Wide Area Monitoring System Enhancement

Transcription

1 Wide Area onitoring System Enhancement Wide Area onitoring System Enhancement Prepared for Entergy Transmission Principal Authors Steven. Rovnyak, Guang Li, Kejun ei, Louisiana Tech University September 00 This research was supported by matching funds from the National Science Foundation under Grant No. ECS Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

2 Wide Area onitoring System Enhancement Table of Contents. Introduction page. Getting Started page. Using DSI Toolbox and Prony analysis page. Using search program page 4.3 Using event analyzer program page 4 3. Technical Information page 5 3. Filtering page 5 3. Downsampling page Normalizing signals page Finding events page. Introduction This document describes programs that process wide-area monitoring system (WAS) data on the Entergy Transmission network. Some notes are given for starting the Dynamic System Identification (DSI) Toolbox that is maintained by John Hauer and supported by the DOE/CERTS WAS Outreach program. The DSI Toolbox collection of programs was written by John Hauer and others at PNNL and BPA. The DSI Toolbox contains a Prony analysis GUI. This text also describes a program written by Guang Li to search data for events, and a program written by Kejun ei to analyze events according to their frequency signature. The function of the computer program that analyzes frequency records is very similar to the event analyzer program implemented by Joe Chow and Alexander Bykhovsky.. Getting Started. Using DSI Toolbox and Prony Analysis Set Path -- The directory of files provided by John Hauer should be copied onto the hard disk. The dir name is 'DSItools FTP050'. In a ATLAB window click on File and select Set Path. Click on the button Open with Subfolders. Select the directory 'DSItools FTP050' on the hard disk and click OK. If you click Save first then the directory will also be included in the path when ATLAB is started again. DSItools -- These programs can be used for the extraction, integration, display and basic analysis of measured signals. The menu-driven interface is contained in the ATLAB script file PSbrowser.m. This file can be run by typing just psmbrowser if the path has been set correctly. ATLAB is not sensitive about case in filenames. However, ATLAB is casesensitive with variable names. PSbrowser is self-explanatory enough that much of it can be learned without documentation or training. There are also tutorial programs that quickly lead the user into PSbrowser. At the ATLAB prompt try typing one of the following: PDCbrowse_Ex

3 Wide Area onitoring System Enhancement PPSbrowse_Ex PSbrowser There is 70-page User Guide to PS Tools in the document PStools_UserGuide in the directory DSI_UserGuides that is very informative about the features of PSbrowser and their technical details. Another good starting point is the document DSI_JumpStart in the same directory. Prony Analysis -- If the folder 'DSItools FTP050' has been copied to the hard disk and the path has been set correctly, then the Ringdown tool is ready to run as described here. The words ringdown and Prony are usually interchangeable. The document Ringdown_UGuideA in directory DSI_UserGuides provides basic directions for operating the Ringdown Analysis Tool. The document Ringdown_UGuideB provides guidelines and examples for applying the Ringdown Analysis Tool to modal analysis problems. Prony analysis fits a model consisting of a sum of complex exponentials to samples of one or more signals. The following directions can be used to start the Prony GUI for one signal. If event is an L x matrix like this: 0 y(0) T y( T ) event =, : : ( L ) T y(( L ) T ) then Prony analysis can be run by typing at the ATLAB prompt: ringdown(event). The following ATLAB script extracts an L x matrix Reducedfrom an x N matrix PSsigsX. After data is loaded in the DSItools menu-driven interface PSbrowser, you can request the keyboard and perform operations on variables in the workspace. In DSItools, the name of the array containing signals extracted from the PPS files is PSsigsX. % This script extracts an L x array from an % x N array PSsigsX; 'tcol' and 'vcol' refer % to columns of PSsigsX; L is 'length' below. % PSsigsX is the signal array name in DSItools. % After running this script you can type ringdown(reduced) % Setting length < 0 helps eliminate error messages % in ringdown about too many points. tcol = ; % this column contains time variable vcol = 4; % this column contains variable to analyze start = 366; % this row is where extraction starts length = 400; % length of extracted signal in samples finish = start + length - ; var=pssigsx(start:finish,tcol); var = var - PSsigsX(start,tcol); 3

4 Wide Area onitoring System Enhancement var=pssigsx(start:finish,vcol); Reduced = [var var];. Using Search Program The following files are necessary to run the Allback search program. The DSI Tools analysis package and the event analyzer program called Amanda are also necessary for full functionality. allback.p --- ATLAB GUI application for Allback Event Scan Tool allback.fig --- ATLAB figure file storing the graph components for allback.p abcover.fig --- ATLAB figure file storing the version information for allback.p autoback.p --- ATLAB CUI application for Autoback Event Scan Tool simback.p --- ATLAB CUI application for Simback Event Collector Tool sincfilt.exe --- executable file to filter data PPSREAD.P --- ATLAB function to retrieve data from PPS format files After these files are copied into a folder, add that folder directory into the ATLAB search path. There are instructions for adding directories to the ATLAB search path in the previous section on getting started with DSI Toolbox and Prony analysis. Create a file with.cfg extension in an editor application. See the Allback documentation for explanation of the.cfg file parameters. Examples include grimes.cfg and waterford.cfg In the command window of ATLAB, type allback, then click enter/return key. After the initial version information window, you select a.cfg file and then the main window will be displayed. Further instructions are available in the Allback program documentation..3 Using Event Analyzer Program The following files are necessary in order to run the event analyzer program. amanda.p --- event analyzer loader update.p --- GUI update loadrule.p --- DT rule understanding amanda.fig --- default figure file noise.p --- noise preprocessing sevt.p --- event data loading and displaying *.dat --- various event example data After these files are copied into a folder, add that folder directory into the ATLAB search path. There are instructions for adding directories to the ATLAB search path in the section on getting started with DSI Toolbox and Prony analysis. 4

