Transient Stability: Result Analyzer - PowerWorld

Transient Stability: Result Analyzer

Jamie WeberDirector of Software Development

PowerWorld WECC User’s Group Meeting

July 14, 2020

2© 2020 PowerWorld Corporation

Previous Tools for Looking at Transient Stability Results

• Plotting– Build PlotSeries that specify an Object and Field to show

• Transient Limit Monitors– Object Type (Gen, Bus, Load, etc…)– Field to monitor– Filter to determine which objects to monitor

• Minimum / Maximum Statistical Results– For every Bus tracks

Voltage and Frequency – For every Generator tracks

Rotor Angle, Field Current, Field Voltage, Mechanical Power, Speed, and Stabilizer Output


Power System Oscillations

• Power systems can experience a wide range of oscillations, ranging from highly damped and high frequency switching transients to sustained low frequency (< 2 Hz) inter-area oscillations affecting an entire interconnect

• Types of oscillations include– Transients: Usually high frequency and highly damped– Local plant: Usually from 1 to 5 Hz– Inter-area oscillations: From 0.15 to 1 Hz– Slower dynamics: Such as AGC, less than 0.15 Hz– Subsynchronous resonance: 10 to 50 Hz (less than

synchronous)


Example Oscillations

• The below graph shows an oscillation that was observed during a 1996 WECC Blackout


Example Oscillations

• The below graph shows oscillations on the Michigan/Ontario Interface on 8/14/03


User Requests whichled to Result Analyzer

• We like the Min/Max result reporting, but…– Want to use different time-windows for reporting– Want to monitor more objects and fields

• Desire to automatically incorporate damping calculations into result analysis– Modal Analysis tools work very well– This just simplifies the user interface and automates

some of the calculation• This led to new tool that meets both of these

requests: The Transient Results Analyzer


Result Analyzer:Available in Simulator Version 22

• Available on the left-hand side of the Transient Stability Dialog: under Result Analyzer– Time Window Definitions– Signal Statistics– Signal Damping and Modes– Modes


Some Theory:Time Windows

• Define a Time Window over which you want to calculate statistics and/or perform modal analysis– Generator Speeds– 7 and 10 seconds

Time Window


First: The Easy StuffStatistics

• Over a Time Window calculate– Maximum, Time of Maximum– Minimum, Time of Minimum– Original– Maximum Increase

• (Maximum – Original)– Maximum Decrease

• (Original – Minimum)– (Maximum – Minimum)– Average– Standard Deviation

• Similar to the “max/min” reporting available for specific hard-code bus and generator fields

• Time Windows Definitions allow anything you can look at with withTransient Limit Monitors or Transient Plot Definitions


Signal Statistics in PowerWorld Simulator

• Statistics are available under– Signal Statistics


Dialog and Case Information Displays for Statistics


Signal Statistics Wrap-up

• The rest of the presentation mathematics and pictures on Modal Analysis are more flashy– But don’t forget the plain old statistics!

• This is all I’m going to say about the Signal Statistics

• They are very easy to understand and use• They are very useful


Second: What about Damping?Modal Analysis of Signals

• First we need to talk about “signals” and “modes”• What is a signal?

– For the purposes of transient stability analysis, a signal is a time-series of a numeric value

– For example: The rotor speed of Generator XYZ between 3 and 10 seconds

– Other fields of study use the same mathematics and concepts

• A spatial sequence of colors: Image processing/Image compression

• Audio signals• Pattern Recognition (Facial Recognition)• We will not talk about that stuff today though!


