## All Solar PV Calculations Under the Sun

Whether you here as a student learning about solar or someone just brushing up their knowledge, here are some of the most used calculation used in the solar industry. We will continue to add to this list so please keep coming back to see what is new. Let’s dive into the primary calculations needed for a simple residential PV design.

## 1. Solar Irradiance Calculation

To figure out how much solar power you’ll receive, you need to calculate solar irradiance. This can be calculated using:

`E = H * r * A`

**Where**:

`E`

= energy (kWh)`H`

= annual average solar radiation (kWh/m²/year)`r`

= PV panel efficiency (%)`A`

= area of PV panel (m²)

For example, a PV panel with an area of 2.3 m², efficiency of 22% and annual average solar radiation of 1700 kWh/m²/year would generate:

`E = 1700 * 0.22 * 2.3 = 860.2 kWh/year`

## 2. Energy Demand Calculation

Knowing the power consumption of your house is crucial. The formula is:

`D = P * t`

**Where**:

`D`

= total energy demand (kWh)`P`

= power of the appliance (kW)`t`

= usage time (hours)

For example, a 0.5 kW refrigerator used for 6 hours would consume:

`D = 0.5 * 6 = 3 kWh`

## 3. PV System Size Calculation

To estimate the size of the PV system required, use:

`S = D / (365 * H * r)`

**Where**:

`S`

= size of PV system (kW)`D`

= total energy demand (kWh)`H`

= average daily solar radiation (kWh/m²/day)`r`

= PV panel efficiency (%)

For a house that consumes 20 kWh per day, with average daily solar radiation of 5 kWh/m²/day and panel efficiency of 22%:

`S = 20 / (365 * 5 * 0.22) = 4.98 kW`

## 4. Structural Calculations

These calculations help understand if the roof can support the PV system’s weight.

`L = W / A`

**Where**:

`L`

= load (kg/m²)`W`

= weight of PV system (kg)`A`

= area of PV system (m²)

If a 7.3 kW PV system weighing 350 kg is spread over 45 m², the load will be:

`L = 350 / 45 = 7.78 kg/m²`

## 5. Electrical Calculations

A crucial calculation involves the current flowing through your PV system, defined by Ohm’s law:

`I = P / V`

**Where**:

`I`

= current (Amperes)`P`

= power (Watts)`V`

= voltage (Volts)

For a 7.3 kW system operating at a voltage of 400 V:

```
I = 7300 / 400 = 18.
25 A
```

## 6. Battery Capacity Calculation

If you’re planning to include a storage system, calculating the battery capacity is essential. This calculation takes into account the average daily consumption and desired autonomy (number of days you want your system to operate when there’s no sun).

`C = D * N / V`

**Where**:

`C`

= Battery capacity (Ah)`D`

= Daily energy demand (kWh)`N`

= Days of autonomy (days)`V`

= Battery voltage (V)

For example, if your daily energy demand is 5 kWh, you want a battery autonomy of 3 days, and you’re using a 48V battery:

`C = (5 * 3) / 48 = 0.3125 Ah`

## 7. Inverter Size Calculation

The inverter converts the DC electricity from the panels (and battery if present) into AC electricity for home use. Its size should be at least as large as the PV array output under peak conditions.

`I = P / V`

**Where**:

`I`

= Inverter size (kVA)`P`

= Peak power from the PV array (kW)`V`

= Voltage (V)

For a system with peak power output of 5 kW and a voltage of 230V:

`I = 5 / 0.230 = 21.74 kVA`

## 8. Cable Size Calculation

Correct cable sizing minimizes energy losses during transmission from the panels to the inverter and battery.

`A = (2 * I * L * K) / V`

**Where**:

`A`

= Cable cross-sectional area (mm²)`I`

= Current (A)`L`

= Cable length (m)`K`

= Allowable voltage drop (expressed as a decimal)`V`

= Voltage drop (V)

For a system with 18.25 A current, 50 m cable length, 3% allowable voltage drop (0.03), and 10 V voltage drop:

`A = (2 * 18.25 * 50 * 0.03) / 10 = 5.475 mm²`

## 9. Return on Investment (ROI) Calculation

While this isn’t an engineering calculation, it’s an essential aspect for homeowners. The ROI helps understand the cost-effectiveness of the PV system:

`ROI = (Savings per year / Initial cost) * 100`

**Where**:

`ROI`

= Return on investment (%)`Savings per year`

= Annual energy savings from the PV system (USD)`Initial cost`

= Total upfront cost of the PV system (USD)

If your PV system saves $800 per year and cost $12,000 to install:

`ROI = (800 / 12000) * 100 = 6.67%`

## 10. Angle of Incidence Calculation

The angle of incidence affects the amount of solar energy received by the PV panel. It’s the angle between the sun’s rays and a line perpendicular to the panel:

`θ = cos^-1((sin δ sin φ) + (cos δ cos φ cos h))`

**Where**:

`θ`

= Angle of incidence (degrees)`δ`

= Solar declination angle (degrees)`φ`

= Latitude of the location (degrees)`h`

= Hour angle (degrees)

Let’s say `δ`

= 23.45° (at the peak of summer), `φ`

= 40° (latitude of New York), and `h`

= -30° (2 hours before solar noon):

