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Power Grids as Complex Networks: Formulating Problems for Useful Science and Science Based Engineering - Titles & Abstracts

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Ian Dobson, pedagogical talk

How can we model power systems for cascading blackouts?… considerable complications, cutting corners, and validation with data.

Abstract: Traditional detailed modeling procedures in power systems engineering are overwhelmed by the extreme complications of cascading blackouts, and the fine analytic advances in complex networks do not yet apply to power systems because of modeling problems. After briefly reviewing the full horror of the modeling difficulties, I will discuss how the nature of cascading blackouts shapes modeling choices, and how one might proceed to cut corners but nevertheless move forward towards some science and engineering applicable to cascading blackouts with validated models.


Adilson E. Motter

Synchronization in Oscillator and Power-Grid Networks

An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Power grids deliver a growing share of the energy consumed in the world and will soon undergo substantial changes owing to the increased harnessing of intermittent energy sources, the commercialization of plug-in electric automobiles, and the development of real-time pricing and two-way energy exchange technologies. These advances will further increase the economical and societal importance of power grids, but they will also lead to new disturbances associated with fluctuations in production and demand. Disturbances can prompt desynchronization of power generators, which is a leading cause of large power outages. In this talk, after reviewing some pertinent advances in the study of synchronization of coupled oscillators, I will discuss a condition under which the desired synchronous state of a power grid is stable. This condition can be used to specify tunable parameters of the generators that enhance spontaneous synchronization. Because these results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection, and for contributing to the development of networks that can recover from failures in real time.

In the second part of the talk, I will discuss our recent contributions to the control of power-grid dynamics through compensatory perturbations. A fundamental property of networks is that the perturbation of one node can affect other nodes, in a cascading process that may cause the entire or a substantial part of the system to change behavior and possibly collapse. Here, I will show how damage caused by external perturbations can often be mitigated or reversed by the application of compensatory perturbations that conform to the constraints of being physically admissible and amenable to implementation on the network. Our approach accounts for the full nonlinear behavior of real complex networks and can bring the system to a desired target state even when this state is not directly accessible. The effectiveness of this methodology is demonstrated through the identification of interventions that can control desynchronization instabilities in power-grid networks.


Zhifang Wang

Power Grid Network Analysis for Smart Grid Applications

Smart Grid is an umbrella term which refers to the modernization of electricity delivery systems with enhanced monitoring, analysis, control, and communication capabilities in order to improve the efficiency, reliability, economics, and sustainability of electricity services. The modernization happens at both the High Voltage transmission and the Medium or Low Voltage distribution grids.

This talk will present our investigation results on the statistical properties of power-grid based on a number of synthetic and real-world power systems, including the Small-World Properties, the Nodal Degree Distribution, the Graph Spectrum and Connectivity Scaling Property, and the Distribution of Line Impedance. It will also introduce an algorithm which is able to generate random topology power grids featuring the same topology and electrical characteristics found from the real data.The second part of this talk will cover various electrical centrality measures for power grids (which have been proposed in our past studies) and discuss their potential advantages in Smart Grid applications, such as the decentralized monitoring/controls and the implementation of Synchronous Phasor Measurement Units (Syn-PMUs).


Anna Scaglione

Cascading Overload Failures in Power Grid

Cascading failure in power grids has long been recognized as a sever security threat to national economy and society, which happens infrequent but results in costly damage. The triggering causes of cascading phenomena can be extremely complicated due to the many different and interactive mechanisms such as transmission overloads, protection equipment failures, transient instability, voltage collapse, etc. In the literature a number of models have been proposed to study the cascading overload failures in power grids. The first part of this talk will discuss the power flow distribution/redistribution in power grids through a couple of visualized examples, so that one may understand the special properties of power grids and realize the limitations of graph theoretic approaches.

Then we will introduce a stochastic Markov model of cascading overload failures in power grids, whose transition probabilities are derived from a stochastic model for the flow redistribution, and that can potentially capture the progression of cascading failures and its time span. Finally we wish to trigger an open discussion on the affecting factors that contribute to the grid vulnerability to such kind of cascading failures.


