Mahdi Khodayar

Mahdi Khodayar, Jianhui Wang, Zhaoyu Wang

Power system studies require the topological structures of real-world power networks; however, such data is confidential due to important security concerns. Thus, power grid synthesis (PGS), i.e., creating realistic power grids that imitate actual power networks, has gained significant attention. In this letter, we cast PGS into a graph distribution learning (GDL) problem where the probability distribution functions (PDFs) of the nodes (buses) and edges (lines) are captured. A novel deep GDL (DeepGDL) model is proposed to learn the topological patterns of buses/lines with their physical features (e.g., power injection and line impedance). Having a deep nonlinear recurrent structure, DeepGDL understands complex nonlinear topological properties and captures the graph PDF. Sampling from the obtained PDF, we are able to create a large set of realistic networks that all resemble the original power grid. Simulation results show the significant accuracy of our created synthetic power grids in terms of various topological metrics and power flow measurements.

Mahdi Khodayar, Saeed Mohammadi, Mohammad Khodayar et al.

Machine Learning on graph-structured data is an important and omnipresent task for a vast variety of applications including anomaly detection and dynamic network analysis. In this paper, a deep generative model is introduced to capture continuous probability densities corresponding to the nodes of an arbitrary graph. In contrast to all learning formulations in the area of discriminative pattern recognition, we propose a scalable generative optimization/algorithm theoretically proved to capture distributions at the nodes of a graph. Our model is able to generate samples from the probability densities learned at each node. This probabilistic data generation model, i.e. convolutional graph auto-encoder (CGAE), is devised based on the localized first-order approximation of spectral graph convolutions, deep learning, and the variational Bayesian inference. We apply our CGAE to a new problem, the spatio-temporal probabilistic solar irradiance prediction. Multiple solar radiation measurement sites in a wide area in northern states of the US are modeled as an undirected graph. Using our proposed model, the distribution of future irradiance given historical radiation observations is estimated for every site/node. Numerical results on the National Solar Radiation Database show state-of-the-art performance for probabilistic radiation prediction on geographically distributed irradiance data in terms of reliability, sharpness, and continuous ranked probability score.

Mahdi Khodayar, Jianhui Wang, Zhaoyu Wang

This paper addresses the energy disaggregation problem, i.e. decomposing the electricity signal of a whole home to its operating devices. First, we cast the problem as a dictionary learning (DL) problem where the key electricity patterns representing consumption behaviors are extracted for each device and stored in a dictionary matrix. The electricity signal of each device is then modeled by a linear combination of such patterns with sparse coefficients that determine the contribution of each device in the total electricity. Although popular, the classic DL approach is prone to high error in real-world applications including energy disaggregation, as it merely finds linear dictionaries. Moreover, this method lacks a recurrent structure; thus, it is unable to leverage the temporal structure of energy signals. Motivated by such shortcomings, we propose a novel optimization program where the dictionary and its sparse coefficients are optimized simultaneously with a deep neural model extracting powerful nonlinear features from the energy signals. A long short-term memory auto-encoder (LSTM-AE) is proposed with tunable time dependent states to capture the temporal behavior of energy signals for each device. We learn the dictionary in the space of temporal features captured by the LSTM-AE rather than the original space of the energy signals; hence, in contrast to the traditional DL, here, a nonlinear dictionary is learned using powerful temporal features extracted from our deep model. Real experiments on the publicly available Reference Energy Disaggregation Dataset (REDD) show significant improvement compared to the state-of-the-art methodologies in terms of the disaggregation accuracy and F-score metrics.