Federal Institute of Santa Catarina

Electrical Engineering

A Teaching Tool for Phasor Measurement

Estimation
December, 2013

Daniel Dotta
Electrical Engineering Department
Federal Institute of Santa Catarina (IFSC), Brazil

Nov-Dec 2013, DD

Federal Institute of Santa Catarina

Electrical Engineering

Outline
Objective

Motivation
Phasor Measurement Process
Phasor Definition
PMU Architectures
PMU Simulink Simulator

Simulations
Conclusions
Future Developments
Nov-Dec 2013, DD

Federal Institute of Santa Catarina

Electrical Engineering

Objective
To present the design of a Simulink-based Phasor
Measurement Unit (PMU) Simulator

Nov-Dec 2013, DD

Federal Institute of Santa Catarina

Electrical Engineering

Motivation
PMUs are spread around world
Over thousand PMUs installed in USA and China

Dissemination of phasor processing techniques

inside a PMU is quite limited
NASPI Research Task Team

Education
Necessity on modernize power system education
courses
CURENT Project at RPI (Rensselaer Polytechnic Institute)
IEEE Power and Energy Education Initiative

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Federal Institute of Santa Catarina

Electrical Engineering

What is a Phasor?

t 0
x t 2 A cos 2 60 t
Re

2 Ae j

Phasor representation of a sinusoidal wave form

Complex number that represents a sine wave whose amplitude

(X) and angular frequency () are time-invariant
The power system frequency is not time-invariant (PMUs must
deal with it)
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Federal Institute of Santa Catarina

Electrical Engineering

Anatomy of a PMU

There is no standardization on the algorithms used inside a

PMU or the number of cycles used in computing a phasor
Adapted from Ken Martin and Arun Phadke
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Federal Institute of Santa Catarina

Electrical Engineering

PMU Architectures
x(t)

x(t)

Analog
Filter

A/D
Converter

Non-Uniform
Sampling

Analog
Filter

Sampling
Clock
Frequency
Estimator

x(k)

A/D
Converter

Frequency
Estimator

x(k)

Digital
Filter

Digital
Filter

Phasor
Estimator

Phasor
Estimator

Uniform
Sampling
(first one)

X(k)

X(k)

Frequency Tracking

Sampling
Clock

Frequency Compensation
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Electrical Engineering

Phasor Measurement Process

Sine Wave
Time-Domain Signal

1.5

N 12

N=12

Magnitude (pu)

Window Size
(points)

0.5

Regular sampling
period (Ts)

-0.5

-1

-1.5
0.014

1/fs
0.016

0.018

Sampling rate
For N=12

0.02

0.022

0.024

Time(s)

0.026

f s Nf

0.028

0.03

0.032

Sampling period

f s 12 60 720Hz
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Ts 0.0014s

1
Ts
fs
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Electrical Engineering

Phasor Measurement Process

Frequency Domain

N 12

Time Domain
Time-Domain Signal

1.5

Magnitude (pu)

DFT

N=12

0.5

-0.5

-1

1/fs

-1.5
0.014

0.016

0.018

Samples
where

0.02

0.022

0.024

Time(s)

0.026

0.028

0.03

0.032

xn x(tn )

X m X (e jm )

tn nTs , n 0,, N -1
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2
m m , m 0,, N -1
N
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Electrical Engineering

Phasor Estimation
Definition of DFT

N 1

2
Xm
xn e

N n 0

Fundamental frequency
component, set m=1

2
j nm
N

N 1

2
X
xn e

N n 0

2
n
N

Discrete Fourier Transform is a simple widely used method for phasor

estimation

Other methods have been discussed

Kalman filters, weighted least squares and neural networks
Currently used in the commercial PMUs

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Frequency Estimation
Frequency Estimation is a key role in the both architectures
Changing the sampling window
Providing the frequency for phasor correction

Several methods are found in the literature

Zero Crossing
Least Error Squares
Kalman Filters
Demodulation

Phasor measurement angle changing

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Electrical Engineering

Frequency Estimation
Zero-Crossing
Good performance for well filtered or perfect waves
High sensible to noise

