IEEE Electrification Magazine - September 2017 - 62

Because the signal
is binary, it has the
lowest possible peak
factor; therefore, the
signal is well-suited
for sensitive systems,
which require
small-amplitude
perturbation.

measurement of impedances related to system stability. Online monitoring yields information about the
converter system and surrounding
electrical distribution system in real
time, enabling the targeting of a specific problem in an intelligent manner as the system changes (see
Figure 3). These methods consist in
generating a wideband perturbation
controlled in both magnitude and
duration and then in applying
advanced digital signal processing
techniques to identify the transfer
function or impedance of interest.
Among the several types of
wideband injection signals available, a small-signal PRBS injection is considered and
used to obtain the desired small-signal transfer functions. The PRBS has many attractive properties; the frequency resolution, the number of signal harmonics, and
injection bandwidth can be defined by the user. Because
the signal is binary, it has the lowest possible peak factor;
therefore, the signal is well suited for sensitive systems,
which require small-amplitude perturbation. Furthermore, due to its binary form, the injection can be easily
implemented even with a low-cost injection system,
whose output can only cope with a small number of signal levels. Finally, the PRBS can be easily generated using
feedback shift registers.
Figure 9 shows the conceptual block diagram of the
implementation of the WSI technique. In this representation, the switching power converter serves as perturbation

Switching
Power
Converter

Load
Subsystem
Zload(s)

PWM
- +
- +
+
Vref
CC
VC
+
+
+

V, I
Measurements

Controller
Embedded
Control
Platform

Test Signal
Processing
Zload(s)

Figure 9. A conceptual block diagram showing the injection of PRBS
over the converter control and embedded control platform for online
parametric identification of source and load impedances as well as
control loop gains.

I E E E E l e c t r i f i c ati o n M agaz ine / SEPTEMBER 2017

source, and the embedded control
platform hosts the processing routines acting as signal analyzer to
measure small-signal transfer functions and impedances of interest.
The converter has a closed-loop controller with an inner current control
loop (CC block) and outer voltage
control loop (VC block). In practice, a
small-signal PRBS test signal is added
to the duty cycle and to both the current and voltage reference signals of
the controller of the switching power
converter. The reason for such a
choice is linked to the frequency
response of the closed-loop converter. If the PRBS is injected into the
duty cycle only, the PRBS signal, seen as a disturbance, is
rejected within the outer control bandwidth as an effect of
the nested control loops, while it is not rejected beyond the
bandwidth of the outer control loop. On the other hand, if
the PRBS is injected into the current and voltage reference
signals, it is not rejected within the current and voltage
control bandwidths. Therefore, injecting the PRBS into the
duty cycle and into both the current and voltage reference
signals ensures that the PRBS is not rejected by the control
action over a wide frequency range.
While the PRBS is injected, output voltage/current
measurements are performed and processed by the
embedded control platform to calculate the load impedance. Note that this is a measurement of the load subsystem impedance only [refer to Figure 4(b)]. To measure the
source subsystem impedance, which in this case is the
output impedance of the switching power converter of
Figure 9, the load subsystem will need to be perturbed. If
a parametric representation of the impedances is desired,
a least-square algorithm can be applied to the nonparametric impedances obtained from the FFT algorithm.

Practical Considerations and Limitations
As explained in reference to Figure 8, commercial network analyzers used to measure frequency responses are
most often based on single sine sweeps, where the system under study is analyzed one frequency at a time.
Comparing the broadband excitations with single sine
sweeps, there are certain drawbacks that need to be
emphasized. First, the possible nonlinearities should be
carefully considered. Perturbing a system at a speciﬁc frequency may create harmonics at other frequencies, e.g.,
due to saturation nonlinearities. This is not an issue with
single sine sweeps. However, using broadband excitation
and computing the frequency response simultaneously at
multiple frequencies, the nonlinearities may create distortions to the measured response.
Using the PRBS, one of the major challenges is to ﬁnd
an appropriate injection amplitude. The amplitude must

Table of Contents for the Digital Edition of IEEE Electrification Magazine - September 2017