blockBasic3phasePLL

Basic version of three phase phase-locked loop

Extends from Modelica.Blocks.Interfaces.MIMO (Multiple Input Multiple Output continuous control block), Interfaces.w_theta (Signal output w and theta).

Information

The basic version of the three phase PLL assumes that a Clarke transformation is performed, then feeding the α- and β-component to this block. Here a Park transformation on the inputs u[1..2] is applied, using the angle θ determined by the control loop. The d- and the q-component are divided by the estimated amplitude to obtain an amplitude of 1. Subsequently, the q-component is controlled to become 0, ie. determining the desired angle θ as well as the frequency resp. angular velocity ω = 2 π f = w.

The output y[1] is a cosine signal in phase with the input u, the output y[2] is a sine signal 90° phase shifted to y[1]. Result of the Clarke - Park - transformation can be inspected with u0, ud and uq.

Problems: especially a double-frequency ripple on the estimated frequency under distorted conditions, i.e. when the input signals contain not only a positive sequence but also a negative sequence and / or zero component. For symmterical components, see [Fortescue1918].

Parameters

TypeNameDefaultDescription
Integernin (from MIMO)1Number of inputs
Integernout (from MIMO)1Number of outputs
RealA01Rated amplitude of input
SI.Frequencyf050Rated frequency
SI.AngularVelocitywn0.25*2*pi*f0Natural angular velocity
Realzeta0.5Damping ratio
Realkp2*zeta*wnProportional gain
Realkiwn^2Integral gain
Realepsilon0.001Avoid division by 0
Reallamda0Factor for adaptive integrator

Connectors

TypeNameDefaultDescription
RealInput[nin]u (from MIMO)Connector of Real input signals
RealOutput[nout]y (from MIMO)Connector of Real output signals
Modelica.Blocks.Interfaces.RealOutputw (from w_theta)Estimated angular velocity
Modelica.Blocks.Interfaces.RealOutputtheta (from w_theta)Estimated angle
Modelica.Blocks.Interfaces.RealOutput[2]udqud, uq

Components

TypeNameDefaultDescription
Modelica.Electrical.Machines.SpacePhasors.Blocks.Rotatorrotator
Modelica.Blocks.Math.Divisiondivision
Modelica.Blocks.Math.Absabs1
Auxilliary.AddOffsetaddOffset
Modelica.Blocks.Continuous.Integratorintegrator1
Auxilliary.AddOffsetaddOffset1
Modelica.Blocks.Math.Gaingain
Auxilliary.Addadd2
Modelica.Blocks.Continuous.Integratorintegrator2
Modelica.Blocks.Math.Sinsin
Modelica.Blocks.Math.Coscos
Modelica.Blocks.Math.Productproduct1
Modelica.Blocks.Sources.RealExpressionrealExpression