This paper presents a generative artificial intelligence approach to probabilistic forecasting of electricity market signals, such as real-time locational marginal prices and area control error signals. Inspired by the Wiener-Kallianpur innovation representation of nonparametric time series, we propose a weak innovation autoencoder architecture and a novel deep learning algorithm that extracts the canonical independent and identically distributed innovation sequence of the time series, from which samples of future time series are generated. The validity of the proposed approach is established by proving that, under ideal training conditions, the generated samples have the same conditional probability distribution as that of the ground truth. Three applications involving highly dynamic and volatile time series in real-time market operations are considered: (i) locational marginal price forecasting for self-scheduled resources such as battery storage participants, (ii) interregional price spread forecasting for virtual bidders in interchange markets, and (iii) area control error forecasting for frequency regulations. Numerical studies based on market data from multiple independent system operators demonstrate the superior performance of the proposed generative forecaster over leading classical and modern machine learning techniques under both probabilistic and point forecasting metrics.

Purpose This article presents a case for a next-generation grid monitoring and control system, leveraging recent advances in generative artificial intelligence (AI), machine learning, and statistical inference. Advancing beyond earlier generations of wide-area monitoring systems built upon supervisory control and data acquisition (SCADA) and synchrophasor technologies, we argue for a monitoring and control framework based on the streaming of continuous point-on-wave (CPOW) measurements with AI-powered data compression and fault detection. Methods and Results: The architecture of the proposed design originates from the Wiener-Kallianpur innovation representation of a random process that transforms causally a stationary random process into an innovation sequence with independent and identically distributed random variables. This work presents a generative AI approach that (i) learns an innovation autoencoder that extracts innovation sequence from CPOW time series, (ii) compresses the CPOW streaming data with innovation autoencoder and subband coding, and (iii) detects unknown faults and novel trends via nonparametric sequential hypothesis testing. Conclusion: This work argues that conventional monitoring using SCADA and phasor measurement unit (PMU) technologies is ill-suited for a future grid with deep penetration of inverter-based renewable generations and distributed energy resources. A monitoring system based on CPOW data streaming and AI data analytics should be the basic building blocks for situational awareness of a highly dynamic future grid.

The main challenge of applying Wiener-Kallianpur innovation Whereas standard probabilistic forecasting aims to estimate representation for inference and decision-making is the conditional probability distribution of the time series at twofold. First, obtaining a causal encoder to extract the a future time, GPF obtains a generative model capable of innovation process requires knowing the marginal and joint producing arbitrarily many Monte Carlo samples of future distributions of the time series, which is rarely possible without time series realizations according to the conditional probability imposing some parametric structure. Furthermore, even when distribution of the time series given past observations. As the probability distribution is known, there is no known computationally a nonparametric probabilistic forecasting technique, GPF is tractable way to construct the causal encoder to essential for decision-making under uncertainty where datadriven obtain an innovation process. Second, the Wiener-Kallianpur risk-sensitive optimization requires conditional samples innovation representation may not exist for a broad class of of future randomness. The Monte Carlo samples generated random processes, including some of the important cases of from GPF can be used to produce any form of point forecast.

Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. Such techniques are critical in risk-based decision-making and planning under uncertainties. Existing approaches are primarily based on parametric or semi-parametric time-series models that are restrictive, difficult to validate, and challenging to adapt to varying conditions. This paper proposes a nonparametric method based on the classic notion of {\em innovations} pioneered by Norbert Wiener and Gopinath Kallianpur that causally transforms a nonparametric random process to an independent and identical uniformly distributed {\em innovations process}. We present a machine-learning architecture and a learning algorithm that circumvent two limitations of the original Wiener-Kallianpur innovations representation: (i) the need for known probability distributions of the time series and (ii) the existence of a causal decoder that reproduces the original time series from the innovations representation. We develop a deep-learning approach and a Monte Carlo sampling technique to obtain a generative model for the predicted conditional probability distribution of the time series based on a weak notion of Wiener-Kallianpur innovations representation. The efficacy of the proposed probabilistic forecasting technique is demonstrated on a variety of electricity price datasets, showing marked improvement over leading benchmarks of probabilistic forecasting techniques.

An innovations sequence of a time series is a sequence of independent and identically distributed random variables with which the original time series has a causal representation. The innovation at a time is statistically independent of the history of the time series. As such, it represents the new information contained at present but not in the past. Because of its simple probability structure, an innovations sequence is the most efficient signature of the original. Unlike the principle or independent component analysis representations, an innovations sequence preserves not only the complete statistical properties but also the temporal order of the original time series. An long-standing open problem is to find a computationally tractable way to extract an innovations sequence of non-Gaussian processes. This paper presents a deep learning approach, referred to as Innovations Autoencoder (IAE), that extracts innovations sequences using a causal convolutional neural network. An application of IAE to the one-class anomalous sequence detection problem with unknown anomaly and anomaly-free models is also presented.

Abstract--The problem of state estimation for unobservable distribution systems is considered. A Bayesian approach is proposed that implements Bayesian inference with a deep neural network to achieve the minimum mean squared error estimation of network states for real-time applications. The proposed technique consists of distribution learning for stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad data detection and cleansing algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors of power injection distributions and the presence of bad data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation with deep neural networks outperforms existing benchmarks. We consider the problem of state estimation for distribution systems that have limited measurements. This problem is motivated by the need of coping with the rising presence of distributed energy resources (DER) in distribution systems.

We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $\Omega(\sqrt{T})$ for any strategy, we conclude that DPDS is order optimal up to a $\sqrt{\log{T}}$ term. We evaluate the performance of DPDS empirically in the context of virtual trading in wholesale electricity markets by using historical data from the New York market. Empirical results show that DPDS consistently outperforms benchmark heuristic methods that are derived from machine learning and online learning approaches.

The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new technique based on online dictionary learning (ODL) is proposed. The ODL approach incorporates real-time measurements and historical traces to produce forecasts of joint and marginal probability distributions of future locational marginal prices, power flows, and dispatch levels, conditional on the system state at the time of forecasting. Compared with standard Monte Carlo simulation techniques, the ODL approach offers several orders of magnitude improvement in computation time, making it feasible for online forecasting of market operations. Numerical simulations on large and moderate size power systems illustrate its performance and complexity features and its potential as a tool for system operators.

The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual information quantities as the edge weights. Using the theory of large-deviations, we analyze the exponent associated with the error probability of the event that the ML-estimate of the Markov tree structure differs from the true tree structure, given a set of independently drawn samples. By exploiting the fact that the output of ML-estimation is a tree, we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event. We prove that in this dominant crossover event, a non-neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non-neighbor pair. Using ideas from Euclidean information theory, we then analyze the scenario of ML-estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio, which is interpreted as the signal-to-noise ratio (SNR) for learning tree distributions. We show via numerical experiments that in this regime, our SNR approximation is accurate.