modelSimpleGen

Information

Simple Generator Model

Simple model of an ideal generator with friction based on angular momentum balance.

Energy Balance

The kinetic energy stored in the rotating generator is \(K_a = \frac{1}{2}J_a\omega_a^2\), where ω_a is angular velocity and J_a is moment of inertia.

From energy balance:

$$ \frac{\mathrm{d}K_a}{\mathrm{d}t} = \dot{W}_s - \dot{W}_{f,a} - \dot{W}_g $$

where:

• Ẇ_s is turbine shaft power
• Ẇ_f,a is frictional power loss
• Ẇ_g is power taken by generator

Friction

Frictional power loss (mainly from bearings):

$$ \dot{W}_{f,a} = \frac{1}{2}k_{f,b}\omega_a^2 $$

where k_f,b is the bearing friction factor.

Electric Power

Electric power available on grid:

$$ \dot{W}_e = \eta_e \dot{W}_g $$

where η_e is electrical efficiency.

Loading Options

The generator can be loaded either:

• via the mechanical shaft connector (e.g., using the Grid model). Set Pload input to 0 in this case.
• or via the input connector Pload specifying the connected electrical load.

Connectors

• RealInput: grid power (Pload) and shaft power
• RealOutput: angular velocity and frequency

Parameters

User specifies: moment of inertia, electrical efficiency, bearing friction factor, number of poles, and initial angular velocity.

Parameters

Connectors

Components