5 Wide Area onitoring System Enhancement The argument passed to the event analyzer has the same format as for the ringdown program. If event is an L x matrix like this: 0 y(0) T y( T ) event =, : : ( L ) T y(( L ) T ) where the y(kt) are power system frequency measurements, then the event analyzer can be run by typing at the ATLAB prompt: amanda(event) After the program has started you can also load a new event by clicking the 'Load Event' button. The frequency measurements from the selected event are plotted with a solid blue curve. To analyze this event, click the 'Analyze' button. A red plot of measurements averaged over a few seconds is added to the display after an event is analyzed, and all the calculated results are updated at the same time. 'Calc. Power' is intended to estimate the power change according to the frequency shift and the beta value; the beta parameter reflects the frequency sensitivity to power changes in the system [refs]. Users can specify a value for beta and the program will estimate the amount of power change corresponding to the change in average frequency. Alternatively, users can specify a value for the power change and the program will calculate beta. The four edit boxes are for zooming in and zooming out of the figure. The 'Load Rule' button was designed to use Decision Trees originally; however, this button is not useful for non-developers at the present time. Application Notes This program requires ATLAB 6. (Release ) There should be no more than one event in the window, and there should be a few seconds of data included both before and after the event. The output file is called 'report.txt'. The event type is encoded as follows: : a nearby load trip : a remote load trip 3: a nearby generator trip 4: a remote generator trip 5: a nearby line fault 6: a remote line fault 7: an oscillation or unknown event This program is modeled after the function of the event analyzer program that was implemented by Joe Chow and Alexander Bykhovsky. 3. Technical Information 3. Filtering Low-pass filtering can reduce noise through a process of averaging. Filtering can make data appear much cleaner but it can also introduce false oscillations around a large step change. 5

6 Wide Area onitoring System Enhancement These features of filtering are described here. Ideal low pass filtering results from the convolution of a signal with a sinc function, which is defined as: sinc(t) ( sin t ) / t, t 0,, t = 0. sinc(t) t Figure : Graph of sinc(t). The Fourier transform of sinc(t) is a function of ω that is constant between - and radians/sec and zero everywhere else. This boxcar shaped function is sometimes called rect(ω / ). Convolution of two functions in the time domain corresponds to multiplication of their Fourier transforms. ultiplying a function by rect(ω / ) makes it zero for ω > rad/sec. Thus the convolution of a signal with sinc(t) removes frequencies above rad/sec (and below - rad/sec). The effect on negative frequencies is implicit and is usually not stated, because the Fourier transform of a real function has magnitude that is symmetric around ω =0. Similarly, convolution with the function sinc(wt) removes frequencies above W rad/sec. Note that W rad/sec is W/π Hz; the parameter corner in the filter program is in Hz so corner = W/π. Let y(t) represent the filter output before scaling. From the definition of convolution: y(t) sinc(wt) * f (t) = sinc(wτ) f (t-τ) dτ. For t = n t, this integral can be calculated from samples as y(n t) sinc(wk t) f((n - k) t) t. k = 6

7 Wide Area onitoring System Enhancement In practice this sum is truncated when k becomes large enough that sinc(wk t) 0. In this application, the sinc function is truncated for Wk t > 6π, which translates into k > 6π /(W t) = N. Thus y(n t) N k = N sinc(wk t) f((n - k) t) t Near the beginning or end of a signal the sum is truncated further on one side and so k ranges from - to N (or from -N to ). Proper scaling of the output can be accomplished using the following observation. When f(t) = for all t, then the filtered result sinc(wt) * f(t) should also equal one. The following formula for the filtered signal clearly has this property: N f filt (n t) sinc(wk t) f((n - k) t) / sinc(wk t) k = N k = The smoothing action of filtering can be seen in the following example where the cutoff frequency is Hz. unfiltered data time (seconds) filtered data time (seconds) Figure : Noisy step change with and without filtering. The oscillations introduced near a sudden jump are very similar to a partial Fourier series approximation to a square wave. 7

