Database-Assisted Frequency Estimation for Power System Measurement

Transcription

1 Database-Assisted Frequency Estimation for Power System Measurement 12 th October2012 Prof. Dr.-Ing. Jürgen Götze Information Processing Lab Faculty of Electrical Engineering and Information Technology TU Dortmund University 1/20

2 Overview Motivation Introduction An Exemplary Power Net Signal Model Estimation Common Approaches PAST&ESPRIT&DaPT Symmetrical Components Transform Simulation Conclusion& Future Work 2/20

3 Motivation Power System Measurement with PMU Synchrophasor on basis of 50Hz/60Hz fundamental Smart and cheap devices could do more System health monitoring and event detection other PMUs measuring Device ESPRIT etc. Collector Sammler Klassifikation Classification rule-based Actions Synchrophasor 3/20

4 An Exemplary Power Net 39-node New England Test System(aka. NETS) /20

5 An Exemplary Power Net 39-node New England Test System(aka. NETS) Scenario: Line-switching(between nodes 22 and 23) // 36 4/20

6 An Exemplary Power Net 39-node New England Test System(aka. NETS) Scenario: Line-switching(between nodes 22 and 23) Focused Node: 16(and 21) // 36 4/20

7 An Exemplary Power Net 1 39-node New England Test System(aka. NETS) Scenario: Line-switching(between nodes 22 and 23) Focused Node: 16(and 21) Oscillation meshes horizon // 36 4/20

8 Line Modeling Line modeling with inductances(l) and capacitances(c) C /2 L Pi C /2 MeshesofcircuitincludingbothLandCcanoscillate Events like switchings, line faults etc. can excite such mesh Oscillating mesh has characteristic frequency 5/20

9 Signal Model Signal model of superposed sinusoids p x(n) = a i (n)e jnω i+jϕ i +w awgn (n) = i=1 p c i (n)e jnω i +w awgn (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 meshes Beat partners by electromagnetic components etc. There are non-linear events that cannot be modeled like this For convenience, additional white random noise is assumed i=1 6/20

10 Common Approaches for Frequency Estimation Transforms(DFT/WT/...) Transform-based frequency estimation like discrete Fourier or Wavelet transform can be accurate for well-separated frequencies(with interpolation incorporated), but mask close frequencies(spectral masking) 7/20

11 Common Approaches for Frequency Estimation Transforms(DFT/WT/...) Transform-based frequency estimation like discrete Fourier or Wavelet transform can be accurate for well-separated frequencies(with interpolation incorporated), but mask close frequencies(spectral masking) Prony s method Prony s method estimates the coefficients of a polynomial whose roots lead to the frequencies. Although it is common and useful, literature states noise sensibility. 7/20

12 Common Approaches for Frequency Estimation Transforms(DFT/WT/...) Transform-based frequency estimation like discrete Fourier or Wavelet transform can be accurate for well-separated frequencies(with interpolation incorporated), but mask close frequencies(spectral masking) Prony s method Prony s method estimates the coefficients of a polynomial whose roots lead to the frequencies. Although it is common and useful, literature states noise sensibility. Subspace-based For the autocorrelation of a signal, a space basis canbederivedwhichcanbesplitinnoiseandsignal subspace. The basis vectors lead to the frequencies. 7/20

13 PAST&ESPRIT&DaPT samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies LS ampl. + phase OPAST From windowed input samples, a specific number (rank) of basis vectors is generated ESPRIT The one-time-step rotation of these vectors is connected to the frequencies via an exponential function DaPT The frequencies are rated and tracked over time to separate noise vectors and counted for rank LS ThesignalmodelcanbeusedwithaLeastSquares approach for estimating amplitude and phase 8/20

14 PAST(Subspace Estimation) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies LS ampl. + phase Common basis of signal EVD of autocorrelation matrix Expensive Not only one basis describing the space Subspace estimators produce basis usually a lot cheaper(but not necessarily orthonormal) 9/20

15 PAST(Subspace Estimation) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies LS ampl. + phase Projection Approximation Subspace Tracking(Yang) Minimizes cost function of minimal distance between samples and 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 10/20

16 ESPRIT(Parameter Estimation) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies LS ampl. + phase Estimating Signal Param. via Rotational Invariance Techniques W i([1... N-1]) W i([2... N]) n n+1 Rotational Invariance: 1 time-step: Eigenvector differs... FirstN 1elements lastn 1: vectorsdiffer......inconstantrotationψ i = e j2π f i/fs 11/20

17 ESPRIT(Parameter Estimation) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies LS ampl. + phase Estimating Signal Param. via Rotational Invariance Techniques W i([1... N-1]) W i([2... N]) n n+1 Rotational Invariance: 1 time-step: Eigenvector differs... FirstN 1elements lastn 1: vectorsdiffer......inconstantrotationψ i = e j2π f i/fs Parameter Estimation Ψ =min Ψ W + ΨW 2 (W basisvectors) 11/20

