Impact of Targeted Cyber Attacks on Electrical Power Systems

Abstract

This paper formulates targeted and coordinated attacks on an electrical power system infrastructure as an optimization problem to (a) investigate the impacts of such attacks on the electric power grid and (b) to study the extent of damages to the grid depending on attacker’s resources and level of protection employed in the grid. In this research, we consider the coordinated load redistribution (LR) attack, which is a variant of false data injection attack on electrical power systems. The bi-level formulation is investigated through a problem in which the goal of the hacker is to maximize load curtailment and that of the power system operator is to minimize load curtailment. The resulting nonlinear mixed-integer bilevel programming formulation is converted into an equivalent single-level mixed-integer linear program by solving the inner optimization by KKT optimality conditions. The case studies are conducted based on an IEEE 14-bus system. From the results, it is observed that the hacker could maximize the damages to the power grid, even with limited attack resources, by simultaneously targeting the physical system and deceiving the operator with a false power dispatch. This study can provide meaningful insights on the relation between hacker’s available resources, existing security measures and resulting disruption in the power system. The results can be used to design methods to prevent and mitigate such coordinated attacks to improve the reliability of the electric grid.

Appendix A

Indices	Definitions
$d$	Index for load demands
$g$	Index for generators on each bus
$l$	Index for transmission lines
Constants
$N_{d}$	Number of loads
$N_{g}$	Number of generators
$N_{l}$	Number of transmission lines
$P_{g}^{max}$	Maximum generation output of generator ‘g’
$P_{g}^{min}$	Minimum generation output of generator ‘g’
$PL_{l}^{max}$	Maximum capacity of transmission line ‘l’
$C_{D,d}$	Cost required to attack load demand measurements
$C_{F,l}$	Cost required to attack line flow measurements
$C_{G,g}$	Cost required to attack the generators
$\Delta D_{d}$	Attack on the load demand measurements
$SF$	Shifting factor matrix
$KP$	Bus-generator incidence matrix
$KD$	Bus-load incidence matrix
$M$	Sufficiently large positive constant
$R_{C}$	Cyber-attack resource
$\varepsilon$	Sufficiently small positive constant
$\tau$	Upper bound of the attack magnitude on the load demand measurements
$C_{0} , C_{1} , C_{2}$	Cost coefficients of generators
Variables
$S_{d}$	Load shedding of load ‘d’
$\Delta D_{d}$	Attack on the load demand measurements
$P_{g}$	Generation output of generator ‘g’
$PL_{l}$	Power flow on line ‘l’
$\Delta PL_{l}$	Attack on power flow measurements
$\nu_{G,g}$	Binary variable indicating whether the ‘g’th generator is attacked
$\left( {\delta_{D + ,d} , \delta_{D - ,d} ,\delta_{D,d} } \right)$	Binary variables indicating whether the load measurement at ‘d’th generator is attacked
$(\delta_{PL + ,l} , \delta_{PL - ,l} ,\delta_{PL,l} )$	Binary variables indicating whether the load measurement at ‘d’th generator is attacked
$\lambda$	LaGrange multiplier associated with the power balance equation of the system
$\mu_{l}$	LaGrange multiplier associated with the power flow equation of line ‘l’
$\left( {\underline{\gamma }}_{d} ,\underline{\gamma }_{d} \right)$	LaGrange multipliers associated with the lower and upper bounds for the shedding of load ‘d’
$\left( {\underline{\alpha }}_{l} ,\underline{\alpha }_{l} \right)$	LaGrange multipliers associated with the lower and upper bounds for power flow of line ‘l’
$(\underline{\beta }_{g} ,\underline{\beta }_{g} )$	LaGrange multipliers associated with the lower and upper bounds for power output of generator ‘g’
$(\omega_{{\underline{\alpha } ,l}} ,\omega_{{\underline{\alpha } ,l}} )$	Binary variables to represent the complementary slackness of the power flow constraints of line ‘l’
$(\omega_{{\underline{\beta } ,g}} ,\omega_{{\underline{\beta } ,g}} )$	Binary variables to represent the complementary slackness of the generation output constraints of generator ‘g’
$(\omega_{{\underline{\gamma } ,d}} ,\omega_{{\underline{\gamma } ,d}} )$	Binary variables to represent the complementary slackness of the load shedding constraints of load ‘d’