Page 64 - Modern Control of DC-Based Power Systems

Small-Signal Analysis of Cascaded Systems 29

in [17] under the assumption that the closed-loop buck converter is PI
controlled. The destabilizing load forms, which were proposed by the
authors in [17] will be extended to match a PID regulator. Those load
forms represent destabilizing characteristics under certain parameter varia-
tions and dynamic conditions which exhibit a different dynamic behavior
in contrast to the CPL assumption. It should also be highlighted that next
to the employed Canonical Model, an alternative approach is possible
which is advocated in [15], where the load Z is taken out of the canonical
model and modeled through the corresponding deviation in the output
current; therefore, the converter equations show the real internal dynam-
ics of the converter without load and thus makes an interconnection of
systems easier.

2.4.1 Constant Power Load Model
Due to the integration in DC grids of LRC and POL converters the effi-
ciency of the network is increased and due to the control algorithm
implemented in the converters these grids are able to handle a wide varia-
tion in either load or source [18].
As an example, a buck POL converter is used with a resistive load as
shown in Fig. 2.10, where Z L sðÞ 5 R. Power converters such as a buck
converter are used because of their tight output voltage control capability,
which enables them to respond almost immediately to system changes.
On the other hand, under these conditions, the converter tends to oper-
ate as a CPL. When averaging the states and applying the canonical
model with the parameters of Table 2.1 and Eq. (2.1) the linearized
impedance model of the buck converter systems for a given operating
point is given in (2.25). As all denominator coefficients are positive and
not zero the perturbation transfer function for a single POL converter
which is supplied by an ideal voltage source satisfies the Hurwitz criteria
for stability.

L

V in V C C V out R

Figure 2.10 Simplified model of a CPL.