Development of Stochastic Models for Flows of Kainji Reservoir System

Abstract

Dams are infrastructural systems critical for hydropower generation, flood control and river navigation. They are systems branded by their multifarious, dynamic, and stochastic behaviors. The recurrent variation in the hydrological and meteorological variables poses a higher probability of dam failure, highlighting the need to improve pertinent risk valuation approaches to forecast failure risks, bearing in mind the uncertain states of such variables. This study Develops stochastic models for reservoir system state. It relates system storage, dependability, and yield to the incidence, scale, and period of reservoir system let-downs and similarly to associate unchanging -state reliability 1-q, to the N-year no-failure system reliability p. A two – state Markov process was employed in the development of the stochastic reservoir models. Two states of the reservoir system were defined, the states are failure state and non-failure. Specifying entirely the dualistic Markov equation, an estimation of (r) and (f) were done. The relationship between the resilience index and the probability that a regular year follows a failure year (r) and the likelihood that a failure year follows a regular year f were established using linear regression models. Correlation coefficients R² and standard error estimates were used to determine the extent of correlation and linearity of the models. Furthermore, the general regression models for establishing relationship between the reservoir system states i.e., failure state and non-failure state were developed. The value of Annual reliability (Ra) obtained depicts that the reservoir is substantially reliable at 0.96 reliability; also the unconditional return period of failure years (72years) substantiates the reliability of the reservoir. Again, the r, f and Average length of reservoir failure (UL) values obtained indicates strong reliability of Kainji reservoir. From the analysis of the reservoir system state the probability of failure years following a regular year was determined to be 0.014 which implies low probability of occurrence of system state f, the probability of regular year following a failure year was estimated as 0.99. The annual reliability Ra was estimated as 0.96, this indicated that the reservoir is significantly reliable. This can be seen from the estimate of the unconditional return period of failure years (72 years) and the average length of return period of 1 year. From the parameter values computed for the reservoir system state it is clear that the reservoir system is significantly reliable. In conclusion stochastic models were developed for the reservoir system state, and used to evaluate the state of the reservoir.