Quantifying Forecast Uncertainty in the Energy Domain

This dissertation focuses on quantifying forecast uncertainties in the energy domain, especially for the electricity and natural gas industry. Accurate forecasts help the energy industry minimize their production costs. However, inaccurate weather forecasts, unusual human behavior, sudden changes in economic conditions, unpredictable availability of renewable sources (wind and solar), etc., represent uncertainties in the energy demand-supply chain. In the current smart grid era, total electricity demand from non-renewable sources influences by the uncertainty of the renewable sources. Thus, quantifying forecast uncertainty has become important to improve the quality of forecasts and decision making. In the natural gas industry, the task of the gas controllers is to guide the hourly natural gas flow in such a way that it remains within a certain daily maximum and minimum flow limits to avoid penalties. Due to inherent uncertainties in the natural gas forecasts, setting such maximum and minimum flow limits a day or more in advance is difficult. Probabilistic forecasts (cumulative distribution functions), which quantify forecast uncertainty, are a useful tool to guide gas controllers to make such tough decisions. Three methods (parametric, semi-parametric, and non-parametric) are presented in this dissertation to generate 168-hour horizon probabilistic forecasts for two real utilities (electricity and natural gas) in the US. Probabilistic forecasting is used as a tool to solve a real-life problem in the natural gas industry. A benchmark was created based on the existing solution, which assumes forecast error is normal. Two new probabilistic forecasting methods are implemented in this work without the normality assumption. There is no single popular evaluation technique available to assess probabilistic forecasts, which is one reason for people’s lack of interest in using probabilistic forecasts. Existing scoring rules are complicated, dataset dependent, and provide less emphasis on reliability (empirical distribution matches with observed distribution) than sharpness (the smallest distance between any two quantiles of a CDF). A graphical way to evaluate probabilistic forecasts along with two new scoring rules are offered in this work. The non-parametric and semi-parametric probabilistic forecasting methods outperformed the benchmark method during unusual days (difficult days to forecast) as well as on other days

Short Term Probabilistic Load Forecasting at Local Level in Distribution Networks

Along with the growing inclusion of smart technologies into the electrical power grids, benefits, which can be originated form advanced metering infrastructure (AMI), have grabbed noticeable attention from distribution utilities. Since the number of meters are severely ample in practical systems, the utilities now is able to create virtual meter data by aggregating loads for distribution substations, feeders, transformers, or regions with the help of geographic information system. Such an important change brought by smart meter rollout is considered as the main factor which motivates this thesis to delve more into the load pattern modeling and forecasting at local level and find approaches which can yield to the enhanced applications in distribution networks. However, low aggregation level leads to high volatile load characteristic. In this regard, this thesis proposes a comprehensive methodology for uncertainty modeling and short-term probabilistic load forecasting (STPLF) in distribution networks. Existing methods related to uncertainty modeling and forecasting are rarely applied to local level loads and they suffer from over- or under-fitting of data when there is a misfit between the complexity of the model and the amount of data available. These models are limited to specific situations due to the great diversity of loads in distribution networks and need to be tuned every time when the load aggregation level changes. They also need a relatively large data set to support the recovery of the predictive densities. Our proposed method addresses this issue and is based on Bayesian nonparametric model which has unbounded complexity and allow the complexity to automatically grow and be inferred from the observed data. The uncertainty underlying load patterns can be endowed with any type of prior distribution and is given in a nonparametric form, i.e. a mixture model with countably infinite number of mixtures, inferred from the posterior using the Gibbs Sampling, which is a Markov Chain Monte Carlo (MCMC) technique. All effective samples from the sampling procedure along with the exogenous variables are fed to an ensemble learning machine. The final result of the probabilistic load forecasting (PLF) is averaged on the outputs of all learning models, thus reducing the model variance and enhancing the model consistency. The proposed method is tested on both a public data set and a local data set from the Saskatoon Light &Power AMI Meter Replacement Program which offers electricity consumption at a granularity of 30 minutes of more than 65,000 electricity customers including industrial, commercial and residential sectors in the city of Saskatoon, Canada

Non-Gaussian residual based short term load forecast adjustment for distribution feeders

The evolving role for electricity network operators means that load forecasting at the distribution level has become increasingly important, presenting the need for anticipation of the behavior of highly dynamic and diversely distributed loads. The commonly held assumption of Gaussian residuals in forecasting does not always hold for distribution network loads, increasing the uncertainty in balancing a system at this network level. To reduce the operational impact of forecast errors, this paper utilizes different multivariate joint probability distributions to capture the intra-day dependency structure of forecast residuals. Transforming these to the conditional form enables forecast corrections to be made at variable horizons even in the absence of the forecast model. Improvements in accuracy are demonstrated on benchmark load forecast models at distribution level low voltage substations. A practical distribution system application on scheduling embedded energy storage shows substantial reductions in grid imports and hence costs to distribution level customers from utilizing the proposed intraday correction approach

