Database-Assisted Frequency Estimation for Power System Measurement · ·...

Database-Assisted Frequency Estimation forPower SystemMeasurement

Matthias [email protected]

| EPEC 2012 | 12th October 2012

Prof. Dr.-Ing. Jürgen GötzeInformation Processing LabFaculty of Electrical Engineering and Information TechnologyTU Dortmund University

technische universitätdortmund DT/IPLDT/IPLDT/IPL

Information Processing LabMatthias Lechtenberg

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Overview| EPEC 2012

MotivationIntroductionAn Exemplary Power NetSignal Model

EstimationCommon ApproachesPAST & ESPRIT & DaPTSymmetrical Components Transform

Simulation

Conclusion & Future Work



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Motivation| EPEC 2012

Power SystemMeasurement with PMU

Synchrophasor on basis of 50Hz/60Hz fundamental

Smart and cheap devices could do more

System health monitoring and event detection

Sammler

other PMUs

Collector KlassifikationClassificationrule-based

Actions

Synchrophasor

measuring

DeviceESPRIT etc.



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An Exemplary Power Net| EPEC 2012

39-node New England Test System (aka. NETS)

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39-node New England Test System (aka. NETS)Scenario: Line-switching (between nodes 22 and 23)

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39-node New England Test System (aka. NETS)Scenario: Line-switching (between nodes 22 and 23)Focused Node: 16 (and 21)

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39-node New England Test System (aka. NETS)Scenario: Line-switching (between nodes 22 and 23)Focused Node: 16 (and 21)Oscillation meshes

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9horizon



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LineModeling| EPEC 2012

Line modeling with inductances (L) and capacitances (C)

C/2

L

C/2Pi

Meshes of circuit including both L and C can oscillate

Events like switchings, line faults etc. can excite such mesh

→ Oscillating mesh has characteristic frequency



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Signal Model| EPEC 2012

Signal model of superposed sinusoids

x(n) =p∑

i=1

ai(n)ejnωi+jϕi + wawgn(n) =

p∑

i=1

ci(n)ejnωi + wawgn(n)

Multiple events can be described by sinusoids:

Of course fundamental system frequency (50Hz/60Hz)Harmonics of system’s fundamental (e.g. by power electronics)Characteristic frequencies of oscillation meshesBeat partners by electromagnetic componentsetc.

There are non-linear events that cannot be modeled like this

For convenience, additional white random noise is assumed



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Common Approaches for Frequency Estimation| EPEC 2012

Transforms (DFT/WT/...) Transform-based frequency estimationlike discrete Fourier or Wavelet transform can beaccurate for well-separated frequencies (withinterpolation incorporated), but mask closefrequencies (spectral masking)



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Prony’s method Prony’s method estimates the coefficients of apolynomial whose roots lead to the frequencies.Although it is common and useful, literature statesnoise sensibility.



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Prony’s method Prony’s method estimates the coefficients of apolynomial whose roots lead to the frequencies.Although it is common and useful, literature statesnoise sensibility.

Subspace-based For the autocorrelation of a signal, a space basiscan be derived which can be split in noise and signalsubspace. The basis vectors lead to the frequencies.



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PAST & ESPRIT & DaPT| EPEC 2012

OPAST ESPRIT

LS

samples

subspace basis vectors frequency candidates

rank/number

ampl. + phase

frequenciesDaPT

OPAST From windowed input samples, a specific number(rank) of basis vectors is generated

ESPRIT The one-time-step rotation of these vectors isconnected to the frequencies via an exponentialfunction

DaPT The frequencies are rated and tracked over time toseparate noise vectors and counted for rank

LS The signal model can be used with a Least Squaresapproach for estimating amplitude and phase



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PAST (Subspace Estimation)| EPEC 2012

OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Common basis of signal → EVD of autocorrelation matrix

→ Expensive

Not only one basis describing the space

Subspace estimators produce basis usually a lot cheaper (butnot necessarily orthonormal)



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PAST (Subspace Estimation)| EPEC 2012

OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Projection Approximation Subspace Tracking (Yang)

Minimizes cost function of minimal distance between samplesand predicted projection

Within, two pseudo correlation matrices are tracked(exponential weighting)

An RLS algorithm approximates an inversion

→ Iteratively produces an orthonormal basis

Variants with more sophisticated properties available



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ESPRIT (Parameter Estimation)| EPEC 2012

OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Estimating Signal Param. via Rotational Invariance Techniques

n

n+1

4 8 12 16−0.3

−0.28

−0.26

−0.24

−0.22

−0.2

−0.18

−0.16Wi([1 ... N-1])

Wi([2 ... N])

Rotational Invariance:

1 time-step: Eigenvector differs . . .

FirstN − 1 elements↔ lastN − 1:vectors differ . . .

→ . . . in constant rotation ψi = ej2π·fi/fs



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ESPRIT (Parameter Estimation)| EPEC 2012

OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Estimating Signal Param. via Rotational Invariance Techniques

n

n+1

4 8 12 16−0.3

−0.28

−0.26

−0.24

−0.22

−0.2

−0.18

−0.16Wi([1 ... N-1])

Wi([2 ... N])

Rotational Invariance:

1 time-step: Eigenvector differs . . .

