Parameters
Formula
E_month = Pw × N × PSH × η × tilt_factor × 30 / 1000CO₂ saved ≈ E_annual × 0.42 kg/kWh
Payback = Cost / (E_annual × price)
Enter panel power, count, tilt angle, latitude, efficiency, and electricity price to calculate monthly generation, annual kWh, CO₂ savings, and payback period.
The core calculation estimates the monthly energy output of a photovoltaic (PV) system. It starts with the panel's rated power and scales it by the available solar resource and system losses.
$$E_{\text{month}}= P_w \times N \times \text{PSH}\times \eta \times f_{\text{tilt}}\times \frac{30}{1000}$$Where:
$E_{\text{month}}$ = Monthly energy generation (kWh)
$P_w$ = Power rating of one panel (W)
$N$ = Number of panels
PSH = Average daily Peak Sun Hours for the location/month (h)
$\eta$ = Overall system efficiency (%)
$f_{\text{tilt}}$ = Tilt correction factor (dimensionless, ≤1)
The factor 30 converts daily to monthly, and /1000 converts Watt-hours to kilowatt-hours.
The financial and environmental impacts are derived from the annual energy total. The payback period is a simple return-on-investment metric, while CO₂ savings use a grid emission factor.
$$ \text{Payback Period (years)}= \frac{\text{Installation Cost}}{E_{\text{annual}}\times \text{Electricity Price}}$$Where:
$E_{\text{annual}}$ = Sum of monthly energy over 12 months (kWh)
Electricity Price = Local cost per kWh ($/kWh)
CO₂ Saved ≈ $E_{\text{annual}} \times 0.42$ kg/kWh. The 0.42 kg/kWh is an average emission factor for electricity displaced from a fossil-fuel-heavy grid.
Residential Solar Feasibility: Homeowners use this exact type of calculation to decide if solar is right for them. By inputting their roof size (as number of panels), local latitude, and current utility rate, they can estimate monthly savings and how long it will take to recoup the installation cost, which is critical for financing.
System Design and Optimization: Installers use these models to design systems for clients. They experiment with different panel wattages (Pw) and tilt angles to find the best balance between higher initial cost (more powerful panels) and faster payback (more energy generation) for a specific property.
Policy and Incentive Analysis: Governments and utilities run these calculations to forecast the impact of solar incentives. For example, they can model how a change in the electricity price (like a rate hike) or a subsidy that lowers the effective installation cost affects the adoption rate by improving the payback period.
Educational Tool for Siting: Urban planners and architects use the principles here to understand the solar potential of different building orientations and locations. The strong dependence on latitude and tilt informs building codes and the design of solar-ready structures.
When you start using this simulator, there are several common pitfalls, especially for beginners. The first is "underestimating the regional characteristics of solar radiation data." While the tool uses nationwide average data, in reality, it's not uncommon for "power generation to vary by more than 10% between coastal and mountainous areas within the same prefecture." Particularly in areas with shorter daylight hours, such as the Sea of Japan side or basins, it's crucial not to take simulation results at face value and to compare them with local meteorological data and actual performance records.
The second point is "overly optimistic estimation of system efficiency." It's tempting to set it high at 85% for a new system, but considering wiring losses (approx. 3%), power conditioner efficiency (approx. 95%), and annual degradation (approx. 0.5% per year), a long-term average below 80% is more realistic. For example, if you calculate the payback period based on 85% efficiency, actual power generation may be lower than expected, potentially extending the payback period by 1-2 years.
The third is the danger of "focusing solely on the payback period." This figure heavily depends on the settings for electricity cost and feed-in tariff rates. For instance, calculating with an electricity cost of 25 yen/kWh yields a shorter payback period, but in reality, the rate fluctuates based on time of use and contract type. Furthermore, a plan where the payback period exceeds the panel's lifespan (typically 20-30 years) is inherently high-risk. For economic evaluation, alongside the payback period, you also need the perspective of considering the "net profit over the system's lifetime (LCOE: Levelized Cost of Electricity)".
Behind this seemingly simple simulator lies knowledge from a wide range of engineering fields. At its core is "Solar Energy Engineering." This field involves understanding the spectrum and intensity of sunlight and pursuing how to convert it into electricity efficiently, forming the basis for improving panel conversion efficiency.
Next, in calculating the relationship between tilt angle and solar radiation, knowledge from "Architectural Environmental Engineering" and "Meteorology" comes into play. Methods developed for building energy-efficient design, such as calculating solar heat gain (solar load coefficient) and sky luminance distribution models (considering clear sky ratio), are applied. Also, when handling regional meteorological data, the methodology for dealing with long-term statistical data from meteorology is crucial.
Furthermore, "Power Engineering and Power Electronics" are essential for considering overall system efficiency. In the background are technologies for efficiently connecting generated power to the grid, such as the power conditioner's conversion efficiency curve (characteristics where efficiency changes with load factor) and calculating voltage drop in DC wiring. Even the single "system efficiency" parameter in this tool can be said to be a result synthesizing these fields.
If you become interested in this tool's calculations and want to learn more, consider taking the next step. First, we recommend starting by learning the mathematical background of the "solar radiation correction factor," which is at the heart of the calculation. This involves representing the temporal and seasonal changes in the sun's altitude and azimuth angles using trigonometric functions to find the angle of incidence on an inclined surface. For example, the correction factor at noon on the summer solstice for a tilt angle β and latitude φ can be approximated using the solar altitude angle. Learning this element of "astronomical calculation" will help you understand the simulation results more deeply.
Next, if you aim for simulations closer to reality, learn about "shading impact assessment." Partial shading from neighboring houses, chimneys, or trees reduces power generation more than you might think. This is because panels are connected in series in "strings," so shading a part significantly reduces the entire output. To understand this phenomenon, basic knowledge of "electronics," such as the equivalent circuit model of solar cells and the operating principle of bypass diodes, is helpful.
Ultimately, to move towards professional system design or business evaluation, it's important to know about specialized simulation software (e.g., PVsyst or PV*SOL). These tools come with more detailed meteorological databases, shading analysis, detailed models of power conditioner characteristics, and economic analysis functions, allowing you to model complex realities that this free tool cannot fully consider. It's a good approach to first grasp the basic principles with this simple tool, understand its limitations, and then consider stepping up to more advanced tools as needed.