|
|
Sort by:
Number
Name
|
Author
|
Date
|
Size
|
Type
|
| 04-01 | A Loading-Dependent Model of Probabilistic Cascading Failure Large blackouts of electric power transmission systems are typically caused by cascading failure of loaded system components. We propose an analytically tractable model of loading dependent cascading failure that captures some of the salient features of large blackouts. This leads to
a new application and derivation of the quasibinomial distribution and its generalization to a saturating form with an extended parameter range. Suitably loading the model of cascading failure yields a power law region in the distribution of the number of failures similar to the distribution of blackout sizes observed in blackout data and simulations. The cascading failure model has many identical components randomly loaded. An initial disturbance adds load to each component and causes some
components to fail by exceeding their loading limit. Failure of a component causes a fixed load increase for other components. As components fail, the system becomes more loaded and cascading failure of further components
becomes likely. The probability distribution of the number of failed components is a saturating quasibinomial distribution. The saturation extends the parameter range of the quasibinomial distribution and the saturated distribution can represent highly stressed systems with a high probability of all components failing. Explicit formulas for the saturating quasibinomial distribution are derived using a recursion and via the quasimultinomial distribution of the number of failures in each stage of the cascade. The application of the saturating quasibinomial distribution is illustrated by increasing average initial component load. At low load, the probability distribution of the number of failed components has an exponential tail. At a critical load the distribution has a power law region that indicates a substantial risk of a large cascading failure. | Ian Dobson, Ben Carreras, David Newman | 1/20/2004 | 474.7k | PDF |
| 04-02 | Modifying Eigenvalue Interactions Near Weak Resonance In electric power system instabilities such as subsynchronous resonance or interarea oscillations, two complex modes can approach each other in frequency and then interact by changing damping so that one of the modes becomes unstable. Selecting changes in parameters to minimize this interaction is difficult by trial and error. By analyzing the interaction as a perturbation of a weak resonance, we calculate sensitivities that indicate the parameters to be changed to minimize the interaction and stabilize the system. The method is illustrated with a simple example of two coupled linear oscillators. The use of sensitivity methods to change the type of the interaction is also demonstrated. | Vincent Auvray, Ian Dobson, Louis Wehenkel | 1/23/2004 | 938.9k | PDF |
| 04-03 | Probabilistic load-dependent cascading failure with limited component interactions We generalize an analytically solvable probabilistic model of cascading failure in which failing components interact with other components by increasing their load and hence their chance of failure. In the generalized model, instead of a failing component increasing the load of all components, it increases the load of a random sample of the components. The size of the sample describes the extent of component interactions within the system. The generalized model is approximated by a saturating branching process and this leads to a criticality condition for cascading failure propagation that depends on the size of the sample. The criticality condition shows how the extent of component interactions controls the proximity to catastrophic cascading failure. Implications for the complexity of power transmission system design to avoid cascading blackouts are briefly discussed. | Ian Dobson, Ben Carreras, David Newman | 1/25/2004 | 110.9k | PDF |
| 04-04 | Visualizations for Power System Contingency Analysis Data Contingency analysis (CA) is critical in many routine power system and market analyses to show potential problems with the system. Due to the tremendous and yet increasing amount of data computed by CA, effective visualizations are needed to present the CA results to assist the system operators and engineers to comprehend the static security status of the system in a quick and intuitive manner. The desirable functionalities of such visualizations include showing the overall system security status, showing the severity levels of the contingencies in terms of their associated limit violations, and showing the geographic connection between the violated elements and the contingent elements. The traditional EMS display of CA results is a tabular list of elements with limit violations. This paper explores interactive 3D visualizations for contingency data. We visualize vulnerability levels of power system elements and severity information of outages separately. The overall situation of the whole system is conveyed “at a glance” by the overview visualizations, while more detailed information is displayed as needed. | Yan Sun, Tom Overbye | 3/2/2004 | 976.5k | PDF |
| 04-05 | Microgrid: A Conceptual Solution Application of individual distributed generators can cause as many problems as it may solve. A better way to realize the emerging potential of distributed generation is to take a system approach which views generation and associated loads as a subsystem or a “microgrid”. During disturbances, the generation and corresponding loads can separate from the distribution system to isolate the microgrid’s load from the disturbance (providing UPS services) without harming the transmission grid’s integrity. This ability to island generation and loads together has a potential to provide a higher local reliability than that provided by the power system as a whole. In this model it is also critical to be able to use the waste heat by placing the sources near the heat load. This implies that a unit can be placed at any point on the electrical system as required by the location of the heat load. | R. H. Lasseter & Paolo Piagi | 4/2/2004 | 382.9k | PDF |
| 04-06 | Implications of Cost and Bid Format on Electricity Market Studies: Linear Versus Quadratic Costs One important assumption in a model of an electricity market is the format of bids and costs. Most literature on electricity markets uses piecewise linear or quadratic functions to represent costs and bids. Economic theory holds that a firm in a perfectly competitive market maximizes its profit when it sells at marginal cost. This implies that profit-maximizing generators will bid at marginal cost. Different markets have varying rules regarding bid formats. Piecewise linear bid curves are compatible with physical characteristics of electricity generators, but cause difficulties in certain analysis techniques. Quadratic bid curves provide smooth dispatch, revenue, and profit curves that facilitate calculus-based analysis. In profit calculations, bids and marginal costs may either be coupled or independent of each other. The relation between bids and marginal costs impacts the profit-maximizing bid, and thus impacts generator strategies. These assumptions are particularly important for marginal generators, since different bid structures may yield different dispatch results, especially if the system is constrained. We compare markets with all piecewise linear bids, all quadratic bids, and a mixture of bids, and study the impacts of bid format and profit calculation on market outcomes in different scenarios. | Mary Cain and Fernando Alvarado | 4/19/2004 | 92.7k | PDF |
| 04-07 | Estimation of Synchronous Generator Parameters Using an Observer for Damper Currents and a Graphical User Interface This paper presents a method to identify synchronous generator parameters from on-line
data. An observer for estimation of synchronous machine damper currents is designed.
The observer-estimator is used in a Graphical User Interface (GUI) application. Possible
internal machine fault conditions can be detected and remedial action can be undertaken.
It is desired that an algorithm be developed such that it will enable bad measurement
detection and rejection so as to increase the reliability of the results. Secondary
objectives include calculation of the error characteristics of the estimation, development
of an index of confidence, study of which machine parameters can be estimated, and
which cannot, and evaluation of alternative GUI features.
