# State-of-Charge Effects on Standalone Solar-Storage Systems in Hot Climates: A Case Study in Saudi Arabia

^{*}

## Abstract

**:**

## 1. Introduction

^{2}), a considerable number of communities, villages, and rural areas are powered by diesel generators through an isolated grid given that connecting these remote locations to the main grid with transmission lines is prohibitively costly [1,2]. According to 2016 data, over 50 remote locations kingdom-wide were diesel-powered. In addition, nearly 19,000 homes were relying on on-site diesel generation for their energy needs as per the 2017 Saudi household energy survey. Some of these homes would obtain their diesel from gas stations, which means that they use (subsidized) diesel that is allocated for the transportation sector. Renewable technologies hold potential in providing energy for these remote locations cost effectively, and this includes solar photovoltaics (PV).

## 2. Review and Motivation

## 3. Methodology

#### 3.1. Financial Assumptions

#### 3.2. Load, Irradiation, and Temperature Profiles

#### 3.3. Technical Assumptions

#### 3.3.1. Overall System Assumptions

#### 3.3.2. PV Assumptions

#### 3.3.3. Battery Assumptions

^{−4}and 1.169, respectively. From Equation (1), an estimated throughput is derived via the Rainflow Counting Algorithm as detailed previously [50]. Note that the throughput is different from the calendar lifetime. The replacement of the battery will occur when the throughput or lifetime is reached, whichever comes first.

_{0,1,2}are the fitted parameters based on the data available, and T

_{c}is the temperature in degrees Celsius. Based on the provided data sheet, the fitted parameters were calculated as: δ

_{0}= 0.706, δ

_{1}= 0.0113, δ

_{2}= −6.3981 × 10

^{−5}.

_{1,2}are fitted parameters, and T

_{k}is the temperature in degrees kelvin. Based on the typical characteristics of lifetime of lead acid batteries versus temperature [51], μ

_{1}and μ

_{2}were calculated as 71,165.2 and 7234.3 respectively.

## 4. Results and Discussion

#### 4.1. Diurnal Load Results

#### 4.2. Nocturnal Load Results

## 5. Discussion and Policy Implications

#### 5.1. Nocturnal Load Results

#### 5.2. The Diesel Alternative

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Disclaimer

## Appendix A

Appliance/Load | Quantity | AC Watts | Hours On per Day | Wh/Day |
---|---|---|---|---|

Coffee maker | 1 | 800 | 0.2 | 160 |

Microwave | 1 | 1300 | 0.15 | 195 |

Iron | 1 | 900 | 0.25 | 225 |

TV | 1 | 130 | 4 | 520 |

Dishwasher | 1 | 1500 | 0.4 | 600 |

Washing machine | 1 | 500 | 0.4 | 200 |

Vacuum cleaner | 1 | 700 | 0.25 | 175 |

Air conditioner (Room) | 1 | 1500 | 10 | 15,000 |

Ceiling fan (AC) | 2 | 50 | 5 | 500 |

Laptop | 1 | 50 | 3 | 150 |

Lights (25 W) | 8 | 25 | 6 | 1200 |

Refrigerator (22 ft^{3}) | 1 | 68 | 24 | 1632 |

Toaster | 1 | 1300 | 0.08 | 104 |

Blender | 1 | 300 | 0.08 | 24 |

Total | 20,685 |

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**Figure 1.**The average load profiles that will be considered for the analysis. Note the diurnal and nocturnal trends.

**Figure 2.**The average monthly temperatures in the city of Riyadh, Saudi Arabia. Note that for the purposes of the model, 8760 temperature data points were used for the year (not shown for brevity). Further, the bars show the maximum and minimum temperatures experienced.

**Figure 3.**The number of cycles of the battery versus the depth-of-discharge (DOD) (DOD = 1ߞstate of charge (SOC)) based on data provided by the manufacturer. Note that the lower the battery discharges, the shorter the lifetime is.

**Table 1.**Review of papers that designed photovoltaic-battery system (PVBs). The cell with ‘Yes’ are highlighted in gray.