David P. Chassin

GridLAB-D: A Smart Grid Simulation Tool

ABSTRACT GridLAB-D is a new power distribution system simulation and analysis tool that provides information to those who design and operate smart grid systems. It is an agent-based simulation environment that incorporates advanced modeling techniques and high-performance algorithms to couple with powerflow, market, control system and load models. GridLAB-D™ was developed by the U.S. Department of Energy (DOE) at Pacific Northwest National Laboratory (PNNL), under funding from the Office of Electricity, in collaboration with industry and academia. David will discuss how GridLAB-D works and how it has been applied to the study of smart grid business cases, volt-VAR control, distribution automation, energy storage, renewable integration, and demand response.

BIOGRAPHY: David Chassin is the manager for Electric Power Systems Engineering team at Pacific Northwest National Laboratory and has more than 25 years of experience in the research and development of computer applications software for the architecture, engineering and construction industry. His research focuses on non-linear system modeling, high-performance simulation of energy and power systems, controls, and diagnostics. He is the principle investigator and project manager of DOE's SmartGrid simulation environment, called GridLAB-D and was the architect of the Olympic Peninsula SmartGrid Demonstration's real-time pricing system. He was granted several U.S. and international patents relating to Grid Friendly(TM) appliance technology. He is a Senior Member of IEEE, a member of the NASPI Data Network Management Task Team, the Western Electric Coordinating Council (WECC) Load Modeling Task Force and Market Integration Committee, and the North American Electricity Reliability Council (NERC) Load Forecasting Work Group.


Ali Pinar

Security-constrained Optimization for Electric Power Systems

The need for improving security standards for electric power systems is well recognized. Such efforts however, are hindered by lack of decision support tools that can incorporate security into the decision making process. The current practice is to protect the system against known or anticipated failures either by using a post?processing phase or byexplicit enumeration of the know cases. These approaches not only lack scalability to larger systems or higher security standards, but also are limited to predicted failures, which is a significant shortcoming with the uncertainty of the renewable generation.

In our earlier work, we have developed efficient techniques for vulnerability analysis of electric power systems. We are now in the process of adding our vulnerability analysis techniques into the decision making process. Specifically, we are investigating transmission and generation expansion and unit commitment problems with contingency constraints. The key to our approach is our ability to compactly represent security constraints.


Ian Hiskens

Grid Control (pedagogical talk)

  • Fundamentals of power system angle stability and voltage collapse.
  • Impact of load on power system dynamics, load modeling.
  • Generator controls: AVR, PSS, governor, AGC
  • Grid voltage regulation.
  • Demand response for peak shaving.
  • Fully responsive load control.

Steven Low, Caltech

Some Problems in Demand Response

We present a sample of problems in demand side management in future power systems and illustrate how they can be solved in a distributed manner using local information. First, we consider a set of users served by a single load-serving entity (LSE). The LSE procures capacity a day ahead. When random renewable energy is realized at delivery time, it manages user load through real-time demand response and purchases balancing power on the spot market to meet the aggregate demand. Hence optimal supply procurement by the LSE and the consumption decisions by the users must be coordinated over two timescales, a day ahead and in real time, in the presence of supply uncertainty. Moreover, they must be computed jointly by the LSE and the users since the necessary information is distributed among them. We present distributed algorithms to maximize expected social welfare. Instead of social welfare, the second problem is to coordinate electric vehicle charging to fill the valleys in aggregate electric demand profile, or track a given desired profile. We present synchronous and asynchronous algorithms and prove their convergence. Finally, we show how loads can use locally measured frequency deviations to adapt in real time their demand in response to a shortfall in supply. We design decentralized demand response mechanism that, together with the swing equation of the generators, jointly manimize disutility of demand rationing, in a decentralized manner.

(Joint work with Lingwen Gan, Libin Jiang, Ufuk Topcu, Changhong Zhao, Caltech)


Daniel Kirschen, pedagogical talk

Power system operation

Abstract: A power system consists not only of the visible infrastructure of power plants, transmission lines, transformers and substations but also of a very large and complex information and control infrastructure. On top of that, there is also a human infrastructure that takes care of the real-time operation and of the operational planning of the system. This talk will describe how these various infrastructures interact and will pay particular attention to the the tools and procedures that are used to maintain the reliability and optimize the economy of the system.


Lise Getoor Computer Science Department and Institute for Advanced Computing Studies University of Maryland, College Park

Graph Alignment, Identification and Summarization

There is a growing need to analyze data describing networks -- biological networks, social networks, sensor networks, and more. This data comes from multiple heterogeneous sources, is usually noisy and incomplete, and often the data is at the wrong level of abstraction for meaningful analysis, In this talk, I will argue that viewing the problem as a statistical inference problem of inferring the "hidden" network has great utility. In this context, I will describe our work on collective graph identification and describe the inference tasks involed, including approaches for performing entity resolution, link prediction and collective node labeling.


