# A Novel Framework for Synchrophasor Based Online Recognition and Efficient Post-Mortem Analysis of Disturbances in Power Systems

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## Abstract

**:**

## Featured Application

**Synchrophasor based data compression and post-mortem analysis as well as online detection and classification of grid disturbances.**

## Abstract

## 1. Introduction

## 2. Synchrophasor Technology and State of the Art Applications

#### 2.1. Application of Synchrophasors in Modern Control Centers

- A clear determination of accurate, dynamic operating limits (i.e., phase-angle differences, or oscillations) is not available, which diminishes the value of the information gain for the system operation.
- The data quality still strongly depends on the quality of the instrument transformers, as well as the ICT infrastructure.
- The rising observability due to a newly installed WAMS can lead to an exposition of new issues, which can lead to a commitment of valuable personnel to investigate the problems.
- Unless some TSOs exchange data of strategic important PMUs, the data exchange is often subject to cyber security issues or other sensitivities.
- A separate development of EMS and WAMS lead to challenges for human operators, who prefer a single unified user interface to support a smoother workflow and a clear decision-making.
- A general evaluation scheme of system dynamics and correlating actions still needs to be defined.
- An operator training, addressing the understanding and the interpretation of dynamic phenomena, needs to be established to raise the level of operator awareness and to establish a flexible response to events, instead of a mainly rule-based operation.

#### 2.2. Enhanced Situational Awareness

#### 2.3. State of the Art Analysis of Synchrophasor Based Detection and Mitigation of Critical Events

## 3. Novel Framework for Advanced Synchrophasor Analysis in Modern Control Centres

#### 3.1. Framework Architecture and Analysis Modules

#### 3.2. Spatiotemporal Synchrophasor Data Compression

#### 3.3. Disturbance Extraction (Post-Mortem Analysis)

#### 3.4. Disturbance Detection

#### 3.5. Disturbance Classification

- preprocessing: normalize the input data into a suitable data range,
- feature extraction: extract relevant features to distinguish between the given classes,
- classification: compute affiliation values (e.g., probabilities) for each class using the features and
- decision-making: final class assignment of the current observation based on the maximum affiliation value.

#### 3.6. Curative Actions

## 4. Results from Case Studies

#### 4.1. Dynamic Grid Simulations

#### 4.1.1. Grid Topology and Key Assumptions

^{®}Programming Language (DPL) script controls the simulations with regard to events creation, stability check and saving of the results. For each operational point, about 440 different contingencies are simulated considering generator outages, line trips, short circuits at different line positions, partial photovoltaic (PV) outages as well as partial load losses. An online assessment of the simulated signals checks the system stability and aborts the current simulation in case of violations of predefined frequency or voltage limits. The RMS values are averaged to extract PMU signals at the given temporal resolution of 40 ms (corresponds to 25 f.p.s.). Compared to field measurements, the phasor estimation procedure and consequent signal deviations (e.g., filtering effects) are neglected.

#### 4.1.2. Dynamic Simulation Results

#### 4.2. Validation of Synchrophasor Applications Using Field Measurements

#### 4.2.1. Results from Spatiotemporal Synchrophasor Data Compression

^{®}with the implementation of an additional toolbox for wavelet decomposition [63].

#### 4.2.2. Results from Synchrophasor Disturbance Extraction

^{®}with an additional open-source implementation for the S transform [63,64] and a JAVA

^{®}based library for Isometric mapping [65]. The outlier detection methods were taken from the JAVA

^{®}based ELKI (Environment for Developing KDD-Applications Supported by Index-Structures) data mining framework [66].

#### 4.3. Validation of Synchrophasor Applications Using Dynamic Grid Simulations

#### 4.3.1. Results from Synchrophasor Disturbance Detection

^{®}with additional packages for wavelet decomposition [67] and statistical analysis [68].

#### 4.3.2. Results from Synchrophasor Disturbance Classification

^{®}with additional packages for statistical analysis [68] as well as for creating and training of neural networks [70].

