19. Production Modeling

Learning objectives

• Select the right modeling tool for the stage of work.
• Understand the loss tree behind the derate factor.
• Read P50/P90 and use modeling to sanity-check quotes.

19.1 The toolchain

• PVWatts (NREL, free): fast preliminary estimates from a handful of inputs (location, DC size, tilt, azimuth, losses, array type). The industry’s quick-check standard; v8 adds bifacial support and updated weather data.
• SAM (NREL, free): detailed hourly performance and economics; the next step up for serious design and financial modeling.
• PVsyst (commercial): the bankability standard for large/utility projects, with granular shading and loss modeling lenders expect.

19.2 The loss tree behind the derate

The ~14% PVWatts default isn’t a guess. It’s a stack of named losses combined multiplicatively (1 − ∏(1 − lᵢ)). A representative breakdown: soiling ~2%, shading ~3%, mismatch ~2%, wiring ~2%, connections ~0.5%, light-induced degradation ~1.5%, nameplate tolerance ~1%, availability ~3%. The temperature penalty is modeled separately on top. Editing these to match the actual site (heavy soiling, snow, measured shading) is what turns a generic estimate into a credible one.

19.3 Bankability: P50 and P90

Modeled output is a distribution, not a single number:

• P50: the median estimate (50% chance of exceeding). Used for expected-value planning.
• P90: the conservative estimate exceeded 90% of years. Lenders underwrite to P90 because it bounds downside risk.

19.4 Using modeling to check a quote

A fast integrity test on any proposal: run the proposed DC size, tilt, azimuth, and location through PVWatts at default losses and compare to the salesperson’s promised annual kWh. A quote far above the PVWatts P50 is a red flag. For example, a quote implying an unrealistic derate or ignoring shade signals a problem. This “reality check before signing” is what makes the tool valuable to customers and inspectors alike.

Example 19.A: The 8.36 kW design (Ch 14) at 4.6 PSH, default ~14% losses, modeled in PVWatts returns ≈ 11,400 kWh/yr, matching the load target and confirming the whole design chain closes.

19.5 The loss tree, visualized

 DC nameplate (100%)
   ├─ soiling        −2%
   ├─ shading        −3%
   ├─ mismatch       −2%
   ├─ wiring         −2%
   ├─ connections    −0.5%
   ├─ light-induced  −1.5%
   ├─ nameplate tol. −1%
   └─ availability   −3%
        │  (losses combine MULTIPLICATIVELY, not additively)
        ▼
 ≈ 86% DC  ──► inverter ──► ≈ 83% AC at the meter  (PVWatts ~14% default)
        +  temperature penalty modeled separately on top

⚠️ The classic error is adding the percentages (which would imply ~15%); they actually compound as 1 − ∏(1 − lᵢ) ≈ 14%. Edit each line to the real site (heavy soiling, snow, measured shading) to turn a generic estimate into a credible one.

Chapter 19 summary

Use PVWatts to estimate and sanity-check, SAM for detailed design/economics, PVsyst for bankable projects. The derate is a multiplicative loss tree, editable to the site, with temperature handled separately. Report P50 for expectations and P90 for financing, and always cross-check a sales quote against an independent model.

Practice Problems: Chapter 19

1. Which tool would you use for: (a) a fast homeowner estimate, (b) a lender-grade bankability study, (c) detailed design + economics?
2. A salesperson promises 14,500 kWh/yr from a 9 kW array at a 4.6 PSH site. A PVWatts run at default losses returns ~11,400 kWh/yr. What should you conclude?
3. Why is P90 the figure lenders underwrite to, rather than P50?
4. Two loss factors are 3% and 2%. Combined multiplicatively, what is the total loss (to one decimal)?
5. Where does the temperature penalty enter the PVWatts model: inside the 14% system-loss figure, or separately?

Solutions: Chapter 19

1. (a) PVWatts, (b) PVsyst, (c) SAM.
2. The promise is ~27% above an independent model at default losses, a red flag; it implies an unrealistic derate or ignores shading. Re-model with site-specific inputs before trusting it.
3. P90 is the conservative output exceeded in 90% of years, bounding downside risk for debt service; P50 (median) is for expected-value planning, not underwriting.
4. 1 − (0.97 × 0.98) = 1 − 0.9506 = 4.9% (not 5.0%).
5. Separately: PVWatts models temperature in the module performance step; the editable “system losses” (~14%) covers soiling, shading, wiring, mismatch, etc., but not temperature.