Maggie Eppstein and Paul Hines

Looking for trouble – and finding it!

Power systems are generally operated such that the failure of a single component (an “n-1 contingency”) does not result in a blackout. However multiple simultaneous component outages (“n-k contingencies”) can trigger large cascading blackouts, and grid operators are now required to protect against such problems. Identifying which combinations of component failures will cause large blackouts, however, is a hard problem due to the combinatorial size of the search space, and because of the complicated paths that cascading failures can take. We describe a stochastic ``Random Chemistry algorithm that can identify large sets of n-k contingencies that initiate cascading failures in a simulated power system. The method requires only O(log n) simulations per contingency identified, which is orders of magnitude faster than random search. We applied the method to a model of cascading failure in a power network with n=2896 transmission lines and identify 148,243 unique, minimal n-k branch contingencies (2 ≤ k ≤ 5) that cause large cascades, many of which would not be found by using pre-contingency flows, linearized line outage distribution factors, or performance indices as screening factors and which cannot be predicted from simple graph-theoretic metrics. Within each n-k collection, the frequency with which individual branches appear follows a power-law (or nearly so) distribution, indicating that a relatively small number of components contribute disproportionately to system vulnerability. We discuss a number of implications for modeling and assessing cascading failure risk in power systems.


David Newman, Ben Carreras and Ian Dobson

The Dynamics of a Power Transmission Grid Model: The impact of size, structure, operation and upgrades

Many of the complex systems characteristics found in the US power grid have been found to be captured by a dynamically evolving model (OPA) of the grid. Using OPA, one can investigate the how these characteristics change as the transmission grid system is modified. As examples of this, we investigate the impact of size and network homogeneity on the grid robustness, the change in risk of failure as generation mix (more distributed vs centralized for example) changes, as well as the effect of operational changes such as the changing the operational risk aversion or grid upgrade strategies. Finally, one of the important potential uses of these complex systems models of critical infrastructures like the power transmission grid is the ability to identify vulnerabilities of the system. We will briefly discuss techniques used to find vulnerabilities in the real US (western region) power grid using OPA.


Aaron Clauset

Computer Science, UC Boulder

A generative model for hierarchical structure


Leonardo Duenas-Osorio

Probabilistic Risk Assessment for Critical Infrastructures Enabled by Complex Systems Tools

While critical infrastructure systems continue to be the lifelines for modern society, both during normal operation and in the aftermath of disasters, they are reaching their design life, their design capacities, and are becoming more interconnected and geographically exposed. These conditions heighten the need for infrastructure system models with predictive power that are also capable of handling uncertainty so as to design, manage, and plan for infrastructure expansions and retrofits. However, sophisticated models for lifeline systems such as power grids and telecommunication networks are too computationally demanding for probabilistic performance analyses as desired by infrastructure engineering analysts and designers. Hence, exploiting concepts from network theory and complex systems it is possible to reduce the computational demands of lifeline system models while capturing the essential features of uncertainty in hazards, response, and interactions. For example, clustering for system decentralization and autonomous decision making mimic well processes seen in practical system operation and restoration, while ranking methodologies that combine topology with physical system fragility enable criticality analysis of components within and across lifeline systems. Applications of these enabling tools are presented in the context of the resilience of the Chilean power system after the 2010 earthquake, as well as the Houston power and gas systems under the possibility of hurricane hazards. Potential applications to other utility systems are also highlighted to showcase the potential of network theory in supporting the upcoming standards for infrastructure resilience in the US.


Misha Chertkov (pedagogical talk)

Applied Math and Physics for Smart (Power) Grids

We are asking modern power grids to serve under conditions for which they were not originally designed. We also expect the grids to be smart, in how they function, how they withstand contingencies, how they respond to fluctuations in generation and load, and how the grids are controlled. To meet these ever-increasing expectations requires extending power grid models beyond the scope of traditional power engineering.

In this pedagogical talk aimed at applied mathematicians and physicists I first review basics of power flows (in a way to complement preceding pedagogical talks), and then outline a number of new approaches in modeling power grids originating from applied math and physics. In particular, I describe (a) probabilistic distance to failure in transmission (high voltage) system; and if time permits (b) ode/pde approach to reduced modeling of voltage stability/collapse in distribution (low voltage) system.


