Optimal Economic Dispatch in Microgrids with Renewable Energy Sources
Abstract
:1. Introduction
2. Literature Review
3. Economic Dispatch Algorithm
4. Case Study
- The microgrid is synchronized to the main grid.
- Each element of the system has its self-protection devices working properly.
- It is assumed that the microgrid contains instrumentation for monitoring and equipment for all control actions.
- All generating plants operate in the ramp form and consequently contain their control system.
- It has communication interfaces and protocols for proper operation in monitoring and management.
- The load limitation values have been defined by the customer and do not affect the profitability of their operation in such a way that the resulting bonus represents a real benefit in the DR program.
- The microgrid has access to a self-contained pollutant processing system that allows it to comply with the restrictions of the environmental contingency plan.
- For the optimization analysis, a one-day study interval divided into 24 one-hour periods is considered.
5. Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
Indices/Sets: | |
I | Set of conventional generators |
J | Set of customers connected to the micro-grid, client connected to the micro-grid with EDR program. |
T | Set of periods for study |
K | Set of pollutants to regenerate |
Parameters: | |
lower ramp power limit of the conventional generator | |
upper ramp power limit of conventional generator | |
quadratic coefficient of the cost function of the conventional generator i | |
linear coefficient of the cost function of the conventional generator | |
total demand in the microgrid in the time | |
binary coefficient activation of the environmental contingency plan during at t time, | |
photovoltaic energy available in the period t | |
wind energy available in the period t | |
quadratic coefficient of cost function to the client | |
linear coefficient of the cost function to the client | |
customer classification client in DR program | |
energy restriction of client in DR program | |
interruptibility factor of client at time in DR program | |
purchase price of energy (kVA) from the main grid | |
sale price of energy (kVA) from the main grid | |
is the coefficient of pollutant emissions in USD Kg/kVA [18] | |
Decision variables: | |
conventional generator power at time | |
power production of the photo voltaic plant at time | |
power output of the wind power plant at time | |
power transferred with the upper main grid at time | |
reduced energy per participating client at time | |
value of the monetary compensation for the client at time |
Appendix A. Lingo Source Code Program
References
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i | ||||||
---|---|---|---|---|---|---|
1 | 0.06 | 0.5 | 0 | 4 | 1 | 3 |
2 | 0.03 | 0.25 | 0 | 6 | 1 | 5 |
3 | 0.04 | 0.3 | 0 | 9 | 1 | 8 |
j | ||||
---|---|---|---|---|
1 | 1.079 | 1.32 | 0 | 30 |
2 | 1.078 | 1.63 | 0.45 | 35 |
3 | 1.847 | 1.64 | 0.9 | 40 |
