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Forecasting number of natural gas consumers and their total consumption with R

Ondřej Konár, Marek Brabec, Ivan Kasanický, Marek Malý, Emil Pelikán

Czech Technical University in Prague Czech Institute of Informatics, Robotics, and Cybernetics Academy of Sciences of the Czech Republic Institute of Computer Science

Modelling Smart Grids 2015: A New Challenge for Stochastics and Optimization Prague, September 11, 2015

Forecasting number of natural gas consumers and their total consumption with R

Motivation

• Total consumption and price per unit are essential

inputs for forecasting the revenues from delivered energy.

• Energy retail prices can differ for various tariffs.
• Larger customers get usually lower price and vice

versa.

• The tariffs can be assigned automatically based on

historical consumption.

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Forecasting number of natural gas consumers and their total consumption with R

Goal of our research

We wanted to develop a prediction model with the following properties:

1 we forecast customer counts and their total

consumption within each tariff class

2 tariffs are assigned to customers based on their

consumption level

3 forecasts are based on regular invoicing data 4 forecast is conditioned by a long-term normal

temperature

5 model should be implemented in a user-friendly way

and run on standard PC

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Forecasting number of natural gas consumers and their total consumption with R

Challenges

Factors that make reaching the goal difficult

• Forecast variables are not independent:

1 total consumptions (naturally) depends on the

customer count

2 customers can switch between tariffs (as a result of

consumption level variability)

Result: covariance structure should be considered

• Invoicing periods differ between various customers

Result: data need to be transformed

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Forecasting number of natural gas consumers and their total consumption with R

Package structure

1 Data preprocessing – conversion of invoicing data to

input data

2 Parameter estimation 3 Forecasting

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Forecasting number of natural gas consumers and their total consumption with R

Standardized load profiles

• Model for disaggregation of consumption
• Makes daily consumptions from time aggregates, e.g.

annual

• GAM with temperature and calendar as explanatory

variables

• Brabec et. al (2015). Statistical Models for

Disaggregation and Reaggregation of Natural Gas Consumption Data. Journal of Applied Statistics 42(5)

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Forecasting number of natural gas consumers and their total consumption with R

Prediction model construction

Basic ideas I

1 Two-level model – customer counts forecast (incl.

tariff switches) as the first level, consumption totals forecast as the second

2 Transition from the forecast time series to a new one

– time series of tariff assignment for a particular customer

3 Forecasting based on Markov property

ˆ pt+1 = ptPt

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Forecasting number of natural gas consumers and their total consumption with R

Prediction model construction

Basic ideas II

1 Probability can be estimated using relative frequency

ˆ pct = Nct/N•t we can invert the procedure and work with ˆ Nct = pctN•t

2 Number of new customers forecast as a separate

module

3 Customer counts forecasts are multiplied by average

consumption forecasts

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Forecasting number of natural gas consumers and their total consumption with R

Data preprocessing

NORMALIZED DATA . . .

consumption

. . .

tariff

INVOICING DATA . . .

consumption

SLP MODEL

INPUT DATA

frequencies of transition between tariffs

...

daily counts of customers average consumption within tariffs

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Forecasting number of natural gas consumers and their total consumption with R

Estimation of parameters

frequencies of transition between tariffs

...

daily counts of customers average consumption within tariffs average number of new customers 1 2 3 4 5 6 7 8 9 10 11 12 average annual consumption 1 2 3 4 5 6 7 8 9 10 11 12 13

INPUT DATA PARAMETERS ...

transition probability matrices

january february december

tariff month

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Forecasting number of natural gas consumers and their total consumption with R

Forecasting

Level 1

average number of new customers 1 2 3 4 5 6 7 8 9 10 11 12

PARAMETERS ...

transition probability matrices

january february december

1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 data forecast next month – data are replaced by forecast

FORECASTING OF COUNTS

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Forecasting number of natural gas consumers and their total consumption with R

Forecasting

Level 2

PARAMETERS ...

monthly counts forecasts

jan feb dec 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13

average annual consumption within tariffs 1 2 3 4 5 6 7 8 9 10 11 12 13

1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13

averageing annual counts forecast

1 2 3 4 5 6 7 8 9 10 11 12 13

product tariff by tariff

1 2 3 4 5 6 7 8 9 10 11 12 13

annual consumption forecast

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Forecasting number of natural gas consumers and their total consumption with R

Thank you for your attention.

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