## 5. Synchrophasor Online Visualization Tool for Enhanced Operator Guidance

^{®}database and continuously updated at the front end applying the Highcharts

^{®}visualization framework. This enables a good interpretability of the results and gives the operator access to the online PMU streaming data as well as notifications for potential disturbances or critical system states. Some exemplary visualization charts for the disturbance detection module and disturbance classification module are given in Figure 24.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$\mathit{X}$, ${\mathit{X}}_{\mathrm{N}}$ | raw PMU measurement matrix, normalized PMU measurement matrix |

$N$ | number of PMU measurement samples |

$\mathit{H}$, $\underset{\_}{h}$ | hidden state matrix, hidden state vector |

$T$, $t$ | number of PMU measurement time steps, single time step |

$Q$, $P$, $K$ | number of hidden dimensions, number of features, number of measurements |

$\alpha $, $s$ | attention weight and score value |

${\underset{\_}{x}}_{\mathrm{F}}$, ${\mathit{X}}_{\mathrm{F}}$ | feature vector, feature matrix |

${\underset{\_}{x}}_{\mathrm{P}}$ | class probability vector |

$\underset{\_}{z}$ | z-score vector |

$\mu $, $\sigma $ | sampled mean, sampled standard deviation |

$y$, ${y}_{\mathrm{Loc}}$, ${y}_{\mathrm{Type}}$ | disturbance event, event location, event type |

${\underset{\_}{\theta}}_{\mathrm{F}}$, ${\underset{\_}{\theta}}_{\mathrm{E}}$, ${\underset{\_}{\theta}}_{\mathrm{C}}$ | parameter for feature extraction, embedding, classification |

