I will describe and demonstrate a new open-source R package that implements the Monash Electricity Forecasting Model, a semi-parametric probabilistic approach to forecasting long-term electricity demand. The underlying model proposed in Hyndman and Fan (2010) is now widely used in practice, particularly in Australia. The model has undergone many improvements and developments since it was first proposed, and these have been incorporated in this R implementation.
The package allows for ensemble forecasting of demand based on simulations of future sample paths of temperatures and other predictor variables. It requires the following data as inputs: half-hourly/hourly electricity demands; half-hourly/hourly temperatures at one or two locations; seasonal (e.g., quarterly) demographic and economic data; and public holiday data.
Peak electricity demand forecasting is important in medium and long-term planning of electricity supply. Extreme demand often leads to supply failure with consequential business and social disruption. Forecasting extreme demand events is therefore an important problem in energy management, and this package provides a useful tool for energy companies and regulators in future planning.
Probabilistic forecasting of long-term peak electricity demandRob Hyndman
This document describes a probabilistic forecasting model for long-term peak electricity demand in South Australia. The model uses 15 years of half-hourly electricity demand and temperature data, as well as economic and demographic data, to forecast peak demand 20 years into the future. It is a semi-parametric additive model that accounts for calendar effects, temperature effects, and annual trends related to GDP, price, heating and cooling degree days. The model generates probabilistic forecasts to capture the uncertainty in long-term peak demand predictions.
ARX models for Building Energy Performance Assessment Based on In-situ Measur...Christoffer Rasmussen
(1) The document describes using ARX models to identify physical parameters for building energy performance assessment based on in-situ measurements. (2) It finds that the best model uses nighttime indoor temperature, outdoor temperature, and heating power data to estimate the building's heat loss coefficient. (3) Applying the model to different occupancy periods, it estimates the heat loss coefficient as 63.2 W/K with a standard deviation of 5.1 W/K.
This document amends regulations related to the Renewable Heat Incentive Scheme in the UK. It makes several changes to definitions in the regulations, including adding new definitions for terms like "air source heat pump", "deep geothermal", and "large installation". It also amends eligibility requirements for installations generating heat from different renewable sources.
This document describes the generation of a typical meteorological solar radiation year (TMY) for Armidale, New South Wales, Australia using 23 years of daily global solar radiation data. The Finkelstein-Schafer statistical method was used to select the most representative year of data for each month based on how closely its cumulative frequency distribution matched the long-term monthly average. The resulting typical year showed monthly average radiation values ranging from a low of 10.41 MJ/m2 in June to a high of 25.88 MJ/m2 in December. Comparison of the TMY data to the long-term monthly averages showed good agreement, indicating the TMY successfully captured typical solar conditions for Armidale
Automatic algorithms for time series forecastingRob Hyndman
Many applications require a large number of time series to be forecast completely automatically. For example, manufacturing companies often require weekly forecasts of demand for thousands of products at dozens of locations in order to plan distribution and maintain suitable inventory stocks. In these circumstances, it is not feasible for time series models to be developed for each series by an experienced analyst. Instead, an automatic forecasting algorithm is required.
In addition to providing automatic forecasts when required, these algorithms also provide high quality benchmarks that can be used when developing more specific and specialized forecasting models.
I will describe some algorithms for automatically forecasting univariate time series that have been developed over the last 20 years. The role of forecasting competitions in comparing the forecast accuracy of these algorithms will also be discussed.
Exploring the feature space of large collections of time seriesRob Hyndman
It is becoming increasingly common for organizations to collect very large amounts of data over time. Data visualization is essential for exploring and understanding structures and patterns, and to identify unusual observations. However, the sheer quantity of data available challenges current time series visualisation methods.
For example, Yahoo has banks of mail servers that are monitored over time. Many measurements on server performance are collected every hour for each of thousands of servers. We wish to identify servers that are behaving unusually.
Alternatively, we may have thousands of time series we wish to forecast, and we want to be able to identify the types of time series that are easy to forecast and those that are inherently challenging.
I will demonstrate a functional data approach to this problem using a vector of features on each time series, measuring characteristics of the series. For example, the features may include lag correlation, strength of seasonality, spectral entropy, etc. Then we use a principal component decomposition on the features, and plot the first few principal components. This enables us to explore a lower dimensional space and discover interesting structure and unusual observations.
The document discusses techniques for visualizing large collections of time series data. It describes some of the challenges in plotting thousands of time series simultaneously. The key idea presented is to first extract features or characteristics from the time series, such as trends, seasonality, and correlations. These features can then be visualized to explore patterns and relationships across the large collection of time series. Examples are provided analyzing tourism demand data from Australia containing over 300 time series. Decomposition, trend analysis, and correlation techniques are demonstrated.
Forecasting electricity demand distributions using a semiparametric additive ...Rob Hyndman
The document describes forecasting electricity demand distributions using a semi-parametric additive model. It aims to forecast peak electricity demand 20 years into the future based on 15 years of half-hourly electricity, temperature, economic and demographic data from South Australia, which has highly volatile demand. The model predicts each half-hour period separately for each season using calendar effects, temperature variables, and other predictors selected through cross-validation to provide the best out-of-sample predictions. The goal is to generate forecasts of the entire demand distribution, not just the mean or median.
