**TABLE OF CONTENTS**

**1.0** **Preface [2](#preface)**

2.0 Summary [2](#summary)

3.0 Introduction [3](#introduction)

4.0 Test Overview [4](#test-overview)

5.0 Observed Values of Interarea Modes
[8](#observed-values-of-interarea-modes)

6.0 Some Basic Aspects of Modal Analysis
[11](#some-basic-aspects-of-modal-analysis)

7.0 Observability of Chief Joseph Brake Insertions
[14](#observability-of-chief-joseph-brake-insertions)

8.0 Observability of Random Probing Signals
[16](#observability-of-random-probing-signals)

9.0 Ambient Correlation Signatures [22](#ambient-correlation-signatures)

10.0 Correlation Analysis for HVDC Probing with Low Level Noise
[26](#correlation-analysis-for-hvdc-probing-with-low-level-noise)

11.0 Transfer Functions for PDCI Terminal Response to Low Level
Modulation
[30](#transfer-functions-for-pdci-terminal-response-to-low-level-modulation)

12.0 Prony Analysis of Brake Insertion on C1 on August 19, 2008
[30](#prony-analysis-of-brake-insertion-on-c1-on-august-19-2008)

12.1. Modal Analysis of Ringdown Signals for Brake Insertions \[update
this section\]
[33](#modal-analysis-of-ringdown-signals-for-brake-insertions-update-this-section)

12.2. Integrated Modal Analysis of Ringdown Signals for the Western
Interconnection
[36](#integrated-modal-analysis-of-ringdown-signals-for-the-western-interconnection)

12.3. Discussion of Ringdown Results
[40](#discussion-of-ringdown-results)

13.0 Cross Validation of Recording Devices
[42](#cross-validation-of-recording-devices)

13.1. Cross Validation of PDC Records
[42](#cross-validation-of-pdc-records)

13.2. Cross Validation of Records from the Celilo PPSM
[42](#cross-validation-of-records-from-the-celilo-ppsm)

13.3. Cross Validation of Records from the Dittmer PPSM
[43](#cross-validation-of-records-from-the-dittmer-ppsm)

13.4. Cross Validation of Records from Special PPSM Units
[45](#cross-validation-of-records-from-special-ppsm-units)

14.0 Actuator Performance of the Pacific HVDC Intertie
[45](#actuator-performance-of-the-pacific-hvdc-intertie)

15.0 Initial Results with ModeMeter Codes
[49](#initial-results-with-modemeter-codes)

16.0 Conclusions [49](#conclusions)

17.0 Acknowledgements [51](#acknowledgements)

18.0 Glossary of Terms [51](#glossary-of-terms)

19.0 APPENDIX A. Test Sequence for August 19, 2008
[54](#appendix-a.-test-sequence-for-august-19-2008-adjust-timing-data)

19.1. Test Series A: Calibration Checks on PDCI Probing Signals
[54](#test-series-a-calibration-checks-on-pdci-probing-signals)

19.2. Test Series B: Noise Probing [54](#test-series-b-noise-probing)

19.3. Test Series C: Cross Validation of Probing Methods
[54](#test-series-c-cross-validation-of-probing-methods)

19.4. Test Series D: Noise Probing [54](#test-series-d-noise-probing)

19.5. Test Series E: Noise Probing [55](#test-series-e-noise-probing)

19.6. Test Series F: Noise Probing [55](#test-series-f-noise-probing)

19.7. Test Series G: Brake Application
[55](#test-series-g-brake-application)

20.0 APPENDIX B. Playback Files for HVDC Probing
[56](#appendix-b.-playback-files-for-hvdc-probing)

21.0 APPENDIX D. DSA Applications During Low Level HVDC Probing
[57](#appendix-d.-dsa-applications-during-low-level-hvdc-probing)

References [61](#references)

# Preface

This is a summary report on the probing tests of August 19, 2008. It
provides a general description of the tests, the observed effects of the
test procedures, and a brief cross section of analysis results produced
to this point. General methodology and a detailed summary of earlier
test results are provided in \[[^1]\]; an overview is provided in
\[[^2]\]. More detailed analysis will be presented in future reports,
which will make wider use of analysis tools being developed under the
ModeMeter effort \[[^3],[^4]\].

Though not exhaustive, the underlying analysis summarized in this report
is already very extensive. Much of this consists of annotated PowerPoint
slides that serve as a running log of analysis results. Such materials
are embedded within the WAMS event archives, in folders such as
\_ACDCtests081908_Reports. The events are "date stamped" there in the
format YYMMDD, rather than MMDDYY.

This Report is intended for general use by the DOE, CERTS, and
associated technical groups of the Western Electricity Coordinating
Council (**WECC**). Many of the reference documents represent a
collective effort by one or more WECC technical groups, and in many
cases the work is still ongoing. Access to those documents that have not
been generally distributed is controlled by the appropriate WECC
authority.

# Summary

During 2005, 2006, and 2008 the Bonneville Power Administration
(**BPA**), in coordination with WECC technical groups such as the DMWG
and the M&VWG, performed four major tests of western system dynamics.
The primary objectives of these tests include the following:

A. Obtain seasonal benchmarks for dynamic performance of the WECC system

B. Develop comparative data to evaluate and refine the realism of WECC
modeling tools

C. Refine and validate methods that identify power system dynamics with
minimal or no use of probing signals

All data for the test were recorded automatically by the WECC WAMS, or
with ordinary SCADA systems. System conditions during the tests were
within normal limits, though testing in September 2005 was done with the
Alberta system was islanded from the remainder of the grid. Though not
common, this is a normal condition that usually occurs for several days
each year.

The tests produced an excellent profile of WECC dynamics across the
entire grid. Response to probing signals was strongly observable in the
western regions, and clearly apparent at eastern locations such as Four
Corners and NE Colorado. The most recent tests, in August 2006 and
August 2008, benefited from newly installed PMUs at several generation
sites in western Canada. Several of these plants are critical to wide
area dynamics \[[^5]\], and this extension to WAMS coverage is a major
contribution to surveillance of wide area interactions across the
western interconnection.

Spectral signatures for brake insertions in 2006 and 2008 fit a general
pattern that extends back to energization of the 500 KV Alberta
connection in 1987. The insertions on 09/14/05 match a different but
equally consistent pattern that results when the Alberta connection is
not in service. *It is strongly recommended that the M&VWG use these
patterns as a general check on the realism of WECC planning models.*

As shown in Table 1, damping for the primary interarea modes was rather
high for brake insertions during all of these tests. By comparison,
during the late 1990's damping for the first three modes was often near
to 6%.; prior to that time a damping of 4.5% for the North-South mode
was not unusual.

System conditions on 09/14/05 represented a normal but uncommon system
topology, for which the Alberta mode is not present and frequency of the
North-South mode is much higher. Data from the tests in 2005 and 2006
were subjected to very thorough analysis, and the values shown for them
in Table 1 are benchmark results that are representative for a number of
signal combinations and analysis procedures. While results for the 2008
test represent work in progress, final results are not expected to
differ materially from those shown in the table.

Table 1. Primary modes from Brake Insertions

**[Mode]{.underline} D1 on 09/14/05 B1 on 06/13/06 B1 on 08/22/06 C1 on
08/19/08**

North-South 0.318 Hz @ 8.3% 0.244 Hz @ 9.1% 0.244 Hz @ 9.6% 0.247 Hz @
9.7%

Alberta (not present) 0.376 Hz @ 9.1 0.373 Hz @ 8.1% 0.363 Hz @ 9.3%

Kemano 0.626 Hz @ 15.4% 0.620 Hz @ 8.8% 0.642 Hz @ 9.9% 0.629 Hz @ 13.3%

Colstrip 0.889 Hz @ 10.7% 0.776 Hz @ 10.2% 0.830 Hz @ 10.9% 0.791 Hz @
\~20%

Of particular note, the tests with low level noise demonstrated good
results with a probing signal that roughly doubles the apparent noise
that is natural to the power system. This additional noise is
essentially invisible to all but the closest examination, and would
probably be acceptable for general use as a background tool for
surveillance of system dynamic conditions.

ModeMeter codes for this purpose are briefly examined in a separate
section, where results consistent with Table 1 are obtained by time
series analysis of system noise records. Such results seem to require a
record length of roughly 20 minutes. The development of these algorithms
is being pursued very actively, and detailed progress is reported in a
separate series of documents.

The processing and many of the results for the August 2008 tests are
closely similar to those for the tests in August 2006. The earlier
report \[Error: Reference source not found\] presents many processing
details that are not repeated here.

# Introduction

Performance validation of power system dynamics makes integrated use of
measurements and models, and it must address many aspects of system
behavior in which oscillatory dynamics are not a key issue. Probing
tests, and the accompanying analysis of oscillation modes, must be
designed and conducted within this broader context.

However, within the narrower context of oscillatory behavior, the
following attributes of wide area oscillation dynamics are of paramount
importance:

a\) **Mode parameters** (eigenvalues). Usually characterized in terms of
frequency and damping.

b\) **Mode shape** (eigenvectors). Characterized by the relative phasing
and strengths of generator oscillations for each mode. Eigenvector
signatures are specific to associated system events.

c\) **Interaction paths**. The specific lines, buses, and controllers
through which generators exchange energy during oscillatory behavior.

d\) **Response to control**. Modification of oscillatory behavior due to
control action, including changes to network parameters and load
characteristics. Usually characterized in terms of transfer function
poles and zeros.

A fully realistic model for wide area oscillation dynamics must, *for
all important modes*, replicate and predict all of these attributes for
the actual system. Probing tests, and the accompanying analysis of
oscillation modes, must address these same attributes and extract key
information for real time use.