## Appendix A

## References

- Tielens, P.; van Hertem, D. The relevance of inertia in power systems. Renew. Sustain. Energy Rev.
**2016**, 55, 999–1009. [Google Scholar] [CrossRef] - Rezkalla, M.; Pertl, M.; Marinelli, M. Electric power system inertia: Requirements, challenges and solutions. Electr. Eng.
**2018**, 100, 2677–2693. [Google Scholar] [CrossRef][Green Version] - Grossman, P.Z.; Cole, D.H. (Eds.) The End of A Natural Monopoly: Deregulation and Competition in the Electric Power Industry; Routledge: London, UK, 2014. [Google Scholar]
- Brahma, S.; Kavasseri, R.; Cao, H.; Chaudhuri, N.R.; Alexopoulos, T.; Cui, Y. Real-Time Identification of Dynamic Events in Power Systems Using PMU Data, and Potential Applications—Models, Promises, and Challenges. IEEE Trans. Power Deliv.
**2017**, 32, 294–301. [Google Scholar] [CrossRef] - Sass, F.; Sennewald, T.; Brosinsky, C.; Westermann, D.; Mangold, M.; Heyde, C.; Becher, S.; Krebs, R. Control Center Implementation of Advanced Optimization and Decision Support Applications. In Proceedings of the 2018 International Conference on Smart Energy Systems and Technologies (SEST), Sevilla, Spain, 13–14 November 2018; pp. 1–6. [Google Scholar]
- Liu, Y.; Wu, L.; Li, J. D-PMU based applications for emerging active distribution systems: A review. Electr. Power Syst. Res.
**2020**, 179, 106063. [Google Scholar] [CrossRef] - Dahal, N.; Abuomar, O.; King, R.; Madani, V. Event stream processing for improved situational awareness in the smart grid. Expert Syst. Appl.
**2015**, 42, 6853–6863. [Google Scholar] [CrossRef] - IEEE Standard for SCADA and Automation Systems; C37.1-2007; IEEE: Piscataway, NJ, USA, 2008.
- Maghsoodlou, F.; Masiello, R.; Ray, T. Energy management systems. IEEE Power Energy Mag.
**2004**, 2, 49–57. [Google Scholar] [CrossRef] - Nuthalapati, S. Power System Grid Operation Using Synchrophasor Technology; Springer International Publishing: Cham, Switzerland, 2019. [Google Scholar]
- Fernwirkeinrichtungen und -systeme—Teil 5-104: Übertragungsprotokolle—Fernwirkeinrichtungen und -systeme —Teil 5-104: Übertragungsprotokolle—Zugriff für IEC 60870-5-101 auf Netze mit genormten Transportprofilen. DIN EN 60870-5-104:2006 (IEC 60870-5-104:2006). Available online: https://webstore.iec.ch/publication/3746 (accessed on 10 September 2018).
- IEEE Standard for Electric Power Systems Communications-Distributed Network Protocol (DNP3); IEEE: Piscataway, NJ, USA, 2012; pp. 1815–2012.
- Morisson, K.; Kamwa, I.; Glavic, M. Review of On-Line Dynamic Security Assessment Tools and Techniques: Cigré WG C4.601; Technical Brochure No. 325; CIGRE: Paris, France, 2007. [Google Scholar]
- Phadke, A.G.; Pickett, B.; Adamiak, M.; Begovic, M.; Benmouyal, G.; Burnett, R.O.; Cease, T.W.; Goossens, J.; Hansen, D.J.; Kezunovic, M.; et al. Synchronized sampling and phasor measurements for relaying and control. IEEE Trans. Power Deliv.
**1994**, 9, 442–452. [Google Scholar] [CrossRef] - IEEE/IEC International Standard—Measuring Relays and Protection Equipment—Part 118–1: Synchrophasor for Power Systems—Measurements; IEEE: Piscataway, NJ, USA, 2011.
- Khan, R.; McLaughlin, K.; Laverty, D.; Sezer, S. IEEE C37.118-2 Synchrophasor Communication Framework —Overview, Cyber Vulnerabilities Analysis and Performance Evaluation. In Proceedings of the 2nd International Conference on Information Systems Security and Privacy, Rome, Italy, 19 February 2016; pp. 167–178. [Google Scholar]
- Power System Relaying Committee. IEEE Guide for Phasor Data Concentrator Requirements for Power System Protection, Control, and Monitoring; IEEE: Piscataway, NJ, USA, 2013. [Google Scholar]
- IEEE Standard for Synchrophasor Data Transfer for Power Systems; C37.118.2-2011; IEEE: Piscataway, NJ, USA, 2011.
- Baigent, D.; Adamiak, M.; Mackiewicz, R.; Sisco, G. IEC 61850 communication networks and systems in substations: An overview for users. SISCO Syst.