Probabilistic forecasting of long-term peak electricity demandRob Hyndman
This document describes a probabilistic forecasting model for long-term peak electricity demand in South Australia. The model uses 15 years of half-hourly electricity demand and temperature data, as well as economic and demographic data, to forecast peak demand 20 years into the future. It is a semi-parametric additive model that accounts for calendar effects, temperature effects, and annual trends related to GDP, price, heating and cooling degree days. The model generates probabilistic forecasts to capture the uncertainty in long-term peak demand predictions.
ARX models for Building Energy Performance Assessment Based on In-situ Measur...Christoffer Rasmussen
(1) The document describes using ARX models to identify physical parameters for building energy performance assessment based on in-situ measurements. (2) It finds that the best model uses nighttime indoor temperature, outdoor temperature, and heating power data to estimate the building's heat loss coefficient. (3) Applying the model to different occupancy periods, it estimates the heat loss coefficient as 63.2 W/K with a standard deviation of 5.1 W/K.
This document amends regulations related to the Renewable Heat Incentive Scheme in the UK. It makes several changes to definitions in the regulations, including adding new definitions for terms like "air source heat pump", "deep geothermal", and "large installation". It also amends eligibility requirements for installations generating heat from different renewable sources.
This document describes the generation of a typical meteorological solar radiation year (TMY) for Armidale, New South Wales, Australia using 23 years of daily global solar radiation data. The Finkelstein-Schafer statistical method was used to select the most representative year of data for each month based on how closely its cumulative frequency distribution matched the long-term monthly average. The resulting typical year showed monthly average radiation values ranging from a low of 10.41 MJ/m2 in June to a high of 25.88 MJ/m2 in December. Comparison of the TMY data to the long-term monthly averages showed good agreement, indicating the TMY successfully captured typical solar conditions for Armidale
Automatic algorithms for time series forecastingRob Hyndman
Many applications require a large number of time series to be forecast completely automatically. For example, manufacturing companies often require weekly forecasts of demand for thousands of products at dozens of locations in order to plan distribution and maintain suitable inventory stocks. In these circumstances, it is not feasible for time series models to be developed for each series by an experienced analyst. Instead, an automatic forecasting algorithm is required.
In addition to providing automatic forecasts when required, these algorithms also provide high quality benchmarks that can be used when developing more specific and specialized forecasting models.
I will describe some algorithms for automatically forecasting univariate time series that have been developed over the last 20 years. The role of forecasting competitions in comparing the forecast accuracy of these algorithms will also be discussed.
Exploring the feature space of large collections of time seriesRob Hyndman
It is becoming increasingly common for organizations to collect very large amounts of data over time. Data visualization is essential for exploring and understanding structures and patterns, and to identify unusual observations. However, the sheer quantity of data available challenges current time series visualisation methods.
For example, Yahoo has banks of mail servers that are monitored over time. Many measurements on server performance are collected every hour for each of thousands of servers. We wish to identify servers that are behaving unusually.
Alternatively, we may have thousands of time series we wish to forecast, and we want to be able to identify the types of time series that are easy to forecast and those that are inherently challenging.
I will demonstrate a functional data approach to this problem using a vector of features on each time series, measuring characteristics of the series. For example, the features may include lag correlation, strength of seasonality, spectral entropy, etc. Then we use a principal component decomposition on the features, and plot the first few principal components. This enables us to explore a lower dimensional space and discover interesting structure and unusual observations.
The document discusses techniques for visualizing large collections of time series data. It describes some of the challenges in plotting thousands of time series simultaneously. The key idea presented is to first extract features or characteristics from the time series, such as trends, seasonality, and correlations. These features can then be visualized to explore patterns and relationships across the large collection of time series. Examples are provided analyzing tourism demand data from Australia containing over 300 time series. Decomposition, trend analysis, and correlation techniques are demonstrated.
Forecasting electricity demand distributions using a semiparametric additive ...Rob Hyndman
The document describes forecasting electricity demand distributions using a semi-parametric additive model. It aims to forecast peak electricity demand 20 years into the future based on 15 years of half-hourly electricity, temperature, economic and demographic data from South Australia, which has highly volatile demand. The model predicts each half-hour period separately for each season using calendar effects, temperature variables, and other predictors selected through cross-validation to provide the best out-of-sample predictions. The goal is to generate forecasts of the entire demand distribution, not just the mean or median.
This document outlines examples of big time series data and techniques for visualizing and forecasting them. It discusses four examples of hierarchical and grouped time series data: Australian tourism demand, Australian labor market participation, PBS pharmaceutical sales, and spectacle sales. It then covers various visualization methods like kite diagrams, STL decomposition, seasonal stacked bar charts, and correlation graphs to explore patterns in large time series datasets.