# Test Overview

During 2005, 2006, and 2008 the Bonneville Power Administration
(**BPA**), in coordination with WECC technical groups such as the DMWG
and the M&VWG, performed four major tests of western system dynamics.
The primary objectives of these tests include the following:

A. Obtain seasonal benchmarks for dynamic performance of the WECC system

B. Develop comparative data to evaluate and refine the realism of WECC
modeling tools

C. Refine and validate methods that identify power system dynamics with
minimal or no use of probing signals

Distinguishing features of these tests were a strong focus on Objective
C, plus greatly improved instrumentation and software for achieving this
objective \[Error: Reference source not found,[^6],[^7],[^8],[^9]\]. All
data for the test were recorded automatically by the WECC WAMS, or with
ordinary SCADA systems.

The tests included the following staged events:

• Energizations (\"insertions\") of the Chief Joseph dynamic brake

• Insertions of brief sine waves and square waves by modulation of the
Pacific HVDC Intertie

• Insertions of sustained random noise by modulation of the Pacific HVDC
Intertie

• Synchronized recording of ambient background activity in network
signals

General guidelines for such tests are presented in \[[^10]\]. Previous
versions of these tests are described in WECC documents such as
\[[^11]\], and a concise summary of tests performed in June 2000 is
available as \[[^12]\]. Detailed reports on various aspects of all
recent tests are available or in progress as \[[^13],[^14]\] and similar
documents.

The tests were performed on the dates shown below:

• Test05A: September 13 -14, 2005 (Alberta system islanded)

• Test06A: June 13, 2006 (Alberta strongly connected)

• Test06B: August 22, 2006 (Alberta strongly connected)

• Test08A: August 19, 2008 (Alberta strongly connected)

Test05A followed the two day schedule shown in \[[^15]\] and \[[^16]\].
The tests in 2006 and 2008 followed one day schedules such as that shown
in \[[^17]\] and in Appendix A.

System conditions during the tests were within normal limits. Conditions
for Test05A were not typical, in that the Alberta system was islanded
from the remainder of the grid. This condition persisted throughout the
test period, and it shifted the interarea modes into a configuration
that is expected for only a few days per year.

The tests produced an excellent profile of WECC dynamics across the
entire grid. Response to probing signals was strongly observable in the
western regions, and clearly apparent at eastern locations such as Four
Corners and NE Colorado. Table 2 and Fig. 1 are summary guides to the
many geographical locations that are indicated in this Report[^18].

Of particular note, the tests with low level noise demonstrated good
results with a probing signal that roughly doubles the apparent noise
that is natural to the power system. As illustrated in Fig. 2and Fig. 3,
this additional noise is essentially invisible to all but the closest
examination, and it would probably be acceptable for general use as a
background tool for surveillance of system dynamic conditions.

Table 2. Summary of PMU names and locations

**WSN1 Williston Central BC**

**MIN1 Minette West central BC (near Skeena)**

**GMS1 GMShrum1 Central BC**

**GMS2 GMShrum2 Central BC**

**MCA1 Mica South central BC**

**REV1 Revelstoke South central BC**

**NIC1 Nicola South central BC**

**SEL1 Selkirk SE BC (north of Boundary)**

**LA01 Langdon Calgary Alberta**

**ING1 Ingledow SW British Columbia**

**CST5 Custer 500 NW Washington**

**BEL5 Bell 500 Spokane WA**

**COLS Colstrip SE Montana**

**GC50 Grand Coulee500 Central Washington**

**BE50 Big Eddy 500 Lower Columbia river**

**JDAY John Day Lower Columbia river**

**MALN Malin California-Oregon**

**SYLM Sylmar Los Angeles basin**

**SCE1 SCE Devers Los Angeles basin**

**PV50 Palo Verde 500 Near Phoenix AZ**

**FC50 Four Corners 500 NE New Mexico**

**BEAR Bears Ears NE Colorado**

![](media/image1.png){width="3.5722222222222224in"
height="4.707638888888889in"}

Fig. 1. Key locations in the ACDC tests of 2005-2006

![](media/image2.png){width="4.510416666666667in" height="3.71875in"}

Fig. 2. Event timing for test steps C on 081908

![](media/image3.png){width="4.510416666666667in" height="3.6875in"}

Fig. 3. Event timing for test steps G on 081908

# Observed Values of Interarea Modes

Test insertions of the 1400 MW Chief Joseph dynamic brake provide a
quick view of modal parameters, together with \"ringdown signatures\"
that are readily compared against historical data. These signatures also
produce convenient benchmarks for validation of transient stability
programs.

All of the tests reported here involved two or more insertions of the
Chief Joseph dynamic brake. The modal parameters shown in Table 3
summarize analysis results at this point. Though subject to refinement
as analysis methodology evolves, these parameter values are consistent
with tests in 1999 and 2000, and with a variety of other observations
that have accumulated over the years. A summary description of the 1999
tests is provided in \[Error: Reference source not found\] Appendix F,
*A* *Primary Benchmark on Effects of the Alberta Connection*.

Table 3. Primary modes from Brake Insertions

**[Mode]{.underline} D1 on 09/14/05 B1 on 06/13/06 B1 on 08/22/06 C1 on
08/19/08**

North-South 0.318 Hz @ 8.3% 0.244 Hz @ 9.1% 0.244 Hz @ 9.6% 0.247 Hz @
9.7%

Alberta (not present) 0.376 Hz @ 9.1 0.373 Hz @ 8.1% 0.363 Hz @ 9.3%

Kemano[^19] 0.626 Hz @ 15.4% 0.620 Hz @ 8.8% 0.642 Hz @ 9.9% 0.629 Hz @
13.3%

Colstrip 0.889 Hz @ 10.7% 0.776 Hz @ 10.2% 0.830 Hz @ 10.9% 0.791 Hz @
\~20%

Fig. 4 shows that spectral signatures for the brake insertions on
08/19/08 are quite consistent with those extending back to 1997. The
same general pattern extends back to energization of the 500 KV Alberta
connection in 1987. The insertions on 09/14/05 match a different but
equally consistent pattern that results when this connection is not in
service.

Fig. 5 through Fig. 7 show representative ringdown transients on the
Malin-Round Mountain. Most of the waveform changes in these figures
represent normal variability in power system response. While the
transients in Fig. 6 are very similar in the short term, Fig. 7 shows
longer term differences suggesting that some kind of control action may
have occurred as a "hidden input" to the system.

The ringdown characteristics in Fig. 5, which are notably different from
those in Fig. 6, represent normal behavior when the Alberta system is
islanded from the remainder of the grid. The differences are conspicuous
in the frequency domain profile of Fig. 8, in which there is no spectral
peak for the Alberta mode and the North-South mode has increased in both
strength and frequency.

![](media/image4.wmf){width="4.5in" height="3.151388888888889in"}

Fig. 4. Ringdown signatures for recent insertions of the Chief Joseph
dynamic brake

(Alberta strongly connected)

![](media/image5.wmf){width="4.082638888888889in" height="3.5in"}

Fig. 5. Ringdown transients on 09/14/05

![](media/image6.wmf){width="4.0in" height="3.4854166666666666in"}

Fig. 6. Ringdown transients on 08/19/08

![](media/image7.wmf){width="4.5in" height="3.890277777777778in"}

Fig. 7. Ringdown transients on 08/19/08 (extended view)

![](media/image8.wmf){width="4.499305555555556in"
height="3.813888888888889in"}

Fig. 8. Ringdown autospectra for test brake insertions, 2005-2008

# Some Basic Aspects of Modal Analysis

Modal analysis of oscillatory dynamics builds upon a tentative
assumption that the dynamics are essentially linear for small motions
about the equilibrium state. To the extent that this assumption is
valid, the \"swings\" following a brief disturbance will be a sum of
modal response terms like

![](media/image9.wmf) (1)

Here (*σ, ω*) are *mode parameters* that denote the frequency and
damping of a mode, and (*M, θ*) are *mode shape parameters* (signal
residues) that denote the strength and phase of that mode within signal
*m(t)*. Table 4 and Fig. 9 show the decomposition of a ringdown signal
into four oscillatory modes.

Table 4. Modal components for ringdown signal in Fig. 9

**Mode Freq in Hz Damping Ratio (%)**

N-S 0.244 9.6

Alberta 0.363 9.2

Kemano 0.646 13.9

Colstrip 0.853 22.2

![](media/image10.wmf){width="4.499305555555556in" height="4.0in"}

Fig. 9. Decomposition of a ringdown signal into four oscillatory modes

Mathematically, the mode parameters are expressed as a complex
*eigenvalu*e λ = *σ+jω* and the mode shape parameters are expressed as
*residues*. The more specific term *signal residue* is sometimes applied
to distinguish them from residues which appear in the eigenanalysis
below.

Underlying equation (1) are the system equations *=Ax+Bu* and *y=Cx+Du*,
where denotes differentiation of x with respect to time. Variables u and
y are respectively the *input* and the *output* of the system; x, the
*internal state* of the system, is usually taken to be a vector of n
elements.

Full eigenanalysis is based upon modal decompositions of the A matrix,
which in turn requires a source model from which to extract it. This
produces a full set of eigenvalues plus associated eigenvectors. The
eigenvalues lead to residue matrices with mode shape information that is
specific to very special kinds of inputs and outputs.

Prony analysis, by contrast, is based upon modal decompositions of
output vector y(t). The modes and the modal parameters are those for a
subset of A that is estimated from a subset of y(t); the mode shape
parameters are specific to whatever stimulus may have produced the
output. Given sufficient knowledge of u(t), an approximating subset can
be constructed for {*A,B,C.D*} \[[^20],[^21]\].

In practice u(t) is usually a sequence of discrete switching events that
are not immediately known. Small signal analysis assumes that the
response to each event is a free ringdown of form

![](media/image11.wmf) (2)

where R^(i)^ is a residue matrix and state x~0~ is the deviation from
final equilibrium. Most events will redefine x~0~ , and some events or
discrete control actions may significantly alter the underlying system
parameters. Hence some kinds of analysis must proceed on a piecewise
basis.

Prony analysis generally fits a tandem model to several measured
components of y(t). One objective in this is to enhance the modal
estimates. Another is to obtain an interaction pattern revealing how the
activity of each mode is distributed across the signal set. An example
of this is shown in the "compass plot" of Fig. 10, which displays the
length and the angle of each signals residue for response of the Kemano
mode to bake insertion B1 on August 22, 2006. The reader is cautioned
that this mode shape is that for a signal y(t) responding to an initial
offset state x~0~. Mode shapes associated with direct eigenanalysis of
the A matrix are not quite the same thing.

