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Roscoe, Andrew (2014) Adaptive-window PMU algorithms using cascaded boxcar filters to meet and exceed C37.118.1(a) requirements. In: Synchrophasor estimation processes for Phasor Measurement Units: algorithms and metrological characterisation, 2014-12-09 - 2014-12-09, École Polytechnique Fédérale de Lausanne. ,

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Adaptive-window PMU algorithms using

cascaded boxcar filters to meet and exceed

C37.118.1(a) requirements

Dr. Andrew Roscoe

Workshop on “Synchrophasor estimation processes for Phasor Measurement

Units: algorithms and metrological characterisation”

Swiss Federal Institute of Technology of Lausanne (EPFL).

December 9th 2014, Lausanne, Switzerland

Contributors to recent and

forthcoming work

Andrew Roscoe,

University of Strathclyde

Bill Dickerson,

Arbiter Systems

Ken Martin,

Chair, IEEE Synchrophasor Working Group

Steven Blair,

University of Strathclyde

ENG52 Researcher

http://personal.strath.ac.uk/steven.m.blair/




C37.118.1a-2014

IEC/IEEE 60255-118-1

General PMU architecture

(single phase section)

Analogue

filtering ADC

X

X

FIR filter

FIR filter

+

+ j

Time

Synchronised

to UTC

Quadrature

oscillator

cos(2ヾfTt) -sin(2ヾfTt)

Tuned frequency fT

f0 = Nominal frequency (Hz)

f = Actual fundamental frequency (Hz)

fT = Tuned frequency (Hz)

Fixed-filter PMU architecture


Analogue

filtering ADC

X

X

FIR filter

FIR filter

+

+ j

Time

Synchronised

to UTC

Quadrature

oscillator


Tuned frequency fT=f0




fT=f0

f f (f-f0 ≈ 0) , (f+f0 ≈ 2f0)

Frequency-tracking PMU architecture


Analogue

filtering ADC

X

X

FIR filter

FIR filter

+

+ j

Time

Synchronised

to UTC

Quadrature

oscillator


Tuned frequency fT=f




fT=f

f f (f-fT=0) , (f+fT=2f)

Reference vs. Tracking filter example

f0=50, Reporting rate 50 Hz

The effect of modulation in the

bandwidth test

(1+0j)

0.9 1.1

0.1 pu amplitude modulation

0.1 rad phase modulation

M

TVEfF

Limit

M 1

1.0

03.01MfF

7.0MfF

F(fM) > -3.098 dB

tfjtfj MM eM

eM

V 22

22

tfj

M

tfj

MMeasMM e

MfFe

MfFV

22

22

VVTVE Meas

Bandwidth test – TVE

Bandwidth testing

F & ROCOF

performance

limits

Error requirements for Compliance

P Class M Class

Reporting Rate

FS (Hz) Fr (Hz) Max FE Max RFE Fr (Hz) Max FE Max RFE

10 1 0.03 0.6 2 0.12 2.3

12 1.2 0.04 0.8 2.4 0.14 3.3

15 1.5 0.05 1.3 3 0.18 5.1

20 2 0.06 2.3 4 0.24 9.0

25 2 0.06 2.3 5 0.30 14

30 2 0.06 2.3 5 0.30 14

50 2 0.06 2.3 5 0.30 14

60 2 0.06 2.3 5 0.30 14

Formulas min(FS/10,2) 0.03 *Fr 0.18*ヾ*Fr 2 min(Fs/5,5) 0.06 *Fr 0.18*ヾ*Fr 2

C37.118.1a-2014

Bandwidth test – Frequency Error (FE)

& ROCOF ERROR (RFE)


f0=50, Reporting rate FS=50 Hz

Frequency error during OOB testing

(1+0j)

Interharmonic at 2ヾfIH

Radius AF(fIH-fT)

• where A=0.1 pu

• F(fIH-fT) is filter gain at (fIH-fT)

• Deviation rotates at 2ヾ∙(fIH-f)

(1- AF(fIH-fT))

Trajectory speed

at closest approach

2ヾ∙(fIH-f) ∙ AF(fIH-fT)

Frequency deviation にヾゲ (fIH−f) ゲ AF(fIH−fT)にヾゲ (1− AF(fIH−fT))

Determining the required filter Mask

for OOB testing

繋血彫張伐血脹隼繋継陳銚掴畦ゲ血彫張伐血

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 血彫張伐血脹 is minimum,

sets the gain (attenuation)

Required at the “closest” mask point.



