Daniel J. Trudnowski

Making Prony analysis more accurate using multiple signals

Prony analysis has proven to be a valuable tool in estimating the modal content of power oscillations from measured ringdowns. The accuracy of the mode estimates is limited by the noise content always found in field measured signals. Current Prony analysis methods assume the system to be single output, and individual signals are analyzed independently often resulting in conflicting frequency and damping estimates (due to noise effects). This paper considers a simple extension to Prony analysis that allows multiple signals to be analyzed simultaneously resulting in one set of mode estimates. Examples are used to show that this extension improves the accuracy of modal estimates and simplifies the analysis steps. The first example uses a Monte Carlo type simulation model and the second analyzes field measured data from the western North American power system.

Initial results in electromechanical mode identification from ambient data

Power system loads are constantly changing. Over a time-span of a few minutes, these changes are primarily random. The random load variations act as a constant low-level excitation to the electromechanical dynamics of the power system which shows up as ambient noise in field measured voltage, current and power signals. Assuming the random variations are white and stationary over an analysis window, it is theoretically possible to estimate the electromechanical modal frequencies and damping from the spectral content of the ambient noise. In this paper, field collected ambient noise is analyzed by solving the Wiener-Hopf linear prediction equations to estimate the modal frequency and damping. These estimates are then compared with results from a Prony analysis on a ringdown resulting from a 1400 MW brake insertion under the same operating conditions as the ambient data. Results show that estimates are consistent between the ambient and ringdown analysis indicating that it is possible to estimate a power systems electromechanical characteristics simply from ambient data. These results demonstrate that it may be possible to provide power system control and operation algorithms with a real-time estimate of modal frequency and damping.

Performance of Three Mode-Meter Block-Processing Algorithms for Automated Dynamic Stability Assessment

The frequency and damping of electromechanical modes offer considerable insight into the dynamic stability properties of a power system. The performance properties of three mode-estimation block-processing algorithms from the perspective of near real-time automated stability assessment are demonstrated and examined. The algorithms are: the extended modified Yule Walker (YW); extended modified Yule Walker with spectral analysis (YWS); and sub-space system identification (N4SID). The YW and N4SID have been introduced in previous publications while the YWS is introduced here. Issues addressed include: stability assessment requirements; automated subset selecting identified modes; using algorithms in an automated format; data assumptions and quality; and expected algorithm estimation performance.

Electromechanical Mode Online Estimation Using Regularized Robust RLS Methods

This paper proposes a regularized robust recursive least squares (R3LS) method for online estimation of power-system electromechanical modes based on synchronized phasor measurement unit (PMU) data. The proposed method utilizes an autoregressive moving average exogenous (ARMAX) model to account for typical measurement data, which includes low-level pseudo-random probing, ambient, and ringdown data. A robust objective function is utilized to reduce the negative influence from nontypical data, which include outliers and missing data. A dynamic regularization method is introduced to help include a priori knowledge about the system and reduce the influence of under-determined problems. Based on a 17-machine simulation model, it is shown through the Monte Carlo method that the proposed R3LS method can estimate and track electromechanical modes by effectively using combined typical and nontypical measurement data.

Fixed-speed wind-generator and wind-park modeling for transient stability studies

Increasing levels of wind-turbine generation in modern power systems is initiating a need for accurate wind-generation transient stability models. Because many wind generators are often grouped together in wind parks, equivalence modeling of several wind generators is especially critical. In this paper, a reduced-order dynamic fixed-speed wind-generator model appropriate for transient stability simulation is presented. The model is derived using a model reduction technique of a high-order finite-element model. Then, an equivalencing approach is presented that demonstrates how several wind generators in a wind park can be combined into a single reduced-order model. Simulation cases are presented to demonstrate several unique properties of a power system containing wind generators. The results in this paper focus on horizontal-axis turbines using an induction machine directly connected to the grid as the generator.

Use of ARMA block processing for estimating stationary low-frequency electromechanical modes of power systems

Accurate knowledge of low-frequency electromechanical modes in power systems gives vital information about the stability of the system. Current techniques for estimating electromechanical modes are computationally intensive and rely on complex system models. This research complements model-based approaches and uses measurement-based techniques. This paper discusses the development of an auto-regressive moving average (ARMA) block processing technique to estimate these low-frequency electromechanical modes from measured ambient power system data without requiring a disturbance. This technique is applied to simulated data containing a stationary low-frequency mode generated from a 19-machine test model. The frequency and damping factor of the estimated modes are compared with the actual modes for various block sizes. This technique is also applied to 35-minute blocks of actual ambient power system data before and after a disturbance and compared to results from Prony analysis on the ringdown from the disturbance.

Impacts of the distributed utility on transmission system stability

The distributed (or dispersed) utility concept is rapidly becoming a reality in some service areas. In this framework, modular generation and storage assets along with selected demand-side management programs are used in place of the more traditional infrastructure upgrades to ensure reliable service to a group of utility customers. From among the many technical challenges associated with the proliferation of distributed resources, this paper deals with the impacts of distributed architectures upon the bulk transmission system. Bulk transmission system transient and small-signal stability are addressed through the use of extensive case studies. Planning tools and methods are discussed, and some general conclusions related to stability issues are drawn.

Estimating Electromechanical Mode Shape From Synchrophasor Measurements

A theoretical basis and signal-processing approach for estimating a power systems electromechanical mode-shape properties using time-synchronized phasor measurements are presented. The relationship between modal eigenvectors and measurable power system quantities are derived. Spectral correlation analysis is used to implement the approach with demonstrative examples. This includes simulation examples as well as measured data from the western North American power system.

Robust RLS Methods for Online Estimation of Power System Electromechanical Modes

This paper proposes a robust recursive least square (RRLS) algorithm for online identification of power system modes based on measurement data. The measurement data can be either ambient or ringdown. Also, the mode estimation is provided in real-time. The validity of the proposed RRLS algorithm is demonstrated with both simulation data from a 17-machine model and field measurement data from a wide area measurement system (WAMS). Comparison with the conventional recursive least square (RLS) and least mean square (LMS) algorithms shows that the proposed RRLS algorithm can identify the modes from the combined ringdown and ambient signals with outliers and missing data in real-time without noticeable performance degradation. An adaptive detrend algorithm is also proposed to remove the signal trend based on the RRLS algorithm. It is shown that the algorithm can keep up with the measurement data flow and work online to provide real-time mode estimation.

Use of the WECC WAMS in Wide-Area Probing Tests for Validation of System Performance and Modeling

During 2005 and 2006, the western electricity coordinating council (WECC) performed three major tests of western system dynamics. These tests used a wide-area measurement system (WAMS) based primarily on phasor measurement units (PMUs) to determine response to events including the insertion of the 1400-MW Chief Joseph braking resistor, probing signals, and ambient events. Test security was reinforced through real-time analysis of wide-area effects, and high-quality data provided dynamic profiles for interarea modes across the entire western interconnection. The tests established that low-level optimized pseudo-random plusmn20 -MW probing with the pacific DC intertie (PDCI) roughly doubles the apparent noise that is natural to the power system, providing sharp dynamic information with negligible interference to system operations. Such probing is an effective alternative to use of the 1400-MW Chief Joseph dynamic brake, and it is under consideration as a standard means for assessing dynamic security.