Stability of primary frequency control with on-off load side participation in power networks

We consider the problem of load side participation providing ancillary services to the power network within the primary frequency control timeframe. In particular, we consider on-off loads that switch when prescribed frequency thresholds are exceeded in order to assist existing primary frequency control mechanisms. However, such control policies are prone to chattering, which limits their practicality. To resolve this issue, we propose loads that follow a hysteretic on-off policy, and show that chattering behavior is not observed within such setting. Furthermore, we provide design conditions that ensure the existence of equilibria when such loads are implemented. However, as numerical simulations demonstrate, hysteretic loads may exhibit limit cycle behavior, which is undesirable. This is resolved by proposing a novel control scheme for hystertic loads. For the latter scheme, we provide asymptotic stability guarantees and show that no limit cycle or chattering will be exhibited. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system.