  This paper proposes a hydraulic model based on the Euler turbine equations
suitable for the purpose of grid integration studies of variable speed
hydropower (VSHP). The work was motivated by the need to assess how the dynamic
performance might change when a hydropower plant is operated at variable speed.
The Euler model considers the water flow dependency on the turbine rotational
speed and calculates the turbine power as a non-linear function of water flow,
turbine rotational speed and guide vane opening. A waterway model is included,
based on the 1-D momentum and continuity balance for a water-filled elementary
pipe to simulate water hammer, mass oscillation and tunnel losses. These
detailed and accurate models are necessary for recognising possible limitations
in the hydraulic system, to model the turbine power and rotational speed
correctly and thereby to be able to maximise power delivery for system control
purposes. All Euler model parameters can be derived from the physical
dimensions of the turbine and waterway, ensuring easy implementation.
State-space representation of the Euler model is approximated by utilising a
lumped-parameter equivalent of the penstock dynamics. Dynamic simulations and
eigenvalue analysis show the strength of the Euler model compared to
conventional hydropower models.
