4. Determining the Size of the Solar Array and Designing the System
Designing a photovoltaic (PV) system involves careful planning and equipment selection based on factors such as location, solar radiation, and energy storage needs. In off-grid regions of Sudan, all electricity must be produced and stored locally to ensure a stable supply, especially during the night or cloudy periods. Therefore, the system must be sized to handle maximum demand during times of minimal solar generation. Proper system sizing establishes the required voltage and current ratings for each component, accounting for installation and operational costs [
21].
Key Factors Influencing System Sizing:
Load Profile: Determined by listing all household appliances and their daily usage in watt-hours.
Panel Positioning: Affects tilt angle, orientation, and daily solar exposure.
Home Design: Optimizing sunlight exposure by clearing the southern side, orienting windows southward, and using good insulation reduces energy loss.
Energy Efficiency: Using low-consumption appliances such as CFLs helps minimize energy needs. Cooking and water heating can be handled separately using gas or thermal systems.
Appliance Type: Choosing low-voltage DC appliances reduces system cost and minimizes the need for high-rated inverters.
Startup Loads: High-surge appliances like refrigerators and pumps require special consideration due to their high initial current draw [
22].
Solar Array Dimensioning
Calculate the average number of hours in the sun each day (Tmin) and the amount of energy used each day in Watt-hours (E) before designing the array. To determine losses and acquire the necessary energy, to avoid under-sizing, divide the total daily power consumption in watt-hours by the product of all individual efficiencies within the system .
Divide the preceding value by the mean number calculate the maximum available power by multiplying the number of sunlight hours per day for the geographical region by Tmin.[
5].
To find the total required current, simply divide the maximum power by the system's DC voltage.
To get the required voltage and current, units should be linked in series and parallel as needed. Use the formula: Divide the total DC voltage of the system by the rated voltage (Vr) of each individual module to calculate the number of series modules.
Ultimately, the sum of the series and parallel modules equals the overall number of modules,
The PV module chosen in this study is Monocrystalline photovoltaic solar panel Longi LNGLR4-72HPH-455M, 144 cells, 455 W455M. It has 144 cells (6x24) monocrystalline type and provides an upper limit of 455 watts for the power output monocrystalline panel is a high one of approx. 20.9%, with very little energy loss. LNGLR4-72HPH-455M has a very big advantage compared to other photovoltaic panels, and this consists in the fact that it minimizes the impact of microcracks, showing a high tolerance to shading. The innovative technology offers superior performance and low radiation both mornings, evenings, and overcast days [
6,
7].
The panel is 209.4 cm x 103.8 cm x 3.5 cm, Also, the panel helps to increase energy production, increasing the general effectiveness of the PV system. The load borne for the snow is quite important, namely 5400 Pa (on the front of the panel), and the wind load is up to 2400 Pa (behind the panel). The degree of protection is guaranteed by the IP 68 standard, the panel being resistant to adverse weather conditions, such as water and dust. The frame of the panel is made of anodized aluminum, and the surface of 3.2 mm tempered glass. The dimensions are: 209.4 x 103.8 x 3.5 cm,
Figure 5.
Current- Voltage Curve.
Figure 5.
Current- Voltage Curve.
Figure 6.
Current- Voltage Curve.
Figure 6.
Current- Voltage Curve.
A Current-Voltage (I-V) curve is a graphical representation of the relationship between the current passing through panel and the voltage applied across it. Figure depicts a specific I-V curve relevant to a system [
23].
Figure depicts the Current-Voltage (I-V) curve of a solar cell. This curve is crucial in understanding the behavior and performance of solar cells under different operating conditions. Error! Reference source not found. Represent the Electrical and mechanical characteristics of the panel [
7].
Table 6.
Electrical and mechanical characteristics.
Table 6.
Electrical and mechanical characteristics.
| Testing Condition |
STC |
NOCT |
| Power greatest (Pmax/W) |
455 |
339.8 |
| Voltage on an open circuit (Voc/V) |
48.5 |
46.4 |
| Current on a short circuit (Isc/A) |
12.66 |
9.43 |
| The highest possible voltage (Vmp/V) |
42.7 |
38.8 |
| current (Imp/A) at highest power |
11.92 |
8.75 |
| Efficiency of the module (%) |
20.9 |
Standard Test and Operating Conditions:
Under Standard Test Conditions (STC), the panel operates at an irradiance of 1000 W/m², with a cell temperature of 25°C, and solar spectrum measured at AM1.5. Under Normal Operating Cell Temperature (NOCT), irradiance is 800 W/m², ambient temperature is 20°C, and the spectrum remains at AM1.5, with a wind speed of 1 m/s.
