Modelica.Electrical.Machines.SpacePhasors.Functions

Functions for space phasor transformation

Information

This package contains space phasor transformation functions for use in calculations:

ToSpacePhasor: transforms a set of three-phase values to space phasor and zero sequence system
FromSpacePhasor: transforms a space phasor and zero sequence system to a set of three-phase values
Rotator: rotates a space phasor (from one coordinate system into another)
ToPolar: Converts a space phasor from rectangular coordinates to polar coordinates
FromPolar: Converts a space phasor from polar coordinates to rectangular coordinates

Space phasors are defined as vectors of length = 2, the first element representing the real part and the second element representing the imaginary part of the space phasor.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
ToSpacePhasor	Conversion: three phase -> space phasor
FromSpacePhasor	Conversion: space phasor -> three phase
Rotator	Rotates space phasor
ToPolar	Converts a space phasor to polar coordinates
FromPolar	Converts a space phasor from polar coordinates
quasiRMS	Calculate quasi-RMS value of input
activePower	Calculate active power of voltage and current input

Modelica.Electrical.Machines.SpacePhasors.Functions.ToSpacePhasor

Conversion: three phase -> space phasor

Information

Transformation of three phase values (voltages or currents) to space phasor and zero sequence value:
y[k] = X0 + {cos(-(k - 1)/m*2*pi),-sin(-(k - 1)/m*2*pi)}*X[Re,Im]
were y designates three phase values, X[Re,Im] designates the space phasor and X0 designates the zero sequence system.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

x[3]

Name	Description
x[3]

Outputs

Name Description

y[2]

y0

Name	Description
y[2]
y0

Modelica.Electrical.Machines.SpacePhasors.Functions.FromSpacePhasor

Conversion: space phasor -> three phase

Information

Transformation of space phasor and zero sequence value to three phase values (voltages or currents):
Y0 = sum(x[k])/m
Y[Re,Im] = sum(2/m*{cos((k - 1)/m*2*pi),sin((k - 1)/m*2*pi)}*x[k])
were x designates three phase values, Y[Re,Im] designates the space phasor and Y0 designates the zero sequence system.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

x[2]

x0

Name	Description
x[2]
x0

Outputs

Name Description

y[3]

Name	Description
y[3]

Modelica.Electrical.Machines.SpacePhasors.Functions.Rotator

Rotates space phasor

Information

Rotates a space phasor (voltage or current) by the angle provided by input argument "angle" from one coordinate system into another:
y[Re,Im] := {{+cos(-angle),-sin(-angle)},{+sin(-angle),+cos(-angle)}}*x[Re,Im]
where y[Re,Im] designates the space phasor in the new coordinate system (twisted by angle against old coordinate system) and y[Re,Im] designates the space phasor in the old coordinate system.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

x[2]

angle [rad]

Name	Description
x[2]
angle	[rad]

Outputs

Name Description

y[2]

Name	Description
y[2]

Modelica.Electrical.Machines.SpacePhasors.Functions.ToPolar

Converts a space phasor to polar coordinates

Information

Converts a space phasor from rectangular coordinates to polar coordinates, providing angle=0 for {0,0}.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

x[2]

Name	Description
x[2]

Outputs

Name Description

absolute

angle [rad]

Name	Description
absolute
angle	[rad]

Modelica.Electrical.Machines.SpacePhasors.Functions.FromPolar

Converts a space phasor from polar coordinates

Information

Converts a space phasor from polar coordinates to rectangular coordinates.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

absolute

angle [rad]

Name	Description
absolute
angle	[rad]

Outputs

Name Description

x[2]

Name	Description
x[2]

Modelica.Electrical.Machines.SpacePhasors.Functions.quasiRMS

Calculate quasi-RMS value of input

Information

Transformation of three phase values (voltages or currents) to space phasor and calculate length of space phasor.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

x[3]

Name	Description
x[3]

Outputs

Name Description

y

Name	Description
y

Modelica.Electrical.Machines.SpacePhasors.Functions.activePower

Calculate active power of voltage and current input

Information

Transformation of three phase voltages and currents to space phasors and calculate active power.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Name Description

v[m] phase voltages [V]

i[m] phase currents [A]

Name	Description
v[m]	phase voltages [V]
i[m]	phase currents [A]

Outputs

Name Description

p Active power [W]

Name	Description
p	Active power [W]

Automatically generated Mon Sep 23 17:20:31 2013.