Page 102 - Modern Control of DC-Based Power Systems

66 Modern Control of DC-Based Power Systems

Guy(s)

u(t) System under y(t)
test

Figure 2.44 A dynamic system under test to find the input-to-output transfer func-
tion G uy sðÞ:

correspondence of a VSI symmetric three-phase load step from 20Ω to
10Ω. An unstable performance is evident.

2.6.2 Online Wideband System Identification Technique
In order to apply the Nyquist Stability Criterion to the minor loop gain
defined in (2.94), it is necessary to know the interface impedances of the cas-
cade system. Offline analytical methods to study the stability provide some
limitations because in real systems the impedances continuously vary over
time and in relation to too many parameters. Therefore, online methods to
measure impedances are required in order to monitor system stability mar-
gins in real time and take stabilizing actions if needed. The online technique
1
to measure impedances presented in this section has the following charac-
teristics. First, it is able to complete the impedance measurement in a short
time, allowing fast response to system variations. Additionally, it utilizes the
existing power converters of the cascade system and their sensors to perform
the impedance measurement (it is not needed to add specialized equipment
with the associated extra cost, size and weight).
Before focusing on how to measure an impedance, let us briefly
review the fundamental principle for measuring a transfer function of a
dynamic system. In order to measure the input-to-output transfer func-
tion G uy ðsÞ of the dynamic system under test shown in Fig. 2.44, an exci-
tation signal with a desired frequency content is applied to the system
input uðtÞ and the system response yðtÞ is measured. The time-domain
measurements of the signals uðtÞ and yðtÞ are processed to calculate the
G uy sðÞ 5 yðsÞ=uðsÞ in the frequency domain. The excitation signal can be
either narrowband or broadband as shown in Fig. 2.45. An example of a
narrowband signal is a sine wave, which ideally has power only at a single
frequency. An example of a wideband signal is white noise, which has
power over a wide frequency range. The pseudo-random binary signal
(PRBS) shown in Fig. 2.45 is a digital approximation of white noise and

1
Other small-signal transfer functions can also be measured.