Forecasting number of natural gas consumers and their total - PowerPoint PPT Presentation

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. Smart Grids 2015 Prague 2 / 19

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 Smart Grids 2015 Prague 3 / 19

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 Smart Grids 2015 Prague 4 / 19

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 Smart Grids 2015 Prague 5 / 19

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) Smart Grids 2015 Prague 6 / 19

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 p t +1 = p t P t ˆ Smart Grids 2015 Prague 7 / 19

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 p ct = N ct /N • t ˆ we can invert the procedure and work with ˆ N ct = p ct N • t 2 Number of new customers forecast as a separate module 3 Customer counts forecasts are multiplied by average consumption forecasts Smart Grids 2015 Prague 8 / 19

Forecasting number of natural gas consumers and their total consumption with R Data preprocessing INVOICING DATA INPUT DATA consumption frequencies of transition between tariffs ... . . . SLP MODEL daily counts of customers NORMALIZED DATA consumption tariff average consumption within tariffs . . . . . . Smart Grids 2015 Prague 9 / 19

Forecasting number of natural gas consumers and their total consumption with R Estimation of parameters INPUT DATA PARAMETERS transition probability matrices frequencies of transition between tariffs ... ... january february december daily counts of customers average number of new customers 1 2 3 4 5 6 7 8 9 10 11 12 month average consumption within tariffs average annual consumption 1 2 3 4 5 6 7 8 9 10 11 12 13 tariff Smart Grids 2015 Prague 10 / 19

Forecasting number of natural gas consumers and their total consumption with R Forecasting Level 1 FORECASTING OF COUNTS PARAMETERS transition probability matrices 0 1 1 2 2 3 ... 3 4 4 5 5 6 6 7 7 january february december 8 8 9 9 10 10 average number of new customers 11 11 12 12 13 13 1 2 3 4 5 6 7 8 9 10 11 12 data forecast next month – data are replaced by forecast Smart Grids 2015 Prague 11 / 19

Forecasting number of natural gas consumers and their total consumption with R Forecasting Level 2 monthly counts forecasts annual counts forecast annual consumption forecast 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 averageing 6 6 6 product 6 6 ... 6 7 7 7 7 7 7 8 8 8 8 8 tariff by tariff 8 9 9 9 9 9 9 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 12 13 13 13 13 13 13 jan feb dec PARAMETERS average annual consumption within tariffs 1 2 3 4 5 6 7 8 9 10 11 12 13 Smart Grids 2015 Prague 12 / 19

Forecasting number of natural gas consumers and their total consumption with R Thank you for your attention. Smart Grids 2015 Prague 13 / 19