Multi-Period Fast Robust Optimization for Partial Distributed Generators (DGs) Providing Ancillary Services
Abstract
:1. Introduction
2. Robust Model for Partial DGs Providing Ancillary Services
2.1. Deterministic Optimization Model
2.2. Robust Optimization Model
3. Solving Method
3.1. Master Problem
3.2. Sub-Problem
3.3. Solution Steps
4. Numerical Analysis
4.1. Case 1
4.2. Case 2
4.3. Case 3
4.4. Case 4
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Objective Function Values (p.u.) | ||||
---|---|---|---|---|
Improved CCG | Proposed Method | |||
MP | SP | MP | SP | |
0.1 | −0.0933 | −0.0934 | −0.0934 | −0.0934 |
0.2 | 0.0072 | 0.0072 | 0.0072 | 0.0072 |
0.3 | 0.1194 | 0.1194 | 0.1184 | 0.1184 |
0.4 | 0.2408 | 0.2409 | 0.2408 | 0.2409 |
0.5 | 0.3754 | 0.3755 | 0.3754 | 0.3755 |
0.6 | 0.5231 | 0.5232 | 0.5231 | 0.5232 |
Improved CCG | Proposed Method | |||
---|---|---|---|---|
Iterations | Time (s) | Iterations | Time (s) | |
0.1 | 3 | 46.155 | 2 | 35.662 |
0.2 | 2 | 33.772 | 2 | 36.256 |
0.3 | 5 | 100.713 | 2 | 33.577 |
0.4 | 2 | 19.926 | 2 | 35.015 |
0.5 | 2 | 19.734 | 2 | 33.844 |
0.6 | 2 | 21.128 | 2 | 28.190 |
Objective Function Values (p.u.) | ||||
---|---|---|---|---|
Improved CCG | Proposed Method | |||
MP | SP | MP | SP | |
0.1 | −0.0660 | −0.0661 | −0.0660 | −0.0661 |
0.2 | 0.0270 | 0.0269 | 0.0269 | 0.0267 |
0.3 | 0.1464 | 0.1462 | 0.1440 | 0.1439 |
0.4 | 0.2694 | 0.2692 | 0.2656 | 0.2654 |
0.5 | 0.4080 | 0.4072 | 0.4016 | 0.4014 |
0.6 | 0.5561 | 0.5544 | 0.5502 | 0.5501 |
Improved CCG | Proposed Method | |||
---|---|---|---|---|
Iterations | Time (s) | Iterations | Time (s) | |
0.1 | 2 | 65.025 | 2 | 77.585 |
0.2 | 2 | 75.127 | 2 | 82.130 |
0.3 | 3 | 110.968 | 2 | 69.863 |
0.4 | 3 | 113.343 | 2 | 69.791 |
0.5 | 5 | 264.499 | 4 | 139.552 |
0.6 | 5 | 272.656 | 3 | 111.973 |
Objective Function Values (p.u.) | ||||||
---|---|---|---|---|---|---|
Improved CCG | CCG | Proposed Method | ||||
MP | SP | MP | SP | MP | SP | |
0.1 | −2.0870 | −2.0466 | −2.1100 | −2.0377 | −2.0633 | −2.0634 |
0.2 | −2.0613 | −2.0277 | −2.0645 | −2.0213 | −2.0403 | −2.0403 |
0.3 | −2.0101 | −2.0061 | −2.0135 | −1.9599 | −2.0159 | −2.0164 |
0.4 | −1.9388 | −1.9072 | −1.9418 | −1.8868 | −1.9240 | −1.9240 |
0.5 | −1.8582 | −1.8268 | −1.8617 | −1.8068 | −1.8447 | −1.8450 |
0.6 | −1.7764 | −1.7321 | −1.7752 | −1.7144 | −1.7568 | −1.7573 |
Improved CCG | CCG | Proposed Method | ||||
---|---|---|---|---|---|---|