8 Wide Area onitoring System Enhancement square wave approximation Figure 3: Partial Fourier series approximation to a step change. One should take care not to perform Prony analysis on the oscillations introduced by low-pass filtering a step change. 3. Downsampling aximum Frequency -- This is the highest frequency that can be represented for a particular sampling rate and it is one half the sampling frequency. Downsampling lowers the maximum frequency and it is important to filter out frequencies above the new maximum frequency before downsampling. Example: If the sampling frequency is 0 times per second then the maximum frequency is 0 Hz. If the downsampling factor is four, that is if every fourth sample is retained, then the new sampling frequency is 5Hz and the new maximum frequency is.5 Hz. One should process the original data through a lowpass filter that cuts out frequencies above.5 Hz before downsampling by a factor of four. 3.3 Normalizing Signals Normalization is performed in order to account for different scales of different measurements such as 60 Hz and 500 kv. The formula for normalization can be written in terms of vector norms, signal RS values, and second moments. All these formulations are described beginning with second moments. Let x[k] be a discrete-time function containing samples of x c (t) in the interval [0, T]. Specifically, T = t, and x[k] = x c (k t), for integer values of k between and. Let the variable x written by itself represent the entire vector: x[] x = x[]. : x[ ] 8

9 Wide Area onitoring System Enhancement The equation for the second moment µ (x) relative to the mean value x is: µ (x) = ( x[ k] x) k = x = ( x[ k]). k =, This second central moment is a reasonable estimate of the variance of the data. The term central refers to the moment being calculated about the mean value. For simplicity, we will just call µ (x) the variance and µ ( x ) the standard deviation. In ATLAB, the variance of a vector z can be calculated as var(z,) or as var(z). The variance used in this discussion exactly equals var(z,) and approximately equals var(z). The formula for var(z) is the same as for var(z,) except that the factor / is replaced by /(-). Subtracting the mean from a signal and dividing the result by the standard deviation produces a signal with mean equal to zero and variance equal to one. Then the mean of z is Let z[k] = ( x[k] - x ) / µ ( ), k =,...,. x z = ( z[ k]). k = = ( x[ k] x ) µ ( x) k = = 0, because k = x [ k] = x = x ; it may help to recall the definition x = k = k = ( x[ k]). The variance of z is defined as µ (z) = ( z[ k] z ) k =, which is simplified by the fact that z = 0. Thus µ (z) = ( x[ k] x) µ ( x) k = =, because µ (x) = k= ( x[ k] x) by definition. 9

10 Wide Area onitoring System Enhancement Normalizing signals places them on the same scale and their correlations are sometimes clearly apparent as in the figure shown here. filtered & normalized signals time (seconds) Figure 4: Normalized signals. The normalization can also be expressed in terms of vector norms and RS values. The standard Euclidean norm of an -element vector y is: y = y [] + y [] + L + y [ ]. Vectors are often divided by their norm as follows which makes their length equal to one. Then they are called unit vectors: y n = y / y. The normalization in terms of variance can also be expressed in terms of the Euclidean norm. Let y[k] = ( x[k] - x ) so that we can write quantities such as y more easily. Then µ (x) = k= ( x[ k] x) = y /. So z[k] = ( x[k] - x ) / µ ( ) = y / y. x Finally, the normalization can also be expressed in terms of the RS value of y. RS stands for root mean square. Some notation first: vector x was obtained from samples of a continuous function x c (t). Similarly vector y can be thought to contain samples of function y c (t) = x c (t) - x. 0

11 Wide Area onitoring System Enhancement The mean of a function y c (t) over the interval [0,T] is y m = T T 0 y c (t) dt. The integral can be calculated from samples as T 0 y c (t) dt k = yc(k t) t = y[k] t. k = The mean square is T y ms = T y c (t) dt = y [k] t = y [k] = y /. 0 T k = k = It may help to recall that T = t. Finally the root mean square is So z[k] = y / y = y / y rms. y rms = y /. The resulting signal has RS value equal to one. If the signal were a sine wave then it would have amplitude. For typical signals, most z[k] values are between - and. 3.4 Finding Events This section describes the algorithm for finding events. Please note that many of the equations below contain vector quantities and/or a calculation that must be carried out for each c =,...,P. We assume that for each channel c =,...,P, there are samples spaced uniformly: sc[] s c = sc[]. : sc[ ] We also assume that values for the parameters ev-thresh and wv c for c =,...,P have been specified. Parameter ev-thresh is the value that must be exceeded in order for an event to be classified as significant in a particular channel; its range is from 0 to 00. The wv c are voting weights for the P channels. Only the relative size between wv c variables is significant; otherwise, their scale does not matter.

12 Wide Area onitoring System Enhancement The absolute difference between neighboring points, also called the point-to-point difference, is 0 d c = sc[] sc[]. : sc[ ] sc[ ] The search program normalizes these vectors through dividing every element by the largest element. The largest element of d c is also referred to as the L norm of d c, and is denoted d c. The percent point-to-point difference is: The average of dp c is: dp c = 00 d c / d c. dp c = k = dp c [k]. After observing that channels with relatively large peaks have lower weights are modified through dividing them by dp c : dpc numbers, the channel wm c = wv c / dp c. The maximum of the wm c is used to scale the weights to be between zero and one. ws c = wm c / wmax, where wmax = The weighted point-to-point differences are: max c =,...,P { wmc }. dw c = ws c * dp c. If dw c [k] > ev-thresh then output: "Potential event exists at time point k and is significant in channel c."