Reference | Has the Paper Considered Temperature Effects on Battery Capacity? | Has the Paper Considered Temperature Effects on Lifetime, i.e., Calendar Life and Cyclical Degradation? | Has the Paper Considered Different MSOC Levels for Sizing Optimization? | Has the Paper Tested for Differed Load Profiles? | Was the System Fully Standalone, i.e., No Grid and No Diesel Generation? |
---|---|---|---|---|---|

[39] | Yes | Yes | No | No | No |

[9] | No | No | No | No | Yes |

[10] | Yes | No | No | No | Yes |

[40] | Yes | No | No | Yes | No |

[41] | No | No | No | No | Yes |

[42] | No | No | No | No | No |

[1] | No | No | No | No | No |

[43] | No | Yes | No | No | No |

[20] | No | No | No | No | No |

[21] | No | No | No | No | No |

[44] | No | No | No | No | Yes |

[15] | No | Yes | No | No | Yes |

[14] | No | No | Yes | No | No |

[45] | No | No | No | Yes | No |

This work | Yes | Yes | Yes | Yes | Yes |

Parameter | Value |
---|---|

Discounting rate | 5 percent |

Inflation rate | 2 percent |

System lifetime | 25 years |

Supply shortage | 0 percent |

Parameter | Value |
---|---|

CAPEX (excluding inverter) ($/W) | 1.8 $/W |

Inverter CAPEX | 0.2 $/W |

Module efficiency (%) | 16 percent |

Annual panel degradation (%) | 0.5 percent |

Temperature power loss coefficient (%/C) | 0.4%/°C |

Nominal operating cell temperature | 47 °C |

Maintenance costs ($/kW/year) | 10 $/kW/year |

Derating factor (including inverter losses) (%) | 85 percent |

Panel slope from the horizontal | 25° |

Azimuth degree from the north | 180° |

Solar irradiation | Hourly irradiation data for Riyadh |

Parameter | Value |
---|---|

Battery model | Trojan SIND 061225 (lead acid) |

Battery cost (including installation) | $2205 (300 $/kW h) |

Nominal voltage | 6 V |

Energy rating | 7.35 kW h |

Capacity (current rating) | 1225 Ah |

Bus voltage | 24 V |

Days of autonomy | 2 days |

Allowable throughput | 14,598 kW h (see text for details) |

Degradation limit | 20 percent |

Round trip efficiency | 85 percent |

Temperature effect on capacity | See text for details |

Temperature effect on calendar lifetime | See text for details |

**Table 5.**Optimum size of the PVB minimizing the net present cost (NPC) for a diurnal load profile based on different minimum allowable state of charge (MSOC) constraints. Any slight discrepancies are due to rounding.

Results Incorporating Temperature Effects | |||||||

MSOC (%) | PV Size (kW) | Total Number of Batteries in the Bank | Average Cost of Energy ($/kW h) | Net Present Cost ($) | Initial Capital ($) | Number of Battery Replacements | Total Number of Batteries Used throughout Project Lifetime |

20 | 6.7 | 8 | 0.435 | 69,985 | 31,025 | 3 | 32 |

30 | 8.0 | 8 | 0.453 | 72,898 | 33,566 | 3 | 32 |

40 | 9.9 | 8 | 0.480 | 77,315 | 37,529 | 3 | 32 |

50 | 7.1 | 16 | 0.728 | 117,287 | 49,499 | 2 | 48 |

60 | 9.4 | 20 | 0.908 | 146,165 | 62,913 | 2 | 60 |

70 | 10.8 | 108 * | 4.208 | 677,471 | 259,781 | 2 | 324 |

Results without Incorporating Temperature Effects | |||||||

MSOC (%) | PV Size (kW) | Total Number of Batteries in the Bank | Average Cost of Energy ($/kW h) | Net Present Cost ($) | Initial Capital ($) | Number of Battery Replacements | Total Number of Batteries Used throughout Project Lifetime |

20 | 6.2 | 8 | 0.244 | 39,306 | 29,961 | 1 | 16 |

30 | 6.9 | 8 | 0.254 | 40,928 | 31,421 | 1 | 16 |

40 | 8.5 | 8 | 0.277 | 44,549 | 34,682 | 1 | 16 |

50 | 11.7 | 8 | 0.321 | 51,655 | 41,082 | 1 | 16 |

60 | 6.6 | 20 | 0.488 | 78,637 | 57,225 | 1 | 40 |

70 | 13.9 | 20 | 0.590 | 94,992 | 71,954 | 1 | 40 |

**Table 6.**Optimum size of the PVB minimizing the NPC for a nocturnal load profile based on different SOC constraints. Any slight discrepancies are due to rounding.

