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α 1 1 α 2
@ 1 5 ð4:11Þ
α 1
where α 1 and α 2 are the coefficients defining the rated capacity of the DGs,
so application of @ 1 sharing factor will ensure the proportional sharing of
power (current) between two MFDGs.
In (4.10), S sw ðkÞ is the switching state of instant t k , and it would be calcu-
lated in a different way for each converter, but the main idea is to sum the
switching state of all the power electronic switches of the converter topol-
ogy, that is, for a parallel operation of two, three-level H-bridge converter,
S sw ðkÞ 5 2 means that both converters are at their positive output state at
instant t k and S sw ðkÞ 5 0, means that both converters are operating in zero
output state, or one is operating in positive and the other one is operating in
negative output state. Therefore f sw ðS sw ðkÞ; S sw ðk 1 1ÞÞ is the mathematical
function, relating the number of changes in switching states from instant t k
to t k11 .
It is obvious that, in multiobjective operation of a controller, different pri-
orities will result in different switching outputs; so to have an acceptable rate
of satisfaction for all of the objectives, there should be an effort to set the
best weighting factors for each application. This kind of controller is a very
good solution for the cases with multiple objectives, which need a fast
dynamic response, such as parallel MFDGs and modular APFs.
A comparison between different control methods applied to MFDGs is
provided in Table 4.2. As can be observed, each method has its advantages
and drawbacks, compared all together will make the selection of control
method proper for the control cases.
A comprehensive comparison is done to clarify the advantages, disadvan-
tages, and other PQI indexes between all generations of PQI devices in
Table 4.3.
In Table 4.3 the devices based on cost-effectiveness factor are not only
ranked based on the price but also on a price-to-capability ratio, so the pas-
sive filter is less cost effective in comparison to MFDGs, although passive
filter will cost much lower.

4.4 Conclusion

To study the concept of power quality in smart grids, first, a definition of
power quality and smart grid was proposed, new challenges and tools that
smart grids will bring to traditional grids have been also discussed. There
has been much research on power quality of smart grids, but less has been
focused on smart grid concept; in this chapter, it has been tried to include
the smart grid technology while studying power quality of smart grids. In
this regard, almost all the PQI devices were discussed. The advantages, dis-
advantages, and applications in the case of each device were studied, and a