Least Error Squares

Based on least squares and Taylor series expansion
in the neighborhood of the nominal frequency
Do not work very well for frequencies out of nominal

Relative Error - LES

12

neighborhood
10

Relative Error (%)

0
45

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50

55

60
Frequency (Hz)

65

70

75

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Electrical Engineering

Frequency Estimation
Kalman Filters
Suitable for noise rejection
Slow compared with the other methods
Dependent from the model parameters adjustment (variance and covariance noise
matrices)

Demodulation
The main idea is to multiply the scalar input with a sine and cosine signal with a
know frequency

Z (k ) e j (0tk )

Sensible to large negative sequence component

Fault conditions

V (k ) Ae

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j (1tk )

Y (k ) Ae j[(1 0 )tk ]

X
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Electrical Engineering

Frequency Estimation
Phasor Angle Changing
Based on the idea that

1
f (t )
2 t

Use positive sequence phasor estimation

Present satisfactory results under large frequency variations
Used in commercial PMUs

Phasor angle changing and demodulation presented

satisfactory results

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Electrical Engineering

Frequency Estimation
Results for frequency ramp
Demodulation

Angle Changing

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Electrical Engineering

Pos-Processing
Under off-nominal operation the phasor measured (Xmes) is
different from the true value (Xtrue)
The effect of the off-nominal frequency can be expressed by a P

and Q factor.

Phasor correction

N ( 0 )t
( 0 ) t
j ( N 1)
2
2
P {
}e
( 0 )t
Nsin
2
N ( 0 )t
sin
( 0 ) t
j ( N 1)
2
2
Q {
}e
where
( 0 )t
Nsin
2
N - window size

X mes PX true QX

sin

w actual frequency
w0 nominal frequency

*
true
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Electrical Engineering

Pos-Processing
The P factor is directly influence by N and frequency value
P behavior under frequency variation (N=48)
Complex Gain P

Magnitude

1.005
1
0.995
0.99

Angle (degress)

0.985
-5

-4

-3

-2

-1

-4

-3

-2

-1

20
10
0
-10
-20
-5

Frequency Variation (Hz)

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Electrical Engineering

PMU Block Diagram

Frequency Compensation
filtering

X N n X N n 1

2
( xN n xn )e
N

Xn

Pn

X ntrue

2
n
N

Post-Processing
measured

xn (t )

Xn

X nfiltering

Filtering*

DFT

Frequency
estimation

X ntrue

Look up table with

calibration factor

Pn

Filtering*
A Average Filter
B Windowing
(C) Least Squares

N ( 0 )t
( 0 ) t
j ( N 1)
2
2
Pn {
}e
( 0 )t
N sin
2
sin

t sampling period
Fixed
N - window size

*D. Dotta and J. H. Chow. Phasor Measurement Estimation Second Harmonic

Filtering. IEEE Trans. Power Delivery, 2013.
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PMU Simulink Simulator

First version was written in Matlab code
Applied in classroom (RPI)
Mainly used for research

Described in IEEE PES GM 2013 paper

Second version in Matlab Simulink (2013)

Applied in classroom at IFSC
Application at CURENT courses is under discussion
Paper under revision IEEE Transactions on Power Systems

(Education)

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PMU Simulink Simulator

Main Advantages
Composed of only one file
Can be easily executed in a students laptop

Real digital data processing (Digital Recorders)

SIMULINK diagrams removed most of the drudgery of keeping
track of the block-diagrams and feedback

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Teaching Tool
PMU Simulink Simulator
Main Window
0

