Optimal Battery Storage Participation in European Energy and Reserves Markets
Abstract
:1. Introduction
2. Literature Review and Contributions
3. Mathematical Formulation
3.1. Nomenclature
I | Set of generation units, indexed by i. |
J | Set of battery charging curve linear parts, indexed by j. |
S | Set of reserve activation scenarios, indexed by s. |
T | Set of time periods, indexed by t. |
Generator i down reserve activation price (€/MWh). | |
Generator i up reserve activation price (€/MWh). | |
Battery storage down reserve activation price (€/MWh). | |
Battery storage up reserve activation price (€/MWh). | |
Battery storage down reserve capacity price (€/MW). | |
Battery storage up reserve capacity price (€/MW). | |
Generator i down reserve capacity price (€/MW). | |
Generator i up reserve capacity price (€/MW). | |
Generator i maximum down reserve capacity (MW). | |
Generator i maximum up reserve capacity (MW). | |
Maximum amount of energy that can be charged at specific state-of-energy breakpoint as a portion of . | |
P | Battery storage maximum charging and discharging power (MW). |
Capacity of each state-of-energy segment j as a portion of the maximum state-of-energy . | |
Required down reserve capacity (MW). | |
Required up reserve capacity (MW). | |
Activated down reserve energy (MWh). | |
Activated up reserve energy (MWh). | |
Battery storage charging efficiency. | |
Battery storage discharging efficiency. | |
Day-ahead market price (€/MW). |
Generator i activated down energy (MWh). | |
Generator i activated up energy (MWh). | |
Generator i down capacity reserved quantity (MW). | |
Generator i up capacity reserved quantity (MW). | |
Battery storage down reserve capacity bid (MW). | |
Battery storage up reserve capacity bid (MW). | |
Battery storage activated down reserve quantity in scenario s (MWh). | |
Battery storage activated up reserve quantity in scenario s (MWh). | |
Battery storage down reserved capacity (MW). | |
Battery storage up reserved capacity (MW). | |
Battery storage charging quantity (MW). | |
Battery storage discharging quantity (MW). | |
Battery storage state-of-energy (MWh). | |
Down reserve activation clearing price in scenario s (€/MWh). | |
Up reserve activation clearing price in scenario s (€/MWh). | |
Down reserve capacity clearing price (€/MW). | |
Up reserve capacity clearing price (€/MW). |
3.2. Initial Problem Formulation
3.3. KKT Conditions of the Lower-Level Problem
4. Case Study
4.1. Input Data
4.2. Results
4.3. Sensitivity Analysis
4.4. Comparison to a Baseline Model
- First we solve only the lower-level problem (2) without battery storage bids, i.e., setting and to zero. This is needed to obtain the capacity reservation and activation prices , , and .
- Then we solve the upper-level problem (1) using the capacity reservation and activation prices , , and from the previous step. Note that the capacity reservation and activation prices are treated as parameters as opposed to being treated as variables in the proposed formulation. The outcome is the battery storage day-ahead and reserves bids.
