We present a data-driven approach for probabilistic wind power forecasting based on conditional normalizing flow (CNF). In contrast with the existing, this approach is distribution-free (as for non-parametric and quantile-based approaches) and can directly yield continuous probability densities, hence avoiding quantile crossing. It relies on a base distribution and a set of bijective mappings. Both the shape parameters of the base distribution and the bijective mappings are approximated with neural networks. Spline-based conditional normalizing flow is considered owing to its non-affine characteristics. Over the training phase, the model sequentially maps input examples onto samples of base distribution, given the conditional contexts, where parameters are estimated through maximum likelihood. To issue probabilistic forecasts, one eventually maps samples of the base distribution into samples of a desired distribution. Case studies based on open datasets validate the effectiveness of the proposed model, and allows us to discuss its advantages and caveats with respect to the state of the art.
Greater direct electrification of end-use sectors with a higher share of renewables is one of the pillars to power a carbon-neutral society by 2050. However, in contrast to conventional power plants, renewable energy is subject to uncertainty raising challenges for their interaction with power systems. Scenario-based probabilistic forecasting models have become a vital tool to equip decision-makers. This paper presents to the power systems forecasting practitioners a recent deep learning technique, the normalizing flows, to produce accurate scenario-based probabilistic forecasts that are cruci…
Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long time horizons as errors accumulate. One such application is with resource scheduling under uncertainty in a grid environment, which requires forecasting electricity demand that is inherently noisy, but often cyclic. In this paper, we introduce the conditional approximate normalizing flow (CANF) to make probabilistic multi-step time-series forecasts when corr…
Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows
HTWG Konstanz - University of Applied Sciences（康斯坦茨应用科学大学HTWG）；TU Berlin（柏林工业大学）；Birds on Mars GmbH（火星上的鸟有限公司）；University of Zurich（苏黎世大学）；Zurich University of Applied Sciences（苏黎世应用科学大学）；Bosch.IO GmbH（博世物联网有限公司）
Forschungszentrum Jülich GmbH（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；University of Cologne（科隆大学）；JARA-ENERGY（于利希-亚琛研究联盟能源部）
Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the European Power EXchange (EPEX) spot markets in a distinct hourly pattern. This work proposes a probabilistic modeling approach that models the intraday price difference to the day-ahead contracts. The model captures the emerging hourly pattern by considering the four 15 min intervals in each day-ahead price in…
Forschungszentrum Jülich GmbH（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；Technical University of Berlin（柏林工业大学）；JARA-ENERGY（于利希-亚琛研究联盟能源部）
We present a specialized scenario generation method that utilizes forecast information to generate scenarios for day-ahead scheduling problems. In particular, we use normalizing flows to generate wind power scenarios by sampling from a conditional distribution that uses wind speed forecasts to tailor the scenarios to a specific day. We apply the generated scenarios in a stochastic day-ahead bidding problem of a wind electricity producer and analyze whether the scenarios yield profitable decisions. Compared to Gaussian copulas and Wasserstein-generative adversarial networks, the normalizing flo…
Forschungszentrum Jülich GmbH（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；JARA-ENERGY（于利希-亚琛研究联盟能源组）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Neural networks-based learning of the distribution of non-dispatchable renewable electricity generation from sources such as photovoltaics (PV) and wind as well as load demands has recently gained attention. Normalizing flow density models are particularly well suited for this task due to the training through direct log-likelihood maximization. However, research from the field of image generation has shown that standard normalizing flows can only learn smeared-out versions of manifold distributions. Previous works on normalizing flow-based scenario generation do not address this issue, and the…
TrajFlow: A Generative Framework for Occupancy Density Estimation Using Normalizing Flows
Department of Computer Science University of Minnesota（计算机科学系明尼苏达大学）；Department of Civil Environmental and Geo- Engineering University of Minnesota（土木环境与地球工程系明尼苏达大学）
This paper introduces an R package ForecastTB that can be used to compare the accuracy of different forecasting methods as related to the characteristics of a time series dataset. The ForecastTB is a plug-and-play structured module, and several forecasting methods can be included with simple instructions. The proposed test-bench is not limited to the default forecasting and error metric functions, and users are able to append, remove, or choose the desired methods as per requirements. Besides, several plotting functions and statistical performance metrics are provided to visualize the comparat…
We discuss an approach to probabilistic forecasting based on two chained machine-learning steps: a dimensional reduction step that learns a reduction map of predictor information to a low-dimensional space in a manner designed to preserve information about forecast quantities; and a density estimation step that uses the probabilistic machine learning technique of normalizing flows to compute the joint probability density of reduced predictors and forecast quantities. This joint density is then renormalized to produce the conditional forecast distribution. In this method, probabilistic calibrat…
Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation
Department of Computer Science and Engineering University of Notre Dame（计算机科学与工程系诺特达姆大学）；Department of Pediatrics Stanford University（儿科系斯坦福大学）；Department of Applied and Computational Mathematics and Statistics University of Notre Dame（应用与计算数学与统计系诺特达姆大学）
University of Pennsylvania（宾夕法尼亚大学）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）
Forecasting complex vehicle and pedestrian multi-modal distributions requires powerful probabilistic approaches. Normalizing flows (NF) have recently emerged as an attractive tool to model such distributions. However, a key drawback is that independent samples drawn from a flow model often do not adequately capture all the modes in the underlying distribution. We propose Likelihood-Based Diverse Sampling (LDS), a method for improving the quality and the diversity of trajectory samples from a pre-trained flow model. Rather than producing individual samples, LDS produces a set of trajectories in…
BEACON: Bayesian Experimental design Acceleration with Conditional Normalizing flows $-$ a case study in optimal monitor well placement for CO$_2$ sequestration
Romanian Institute of Science and Technology（罗马尼亚科学技术研究院）
The next generation 21 cm surveys open a new window onto the early stages of cosmic structure formation and provide new insights about the Epoch of Reionization (EoR). However, the non-Gaussian nature of the 21 cm signal along with the huge amount of data generated from these surveys will require more advanced techniques capable to efficiently extract the necessary information to constrain the Reionization History of the Universe. In this paper we present the use of Bayesian Neural Networks (BNNs) to predict the posterior distribution for four astrophysical and cosmological parameters. Besides…
Northeast Electric Power University（东北电力大学）；State Grid Jilin Electric Power Co., Ltd. Jilin Power Supply Company（国网吉林省电力有限公司吉林供电公司）；Huazhong University of Science and Technology（华中科技大学）；Naval University of Engineering（海军工程大学）；Cranfield University（克兰菲尔德大学）
In a modern power system with an increasing proportion of renewable energy, wind power prediction is crucial to the arrangement of power grid dispatching plans due to the volatility of wind power. However, traditional centralized forecasting methods raise concerns regarding data privacy-preserving and data islands problem. To handle the data privacy and openness, we propose a forecasting scheme that combines federated learning and deep reinforcement learning (DRL) for ultra-short-term wind power forecasting, called federated deep reinforcement learning (FedDRL). Firstly, this paper uses the de…
Improving the Accuracy and Interpretability of Neural Networks for Wind Power Forecasting
Ecole Polytechnique Federale de Lausanne (EPFL)（洛桑联邦理工学院）；Aalborg University（奥尔堡大学）；The Hong Kong Polytechnic University（香港理工大学）；The University of Hong Kong（香港大学）
This paper proposes a regression market for wind agents to monetize data traded among themselves for wind power forecasting. Existing literature on data markets often treats data disclosure as a binary choice or modulates the data quality based on the mismatch between the offer and bid prices. As a result, the market disadvantages either the data sellers due to the overestimation of their willingness to disclose data, or the data buyers due to the lack of useful data being provided. Our proposed regression market determines the data payment based on the least absolute shrinkage and selection o…
Forecasting a particular variable can depend upon temporal or spatial scale. Temporal variations that indicate variations with time, reflect the stochasticity present in the variable. Spatial variation usually are dominant in climatology and meteorology. Temporal scale for a variable can be modeled in terms of time-series. A time series is a successively ordered sequence of numerical data points, and can be taken on any variable changing with time. Wind speed forecasting applications lie majorly in the area of electricity market clearing, economic load dispatch and scheduling, and sometimes to…
Marginalize, Rather than Impute: Probabilistic Wind Power Forecasting with Incomplete Data
School of Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电气工程学院）；Dyson School of Design Engineering, Imperial College London（帝国理工学院设计工程学院）；Department of Technology, Management and Economics, Technical University of Denmark（丹麦技术大学技术、管理与经济系）；Centre for Energy Research – CoRE, Aarhus University（奥胡斯大学能源研究中心）
Islamic Azad University（伊斯兰阿扎德大学）；Iranian University of Science and Technology（伊朗科技大学）；Shiraz University of Technology（设拉子理工大学）；Electric reliability council of Texas（得克萨斯州电力可靠性委员会）
In terms of the operation of microgrids, optimal scheduling is a vital issue that must be taken into account. In this regard, this paper proposes an effective framework for optimal scheduling of renewable microgrids considering energy storage devices, wind turbines, micro turbines. Due to the nonlinearity and complexity of operation problems in microgrids, it is vital to use an accurate and robust optimization technique to efficiently solve this problem. To this end, in the proposed framework, the teacher learning-based optimization is utilized to efficiently solve the scheduling problem in th…
Renewable energy sources, such as wind and solar power, are increasingly being integrated into smart grid systems. However, when compared to traditional energy resources, the unpredictability of renewable energy generation poses significant challenges for both electricity providers and utility companies. Furthermore, the large-scale integration of distributed energy resources (such as PV systems) creates new challenges for energy management in microgrids. To tackle these issues, we propose a novel framework with two objectives: (i) combating uncertainty of renewable energy in smart grid by lev…