Iterations | Time (s) | Iterations | Time (s) | Iterations | Time (s) | |
0.1 | 10 | 3524.916 | 10 | 3810 | 2 | 183.664 |
0.2 | 10 | 3152.919 | 10 | 4248 | 2 | 195.945 |
0.3 | 10 | 3318.348 | 10 | 4258 | 2 | 193.753 |
0.4 | 10 | 3151.459 | 10 | 4606 | 2 | 192.636 |
0.5 | 10 | 3091.671 | 10 | 4017 | 2 | 192.460 |
0.6 | 10 | 3010.364 | 10 | 4154 | 3 | 299.966 |
33-Bus System | 69-Bus System | 123-Bus System | |
---|---|---|---|
0.1 | 6.3948 × 10−9 | 7.9871 × 10−7 | 6.4669 × 10−8 |
0.2 | 8.8074 × 10−9 | 3.6889 × 10−8 | 5.0020 × 10−9 |
0.3 | 7.8910 × 10−9 | 4.1979 × 10−8 | 1.3896 × 10−8 |
0.4 | 8.4152 × 10−9 | 5.3522 × 10−8 | 3.1927 × 10−8 |
0.5 | 9.4049 × 10−9 | 8.7201 × 10−7 | 7.4779 × 10−8 |
0.6 | 8.0618 × 10−9 | 7.3739 × 10−7 | 7.8610 × 10−8 |
Time | PV Bus Number | Time | PV Bus Number | Time | PV Bus Number |
---|---|---|---|---|---|
1 | 7, 23, 26, 31, 32 | 9 | 7, 23, 26, 31, 32 | 17 | 7, 23, 26, 31, 32 |
2 | 7, 23, 26, 31, 32 | 10 | 7, 23, 26, 31, 32 | 18 | 6, 7, 26, 31, 32 |
3 | 20, 23, 26, 31, 32 | 11 | 7, 23, 26, 31, 32 | 19 | 6, 7, 26, 31, 32 |
4 | 14, 20, 26, 31, 32 | 12 | 7, 23, 26, 31, 32 | 20 | 6, 7, 26, 31, 32 |
5 | 14, 20, 26, 31, 32 | 13 | 7, 23, 26, 31, 32 | 21 | 7, 23, 26, 31, 32 |
6 | 14, 20, 26, 31, 32 | 14 | 7, 23, 26, 31, 32 | 22 | 7, 23, 26, 31, 32 |
7 | 20, 23, 26, 31, 32 | 15 | 7, 23, 26, 31, 32 | 23 | 7, 23, 26, 31, 32 |
8 | 7, 23, 26, 31, 32 | 16 | 7, 23, 26, 31, 32 | 24 | 7, 23, 26, 31, 32 |
Time | PV Bus Number | Time | PV Bus Number | Time | PV Bus Number |
---|---|---|---|---|---|
1 | 39, 44, 48, 52, 54 | 9 | 39, 44, 48, 52, 53 | 17 | 44, 48, 52, 53, 54 |
2 | 25, 39, 44, 48, 52 | 10 | 44, 48, 52, 53, 54 | 18 | 44, 48, 52, 53, 54 |
3 | 25, 39, 44, 48, 52 | 11 | 44, 48, 52, 53, 54 | 19 | 44, 48, 52, 53, 54 |
4 | 25, 39, 44, 48, 52 | 12 | 44, 48, 52, 53, 54 | 20 | 44, 48, 52, 53, 54 |
5 | 15, 39, 44, 48, 52 | 13 | 44, 48, 52, 53, 54 | 21 | 39, 48, 52, 53, 54 |
6 | 25, 39, 44, 48, 52 | 14 | 44, 48, 52, 53, 54 | 22 | 39, 48, 52, 53, 54 |
7 | 25, 39, 44, 48, 52 | 15 | 44, 48, 52, 53, 54 | 23 | 39, 48, 52, 53, 54 |
8 | 25, 39, 44, 48, 52 | 16 | 44, 48, 52, 53, 54 | 24 | 44, 48, 52, 53, 54 |
Time | WT Bus Number | Time | WT Bus Number | Time | WT Bus Number |
---|---|---|---|---|---|
1 | 71, 85, 104, 107, 114 | 9 | 70, 71, 104, 107, 114 | 17 | 33, 48, 56, 66, 122 |
2 | 70, 71, 104, 107, 114 | 10 | 48, 56, 66, 78, 122 | 18 | 39, 48, 56, 66, 122 |
3 | 71, 85, 104, 107, 114 | 11 | 33, 48, 56, 66, 122 | 19 | 39, 48, 56, 66, 122 |
