Optimal Asset Planning for Prosumers Considering Energy Storage and Photovoltaic (PV) Units: A Stochastic Approach
Abstract
:1. Introduction
1.1. State of the Art
1.2. Contributions
- A novel optimization algorithm for prosumer asset planning that determines optimal sizes for PV generation, BESS maximum power, and BESS storage capacity, based on a MILP formulation which minimizes costs associated with investment, maintenance, and operation of the system over a 25-year period.
- A deterministic and stochastic MILP model which guarantees that the optimal solution is obtained and can cope with uncertainties associated with PV generation.
2. Optimal Prosumer Asset Planning
2.1. Solar PV
2.2. Energy Storage
3. Mathematical Formulation
3.1. Deterministic Approach
3.1.1. Objective Function
3.1.2. Load
3.1.3. Power Balance
3.1.4. PV Generators
3.1.5. Energy Storage
3.1.6. Electricity Cost
3.2. Stochastic Formulation
3.2.1. Objective Function
3.2.2. Load
3.2.3. Power Balance
3.2.4. PV Generators
3.2.5. Energy Storage
3.2.6. Electricity Cost
4. Test and Results
4.1. Deterministic Approach
4.1.1. Case Study 1: Grid Exclusively
4.1.2. Case Study 2: Solar PV and Grid
4.1.3. Case Study 3: Solar PV, Energy Storage, and Grid
4.2. Stochastic Approach
4.2.1. Case Study 2: Solar PV and Grid
4.2.2. Case Study 3: Solar PV, Energy Storage, and Grid
5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
, | Charging coefficient. |
Discharging coefficient. | |
Self-discharging of BESS, in %. | |
Electricity rates, in $/kWh. | |
Cost per panel, including cost of installation, in CAD. | |
Cost of electricity supplied by the grid over a period of analysis. | |
Cost of BESS over a period of analysis. | |
Cost of solar PV system over a period of analysis. | |
Total cost of the prosumer model. | |
Hourly demand, in %. | |
Initial energy stored, in kWh. | |
Energy capacity of the BESS, in kWh. | |
Expected energy from the grid, in kWh. | |
, | Energy stored in the BESS, in kWh. |
Present value maintenance costs of the BESS, in $, over a period of analysis. | |
Annual maintenance costs of the BESS, in $. | |
Rate of inflation. | |
Energy cost coefficient, in $/kWh. | |
Power cost coefficient, in $/kW. | |
Charging efficiency, in %. | |
Discharging efficiency, in %. | |
, | Charging power, in kW. |
, | Discharging power, in kW. |
Power capacity of the BESS, in kW. | |
, | Power supplied by the BESS, in kW. |
Power factor. | |
Load power, in kW. | |
Power supplied by the grid, in kW. | |
Peak-load requirement, in kW. | |
, | PV power potential, in kW. |
, | Power supplied by the PV units, in kW. |
Probability of each scenario, in %. | |
Present value maintenance costs of the solar PV system, in $, over a period of analysis. | |
Annual maintenance costs of the solar PV system, in $. | |
Index for seasons. | |
Peak-load requirement, in kVA. | |
Size of the solar panel, in kW. | |
PV size, in kW. | |
Index for time zones. | |
Index for scenarios. | |
Period of analysis, in years. |
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Case Study | Solar PV | Energy Storage | Grid |
---|---|---|---|
