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

TL;DR

The paper addresses financial risk in renewable-rich distribution grids exposed to load variability and load-altering attacks by proposing a cyber insurance framework priced with VaR and TVaR. It combines Monte Carlo sampling, a bi-level max-impact optimization, and a semi-Markov process to quantify extreme-cost risk, and validates the approach on IEEE 118-bus and IEEE European LV networks. Key contributions include worst-case impact assessment under load variations, SMP-based risk probabilities, and a VaR/TVaR-based insurance design that requires a modest premium. The results demonstrate practical hedging potential against elevated operational costs and show scalability to larger networks, highlighting cyber insurance as a complementary protective layer to defenses. The work provides a quantitative, adaptable mechanism for operators to manage financial exposure in highly renewable distribution grids.

Abstract

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-bus test system and the IEEE European low-voltage (LV) test feeder 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.

Figures (10)

• Figure 1: Operational overview of the grid model under consideration.
• Figure 2: Semi-Markov process (SMP) model for risk probability estimation. P(·) defines the CDF of the state transition time.
• Figure 3: Illustration of the operational cost distribution $g(x)$, highlighting $VaR_\alpha$ as the insurance activation threshold, and $TVaR_\alpha$ as the expected loss in the tail region (blue area).
• Figure 4: Detailed insurance framework.
• Figure 5: (a) PV, load factors and electricity prices over 24h, (b) Total operational cost of the modified IEEE 118-bus system using the cost function $\boldsymbol{c}^{LC}$ with different $a$, and $b=0$, (c) Total curtailed loads and net purchased electricity of a day in the modified IEEE 118-bus system for different $a$, (d) Bus voltages of the modified IEEE 118-bus system after optimization with $a=1$.