![](media/image12.wmf){width="4.206944444444445in"
height="3.5972222222222223in"}

Fig. 10. Pattern for Kemano mode in WECC local frequency signals

Brake insertion B1, 08/22/06

Modal analysis methods are approximate, and none can generate results of
higher quality than the information provided to them. Results from
model-based eigenanalysis are colored by errors in the model, and by
linear approximations to nonlinear phenomena such as saturation and dead
zones. Results from measurement-based eigenanalysis are colored by the
extent and quality of the available signals. Some modes may not be
sufficiently observable within the signal set. Those which are
observable may be obscured by noise, by dynamic nonlinearities, and by
hidden inputs to the system.

Prony analysis, in the present context, is considered to include any
algorithm that directly fits time domain signals with the \"Prony
model\" of equation (1). This model generalizes that of Fourier
analysis, and can sometimes be used for the same purposes. Fourier
methods remain a mainstay of WAMS analysis, however.

General indications for modal frequencies can be obtained by Fourier
analysis of random variations in power system quantities, under ambient
(that is, undisturbed) conditions. Fig. 11 shows typical results for
real power on the Malin-Round Mountain line. Note that the major peaks
in Fig. 11 align with those of Fig. 8, and that the strength of the
peaks change with power system conditions. Somewhat sharper results are
obtained by correlation analysis of multiple signals.

![](media/image13.wmf){width="4.497222222222222in" height="3.88125in"}

Fig. 11. Autospectra for random fluctuations on the Malin-Round Mountain
line

# Observability of Chief Joseph Brake Insertions

Insertions of the Chief Joseph dynamic brake are clearly observable
across the entire power system. This is illustrated by the response
summary of Fig. 12. The signals depicted were selected to provide an
overall profile for the system, and they do not represent the entire
collection of PMUs from which data were obtained.

Fig. 13 shows the response in each signal as beginning at the time of
brake insertion. This demonstrates that the various phasor networks were
operating in synchronism, and that such disturbances "propagate" across
the grid with no appreciable time delays.

It should be noted that the frequencies in these figures are of type
EFreqL_FD, whereas the local frequencies measured by the PMUs themselves
are of type FreqL The prefix 'E' in the type tag indicates that the
frequency has been estimated from the bus angle, and the postfix '\_FD'
indicates that the estimation logic is based upon forward difference
calculations. This substitution assures that all frequencies are
calculated in the same manner[^22], and it often enhances quality of the
data.

![](media/image14.wmf){width="4.497916666666667in"
height="4.649305555555555in"}

Fig. 12. Frequency swings for Brake Insertion Event C1, 081908

(frequencies estimated as forward difference of bus angle signals)

![](media/image15.png){width="5.010416666666667in" height="5.0in"}

Fig. 13. Timing Checks: Brake Insertion Event C1, 081908

(frequencies estimated as forward difference of bus angle signals)

# Observability of Random Probing Signals

The basic strategy in low level probing is to start with a very weak
probing signal, and to progressively adjust that signal to the minimum
level that produces acceptable results. Key real-time resources for this
are PDC StreamReaders, accompanied by an add-on Dynamic Signal Analyzer
(**DSA**) tool for spectral analysis (shown in Section 15.0). Many of
these same functionalities are being incorporated into the PNNL
ModeMeter and the Real Time Dynamic Monitoring System (**RTDMS**)
\[Error: Reference source not found\]. Off line tools for full analysis
include SYSFIT \[[^23]\], for transfer function fitting, plus a range of
advanced tools that are applied in time domain \[[^24],[^25],[^26]\].

The probing tests of 2005 through 2008 establish that good results can
be obtained with band limited white noise having limits on the order of
±20 MW dc and a standard deviation of 14 MW. This probing signal roughly
doubles the apparent noise that is natural to the power system, and is
essentially invisible to all but the closest examination. Typical
waveforms for the tests in August 2008 are shown in Fig. 14. Fig. 15
shows gain response for bandpass filter BP1, which is used in much of
the analysis reported here. Fig. 16 and Fig. 17 show the effects of
filter BP1 upon signal waveforms, and Fig. 18 shows that spectra are not
significantly changed across the frequency range of interest.

The general observability of random noise probing depends quite strongly
upon the means that are used to examine power system activity. This is
illustrated by Fig. 17 and \*\*\*, together with a series of related
examples.

![](media/image16.png){width="4.510416666666667in"
height="3.6354166666666665in"}

Fig. 14. Startup of ±20 MW noise modulation, test step B2 on August 19,
2008

![](media/image17.wmf){width="4.084722222222222in"
height="3.497916666666667in"}

Fig. 15. Bandpass filter BP1 (set to \[0.08 1.0\] Hz)

![](media/image18.png){width="4.510416666666667in"
height="3.6041666666666665in"}

Fig. 16. Startup of ±20 MW noise modulation, test step B2 on August 19,
2008

(Signals have been filtered with BP1)

![](media/image19.png){width="4.510416666666667in" height="3.5625in"}

Fig. 17. Filter effects on COI MW signals

![](media/image20.wmf){width="4.500694444444444in"
height="3.6944444444444446in"}

Fig. 18. Autospectrum for fluctuations in COI Total MW, ambient
conditions of step B1

(raw vs. filtered data)

Fig. 19, which is based upon the bandpassed data, shows that the
variation in total COI MW is 11.01 MW during the ambient conditions of
test step B1. Applying ±20 MW probing during test step B2 increases the
variation to 13.81 MW, which is scarcely noticeable to ordinary
observations.

Fig. 20 shows a histogram for the probing signal obtained by PDCI
modulation. The range of the raw data is close to ±20 MW, with a
standard deviation of 15.10 MW. Filtering the data with BP1 extends the
range to ±32 MW, with a standard deviation of 14.01MW.

Fig. 21 provides a frequency domain view of the effects that ±20 MW
noise probing has upon random variations in COI MW. Activity in the N-S
mode is almost unchanged; the broadened peak suggests that the frequency
of this mode may have shifted during the probing interval. The increase
in spectral levels is about 4 dB for the Alberta mode, and substantially
higher than that for modes above that. Though modest, such changes in
spectral levels are fairly apparent in spectral waterfalls.

![](media/image21.wmf){width="4.498611111111111in"
height="3.723611111111111in"}

Fig. 19. Histograms for activity in COI total MW

(BP filtered data, without and with ±20 MW probing)

![](media/image22.wmf){width="4.497222222222222in"
height="3.723611111111111in"}

Fig. 20. Histogram for PDCI variations during ±20 MW noise probing (B2)

(raw vs. filtered data)

![](media/image23.wmf){width="4.501388888888889in"
height="3.7083333333333335in"}

Fig. 21. Autospectra for activity in COI MW

(filtered data, with and without ±20 MW probing)

\[continue here\]

# Ambient Correlation Signatures

Correlation analysis provides various measures of the way in which the
activity in other signals relate to the activity in a selected reference
signal \[Error: Reference source not found,Error: Reference source not
found\]. The results shown in this section are based upon Test step B1
on August 19, 2008, and generally use MW swings on Malin-Round Mountain
circuit 1 as the reference signal. The results are very similar to those
of step C1 on August 22, 2006.

Fig. 22 shows that MW swings on Custer-Ingledow circuit 1 are strongly
coherent with those at Malin for the North-South mode and for several
modes above 0.5 Hz. Coherency is small for the Alberta mode (near 0.38
Hz). The corresponding autospectra show a peak in that region for
Malin-Round Mountain activity, but not for Custer-Ingledow activity.

Fig. 23 through Fig. 25 show similar results for other interchange
signals that, when combined with those at Malin and Ingledow, provide a
good basic summary of modal signatures. However, for a sharper view of
modes above 0.5 Hz, it is highly desirable to include signals that have
recently become available in western Canada (BCH and the Alberta ISO).
Fig. 26 through Fig. 28 demonstrate this, and the general issue is given
special attention in \[Error: Reference source not found\].

While Fig. 22 shows little evidence of the Alberta mode on
Custer-Ingledow circuits, Fig. 26 does show such activity on
Williston-Kelly Lake circuits. Fig. 27 and Fig. 28 show that the
associated interaction path is predominantly east-west, along the
Selkirk-Cranbrook-Langdon connection. These figures also show strong
interactions of the North-South mode along this path.

![](media/image24.wmf){width="4.500694444444444in"
height="3.6256944444444446in"}

Fig. 22. Ambient correlations: Custer-Ingledow vs. Malin-Round Mountain

![](media/image25.wmf){width="4.502083333333333in"
height="3.6256944444444446in"}

Fig. 23. Ambient correlations: Bell2-Boundary vs. Malin-Round Mountain

![](media/image26.wmf){width="4.501388888888889in"
height="3.8305555555555557in"}

Fig. 24. Ambient correlations: Colstrip-Broadview vs. Malin-Round
Mountain

![](media/image27.wmf){width="4.498611111111111in"
height="3.6256944444444446in"}

Fig. 25. Ambient correlations: Palo Verde-Devers vs. Malin-Round
Mountain

![](media/image28.wmf){width="4.500694444444444in" height="3.625in"}

Fig. 26. Ambient correlations: Williston-Kelly Lake vs. Malin-Round
Mountain

![](media/image29.wmf){width="4.502083333333333in"
height="3.6256944444444446in"}

Fig. 27. Ambient correlations: Selkirk-Cranbrook vs. Malin-Round
Mountain

![](media/image30.wmf){width="4.500694444444444in" height="3.625in"}

Fig. 28. Ambient correlations: Langdon-Cranbrook vs. Malin-Round
Mountain

# Correlation Analysis for HVDC Probing with Low Level Noise

Correlation analysis can also provide useful transfer function data
showing how the activity in one signal is related to the activity in a
selected reference signal. Fig. 29 and Fig. 30 show this for the
response of total COI MW to ±20 MW PDCI probing noise, during test step
B2 on 08/19/08.