For a Power System Engineer, This is a Signal

• Gen Rotor Speed between 3 and 10 seconds


Description of a Signal

• To describe a signal, we will treat it as the summation of modes

• First let’s define a “Mode”– We will define a mode as an exponential multiplied

by a sinusoidal wave• (that’s convenient for us to choose)

– Mode 𝑚𝑚 𝑡𝑡 = 𝑒𝑒𝜆𝜆 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 cos 2𝜋𝜋𝜋𝜋 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡


Example Mode

• 𝑚𝑚 𝑡𝑡 = 𝑒𝑒𝜆𝜆 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 cos 2𝜋𝜋𝜋𝜋 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡• Consider two example waveforms • 𝜆𝜆 = 0.2 or -0.2 ; 𝜋𝜋 = 2Hz

𝑒𝑒−0.2𝑡𝑡 𝑒𝑒+0.2𝑡𝑡

𝑒𝑒−0.2𝑡𝑡 cos 2𝜋𝜋2𝑡𝑡 𝑒𝑒+0.2𝑡𝑡 cos 2𝜋𝜋2𝑡𝑡

𝜆𝜆 < 0 means Damped 𝜆𝜆 > 0 means Undamped

𝝀𝝀 = −𝟎𝟎.𝟐𝟐 𝝀𝝀 = +𝟎𝟎.𝟐𝟐


Damping Ratio %

• 𝑚𝑚 𝑡𝑡 = 𝑒𝑒𝜆𝜆 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 cos 2𝜋𝜋𝜋𝜋 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡• 𝜆𝜆 is a measure of damping, but the units depend on

the frequency of the oscillation too• Engineers commonly define a

“Damping Ratio”

• Damping Ratio = −𝜆𝜆𝜆𝜆2+ 2𝜋𝜋𝜋𝜋 2 (may see 𝜉𝜉 symbol)

– Note that 𝜆𝜆 < 0 gives Damping Ratio > 0– For mathematics we’ll talk about 𝜆𝜆, but as engineers

we’ll mostly talk about “Damping Ratio %”• If Damping ratio is 0.02, we will say 2%• Values of damping ratio are between –100% and +100%


Damping Ratio % References

• Taking the Damping Ratio and multiplying by 100 to refer to a “Damping Ratio Percentage” is common within the WECC community– https://www.wecc.org/Reliability/WECCmodesPaper130113Trudnowski.

pdf– https://www.wecc.org/Administrative/InterconnectionOscillationAnalysi

s.pdf– http://web.eecs.utk.edu/~kaisun/TF/Panel_2018IEEEPESGM/7-

Hongming_PeakRC_OscillationAnalysis.pdf– https://ieeexplore.ieee.org/document/6644309

• WECC doesn’t formally define a threshold at which things are considering “undamped”.

• WECC TPL-001-WECC-CRT-3.1 – WR1 1.6

• All oscillations that do not show positive damping within 30-seconds after the start of the studied event shall be deemed unstable.

– https://www.wecc.org/Reliability/TPL-001-WECC-CRT-3.1.pdf

https://www.wecc.org/Reliability/WECCmodesPaper130113Trudnowski.pdf

https://www.wecc.org/Administrative/InterconnectionOscillationAnalysis.pdf

http://web.eecs.utk.edu/%7Ekaisun/TF/Panel_2018IEEEPESGM/7-Hongming_PeakRC_OscillationAnalysis.pdf

https://ieeexplore.ieee.org/document/6644309

https://www.wecc.org/Reliability/TPL-001-WECC-CRT-3.1.pdf


Careful when saying “Damping %”

• Engineers often loosely discuss damping percentage– They might mean something different

• Example: Southwest Power Pool – https://www.spp.org/documents/28859/spp%20disturbance

%20performance%20requirements%20(twg%20approved).pdf

– They have requirement for 5% – But they mean that each subsequent peak is 5% lower than

the previous– Good description by Southwest Power Pool at the link above.

