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Power Grid Kinetic Energy Analysis for Smaller Systems
Grid Cruise Control
Kinetic Energy and Inertia
Kinetic Energy Analysis
Kinetic Energy Analysis for Smaller Systems
This analysis is intended for a system with fewer generators and with power supplies that have no inherent inertia, e.g., wind farms.  Starting with individual power supplies, we develop the composite of all the sources.
The stored energy for an individual “real” generator is expressed as follows:
Eg = Hg * ( F / F0 )^2 * Sg
The stored energy for an individual conventional wind farm is expressed as follows:
Ew = Hw * ( F / F0 )^2 * Sw
To get the system stored energy of the interconnected resources, we add up the individual stored energies:
Es = ∑ Hg * ( F / F0 )^2 * Sg + ∑ Hw * ( F / F0 )^2 * Sw
At this point we “remove” the wind farms since they have no stored energy, i.e., their “H” is zero:
Es = ∑ Hg * ( F / F0 )^2 * Sg
This is where we can derive a composite “Hs” and a composite “Ss”.  Notice that the system stored energy does not include the effect of wind farms:
Es = Hs * ( F / F0 )^2 * Ss
Note that:
Hs * Ss = ∑ Hg * Sg
This is an opinion for how to derive a “weighted average” for system “H” for simulation studies.
In conclusion, the inertia of the system does not change with the addition of conventional wind farms. Consider a shaft with large heavy flywheels and some light thin disks. Where will most of the stored energy reside?

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Session # 178923 Copyright 2008-2010, GridTrak Updated: July 22, 2009