4 | 71, 85, 104, 107, 114 | 12 | 33, 48, 56, 66, 122 | 20 | 39, 48, 56, 66, 122 |
5 | 71, 85, 104, 107, 114 | 13 | 33, 48, 56, 66, 122 | 21 | 39, 48, 56, 66, 122 |
6 | 71, 85, 104, 107, 114 | 14 | 48, 56, 66, 78, 122 | 22 | 39, 48, 56, 66, 122 |
7 | 70, 71, 104, 107, 114 | 15 | 33, 48, 56, 66, 122 | 23 | 48, 56, 66, 78, 122 |
8 | 70, 71, 104, 107, 114 | 16 | 33, 48, 56, 66, 122 | 24 | 48, 56, 66, 78, 122 |
Active Power of Each PV (MW) | Proposed Method | Method in [23] | Method in [25] | Method in [29] |
---|---|---|---|---|
1.5 | 5 | 30 | 14 | 30 |
2.5 | 5 | 30 | 30 | 30 |
3.5 | 4 | 30 | 30 | 30 |
4.5 | 5 | 30 | 30 | 30 |
5.5 | 4 | 30 | 30 | 30 |
6.5 | 4 | 30 | 30 | 30 |
Objective Function (p.u.) | ||||
---|---|---|---|---|
Method in [25] | Proposed Method | |||
MP | SP | MP | SP | |
0.1 | −0.7654 | −0.7654 | −0.7655 | −0.7655 |
0.2 | −0.7323 | −0.7323 | −0.7323 | −0.7323 |
0.3 | −0.6992 | −0.6992 | −0.6992 | −0.6992 |
0.4 | −0.6660 | −0.6660 | −0.6660 | −0.6660 |
0.5 | −0.6329 | −0.6329 | −0.6329 | −0.6329 |
0.6 | −0.5997 | −0.5997 | −0.5997 | −0.5997 |
Method in [25] | Proposed Method | |||
---|---|---|---|---|
Iterations | Time (s) | Iterations | Time (s) | |
0.1 | 2 | 31.433 | 2 | 13.896 |
0.2 | 2 | 31.894 | 2 | 15.148 |
0.3 | 2 | 31.938 | 2 | 11.402 |
0.4 | 2 | 29.879 | 2 | 13.179 |
0.5 | 2 | 31.046 | 2 | 11.724 |
0.6 | 2 | 33.076 | 2 | 11.168 |
Objective Function Values (p.u.) | ||||
---|---|---|---|---|
Method in [23] | Method in [29] | |||
MP | SP | MP | SP | |
0.1 | −0.7619 | −0.7655 | Infeasible | −0.7655 |
0.2 | Infeasible | 58.4681 | Infeasible | −0.7323 |
0.3 | Infeasible | 60.6725 | Infeasible | −0.6992 |
0.4 | Infeasible | 62.8792 | Infeasible | −0.6660 |
0.5 | Infeasible | 65.0870 | Infeasible | −0.6329 |
0.6 | Infeasible | 67.2952 | Infeasible | −0.5997 |
Method in [23] | Method in [29] | |||
---|---|---|---|---|
Iterations | Time (s) | Iterations | Time (s) | |
0.1 | 5 | 46.240 | 2 | 57.417 |
0.2 | 5 | 20.606 | 2 | 56.451 |
0.3 | 5 | 23.765 | 2 | 53.611 |
0.4 | 5 | 22.276 | 2 | 56.217 |
0.5 | 5 | 20.324 | 2 | 56.976 |
0.6 | 5 | 20.741 | 2 | 56.599 |
Objective Function Values (p.u.) | ||||
---|---|---|---|---|
69-Bus System | 123-Bus System | |||
MP | SP | MP | SP | |
0.5 | −1.2676 | −1.2679 | −3.7354 | −3.7379 |
69-Bus System | 123-Bus System | |||
---|---|---|---|---|
Iterations | Time (s) | Iterations | Time (s) | |
0.5 | 3 | 495.609 | 3 | 1985.721 |
