I am working on the analytic signal concept for observing the frequency variation in the faulted phase current waveform in MATLAB/Simulink model. In MATLAB/Simulink model, I have used analytic signal block and hilbert's transform method to calculate the real and imaginary components of the faulted phase current. After that I have used the data of real and imaginary components of the faulted phase current to calculate the magnitude, phase, and instantaneous frequency. When I plotted the curve between the instantaneous frequency variation vs time for the faulted phase current, I observed that the frequency variation is negative in the curve of instantaneous frequency vs time for the faulted phase current. Why it is so ?
Siddharth Kamila The analytic signal is a complex-valued signal created by using the Hilbert transform on a real-valued signal. The analytic signal is defined as x a(t) = x(t) + jx h(t), where x(t) is the original real-valued signal and x h(t) is x h(t) (t). x r(t) = (x(t) + x h(t))/2 and x i(t) = (x(t) - x h(t))/2j are the real and imaginary components of the analytic signal, respectively. The magnitude of the analytic signal is given by |x a(t)| = sqrt[x r(t)2 + x i(t)2], the phase is supplied by phi(t) = atan(x i(t)/x r(t)), and the instantaneous frequency is given by f(t) = (1/2pi) * d(phi(t))/dt.
In general, the analytic signal has the same frequency as the original real-valued signal. If the original real-valued signal has a non-zero mean value, the frequency of the analytic signal may deviate somewhat from that of the original real-valued signal. Furthermore, if the original real-valued signal contains a non-zero DC component, the frequency of the analytic signal may deviate somewhat from that of the original real-valued signal.
If the curve of the faulty phase current's instantaneous frequency vs time is negative, it might be owing to the presence of a non-zero DC component or a non-zero mean value in the original real-valued signal. It is also conceivable that the negative frequency change is caused by anything else in the signal, such as noise or interference.
I hope this was helpful. Please let me know if you have any more inquiries.
In a power system, the instantaneous frequency of a current signal is a measure of the rate of change of the phase angle of the current. The instantaneous frequency is calculated as the derivative of the phase angle with respect to time.
In the case of a faulted phase current, the instantaneous frequency curve will show a negative frequency variation because the phase angle of the current is decreasing with time. This is due to the fact that during a fault, the current is rapidly decreasing and the voltage is also rapidly decreasing, resulting in a decreasing phase angle.
It is important to note that the negative frequency variation during a fault is a sign of an abnormal condition in the power system and indicates that a fault has occurred. This negative frequency variation can be used as an indication for the protection system to trip the breaker and clear the fault.
Also, the instantaneous frequency curve can be used to identify the type of fault, for example, a negative slope in the curve can indicate a single-phase-to-ground fault, while a positive slope indicates a three-phase fault.
Keep in mind that this is a general explanation, there might be variations depending on the type of fault, location of the fault and the system impedance. Also, some advanced protection systems use the frequency deviation instead of the instantaneous frequency for fault detection.
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