Table 1 List of the symbols of the system elements

Power network

Model

Ω

State

T

Power generators and consumers

Combined set

\(\mathcal {P}=\mathcal {P}^{G} \cup \mathcal {P}^{C}\)

Set of power generators

\(\mathcal {P}^{G}=\left \{P_{1}^{G},...,P_{|\mathcal {P}^{G}|}^{G}\right \}\)

Set of power consumers

\(\mathcal {P}^{C}=\left \{P_{1}^{C},...,P_{|\mathcal {P}^{C}|}^{C}\right \}\)

Position

\(P_{i}^{x}.pos = L_{j}\) for x∈{G,C}

Power value

\(P_{i}^{x}.pv\) for x∈{G,C}

Vector of all power values

P

Buses

Set of buses

\(\mathcal {B}= \left \{B_{1},..., B_{|\mathcal {B}|} \right \}\)

Vector of incoming lines

B_i.in=[L_j,...,L_n]

Vector of outgoing lines

B_i.out=[L_c,...,L_h]

Transformers

Set of transformers

\(\mathcal {T} = \left \{ T_{1},..., T_{|\mathcal {T}|}\right \}\)

Transformer rate

T_i.r

Tap switch position

T_i.p

Vector of all tap positions

T

Power lines

Set of power lines

\(\mathcal {L} = \left \{L_{1},...,L_{|\mathcal {L}|}\right \}\)

Position

L_i.pos=(Bk,B_n)

Maximum current

L_i.I_max

Reference voltage

L_i.V_ref

Meter (side of B_k)

L_i.B_k.M=M_d

Vector of meters on line L_i

L_i.M=[M_d,...,M_h]

Switch (side of B_k)

L_i.B_k.S=S_e

Vector of switches on line L_i

L_i.S=[S_e,...,S_o]

Fuse (side of B_k)

L_i.B_k.F=F_u

Vector of fuses on line L_i

L_i.F=[F_u,...,F_y]

Meters

Set of meters

\(\mathcal {M} = \left \{M_{1},...,M_{|\mathcal {M}|}\right \}\)

Position

M_i.pos=L_i.B_n

Measured current

M_i.I

Measured voltage

M_i.V

Vector of states of all readings

M

Switches

Set of switches

\(\mathcal {S} = \left \{S_{1},...,S_{|\mathcal {S}|}\right \}\)

Position

S_i.pos=L_i.B_n

State of the switch

S_i.st

Vector of states of all the switches

S

Fuses

Set of fuses

\(\mathcal {F} = \left \{F_{1},..., F_{|\mathcal {F}|}\right \}\)

Position

F_i.pos=L_i.B_n

State of the fuse

F_i.st

Vector of states of all fuses

F

Protective relays(circuit breakers)

Set of protective relays

\(\mathcal {R} = \left \{ R_{1},...,R_{|\mathcal {R}|}\right \}\)

Position (on a switch)

R_i.S=S_j

Cutting current

R_i.I_max