Hardware integration of solar panel power.

In this article we will try to analyze real power panel set up and power transfer in to battery storage.

The average power delivered by the solar panel is:

Solar Panel Specifications:

• Number of Cells/pannels: 3 in series
  
• Maximum Power (Pmax) per Cell: 7.5 W
• Total Maximum Power (Pmax): $7.5\text{W}\times 3=22.5\text{W}$
• Max Voltage (Vmpp) per Cell: 1.60 V
• Total Max Voltage (Vmpp): $1.60\text{V}\times 3=4.80\text{V}$
• Max Current (Impp) per Cell: 3.875 A (current remains the same in series). Observed 4.5A when doing real test on short circuit.
  
• Open Circuit Voltage (Voc) per Cell: 2.05 V
• Total Open Circuit Voltage (Voc): $2.05\text{V}\times 3=6.15\text{V}$ (matches our real measurements)
• Short Circuit Current (Isc) per Cell: 5.397 A
• Cell Size: 14" L x 10" W = 0.0903 m² per cell
• Total Panel Area: $0.0903\text{m²}\times 3=0.2709\text{m²}$

Battery Specifications:

• Capacity: 12 Ah (3 x4Ah in parallel)
  
• Nominal Voltage: 3.7 V, Max Voltage 4.2V
  
• Fully discharged initially , then charged until disconnected at 11:30 AM .Location and Date:

• Location: Salt Lake City, Utah, USA
• Date: February 28
• Latitude: ~40.76° N
• Day of Year: February 28 is the 59th day of the year (non-leap year).

We will calculate the theoretical power output by using this calculator.

Step 2.1: Solar Declination Angle (δ)

The solar declination angle for February 28 is:$$\delta =-8.49^{\circ }$$

The daylight duration is approximately: $$10.8\text{hours}$$

Solar Elevation Angle (α)

At solar noon (12:00 PM), the solar elevation angle is: $$\alpha \approx 40.75^{\circ }$$

Effective Irradiance

Using the cosine of the angle of incidence ($\cos \theta$):

$$\cos \theta \approx 0.91$$

The effective irradiance is:

$$G_{\text{effective}}=G_0\cdot \tau \cdot \cos \theta$$

Where:

• $G_0=1361\text{W/m²}$,
• $\tau \approx 0.7$ (atmospheric transmittance).

$$G_{\text{effective}}=1361\cdot 0.7\cdot 0.91\approx 876\text{W/m²}$$

Theoretical Power Output

$$P_{\text{theoretical}}=G_{\text{effective}}\cdot A\cdot \eta$$

Where:  $A=0.2709\text{m²}$ (total panel area),

$$P_{\text{theoretical}}=876\cdot 0.2709\cdot 0.0605\approx 14.3\text{W}$$

The lithium-ion battery consists of three

4.2 V, 4 Ah cells connected in parallel :

• Nominal Voltage: $4.2\text{V}$ (fully charged voltage)
• Capacity: $12\text{Ah}$ (since the cells are connected in parallel, their capacities add up).

From our experiment:

• The battery was fully charged by 11:30 AM .
• Assuming sunrise occurred around 7:00 AM , the total charging time was approximately 4.5 hours .

we confirmed energy stored in the battery pack by discharging in computerized discharge station, which confirmed 43.7Wh or 12Ah stored energy:

Average Power Delivered:

So, the real power output of the solar panel during charging was approximately 9.7 W .

This can be derived from the following:

The lithium-ion battery consists of 4.2 V, 4 Ah cells connected in parallel :

• Nominal Voltage: $4.2\text{V}$ (fully charged voltage)
• Capacity: $12\text{Ah}$ (since the cells are connected in parallel, their capacities add up).

The total energy stored in the battery is:

$$E_{\text{battery}}=$$$$\text{43.7Wh in reality after measurement and that is within 4.5hours.}$$

Comparison theory and experimental.

• Theoretical Power Output: $14.3\text{W}$
• Real Power Output: $9.7\text{W}$

The real power output is slightly lower than the theoretical value. This discrepancy could be explained by:

1. System Losses: Wiring resistance, mosfet losses in BMS, or inefficiencies in the battery charging process.
2. Suboptimal Operating Conditions: The panel may not have been operating at its maximum power point (MPP) due to varying sunlight or temperature effects.
3. Partial Shading or Dirt: Any shading or dirt on the panel would reduce its output.

Salt Lake City in late February often has clear skies, but other factors like snow reflection or haze could influence the results:

• If snow reflection increased the effective irradiance (e.g., albedo of 0.8), the theoretical power output could increase:$$G_{\text{effective}}=876+(1361\cdot 0.7\cdot 0.8)\approx 1637\text{W/m²}$$$$P_{\text{theoretical}}=1637\cdot 0.2709\cdot 0.0605\approx 27.1\text{W}$$

That day there was no snow and reflection may not have played a significant role.

Conclusion

Our experimental setup aligns reasonably well with the theoretical model:

• The real power output ($9.7\text{W}$) is slightly lower than the theoretical power output ($14.3\text{W}$), likely due to system losses or suboptimal conditions. Our calculator describes accurately all factors which plays significant role in solar generation.