A Distributed Optimization and Control Framework for a Network of Constraint Coupled Residential BESSs

Resilient and Privacy-Preserving Multi-Agent Optimization and Control of a Network of Battery Energy Storage Systems Under Attack

“…The first setting, introduced in [23] and [24], is represented as g 1 n n i=1 x i ≤ 0. Another setting, presented in [25], is expressed as 1 n n i=1 x i ≤ s. It is important to note that neither of these settings aligns with (15), which is n i=1 g i (x i ) ≤ 0. ■…”

“…According to the constraints defined in Section III, X i is compact. Furthermore, (15) implies that g(.) is L-Lipschitz in the compact set, X i , therefore there exists a constant L such that…”

“…Remark 2: To ensure that the coupling constraints are satisfied, we account for the worst-case behavior of the 2F filtered agents in the network. Specifically, we modify both g 1 (x i ) and g 2 (x i ) in (15) based on the maximum allowable power transfer of each agent, denoted as p l max i . Let us define P M as the maximum value of p l max i across all agents, i.e., P M = max i∈V p l max i .…”

“…In the worst-case scenario, the neglected agents can consume or inject a total power of P M into the network, thereby occupying the common resources. Therefore, we replace L max with L max − 2F • P M in (15) to ensure that the coupling constraints are not violated. ■ In this section, we evaluate the performance of Algorithm 1 and compare it with the non-resilient resource allocation algorithm introduced in [26].…”

“…In the last decade, decentralized and distributed optimization has been introduced as a suitable solution to address the aforementioned drawbacks [9], [10], [11], [12]. Numerous articles from various perspectives have tackled power system-related issues using distributed optimization algorithms [13], [14], [15], [16], [17]. However, one concern when utilizing networked systems is the potential for cyberattacks.…”