Probabilistic forecasting and interpretability in power load applications

Power load forecasting is a fundamental tool in the modern electric power generation and distribution industry. The ability to accurately predict future behaviours of the grid, both in the short and long term, is vital in order to adequately meet demand and scaling requirements. Over the past few decades Machine Learning (ML) has taken center stage in this context, with an emphasis on short-term forecasting using both traditional ML as well as Deep-Learning (DL) models. In this dissertation, we approach forecasting not only from the angle of improving predictive accuracy, but also with the goal of gaining interpretability of the behavior of the electric load through models that can offer deeper insight and extract useful information. Specifically for this reason, we focus on the use of probabilistic models, which can shed light on valuable information about the underlying structure of the data through the interpretation of their parameters. Furthermore, the use of probabilistic models intrinsically provides us with a way of measuring the confidence in our predictions through the predictive variance. Throughout the dissertation we shall focus on two specific ideas within the greater field of power load forecasting, which will comprise our main contributions. The first contribution addresses the notion of power load profiling, in which ML is used to identify profiles that represent distinct behaviours in the power load data. These profiles have two fundamental uses: first, they can be valuable interpretability tools, as they offer simple yet powerful descriptions of the underlying patterns hidden in the time series data; second, they can improve forecasting accuracy by allowing us to train specialized predictive models tailored to each individual profile. However, in most of the literature profiling and prediction are typically performed sequentially, with an initial clustering algorithm identifying profiles in the input data and a subsequent prediction stage where independent regressors are trained on each profile. In this dissertation we propose a novel probabilistic approach that couples both the profiling and predictive stages by jointly fitting a clustering model and multiple linear regressors. In training, both the clustering of the input data and the fitting of the regressors to the output data influence each other through a joint likelihood function, resulting in a set of clusters that is much better suited to the prediction task and is therefore much more relevant and informative. The model is tested on two real world power load databases, provided by the regional transmission organizations ISO New England and PJM Interconect LLC, in a 24-hour ahead prediction scenario. We achieve better performance than other state of the art approaches while arriving at more consistent and informative profiles of the power load data. Our second contribution applies the idea of multi-task prediction to the context of 24- hour ahead forecasting. In a multi-task prediction problem there are multiple outputs that are assumed to be correlated in some way. Identifying and exploiting these relationships can result in much better performance as well as a better understanding of a multi-task problem. Even though the load forecasting literature is scarce on this subject, it seems obvious to assume that there exist important correlations between the outputs in a 24-hour prediction scenario. To tackle this, we develop a multi-task Gaussian process model that addresses the relationships between the outputs by assuming the existence of, and subsequently estimating, both an inter-task covariance matrix and a multitask noise covariance matrix that capture these important interactions. Our model improves on other multi-task Gaussian process approaches in that it greatly reduces the number of parameters to be inferred while maintaining the interpretability provided by the estimation and visualization of the multi-task covariance matrices. We first test our model on a wide selection of general synthetic and real world multi-task problems with excellent results. We then apply it to a 24-hour ahead power load forecasting scenario using the ISO New England database, outperforming other standard multi-task Gaussian processes and providing very useful visual information through the estimation of the covariance matrices.La predicción de carga es una herramenta fundamental en la industria moderna de la generación y distribución de energía eléctrica. La capacidad de estimar con precisión el comportamiento futuro de la red, tanto a corto como a largo plazo, es vital para poder cumplir con los requisitos de demanda y escalado en las diferentes infraestructuras. A lo largo de las últimas décadas, el Aprendizaje Automático o Machine Learning (ML) ha tomado un papel protagonista en este contexto, con un marcado énfasis en la predicción a corto plazo utilizando tanto modelos de ML tradicionales como redes Deep-Learning (DL). En esta tesis planteamos la predicción de carga no sólo con el objetivo de mejorar las prestaciones en la estimación, sino también de ganar en la interpretabilidad del comportamiento de la carga eléctrica a través de modelos que puedan extraer información útil. Por este motivo nos centraremos en modelos probabilísticos, que por su naturaleza pueden arrojar luz sobre la estructura oculta de los datos a través de la interpretación de sus parámetros. Además el uso de modelos probabilísticos nos proporciona de forma intrínseca una medida de confianza en la predicción a través de la estimación de la varianza predictiva. A lo largo de la tesis nos centraremos en dos ideas concretas en el contexto de la predicción de carga eléctrica, que conformarán nuestras aportaciónes principales. Nuestra primera contribución plantea la idea del perfilado de la carga eléctrica, donde se utilizan modelos de ML para identificar perfiles que representan comportamientos diferenciables en los datos de carga. Estos perfiles tienen dos usos fundamentales: en primer lugar son herramientas útiles para la interpretabilidad del problema ya que ofrecen descripciones sencillas de los posibles patrones ocultos en los datos; en segundo lugar, los perfiles pueden ser utilizados para mejorar las prestaciones de estimación, ya que permiten entrenar varios modelos predictivos especializados en cada perfil individual. Sin embargo, en la literatura el perfilado y la predicción se presentan como eventos en cascada, donde primero se entrena un algoritmo de clústering para detectar perfiles que luego son utilizados para entrenar los modelos de regresión. En esta tesis proponemos un modelo probabilístico novedoso que acopla las dos fases ajustando simultáneamente un modelo de clústering y los correspondientes modelos de regresión. Durante el entrenamiento ambas partes del modelo se influencian entre sí a través de una función de verosimilitud conjunta, resultando en un conjunto de clusters que está mucho mejor adaptado a la tarea de predicción y es por tanto mucho más relevante e informativo. En los experimentos, el modelo es entrenado con datos reales de carga eléctrica provinientes de dos bases de datos públicas proporcionadas por las organizaciónde de transmisión regional estadounidenses ISO New England y PJM Interconect LLC, en un escenario de predicción a 24 horas. El modelo obtiene mejores prestaciones que otros algoritmos competitivos, proporcionando al mismo tiempo un conjunto de perfiles del comportamiento de la carga más consistente e informativo. Nuestra segunda contribución aplica la idea de predicción multi-tarea al contexto de la estimación a 24 horas. Los problemas multi-tarea presentan múltiples salidas que se asume están de alguna forma correladas entre sí. Identificar y aprovechar estas relaciones puede incurrir en un incremento de las prestaciones así como un mejor entendimiento del problema multi-tarea. A pesar de que la literatura de predicción de carga es escasa en este sentido, parece lógico pensar que deben existir importantes correlaciones entre las salidas de un escenario de predicción a 24 horas. Por este motivo hemos desarrollado un proceso Gaussiano multi-tarea que recoge las relaciones entre salidas asumiendo la existencia de de una covarianza inter-tarea así como un ruido multi-tarea. Nuestro modelo ofrece mejoras con respecto a otras formulaciones de procesos Gaussianos multi-tarea al reducir el número de parámetros a estimar mientras se mantiene la interpretabilidad proporcionada por la estimación y visualizacion de las matrices de covarianza y ruido inter-tarea. Primero, en la fase de experimentos nuestro modelo es puesto a prueba sobre una batería de bases de datos tanto sintéticas como reales, obteniendo muy buenos resultados. A continuación se aplica el modelo a un problema de predicción de carga a 24 horas utilizando la base de datos de ISO New England, batiendo en prestaciones a otros procesos Gaussianos multi-tarea y proporcionando información visual útil mediante la estimación de las matrices de covarianza inter-tarea.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Pablo Martínez Olmos.- Secretario: Pablo Muñoz Moreno.- Vocal: José Palacio

