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The concept of hydraulic impedance is widely used for periodic or oscillating flow scenarios in applied hydraulic transients. This paper proposes an equivalent circuit-based discrete hydraulic impedance model for the hydraulic system of the power station. The equivalent hydraulic circuit is established by an analogy between the water hammer wave propagation in pressurized pipes and the electromagnetic wave propagation in conductors. The discrete hydraulic impedance at a given location is obtained by calculating the total specific impedance of the series and parallel circuits from one end to the other. In addition, the numerical solution process to obtain the natural frequencies of the system via the proposed model is designed in detail. Furthermore, oscillation characteristics of the pipelines in the hydropower station are investigated. The variation trends of the decay coefficients of different orders of oscillation of the system and the influence of turbine impedance on the oscillation frequencies are discussed, respectively. [ABSTRACT FROM AUTHOR]

Mathematical modeling is widely used for the time‐and frequency‐domain analysis of hydraulic systems. To explore the complicated hydraulic transients of the piping system under various operating conditions, different formulations of the equivalent circuit model (ECM) are systematically discussed in this study. In particular, comparative studies are performed regarding the restrictions on the tempo‐spatial discretization of the time‐domain ECM and the state‐of‐the‐art numerical schemes. In addition, the eigenanalysis of the free oscillation response and frequency features of the forced oscillation response were discussed in detail, respectively. Furthermore, the influence of spatial discretization on the frequency response precision for ECM is also quantified. Analytical results indicate that the ECM can achieve satisfactory performances in both numerical simulation and frequency analysis with affordable computational effort and relatively loose tempo‐spatial discretization restriction. [ABSTRACT FROM AUTHOR]

In order to realize the automatic selection of rule number in fuzzy space partition in the identification of the Takagi–Sugeno (T–S) fuzzy model, a new fuzzy clustering method is proposed in this paper. With the purpose of searching for the optimal fuzzy cluster number and the corresponding cluster centers simultaneously, a novel improved hybrid backtracking search algorithm (IHBSA) has been proposed by introducing the idea of a hybrid encoding scheme as well as a variable valid length chromosome to this optimization algorithm. With a proper cluster validity index taken as the objective function, IHBSA is capable of partitioning the fuzzy space and identifying premise parameters of the T–S fuzzy model without setting a deterministic value of cluster number as a priori. Through the experimental analysis, it is demonstrated that the proposed method possesses higher approximation accuracy with relatively fewer rule number in comparison with traditional ones. Moreover, the T–S fuzzy model is implemented to the practical data of hydroelectric generating units (HGU), and preponderant trajectory matching performance has also been achieved when utilizing the proposed method. [ABSTRACT FROM AUTHOR]