synchrophasor characteristics & terminology
DESCRIPTION
Ken Martin, Senior P rincipal Engineer Electric Power Group, LLC (EPG ) Presented to ERCOT Synchrophasor Work Group. Synchrophasor Characteristics & Terminology. March 7, 2014. Phasor Grid Dynamics Analyzer. e nhanced PDC. Real Time Dynamics Monitoring System Alarming. Bill’s suggestions. - PowerPoint PPT PresentationTRANSCRIPT
SYNCHROPHASOR CHARACTERISTICS & TERMINOLOGY
Ken Martin, Senior Principal EngineerElectric Power Group, LLC (EPG)
Presented to ERCOT Synchrophasor Work Group
March 7, 2014
Real Time Dynamics Monitoring
System Alarming
Phasor Grid Dynamics Analyzer
enhanced PDC
Bill’s suggestions P-Class vs M-Class measurements; what is the difference? Which one do we want for
what application? How do we configure PMUs to produce one or the other?
Lessons learned from working with or testing PMUs in the field. Suggested PMU testing/validation/commissioning procedures in the field (not the lab).
Personal experience on best vs worst performing PMUs (brand/model/firmware version) as far as data quality is concerned.
The role of “network latency” and PDC wait time on data quality.
The role of the GPS clock on data quality; sensitivity of PMUs to clock “jitter”.
Pros and Cons of different Synchrophasor system architectures: PMU-Local PDC-Central PDC–ERCOT vs PMU-ERCOT vs PMU-Central PDC-ERCOT, etc.
There was a presentation at the January 16, 2013 Power System Relaying Committee Main meeting on the recently completed IEEE “Guide for Phasor Data Concentrator Requirement for Power Systems Protection Control and Monitoring C37.244-2013” by Galina Antonova (ABB), chairperson of the working group that developed this guide. Ken Martin is a member of this working group and I believe this would also be a good presentation for the ERCOT Synchrophasor Work Group.
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Synchrophasor Fundamentals
Introduction of phasors Calculation of synchrophasors Synchrophasor characteristics Errors and their impacts Measurement classes
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Phasor Representation
A phasor is a complex value representing and AC signalIt includes the magnitude and phase angle of the sinusoid
√2 A cos (2 ω0 t + ) A ej
A
√2 A
So how do we get phasors?
Given the AC waveform formula, the phasor value can be determined by inspection:
If there is no formula, only a waveform, how do we determine the phasor value?
In a waveform there is no inherent frequency or phase reference
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v(t) = √2 A cos (2 ω0 t + ) V = A ej
????
Phasor calculation with a DFT Discrete Fourier Transform (DFT) Fourier coefficients from cos (black)
& sine (red) waves (kø) Multiply & sum with samples from
waveform (blue) (xk) Result is phasor (complex number)
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kxN
X kr cos2
ir jXX X
kxN
X ki sin2
Measurement Window
Traditional phasor calculation One set of Fourier coefficients (example - 1 cycle window) Reference waveforms move with calculation Phasor rotates CW at system frequency
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Synchrophasor calculation Reference waveforms fixed in time New Fourier coefficients at each window At nominal frequency, angle is constant Windows may or may not overlap
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WINDOW 1
WINDOW 2
WINDOW 3
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Synchrophasor off nominal frequency Example: f0 + 5 Hz (65 Hz) Phasor rotates: rotation = f – fnominal CCW for f > fnominal & CW for f < fnominal
WINDOW 1 WINDOW 3WINDOW 2
Signal specification Phasor is a shorthand for sinusoid formula
– Specifies magnitude and phase– Assumes frequency, based on nominal f0
We are used to seeing constant phase and amplitude– Xm & φ give phasor:
A true dynamic system has changing parameters:– Amplitude: Xm(t)– Frequency: g(t)– Phase: φ(t)
Giving a dynamic phasor: X (t) = (Xm(t)/√2)ej(2π∫gdt +φ(t))
X = Xm ejφ
Signal implementation The dynamic phasor defines the sinusoid formula The formula specifies the waveform
The phasor value can be specified at an instant of time t1:
X (t1) = (Xm(t1)/√2)ej(2π∫gdt +φ(t1))
x(t1) = Xm(t1) cos(2πf0 t1 + (2π ∫gdt +φ(t1)))
Phasor value:
Determines the sinusoidal formula:
Which generates a point t1 on the waveform:t1
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Phasor estimation Given waveform, what is phasor?
– There is no phasor in waveform– We cannot measure an instantaneous phasor
Observe waveform over interval– There is no way to recover the phasor value at t1– It is estimated over an interval around t1
Phasor value is instantaneous but estimated over an interval
X (t1) = (Xm/√2)ejφEstimate the phasor over interval:
Sample the given waveform:
t1
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Window & timetag Example: f0 + 5 Hz (65 Hz)
Window X averages windows 1-3 – Phase rotation speed constant, angle same as #2 Timetag best represents measurement in center
WINDOW 1 WINDOW 3WINDOW 2
WINDOW X
Reporting latency (delay) Real measurement latency
in depends on window length– Generally ½ window length
For latency calculated by time stamp (center of window)– Processing < 2 ms– P class ~17 ms (1 cycle)– M class depends on
reporting• 50 ms for Fs = 60/s• 414 ms for Fs = 10/s
F & ROCOF estimates can add 1-5 ms
4.85 4.9 4.95 5 5.05 5.1 5.15
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Time (Sec)
signal
signal, A phase
Phasor est.
