Page 114 - Modern Control of DC-Based Power Systems

78 Modern Control of DC-Based Power Systems

A special section was devoted to the so-called CPL. There, its behav-
ior was derived and its boundary conditions explained. An important fact
that could be drawn from this analysis is that when using dynamic models
an ideal CPL representation does not represent the worst case condition.
Additionally, the CPL does not exhibit infinite bandwidth but takes over
the bandwidth characteristics of the LRC.
An extension of the procedure presented in this chapter to other con-
verter topologies is possible. For example, if unidirectional power flow is
sufficient according to the system requirements, Single Active Bridge (SAB)
converters could be used; their modeling in small-signal was presented by
Demetriades [51]. When the system requires bidirectional power flow, Dual
Active Bridge (DAB) converters could be considered. There exist different
modeling approaches for DAB in literature, the primary difference among
them lies in the set of state variables selected. In [52], De Doncker intro-
duced the DAB model as a first-order system; after, Demetriades [53] pro-
posed a second-order model; in [54] Alonso presented a third-order model
which is further expanded by Krismer up to a fifth-order model [55].
Recently, Qin [56,57] presented an open-loop third-order model based on
the DAB generalized state-space modeling and a sixth-order model which
takes Equivalent Series Resistance into account. The generalized state-space
modeling approach, which was introduced in [58,59], uses more terms of
the Fourier series than the conventional averaging approach in the state vari-
ables; thus enabling a full order continuous time state-space average model
which could include the transformer current [56,57].
The aforementioned models can be used to derive the different trans-

fer functions of SAB and DAB converters in analogy to the Eqs. (2.1)
(2.7), and following a similar procedure to the presented in this chapter,
although using the phase shift angle instead of the duty cycle as the con-
trol variable.
In this context, it can be said that even when changing the converter
topology, the methodology presented throughout this chapter would
remain unaltered.
Furthermore, we gave an introduction to the linear control design and
validation procedure for voltage and current mode control, followed by a
simulation example. We highlighted the different stability criteria and
their application when combining different sources and load converters.
With the online wideband system identification technique, we displayed a
powerful tool for the engineers, as this can be incorporated into a real-
world converter setup and generate the stability analysis during operation.