Solar Array Engineering: Photovoltaic Sizing Models
Understand the meteorological impacts of Peak Sun Hours and Derating Factors on Solar Panel (PV) output.
The Mathematics of Photovoltaic Array Sizing
Translating your monthly electrical utility bill directly into a physical array of roof-mounted solar panels is not a direct 1:1 conversion. An electrical engineer must navigate weather intermittency, specific geographic latitude sun-paths, and the unavoidable laws of thermodynamics. While your monthly bill gives you an absolute Kilowatt-Hour (kWh) consumption figure, sizing a solar array requires reverse-engineering that consumption against the strict reality of localized Peak Sun Hours.
What Exactly is a "Peak Sun Hour"?
A "Peak Sun Hour" is distinctly not the raw duration of daylight hours your city experiences. It is a strict industry-standard meteorological measurement defined as precisely one hour of $1000 \text{ Watts per square meter} (W/m^2)$ of solar irradiance striking a flat surface.
While the sun may technically be over the horizon for 12 continuous hours during a summer day, the intensity of light during sunrise and sunset is incredibly weak. When you mathematically integrate the low-intensity morning light, the intense noon light, and the fading evening light, the total energy often only equates to 4 or 5 consolidated "Peak Sun Hours" per day. In a sunny region like Arizona, you may average 6.0 Peak Sun Hours/Day annually, whereas London may only average 2.5. This single meteorological variable explicitly dictates whether your roof requires 15 panels or 45 panels to accomplish the exact same objective.
The Photovoltaic (PV) Yield Formula
To explicitly model the kW capacity of the required DC array, engineers build a cascading sequence of requirements, beginning with the raw utility demand and ending with meteorological limits.
- Gross Model kWh: To ensure the system physically produces the required net load, we must intentionally oversize the daily target limit up front in the math by incorporating the Loss Margin.
- Array Capacity (kWp): The final "Nameplate" Kilowatt Peak rating. If the math states $6.5\text{ kWp}$, you must purchase $6500\text{ Watts}$ worth of actual physical panels.
System Losses (The Internal Derating Factor)
Why do we artificially inflate the required energy model by 20% to 25%? Solar panels are tested and branded under pristine laboratory parameters called Standard Test Conditions (STC). STC dictates an artificially perfect $25^\circ C (77^\circ F)$ cell temperature and zero dust. When deployed into the real environment, PV output dramatically decreases due to inescapable physical laws. Engineers universally insert a standard 20% to 25% internal derating factor directly into their capacity models to account for:
- Thermal Degradation (Heat Loss): It sounds contradictory, but intense heat destroys solar efficiency. Silicon photovoltaics systematically lose efficiency (typically $-0.4\%$ per degree Celsius) as their surface temperature sharply rises. On a $100^\circ F$ day, a black solar panel resting on asphalt shingles can easily reach $150^\circ F$, sapping nearly $15\%$ of its nameplate capacity instantly.
- DC to AC Inversion Loss: Your home appliances cannot run on the raw DC voltage produced by the panels. Routing the power through a solid-state inverter to generate $120\text{V} / 240\text{V}$ AC incurs a mandatory $3\%$ to $5\%$ thermodynamic drop, which must be counteracted. (See our Solar Inverter Sizing Calculator for deep-dive inverter clipping mathematics).
- Soiling and Shading: Micro-dust buildup on glass, localized shading from distant trees at $4\text{ PM}$, and inherent Ohmic $I^2R$ Voltage Drop resistance occurring over the long copper wires running from your roof down to your basement panel.
- Battery Cycling (If Off-Grid): If you are charging an off-grid Battery Bank, pushing current into the chemistry and pulling it back out later incurs a brutal round-trip efficiency penalty. You must add another $5\%$ to $10\%$ loss margin to compensate.
Frequently Asked Questions (FAQ)
What is the difference between kW and kWh?
Kilowatt (kW) is a measure of instantaneous capacity or speed. It is the size of the hose. Kilowatt-Hour (kWh) is a measure of volume or total energy delivered over time. If a $5\text{ kW}$ solar array operates in perfect direct sunlight for exactly $2\text{ hours}$, it has delivered $10\text{ kWh}$ of total energy into the building.
Should I size my system for Summer or Winter months?
If you are grid-tied and have Net Metering, you should size the system using your Annual Average kWh bill and Average Peak Sun Hours. The utility grid acts as an infinite battery—you overproduce massively in the Summer, build up financial credits, and slowly burn through those credits during the miserable Winter. If you are deeply Off-Grid, you must explicitly size the array using strictly December's horrible Peak Sun Hours, otherwise, the system will crash during winter storms.
Why does the calculator round up the Total Panels physically needed?
Because you cannot purchase $14.3$ solar panels. Once the mathematically perfect total wattage is calculated (e.g., $5720\text{ Watts}$ needed), we divide that by the wattage of the specific panel you intend to buy (e.g., $400\text{ Watts}$). $5720 / 400 = 14.3$. Because falling short will result in power failure, engineers must round the hardware up to $15$ full $400\text{W}$ panels. Your final array actually becomes $6000\text{W}$, slightly safer than your minimum requirement.