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A peer-reviewed article of this preprint also exists.
This version is not peer-reviewed
Nodal | Di | Number of instabilities | Nodal | Di | Number of instabilities | Nodal | Di | Number of instabilities |
1 | 0.0000 | 0 | 14 | 16.7118 | 6 | 27 | 1.7394 | 1 |
2 | 0.0000 | 0 | 15 | 4.2450 | 3 | 28 | 0.0000 | 1 |
3 | 0.5803 | 1 | 16 | 2.5523 | 1 | 29 | 0.0000 | 1 |
4 | 11.7646 | 6 | 17 | 2.3568 | 1 | 30 | 0.0000 | 0 |
5 | 10.3804 | 6 | 18 | 2.0995 | 1 | 31 | 7.3380 | 5 |
6 | 10.6489 | 6 | 19 | 1.5516 | 1 | 32 | 7.4773 | 5 |
7 | 9.9658 | 5 | 20 | 1.4768 | 1 | 33 | 0.0000 | 0 |
8 | 9.5830 | 5 | 21 | 2.1258 | 1 | 34 | 0.0000 | 0 |
9 | 0.0000 | 0 | 22 | 1.6480 | 1 | 35 | 0.0000 | 0 |
10 | 11.2007 | 6 | 23 | 1.7070 | 1 | 36 | 0.0000 | 0 |
11 | 11.5400 | 6 | 24 | 2.6959 | 1 | 37 | 0.0000 | 0 |
12 | 11.2962 | 6 | 25 | 0.0000 | 0 | 38 | 0.0000 | 0 |
13 | 10.8595 | 6 | 26 | 0.3354 | 2 | 39 | 0.0000 | 0 |
Failure Number | DΓ,l | Failure Number | DΓ,l | Failure Number | DΓ,l |
1 | 0.0909 | 17 | 0.9490 | 33 | 0.2714 |
2 | 0.0796 | 18 | 0.9148 | 34 | 1.7133 |
3 | 0.4212 | 19 | 0.7055 | 35 | 0.8796 |
4 | 0.4380 | 20 | 0.8705 | 36 | 0.3278 |
5 | 0.6902 | 21 | 0.9528 | 37 | 0.5423 |
6 | 0.4949 | 22 | 0.6184 | 38 | 0.6378 |
7 | 0.8572 | 23 | 0.6772 | 39 | 0.3311 |
8 | 0.8787 | 24 | 0.8356 | 40 | 0.2553 |
9 | 0.9739 | 25 | 0.6696 | 41 | 0.3781 |
10 | 0.8299 | 26 | 0.4717 | 42 | 0.2440 |
11 | 0.8614 | 27 | 0.5254 | 43 | 0.1699 |
12 | 0.9562 | 28 | 0.5051 | 44 | 0.2006 |
13 | 0.7955 | 29 | 0.3624 | 45 | 0.2976 |
14 | 0.3163 | 30 | 0.3121 | 46 | 0.3557 |
15 | 0.0928 | 31 | 0.3784 | ||
16 | 0.9501 | 32 | 0.2797 |
Nodal | Γ | SΓ,i | Nodal | Γ | SΓ,i |
1 | -5.48855 | 0.003469 | 16 | -4.96675 | 0.013905 |
2 | -5.15575 | 0.010125 | 17 | -4.8989 | 0.015262 |
3 | -5.0114 | 0.013012 | 18 | -4.9498 | 0.014244 |
4 | -4.9407 | 0.014426 | 19 | -5.09815 | 0.011277 |
5 | -4.99185 | 0.013403 | 20 | -5.23305 | 0.008579 |
6 | -5.0139 | 0.012962 | 21 | -5.04085 | 0.012423 |
7 | -5.05725 | 0.012095 | 22 | -5.10995 | 0.011041 |
8 | -5.05815 | 0.012077 | 23 | -5.0916 | 0.011408 |
9 | -5.4201 | 0.004838 | 24 | -4.94405 | 0.014359 |
10 | -4.9501 | 0.014238 | 25 | -5.1098 | 0.011044 |
11 | -4.97635 | 0.013713 | 26 | -4.84815 | 0.016277 |
12 | -4.8839 | 0.015562 | 27 | -4.8134 | 0.016972 |
13 | -4.947 | 0.0143 | 28 | -4.9461 | 0.014318 |
14 | -4.9066 | 0.015108 | 29 | -4.8698 | 0.015844 |
15 | -4.89625 | 0.015315 |
Device type | Operational life / a | Installation costs / $ | Reimbursement unit price / [$∙Mvar-1] |
SVC | 10 | 1.3×107 | 3×104 |
