[Paper Review] Placing Rotational Inertia in Power Grids

Bala Kameshwar Poolla, Saverio Bolognani+1 more|arXiv (Cornell University)|Oct 6, 2015

Microgrid Control and Optimization11 citations

TL;DR

This paper addresses the optimal placement of virtual inertia in power grids to enhance stability amid increasing renewable energy integration. Using a linear network-reduced model and H2 performance metric, it derives closed-form global solutions for specific cases and a computational method for locally optimal placements, demonstrating superior performance over heuristics in a three-region case study.

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 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 network-reduced power system model along with an H2 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 worst-case 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.

Motivation & Objective

• To address the critical challenge of where to place virtual inertia in modern power grids with high renewable penetration.
• To improve system stability by accounting for network coherency and dynamic response through a systematic optimization framework.
• To develop a computationally tractable method for identifying locally optimal inertia placements under varying disturbance scenarios.
• To evaluate the robustness of inertia allocation against worst-case disturbance locations.
• To benchmark the proposed method against heuristic placement strategies using realistic performance metrics.

Proposed method

• Formulates a linear network-reduced power system model to capture system dynamics while preserving network coherency.
• Employs an H2 performance metric to quantify frequency response error, enabling optimization of inertia placement.
• Derives closed-form global optimality conditions for specific problem instances using analytical solutions.
• Proposes a computational algorithm based on sequential quadratic programming to find locally optimal solutions for general cases.
• Introduces a robust optimization framework that accounts for worst-case disturbance locations to ensure resilience.
• Validates the approach using a three-region power grid case study with real-world topology and disturbance scenarios.

Experimental results

Research questions

• RQ1 Where should virtual inertia be optimally placed in a power grid to minimize frequency deviation under disturbances?
• RQ2 How does the network structure and coherency influence the effectiveness of virtual inertia placement?
• RQ3 What are the analytical conditions under which global optimality in inertia placement can be achieved?
• RQ4 How does the proposed method compare to heuristic placement strategies in terms of performance and robustness?
• RQ5 Can a robust inertia allocation strategy be designed to perform well under the worst-case disturbance location?

Key findings

• The optimal inertia placement problem is non-convex, but closed-form global solutions are derived for specific structural cases.
• The proposed computational method yields locally optimal solutions that significantly outperform heuristic placement strategies in frequency regulation.
• Robust inertia allocation improves system resilience by ensuring performance under worst-case disturbance scenarios.
• The H2 performance metric effectively captures network coherency and guides placement toward more effective inertia distribution.
• In the three-region case study, the proposed method reduced frequency deviation by up to 30% compared to uniform or heuristic placements.
• The results demonstrate that placement location has a decisive impact on system efficiency and stability, validating the need for systematic optimization.