Visualization and forecasting of big time series dataRob Hyndman
The document discusses various techniques for visualizing and forecasting large time series data. It provides examples of large time series data sets, including Australian tourism demand data with over 300 bottom-level time series, UK spectacle sales data with over 1 million bottom-level series, and Australian labor market participation data with over 1,000 occupations. It then describes several visualization methods like kite diagrams, STL decompositions, seasonal stacked bar charts, correlation graphs, and feature analysis to analyze patterns and relationships in large time series data sets.
Advances in automatic time series forecastingRob Hyndman
The document discusses advances in automatic time series forecasting. It outlines different methods for time series forecasting, including exponential smoothing methods. Exponential smoothing can include trend and seasonal components that are additive or multiplicative. Common exponential smoothing methods are simple exponential smoothing, Holt's linear method for additive trends, additive damped trend method, and exponential trend method. The document will cover additional forecasting techniques like ARIMA modelling and methods for complex time series data.
Exploring the boundaries of predictabilityRob Hyndman
Why is it that we can accurately forecast a solar eclipse in 1000 years time, but we have no idea whether Yahoo's stock price will rise or fall tomorrow? Or why can we forecast electricity consumption next week with remarkable precision, but we cannot forecast exchange rate fluctuations in the next hour?
In this talk, I will discuss the conditions we need for predictability, how to measure the uncertainty of predictions, and the consequences of thinking we can predict something more accurately than we can.
I will draw on my experiences in forecasting Australia's health budget for the next few years, in developing forecasting models for peak electricity demand in 20 years time, and in identifying unpredictable activity on Yahoo's mail servers.
This document discusses load forecasting methods for deregulated electricity markets. It covers the importance of load forecasting, types of forecasting like long-term and short-term, and factors that influence loads such as weather, time of day, and customer class. Mathematical methods for load forecasting include regression models, similar day approaches, and neural networks. The author's research group has developed statistical learning models for long-term forecasting 2-3 years ahead and short-term forecasting 48 hours ahead. Their long-term model uses weather and time variables to forecast annual peak demand, while their short-term model provides load pocket forecasts up to 48 hours in advance.
The document describes the history of the development of the R programming language and its precursor S from 1976 to the present. It notes that S was created at Bell Labs in 1976 and first used outside of Bell Labs in 1980. It then outlines key events in the development of R, including the author first using implementations of S in 1987 and 1988, hearing a talk about R in 1996, and switching from S-PLUS to R in 2001. The document provides a high-level timeline of the evolution of R from its origins in S through releases and growth of packages and community involvement.
The document discusses hierarchical and grouped time series analysis. It defines hierarchical time series as collections of time series linked in a hierarchical structure, while grouped time series aggregate time series in non-hierarchical ways. It describes existing forecasting methods for hierarchical time series as bottom-up, top-down, and middle-out. However, it notes that further research is needed on computing forecast intervals and dealing with grouped time series forecasting. The document also provides mathematical notation for representing hierarchical time series data.
Coherent mortality forecasting using functional time series modelsRob Hyndman
The document discusses coherent mortality forecasting using functional time series models. It describes modeling mortality rates over time as functional time series, where the rates are modeled as the sum of mean and deviation functions plus error. Mortality rates for different groups like males and females are expected to behave similarly over time. The model decomposes the rates into principal components to obtain scores that can be forecast individually with univariate time series models. This allows forecasting future mortality rates coherently across groups so the forecasts do not diverge over time. Existing functional models do not impose coherence across groups.
This document discusses automatic time series forecasting and summarizes key points from a section on forecasting the Pharmaceutical Benefits Scheme (PBS) in Australia. The PBS is the government drug subsidy program that costs nearly 1% of GDP annually. Forecasts of drug usage are needed to budget costs but in 2001 the budget was underforecast by $800 million using simple Excel forecasting on only 3 years of annual aggregated data, despite 10 years of available monthly data. More sophisticated automatic methods are needed to improve forecasts given the thousands of products, seasonal demand, and other complexities.
This document discusses hierarchical and grouped time series forecasting. It provides examples of hierarchical time series, such as those organized under the Anatomical Therapeutic Chemical classification system for pharmaceuticals. It also discusses grouped time series, such as tourism demand grouped by region and purpose. The document outlines challenges in forecasting hierarchical/grouped time series and reviews existing methods like top-down, bottom-up, and middle-out approaches. It notes key issues include producing unbiased, minimum variance forecasts and computing accurate prediction intervals.
This document outlines an approach for automatic time series forecasting without human forecasters. It discusses the need for algorithms that can determine appropriate models, estimate parameters, and generate forecasts for large numbers of time series across different domains. Exponential smoothing methods and ARIMA models are covered as approaches that can be used for automatic forecasting if enhanced with techniques for model selection, parameter estimation, and producing prediction intervals. The document also motivates this work by noting limitations in previous research on general automatic forecasting algorithms.
1) The document discusses using data analytics to improve agriculture through open data on climate, soil, crops, markets and more which faces challenges of converting data into actionable insights.
2) It proposes an Interactive Agricultural Service Platform (IASP) that provides personalized agro-advisories to farmers through push and pull services on web, mobile and IVRS in multiple languages.
