Adaptive-window PMU algorithms using cascaded boxcar filters to meet and exceed C (a) requirements. Dr. Andrew Roscoe

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1 Adaptive-window PMU algorithms using cascaded boxcar filters to meet and exceed C (a) requirements Dr. Andrew Roscoe

2 Contributors to recent and forthcoming work Andrew Roscoe, University of Strathclyde Bill Dickerson, Arbiter Systems Steven Blair, University of Strathclyde ENG5 Researcher Ken Martin, Chair, IEEE Synchrophasor Working Group

3 C a-014 IEC/IEEE

4 f 0 = Nominal frequency (Hz) f = Actual fundamental frequency (Hz) f T = Tuned frequency (Hz) General PMU architecture (single phase section) Analogue filtering ADC X X FIR filter FIR filter j + + Time Synchronised to UTC -sin(πf T t) Quadrature oscillator cos(πf T t) Tuned frequency f T

5 f 0 = Nominal frequency (Hz) f = Actual fundamental frequency (Hz) f T = Tuned frequency (Hz) f T =f 0 f Analogue filtering Fixed-filter PMU architecture (single phase section) ADC X X FIR filter f (f-f 0 0), (f+f 0 f 0 ) FIR filter j + + Time Synchronised to UTC -sin(πf T t) Quadrature oscillator cos(πf T t) Tuned frequency f T =f 0

6 f 0 = Nominal frequency (Hz) f = Actual fundamental frequency (Hz) f T = Tuned frequency (Hz) f T =f f Analogue filtering Frequency-tracking PMU architecture (single phase section) ADC f X X FIR filter (f-f T =0), (f+f T =f) FIR filter j + + Time Synchronised to UTC -sin(πf T t) Quadrature oscillator cos(πf T t) Tuned frequency f T =f

7 Reference vs. Tracking filter example f 0 =50, Reporting rate 50 Hz

8 The effect of modulation in the bandwidth test V Meas F M V e M j f M e j f t j f M M e fm t j f M t F f e M M t M 0.1 pu amplitude modulation TVE V F f M Meas V TVE 1 M Limit 0.1 rad phase modulation (1+0j) F f M 1 F f M F(f M ) > db

9 Reference vs. Tracking filter example f 0 =50, Reporting rate 50 Hz

10 Bandwidth test TVE

11 Bandwidth testing C a-014 F & RCF performance limits Error requirements for Compliance P Class M Class Reporting Rate F S (Hz) F r (Hz) Max FE Max RFE F r (Hz) Max FE Max RFE Formulas min(f S /10,) 0.03 *F r 0.18*π*F r min(f s /5,5) 0.06 *F r 0.18*π*F r

12 Bandwidth test Frequency Error (FE) & RCF ERRR (RFE)

13 Reference vs. Tracking filter example f 0 =50, Reporting rate F S =50 Hz

14 Reference vs. Tracking filter example f 0 =50, Reporting rate 50 Hz

15 Frequency error during B testing Interharmonic at πf IH Radius AF(f IH -f T ) where A=0.1 pu F(f IH -f T ) is filter gain at (f IH -f T ) Deviation rotates at π (f IH -f) (1- AF(f IH -f T )) (1+0j) Frequency deviation π (f IH f) AF(f IH ft) π (1 AF(f IH ft)) Trajectory speed at closest approach π (f IH -f) AF(f IH -f T )

16 Determining the required filter Mask for B testing Frequency deviation π (f IH f) AF(f IH ft) π (1 AF(f IH ft)) Frequency deviation π (f IH f) AF(f IH ft) π (1 AF(f IH ft)) F f IH f T < FE max A f IH f Minimum separation of the interharmonic from the tuned (heterodyne) frequency. Sets the width of the mask. Maximum separation of the interharmonic from the fundamental frequency, when f IH f T is minimum, sets the gain (attenuation) Required at the closest mask point.

17 ut-of-band testing, f=f 0 All algorithms f 0 = Nominal frequency (Hz) f = Actual fundamental frequency (Hz) f T = Tuned frequency (Hz) Minimum f IH (upper) = f 0 + F S Minimum ( f IH - f T ) = f 0 + F S f 0 = F S Frequency in filter = ( f IH - f T ) f 0 F S f = f T = f 0 f 0 + F S Frequency Maximum ( f IH - f ) = f 0 + F S f 0 = F S Mask width is normal F S and ( f IH - f ) tracks exactly with ( f IH - f T ).

