Interval Load Flow for Uncertainty Consideration in Power Systems Analysis
Abstract
1. Introduction
2. Interval Arithmetic
3. Interval Load Flow
3.1. Algorithm Description
3.2. Illustrative Example
4. Probabilistic Load Flow
5. Test and Results
5.1. IEEE 34-Bus Radial TEST System
5.2. IEEE 69-Bus Distribution Network
5.3. 192-Bus Brazilian Distribution Network
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Bus | Method | Lower Angle (°) | Upper Angle (°) | Deterministic Angle (°) |
---|---|---|---|---|
5 | MCS | 0.23615 | 0.35810 | 0.31588 |
ILF | 0.26275 | 0.36900 | ||
9 | MCS | 0.48285 | 0.67387 | 0.61611 |
ILF | 0.53320 | 0.69891 | ||
23 | MCS | 0.70353 | 1.00872 | 0.90243 |
ILF | 0.78490 | 1.01959 | ||
27 | MCS | 0.79289 | 1.13820 | 1.00895 |
ILF | 0.88240 | 1.13499 | ||
33 | MCS | 0.52957 | 0.72857 | 0.66792 |
ILF | 0.58067 | 0.75503 |
Bus | Method | Lower Magnitude (p.u.) | Upper Magnitude (p.u.) | Deterministic Magnitude (p.u.) |
---|---|---|---|---|
5 | MCS | 0.97556 | 0.97868 | 0.97603 |
ILF | 0.97479 | 0.97729 | ||
9 | MCS | 0.96113 | 0.96639 | 0.96197 |
ILF | 0.95999 | 0.96396 | ||
23 | MCS | 0.94417 | 0.95144 | 0.94601 |
ILF | 0.94318 | 0.94885 | ||
27 | MCS | 0.93963 | 0.94997 | 0.94166 |
ILF | 0.93861 | 0.94474 | ||
33 | MCS | 0.95896 | 0.96466 | 0.95992 |
ILF | 0.95784 | 0.96201 |
Bus | Method | Lower Angle (°) | Upper Angle (°) | Deterministic Angle (°) |
---|---|---|---|---|
2 | MCS | −0.00140 | −0.00089 | −0.00122 |
ILF | −0.00133 | −0.00223 | ||
29 | MCS | −0.00587 | −0.00421 | −0.00530 |
ILF | −0.00578 | −0.00482 | ||
48 | MCS | −0.06559 | −0.03440 | −0.05247 |
ILF | −0.05724 | −0.04770 | ||
54 | MCS | 0.00461 | 0.37110 | 0.19470 |
ILF | 0.12409 | 0.26530 | ||
63 | MCS | 0.33813 | 187.126 | 112.526 |
ILF | 0.90650 | 134.402 |
Bus | Method | Lower Magnitude (p.u.) | Upper Magnitude (p.u.) | Deterministic Magnitude (p.u.) |
---|---|---|---|---|
2 | MCS | 0.99996 | 0.99997 | 0.99996 |
ILF | 0.99996 | 0.99997 | ||
29 | MCS | 0.99984 | 0.99987 | 0.99985 |
ILF | 0.99984 | 0.99986 | ||
48 | MCS | 0.99840 | 0.99883 | 0.99854 |
ILF | 0.99847 | 0.99980 | ||
54 | MCS | 0.96770 | 0.97738 | 0.97141 |
ILF | 0.96985 | 0.97296 | ||
63 | MCS | 0.89464 | 0.93411 | 0.91165 |
ILF | 0.90679 | 0.91652 |
Bus | Method | Lower Angle (°) | Upper Angle (°) | Deterministic Angle (°) |
---|---|---|---|---|
8 | MCS | −0.24610 | −0.21364 | −0.24170 |
ILF | −0.27692 | −0.20648 | ||
36 | MCS | −0.90111 | −0.76996 | −0.87943 |
ILF | −100.956 | −0.75299 | ||
64 | MCS | −0.44769 | −0.38699 | −0.43892 |
ILF | −0.50307 | −0.37477 | ||
113 | MCS | −0.86144 | −0.73693 | −0.84702 |
ILF | −0.97206 | −0.72197 | ||
187 | MCS | −0.91812 | −0.78600 | −0.89612 |
ILF | −102.858 | −0.76365 |
Bus | Method | Lower Magnitude (p.u.) | Upper Magnitude (p.u.) | Deterministic Magnitude (p.u.) |
---|---|---|---|---|
8 | MCS | 0.98727 | 0.98888 | 0.98795 |
ILF | 0.98732 | 0.99176 | ||
36 | MCS | 0.95602 | 0.96027 | 0.95686 |
ILF | 0.95461 | 0.95911 | ||
64 | MCS | 0.97824 | 0.97994 | 0.97827 |
ILF | 0.97713 | 0.97939 | ||
113 | MCS | 0.95754 | 0.96171 | 0.95849 |
ILF | 0.95632 | 0.96066 | ||
187 | MCS | 0.95603 | 0.95959 | 0.95612 |
ILF | 0.95612 | 0.95842 |
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Nogueira, W.C.; Garcés Negrete, L.P.; López-Lezama, J.M. Interval Load Flow for Uncertainty Consideration in Power Systems Analysis. Energies 2021, 14, 642. https://doi.org/10.3390/en14030642
Nogueira WC, Garcés Negrete LP, López-Lezama JM. Interval Load Flow for Uncertainty Consideration in Power Systems Analysis. Energies. 2021; 14(3):642. https://doi.org/10.3390/en14030642
Chicago/Turabian StyleNogueira, Wallisson C., Lina Paola Garcés Negrete, and Jesús M. López-Lezama. 2021. "Interval Load Flow for Uncertainty Consideration in Power Systems Analysis" Energies 14, no. 3: 642. https://doi.org/10.3390/en14030642
APA StyleNogueira, W. C., Garcés Negrete, L. P., & López-Lezama, J. M. (2021). Interval Load Flow for Uncertainty Consideration in Power Systems Analysis. Energies, 14(3), 642. https://doi.org/10.3390/en14030642