18 DaPT(Parameter Rating) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies LS ampl. + phase Database-assisted Parameter Estimation Rule-based post-processing for parameter estimation like ESPRIT Rating temporal presence of a parameter Tracking of dynamic parameters start get estimations from e.g. ESPRIT iterate (i) end through while database if yes no (fdb(i) ϵ [fest]) iterate (j) update db-entry of end through while update db-entry of fdb(i): [fest] fdb(i): inc(qdb(i)) dec(qdb(i)) upd(ddb(i)) Assessment of parameters to decide whether signal or noise yes if (valid(j)) create new dbentry for fest(j) no mark current if yes estimation invalid (qdb(i) = 0) delete entry of fdb(i) no 12/20

19 DaPT(Parameter Rating) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies Dynamic aspects: LS ampl. + phase Difference of frequency input to field exponentially weighted Severity: Endurance of significant difference(signed) Correct frequency field in case of high severity DaPT Entry 1 Entry 2 Frequency Drift Drift severity Phase diff. P. diff. sev. Rating Entry /20

20 DaPT(Parameter Rating) samples OPAST subspace basis vectors ESPRIT frequency candidates DaPT rank/number frequencies Dynamic aspects: LS ampl. + phase 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 estimations based on current frequency Severity: Endurance of significant phase drift (signed) Correct frequency field in case of high severity DaPT Entry 1 Entry 2 Frequency Drift Drift severity Phase diff. P. diff. sev. Rating Entry /20

21 Symmetrical Components Transform To evaluate delay of signal processing Phasesareswitchedwithdelayof120 offundamentalcycle In case of event, zero-component not zero Simple threshold indicator Symmetrical Components Transform, SCT U + 1 a a 2 U A U = a 2 a U B with a = e j 2π/3 U U C 14/20

22 An Exemplary Power Net 1 39-node New England Test System(aka. NETS) Scenario:Linebetween22&23openedafter1sofnominal service(and closed again 2s later) Focused node for signal processing: 16(and 21) // 36 15/20

23 Frequency Estimation [Hz] frequency [V] B symmetric components C negative sequence [s] As expected: fundamental system frequency permanently present 16/20

24 Frequency Estimation [Hz] frequency [V] B symmetric components C negative sequence [s] As expected: fundamental system frequency permanently present Region C: another component near fundamental both produce beat(electromagnetic influence, AM) 16/20

25 Frequency Estimation [Hz] frequency [V] B symmetric components C negative sequence [s] As expected: fundamental system frequency permanently present Region C: another component near fundamental both produce beat(electromagnetic influence, AM) Region B: Some additional, temporary components after switching 16/20

26 Frequency Estimation [Hz] frequency [V] B symmetric components C negative sequence [s] As expected: fundamental system frequency permanently present Region C: another component near fundamental both produce beat(electromagnetic influence, AM) Region B: Some additional, temporary components after switching Region A: SCT indicates switching; 0.02s later, DaPT reacts PASTwindow(128)+exp.window(20)+DaPTthresh.(100)= 248 samples(24.8ms) worst-case consistent 16/20

27 Amplitude Estimation 500 [Hz] B frequency 0 [V] 400 amplitude [s] C 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 AM magnitude 17/20

28 Closeness Problem [Hz] frequency 49.5 [V] 1k 500 A B amplitude [s] 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 18/20

29 Conclusion& Future Work Variable-rank parameter estimation helps characterizing transient processes Signal model superposed sinusoids provides information on fundamental, harmonics, beats(am)& oscillation meshes 19/20

30 Conclusion& Future Work Variable-rank parameter estimation helps characterizing transient processes Signal model superposed sinusoids provides information on fundamental, harmonics, beats(am)& oscillation meshes However, problems occur for very close parameters 19/20

31 Conclusion& Future Work Variable-rank parameter estimation helps characterizing transient processes Signal model superposed sinusoids provides information on fundamental, harmonics, beats(am)& oscillation meshes However, problems occur for very close parameters In parallel, research associates do theoretical net calculation for verification 19/20

32 Conclusion& Future Work Variable-rank parameter estimation helps characterizing transient processes Signal model superposed sinusoids provides information on fundamental, harmonics, beats(am)& oscillation meshes However, problems occur for very close parameters In parallel, research associates do theoretical net calculation for verification In future, event identification with look-up-table 19/20

33 Discussion Do you have questions? other PMUs measuring Device ESPRIT etc. Collector Sammler Klassifikation Classification rule-based Actions Synchrophasor c 2012 by M. Lechtenberg, Information Processing Lab, TU Dortmund. Permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or toreuseanycopyrightedcomponentofthisworkinotherworksmustbeobtainedfromipl. This work was supported by (German Research Foundation). 20/20