Step
1
Ramp

Disturbance

Switch 1

60
Nominal
Frequency
59

Frequency Goal

SP_MF

SP_MF

SP_MnF

SP_MnF

PS_M

PS_M

PS_Md

PS_Md

PS_A

PS_A

PS_Ad

PS_Ad

Switch 2
Frequency Deviation

PMU

Frequency
Goal
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FD

Ploting
Area

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Electrical Engineering

PMU Simulink Simulator

Main Components
Phasor A
CF

SP_MF

1
SP_MF

SP_MnF

Single-PhaseProcessing

2
SP_MnF

3 PS_M
2
Frequency
Goal

Phase A
Frequency

Phase A

Phasor A

Phasor A

Phase B

Phase B

Phasor B

Phasor B

Phase C

Phase C

Phasor C

Phasor C

P_PS

PS_M
P_PS

1
Disturbance

Type

Three-Phase
Signal Producer

CF

P_ PS

Phasor
Estimation

Symmetrical
Components

FD

Frequency
Estimation

Nov-Dec 2013, DD

FD

PS_M

PS_Md

4
PS_Md

PS_A

PS_Ad

6
PS_Ad

PS_A

Lookup
Table
7
Frequency
Deviation

Downsampling
5 PS_A

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Simulations
Frequency Step (1 Hz)
Phase A - Signal Input
Magnitude

2
1
0
-1
-2
1.5

1.6

1.7

1.8

1.9

2.1

2.2

2.3

2.4

2.5

Frequency
60

Hz

Estimated
Reference
59.5

59
1.5

1.6

1.7

1.8

1.9

2.1

2.2

2.3

2.4

2.5

Time(s)

Frequency Sampling = 2.88 kHz

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Simulations
Positive Sequence
Positive Sequence Magnitude - Downsampling
1.1

Magnitude (pu)

1.05

0.95

0.9
0

0.5

1.5

2.5

3.5

4.5

4.5

Time
(s) - Downsampling
Positive Sequence
Angle
250

200

Angle (degrees)

150
100
50
0
-50
-100
-150
-200
0

0.5

1.5

2.5

3.5

Time (s)

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Simulations
Positive Sequence (Ramp +1Hz)
Downsampling Angle - Ramp Disturbance
150

Angle (degrees)

100
50
0
-50
-100
-150
1.5

2.5

3.5

4.5

Time (s)

Positive Frequency Ramp between 2-3 seconds

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Simulations
Positive Sequence Complex Gain P Influence
PS Magnitude - Before Correction
1.0002
1.0001

Magnitude (pu)

1
0.9999
0.9998
0.9997
0.9996
0.9995
0.9994
1.8

1.9

2.1

2.2

2.3

Time (s)

Frequency Step Disturbance

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Electrical Engineering

Simulations
Positive Sequence Complex Gain P Influence
PS Magnitude - Before Correction

Magnitude (pu)

1
0.9999
0.9998
0.9997
0.9996
0.9995
1.6

1.8

2.2

2.4

2.6

2.8

3.2

3.4

3.6

Time (s)

Frequency Ramp Disturbance

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Simulations
Single-Phase Complex Gain Q Influence

Frequency Step Disturbance

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Simulations
Single-Phase Complex Gain Q Influence
Single-Phase Magnitude

1.008

Magnitude (pu)

1.006
1.004
1.002
1
0.998
0.996
0.994
0.992
0.99
1.99

2.01

2.02

2.03

2.04

2.05

2.06

2.07

Time (s)

Before Downsampling
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Simulations
Single-Phase Complex Gain Q Influence
Single-Phase Filtering and Downsampling

Mangnitude (pu)

1.01
1.005
1
0.995
0.99
0.985
2

2.5

3.5

Time (s)

After Downsampling
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Simulations
Positive Sequence Complex Gain Q Influence
Positive Sequence - Unbalanced Operation

Magnitude (pu)

1.0002

0.9998

0.9996

0.9994
1.5

2.5

3.5

4.5

Time (s)

Unbalanced Operation (5%)

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Real Data
Frequency Step
Real Data - Frequency
51

50.5

Hz

50

49.5

49

48.5

48
0

10

15

20

25

30

35

40

Time (s)

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Real Data
Single-Phase Performance
Single-Phase - Real Data
11.3

Magnitude (V)

11.2
11.1
11
10.9
10.8
10.7
10.6
10

15

20

25

30

35

40

Time(s)

1 Hz Oscillation
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Real Data
Single-Phase Performance Zoom
Single-Phase - Real Data
11.325

Magnitude (V)

