Exploration of a Scalable Holomorphic Embedding Method Formulation for Power System Analysis Applications

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/ThesisDoctoral Dissertation Electrical Engineering 201

Numerical Performance of the Holomorphic Embedding Method

abstract: Recently, a novel non-iterative power flow (PF) method known as the Holomorphic Embedding Method (HEM) was applied to the power-flow problem. Its superiority over other traditional iterative methods such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and their variants is that it is theoretically guaranteed to find the operable solution, if one exists, and will unequivocally signal if no solution exists. However, while theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not. Numerically, the HEM may require extended precision to converge, especially for heavily-loaded and ill-conditioned power system models. In light of the advantages and disadvantages of the HEM, this report focuses on three topics: 1. Exploring the effect of double and extended precision on the performance of HEM, 2. Investigating the performance of different embedding formulations of HEM, and 3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements. The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance. A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems. The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Modelling and control of united power flow controller for reinforcement of transmission systems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The work involved in the thesis is concentrated on modelling and control of UPFC. The overall objective is to provide effective methods and tools for assessing the impact of UPFC in the reinforcement of transmission systems. The thesis clarifies modelling and control of UPFC into several subproblems, in which the associated models, algorithms and control strategies of UPFC have been systematically reviewed. An electromagnetic transient prototype model of the UPFC has been set up by using its detailed power electronic device as well as its internal closed-loop controller. The problems encountered in the process of building such a model and the way of handling them by EMTP have been discussed. This EMTP-based simulator of SPWM UPFC implemented has provided a useful tool to assist the development and validation of more detailed and practical model of the UPFC for further studies. The steady-state modelling and control for the UPFC has been developed, including: (i) The power injection model of the UPFC suitable for its implementation in an optimal multiplier power flow computation method has been derived in rectangular form. The effectiveness of the proposed algorithm has been compared with the user defined model method. (ii) A systematic method for deriving the control capabilities of the UPFC has been proposed based on predicting the feasibility limit of the system. Using an index derived from optimal multiplier, three dimensional diagrams describing the ranges have been obtained. The results are also verified through the singular value decomposition algorithm. (iii) A power injection model based control method (PIM) has been proposed and implemented to directly derive the UPFC parameters as so to achieve the control objectives. The assumptions, algorithmic process and validation of the PIM have been investigated in detail. Its pros and cons are also discussed. (iv) Five internal limits of the UPFC device have been derived as the constraints to its performance. A complete set of control rules considering these limits as well as their implementation in the PlM have been constructed to form the basis of optimal UPFC control strategies for its steady-state local control. All the above proposed methods are tested and validated on the IEEE 30-bus system, a practical 306-bus system and a meshed network. The thesis concludes by suggesting the future research areas in further UPFC studies

Design and laboratory implementation of robust FACTS controller for inter-connected power systems

Imperial Users onl

Measurement-Based Monitoring and Control in Power Systems with High Renewable Penetrations

Power systems are experiencing rapid changes in their generation mixes because of the increasing integration of inverter-based resources (IBRs) and the retirement of traditional generations. This opens opportunities for a cleaner energy outlook but also poses challenges to the safe operation of the power networks. Enhanced monitoring and control based on the increasingly available measurements are essential in assisting stable operation and effective planning for these evolving systems. First, awareness of the evolving dynamic characteristics is quintessential for secure operation and corrective planning. A quantified monitoring study that keeps track of the inertial response and primary frequency response is conducted on the Eastern Interconnection (EI) for the past decade with field data. Whereas the inertia declined by at least 10%, the primary frequency response experienced an unexpected increase. The findings unveiled in the trending analysis also led to an improved event MW size estimation method, as well as discussions about regional dynamics. Experiencing a faster and deeper renewable integration, the Continental Europe Synchronous Area (CESA) system has been threatened by more frequent occurrences of inter-area oscillations during light-load high-renewable periods. A measurement-based oscillation damping control scheme is proposed for CESA with reduced reliance on system models. The design, implementation, and hardware-in-the-loop (HIL) testing of the controller are discussed in detail. Despite the challenges, the increasing presence of IBRs also brings opportunities for fast and efficient controls. Together with synchronized measurement, IBRs have the potential to flexibly complement traditional frequency and voltage control schemes for improved frequency and voltage recovery. The design, implementation, and HIL testing of the measurement-based frequency and voltage control for the New York State Grid are presented. In addition to the transmission level development, IBRs deployed in distribution networks can also be valuable assets in emergency islanding situations if controlled properly. A power management module is proposed to take advantage of measurements and automatically control the electric boundaries of islanded microgrids for maximized power utilization and improved frequency regulation. The module is designed to be adaptive to arbitrary non-meshed topologies with multiple source locations for increased flexibility, expedited deployment, and reduced cost