Panel Construction and Cable Specifications:
The module features a 4 mm² output cable, 1400 mm in length. Its frame is built from anodized aluminum alloy, while the front surface is made of 3.2 mm tempered glass. The panel operates within a temperature range of -40°C to +85°C and weighs 23.5 kg.
Panel Quantity and Cost:
Using the Longi LR4-72HPH-455M model (455W, 144 cells), each building requires 8 panels. For 33 buildings (30 houses, a clinic, a supermarket, and public lighting), the total number of panels is 264. At a cost of 100 USD per panel, the total investment in PV panels is approximately 26,000 USD.
Battery Bank Sizing:
The required battery storage capacity is calculated by multiplying the total daily energy consumption by the number of autonomy days (days without solar production). The result is then divided by the maximum allowable depth of discharge to ensure safe and efficient battery operation.
To determine the nominal voltage (Vb) of each battery to be used in the battery bank, we need to decide based on the required safe energy storage. This can be achieved by dividing the necessary safe energy storage by the DC voltage of one of the chosen batteries, resulting in the required capacity of the battery bank in ampere-hours (C)[
9]
Once the capacity of the battery bank has been determined, the capacity (Cb) of each individual battery within the bank needs to be established. Based on the battery voltage rating and system requirements, the battery bank is constructed by connecting batteries in both series and parallel configurations [
24]. To calculate the total number of batteries required, the capacity of the battery bank (C) in ampere-hours is divided by the capacity of one of the selected batteries (
):
At that point, it is simple to ascertain the battery bank's arrangement[
10]. The rating of the voltage of one selected battery is subtracted by the system's DC voltage to obtain the number of batteries
linked in series:
The number of parallel paths Np is then calculated by dividing the total number of batteries by the number of batteries connected in sequence [
11].
We will move on to the next system component as soon as the bank's battery size is known.
According to the system the battery size is approximative 80000 /12V = 6600Ah. In this system we can use 100Ah. Number of batteries = 66 batteries.
Lithium Battery 12V, 100Ah Storage Box Case Organizer Apply for Energy Solar, off grid, RV, etc.[
12]. One battery cost
$75, making the total cost of the purchase
$5000.
Sizing of the Voltage Regulator
Its job is to control the flow of current. The highest current of the arrays and the maximum current of the load must both be tolerated by an effective voltage regulator. [
13]. A safety factor
can be used to double the short circuit current of the parallel modules. The rated current I of the voltage controller is the outcome:
where Np is the number of parallel modules, Isc is the short-circuit current of an individual module, and
is the safety factor The safety factor is utilized to guarantee that the regulator can handle the highest current produced by the array, which could surpass the calculated amount. It also allows for the addition of new equipment or a larger load current than originally anticipated. This safety factor essentially permits a little system growth [
25].
Sizing of the Inverter
Figuring out how much power the appliances that will be operating simultaneously actually need is a crucial first step in sizing the inverter [
14]. Secondly, we must double the power of big motors by three to account for their beginning current. The two preceding numbers are then added together and multiplied by 1.25 as a safety precaution to allow for system growth[
15]
Based on the load, a Solar Hybrid Inverter with an output power of 800W in each building is deemed suitable. The cost of each inverter is 100USD which included 33 inverters costing $3300 USD in total. The technical specification of the inverter as shown in Error! Reference source not found.
Table 7.
Technical specification Solar Hybrid Inverter.
Table 7.
Technical specification Solar Hybrid Inverter.