1 | – | – | × |
2 | × | – | × |
3 | × | × | × |
Item | Value |
---|---|
Cost per panel, ($/panel) | 361.89 |
Size per panel, (kW/panel) | 0.325 |
Solar PV system maintenance percentage of capital cost (%) | 1 |
Rate of inflation (%/ year) | 2 |
Item | Value |
---|---|
Charging efficiency of BESS | 0.7975 |
Discharging efficiency of BESS | 1/0.8829 |
Self-Discharge of BESS | 0.0188 |
Power cost coefficient ($/kW) | 402 |
Energy cost coefficient ($/kWh) | 120.6 |
BESS maintenance cost ($/kW/year) | 33.5 |
Rate of inflation (%/year) | 2 |
Time Periods | Electricity Rates (¢/kWh) |
---|---|
off-peak | 6.5 |
mid-peak | 9.4 |
on-peak | 13.2 |
Season | Time Periods | ||
---|---|---|---|
off-peak | mid-peak | on-peak | |
1 | 7 pm–7 am | 11 am–5 pm | 7 am–11 am, 5 pm–7 pm |
2 | 7 pm–7 am | 11 am–5 pm | 7 am–11 am, 5 pm–7 pm |
3 | 7 pm–7 am | 7 am–11 am, 5 pm–7 pm | 11 am–5 pm |
4 | 7 pm–7 am | 7 am–11 am, 5pm–7 pm | 11 am–5 pm |
Case Study | PV Size (kW) | Power Capacity of BESS (kW) | Energy Capacity of BESS (kWh) | Initial Energy in BESS (kWh) | Total Cost ($) in Millions |
---|---|---|---|---|---|
1 | – | – | – | – | 22.9364 |
2 | 4888.98 | – | – | – | 18.0665 |
3 | 4903.28 | 231.04 | 716.49 | 0.0 | 18.0148 |
Case Study | PV Size (kW) | Power Capacity of BESS (kW) | Energy Capacity of BESS (kWh) | Initial Energy in BESS (kWh) | Total Cost ($) in Millions |
---|---|---|---|---|---|
1 | – | – | – | – | 22.9364 |
2 | 3671.53 | – | – | – | 19.1753 |
3 | 4124.57 | 1650.70 | 12,788.68 | 4656.70 | 16.9039 |
Case | Variation in Electricity Rates (%) | PV Size (kW) | Power Capacity of BESS (kW) | Energy Capacity of BESS (kWh) | Initial Energy in BESS (kWh) | Total Cost ($) in Millions |
---|---|---|---|---|---|---|
1 | –20 | 3153.15 | 1565.48 | 11,479.7 | 3675.43 | 15.1317 |
2 | –15 | 3451.83 | 1620.57 | 12,011.8 | 3951.07 | 15.6062 |
3 | –10 | 3687.12 | 1620.57 | 11,975.9 | 3910.09 | 16.0582 |
4 | −5 | 3931.20 | 1641.24 | 12,738.8 | 4656.70 | 16.4914 |
5 | 0 | 4124.57 | 1650.70 | 12,788.7 | 4656.70 | 16.9039 |
6 | +5 | 4420.00 | 1663.51 | 12,856.3 | 4656.70 | 17.2969 |
7 | +10 | 4508.07 | 1695.28 | 13,023.9 | 4656.70 | 17.6778 |
8 | +15 | 4765.80 | 1780.35 | 13,472.9 | 4656.70 | 18.0461 |
9 | +20 | 4802.20 | 1787.09 | 13,508.4 | 4,656.70 | 18.4006 |
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Achiluzzi, E.; Kobikrishna, K.; Sivabalan, A.; Sabillon, C.; Venkatesh, B. Optimal Asset Planning for Prosumers Considering Energy Storage and Photovoltaic (PV) Units: A Stochastic Approach. Energies 2020, 13, 1813. https://doi.org/10.3390/en13071813
Achiluzzi E, Kobikrishna K, Sivabalan A, Sabillon C, Venkatesh B. Optimal Asset Planning for Prosumers Considering Energy Storage and Photovoltaic (PV) Units: A Stochastic Approach. Energies. 2020; 13(7):1813. https://doi.org/10.3390/en13071813
Chicago/Turabian StyleAchiluzzi, Eleonora, Kirushaanth Kobikrishna, Abenayan Sivabalan, Carlos Sabillon, and Bala Venkatesh. 2020. "Optimal Asset Planning for Prosumers Considering Energy Storage and Photovoltaic (PV) Units: A Stochastic Approach" Energies 13, no. 7: 1813. https://doi.org/10.3390/en13071813