Power system dynamic modeling and synchrophasor measurements

Electric power is fully interwoven into the fabric of American life. Its loss for extended periods has profound impacts upon public safety, health and welfare. The power system has been termed the most complex machine built by man. Not surprisingly, the measures to address the range of power system downtime causes are as diverse as the causes themselves. One important arc of effort is providing power system operators with full knowledge of the system's operating state, timely warning when changing conditions threaten system stability, and tools guiding control actions to maintain stable operations. This research is motivated, in part, by the need to explore opportunities for leveraging nascent synchrophasor data streams against known power system stability challenges. Over the past half-decade, power system operators have aggressively installed large networks of phasor measurement units (PMUs) and phasor data concentrators (PDCs) across the United States and Canada. Today, the synchrophasor data network has reached a state of maturity that opens the door to useful application. This dissertation investigates power system stability along three lines of effort. The first two efforts address steady-state power system stability – specifically methods for assessing system vulnerabilities arising from the phase angle difference between two buses connected by a transmission line. The third effort investigates the information that can be gleaned from synchrophasor measurements during a system's dynamic system response to changing system conditions. The first line of investigation extends steady-state distribution factor theory. Distribution factors are computed from a known non-linear power system load flow solution. They provide a computationally light method for estimating new system conditions under different operating circumstances. Distribution factors are extremely useful for very rapidly screening the impact of unexpected changes in power system configuration – e.g. a transmission line dropping out of service due to environmental conditions. The Line Outage Angle Factor (LOAF) developed herein provides a method for fast computation of bus voltage angle changes after a line outage. The Line Outage Generator Factor (LOGF) modifies the simulated circuit topology to include synchronous machine transient reactances, enabling rapid screening of operating states in which line opening (or re-closure) risks damaging equipment. The LOAF and LOGF provide promising results in MATLAB simulation of the Western System Coordinating Council 3-Machine, 9-Bus System. The second investigative line seeks to develop a Thevenin equivalent model to be used in tandem with synchrophasor data streams to provide real-time bus angle difference information for buses connected by a transmission line. The appeal is that real-time bus angle difference information could be computed on-site and very rapidly – and significantly, independent of other network bus measurements. The results show that developing a Thevenin equivalent that provides a useful angle difference measure often works well on paper, but is challenging using actual synchrophasor data. Efforts to develop a Thevenin equivalent using Monte Carlo methods show promise, but require further investigation. The third line of effort shifts to investigate the useful information that a PMU can produce during a power system disturbance event. A synchrophasor is defined at a specific frequency, i.e. the system steady-state operating frequency. Thus a PMU produces a data stream recording power system changes progressing slower than the nominal system frequency; consequently, this is an “off-label” synchrophasor data application. The test system is a generator with electrical and mechanical controls connected by a pair of identical transmission lines to an infinite bus. The synchronous generator is modeled as a three-damper-winding synchronous machine. A MATLAB simulation was written to simulate both the full 14 dynamic state and the reduced order 11 dynamic state system models. A Real-Time Digital Simulator (RTDS) simulation emulating the test system provides the capability to produce real-time analog generator terminal waveforms to be sampled by a commercial off-the-shelf PMU to produce synchrophasor data. We find that the RTDS generated synchrophasor data stream is similar to the MATLAB reduced order model voltage and current generator terminal data in the dqo reference frame – reflecting parallel, but distinct, filtering processes