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Table 2 Physical consistency constraints

From: An integrated testbed for locally monitoring SCADA systems in smart grids

Physical consistency constraint Explanation
\(\forall B_{i} \in \mathcal {B} \left (\sum \limits _{L_{j} \in {{B}_{i}}.in}{{L_{j}.B_{i}.M.I}} =\sum \limits _{L_{k} \in {{B}_{i}}.out}{{L_{k}.B_{i}.M.I}} \right)\) Kirchoff’s current law
\(\forall L_{i} \in \mathcal {L} ~ \left (\forall S_{j} \in {L}_{i}.S ~ \left (\left (S_{j}.st = 0\right) \Rightarrow \left (\forall M_{k} \in {L}_{i}.M \left (\left (M_{k}.I = 0 \right) \wedge \left (M_{k}.V = 0 \right) \right) \right) \right) \right) \) If all switches on a line are open, the values of current and voltage on this line have to be zero
\(\forall T_{i} \in \mathcal {T}, M_{x}, M_{y} : M_{x} = L_{x}.T_{i}.M \wedge M_{y} = L_{y}.T_{i}.M \left (T_{i}.r = M_{x}.V / M_{y}.V = M_{y}.I / M_{x}.I \right)\) for Mx.V>My.V Assuming no losses, the transformer changes the voltage and current value with its predefined ratio r
P=V·I, e.g., \(P_{1}^{G}.pv = P_{1}^{G}.pos.P_{1}^{G}.M.I \cdot P_{1}^{G}.pos.P_{1}^{G}.M.V \) Electric power is equal to voltage times current