3) The IASP would integrate data collection, analytics, knowledge services and delivery across platforms to help farmers with customized advice, access inputs and credit, and sell produce.
This document describes the LongWave Radiation Balance (LWRB) component for estimating downwelling (L ↓) and upwelling (L ↑) longwave atmospheric radiation. Ten simplified models are implemented for estimating L ↓ using inputs like air temperature, relative humidity, and cloud cover. One model estimates L ↑. The component is integrated into the JGrass-NewAge modeling framework and can produce time series or raster outputs of L ↓, L ↑, and total longwave radiation. Examples and documentation are provided to help users configure and run the LWRB component.
Robust model reference adaptive control for a second order system 2IAEME Publication
This document discusses robust model reference adaptive control for a second order system using the MIT rule. It begins by introducing model reference adaptive control and the MIT rule adaptation mechanism. It then presents the mathematical modeling of an MRAC scheme for a second order plant in the presence of first-order and second-order noise/disturbances. Simulation results are shown for the MIT rule MRAC controlling a second order system for different adaptation gain values without noise, demonstrating the effect of the gain on system stability and performance.
Robust model reference adaptive control for a second order system 2IAEME Publication
This document discusses robust model reference adaptive control for a second order system using the MIT rule. It begins by introducing model reference adaptive control and the MIT rule adaptation mechanism. It then presents the mathematical modeling of an MRAC scheme for a second order plant in the presence of first-order and second-order noise/disturbances. Simulation results are shown for the MIT rule MRAC controlling a second order system for different adaptation gain values without noise, demonstrating the effect of the gain on system stability and performance.
In recent years we witnessed a rapid growth of the weather derivatives market.
These derivatives are used to hedge energy contracts and distribute weather
risk. While most derivative markets are complete and contingent climes
replications are standard procedure, this special market is incomplete, and
therefore modeling the weather is a more appropriate approach to pricing. In
this work, we base our modeling on a widely accepted physical approach. We
base our analysis on Navier-Stokes equations applied to a thin atmosphere as
presented by Lorentz 1962. This modeling is considered by meteorologists a
“very-long-weather” prediction, allowing for accurate and robust
temperature forecasting. We show that under this setting we empirically
outperform the standard approach to weather derivative pricing.In recent years we witnessed a rapid growth of the weather deriv
This document discusses differential equations and their application. It begins by defining what a differential equation is and provides examples of first order differential equations. It then discusses Newton's Law of Cooling, providing the derivation and formulation of the law. Several applications of Newton's Law of Cooling are presented, including using it to estimate time of death from temperature readings and determining cooling system specifications for computer processors. Other topics covered include the Mean Value Theorem, precalculus concepts, and examples of how calculus is applied in various fields such as credit cards, biology, engineering, architecture, and more.
The document summarizes recent results from WZ, Higgs, and top analyses for upcoming summer conferences. For WZ analyses, cross sections are being updated in the electron and muon channels and combined with other experiments. For top analyses, improvements are being made to measurements of the cross section using topological cuts, dilepton events, and b-tagging. The top mass is also being measured. For Higgs analyses, searches are ongoing in the W/ZH to electrons/muons channels with additional b-tagging, and in decay modes like H to gamma gamma and WW.
This document discusses load forecasting methods for electric utilities. It describes short, medium, and long-term load forecasts and factors like weather, time, and customer class that influence accurate forecasts. Mathematical regression models are used to develop statistical learning models for long-term (2-3 years ahead) and short-term (48 hours ahead) load forecasting. Performance is evaluated based on correlation, R-squared value, and normalized distance between actual and predicted loads.
The document discusses various forecasting techniques including exponential smoothing, linear regression, and simulation. It provides examples of how to calculate forecasts using simple and double exponential smoothing as well as linear, parabolic, and multiple regression models. It also presents a simulation example to compare the costs of different maintenance policies for vacuum tubes in a machine.
Short-term Load Forecasting based on Neural network and Local RegressionJie Bao
The document outlines different approaches to short-term load forecasting (STLF), including neural networks, moving averages, and local regression. It discusses using neural networks to model the complex relationships between load and determining factors like weather, calendar effects, and past loads. Moving averages are also explored, with modifications like temperature shifting to improve accuracy. Combining neural networks and local regression is proposed to better capture different timescales in load patterns.
Performance analysis of a second order system using mraciaemedu
The document analyzes the performance of a second-order system using model reference adaptive control (MRAC) with two different adaptation rules - MIT rule and Lyapunov rule. It first describes the MRAC scheme and the two adaptation rules. It then models a second-order underdamped plant and a critically damped reference model. Lastly, it applies the MIT rule to the system and derives the adaptation laws to minimize the error between the plant and reference model outputs. The analysis aims to improve the dynamic performance of the underdamped plant using MRAC.
This document outlines examples of big time series data and techniques for visualizing and forecasting them. It discusses four examples of hierarchical and grouped time series data: Australian tourism demand, Australian labor market participation, PBS pharmaceutical sales, and spectacle sales. It then covers various visualization methods like kite diagrams, STL decomposition, seasonal stacked bar charts, and correlation graphs to explore patterns in large time series datasets.
