Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal placement of inertia and primary control : a matrix perturbation
  theory approach   The increasing penetration of inertialess new renewable energy sources
reduces the overall mechanical inertia available in power grids and accordingly
raises a number of issues of grid stability over short to medium time scales.
It has been suggested that this reduction of overall inertia can be compensated
to some extent by the deployment of substitution inertia - synthetic inertia,
flywheels or synchronous condensers. Of particular importance is to optimize
the placement of the limited available substitution inertia, to mitigate
voltage angle and frequency disturbances following a fault such as an abrupt
power loss. Performance measures in the form of H2-norms have been recently
introduced to evaluate the overall magnitude of such disturbances on an
electric power grid. However, despite the mathematical conveniance of these
measures, analytical results can be obtained only under rather restrictive
assumptions of uniform damping ratio, or homogeneous distribution of inertia
and/or primary control in the system. Here, we introduce matrix perturbation
theory to obtain analytical results for optimal inertia and primary control
placement where both are heterogeneous. Armed with that efficient tool, we
construct two simple algorithms that independently determine the optimal
geographical distribution of inertia and primary control. These algorithms are
then implemented on a model of the synchronous transmission grid of continental
Europe. We find that the optimal distribution of inertia is geographically
homogeneous but that primary control should be mainly located on the slow modes
of the network, where the intrinsic grid dynamics takes more time to damp
frequency disturbances.

14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc