The Hausdorff dimension as a tool of step-by-step prediction

Abstract

Forecasts of the random processes occurring in power systems should be characterized by very high accuracy—inaccurate forecasts always cause serious economic losses for electrical energy producers and distributors. The processes of power demand, electrical energy demand, and development of power networks exhibit self-similar features. This peculiarity enables the Hausdorff dimension to be applied to formulate prediction models of the above-mentioned quantities. The models are characterized by simplicity and high accuracy. This work deals with models of step prediction of random linear and periodic functions characterized by self-similarity. The definition of the Hausdorff dimension and the principles of generating self-similar geometrical forms and formulating the prediction models for self-similar processes are presented. Examples of prediction models and their application in electrical power engineering are given. The problem of predicting power demands in state and local electrical power systems is described in detail. The reader is also provided with an annotated list of English-language papers issued in 1918–1980 concerning the prediction of power demands, as well as the most important American and Polish works of the last few years.