Visualization and forecasting of big time series dataRob Hyndman
The document discusses various techniques for visualizing and forecasting large time series data. It provides examples of large time series data sets, including Australian tourism demand data with over 300 bottom-level time series, UK spectacle sales data with over 1 million bottom-level series, and Australian labor market participation data with over 1,000 occupations. It then describes several visualization methods like kite diagrams, STL decompositions, seasonal stacked bar charts, correlation graphs, and feature analysis to analyze patterns and relationships in large time series data sets.
Advances in automatic time series forecastingRob Hyndman
The document discusses advances in automatic time series forecasting. It outlines different methods for time series forecasting, including exponential smoothing methods. Exponential smoothing can include trend and seasonal components that are additive or multiplicative. Common exponential smoothing methods are simple exponential smoothing, Holt's linear method for additive trends, additive damped trend method, and exponential trend method. The document will cover additional forecasting techniques like ARIMA modelling and methods for complex time series data.
Exploring the boundaries of predictabilityRob Hyndman
Why is it that we can accurately forecast a solar eclipse in 1000 years time, but we have no idea whether Yahoo's stock price will rise or fall tomorrow? Or why can we forecast electricity consumption next week with remarkable precision, but we cannot forecast exchange rate fluctuations in the next hour?
In this talk, I will discuss the conditions we need for predictability, how to measure the uncertainty of predictions, and the consequences of thinking we can predict something more accurately than we can.
I will draw on my experiences in forecasting Australia's health budget for the next few years, in developing forecasting models for peak electricity demand in 20 years time, and in identifying unpredictable activity on Yahoo's mail servers.
This document discusses load forecasting methods for deregulated electricity markets. It covers the importance of load forecasting, types of forecasting like long-term and short-term, and factors that influence loads such as weather, time of day, and customer class. Mathematical methods for load forecasting include regression models, similar day approaches, and neural networks. The author's research group has developed statistical learning models for long-term forecasting 2-3 years ahead and short-term forecasting 48 hours ahead. Their long-term model uses weather and time variables to forecast annual peak demand, while their short-term model provides load pocket forecasts up to 48 hours in advance.
The document describes the history of the development of the R programming language and its precursor S from 1976 to the present. It notes that S was created at Bell Labs in 1976 and first used outside of Bell Labs in 1980. It then outlines key events in the development of R, including the author first using implementations of S in 1987 and 1988, hearing a talk about R in 1996, and switching from S-PLUS to R in 2001. The document provides a high-level timeline of the evolution of R from its origins in S through releases and growth of packages and community involvement.
The document discusses hierarchical and grouped time series analysis. It defines hierarchical time series as collections of time series linked in a hierarchical structure, while grouped time series aggregate time series in non-hierarchical ways. It describes existing forecasting methods for hierarchical time series as bottom-up, top-down, and middle-out. However, it notes that further research is needed on computing forecast intervals and dealing with grouped time series forecasting. The document also provides mathematical notation for representing hierarchical time series data.
Coherent mortality forecasting using functional time series modelsRob Hyndman
The document discusses coherent mortality forecasting using functional time series models. It describes modeling mortality rates over time as functional time series, where the rates are modeled as the sum of mean and deviation functions plus error. Mortality rates for different groups like males and females are expected to behave similarly over time. The model decomposes the rates into principal components to obtain scores that can be forecast individually with univariate time series models. This allows forecasting future mortality rates coherently across groups so the forecasts do not diverge over time. Existing functional models do not impose coherence across groups.
This document discusses automatic time series forecasting and summarizes key points from a section on forecasting the Pharmaceutical Benefits Scheme (PBS) in Australia. The PBS is the government drug subsidy program that costs nearly 1% of GDP annually. Forecasts of drug usage are needed to budget costs but in 2001 the budget was underforecast by $800 million using simple Excel forecasting on only 3 years of annual aggregated data, despite 10 years of available monthly data. More sophisticated automatic methods are needed to improve forecasts given the thousands of products, seasonal demand, and other complexities.
This document discusses hierarchical and grouped time series forecasting. It provides examples of hierarchical time series, such as those organized under the Anatomical Therapeutic Chemical classification system for pharmaceuticals. It also discusses grouped time series, such as tourism demand grouped by region and purpose. The document outlines challenges in forecasting hierarchical/grouped time series and reviews existing methods like top-down, bottom-up, and middle-out approaches. It notes key issues include producing unbiased, minimum variance forecasts and computing accurate prediction intervals.
This document outlines an approach for automatic time series forecasting without human forecasters. It discusses the need for algorithms that can determine appropriate models, estimate parameters, and generate forecasts for large numbers of time series across different domains. Exponential smoothing methods and ARIMA models are covered as approaches that can be used for automatic forecasting if enhanced with techniques for model selection, parameter estimation, and producing prediction intervals. The document also motivates this work by noting limitations in previous research on general automatic forecasting algorithms.
1) The document discusses using data analytics to improve agriculture through open data on climate, soil, crops, markets and more which faces challenges of converting data into actionable insights.
