  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.
