It has been shown that a typical electrical power transmission system exhibits a scale invariant feature at
intermediate frequencies. This invariance is characterized by the spectral dimension which is a key parameter for
identifying a frequency equivalent of the network. Beyond its accuracy, the main interest of the scale invariant
equivalent is to integrate an explicit knowledge of the inner dynamic couplings of the network. Through powerlaws,
an essential link between the topology and the dynamic behavior is simply described with very few parameters.
This ability to reveal how complex dynamics emerges from the network is an important result for the dynamic studies
of power systems. It could be very helpful for power engineers when assessing what could be the consequences of a
smart grid architecture on the dynamic performances.
Of course, further works are required to consolidate the approach. In particular, loads, generators and their
regulators have not been considered in the present work. Upcoming studies should confirm that the integration of these
multiple components has not a major impact. In addition, an effort could be done to reduce the size of the frequency
equivalent by coupling the scale invariant approach with modal reduction techniques with the aim of canceling the
weakest modes in the frequency approximation.
Then, the next important step will be to integrate the scale invariant equivalent into a smart grid simulation platform
for off-line or real-time computations. For that purpose, a time implementation of the non-integer impedance that
represents the asymptotic behavior at intermediate frequencies should be performed [23].
And, at long-term, the scaling approach should be extended to model the ICT networks too. This would be the
opportunity to develop a universal modeling framework for representing dynamic behaviors of smart grids, including
both power and communication networks.