The gain data in Fig. 30 show that response on the COI circuits is
chiefly associated with the N-S and the Alberta modes. Unlike the
response for step C2 on 08/22/06, the associated phase data shows no
abrupt steps suggesting a transfer function zero close to the imaginary
axis.

Analytical models can be extracted directly from the transfer function
data, either by direct model fitting or by Prony analysis of the
transfer function's time domain inverse. A later section will show
preliminary results for extracting models from the signals themselves.

Fig. 31 through Fig. 35 show additional transfer functions for ±20 MW
PDCI probing noise during test step B2. These are provided as examples
to show that different lines can produce rather different transfer
functions, and that a mode which is highly responsive in one signal may
be nearly invisible in another.

![](media/image31.wmf){width="4.499305555555556in"
height="3.6256944444444446in"}

Fig. 29. Response correlations: Malin-Round Mountain vs. ±20 MW PDCI
probing noise

step B2 on 08/19/08

![](media/image32.wmf){width="4.501388888888889in"
height="3.5805555555555557in"}

Fig. 30. Transfer function for Malin-Round Mountain MW vs. ±20 MW PDCI
probing noise

![](media/image33.wmf){width="4.497222222222222in"
height="3.527083333333333in"}

Fig. 31. Transfer function for Bell2-Boundary MW vs. ±20 MW PDCI probing
noise

![](media/image34.wmf){width="4.502083333333333in"
height="3.542361111111111in"}

Fig. 32. Transfer function for Colstrip-Broadview MW vs. ±20 MW PDCI
probing noise

![](media/image35.wmf){width="4.499305555555556in" height="3.58125in"}

Fig. 33. Transfer function for Palo Verde-Devers MW vs. ±20 MW PDCI
probing noise

![](media/image36.wmf){width="4.499305555555556in"
height="3.5805555555555557in"}

Fig. 34. Transfer function for Williston-Kelly Lake MW vs. ±20 MW PDCI
probing noise

![](media/image36.wmf){width="4.499305555555556in"
height="3.5805555555555557in"}

Fig. 35. Transfer function for Langdon-Cranbrook MW vs. ±20 MW PDCI
probing noise

# Transfer Functions for PDCI Terminal Response to Low Level Modulation

The transfer functions shown in Fig. 36 show that PDCI angles (and
therefore frequencies) contain much the same dynamic information as do
COI MW and other more remote signals. This is important when PDCI
modulation tests are supervised at the terminal where the test signals
are applied, and it has potential applications to HVDC damping controls.

![](media/image37.wmf){width="4.499305555555556in"
height="3.692361111111111in"}

Fig. 36. Transfer function for PDCI terminal angles vs. ±20 MW PDCI
probing noise

# Prony Analysis of Brake Insertion on C1 on August 19, 2008 

This section provides a detailed modal analysis of brake insertion C1 on
August 19, 2008. The key tool for this is Prony analysis via the DSI
Toolbox. Fourier analysis is, as usual, used to select the signals for
analysis and to assess quality of the fitted Prony models.

The methodology and many of the results resemble those detailed in
\[Error: Reference source not found\]. Further details concerning the
analysis procedure are available in \[[^27],[^28]\] and in various
application examples that are distributed with the DSI Toolbox.

The appropriate signals and methodology for modal analysis depend upon
the nature of the event, the signals that are available, and the
information to be extracted from them. The Introduction listed the
following "information targets" for modal analysis:

a\) Mode parameters

b\) Mode shape

c\) Interaction paths

d\) Response to control

General analysis usually begins with a first estimate of interarea *mode
parameters*. This is usually done with a fairly small collection of
signals that, overall, provide a good overview of interarea modes. Line
MW are usually selected as a starting point for this, partly for
historical reasons (comparative data for earlier events is abundant) but
also because they are a sensitive indicator of generator accelerating
power. Care must be taken to avoid data that are significantly impacted
by secondary control actions, however.

*Mode shapes* are usually determined from bus angles and frequencies
across wide regions of the power system. These signals are sometimes
made relative to some selected reference, such as the Sylmar 230 KV bus
in the Los Angeles basin. The analyst should be aware that signals for
estimated frequency are more reliable those produced at PMU level, and
that modes which are coherent within some region of the power system may
not be very observable within relative signals for that region.

*Interaction paths* are usually determined from MW signals on key lines,
and sometimes from MVar or other signals associated with major control
systems. The analysis procedure is similar to that for mode shapes, but
the context is more oriented to the equipment level.

*Response to control* is determined as an extension of interaction path
analysis. The chief differences are that there is a known controlled
input to the power system, and that the design of this input is
important for testing the system and, perhaps, for enhancing system
dynamic performance.

The remainder of this section uses increasingly large signal collections
to address information targets (a) through (c) in turn. This is typical
for major system events, where the scope of analysis expands as
additional data become available and interim results guide the direction
of inquiry. The analysis begins with signals which are immediately
available on BPA's PDC.

The timing for Prony analysis is usually determined by inspecting the
transient ringdown in COI MW signals. Fig. 37 and Fig. 38 are typical.
The transient usually merges into the ambient noise level within some 20
seconds, and it is important that the Prony analysis not continue beyond
that time.

It is also important that the Prony analysis start after the brake has
been disconnected, and long enough after that for saturation or other
nonlinear effects to be unlikely. A general guideline for this is shown
in Fig. 37 , where A and B approximate the first two times when the
transient crosses the mean value of the post-disturbance signal.

A first analysis would usually start at A and last for 14 seconds -- in
Matlab notation, the analysis interval is A+\[0 14\]=\[tstart  tstop1\]
seconds. Then, as a check on nonlinearities and hidden inputs, analyses
are also performed on the intervals A+\[0 12\]=\[tstart  tstop2\],
\[B  tstop1\], and \[B  tstop2\]. If results are not consistent then it
becomes necessary to examine voltage magnitudes and other signals for
evidence of control actions during the ringdown, and to base the
analysis on signals which are remote from the suspected problem. Modal
damping for the August 19 tests was extremel;y high, however, and best
results were found with a processing interval of just 10 seconds.

A few important signals usually merge into the ambient noise rather
quickly. The Colstrip MW signal is a leading case of this, and the
analysis interval is usually set at A+\[0 6\] seconds.

**\[expand discussion & examples\]**

![](media/image38.wmf){width="4.497222222222222in"
height="3.6506944444444445in"}

Fig. 37. Merging of transient ringdown into ambient noise

![](media/image39.wmf){width="4.497222222222222in"
height="3.692361111111111in"}

Fig. 38. Analysis timing for brake event ringdown

## Modal Analysis of Ringdown Signals for Brake Insertions \[update this section\] 

A basic set of BPA signals for determination of modal parameters is
shown in Fig. 39. Power flowing on the Devers-Palo Verde line is
sometimes added to this basic set. However, the associated voltage
signals often indicate that some discrete control action has occurred
nearby, and the data received from SCE is prone to communication
problems[^29].

Spectral signatures for these signals are shown in Fig. 40, where the
dotted vertical lines are at frequencies for interarea modes as
determined by Prony analysis.

Setup of the Prony tool (called the Ringdown GUI) is shown in Fig. 41.
The analysis starts at 611.9 seconds after 22-Aug-2006 20:00:00.000
(1300 hrs. PST), and most signals are processed for 14 seconds. The
Colstrip-Broadview signal is an exception to this; the transient fades
into the ambient noise level quite rapidly, so only the first 6 seconds
is included in the analysis.

Basic Prony Solution (**PRS**) results are shown graphically in Fig. 42,
which displays the Results Screen for output signal 2. The selected
modes provide a quite reasonable fit to the time domain record, and also
to the amplitude and phase of its FFT equivalent.

Table 5 and Table 6 provide the results of this particular analysis in
tabular form. The mode shape information contained in Table 6 can also
be presented graphically. The use of this display is deferred until
later portions of this section, where it is of more immediate interest.

[Table 5]{.underline}: PRS results #1 for Brake Event B1 on 08/22/06-- 4
BPA MW signals

**Sorted Mode Table for MALN Round Mountain 1 Current MW**

**Pole Freq in Hz Damp Ratio (pu) Res Mag Res Angle**

1 0.24457386 0.09650302 42.97790323 -125.37057786

3 0.37325895 0.08149476 68.49721288 -72.72228997

5 0.64201579 0.09875745 16.14141450 125.19810557

7 0.83040170 0.10946506 18.97985859 -77.01778871

9 1.11656352 0.04238910 3.02749942 84.33755476

11 1.53552436 0.06452895 4.43331587 -167.53833977

13 1.79599955 0.04307541 0.91672141 133.96171028

[Table 6]{.underline}. PRS results #2 for Brake Event B1 on 08/22/06 --
4 BPA MW signals

Sorted Mode Table for pole1: Interarea oscillation

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.24457386 0.09650302 42.97790323
-125.37057786

COLS Broadview 1 & 2 Current MW 0.24457386 0.09650302 1.21022959
100.86639055

CST5 Ingledow 1 current MW 0.24457386 0.09650302 47.80477662 60.36275167

BEL2 Boundary 1 current MW 0.24457386 0.09650302 11.45821475 60.29963754

Sorted Mode Table for pole3: Interarea oscillation

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.37325895 0.08149476 68.49721288
-72.72228997

COLS Broadview 1 & 2 Current MW 0.37325895 0.08149476 17.39058635
-72.00060141

CST5 Ingledow 1 current MW 0.37325895 0.08149476 9.33029729 -50.05551250

BEL2 Boundary 1 current MW 0.37325895 0.08149476 8.96498776 -56.42918534

Sorted Mode Table for pole5: Interarea oscillation

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.64201579 0.09875745 16.14141450
125.19810557

COLS Broadview 1 & 2 Current MW 0.64201579 0.09875745 38.88079850
148.48926522

CST5 Ingledow 1 current MW 0.64201579 0.09875745 67.63853435
145.29027330

BEL2 Boundary 1 current MW 0.64201579 0.09875745 8.12245478 144.16787447

Sorted Mode Table for pole7: Interarea oscillation

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.83040170 0.10946506 18.97985859
-77.01778871

COLS Broadview 1 & 2 Current MW 0.83040170 0.10946506 83.80291035
36.01057180

CST5 Ingledow 1 current MW 0.83040170 0.10946506 26.27893330
-106.27017852

BEL2 Boundary 1 current MW 0.83040170 0.10946506 1.93913847
-110.75277817

![](media/image40.png){width="4.510416666666667in"
height="3.5833333333333335in"}

Fig. 39. BPA line MW signals for initial Prony analysis of Brake Event
B1, 082206

![](media/image41.wmf){width="4.500694444444444in"
height="3.7472222222222222in"}

Fig. 40. Signatures of BPA line MW for initial Prony analysis of Brake
Event B1, 082206

![](media/image42.wmf){width="5.002083333333333in"
height="3.751388888888889in"}

Fig. 41. Ringdown setup for Prony analysis of Brake Event B1, 082206

![](media/image43.wmf){width="5.002083333333333in"
height="3.751388888888889in"}

Fig. 42. Partial results for Prony analysis of Brake Event B1, 082206

## Integrated Modal Analysis of Ringdown Signals for the Western Interconnection

This subsection extends ringdown analysis to the entire western
interconnection. The primary objective is to determine mode shapes, both
as "signature" information and as a step toward identifying the
participation of particular plants in the associated modes.

