Influence of Degradation Processes in Lead–Acid Batteries on the Technoeconomic Analysis of Photovoltaic Systems
<p>Relationship among photovoltaic (PV) system parameters, battery performance, Net Present Value (NPV), PayBack Period (PBP), and Discounted PayBack Period (DPBP).</p> "> Figure 2
<p>Energy flows in the PV system with the battery.</p> "> Figure 3
<p>PV system distribution.</p> "> Figure 4
<p>Solar Irradiance, ambient temperature, and load demand profiles for the selected day.</p> "> Figure 5
<p>Combination of the scenarios that have been analysed.</p> "> Figure 6
<p>Daily energy balances according to the battery and PV system sizes for Cases 1 and 2. When the stored energy is lower than the PV, the energy yield in an hour, the bars show in a dark blue colour the PV energy yield and in light blue colour the stored energy. Otherwise, the PV energy yield is shown in a greenish-blue colour.</p> "> Figure 7
<p>Daily energy balances according to the battery and PV system sizes for Case 3. When the stored energy is lower than the PV energy yield in an hour, the bar shows in a dark blue colour the PV energy yield and in a greenish-blue colour the stored energy. Otherwise, the PV energy yield is shown in a greenish-blue colour.</p> "> Figure 8
<p>Daily energy balances according to the PV system size for Case 0.</p> "> Figure 9
<p>Battery lifetime for all scenarios.</p> "> Figure 10
<p>Evolution of the battery cycles over the battery lifetime for all scenarios.</p> "> Figure 11
<p>Battery efficiency evolution over its lifetime for all scenarios.</p> "> Figure 12
<p>Accumulated cash flow over the PV system lifetime for all scenarios within the High Electricity Price (HEP).</p> "> Figure 13
<p>Accumulated cash flow over the PV system lifetime for all scenarios within the Low Electricity Price (LEP).</p> ">
Abstract
:1. Introduction
2. Model, Battery Parameters, and Photovoltaic Integration
2.1. Battery Performance Parameters Versus PV System Operating Conditions
2.2. Battery Performance Parameters
2.3. Battery Operation Scenarios According to PV System Operating Conditions
- (1)
- Low Battery and High PV yield (LB + HPV): This happens when the battery capacity is small with respect to the PV array yield and the PV array yield is in the same order of magnitude or higher than the load demand.
- (2)
- Low Battery and Low PV yield (LB + LPV): This happens when the battery capacity is small with respect to the PV array yield and the PV array yield is smaller than the load demand.
- (3)
- High Battery and High PV yield (HB + HPV): This happens when the battery capacity is high with respect to the PV array yield and the PV array yield is in the same order of magnitude or higher than the load demand.
- (4)
- High Battery and Low PV yield (HB + LPV): This happens when the battery capacity is high with respect to the PV array yield and the PV array yield is smaller than the load demand.
- Case 0—Technoeconomic analysis assumes that the PV system does not have a battery. This will be the reference case.
- Case 1—Technoeconomic analysis assumes that battery lifetime and battery efficiency depend on degradation factors, σ(T), α, γd, and γc.
- Case 2—Technoeconomic analysis assumes that battery lifetime and battery efficiency depend on degradation factors σ(T) but not on α, γd, and γc.
- Case 3—Technoeconomic analysis assumes that battery lifetime and battery efficiency are constants according to the manufacturer datasheet. So, they do not depend on the degradation factors σ(T), α, γd, and γc.
3. Energy Balance
- -
- The annual hourly solar irradiance on the PV array and load demand profiles are the same during all days and years. PV system lifetime is set at 30 years. PV module degradation over the years has been despised.
- -
- A typical day has been selected with a solar radiation, ambient temperature, and load demand profile.
- -
- The Inverter efficiency is constant over its lifetime and set at 90%. The inverter lifetime is set at 15 years.
- -
- The Performance Ratio (PR) is constant over the PV system lifetime and is set at 90% [45].
- -
- The battery self-discharge rate is depreciable. The upper and lower state of charge (SoC) of the battery should be defined. The suggested values (used for this study) are 100% and 20%, respectively.