Paper printed in J. Electric Power Systems Research, No. 69, v. 2004, pp. 7-16, February 2004 . | Elias Kyriakides and G.T. Heydt | 4/19/2004 | 107.0k | PDF |
| 04-08 | Fault Current Issues for Market Driven Power Systems with Distributed Generation This paper presents the consequences and operating limitations of installing distributed generation (DG) to electric power systems. The proliferation of new generators creates new operating conditions, some not seen before, that are limited by fault interruption capability. Increased system fault currents resulting from DG installation and the effects of increased fault currents are discussed. A technique used to evaluate fault current in the system after installing DGs is analyzed, and an example is given. The responsibility for the system change and safety degradation is discussed.
Prepared for NAPS 2004. | N. Nimpitiwan, G. Heydt | 4/20/2004 | 125.8k | PDF |
| 04-09 | Auto Tuning of Measurement Weights in WLS State Estimation This paper describes an approach for choosing and updating measurement weights used in weighted least squares (WLS) state estimation. Since the weights are related to the measurement error variances, sample variances are estimated using historical data from previous measurement scans and the corresponding WLS estimation results. The proposed approach can be implemented as a one-time estimation function for off-line execution or as a recursive function for updating the meas-urement weights on-line. Simulated measurement data and state estimation results are used to test and verify the accuracy of the proposed method. The proposed method can be inte-grated into an existing WLS state estimator as an added feature.
Uploaded 4/22/2004 | S. Zhong and Ali Abur | 4/24/2004 | 871.9k | PDF |
| 04-10 | Innovative concepts for on-line synchronous generator parameter estimation Ph.D. dissertation completed as part of the project "Extended State Estimation for Synchronous Generator Parameters."
A method to identify synchronous generator parameters from on-line
measurements is presented. Generator parameters are employed in the construction of
models used in transient stability studies and other routine power engineering studies.
These studies are critical for the operation of the power system, and therefore accurate
representation of synchronous generators and their parameters is important. The existing
off-line techniques are often not practical and do not capture the behavior of the generator
at all operating levels. Generator parameters vary due to aging, changes of the generator
internal temperature, magnetic saturation, and coupling between the generator and
external systems. The method proposed in this dissertation estimates generator
parameters at any operating level, taking into consideration the effect of saturation and
other phenomena in the operation of the synchronous generator.
Uploaded 4/22/2004 | Elias Kyriakides | 7/14/2004 | 5.2M | PDF |
| 04-11 | Combined State Estimation and Measurement Calibration A measurement calibration method is described in this paper. The proposed method identifies calibration models for the uncalibrated measurements and estimates the calibration model parameters along with the system states. The permanent nature of calibration errors allows their estimation by using multiple scans of measurements. The parametric models of the meas-urements can be estimated by reformulating the conventional system state estimation problem and incorporating calibration models. The paper also addresses the issues of network and parameter observability and provides simulation results for cases involving the IEEE-14 bus test system.
Uploaded 4/22/2004 | Shan Zhong and Ali Abur | 5/8/2004 | 707.0k | PDF |
| 04-12 | Voltage Stability Enhancement via Model Predictive Control of Load Impending voltage collapse can often be avoided by appropriate control of loads. However the traditional form of load control (shedding) is unpopular due to the resulting consumer disruption. Advances in communications and computer systems allow more selective load control though. Individual loads that are sacrificeable in the short-term can be switched with minimal consumer disruption. The paper considers the use of such non-disruptive load control for improving voltage stability. A control strategy that is based on model predictive control (MPC) is proposed. MPC utilizes an internal model to predict system dynamic behaviour over a finite horizon. Control decisions are based on optimizing that predicted response. MPC is a discrete-time form of control, so inaccuracies in predicted behaviour are corrected at the next control interval. A standard 10 bus voltage collapse example is used to illustrate this control strategy.
Original Submittal: Dec. 2003. Also appears in the Journal of Intelligent Automation and Soft Computing. | Ian Hiskens and B. Gong | 3/16/2006 | 182.5k | PDF |
| 04-13 | Three-Dimensional Displays as an Effective Visualization Technique for Power Systems Monitoring and Control Due to recent reconfiguration of the interconnected North American electric
power grid, operators must now comprehend a vast and growing amount of
multivariate data over more extensive network regions. Power systems
engineers and designers have thus begun to develop visualization tools to
aid these operators in managing such regions. In this study, we
investigated the use of three-dimensionality as a potential display
enhancement to support the tasks of fault detection and diagnosis across an
integrated one-line diagram. The participants were first required to
acknowledge all overloaded transmission lines for a given scenario and then
solve the scenario by reducing all line loadings to 100% of capacity or
less. Participants performed the tasks using one of three display types:
2-D numerical, 2-D graphical, and 3-D. Although the display type did not
have a significant effect on acknowledgment time, a 3-D advantage was
apparent for solution time. Accuracy results indicated a significant 3-D
advantage for the number of attempted output increases of maxed-out
generators. However, no significant effects of display type were found on
the number of erroneous generator output adjustments during the solution
task. More difficult tasks that require both focused attention and parallel
processing may further reveal whether three-dimensional displays can indeed
enhance accuracy. Workload was not affected by display dimensionality.
Overall, our results support the claim that three-dimensional displays can
improve performance in tasks that require monitoring and controlling
variables of complex systems. Uploaded 4/30/2004 | Stephan Hoppe, Gavin Essenberg, Doug Wiegmann, and Tom Overbye | 4/30/2004 | 1.0M | PDF |
| 04-14 | The Impact of Uncertainty on Incentives to Collude in Electricity Markets Market power in any market can result in higher prices than in a truly competitive market. Electricity markets pose unique problems to detection of market power due to the properties of electricity: it cannot be stored, which implies that the amount of energy supplied must always equal the amount demanded, and it must obey the laws of physics. A group of generators may exercise market power through tacit collusion, all raising prices together without communicating their intentions. Generators will use their expectations of market conditions to choose a competitive (low) bid, or a non-competitive (high) bid. We use expected residual demand to describe market conditions, and calculate threshold levels where a generator would decide to change from low to high bid. We examine the effects of uncertainty in load and competitor behavior on collusion decisions in both uniform price and discriminatory price auctions.
