Calculation of solar panel output

📐 The Foundational Solar Output Equation

A widely used formula to estimate the energy output of a photovoltaic (PV) system is the following [1]:$$E=A\times r\times H\times PR$$

However, to better integrate your specific variables, we can expand this into a more detailed form, commonly used for system sizing and implemented in recognized models like NREL’s PVWatts [4]:$$P_{pv}=H_{tilt}\times P_{stc}\times f_{temp}\times f_{other}$$​

Let’s define each term in this expanded equation [4, 8]:

• PpvPpv​ : The total energy output (in kWh) over a given period (e.g., daily, monthly, or annually) or the power output (in W) [4].
• PstcPstc​ : The total rated power of your solar array (in kWdc) under Standard Test Conditions (STC: irradiance of 1000 W/m², cell temperature of 25°C) [1, 4]. This is the “size” of your system.
• HtiltHtilt​ : The daily, monthly, or annual solar irradiation (in kWh/m²) on the plane of your solar array (Plane of Array or POA). This is where latitude and panel angle are used to calculate the sunlight your specific setup receives [5, 7].
• ftempftemp​ : The temperature derating factor (a decimal between 0 and 1). This accounts for the loss in efficiency as the solar panel’s cell temperature rises above 25°C [1, 2, 8].
• fotherfother​ : A combined factor for all other system losses (a decimal between 0 and 1). This includes soiling (dust), shading, wiring losses, inverter efficiency, and more [1, 4].

🔍 Breaking Down the Key Components

To make this equation work, you need to determine the specific values for $H_{tilt}$Htilt​ and $f_{temp}$ftemp​.

1. Irradiation on a Tilted Surface ($H_{tilt}$Htilt​)

This is the most complex part, as it combines your location (latitude) and panel angle. The annual optimal fixed tilt angle for a location is often approximated by its latitude [5]. However, for maximum accuracy, a more nuanced approach is needed.

• Fixed Tilt Angle: The “golden rule” is to set the tilt angle equal to your latitude. For example, at a latitude of 35°N, panels are often installed with a 35° tilt [5].
• Calculating HtiltHtilt​: Manually calculating the irradiation on a tilted plane is complex. It requires splitting horizontal solar radiation data into its direct and diffuse components and then transposing them to the tilted plane [7]. For this reason, professionals use tools like the European Commission’s PVGIS (Photovoltaic Geographical Information System) [3] or NREL’s PVWatts in the United States [4]. By inputting your location (latitude/longitude), panel tilt, and orientation (azimuth), these tools provide an accurate value for $H_{tilt}$Htilt​. More recent approaches even use machine learning to improve the accuracy of these estimates compared to traditional isotropic models [7].

2. The Temperature Derating Factor ($f_{temp}$ftemp​)

Solar panels operate less efficiently as they get hot. This factor corrects for this effect [1, 2]. The formula, implemented in models like PVWatts, is as follows [4, 8]:$$f_{temp}=1+[\gamma \times (T_{cell}-T_{stc})]$$

• γγ : The power temperature coefficient provided by the manufacturer. For crystalline silicon, it is typically expressed in %/°C and is negative [6, 10].
• TcellTcell​ : The estimated operating cell temperature (°C). More sophisticated models also account for wind speed and irradiance [1, 9].
• TstcTstc​ : The cell temperature at standard test conditions (STC), which is always 25°C [4].

For example, according to industry data, for a module with $\gamma =-0.4\mathrm{\%}\mathrm{/}\mathrm{°}C$γ=−0.4%/°C, $T_{cell}=65\mathrm{°}C$Tcell​=65°C, and $T_{stc}=25\mathrm{°}C$Tstc​=25°C, the power loss is significant [6]. The calculation is:$$f_{temp}=1+[-0.004\times (65-25)]=1+(-0.16)=0.84$$

This means the panel is operating at only 84% of its rated power due to the high temperature.