FirstN − 1 elements↔ lastN − 1:vectors differ . . .

→ . . . in constant rotation ψi = ej2π·fi/fs

Parameter Estimation

Ψ = minΨ

‖W+ −ΨW−‖2 (W basis vectors)



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DaPT (Parameter Rating)| EPEC 2012

OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Database-assisted Parameter Estimation

Rule-based post-processing forparameter estimation like ESPRIT

→ Rating temporal presence of aparameter

→ Tracking of dynamic parameters

Assessment of parameters todecide whether signal or noise

start

get estimations from e.g. ESPRIT

if (fdb(i) ϵ [fest])

update db-entry of fdb(i):

≥ inc(qdb(i))≥ upd(ddb(i))

mark current estimation invalid

update db-entry of fdb(i):

≥ dec(qdb(i))

if (qdb(i) = 0)

delete entry of fdb(i)

iterate (i) through

database

iterate (j) through

[fest]

if (valid(j))

create new db-entry for fest(j)

while

yes no

yes no

end

while

yes no

end



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OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Dynamic aspects:

Difference of frequency input to field exponentially weighted

Severity: Endurance of significant difference (signed)

→ Correct frequency field in case of high severityDaPT

Entry 1Entry 2

Entry 3

Frequency

Rating

DriftDrift severityPhase diff.P. diff. sev.

...



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OPAST ESPRIT

LS

samples


rank/number

ampl. + phase

frequenciesDaPT

Dynamic aspects:

Difference of frequency input to field exponentially weighted

Severity: Endurance of significant difference (signed)

→ Correct frequency field in case of high severity

Difference of subsequent phase estimationsbased on current frequency

Severity: Endurance of significant phase drift(signed)

→ Correct frequency field in case of high severity

DaPTEntry 1Entry 2

Entry 3

Frequency

Rating

DriftDrift severityPhase diff.P. diff. sev.

...



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Symmetrical Components Transform| EPEC 2012

→ To evaluate delay of signal processing

Phases are switched with delay of 120◦ of fundamental cycle

→ In case of event, zero-component not zero

→ Simple threshold indicator

Symmetrical Components Transform, SCT

U+

U−

U0

= 1

3

1 a a2

1 a2 a

1 1 1

UA

UB

UC

with a = ej2π/3



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39-node New England Test System (aka. NETS)Scenario: Line between 22 & 23 opened after 1s of nominalservice (and closed again 2s later)Focused node for signal processing: 16 (and 21)

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Frequency Estimation| EPEC 2012

0

500

012

0.8 1 1.2 1.4 1.6 1.8 [s]

frequency

Csymmetric components negative sequence

[Hz]

[V] B

As expected: fundamental system frequency permanentlypresent



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0

500

012

0.8 1 1.2 1.4 1.6 1.8 [s]

frequency


[Hz]

[V] B


Region C: another component near fundamental

→ both produce beat (electromagnetic influence, AM)



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0

500

012

0.8 1 1.2 1.4 1.6 1.8 [s]

frequency


[Hz]

[V] B




Region B: Some additional, temporary components afterswitching



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0

500

012

0.8 1 1.2 1.4 1.6 1.8 [s]

frequency


[Hz]

[V] B




Region B: Some additional, temporary components afterswitching

Region A: SCT indicates switching;≈ 0.02s later, DaPT reacts

→ PAST window (128) + exp. window (20) + DaPT thresh. (100) =248 samples (24.8ms) worst-case → consistent



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Amplitude Estimation| EPEC 2012

0

500

0200400

0.8 1 1.2 1.4 1.6 1.8 [s]

frequency

C amplitude

[Hz]

[V] B

Amplitude estimation shows...

1 very strong fundamental component (green)

2 some barely visible components (orange)

→ explains the uncertainty about the additional components

→ Region C: beat partner small → small AMmagnitude



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Closeness Problem| EPEC 2012

A49.5

50

50.5

B2.2 2.3 2.4 2.5 2.6 2.7 [s]0

500

1k

frequency[Hz]

amplitude[V]

As mentioned, another component close to fundamental

Here, additional (orange) crosses fundamental (green)

Region A: When estimations cross

Region B: Estimations more separated than in true

→ Angle between basis vectors small

→ high matrix condition → inaccuracy



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Conclusion & Future Work| EPEC 2012

Variable-rank parameter estimation helps characterizingtransient processes

Signal model superposed sinusoids provides information onfundamental, harmonics, beats (AM) & oscillation meshes



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However, problems occur for very close parameters



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In parallel, research associates do theoretical net calculationfor verification



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In parallel, research associates do theoretical net calculationfor verification

In future, event identification with look-up-table



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Discussion| EPEC 2012

Do you have questions?

Sammler

other PMUs

Collector KlassifikationClassificationrule-based

Actions

Synchrophasor

measuring

DeviceESPRIT etc.

Matthias [email protected]+49 231 755-7017

c© 2012 by M. Lechtenberg, Information Processing Lab, TU Dortmund. Permission to reprint/republish this material foradvertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, orto reuse any copyrighted component of this work in other works must be obtained from IPL.This work was supported by (German Research Foundation).



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Database-Assisted Frequency Estimation for Power System Measurement · ·...

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