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Hey there,

i want to calculate the power output of a 3 phase inverter. Therefore i have to do a FFT on my voltage Signals, to get the amplitude of the fundamental.

In comparison to the FFT Tool from the Simulink powergui, my amplitude is always lower. I searched for some examples for a correct scaled FFT, but i cant find differences to my code.

f1 = ac_voltage_a.data(SteadyState:1:SteadyState+2^15); % A Timeseries vector is used when system is in steady state

g1 = hanning(length(f1)).*f1; % Using the hanning window

dt=Tsample % Tsample = 1e-6

vac_fenstera_Nfft = length(g1); % Sampled values

J = fft(g1); % FFT

vac_fenstera_sfft = 2*abs(J)/vac_fenstera_Nfft; %

plot(1/dt * (0:(vac_fenstera_Nfft/2-1)) / vac_fenstera_Nfft, (vac_fenstera_sfft(1:vac_fenstera_Nfft/2)));

In comparison to the FFT analysis tool from powergui, the value of my fundamental amplitude is only half the size, even i mutiplied the abs*2.

Where is my fault?

Is it nessesary that the length of g1 is a multiple of 2? I think a DFT could also work out.

Regards

David Goodmanson
on 17 May 2021

Edited: David Goodmanson
on 17 May 2021

Hi Meikel,

You are multiplying your signal times a window, which reduces the signal amplitude. That has to have a significant effect on the fft. The code below shows the effect, which for the (misnamed) hanning window drops the fundamental by a factor of 2.

For an oscillation at one frequency, the peak amplitude in the frequency domain is reduced by a factor equal to the average value of the window function. Since the Hann window is a cos^2 function, and since the average value of cos^2 is 1/2, the frequency domain peak is reduced by that amount.

N = 1000; % signal length

t = (0:N-1)/N;

f0 = 40;

y = cos(2*pi*f0*t)/N;

yH = (cos(2*pi*f0*t)/N).*hanning(N)';

f = (0:N-1);

yf = fft(y);

yfH = fft(yH);

ind = 1:N/2;

figure(1)

stem(f(ind),2*abs(yf(ind)))

grid on

figure(2)

stem(f(ind),2*abs(yfH(ind)))

grid on

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