Aranya Chakrabortty

A Measurement-Based Framework for Dynamic Equivalencing of Large Power Systems Using Wide-Area Phasor Measurements

Wide-area analysis and control of large-scale electric power systems are highly dependent on the idea of aggregation. For example, one often hears power system operators mentioning how northern Washington oscillates against southern California in response to various disturbance events. The main question here is whether we can analytically construct dynamic electromechanical models for these conceptual, aggregated generators representing Washington and California, which in reality are some hypothetical combinations of thousands of actual generators. In this paper we address this problem, and present a concise overview of several new results on how to construct simplified interarea models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our examples of study are motivated by widely encountered power transfer paths in the Western Electricity Coordinating Council (WECC), namely, a two-area radial system representing the WA-MT flow, and a star-connected three-area system resembling the Pacific AC Intertie.

Synchronized Phasor Data Based Energy Function Analysis of Dominant Power Transfer Paths in Large Power Systems

Many large interconnected power systems such as the U.S. eastern interconnection and the U.S. western power system are characterized by many power transfer paths or interfaces with high loading. Disruptions of these transfer paths frequently lead to increased loading on neighboring transfer paths, which themselves will become less secure and could cause further disruptions. State estimators have limited performance under large system disruptions, because of low sampling rates and potentially poor solution quality due to topology errors. Furthermore, disruptions in external power systems cannot be readily seen by control room operators because most state estimators only use reduced models for external systems. A system of well-placed phasor measurement units (PMUs) that provide voltage and current magnitude and phase at a high sampling rate can provide useful system dynamic security information. In this paper we apply energy function analysis using phasor data to monitor the dynamic status of power transfer paths. The ideas will be illustrated using actual data captured by several PMUs in the U.S. western power system

Introduction to wide-area control of power systems

A key element in the development of smart power transmission systems over the past decade is the tremendous advancement of the Wide-Area Measurement System (WAMS) technology, also commonly referred to as the Synchrophasor technology. Sophisticated digital recording devices called Phasor Measurement Units or PMUs are currently being installed at different points in the North American grid, especially under the smart grid initiatives of the US Department of Energy, to record and communicate GPS-synchronized, high sampling rate (6-60 samples/sec), dynamic power system data. Significant research efforts have been made on techniques to useWAMS for monitoring and situational awareness of large power networks dispersed across wide geographical areas. In contrast, use of WAMS for automatic feedback control has received less attention from the research community. The objective of this paper is to bridge this gap by formulating wide-area control problems for oscillation damping, voltage control, wide-area protection, and disturbance localization. We present the main research challenges that need to be overcome to realize the benefits of wide area control in power systems. Our discussion begins with a review of the fundamental physical models of different characteristic components of a large transmission-level power grid such as synchronous generators, transmission lines, and loads, followed by a description of how these subsystem-level models can be integrated to form the overall system model. We pose ten distinct control-theoretic problems. The first two problems are on using PMU measurements from selected nodes in the system to identify such system models in different resolutions in real-time, and the remaining on how the identified models can be used for designing output-feedback based damping controllers, for understanding voltage fluctuations at different nodes of the network graph, and for detecting malicious inputs entering the system dynamics via faults or extraneous attacks. We also propose two new control paradigms, namely a scheduling approach for appropriate controller selection based on online estimation of oscillation modes, and distributed phasor-based control using model estimation. We illustrate our ideas via representative examples, many of which are inspired by well-known power transfer paths in the US west coast grid, also referred to as the Western Electricity Coordinating Council (WECC).

Time-scale separation redesigns for stabilization and performance recovery of uncertain nonlinear systems

In this paper we propose two different time-scale separation based robust redesign techniques which recover the trajectories of a nominal control design in the presence of uncertain nonlinearities. We first consider additive input uncertainties and design a high-gain filter to estimate the uncertainty. We then employ the fast variables arising from this filter in the feedback control law to cancel the effect of the uncertainties in the plant. We next extend this design to systems with uncertain input nonlinearities in which case we design two sets of high gain filters-the first to estimate the input uncertainty over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. Using singular perturbation theory we prove that the trajectories of the respective two-time-scale and three-time scale redesigned systems approach those of the nominal system when the filter gains are increased. We illustrate the redesigns by applying them to various physically motivated examples.

Wide-Area Damping Control of Power Systems Using Dynamic Clustering and TCSC-Based Redesigns

In this paper we present a FACTS (Flexible AC Transmission Systems)-based control design for electromechanical oscillation damping in large power systems, facilitated by aggregate models that can be constructed using Synchronized phasor measurements. Our approach consists of three steps, namely-1. Model Reduction, where Synchrophasors are used to identify second-order models of the oscillation clusters of the power system retaining the inter-ties on which FACTS devices such as Thyristor Controlled Series Compensators (TCSC) are installed, 2. Aggregate Control, where feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally 3. Control Inversion, where the aggregate control design is distributed and tuned to actual TCSC controllers in the full-order model until its inter-area responses match the respective inter-machine responses of the reduced-order system. It is shown that the inversion problem can be posed equivalently as decomposing the swing dynamics into fast and slow states, and designing the controllers such that the slow dynamics can optimally track a desired closed-loop signal designed for the aggregate model. Application of the approach to two-area power systems is demonstrated through topological examples inspired by the US west coast grid.

Local energy storage sizing in plug-in hybrid electric vehicle charging stations under blocking probability constraints

Plug-in hybrid electric vehicles (PHEV) are becoming gradually more attractive than internal combustion engine vehicles, even though the current electrical grid is not potentially able to support the required power demand increase to introduce charging stations. Acknowledging that design and development of charging stations has crucial importance, this paper introduces a candidate PHEV charging station architecture, along with a quantitative stochastic model, that allows us to analyze the performance of the system by using arguments from queuing theory and economics. A relevant component of the proposed architecture is the capability of the charging stations to store excess power obtained from the grid. The goal is to design a general architecture which will be able to sustain grid stability, while providing a required level of quality of service; and to describe a general methodology to analyze the performance of such stations with respect to the traffic characteristics, energy storage size, pricing and cost parameters. Our results indicate that significant gains in net cost/profit and useful insights can be made with the right choice of storage size. Such considerations are crucial in this early stage of designing the smart grid and charging stations of the future.

Estimation of Radial Power System Transfer Path Dynamic Parameters Using Synchronized Phasor Data

This paper develops a measurement-based method for estimating a two-machine reduced model to represent the interarea dynamics of a radial, multimachine power system. The method uses synchronized bus voltage phasor measurements at two buses and the line current on the power transfer path. The innovation is the application of the interarea oscillation components in the voltage variables resulting from disturbances for extrapolating system impedances and inertias beyond the measured buses. Expressions for the amplitudes of the bus voltage and bus frequency oscillations as functions of the location on the transmission path are derived from a small-signal perturbation approach. The reduced model provides approximate response to disturbances on the transfer path and offers an alternative to model reduction techniques based on detailed system models and data.

Co-Optimization of Power and Reserves in Dynamic T&D Power Markets With Nondispatchable Renewable Generation and Distributed Energy Resources

Marginal-cost-based dynamic pricing of electricity services, including real power, reactive power, and reserves, may provide unprecedented efficiencies and system synergies that are pivotal to the sustainability of massive renewable generation integration. Extension of wholesale high-voltage power markets to allow distribution network connected prosumers to participate, albeit desirable, has stalled on high transaction costs and the lack of a tractable market clearing framework. This paper presents a distributed, massively parallel architecture that enables tractable transmission and distribution locational marginal price (T&DLMP) discovery along with optimal scheduling of centralized generation, decentralized conventional and flexible loads, and distributed energy resources (DERs). DERs include distributed generation; electric vehicle (EV) battery charging and storage; heating, ventilating, and air conditioning (HVAC) and combined heat & power (CHP) microgenerators; computing; volt/var control devices; grid-friendly appliances; smart transformers; and more. The proposed iterative distributed architecture can discover T&DLMPs while capturing the full complexity of each participating DERs intertemporal preferences and physical system dynamics.

Distributed Optimization Algorithms for Wide-Area Oscillation Monitoring in Power Systems Using Interregional PMU-PDC Architectures

In this paper, we present a set of distributed algorithms for estimating the electro-mechanical oscillation modes of large power system networks using synchrophasors. With the number of phasor measurement units (PMUs) in the North American grid scaling up to the thousands, system operators are gradually inclining toward distributed cyber-physical architectures for executing wide-area monitoring and control operations. Traditional centralized approaches, in fact, are anticipated to become untenable soon due to various factors such as data volume, security, communication overhead, and failure to adhere to real-time deadlines. To address this challenge, we propose three different communication and computational architectures by which estimators located at the control centers of various utility companies can run local optimization algorithms using local PMU data, and thereafter communicate with other estimators to reach a global solution. Both synchronous and asynchronous communications are considered. Each architecture integrates a centralized Prony-based algorithm with several variants of alternating direction method of multipliers (ADMM). We discuss the relative advantages and bottlenecks of each architecture using simulations of IEEE 68-bus and IEEE 145-bus power system, as well as an Exo-GENI-based software defined network.

Coordinating Wind Farms and Battery Management Systems for Inter-Area Oscillation Damping: A Frequency-Domain Approach

This paper presents a set of linear control designs for shaping the inter-area oscillation spectrum of a large radial power system through coordinated control of a wind farm and a battery energy system (BES). We consider a continuum representation of the power system with the wind and battery power modeled as point-source forcings. A spectral analysis of the system demonstrates that its oscillation spectrum strongly depends on the locations of these power injections, implying that there are siting locations that produce more favorable spectral responses. However, the ability to site a wind farm or BES at a specific location may be limited by geographic, environmental, economic or other considerations. Our work provides a means to circumvent this problem by designing co-ordinated controllers for the power outputs of the wind farm and the BES by which one can shape the spectral response of the system to a desired response. The design is posed as a parametric optimization problem that minimizes the error between the two spectral responses over a finite range of frequencies. The approach is independent of the locations of the wind farm and the BES, and can be implemented in a decentralized fashion.