• Also mentions that this 5% is different than our “Damping Ratio”• Shows that their 5% maps to a damping ratio of 0.0081633

https://www.spp.org/documents/28859/spp%20disturbance%20performance%20requirements%20(twg%20approved).pdf


SPPR1 and SPPR5“Successive Positive Peak Ratio”

• In SPP, to be considered “damped”, one of the following two require must be met– Peak to peak magnitude decreased 5% over one

cycle

– Peak to peak decreases by 22.6% over 5 cycles


Conversion of Damping Ratio to Damping Mag %

• Assume we want 5% drop peak to peak• 0.95 = 𝑒𝑒λ 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

• Time for one cycle is 1/freq 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡 = 1𝜋𝜋

• 0.95 = 𝑒𝑒λ/𝜋𝜋 ln 0.95 = λ𝜋𝜋 λ = ln 0.95 𝜋𝜋

• Plug this into Damping Ratio calculation• Damping Ratio = −ln 0.95 𝜋𝜋

ln 0.95 𝜋𝜋 2+ 2𝜋𝜋𝜋𝜋 2

• The frequency cancels out in this equation

• Damping Ratio = −ln 0.95ln 0.95 2+ 2𝜋𝜋 2 = 0.0081633


Be Careful! Do you agree what “%” means?

• Define a “Damping Factor %”• Damping Factor % = 100 1 − 𝑒𝑒λ/𝜋𝜋

– This represents the factor by which the peak-to-peak magnitudes decrease each cycle

– 5% is the factor folks seem to like to use• Following are the same

– 5.000% “Damping Factor %” (SPP term)– 0.816% “Damping Ratio %” (WECC term)

• PowerWorld Simulator is going to stick with the Damping Ratio %– Nice because it varies between -100 and +100.


Mapping from Damping Ratio to Damping Factor %

• 𝜉𝜉 = −𝜆𝜆𝜆𝜆2+ 2𝜋𝜋𝜋𝜋 2 𝜆𝜆 = −2𝜋𝜋𝜋𝜋𝜉𝜉

1−𝜉𝜉2– Damping Ratio varies between

–1.00 and +1.00– Damping Ratio % varies between

–100% and +100%

• 𝐷𝐷𝐷𝐷𝑚𝑚𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐹𝐹𝐷𝐷𝐹𝐹𝑡𝑡𝐹𝐹𝐹𝐹 % = 100 1 − 𝑒𝑒

−2𝜋𝜋𝜉𝜉

1−𝜉𝜉2

– Damping Factor % varies between – infinity and + 100%

• We will stick with Damp Ratio %, as is done in WECC

• Be careful when talking to others


Does a Signal have only 1 Mode?

• No! A signal is made up of many modes


Approximating a Signal using multiple Modes

• A signals will be made up of a summation of modes• As example assume 3 modes

• 𝑚𝑚1 𝑡𝑡 = 𝑒𝑒𝜆𝜆1 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 cos 2𝜋𝜋𝜋𝜋1 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡• 𝑚𝑚2 𝑡𝑡 = 𝑒𝑒𝜆𝜆2 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 cos 2𝜋𝜋𝜋𝜋2 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡• 𝑚𝑚3 𝑡𝑡 = 𝑒𝑒𝜆𝜆3 𝑡𝑡−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 cos 2𝜋𝜋𝜋𝜋3 𝑡𝑡 − 𝑇𝑇𝑠𝑠𝑡𝑡𝑠𝑠𝑠𝑠𝑡𝑡

• Signal is a complex number combination of the modes– Given 3 modes, signal x(t) is defined by 3 complex numbers

• Signal x(t) = +𝐴𝐴𝑥𝑥1𝑒𝑒𝜆𝜆1 𝑡𝑡−𝑇𝑇𝑠𝑠 cos 2𝜋𝜋𝜋𝜋1 𝑡𝑡 − 𝑇𝑇𝑠𝑠 + 𝜃𝜃𝑥𝑥1+𝐴𝐴𝑥𝑥2𝑒𝑒𝜆𝜆2 𝑡𝑡−𝑇𝑇𝑠𝑠 cos 2𝜋𝜋𝜋𝜋2 𝑡𝑡 − 𝑇𝑇𝑠𝑠 + 𝜃𝜃𝑥𝑥2+𝐴𝐴𝑥𝑥3𝑒𝑒𝜆𝜆3(𝑡𝑡−𝑇𝑇𝑠𝑠) cos 2𝜋𝜋𝜋𝜋3 𝑡𝑡 − 𝑇𝑇𝑠𝑠 + 𝜃𝜃𝑥𝑥3


