Publication: Generación de escenarios de producción eólica para el análisis probabilístico de la operación de sistemas de energía eléctrica
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2012-06
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2012-07-10
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Abstract
El objetivo general de la tesis consiste en generar trayectorias de la producción eólica futura para el análisis probabilístico de los sistemas de energía eléctrica. Esta información puede ser utilizada para el comercio en los mercados de energía, para la determinación y la resolución de restricciones en la operación del sistema, para la estimación de las reservas de energía, entre otros usos. De esta forma, se facilita la integración de las fuentes no gestionables, y en particular, de la energía eólica. Para conseguir este objetivo se desarrolló un modelo estocástico de la producción eólica. Este modelo genera escenarios de producción condicionados por la predicción a corto plazo. El modelo caracteriza las trayectorias simuladas basándose en la información obtenida del comportamiento pasado del parque eólico: producciones reales y sus respectivas previsiones a diferentes horizontes de predicción. Este tipo de información es la que usualmente poseen los productores eólicos y el operador del sistema, de forma que son los únicos datos disponibles para obtener el modelo. El modelo se desarrolla partiendo de la teoría de las funciones cópula, como una herramienta para el modelado multivariante de variables aleatorias. Para el modelo multivariante es necesario obtener los modelos para las funciones de densidad univariantes de los errores de la predicción. Para obtener estos modelos se parte de los datos de un parque eólico, predicciones y producciones donde se identifican las características de las variables. Para las funciones marginales univariantes, primero se considera un modelo paramétrico basado en la distribución beta; como segunda alternativa, se considera una técnica de estimación de la función de densidad mediante funciones kernel, siendo este un método no paramétrico. Los dos modelos, paramétrico y no paramétrico, no consiguen modelar de forma adecuada los errores de la predicción eólica cuando la producción real del parque es cero. Para resolver este problema se utiliza la regresión logística, un método que permite estimar la probabilidad de una variable con respuesta cualitativa, en este caso, de las producciones nulas. Una vez que se estima el modelo que obtiene la probabilidad de que ocurra una producción nula, dada la predicción, se adaptan los modelos antes descritos para obtener las funciones de densidad que modelan correctamente los errores en la predicción de producción eólica. En ambos modelos, paramétrico y no paramétrico, se implementaron estimaciones adaptativas de los parámetros. A medida que pasa el tiempo, el modelo obtiene nueva información del comportamiento del parque, en este caso, de las producciones reales y sus respectivas predicciones. Los nuevos datos son incluidos y ponderados de acuerdo a su relevancia y antigüedad, dando una característica adaptativa al modelo, de forma que logran replicar los comportamientos estacionales de la producción eólica. Los modelos estimados para las funciones marginales univariantes son evaluados y comparados durante el procedimiento. Se determina que el modelo no paramétrico, mediante funciones kernel y la regresión logística, tiene un mejor desempeño que la técnica de modelado paramétrica, que utiliza la distribución beta y la regresión logística. Finalmente, se estima la estructura de dependencia de las variables aleatorias desde el dominio uniforme. Se convierten las variables aleatorias al dominio uniforme, mediante la función de distribución de probabilidad obtenida con las funciones kernel y la regresión logística. De esta forma, se elimina la influencia del dominio original de las variables aleatorias. Con las funciones de densidad univariantes y la estructura de dependencia, se construye un modelo multivariante para la producción eólica, usando las funciones cópula. Con el modelo propuesto se pueden generar trayectorias posibles de la producción y obtener los intervalos de confianza. Dos modelos han sido desarrollados, el primero representa la dependencia temporal (corto plazo) en la producción de un parque y el segundo representa la dependencia espacial-temporal de varios parques en una misma zona. Con un número considerable de escenarios simulados es posible estimar la incertidumbre de la producción, no solo en términos de potencia, sino también en cantidad de energía desviada. Esta información es utilizada para desarrollar medidas de compensación de los desvíos en la producción eólica, aplicadas a problemas de complejidad real. En el primer problema se propone la utilización de un método de optimización, buscando maximizar los ingresos de la operación conjunta de una central hidroeléctrica reversible y un parque eólico. En el segundo problema se representan diversas medidas de compensación como problemas de optimización, donde se busca cubrir los desvíos de la producción de un grupo de parques eólicos. En los problemas de optimización, el modelo del sistema eléctrico es representado explícitamente. A partir de las trayectorias simuladas de la producción eólica futura se determinan los niveles de incertidumbre, en términos tanto de potencia como de energía futura. La incertidumbre de la producción es incluida en un problema de optimización que usa una central hidroeléctrica reversible con el objetivo de reducir el costo de los desvíos. En todos los resultados obtenidos para este problema, se consiguió un beneficio al comparar la operación independiente respecto a la operación conjunta. El método propuesto puede ser extendido a otros aspectos de la operación de sistemas de energía eléctrica. La central hidroeléctrica reversible se usa para minimizar los desvíos debidos a los errores en la predicción de la potencia eólica, cuando el productor eólico participa en el mercado. De esta forma, los agentes pueden reducir el riesgo al que están expuestos debido a la incertidumbre asociada a la producción eólica y a los precios de la energía de reserva. Finalmente, se comparan diferentes alternativas para compensar los desvíos de la producción eólica en un sistema de energía eléctrica. Las medidas propuestas se prueba en un sistema basado en el caso «IEEE 30 Bus Test Case», incluido en MATPOWER, con el objetivo de simular la complejidad de un pequeño sistema real. Las diferentes alternativas se validan mediante un Flujo de Potencia Probabilístico (FPP), empleando el método de Monte Carlo, donde se considera la incertidumbre de la producción eólica de un grupo de parques eólicos. Mediante este método se puede estimar el valor de cualquiera de las variables del sistema de energía eléctrica por medio de su función de densidad de probabilidad, por ejemplo, el nivel de carga de las líneas de transmisión, las pérdidas del sistema, el uso de los elementos de almacenamiento, etc. La influencia de la producción eólica y los efectos del almacenamiento en el sistema de energía eléctrica pueden apreciarse comparando las variables de salida (generación, intercambio entre áreas, pérdidas del sistema y uso del almacenamiento) del Flujo de Potencia Probabilístico (FPP). ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