18 f 0 = Nominal frequency (Hz) f = Actual fundamental frequency (Hz) f T = Tuned frequency (Hz) Frequency in filter = ( f IH - f T ) ut-of-band testing, f=f 0 - F S 0 Fixed-filter algorithm Minimum f IH (upper) = f 0 + F S Minimum ( f IH - f T ) = f 0 + F S f 0 = F S f 0 F S f T = f 0 f 0 + F S Frequency f =f 0 - F S 0 Maximum ( f IH - f) = f 0 + F S Mask width is normal F S but gain needs to be reduced by 0 log 1 at the closest frequency, from what you might expect. 1.1 (f 0 F S ) = 1.1 F S 0 = 0.83 db,

19 f 0 = Nominal frequency (Hz) f = Actual fundamental frequency (Hz) f T = Tuned frequency (Hz) Frequency in filter = ( f IH - f T ) ut-of-band testing, f=f 0 + F S 0 Frequency-tracking algorithm Minimum ( f IH - f T ) = f 0 + F S Minimum f IH (upper) = f 0 + F S f 0 + F S = 0.9 F S 0 f 0 F S f 0 f 0 + F S Frequency f =f T =f 0 + F S 0 Maximum ( f IH - f) = f 0 + F S Mask frequency width is reduced by 10% from F S but gain can be 0 log at the closest frequency, from what you might expect. (f 0 + F S ) = 0.9 F S 0 = 0.9 db higher,

20 Simplified B requirements and examples, f 0 =50 Hz, F S =50 Hz

21 Simplified B requirements and examples, f 0 =50 Hz, F S =50 Hz 0.9 db 0.83 db 14.8% narrower f 0 = 50 Hz F S = 50 Hz

22 Cascaded boxcar filters, f 0 =50 Hz, F S =50 Hz

23 Boxcar filter properties

24 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz

25 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz Primary filter zeros

26 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz Primary filter zeros Frequency filter Additional zeros

27 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz Primary filter zeros Harmonic zeros Frequency filter Additional zeros Frequency filter harmonic zeros

28 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz

29 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz

30 Cascaded boxcar filters example, f 0 =50 Hz, F S =50 Hz 1 1 ½ 1½ 1 Primary filter 10 cycles, ~00ms at f=50 Hz Latency ~5 cycles, ~100ms at f=50 Hz Additional Frequency (and RCF) filtering Response time

31 Example software architecture

32 Code execution speed 30-60μs Typical execution time per frame for M class PMU (Motorola MVME5500). Supports >10kHz reporting. Calculation rate does NT increase for longer-window (lower reporting rate) devices, as long as the NUMBER of cascaded boxcar filter sections is kept constant. But fast-access memory requirement does ( Window length). Can easily be extended to Harmonic PMU applications. # Calculations expand N harmonics, memory expands N harmonics and Window length Compare with Least Squares and TFT algorithms, # calculations proportional to window length FFT algorithms for harmonic PMUs, # calculations proportional to (window length)*log(window length) Kalman filter methods, # calculations proportional to the number of filter zeros squared (matrix multiplications).

33 Non-standard tests and real-world conditions

34 Unfinished work - Increased fault tolerance for frequency and RCF - 7 th August 013 example P class

35 Unfinished work - Increased fault tolerance for frequency and RCF - 7 th August 013 example P class

36 Unfinished work - Increased fault tolerance for frequency and RCF - 7 th August 013 example P class

37 Future considerations/work: Implement in hardware! Continuing input to standards development. Accurate revenue metering. Synchronised Power Quality assessment and PQ metering! Combinations of adaptive and fixed boxcars to provide Uniform Aggregated Weighting (Welch s method) via repeated windows at fixed (i.e. 0ms) intervals, while also providing adaptive-zero-placement for off-nominal frequency. Integrating PMU algorithms within HVDC controllers? Aggregation of PMU RCF data across a geographically wide network to determine system RCF and required inertial responses. Enhanced Frequency Control Capability (EFCC) with National Grid, Alstom, Belectric, Centrica, Flextricity & University of Manchester.

38 END

PMU (algorithm) Testing to C (a) in software. Dr. Andrew Roscoe

PMU (algorithm) Testing to C (a) in software. Dr. Andrew Roscoe PMU (algorithm) Testing to C37.118.1(a) in software Dr. Andrew Roscoe Rough Agenda C37.118.1 (2011) & C37.118.1a (2014) Description of the six main tests in order Making references to C37.118.1a and the