Results Incorporating Temperature Effects | |||||||

MSOC (%) | PV Size (kW) | Total Number of Batteries in the Bank | Average Cost of Energy ($/kW h) | Net Present Cost ($) | Initial Capital ($) | Number of Battery Replacements | Total Number of Batteries Used throughout Project Lifetime |

20 | 6.8 | 12 | 0.615 | 99,044 | 40,023 | 3 | 48 |

30 | 7.2 | 12 | 0.622 | 100,192 | 40,880 | 3 | 48 |

40 | 6.9 | 16 | 0.751 | 120,992 | 49,061 | 3 | 64 |

50 | 7.8 | 20 | 0.906 | 145,879 | 59,631 | 3 | 80 |

60 | 10.2 | 28 * | 1.231 | 198,166 | 82,161 | 2 | 84 |

70 | 7.0 | 148 * | 5.653 | 910,114 | 340,321 | 2 | 444 |

Results without Incorporating Temperature Effects | |||||||

MSOC (%) | PV Size (kW) | Total Number of Batteries in the Bank | Average Cost of Energy ($/kW h) | Net Present Cost ($) | Initial Capital ($) | Number of Battery Replacements | Total Number of Batteries Used throughout Project Lifetime |

20 | 8.8 | 8 | 0.281 | 45,188 | 35,258 | 1 | 16 |

30 | 11.1 | 8 | 0.312 | 50,195 | 39,767 | 1 | 16 |

40 | 7.8 | 12 | 0.347 | 55,859 | 42,149 | 1 | 24 |

50 | 7.5 | 16 | 0.422 | 68,011 | 50,374 | 1 | 32 |

60 | 9.4 | 20 | 0.528 | 84,953 | 62,913 | 1 | 40 |

70 | 10.7 | 36 * | 0.864 | 139,118 | 100,818 | 1 | 72 |

Parameter | Value for Independent Generator | Value for Microgrid Generator |
---|---|---|

Capital cost | 0.70 $/W | 0.20 $/W |

Fuel cost | 0.10, 0.50, 1.00, 1.50 $/L | 0.10, 0.50, 1.00, 1.50 $/L |

Lifetime of generator | 2500 h | 15,000 h |

Minimum load ratio | 25 percent | 25 percent |

Maintenance intervals | Every 400 h of operation | Every 400 h of operation |

Maintenance cost | $25 | $400 |

Operation cost | 0.10 $/h of operation | 0.45 $/h of operation |

**Table 8.**Net Present Cost, in millions of dollars, of delivering energy to 1000 homes using individual diesel generators provided for each home, a microgrid powering the whole community, and individual PVB systems.

Scenario | Diesel Price ($/L) | Diesel Consumption Per Year (Million Liters) | Carbon Emissions Per Year (Thousand Tons) | Comments | |||
---|---|---|---|---|---|---|---|

0.10 | 0.50 | 1.00 | 1.50 | ||||

Individual generator for each home | 111 | 133 | 159 | 185 | 3.03 | 7900 | - No grid investment or maintenance costs required - Model run for two generators each with a capacity of 2 kW |

Microgrid powering complete community | 91 | 105 | 122 | 139 | 1.94 | 5100 | - Cost of supplying diesel, maintaining and upgrading grid, and externalities not included - Model chooses two generators with capacities of 1 MW and 1.75 MW to meet the load |

PVB: 30% MSOC with temperature effects incorporated | 99 (maximum) | 0 | - No grid investment or maintenance costs required - Learning curve of battery technology not considered | ||||

PVB: 30% MSOC with temperature effects NOT incorporated | 50 (maximum) |

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## Share and Cite

**MDPI and ACS Style**

Elshurafa, A.M.; Aldubyan, M.H.
State-of-Charge Effects on Standalone Solar-Storage Systems in Hot Climates: A Case Study in Saudi Arabia. *Sustainability* **2019**, *11*, 3471.
https://doi.org/10.3390/su11123471

**AMA Style**

Elshurafa AM, Aldubyan MH.
State-of-Charge Effects on Standalone Solar-Storage Systems in Hot Climates: A Case Study in Saudi Arabia. *Sustainability*. 2019; 11(12):3471.
https://doi.org/10.3390/su11123471

**Chicago/Turabian Style**

Elshurafa, Amro M., and Mohammad H. Aldubyan.
2019. "State-of-Charge Effects on Standalone Solar-Storage Systems in Hot Climates: A Case Study in Saudi Arabia" *Sustainability* 11, no. 12: 3471.
https://doi.org/10.3390/su11123471