The overall objective of the thesis is the generation of trajectories of future wind power production (for a short term horizon, one or two days in advance) for the probabilistic analysis of power systems. This information can be used for trading into markets, for the identification and resolution of constraints on the operation of the system, to estimate energy reserves, among others. This results will facilitate the integration of intermittent energy into the system, in particular the wind energy. To achieve this objective, a stochastic model of the wind production. This model generates possible production trajectories, conditioned by the short-term wind power prediction has been developed. The model characterizes the simulated trajectories, based on the historical data of the wind farm, namely power production and their forecasts for different horizons. This information is usually held by wind farms owners and system operators. The model is based on the copula function theory, which is a tool for modeling multivariate random variables. For the multivariate model the univariate density functions of the forecasted error of the wind power is required. These functions have been estimated in this work from the data of a wind farm, predictions and productions, from also the characteristics of the variables were identified. For univariate marginal functions, a parametric model based on the beta distribution was considered in a first trial. As second alternative, the estimation technique called Kernel Density Estimation (KDE), a non-parametric method, was considered. The two models, parametric and nonparametric, failed to correctly represent the prediction errors of the wind power when the real production is zero. To solve this problem, logistic regression was used, to estimate the probability of a qualitative response variable (in this case the null productions). Once the model for the probability of null production was estimated, for a given value of the prediction, the models described above were adapted for modeling correctly the forecast error of the wind power production. In both models, parametric and nonparametric, adaptive estimates of the parameters were implemented. This means that a new information obtained from data of the wind farm, in this case of new productions and their predictions, are included and weighted according to their relevance and age, giving to the model an adaptive feature, so the model is able to represent the seasonal behavior of wind production. The proposed models for the univariate marginal functions were evaluated and compared with real data. It was determined that the non-parametric model using kernel functions and logistic regression performs better than the parametric modeling technique, using the beta distribution and logistic regression. Finally, the dependence structure of the random variables from the uniform domain was estimated. The forecasted errors were transformed to uniform domain by using the Probability Density Function (PDF), obtained with kernel functions and logistic regression. Through this transformation, the influence of the original domain of the random variables was eliminated. With these elements a multivariate model for the wind power production using the copula function can be built, to generate possible trajectories and to obtain the confidence intervals of the wind power production. The first developed model represents the time dependence (short term) in the wind power production of a wind farm, and the second model represents the spatialtemporal dependence for several wind farms in the same region. With a considerable number of simulated trajectories, it is possible to estimate the uncertainty of the wind production, not only in terms of power but also in terms of energy. This information is used to develop actions for compensating the wind power deviations in complex problems. As a first problem, the use of an optimization method is propose, which seeks to maximize the revenues of a wind power producer, reducing the wind power deviations by the joint operation with a hydro-pump plant. In the second problem, different actions of compensation are formulated as optimization problems, in order to reduce the deviations of a group of wind farms. In all the actions, the power system model is explicitly considered in the optimization problem. The statistical information obtained with the simulated trajectories makes possible to calculate the joint optimal operation of a hydropump plant and a wind power producer. The wind power production uncertainty is included in an optimization problem that uses a hydro-pump plant in an optimal way, reducing the imbalance costs. In all the results of this problem, an economic gain was achieved for the operation in cooperation. The procedure can be expanded to independent control centers for renewable energy and some other operational issues. The hydro-pump plant is used to minimize the imbalances due to the errors in the wind power forecasting when the wind producer trades in energy markets. In this way, the utilities may reduce the risk due to the uncertainty in the wind power prediction and in prices of the reserve market. Eventually, the imbalances in the wind power production could be fully avoided by the action of the hydro-pump plant and others storages devises. Finally, different alternatives to compensate wind power deviations in power systems are compared. The different approaches were tested on a modified MATPOWER 30-bus test system modeling the complexity of a real system. The different alternatives were validated by using the Probabilistic Load Flow in the electrical power system where wind power uncertainty is considered. With this method the probability density function of any variable in the power system can be estimated. These variables might be the charge level of the transmission line, the losses in the system, the use of storage devices, etc. The wind power and storage effects in the power systems can be observed by comparing the output variables (generation, area interchange flows, system losses and storage use) of the Monte Carlo method in the power systems.