(h) | (kVA) | (kVA) | (kVA) | ($/kVA) | ($/kVA) | ($/kVA) | |
---|---|---|---|---|---|---|---|
1 | 8.5 | 0 | 35.8 | 1.7 | 3.7 | 2.7 | 0 |
2 | 8.5 | 0 | 36.1 | 1.4 | 2.7 | 1.9 | 0 |
3 | 9 | 0 | 34.7 | 2.2 | 3.2 | 1.8 | 0 |
4 | 7 | 0 | 35.2 | 3.7 | 2.6 | 1.9 | 0 |
5 | 7.5 | 0 | 35.5 | 4.5 | 3.8 | 2.3 | 0 |
6 | 8 | 0 | 34.9 | 4.7 | 1.7 | 0.7 | 0 |
7 | 9 | 0 | 35.1 | 5.1 | 2.3 | 1.4 | 1 |
8 | 11 | 7 | 40.8 | 5.3 | 1.5 | 0.5 | 1 |
9 | 12 | 13 | 47.5 | 6.7 | 4.3 | 2.9 | 1 |
10 | 10 | 18 | 48.3 | 6.6 | 4.6 | 1.6 | 0 |
11 | 10 | 21 | 48.5 | 6.8 | 3.5 | 4.3 | 0 |
12 | 10 | 21.5 | 51.1 | 6.2 | 4.2 | 4.8 | 0 |
13 | 11 | 20.5 | 59.7 | 7.3 | 4.3 | 5.1 | 0 |
14 | 14 | 19.5 | 61.7 | 7.8 | 6.3 | 5.4 | 0 |
15 | 13 | 19 | 58.1 | 0.5 | 3.5 | 5.5 | 0 |
16 | 18 | 19 | 56.6 | 5.2 | 5.3 | 6.1 | 0 |
17 | 20 | 17 | 52.7 | 6.8 | 5.3 | 5.6 | 1 |
18 | 22 | 16 | 50.7 | 5.7 | 6.1 | 6.3 | 1 |
19 | 13 | 7 | 42.6 | 4.8 | 2.6 | 4.5 | 0 |
20 | 12 | 0 | 39.4 | 3.9 | 3.6 | 4.2 | 0 |
21 | 11 | 0 | 34.8 | 3.8 | 4.2 | 3.9 | 0 |
22 | 8.5 | 0 | 34.1 | 3.1 | 3.8 | 3.2 | 0 |
23 | 8 | 0 | 35.2 | 2.5 | 2.3 | 2.8 | 0 |
24 | 8.5 | 0 | 35.6 | 1.9 | 3.8 | 4.2 | 0 |
Total Power | EDR | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 8.5 | 0.0 | 4.0 | 8.0 | 12.0 | 0.8 | 33.3 | 2.5 | 0.0 | 1.2 | 1.3 |
2 | 8.5 | 0.0 | 4.0 | 8.0 | 12.0 | 1.7 | 34.2 | 1.9 | 0.0 | 0.8 | 1.1 |
3 | 9.0 | 0.0 | 4.0 | 8.0 | 12.0 | −0.4 | 32.6 | 2.1 | 0.0 | 1.0 | 1.1 |
4 | 7.0 | 0.0 | 4.0 | 8.0 | 12.0 | 1.8 | 32.8 | 2.4 | 0.5 | 0.8 | 1.1 |
5 | 7.5 | 0.0 | 4.0 | 8.0 | 12.0 | 0.7 | 32.2 | 3.3 | 0.9 | 1.2 | 1.2 |
6 | 8.0 | 0.0 | 4.0 | 8.0 | 12.0 | 0.7 | 32.7 | 2.2 | 1.0 | 0.5 | 0.8 |
7 | 9.0 | 0.0 | 0.3 | 5.0 | 3.0 | 14.0 | 31.3 | 3.9 | 1.6 | 1.0 | 1.2 |
8 | 11.0 | 7.0 | 0.0 | 3.5 | 1.9 | 14.0 | 37.4 | 3.3 | 1.7 | 0.7 | 1.0 |
9 | 12.0 | 13.0 | 0.0 | 2.1 | 0.9 | 14.0 | 42 | 5.5 | 2.3 | 1.7 | 1.6 |
10 | 10.0 | 18.0 | 4.0 | 8.0 | 12.0 | −8.1 | 43.9 | 4.4 | 1.9 | 1.5 | 1.0 |
11 | 10.0 | 21.0 | 4.0 | 8.0 | 12.0 | −11.3 | 43.7 | 4.8 | 2.0 | 1.1 | 1.7 |
12 | 10.0 | 21.5 | 4.0 | 8.0 | 12.0 | −9.3 | 46.2 | 4.9 | 1.7 | 1.4 | 1.9 |
13 | 11.0 | 20.5 | 4.0 | 8.0 | 12.0 | −1.4 | 54.1 | 5.6 | 2.2 | 1.4 | 2.0 |
14 | 14.0 | 19.5 | 4.0 | 8.0 | 12.0 | −2.4 | 55.1 | 6.6 | 2.4 | 2.1 | 2.0 |
15 | 13.0 | 19.0 | 4.0 | 8.0 | 12.0 | −1.1 | 54.9 | 3.2 | 0.0 | 1.1 | 2.1 |
16 | 18.0 | 19.0 | 4.0 | 8.0 | 12.0 | −9.6 | 51.4 | 5.2 | 1.2 | 1.8 | 2.2 |
17 | 20.0 | 17.0 | 0.0 | 0.0 | 0.0 | 9.9 | 46.9 | 5.8 | 2.0 | 1.8 | 2.1 |
18 | 22.0 | 16.0 | 0.0 | 0.0 | 0.0 | 6.9 | 44.9 | 5.8 | 1.4 | 2.1 | 2.3 |
19 | 13.0 | 7.0 | 4.0 | 8.0 | 12.0 | −5.0 | 39 | 3.6 | 1.0 | 0.8 | 1.8 |
20 | 12.0 | 0.0 | 4.0 | 8.0 | 12.0 | −0.1 | 35.9 | 3.5 | 0.6 | 1.2 | 1.7 |
21 | 11.0 | 0.0 | 4.0 | 8.0 | 12.0 | −3.8 | 31.2 | 3.6 | 0.6 | 1.4 | 1.6 |
22 | 8.5 | 0.0 | 4.0 | 8.0 | 12.0 | −1.3 | 31.2 | 2.9 | 0.2 | 1.2 | 1.4 |
23 | 8.0 | 0.0 | 4.0 | 8.0 | 12.0 | 1.2 | 33.2 | 2.0 | 0.0 | 0.7 | 1.3 |
24 | 8.5 | 0.0 | 4.0 | 8.0 | 12.0 | 0.1 | 32.6 | 3.0 | 0.0 | 1.2 | 1.7 |
(USD) | |||
---|---|---|---|
1 | 0.0 | 3.4 | 4.0 |
