modelTurbine

Information

Simple Turbine Model

This is a simple model of the turbine that gives possibilities for simplified modelling of the turbine unit. The model is based on a look-up table for turbine efficiency vs. guide vane opening.

Figure: Simple turbine model schematic.

Power Calculation

The mechanical turbine shaft power is:

$$ \dot{W}_\mathrm{tr} = \eta_\mathrm{h} \Delta p_\mathrm{tr} \dot{V}_\mathrm{tr} $$

where η_h is hydraulic efficiency (from lookup table or constant value), Δp_tr is pressure drop, and V̇_tr is volumetric flow rate.

The turbine efficiency is in per-unit values from 0 to 1, where 1 means that there are no losses. The model can use a constant efficiency or varying efficiency from a lookup-table.

Flow Relationship

This model is based on the energy balance and a simple valve-like expression. The turbine flow rate relates to pressure drop through:

$$ \dot{V}_\mathrm{tr} = C_\mathrm{v} u_\mathrm{v} \sqrt{\frac{\Delta p_\mathrm{tr}}{p^\mathrm{atm}}} $$

where C_v is the guide vane "valve capacity", u_v is guide vane opening signal (0 to 1), and p^atm is atmospheric pressure.

The guide vane valve capacity can either be specified directly by the user via C_v or it will be calculated from the nominal turbine net head H_n and nominal flow rate Vdot_n.

Usage

Besides hydraulic input and output, there are inputs as the control signal for the opening and also output as the turbine shaft power.

Efficiency Options

Two modes are available, controlled by the Boolean parameter ConstEfficiency in the Efficiency data group:

• Constant efficiency (ConstEfficiency = true, default): The hydraulic efficiency is fixed at the value given by eta_h (default 0.9). This is suitable for quick studies where a single representative efficiency value is sufficient.
• Variable efficiency table (ConstEfficiency = false): Efficiency varies with guide-vane opening according to a lookup table stored in the replaceable record VarEfficiency of type Types.Efficiency.

Defining a Custom Efficiency Record

To supply turbine-specific efficiency data, create a new record that extends OpenHPL.Types.Efficiency and override EffTable. The table must have exactly two columns:

1. Guide-vane opening in per-unit (0 = fully closed, 1 = fully open).
2. Corresponding turbine efficiency in per-unit (0 = no conversion, 1 = lossless).

Rows must be sorted in ascending order of the first column. Extrapolation beyond the defined range uses the slope of the last two points (Modelica.Blocks.Types.Extrapolation.LastTwoPoints), and the curve is interpolated with a continuous derivative (Modelica.Blocks.Types.Smoothness.ContinuousDerivative).

Example record:

record MyTurbineEfficiency
  extends OpenHPL.Types.Efficiency(
    EffTable = [0.00, 0.00;
                0.20, 0.72;
                0.50, 0.91;
                0.80, 0.94;
                1.00, 0.91]);
end MyTurbineEfficiency;

Place this record in your own package (or directly in the model), then in the Efficiency data group of the Turbine:

1. Uncheck ConstEfficiency.
2. Set VarEfficiency to redeclare MyTurbineEfficiency VarEfficiency (or use the drop-down in the parameter dialog, which lists all records compatible with Types.Efficiency).

The base record Types.Efficiency already contains a representative default table that can be used as a starting point when no measured data are available.

Parameters

Connectors

Components