Uploaded 5/4/2004 | Mary B. Cain and Fernando L. Alvarado | 5/4/2004 | 128.2k | PDF |
| 04-15 | An Efficient Procedure For The Rational Buyer Approach For The Acquisition Of Capacity-Based Ancillary Services This paper addresses the competitive procurement
of capacity-based ancillary services (AS) in unbundled
markets by the Independent Grid Operator (IGO).
These AS include upward frequency control, load following
and the range of reserve services, which may be procured
from unloaded capacity offered by both on-line and
off-line sources. The capacity-based AS are prioritized in
order of ascending response times. Prioritization allows
substitutability of the AS by automatically making the
unused capacity of a higher priority AS usable for any
lower priority AS without the need of submitting additional
offers. This paper discusses the formulation of the
auction structures for the acquisition of the prioritizable
capacity-based AS and presents an efficient scheme for
minimizing the costs incurred by the IGO by using the
rational buyer procedure. The proposed scheme adopts
effective discrete programming techniques that exploit the
structural characteristics of the problem for handling the
multi-auction formulation. The proposed bounding scheme
takes fully advantage of critical physical constraints such
as ramp rate, capacity limits, and inter-zonal constraints.
The effectiveness and computational efficiency of the proposed
scheme are illustrated and discussed with numerical
examples.
Uploaded 05/8/2004 | Gianfranco Chicco and George Gross | 5/8/2004 | 223.1k | PDF |
| 04-16 | Comparative Analysis of Congestion Management Schemes under a Unified Framework The restructuring of the electricity industry has spawned the introduction of new independent grid operators or IGOs, typically called transmission system operators (TSOs), independent system operator (ISOs) or regional transmission organizations (RTOs), in various parts of the world. An important task of an IGO is congestion management (CM) and pricing. This activity has significant economic implications on every market participant in the IGO’s region. The paper briefly reviews the congestion management schemes and the associated pricing mechanism used by the IGO’s in five representative schemes. These were selected to illustrate the various CM approaches in use: England and Wales, Norway, Sweden, PJM and California. We develop a unified framework for the mathematical representation of the market dispatch and redispatch problems that the IGO must solve in CM in these various jurisdictions. We use this unified framework to develop meaningful metrics to compare the various CM approaches so as to assess their efficiency and the effectiveness of the market signals provided to the market participants. We compare, using a small test system, side by side, the performance of these schemes.
Uploaded 5/8/2004 | Ettore Bompard, Pedro Correia, George Gross, and Mikael Amelin | 5/8/2004 | 605.5k | PDF |
| 04-17 | Competitive Acquisition of Prioritizable Capacity-Based Ancillary Services The rational buyer procedure provides the competitive procurement of capacity-based ancillary services (AS) in unbundled markets by the Independent Grid Operator (IGO). The capacity-based AS are prioritized in order of ascending response times. Prioritization allows substitutability of the AS by automatically making the unused capacity of a higher priority AS usable for any lower priority AS without the need of submitting additional offers. We develop an efficient scheme for the rational buyer procedure for the acquisition of the prioritizable capacity-based AS. The scheme allows the simultaneous determination of the successful offers in the multi-auction procedure through the effective deployment of discrete programming notions and the exploitation of the structural characteristics of the formulation. A key feature is the incorporation of physical constraints such as capacity and inter-zonal constraints. The use of bounding techniques combined with procedures for the quick detection of infeasible combinations of the offer prices and the identification of avoidable calculations leads to reducing the computational burden. The effectiveness and computational efficiency of the scheme are illustrated with representative numerical results including case studies based on he IEEE 118-bus network.
Uploaded 5/8/2004 | Gianfranco Chicco and George Gross | 5/8/2004 | 514.2k | PDF |
| 04-18 | Framework for the Design and Analysis of Congestion Revenue Rights The capability to deal effectively with the uncertainty
associated with locational marginal prices (LMPs) in congestion
management schemes requires the development of appropriate
financial tools. Congestion revenue rights (CRR) are
hedging tools that provide the holder reimbursement of the congestion
charges in the day-ahead market and thereby provide
transmission service customers with price certainty. In this paper,
we construct a framework for the design and analysis of the
CRR by marrying finance theory notions with salient characteristics
of electric power systems and electricity markets. The
framework consists of three interconnected layers with one layer
each to represent the models of the transmission network, the
commodity markets and the CRR financial markets. The interaction
between the layers is represented as information flows. The
framework has sufficient scope to allow the analysis of a broad
range of problems associated with ensuring price certainty for
transmission services. The structural modularity of the framework
provides the flexibility to analyze issues and design structures
for the provision of transmission services in the competitive
environment. We introduce a new notion of CRR payoff parity
and a practical pricing scheme, which are used as the basis for
the design of more liquid CRR markets. The application of the
framework is further illustrated by the analysis of the conditions
that guarantee the revenue adequacy for the CRR issuer.
Uploaded 5/8/2004 | Minghai Liu and George Gross | 5/8/2004 | 256.1k | PDF |
| 04-19 | Computing Cournot Equilibria in Two Settlement Electricity Markets with Transmission Constraints We formulate a two-settlement equilibrium in competitive electricity markets as a subgame-perfect Nash equilibrium in which each generation firm solves a Mathematical Program
with Equilibrium Constraints (MPEC), given other firms’ forward and spot strategies. We implement two computational approaches, one of which is based on a Penalty Interior Point Algorithm and the other is based on a steepest descent approach. We apply the algorithm to a six node illustrative example.
Initial upload: 5/14/2004 | Jian Yao, Shmuel S. Oren, Ilan Adler | 5/14/2004 | 150.9k | PDF |
| 04-20 | The Inherent Inefficiency of Simultaneously Feasible Financial Transmission Rights Auctions Empirical evidence shows that the clearing prices for point-to-point congestion revenue rights, also known as financialtransmission rights (FTRs), resulting from centralized auctions conducted by Independent System Operators differ significantly and systematically from the realized congestion revenues that determine the accrued payoffs of these rights. The question addressed by this paper is whether such deviations are due to price
discovery errors which will eventually vanish or due to inherent inefficiencies in the auction structure. We show that even with perfect foresight of average congestion rents the clearing prices for the FTRs depend on the bid quantity and therefore may not be priced correctly in the financial transmission
right (FTR) auction. In particular, we demonstrate that if all FTR bid quantities are equal to the corresponding average transaction volumes and the bid values are set at the expected congestion rent level, then the resulting auction prices systematically
deviate from the known FTR values. We conclude that price discovery alone would not remedy the discrepancy between the auction prices and the realized values of the FTRs. Secondary markets
or frequent reconfiguration auctions are necessary in order to achieve such convergence.
