innovation

Federal Institute of Santa Catarina Electrical Engineering

Nov-Dec 2013, DD 1

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 2

Outline

Objective

Motivation

Phasor Measurement Process

Phasor Definition

PMU Architectures

PMU Simulink Simulator

Simulations

Conclusions

Future Developments


Nov-Dec 2013, DD 3

Objective

To present the design of a Simulink-based Phasor

Measurement Unit (PMU) Simulator


Nov-Dec 2013, DD 4

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


Nov-Dec 2013, DD 5

What is a Phasor?

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)

0t

A

Phasor representation of a sinusoidal wave form

A

2 cos 2 60

Re 2 j

x t A t

Ae


Nov-Dec 2013, DD 6

Anatomy of a PMU

Adapted from Ken Martin and Arun Phadke

There is no standardization on the algorithms used inside a PMU or the number of cycles used in computing a phasor


Nov-Dec 2013, DD 7

PMU Architectures

Analog

Filter

A/D

Converter

Digital

Filter

Phasor

Estimator

Frequency

Estimator

Sampling

Clock

Analog

Filter

A/D

Converter

Digital

Filter

Phasor

Estimator

Frequency

Estimator

Sampling

Clock

x(t)

X(k)

x(t)

x(k)

X(k)

x(k)

Frequency Tracking Frequency Compensation

Non-Uniform Sampling

Uniform Sampling (first one)


Nov-Dec 2013, DD 8


Sine Wave Window Size (points)

sf NfSampling rate

For N=12

0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03 0.032-1.5

-1

-0.5

0

0.5

1

1.5

Time(s)

Mag

nit

ud

e (p

u)

Time-Domain Signal

1/fs

N=12

12N

Sampling period 1

s

s

Tf

Regular sampling period (Ts)

12 60 720sf Hz 0.0014sT s


Nov-Dec 2013, DD 9


Time Domain

Frequency Domain

( )n nx x tSamples

, 0, , -1n st nT n N

( )mj

mX X e

2, 0, , -1m m m N

N

where

DFT

0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028 0.03 0.032-1.5

-1

-0.5

0

0.5

1

1.5

Time(s)

Mag

nit

ud

e (p

u)

Time-Domain Signal

1/fs

N=12

12N


Nov-Dec 2013, DD 10

Definition of DFT

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

Phasor Estimation

21

0

2 N j nmN

m n

n

X x eN

21

0

2 N j nN

n

n

X x eN

Fundamental frequency component, set m=1


Nov-Dec 2013, DD 11

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

Frequency Estimation


Nov-Dec 2013, DD 12

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

neighborhood


45 50 55 60 65 70 750

2

4

6

8

10

12Relative Error - LES

Frequency (Hz)

Re

lative

Err

or

(%)


Nov-Dec 2013, DD 13

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

Sensible to large negative sequence component

Fault conditions


X1( )( ) k

j tV k Ae

0( )( ) kj t

Z k e

1 0[( ) ]( ) kj t

Y k Ae


Nov-Dec 2013, DD 14

Phasor Angle Changing

Based on the idea that

Use positive sequence phasor estimation

Present satisfactory results under large frequency variations

Used in commercial PMUs

Phasor angle changing and demodulation presented

satisfactory results


1( )

2f t

t


Nov-Dec 2013, DD 15

Results for frequency ramp


Demodulation Angle Changing


Nov-Dec 2013, DD 16

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.

Pos-Processing

where

N - window size w actual frequency w0 nominal frequency

*

mes true trueX PX QX

Phasor correction

0

0

0( )

( 1)2

0

0( )

( 1)2

0

( )

2{ }( )

2

( )

2{ }( )

2

tj N

tj N

N tsin

P et

Nsin

N tsin

Q et

Nsin


Nov-Dec 2013, DD 17

The P factor is directly influence by N and frequency value

P behavior under frequency variation (N=48)

Pos-Processing

-5 -4 -3 -2 -1 0 1 2 3 4 50.985

0.99

0.995

1

1.005

Mag

nit

ude

Complex Gain P

-5 -4 -3 -2 -1 0 1 2 3 4 5-20

-10

0

10

20

Frequency Variation (Hz)

Angle

(d

egre

ss)


Nov-Dec 2013, DD 18

PMU Block Diagram Frequency Compensation

DFT

Frequency

estimation

Filtering*

Look up table with

calibration factor

X

2

1 2 ( )j n

N n N n NN n nX X x x e

N

measured

nX

nP

( )nx t

0

0( )

( 1)2

0

( )sin

2{ }( )

sin2

tj N

n

N t

P et

N

filtering

true nn

n

XX

P

filtering

nXtrue

nX

sampling period

N - window size

0

tFixed

Post-Processing

1

2

Filtering*

A Average Filter

B Windowing

(C) Least Squares

*D. Dotta and J. H. Chow. Phasor Measurement Estimation Second Harmonic Filtering. IEEE Trans. Power Delivery, 2013.


