Power plant Mother of Macedonia:
kolektiv autorů, 2005
Existing HPP Matka is located downstream, near to the dam body. Upstream, starting from this plant, HPP Kozjak, which is under construction, has larger installed flow of 100 m3/s. To avoid overflows and permanent oscillation of the water level in the storage this existing power plant will be enlarged. The purpose of the project is to produce electricity and to secure constant and favorable flow in the Treska River and in the main river in Republic 
of Macedonia, the river Vardar. HPP Matka enlargement will increase the installed capacity of the plant as a whole and use a part of economically usable water energy. Also it will optimize water regime in the river Treska and the river Vardar, and avoid large overflows and permanent oscillations in the storage Matka that will automatically avoid problems with stability of the slopes of the storage, environmental problems along the coast and in the lake. Option 3 includes construction of completely new power plant of total discharge 42 m3/s. Water to new HPP shall be supplied by newly constructed penstocks, connected to present intake tunnel in front of water chamber. Two new Kaplan spiral turbines 2x21 m3/s with all associated appliances will be installed in the powerhouse. New generators, power step-up transformers, electrical equipment and complete power plant automation will be installed. After commissioning of new HPP, the present HPP shall never be operated and can be preserved as a museum.
Subject of calculation was to determine the first natural frequencies and eigenmodes of vibrations for the reinforced concrete structure of the lower construction in the restored Matka HPP (Macedonia). Calculation was performed for 7 LCi, with LC1 to LC6 representing different operating modes of HP. For LC0 the task submitter was interested in behaviour of the unloaded reinforced concrete structure of the lower construction without influence of surroundings and foundations and without additional loads from the steel structure of the upper construction and machinery. Accuracy of calculated results should be assessed according to an internationally reputable norm. Because no such corresponding assessment exists in 
foreign 
norms (e.g. in Eurocode or DIN), the natural frequencies values were corrected according to the norm [4] ČSN 73 0032, with respect to influence of incorrect determination of input values for calculation, i.e. physical constants and their potential change within lifetime of the construction, the computing model and possible load variants (LC). Considering that 4 excitation sources are known, the first 100 natural frequencies and eigenmodes of vibrations were calculated for the reinforced concrete structure of the lower construction. The excitation sources are as follows:
1) Exciting frequency of rotor machinery at nominal speed of the rotor – fmin = 5,56 Hz. This frequency is the most dangerous.
2) Blade exciting frequency of the turbine impellor – fimp = 33,33 Hz; from the energy viewpoint this excitation is of minor importance.
3) Exciting frequency of the segments of thrust bearing of generator – fg = 55,56 Hz; from the energy viewpoint this excitation is of minor importance, too.
4) Maximal exciting frequency of the diaphragm of turbine – fgw = 133,32 Hz, from the energy viewpoint this excitation is of minor importance, too.
