Page 89 - Modern Control of DC-Based Power Systems

54 Modern Control of DC-Based Power Systems

Im

GMPM criterion

PM Unit circle
Maximum peak criteria
–1
ESAC criterion Re
Middlebrook criterion
RESC

1/GM
Opposing argument
criterion
Figure 2.29 Stability criteria: boundaries between forbidden regions and allowable
regions.

To assess overall system stability, several stability criteria for DC sys-
tems based on forbidden regions for the minor loop gain have been pro-
posed in the literature, such as the Middlebrook Criterion [29], and its
various extensions, such as the Gain and Phase Margin (GMPM)
Criterion [30], the Opposing Argument Criterion [31 33], the Energy
Source Analysis Consortium (ESAC) Criterion [34,35], and its extension
the Root Exponential Stability Criterion (RESC) [36]. All these criteria
have been reviewed in [37], which presents a discussion, for each crite-
rion, of the artificial conservativeness of the criterion in the design of DC
systems, and the design specifications that ensure system stability.
Shortcomings of all these criteria (also discussed in [37]) are that they lead
to artificially conservative designs, encounter difficulties when applied to
multiconverter systems (more than two interconnected subsystems) espe-
cially in the case when power flow direction changes, and are sensitive to
component grouping. Moreover, all these criteria, with the exception of
the Middlebrook Criterion, are not conducive to an easy design formula-
tion. Another significant practical difficulty present with all the prior sta-
bility criteria is the minor loop gain online measurement [38]. It requires
two separate measurements, source subsystem output impedance and load
subsystem input impedance, and then some postprocessing. Due to the
complexity in the calculation, this approach is not suitable for online sta-
bility monitoring. (Only in the work [39], a practical approach to mea-
sure the stability margins of the minor loop gain was proposed. However,