Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation
Abstract
:1. Introduction
2. Problem Formulation
2.1. Wind Output Characteristics
2.1.1. Variability
2.1.2. Uncertainty
2.2. Auxiliary Services Eased by BESS
2.2.1. BESS Participation in the Scheduling Plan
2.2.2. Quantification the Ancillary Services Cost
2.3. Mathematical Description of BESS
2.3.1. Equivalent Loss of Cycle Life
2.3.2. Constraints of BESS Accounting to the Scheduling
3. Optimal Model
3.1. Objective Function
3.2. Constraints
3.3. System Performance Indices
4. Case Study
4.1. Basic Data
4.2. Operation Results Without BESS
- Case 1: The optimal scheduling results of systems without wind power integration is calculated.
- Case 2: With allowing wind power curtailment, the scheduling results with wind power integration is considered.
4.3. Operation Results with BESS
- Case 3: both the auxiliary service compensation and BESS reserve wind forecast error are considered, that is, the proposed model;
- Case 4: without auxiliary service compensation and with BESS reserve wind uncertainty;
- Case 5: with auxiliary service compensation, and without BESS reserve wind uncertainty; and,
- Case 6: neither auxiliary service compensation nor BESS reserve wind uncertainty is considered.
4.4. Sensitivity Analysis
4.4.1. On-grid Price of Wind Power
4.4.2. Investment Cost and Cycle Life of BESS
4.4.3. Reserve Level of BESS
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
Pnet,t | net load of systems with wind power integration in hour t |
Pload,t | forecast value of load demand in hour t |
Pwind,t | forecast output of wind farm in hour t |
up/down ramp demand of the net load in hour t | |
maximum/minimum output of unit i | |
ui,t | on-off state of unit i in hour t |
Pgi,t | output of unit i in hour t |
△Pload,t | spinning reserve demand of the load demand in hour t |
upper and down limitation of wind prediction interval | |
Ng | number of conventional units |
Ponline,max/Ponline,min | upper/lower limitation of the online units |
Ponline,total | total output of the online conventional units |
P’net | net load of systems with wind farm configuration BESS |
R | total spinning reserve capacity required by the system |
Pcap | rated power of BESS |
Scap | rate capacity of BESS |
Cserve | difference auxiliary service cost of systems with and without BESS |
Cfixed | fixed cost item of auxiliary service |
Cvary | variable cost item of auxiliary service |
CAI | daily investment cost per capacity of conventional units |
rated power of the conventional unit i | |
output of unit i with configuration BESS in hour t | |
MBESS/M | number of units participating the auxiliary service with/without BESS |
unit coal cost of conventional units with/without BESS | |
T | one scheduling period |
D | charge/discharge depth of BESS |
Lcyc,D | cycle life of BESS under the charge/discharge depth of D |
Lcyc,N | cycle life of BESS with fully charge/discharge |
NB | charge/discharge number of BESS though the life cycle |
Tlife | equivalent operation years of BESS |
Ps,t | output of BESS in hour t |
Punion,t | output of wind energy union system in hour t |
Ssoc,t | state of charge (SOC) of BESS in hour t |
△t | scheduled interval |
charge/discharge status of BESS at time t | |
charge/discharge effectiveness of BESS | |
Cost | total investment cost of BESS |