Forecast-informed power load profiling: A novel approach

Power load forecasting plays a critical role in the context of electric supply optimization. The concept ofload characterization and profiling has been used in the past as a valuable approach to improve forecasting performance as well as problem interpretability. This paper proposes a novel, fully fledged theoretical framework for a joint probabilistic clustering andregression model, which is different from existing models that treat both processes independently. The clustering process is enhanced by simultaneously using the input data and the prediction targets during training. The model is thus capable of obtaining better clusters than other methods, leading to more informativedata profiles, while maintaining or improving predictive performance. Experiments have been conducted using aggregated load data from two U.S.A. regional transmission organizations, collected over 8 years. These experiments confirm that the proposed model achieves the goalsset for interpretability and forecasting performance.This work is partially supported by the National Science Foundation EPSCoR Cooperative Agreement OIA-1757207 and the SpanishMINECO grants TEC2014-52289-R and TEC2017-83838-R

Evaluation of dimensionality reduction methods applied to numerical weather models for solar radiation forecasting

The interest in solar radiation prediction has increased greatly in recent times among the scientific community. In this context, Machine Learning techniques have shown their ability to learn accurate prediction models. The aim of this paper is to go one step further and automatically achieve interpretability during the learning process by performing dimensionality reduction on the input variables. To this end, three non standard multivariate feature selection approaches are applied, based on the adaptation of strong learning algorithms to the feature selection task, as well as a battery of classic dimensionality reduction models. The goal is to obtain robust sets of features that not only improve prediction accuracy but also provide more interpretable and consistent results. Real data from the Weather Research and Forecasting model, which produces a very large number of variables, is used as the input. As is to be expected, the results prove that dimensionality reduction in general is a useful tool for improving performance, as well as easing the interpretability of the results. In fact, the proposed non standard methods offer important accuracy improvements and one of them provides with an intuitive and reduced selection of features and mesoscale nodes (around 10% of the initial variables centered on three specific nodes).This work has been partially supported by the projects TIN2014-54583-C2-2-R, TEC2014-52289-R and TEC2016-81900-REDT of the Spanish Interministerial Commission of Science and Technology (MICYT), and by Comunidad Autónoma de Madrid, under project PRICAM P2013ICE-2933