Supplementary file for “ Defending Against Unidentifiable Attacks in Electric Power Grids ”
نویسندگان
چکیده
Therefore, we first need to find the regions that require fewest compromised meters for an undetectable attack. In [6], Liu et al. proposed a heuristic algorithm for desirable attack region in DC model, where z = Hx+e and H is fixed; with column transformation of H matrix, they aimed to find a column vector with the greatest number of zero elements. However, in our AC model case, there is no such fixed H matrix and the relations between measurements and state variables are non-linear. Instead, we examine the Jacobian matrix ∂h/∂x, denoted by J. Similar to [6], we apply column transformations on the Jacobian matrix to find a column vector with the greatest number of zero elements, say vector u. Then, we figure out the rows with non-zero elements in u. Finally the attack region is the region containing meters i such that ui = 0. The algorithm is summarized as follows. ————————————————————————— Alg. 1: Finding the best attack region 1: Calculate J at the pre-attack point; 2: u =the column vector in J with most zeros; 3: For each column vector j ∈ J, j = u, 4: Find u′ = u+ c· j that results in most zero elements, where c can be any scalar; 5: Endfor 6: If u′ has more zero elements than u, go to line 3; 7: Find the set of meters with indices {i|ui = 0}; the attack region is the region where these meters are. ————————————————————————— Different from H, which is fixed, our Jacobian matrix is different at different starting points. Here, we assume a simple starting scenario that all voltages are 1 and all phases are 0, which is a feasible solution to power systems. We examine three IEEE bus systems: 9-bus system, 14-bus system, and 30-bus system. The results
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