A first issue in modeshape analysis is to determine appropriate signals
for analysis. By choice, one would use local bus frequencies. But, as
mentioned earlier, "one sided" disturbances such as a brake insertion
(or a generator trip) produce a frequency dip followed by a slow
exponential recovery. The transient in Fig. 43 is typical in this
regard. The exponential terms associated with frequency recovery usually
reduce the accuracy of Prony analysis[^30].

Fig. 44 shows a useful set of line MW signals for estimating modal
parameters and interaction paths. Results are shown in Table 7 plus Fig.
45 through Fig. 48. Mode shape results for frequencies and relative
angles will be provided in later versions of this Report.

![](media/image44.wmf){width="4.497222222222222in"
height="4.040972222222222in"}

Fig. 43. Exponential transient in frequency recovery after brake
insertion C1

![](media/image45.png){width="4.510416666666667in"
height="3.6354166666666665in"}

Fig. 44. Signal set A for wide area Prony analysis

Table 7. PRS results for Brake Event C1 on 08/19/08 -- 7 line MW signals
(TRange=\[612.3 622.3\])

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.24660169 0.09735930 40.27757008
-138.42419562

CST5 Ingledow 1 current MW 0.24660169 0.09735930 48.16624603 46.54435272

COLS Broadview 1 & 2 Current MW 0.24660169 0.09735930 1.86777773
19.36671429

BEL2 Boundary 1 current MW 0.24660169 0.09735930 10.81920672 47.43308208

WSN1 5L13 WSN/KLY Current MW 0.24660169 0.09735930 3.22118039
-118.16602815

LA01 1201L MW 0.24660169 0.09735930 78.12707051 -125.69336216

PV50 DEV Line Current MW 0.24660169 0.09735930 11.33824895 48.73510923

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.36272829 0.09293383 69.17894441
-64.39121003

CST5 Ingledow 1 current MW 0.36272829 0.09293383 5.45297235 135.65753313

COLS Broadview 1 & 2 Current MW 0.36272829 0.09293383 18.22457087
-71.19764563

BEL2 Boundary 1 current MW 0.36272829 0.09293383 5.90362515 -55.91167540

WSN1 5L13 WSN/KLY Current MW 0.36272829 0.09293383 19.34501084
-46.84293030

LA01 1201L MW 0.36272829 0.09293383 149.91089762 136.34980975

PV50 DEV Line Current MW 0.36272829 0.09293383 36.43266652 136.08568880

Signal Freq in Hz Damp Ratio (pu) Res Mag Res Angle

MALN Round Mountain 1 Current MW 0.62861443 0.13308578 17.15869579
174.13846681

CST5 Ingledow 1 current MW 0.62861443 0.13308578 50.45048919
152.71660038

COLS Broadview 1 & 2 Current MW 0.62861443 0.13308578 26.68462218
176.47310062

BEL2 Boundary 1 current MW 0.62861443 0.13308578 6.08700037 160.76265116

WSN1 5L13 WSN/KLY Current MW 0.62861443 0.13308578 39.32152258
-33.29675888

LA01 1201L MW 0.62861443 0.13308578 9.97750695 86.59401301

PV50 DEV Line Current MW 0.62861443 0.13308578 10.56176850 80.14677280

MALN Round Mountain 1 Current MW 0.79064347 0.20463077 19.79424299
24.81474731

CST5 Ingledow 1 current MW 0.79064347 0.20463077 30.14280005
-177.81461189

COLS Broadview 1 & 2 Current MW 0.79064347 0.20463077 71.60348115
96.15874880

BEL2 Boundary 1 current MW 0.79064347 0.20463077 4.95768246 178.57898924

WSN1 5L13 WSN/KLY Current MW 0.79064347 0.20463077 17.19895340
157.87364322

LA01 1201L MW 0.79064347 0.20463077 35.57653380 -143.98978428

PV50 DEV Line Current MW 0.79064347 0.20463077 12.03309321 40.14429535

![](media/image46.wmf){width="4.496527777777778in"
height="3.4472222222222224in"}

Fig. 45. Pattern for N-S mode in line MW signals

Brake insertion C1, 08/19/08

![](media/image47.wmf){width="4.496527777777778in"
height="3.4458333333333333in"}

Fig. 46 Pattern for Alberta mode in line MW signals

Brake insertion C1, 08/19/08

![](media/image48.wmf){width="4.496527777777778in"
height="3.4458333333333333in"}

Fig. 47. Pattern for Kemano mode in line MW signals

Brake insertion C1, 08/19/08

![](media/image49.wmf){width="4.496527777777778in"
height="3.4458333333333333in"}

Fig. 48. Pattern for Colstrip mode in line MW signals

Brake insertion C1, 08/19/08

## Discussion of Ringdown Results

Prony analysis for brake insertions C1 and C2 produced similar results
for a variety of signal combinations. Fig. 49 and Fig. 50 show that the
underlying "trends" for these two events are not quite the same,
however. These differences affect the modal estimates, and they are a
major consideration in selecting the best data for reliable analysis.

The customary search for "hidden inputs" during the ringdowns has, as
yet, not produced a cause for the different trends. Review of those few
SVC signals that are collected on the WAMS backbone produced a few small
differences, such as that shown in Fig. 51 for the Langdon SVC. This
suggests that hidden inputs, if any, may be associated with a prime
mover, or perhaps AGC.

![](media/image7.wmf){width="4.5in" height="3.890277777777778in"}

Fig. 49. Ringdown transients in Malin MW on 08/19/08 (extended view)

![](media/image50.png){width="4.510416666666667in" height="3.59375in"}

Fig. 50. Frequency recovery for Brake Events C1 & C2

![](media/image51.png){width="4.510416666666667in"
height="3.8854166666666665in"}

Fig. 51. SVC responses for Brake Events C1 & C2

# Cross Validation of Recording Devices

The WECC WAMS has a primary backbone of synchronized phasor measurement
units (**PMU**s) that continuously stream data to Phasor Data
Concentrators (**PDC**s) at central locations for integration,
recording, and further distribution. In addition to a range of other
recording devices, the WECC WAMS also employs a variety of Portable
Power System Monitor (**PPSM**) units as a secondary backbone to
continuously record point-on-wave or analog transducer signals on a
local basis. Though most of these recorders are GPS synchronized, any in
depth analysis should be prefaced by a cross validation of recorder
timing and response.

## Cross Validation of PDC Records

Fig. 13 in Section 7.0 demonstrates the general observation that all
PMUs in the WECC WAMS were well synchronized during the tests. Despite
this, processing differences between PMUs of different types---or by
PMUs of the same type but with different software editions---can produce
small inconsistencies in the phasor measurements that become apparent
under very close examination \[Error: Reference source not found\].
These are disregarded for present purposes. Corresponding differences in
PMU frequency measurements can be much larger, however, so these
measurements have been replaced by estimates based upon bus angles when
close analysis is required.

## Cross Validation of Records from the Celilo PPSM

The Celilo PPSM is an important recording device for control and line
flow quantities at the Celilo terminal of the PDCI. In extended mode it
also records a number of point-on-wave AC quantities. For the data shown
in this Report the unit was operated at 960 sps. Fig. 52 indicates that
the Celilo PPSM was well synchronized to the phasor networks.

![](media/image52.wmf){width="4.5in" height="3.873611111111111in"}

Fig. 52. Celilo PPSM vs. Big Eddy PMUs: Step A7

## Cross Validation of Records from the Dittmer PPSM

The Dittmer PPSM is located at the Dittmer Control Center, and is
usually set to collect data at 30 sps. Fig. 53 through Fig. 55 show that
this unit was well synchronized to the phasor networks.

![](media/image53.png){width="4.510416666666667in"
height="3.2604166666666665in"}

Fig. 53. Dittmer PPSM vs. Malin PMU: Brake insertions C1 & C2

![](media/image54.png){width="4.510416666666667in" height="3.375in"}

Fig. 54. Dittmer PPSM vs. Malin PMU: Brake insertion C1

![](media/image55.png){width="4.510416666666667in"
height="3.5416666666666665in"}

Fig. 55. Dittmer PPSM frequencies vs. Maple Valley PMU: Brake insertion
C1

## Cross Validation of Records from Special PPSM Units

\[need data from the Kemano PPSM and similar point-on-wave units\]

# Actuator Performance of the Pacific HVDC Intertie

Modulating the current on an HVDC line produces real and reactive power
injections into the ac system at each terminal So, considered as an
actuator for the current modulation signal, the PDCI has one controlling
input but six cross coupled outputs.

