blockSimpledqPLL
Extends from Modelica.Blocks.Interfaces.MIMOs (Multiple Input Multiple Output continuous control block with same number of inputs and outputs), Interfaces.w_theta (Signal output w and theta).
Information
This block calculates angle and angular velocity of the input u[2] in α,β-frame.
The used calculation method is based on an angle tracking observer as common in electrical engineering. This implementation is very robust. It determines the angle of the input space phasor.
The angle of a complex space phasor is controlled in such a way that its imaginary part is equal to zero.
The controlled angle theta is the unwrapped continuous angle.
The output theta approximates the desired angle by a first order system
which time constant is the integral time constant of the controller:
Im(ej*(u-y)) = sin(u - y)
This expression can be approximated for small differences by
(u - y).
Using an integral controller, the transfer function of the closed loop can, thus, be
determined as:
y = u / (1 + s*Ti).
The derivative of the output theta is the angular velocity w,
provided as an output signal as well.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Integer | n (from MIMOs) | 1 | Number of inputs (= number of outputs) |
| Modelica.Units.SI.Time | Ti | 1e-6 | Integral time constant of controller |
| Modelica.Units.SI.Angle | phi0 | 0 | Initial angle |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| RealInput[n] | u (from MIMOs) | Connector of Real input signals | |
| RealOutput[n] | y (from MIMOs) | Connector of Real output signals | |
| Modelica.Blocks.Interfaces.RealOutput | w (from w_theta) | Estimated angular velocity | |
| Modelica.Blocks.Interfaces.RealOutput | theta (from w_theta) | Estimated angle |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Electrical.Machines.SpacePhasors.Blocks.Rotator | rotator | ||
| Modelica.Blocks.Continuous.Integrator | integralController | ||
| Modelica.Blocks.Math.Gain | gain |