- Finally, we solve the lower-level problem (2) again, but this time with battery storage bids and from the previous step. This calculation provides actual reserve capacity and activation prices (note that these may differ from those obtained in step 1) as well as cleared battery storage quantities and profit.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
AESO | Alberta Electric System Operator |
aFRR | Automatic Frequency Restoration Reserve |
FCR | Frequency Containment Reserve |
KKT | Karush–Kuhn–Tucker |
MILP | Mixed-Integer Linear Program |
MOL | Merit Order List |
SOE | State-Of-Energy |
TSO | Transmission System Operator |
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Hour | Price (€/MWh) | Hour | Price (€/MWh) | Hour | Price (€/MWh) | Hour | Price (€/MWh) |
---|---|---|---|---|---|---|---|
1 | 5.5 | 7 | 2.54 | 13 | 0.35 | 19 | 18.99 |
2 | 5.35 | 8 | 1.50 | 14 | −2.04 | 20 | 23.50 |
3 | 3.82 | 9 | −1.57 | 15 | −2.06 | 21 | 28.43 |
4 | 2.63 | 10 | −2.43 | 16 | −0.04 | 22 | 26.88 |
5 | 1.56 | 11 | −2.89 | 17 | 1.95 | 23 | 20.91 |
6 | 2.46 | 12 | −2.47 | 18 | 7.88 | 24 | 16.00 |
Hours 1–4 | Hours 5–8 | Hours 9–12 | Hours 13–16 | Hours 17–20 | Hours 21–24 | |
---|---|---|---|---|---|---|
Up reserve (MW) | 2359 | 2334 | 2355 | 2344 | 2357 | 2360 |
Down reserve (MW) | 2247 | 2295 | 2338 | 2354 | 2316 | 2303 |
Hour | s1 | s2 | s3 | s4 | s5 | s6 | s7 | s8 | s9 | s10 |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0.4/400 | 0/0 | 0.4/327 | 0.4/8 | 0.4/2 | 0.4/17 | 0.4/38 | 0.4/116 | 0.4/79 | 0.4/10 |
2 | 16/377 | 10/10 | 16/341 | 16/21 | 8/8 | 16/16 | 13/13 | 16/70 | 16/69 | 16/177 |
3 | 10/170 | 10/10 | 10/156 | 10/32 | 10/23 | 10/38 | 10/34 | 10/28 | 10/129 | 10/107 |
4 | 17/67 | 0/0 | 17/32 | 7/7 | 17/68 | 17/53 | 12/12 | 17/74 | 17/62 | 2/2 |
5 | 1/1 | 2/2 | 5/7 | 0/0 | 5/11 | 5/17 | 5/223 | 5/5 | 5/15 | 4/4 |
6 | 0/0 | 0/3 | 0/34 | 0/39 | 0/4 | 0/5 | 0/72 | 0/0 | 0/2 | 0/9 |
7 | 2/5 | 2/13 | 2/80 | 2/28 | 2/52 | 2/48 | 2/182 | 2/2 | 0/0 | 2/5 |
8 | 0/4 | 0/47 | 0/44 | 0/17 | 0/48 | 0/33 | 0/35 | 0/0 | 0/0 | 0/213 |
9 | 1/2 | 1/17 | 1/6 | 1/279 | 1/138 | 1/33 | 1/9 | 1/1 | 0/0 | 1/489 |
10 | 0/0 | 8/20 | 1/1 | 8/50 | 8/54 | 8/16 | 8/118 | 1/1 | 2/2 | 8/102 |
11 | 7/7 | 1/1 | 7/31 | 7/57 | 7/263 | 7/7 | 7/25 | 7/13 | 0/0 | 7/8 |
12 | 0/554 | 0/2 | 0/841 | 0/63 | 0/108 | 0/7 | 0/10 | 0/0 | 0/4 | 0/1 |
13 | 1/123 | 1/23 | 1/74 | 1/57 | 1/58 | 1/5 | 1/89 | 1/17 | 1/104 | 1/0 |
14 | 4/336 | 4/192 | 0/0 | 4/110 | 4/22 | 4/4 | 4/17 | 4/125 | 4/124 | 0/0 |
15 | 3/349 | 3/484 | 1/1 | 3/69 | 3/148 | 3/3 | 0/0 | 3/15 | 3/116 | 3/753 |
16 | 13/260 | 13/86 | 2/2 | 13/219 | 1/1 | 7/7 | 3/3 | 5/5 | 13/76 | 13/1119 |
17 | 9/477 | 9/375 | 9/157 | 9/50 | 2/2 | 2/2 | 4/4 | 9/27 | 3/3 | 9/37 |
18 | 2/97 | 2/115 | 2/263 | 2/27 | 2/14 | 2/2 | 2/89 | 2/42 | 2/10 | 2/165 |
19 | 6/20 | 6/67 | 6/163 | 6/6 | 6/52 | 6/6 | 6/139 | 6/27 | 6/13 | 6/74 |
20 | 4/98 | 4/69 | 4/125 | 3/3 | 4/226 | 4/129 | 4/103 | 2/2 | 4/5 | 2/2 |
21 | 1/157 | 1/30 | 1/84 | 1/20 | 1/23 | 1/70 | 1/93 | 1/1 | 1/142 | 1/5 |
22 | 0/0 | 3/76 | 3/131 | 3/15 | 3/62 | 3/205 | 3/508 | 3/17 | 3/128 | 3/3 |
23 | 7/12 | 1/1 | 7/27 | 7/43 | 2/2 | 7/30 | 7/68 | 7/10 | 7/40 | 7/158 |
24 | 6/74 | 6/16 | 6/190 | 6/8 | 6/10 | 6/6 | 6/23 | 6/29 | 6/17 | 6/148 |
Hour | s1 | s2 | s3 | s4 | s5 | s6 | s7 | s8 | s9 | s10 |
---|---|---|---|---|---|---|---|---|---|---|