- -
- The Electricity retail price and electricity surplus price are constants over the PV system lifetime.
- (a)
- Situation A: PV system with battery. The PV system yield is higher or equal to the load demand, When the PV system yield is higher than load demand, the entire load demand is met by the PV system. In this case, the energy self-consumed by household, the bought energy from the national grid, the discharged energy from the battery for an hour t of the year n, , and
- (b)
- Situation B—PV system with battery. The PV system yield is lower than the load demand, . When the PV system yield is lower than the load demand, the load demand should be met by the PV system, battery, and the grid. In this scenario, , , and
- (c)
- Situation C—PV system without battery and PV system yield is higher or equal to the load demand, In this situation, load demand is met by the PV system. Consequently, and and are given by Equations (32) and (33):
- (d)
- Situation D—PV system without battery and PV system yield is lower to the load demand, In this situation, the load demand should be met by the PV system and the grid. Consequently, and and are given by Equations (34) and (35):
4. Economic Analysis
5. Results and Discussion
- -
- Electricity retail price and electricity surplus price have a significant influence on results. For this reason, two price scenarios have been analysed:
- -
- Low Electricity Price (LEP): 7.5 c€/kWh for bought energy from the national grid and 2.5 c€/kWh for energy sold to the grid from the PV system.
- -
- High Electricity Price (HEP): 15 c€/kWh for bought energy from the national grid and 5 c€/kWh for energy sold to the grid from the PV system.
- -
- The interest rate is set at 2%.
- -
- PV array investment cost = 0.9 €/Wp. Battery investment cost = 200 €/kWh [13], BoS investment cost = 0.6 €/W.
- -
- PV array operation and maintenance cost is set at 1% of investment PV array cost. Battery operation and maintenance cost is set at 1% of the investment battery cost. BoS operation and maintenance cost is set at 1% of the investment BoS cost.
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Abbreviations | |
AGM | Absorbed Glass Mat battery |
BoS | Balance of System |
HB | Large battery scenario |
HEP | High Electricity Price scenario |
HPV | High PV system energy yield scenario |
KPI | Key Performance Indicators |
PV | Photovoltaic |
LB | Small battery scenario |
LEP | Low Electricity Price scenario |
LPV | Low PV system energy yield scenario |
NOCT | Nominal Operating Cell Temperature |
PBP | PayBack Period |
SLA | Sealed lead–acid battery |
VRLA | Valve-regulated lead–acid battery |
Parameters and Variables | |
N | PV system lifetime (year) |
Battery lifetime (year) | |
Service year of the battery (year) | |
Battery State of Charge (%/100) | |
Battery Deep of Discharge (%/100) | |
Battery energy in the battery at the end of the hour t and year n (kWh) | |
Load demand for the hour t of the year n (kWh) | |
Surplus energy price injected into the grid (€/kWh) | |
Retail energy price (€/kWh) | |
Photovoltaic self-consumption ratio in the hour t of the year n (100/%) | |
Load self-consumption ratio in the hour t of the year n (100/%) | |
Self-consumed energy from the PV system for the hour t of the year n (kWh) | |
Surplus energy sold to the grid for the hour t of the year n (kWh) | |
