IEEE Electrification Magazine - September 2017 - 57

Figure 2 contrasts the voltage-current characteristic of a
conventional resistive load versus a CPL. For the resistive
load case, if the bus voltage changes, the load current
changes in the same direction in a linear fashion. For
example, if the bus voltage decreases, the load current
decreases as well. In contrast, for the CPL case, voltage and
current change in opposite directions. If the voltage
decreases, the current increases. The linearized behavior
around a certain operating point is given by a negative
incremental resistance, as shown in Figure 2. The reason
for this behavior is the closed-loop control action. The
closed-loop control keeps the output voltage constant,
rejecting input voltage variations; this implies that the
output power is also constant. The input power is thus
required to be approximately constant as well, hence the
CPL characteristic.
An important note is that a power electronics system
decouples the inertia, which is present in the generators
from the main dc-bus. This means that these systems
have no inertia in contrast to classical power systems. As a
consequence, the damping of oscillations due to the inertia of the electrical machines is not present on the dc-bus,
unless such behavior is programed into the closed-loop
control of the power electronics system.
When switching converters are connected to a common bus, dc distribution systems may suffer from stability
degradation. This stability problem can be explained in
two ways. The first explanation considers the stability
problem as due to the previously described CPL effect,
which introduces a destabilizing equivalent negative resistance behavior at the dc-bus. The second explanation considers the instability as arising from the interactions of the
different converters and their respective control loops.
This interaction can be observed when plotting the
impedances of each subsystem. If the impedances of each
subsystem overlap, i.e., have similar amplitudes in a certain frequency range, an interaction takes place that may
lead to instability.
Each individual subsystem or converter in the power
distribution system is typically independently designed in
such way that it is stable. Instability arises from dynamic
effects due to interactions among subsystems. This means
that the system designer who is integrating the power distribution system is responsible for the necessary damping
and stability.
In the study of stability, one can distinguish between
large- and small-signal stability. Large-signal stability considers the effects of large perturbations and includes nonlinear effects. The full nonlinear system needs to be
considered. The behavior of nonlinear systems is significantly more complicated than that of linear systems. For
example, stability is not a global property, as it is in linear
systems, and is restricted to certain trajectories of the system. A very often used large-signal stability concept is
based on the theory introduced by Lyapunov. In general,
evaluating nonlinear stability is a difficult problem. For

Constant Power
Load P = VI = Constant
Resistive
Load

-RCPL
I0

Figure 2. The characteristic VI curve of a CPL.

example, the evaluation of Lyapunov stability requires
finding a so-called Lyapunov function, but no general
method to find such a function is available. For ac power
systems, the study of large-signal stability is known as
transient stability or dynamic stability.
Given the difficulties with large-signal stability, a common approach is to study a simpler problem, i.e., smallsignal linearized stability. A nonlinear system can be
linearized around a given operating point, and linear theory can be applied to the resulting linearized system.
Traditionally, the voltage stability assessment of dc systems is focused on ensuring stability for small variations
around a given operating point, thus small-signal stability.
The small-signal stability assessment in cascaded systems has been performed in the frequency domain using
the Middlebrook stability criterion and its extensions.
Now, the classification societies state only functional
requirements for the safe operation of a maritime electrical installation. These classification societies are organizations within the maritime industry that establish and
maintain technical standards for the construction and
operation of ships and offshore structures. Consequently,
there are no further standards besides IEEE Standard 1709
(IEEE Recommended Practice for 1 kV to 35 kV Medium-Voltage
dc Power Systems on Ships) (Recommended Practice) from
2010, which covers the main aspects of the MVdc distribution system.
The main reason for the lack of well-established standards is that this is still an emerging field. Emerging solutions from different power distribution manufacturers all
have different approaches using different technologies and
approaches. The dc distribution systems in a new ship will
be built entirely by one manufacturer and will not necessarily use standard components. Due to the absence of
widespread standards, manufacturers have a certain
amount of freedom in meeting these standards, and they
can receive a formal approval if they meet the functional
requirements specified in the existing standards.
IEEE Elec trific ation Magazine / S EP T EM BE R 2 0 1 7

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