Out-of-Band testing, f=f0

All algorithms




Frequency in filter = ( fIH - fT )

Frequency

f = fT = f0

血待髪繋聴に血待伐繋聴に

Minimum ( fIH - fT ) = 血待髪庁縄態伐血待噺庁縄態

Minimum fIH (upper) = 血待髪庁縄態

Maximum ( fIH - f ) = 血待髪庁縄態伐血待噺庁縄態

Mask width is “normal” 庁縄態 and ( fIH - f ) tracks exactly with ( fIH - fT ).

Out-of-Band testing, f=f0-庁縄態待

Fixed-filter algorithm





Frequency

fT = f0


Minimum ( fIH - fT ) = 血待髪庁縄態伐血待噺庁縄態


Maximum ( fIH - f) = 血待髪庁縄態伐 (f0−庁縄態待 ) 噺な┻な庁縄態

f =f0-庁縄態待

Mask width is “normal” 庁縄態 but gain needs to be reduced by にどゲ健剣訣怠怠┻怠 = 0.83 dB,

at the closest frequency, from what you might expect.

Out-of-Band testing, f=f0+庁縄態待

Frequency-tracking algorithm





Frequency

f0


Minimum ( fIH - fT ) = 血待髪庁縄態伐血待髪庁縄態待噺ど┻ひ庁縄態


Maximum ( fIH - f) = 血待髪庁縄態伐 (f0+庁縄態待 ) 噺ど┻ひ庁縄態 f =fT=f0+

庁縄態待

Mask frequency width is reduced by 10% from 庁縄態 but gain can be にどゲ健剣訣怠待┻苔 = 0.92 dB higher,

at the closest frequency, from what you might expect.

Simplified OOB requirements and

examples, f0=50 Hz, FS=50 Hz

Simplified OOB requirements and

examples, f0=50 Hz, FS=50 Hz

f0 = 50 Hz

FS = 50 Hz

0.92 dB

0.83 dB

14.8% narrower

Cascaded boxcar filters,

f0=50 Hz, FS=50 Hz

Boxcar filter properties

Cascaded boxcar filters example,

f0=50 Hz, FS=50 Hz


f0=50 Hz, FS=50 Hz

O

O

O O

O

O

O Primary filter zeros


f0=50 Hz, FS=50 Hz

O

O

O O

O

O

O


O Frequency filter

Additional zeros


f0=50 Hz, FS=50 Hz

O

O

O O

O

O

O

O

O

O

O O O O

O O

O

O

O

O

O

O


O Frequency filter

Additional zeros

O “Harmonic” zeros

O Frequency filter

“harmonic” zeros


f0=50 Hz, FS=50 Hz


f0=50 Hz, FS=50 Hz

1 1 2 2½ 2 1½ 1

Primary filter

10 cycles, ~200ms at f=50 Hz

Latency ~5 cycles, ~100ms at f=50 Hz Additional

Frequency (and ROCOF)

filtering

Response time

Example software architecture

Code execution speed

• 30-60たs Typical execution time per frame for M class PMU (Motorola MVME5500). Supports >10kHz reporting.

• Calculation rate does NOT 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 (服 Window length).

• Can easily be extended to “Harmonic PMU” applications. – # Calculations expand 服N harmonics, memory expands 服N

harmonics and 服 Window length

呑 Compare with 椴 Least Squares and 惇TFT敦 algorithms, # calculations proportional to

window length

椴 FFT algorithms for harmonic PMUs, # calculations proportional to (window length)*log(window length)

椴 Kalman filter methods, # calculations proportional to the number of filter zeros squared (matrix multiplications).

Non-standard tests and real-world conditions

Unfinished work - Increased fault tolerance for frequency

and ROCOF - 27th August 2013 example – P class

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. 20ms) intervals, while also providing adaptive-zero-placement for off-nominal frequency.

• Integrating PMU algorithms within HVDC controllers?

• Aggregation of PMU ROCOF data across a geographically wide network to determine “system ROCOF” and required “inertial” responses.

– “Enhanced Frequency Control Capability (EFCC)” with National Grid, Alstom, Belectric, Centrica, Flextricity & University of Manchester.

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