PR | Performance Ratio (100/%) |
Photovoltaic energy yield for the hour t of the year n (kWh) | |
Bought energy to the grid for the hour t of the year n (kWh) | |
Discharged energy from the battery for the hour t of the year n (kWh) | |
Charged energy into the battery for the hour of the year n (kWh) | |
Battery discharge efficiency for the hour t of the year n (100/%) | |
Battery charge efficiency for the hour t of the year n (100/%) | |
Inverter efficiency (100/%) | |
Average module temperature for the hour t of the year n (°C) | |
PV array yield for the hour t of the year n (kWh) | |
Average ambient temperature for the hour t of the year n (°C) | |
Battery discharge efficiency degradation factor | |
Battery charge efficiency degradation factor | |
Battery lifetime degradation factor | |
Battery capacity degradation factor | |
Vbn | Battery nominal voltage (V) |
Maximum energy that the battery could store (kWh) | |
Minimum energy that the battery should keep according to a fixed DoD (kWh) | |
Battery lifetime (years) | |
Battery cycles from the manufacturer datasheet at a given DoD and 25 °C (cycles) | |
Battery annual cycles at a given DoD and temperature T (cycles/y) | |
Battery temperature dependent correction factor (-) | |
Battery charge current (A) | |
Battery charge current in 10 h (A) | |
Battery capacity at temperature T1 and a discharge time t (Ah) | |
PV module power temperature coefficient (%/(100 °C)) | |
PV system operation and maintenance costs in the year n (€) | |
Battery operation and maintenance cost in the year n (€) | |
Battery reposition cost in the year n (€) | |
Balance of System reposition cost in the year n (€) | |
PV array investment cost in Year 1 (€) | |
Battery investment cost in Year 1 (€) | |
BoS investment cost in Year 1 (€) | |
Cash flow out for the hour t of the year n (€) | |
Cash flow in for the hour t of the year n (€) | |
Capital investment cost in Year 1 (€) | |
Net Present Value (€) | |
PayBack Period (year) | |
Discounted PayBack Period (year) |
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1 | 0.69 | 0.51 | 0.37 | 0.25 | 0.14 |
Scenario | LB + HPV | LB + LPV | HB + HPV | HB + LPV |
---|---|---|---|---|
0.3 | 0.2 | 0.1 | 0.05 |
Scenario | LB + HPV | LB + LPV | HB + HPV | HB + LPV |
---|---|---|---|---|
0.3 | 0.2 | 0.1 | 0.05 |
Scenario | LB + HPV | LB + LPV | HB + HPV | HB + LPV |
---|---|---|---|---|
0.7 | 0.8 | 0.9 | 1 |
Equipment | Scenarios | |||
---|---|---|---|---|
LB + HPV | LB + LPV | HB + HPV | HB + LPV | |
Peak Power (Wp) | 7.50 | 3.00 | 7.50 | 3.00 |
BoS (W) | 7.50 | 3.00 | 7.50 | 3.00 |
Battery Size, C10 (kWh) | 4.85 | 4.85 | 14.54 | 14.54 |
Energy Balances | LB + HPV | LB + LPV | ||||||
---|---|---|---|---|---|---|---|---|
Case 3 | Case 2 | Case 1 | Case 0 | Case 3 | Case 2 | Case 1 | Case 0 | |
PV array production (kWh/d), | 32.34 | 32.34 | 32.34 | 32.34 | 12.94 | 12.94 | 12.94 | 12.94 |
PV self-consumption (kWh/d), | 17.80 | 17.80 | 17.80 | 17.80 | 10.72 | 10.72 | 10.72 | 10.72 |
Battery self-consumption (kWh/d), | 6.17 | 6.05 | 6.05 | N/A | 1.93 | 1.77 | 1.93 | N/A |
Total self-consumption (kWh/d) | 23.97 | 23.85 | 23.85 | 17.80 | 12.65 | 12.49 | 12.65 | 10.72 |
Load demand (kWh(day), | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 |
