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 Development of Hydro Power Systems
Dr Slobodan Stojković
Mathematical Model of Dynamic Behavior of the Hydro Power Aggregates

A few words about the contents of this paper.
In the initial part are given: Types and Parameters of Hydro Turbine, Theory of Banki Turbine (Description of turbines, Stream flow through a turbine, Effectiveness and Constructive proportions) and Basic Parameters of Banki Turbine as well as Banki Turbine BT90.k (functional and structural characteristics of the turbine).

A key part of the paper is:
Mathematical model of dynamic behavior of the hydro turbine aggregates (complete mathematical model to define the dynamic behavior of components and assembly of this complex system).
Within the mathematical model are in detail all the components described:
- Electric actuator of water distributor,
- Reducer,
- Lever system of the distributor with counterweight,
- Synchronous generator,
- Turbine,
- Transmission function of the system,
- The equation of motion,
- Control system and
- Defining and optimization of PID controller.

At the end of this part of the paper the stability problem is treated (unit step response, logarithmic frequency and phase frequency characteristic (bode diagrams), Nyquist criterion, Routh-Hurwitz stability criterion).
Calculation of parameters and coefficients creates the possibility the results of model testing of a prototype turbine utilize in order to define parameters and coefficients of a mathematical model for implemented turbine (based on the characteristic curve of the prototype turbine and parametars of system components).

At the end of the paper modifications of the model that relate primarily to the higher power generators are described: Hydro actuator of water distributor, Active and passive pneumo balancing device of distributor apparatus and Induction generator (The difference between asynchronous and synchronous generator, D-q model of induction generator, The stabilization of the supply voltage using the active filter).

Although this article treats a Banki turbine, created mathematical model can be applied to any power unit and that fact gives him a universal value.

Mathematical Model of the Dynamic Hydro Power Unit’s behavior [PDF]