14. Array Sizing & Energy Yield

Learning objectives

Convert an energy target into a required array size in kW.
Apply peak sun hours and a realistic derate factor.
Interpret specific yield and capacity factor as sanity checks.

14.1 The master sizing relationship

From Chapters 1–2, energy = power × time, adjusted for real-world losses. The working form:

Annual kWh ≈ Array kW(DC) × PSH(daily) × 365 × Derate

Rearranged to size the array:

Array kW(DC) = Target Annual kWh ÷ (PSH × 365 × Derate)

Where PSH is the site’s average daily peak sun hours (Chapter 2.3, from NREL data) and Derate bundles all real-world losses.

PVWatts: NREL's free online energy simulation tool. Enter location, array size, tilt, and azimuth, and it returns estimated annual kWh output using satellite-derived solar resource data. It is the industry standard reference for derate defaults and production estimates.

The derate converts a DC nameplate into the AC energy your meter actually counts. The industry anchor is NREL PVWatts, whose default total system loss is ~14%. Note that these losses stack multiplicatively, not additively (a frequent error). The 14% default corresponds to roughly:

0.86 DC-side derate,
~0.83 including inverter losses (the PVWatts v8 default), and
0.77 as the classic conservative value with extra safety margin.

A defensible quick estimate uses 0.80–0.83; a conservative bid uses 0.77. (The detailed loss tree behind this number is Chapter 19.)

Example 14.A: Size an array for the 11,400 kWh/yr target (Ex 13.A) at a 4.6 PSH site, derate 0.82. Array kW = 11,400 ÷ (4.6 × 365 × 0.82) = 11,400 ÷ 1,377 = 8.28 kW DC. At 440 W modules: 8,280 ÷ 440 = 18.8 → 19 modules (≈ 8.36 kW). The next chapters confirm this array can be wired within the chosen inverter’s limits.

14.3 Sanity checks: specific yield and capacity factor

Specific yield = annual kWh ÷ kW(DC) (units kWh/kWp). Typical fixed-tilt values run ~1,100–1,800 kWh/kWp depending on climate; a number far outside this signals an input error.
Capacity factor = actual annual energy ÷ (kW × 8,760 h). Fixed PV typically lands ~13–22%. Another quick plausibility gate.

Example 14.B: 11,400 kWh ÷ 8.36 kW = 1,364 kWh/kWp, squarely typical, so the design is plausible.

14.4 The sizing flow, visualized

  Annual kWh target ──┐
                      ├──►  Array kW = target ÷ (PSH × 365 × derate)
  Site PSH ───────────┤
                      │
  Derate (~0.80–0.83)─┘            │
                                   ▼
                       Array kW ÷ module W = module count (round to fit roof/strings)
                                   │
                                   ▼
                       Sanity-check: specific yield 1,100–1,800 kWh/kWp ?  capacity factor 13–22% ?

14.5 More worked examples

Example 14.C (high-sun vs low-sun site, same load): A 14,000 kWh/yr target, derate 0.82.

Phoenix (≈6.5 PSH): 14,000 ÷ (6.5 × 365 × 0.82) = 7.2 kW
Seattle (≈3.7 PSH): 14,000 ÷ (3.7 × 365 × 0.82) = 12.6 kW The same energy need requires a 75% larger array in Seattle. This is a vivid reminder that location, not load alone, sets system size.

Example 14.D (module count and roof reality): An 8.2 kW target at 440 W/module = 18.6 → round to 19 modules (8.36 kW). If the usable roof only fits 16 modules (7.04 kW), the design is roof-constrained. In that case, you either accept a partial offset (~84%), switch to higher-wattage modules, or add a second roof plane (Ch 18).

Chapter 14 summary

Array kW = target kWh ÷ (PSH × 365 × derate). Use ~0.80–0.83 derate (PVWatts-aligned) or 0.77 conservative, remembering losses multiply. Convert kW to a module count, then validate with specific yield (~1,100–1,800 kWh/kWp) and capacity factor (~13–22%) before moving on.

PSH (Peak Sun Hours): daily equivalent hours of full 1,000 W/m² irradiance at a site; the solar resource input to the sizing formula.
Derate factor: a multiplier (typically 0.77–0.83) that converts DC nameplate output to metered AC energy by accounting for all real-world losses stacked multiplicatively.
PVWatts: NREL’s online energy simulation tool; the industry standard for derate defaults and annual production estimates.
Specific yield: annual kWh output divided by DC array size (kWh/kWp); typical range is 1,100–1,800 kWh/kWp for fixed-tilt systems.
Capacity factor: actual annual energy divided by the energy the array would produce running at nameplate power for 8,760 hours; typical PV range is 13–22%.
Roof-constrained design: a layout where available roof space limits array size below the load-matched ideal, requiring a tradeoff on offset percentage or module selection.

Full definitions: Appendix A (glossary).

Practice Problems: Chapter 14

Size an array for a 10,000 kWh/yr target at 5.0 PSH, derate 0.82.
Convert that to a module count using 450 W modules.
A 9 kW array at 4.8 PSH and 0.80 derate produces how much annual energy?
Compute that array’s specific yield (kWh/kWp). Is it in the normal range?
The customer’s roof fits only 18 modules (450 W). What array size is that, and what % of a 10,000 kWh/yr need would it offset at 5.0 PSH / 0.82 derate?
Why does using a 0.77 derate instead of 0.83 make a larger recommended array for the same energy target?

Solutions: Chapter 14

10,000 ÷ (5.0 × 365 × 0.82) = 10,000 ÷ 1,496.5 = 6.68 kW.
6,680 ÷ 450 = 14.8 → 15 modules (6.75 kW).
9 × 4.8 × 365 × 0.80 = 12,614 kWh/yr.
12,614 ÷ 9 = 1,402 kWh/kWp. Yes, squarely in the 1,100–1,800 range.
18 × 450 = 8,100 W = 8.1 kW; annual = 8.1 × 5.0 × 365 × 0.82 = 12,118 kWh → that exceeds 10,000 kWh, so it offsets 100% (with margin). (If the need were larger, you’d compute the fraction.)
A lower derate assumes more losses, so more DC capacity is needed to deliver the same AC energy: the target kWh is divided by a smaller number, yielding a larger kW.

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