Fred C. Schweppe

Power System Static-State Estimation, Part I: Exact Model

The static state of an electric power system is defined as the vector of the voltage magnitudes and angles at all network buses. The static-state estimator is a data processing algorithm far converting redundant meter readings and other available information into an estimate of the static-state vector. Discussions center on the general nature of the problem, mathematical modeling, an interative technique for calculating the state estimate, and concepts underlying the detection and identification of modeling errors. Problems of interconnected systems are considered. Results of some initial computer simulation tests are discussed.

Bad data analysis for power system state estimation

The state estimation problem in electric power systems consists of four basic operations: hypothesize structure; estimate; detect; identify. This paper addresses the last two problems with respect to the bad data and structural error problem. The paper interrelates various detection and identification methods (sum of squared residuals, weighted and normalized residuals, nonquadratic criteria) and presents new results on bad data analysis (probability of detection, effect of bad data). The theoretical results are illustrated by means of a 25 bus network.

Optimal pricing in electrical networks over space and time

An electrical system is modelled with a transmission network, customers, central generators, and independent generators. The system is subject to stochastic failures and stochastic demand parameters. Optimal spot prices are derived for the system. They vary stochastically with space and time, and depend on electrical load flow patterns. The price difference between two locations or two voltage levels, and the wheeling charge between them, will change magnitude and sometimes sign over time, as a function of events throughout the network. Current spatial pricing methods are significantly different from the spot-price-based methods derived here.

Power System Static-State Estimation, Part II: Approximate Model

The static state of an electric power system is defined as the vector of the voltage magnitudes and angles at all network buses. The static-state estimator is a data-processing algorithm for converting redundant meter readings and other available information into an estimate of the static-state vector. Discussions center on an approximate mathematical model (related to the dc load-flow model). This model yields noniterative-state estimation equations, simplified prediction of effects of network and generation-load pattern changes on network flow, and simplified detection and identification of modeling errors. Results of some initial computer studies on the real power-voltage angle portion of the approximate model are discussed.

Power System Static-State Estimation, Part III: Implementation

The static state of an electric power system is defined as the vector of the voltage magnitudes and angles at all network buses. The static-state estimator is a data processing algorithm for converting redundant meter readings and other available information into an estimate of the static-state vector. Discussions center on implementation problems associated with computation time requirements, dimensionality resulting from a large number of buses, and the actual time-varying (nonstatic) character of power systems. Various potentially useful approaches are discussed and compared.

Physically Based Modeling of Cold Load Pickup

A general, physically based, probabilistic model of power system load has been developed [1]. The model is suitable for short-term prediction of system demand by composition, and accounts for lifestyle dependency and weather dependency as well as effects of other exogenous processes. The conceptual framework and notation applicable to a wide range of load modeling problems have been the key issues in developing a general model.

Bad Data Suppression in Power System Static State Estimation

The presence of bad data points may severely degrade the performance of any of the power system static state estimators currently being proposed. This paper discusses a BDS (bad data suppression) estimator which is based on a non-quadratic cost function but which reduces to the weighted least squares estimator in the absence of bad data. In the presence of bad data, the BDS algorithm provides state estimates comparable to those provided by the weighted least squares method when all data is good. Computer storage and computational requirements and convergence time are equivalent for the BDS and weighted least squares estimators.

Selective Modal Analysis With Applications to Electric Power Systems, Part II: The Dynamic Stability Problem

Selective Modal Analysis (or SMA) is a physically motivated framework for understanding, simplifying and analyzing complicated linear time-invariant (or LTI) models of dynamic systems [1,2,3]. SMA allows one to focus on any prespecified dynamic pattern of intrest in the model. In particular, One can efficiently and accurately compute the eigene values and eigenvectors of the natural modes of interest and their sensitivities, and also determine physically meaningful reduced order models containing these natural modes. SMA is particularly suitable for dealing with composite models, i.e. models consisting of several dynamic subsystems interrelated by static constraints. An introduction to the basic concepts of SMA pertinent to the applications being considered here is presented in the companion paper [3]. This paper concerns the application of SMA to the Dynamic Stability problem in electric power systems; it is shown how SMA is well suited to meet the demanding requirements of Dynamic Stability analysis. This is illustrated in [3] with examples, including a 60-machine model of a dynamic instability occurrence in an actual power system.

Real time pricing to assist in load frequency control

We study the use of real time prices to assist in the control of frequency and tie line deviations in electric power systems. The role of such prices, if any, would yield the practical limit to the trend in electric power systems of varying prices on ever faster time scales. The application of prices in electric power systems to increase the efficient use of resources is an established technique. The pricing schemes can be classified by time scales. Energy adjustment charges vary seasonally or monthly, while time of day rates vary two or three times per day. The power brokering system of 18 Florida Utilities operates on an hourly time scale. In a spot price market of buyers and sellers of electric power, prices adapt to system operation conditions such as changes in system lambda, the effect of generation shortages, and the effect of line overloads. The fastest spot price that has been implemented to date is 30 minutes (most implementations involve 1 hour time steps, which may be prespecified 24 hours in advance). On a five minute time scale is system lambda, a shadow price, used internally by electric utilities for economic dispatch. A key assumption of spot pricing and economic dispatch is that the power system is in quasi-steady state; i.e. power system dynamics involving frequency, voltage, etc. are ignored, and only Kirchoffs laws for network are considered. The paper explores pricing at time scales where the quasi-steady state assumption is no longer valid.

Distance Measures and Coherency Recognition for Transient Stability Equivalents

Existing methods for transient stability equivalents all lack a means of drawing a consistent boundary between the equivalized area and the area represented in detail. In most methods, it is assumed that the generators equivalized are coherent. However, no simple method to identify them has been offered, which does not require a transient stability study of the entire system. A method using distance measures to draw boundaries and pattern recognition concepts to identify coherency is presented. Computation required is minimal. The method is incorporated in a computer program which is a useful tool for transient stability studies in power system planning.