2) It proposes an Interactive Agricultural Service Platform (IASP) that provides personalized agro-advisories to farmers through push and pull services on web, mobile and IVRS in multiple languages.
3) The IASP would integrate data collection, analytics, knowledge services and delivery across platforms to help farmers with customized advice, access inputs and credit, and sell produce.
This document describes the LongWave Radiation Balance (LWRB) component for estimating downwelling (L ↓) and upwelling (L ↑) longwave atmospheric radiation. Ten simplified models are implemented for estimating L ↓ using inputs like air temperature, relative humidity, and cloud cover. One model estimates L ↑. The component is integrated into the JGrass-NewAge modeling framework and can produce time series or raster outputs of L ↓, L ↑, and total longwave radiation. Examples and documentation are provided to help users configure and run the LWRB component.
Robust model reference adaptive control for a second order system 2IAEME Publication
This document discusses robust model reference adaptive control for a second order system using the MIT rule. It begins by introducing model reference adaptive control and the MIT rule adaptation mechanism. It then presents the mathematical modeling of an MRAC scheme for a second order plant in the presence of first-order and second-order noise/disturbances. Simulation results are shown for the MIT rule MRAC controlling a second order system for different adaptation gain values without noise, demonstrating the effect of the gain on system stability and performance.
Robust model reference adaptive control for a second order system 2IAEME Publication
This document discusses robust model reference adaptive control for a second order system using the MIT rule. It begins by introducing model reference adaptive control and the MIT rule adaptation mechanism. It then presents the mathematical modeling of an MRAC scheme for a second order plant in the presence of first-order and second-order noise/disturbances. Simulation results are shown for the MIT rule MRAC controlling a second order system for different adaptation gain values without noise, demonstrating the effect of the gain on system stability and performance.
In recent years we witnessed a rapid growth of the weather derivatives market.
These derivatives are used to hedge energy contracts and distribute weather
risk. While most derivative markets are complete and contingent climes
replications are standard procedure, this special market is incomplete, and
therefore modeling the weather is a more appropriate approach to pricing. In
this work, we base our modeling on a widely accepted physical approach. We
base our analysis on Navier-Stokes equations applied to a thin atmosphere as
presented by Lorentz 1962. This modeling is considered by meteorologists a
“very-long-weather” prediction, allowing for accurate and robust
temperature forecasting. We show that under this setting we empirically
outperform the standard approach to weather derivative pricing.In recent years we witnessed a rapid growth of the weather deriv
This document discusses differential equations and their application. It begins by defining what a differential equation is and provides examples of first order differential equations. It then discusses Newton's Law of Cooling, providing the derivation and formulation of the law. Several applications of Newton's Law of Cooling are presented, including using it to estimate time of death from temperature readings and determining cooling system specifications for computer processors. Other topics covered include the Mean Value Theorem, precalculus concepts, and examples of how calculus is applied in various fields such as credit cards, biology, engineering, architecture, and more.
The document summarizes recent results from WZ, Higgs, and top analyses for upcoming summer conferences. For WZ analyses, cross sections are being updated in the electron and muon channels and combined with other experiments. For top analyses, improvements are being made to measurements of the cross section using topological cuts, dilepton events, and b-tagging. The top mass is also being measured. For Higgs analyses, searches are ongoing in the W/ZH to electrons/muons channels with additional b-tagging, and in decay modes like H to gamma gamma and WW.
This document discusses load forecasting methods for electric utilities. It describes short, medium, and long-term load forecasts and factors like weather, time, and customer class that influence accurate forecasts. Mathematical regression models are used to develop statistical learning models for long-term (2-3 years ahead) and short-term (48 hours ahead) load forecasting. Performance is evaluated based on correlation, R-squared value, and normalized distance between actual and predicted loads.
The document discusses various forecasting techniques including exponential smoothing, linear regression, and simulation. It provides examples of how to calculate forecasts using simple and double exponential smoothing as well as linear, parabolic, and multiple regression models. It also presents a simulation example to compare the costs of different maintenance policies for vacuum tubes in a machine.
Short-term Load Forecasting based on Neural network and Local RegressionJie Bao
The document outlines different approaches to short-term load forecasting (STLF), including neural networks, moving averages, and local regression. It discusses using neural networks to model the complex relationships between load and determining factors like weather, calendar effects, and past loads. Moving averages are also explored, with modifications like temperature shifting to improve accuracy. Combining neural networks and local regression is proposed to better capture different timescales in load patterns.
Performance analysis of a second order system using mraciaemedu
The document analyzes the performance of a second-order system using model reference adaptive control (MRAC) with two different adaptation rules - MIT rule and Lyapunov rule. It first describes the MRAC scheme and the two adaptation rules. It then models a second-order underdamped plant and a critically damped reference model. Lastly, it applies the MIT rule to the system and derives the adaptation laws to minimize the error between the plant and reference model outputs. The analysis aims to improve the dynamic performance of the underdamped plant using MRAC.
