Liubomyr Vytvytsky
Department of Electrical engineering, Information Technology and Cybernetics, University College of Southeast Norway, Porsgrunn, Norway
Bernt Lie
Ladda ner artikel
http://dx.doi.org/10.3384/ecp1713820Ingår i: Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58) Reykjavik, Iceland, September 25th – 27th, 2017
Linköping Electronic Conference Proceedings 138:2, s. 20-28
Publicerad: 2017-09-27
ISBN: 978-91-7685-417-4
ISSN: 1650-3686 (tryckt), 1650-3740 (online)
The possibility for modelling and simulating
hydropower systems as accurately as possible take an
important role in order to develop a control structure and
to make efficient analysis tools for testing a designed
controller for stability and performance in different
operating regimes. Both the simulation time for such
models as well as the accuracy are important.
A high head hydropower system is considered for this
study. The pipe with the main part of the height drop is
known as pressure shaft or penstock, and it can be
modeled with two levels of accuracy which have been
compared in this studying. A simple model with one
nonlinear ODE considers inelastic walls of the penstock
and incompressible water. A more realistic model for
large pressure variations assumes a penstock with elastic
walls and compressible water column in the penstock.
This more detailed model of a penstock is described
with two nonlinear PDEs which have been solved using
the Kurganov-Petrova scheme.
Comparing results from these two models it can be
concluded that the simple ODE model shows by and
large the same results as the PDE model with just
slightly smoothed dynamics. Obviously, the simulation
time for the inelastic penstock model is considerably
smaller. Both models show reasonable results and can
be further used for control synthesis and analysis. In
cases where the time consumption is most important, the
simple ODE model for the penstock is preferred. On the
other hand, for more accurate studies the
elastic/compressible model for the penstock or even for
other waterway units, such as conduit, is more useful.
The modeling part for both cases was done in
OpenModelica using our own hydropower library,
where all models for different units of the hydropower
system have been developed and collected.
High head hydropower, penstock/pressure
shaft, Kurganov-Petrova scheme, OpenModelica
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