A Cyber Insurance Policy for Hedging Against Load-Altering Attacks and Extreme Load Variations in Distribution Grids

Uncertainties in renewable energy resources (RES) and load variations can lead to elevated system operational costs. Moreover, the emergence of large-scale distributed threats, such as load-altering attacks (LAAs), can induce substantial load variations, further exacerbating these costs. Although traditional defense measures can reduce the likelihood of such attacks, considerable residual risks remain. Thus, this paper proposes a cyber insurance framework designed to hedge against additional operational costs resulting from LAAs and substantial load variations in renewable-rich grids. The insurance framework determines both the insurance coverage and premium based on the Value at Risk (VaR) and Tail Value at Risk (TVaR). These risk metrics are calculated using the system failure probability and the probability density function (PDF) of the system operation cost. The system failure probability is assessed through a semi-Markov process (SMP), while the cost distribution is estimated through a cost minimization model of a distribution grid combined with a Monte-Carlo simulation to capture load variability. Furthermore, we employ a bi-level optimization scheme that identifies the specific load distribution leading to the maximum system cost, thereby enhancing the accuracy of the operation cost PDF estimation. The effectiveness and scalability of the proposed cyber insurance policy are evaluated considering a modified IEEE-118 test bus system and the IEEE European low-voltage (LV) test feeders model. The case study shows that with a relatively low premium, the network operator can hedge against additional operational costs caused by malicious load manipulations.