Quick Aside: Detrending

• PowerWorld also does some “detrending” using a polynomial function– Modal Analysis we have had for many years allows a

constant, linear, or quadratic function– The Time Window features for now just always uses

a linear function

0.1𝑡𝑡 + cos 2𝜋𝜋2𝑡𝑡


Final Approximation for Signals

• x(t) =𝑇𝑇𝐹𝐹𝑒𝑒𝐷𝐷𝑇𝑇𝐴𝐴 + 𝑇𝑇𝐹𝐹𝑒𝑒𝐷𝐷𝑇𝑇𝑇𝑇 ∗ 𝑡𝑡 − 𝑇𝑇𝑠𝑠 + 𝑇𝑇𝐹𝐹𝑒𝑒𝐷𝐷𝑇𝑇𝑇𝑇 ∗ 𝑡𝑡 − 𝑇𝑇𝑠𝑠 2

+ �𝑚𝑚=𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠

𝐴𝐴𝑥𝑥𝑚𝑚𝑒𝑒𝜆𝜆m 𝑡𝑡−𝑇𝑇𝑠𝑠 cos 2𝜋𝜋𝜋𝜋𝑚𝑚 𝑡𝑡 − 𝑇𝑇𝑠𝑠 + 𝜃𝜃𝑥𝑥𝑚𝑚

• Each mode is defined by a 𝜆𝜆m and 𝜋𝜋𝑚𝑚• Each signal is approximated as a

– Trend polynomial (𝑇𝑇𝐹𝐹𝑒𝑒𝐷𝐷𝑇𝑇𝐴𝐴, 𝑇𝑇𝐹𝐹𝑒𝑒𝐷𝐷𝑇𝑇𝑇𝑇, and 𝑇𝑇𝐹𝐹𝑒𝑒𝐷𝐷𝑇𝑇𝑇𝑇)– Set of complex numbers assigned to each mode (𝐴𝐴𝑥𝑥𝑚𝑚

and 𝜃𝜃𝑥𝑥𝑚𝑚)


Summation of two damped exponentials

• Initially looks undamped

• But actually 2 damped signals summed


Visualization of this in Simulator

• Let’s look at our signal. – Blue line is the RAW signal we are fitting– Red line is the Reproduced Signal using a summation of

the detrend and various modes• Let’s start with only the Linear Trend line

– We will then slowly add signals from there– Available in PowerWorld under Signal and Damping

Modes


Examining One Signal


Useful Interface Demonstrating Combining Modes

• First column of “Mode Include Reproduce” can be toggled to change which signals are included in the summation for the reproduced signal

Toggle to visualize signal reproduction


Useful Interface Demonstrating Combining Modes

• Modes are sorted by “Rank”– Rank is a normalized value that sums to 100% for

each signal– Every mode will have a rank, but some are very

smallOrdered by “Rank”


Definition of “Rank”

• This is an approximate measure describing for each signal which modes contribute the most to that signal

• The contribution to the reproduced signal from a mode for a particular signal is 𝐴𝐴𝑥𝑥𝑚𝑚𝑒𝑒𝜆𝜆m 𝑡𝑡−𝑇𝑇𝑠𝑠 cos 2𝜋𝜋𝜋𝜋𝑚𝑚 𝑡𝑡 − 𝑇𝑇𝑠𝑠 + 𝜃𝜃𝑥𝑥𝑚𝑚

• The sinusoid is just going to oscillate, so we only want the magnitude, so that leaves

𝐴𝐴𝑥𝑥𝑚𝑚𝑒𝑒𝜆𝜆m 𝑡𝑡−𝑇𝑇𝑠𝑠


For damped signals, use the start magnitude𝐴𝐴𝑥𝑥𝑚𝑚

Definition of “Rank”

• 𝐴𝐴𝑥𝑥𝑚𝑚𝑒𝑒𝜆𝜆m 𝑡𝑡−𝑇𝑇𝑠𝑠

• We can’t just use 𝐴𝐴𝑥𝑥𝑚𝑚 alone to rank – for undamped mode 𝐴𝐴𝑥𝑥𝑚𝑚 may be small, but it grows

exponentiallyFor undamped signals, use the end magnitude𝐴𝐴𝑥𝑥𝑚𝑚𝑒𝑒𝜆𝜆m 𝑇𝑇𝑒𝑒𝑒𝑒𝑒𝑒−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠


What is a “Rank”?

