forecasting prices in electricity markets · exploratory analysis. electricity prices. v modelling...
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Forecasting prices in electricity markets
V Modelling WeekForecasting prices in electricity markets
V Modelling WeekComplutense University of MadridTuesday, 21 July 2011
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Contents
V Modelling WeekForecasting prices in electricity markets
• Introduction to the problem
• Exploratory Analysis
• Arima Model
• Refinements
• KNN Model
• Conclusions
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Introduction to the problem
V Modelling WeekForecasting prices in electricity markets
![Page 4: Forecasting prices in electricity markets · Exploratory analysis. Electricity prices. V Modelling Week Forecasting prices in electricity markets In this plot we recognize some points](https://reader034.vdocuments.net/reader034/viewer/2022042806/5f741e1df27c25522a4bd922/html5/thumbnails/4.jpg)
Introduction to the problem
V Modelling WeekForecasting prices in electricity markets
![Page 5: Forecasting prices in electricity markets · Exploratory analysis. Electricity prices. V Modelling Week Forecasting prices in electricity markets In this plot we recognize some points](https://reader034.vdocuments.net/reader034/viewer/2022042806/5f741e1df27c25522a4bd922/html5/thumbnails/5.jpg)
Introduction to the problem
V Modelling WeekForecasting prices in electricity markets
Aim Hourly electricity price prediction model
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Exploratory analysis. Data and variables
V Modelling WeekForecasting prices in electricity markets
![Page 7: Forecasting prices in electricity markets · Exploratory analysis. Electricity prices. V Modelling Week Forecasting prices in electricity markets In this plot we recognize some points](https://reader034.vdocuments.net/reader034/viewer/2022042806/5f741e1df27c25522a4bd922/html5/thumbnails/7.jpg)
Exploratory analysis. Data and variables
V Modelling WeekForecasting prices in electricity markets
Data Estimate
the model Validate the model
Data to estimate the model: June 2010 –May 2011
Data to validate the model: 1 – 12 of June 2011
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Exploratory analysis. Data and variables.
V Modelling WeekForecasting prices in electricity markets
In this plot we can observe the distribution per months of the electricity prices between January 2007 and May 2011
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Exploratory analysis. Data and variables
V Modelling WeekForecasting prices in electricity markets
Taking into account the last plot we create a new variable call “Season” thatclassifies the data in two categories, “Spring” and “Rest of the year”
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Exploratory analysis. Data and variables
V Modelling WeekForecasting prices in electricity markets
In this plot we can observe the distribution of the electricity demand, Prices and temperature for the different hours of a day.
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Exploratory analysis. Data and variables
V Modelling WeekForecasting prices in electricity markets
Looking to the last plot we can create a new variable called “period of a day “ that classifies the 24 hours in three periods
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Exploratory analysis. Data and variables
V Modelling WeekForecasting prices in electricity markets
In this plot we can observe the distribution per month of the electricity demand during the last four years.
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Exploratory analysis. Correlations.
V Modelling WeekForecasting prices in electricity markets
Here we represent the higher correlations between the different variables.
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V Modelling WeekForecasting prices in electricity markets
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Exploratory analysis. Electricity prices.
V Modelling WeekForecasting prices in electricity markets
In this plot we recognize some points that breaks the tendence of the Series.The horizontal axis represent all the weeks from 2007 to 2011
All these days corresponde to holidays in Spain (Christmas day, easter,… )
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Prediction model building
V Modelling WeekForecasting prices in electricity markets
‐ARIMA Model
‐ K‐ Nearest Neighbors (KNN)
‐Measures of the error
‐ Methods
‐ Data‐Training dataset: 1 year
‐ Validation dataset: 2 weeks
24
1
ˆ
241MDE
h h
hh
P
PP
168
1
ˆ
1681MWE
h h
hh
P
PP
‐ Mean Daily Error
‐ Mean Weekly Error
‐Previous works on forecasting electricity prices (Weron, 2008) MWE 10‐15%
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V Modelling WeekForecasting prices in electricity markets
ARIMA Model
‐ Correlation between weeks = 0.557 Lag 168 = hours of a week
‐ Seasonality of 24 hours
‐ ARIMA (3, 0, 10) x (1, 1, 1)24 x (0, 1, 0)168
3 4 5 7 8 9, 0.
FINAL MODEL FOR FULL SERIE:
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V Modelling WeekForecasting prices in electricity markets
FORECAST FOR PRICE USING THE VARIABLE PRICE AND ARIMA MODEL
Mean Weekly Error: 2.3 % for both weeks
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V Modelling WeekForecasting prices in electricity markets
Maximum = 2.46 % in 6 June 2011
FORECAST FOR PRICE USING THE VARIABLE PRICE AND ARIMA MODEL
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V Modelling WeekForecasting prices in electricity markets
FORECAST FOR PRICE USING THE VARIABLE PRICE AND NATIONAL DEMAND
Mean Weekly Error: 2.0 % for both weeks
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V Modelling WeekForecasting prices in electricity markets
ARIMA Model
‐ ARIMA (3, 0, 10) x (1, 1, 1)24 x (0, 1, 0)168
3 4 5 7 8 9, 0.
FINAL MODEL FOR FULL SERIE:
No mean term in this model.
Autoregressive Factors
Factor 1: 1 + 0.28912 B**(3)Factor 2: 1 ‐ 0.82937 B**(1)
Moving Average Factors
Factor 1: 1 ‐ 0.46842 B**(1) + 0.34295 B**(2) ‐ 0.05455 B**(6) + 0.06695 B**(10)Factor 2: 1 + 0.62342 B**(1)
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V Modelling WeekForecasting prices in electricity markets
ARIMA by days.
MWE1 5,32 %
MWE2 6,02 %
‐ 7 time series, one for each day
‐ Problem: no information about the previous day
DAY OF THE WEEK ARIMA MODEL
MONDAY (0,1,2)(0,1,1)
TUESDAY (0,1,3)(0,1,1)
WEDNESDAY (2,1,0)(0,1,1)
THURSDAY (1,0,2)(0,1,1)
FRIDAY (2,1,1)(0,1,1)
SATURDAY (1,1,1)(0,1,1)
SUNDAY (2,1,3)(0,1,1)
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V Modelling WeekForecasting prices in electricity markets
KNN method
We take the data for the price each day to be a vector of 24 entries.
Training set of data, say {p1,p2,p3,....pt}.
Rank each day in order of similarity to today, choose k Nearest Neighbours say {v1, v2,..., vk,}
Day next to a nearest neighbour of today will be nearest neighbour of tomorrow. {v1, v2,..., vk,}
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V Modelling WeekForecasting prices in electricity markets
KNN method
Tomorrow's price is a weighted linear combination of its k nearest neighbours.
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V Modelling WeekForecasting prices in electricity markets
KNN method
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V Modelling WeekForecasting prices in electricity markets
KNN method
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V Modelling WeekForecasting prices in electricity markets
KNN method by Demand
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V Modelling WeekForecasting prices in electricity markets
KNN method by Demand
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V Modelling WeekForecasting prices in electricity markets
Conclusion
Lots of future investigation….
ARIMA ARIMA +
Demand
ARIMA + Demand ,
by days
KNN KNN by demand
MWE 1 2.05% 2.0% 5% 7.3% 14%
MWE 2 2.1% 2.0% 6% 6.4% 8.4%
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V Modelling WeekForecasting prices in electricity markets
Thank you!
StudentsCarlos González Salcedo Diana Edith Guere Lettich Natalie KeatingIgnacio Martínez Calvo Charmi Devendra PanchalVíctor Puente García
InstructorsJuan TejadaHugo Marrao