Fourier#

The Fourier block performs Fourier analysis of the input signal during one period of the fundamental frequency of the signal. This block can be used to calculate the amplitude and phase of the zero, first or any other harmonic component of the input signal.

See also

An example of using this block can be found in subsection Power industry of section Electrical equipment practical guide Modeling of zero-sequence current directional protection of 220 kV power transmission lines.

Harmonic numbers, initial values of amplitudes and arguments are specified in the form of an array. If you specify more than one element in the arrays, the output signals become vector signals. To obtain data for each harmonic in this case, it is necessary to use the block Demux indicating in it the number of output ports equal to the number of harmonics.

The input signal f(t) can be represented as a Fourier series (1):

(1)#\[f(t)=\frac{a_0}{2}+\sum_{n=1}^{ \bowtie}a_n\cdot cos(n\cdot\omega \cdot t)+b_n\cdot cos(n\cdot\omega \cdot t)\]

where:

n - harmonic number, n = 1 corresponds to the fundamental harmonic.

The amplitude and phase of the selected harmonic are calculated using the formulas below (2), (3) :

(2)#\[|H_n|=\sqrt{a_n^2+b_n^2}\]

(3)#\[\angle H_n=arctg(\frac{a_n}{b_n})\]

where (4), (5) :

(4)#\[a_n=\frac{2}{T}\cdot\int_{t-T}^{t}f(t)sin(n\cdot\omega \cdot t)dt\]

(5)#\[T=\frac{1}{f_1}\]

\(f_1\) - fundamental signal frequency.

During the first period of the fundamental frequency of the signal, the output amplitude and phase values will be equal to the indicated initial input parameters, because in order to obtain the calculated values, the first period of the fundamental frequency must be completed.

1. Properties#

Property	Default Value	Description	Units of measurement
Calculatable harmonics	1.0; 3.0; 5.0	-	-
Initial values of magnitudes	0.0; 0.0; 0.0	-	-
Initial values of angles	0.0; 0.0; 0.0	-	deg
Fundamental frequency	50.0	-	Hz
Sampling type: Fundamental project frequency decimation; Sample time; Sampling frequency	Fundamental project frequency decimation	-	-
Decimation factor of project fundamental discretization frequency, available when selecting `Sampling type` - `Fundamental project frequency decimation`	1	-	-
Sample time, available when selecting `Sampling type` - `Sample time`	0.05	-	s
Sampling frequency, available when selecting `Sampling type` - `Sampling frequency`	20.0	-	Hz

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input signal	Input	-	-	Automation
Magnitudes	Output	-	-	Automation
Angles	Output	-	deg	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports