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The availability of data for monitoring and controlling the electrical grid has increased exponentially over the years in both resolution ...
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Model-Based Machine Learning for the Power Grid
by Raksha Ramakrishna
A Dissertation Presented in Partial Fulfillment of the Requirement for the Degree Doctor of Philosophy
Approved September 2020 by the Graduate Supervisory Committee: Anna Scaglione, Chair Douglas Cochran Andreas Spanias Vijay Vittal Junshan Zhang
December 2020
The availability of data for monitoring and controlling the electrical grid has increased exponentially over the years in both resolution and quantity leaving a large data foot- print. This dissertation is motivated by the need for equivalent representations of grid data in lower-dimensional feature spaces so that machine learning algorithms can be employed for a variety of purposes. To achieve that, without sacrificing the inter- pretation of the results, the dissertation leverages the physics behind power systems, well-known laws that underlie this man-made infrastructure, and the nature of the underlying stochastic phenomena that define the system operating conditions as the backbone for modeling data from the grid. The first part of the dissertation introduces a new framework of graph signal processing (GSP) for the power grid, Grid-GSP, and applies it to voltage phasor measurements that characterize the overall system state of the power grid. Concepts from GSP are used in conjunction with known power system models in order to high- light the low-dimensional structure in data and present generative models for voltage phasors measurements. Applications such as identification of graphical communities, network inference, interpolation of missing data, detection of false data injection at- tacks and data compression are explored wherein Grid-GSP based generative models are used. The second part of the dissertation develops a model for a joint statistical de- scription of solar photo-voltaic (PV) power and the outdoor temperature which can lead to better management of power generation resources so that electricity demand such as air conditioning and supply from solar power are always matched in the face of stochasticity. The low-rank structure inherent in solar PV power data is used for forecasting and to detect partial-shading type of faults in solar panels.
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I am deeply indebted to my advisor, Prof. Anna Scaglione for her wonderful guid- ance, patience and support. This work has greatly benefited from her scrutiny and insight. Her creativity in formulating problems, courage in venturing out seeking to connect seemingly different areas of study while doing multidisciplinary work and her excitement for research will continue to motivate me. I also thank my dissertation committee- Prof. Douglas Cochran, Prof. Andreas Spanias, Prof. Vijay Vittal and Prof. Junshan Zhang for their input, feedback and collaboration. I am also grateful to all the Professors I have taken courses with at ASU who helped me establish a strong technical foundation. My first brush with research was at the Signal Processing for Communications (SPC) lab at the Indian Institute of Science under the tutelage of Prof. Chandra Murthy. I want to thank him for providing me the opportunity to explore various facets of research ranging from writing papers, data analysis to developing software. Huge thanks to all the members of SPC lab I overlapped with and particularly to Karthik and Geethu for being my very first collaborators and co-authors. I would like to thank all my collaborators and internship hosts Prof. Emiliano Dall’Anese, Dr. Andrey Bernstein, Dr. Sean Peisert and Dr. Aram Shumavon for their ideas, encouragement and support. A big thank you to all the past and present SINE lab members-To, Reinhard, Lorenzo, Mahdi, Kari, Eran, Bita, Sissi, Tech, Nikhil, Nurullah, Ignacio and Sham- mya. They made work and leisure so much fun and I made friends for life. You guys are simply the best! Thanks to my longtime friends-Ayesha, Saraswati, Manoj, Anisha, Ashwin, Sushma, Vivek, Shivarama, Suhas, Suleman and Sunil for believing in me and offering me kind words of encouragement from time to time.
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I am also extremely grateful to all my friends in Tempe and roommates-Karthigayani, Anushree, Vaishnavi, Subramanian, Niveditha, Suhas, Saranya, Pratyusha, Rakshith, Parth and Dheeraj. They made Tempe feel like home, and were my local family! I thank my parents, Ramakrishna and Mangala, sister Varsha and my in-laws Surendra Rao and Vijayalakshmi for their relentless cheering and great support. Last but not the least, I would not have made it this far if not for my husband Harish’s love, patience, understanding and optimism. Thank you my dear, for enduring our long periods of separation and for moving countries for me! Lastly, I want to thank the ASU ECEE Graduate advisors, Business Operations Specialists, ASU IT, Tax advisors and the International Scholars and Student Center who helped a great deal with all the bureaucratic tasks. I am also grateful for the expansive ASU library and the Sun Devil Fitness Center that hosted great group fitness classes which kept me in good health.