Performance analysis of a second order system using mracIAEME Publication
The document analyzes the performance of a second-order system using model reference adaptive control (MRAC) with two different adaptation rules - MIT rule and Lyapunov rule. Simulation results in MATLAB show that:
1) Using MRAC with the MIT rule reduces the overshoot and undershoot of the second-order system to zero and improves settling time, provided the adaptation gain is within a suitable range.
2) Both MIT rule and Lyapunov rule derive similar parameter update laws for the adaptive controller, with the main difference being an additional filter for the reference model in the MIT rule.
3) Simulation for different adaptation gains shows the system performance is optimal within a certain range,
MATHEMATICAL MODELING OF COMPLEX REDUNDANT SYSTEM UNDER HEAD-OF-LINE REPAIREditor IJMTER
Suppose a composite system consisting of two subsystems designated as ‘P’ and
‘Q’ connected in series. Subsystem ‘P’ consists of N non-identical units in series, while the
subsystem ‘Q’ consists of three identical components in parallel redundancy.
Optimal Budget Allocation: Theoretical Guarantee and Efficient AlgorithmTasuku Soma
The document presents two main results:
1. A general framework for submodular function maximization over integer lattices with a (1-1/e)-approximation algorithm that runs in pseudo polynomial time. This extends budget allocation to more complex scenarios.
2. A faster algorithm for budget allocation when influence probabilities are non-increasing, running in almost linear time compared to previous polynomial time algorithms. Experiments on real and large synthetic graphs show it outperforms heuristics by up to 15%.
This document presents a mathematical model of solar radiation effects on loamy soil temperature. The model considers thermal conductivity that varies linearly with soil depth and an exponentially varying boundary condition. A perturbation method is used to reduce the partial differential equation to an ordinary differential equation, which is then solved analytically. The model shows that increasing solar radiation (represented by the radiation parameter) increases loamy soil temperature. Numerical results from the model using MATLAB demonstrate the effects of varying the radiation and internal heat generation parameters on soil temperature profiles at increasing depths.
This document discusses modal analysis and parameter estimation. It introduces single degree of freedom (SDOF) and multi degree of freedom (MDOF) system theory, including equations of motion, transfer functions, frequency response functions, and impulse responses. Parameter estimation can be performed in the frequency domain using FRFs or the time domain using impulse response functions. The goal is to estimate modal parameters like natural frequencies, damping ratios, and mode shapes.
Climate Analysis Workshop for weather filesAPSanyal1
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MEFM: An R package for long-term probabilistic forecasting of electricity demand
1. Rob J Hyndman
Joint work with Shu Fan
MEFM: long-term probabilistic demand forecasting 1
MEFM: An R package for
long-term probabilistic
forecasting of electricity demand
3. South Australian demand data
MEFM: long-term probabilistic demand forecasting 3
SA State wide demand (summer 2015)
SAStatewidedemand(GW)
1.01.52.02.53.0
Oct Nov Dec Jan Feb Mar
6. Temperature data (Sth Aust)
MEFM: long-term probabilistic demand forecasting 5
10 20 30 40
1.01.52.02.53.03.5
Time: 12 midnight
Temperature (deg C)
Demand(GW)
Workday
Non−workday
7. Predictors
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately for
each season.
MEFM: long-term probabilistic demand forecasting 6
8. Predictors
calendar effects
prevailing and recent weather conditions
climate changes
economic and demographic changes
changing technology
Modelling framework
Semi-parametric additive models with
correlated errors.
Each half-hour period modelled separately for
each season.
MEFM: long-term probabilistic demand forecasting 6
9. Monash Electricity Forecasting Model
y∗
t = yt/¯yi
yt denotes per capita demand at time t
(measured in half-hourly intervals);
¯yi is the average demand for quarter i where t
is in quarter i.
y∗
t is the standardized demand for time t.
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
MEFM: long-term probabilistic demand forecasting 7
10. Monash Electricity Forecasting Model
y∗
t = yt/¯yi
yt denotes per capita demand at time t
(measured in half-hourly intervals);
¯yi is the average demand for quarter i where t
is in quarter i.
y∗
t is the standardized demand for time t.
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
MEFM: long-term probabilistic demand forecasting 7
16. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
MEFM: long-term probabilistic demand forecasting 10
17. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
MEFM: long-term probabilistic demand forecasting 10
18. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Calendar effects
“Time of summer” effect (a regression spline)
Day of week factor (7 levels)
Public holiday factor (4 levels)
MEFM: long-term probabilistic demand forecasting 10
19. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
20. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
21. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
22. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
23. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
24. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
25. Half-hourly sub-model
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Temperature effects
Ave temp across two sites, plus lags for previous 3
hours and previous 3 days.
Temp difference between two sites, plus lags for
previous 3 hours and previous 3 days.
Max ave temp in past 24 hours.
Min ave temp in past 24 hours.
Ave temp in past seven days.
Each function estimated using boosted regression splines.