Chris DeMarco, University of Wisconsin-Madison

The Network Graph in Power Grid Phenomena: Unifying Power Flow Structure from Locational Marginal Prices to Electromechanical Coherency

At the core of many phenomena of interest in the electric power grid lie the coupling and transfer limits imposed by the network's power flow. In many ways, challenges in study of the electric grid arise from the fact that power, determined by the voltage-current product, is the quantity of interest driving both grid economics in the steady state, and grid dynamics under transient conditions. The well-known power flow equations characterize the power absorbed by the network at each node, as a function of magnitude and phase information for the (assumed) sinusoidal voltages at each node. The graph of the transmission network determines the structure of these equations, and their linearized, local behavior about an equilibrium is characterized by a Jacobian that may be well-approximated as a weighted Laplacian matrix.

This talk will illustrate how the local Laplacian structure may be exploited to explain two interesting qualitative features that appear in seemingly very different facets of grid behavior. First, in the context of power market calculations for Locational Marginal Prices (LMPs), we will show how the null space of an augmented power flow Jacobian determines an admissible set from which the dual variables of LMPs must be drawn. We then make use of the properties of the Fieldler vector associated with a weighted Laplacian to show how this gives rise to easily predicted graph partitions of differentiated LMPs when one or more transmission line(s) are constrained.

In a very different context, we illustrate how the power flow Jacobian plays a key role in predicting the eigenstructure for a generalized eigenvalue problem, associated with the electromechanical dynamics of the grid (i.e., the typically oscillatory exchange of power between generators following a system disturbance). In this context we will show how the Fielder vector associated with the weighted Laplacian for the power flow predicts the phenomena of "coherency," -- that is, the tendency of groups of generators on either side of a cutset of transmission lines to experience near equal deviations in frequency, with one group oscillating against the other. This class of "inter-area" modes are of particular interest because they can affect groups of generators hundreds of kilometers apart, and are often problematic due to their low damping.


Cristopher Moore, Santa Fe Institute, TBA


Raissa D'Souza, TBA


Charlie Brummitt

Optimal interdependence among power grids

Interdependence among power grids offers benefits such as long distance trade and sharing risk. But interdependence also enables failures to spread widely. We are trying to determine how much interdependence might balance tradeoffs like these. Cascades in a highly stylized model, the sandpile model, on interdependent networks suggest that an intermediate amount of interdependence mitigates each network's risk to large cascades. Now we are seeking similar behavior in more realistic models of interdependent power grids. Cascading line outages in the DC model have monotonic relationships between risk and interdependence, unlike the sandpile model. Insight from domain experts could steer this work to relevance and more interesting behavior. What is the right scale to consider networks that mitigate their own risk to blackouts: The ISO? Countries? What happens at connections between them (and how do we model such connections)? What dynamical models and time scales might be relevant at the scale of interdependent grids?


Clayton Barrows Ph.D. Candidate, Penn State University

Marginal Transmission Switching


Removal of specific transmission lines from operation (“transmission switching”) can reduce the costs associated with power system operation. This phenomenon, known as Braess’ Paradox, could be avoided in electric transmission networks through the use of high-quality “smart grid” data and emerging technologies that would make the topology of the power grid adaptable to real-time system conditions. The “optimal transmission topology” problem has been posed in previous research, but is infeasible to solve globally due to the size of real power systems. We analyze the optimal transmission switching results of previous research on the RTS-96 network to determine network properties that identify the optimal number and location of transmission switches. Additionally, we decompose the results of Optimal Transmission Switching to determine the marginal contribution of each switched line to cost savings. As expected, none of the examined network properties successfully identify optimally switched lines. However, our analysis of marginal switching contribution draws conclusions that will enable solution heuristics for the optimal transmission switching problem on larger systems.


Eduardo Cotilla-Sanchez

Measures of performance and clustering of power networks based on electrical distance

Abstract: Electric power grids have a topological structure that is straightforward to represent and analyze with metrics and methods from network science. However, simple graph models neglect the comprehensive connections between components that result from Ohm's and Kirchhoff's laws. In this talk, we will first discuss a method to represent electrical networks using electrical distances rather than topological distances. Then, we will obtain performance metrics for the North American power grid using the proposed approach and compare against more traditional network metrics. Lastly, we will present an application of this electrical representation consisting in the partinioning of power networks into electrically cohesive clusters that are favorable for zone-based planning analyses.