Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm
Abstract
1. Introduction
2. Component Models and Energy Management Strategy
2.1. Wind turbine
2.2. PV Panel
2.3. Battery System
2.4. Load Profile
2.5. Economic Model
2.6. Rule-Based Energy Management Strategy
2.7. Objective Function and Constraints
3. Optimization Algorithm
3.1. MOEA/DADE
3.1.1. Differential Evolution Mechanism
3.1.2. Parameter Adaptive Mechanism
3.2. Algorithm Contrast
4. Case Study
4.1. Data
4.2. Techno-Economic Analysis
4.3. Sensitivity Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
DOD | BS’s allowable depth of discharge |
PV derating factor (%) | |
solar incident radiation on the PV (kW/m2) | |
solar radiation under standard test conditions ( = 1 kW/m2) | |
turbine hub altitude (m) | |
anemometer altitude (m) | |
initial capital cost ($/kW) | |
real discount rate (%) | |
perturbation factor of load | |
maintenance and operation cost ($/kW) | |
electrical load (kW) | |
output power of PV (kW) | |
rated output power of WT (kW) | |
output power of WT (kW) | |
nominal discount rate (%) | |
replacement cost ($/kW) | |
salvage value($/kW) | |
a binary variable denoting whether the converter capacity is sufficient | |
a binary variable denoting whether the electric power generated is sufficient | |
SOC BS’s state of charge | |
u | expected inflation rate (%) |
wind speed at the turbine hub altitude (m/s) | |
cut-in speed (m/s) | |
cut-out speed (m/s) | |
nominal speed (m/s) | |
wind speed measured by anemometer (m/s) | |
daily variation percent of load | |
hourly variation percent of load | |
charge efficiency of BS | |
discharge efficiency of BS | |
converter efficiency |
Abbreviation
BS | battery system |
CRF | capital recovery factor |
DG | diesel system |
EMS | energy management strategy |
HRES | hybrid renewable energy systems |
LCC | life cycle cost |
LCOE | levelized cost of electricity |
LPSP | loss of power supply probability |
WT | wind turbine |
PF | Pareto frontier |
PS | Pareto set |
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Algorithm | Parameters |
---|---|
NSGA-II | Pc = 0.9, Pm = 1/D, ηc = 20, ηm = 20 |
MOEA/D | T = 10, Pc = 0.9, Pm = 1/D, ηc = 20, ηm = 20 |
MOEA/DADE | T = 10, , , δ = 0.9 |
Function | NSGA-II Mean (std) | MOEA/D Mean (std) | MOEA/DADE Mean (std) |
---|---|---|---|
ZDT1 | 1.7218 × 10−1 (1.10 × 10−1) − | 1.6737 × 10−1 (5.91 × 10−2) − | 4.7928 × 10−2 (1.62 × 10−2) |
ZDT 2 | 5.5298 × 10−1 (1.01 × 10−1) − | 3.2507 × 10−1 (1.88 × 10−1) − | 1.2261 × 10−1 (1.63 × 10−1) |
ZDT 3 | 1.3700 × 10−1 (8.06 × 10−2) − | 2.1748 × 10−1 (1.12 × 10−1) − | 6.6407 × 10−2 (3.45 × 10−2) |
ZDT 4 | 1.4230 × 101 (4.08 × 100) + | 1.4189 × 101 (4.79 × 100) + | 3.8489 × 101 (9.88 × 100) |
ZDT 6 | 3.8877 × 100 (3.78 × 10−1) − | 2.3380 × 100 (4.81 × 10−1) − | 1.8724 × 100 (3.83 × 10−1) |
+/-/= | 1/4/0 | 1/4/0 |
Factor | Value | Factor | Value | ||
---|---|---|---|---|---|
Project | Lifetime (year) | 25 | Battery | Lifetime (year) | 10 |
Discount rate (%) | 6 | Initial capital ($/kW∙h) | 160 | ||
Inflation rate (%) | 2 | Replacement ($/kW∙h) | 128 | ||
PV | Lifetime (year) | 25 | O&M ($/year/kW∙h) | 1 | |
Initial capital ($/kW) | 1857 | Round trip efficiency (%) | 80 | ||
Replacement ($/kW) | 1486 | Converter | Lifetime (year) | 15 | |
O&M ($/year/kW) | 18 | Initial capital ($/kW) | 890 | ||
Wind Turbine | Lifetime (year) | 20 | Replacement ($/kW) | 800 | |
Initial capital ($/kW) | 1610 | O&M ($/year/kW) | 10 | ||
Replacement ($/kW) | 1288 | Efficiency (%) | 95 | ||
O&M ($/year/kW) | 32 |
Algorithm | NSGA-II | MOEA/D | MOEA/DADE |
---|---|---|---|
IGD | 4.7809 × 10−4 | 1.3926 × 10−3 | 7.5655 × 10−5 |
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Yang, Y.; Li, R. Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm. Energies 2020, 13, 1585. https://doi.org/10.3390/en13071585
Yang Y, Li R. Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm. Energies. 2020; 13(7):1585. https://doi.org/10.3390/en13071585
Chicago/Turabian StyleYang, Yong, and Rong Li. 2020. "Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm" Energies 13, no. 7: 1585. https://doi.org/10.3390/en13071585
APA StyleYang, Y., & Li, R. (2020). Techno-Economic Optimization of an Off-Grid Solar/Wind/Battery Hybrid System with a Novel Multi-Objective Differential Evolution Algorithm. Energies, 13(7), 1585. https://doi.org/10.3390/en13071585