11.32

11.315

11.31

11.305

11.3

11.295
24

26

28

30

32

34

36

38

Time(s)

1 Hz Oscillation - Show up in Frequency Spectrum

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Real Data
Positive Sequence
Magnitude - Positive Sequence
11.3

Magnitude (V)

11.2
11.1
11
10.9
10.8
10.7
10.6
15

20

25

30

Time(s)
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Conclusions
PMU Simulink Simulator
Phasor measurement process understanding (data analysis)
Maybe helpful to include PMU measurement in state estimators
Maybe helpful to better design future advanced protection and
control applications
Real data processing
Can be used in classroom for WAMS teaching
Validated in classroom set with students from IFSC and USP-SC

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Future Developments
Hybrid state estimator using both SCADA and PMU data
increases the reliability (solution convergence) of a
state estimator by a few percent because of better
observability (Prof. Ali Abur)
Phasor state estimator
State estimator using only PMU data
Very few US ISOs can have this capability except for
New York: Full coverage for 765/345/230 kV; most
PMUs have multiple current channels
Perhaps New England also

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Power Transfer Paths/Interfaces

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State Estimator
PMU
Network
Parameters
PMU

PMU

Phasor
Data

State
Estimator

PDC

(Only Phasors)

Trustable Data
for
Applications

Network
Status

PMU

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Contact
Contact
Daniel Dotta: dotta@ifsc.edu.br

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WAMS Overview
USA
Selective coverage of HV buses
Old PMUs (some close to 20 years); New PMUs: DOE Smart
Grid Investment Program (SGIG) adding over 1000 PMUs
Deregulated markets no direct monitoring of generator
variables; in New York, the norm is no PMU on a generator
substation
Concerns with sharing PMU data between different ISOs
PMU data communication over both private and public
networks

China (based on several presentations by Prof. Bi)

New generation of PMUs on every HV substation bus
Monitoring of synchronous generator variables, including
the rotor angle

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Time Synchronization
GOES (Geostationary
Operational
Environmental Satellite
(NASA)): 25-100 microsecond accuracy
GPS (Global Positioning
System, 1973, originally 24
satellites) 32 satellites in
medium Earth orbit: 2
micro-second accuracy
IRIG-B pulses
IEEE 1588: distributed by
Ethernet

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Introduction
US power system: 3 phase sinusoidal AC voltages and
currents at a frequency of 60 Hz

Phase a quantities (voltages and currents) lead phase b

quantities by 120 degrees, which lead phase c by 120
degrees

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Voltage and Current Measurements

What operators see on the EMS screens

V and P,Q are sampled every 5 sec (or less frequently). An RTU will transmit the
data via modems, microwave, or internet in ICCP directly to control rooms or
NERC Net (USA).
The data from different locations are not captured at precisely the same time.
However, V, P, and Q normally do not change abruptly (unless there is a large
disturbance nearby). These data can be used in the State Estimator to validate
the measured data and calculate the non-metered voltages and line power flows.
The parameter that is still varying in steady-state is the system frequency f which
is not exactly at 50 or 60 Hz, and as a result, the phase of the voltages and
currents would change rapidly.
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Phasor Measurement Equipment

Macrodyne Model 1690

Phasor Measurement Unit

Schweitzer Engineering Laboratories

SEL-421 Protection, Automation, and
Control System

Arbiter Power Sentinel 1133A

ABB Phasor Measurement Unit

RES 521
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Phasor Measurement Equipment

1. Generically known as a Phasor Measurement Unit (PMU)
2. Sample AC waveform using A/D converter
3. High internal sampling rate (like 2.88 or 5.76 kHz); writes/exports
data at 6-60 samples per second; USA is using 30 sps
4. Time stamped with GPS signals, high bandwidth, high accuracy
1% Total Vector Error
0.2% magnitude resolution
0.3 degree phase resolution

Frequency measurement to 0.001 Hz (1 mHz)

1 cycle (or more) measurement time
5. Phasor Data Concentrator (PDC) collects data from multiple PMUs
6. Off-nominal frequency phasor calculation

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