Grid consumption (kWh/d), | 13.61 | 14.44 | 14.44 | 18.05 | 23.62 | 23.85 | 23.62 | 25.13 |
Grid energy sale (kWh/d), | 6.83 | 7.46 | 7.46 | 14.55 | 0.00 | 0.00 | 0.00 | 2.12 |
PV array production (kWh/d), | 32.34 | 32.34 | 32.34 | 32.34 | 12.94 | 12.94 | 12.94 | 12.94 |
PV self-consumption (kWh/d), | 17.80 | 17.80 | 17.80 | 17.80 | 10.72 | 10.72 | 10.72 | 10.72 |
Battery self-consumption (kWh/d), | 11.64 | 12.65 | 12.65 | N/A | 1.77 | 1.93 | 1.93 | N/A |
Total self-consumption (kWh/d) | 29.43 | 30.45 | 30.45 | 17.80 | 12.49 | 12.65 | 12.65 | 10.72 |
Load demand (kWh(day), | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 | 35.85 |
Grid consumption (kWh/d), | 9.67 | 8.20 | 8.20 | 18.05 | 23.85 | 23.62 | 23.62 | 25.13 |
Grid energy sale (kWh/d), | 0.00 | 0.00 | 0.00 | 14.55 | 0.00 | 0.00 | 0.00 | 2.21 |
NPV and ΔNPV | ||||||||
---|---|---|---|---|---|---|---|---|
HEP: High Electricity Price | LEP: Low Electricity Price | |||||||
Case 0 | Case 1 | Case 2 | Case 3 | Case 0 | Case 1 | Case 2 | Case 3 | |
LB + HPV | 10,961.99 | −2832.98 | 1321.60 | 9430.54 | −7919.82 | −25,462.99 | −20,638.37 | −12,454.17 |
−126% | −88% | −14% | 222% | 161% | 57% | |||
LB + LPV | 7391.51 | 285.53 | 9586.18 | 8479.48 | −21,65.69 | −9698.91 | −6793.38 | −7770.90 |
−96% | 30% | 15% | 348% | 214% | 259% | |||
HB + HPV | 10,961.99 | −22,666.76 | −22,052.22 | 2613.27 | −7919.82 | −47,644.67 | −47,439.83 | −22,774.34 |
−307% | −301% | −76% | 502% | 499% | 188% | |||
HB + LPV | 7391.51 | 2710.86 | 3370.07 | −7762.89 | −2165.69 | -7397.23 | −7144.49 | −18,181.28 |
−63% | −54% | −205% | 242% | 230% | 740% |
Payback Period (Years) | ||||||||
---|---|---|---|---|---|---|---|---|
HEP: High Electricity Price | LEP: Low Electricity Price | |||||||
Case 0 | Case 1 | Case 2 | Case 3 | Case 0 | Case 1 | Case 2 | Case 3 | |
LB + HPV | 11 | >30 | 23 | 12 | >30 | >30 | >30 | >30 |
109% | 9% | |||||||
LB + LPV | 8 | 23 | 12 | 14 | >30 | >30 | >30 | >30 |
188% | 50% | 75% | ||||||
HB + HPV | 11 | >30 | >30 | 20 | >30 | >30 | >30 | >30 |
82% | ||||||||
HB + LPV | 8 | 13 | 13 | >30 | >30 | >30 | >30 | >30 |
63% | 63% |
Discounted Payback Period (Years) | ||||||||
---|---|---|---|---|---|---|---|---|
HEP: High Electricity Price | LEP: Low Electricity Price | |||||||
Case 0 | Case 1 | Case 2 | Case 3 | Case 0 | Case 1 | Case 2 | Case 3 | |
LB + HPV | 12 | >30 | 23 | 12 | >30 | >30 | >30 | >30 |
92% | 0% | |||||||
LB + LPV | 9 | 28 | 17 | 20 | >30 | >30 | >30 | >30 |
211% | 89% | 122% | ||||||
HB + HPV | 12 | >30 | >30 | 25 | >30 | >30 | >30 | >30 |
108% | ||||||||
HB + LPV | 9 | 23 | 23 | >30 | >30 | >30 | >30 | >30 |
156% | 156% |
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Delgado-Sanchez, J.-M.; Lillo-Bravo, I. Influence of Degradation Processes in Lead–Acid Batteries on the Technoeconomic Analysis of Photovoltaic Systems. Energies 2020, 13, 4075. https://doi.org/10.3390/en13164075
Delgado-Sanchez J-M, Lillo-Bravo I. Influence of Degradation Processes in Lead–Acid Batteries on the Technoeconomic Analysis of Photovoltaic Systems. Energies. 2020; 13(16):4075. https://doi.org/10.3390/en13164075
Chicago/Turabian StyleDelgado-Sanchez, Jose-Maria, and Isidoro Lillo-Bravo. 2020. "Influence of Degradation Processes in Lead–Acid Batteries on the Technoeconomic Analysis of Photovoltaic Systems" Energies 13, no. 16: 4075. https://doi.org/10.3390/en13164075