  An increase in the integration of Inverter Based Resources (IBRs) to the
electric grid, will lead to a corresponding decrease in the amount of connected
synchronous generators, resulting in a decline in the available rotational
inertia system-wide. This can lead to pronounced frequency deviations when
there are disturbances and faults in the grid. This decline in available
rotational inertia can be compensated for by fast acting IBRs participating in
frequency response services, by rapidly injecting into or removing power from
the grid. Currently, there are still relative small number of sizable IBRs in
the grid. Therefore, the placement of the IBRs in the system, as well as the
inverter configuration type and controller, will have a material impact on the
frequency response of the grid. In this work, we present an optimal placement
algorithm that maximizes the benefits of utilizing IBRs in providing frequency
response services. That is, we minimize the overall system frequency deviation
while using a minimal amount of electric power injection from the IBRs. The
proposed algorithm uses the resistance distance to place the IBRs at nodes that
are central to the rest of the nodes in the network thus minimizing the
distance of power flow. The proposed greedy algorithm achieves a near optimal
performance and relies on the supermodularity of the resistance distances. We
validate the performance of the placement algorithm on three IEEE test systems
of varying sizes, by comparing its performance to an exhaustive search
algorithm. We further evaluate the performance of the placed IBRs on an IEEE
test system, to determine their impact on frequency stability. The IBRs are
configured in a grid-forming mode and equipped with a model predictive control
(MPC)-based inverter power control.
