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20 UEC Int’l Mini-Conference No.52

a combination of the flexibility regions of the 3.2 Maliciously Changed Power Mea-
lower level. The proposed flexibility region surements
attack does not manipulate the aggregated
flexibility regions of the upper layers due to The sum of a i in the bus controller equation (5)
changes in DER flexibility regions; rather, is to minimize. This is shown for a bus with
it aims to find invalid solutions for a valid three DERs connected:
reference signal transmitted by the SPC-Level
Controller.
a 1 = R 2 T 2 T 3 + R 2 T 1 T 3 + R 3 T 2 T 1
a 2 = R 1 (T 2 + T 3 ) + R 2 (T 1 + T 3 )+ (10)
R 3 (T 2 + T 1 )
Enlarging Flexibility Region
with R i = (r i −y i ). A manipulation of y i does
Enlarging the flexibility region of DER k is given
by: not cause any problem in following the reference
signal set by the SPC-controller, as the steady
state is ensured by the equality constraint. Con-
sidering equation (10), a maliciously changed
|r min,a,k (t)| > |r min,k (t)| ∨
power signal of the DER results R i,a ̸= R i and
|r max,a,k (t)| > |r max,k (t)|
(7) may lead to an over and undershoot, as the op-
REF a = {r | r min,a,i < r i < r max,a,i } timization is performed over falsified a i . R i,a is
⇒ |REF a | > |REF| the power error under attack.

with r min/max,k,a (t) as the attacked reference
signal, and i ∈ {1, 2, 3, .., k, .., n−1, n} the num- 4 Simulation Setup and Re-
ber of DERs connceted to the bus. The attack sults
is considered successful if the equation
The simulations are performed in Matlab. A bus
r ∈ REF a \REF (8) with two connected DERs is considered, with
one generator and one storage. The flexibility
is satisfied. region of a storage is defined by:

ref s = {(r P , r Q )|r max,P ≥ r P ≥ r min,P ,
Shrinking Flexibility Region (11)
r max,Q ≥ r Q ≥ r min,Q }
Shrinking the flexibility region of DER k is given
by: The flexibility region of a generator is defined
as follows:

ref g = {(r P , r Q )|cos(ϕ)r max,P ≥ r P ≥ 0,
|r min,a,k (t)| < |r min,k (t)| ∨ (12)
sin(ϕ)r max,Q ≥ r Q ≥ 0}
|r max,a,k (t)| < |r max,k (t)|
(9)
REF a = {r | r min,a,i < r i < r max,a,i } ϕ is the power factor of generators and the angle
⇒ |REF a | < |REF| between the voltage of the grid and the injected
current at the point of common coupling. For
The shrinking of the REF resulting in REF a
leads to the following two scenarios: i) the SPC Table 2: DER Lower- Upper Bound and Time
reference signal cannot be followed by r, as there Constants
exists no r which satisfies both the equality con-
straint and the inequality constraint of the opti- Generator Storage
mization problem (5), ii) the SPC reference sig- P [MW] ϕ[deg] P [MW] Q [MVar]
nal can be followed, but r is not optimal regard- LB UB 2 90 2.5 2.5
ing equation (5). T 0.1 0.1 0.01 0.02