Calculation of solar panel output | 国际电能质量论坛

📐 The Foundational Solar Output Equation

A widely used formula to estimate the energy output of a photovoltaic (光伏) system is the following [1]: $它 = 一 \times r \times Ĥ \times P ŕ$

然而, 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]: $P_{p 在} = Ĥ_{ţ 我 l ţ} \times P_{小号 ţ Ç} \times f_{ţ 和米 p} \times f_{该 ţ Ĥ 和 r}$

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

PpvPp在 : The total energy output (in kWh) over a given period (例如, daily, monthly, or annually) or the power output (in W) [4].
PstcP小号ţÇ : 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.
HtiltĤţ我COM : 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 和 panel angle are used to calculate the sunlight your specific setup receives [5, 7].
ftempfţ和米p : The temperature derating factor (a decimal between 0 和 1). This accounts for the loss in efficiency as the solar panel’s cell temperature rises above 25°C [1, 2, 8].
fotherf该ţĤer : A combined factor for all other system losses (a decimal between 0 和 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 $Ĥ_{ţ 我 l ţ}$ Ĥţ我COM and $f_{ţ 和米 p}$ fţ和米p.

1. Irradiation on a Tilted Surface ( $Ĥ_{ţ 我 l ţ}$ Ĥţ我COM)

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]. 然而, for maximum accuracy, a more nuanced approach is needed.

Fixed Tilt Angle: “ “golden rule” is to set the tilt angle equal to your latitude. 例如, at a latitude of 35°N, panels are often installed with a 35° tilt [5].
Calculating HtiltĤţ我COM: 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]. 为此, 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 $Ĥ_{ţ 我 l ţ}$ Ĥţ我COM. 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 ( $f_{ţ 和米 p}$ fţ和米p)

Solar panels operate less efficiently as they get hot. This factor corrects for this effect [1, 2]. The formula, implemented in models like PVWatts, 是如下所示 [4, 8]: $f_{ţ 和米 p} = 1 + [γ \times (Ţ_{Ç 和 l l} - Ţ_{小号 ţ Ç})]$

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

例如, according to industry data, for a module with $γ = - 0.4 % / ° Ç$ γ=−0.4%/°Ç, $Ţ_{Ç 和 l l} = 65 ° Ç$ Tcell=65°Ç, 和 $Ţ_{小号 ţ Ç} = 25 ° Ç$ Tstc=25°Ç, the power loss is significant [6]. The calculation is: $f_{ţ 和米 p} = 1 + [- 0.004 \times (65 - 25)] = 1 + (- 0.16) = 0.84$

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

Typical Temperature Coefficient ( $γ$ 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 ( $γ$ γ)	笔记
Monocrystalline Silicon (Older BSF)	-0.45% 至 -0.50% /°C	Older technology with higher temperature losses [6].
Monocrystalline Silicon (Modern PERC)	-0.35% 至 -0.40% /°C	Common technology with improved performance [6].
Monocrystalline Silicon (N-type TOPCon)	-0.29% 至 -0.35% /°C	Advanced technology with a very good coefficient [6].
Monocrystalline Silicon (HJT – Heterojunction)	-0.25% 至 -0.30% /°C	Premium technology with the best coefficient [6].
Polycrystalline Silicon	-0.40% 至 -0.50% /°C	Older technology, generally higher coefficient [6].
Thin-Film (CdTe)	-0.24% 至 -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 ( $f_{该 ţ Ĥ 和 r}$ f该ţĤer)

This is a catch-all for real-world inefficiencies. A typical value for a well-designed system might be around0.75 至 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 a1 kWdc system using the PVWatts formula [4, 8].

Array Power (PstcP小号ţÇ): 1 kWdc
Tilted Irradiation (HtiltĤţ我COM): Let’s assume you’ve used an online tool like PVGIS [3] for your specific latitude and chosen tilt. The tool outputs an annual HtiltĤţ我COM of 1700 kWh/m².
Temperature Factor (ftempfţ和米p): Based on your local climate and panel specifications (例如, $γ = - 0.4 % / ° Ç$ γ=−0.4%/°Ç [6]), you calculate an average annual $f_{ţ 和米 p}$ fţ和米p of 0.90.
Other Losses (fotherf该ţĤer): You estimate a combined factor of 0.80 for inverter losses, soiling, wiring, 等. [1, 4].

Your estimated annual energy output ( $P_{p 在}$ Pp在) would be [4]: $P_{p 在} = 1 kWdc \times 1700 kWh/m² \times 0.90 \times 0.80 = 1224 kWh$ Pp在=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 $Ĥ_{ţ 我 l ţ}$ Ĥţ我COM values, I strongly recommend using established tools like PVGIS [3] 或 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 ( $γ$ 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” 或 “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). 表 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., 有限公司.

[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

📐 The Foundational Solar Output Equation

🔍 Breaking Down the Key Components

1. Irradiation on a Tilted Surface (Ĥţ我lţĤţ我COM​)

2. The Temperature Derating Factor (fţ和米pfţ和米p​)

Typical Temperature Coefficient (γγ) Values

3. Other Derating Factors (f该ţĤ和rf该ţĤer​)