**2004**, 1–8. [Google Scholar] - TC 57—Power Systems Management and Associated Information Exchange, Ed., IEC TR 61850-90-5:2012: Communication Networks and Systems for Power Utility Automation—Part 90-5: Use of IEC 61850 to transmit synchrophasor information according to IEEE C37.118. Technical Report. May 2012. Available online: https://webstore.iec.ch/publication/6026 (accessed on 4 March 2020).
- Sass, F.; Sennewald, T.; Westermann, D. Automated Corrective Actions by VSC-HVDC-Systems: A Novel Remedial Action Scheme. IEEE Trans. Power Syst.
**2020**, 35, 385–394. [Google Scholar] [CrossRef] - Patel, M.A.; Aivaliotis, S.; Ellen, E. North American Electric Reliability Corporation Nerc. Real-Time Application of Synchrophasors for Improving Reliability; North American Electric Reliability Corporation (NERC): Princeton, NJ, USA, 2010. [Google Scholar]
- Brosinsky, C.; Kummerow, A.; Naumann, A.; Kronig, A.; Balischewski, S.; Westermann, D. A new development platform for the next generation of power system control center functionalities for hybrid AC-HVDC transmission systems. In Proceedings of the 2017 IEEE Power & Energy Society General Meeting, Chicago, IL, USA, 16–20 July 2017; pp. 1–5. [Google Scholar]
- Kummerow, A.; Brosinsky, C.; Monsalve, C.; Nicolai, S.; Bretschneider, P.; Westermann, D. PMU-based online and offline applications for modern power system control centers in hybrid AC-HVDC transmission systems. In Proceedings of the International ETG Congress, Esslingen am Neckar, Germany, 8–9 May 2019; Vde Verlag Gmbh Berlin Offenbach: Offenbach am Main, Germany, 2019; pp. 405–410. [Google Scholar]
- Cigré, Wide Area Monitoring Systems—Support for Control Room Applications; Technical Brochure 750; Cigrè Working Group C2.17: Germany; CIGRE: Paris, France, 2018.
- Endsley, M.R. Toward a Theory of Situation Awareness in Dynamic Systems. Hum. Factors
**1995**, 37, 32–64. [Google Scholar] [CrossRef] - Prostejovsky, A.M.; Brosinsky, C.; Heussen, K.; Westermann, D.; Kreusel, J.; Marinelli, M. The future role of human operators in highly automated electric power systems. Electr. Power Syst. Res.
**2019**, 175, 105883. [Google Scholar] [CrossRef][Green Version] - Li, W.; Wang, M.; Chow, J.H. Real-Time Event Identification Through Low-Dimensional Subspace Characterization of High-Dimensional Synchrophasor Data. IEEE Trans. Power Syst.
**2018**, 33, 4937–4947. [Google Scholar] [CrossRef] - Yadav, R.; Pradhan, A.K.; Kamwa, I. Real-Time Multiple Event Detection and Classification in Power System using Signal Energy Transformations. IEEE Trans. Ind. Inf.
**2018**, 10. [Google Scholar] [CrossRef] - Biswal, M.; Brahma, S.M.; Cao, H. Supervisory Protection and Automated Event Diagnosis Using PMU Data. IEEE Trans. Power Deliv.
**2016**, 31, 1855–1863. [Google Scholar] [CrossRef] - Li, M. Transient Stability Prediction based on Synchronized Phasor Measurements and Controlled Islanding; Doctor of Philosophy, Electrical Engineering; Virginia Polytechnic Institute and State University: Blacksburg, VA, USA, 2013. [Google Scholar]
- Zhou, Y.; Wu, J.; Yu, Z.; Ji, L.; Hao, L. A Hierarchical Method for Transient Stability Prediction of Power Systems Using the Confidence of a SVM-Based Ensemble Classifier. Energies
**2016**, 9, 778. [Google Scholar] [CrossRef][Green Version] - Terzija, V.; Valverde, G.; Cai, D.; Regulski, P.; Madani, V.; Fitch, J.; Skok, S.; Begovic, M.M.; Phadke, A. Wide-Area Monitoring, Protection, and Control of Future Electric Power Networks. Proc. IEEE
**2011**, 99, 80–93. [Google Scholar] [CrossRef] - Singh, B.; Sharma, N.K.; Tiwari, A.N.; Verma, K.S.; Singh, S.N. Applications of phasor measurement units (PMUs) in electric power system networks incorporated with FACTS controllers. Int. J. Eng. Sci. Tech.
**2011**, 3. [Google Scholar] [CrossRef][Green Version] - Muller, S.C.; Kubis, A.; Brato, S.; Hager, U.; Rehtanz, C.; Gotze, J. New applications for Wide-Area Monitoring, Protection and Control. In Proceedings of the 2012 3rd IEEE PES Innovative Smart Grid Technologies Conference Europe, Berlin, Germany, 14–17 October 2012; pp. 1–8. [Google Scholar]
- Pinte, B.; Quinlan, M.; Reinhard, K. Low Voltage Micro-Phasor Measurement Unit (μPMU). In 2015 IEEE Power and Energy Conference at Illinois (PECI): PECI 2015: University of Illinois at Urbana-Champaign, Proceedings of the I-Hotel and Conference Center, Champaign, IL, USA, 20–21 February 2015; IEEE: Champaign, IL, USA, 2015; pp. 1–4. [Google Scholar]
