Page 103 - Modern Control of DC-Based Power Systems

Small-Signal Analysis of Cascaded Systems 67

Figure 2.45 A wideband PRBS signal (red (light gray in print version)) and a narrow-
band sinusoidal signal (blue (dark gray in print version)) in the time domain (top)
and in the frequency domain (bottom)

has an approximately flat signal content in the frequency domain (the sig-
nal energy drops to zero at signal generation frequency which is 1000 Hz
in this example). Specialized equipment used to measure transfer func-
tions of dynamic systems, such as network analyzers, frequently uses nar-
rowband excitation signals. This gives measurement with accuracy and
reduced noise, but the measurement typically requires long time, because
the measurement is performed one frequency at a time and the excitation
frequency must be swept across the frequency range of interest.
Conversely, wideband signals, such as the PRBS, excite all frequencies of
interest simultaneously, allowing a much faster measurement using Fast
Fourier Transform (FFT) techniques. This latter solution is described
hereafter in this section, since a fast measurement technique is desired.
The online method to measure system impedances by using the wide-
band excitation signal PRBS is called the online WSI technique [47,48].
The online WSI technique can generate the wideband excitation which
can be controlled in both magnitude and duration for both voltage and
current at the impedance measurement point. Then, FFT techniques can
be applied on the measured voltage and current to identify the impedance
of the system under test. This technique to measure impedances is used
in conjunction with existing power electronics converters which serve as
power amplifiers for the excitation signal PRBS. Moreover, since the
converters have digital control and sensing, they may also be used to
monitor the evolution of impedances on the top of their power