| Nature of Source Flow: |
Active Inverter |
| Model No. |
VG1012 |
| Key Features |
Energy-saving Solar Inverter and Hybrid Inverter |
| Application |
Residential Solar Power Systems |
| Circuit Topology |
Full-Bridge Type |
| Rated Power |
800W |
| Voltage |
220VAC |
| Frequency |
50/60Hz |
| Output Voltage Regulation |
±10% |
| Efficiency |
>98% |
| Input/output Protection |
Circuit Breaker |
| Low-Level Disconnect (Selectable) |
20V or 21V |
| PWM Controller Voltage |
30VDC−60VDC
|
| Max PV Open Circuit Voltage |
PWM: 60VDC, MPPT: 150VDC
|
| Max Solar Charge Current |
60A |
| Protections |
Overload, Over Temperature, Overcharging, Low Battery, Battery Reverse Connection, High AC Voltage, etc. |
| LCD Indicator Status |
AC Input Voltage, AC Input Frequency, PV Voltage, PV Current, Output Voltage, Output Frequency, etc. |
| LED Indicator Status |
AC Line In: Green/Inverter: Green/Charging: Yellow/Alarm: Red |
| Temperature |
0-40ºC |
| Humidity |
−10ºC~90ºC Noncondensing |
| Packing Size (LWH) |
470335210mm |
Error! Reference source not found. outlines the technical specifications of the Solar Hybrid Inverter (Model No. VG1012), featuring key attributes such as rated power, voltage, frequency, efficiency, input/output protection, and various alarm indicators.
Diesel Generator Group
The same life cycle cost analysis is used to determine the cost of 80 kWh generated considering the following remarks:
- It is necessary to use five separate diesel units, one as reserve, which will increase the kWh cost of diesel [
16]. At the same time, due to the minimum practical size for small loads, diesel generators are often oversized, as in our case. Due to oversizing, the diesel generator runs with low utilization, which in addition to the frequent need for spare parts and overhauls leads to an increase in maintenance and repair costs [
26].
The five diesel it consists of 2 x 5 kW+3x20kW= 70kW
5kW diesel generator
Soundproof single-phase diesel generator 5kW, 18A, 3000rpm, engine YD186FAG, Stager YDE7000TD.
20kW diesel generator
Table 8.
Technical specification of 20 kW diesel generator.
Table 8.
Technical specification of 20 kW diesel generator.
| Nominal power |
20kVA |
Dimensions (LxWxH) |
1890*910*1160 mm |
| Maximum power |
22kVA |
Net weight |
830 kg |
| Nominal voltage |
(AC) 230V |
Starting system |
12V Electric |
| Power factor (cos Φ) |
1 |
Compression ratio |
18.2:1 |
| Rated current |
86.9 A |
Cylinder capacity |
2.672 L |
| Nominal frequency |
50 Hz |
Oil bath capacity |
7.6 L |
| Tank capacity |
92 L |
Insulation grade |
H |
| Noise level (LWA) |
93 dB(A) |
Product code |
1158000022S |
Error! Reference source not found. The technical specifications of the 20-kW diesel generator, priced at
$10000 USD per unit, detail its rated power and fuel type as diesel. When considering the total cost for five generators, including the cost of diesel, the sum amounts to
$34000 USD [
27].
System Components Summary
The equipment needed to construct the standalone photovoltaic system for the hypothetical distant home mentioned above is included in Error! Reference source not found. together with certain specs and details. This is not the only equipment’s on the market, and there are many manufacturers who sell them.
Table 9.
Summary of the System Components.
Table 9.
Summary of the System Components.
| Component |
Model |
Component Rating |
Size (inch) |
Unit Price USD |
Total Price |
Warranty |
| W/Ah |
A |
V |
| Panels |
Longi LNGLR4-72HPH-455M |
455 /339W |
10.92/8.75 |
41.7/38.8 |
209.4 x 103.8 x 3.5 cm |
100 |
26000 |
25 |
| Batteries |
Lithium Battery |
100 Ah |
~ |
12 |
3.3x1.7x2.2 |
75 |
5000 |
2 |
| Inverter |
VG1012 |
800W |
~ |
24/220 |
4.7x3.35x2.1 |
100 |
3300 |
5 |
| Wires |
#02 AWG |
|
|
|
Diameter= 6.54 mm, Area= 32.0 mm2
|
50 |
100 |
|
| #10 AWG |
|
|
|
Diameter= 2.59 mm, Area= 5.27 mm2
|
50 |
100 |
|
| Diesel |
Stager |
5000 |
18 |
230 |
9.50 x 5.50 x 7.65 |
2000 |
4000 |
2 |
| Diesel |
Stager |
20000 |
86.9 |
230 |
18.9x9.1x11.6 |
10000 |
30000 |
2 |
This means that equipment ratings and prices will differ. However, to achieve optimal performance, equipment ratings, quality, and prices are used to select this equipment.
Cost estimate of the system
The equipment used in the system costs a total of 34300USD PV and 34000 USD diesel. Additional costs must be added for design, labor, wiring, metering, monitoring, disconnect devices, and shipment, this additional expense is estimated to cost 4000USD on diesel.