With reference to the unsymmetrical fault analysis in power system, factors 'a'= -0.5+j0.866, 'a2'=-0.5-j0.866. Suppose I wish to generate the signal a2*Vb, where Vb is one of the phase voltage in the three phase system.
How can I model the same in Matlab/Simulink?
I have attached a diagram for ease of understanding.
The complex numbers can be represented either by Cartesian coordinates x+j y, or in a polar form z= a exp j theta, with a is the magnitude and theta is the phase.
Concerning the three phase source they can be best expressed in a polar form V, Vexp j120 degree, Vexp -j120 degrees. They can be converted into the Cartesian form as:
z = a cos theta + j a sin theta.
Best wishes
I would suggest using a basic "gain" block, setting the gain to "-0.5-sqrt(3)/2*i"
I agree with Dr. Wolfgang, you can use the gain block in simulink and can define its value either in the simulink itself or in matlab workspace.
Thanks for the inputs, I have tried to use the basic gain block and entered the value -0.5-sqrt(3)/2*i, then I am passing a sinusoidal signal of frequency 314 rad/s, and then connecting a scope; the error "Complex signal mismatch. Output port 1 of 'untitled/Gain' is a signal of numeric type complex. However, it is driving a signal of numeric type real" comes.
To over come the same I have used a complex to real-imag block.
I have enclosed the snapshot of the input and output signals. Should I take the real part and consider as the output a2Vb ?
Dear Amit,
you should not consider the real part only, as it is not the entire output of a²V_b, which is obviously a complex number (BTW, you solved the signal mismatch issue correctly).
It seems that, as you investigate unsymmetrical faults, you try to calculate the negative sequence component using a²V_b (and aV_c and V_a, I would assume), but the input to such a transformation for the voltages usually is the phasor (or complex amlitude) of the phase voltages, i.e. complex numbers itself. So, you should not use the time characteristic of the voltage as input signal, but the related phasor which can be derived from amplitude and phase of the sine wave.
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