STATCOM | 10 | 2.6×107 | 9×104 |
Compensation nodal |
Scheme 1 | Scheme 2 | Scheme 3 | Scheme 4 | Scheme 5 | |||||
Capacity /Mvar |
Type | Capacity /Mvar |
Type | Capacity /Mvar |
Type | Capacity /Mvar |
Type | Capacity /Mvar |
Type | |
Bus-12 | 463 | SVC | 372 | STATCOM | 438 | SVC | 306 | STATCOM | 433 | SVC |
Bus-15 | 453 | STATCOM | 255 | SVC | 225 | SVC | 206 | SVC | 460 | STATCOM |
Bus-17 | 478 | SVC | 456 | SVC | 114 | SVC | 300 | SVC | 418 | STATCOM |
Bus-26 | 238 | STATCOM | 310 | SVC | 363 | SVC | 240 | SVC | 91 | SVC |
Bus-27 | 406 | SVC | 402 | SVC | 395 | SVC | 397 | SVC | 454 | SVC |
Bus-29 | 201 | STATCOM | 115 | SVC | 85 | SVC | 195 | SVC | 318 | STATCOM |
Scheme | Cost /$ | Γ | Closeness value |
1 | 2.3769×108 | 3.9567 | 0.4179 |
2 | 1.6360×108 | 3.5939 | 0.7707 |
3 | 1.4310×108 | 2.7685 | 0.6202 |
4 | 1.5268×108 | 3.1681 | 0.6894 |
5 | 2.5398×108 | 3.9922 | 0.3798 |
Method of compensation | Cost/$ | Γ | Total number of instabilities |
Uncompensated | 0 | -5.6620 | 106 |
Traditional compensation method | 2.1008×108 | 3.6032 | 78 |
Differentiated compensation method | 1.6360×108 | 3.5939 | 79 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
Submitted:
28 July 2023
Posted:
31 July 2023
You are already at the latest version
A peer-reviewed article of this preprint also exists.
This version is not peer-reviewed
Submitted:
28 July 2023
Posted:
31 July 2023
You are already at the latest version
Nodal | Di | Number of instabilities | Nodal | Di | Number of instabilities | Nodal | Di | Number of instabilities |
1 | 0.0000 | 0 | 14 | 16.7118 | 6 | 27 | 1.7394 | 1 |
2 | 0.0000 | 0 | 15 | 4.2450 | 3 | 28 | 0.0000 | 1 |
3 | 0.5803 | 1 | 16 | 2.5523 | 1 | 29 | 0.0000 | 1 |
4 | 11.7646 | 6 | 17 | 2.3568 | 1 | 30 | 0.0000 | 0 |
5 | 10.3804 | 6 | 18 | 2.0995 | 1 | 31 | 7.3380 | 5 |
6 | 10.6489 | 6 | 19 | 1.5516 | 1 | 32 | 7.4773 | 5 |
7 | 9.9658 | 5 | 20 | 1.4768 | 1 | 33 | 0.0000 | 0 |
8 | 9.5830 | 5 | 21 | 2.1258 | 1 | 34 | 0.0000 | 0 |
9 | 0.0000 | 0 | 22 | 1.6480 | 1 | 35 | 0.0000 | 0 |
10 | 11.2007 | 6 | 23 | 1.7070 | 1 | 36 | 0.0000 | 0 |
11 | 11.5400 | 6 | 24 | 2.6959 | 1 | 37 | 0.0000 | 0 |
12 | 11.2962 | 6 | 25 | 0.0000 | 0 | 38 | 0.0000 | 0 |
13 | 10.8595 | 6 | 26 | 0.3354 | 2 | 39 | 0.0000 | 0 |
Failure Number | DΓ,l | Failure Number | DΓ,l | Failure Number | DΓ,l |
1 | 0.0909 | 17 | 0.9490 | 33 | 0.2714 |
2 | 0.0796 | 18 | 0.9148 | 34 | 1.7133 |
3 | 0.4212 | 19 | 0.7055 | 35 | 0.8796 |
4 | 0.4380 | 20 | 0.8705 | 36 | 0.3278 |
5 | 0.6902 | 21 | 0.9528 | 37 | 0.5423 |
6 | 0.4949 | 22 | 0.6184 | 38 | 0.6378 |