The relative strengths and phases of the complex power injections depend
upon the nature of the modulation, and upon existing power system
conditions. System conditions also affect dynamic response to the
individual injections. Results summarized in \[Error: Reference source
not found\] suggest that system response to reactive power injections
can approach that for real power injections, and that this response may
be strongly affected by voltage support at the terminal.

PDCI activity is rich in harmonics, not all of which are at multiples of
the power system frequency. Measurements and analysis must be done with
close attention to this environment, and with an expectation that some
harmonics above the fundamental might be modulated by the probing
signal.

Fig. 56 through Fig. 61 indicate the PDCI signal environment for ambient
conditions during step B1 on August 19, 2008. The Celilo PPSM unit was
set to record at 960 sps, and is GPS synchronized to the WECC phasor
networks.

Fig. 56 shows a conspicuous peak, near 0.75 Hz, which was conspicuous in
spectral analyses throughout the test period. It is also visible in the
waterfall plot of Fig. 57, which shows the spectral content for low
level probing with playback file MSF-1/6/100 in test step B2. Post
analysis shows that the peak is present in all three PMUs that meter the
PDCI. The full extent of this activity is still under investigation.

Fig. 58 and Fig. 59 show signals that are typical for ambient conditions
during the test period. The autospectrum in Fig. 60, which shows
conspicuous activity at the first four harmonics, is typical as well.
Fig. 61 argues that the PMUs are relatively immune to the extraneous
noise seen by the Celilo PPSM, probably because the (Macrodyne) filters
provide good rejection at harmonics of 60 Hz. Fig. 60 shows substantial
noise between the harmonics, however, and analysis will be made to
determine the extent to which this is aliased into the PMU outputs.
\[need graphics, discussion of PMU simulation\]

The PDCI noise levels shown here seem substantially higher than those
noted in earlier tests. This too is a matter for further attention.

![](media/image56.wmf){width="4.0in" height="3.4194444444444443in"}

Fig. 56. Ambient autospectra during test event B1 on August 19, 2008

(PMU data, TRange=\[0 1700\] seconds)

![](media/image57.png){width="4.499305555555556in"
height="3.3895833333333334in"}

Fig. 57. Waterfall plot for variations in PDCI power---steps B

(bandpassed data)

![](media/image58.png){width="4.010416666666667in"
height="3.2916666666666665in"}

Fig. 58. Ambient signals during test event B1 on August 19, 2008

(PMU data for the PDCI)

![](media/image59.png){width="4.010416666666667in"
height="3.3020833333333335in"}

Fig. 59. Ambient signals during test event B1 on August 19, 2008

(data from Celilo PPSM)

![](media/image60.wmf){width="4.000694444444444in"
height="3.4583333333333335in"}

Fig. 60. Ambient autospectra during test event B1 on August 19, 2008

(data from Celilo PPSM)

![](media/image61.png){width="4.510416666666667in" height="3.1875in"}

Fig. 61. Signal noise at start of test event B2: Celilo PPSM vs. PMUs

# Initial Results with ModeMeter Codes

Broadly described, a ModeMeter is an integrated suite of analysis and
display tools for real-time tracking of oscillatory dynamics. A
perspective on the ModeMeter functionalities and technology is presented
in \[Error: Reference source not found\], and is based upon long term
experience in the WECC WAMS \[Error: Reference source not found\].

\[need material here\]

# Conclusions

The tests produced an excellent profile of WECC dynamics across the
entire grid. Response to probing signals was strongly observable in the
western regions, and clearly apparent at eastern locations such as Four
Corners and NE Colorado. The most recent tests, in August 2006 and
August 2008, benefited from newly installed PMUs at several generation
sites in western Canada. Several of these plants are critical to wide
area dynamics, and this extension to WAMS coverage is a major
contribution to surveillance of wide area interactions across the
western interconnection.

Spectral signatures for brake insertions in the tests of 2006 and 2008
fit a general pattern that extends back to energization of the 500 KV
Alberta connection in 1987. The insertions on 09/14/05 match a different
but equally consistent pattern that results when the Alberta connection
is not in service. *It is strongly recommended that the M&VWG use these
patterns as a general check on the realism of WECC planning models.*

The damping for the principal interarea modes was rather high for brake
insertions during all three tests. By comparison, during the late 1990's
damping for the first three modes was often near to 6%.; prior to that
time a damping of 4.5% for the North-South mode was not unusual.

System conditions on 09/14/05 represented a normal but uncommon system
topology, for which the Alberta mode is not present and frequency of the
North-South mode is much higher. Data from the tests in 2005 and 2006
were subjected to very thorough analysis, and the values shown for them
in Table 1 are benchmark results that are representative for a number of
signal combinations and analysis procedures. While results for the 2008
test represent work in progress, final results are not expected to
differ materially from those shown in the table.

Of particular note, the tests with low level noise demonstrated good
results with a probing signal that roughly doubles the apparent noise
that is natural to the power system. This additional noise is
essentially invisible to all but the closest examination, and would
probably be acceptable for general use as a background tool for
surveillance of system dynamic conditions.

ModeMeter codes for this purpose were applied to system noise records.
Results consistent with those for Prony analysis of brake insertions
appears to require a record length of roughly 20 minutes. The
development of these algorithms is being pursued very actively, and
detailed progress is reported in a separate series of documents.

The data employed in the analysis were collected on just three PDC units
plus a few secondary monitors. Even so, the data were contributed by
eight or more operating utilities and provide a good overview of wide
area dynamics for the entire system. Additional records, provided by
other data owners, are available as backup to those shown here and for
more detailed analyses that will be performed in the future.

# Acknowledgements

The work reported here draws upon the contributions of far more people
than are indicated in the author list. Existence of the WECC WAMS itself
is largely due to efforts of the DMWG, the M&VWG, and other technical
groups with an interest in the measurement, modeling, and control of
wide area dynamics. The performance of staged tests would not be
feasible without the endorsement of these same groups, together with the
direct assistance of grid operators and data owners across the WECC
system. These contributions are recognized and greatly appreciated.

# Glossary of Terms

Table 8. Guide to general acronyms

DSA Dynamic Signal Analyzer

DSM Dynamic System Monitor

GPS global positioning satellite

IMU Information Management Unit

PDC Phasor Data Concentrator

PMU Phasor Measurement Unit

PPSM Portable Power System Monitor

PSM Power System Monitor (primary definition)

\" Power System Measurements (secondary definition)

RTDMS Real Time Dynamic Monitoring System

SCADA Supervision Control and Data Acquisition

SPM Synchronized Phasor Measurements

SSM Synchronized System Measurements

AGC automatic generation control

FACTS Flexible AC Transmission System

HVDC high voltage direct current

PSS power system stabilizer

SVC static VAR compensator

TCSC thyristor controlled series capacitor

EIPP Eastern Interconnection Phasor Project

WACS Wide Area Control System

WAMS Wide Area Measurement System

ISO Independent System Operator

NERC North American Electric Reliability Council

WECC Western Electricity Coordinating Council

WSCC Western Systems Coordinating Council (predecessor to WECC)

AEP American Electric Power Co.

APS Arizona Public Service Co.

BCH British Columbia Hydro & Power Authority

BPA Bonneville Power Administration

PNNL Pacific Northwest National Laboratory

WAPA Western Area Power Administration

MT Montana Tech

DMWG Disturbance Monitoring Work Group of the WECC

M&VWG Monitoring & Validation Work Group of the WECC

PVTF Performance Validation Task Force of the M&VWG

COI California-Oregon Interconnection

PACI Pacific AC Intertie

PDCI Pacific DC Intertie

pow point on wave

sps samples per second

DSI Dynamic System Identification

FFT Fast Fourier Transform

PRS Prony Solution

LMS Least Mean Square

N4SID Numerical algorithms for Subspace State Space System
Identification

RLS Recursive Least Squares

RRLS Robust RLS

YW Yule-Walker

YWS Yule-Walker Spectral

Table 9. PMU names and locations

**PMU tags in configuration file BPA2_060508m.ini**

GC50 Grand Coulee500

JDAY John Day

MALN Malin

COLS Colstrip

BE23 Big Eddy 230

BE50 Big Eddy 500

SYLM Sylmar

MPLV Maple Valley

KEEL Keeler

CPJK Captain Jack

SUML Summer Lake

SLAT Slatt

SCE1pmu0 SCE Vincent

SCE1pmu1 SCE Devers

MCN2 McNary 230

MCN5 McNary 500

ASHE Ashe 500

BEL5 Bell 500

BEL2 Name=Bell 230_A

BEL3 Bell 230_B

CHJ5 Chief Joe 500

CHJ2 Chief Joe 230_A

CHJ3 Chief Joe 230_B

CST5 Custer 500

CST2 Custer 230

AULT Ault

BEAR Bears Ears

SHIP Shiprock

YELT Yellowtail

MDW5 MIDWAY 500

DCPP Diablo Canyon

TSL5 Tesla 500

ML50 Moss Landing 500

PTSB Pittsburg 230

**PMU tags in configuration file \_BCH062006X.ini**

ING1 Ingledow

DMR1 Dunsmuir

NIC1 Nicola

WSN1 Williston

SEL1 Selkirk

MIN1 Minette

REV1 Revelstoke

MCA1 Mica

GMS1 GMShrum1

GMS2 GMShrum2

LA01 Langdon

LAB1 Test PMU in BCH Lab

**PMU tags in configuration file \_APS1_060725.ini**

FC50 Four Corners 500

FC30 Four Corners 345

NV50 Navajo 500

PP30 Pinnacle Peak 345

PV50 Palo Verde 500

HA50 Hassayampa 500

KY50 Kyrene 500

WW51 West Wing500-Navajo

WW52 West Wing500-Yavapai

WW53 West Wing500-Palo Verde1

WW54 West Wing500-Palo Verde2

WW25 WWG XFMR 1 230

WW26 WWG XFMR 4 230

WW27 WWG XFMR10 230

# APPENDIX A. Test Sequence for August 19, 2008 \[adjust timing data\]

All times shown below are in Pacific Daylight Time (**PDT**), and seven
hours behind GMT (or universal time).