PART IV: CAPSTONE CASE STUDIES

These two integrated case studies chain every Part IV chapter end to end, the textbook payoff of the design sequence.

Case Study A: Residential grid-tied, 100% offset

Inputs: Home uses 11,400 kWh/yr; site 4.6 PSH, record low −18 °C, hot cell max 70 °C; 440 W modules (Voc 49.5 V, Vmp 41.2 V, Isc 13.85 A, β(Voc) −0.25%/°C, Vmp coeff −0.34%/°C, max series fuse 25 A); inverter 7.6 kW AC, max DC 600 V, MPPT 60–550 V, 32 A AC out; 200 A busbar with 200 A main.

1. Energy target (Ch 13): 11,400 kWh/yr (full offset).
2. Array size (Ch 14): 11,400 ÷ (4.6 × 365 × 0.82) = 8.28 kW → 8,280 ÷ 440 = 18.8 → 19 modules (8.36 kW).
3. String sizing (Ch 15):
   • Cold Voc = 49.5 × [1 + (−0.0025)(−18 − 25)] = 49.5 × 1.1075 = 54.8 V → max = 600 ÷ 54.8 = 10.9 → ≤10/string.
   • Hot Vmp = 41.2 × [1 + (−0.0034)(45)] = 41.2 × 0.847 = 34.9 V → min = 60 ÷ 34.9 = 1.7 → ≥2/string (MPPT floor is low here, so the cold-Voc ceiling dominates).
   • Wiring: 19 modules → two strings of 9 and 10 (both ≤10 ✓).
4. Conductor/OCPD (Ch 16): 13.85 × 1.5625 = 21.6 A min ampacity (derate for heat/fill, likely 10 AWG); series fuse ≤ 25 A (module limit) ✓.
5. Interconnection (Ch 16): PV breaker ≤ (1.20 × 200) − 200 = 40 A; inverter needs 32 × 1.25 = 40 A → fits load-side exactly.
6. Production check (Ch 19): 8.36 kW × 4.6 × 365 × 0.82 ≈ 11,500 kWh/yr, matching the target. Design closes. ✓

Case Study B: Small commercial, roof-constrained

Inputs: Business wants to offset as much of 90,000 kWh/yr as a 400 m² flat roof allows; site 5.2 PSH; 440 W modules (~2 m² each); 1,000 V three-phase string inverter, MPPT 250–950 V; cold string limit gives ≤17 modules/string (from Example 15.A second case).

1. Roof capacity: at ~2 m²/module with walkway/setback losses (~60% usable), ~120 modules fit → 120 × 440 = 52.8 kW (roof-constrained, below a full offset).
2. Energy (Ch 14): 52.8 × 5.2 × 365 × 0.82 ≈ 82,200 kWh/yr → offsets ~91% of the 90,000 kWh need, acceptable when the roof is the binding constraint.
3. Stringing (Ch 15): 120 modules ÷ 15 per string = 8 strings of 15 (≤17 ✓), distributed across the inverter’s MPPT inputs.
4. Takeaway: unlike the residential case (sized to load), this design is sized to the roof, a common commercial reality where available area sets the system rather than energy appetite. The remaining ~9% comes from the grid (or a future carport/ground array).

⚠️ Both case studies assume one adopted code edition and one set of site temperatures. Real projects re-run every step against the actual AHJ edition, ASHRAE site data, and equipment datasheets.

PART IV: CONSOLIDATION

You can now take a project from a utility bill to a proven design. Establish the energy target (Ch 13), size the array (Ch 14), determine legal string lengths against the inverter’s voltage window (Ch 15), size the inverter, conductors, and OCPD to code (Ch 16), size storage to its purpose (Ch 17), optimize for shade/tilt/azimuth (Ch 18), and model the result for proof and bankability (Ch 19). This is the heart of the installer-designer’s competence.

Part V takes the design into the realm of law and safety: the electrical theory behind it, the structure of NEC Articles 690/705/706, grounding and rapid shutdown, and the overcurrent/wiring methods that make a design not just functional but code-compliant and inspector-ready.

A design that works on paper still has to be legal and inspectable. This part covers the electrical theory an installer applies daily and the code framework (primarily the NEC) that governs every connection. Code content here was verified against current code-education sources in mid-2026. The single most important rule in this entire part: the code that applies is the edition your AHJ has adopted, plus local amendments. Confirm it before every plan set.