2 | 0.0 | 1.9 | 2.9 |
3 | 0.0 | 2.6 | 2.8 |
4 | 1.0 | 1.8 | 2.9 |
5 | 2.0 | 3.5 | 3.5 |
6 | 2.3 | 0.9 | 1.6 |
7 | 4.9 | 2.7 | 3.5 |
8 | 5.2 | 1.5 | 2.3 |
9 | 8.5 | 6.0 | 5.6 |
10 | 6.2 | 5.0 | 2.6 |
11 | 6.7 | 3.1 | 6.8 |
12 | 5.2 | 4.2 | 7.8 |
13 | 8.0 | 4.4 | 8.4 |
14 | 9.5 | 8.8 | 9.0 |
15 | 0.0 | 3.1 | 9.3 |
16 | 3.2 | 6.4 | 10.7 |
17 | 6.7 | 6.4 | 9.5 |
18 | 4.1 | 8.3 | 11.1 |
19 | 2.5 | 1.8 | 7.2 |
20 | 1.2 | 3.2 | 6.6 |
21 | 1.1 | 4.2 | 6.0 |
22 | 0.4 | 3.5 | 4.8 |
23 | 0.0 | 1.5 | 4.2 |
24 | 0.0 | 3.5 | 6.6 |
Case | Considered Characteristics |
---|---|
a (Base case) | All parameters of the initial study are considered. |
b | It is considered a sale price = $1 and purchases = $1 in the transfer of energy with the main grid. |
c | It is considered = 0 as the interruptibility coefficient for all customers |
d | It is considered = 0 with the same priority for customers as well = 0 in the EDR plan |
e | It is considered = 0 without environmental contingency |
f | It is considered = 1 in the 24 h with environmental contingency |
g | It is considered = = 1, = 1, 24 h and = 30 kVA |
Variables | a | b | c | d | e | f | g | Standard Deviation |
---|---|---|---|---|---|---|---|---|
(kVA) | 1044.7 | 1044.7 | 1044.7 | 1044.7 | 1044.7 | 1044.7 | 1044.7 | 0.00 |
(kVA) | 269.5 | 269.5 | 269.5 | 269.5 | 269.5 | 269.5 | 269.5 | 0.00 |
(kVA) | 198.5 | 198.5 | 198.5 | 198.5 | 198.5 | 198.5 | 198.5 | 0.00 |
(kVA) | 76.3 | 76 | 76.6 | 76.7 | 96 | 9.1 | 0 | 37.75 |
(kVA) | 162.6 | 160.5 | 164.7 | 165.3 | 192 | 92.7 | 0 | 66.42 |
(kVA) | 233.8 | 170.6 | 235.6 | 236.1 | 286.5 | 56.8 | 0 | 106.38 |
(kVA) | 11.8 | 87.7 | 52.1 | 61.1 | −88.9 | 325.6 | 496.8 | 202.94 |
(kVA) | 92.3 | 82 | 47.8 | 37.5 | 91 | 92.5 | 79.9 | 22.66 |
(USD) | 309.9 | 257.1 | 96.1 | 83.8 | 301.2 | 308.3 | 243.6 | 98.14 |
(h) | 5 | 5 | 5 | 5 | 0 | 24 | 24 | 9.93 |
(USD) | 144.6 | 123.7 | 312.7 | 321.6 | 12 | 687.5 | 179.7 | 219.46 |
Iterations | 607 | 362 | 174 | 159 | 361 | 274 | 290 | 150.58 |
Seconds | 1.12 | 0.33 | 0.28 | 0.22 | 0.24 | 0.19 | 0.2 | 0.33 |
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Share and Cite
Santillán-Lemus, F.D.; Minor-Popocatl, H.; Aguilar-Mejía, O.; Tapia-Olvera, R. Optimal Economic Dispatch in Microgrids with Renewable Energy Sources. Energies 2019, 12, 181. https://doi.org/10.3390/en12010181
Santillán-Lemus FD, Minor-Popocatl H, Aguilar-Mejía O, Tapia-Olvera R. Optimal Economic Dispatch in Microgrids with Renewable Energy Sources. Energies. 2019; 12(1):181. https://doi.org/10.3390/en12010181
Chicago/Turabian StyleSantillán-Lemus, F. Daniel, Hertwin Minor-Popocatl, Omar Aguilar-Mejía, and Ruben Tapia-Olvera. 2019. "Optimal Economic Dispatch in Microgrids with Renewable Energy Sources" Energies 12, no. 1: 181. https://doi.org/10.3390/en12010181
APA StyleSantillán-Lemus, F. D., Minor-Popocatl, H., Aguilar-Mejía, O., & Tapia-Olvera, R. (2019). Optimal Economic Dispatch in Microgrids with Renewable Energy Sources. Energies, 12(1), 181. https://doi.org/10.3390/en12010181