John W. Pierre

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.

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.

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.

Bootstrap-based confidence interval estimates for electromechanical modes from multiple output analysis of measured ambient data

Previously, variations of the Yule-Walker techniques have been applied successfully to give point estimates of electromechanical modes of a power system based on measured ambient data. This paper introduces a bootstrap method to give confidence interval estimates for the electromechanical modes. Simulation results from a 19-machine model show the validation of the bootstrap method and its consistence to Monte Carlo methods. Actual measurement data taken from western North American Power Grid in 2000 are processed using the bootstrap method to give confidence interval estimates for interarea mode damping ratios. The use of multiple outputs is shown to improve the performance and tighten the confidence intervals.

Overview of algorithms for estimating swing modes from measured responses

Linear-system formulations are often used to describe power-system small-signal electromechanical dynamic properties. Over the past two decades, many techniques have been developed to conduct modal analysis using only actual-system measurements. Some techniques are appropriate for transient signals, others are for ambient signal conditions, and some are for conditions where a known probing signal is exciting the system. An overview of many of the more successful analysis techniques is presented. The theoretical background for these methods is summarized as well as application properties. Examples include computer simulations and actual system experiments from the western North American power system. Analysis goals center on estimating the modal frequency and damping.

A Stepwise Regression Method for Estimating Dominant Electromechanical Modes

Summary form only given. Prony analysis has been applied to estimate inter-area oscillation modes using phasor measurement unit (PMU) measurements. To suppress noise and signal offset effects, a high-order Prony model usually is used to over-fit the data. As such, some trivial modes are intentionally added to improve the estimation accuracy of the dominant modes. Therefore, to reduce the rate of false alarms, it is important to distinguish between the dominant modes that reflect the dynamic features of a power system and the trivial modes that are artificially introduced to improve the estimation accuracy. In this paper, a stepwise-regression method is applied to automatically identify the dominant modes from Prony analysis. A Monte-Carlo method is applied to evaluate the performance of the proposed method using data obtained from simulations. Field-measured PMU data are used to verify the applicability of the proposed method. A comparison of results obtained using the proposed approach with results from a traditional energy-sorting method shows the improved performance of the proposed method.

Quadrature receiver mismatch calibration

This article introduces nonlinear regression techniques to estimate gain and phase mismatches between the in-phase (I) and quadrature (Q) branches of a quadrature receiver. Under modest assumptions, the system intrinsically follows a nonlinear regression model. The algorithm is effective, easily implemented, customizable, and requires few assumptions. Large-sample, jackknife, and bootstrap techniques provide on-line error assessment and parameter inference.