1. 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

2. 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. Page 1

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

4. 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

5. 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  ????

6. 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

7. Traditional phasor calculation  One set of Fourier coefficients (example - 1 cycle window)  Reference waveforms move with calculation  Phasor rotates CW at system frequency   

8. 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 

9. Synchrophasor off nominal frequency  Example: f 0 + 5 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

10. 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

11. 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: t1t1 -0.5 0 0.5 1 -0.012-0.008-0.00400.0040.0080.012

12. 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: t1t1 -0.5 0 0.5 1 -0.012-0.008-0.00400.0040.0080.012

13. Window & timetag  Example: f 0 + 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 3 WINDOW 2 WINDOW X

14. 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

15. 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

16. 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

17. 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 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  

18. 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

19. 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

20. 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

21. 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  

22. Noise Frequency & ROCOF  Voltage very smooth  Frequency with a little noise  ROCOF follows swing significant noise – Note ~ 90° offset from frequency

23. 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 Page 22

24. 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

25. 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

26. Thank You! Page 25 201 S. Lake Ave., Ste. 400 Pasadena, CA 91101 626-685-2015 Ken Martin martin@electricpowergroup.com Prashant Palayam palayam@electricpowergroup.com Heng (Kevin) Chen chen@electricpowergroup.com John Ballance ballance@electricpowergroup.com

27. Reserve  Leftover slides Page 26

28. 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

29. 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  