Semi-Markov model for the Kaplan preventive repair system for water turbines with periodic inspection of the technical condition

Klaudiusz Migawa,Agnieszka Sołtysiak,Sylwester Borowski,Maciej Woropay,Magda Czyżewska,J Musiał,T Kałaczyński,Ł Muślewski

doi:10.1051/matecconf/202135101002

Klaudiusz Migawa, Agnieszka Sołtysiak + Show 6 more

Open Access

https://doi.org/10.1051/matecconf/202135101002

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Abstract

The paper presents a semi-Markow model of a preventive repair system by age, implemented in hydroelectric power plants with Kaplan turbines. In the case of the analyzed technical objects, the profit per time unit is considered as the criterion of the quality of functioning. On the basis of the adopted assumptions, for the developed mathematical model, formulas describing the criterion function were determined and the conditions for the existence of the extreme (maximum) of this function were formulated. The proposed method makes it possible to determine the optimal time for preventive repair of the considered technical objects. The theoretical considerations presented in the work are illustrated by a computational example developed on the basis of data obtained from the actual operating system of Kaplan water turbines with a rated power of 120 kW.

Highlights

Proper and effective operation of hydropower plants is possible only if the continuity of electricity production is ensured
The results presented in this paper are a continuation of the considerations presented in [11,12,13], in which the results were obtained on the basis of the research of semiMarkov models, in which the profit of the exploitation system or the cost of preventive replacement per time unit were considered as criterion functions
The considerations presented in the paper allowed for the development of a mathematical model of preventive repairs of Kaplan water turbines

Summary

Introduction

Proper and effective operation of hydropower plants is possible only if the continuity of electricity production is ensured. The results presented in this paper are a continuation of the considerations presented in [11,12,13], in which the results were obtained on the basis of the research of semiMarkov models, in which the profit of the exploitation system or the cost of preventive replacement per time unit were considered as criterion functions. The purpose of this manuscript is to develop and examine a 5-state semi-Markov model of preventive repairs with the use of periodic assessment of the technical condition of the technical facilities in use. The results of the model tests, developed on the basis of real data, may constitute the basis for making decisions in the analyzed exploitation system

States in the Kaplan water turbine operation model

Mathematical model for the operation of Kaplan water turbines

Determination of the criterion function

Conclusion

Sample test results

Conclusions