Nov-Dec 2013, DD 19

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)



Nov-Dec 2013, DD 20

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



Nov-Dec 2013, DD 21

Main Window

Teaching Tool PMU Simulink Simulator

Switch 2

Switch 1

Step

0

Ramp

1

PlotingArea

SP_MF

SP_MnF

PS_M

PS_Md

PS_A

PS_Ad

FD

PMU

Disturbance

Frequency Goal

SP_MF

SP_MnF

PS_M

PS_Md

PS_A

PS_Ad

Frequency Deviation

NominalFrequency

60

FrequencyGoal

59


Nov-Dec 2013, DD 22

Main Components


Frequency

Deviation

7

PS_Ad6

PS_A5

PS_Md4

PS_M3

SP_MnF2

SP_MF1

Three-Phase

Signal Producer

Frequency

Type

Phase A

Phase B

Phase C

Symmetrical

Components

Phasor A

Phasor B

Phasor C

P_PS

Single-PhaseProcessing

Phasor A

CF

SP_MF

SP_MnF

Phasor

Estimation

Phase A

Phase B

Phase C

Phasor A

Phasor B

Phasor CLookup

Table

P_ PS

FD

CF

PS_M

PS_A

Frequency

Estimation

P_PS FD

Downsampling

PS_M

PS_A

PS_Md

PS_Ad

Frequency

Goal

2

Disturbance1


Nov-Dec 2013, DD 23

Frequency Step (1 Hz)

Simulations

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5-2

-1

0

1

2Phase A - Signal Input

Ma

gn

itu

de

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.559

59.5

60

Time(s)

Hz

Frequency

Estimated

Reference

Frequency Sampling = 2.88 kHz


Nov-Dec 2013, DD 24

Positive Sequence

Simulations

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.9

0.95

1

1.05

1.1

Time (s)

Ma

gn

itu

de

(p

u)

Positive Sequence Magnitude - Downsampling

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200

-150

-100

-50

0

50

100

150

200

250

Time (s)

An

gle

(d

eg

ree

s)

Positive Sequence Angle - Downsampling

2


Nov-Dec 2013, DD 25

Positive Sequence (Ramp +1Hz)

Simulations

1.5 2 2.5 3 3.5 4 4.5

-150

-100

-50

0

50

100

150

Time (s)

An

gle

(d

eg

ree

s)

Downsampling Angle - Ramp Disturbance

Positive Frequency Ramp between 2-3 seconds


Nov-Dec 2013, DD 26

Positive Sequence Complex Gain P Influence

Simulations

Frequency Step Disturbance

1.8 1.9 2 2.1 2.2 2.3

0.9994

0.9995

0.9996

0.9997

0.9998

0.9999

1

1.0001

1.0002

Time (s)

Ma

gnitu

de (

pu)

PS Magnitude - Before Correction


Nov-Dec 2013, DD 27

Positive Sequence Complex Gain P Influence

Simulations

Frequency Ramp Disturbance

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6

0.9995

0.9996

0.9997

0.9998

0.9999

1

Time (s)

Ma

gn

itu

de

(p

u)

PS Magnitude - Before Correction


Nov-Dec 2013, DD 28

Single-Phase Complex Gain Q Influence

Simulations

Frequency Step Disturbance


Nov-Dec 2013, DD 29


Simulations

Before Downsampling

1.99 2 2.01 2.02 2.03 2.04 2.05 2.06 2.07

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

Time (s)

Ma

gn

itu

de

(p

u)

Single-Phase Magnitude


Nov-Dec 2013, DD 30


Simulations

After Downsampling

2 2.5 3 3.5 4

0.985

0.99

0.995

1

1.005

1.01

Ma

ng

nitu

de

(p

u)

Time (s)

Single-Phase Filtering and Downsampling


Nov-Dec 2013, DD 31

Positive Sequence Complex Gain Q Influence

Simulations

Unbalanced Operation (5%)

1.5 2 2.5 3 3.5 4 4.5

0.9994

0.9996

0.9998

1

1.0002

Time (s)

Ma

gn

itu

de

(p

u)

Positive Sequence - Unbalanced Operation


Nov-Dec 2013, DD 32

Frequency Step

Real Data

0 5 10 15 20 25 30 35 4048

48.5

49

49.5

50

50.5

51

Time (s)

Hz

Real Data - Frequency


Nov-Dec 2013, DD 33

Single-Phase Performance

Real Data

10 15 20 25 30 35 4010.6

10.7

10.8

10.9

11

11.1

11.2

11.3

Time(s)

Mag

nit

ud

e (V

)

Single-Phase - Real Data

1 Hz Oscillation


Nov-Dec 2013, DD 34

Single-Phase Performance Zoom

Real Data

1 Hz Oscillation - Show up in Frequency Spectrum

24 26 28 30 32 34 36 38

11.295

11.3

11.305

11.31

11.315

11.32

11.325

Time(s)

Mag

nit

ud

e (V

)

Single-Phase - Real Data


Nov-Dec 2013, DD 35

Positive Sequence

Real Data

15 20 25 3010.6

10.7

10.8

10.9

11

11.1

11.2

11.3

Time(s)

Mag

nit

ud

e (V

)

Magnitude - Positive Sequence


Nov-Dec 2013, DD 36

Conclusions


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


Nov-Dec 2013, DD 37

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


Nov-Dec 2013, DD 38

Power Transfer Paths/Interfaces


Nov-Dec 2013, DD 39

State Estimator

PMU

PMU

PMU

PMU

PDC

State

Estimator

(Only Phasors)

Phasor

Data

Network

Status

Network

Parameters

Trustable Data

for

Applications


Nov-Dec 2013, DD 40

Contact

Contact Daniel Dotta: [email protected]


Nov-Dec 2013, DD 41

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


Nov-Dec 2013, DD 42


Nov-Dec 2013, DD 43

Time Synchronization

GOES (Geostationary Operational Environmental Satellite (NASA)): 25-100 micro-second 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


Nov-Dec 2013, DD 44

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


Nov-Dec 2013, DD 45

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.


Nov-Dec 2013, DD 46

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


Nov-Dec 2013, DD 47

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

Documents

innovation