- Arghandeh, R. Micro-Synchrophasors for Power Distribution Monitoring, A Technology Review. 2016. Available online: https://arxiv.org/pdf/1605.02813 (accessed on 4 March 2020).
- Konakalla, S.A.R.; de Callafon, R.A. Feature Based Grid Event Classification from Synchrophasor Data. Procedia Comput. Sci.
**2017**, 108, 1582–1591. [Google Scholar] [CrossRef] - Ma, R.; Basumallik, S.; Eftekharnejad, S. A PMU-Based Multivariate Model for Classifying Power System Events. 2018. Available online: https://arxiv.org/pdf/1812.00246 (accessed on 18 April 2020).
- Hannon, C.; Deka, D.; Jin, D.; Vuffray, M.; Lokhov, A.Y. Real-Time Anomaly Detection and Classification in Streaming PMU Data. 2019. Available online: https://arxiv.org/pdf/1911.06316 (accessed on 18 April 2020).
- Gharavi, H.; Hu, B. Space-Time Approach for Disturbance Detection and Classification. IEEE Trans. Smart Grid
**2018**, 9, 5132–5140. [Google Scholar] [CrossRef] - Singh, A.K.; Fozdar, M. Supervisory Framework for Event Detection and Classification using Wavelet Transform. In Proceedings of the Institute of Electrical and Electronics Engineers, Power & Energy Society General Meeting, Chicago, IL, USA, 16–20 July 2017; pp. 1–5. [Google Scholar]
- Negi, S.S.; Kishor, N.; Uhlen, K.; Negi, R. Event Detection and Its Signal Characterization in PMU Data Stream. IEEE Trans. Ind. Inf.
**2017**, 13, 3108–3118. [Google Scholar] [CrossRef][Green Version] - Kummerow, A.; Nicolai, S.; Bretschneider, P. Spatial and Temporal PMU Data Compression for Efficient Data Archiving in Modern Control Centres. In Proceedings of the 2018 IEEE International Energy Conference (ENERGYCON), Limassol, Cyprus, 3–7 June 2018; pp. 1–6. [Google Scholar]
- Marteau, P.-F. Time warp edit distance with stiffness adjustment for time series matching. IEEE Trans. Pattern Anal. Mach. Intell.
**2009**, 31, 306–318. [Google Scholar] [CrossRef] [PubMed][Green Version] - Han, J.; Kamber, M.; Pei, J. Data Mining: Concepts and Techniques, 3rd ed; Amsterdam: Elsevier/Morgan Kaufmann. 2012. Available online: http://ebookcentral.proquest.com/lib/subhh/detail.action?docID=729031 (accessed on 18 April 2020).
- Breunig, M.M.; Kriegel, H.-P.; Ng, R.T.; Sander, J. LOF: Identifying Density-Based Local Outliers. In Proceedings of the 2000 ACM SIGMOD International Conference on Management of data, Dallas, TX, USA, 16–18 May 2000; pp. 93–104. [Google Scholar]
- Kriegel, H.-P.; Kroger, P.; Schubert, E.; Zimek, A. Outlier Detection in Arbitrarily Oriented Subspaces. In Proceedings of the IEEE 12th International Conference on Data Mining (ICDM), Brussels, Belgium, 10–13 December 2012; proceedings: Brussels, Belgium, 2012; pp. 379–388. [Google Scholar]
- Kummerow, A.; Nicolai, S.; Bretschneider, P. Outlier Detection Methods for Uncovering of Critical Events in Historical Phasor Measurement Records. E3S Web. Conf.
**2018**, 64. [Google Scholar] [CrossRef] - Kummerow, A.; Nicolai, S.; Bretschneider, P. Ensemble approach for automated extraction of critical events from mixed historical PMU data sets. In Proceedings of the 2018 IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, USA, 5–10 August 2018; pp. 1–5. [Google Scholar]
- Pimentel, M.A.F.; Clifton, D.A.; Clifton, L.; Tarassenko, L. A review of novelty detection. Signal Process.
**2014**, 99, 215–249. [Google Scholar] [CrossRef] - Janssens, J.H.M. Outlier Selection and One-Class Classification, Dissertation; Tilburg University: Tilburg, The Netherlands, 2013. [Google Scholar]
- Bagnall, A.; Lines, J.; Bostrom, A.; Large, J.; Keogh, E. The great time series classification bake off: A review and experimental evaluation of recent algorithmic advances. Data Min. Knowl. Disc.
