A mathematical model for the virtual simulator of the power unit electrical part

The mathematical model is developed for a virtual training system (simulator) of the power unit electrical part operators of a thermal (nuclear) power plant. The model is used to simulating the main operating conditions of the power unit electrical part: generator idling, generator synchronization with the power system, excitation shifting from the main unit to the backup one and vice versa, switching in the power unit auxiliary system, and others. Furthermore, it has been implemented modelling some probable emergency conditions within a power plant: incomplete phase switching, damage to standard power unit equipment, synchronous oscillations, asynchronous mode, etc. The model of the power unit electrical part consists of two interacting software units: models of power equipment (turbine, generator with excitation systems, auxiliary system) and models of its control systems, automation, relay protection and signalling. The models are represented by the corresponding algebraic-differential equations that provide real-time mapping power unit processes at the operator’s request. The developed model uses optimal solving algebraic-differential equations to ensure the virtual process behaviour in real-time. In particular, the implicit Euler method is used to solve differential equations, which is stable when simulating processes in significant disturbances, such as accidental disconnection of the unit from the power system, tripping and energizing loads, generator excitation loss, etc.

On the Diachrony of the Clitic Cluster in Bulgarian

The article traces back the formation of the clitic cluster in Bulgarian starting from the Old Church Slavonic through Middle Bulgarian up to the Early Modern Bulgarian and beyond. It offers a hypothetical two-layer structure of the cluster – with the main layer consisting of a (pronominal) core and a (verbal) periphery, and a secondary layer hosting (‘quasi-clitical’) elements that exhibit, both diachronically and synchronically, a behaviour that is not strictly consistent with that of the clitical elements. The language material from three corpora shows that there was no change in the positions of the elements in the core, and the changes in the periphery observed are mainly due to the changes in the set of the elements (as a result of the restructuring of the pronoun system and changes in the auxiliary system, as well as the loss of some early clitics, such as the discourse markers).