1 | 1/8 | 1/209 | 1/6 | 1/250 | 1/430 | 1/37 | 1/88 | 1/57 | 1/10 | 1/57 |
2 | 0/5 | 0/132 | 0/4 | 0/118 | 0/72 | 0/43 | 0/23 | 0/15 | 0/10 | 0/8 |
3 | 0/4 | 0/28 | 0/5 | 0/32 | 0/65 | 0/20 | 0/31 | 0/12 | 0/6 | 0/8 |
4 | 0/15 | 0/166 | 0/5 | 0/68 | 0/20 | 0/27 | 0/16 | 0/6 | 0/12 | 0/77 |
5 | 0/201 | 0/48 | 0/9 | 0/200 | 0/18 | 0/49 | 0/6 | 0/56 | 0/81 | 0/12 |
6 | 18/72 | 5/40 | 13/48 | 18/55 | 18/69 | 5/40 | 0/15 | 18/407 | 18/247 | 18/64 |
7 | 0/7 | 0/100 | 0/4 | 0/84 | 0/21 | 0/66 | 0/26 | 0/373 | 0/214 | 0/24 |
8 | 0/8 | 0/4 | 0/14 | 2/63 | 2/65 | 2/112 | 2/105 | 2/516 | 2/477 | 0/5 |
9 | 16/380 | 0/29 | 0/27 | 0/20 | 0/32 | 16/173 | 16/183 | 16/403 | 16/181 | 0/4 |
10 | 11/163 | 11/57 | 11/71 | 11/42 | 0/15 | 11/444 | 0/14 | 11/648 | 11/237 | 10/41 |
11 | 2/38 | 2/148 | 0/12 | 0/27 | 0/4 | 2/455 | 2/33 | 2/369 | 2/333 | 2/384 |
12 | 0/5 | 6/84 | 0/4 | 0/24 | 0/5 | 6/108 | 6/58 | 6/827 | 6/65 | 6/504 |
13 | 10/30 | 10/119 | 10/28 | 4/9 | 10/89 | 10/54 | 2/7 | 10/169 | 2/7 | 10/651 |
14 | 9/14 | 11/20 | 11/246 | 11/49 | 11/179 | 11/387 | 11/253 | 11/70 | 1/6 | 11/392 |
15 | 0/1 | 0/2 | 28/60 | 16/21 | 28/180 | 28/198 | 28/603 | 4/9 | 0/5 | 9/14 |
16 | 0/2 | 0/4 | 6/74 | 0/5 | 6/559 | 6/99 | 6/271 | 6/32 | 3/8 | 1/6 |
17 | 0/0 | 0/2 | 0/36 | 0/8 | 0/165 | 0/394 | 0/127 | 0/119 | 0/134 | 0/62 |
18 | 0/5 | 0/8 | 0/6 | 0/11 | 0/186 | 0/292 | 0/290 | 0/231 | 0/284 | 0/30 |
19 | 11/83 | 11/32 | 0/14 | 11/133 | 11/127 | 11/546 | 11/32 | 11/104 | 11/113 | 0/11 |
20 | 1/21 | 0/9 | 0/5 | 7/231 | 0/19 | 7/121 | 7/92 | 7/293 | 7/85 | 7/234 |
21 | 0/30 | 0/12 | 0/5 | 0/124 | 0/9 | 0/16 | 0/3 | 0/165 | 0/6 | 0/48 |
22 | 7/498 | 0/40 | 0/16 | 7/103 | 0/36 | 0/45 | 0/8 | 7/159 | 0/18 | 7/155 |
23 | 10/167 | 10/274 | 0/27 | 1/47 | 10/341 | 10/89 | 3/49 | 10/223 | 10/118 | 0/7 |
24 | 0/23 | 2/125 | 0/15 | 2/151 | 2/145 | 2/141 | 2/173 | 2/163 | 2/155 | 2/53 |
Day-Ahead Revenue | Up Capacity Res. Revenue | Up Capacity Act. Revenue | Down Capacity Res. Revenue | Down Capacity Act. Revenue | Overall Revenue | |
---|---|---|---|---|---|---|
(0,0,0,0) | −372 | 21 | 8507 | 6724 | 7291 | 22,172 |
(1,1,0,0) | −368 | 22 | 8835 | 6511 | 7163 | 22,162 |
(1,1,25,0) | −354 | 21 | 8684 | 6804 | 7274 | 22,429 |
(1,1,25,15) | −366 | 21 | 8316 | 5568 | 5630 | 19,168 |
(5,5,0,0) | −360 | 22 | 8588 | 6703 | 7205 | 22,158 |
(5,5,25,0) | −327 | 21 | 8066 | 7162 | 7515 | 22,438 |
(5,5,25,15) | −360 | 22 | 8096 | 5713 | 5698 | 19,169 |
(5,5,50,0) | −7 | 5 | 5386 | 5605 | 6352 | 17,342 |
(10,10,50,−15) | 1033 | 7 | 3585 | 9172 | 12,416 | 26,212 |
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Pandžić, K.; Pavić, I.; Andročec, I.; Pandžić, H. Optimal Battery Storage Participation in European Energy and Reserves Markets. Energies 2020, 13, 6629. https://doi.org/10.3390/en13246629
Pandžić K, Pavić I, Andročec I, Pandžić H. Optimal Battery Storage Participation in European Energy and Reserves Markets. Energies. 2020; 13(24):6629. https://doi.org/10.3390/en13246629
Chicago/Turabian StylePandžić, Kristina, Ivan Pavić, Ivan Andročec, and Hrvoje Pandžić. 2020. "Optimal Battery Storage Participation in European Energy and Reserves Markets" Energies 13, no. 24: 6629. https://doi.org/10.3390/en13246629