`θ = cos^-1((sin 23.45 sin 40) + (cos 23.45 cos 40 cos -30)) = 31.9°`

## 11. Cable Loss Calculation

Cable losses occur due to the resistance in the conductor, reducing the efficiency of the PV system:

`L = I² * R`

**Where**:

`L`

= Cable loss (W)`I`

= Current (A)`R`

= Resistance (Ohms)

For a system with 18.25 A current and 0.1 Ohms resistance:

`L = 18.25² * 0.1 = 33.26 W`

## 12. Number of PV Panels Calculation

To meet your energy demands, you need to calculate the number of solar panels required:

`N = P / (E * r)`

**Where**:

`N`

= Number of panels`P`

= Total power requirement (kW)`E`

= Solar panel rated power (kW)`r`

= Solar panel efficiency (%)

For example, if your home requires a 5 kW system, and you’re using 300 W panels with an efficiency of 22%:

`N = 5 / (0.3 * 0.22) = 75.76`

So, you would need approximately 112 panels.

## 13. Solar Payback Period Calculation

The payback period is the time it takes for the savings from the solar system to equal its cost:

`PB = C / S`

**Where**:

`PB`

= Payback period (years)`C`

= System cost (USD)`S`

= Annual savings (USD)

For a system that costs Rs.1,200,000 and provides annual savings of Rs. 500,000:

`PB = 1200000 / 500000 = 2.4 years`

## 14. Sun Hours Calculation

The number of sun hours affects how long your panels can generate electricity each day:

`SH = I / H`

**Where**:

`SH`

= Sun hours (hours)`I`

= Solar insolation (kWh/m²/day)`H`

= Peak sun hours (hours)

For a location with solar insolation of 5 kWh/m²/day and peak sun hours of 4:

`SH = 5 / 4 = 1.25 hours`

## 15. Grid Electricity Offset Calculation

This calculates how much of your home’s electricity usage can be offset by the solar system:

`O = (E * 365) / D * 100`

**Where**:

`O`

= Grid electricity offset (%)`E`

= Daily energy production from the PV system (kWh)`D`

= Daily energy demand (kWh)

For a system that produces 5 kWh per day and a home that consumes 20 kWh per day:

`O = (5 * 365) / (20 * 365) * 100 = 25%`

## 16. Array Tilt Angle Calculation

Optimizing the tilt angle of your PV array can help maximize solar energy capture:

`β = φ - arctan[(tan δ cos h) / cos(φ - δ)]`

**Where**:

`β`

= Array tilt angle (degrees)`φ`

= Latitude of the location (degrees)`δ`

= Solar declination angle (degrees)`h`

= Hour angle (degrees)

Assuming `φ`

= 40°, `δ`

= 23.45° (at the peak of summer), `h`

= -30° (2 hours before solar noon):

`β = 40 - arctan[(tan 23.45 cos -30) / cos(40 - 23.45)] = 36.3°`

## 17. Fuses and Circuit Breakers Calculation

Choosing the correct fuse or circuit breaker size is critical for safety:

`F = I * 1.25`

**Where**:

`F`

= Fuse/Circuit breaker size (A)`I`

= Current (A)

For a system with a current of 18.25 A:

`F = 18.25 * 1.25 = 22.81 A`

## 18. Shadow Impact Calculation

Shadows can significantly reduce a solar panel’s output. Calculate the impact using:

`SI = (1 - (s / A)) * 100`

**Where**:

`SI`

= Shadow impact (%)`s`

= Shadow area (m²)`A`

= Total panel area (m²)

If a shadow covers 2 m² of a 10 m² panel:

`SI = (1 - (2 / 10)) * 100 = 80%`

## 19. System Lifespan Calculation

The lifespan of a solar system can be approximated using:

`L = E / (P * H * r)`

**Where**:

`L`

= Lifespan (years)`E`

= Energy over lifetime (kWh)`P`

= Peak power (kW)`H`

= Annual solar hours (hours)`r`

= Degradation rate (%)

For a system with a lifetime energy production of 100,000 kWh, peak power of 5 kW, 4 solar hours per day, and a degradation rate of 0.5%:

`L = 100000 / (5 * 4 * 365 * 0.005) = 13.7 years`

## 20. Load Factor Calculation

The load factor indicates how efficiently your PV system operates:

`LF = (E / (P * T)) * 100`

**Where**:

`LF`

= Load factor (%)`E`

= Actual energy output (kWh)`P`

= Rated capacity of PV system (kW)`T`

= Time (hours)

For a system that generates 4000 kWh in a year, with a rated capacity of 5 kW:

`LF = (4000 / (5 * 24 * 365)) * 100 = 9.13%`

## 21. Solar Heat Gain Coefficient (SHGC) Calculation

The SHGC determines how much solar heat gain your house can block:

`SHGC = SC * 0.87`

**Where**:

`SHGC`

= Solar Heat Gain Coefficient`SC`

= Shading Coefficient

For a house with a shading coefficient of 0.5:

`SHGC = 0.5 * 0.87 = 0.435`

## 22. Bypass Diode Calculation

Determining the number of bypass diodes can prevent your panels from overheating:

`D = N / 20`

**Where**:

`D`

= Number of diodes`N`

= Number of cells in a panel

For a panel with 60 cells:

`D = 60 / 20 = 3 diodes`

## 23. Solar Constant Calculation

The solar constant is the amount of solar radiation received outside the Earth’s atmosphere:

`SC = 1361 W/m² (fixed value)`

## 24. Greenhouse Gas (GHG) Emissions Reduction Calculation

Solar energy significantly reduces the GHG emissions that would have been produced by traditional energy sources:

`G = E * F`

**Where**:

`G`

= GHG emissions reduction (kg CO2e)`E`

= Energy produced by the solar system (kWh)`F`

= CO2e factor of the grid (kg CO2e/kWh)

If your solar system produces 5,000 kWh/year and your local grid’s CO2e factor is 0.7 kg CO2e/kWh:

`G = 5000 * 0.7 = 3500 kg CO2e`

## 25. Solar Panel Yield Calculation

Solar panel yield refers to the ratio of energy that a panel can produce compared to its nominal power:

`Y = E / (A * S)`

**Where**:

`Y`

= Solar panel yield`E`

= Energy produced by the panel (kWh)`A`

= Area of the solar panel (m²)`S`

= Solar irradiation (kWh/m²)

If your solar panel (2 m²) produces 500 kWh/year and the solar irradiation is 1000 kWh/m²:

`Y = 500 / (2 * 1000) = 0.25 or 25%`

## 26. Solar Irradiance Calculation

Solar irradiance measures the power per unit area (surface power density):

`I = P / A`

**Where**:

`I`

= Solar irradiance (W/m²)`P`

= Power (W)`A`

= Area (m²)

For a system that generates 1000 W over an area of 10 m²:

`I = 1000 / 10 = 100 W/m²`

## 27. System Efficiency Calculation

The overall efficiency of your solar system can be calculated as follows:

`SE = (OE * IE * BE) * 100`

**Where**:

`SE`

= System efficiency (%)`OE`

= Optical efficiency (%)`IE`

= Inverter efficiency (%)`BE`

= Battery efficiency (%)

If your system has an optical efficiency of 75%, an inverter efficiency of 90%, and a battery efficiency of 85%:

`SE = (0.75 * 0.90 * 0.85) * 100 = 57.375%`

## 28. Battery Bank Size Calculation

It’s important to ensure that your battery bank can handle your system’s energy needs:

`B = (C * H) / V`

**Where**:

`B`

= Battery bank size (Ah)`C`

= Total daily consumption (kWh)`H`

= Autonomy hours (hours)`V`

= Battery voltage (V)

Assuming a daily consumption of 10 kWh, autonomy hours of 48, and a battery voltage of 48 V:

`B = (10 * 48) / 48 = 10 Ah`

## 29. Inverter Size Calculation

The size of your inverter needs to match the peak load and the PV array’s total wattage:

`I = P * 1.25`

**Where**:

`I`

= Inverter size (W)`P`

= Peak load (W)

Assuming a peak load of 4000 W:

`I = 4000 * 1.25 = 5000 W`

## 30. Battery Life Cycle Calculation

Understanding your battery’s life cycle can help in scheduling replacements and maintenance:

`L = N / (D * 365)`

**Where**:

`L`

= Battery life (years)`N`

= Battery life cycle (cycles)`D`

= Number of discharge cycles per day

If your battery has a life cycle of 5000 cycles and discharges twice per day:

`L = 5000 / (2 * 365) = 6.85 years`

## 31. Maximum Power Point (MPP) Calculation

The MPP is the point on an I-V curve where the product of current and voltage is maximum:

`MPP = V * I`

**Where**:

`MPP`

= Maximum power point (W)`V`

= Voltage at MPP (V)`I`

= Current at MPP (A)

For a system with a voltage of 30 V and a current of 8.3 A at MPP:

`MPP = 30 * 8.3 = 249 W`

## 32. Maximum System Voltage Calculation

This is the highest system voltage based on the lowest expected ambient temperature:

`Vmax = Voc * (1 + ((Tmin - 25) * β))`

**Where**:

`Vmax`

= Maximum system voltage (V)`Voc`

= Open-circuit voltage at standard test conditions (STC) (V)`Tmin`

= Lowest expected ambient temperature (°C)`β`

= Temperature coefficient of Voc (1/°C)

If the Voc is 40V, Tmin is -10°C, and β is -0.0035 1/°C:

`Vmax = 40 * (1 + ((-10 - 25) * -0.0035)) = 42.875V`

## 33. Minimum System Voltage Calculation

This is the lowest system voltage based on the highest expected ambient temperature:

`Vmin = Vmp * (1 + ((Tmax - 25) * α))`

**Where**:

`Vmin`

= Minimum system voltage (V)`Vmp`

= Maximum power point voltage at STC (V)`Tmax`

= Highest expected ambient temperature (°C)`α`

= Temperature coefficient of Vmp (1/°C)

If the Vmp is 30V, Tmax is 50°C, and α is -0.003 1/°C:

`Vmin = 30 * (1 + ((50 - 25) * -0.003)) = 22.5V`

## 34. Battery Capacity Calculation

This is the required battery capacity to meet your energy storage needs:

`Bc = (El * Nd) / DOD`

**Where**:

`Bc`

= Battery capacity (Ah)`El`

= Energy load per day (kWh)`Nd`

= Number of autonomy days`DOD`

= Depth of discharge

If the energy load per day is 3kWh, the number of autonomy days is 2, and DOD is 0.5:

`Bc = (3 * 2) / 0.5 = 12Ah`

## 35. Carbon Footprint Reduction Calculation

This is the reduction in carbon footprint as a result of your solar system:

`CFR = E * EG * EF`

**Where**:

`CFR`

= Carbon footprint reduction (kg CO2/year)`E`

= Annual energy production (kWh/year)`EG`

= Emission factor for grid electricity (kg CO2/kWh)`EF`

= Emission factor for solar electricity (kg CO2/kWh)

Assuming your solar system produces 5000 kWh/year, the emission factor for grid electricity is 0.5, and the emission factor for solar electricity is 0.07:

`CFR = 5000 * (0.5 - 0.07) = 2150 kg CO2/year`

## 36. Solar Cell Efficiency Calculation

Solar cell efficiency represents how much of the incoming solar energy is converted into electrical energy:

`E = (Pout / Pin) * 100`

**Where**:

`E`

= Solar cell efficiency (%)`Pout`

= Power output (W)`Pin`

= Incident solar power (W)

If a solar cell produces 150W of power from 1000W of incident solar power:

`E = (150 / 1000) * 100 = 15%`

## 37. Payback Period Calculation

The payback period is the time it takes for the savings generated by the solar system to cover its cost:

`P = C / S`

**Where**:

`P`

= Payback period (years)`C`

= Total cost of the solar system ($)`S`

= Annual savings from the solar system ($)

If the total system cost is $15,000 and annual savings are $1,500:

`P = 15000 / 1500 = 10 years`

## 38. Incident Angle Modifier (IAM) Calculation

The IAM quantifies how well a solar panel can convert off-angle light:

`IAM = cos θ`

**Where**:

`IAM`

= Incident Angle Modifier`θ`

= Angle of incidence (degrees)

If the angle of incidence is 30 degrees:

`IAM = cos 30 = 0.866`

## 39. Energy Payback Time (EPBT) Calculation

The EPBT is the time over which the energy saved equals the energy invested in the system:

`EPBT = Ei / (Ea - Ep)`

**Where**:

`EPBT`

= Energy payback time (years)`Ei`

= Primary energy investment (kWh)`Ea`

= Annual energy production (kWh/year)`Ep`

= Annual primary energy needed for system maintenance (kWh/year)

If the primary energy investment is 50,000 kWh, annual energy production is 5,000 kWh/year, and annual energy for maintenance is 100 kWh/year:

`EPBT = 50000 / (5000 - 100) = 10.64 years`

## 40. Energy Density Calculation

The energy density gives an idea about how much energy can be stored per unit weight in the battery:

`ED = E / W`

**Where**:

`ED`

= Energy density (Wh/kg)`E`

= Total energy stored in the battery (Wh)`W`

= Weight of the battery (kg)

For a battery storing 5000Wh of energy and weighing 50kg:

`ED = 5000 / 50 = 100 Wh/kg`

## 41. Solar Panel Degradation Calculation

Solar panels typically degrade over time, reducing their output:

`DP = P * D * T`

**Where**:

`DP`

= Degraded power output (W)`P`

= Initial power output (W)`D`

= Degradation rate per year (expressed as a fraction of 1)`T`

= Time (years)

If your panel initially produces 250W and degrades at a rate of 0.005 per year, after 10 years:

`DP = 250 * 0.005 * 10 = 12.5W`

## 42. Fuse Rating Calculation

Fuse rating should be 25% higher than the maximum current of the system:

`F = I * 1.25`

**Where**:

`F`

= Fuse rating (A)`I`

= Maximum current (A)

If your system has a maximum current of 20A:

`F = 20 * 1.25 = 25A`

## 43. Cost Per Watt Calculation

The cost per watt is a common way to compare the cost of different solar systems:

`CPW = TC / PC`

**Where**:

`CPW`

= Cost per watt ($/W)`TC`

= Total cost of the solar system ($)`PC`

= Power capacity of the solar system (W)

If your system cost $10,000 and has a power capacity of 5kW (5000W):

`CPW = 10000 / 5000 = $2/W`

## 44. Solar Array Ground Coverage Ratio (GCR) Calculation

The GCR helps to decide how closely to place the solar panel rows to each other:

`GCR = Ap / At`

**Where**:

`GCR`

= Ground coverage ratio`Ap`

= Total area of all solar panels (m²)`At`

= Total area of ground where panels are installed (m²)

If your panels total 200m² and they’re installed over 500m² of land:

`GCR = 200 / 500 = 0.4 or 40%`

## 45. Temperature Coefficient Calculation

The temperature coefficient tells how much the power output decreases for each degree above 25°C:

`ΔP = Pstc * Tc * (Tm - 25)`

**Where**:

`ΔP`

= Power output change (W)`Pstc`

= Power at standard test conditions (W)`Tc`

= Temperature coefficient (%/°C)`Tm`

= Module temperature (°C)