**2017**, 31, 606–660. [Google Scholar] [CrossRef][Green Version] - Esling, P.; Agon, C. Time-series data mining. ACM Comput. Surv.
**2012**, 45, 1–34. [Google Scholar] [CrossRef][Green Version] - Gamboa, J.C.B. Deep Learning for Time-Series Analysis; CoRR, abs/1701.01887, 2017. Available online: http://arxiv.org/abs/1701.01887, (accessed on 18 April 2020).
- Wang, Z.; Yan, W.; Oates, T. Time series classification from scratch with deep neural networks: A strong baseline. In Proceedings of the IJCNN 2017: The International Joint Conference on Neural Networks, Anchorage, AK, USA, 14–19 May 2017; pp. 1578–1585. [Google Scholar]
- Goodfellow, I.; Bengio, Y.; Courville, A. Deep Learning; MIT Press: Cambridge, MA, USA; London, UK, 2016; Available online: http://www.deeplearningbook.org/ (accessed on 4 April 2020).
- Kummerow, A.; Monsalve, C.; Nicolai, S.; Bretschneider, P. Simultaneous Online Identification and Localization of Disturbances in Power Transmission Systems. In Proceedings of the 2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT-Europe), Bucharest, Romania, 29 September 2019; pp. 1–5. [Google Scholar]
- Kummerow, A. Robuste Online-Klassifikation kritischer Netzereignisse unter Berücksichtigung von Störgrößen. In Proceedings of the 29. Workshop Computational Intelligence, Dortmund, Germany, 28–29 November 2019; Hoffmann, F., Hüllermeier, E., Mikut, R., Eds.; KIT Scientific Publishing: Karlsruhe, Baden, 2019; pp. 189–208. [Google Scholar]
- Zhou, P.; Shi, W.; Tian, J.; Qi, Z.; Li, B.; Hao, H.; Xu, B. Attention-Based Bidirectional Long Short-Term Memory Networks for Relation Classification. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), Berlin, Germany, 7–12 August 2016; pp. 207–212. [Google Scholar]
- Westermann, D.; Schlegel, S.; Sass, F.; Schwerdfeger, R.; Wasserrab, A.; Haeger, U.; Dalhues, S.; Biele, C.; Kubis, A.; Hachenberger, J. Curative actions in the power system operation to 2030. In Proceedings of the International ETG Congress, Esslingen am Neckar, Germany, 8–9 May 2019; VDE Verlag GMBH Berlin Offenbach: Offenbach am Main, Germany, 2019. [Google Scholar]
- Allen, A.; Singh, M.; Nrel, E.M.; Santoso, S. University of Texas at Austin, PMU Data Event Detection: A User Guide for Power Engineers, Technical Report, NREL National Renewable Energy Laboratory, The University of Texas at Austin NREL/TP-5D00-61664. 2014. Available online: https://www.osti.gov/biblio/1160181 (accessed on 10 September 2018).
- I. The MathWorks (Ed.) MATLAB 7.5 and Signal Processing Toolbox 6.1, Statistics Toolbox 6.1, Wavelet Toolbox 4.1; I. The MathWorks: Natick, MA, USA, 2007. [Google Scholar]
- Sundar, A. Time Frequency Distribution of a Signal Using S-transform: Stockwell Transform, This Function Gives the Time-Frequency Distribution Using S-transform in Matlab. 2015. Available online: https://de.mathworks.com/matlabcentral/fileexchange/51808-time-frequency-distribution-of-a-signal-using-s-transform-stockwell-transform (accessed on 2 August 2018).
- Raff, E. JSAT: Java Statistical Analysis Tool, a Library for Machine Learning. J. Mach. Learn. Res.
**2017**, 18, 1–5. Available online: http://jmlr.org/papers/v18/16-131.html (accessed on 20 September 2017). - Achtert, E.; Goldhofer, S.; Kriegel, H.-P.; Schubert, E.; Zimek, A. Evaluation of Clusterings—Metrics and Visual Support. Washington, DC, USA (Arlington, Virginia). 1–5 April 2012. pp. 1285–1288. Available online: https://doi.org/10.1109/ICDE.2012.128 (accessed on 20 September 2017).
- Lee, G.; Gommers, R.; Wohlfahrt, K.; O’Leary, A.; Nahrstaedt, H. PyWavelets—Wavelet Transforms in Python. 2006. Available online: https://github.com/PyWavelets/pywt (accessed on 18 April 2020).
- Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res.
**2011**, 12, 2825–2830. [Google Scholar] - Tieleman, T.; Hinton, G. Lecture 6.5-RmsProp: Divide the gradient by a running average of its recent magnitude. COURSERA Neural Netw. Mach. Learn.
**2012**, 4, 26–31. [Google Scholar] - Keras, C.F. Keras: GitHub: 2015. Available online: http://github.com/fchollet/keras (accessed on 18 April 2020).