Uploaded 5/14/2004. Updated version of paper 3-33. | Shijie Deng, Shmuel Oren and Sakis Meliopolous | 5/15/2004 | 132.8k | PDF |
| 04-21 | Metrics for Application of Revenue Sensitivity Analysis to Predict Market Power Coalitions in Electricity Markets This paper explores a mathematical method for detecting groups of generators in an electric power system that have the potential to benefit from exercising market power. Applications of this method include metrics for measuring or
detecting the possibility of market power. This paper focuses on the properties of revenue and dispatch to bid sensitivity matrices, and develops methods of identifying load pockets
from the sensitivity matrices, and how the matrices can provide metrics for market power.
Uploaded 5/20/2004 | Mary Cain and Fernando Alvarado | 5/21/2004 | 205.3k | PDF |
| 04-22 | Estimating Failure Propagation in Models of Cascading Blackouts We compare and test statistical estimates of failure propagation in data from versions of a probabilistic model of loading-dependent cascading failure and a power systems blackout model of cascading transmission line overloads. The comparisons suggest mechanisms affecting failure propagation and are an initial step towards monitoring failure propagation from practical system data. Approximations to the probabilistic model describe the forms of probability distributions of cascade sizes. This conference paper will appear in PMAPS 2004. | Ian Dobson, Ben Carreras, Vickie Lynch, Bertrand Nkei, David Newman | 5/31/2004 | 821.2k | PDF |
| 04-23 | Human Factors Aspects of Power System Flow Animation This paper presents experimental results associated with human factors aspects of using animation to display electric power system flow information, including transmission line MW flow and power transfer distribution factor (PTDF) values. The paper’s results are based on two experiments performed at the University of Illinois at Urbana-Champaign using electric power system students. The results indicate that animated motion of power system flows can be used successfully in displays to improve both the speed and accuracy of certain tasks. This effect was most apparent on displays showing PTDFs. However, the results also show that motion may not provide a clear advantage in the visualization of transmission line flows for uncomplicated analysis tasks. | Doug Wiegmann, Gavin Essenberg, Tom Overbye, and Yan Sun | 7/6/2004 | 488.6k | PDF |
| 04-24 | Self-Regulating Electricity Markets? An experimental structure is demonstrated that represents end-use customers in electricity markets who can substitute part of their usage between day and night. Three alternative demand-side market structures are evaluated: 1) customers pay the same fixed price (FP) in all periods - - the base case, 2) a demand response feature (DRP) is added to the fixed price case in periods of supply shortages, wherein buyers receive a pre-specified credit for reduced purchases, and 3) a real time pricing (RTP) case where prices are forecast for the upcoming day/night pair, then buyers select their quantity purchases sequentially and are charged the actual market-clearing price, period-by-period. After demonstrating the ability of buyers to make efficient purchases, six experienced sellers with experience in exercising market power were paired with seventeen buyers over twenty two auctions (eleven day-night pairs) that included heat waves and unit outages. The same periods were repeated under each of the three different market treatments, and the RTP structure resulted in the greatest market efficiency, despite the difficult cognitive problem it poses for buyers. Both DRP and RTP reduced the severity of price spikes as compared to the FP structure. The same periods were repeated under each of the three different market treatments, and the RTP structure resulted in the greatest market efficiency, despite the difficult cognitive problem it poses for buyers. Both DRP and RTP reduced the severity of price spikes as compared to the FP structure. | Nodir Adilov, Thomas Light, Richard Schuler, William Schulze, David Toomey and Ray Zimmerman | 7/7/2004 | 245.8k | PDF |
| 04-28 | Analysis of Angle Stability Problems: A Transmission Protection Systems Perspective Post-fault rotor angle oscillations lead to power swings. Both unstable and stable swings can induce distance relay tripping. For unstable swings, a new computational procedure to locate all of the electrical centers is developed. It simplifies the work associated with visual screening of all the R-X plots. For stable swings, a generic three-tier hierarchy of stability-related norms defined by branch norm, fault norm, and system norm is
proposed. Ranking by branch norm leads to ranking of power swings. Ranking by fault norm leads to ranking of faults or contingencies. Magnitude and rate of change of system norm can be used to detect an out-of-step condition. Results on a ten-machine system and a utility system with detailed models are also presented. | S. A. Soman, T. B. Nguyen, M. A. Pai, and R. Vaidyanathan | 7/27/2004 | 409.7k | PDF |
| 04-29 | Electrical Blackouts: A Systemic Problem Promises to end blackouts have been made for decades, but they ignore the reality that complex systems built and operated by humans will fail. Congress and the Federal Energy Regulatory Commission (FERC) must implement a framework that recognizes that individuals and companies will make errors and create a system that will limit their effects. | Jay Apt, Lester B. Lave, Sarosh Talukdar, M. Granger Morgan, and Marija Ilic | 8/16/2004 | Link | URL |
| 04-30 | Planning of Reconfigurable Power Systems The objectives of this project are to develop (a) theory and method for planning hybrid (discrete, continuous) power system controllers, and (b) economic systems, applicable to power system energy markets, for incentivizing, recovering, and allocating costs of design and installation of such controllers. The paper reports on first year efforts which include (a) application of discrete-event system theory to the reactive power planning problem, illustrated on a nine bus test system, and (b) development of cost allocation rules based on analysis of a cooperative game formulation using locational marginal pricing, illustrated on a 3 bus test system. In addition, we report on our efforts to develop a course for seniors in electrical engineering and in economics on electricity markets, system control, and planning. | J. McCalley, R. Kumar, N. Elia, V. Ajjarapu, V. Vittal, H. Liu, L. Jin, O. Volij, W. Shang | 8/16/2004 | 351.4k | PDF |
| 04-31 | Branching Process Models for the Exponentially Increasing Portions of Cascading Failure Blackouts We introduce branching process models in discrete and continuous time for the exponentially increasing phase of cascading blackouts. Cumulative line trips from real blackout data have portions consistent with these branching process models. Some initial calculations identifying parameters and using a branching process model to estimate blackout probabilities are illustrated.
