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Resilient Distribution Network Planning against Dynamic Malicious Power Injection Attacks

Hampei Sasahara, Tatsuya Yamada, Jun-ichi Imura, Henrik Sandberg

TL;DR

The paper tackles resilience of distribution networks against dynamic malicious power injections at end-user nodes by embedding a grid-level security constraint into the planning problem. It develops a tractable MILP formulation through a two-step reduction: first, a linear dynamical-system-based characterization shows that attack impact depends on the cumulative reactance along the substation-to-node path; second, a bottleneck/shortest-path transformation encodes the path constraint with binary variables. The approach yields a precise, scalable planning tool that combines topology decisions with inverter dynamics to improve voltage volatility resilience. In simulations on a 54-node benchmark, resiliency improves by about $29.3\%$ with only a $2.1\%$ rise in investment costs, demonstrating practical relevance for grid-level cybersecurity. The work provides a foundation for extending to nonuniform lines, multiple targets, and broader network interactions with transmission systems.

Abstract

Active distribution networks facilitating bidirectional power exchange with renewable energy resources are susceptible to cyberattacks due to integration of a diverse array of cyber components. This study introduces a grid-level defense strategy aimed at enhancing attack resiliency based on distribution network planning. Our proposed framework imposes a security requirement into existing planning methodologies, ensuring that voltage deviation from its rated value remains within a tolerable range against dynamically and maliciously injected power at end-user nodes. Unfortunately, the formulated problem in its original form is intractable because it is an infinite-dimensional bi-level optimization problem over a function space. To address this complexity, we develop an equivalent transformation into a tractable form as mixed-integer linear program leveraging linear dynamical system theory and graph theory. Notably, our investigation reveals that the severity of potential attacks hinges solely on the cumulative reactances over the path from the substation to the targeted node, thereby reducing the problem to a finite-dimensional problem. Further, the bi-level optimization problem is reduced to a single-level optimization problem by using a technique utilized in solving the shortest path problem. Through extensive numerical simulations conducted on a 54-node distribution network benchmark, our proposed methodology exhibits a noteworthy 29.3% enhancement in the resiliency, with a mere 2.1% uptick in the economic cost.

Resilient Distribution Network Planning against Dynamic Malicious Power Injection Attacks

TL;DR

The paper tackles resilience of distribution networks against dynamic malicious power injections at end-user nodes by embedding a grid-level security constraint into the planning problem. It develops a tractable MILP formulation through a two-step reduction: first, a linear dynamical-system-based characterization shows that attack impact depends on the cumulative reactance along the substation-to-node path; second, a bottleneck/shortest-path transformation encodes the path constraint with binary variables. The approach yields a precise, scalable planning tool that combines topology decisions with inverter dynamics to improve voltage volatility resilience. In simulations on a 54-node benchmark, resiliency improves by about with only a rise in investment costs, demonstrating practical relevance for grid-level cybersecurity. The work provides a foundation for extending to nonuniform lines, multiple targets, and broader network interactions with transmission systems.

Abstract

Active distribution networks facilitating bidirectional power exchange with renewable energy resources are susceptible to cyberattacks due to integration of a diverse array of cyber components. This study introduces a grid-level defense strategy aimed at enhancing attack resiliency based on distribution network planning. Our proposed framework imposes a security requirement into existing planning methodologies, ensuring that voltage deviation from its rated value remains within a tolerable range against dynamically and maliciously injected power at end-user nodes. Unfortunately, the formulated problem in its original form is intractable because it is an infinite-dimensional bi-level optimization problem over a function space. To address this complexity, we develop an equivalent transformation into a tractable form as mixed-integer linear program leveraging linear dynamical system theory and graph theory. Notably, our investigation reveals that the severity of potential attacks hinges solely on the cumulative reactances over the path from the substation to the targeted node, thereby reducing the problem to a finite-dimensional problem. Further, the bi-level optimization problem is reduced to a single-level optimization problem by using a technique utilized in solving the shortest path problem. Through extensive numerical simulations conducted on a 54-node distribution network benchmark, our proposed methodology exhibits a noteworthy 29.3% enhancement in the resiliency, with a mere 2.1% uptick in the economic cost.

Paper Structure

This paper contains 14 sections, 5 theorems, 25 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Modeling and Problem Description
  3. Distribution network components and structure
  4. Attack model, resiliency metric, and security requirements
  5. Resilient distribution network planning problem
  6. Characterization of Maximally Disruptive Power Injection Signal
  7. Maximally disruptive power injection signal characterization problem
  8. State-space representation of network dynamics
  9. Characterization of maximally disruptive power injection signal
  10. Equivalent Reformulation to MILP
  11. Numerical Simulation
  12. Simulation settings
  13. Simulation results
  14. Conclusion

Key Result

Lemma 1

If the original attack signal satisfies $|a_i(t)|\leq C$ the surrogate attack signal satisfies $|\hat{a}_i(t)|\leq C_0$ where $C_0:=C\sqrt{m^2+1}$. Furthermore, if $|\hat{a}_i(t)|\leq C_0$, then there exists an original signal such that $|a_i(t)|\leq C$.

Figures (8)

  • Figure 1: Illustration of distribution network planning.
  • Figure 2: Consumer node structure and malicious power injection attack.
  • Figure 3: Architectural components of a smart inverter and possible threats.
  • Figure 4: The Maximally disruptive power injection signal.
  • Figure 5: Simulated distribution network.
  • ...and 3 more figures

Theorems & Definitions (9)

  • Lemma 1
  • proof
  • Lemma 2
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 1
  • proof