For a panel with Pstc of 300W, a Tc of -0.5%/°C, and Tm of 40°C:

`ΔP = 300 * -0.005 * (40 - 25) = -22.5W`

## 46. Solar Panel Life Span Calculation

The lifespan of a solar panel can be calculated based on the degradation rate:

`Ls = 1 / D`

**Where**:

`Ls`

= Lifespan of the solar panel (years)`D`

= Degradation rate per year

If your solar panel has a degradation rate of 0.005 per year:

`Ls = 1 / 0.005 = 200 years`

## 47. System Loss Calculation

System loss is the energy loss in the system due to factors like inverter inefficiency, cable losses, dust, and shading:

`L = Ein - Eout`

**Where**:

`L`

= System loss (kWh)`Ein`

= Energy into the system (kWh)`Eout`

= Energy out from the system (kWh)

If 6000kWh is input to your system and 5000kWh is output:

`L = 6000 - 5000 = 1000 kWh`

## 48. Solar Insolation Calculation

The amount of solar radiation energy received on a given surface area in a given time is called solar insolation:

`I = E / (A * T)`

**Where**:

`I`

= Solar insolation (W/m²)`E`

= Energy received (W)`A`

= Area (m²)`T`

= Time (hours)

If a solar panel of 1.6m² receives 800W energy in 4 hours:

`I = 800 / (1.6 * 4) = 125 W/m²`

## 49. Bypass Diode Number Calculation

The number of bypass diodes required is typically one for every 15-20 cells in series:

`D = N / 15`

**Where**:

`D`

= Number of bypass diodes`N`

= Number of cells in series

If your panel has 60 cells in series:

`D = 60 / 15 = 4 diodes`

## 50. PV Array Yield Calculation

The PV array yield gives the total energy produced by the array:

`Y = E * H`

**Where**:

`Y`

= PV array yield (kWh/year)`E`

= System efficiency`H`

= Annual sum of global irradiation on the tilted panels (kWh/m²)

For a system with an efficiency of 0.15 and annual irradiation of 1700kWh/m²:

`Y = 0.15 * 1700 = 255 kWh/year`

## 51. Energy Return Factor (ERF) Calculation

The ERF measures the ratio of the energy produced by a system to the energy invested in its production and maintenance:

`ERF = Eout / Ein`

**Where**:

`ERF`

= Energy Return Factor`Eout`

= Total energy output over lifetime (kWh)`Ein`

= Total energy input for production and maintenance (kWh)

If a system produces 50000kWh over its lifetime and requires 10000kWh for production and maintenance:

`ERF = 50000 / 10000 = 5`

Sure, here are a few more calculations:

## 52. Tilt Angle Calculation

The tilt angle is critical for maximizing the amount of sunlight that hits your panels:

```
θ = Latitude - 15° (Winter)
θ = Latitude (Equinox)
θ = Latitude + 15° (Summer)
```

**Where**:

`θ`

= Tilt angle

For instance, if you’re located at a latitude of 40°, your tilt angle will be:

- Winter:
`40 - 15 = 25°`

- Equinox:
`40°`

- Summer:
`40 + 15 = 55°`

## 53. Shading Impact Calculation

The impact of shading on your system’s output can be calculated as follows:

`ShadingLoss = Pn * (1 - ShadingFactor)`

**Where**:

`ShadingLoss`

= Loss in power output due to shading (W)`Pn`

= Nominal power of the PV array (W)`ShadingFactor`

= Fraction of solar irradiance blocked by shading (ranges from 0 to 1)

For instance, if you have a 1000W system and 30% of the sunlight is blocked due to shading:

`ShadingLoss = 1000 * (1 - 0.3) = 700W`

## 54. Inverter Efficiency Calculation

The efficiency of the inverter can be calculated as follows:

`η = Pout / Pin`

**Where**:

`η`

= Efficiency of the inverter`Pout`

= Output power of the inverter (W)`Pin`

= Input power to the inverter (W)

For instance, if your inverter is consuming 1100W to produce 1000W:

`η = 1000 / 1100 = 0.91 or 91%`

## 55. Peak Sun Hours Calculation

Peak sun hours are the equivalent number of hours per day when solar irradiance averages 1000W/m²:

`PSH = SolarInsolation / 1000`

**Where**:

`PSH`

= Peak sun hours`SolarInsolation`

= Solar insolation in a day (Wh/m²)

For instance, if your location gets 5000Wh/m² in a day:

`PSH = 5000 / 1000 = 5 hours`

## 56. Optimal Orientation Calculation

The optimal orientation or azimuth angle for maximizing the PV system output in the northern hemisphere is generally due south (180°). For the southern hemisphere, it’s due north (0°). However, a more accurate calculation could include the following:

`Azimuth Angle = |Longitude - 180|`

**Where**:

- Azimuth Angle is the optimal orientation for the PV panel

For example, if you are located at a longitude of 75° W:

`Azimuth Angle = |75 - 180| = 105°`

## 57. Solar Noon Calculation

Solar noon is the time of day when the sun is highest in the sky. It can be calculated with the following formula:

`Solar Noon = 12:00 PM + (4 * (Standard Meridian - Local Longitude)) / 60 minutes`

