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Power plants experience distinct dynamic behaviors according to the primary source of energy. Whereas thermal power plants have a slow dynamic, modern renewables such as wind and solar PV are subject to very fast variations, due to environmental factors. Therefore, their availability is not guaranteed. Consequently, it is opportune to take advantage of the intrinsic flexibility of hydropower plants for balancing fast variations caused by modern renewable sources, in order to keep stability and reliability of the power grid. On the other hand, the use of hydropower plants as means of compensating constant variations between electricity generation and consumption leads to off-design operation. Such condition may cause instabilities or undesirable oscillations in the power plant whose origin lies in the hydraulic system. Furthermore, small hydropower plants play a major role in the development of emerging countries, where they may be frequently subjected to islanded or isolated operation. In such context, operating conditions are more critical in terms of reliability and stability. Considering these factors, one can readily understand the importance of predicting the dynamic behavior of power plants under various scenarios and different operating modes. This requires precise, comprehensive mathematical models and efficient computational tools, which are appropriate for planning new installations and better exploiting the existing ones. Thereupon, the purpose of the present work is the development of a novel tool for small-signal stability analysis of hydroelectric systems, with comprehensive modeling of both electrical and hydraulic elements of a hydropower plant. This tool is implemented in SIMSEN, a fully modular, efficient, user-friendly software developed at EPFL, for the simulation of electrical power networks and hydroelectric systems. The originality of this new tool lies not only on the exhaustive and detailed modeling of electrical and hydraulic systems (a multi-physics representation). It lies also on the fact that it is a modular tool, capable of treating systems with any given topology, with automatic generation of the full set of differential equations, based on circuits easily built in an user-friendly GUI. Another distinctive characteristic of the present work is that small-signal models of electrical elements are based on a,b,c-phase variables, different from the traditional d,q,o-axis representation. The procedure to be followed for the derivation of such models is presented in this document. Furthermore, case studies performed with this tool show that substantial interactions happen between electrical, mechanical, hydraulic and regulation elements. These interactions can be either positive or detrimental to the stability of the system. In case of adverse interactions, unstable behaviors may occur. Such instabilities cannot be predicted without a comprehensive, multi-physics model. These conflicting interactions are presented, and their consequences and possible solutions are discussed in this document.