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This paper proposes a hydraulic model based on the Euler turbine equationssuitable for the purpose of grid integration studies of variable speedhydropower (VSHP). The work was motivated by the need to assess how the dynamicperformance might change when a hydropower plant is operated at variable speed.The Euler model considers the water flow dependency on the turbine rotationalspeed 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 elementarypipe to simulate water hammer, mass oscillation and tunnel losses. Thesedetailed and accurate models are necessary for recognising possible limitationsin the hydraulic system, to model the turbine power and rotational speedcorrectly and thereby to be able to maximise power delivery for system controlpurposes. All Euler model parameters can be derived from the physicaldimensions of the turbine and waterway, ensuring easy implementation.State-space representation of the Euler model is approximated by utilising alumped-parameter equivalent of the penstock dynamics. Dynamic simulations andeigenvalue analysis show the strength of the Euler model compared toconventional hydropower models.

Modelling of Variable Speed Hydropower for Grid Integration Studies