**Where**:

- Standard Meridian is the meridian for your local time zone
- Local Longitude is your actual longitudinal coordinate

For instance, if you are located at a longitude of 77° W and the standard meridian for your time zone is 75° W:

```
Solar Noon = 12:00 PM + (4 * (75 - 77)) / 60
= 12:00 PM - 8/60
= 11:52 AM
```

## 58. Solar Heat Gain Coefficient Calculation

Solar heat gain coefficient (SHGC) represents how much solar heat gain a window allows:

`SHGC = Solar Heat Gain / Incident Solar Radiation`

For instance, if your window allows 100W of solar heat gain from 200W of incident solar radiation:

`SHGC = 100 / 200 = 0.5`

## 59. Solar Window Collector Efficiency Calculation

The efficiency of a solar window collector can be calculated as follows:

`η = (Ti - Ta) / (G * A)`

**Where**:

`η`

= Efficiency of the collector`Ti`

= Inlet fluid temperature (°C)`Ta`

= Ambient temperature (°C)`G`

= Solar radiation on the collector (W/m²)`A`

= Surface area of the collector (m²)

For instance, if the inlet temperature is 75°C, ambient temperature is 25°C, solar radiation is 1000 W/m², and the collector area is 2m²:

`η = (75 - 25) / (1000 * 2) = 0.025 or 2.5%`

## Solar PV Calculations Table

Here we compiled this data into a table for you that is easy to copy and paste into your own spreadsheet. **If you do use this data in an online article, while it’s not required, we would appreciate it if you would cite us as a source**.

Calculation | Description | Formula | Variables |
---|---|---|---|

Solar Irradiance |
Measures how much solar power is received per unit area. | E = H * r * A | E = energy (kWh), H = annual average solar radiation (kWh/m²/year), r = PV panel efficiency (%), A = area of PV panel (m²) |

Energy Demand |
Calculates the total energy consumption of an appliance over time. | D = P * t | D = total energy demand (kWh), P = power of the appliance (kW), t = usage time (hours) |

PV System Size |
Determines the capacity of the PV system needed to meet a specific energy demand. | S = D / (365 * H * r) | S = size of PV system (kW), D = total energy demand (kWh), H = average daily solar radiation (kWh/m²/day), r = PV panel efficiency (%) |

Structural Calculations |
Determines the load a structure needs to withstand from a PV system. | L = W / A | L = load (kg/m²), W = weight of PV system (kg), A = area of PV system (m²) |

Electrical Calculations |
Calculates the current based on power and voltage. | I = P / V | I = current (Amperes), P = power (Watts), V = voltage (Volts) |

Battery Capacity |
Determines the capacity of the battery required to support the system for a given number of days. | C = D * N / V | C = Battery capacity (Ah), D = Daily energy demand (kWh), N = Days of autonomy (days), V = Battery voltage (V) |

Inverter Size |
Estimates the size of the inverter needed for a PV system. | I = P / V | I = Inverter size (kVA), P = Peak power from the PV array (kW), V = Voltage (V) |

Cable Size |
Determines the suitable size of the cable for the system, taking into account voltage drop. | A = (2 * I * L * K) / V | A = Cable cross-sectional area (mm²), I = Current (A), L = Cable length (m), K = Allowable voltage drop (expressed as a decimal), V = Voltage drop (V) |

Return on Investment (ROI) |
Determines how quickly the savings from a PV system will cover its initial cost. | ROI = (Savings per year / Initial cost) * 100 | ROI = Return on investment (%), Savings per year = Annual energy savings from the PV system (USD), Initial cost = Total upfront cost of the PV system (USD) |

Angle of Incidence |
Calculates the angle at which sunlight strikes the solar panel. | θ = cos^-1((sin δ sin φ) + (cos δ cos φ cos h)) | θ = Angle of incidence (degrees), δ = Solar declination angle (degrees), φ = Latitude of the location (degrees), h = Hour angle (degrees) |

Cable Loss |
Determines the power lost in the cables due to resistance. | L = I² * R | L = Cable loss (W), I = Current (A), R = Resistance (Ohms) |

Number of PV Panels |
Determines the number of solar panels needed to meet a specific power requirement. | N = P / (E * r) | N = Number of panels, P = Total power requirement (kW), E = Solar panel rated power (kW), r = Solar panel efficiency (%) |

Solar Payback Period |
Estimates the time it takes for a PV system to pay for itself through energy savings. | PP = IC / (E * P) | PP = Payback period (years), IC = Initial cost of the system (USD), E = Energy price (USD/kWh), P = Annual power output of the system (kWh/year) |

Fuse/Circuit Breaker Sizing |
Calculates the size of the fuse or circuit breaker required for the system. | F = I * 1.25 | F = Fuse/Circuit breaker size (A), I = Current (A) |

Shadow Impact |
Measures the percentage of a solar panel’s surface that is obscured by shadows. | SI = (1 – (s / A)) * 100 | SI = Shadow impact (%), s = Shadow area (m²), A = Total panel area (m²) |

System Lifespan |
Estimates the lifespan of the PV system based on its peak power, annual solar hours, and degradation rate. | L = E / (P * H * r) | L = Lifespan (years), E = Energy over lifetime (kWh), P = Peak power (kW), H = Annual solar hours (hours), r = Degradation rate (%) |