• Instead “Rank” is calculated based on the larger value of the Magnitude or the Magnitude at the end of the Time Window

– RankFactor = Maximum �𝐴𝐴𝑥𝑥𝑚𝑚

𝐴𝐴𝑥𝑥𝑚𝑚𝑒𝑒𝜆𝜆m 𝑇𝑇𝑒𝑒𝑒𝑒𝑒𝑒−𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

• Rank shown in PowerWorld takes this value and normalizes it across all modes for each signal.– For a signal, the summation of the Rank values is

100 by definition


Add highest “Rank”


Add 1st and 2nd largest modes

ADDTHEM


Linear Trend Line Only


Trend + Row1


Trend + Row1 + Row2


Trend + Row1 + Row2 + Row4


Add Row 3 which has the1.364 Hz oscillation


Finally Add Row 5 (hard to even tell a difference!)


Damping % for each Mode

• Extremely small frequencies (like 0.000 for instance)– Ignore those damping % values– They are only providing some “shape” to the

trendline


Ignore: Negative Damping for very small Frequencies

• Trend Line Only

• Trend + Row 4 (negatively damped signal)


Multiple Signals: Share the same Modes

• When studying power systems, we have 1000s (even millions) of signals

• Does each Signal have its own modes? No! – Normally 1000s of signals share modal information

Clearly these three signals share the same modal frequencies


Careful in your choice of Signals

• If you are looking for global characteristics of the power system response, you want signals that illustrate these global characteristics– Bus Frequency can be a good choice– Our experience with over 20,000 bus WECC cases is that

even looking across the entire system you don’t see a huge number of modes

– This is also industry experience!• Looking at something like Bus Voltage you will see local

mode information– That means a LOT more modes may show up– Alternative would be to only use 300 kV and higher buses


What is Modal Analysis Calculating?

• Modes– Each mode will have a frequency and lambda

• Signals– Each Signal will have a complex number assigned to

each Mode

• Example:– 5 Mode– 100 Signals– 500 complex numbers must be calculated



• 5 Modes– 2.017 Hz, 1.364 Hz, 0.171 Hz, and two at 0.000 Hz – Note: You can have a 0.0 Hz mode

• Represents a pure exponential with no sinusoid



2.017 Hz

1.364 Hz

Very Small Magnitude

For 1.364 Hz modeBus #1 is 180 degree out of phase with the other 2 buses.

That’s what you see in plot!

0.171 Hz0.0 Hz 0.0 Hz



2.017 Hz1.364 Hz 0.171 Hz

Very Small Magnitude

Notice that the slower frequency modes are all in phase with each other.They share this same shape

0.0 Hz 0.0 Hz


How are Modes calculated?

• Older methods used a Prony approach (1795)• Many other more modern approaches are

available now as well– Matrix Pencil– Iterative Matrix Pencil– Dynamic Mode Decomposition


Hand-Waving Theory

• You’ll read terms like “Hankel Matrix”• The mathematics for this is built around

calculating the “Singular Value Decomposition” (SVD) of matrices

• This is not a theory presentation though

• For now, you can call all this what I call it: It’s Magic!


