Optimal Placement of Virtual Inertia in Power Grids

Abstract

A major transition in the operation of electric power grids is the replacement of synchronous machines by distributed generation connected via power electronic converters. The accompanying "loss of rotational inertia" and the fluctuations by renewable sources jeopardize the system stability, as testified by the ever-growing number of frequency incidents. As a remedy, numerous studies demonstrate how virtual inertia can be emulated through various devices, but few of them address the question of "where" to place this inertia. It is, however, strongly believed that the placement of virtual inertia hugely impacts system efficiency, as demonstrated by recent case studies. In this article, we carry out a comprehensive analysis in an attempt to address the optimal inertia placement problem. We consider a linear networkreduced power system model along with an H 2 performance metric accounting for the network coherency. The optimal inertia placement problem turns out to be non-convex, yet we provide a set of closed-form global optimality results for particular problem instances as well as a computational approach resulting in locally optimal solutions. Further, we also consider the robust inertia allocation problem, wherein the optimization is carried out accounting for the worstcase disturbance location. We illustrate our results with a three-region power grid case study and compare our locally optimal solution with different placement heuristics in terms of different performance metrics.

Distributed Bilayered Control for Transient Frequency Safety and System Stability in Power Grids

“…(Bilayered control with stability and frequency guarantees). Under condition (4), assume that ε i T i < 1 for every i ∈ I u , and x(0) ∈ T , then the system (2) with the bilayered controller defined by (5), (8), (12), (13), and (20) satisfies…”

“…(Time scale in saddle-point dynamics). Since the MPC component updates its output at time instants {∆ w } w∈N according to (8), a requirement on the saddle-point dynamics (28) solving R (or equivalently R aug ) is that it returns the optimal solution within ∆ w+1 − ∆ w seconds starting from ∆ w for every w ∈ N. To achieve this, one may tune ε Y , ε η , and ε µ to accelerate the convergence of the saddle-point dynamics. In practice, this corresponds to running (28) on a faster time scale, which puts requirements on the hardware regarding communication bandwidth and computation time.…”

“…Let I ω = {30, 31, 32, 37} be four generator buses with transient frequency requirements. The safe frequency region is We first show that the bilayered controller defined by (5), (8), (12), (13), (20) is able to maintain the transient frequency of selected nodes within the safe region without changing the equilibrium point (cf. Theorem IV.6(i) and (iii)).…”

Virtual Inertia: Current Trends and Future Directions

“…The change in frequency per generation loss is increasing yearly, and this trend is highly correlated with increased RES penetration over the same time-period. Similarly, the European Network of Transmission System Operators for Electricity (ENTSO-E) has reported increased frequency violations in the Nordic grid correlated with increased RES penetration [9]. As a consequence, inertial response from wind turbines is now mandatory in many countries [10,11] and the trend is extending towards PV plants as well.…”

Primary Frequency Response Enhancement for Future Low Inertia Power Systems Using Hybrid Control Technique

“…This motivates the research community to search for technical solutions to let variable speed wind turbines (VSWTs) contribute to the system inertia and to support primary frequency control. The importance of the frequency regulation needed for such kind of renewable energy technology is emphasized in many works (e.g., [4][5][6][7]). Several control techniques are proposed in the literature to support the system frequency with increasing the penetration of the wind energy in the electric grid.…”