FRUZSINA MÁK VOLUME RISK IN THE POWER MARKET Department of Statistics Supervisors: Beatrix Oravecz, Senior lecturer, Ph.D. András Sugár, Associate professor, Head of Department of Statistics, Ph.D. Copyright © Fruzsina Mák, 2017 Corvinus University of Budapest Doctoral Programme of Management and Business Administration Volume risk in the power market Load profiling considering uncertainty Ph.D. Dissertation Fruzsina Mák Budapest, 2017 TABLE OF CONTENTS INTRODUCTION ................................................................................................................. 2 1. APPLICATION EXAMPLES AND TERMINOLOGY OF CONSUMER PROFILING ...................................................................................................................................... 12 1.1. Price- and volume uncertainty on the energy market ............................................ 12 1.2. Some application examples on profiling ............................................................... 19 1.2.1. Short and long term hedging and pricing ....................................................... 19 1.2.2. Demand side management ............................................................................. 22 1.2.3. Building portfolios and creating balancing groups ........................................ 24 1.3. Profile and profile-related risks ............................................................................. 26 1.3.1. Definition of consumer profile ....................................................................... 26 1.3.2. Profile-related risks ........................................................................................ 28 1.4. The empirical examination of stylized facts in consumption time series .............. 30 1.4.1. Load shape and level ...................................................................................... 31 1.4.2. The intraday distribution of loads .................................................................. 35 1.4.3. Temperature-dependency ............................................................................... 40 1.4.4. Conclusions .................................................................................................... 42 2. PREVIOUS RESEARCH RESULTS ON CONSUMER PROFILING ....................... 44 2.1. The two-step consumption time series clustering ................................................. 44 2.1.1. Time series clustering in general.................................................................... 44 2.1.2. The general framework for profiling.............................................................. 45 2.1.3. Producing curve characteristics to be used in profiling ................................. 47 2.1.4. Clustering algorithms used in profiling.......................................................... 49 2.2. Capturing the effect of weather variables in energy time series ........................... 51 2.2.1. The relationship between weather variables and consumption ...................... 51 2.2.2. Capturing the effect of weather variables in profiling ................................... 53 2.2.3. The extreme (irregular) effect of temperature ................................................ 55 2.2.4. Seasonal adjustment and the removal of extreme (irregular) effect of temperature in the Hungarian natural gas consumption ............................................... 56 I 3. AN OVERVIEW OF METHODS USED IN THIS DISSERTATION AND THEIR APPLICATIONS IN PROFILING .......................................................................................67 3.1. Classical stochastic time series regression models.................................................67 3.1.1. The definition of stationarity and testing for unit root ....................................68 3.1.2. The role of the error term in integrated time series .........................................68 3.1.3. The role of the error term in stationary time series .........................................69 3.1.4. Seasonal autoregressive moving average (SARMA) model ...........................71 3.1.5. Periodic autoregressive (PAR) model .............................................................72 3.2. Mixture models.......................................................................................................75 3.2.1. Description of the mixture model (MM) and the Gaussian mixture model (GMM) .........................................................................................................................76 3.2.2. Expectation-Maximization (EM) estimation procedure .................................77 3.2.3. An empirical example on the daily natural gas consumption data of Budapest . .........................................................................................................................79 3.2.4. Further methodological questions related to the Gaussian mixture model ....83 3.2.5. The regression approach based on the Gaussian mixture model (GMR) .......84 3.2.6. Gaussian mixture regression for time series ...................................................89 3.3. Mixture models and their applications on energy time series ................................90 3.3.1. Construction of typical daily consumption curves ..........................................90 3.3.2. Modelling the distribution of consumption using mixture density function ...93 3.3.3. Modelling the distribution of consumption using mixture density function and regression .......................................................................................................................94 4. CONSIDERING UNCERTAINTY OF CONSUMPTION IN PROFILING – EMPIRICAL RESEARCH RESULTS .................................................................................97 4.1. Creating typical consumption patterns ...................................................................97 4.1.1. Using the mixture model to create typical consumption patterns ...................98 4.1.2. Using classical time series regression to create typical consumption patterns ... .......................................................................................................................107 4.1.3. Creating profile groups .................................................................................111 4.1.4. Results, summary of conclusions ..................................................................117 II 4.2. Modelling the uncertainty of consumption ......................................................... 119 4.2.1. Volume risk in classical time series regression models ............................... 119 4.2.2. Modelling volume risk with mixture regression .......................................... 130 SUMMARY OF THE KEY FINDINGS OF THE DISSERTATION ............................... 152 A) The examination of stylized facts of consumption time series ............................... 152 B) Using the mixture model for creating typical consumption patterns ...................... 153 C) Using heuristic and classical stochastic time series methods to measure uncertainty of consumption ............................................................................................................... 156 D) Using mixture models to measure the uncertainty of consumption ........................ 157 AVENUES FOR FURTHER RESEARCH AND APPLICATION IN PRACTICE ......... 159 APPENDICES ................................................................................................................... 163 A) Statistical software packages and the most important functions used for calculations. ................................................................................................................................. 163 B) Empirical example of the natural gas consumption data of Budapest – some calculation results ........................................................................................................... 165 C) Examination of stylized facts of load time series.................................................... 166 D) SI ratios in the seasonal adjustment of national gas consumption .......................... 168 E) Typical daily profiles and weekly load time series figures ..................................... 169 F) The diversification of volume risk .......................................................................... 171 REFERENCES ................................................................................................................... 173 PUBLICATIONS ............................................................................................................... 178 A) Publications in Hungarian in the field of the dissertation ....................................... 178 B) Publications in English in the field of the dissertation ............................................ 178 C) Most important unpublished works ......................................................................... 178 III INDEX OF FIGURES Figure 1: The historical variation of balancing energy and dayahead hourly prices .......................................... 3 Figure 2: The contour plot of a portfolio time series .......................................................................................... 6 Figure 3: The average of conditional standard errors in a consumer load curve (winter weekdays) .................. 7 Figure 4: Results of mixture clustering on the example of daily average temperature – natural gas consumption.......................................................................................................................................................