Another Aside: Sampling Rate and Aliasing

• The Nyquist-Shannon sampling theory requires sampling at twice the highest desired frequency– For example, to see a 5 Hz frequency we need to

sample the signal at a rate of at least 10 Hz• Sampling shifts the frequency spectrum by 1/T

(where T is the sample time), which causes frequency overlap

• This overlapping of frequencies is known as aliasing, which can cause a high frequency signal to appear to be a lower frequency signal– Aliasing can be reduced by

fast sampling and/or lowpass filters

Image: upload.wikimedia.org/wikipedia/commons/thumb/2/28/AliasingSines.svg/2000px-AliasingSines.svg.png

9 Hz signal looks like a 0.1 Hz


Characteristics of Calculations

• The computation time to find the Modes scale as follows– Linearly with the number of signals (M)– Cubic with the number of time points (N)– 𝑇𝑇𝐷𝐷𝑚𝑚𝑒𝑒 𝑂𝑂𝐹𝐹𝑇𝑇𝑒𝑒𝐹𝐹 = 𝑂𝑂𝐹𝐹𝑇𝑇𝑒𝑒𝐹𝐹 𝑀𝑀 ∗ 𝑁𝑁3

• A second algorithm is then applied– Least squares fit to find complex factors for each

signal that most closely match the actual signal– Signals do not need to be included in the mode

calculation to then calculate the complex factors


What is useful for you to know?

• First, don’t use too many time points (𝑁𝑁3 𝐷𝐷𝑖𝑖 𝑏𝑏𝐷𝐷𝑇𝑇!)– To alleviate that PowerWorld will ask you to specify

the maximum frequency you want to look for– We then sample at 2 times that frequency (Nyquist-

Shannon sampling theory)• Second: Be careful choosing a Time Window• Third: The “Iterative Matrix Pencil” routine

starts with 1 signal and then iteratively adds more signals


Be Careful of Time Window

• What if I choose a Time of 0 to 10 seconds for this signal

• Algorithm is going to try to fit this – including the discrete jump at 1.0 seconds!


Be Careful with Time Window

• This gives you a good fit, but it’s nonsense!– It has severally highly tuned sinusoids that happen

to cancel out values during the 0 to 1 second range


Trend Line Only


Trend+Row1


Trend+Row1+Row2


Trend+Row1+Row2+Row3


Trend+Row1+Row2+Row3+Row4

Basically 4 modes match the curve from 1.5 to 10 seconds


Trend+Row1+Row2+Row3+Row4+Row5


Trend+Row1+Row2+Row3+Row4+Row5+Row6

Modes 5 and 6 magically cancel out signal from 0 to 1 second


Trend+Row1+Row2+Row3+Row4+Row5+Row6+Row7

Mode 7 fits end times better (9 – 10 seconds)


Sampling Example

• If want only 2 Hz modes and slower, sample at 4 Hz (4 times per second)– Time Step of Simulation if 0.004167 (1/240) seconds– Sample Time = 0.25 second– That means we’re only using every 60 time steps, so calculation will be 603 times

faster (216,000 times faster!)– Also means you won’t be finding modes you don’t care about


Iterative Matrix Pencil

• Matrix Pencil algorithm is run on many signals– Calculates the Modes from Multiple Signals– A second algorithm finds the complex factors to fit

signals to modes• Iterative Matrix Pencil

1. Start with ONE signal and add to a Signal List2. Perform Matrix Pencil on Signal List to find modes3. Calculate complex factors to fit signals to modes4. Find the signal that has the worse fit and add it to the

Signal List5. If a user-specified “maximum iterations” is met then

stop, otherwise go back to step 2 and repeat.


Implementation in SoftwareResult Analysis Time Windows

• ObjectName = TSResultAnalysisTimeWindow• Under Result Analyzer\Time Window Definitions



• Include : YES or NO indicating whether to do calculations• Signals to consider

– PlotName: include all signals defined in a plot definition– ObjectType, ObjectField, ObjectFilter: include signals that look at

the ObjectField for a particular ObjectType for all objects that meet an ObjectFilter

• Example: Gen, Speed, “MyFilterName”• TimeStart: time in seconds at which window starts• TimeEnd: time in seconds at which window ends• TimeMeaning: either Absolute or Delta

