Thomas J. Overbye

A comparison of the AC and DC power flow models for LMP calculations

The paper examines the tradeoffs between using a full ac model versus the less exact, but much faster, dc power flow model for LMP-based market calculations. The paper first provides a general discussion of the approximations associated with using a dc model, with an emphasis on the impact these approximations will have on security constrained OPF (SCOPF) results and LMP values. Then, since the impact of the approximations can be quite system specific, the paper provides case studies using both a small 37 bus system and a somewhat larger 12,965 bus model of the Midwest U.S. transmission grid. Results are provided comparing both the accuracy and the computational requirements of the two models. The general conclusion is that while there is some loss of accuracy using the dc approximation, the results actually match fairly closely with the full ac solution.

A two-level optimization problem for analysis of market bidding strategies

Electricity markets involve suppliers (generators) and sometimes consumers (loads) bidding for MWhr generation and consumption. In this market model, a central operator selves an optimal power flow (OPF) based on the maximization of social welfare to determine the generation and load dispatch and system spot prices. In this structure, market participants will choose their bids in order to maximize their profits. This presents a two-level optimization problem in which participants try to maximize their profit under the constraint that their dispatch and price are determined by the OPF. This paper presents an efficient numerical technique, using price and dispatch sensitivity information available from the OPF solution, to determine how a market participant should vary its bid portfolio in order to maximize its overall profit. The paper further demonstrates the determination of Nash equilibrium when all participants are trying to maximize their profit in this manner.

Line Outage Detection Using Phasor Angle Measurements

Although phasor measurement units (PMUs) have become increasingly widespread throughout power networks, the buses monitored by PMUs still constitute a very small percentage of the total number of system buses. Our research explores methods to derive useful information from PMU data in spite of this limited coverage. In particular, we have developed an algorithm which uses known system topology information, together with PMU phasor angle measurements, to detect system line outages. In addition to determining the outaged line, the algorithm also provides an estimate of the pre-outage flow on the outaged line. To demonstrate the effectiveness of our approach, the algorithm is demonstrated using simulated and real PMU data from two systems - a 37-bus study case and the TVA control area.

A power flow measure for unsolvable cases

As power systems become more heavily loaded, there will be an increase in the number of situations where the power flow equations have no real solution, particularly in contingency analysis and planning applications. Since these cases can represent the most severe threats to viable system operation, it is important that a computationally efficient technique be developed to both quantify the degree of unsolvability, and to provide optimal recommendations of the parameters to change to return to a solvable solution. Such an algorithm is developed in the paper. The distance in parameter space between the desired operating point and the closest solvable operating point provides a measure of the degree of unsolvability, with the difference between these two points providing the optimal system parameter changes. The algorithm is based upon a Newton-Raphson power flow algorithm, which provides both computational efficiency and compatibility with existing security analysis techniques. The method is demonstrated on systems of up to 118 buses. >

An energy based security measure for assessing vulnerability to voltage collapse

A security measure is defined to indicate vulnerability to voltage collapse based on an energy function for system models that includes voltage variation and reactive loads. The system dynamic model, the energy function, and the security measure are first illustrated in a simple radial system. Application of the security measure and its computational aspects are then examined in a standard 30-bus example (New England System). The security measure captures nonlinear effects such as VAR limits on generators that can influence the systems vulnerability to collapse. The behavior of the index with respect to network load increases is nearly linear over a wide range of load variation, facilitating prediction of the onset of collapse. >

An Authenticated Control Framework for Distributed Voltage Support on the Smart Grid

Existing and forthcoming devices at the residential level have the ability to provide reactive power support. Inverters which connect distributed generation such as solar panels and pluggable hybrid electric vehicles (PHEVs) to the grid are an example. Such devices are not currently utilized by the power system. We investigate the integration of these end-user reactive-power-capable devices to provide voltage support to the grid via a secure communications infrastructure. We determine effective locations in the transmission system and show how reactive power resources connected at those buses can be controlled. Buses belong to reactive support groups which parallel the regions of the secure communications architecture that is presented. Ultimately, our goal is to present how the smart grid can enable the utilization of available end-user devices as a resource to mitigate power system problems such as voltage collapse.

SCADA Cyber Security Testbed Development

New technologies are increasing the vulnerability of the power system to cyber security threats. Dealing with these threats and determining vulnerabilities is an important task for utilities. This paper presents the development of a testbed designed to assess the vulnerabilities introduced by using public networks for communication.

Improved techniques for power system voltage stability assessment using energy methods

An improved method of assessing power system voltage stability using energy techniques is presented. The concept of an energy function providing a localized measure of voltage security in a particular portion of the system is developed. A crucial factor in the use of the energy function method is the ability to rapidly determine the appropriate low-voltage solution to use in the energy measure calculation. Also, an improved method of locating power alternative solutions with low associated energy measures is presented. Techniques are demonstrated on the IEEE 118 bus system and a 415-bus system. >

An individual welfare maximization algorithm for electricity markets

An algorithm that allows a market participant to maximize its individual welfare in electricity spot markets is presented. The use of the algorithm in determining market equilibrium points, called Nash equilibria, is demonstrated. The start of the algorithm is a spot market model that uses the optimal power flow (OPF), with a full representation of the transmission system and inclusion of consumer bidding. The algorithm utilizes price and dispatch sensitivities available from the Hessian matrix and gradient of the OPF to help determine an optimal change in an individuals bid. The algorithm is shown to be successful in determining local welfare maxima, and the prospects for scaling the algorithm up to realistically sized systems are very good. Nash equilibria are investigated assuming all participants attempt to maximize their individual welfare. This is done by iteratively solving the individual welfare maximization algorithm until all individuals stop modifying their bids.

Power System Level Impacts of PHEVs

This paper presents investigations into various aspects of how plug-in hybrid electric vehicles (PHEVs) could impact the electric power system. The investigation is focused on impacts on the power system infrastructure and impacts on the primary fuel utilizations due to PHEV charging. The investigation is presented in terms of examples of typical systems. Methodologies are presented for computing loss of life of distribution transformers, which sets the basis for needed expansion or upgrades of systems with PHEV penetration. In addition, a methodology is presented for evaluating the impact on primary fuel source utilization considering all the operating constraints of an electric power system. Examples of fuel utilization impact are presented for various levels of PHEV penetration. In general, PHEVs cause a shift of fuel utilization from petroleum to less expensive fuels utilized by electric power utilities.