# Design and Stability of Load-Side Primary Frequency Control in Power Systems

arXiv: https://arxiv.org/abs/1305.0585 · HTML: https://mlsanity.com/paper/1305.0585/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2013.

## Built on by (most cited first, 5 of 5)

- [Predictability and Fairness in Load Aggregation and Operations of Virtual Power Plants](https://mlsanity.com/paper/2110.03001/) (2021)
- [Online Event-Triggered Switching for Frequency Control in Power Grids with Variable Inertia](https://mlsanity.com/paper/2408.15436/) (2024)
- [Revisiting Policy Gradients for Restricted Policy Classes: Escaping Myopic Local Optima with k-step Policy Gradients](https://mlsanity.com/paper/2605.10909/) (2026)
- [Stability of Primal-Dual Gradient Flow Dynamics for Multi-Block Convex Optimization Problems](https://mlsanity.com/paper/2408.15969/) (2024)
- [Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systems](https://mlsanity.com/paper/2602.12592/) (2026)

## Abstract (arXiv)

We present a systematic method to design ubiquitous continuous fast-acting distributed load control for primary frequency regulation in power networks, by formulating an optimal load control (OLC) problem where the objective is to minimize the aggregate cost of tracking an operating point subject to power balance over the network. We prove that the swing dynamics and the branch power flows, coupled with frequency-based load control, serve as a distributed primal-dual algorithm to solve OLC. We establish the global asymptotic stability of a multimachine network under such type of load-side primary frequency control. These results imply that the local frequency deviations at each bus convey exactly the right information about the global power imbalance for the loads to make individual decisions that turn out to be globally optimal. Simulations confirm that the proposed algorithm can rebalance power and resynchronize bus frequencies after a disturbance with significantly improved transient performance.