– Absolute means use TimeStart and TimeEnd in seconds exactly– Delta means they represent the change in time after the final user-

specified event in the transient contingency



• ModalDo: YES or NO indicating whether to calculate the modes• ModalMaxHz : Maximum frequency signal you are concerned with

– Sampling will be at 2X this. Smaller value gives faster calculation• Choose starting signal for mode calculations algorithm

– ModalStartObject : Specify which object to start the calculation with– ModalStartField : Specify which field to start the calculation with– If left unspecified, we just pick the “first one”, probably based on the lowest bus

number• ModalIterations : Iterations of the Iterated Matrix Pencil to do.• Fields for specifying whether a particular signal is considered “undamped”

– UndampMinHz : This is the minimum frequency to consider. For example, the very low (even 0.0 Hz) signals are not really of interest to us.

– UndampDampPerc : Mode is undamped if the Damping Ratio Percentage is below this number

– UndampMinRank : Signal considered undamped if at least one mode has a rank above this value AND that mode is considered undamped (based on UndampMinHz and UndampDampPerc)


Modal Analysis on a Big Case

• Simulated the Outage of 2 large generators in the system at 1.0 seconds.

• Ran the simulation out to 30 seconds• Look at bus frequencies from 20 to 30 seconds

– Only at buses with a generator larger than 50 MW (1084 signals)

• Look at bus voltages from 5 to 15 second– Only at buses at 300 kV and higher (731 signals)


Bus Frequencies(1084 signals)


Closeup of Frequencies from 20 to 30 seconds


Voltage Deviation from Initial(731 signals)


Closeup of Voltage Deviations from 5 to 15 seconds


Worse Approximation for Modal Analysis

Worst Frequency Match Worst Voltage Match

These are both very good matches even though they are the worst match!


Modal Analysis on Frequency and Voltage

• Similar results for voltage and frequency• The “modal information” is in all these signals

Bus Freq 20 - 30 seconds Bus Vpu 5 - 15 seconds

Frequency Damping Ratio % Frequency Damping Ratio %0.609 4.17 0.616 6.12

0.531 7.200.315 9.61 0.329 5.280.236 18.03 0.222 16.270.000 100.000.053 -29.17 0.095 1.34


Comparison to Expectation from Real Measurement

• https://www.wecc.org/Reliability/WECCmodesPaper130113Trudnowski.pdf– North – South Mode A

• 0.25 Hz, 10-15% damping– North – South Mode B (Alberta)

• 0.40 Hz, 5-10% damping– “BC” Mode

• 0.6 Hz– Other Modes

• 0.5 and 0.7 Hz• https://www.wecc.org/Administrative/InterconnectionO

scillationAnalysis.pdf– Similar Results

https://www.wecc.org/Reliability/WECCmodesPaper130113Trudnowski.pdf

https://www.wecc.org/Administrative/InterconnectionOscillationAnalysis.pdf


Screening Signals:What to consider undamped

• All signals have small fractions of all modes

• Damping % threshold for a mode to be considered undamped

• Minimum Frequency for a mode to consider (Ignore very low frequency signals)

• Rank Percentage required for a mode’s contribution to a signal

• A signal is considered undamped if it meets these requirements


Undamped Screening for Bus Frequencies 20 – 30 seconds

• 0.053 Hz signal Ignore because < 0.1 Hz

• Thus the only mode marked to be considered undamped in the 0.609 Hz mode

• Next we only consider a signal undamped if it is has a Rank of 10% for that mode

Bus Freq 20 - 30 seconds

Frequency Damping %0.609 4.170.315 9.610.236 18.030.000 100.000.053 -29.17


Signal Damping and Modes

• Mode 0 is the 0.609 Hz mode• Only the first signals below have a Rank % higher

than 10% for that mode• Those signals show Has Undamped = YES


Future Work

• Integrate this analysis in the Transient Limit Monitors– Automate the process of doing this analysis to point

you at potential problems and their location

• Add more visualization data around this– Visualize Mode angles and Magnitudes can point

you toward what parts are the system are oscillating against one another

– Find the source of an oscillation

Date post:	15-Feb-2022
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