Uploaded 10/6/2004 | Ian Dobson, Ben Carreras, David Newman | 10/6/2004 | 150.5k | PDF |
| 04-32 | Complex Systems Analysis of Series of Blackouts: Cascading Failure, Criticality, and Self-organization We give a comprehensive account of a complex systems approach to large blackouts caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is governed by a power law. This result is consistent with the power system being a complex system designed and operated near criticality.
The power law makes the risk of large blackouts consequential and implies the need for nonstandard risk analysis.
Power system overall load relative to operating limits is a key factor affecting the risk of cascading failure. Blackout models and an abstract model of cascading failure show that there are critical transitions as load is increased. Power law behavior can be observed at these transitions.
The critical loads at which blackout risk sharply increases are identifiable thresholds for cascading failure and we discuss approaches to computing the proximity to cascading failure using these thresholds. Approximating cascading failure as a branching process suggests ways to compute and monitor criticality by quantifying how much failures propagate.
Inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near criticality and confirm this idea using a blackout model. Mitigation of blackout risk should take care to account for counter-intuitive effects in complex self-organized critical systems. For example, suppressing small blackouts could lead the system to be operated closer to the edge and ultimately increase the risk of large blackouts.
Uploaded: 10/6/2004 | Ian Dobson, Ben Carreras, Vickie Lynch, David Newman | 10/6/2004 | 743.1k | PDF |
| 04-36 | Self-Regulating Markets for Electricity: Letting Customers into the Game We are conducting experiments of alternative forms of demand-side participation in the market to understand to what extent electricity markets might be more self-regulating (require fewer regulatory interventions like price caps and AMPS), were customers to become more actively involved. There appears to be beneficial outcomes for everyone from encouraging widespread customer participation in these markets: less volatility in prices and line flows and greater overall efficiency. But that’s not surprising because whoever heard of a market where the customers weren’t allowed to play?
IEEE Power Systems Conference and Exposition, October 10-13, 2004, New York, NY. Uploaded: 11/18/2004. | Richard E. Schuler | 11/18/2004 | 41.4k | PDF |
| 04-37 | The Probability, Identification, and Prevention of Rare Events in Power Systems The objectives of this thesis are to
- Provide a better understanding of the probabilities of rare events in power
systems;
- Develop ways to identify initiating high-order events in addition to N-1
contingencies;
- Provide an operational approach for avoiding or mitigating these types of events.
The focus of this work is on power system rare events that are not caused by
uncontrollable natural forces.
Uploaded 11/19/2004. | Qiming Chen | 11/19/2004 | 1.6M | PDF |
| 04-38 | On the Efficiency of the New York Independent System Operator Market for Transmission Congestion Contracts The physical nature of electricity generation and delivery creates special problems for the
design of efficient markets, notably the need to manage delivery in real time and the volatile
congestion and associated costs that result. Proposals for the operation of the deregulated
electricity industry tend towards one of two paradigms: centralized and
decentralized. Transmission congestion management can be implemented in the more
centralized point-to-point approach, as in New York state, where derivative transmission
congestion contracts (TCCs) are traded, or in the more decentralized flowgate-based approach.
While it is widely accepted that theoretically TCCs have attractive properties as
hedging instruments against congestion cost uncertainty, whether efficient markets for
them can be established in practice has been questioned. Based on an empirical analysis
of publicly available data from years 2000 and 2001, it appears that New York TCCs provided
market participants with a potentially effective hedge against volatile congestion
rents. However, the prices paid for TCCs systematically diverged from the resulting congestion
rents for distant locations and at high prices. The price paid for the hedge not being
in line with the congestion rents, i.e. unreasonably high risk premiums are being paid,
suggests an inefficient market. The low liquidity of TCC markets and the deviation of
TCC feasibility requirements from actual energy flows are possible explanations.
Uploaded: 11/22/2004 (Shmuel Oren) | Afzal S. Siddiqui, Emily S. Bartholomew, Chris Marnay, and Shmuel S. Oren | 11/22/2004 | 1.2M | PDF |
| 04-39 | Joint Energy and Reserves Auction with Opportunity Cost Payment for Reserves System operators in the electricity industry are
required to procure reserve capacity to deal with unanticipated
outages, demand shocks, and transmission constraints. One
traditional method of procuring reserves is through a separate
capacity auction with two-part bids. We analyze an alternative
scheme whereby reserves are procured through the energy
market using only energy bids, and capacity payments are
made based on a generator’s implied opportunity cost. By using
the revelation principle, we are able to derive the equilibrium
bidding function in this market and show that generators have
a clear incentive to understate their costs in order to capture
higher capacity rents. We then show that in spite of making
energy payments based on the marginally procured unit, the
expected energy costs under our scheme are bounded by that
of a disjoint auction. We then give a numerical example for a
special case of uniform demand distributions.
Uploaded: 11/22/04 (Shmuel Oren) | Shmuel Oren and Ramteen Sioshansi | 11/22/2004 | 166.3k | PDF |
| 04-40 | Cournot Equilibrium in Price-capped Two-Settlement Electricity Markets We compare two alternative mechanisms for capping
prices in two-settlement electricity markets. With sufficient
lead time and competitive entry opportunities, forward market
prices are implicitly capped by competitive pressure of potential
entry that will occur when forward prices rise above a certain
level. Another more direct approach is to cap spot prices through
regulatory intervention. In this paper we explore the implications
of the two alternative mechanisms in a two settlement Cournot
equilibrium framework. We formulate the market equilibrium
as a stochastic equilibrium problem with equilibrium constraints
(EPEC) capturing congestion effects, probabilistic contingencies
and market power. As an illustrative test case we use the 53-
bus Belgian electricity network with representative generator
cost but hypothetical demand and ownership assumptions. When
compared to two-settlement systems without price caps we find
that either of the price capping alternatives results in reduced
forward contracting. Furthermore the reduction in spot prices
due to forward contracting is smaller. | Jian Yao, Bert Willems, Shmuel S. Oren, and Ilan Adler | 11/22/2004 | 153.3k | PDF |
| 04-41 | Static Collapse and Topological Cuts This paper explores the relationships between power
system static collapse and flows in topological cuts. It
seeks a “local” detection of this “global” phenomenon.
The paper proposes a method capable of identifying a
limiting cut which has this property. This method is based
on the concepts of “bus through flow” and a bus static
transfer stability limit (BSTSL), both defined here.
Exploration of the limitations of power transfer through
buses and topological cuts provides insight on the
mechanisms for static collapse and points to remedial
actions to extend its margin.
