S YNCHROPHASOR C HARACTERISTICS & T ERMINOLOGY Ken Martin, Senior Principal Engineer Electric Power Group, LLC (EPG) Presented to ERCOT Synchrophasor Work.

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S YNCHROPHASOR C HARACTERISTICS & T ERMINOLOGY Ken Martin, Senior Principal Engineer Electric Power Group, LLC (EPG) Presented to ERCOT Synchrophasor Work Group March 7, 2014 Real Time Dynamics Monitoring System Alarming Phasor Grid Dynamics Analyzer e nhanced 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 C ” 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. Page 1

Synchrophasor Fundamentals  Introduction of phasors  Calculation of synchrophasors  Synchrophasor characteristics  Errors and their impacts  Measurement classes Page 2

Phasor Representation A phasor is a complex value representing and AC signal It includes the magnitude and phase angle of the sinusoid √2 A cos (2  ω 0 t +  ) A e j    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 Page 4 v(t) = √2 A cos (2  ω 0 t +  ) V = A e j  ????

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) (x k )  Result is phasor (complex number) 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   

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 WINDOW 1 WINDOW 2 WINDOW 3 

Synchrophasor off nominal frequency  Example: f Hz (65 Hz)  Phasor rotates: rotation = f – f nominal  CCW for f > f nominal & CW for f < f nominal  WINDOW 1 WINDOW 3 WINDOW 2

Signal specification  Phasor is a shorthand for sinusoid formula – Specifies magnitude and phase – Assumes frequency, based on nominal f 0  We are used to seeing constant phase and amplitude – X m & φ give phasor:  A true dynamic system has changing parameters: – Amplitude: X m (t) – Frequency: g(t) – Phase: φ(t)  Giving a dynamic phasor: X (t) = (X m (t)/√2)e j(2π∫gdt +φ(t)) X = X m e jφ

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 t 1 : X (t 1 ) = (X m (t 1 )/√2)e j(2π∫gdt +φ(t1)) x(t 1 ) = X m (t 1 ) cos(2πf 0 t 1 + (2π ∫gdt +φ(t 1 ))) Phasor value: Determines the sinusoidal formula: Which generates a point t 1 on the waveform: t1t

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 t 1 – It is estimated over an interval around t 1  Phasor value is instantaneous but estimated over an interval X (t 1 ) = (X m /√2)e jφ Estimate the phasor over interval: Sample the given waveform: t1t

Window & timetag  Example: f 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 3 WINDOW 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 Phasor est. timetag Latency = ½ window + processing Data sent 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 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 Two cycle window Many cycle window

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/46x degrees (1° ~ 46 µs at f 0 = 60 Hz)  Note the error ONLY effects phase angle – magnitude ok Page 16 v(t) = √2 A cos (2  ω 0 t +  )  V = A e j   Measurement time t = 0 Measurement angle Actual time t = 0 Actual angle  

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 ESTIMATION WINDOW GPS Timing Clock PMU PowerSignals

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 Page 18

19 Frequency & ROCOF defined in standard  Given the signal: x(t) = X m (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 =  (    -   ) / (t 2 - t 1 ) =  /  t –(can also use zero crossings of sine wave) ROCOF = (F 2 - F 1 )/  t Standard requires minimal delay –Filtering adds delay –Minimal filtering Vt1Vt1  Vt2Vt2  

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 60/s, /s) – Important for situations with higher frequencies present  Both classes – Essentially the same measurement in all other respects Page 22

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 Page 23

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 Page 24

Thank You! Page S. Lake Ave., Ste. 400 Pasadena, CA Ken Martin Prashant Palayam Heng (Kevin) Chen John Ballance

Reserve  Leftover slides Page 26

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 Page 27 Vp = (V a + V b e 120j + V c e -120j )/3 VbVb VaVa VcVc 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 = V x + j V y I e = I x + j I y jj jj  