. To achieve this, FACTS devices such as Static VAR Compensator (SVC), Static Synchronous Compensator (STATCOM), and Thyristor Controlled Series Capacitor (TCSC) are used in the test system as three separate test cases. The results obtained assist in drawing conclusions on the effectiveness of each FACTS devices at generator, load and swing buses, on lines between two load buses, and between a load bus and a generator bus, in terms of metrics such as voltage magnitude profile, PV curves, and active and reactive power losses.

The growing demand for power and increased environmental concerns gave an impetus to the growth of clean and renewable energy sources like wind, solar etc. There is a remarkable increase in the penetration of wind energy systems in the last decade and this trend is bound to increase at a much faster pace in future. This ever increasing penetration of wind power generating systems pose multi-fold challenges related to operational and stability aspects of the grid. Present day wind energy systems mostly comprise of variable speed wind generators. A large fraction of present day variable speed wind turbine generators use doubly fed induction machine (DFIM). This thesis deals with modeling and grid coordination aspects of variable speed wind gener- ators. In particular, the short coming of the existing steady state equivalent circuit of a DFIM is identified and subsequently, an accurate equivalent circuit of a DFIM is proposed. Relevant mathematical basis for the proposed model is presented. The proposed steady state equivalent circuit of a doubly fed induction machine is further validated using dynamic simulations of a standalone machine. Based on the proposed equivalent circuit, two approaches for computing the initial values of state variables of a DFIM is proposed. The first approach is a linear formulation where the losses due to resistance of the stator and rotor windings are neglected. The second approach is a non-linear formulation which takes the losses into consideration. Further, analysis is carried out on grid connected doubly fed induction generators (DFIG). A framework to incorporate DFIG based variable speed wind farms in the steady state power flow analysis is proposed. The proposed framework takes into consideration important aspects such as voltage dependent reactive power limits and mode of reactive power control of associated converters. Some of the challenges in a grid connected DFIG especially during su- persynchronous mode of operation are identified. The advantages of a non-Maximum Power Point Tracking (MPPT) mode of operation under certain operating conditions is highlighted. Finally, aspects pertaining to coordination of grid connected variable speed wind generators are studied. A trust region framework to determine the reference values to the control loops of converters in a variable speed wind generator is proposed. The proposed framework identifies the reference values considering other reactive power controllers in the grid. Moreover, the proposed framework ensures that the steady state voltage stability margin is maximized. On the computational front, trust region algorithms ensure global convergence. The mathematical models and initialization algorithms proposed in this thesis are tested on standalone systems under various control scenarios. The algorithms proposed to incorporate a grid connected DFIG in steady state analysis tools have been tested on a sample 6-bus system and a practical 418-bus equivalent system of Indian southern grid.

The research is motivated by the need to address two major challenges in wind power integration: how to mitigate wind power fluctuation and how to ensure stability of the farm and host grid. It is envisaged that wind farm power output fluctuation can be reduced by using a specific type of buffer, such as an energy storage system (ESS), to absorb its negative impact. The proposed solution, therefore, employs ESS to solve the problems. The key research findings include a new technique for calculating the desired power output profile, an ESS charge-discharge scheme, a novel direct-calculation (optimization-based) method for determining ESS optimal rating, and an ESS operation scheme for improving wind farm transient stability. Analysis with 14 wind farms and a compressed-air energy storage system (CAES) shows that the charge-discharge scheme and the desired output calculation technique are appropriate for ESS operation. The optimal ESSs for the 14 wind farms perform four or less switching operations daily (73.2%-85.5% of the 365 days) while regulating the farms output variation. On average, the ESSs carry out 2.5 to 3.1 switching operations per day. By using the direct-calculation method, an optimal ESS rating can be found for any wind farm with a high degree of accuracy. The method has a considerable advantage over traditional differential-based methods because it does not require knowledge of the analytical form of the objective function. For ESSs optimal rating, the improvement in wind energy integration is between 1.7% and 8%. In addition, a net increase in grid steady-state voltage stability of 8.3%-18.3% is achieved by 13 of the 14 evaluated ESSs. For improving wind farm transient stability, the proposed ESS operation scheme is effective. It exploits the use of a synchronous-machine-based ESS as a synchronous condenser to dynamically supply a wind farm with reactive power during faults. Analysis with an ESS and a 60-MW wind farm consisting of stall-regulated wind turbines shows that the ESS increases the farm critical clearing time (CCT) by 1 cycle for worst-case bolted three-phase-to-ground faults. For bolted single-phase-to-ground faults, the CCT is improved by 23.1%-52.2%. / text