Save | directly benefit from saving wind curtailed energy |
Cc(p,n) | capital recovery factor with annual interest rate p |
CE | unit capacity cost of BESS |
COM | unit operation and maintenance cost of BESS |
amortized power cost per year | |
amortized capacity cost per year | |
r | kW·h/kW cost ratio of BESS |
on-grid price of wind power | |
Pwloss,t/PBwloss,t | curtailed wind energy with and without BESS in hour t |
auxiliary service cost caused by wind power with/without BESS | |
Ri | ramping ability of unit i |
maximum/minimum online time of unit i | |
CGen | operating cost function of conventional units |
f(Pgi,t) | quadratic fuel cost function with coefficients ai, bi, ci |
Si | on-off cost of unit i |
q | curtailed rate of wind power |
Ncyc | equivalent cycle numbers of BESS though a scheduling period |
reserve level provided by BESS for the uncertainty of wind power |
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Discharge Depth (%) | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
---|---|---|---|---|---|
Cycle (time) | 9000 | 7200 | 5700 | 5200 | 4500 |
Units | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Pmax (MW) | 455 | 455 | 130 | 130 | 162 | 80 | 85 | 55 | 55 | 55 |
Pmin (MW) | 150 | 150 | 20 | 20 | 25 | 20 | 25 | 10 | 10 | 10 |
c ($/h) | 1000 | 970 | 700 | 680 | 450 | 370 | 480 | 660 | 665 | 670 |
b ($/MW·h2) | 16.19 | 17.26 | 16.60 | 16.50 | 19.70 | 22.26 | 26.74 | 25.92 | 27.27 | 27.29 |
a (10−3 $/MW·h2) | 0. 48 | 0.31 | 2.0 | 2.1 | 3.98 | 7.12 | 7.9 | 4.13 | 2.22 | 1.73 |
Ri (MW/h) | 130 | 130 | 60 | 60 | 90 | 40 | 40 | 20 | 20 | 20 |
Si ($) | 4500 | 5000 | 550 | 560 | 900 | 170 | 260 | 30 | 30 | 30 |
Initial status (h) | 8 | −8 | −5 | −5 | −5 | −3 | −3 | −1 | −1 | −1 |
Case | cg ($/MW·h) | q (%) | |
---|---|---|---|
1 | 21.201 | - | 382 |
2 | 21.579 | 6.09% | 437 |
Case | cg ($/MW·h) | f ($) | q (%) | Pcap (MW) | Scap (MW·h) | Ncyc (time) |
---|---|---|---|---|---|---|
Case 3 | 21.238 | 2990 | 0.0% | 58 | 122.4 | 1.73 |
Case 4 | 21.305 | −1540 | 0.64% | 55 | 88.9 | 1.71 |
Case 5 | 21.290 | 1790 | 3.61% | 27.75 | 60.25 | 1.85 |
Case 6 | 21.544 | 1050 | 4.32% | 7.15 | 35.75 | 1.56 |
On-Grid Price ($/kW·h) | f ($) | Pcap (MW·h) | Scap (MW·h) |
---|---|---|---|
0.084 | 2990 | 58 | 122.4 |
0.080 | 2321 | 54 | 102.4 |
0.076 | 1845 | 35.25 | 63.25 |
0.072 | 740 | 27.75 | 60.25 |
0.068 | 322 | 7.15 | 14.25 |
0.064 | 0 | 0 | 0 |
cg ($/MW·h) | f ($) | q (%) | Pcap (MW·h) | Scap (MW·h) | |
---|---|---|---|---|---|
100% | 21.238 | 2990 | 0.0% | 58 | 122.4 |
80% | 21.324 | 3160 | 1.10% | 44.8 | 95.2 |
60% | 21.323 | 3930 | 1.84% | 34.8 | 79.6 |
40% | 21.312 | 3560 | 2.54% | 31.2 | 70.35 |
20% | 21.307 | 2910 | 3.23% | 29.5 | 61.25 |
0% | 21.290 | 1790 | 3.61% | 27.75 | 60.25 |
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Jiang, X.; Nan, G.; Liu, H.; Guo, Z.; Zeng, Q.; Jin, Y. Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation. Appl. Sci. 2018, 8, 1957. https://doi.org/10.3390/app8101957
Jiang X, Nan G, Liu H, Guo Z, Zeng Q, Jin Y. Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation. Applied Sciences. 2018; 8(10):1957. https://doi.org/10.3390/app8101957
Chicago/Turabian StyleJiang, Xin, Guoliang Nan, Hao Liu, Zhimin Guo, Qingshan Zeng, and Yang Jin. 2018. "Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation" Applied Sciences 8, no. 10: 1957. https://doi.org/10.3390/app8101957