**Figure 8.**Embedding functions using feedforward neural network (

**left**), parametric attention model (

**middle**) and non-parametric attention model (

**right**).

**Figure 10.**Exemplary simulations of four PMUs for a partial PV outage at station 2D3 (50% loss of installed capacity) including frequencies (

**top and bottom left**) and voltage magnitudes (

**top and bottom right**) for two operational points.

**Figure 11.**Exemplary simulations of four PMUs for a short circuit at line L19 (90% line length) including frequencies (

**top and bottom left**) and voltage magnitudes (

**top and bottom right**) for two operational points.

**Figure 12.**Original vs. reconstructed voltage magnitudes (

**left**) and frequencies (

**right**) after the spatiotemporal data compression.

**Figure 13.**Voltage magnitudes (

**top**), voltage angles (

**bottom left**) and frequency (

**bottom right**) raw signals from the MVField dataset.

**Figure 14.**Outlier scores for different combinations of outlier detection techniques (LOF at

**top and bottom left**, SiLiOd at

**top right**and COP at

**bottom right**) and dimension reduction techniques (PCA at

**top left and right**, Isomap at

**bottom left and right**) using features from time-domain.

**Figure 19.**Example frequency (

**top and bottom left**), voltage magnitude (

**top and bottom middle**) and voltage angle (

**top and bottom right**) patterns for low to medium anomaly scores (

**top left to right**) and high anomaly scores (

**bottom left to right**).

**Figure 21.**Receiver operating characteristics for training (

**left**) and validation (

**right**) predictions.

**Figure 24.**Exemplary online visualization charts for anomaly detection (

**top**) and disturbance classification (

**bottom**) of synchrophasor based applications.

Method | Compression Result | Parameters |
---|---|---|

PCA | PCA scores (principle components) | PCA loadings, sample means |

DWT | approximation and detailed coefficients | low- and high-pass filters, wavelet expansion coefficients |

Method | Main Principle | Outlier Score |
---|---|---|

LOF | Local density of data points and its neighborhoods | Local outlier factor |

COP | Deviation within local correlation model using robust PCA | Correlation outlier probability |

SiLiOd | Hierarchical clustering using shortest distances | Path lengths to final cluster |

Feature | Description |
---|---|

Basis: time-domain values | |

F1 | absolute slope |

F2 | Variance |

Basis: Stockwell transform coefficients | |

F3 | energy variance along time axis |

F4 | energy variance along frequency axis |

Z-Score | Anomaly Level |
---|---|

0–1 | Normal |

1–2 | Low |

2–3 | Medium |

3–4 | High |

>4 | Extreme |

Dataset | # of PMU Stations | Measurement Channels ^{[a]} | Voltage Level | Reporting Rate |
---|---|---|---|---|

LVField | 5 | F, V_{AMP}, V_{ANG}, I_{AMP}, I_{ANG}, FC | 0.4 kV–20 kV | 10 f.p.s. |

MVField [62] | 6 | F, V_{AMP}, V_{ANG} | 0.4 kV–120 kV | 30 f.p.s. |

HVSim | 21 | F, V_{AMP}, V_{ANG} | 400 kV | 25 f.p.s. |

^{[a]}F…frequency, V

_{Amp}…voltage amplitude, V

_{Ang}…voltage angle, I

_{AMP}…current amplitude, I

_{ANG}…current angle, FC…rate of change of frequency.

Hyperparameter | Value |
---|---|

Wavelet function | Db5 |

Decomposition level | 2 |

Coefficient threshold | 0.05 |

Channel | Spatial | Temporal | Total | |||
---|---|---|---|---|---|---|

${\mathit{r}}_{\mathit{C}}$ | ${\mathit{e}}_{\mathit{r}}$ | ${\mathit{r}}_{\mathit{C}}$ | ${\mathit{e}}_{\mathit{r}}$ | ${\mathit{r}}_{\mathit{C}}$ | ${\mathit{e}}_{\mathit{r}}$ | |