HICSS-38 Conference Paper uploaded Dec. 14, 2004. | Santiago Grijalva and Peter W. Sauer | 12/14/2004 | 670.5k | PDF |
| 04-42 | Market Structure and the Predictability of Electricity System Line Flows: An Experimental Analysis This experimental analysis demonstrates that letting
the customers participate fully in the market reestablishes
the predictability of line flows as a function of
system load. In all of these experiments there are no
restrictions on permissible offering behavior by suppliers
(e.g. no price caps, prohibitions on withholding capacity
or automated mitigation procedures). Two alternative
forms of demand side participation are considered: 1) a
demand response program (DRP) where customers are
alerted to high prices in the subsequent period and are
paid a pre-specified amount for each kWh less than their
benchmark level of usage for that period, and 2) a real
time pricing program (RTP) where customers are given
forecasts of prices for each period over the subsequent
day and they then pay the actual period-by-period market
clearing price. As a benchmark, these experiments with
six suppliers and seventeen buyers are also repeated
where customers pay an average constant price in all
periods (FP); although in all cases sellers receive the
market-clearing price in each period.
HICSS-38 Conference Paper uploaded Dec. 14, 2004. | Nodir Adilov, Thomas Light, Richard Schuler, William Schulze, David Toomey, and Ray Zimmerman | 12/14/2004 | 248.9k | PDF |
| 04-43 | Automated Monitoring and Control Using New Data Integration Paradigm This paper introduces a new paradigm for data integration where the substation field data recorded by monitoring and protection Intelligent Electronic Devices (IEDs) is used to supplement Remote Terminal Unit (RTU) data for Supervisory Control and Data Acquisition (SCADA) system, which improves SCADA and other applications. This data integration paradigm allows very detailed monitoring of the power system and subsequently a more comprehensive decision making opportunities for the control applications. The data interfacing between the substation IEDs and EMS SCADA database to allow for such integration is elaborated on indicating various issues in using present IEC standards 61850 and 61970 to accomplish the required data interfacing. The paper ends with a discussion of the benefits of such an approach.
HICSS-38 Conference Paper. Uploaded Dec. 16, 2004. | Mladen Kezunovic, Tanja Djokic, and Tatjana Kostic | 12/16/2004 | 1.2M | PDF |
| 04-44 | Visualization and Animation of State Estimation Performance Reliable real time system “visibility” depends on a reliable and accurate state estimator. Present experience with state estimators indicates that its reliability is below expectations (an average of 5% non-convergent cases). The causes of this poor performance have been identified in earlier work by the authors and alternative robust state estimators have been proposed. For any state estimator, it is important to develop techniques for monitoring the performance of the state estimator and identification of potential problems such as bad sensors, consistent errors, modeling errors, etc. The paper presents visualization and animation methods that assist this process. It is demonstrated that bad data many times can be detected via visualization methods. The methodologies are demonstrated with a hybrid three-phase state estimator which addresses the issue of systematic errors from modeling and imbalance errors. This estimator is enhanced by visualization and animation methods that provide valuable information to users and system operators “at a glance”. The procedure and the visualization techniques are demonstrated on TVA’s 500 kV transmission system.
Conference paper for HICSS-38. Uploaded: Dec. 19, 2004. | A. P. Sakis Meliopoulos, George J. Cokkinides, Mike Ingram, Sandra Bell, and Sherica Mathews | 12/19/2004 | 547.7k | PDF |
| 04-45 | Testing the Effects of Holding Forward Contracts On the Behavior of Suppliers in an Electricity Auction The objective of this paper is to test how
spot prices are affected by forward contracts using
experimental economics. One set of tests used students
to represent suppliers in an electricity auction with 1)
no forward contracts, 2) permanent forward contracts,
and 3) renewable forward contracts. In the latter test,
the price of a new forward contract is affected by
conditions in the spot market. An identical set of tests
was also conducted using computer agents to represent
all of the suppliers. The objective was to demonstrate
that computer agents can be used effectively to test
electricity auctions and do additional sensitivity tests to
supplement the results obtained using humans.
The results show that holding a forward
contract is an effective way to mitigate high prices if the
same contract is held for all trading periods and the
price of this contract is independent of the spot prices
(i.e. is fixed). However, there is more speculation and
the spot prices are higher when a forward contract is
renewed periodically and spot prices influence the
forward price. With a renewable forward contract, a
price spike increases a supplier’s current earnings in
the spot market and expected future earnings from a
new forward contract. The overall conclusion is that
long-term bilateral contracts will reduce speculative
behavior, but this effect will be dissipated in an active
forward market with a large amount of secondary
trading.
Conference paper for HICSS-38. Uploaded Dec. 20, 2004. | Hyungna Oh and Tim Mount | 12/20/2004 | 1.9M | PDF |
| 04-46 | Observability Analysis and Measurement Placement for Systems with PMUs This paper is concerned about the analysis of network observability and phasor measurement unit (PMU) placement when using a mixed measurement set. The measurements will include conventional power flows and injections as well as phasor measurements for voltages and line currents provided by phasor measurement units. The observability analysis is followed by an optimal meter placement strategy for the PMUs.
Proceedings of the IEEE Power Systems Conference and Exposition 2004, October 10 – 13, 2004. Uploaded May 12, 2005. | Bei Xu and Ali Abur | 5/12/2005 | 66.5k | PDF |
| 04-47 | A Comprehensive Contribution Factor Method for Congestion Management This paper introduces a comprehensive method for congestion management by using network, generator and load contribution information. When congestion occurs, the priority is given first to the network contribution factor, then to the generator contribution factor and last to the load contribution factor. If the congestion can be relieved by the network adjustment, only the network control is used. Otherwise, generator re-dispatching is initialized. The method may also be combined with demand side (load) management to solve the congestion. The congestion management scheme is presented in this paper.
