Daily electricity price forecasting (report)

Материал из MachineLearning.

(Различия между версиями)

Версия 18:35, 1 ноября 2009

Введение в проект

Project description

Goal

The goal is to forecast average daily spot price of electricity. Forecasting horizon (the maximal time segment where the forecast error does not exceed given value) is supposed to be one month.

Motivation

For example, one needs precise forecast of electricity consumption for each hour during the next day to avoid transactions on the balancing market.

Data

Daily time series from 1/1/2003 until now. Time series are weather (average-, low-, and high daily temperature, relative humidity, precipitation, wind speed, heating-, and cooling degree day) and average daily price of electricity. There is no data on electricity consumption and energy units prices. The data on sunrise and sunset are coming from the internet.

Quality

The time series splits into the whole history but the last month and the last month. The model is created using the first part and tested with the second. The procedure must be repeated for each month of the last year. The target function is MAPE (mean absolute percentage error) for given month.

Requirements

The monthly error of obtained model must not exceed the error of the existing model, same to customers. It’s LASSO with some modifications.

Feasibility

The average daily price of electricity contains peaks and it is seems there is no information about these peaks in given data. There is no visible correlation between data and responses.

Methods

The model to be generated is a linear combination of selected features. Each primitive feature (of index j) is a set of j+nk-th samples of time series, k is a period. The set of the features includes primitive features and their superpositions.

Problem definition

We have variables matrix $X$ and responses vector $Y$ for this matrix. This is time series. Our goal is to recover regression $\hat{Y}$ for variables matrix $\hat{X}$ . This data is straight after initial data in time. Our goal is to find vector $\beta$ � of linear coefficients between $\hat{X}$ and $\hat{Y}$ , $Y = X\beta^T$ . As quality functional we use MAPE (mean average percent error).

${ Q(\hat{Y}) = \sum_{i=1}^n \frac{|y_i-\hat{y}_i|}{|y_i|}$ ,

Algorithm description

State of art

The main task of this subsection is to describe ways of daily electricity price forecasting and sort of data needed for this task. Also we have a deal with German electricity price market and there is brief survey about it. Let’s start from methods of forecasting daily electricity price. There are many ways to solve this problem. It can be ARIMA models or autoregression [1], [4]. Artificial neural networks are also used in combination with some serious improvements like wavelet techniques or ARIMA models [2]. SVM can be used in a close problem of price spikes forecasting [2]. Models of noise and jump can be constructed in some other ways [3]. Sets of data can be rather different. For neural networks it can be only time series [1], but in most of works some addition data is required. Weather is an important factor in price forecasting [5]. It can be median day temperature, HDD, CDD [4] or wind speed [6]. Dates of sunsets and sunrises can be useful too. Energy consumption and system load has important impact on daily electricity price [4]. Interesting features is prediction $\log(P_t)$ instead of $P_t$ electricity price in €. Our goal is forecasting daily electricity price for German electricity price market EEX, so let’s represent some information about it. Germany has free 2 electricity market, so models for free electricity market can be applied to it. Market of energy producing changes every year, main goals are phasing out nuclear energy and creation new renewable sources manufactures. Germany is one of the largest consumers of energy in the world. In 2008, it consumed energy from the following sources: oil (34.8%), coal including lignite (24.2%), natural gas (22.1%), nuclear (11.6%), renewables (1.6%), and other (5.8%), whereas renewable energy is far more present in produced energy, since Germany imports about two thirds of its energy. This country is the world’s largest operators of non-hydro renewables capacity in the world, including the world’s largest operator of wind generation [7].

References

[1] Hsiao-Tien Pao. A Neural Network Approach to m-Daily-Ahead Electricity Price Prediction

[2] Wei Wu, Jianzhong Zhou,Li Mo and Chengjun Zhu. Forecasting Electricity Market Price Spikes Based on Bayesian Expert with Support Vector Machines

[3] S.Borovkova, J.Permana. Modelling electricity prices by the potential jump-functions

[4] R.Weron, A.Misiorek. Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models

[5] J.Cherry, H.Cullen, M.Vissbeck, A.Small and C.Uvo. Impacts of the North Atlantic Oscillation on Scandinavian Hydropower Production and Energy Markets

[6] Yuji Yamada. Optimal Hedging of Prediction Errors Using Prediction Errors Yuji Yamada

[7] http://en.wikipedia.org/wiki/Energy_in_Germany

Basic hypotheses and estimations

In case of linear regression we assume, that vector of responses $Y$ is linear combination for modified incoming matrix of features $\tilde{X}$ , what we designate as $X$ :

$Y = X\beta^T$ .

This modified matrix we can get from superposition, smoothing and autoregression in initial data set. LARS[8] seems suitable for this kind of problem, so we use it in our work. From state of art and data we get some additional hypotheses. We have a deal with data set with two periodic – week periodic and year periodic. Possible usage of this is generation new features and creation own model for each day of week.

Математическое описание

Варианты или модификации

Описание системы

Ссылка на файл system.docs
Ссылка на файлы системы

Отчет о вычислительных экспериментах

Визуальный анализ работы алгоритма

Анализ качества работы алгоритма

Анализ зависимости работы алгоритма от параметров

Отчет о полученных результатах

Список литературы

Данная статья является непроверенным учебным заданием.

Студент: Участник:Зайцев Алексей

Преподаватель: Участник:В.В. Стрижов

Срок: 15 декабря 2009

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Источник — «http://machinelearning.ru/wiki/index.php?title=Daily_electricity_price_forecasting_%28report%29»

Категория: Непроверенные учебные задания

@@ Строка 107: / Строка 107: @@
 combination for modified incoming matrix of features <tex>\tilde{X}</tex> , what we designate as
 <tex>X</tex>:
-<tex>Y = X\beta^T</tex>
+<tex>Y = X\beta^T</tex>.
 This modified matrix we can get from superposition, smoothing and autoregression
 in initial data set. LARS[8] seems suitable for this kind of problem, so we