## Test Series A: Calibration Checks on PDCI Probing Signals

Step A0 \[9:00\] Celilo instrumentation check using +/-10MW waveform.
Check proper function of PSG using Celilo/Sylmar DC metering.

Step A1 \[9:10\] Calibration check on MSF-20/6/17 for ±5 MW noise
probing to determine HVDC pole response. Noise bandwidth will be 20 Hz.
Adjust scaling of Probing Signal Generator (PSG) if needed.

Step A2 \[9:15\] Apply MSF-20/6/17 for ±5 MW noise probing to determine
HVDC pole response. Expected duration is 5 minutes or less.

Step A3 \[9:20\] Calibration check on MSF-1/6/100 for ±10 MW noise
probing of inter-area modes. Adjust PSG scaling if needed.

Step A4 \[9:25\] Apply MSF-1/6/100 for ±10 MW noise probing of
inter-area modes. Expected duration is 10 minutes, but additional time
may be needed for coordination of real-time observations at remote
locations.

Step A5 \[9:40\] Apply PbfSM2 for single-mode probing ±125 MW. Waveform
will be three cycles of a sine wave at 0.25 Hz.

Step A6 \[9:42\] Apply PbfSM3 for single-mode probing ±125 MW. Waveform
will be three cycles of a sine wave at 0.70 Hz.

Step A7 \[9:44\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

## Test Series B: Noise Probing 

Step B1 \[10:10\] Measurement of ambient noise conditions

Step B2 \[10:30\] Apply a [+]{.underline}20 MW MSF-1/6/100 for a
duration of 12 periods (20 minutes).

## Test Series C: Cross Validation of Probing Methods 

Step C1 \[13:10\] Insertion C1 of the Chief Joseph Dynamic Brake

Step C2 \[13:15\] Insertion C2 of the Chief Joseph Dynamic Brake, five
minutes after insertion B1

Step C3 \[13:20\] Apply a [+]{.underline}20 MW MSF-1/6/100 for a
duration of 15 periods (25 minutes). Additional time may be needed if
powerflow shifts or discrete control actions are noted during the test
interval.

Step C4 \[13:47\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

Step C5 \[13:49\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

## Test Series D: Noise Probing 

Step D1 \[14:10\] Measurement of ambient noise conditions

Step D2 \[14:11\] Apply a [+]{.underline}10 MW MSF-1/6/100 for a
duration of 21 periods (35 minutes).

Step D3 \[14:47\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

Step D4 \[14:49\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

## Test Series E: Noise Probing 

Step E1 \[15:10\] Measurement of ambient noise conditions

Step E2 \[15:11\] Apply a [+]{.underline}20 MW MSF-1/6/100R for a
duration of 21 periods (35 minutes).

Step E3 \[15:47\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

Step E4 \[15:49\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

## Test Series F: Noise Probing 

Step F1 \[16:10\] Measurement of ambient noise conditions

Step F2 \[16:11\] Apply a [+]{.underline}15 MW MSF-1/6/100 for a
duration of 21 periods (35 minutes).

Step F3 \[16:47\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

Step F4 \[16:49\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

## Test Series G: Brake Application 

Step G1 \[17:10\] Insertion G1 of the Chief Joseph Dynamic Brake.

Step G2 \[17:15\] Insertion G2 of the Chief Joseph Dynamic Brake, five
minutes after insertion G1

Step G3 \[17:20\] Apply a [+]{.underline}20 MW MSF-1/6/100 for a
duration of 15 periods (25 minutes).

Step G4 \[17:47\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

Step G5 \[17:49\] Apply PbfSM5 ±125 MW intermediate level short-term
probing wave.

# APPENDIX B. Playback Files for HVDC Probing 

HVDC probing signals were produced by adding a modulation signal to the
HVDC current order for each of the Celilo pole controls. The process
consisted of the following steps:

1\. The test signal was developed in Matlab, with the scaling normalized
to 1 MW.

2\. The normalized test signal was translated into a Comtrade file and
exported to an accessory computer (Matlab utility **PSGwriteA.m**)

3\. The normalized test signal was scaled to the desired magnitude, then
examined for correctness and loaded into a server acting as the Probing
Signal Generator (**PSG**)

4\. The PSG controls were set to play the scaled test signal a certain
number of times.

5\. The PSG utility was activated, thus playing the scaled test signal
through the associated D/A converter and into the pole controls for the
indicated number of times. Scale factor = 8 dc amperes for 1 volt.

A detailed description of the PSG is provided in \[[^31],[^32]\].

**\[Expand discussion here---Greg?\]**

Table 10. Menu of Playback Files for HVDC Probing on August 19, 2008

+-----------+-----+------------------+-----------------+-------------+
| File Name | T   | Type             | Band Width or   | Amplitude   |
|           | est |                  | Frequency       |             |
+-----------+-----+------------------+-----------------+-------------+
| MS        | A   | Multi-sine       | 20 Hz 6^th^     | +/- 5 MW    |
| F-20/6/17 |     | fitted           | filter          |             |
+-----------+-----+------------------+-----------------+-------------+
| MS        | A   | Multi-sine       | 1 Hz 6^th^      | +/- 5 MW    |
| F/1/6/100 |     | fitted           | order filter    |             |
+-----------+-----+------------------+-----------------+-------------+
| MS        | C   | Multi-sine       | 1 Hz 6^th^      | +/- 10 MW   |
| F/1/6/100 |     | fitted           | order filter    |             |
|           |     |                  |                 | (5 x 2      |
|           |     |                  |                 | multiplier) |
+-----------+-----+------------------+-----------------+-------------+
| MS        | E   | Multisine fitted | 1 Hz 6^th^      | +/- 15 MW   |
| F/1/6/100 |     |                  | order filter    | (5 x 3      |
|           |     |                  |                 | multiplier) |
+-----------+-----+------------------+-----------------+-------------+
| MS        | D,  | Multisine fitted | 1 Hz 6^th^      | +/- 20 MW   |
| F/1/6/100 | F,G |                  | order filter    | (5 x 4      |
|           |     |                  |                 | multiplier) |
+-----------+-----+------------------+-----------------+-------------+
| MSF       | D,  | Reverse in time  | 1 Hz 6^th^      | +/- 20 MW   |
| /1/6/100R | F,G | of MSF/1/6/100   | order filter    | (5 x 4      |
|           |     | above            |                 | multiplier) |
+-----------+-----+------------------+-----------------+-------------+
| PbfSM2    | A,B | Sine single mode | 3 cycle 0.25 Hz | +/- 125 MW  |
+-----------+-----+------------------+-----------------+-------------+
| PbfSM3    | A   | Sine single mode | 3 cycle 0.7 Hz  | +/- 125 MW  |
+-----------+-----+------------------+-----------------+-------------+
| PbfSM5    | A-  | Intermediate     | 0.2 to 2.0 Hz   | +/- 125 MW  |
|           | E,G | level            | sweep           |             |
+-----------+-----+------------------+-----------------+-------------+

![](media/image62.wmf){width="4.829861111111111in"
height="3.626388888888889in"}

Figure 10. ±125 MW intermediate level short-term probing wave (PbfSM5)

# APPENDIX D. DSA Applications During Low Level HVDC Probing

The basic strategy in low level probing is to start with a very weak
probing signal, and to progressively adjust that signal to the minimum
level that produces acceptable results. Key real-time resources for this
are PDC StreamReaders, accompanied by an add-on Dynamic Signal Analyzer
(**DSA**) tool for spectral analysis \[[^33]\].

Topology of the HVDC probing tests can be represented by Fig. 62, where
the indicated test points provide the following quantities:

**Test Point A**

HVDC modulation signal, presented to the Celilo pole controls as a
current order. Recorded by the Celilo PPSM at 960 samples per second
(sps).

**Test Point B**

-- HVDC voltages & currents at Celilo converters, plus various HVDC
control signals. Recorded by the Celilo PPSM at 960 sps.

-- AC bus and line quantities at Celilo converters. Recorded by BPA
phasor measurement network at 30 sps.

**Test Point C**

AC bus and line quantities at key locations across the western
interconnection. Recorded by WECC phasor measurement networks at 30 sps,
and by other WECC facilities at a variety of sample rates.

As yet there is no real time integration of the dc and the ac
measurements at test point B. The notation B~dc~ and B~ac~ will be used
to distinguish between the two classes of signals there.

Actuator response of the Celilo pole controls was observed in real time
by means of a hardware DSA[^34] connected from test point A to test
point B~dc~, in addition to other local instruments at Celilo.

AC system response to HVDC modulation was observed in real time with PDC
StreamReaders in combination with the StreamReader DSA. Topology for
this aspect of the system measurements is shown in Fig. 63. The DSA
functionality appears there in two places, as a StreamReader add-on and
as an element of the DSI Toolbox. At present the DSI Toolbox is only
applied off line.

Fig. 64 and Fig. 65 show typical displays for the PDC StreamReader, and
for the StreamReader DSA. While this may not have been necessary, the
spectrogram displays (in Fig. 65) have been turned off to minimize
computational burden on the supporting PC units. FFT settings used in
the DSA are shown in Fig. 66, which expands the lower portion of Fig.
65.

Overviews of underlying mathematics for DSA calculations can be found in
\[[^35],[^36],[^37]\]. Specific documentation for the DSA itself is
desirable.

