In the proposed model, the minimization of the objective function is subject to operational constraints, which are active and reactive power flow constraints, capability limits of the cables, voltage limits for all the buses, radiality constraints.
(11 where ( {P}_{i,j}^{load} ) and ( {Q}_{i,j}^{load} ) respectively denote active and reactive load of bus j at time interval i. V i is vector of bus voltage magnitude and θ i is vector of bus voltage angle at time interval i. F 1 and F 2 are active and reactive power flow functions.
These relation could be expressed as: {C}_j^{BS}={M}_j^{BS,D}+sum_{i=1}^Tleft({lambda}_j^{S,P}{P}_{i,j}^{S,C}+{lambda}_j^{S,Q}{Q}_{i,j}^Sright) (8 where ( {C}_j^{BS} ) and ( {M}_j^{BS,D} ) denote the total operation cost and the depreciation of investment cost of battery storage j. ( {lambda}_j^{S,P} ) and ( {lambda}_j^{S,Q} ) are the active and reactive cost coefficients of battery storage j.
E i ∠θ i (i = 1,2,⋯) is the voltage output of DG i ; P i and Q i are the active and reactive power flowing into loads generated by DG i, respectively; V∠θ is the AC common bus voltage; Z i ∠φ i is the equivalent impedance.
P i_2 and Q i_2 are the active and reactive power of DG i and V g_2 is the AC common bus voltage when the new robust droop control is applied.
A single AC transmission line is shown in Fig. 1, where (dot{U}_{2}) and (dot {U}_{1}) are the voltage phasors of both terminals, (dot {I}_{2}) and (dot {I}_{1}) are the current phasors of both terminals, P and Q are the active and reactive power from the terminal 2 to 1, respectively.
(8 where P i and Q i are the active and reactive power injection at node i; P Li and Q Li are the active and reactive load at node i; V i is the voltage of node i; G ij and B ij are the conductance and susceptance between nodes i and j; δ ij is the phase-angle difference between V i and V j ; and N is the number of nodes.
According to the calculation results in "Appendix A", the constant component in the branch power is P_{{bk{textconst}} = frac{1}{6}(P_{s} - P_{l} ) + ( - 1)^{k} left[frac{sqrt 3 }{18}(Q_{s} + Q_{l} ) - V_{NO} I_{cir} right] (21 where P s and Q s are the active and reactive power of the IF system; and P l and Q l are the active and reactive power of the FF system.
( {P}_{i,j}^{line} ) and ( {Q}_{i,j}^{line} ) are the active and reactive transmission power flow of line j at time interval i. Constraints on bus voltage are expressed as: left{begin{array}{l}{underline{V}}^ble {V}_{i,j}le {overline{V}}^b {V}_{i,j}={V}^{s, set} {theta}_{i,j}=0end{array}right.
Be active in your support, not reactive".
