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 $ϵ$ from the optimal cost, providing a non conservative value for $ϵ$. The practicality of our analytic results is demonstrated with numerical simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system.

在紧急情况下，负载侧的参与可以为电网提供宝贵的支持。在许多情况下，负载自然由开和关状态表示。然而，使用开关负载进行频率控制会导致颤振和不良的极限循环行为，这是此类负载用于网络支持需要解决的问题本文考虑了初级频率调节与辅助频率的问题。为电力网络中的开关负载提供服务，并建立导致收敛保证和网络内适当功率分配的条件。特别是，为了协助现有的频率控制机制，我们考虑了在超过规定的频率阈值时切换的负载。这样的控制策略容易产生喋喋不休，限制了它们的实用性。为了解决这个问题，我们考虑了遵循分散滞后开关策略的负载，并表明在这种情况下不会观察到抖动。然而，滞后负载可能会表现出不希望有的极限循环行为。为了解决这个问题，我们提出了一个适应我们提供收敛保证的滞后控制方案。此外，我们考虑了功率分配的混合整数优化问题，并提出了一个合适的控制策略设计，使得在平衡时产生的成本在$\epsilon$ 从最优成本，提供一个非保守值 $\epsilon$. 东北电力协调委员会 (NPCC) 140 总线系统的数值模拟证明了我们分析结果的实用性。