**\[Expand discussion to include RTDMS & ModeMeter\]**

![](media/image63.wmf){width="5.648611111111111in"
height="3.560416666666667in"}

Fig. 62. General environment for probing tests based upon HVDC
modulation

![](media/image64.png){width="5.65625in" height="3.5104166666666665in"}

Fig. 63. Integration and analysis of WAMS data

![](media/image65.wmf){width="5.998611111111111in"
height="4.206944444444445in"}

Fig. 64. StreamReader window during Test Step E3-7: single-mode square
burst @ 0.3 Hz

![](media/image66.wmf){width="6.002083333333333in" height="4.09375in"}

Fig. 65. StreamReader DSA window during Test Step C3: noise probing @ 20
MW

![](media/image67.png){width="5.998611111111111in"
height="1.9854166666666666in"}

Fig. 66. FFT settings for StreamReader DSA

# References {#references .unnumbered}

[^1]: \[?\] **Use of the WECC WAMS in Staged System Tests for Validation
    of System Performance and Modeling: Summary Report for September
    2005--August 2006,** J. F. Hauer, W. A. Mittelstadt, J W. Burns, K.
    E. Martin, Harry Lee, and D. J. Trudnowski**.** Interim report of
    the WECC Disturbance Monitoring Work Group, April 25, 2007.
    (Available at ftp://ftp.bpa.gov/pub/WAMS_Information/)

[^2]: \[?\] **Use of the WECC WAMS in Wide Area Probing Tests for
    Validation of System Performance & Modeling,** J. F. Hauer, W. A.
    Mittelstadt, K. E. Martin, J. W. Burns, Harry Lee, J. W. Pierre, and
    D. J. Trudnowski in association with the WECC Disturbance Monitoring
    Work Group. Submitted for publication in **IEEE Trans. Power
    Systems**.

[^3]: \[?\] **Integrated Dynamic Information for the Western Power
    System: WAMS Analysis in 2005**, J. F. Hauer, W. A. Mittelstadt, K.
    E. Martin, J. W. Burns, and Harry Lee. Interim report of the WECC
    Disturbance Monitoring Work Group, December 2005. (available at
    [ftp://ftp.bpa.gov/pub/WAMS%20Information/](ftp://ftp.bpa.gov/pub/WAMS Information/),
    and in **The Electric Power Engineering Handbook**, edition 2, L. L.
    Grigsby ed., CRC Press, 2007)

[^4]: \[?\] **WAMS Analysis Tools for Tracking of Oscillatory
    Dynamics,** J. F. Hauer, D. J. Trudnowski, and J. D. DeSteese**.**
    Presented at the 2007 PES General Meeting in Tampa, Florida, June
    24-28, 2007.

[^5]: \[?\] **August 4th Oscillations: Analysis of Possible Effects of
    Control System Tunings**, B. Corm, J. Jardim, and M. Kwok. BCH
    internal report provided to the Disturbance Monitoring Work Group,
    October 31, 2000.

[^6]: \[?\] **"Initial Results in Power System Identification from
    Injected Probing Signals Using a Subspace Method,\"** N. Zhou, John
    Pierre, and J. F. Hauer. **IEEE Trans. Power Systems**, vol.
    21, issue 3, pp. 1296-1302, August 2006.

[^7]: \[?\] **\"Robust RLS Methods for On-Line Estimation of Power
    System Electromechanical Modes,\"** N. Zhou, J. W. Pierre, D.
    Trudnowski, and R. Guttromson. **IEEE Trans. Power Systems,** Volume
    22,  [Issue
    3](http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4282002), 
    Aug. 2007 pp. 1240-1249.

[^8]: \[?\] "**Performance of Three Mode-Meter Block-Processing
    Algorithms for Automated Dynamic Stability Assessment,"** D. J.
    Trudnowski, J. W. Pierre, N. Zhou, J. F. Hauer, and M. Parashar.
    **IEEE Trans. on Power Systems,** vol. 23, no. 2, May 2008, pp.
    680-690.

[^9]: \[?\] "**Estimating Electromechanical Mode Shape from
    Synchrophasor Measurements**", D. J. Trudnowski. **IEEE Transactions
    on Power Systems**, vol. 23, no. 3, pp. 1188-1195, Aug. 2008.

[^10]: \[?\] **A Perspective on Use of the Pacific HVDC Intertie for
    Wide Area Tests of Western Power System Dynamics**, J. F. Hauer.
    WAMS Working Note developed under BPA/EPRI Tailored Collaboration,
    June 10, 1997. (Attachment to WAMS Information Manager Report EPRI
    Report TR-112031, May 1999)

[^11]: \[?\] **Interim Report on the Model Validation Tests of June 7,
    2000 \-- Part 1: Oscillatory Dynamics**, principal investigator J.
    F. Hauer. WSCC Performance Validation Task Force (PVTF) of the
    Modeling and Validation Work Group, October 26, 2000. Available at
    Internet site http://www.wecc.biz/committees/PCC/TSS/MVWG/documents/
    (address out of date?)

[^12]: \[?\] **Dynamic Performance Validation in the Western Power
    System,** J. F. Hauer, M. J. Beshir, and W. A. Mittelstadt in
    association with WSCC work groups. APEx 2000 Conference in
    Kananaskis, Alberta, October 2000. (Available at
    ftp://ftp.bpa.gov/pub/WAMS%20Information/)

[^13]: \[?\] **September 2005 Staged System Tests for Validation of WECC
    System Performance and Modeling---Summary Report,** J. F. Hauer et
    al**.** WAMS Working Note, partial draft of March 23, 2006.

[^14]: \[?\] **September 2005 Staged System Tests for Validation of WECC
    System Performance and Modeling---** **Response of PDCI Terminal
    Quantities to Current Modulation,** J. F. Hauer**.** WAMS Working
    Note, partial draft of June 6, 2006

[^15]: \[?\] **Performance Validation and Noise Injection Staged Tests
    -- Test Plan Comprehensive Report**. WAMS Working Note distributed
    August 30, 2005 and updated Sept 12, 2005 to reflect small changes
    in test schedule.

[^16]: \[?\] **Performance Validation and Noise Injection Staged
    Tests**. BPA Memorandum distributed as a test notice on August 30,
    2005 and updated Sept 12, 2005 to reflect small changes in test
    schedule.

[^17]: \[?\] **Performance Validation and Noise Injection Staged Tests**
    \[TEST PLAN\]. BPA Memorandum distributed to the WECC, May 26, 2006.

[^18]: A more detailed PMU table is provided in 17.0, *Glossary of
    Terms*

[^19]: Damping of the Kemano mode on 09/14/05 was very high, and the
    estimate was quite variable.

[^20]: \[?\] Juang, J. N. 1994. **Applied System Identification.**
    Prentice-Hall, city, state????.

[^21]: \[?\] Van Overshee, P. and B. De Moor. 1996. **Subspace
    Identification for Linear Systems**. Kluwer Academic Publishers,
    city, state??.

[^22]: PMUs of different vintages and types may employ markedly
    inconsistent logic for calculating bus frequency.

[^23]: \[?\] Hauer, J. F, \"Power System Identification by Fitting
    Structured Models to Measured Frequency Response,\" **IEEE Trans.
    PAS**, pp. 915-923, April 1982.

[^24]: \[?\] R.W. Wies, J.W. Pierre, and D.J. Trudnowski, "Use of ARMA
    Block Processing for Estimating Stationary Low-Frequency
    Electromechanical Modes of Power Systems," **IEEE Transactions on
    Power Systems**, vol. 18, no. 1, pp. 167-173, Feb. 2003.

[^25]: \[?\] Anderson, M.G., N. Zhou, J.W. Pierre, and R.W. Wies,
    "Bootstrap-based Confidence Interval Estimates for Electromechanical
    Modes from Multiple Output Analysis of Measured Ambient Data,"
    **IEEE Transactions on Power Systems**, vol. 20, no. 2, pp. 943-950,
    May 2005.

[^26]: \[?\] **\"Initial Results in Power System Identification from
    Injected Probing Signals Using a Subspace Method,\"** N. Zhou, J.
    Pierre, and J. F. Hauer. **IEEE Trans. Power Systems**, vol.
    21, issue 3, pp. 1296-1302, August 2006.

[^27]: \[?\] **A User Guide to PSM Tools: Utilities for Matlab
    Processing of Power System Response Records**, J. F. Hauer and J. M.
    Johnson. Prepared for the U.S. Department of Energy Transmission
    Reliability Program by the Consortium for Electric Reliability
    Solutions (CERTS), February 2001. (Available at
    ftp.bpa.gov/pub/WAMS%20Information/).

[^28]: \[?\] **DSItools User Manual for the Ringdown Analysis Tool**, J.
    M. Johnson and D. J. Trudnowski. Battelle Memorial Institute, 1998.

[^29]: APS data for the Palo Verde-Devers line are a preferred
    alternative, in part because it provides a broader view of system
    voltage quantities.

[^30]: An alternative is to estimate the recovery transient on a long
    window, and the oscillatory modes on short windows. The DSI Toolbox
    provides several mechanisms for doing this.

[^31]: \[?\] **Probe Server User\'s Guide**, K. E. Martin and others.
    BPA internal report, March 1999.

[^32]: \[?\] **Probe Client User\'s Guide**, K. E. Martin and others.
    BPA internal report, March 1999.

[^33]: \[?\] **Report on September 2005 Staged System Tests for
    Validation of WECC System Performance and Modeling\-- Performance of
    the Dynamic Signal Analyzer (DSA) Tool Interfaced to the PDC
    StreamReader**, J. F. Hauer. WAMS Working Note, partial draft of
    October 6, 2005.

[^34]: A Hewlett-Packard HP3562A unit

[^35]: \[?\] **Engineering Applications of Correlation and Spectral
    Analysis,** J. S. Bendat and A. G. Piersol**.** New York: John
    Wiley, 1980.

[^36]: \[?\] **A User Guide to PSM Tools: Utilities for Matlab
    Processing of Power System Response Records**, J. F. Hauer and J. M.
    Johnson. Prepared for the U.S. Department of Energy Transmission
    Reliability Program by the Consortium for Electric Reliability
    Solutions (CERTS), February 2001. (Available at
    ftp.bpa.gov/pub/WAMS%20Information/).

[^37]: \[?\] **\"Using the Coherency Function to Detect Large-Scale
    Dynamic System Modal Observability,\"** D. J. Trudnowski, J. F.
    Hauer, J. Pierre, W. H. Litzenberger, and D. J. Maratukulam.
    **Proceedings of the 1999 American Control Conference**, pp.
    2886-2890, San Diego, CA, June 1999.