Typical Temperature Coefficient ($\gamma$γ) Values

The table below presents typical values for different panel technologies, based on research and industry data [2, 6, 10]:

Panel Technology	Typical Temperature Coefficient ($\gamma$γ)	Notes
Monocrystalline Silicon (Older BSF)	-0.45% to -0.50% /°C	Older technology with higher temperature losses [6].
Monocrystalline Silicon (Modern PERC)	-0.35% to -0.40% /°C	Common technology with improved performance [6].
Monocrystalline Silicon (N-type TOPCon)	-0.29% to -0.35% /°C	Advanced technology with a very good coefficient [6].
Monocrystalline Silicon (HJT – Heterojunction)	-0.25% to -0.30% /°C	Premium technology with the best coefficient [6].
Polycrystalline Silicon	-0.40% to -0.50% /°C	Older technology, generally higher coefficient [6].
Thin-Film (CdTe)	-0.24% to -0.25% /°C	Very good performance in heat [6].
Field-Aged Modules	-0.5% /°C (for ηm)	Measurements on aged modules confirm these orders of magnitude [2].

3. Other Derating Factors ($f_{other}$fother​)

This is a catch-all for real-world inefficiencies. A typical value for a well-designed system might be around 0.75 to 0.85 [1]. You can calculate it by multiplying individual factors together [4].

💡 A Practical Example

Let’s combine these for a simplified annual estimate for a 1 kWdc system using the PVWatts formula [4, 8].

1. Array Power (PstcPstc​): 1 kWdc
2. Tilted Irradiation (HtiltHtilt​): Let’s assume you’ve used an online tool like PVGIS [3] for your specific latitude and chosen tilt. The tool outputs an annual HtiltHtilt​ of 1700 kWh/m².
3. Temperature Factor (ftempftemp​): Based on your local climate and panel specifications (e.g., $\gamma =-0.4\mathrm{\%}\mathrm{/}\mathrm{°}C$γ=−0.4%/°C [6]), you calculate an average annual $f_{temp}$ftemp​ of 0.90.
4. Other Losses (fotherfother​): You estimate a combined factor of 0.80 for inverter losses, soiling, wiring, etc. [1, 4].

Your estimated annual energy output ($P_{pv}$Ppv​) would be [4]:$$P_{pv}=1\text{ kWdc}\times 1700\text{ kWh/m²}\times 0.90\times 0.80=1224\text{ kWh}$$Ppv​=1 kWdc×1700 kWh/m²×0.90×0.80=1224 kWh

This means your 1 kWdc system is expected to generate about 1224 kWh of electricity per year under these conditions.

🧠 Recommendations for the Most Accurate Results

• Use Professional Tools: For the most reliable $H_{tilt}$Htilt​ values, I strongly recommend using established tools like PVGIS [3] or PVWatts [4]. They handle the complex geometry of sun position and radiation conversion for you [7].
• Consult the Datasheet: The most accurate value for the temperature coefficient ($\gamma$γ) will always come from the manufacturer’s datasheet for the specific solar panel model you are using [6, 10]. Look for “Temperature Coefficient of Pmax” or “Power Temperature Coefficient”.
• Gather Quality Input Data: The accuracy of your equation depends on your inputs. Use site-specific data for average temperatures and the exact technical details of your panels [1, 2, 9].

I hope this detailed analysis helps you develop a robust model for your solar energy calculations.

📚 Reference List

[1] MDPI (2022). Implicit Equation for Photovoltaic Module Temperature and Efficiency via Heat Transfer Computational Model. MDPI

[2] NIH (2023). Table 3: Average temperature coefficients of the 3 field-aged PV modules. Heliyon

[3] Scilit (undated). PV-GIS: a web-based solar radiation database for the calculation of PV potential in Europe. Scilit

[4] NREL (2013). PVWatts Version 1 Technical Reference. National Renewable Energy Laboratory (NREL)

[5] Hugging Face (undated). Fiacre/PV-system-expert-500 · Datasets. Hugging Face

[6] Tongwei (2025). Mono Silicon Solar Panel Efficiency丨Temperature Coefficient, Low Light Performance, Attenuation Rate. Tongwei Co., Ltd.

[7] Energy Conversion and Management (2024). A universal tool for estimating monthly solar radiation on tilted surfaces from horizontal measurements: A machine learning approach. Energy Conversion and Management

[8] pvlib-python Documentation (undated). pvlib.pvsystem.pvwatts_dc. Read the Docs

[9] UNT Digital Library (1981). Analytical and experimental system studies of combined photovoltaic/thermal systems. Technical status report No. 12. University of North Texas

[10] IEEE (1997). Temperature coefficients for PV modules and arrays: measurement methods, difficulties, and results. Conference Record of the Twenty-Sixth IEEE Photovoltaic Specialists Conference