Table 3 Pareto front of the suggested grid-connected VPP operation.

From: Multi-objective economic operation of smart distribution network with renewable-flexible virtual power plants considering voltage security index

ωEC

ωEL

ωVS

Energy cost ($)

Energy loss (MWh)

Voltage Security (sum of WSI) (p.u.)

1

0

0

1422.6

3.023

19.8

0

1

0

2943.5

1.354

21.5

0

0

1

2381.2

2.137

23.1

0.75

0.25

0

1923.7

2.479

20.0

0.75

0

0.25

1945.6

2.891

20.4

0

0.75

0.25

2811.3

1.573

21.7

0.25

0.75

0

2683.2

1.897

19.9

0.25

0

0.75

2694.1

2.867

22.5

0

0.25

0.75

2900.4

1.676

22.7

0.5

0.5

0

2018.5

2.094

19.9

0.5

0

0.5

2057.2

2.746

20.9

0

0.5

0.5

2854.8

1.722

22.4

0.33

0.33

0.33

2145.6

2.221

21.2