Load Factor |
Measures the ratio of the actual output of a PV system to its potential maximum output over a period of time. | LF = (E / (P * T)) * 100 | LF = Load factor (%), E = Actual energy output (kWh), P = Rated capacity of PV system (kW), T = Time (hours) |

Solar Heat Gain Coefficient (SHGC) Calculation |
The SHGC determines how much solar heat gain your house can block. | SHGC = SC * 0.87 | SHGC = Solar Heat Gain Coefficient, SC = Shading Coefficient |

Bypass Diode Calculation |
Determining the number of bypass diodes can prevent your panels from overheating. | D = N / 20 | D = Number of diodes, N = Number of cells in a panel |

Solar Constant Calculation |
The solar constant is the amount of solar radiation received outside the Earth’s atmosphere. | SC = 1361 W/m² (fixed value) | SC = Solar Constant |

Greenhouse Gas (GHG) Emissions Reduction Calculation |
Solar energy significantly reduces the GHG emissions that would have been produced by traditional energy sources. | G = E * F | G = GHG emissions reduction (kg CO2e), E = Energy produced by the solar system (kWh), F = CO2e factor of the grid (kg CO2e/kWh) |

Solar Panel Yield Calculation |
Solar panel yield refers to the ratio of energy that a panel can produce compared to its nominal power. | Y = E / (A * S) | Y = Solar panel yield, E = Energy produced by the panel (kWh), A = Area of the solar panel (m²), S = Solar irradiation (kWh/m²) |

Solar Irradiance Calculation |
Solar irradiance measures the power per unit area (surface power density). | I = P / A | I = Solar irradiance (W/m²), P = Power (W), A = Area (m²) |

System Efficiency Calculation |
The overall efficiency of your solar system can be calculated as follows. | SE = (OE * IE * BE) * 100 | SE = System efficiency (%), OE = Optical efficiency (%), IE = Inverter efficiency (%), BE = Battery efficiency (%) |

Battery Bank Size Calculation |
It’s important to ensure that your battery bank can handle your system’s energy needs. | B = (C * H) / V | B = Battery bank size (Ah), C = Total daily consumption (kWh), H = Autonomy hours (hours), V = Battery voltage (V) |

Inverter Size Calculation |
The size of your inverter needs to match the peak load and the PV array’s total wattage. | I = P * 1.25 | I = Inverter size (W), P = Peak load (W) |

Battery Life Cycle Calculation |
Understanding your battery’s life cycle can help in scheduling replacements and maintenance. | L = N / (D * 365) | L = Battery life (years), N = Battery life cycle (cycles), D = Number of discharge cycles per day |

Maximum Power Point (MPP) Calculation |
The MPP is the point on an I-V curve where the product of current and voltage is maximum. | MPP = V * I | MPP = Maximum power point (W), V = Voltage at MPP (V), I = Current at MPP (A) |

Maximum System Voltage Calculation |
This is the highest system voltage based on the lowest expected ambient temperature. | Vmax = Voc * (1 + ((Tmin – 25) * β)) | Vmax = Maximum system voltage (V), Voc = Open-circuit voltage at standard test conditions (STC) (V), Tmin = Lowest expected ambient temperature (°C), β = Temperature coefficient of Voc (1/°C) |

Minimum System Voltage Calculation |
This is the lowest system voltage based on the highest expected ambient temperature. | Vmin = Vmp * (1 + ((Tmax – 25) * α)) | Vmin = Minimum system voltage (V), Vmp = Maximum power point voltage at STC (V), Tmax = Highest expected ambient temperature (°C), α = Temperature coefficient of Vmp (1/°C) |

Battery Capacity Calculation |
This is the required battery capacity to meet your energy storage needs. | Bc = (El * Nd) / DOD | Bc = Battery capacity (Ah), El = Energy load per day (kWh), Nd = Number of autonomy days, DOD = Depth of discharge |

Carbon Footprint Reduction Calculation |
This is the reduction in carbon footprint as a result of your solar system. | CFR = E * EG * EF | CFR = Carbon footprint reduction (kg CO2/year), E = Annual energy production (kWh/year), EG = Emission factor for grid electricity (kg CO2/kWh), EF = Emission factor for solar electricity (kg CO2/kWh) |

Solar Cell Efficiency Calculation |
Solar cell efficiency represents how much of the incoming solar energy is converted into electrical energy. | E = (Pout / Pin) * 100 | E = Solar cell efficiency (%), Pout = Power output (W), Pin = Incident solar power (W) |

Payback Period Calculation |
The payback period is the time it takes for the savings generated by the solar system to cover its cost. | P = C / S | P = Payback period (years), C = Total cost of the solar system ($), S = Annual savings from the solar system ($) |

Incident Angle Modifier (IAM) Calculation |
The IAM quantifies how well a solar panel can convert off-angle light. | IAM = cos θ | IAM = Incident Angle Modifier, θ = Angle of incidence (degrees) |

