Abstract
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.
Highlights
The penetration of new renewable energy sources (RESs), such as photovoltaic panels and wind turbines, is increasing in most electric power grids worldwide
The corresponding optimal placement of primary control can be obtained with Theorem 2, from which we observe that the damping-to-inertia ratios are increased for the buses with large squared components u(α0i)2 of the slow modes of L – those with the smallest λ(α0)
To find the optimal placement of inertia and primary control in electric power grids is a problem of paramount importance
Summary
The penetration of new renewable energy sources (RESs), such as photovoltaic panels and wind turbines, is increasing in most electric power grids worldwide. Jacquod: Optimal Placement of Inertia and Primary Control: Matrix Perturbation Theory Approach new RES with substitution inertia? A numerical optimization can certainly be performed for any given network on a case-bycase basis; it is highly desirable to shed light on the problem with analytical results Such results have either been restricted to small systems or derived assuming homogeneity in the damping and inertia parameters or their ratio. The theory constructed below constitutes an important step forward in the analytical optimization of inertia and primary control placement in low-inertia power grids.
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