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UPFC rating constraints.
The line loading limits and the UPFC rating constraints are provided in the Appendix A.
The objective function is given by (20), which subjects to the voltage constraints given by (17), the line loading constraints given by (18) and UPFC rating constraints given by (19).
Likewise, the line loading constraints (Delta dot{I}_{U}^) has to satisfy are deduced from (2): left| {dot{I}_{k} dot{I}_{k0} + tilde{H}_{k} Delta dot{I}_{U}^ right| le I_{{k, {text{max}}}} (18 where I k,max is the loading limit for line k (k = 1, 2, …, b). 3) UPFC rating constraints .
The UPFC rating constraints (Delta dot{I}_{U}^) has to satisfy are given by: left{ begin{array}{ll}, left| {dot{V}_{se}^ right| le V_{{se, {text{max}}}}^ hfill , left| {dot{I}_{U}^ right| le I_{{U, {text{max}}}}^ hfill , left| {P_{dc}^ right| le P_{{dc, {text{max}}}}^ hfill end{array} right.
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Generation rate constraints: [14].
We first handle rate constraints within a soft constraints framework.
By increasing, the minimum rate constraints are relaxed.
From (19), we obtain the rate constraints in (28).
In that case, the rate constraints are not feasible.
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