Voltage (magnitude) | 1.656 | 0.035 | 3.571 | 0.008 | 5.814 | 0.036 |

Voltage (angle) | 0.001 | 0.001 | 0.001 | |||

Current (magnitude) | 0.034 | 0.006 | 0.035 | |||

Current (angle) | 0.001 | 0.004 | 0.003 | |||

Frequency | 0.006 | 0.008 | 0.010 | |||

ROCOF | 0.058 | 0.016 | 0.060 |

Hyperparameter | Value |
---|---|

S transform max. frequency | 1 Hz |

DWT decomposition level | 12 |

DWT wavelet function | Db5 |

Isomap number of nearest neighbors | 50 |

SiLiOd distance function | Mahalanobis |

LOF & COP distance function | Euclidean |

LOF & COP number of nearest neighbors | 50 |

Hyperparameter | Value |
---|---|

S transform max. frequency | 10 Hz |

# of S transform frequency bins | 50 |

# of samples for feature assessment N | 20 |

# of time steps per sample | 50 |

Location | Type | Label |
---|---|---|

Station 1D1 | Outage of DKW generator | 1D1.DKW_OT |

Station 2D3 | Outage of GKW generator | 2D3.GKW_OT |

Station 4D2 | Outage of GKW generator | 4D2.GKW_OT |

Station 6D1 | Outage of DKW generator | 6D1.DKW_OT |

Station 1D1 | PV partial outage of 25% | 1D1.PV_LC_25 |

Station 2D3 | PV partial outage of 50% | 2D3.PV_LC_50 |

Station 4D2 | PV partial outage of 75% | 4D2.PV_LC_75 |

Station 6D1 | PV partial outage of 50% | 6D1.PV_LC_50 |

Station 1D1 | Load loss of 75% | 1D1.L1_LC_75 |

Station 2D3 | Load loss of 50% | 2D3.L1_LC_50 |

Station 4D2 | Load loss of 25% | 4D2.L1_LC_25 |

Station 6D1 | Load loss of 50% | 6D1.L1_LC_50 |

Line 7 | Line trip | L7_OT |

Line 19 | Line trip | L19_OT |

Line 24 | Line trip | L24_OT |

Line 32 | Line trip | L32_OT |

Line 7 | Short circuit at 10% line length | L7_SC_10 |

Line 19 | Short circuit at 90% line length | L19_SC_90 |

Line 24 | Short circuit at 50% line length | L24_SC_50 |

Line 32 | Short circuit at 10% line length | L32_SC_10 |

Scenario Parameter | Value |
---|---|

Measurement channels | Voltage magnitudes Frequencies |

# of PMUs | 13 |

PMU reporting rate | 25 f.p.s. |

Time window | 2 s |

Post-disturbance time | 10 s |

# of operational points | 3 |

Sample overlapping (training) (%) | 50 |

Sample overlapping (validation) (%) | 50 |

Sample overlapping (test) (%) | 90 |

# of samples (training) | 540 |

# of samples (validation) | 108 |

# of samples (test) | 3060 |

Hyperparameter | Value |
---|---|

# of hidden dimensions $Q$ | 15 |

# of feature dimensions $P$ | 15 |

Optimizer | rmsprop [69] |

Learning rate | 0.01 |

Batch size | 50 |

Maximum # of epochs | 1000 |

Metric | Training | Validation | Test |
---|---|---|---|

Accuracy (%) | 97.92 | 89.81 | 94.80 |

F1-score (macro) (%) | 97.91 | 89.01 | 94.73 |

F1-score (micro) (%) | 97.92 | 89.81 | 94.80 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kummerow, A.; Monsalve, C.; Brosinsky, C.; Nicolai, S.; Westermann, D. A Novel Framework for Synchrophasor Based Online Recognition and Efficient Post-Mortem Analysis of Disturbances in Power Systems. *Appl. Sci.* **2020**, *10*, 5209.
https://doi.org/10.3390/app10155209

**AMA Style**

Kummerow A, Monsalve C, Brosinsky C, Nicolai S, Westermann D. A Novel Framework for Synchrophasor Based Online Recognition and Efficient Post-Mortem Analysis of Disturbances in Power Systems. *Applied Sciences*. 2020; 10(15):5209.
https://doi.org/10.3390/app10155209

**Chicago/Turabian Style**

Kummerow, Andre, Cristian Monsalve, Christoph Brosinsky, Steffen Nicolai, and Dirk Westermann. 2020. "A Novel Framework for Synchrophasor Based Online Recognition and Efficient Post-Mortem Analysis of Disturbances in Power Systems" *Applied Sciences* 10, no. 15: 5209.
https://doi.org/10.3390/app10155209