This work was supported by Pserc poject S-19, “Detection, Prevention and Mitigation of Cascading Events”. It was published in the IEEE PES PSCE 2004, New York, October 2004. Uploaded: July 13, 2005. | Hongbiao Song, Mladen Kezunovic | 7/14/2005 | 384.3k | PDF |
| 04-48 | Relieving Overload and Improving Voltage by the Network Contribution Factor (NCF) Method This paper introduces new Network Contribution Factor (NCF) method for relieving overload and improving voltage by using the network contribution information and base load flow conditions. When line overload or low voltage occurs, irrespective if it is caused by disturbance, load increase, or wheeling, we first find the following network contribution factors: Flow Network Contribution Factor (FNCF) and Voltage Network Contribution Factor (VNCF). Then we choose the most contributing elements and change their parameters, either by line control (Thyristor Controlled Series Capacitor-TCSC, line switching, etc.) or bus control (shunt capacitor, Static Var Compensator-SVC, etc.). The variances of the line flow and bus voltage are calculated. The results are verified by power flow calculation. This method can quickly find the parameter contributing to the largest variance based on the network information and base load flow conditions. It can be used for re-dispatching load flow, solving congestion, relieving overload, improving voltage, controlling emergency, etc.
This work was supported by Pserc project S-19, “Detection, Prevention and Mitigation of Cascading Events”. It was published at NAPS 2004, 36th Annual North America Power Symposium, Moscow, Idaho, August 2004. Uploaded July 13, 2005. | Hongbiao Song, Mladen Kezunovic | 7/14/2005 | 367.6k | PDF |
| 04-49 | Stability Control using PEBS method and Analytical Sensitivity of the Transient Energy Margin This paper introduces a stability control scheme based on a Lyapunov direct method, the Potential Energy Boundary Surface (PEBS) method, and analytical sensitivity of the transient energy margin. It classifies the stability control means into two categories, admittance-based control (ABC) and generator input-based control (GIBC), and uses a comprehensive method to analyze the contribution of each control. The scheme can get the optimal control from all the available control means by sensitivity analysis and then verify it in the transient stability program. Fast and accurate control goal is obtained from this stability control scheme.
This work was supported by Pserc project S-19, “Detection, Prevention and Mitigation of Cascading Events”. It was published in the IEEE PES PSCE 2004, New York, October 2004. Uploaded: July 14, 2005. | Hongbiao Song, Mladen Kezunovic | 7/14/2005 | 369.6k | PDF |
| 04-50 | Verifying the Protection System Operation Using an Advanced Fault Analysis Tool Combined with the Event Tree Analysis Relay misoperations play an important role in
cascading events. This paper proposes a novel strategy to monitor and verify relay operations during disturbances. Neural network based fault detection (NNFD) algorithm and Synchronized sampling based fault location (SSFL) algorithm are combined as an advanced fault analysis tool to give the precise fault information. Event tree analysis (ETA) is used for comparing relay operations in the real system with expected relay actions. Corrective actions are introduced if relay operations are contributing to cascading events. A case study is given in this
paper to help better understanding of the entire strategy.
Paper for Pserc S-19, Detection, Prevention and Mitigation of Cascading Event. In proceeding of NAPS 2004 (36th Annual North American Power Symposium). Uploaded July 7, 2005 | Nan Zhang and Mladen Kezunovic | 7/14/2005 | 120.7k | PDF |
| 04-51 | Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment Power system dynamic performance enhancement can often be formulated as a
dynamic embedded optimization problem. The associated cost function
quantifies performance, and involves dynamically evolving state
variables. The dynamic model is embedded within the constraints. Power
systems form an important example of hybrid systems, with interactions
between continuous dynamics and discrete events playing a fundamental role
in behaviour. However it is shown that for a large class of problems, the
cost function is smooth even though the underlying dynamic response is
non-smooth. Complementing this design-oriented optimization framework,
techniques for assessing power system performance and vulnerability can
often be expressed as boundary value problems, and solved using shooting
methods. it is shown that performance limitations are closely related to
grazing phenomena. Techniques are presented for determining parameter
values that induce limit cycles and grazing.
I.A. Hiskens, J-W. Park and V. Donde, "Dynamic
embedded optimization and shooting methods for power system
performance assessment", in Applied Mathematics for Deregulated
Electric Power Systems: Optimization, Control, and Computational
Intelligence, J. Chow, F. Wu and J. Momoh (Editors), Springer, 2004. Uploaded July 27, 2005. | I.A. Hiskens, J-W. Park and V. Donde | 8/23/2005 | 483.5k | PDF |
| 04-52 | Protecting the Market from ‘‘Hockey Stick’’ Pricing: How the Public Utility Commission of Texas is Dealing with Potential Price Gouging An automatic mitigation procedure called the
Competitive Solution Method offers a way of guarding
against price gouging while keeping the door open to
appropriate scarcity rents and price signals. | David Hurlbut, Keith Rogas and Shmuel Oren | 9/17/2005 | 201.7k | PDF |
| 04-53 | Float Together/ Sink Together? (The Effect of Connectivity on Power Systems) The recent mantra for reorganizing power systems in the U.S. has been to extend the
geographic scope of control centers to span several states, utilities and/or grid operators,
initially for the purpose of expanding the range of economic transfers and more recently
to improve operational reliability, in both cases through the reduction of “seams” at the
borders of control areas. Currently, the power system(s) in the U. S. is a hodge-podge - - institutionally,
economically, physically and in terms of regulatory oversight. It is the epitome of nationwide
de-centralized decision-making about a set of systems that are, nevertheless, highly
centralized locally. This analysis reviews these seeming inconsistencies and examines the
likely consequences for reliability. Conceptually, it compares strongly coordinated
network systems vs. decentralized loosely coupled systems as applied to the vulnerability
of power grids to catastrophic collapse.