The overall objective of the thesis is the generation of trajectories of future wind power production (for a short term horizon, one or two days in advance) for the probabilistic analysis of power systems. This information can be used for trading into markets, for the identification and resolution of constraints on the operation of the system, to estimate energy reserves, among others. This results will facilitate the integration of intermittent energy into the system, in particular the wind energy. To achieve this objective, a stochastic model of the wind production. This model generates possible production trajectories, conditioned by the short-term wind power prediction has been developed. The model characterizes the simulated trajectories, based on the historical data of the wind farm, namely power production and their forecasts for different horizons. This information is usually held by wind farms owners and system operators. The model is based on the copula function theory, which is a tool for modeling multivariate random variables. For the multivariate model the univariate density functions of the forecasted error of the wind power is required. These functions have been estimated in this work from the data of a wind farm, predictions and productions, from also the characteristics of the variables were identified. For univariate marginal functions, a parametric model based on the beta distribution was considered in a first trial. As second alternative, the estimation technique called Kernel Density Estimation (KDE), a non-parametric method, was considered. The two models, parametric and nonparametric, failed to correctly represent the prediction errors of the wind power when the real production is zero. To solve this problem, logistic regression was used, to estimate the probability of a qualitative response variable (in this case the null productions). Once the model for the probability of null production was estimated, for a given value of the prediction, the models described above were adapted for modeling correctly the forecast error of the wind power production. In both models, parametric and nonparametric, adaptive estimates of the parameters were implemented. This means that a new information obtained from data of the wind farm, in this case of new productions and their predictions, are included and weighted according to their relevance and age, giving to the model an adaptive feature, so the model is able to represent the seasonal behavior of wind production. The proposed models for the univariate marginal functions were evaluated and compared with real data. It was determined that the non-parametric model using kernel functions and logistic regression performs better than the parametric modeling technique, using the beta distribution and logistic regression. Finally, the dependence structure of the random variables from the uniform domain was estimated. The forecasted errors were transformed to uniform domain by using the Probability Density Function (PDF), obtained with kernel functions and logistic regression. Through this transformation, the influence of the original domain of the random variables was eliminated. With these elements a multivariate model for the wind power production using the copula function can be built, to generate possible trajectories and to obtain the confidence intervals of the wind power production. The first developed model represents the time dependence (short term) in the wind power production of a wind farm, and the second model represents the spatialtemporal dependence for several wind farms in the same region. With a considerable number of simulated trajectories, it is possible to estimate the uncertainty of the wind production, not only in terms of power but also in terms of energy. This information is used to develop actions for compensating the wind power deviations in complex problems. As a first problem, the use of an optimization method is propose, which seeks to maximize the revenues of a wind power producer, reducing the wind power deviations by the joint operation with a hydro-pump plant. In the second problem, different actions of compensation are formulated as optimization problems, in order to reduce the deviations of a group of wind farms. In all the actions, the power system model is explicitly considered in the optimization problem. The statistical information obtained with the simulated trajectories makes possible to calculate the joint optimal operation of a hydropump plant and a wind power producer. The wind power production uncertainty is included in an optimization problem that uses a hydro-pump plant in an optimal way, reducing the imbalance costs. In all the results of this problem, an economic gain was achieved for the operation in cooperation. The procedure can be expanded to independent control centers for renewable energy and some other operational issues. The hydro-pump plant is used to minimize the imbalances due to the errors in the wind power forecasting when the wind producer trades in energy markets. In this way, the utilities may reduce the risk due to the uncertainty in the wind power prediction and in prices of the reserve market. Eventually, the imbalances in the wind power production could be fully avoided by the action of the hydro-pump plant and others storages devises. Finally, different alternatives to compensate wind power deviations in power systems are compared. The different approaches were tested on a modified MATPOWER 30-bus test system modeling the complexity of a real system. The different alternatives were validated by using the Probabilistic Load Flow in the electrical power system where wind power uncertainty is considered. With this method the probability density function of any variable in the power system can be estimated. These variables might be the charge level of the transmission line, the losses in the system, the use of storage devices, etc. The wind power and storage effects in the power systems can be observed by comparing the output variables (generation, area interchange flows, system losses and storage use) of the Monte Carlo method in the power systems.
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Keywords
Energía eólica, Producción de energía, Análisis probabilístico, Sistemas de energía eléctrica