SIMULATION OF CONTROL PLANT DYNAMIC
CHARACTERISTICS IN THE CASE OF HYDRAULIC
, Atanasko Tuneski
Faculty of Mechanical Engineering, "Sts. Cyril and Methodius" University,P.O. Box 464, 1001
Skopje, Republic of Macedonia. Fax: +389 2 362 298, e-mail:
A linear and nonlinear mathematical
model of hydraulic turbine, including water
supply conduit is proposed. Analysis of static and
dynamic characteristics of models is made.
Modification and analysis of both linear and
nonlinear model was made, using experimental
data from hydraulic turbine model acceptance
tests, with proposal of mathematical model which
has minimal error between simulation results and
static turbine model measurements. These
mathematical models can be used as control
plants in further control design tasks.
Hydraulic turbines, control, PID.
The requests of mathematical model of hydraulic
unrestricted head and tail race, large or no surge tank
and governor of hydraulic turbine are, to assure large
transient stability program simulation, isolated system
operation, system restoration after brake up, load
rejection, load acceptance, water hammer dynamics
and optimal speed control. In this paper are used for
simulation both linear and non-linear mathematical
models of hydraulic plants recommended by IEEE 
and their modifications made with data from
hydraulic turbine model acceptance measurements
. Non-linear models are required where speed and
power changes are large, such as in islanding, load
rejection and system restoration studies although
there are great difficulties designing good governor of
hydraulic turbines, because the hydraulic turbine is
highly non-linear device which characteristics vary
significantly with the unpredictable load on the unit.
Such nonlinearities make the governor design a
nontrivial task because governors designed for one
operating condition may not work at all under other
conditions. Basic elements of a hydraulic turbine
within the power system environment are shown on
the block diagram of figure 1.
Block diagram of hydro prime mover and
2. MATHEMATICAL MODEL OF
Mathematical models of hydraulic turbine with
penstock and without surge tank, modelled assuming
incompressible fluid, recommended by IEEE , 
are presented. Modelling of linear and non-linear
mathematical model of hydraulic turbine is presented
in following subsections.
2.1 Non-linear model of hydraulic turbine
assuming incompressible flow
From the laws of momentum, the rate of change of
flow in the conduit is:
is the volumetric flow rate,
penstock length and
is the mass density of water.