Energy Payback Time (EPBT) Calculation |
The EPBT is the time over which the energy saved equals the energy invested in the system. | EPBT = Ei / (Ea – Ep) | EPBT = Energy payback time (years), Ei = Primary energy investment (kWh), Ea = Annual energy production (kWh/year), Ep = Annual primary energy needed for system maintenance (kWh/year) |

Energy Density Calculation |
The energy density gives an idea about how much energy can be stored per unit weight in the battery. | ED = E / W | ED = Energy density (Wh/kg), E = Total energy stored in the battery (Wh), W = Weight of the battery (kg) |

Solar Panel Degradation Calculation |
Solar panels typically degrade over time, reducing their output. | DP = P * D * T | DP = Degraded power output (W), P = Initial power output (W), D = Degradation rate per year, T = Time (years) |

Fuse Rating Calculation |
Fuse rating should be 25% higher than the maximum current of the system. | F = I * 1.25 | F = Fuse rating (A), I = Maximum current (A) |

Cost Per Watt Calculation |
The cost per watt is a common way to compare the cost of different solar systems. | CPW = TC / PC | CPW = Cost per watt ($/W), TC = Total cost of the solar system ($), PC = Power capacity of the solar system (W) |

Solar Array Ground Coverage Ratio (GCR) Calculation |
The GCR helps to decide how closely to place the solar panel rows to each other. | GCR = Ap / At | GCR = Ground coverage ratio, Ap = Total area of all solar panels (m²), At = Total area of ground where panels are installed (m²) |

Temperature Coefficient Calculation |
The temperature coefficient tells how much the power output decreases for each degree above 25°C. | ΔP = Pstc * Tc * (Tm – 25) | ΔP = Power output change (W), Pstc = Power at standard test conditions (W), Tc = Temperature coefficient (%/°C), Tm = Module temperature (°C) |

Solar Panel Life Span Calculation |
The lifespan of a solar panel can be calculated based on the degradation rate. | Ls = 1 / D | Ls = Lifespan of the solar panel (years), D = Degradation rate per year |

System Loss Calculation |
System loss is the energy loss in the system due to factors like inverter inefficiency, cable losses, dust, and shading. | L = Ein – Eout | L = System loss (kWh), Ein = Energy into the system (kWh), Eout = Energy out from the system (kWh) |

Solar Insolation Calculation |
The amount of solar radiation energy received on a given surface area in a given time is called solar insolation. | I = E / (A * T) | I = Solar insolation (W/m²), E = Energy received (W), A = Area (m²), T = Time (hours) |

Bypass Diode Number Calculation |
The number of bypass diodes required is typically one for every 15-20 cells in series. | D = N / 15 | D = Number of bypass diodes, N = Number of cells in series |

PV Array Yield Calculation |
The PV array yield gives the total energy produced by the array. | Y = E * H | Y = PV array yield (kWh/year), E = System efficiency, H = Annual sum of global irradiation on the tilted panels (kWh/m²) |

Energy Return Factor (ERF) Calculation |
The ERF measures the ratio of the energy produced by a system to the energy invested in its production and maintenance. | ERF = Eout / Ein | ERF = Energy Return Factor, Eout = Total energy output over lifetime (kWh), Ein = Total energy input for production and maintenance (kWh) |

Tilt Angle Calculation |
The tilt angle is critical for maximizing the amount of sunlight that hits your panels. | θ = Latitude – 15° (Winter), θ = Latitude (Equinox), θ = Latitude + 15° (Summer) | θ = Tilt angle |

Shading Impact Calculation |
The impact of shading on your system’s output can be calculated. | ShadingLoss = Pn * (1 – ShadingFactor) | ShadingLoss = Loss in power output due to shading (W), Pn = Nominal power of the PV array (W), ShadingFactor = Fraction of solar irradiance blocked by shading |

Inverter Efficiency Calculation |
The efficiency of the inverter can be calculated. | η = Pout / Pin | η = Efficiency of the inverter, Pout = Output power of the inverter (W), Pin = Input power to the inverter (W) |

Peak Sun Hours Calculation |
Peak sun hours are the equivalent number of hours per day when solar irradiance averages 1000W/m². | PSH = SolarInsolation / 1000 | PSH = Peak sun hours, SolarInsolation = Solar insolation in a day (Wh/m²) |

Optimal Orientation Calculation |
The optimal orientation for maximizing the PV system output is generally due south (180°) for the northern hemisphere and due north (0°) for the southern hemisphere. | Azimuth Angle = | Longitude – 180 |

Solar Noon Calculation |
Solar noon is the time of day when the sun is highest in the sky. | Solar Noon = 12:00 PM + (4 * (Standard Meridian – Local Longitude)) / 60 minutes | Standard Meridian is the meridian for your local time zone, Local Longitude is your actual longitudinal coordinate |

Solar Heat Gain Coefficient Calculation |
Solar heat gain coefficient (SHGC) represents how much solar heat gain a window allows. | SHGC = Solar Heat Gain / Incident Solar Radiation | – |

Solar Window Collector Efficiency Calculation |
The efficiency of a solar window collector can be calculated. | η = (Ti – Ta) / (G * A) | η = Efficiency of the collector, Ti = Inlet fluid temperature (°C), Ta = Ambient temperature (°C), G = Solar radiation on the collector (W/m²), A = Surface area of the collector (m²) |