Certainty of Linear Interrelation of Technical and Economic Parameters of Power Units of 300 МWt Thermal Power Stations

Abstract

For 300 MWt gas-and-oil-burning power units which durability exceeds the estimated one, when comparing and ranking, it is necessary to take into account not only efficiency indicators (for example, the specific consumption of conventional fuel), but also indicators of reliability and safety. In practice, this is exactly what is being done. However, it is being done just by intuition. An intuitive approach solves this problem, but not always certainly. It would seem that there is a quite fully developed mathematical apparatus for regression and correlation analysis, a set of algorithms and calculation programs. But there is one specific feature that, if it is not taken into account, further increases the risk of an erroneous decision. The fact is that the average monthly data on the technical and economic indicators of power units do not belong to the samples from the general population that correspond to the normal distribution law, the latter being a necessary condition for using such methods. This is a non-random sample from a finite set of multidimensional data. Naturally, the methods of classification of multidimensional data are not simple; they require the development of special calculation programs that recommend solutions for maintenance and repair, load distribution, etc. The article presents only one, but very important issue of the problem, viz. the assessment of the reliability of the assumption about the linear relationship of technical and economic indicators. Its solution will simultaneously demonstrate difficulties in comparing the efficiency of aging power units. It is noted that the known and practically used method for assessing the reliability of the linear regression equation, based on the construction of a “confidence corridor” or “uncertainty band”, does not allow one to answer the main question, viz. whether the relationship of the considered technical and economic indicators corresponds to a linear one. A new method for evaluating this relationship is proposed, based on constructing a fiducial domain of possible regression line implementations. It is shown that for small values of the number of sample implementations, a significant part of independent samples has a correlation coefficient exceeding 0.9.