Classification of load forecasting studies by forecasting problem to select load forecasting techniques and methodologies

The key contribution of this paper is to propose a classification into two dimensions of the load forecasting studies to decide which forecasting tools to use in which case. This classification aims to provide a synthetic view of the relevant forecasting techniques and methodologies by forecasting problem. In addition, the key principles of the main techniques and methodologies used are summarized along with the reviews of these papers. The classification process relies on two couples of parameters that define a forecasting problem. Each article is classified with key information about the dataset used and the forecasting tools implemented: the forecasting techniques (probabilistic or deterministic) and methodologies, the data cleansing techniques, and the error metrics. The process to select the articles reviewed in this paper was conducted into two steps. First, a set of load forecasting studies was built based on relevant load forecasting reviews and forecasting competitions. The second step consisted in selecting the most relevant studies of this set based on the following criteria: the quality of the description of the forecasting techniques and methodologies implemented, the description of the results, and the contributions. This paper can be read in two passes. The first one by identifying the forecasting problem of interest to select the corresponding class into one of the four classification tables. Each one references all the articles classified across a forecasting horizon. They provide a synthetic view of the forecasting tools used by articles addressing similar forecasting problems. Then, a second level composed of four Tables summarizes key information about the forecasting tools and the results of these studies. The second pass consists in reading the key principles of the main techniques and methodologies of interest and the reviews of the articles.arXiv versio

Computation of loop flows in electric grids with high wind energy penetration

2013 Fall.Includes bibliographical references.In a deregulated electricity market, the financial transmission rights (FTRs) and the bid-sell principle for energy trades are used to determine the expected power flows on transmission lines. Expected power flows are calculated by applying the superposition theorem on the approved electronic tags (e-tags). Multiple parallel paths in interconnected networks lead to division of power flows determined by the impedances of the parallel paths and the physical laws of electricity. The actual power flows in the network do not conform to the market expectations leading to unscheduled flows (USF) on transmission lines. USF have historically been estimated and accommodated deterministically for a given set of e-tags. However, wide-area interconnections experience variability and uncertainty due to a significant penetration of wind energy connected at the transmission level, thus imparting a stochastic nature to USF. A linear model, from the literature, has been adopted to model USF using a mathematical artifact called `minor loop flows'. This research develops an automated framework that provides accurate estimates of loop flows suitable for both market and network level accommodation of variable USF. This generic framework will be applicable to any power transmission network with intermittent energy resources. A loop detection algorithm (LDA) based on graph theory is proposed to detect loops in a transmission network of any size. The LDA is formulated as a modification of the A-star (A*) algorithm, the lowest ancestor theorem, and Dijkstra's algorithm. The LDA has an order of complexity of V2, where V is the total number of vertices or buses in the network under consideration. An application of a geographical information systems (GIS) technique has been established to obtain the transmission line layouts. The outcome of the LDA (i.e., minor loops) and line layouts (i.e., azimuth) are processed to compute the incidence matrix of the estimator. The variability due to the penetration of wind energy is accounted in the proposed framework using the probabilistic load flow analysis based on Monte Carlo simulations. Three techniques - ordinary least squares (OLS), analytic ridge regression (RR), and robust regression (M-estimators) - are used to estimate minor loop flows. The estimation techniques adhere to the auto-correction of the quality of estimates in case of ill-conditioning of the incidence matrix. Accuracy of loop flow estimates is highly significant, as they may be used for assigning economic responsibility of USF in electricity markets. Wind power generation companies (WGENCOs) employ forecasting models to participate in the primary electricity markets. Forecasting models used to predict the output of wind power plants are inherently erroneous and hence, their impacts on USF are studied. The impact of forecasting errors associated with the output of wind plants is investigated using the concept of prediction intervals rather than point accurate forecasts. Loop flow estimates corresponding to the prediction intervals of power output of wind power plants are computed to provide statistical bounds. The proposed framework is tested on the IEEE 14-bus and the IEEE 30-bus standard test systems with suitable modifications to represent wind energy penetration. Accurate loops are detected for the aforementioned test systems using the LDA. Thus, an automated and generic computation of loop flows is proposed along with a step-wise demonstration on IEEE test systems is provided. Future work and concluding remarks summarize the research work in this dissertation