Primary frequency regulation in power grids with on-off loads: chattering, limit cycles and convergence to optimality

TL;DR

This paper investigates the use of on-off loads for primary frequency regulation in power grids, addressing issues like chattering and limit cycles, and proposes hysteretic control schemes with convergence guarantees and near-optimal cost solutions.

Contribution

It introduces a hysteretic on-off control policy that prevents chattering, analyzes limit cycle behavior, and designs a control scheme ensuring near-optimal power allocation.

Findings

Hysteretic control prevents chattering in on-off loads.

Proposed control schemes guarantee convergence to optimality.

Numerical simulations validate the theoretical results on a 140-bus system.

Abstract

Load side participation can provide valuable support to the power network in case of urgencies. On many occasions, loads are naturally represented by on and off states. However, the use of on-off loads for frequency control can lead to chattering and undesirable limit cycle behavior, which are issues that need to be resolved for such loads to be used for network support. This paper considers the problem of primary frequency regulation with ancillary service from on-off loads in power networks and establishes conditions that lead to convergence guarantees and an appropriate power allocation within the network. In particular, in order to assist existing frequency control mechanisms, we consider loads that switch when prescribed frequency thresholds are exceeded. Such control policies are prone to chattering, which limits their practicality. To resolve this issue, we consider loads that follow a decentralized hysteretic on-off policy, and show that chattering is not observed within such a setting. Hysteretic loads may exhibit, however, limit cycle behavior, which is undesirable. To address this, we propose an adapted hysteretic control scheme for which we provide convergence guarantees. Furthermore, we consider a mixed-integer optimization problem for power allocation and propose a suitable design of the control policy such that the cost incurred at equilibrium is within $\epsilon$ from the optimal cost, providing a non conservative value for $\epsilon$. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system.