MEFM: long-term probabilistic demand forecasting 11
26. Ensemble forecasting
log(yt) = log(¯yi) + log(y∗
t )
log(¯yi) = f(GSP, price, HDD, CDD) + εi
log(y∗
t ) = f(calendar effects, temperatures) + et
Multiple alternative futures created:
Calendar effects known;
Future temperatures simulated
(taking account of climate change);
Assumed values for GSP, population and price;
Residuals simulated (preserving
autocorrelations)
MEFM: long-term probabilistic demand forecasting 12
27. MEFM package for R
Available on github:
install.packages("devtools")
library(devtools)
install_github("robjhyndman/MEFM-package")
Package contents:
seasondays The number of days in a season
sa.econ Historical demographic & economic data for
South Australia
sa Historical data for model estimation
maketemps Create lagged temperature variables
demand_model Estimate the electricity demand models
simulate_ddemand Temperature and demand simulation
simulate_demand Simulate the electricity demand for the next
season
MEFM: long-term probabilistic demand forecasting 13
28. MEFM package for R
Available on github:
install.packages("devtools")
library(devtools)
install_github("robjhyndman/MEFM-package")
Package contents:
seasondays The number of days in a season
sa.econ Historical demographic & economic data for
South Australia
sa Historical data for model estimation
maketemps Create lagged temperature variables
demand_model Estimate the electricity demand models
simulate_ddemand Temperature and demand simulation
simulate_demand Simulate the electricity demand for the next
season
MEFM: long-term probabilistic demand forecasting 13
29. MEFM package for R
Usage
library(MEFM)
# Number of days in each "season"
seasondays
# Historical economic data
sa.econ
# Historical temperature and calendar data
head(sa)
tail(sa)
dim(sa)
# create lagged temperature variables
salags <- maketemps(sa,2,48)
dim(salags)
head(salags)
MEFM: long-term probabilistic demand forecasting 14
30. MEFM package for R
# formula for annual model
formula.a <- as.formula(anndemand ~ gsp + ddays + resiprice)
# formulas for half-hourly model
# These can be different for each half-hour
formula.hh <- list()
for(i in 1:48) {
formula.hh[[i]] <- as.formula(log(ddemand) ~ ns(temp, df=2)
+ day + holiday
+ ns(timeofyear, df=9) + ns(avetemp, df=3)
+ ns(dtemp, df=3) + ns(lastmin, df=3)
+ ns(prevtemp1, df=2) + ns(prevtemp2, df=2)
+ ns(prevtemp3, df=2) + ns(prevtemp4, df=2)
+ ns(day1temp, df=2) + ns(day2temp, df=2)
+ ns(day3temp, df=2) + ns(prevdtemp1, df=3)
+ ns(prevdtemp2, df=3) + ns(prevdtemp3, df=3)
+ ns(day1dtemp, df=3))
}
MEFM: long-term probabilistic demand forecasting 15
31. MEFM package for R
# Fit all models
sa.model <- demand_model(salags, sa.econ, formula.hh, formula.a)
# Summary of annual model
summary(sa.model$a)
# Summary of half-hourly model at 4pm
summary(sa.model$hh[[33]])
# Simulate future normalized half-hourly data
simdemand <- simulate_ddemand(sa.model, sa, simyears=50)
# economic forecasts, to be given by user
afcast <- data.frame(pop=1694, gsp=22573, resiprice=34.65,
ddays=642)
# Simulate half-hourly data
demand <- simulate_demand(simdemand, afcast)
MEFM: long-term probabilistic demand forecasting 16
32. MEFM package for R
plot(ts(demand$demand[,sample(1:100, 4)], freq=48, start=0),
xlab="Days", main="Simulated demand futures")
MEFM: long-term probabilistic demand forecasting 17
38. MEFM package for R
plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)",
main="Density of seasonal maximum demand")
rug(demand$annmax)
MEFM: long-term probabilistic demand forecasting 20
39. MEFM package for R
plot(density(demand$annmax, bw="SJ"), xlab="Demand (GW)",
main="Density of seasonal maximum demand")
rug(demand$annmax)
1.5 2.0 2.5 3.0 3.5
0.00.40.81.2
Density of seasonal maximum demand
Demand (GW)
Density
MEFM: long-term probabilistic demand forecasting 20
40. References
¯ Hyndman, R.J. & Fan, S. (2010)
“Density forecasting for long-term peak electricity demand”,
IEEE Transactions on Power Systems, 25(2), 1142–1153.
¯ Fan, S. & Hyndman, R.J. (2012) “Short-term load forecasting
based on a semi-parametric additive model”.
IEEE Transactions on Power Systems, 27(1), 134–141.
¯ Ben Taieb, S. & Hyndman, R.J. (2013) “A gradient boosting
approach to the Kaggle load forecasting competition”,
International Journal of Forecasting, 29(4).
¯ Hyndman, R.J., & Fan, S. (2015).
“Monash Electricity Forecasting Model”. Technical paper.
robjhyndman.com/working-papers/mefm/
¯ Fan, S., & Hyndman, R.J. (2015). “MEFM: An R package imple-
menting the Monash Electricity Forecasting Model.”
github.com/robjhyndman/MEFM-package
MEFM: long-term probabilistic demand forecasting 21