## 1 Introduction  
Contemporary requirements for as much energy generation and output as possible from renewable sources result in the design and construction of new hydropower plants (HPPs) with increasing installed capacity and maneuvering capabilities, as well as in preferential increase in the existing HPPs maximum installed discharge as a part of their refurbishments [1]. Inevitable activities aiming at their safe, stable and efficient operation are analyses of transient processes which can generally be divided into several categories: water hammer (WH), water-mass oscillations (WMO), turbine governing (TGOV), hydraulic oscillations (HOSC), headwater level governing (LGOV), and open channel (OPCH)analyses [2]. Water-mass oscillations analyses are necessary whenever an HPP is provided with a surge tank. Surge tank, as a safety measure, is a very reliable solution, but often being indispensable and costly, therefore it should be wisely chosen and optimally designed [3; 4; 5]. Hydraulic transients' analyses with the implementation of various types of surge tanks have for a long time been the subject of investigations. In addition to the conventional open-air surge tanks for on-network load-variation stability governing in HPPs, the advantages of closed surge tanks (CSTs), i.e., air-cushion or pressurized-air STs, were observed more than a century ago [6; 7; 8], when the first assumptions about the pertaining isothermal a/o adiabatic thermodynamic processes were made [9; 10]. Later descriptions of these processes in the CSTs were analyzed from the point of polytropic character view [11; 12; 13], Rational Heat Transfer method [14] and combined with the improved Modified Rational Heat Transfer method [15]. With the aim of developing improved HPP protection measures and optimizing surge tanks, modern researches have been conducted through hybrid approaches which include CFD analyses [4; 16; 17] and various optimization methods e.g., [18; 19] together with comprehensive experimental measurements [20; 21]. On the other hand, the conditions of surge tank setting have always been of great significance too [22; 23; 24; 25], due to the fact that surge tank installation is often inevitable in the long derivation HPPs. As one of the possible approaches in the protection of HPP, which has not been given special attention in previous decades, there is also the application of the so-called semi-pneumatic surge tank (SPST). Besides the well-known characteristics of the throttled surge tank [26; 27; 28], the SPST is expected to be an improvement of the currently used open-air surge tank (cylindrical, with chambers, differential, with external over-spill, etc.) by implementing an aeration orifice. The aeration orifice allows convenient use of air in the SPST during transient processes without further investment in additional equipment. In the upper section of the SPST, the rise of the water level induces air compression. The role of the aeration orifice is to enable air outflow into the atmosphere in a choked flow setup inducing energy dissipation of the expelled air, getting pressurized on the account of energy transfer from oscillating water masses. Simultaneously, the lower up-surge of the water level is caused by the pressurized air in the upper section. On the contrary, the aeration orifice also enables chocked in-flow of air and lower air pressure with the effect of reducing minimum water level [29]. The literature survey shows that SPSTs have never been investigated in detail in terms of their capabilities and feasibility in the past. [PERSON], and [PERSON] [30; 31], respectively mentioned and illustrated the SPST as a structural protection measure, however, without any detailed elaboration. In WHAMO software users' manual, developed by [PERSON] and [PERSON] [32], the SPST mathematical model was suggested, however without any specific results of the case-study simulations, detailed analyses nor with the full proposition of the equations.