timetag
Latency = ½ window + processing
Datasent
Process time
Timetag & step change
Timetag center of window
Step response starts in relation to window
Synchrophasor is an estimate of phasor value– Includes data within
window– It is NOT a measurement
response
20% step
Signal magnitude
Window before step – no change
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Time (Sec)
Magnitude (unit value)
AC signal
Window includes ½ step – ½ response
Window includes full step – full response
Windowing & step change
Step centered in window– M & P class the same
Window length– Filtering included in window– Longer window stretches
response– Less sharp, high frequency
excluded
M class reduces frequency for alias protection
P class sharper response, no alias protection
20% step
One cycle window
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Time (Sec)
Magnitude (unit value)
AC signal
Two cycle windowMany cyclewindow
Timing errors The phase angle is determined by the time reference If t = 0 is displaced by x seconds, the phase angle will be
rotated by x/46x10-06 degrees (1° ~ 46 µs at f0 = 60 Hz) Note the error ONLY effects phase angle – magnitude ok
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v(t) = √2 A cos (2 ω0 t + )
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V = A ej
Measurement time t = 0
Measurement angle
Actual time t = 0
Actual angle
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Other timing effects Effects depend on PMU construction
– Internal GPS clock– Internal timing filters
Clock wander (slow changes in clock accuracy)– Phase angle may wander with clock
Clock jitter (instantaneous phase changes in clock)– May have no effect– May increase noise in estimate
Loss of lock – phase angle will drift– Rate of drift depends on local oscillator
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1ESTIMATION WINDOW
GPS GPS Timing Timing
ClockClock
PMUPMUPowerPower
SignalsSignals
Magnitude errors
Primarily due to instrumentation problems– Wrong ratio– Bad connections– Bad termination– Positive sequence errors
• Phasing errors• Phase failure
Noise and harmonics– Noise usually well filtered by Fourier– Harmonics suppressed (standard)
Frequency compensation errors
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52 54 56 58 60 62 64 66 680.85
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Input Frequency (Hz)
Pha
sor
Mag
nitu
de
Phasor Magnitude vs. Frequency
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Frequency & ROCOF defined in standard
Given the signal: x(t) = Xm(t) cos[ψ(t)]
Frequency: f(t) = 1/(2π) dψ(t)/dt ROCOF: ROCOF(t) = df(t)/dt
– ROCOF: Rate of Change of Frequency
Follows usual implementation of F & dF/dt
F not the same as rotor speed!
Derivative subject to noise; can make compliance difficult
Frequency and ROCOF calculation
• Frequency is rate of change of phase angle
• F = (- ) / (t2 - t1) = / t
– (can also use zero crossings of sine wave)
• ROCOF = (F2 - F1)/t
• Standard requires minimal delay– Filtering adds delay
– Minimal filtering
Vt1
Vt2
Noise Frequency & ROCOF
Voltage very smooth
Frequency with a little noise
ROCOF follows swing significant noise– Note ~ 90°
offset from frequency
P class vs. M class
P class– Minimal filtering– Possible aliasing of higher frequency components
• Are there any?– Less delay in estimation (shorter window, 30 – 100 ms less than M
class)– Important for real-time controls requiring minimum delay
M class– Some anti-alias protection– Wider frequency response, lower noise– Latency longer (depends on reporting rate, 30 ms @ 60/s, 100 ms @
30/s)– Important for situations with higher frequencies present
Both classes– Essentially the same measurement in all other respects
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PMU Settings Settings usually defined by filters and/or windows
No production PMUs have fully qualified for classes
Some PMU settings--
SEL– “Fast response” – P class, no filtering– “Narrowband” – M class filtering
Arbiter– Many filter & window options– P class – short window, suggest Hann window– M class – set window 3X reporting period, suggest Hann window
ABB– Offers a number of filters– Filter 0 and 1 should be P Class– Filters 5-6 area around M class
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Synchrophasors – Summary
Synchrophasors provide complete measurement– Magnitude & phase angle of V & I– Power & frequency directly derived– Accurate and high speed
Measurement is well defined and standardized
Provide many benefits to operations & planning– Wide area view with synchronized measurements– View into system dynamics– Precise data for system analysis & planning– System-wide measurement based controls
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Thank You!
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201 S. Lake Ave., Ste. 400
Pasadena, CA 91101
626-685-2015
Ken Martin [email protected]
Prashant Palayam
[email protected] (Kevin) Chen
John Ballance
Reserve
Leftover slides
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Phase & symmetrical components
Both single phase & symmetrical components are used Positive sequence represents normal system
– Matches system models Negative and zero sequence components used for
special applications
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Vp = (Va + Vb e120j + Vc e-120j )/3
Vb
Va
Vc
120
120
Phasors provide MW, MVAR
• Power P = V I cos(VI = Vx Ix + Vy Iy• Reactive Power Q = V I sin() = V (jI)
= Vy Ix - Vx Iy
V e = Vx + j Vy
I e = Ix + j Iy
j
j