Time | PV Bus Number | Time | PV Bus Number | Time | PV Bus Number |
---|---|---|---|---|---|
1 | 15, 39, 44, 48, 52 | 9 | 15, 26, 27, 39, 52 | 17 | 39, 44, 48, 52, 53 |
2 | 15, 39, 44, 48, 52 | 10 | 15, 19, 25, 26, 27 | 18 | 15, 39, 44, 48, 52 |
3 | 15, 39, 44, 48, 52 | 11 | 15, 19, 25, 26, 27 | 19 | 33, 39, 44, 48, 52 |
4 | 15, 39, 44, 48, 52 | 12 | 15, 19, 25, 26, 27 | 20 | 33, 39, 44, 48, 52 |
5 | 15, 39, 44, 48, 52 | 13 | 15, 19, 25, 26, 27 | 21 | 15, 39, 44, 48, 52 |
6 | 15, 39, 44, 48, 52 | 14 | 15, 19, 25, 26, 27 | 22 | 15, 39, 44, 48, 52 |
7 | 15, 39, 44, 48, 52 | 15 | 19, 25, 26, 27, 39 | 23 | 15, 39, 44, 48, 52 |
8 | 39, 48, 52, 53, 54 | 16 | 15, 27, 39, 48, 52 | 24 | 15, 39, 44, 48, 52 |
Time | Reactive Power (kvar) | Time | Reactive Power (kvar) |
---|---|---|---|
1 | 175, 588, 128, 232, 590 | 13 | −106, −172, −426, −480, −508 |
2 | 151, 540, 108, 211, 489 | 14 | −106, −173, −430, −484, −512 |
3 | 130, 498, 92, 192, 401 | 15 | −181, −442, −495, −522, 19 |
4 | 120, 480, 85, 184, 363 | 16 | 88, −406, −415, 175, 415 |
5 | 117, 474, 83, 182, 350 | 17 | 253, −240, 491, 544, −8.9 × 10−4 |
6 | 124, 400, 87, 187, 376 | 18 | 263, 598, 51, 598, 598 |
7 | 95, 496, 61, 180, 369 | 19 | 43, 600, 32, 600, 600 |
8 | −513, 252, 537, −268, 45 | 20 | 71, 600, 57, 600, 600 |
9 | −275, −393, −415, 29, −275 | 21 | 237, 600, −29, 531, 600 |
10 | −107, −175, −435, −489, −517 | 22 | 230, 600, −35, 500, 600 |
11 | −106, −172, −427, −481, −509 | 23 | 206, 600, −58, 376, 600 |
12 | −105, −171, −425, −478, −507 | 24 | 182, 599, −80, 253, 600 |
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Zhang, J.; Cui, M.; He, Y. Multi-Period Fast Robust Optimization for Partial Distributed Generators (DGs) Providing Ancillary Services. Energies 2021, 14, 4911. https://doi.org/10.3390/en14164911
Zhang J, Cui M, He Y. Multi-Period Fast Robust Optimization for Partial Distributed Generators (DGs) Providing Ancillary Services. Energies. 2021; 14(16):4911. https://doi.org/10.3390/en14164911
Chicago/Turabian StyleZhang, Jian, Mingjian Cui, and Yigang He. 2021. "Multi-Period Fast Robust Optimization for Partial Distributed Generators (DGs) Providing Ancillary Services" Energies 14, no. 16: 4911. https://doi.org/10.3390/en14164911
APA StyleZhang, J., Cui, M., & He, Y. (2021). Multi-Period Fast Robust Optimization for Partial Distributed Generators (DGs) Providing Ancillary Services. Energies, 14(16), 4911. https://doi.org/10.3390/en14164911