Distribution Level Phasor Measurement Accuracy Limits

Jiecheng (Jeff) Zhao, Lingwei (Eric) Zhan, Yilu Liu

University of Tennessee, Knoxville Paul Ewing, Joe Gracia

Oak Ridge National Laboratory March 23, 2015

Outline

Introduction

Methodology

Error Analysis

Conclusions

2

Introduction

Looking beyond wide area monitoring Potential value with more generation and load control

at distribution level Measurement accuracy and error impact are issues –

no standard for distribution level measurements Focused on frequency and phase angle

3

FDR (Frequency Disturbance Recorder)

PMU (Phasor Measurement Unit)

Methodology

Error calculations were performed based on typical accuracy values, measurements, and simulations

4

Filter ADC Microprocessor

GPSReceiver

AC Signal

Measurement result

Methodology

Error sources vary – both internal and external

5

Error Sources

Internal factor

External factor

Hardware

Software

Time reference

ADC

Noise inside device

Round error

Algorithm

Noise

Harmonic distorion

White noise

Other noise

Methodology

• Our focus was on errors with larger impact

6

Error Sources

Internal factor

External factor

Hardware

Software

Time reference

ADCNoise inside

device

Round error

Algorithm

Noise

Harmonic distorion

White noiseOther noise

Internal Factors

Main factors

Algorithms

Time reference

ADC

Approach

Calculations based on typical inaccuracies

Simulation

7

Algorithm Error

Fed digitized sinusoidal signal with known frequency, amplitude, and angle into measurement algorithm Measurement algorithm -Discrete Fourier

Transform (DFT) Error obtained by comparing estimated values

and true values Increased simulation time (resampling) until

max positive and negative error converged

8

Algorithm Error

• Result - Sensitive to frequency deviation

9

0.00E+001.00E-072.00E-073.00E-074.00E-075.00E-076.00E-077.00E-078.00E-07

0.00E+002.00E-044.00E-046.00E-048.00E-041.00E-031.20E-03

59.95 59.975 60 60.025 60.05

Freq

uenc

y Er

ror (

Hz)

Angl

e Er

ror (

degr

ee)

Actual Frequency (Hz)

Angle Error Frequency Error

Time Reference Error

• GPS: 1 sec time/frequency reference • PPS signal: typical jitter - 50 ns to 1 μs; held to

10 ns with effort

10

Amplitude

Time

GPS Second

GPS Receiver PPS Signal

Time Reference Error

• Result (f = 59.95 Hz) – jitter matters

11

0.00E+001.00E-052.00E-053.00E-054.00E-055.00E-056.00E-057.00E-05

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

10 ns 50 ns 1 μs

Freq

uenc

y Er

ror (

Hz)

Angl

e Er

ror (

degr

ee)

Time reference Error

Angle Error Frequency Error

ADC Error • Results (f = 59.95 Hz) – better resolution helps • 1 least significant bit (LSB) error

12

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

0.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-03

14 bit 16 bit

Freq

uenc

y Er

ror (

Hz)

Angl

e Er

ror (

degr

ee)

ADC Accuracy

Angle Error Frequency Error

External Factors

Main factors • White noise • Harmonic distortion

Approach • Measure the real noise level • Simulation • f=59.95 Hz

13

White Noise

14

0.00E+001.00E-042.00E-043.00E-044.00E-045.00E-046.00E-04

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

70 dB 80 dB 90 dB

Freq

uenc

y Er

ror (

Hz)

Angl

e Er

ror (

degr

ee)

SNR (Signal-to-Noise Ratio) Angle Error Frequency Error

• Result (f = 59.95 Hz) – SNR matters • Four cases – calculated power spectrum densities

Harmonics Distortion • 2nd - 25th harmonics from 4 cases, (f = 59.95 Hz) • Higher order components contribute more error

15

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

Case 1 Case 2 Case 3 Case 4Angle Error Frequency Error

Angle Error Contribution

• f = 59.95 Hz

16

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

Algorithm GPS ADC White Noise HarmonicDistortion

59.95Hz

10ns 14bit 70dB

Case 1

59.975Hz

50ns 16bit 80dB

Case 2

60Hz 1µs

90dB

Case 3

60.025Hz

Case 4

60.05Hz

Angle Error Contribution of Each Factor (degree)

Frequency Error Contribution

• f = 59.95 Hz

17

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

Algorithm GPS ADC White Noise HarmonicDistortion

59.95Hz

10ns

14bit

70dB

Case 1

59.975Hz 50ns

16bit

80dB

Case 2

60Hz

1µs

90dB

Case 3

60.025Hz

Case 4

60.05Hz

Frequency Error Contribution of Each Factor (Hz)

Thank You!

Questions/Comments?