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Table Page 5.1 Table with Average Score Normalized by the Nameplate Capacity...... 112 5.2 CRPS for Joint Forecast (in (W/m^2 )^2 (◦C)^2 ).......................... 114
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Figure Page
6.0.1 Communication Network Schematic for Distributed Estimation........ 117 6.2.1 Singular Values of Solar PV Power Data Measurement Matrix......... 124 6.2.2 Comparison of Lower Bound with MSE for Synthetic Data............ 124 6.3.1 Partial Shading Fault Detection Performance on Real Data............ 125 6.3.2 Comparison of Lower Bound with MSE for Day d..................... 125
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Algorithm Page 3.1 Optimal Placement Algorithm...................... 46 4.1 Blind Community Detection for Grid Graph Signals.......... 57 4.2 Encoding Algorithm for Compression................... 68 4.3 Decoding Algorithm for Reconstruction................. 69 6.1 Distributed Bayesian Estimation..................... 122
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goal of this dissertation is to go beyond intuition and empirical observation to justify the black box models. Instead it is shown how it is possible to utilize the underlying physics as well as the knowledge of electrical-grid that is a man-made infrastructure to guide the process of abstraction and support the design of model-based machine learning algorithms for power systems. This dissertation explores the topic of modeling data from power systems in a way that their low-dimensional representations become apparent. Then, these mod- els are utilized to address several problems in both transmission and distribution of power systems such as forecasting renewable energy generation and anomaly detec- tion. Well-established theory of power systems, tools from statistical signal processing and validation through a large amount of data from the power grid are the ingredients for the model-based machine learning algorithms proposed in this dissertation. The first part of the dissertation focuses on low-dimensional modeling techniques to voltage phasor measurements that characterize the overall system ‘state’ of the power grid. Given that data from the power grid lies on a graph that is the electric grid, it introduces the framework of graph signal processing (GSP) in general and specializes the tools and ideas from GSP to voltage measurements. It establishes that voltage measurements have a generative model in the realm of GSP which is suggestive of the underlying low-dimensionality in the data. The second part of this dissertation focuses on AMI measurements of power in- jection from solar photo-voltaic (PV) power generation and power consumption of thermostatically controlled loads (TCL) while modeling the statistical dependency that exists between these data. Since both solar PV power and temperature are dependent on weather and the sun, there is natural correlation not just between the two quantities but also in space due to geographical proximity between residential consumers. This induces
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substation
loads
renewables
thermostatically controlled loads
temperature
solar PV power
Chapter 3 : Chapter 4: Applications of GSP frameworkGSP framework for power grid for anomaly detection, data compression
Chapter 5 : power and temperature Joint probabilistic forecasting of PV Chapter 6: Fault detection in PV panels
Graph Signal Processing (GSP) for the power grid
Modeling Solar Photo-voltaic (PV) Power and Temperature for Renewable Integration
Transmission
Distribution
Figure 1.1.1: An Overview Of This Dissertation And The Corresponding Chapters.
correlation in the variability that lies in the heating or cooling power demand and renewable power production. Therefore an equivalent low-dimensional representation of these quantities is possible and the joint modeling of solar PV power and outdoor temperature is studied. In fact, prior works have already applied concepts from GSP to model the spatial correlation in solar radiation [5] and outdoor temperature [6]. The graph considered is based on the geographical distance between multiple locations. This dissertation fill the gap that exists in modeling the temporal structure and coupling between these data sets modeling the correlation between solar PV power and temperature at one location while accounting for temporal stochasticity and then considering the spatial model for locations in close geographical proximity. The models introduced in this dissertation make the low-dimensional representa-
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This characteristic of dimensionality reduction of voltage data can be well modeled by a low-pass graph filter which captures a smoothing operation applied to an input graph signal. As it turns out, this is a common property of processes observed in many physical/social systems. Chapter 2 briefly reviews the concepts entailing low- pass GSP and provides a set of particular examples highlighting the fact that low-pass graph signals often appear in different application domains. Once the general concepts from low-pass GSP are introduced, Grid-GSP: a GSP framework for the power grid is discussed in Chapter 3. It builds upon the exist- ing system-level knowledge of power systems to create a solid foundation to analyze power-grid measurements using tools from GSP. Well-known results for sampling, data interpolation and network-inference in GSP are extended to power system data without losing the associated physical interpretation. The core idea in this chapter is derived by rewriting the differential algebraic equations (DAE) [16] in a way of- ten done in transient stability analysis of power systems, to reveal that the inherent structure in voltage phasor measurements can be explained using a low-pass graph filter, whose inputs are the generator voltages, as a generative model. In Chapter 4, few applications of Grid-GSP are studied namely-identification of community structure in the grid which is a consequence of the low-pass nature of volt- age graph signals, fault localization using under-sampled grid, data data compression and the detection of false data injection attacks using Grid-GSP.
1.2.1 Prior Works and Contributions Several papers have used insights from spectral and algebraic graph theory for problems such as optimal placement [17–20], for generating statistically accurate topologies [21], for grid topology identification [22, 23] and to defend against at- tacks [24, 25]. GSP concepts have been leveraged in [26, 27] to detect false data
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injection (FDI) attacks. Prior work in [28] dealt with performance limits on fault localization with inadequate number of PMUs and connected it with graph signal sampling theory and optimal placement of PMUs for best possible resolution of fault localization in this under-sampled regime. The Kron-reduced network among the generator buses and the associated prop- erties are used in [29, 30] to detect low-frequency oscillations as well as the resulting islanding patterns. In [31], the authors have shed light on the relationship that exists between Graph Laplacian and modes in power systems. Recently, a comprehensive review of graph-theoretical concepts in power systems is presented in [16]. Additionally, there have been several papers adopting graphical models for state estimation [32], topology estimation [33] and optimal power flow [34]. While the modeling approach is valid, the graphical models capture correlation whereas GSP- based method models the underlying cause for that correlation structure thereby opening the door for statistical and non-statistical approaches. Note that with the exception of [26, 27], no other papers make the connection with GSP and even in the aforementioned work, GSP is used in an empirical manner without establishing a foundation, as done in preliminary work [35, 36].
Contributions The overarching goal of Chapters 3 and 4 are to lay down the foundations of Grid-GSP and elucidate properties of power grid signals using tools from GSP. In particular:
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