7 | 0.8572 | 23 | 0.6772 | 39 | 0.3311 |
8 | 0.8787 | 24 | 0.8356 | 40 | 0.2553 |
9 | 0.9739 | 25 | 0.6696 | 41 | 0.3781 |
10 | 0.8299 | 26 | 0.4717 | 42 | 0.2440 |
11 | 0.8614 | 27 | 0.5254 | 43 | 0.1699 |
12 | 0.9562 | 28 | 0.5051 | 44 | 0.2006 |
13 | 0.7955 | 29 | 0.3624 | 45 | 0.2976 |
14 | 0.3163 | 30 | 0.3121 | 46 | 0.3557 |
15 | 0.0928 | 31 | 0.3784 | ||
16 | 0.9501 | 32 | 0.2797 |
Nodal | Γ | SΓ,i | Nodal | Γ | SΓ,i |
1 | -5.48855 | 0.003469 | 16 | -4.96675 | 0.013905 |
2 | -5.15575 | 0.010125 | 17 | -4.8989 | 0.015262 |
3 | -5.0114 | 0.013012 | 18 | -4.9498 | 0.014244 |
4 | -4.9407 | 0.014426 | 19 | -5.09815 | 0.011277 |
5 | -4.99185 | 0.013403 | 20 | -5.23305 | 0.008579 |
6 | -5.0139 | 0.012962 | 21 | -5.04085 | 0.012423 |
7 | -5.05725 | 0.012095 | 22 | -5.10995 | 0.011041 |
8 | -5.05815 | 0.012077 | 23 | -5.0916 | 0.011408 |
9 | -5.4201 | 0.004838 | 24 | -4.94405 | 0.014359 |
10 | -4.9501 | 0.014238 | 25 | -5.1098 | 0.011044 |
11 | -4.97635 | 0.013713 | 26 | -4.84815 | 0.016277 |
12 | -4.8839 | 0.015562 | 27 | -4.8134 | 0.016972 |
13 | -4.947 | 0.0143 | 28 | -4.9461 | 0.014318 |
14 | -4.9066 | 0.015108 | 29 | -4.8698 | 0.015844 |
15 | -4.89625 | 0.015315 |
Device type | Operational life / a | Installation costs / $ | Reimbursement unit price / [$∙Mvar-1] |
SVC | 10 | 1.3×107 | 3×104 |
STATCOM | 10 | 2.6×107 | 9×104 |
Compensation nodal |
Scheme 1 | Scheme 2 | Scheme 3 | Scheme 4 | Scheme 5 | |||||
Capacity /Mvar |
Type | Capacity /Mvar |
Type | Capacity /Mvar |
Type | Capacity /Mvar |
Type | Capacity /Mvar |
Type | |
Bus-12 | 463 | SVC | 372 | STATCOM | 438 | SVC | 306 | STATCOM | 433 | SVC |
Bus-15 | 453 | STATCOM | 255 | SVC | 225 | SVC | 206 | SVC | 460 | STATCOM |
Bus-17 | 478 | SVC | 456 | SVC | 114 | SVC | 300 | SVC | 418 | STATCOM |
Bus-26 | 238 | STATCOM | 310 | SVC | 363 | SVC | 240 | SVC | 91 | SVC |
Bus-27 | 406 | SVC | 402 | SVC | 395 | SVC | 397 | SVC | 454 | SVC |
Bus-29 | 201 | STATCOM | 115 | SVC | 85 | SVC | 195 | SVC | 318 | STATCOM |
Scheme | Cost /$ | Γ | Closeness value |
1 | 2.3769×108 | 3.9567 | 0.4179 |
2 | 1.6360×108 | 3.5939 | 0.7707 |
3 | 1.4310×108 | 2.7685 | 0.6202 |
4 | 1.5268×108 | 3.1681 | 0.6894 |
5 | 2.5398×108 | 3.9922 | 0.3798 |
Method of compensation | Cost/$ | Γ | Total number of instabilities |
Uncompensated | 0 | -5.6620 | 106 |
Traditional compensation method | 2.1008×108 | 3.6032 | 78 |
Differentiated compensation method | 1.6360×108 | 3.5939 | 79 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
Jie Dang
et al.
,
2023
© 2024 MDPI (Basel, Switzerland) unless otherwise stated