Uploaded: Sep. 20, 2005. | Richard E. Schuler | 9/20/2005 | 376.7k | PDF |
| 04-54 | Evolving Nature of Electricity Market Design in the U.S. The introduction of the blueprint for open access transmission operations laid out in the FERC Orders No. 888 and 889 in 1996 was followed by the Order No. 2000 which directed FERC-jurisdictional entities to establish new transmission structures called regional transmission organizations or RTO’s. FERC subsequently invested considerable time and effort to develop a robust wholesale market via the so-called standard design (SMD) proposed rule making. The SMD was a bold, overly prescriptive and overly ambitious undertaking that failed due to various political, regional and stakeholder pressures, including the opposition of those entities who have yet to accept the notion of markets in the electricity sector. FERC withdrew the proposed rulemaking and replaced it with the less ambitious White Paper on the Wholesale Power Market Platform (WPM). While many of the underlying SMD aspects were kept, the overall effect was to move away from the cookie-cutter approach and to encourage regional differences in the market design arena. This paper assesses the thrusts of the SMD proposal and those of its redrafted version as presented in the WPM White Paper. The objective is to examine the FERC’s vision for achieving smoothly functioning electricity wholesale markets in the U.S. and the path taken toward the implementation of that vision. Proceedings of the IERE General Meeting and Central & Eastern European Forum. Krakow, Poland, October 17 - 21, 2004. Uploaded: Sep. 26, 2005. | George Gross | 9/26/2005 | 141.2k | PDF |
| 04-55 | Role of Distribution Factors in Congestion Revenue Rights In the locational marginal price (LMP)-based congestion
management scheme, transmission customers face uncertainty
in the congestion charges they incur. In order to bring certainty to
customers, congestion revenue rights (CRR) such as the fixed transmission
rights (FTR) used in the PJM interconnection and flowgate
rights (FGR) are introduced. These CRR are financial tools
that provide the holder reimbursement of the congestion charges
incurred in the day-ahead market. The implementation of CRR requires
appropriate modeling of the transmission network in which
the distribution factors are extensively used. These factors—the injection
shift factors (ISFs) and the power transfer distribution factors
(PTDFs)—are linear approximations of the sensitivities of the
active power line flows with respect to various variables. The factors
are computed for a specified network topology and parameter
values. In practice, the PTDFs used for the CRR issuance may be
different from those used in the day-ahead market due to changes
in the forecasted network conditions. The PTDF errors may impact
the FTR issuance quantities, the revenue adequacy of the FTR issuer
and the hedging ability of the FGR. In this paper, we explore
analytical characteristics of these distribution factors and investigate
their role in CRR applications. We study the nature of the
PTDF errors and examine their impacts in these applications, both
analytically and experimentally. Our results indicate that the impacts
of the PTDF errors in CRR applications stay in an acceptable
range under a broad spectrum of conditions including contingencies
used to establish 1 security. IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 2, MAY 2004. Uploaded Sep. 26, 2005. | Minghai Liu and George Gross | 9/26/2005 | 310.4k | PDF |
| 04-56 | PowerWeb Testing of Various Auction Clearing Mechanisms for Electricity Testing auction mechanisms using humans in a controlled environment provides an excellent and inexpensive means for evaluating their relative merits. This paper describes a framework for testing the efficacy of various supply-side auctions including one with price-responsive load and a soft-cap market. These are compared to a non-uniform price discriminative auction also inappropriately termed a “pay-as-bid” auction. Experimental evidence to date based on uniform price market testing has shown an ability of price responsive load to mitigate high volatility and average price. IEEE PES Power System Conference and Exposition, Oct. 2004. Uploaded June 27, 2006. | Robert J. Thomas, Timothy D. Mount, Ray D. Zimmerman | 6/27/2006 | 596.0k | PDF |
| 04-57 | Market Efficiency, Competition, and Communication in Electric Power Markets: Experimental Results Economic theory gives no clear indication of the minimum number of producers necessary for a market to define competitive price-quantity equilibria which approximate price equal to marginal cost. Previous work and FERC Guidelines generally suggest that 6 to 10 generators may be workably competitive. Our experiments with PowerWeb suggest that a higher number of suppliers may be necessary to approximate competitive market solutions, this in the absence of any communication among producers. As communications rules are altered to parallel differing types of antitrust enforcement, market results with 24 participants approach pure monopoly values. Ecological Economics March 31, 2004. Uploaded June 27, 2006. | D. Chapman, C. Vossler, T. Mount, V. Barboni, R. Thomas, R. Zimmerman | 6/27/2006 | 1.0M | PDF |
| 04-58 | PowerWeb: A Tool for Evaluating Economic and Reliability Impacts of Electric Power Market Designs This paper describes a web-based electric power market simulation tool called POWERWEB. It can be used as an experimental economics research tool to evaluate the economic and reliability impacts of given market designs as well as to train and educate students, industry professionals and policy makers. It is unique in its ability to combine the human behavior characteristics of a market structure with the operational and reliability aspects of the underlying power system. IEEE PES Power Systems Confernece and Exposition, October 13-14, 2004, Vol. 3. Uploaded: June 27, 2006. | Ray D. Zimmerman, and Robert J. Thomas | 6/27/2006 | 1.4M | PDF |
| 04-59 | Identifying the Potential for Market Power in Electric Power Systems in Real-Time The abuse of market power is a potentially serious problem for market designers. Few if any indices exist to measure the potential for market power in real-time. In references [1-2] an expression for a dispatch-to-price sensitivity matrix, M, was derived. The expression requires information about network topology and parameters as well as the rules used to operate the market. While computing the matrix is conceptually easy for those with all the market and system information (e.g., an ISO), the method is probably impractical for market participants due to the inaccessibility of much of the information. In this paper we suggest a method for estimating the M-matrix by using publicly available data. This suggests that any market participant who does the computation will know when conditions permit them to lower/raise prices through decreased/increased bids and/or offers. Proceedings of the 37th Hawaii International Conference on System Sciences, Jan. 5-8, 2004. Uploaded: June 27, 2006. | A. Kian, R. Thomas, R. Zimmerman, B. Lesieutre, T. Mount | 6/27/2006 | 204.8k | PDF |
| 04-60 | A Virtual Environment for Protective Relaying Evaluation and Testing Protective relaying is a fundamental discipline of power system engineering. At Georgia Tech we offer three courses that cover protective relaying: an undergraduate course that devotes one-third of the semester on relaying, a graduate course entitled “Power System Protection” and a three and a half day short course for practicing engineers. To maximize student understanding and training on the concepts, theory and technology associated with protective relaying, we have developed a number of educational tools, all wrapped in a virtual environment. The virtual environment includes (a) a power system simulator, (b) a simulator of instrumentation for protective relaying with visualization and animation modules, (c) specific protective relay models with visualization and animation modules and (d) interfaces to hardware so that testing of actual relaying equipment can be performed. We refer to this set of software as the “virtual power system”. The virtual power system permits the in-depth coverage of the protective relaying concepts in minimum time and maximizes student understanding. The tool is not used in a passive way. Indeed the students actively participate with well-designed projects such as (a) design and implementation of multifunctional relays, (b) relay testing for specific disturbances, etc. The paper describes the virtual power system organization and “engines”, such as solver, visualization and animation of protective relays, etc. It also discusses the utilization of this tool in the courses via specific application examples and student assignments. IEEE Transactions on Power Systems, Feb. 2004. Uploaded: June 30, 2006. | A.P. Sakis Meliopoulos and George J. Cokkinides | 6/30/2006 | 460.4k | PDF |