Quantitative Design Challenge
This 12-question quiz tests your ability to perform calculations essential for designing solar power systems. Topics include sizing solar arrays, selecting inverters, calculating battery bank capacity, and applying NEC safety factors. Select your answer for each question, then submit to see your score and detailed explanations.
Note: All calculations follow NEC Article 690 requirements and industry best practices.
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Answer Explanations
Question 1: Solar Array Sizing
Correct Answer: C. 7.5 kW
Array Size (kW) = Daily Energy Use (kWh) ÷ Peak Sun Hours ÷ System Efficiency
= 30 kWh ÷ 5 hours ÷ 0.80
= 7.5 kW
This calculation determines the minimum solar array needed to meet daily energy consumption. The 80% efficiency accounts for losses in inverters, wiring, and other system components.
Key Point: Always account for system efficiency (typically 75-85%) when sizing solar arrays. Real-world production is less than theoretical STC ratings.
Question 2: Temperature Voltage Correction
Correct Answer: C. 648V
Temperature difference = 25°C - (-10°C) = 35°C
Voltage increase = 35°C × 0.0035/°C = 0.1225 (12.25%)
Corrected Voc = 45V × (1 + 0.1225) = 50.51V
String voltage = 50.51V × 12 = 606.1V
NEC requires 125% factor: 606.1V × 1.25 = 648V
NEC 690.7 requires calculating maximum system voltage using the lowest expected temperature and applying safety factors to prevent overvoltage conditions.
Question 3: Battery Capacity Calculation
Correct Answer: B. 390.6 Ah
Usable energy = Total energy ÷ Depth of Discharge = 15 kWh ÷ 0.80 = 18.75 kWh
Battery capacity (Ah) = Usable energy (Wh) ÷ System Voltage
= 18,750 Wh ÷ 48V = 390.6 Ah
This calculation ensures the battery bank can deliver the required energy while staying within safe discharge limits. Lithium batteries typically allow 80-90% DoD, while lead-acid is limited to 50%.
Question 4: NEC Conductor Sizing
Correct Answer: C. 46.9A
Total Isc = 10A × 3 strings = 30A
NEC 690.8(A)(1): 125% of Isc = 30A × 1.25 = 37.5A
NEC 690.8(B)(1): Continuous current factor = 37.5A × 1.25 = 46.875A
NEC requires two 125% factors: one for possible current exceeding Isc, and another for continuous operation (3+ hours). This ensures conductors don't overheat.
Question 5: Panel Count with Losses
Correct Answer: B. 29 panels
Required STC rating = System size ÷ (1 - Losses) = 10 kW ÷ 0.85 = 11.76 kW
Number of panels = 11,760W ÷ 400W = 29.4 ≈ 29 panels
Always account for system losses (shading, soiling, wiring, inverter inefficiency) when determining actual panel count needed.
Question 6: Inverter Voltage Window
Correct Answer: C. 22 panels
Temperature difference = 70°C - 25°C = 45°C
Voltage reduction = 45°C × 0.004/°C = 0.18 (18%)
Vmp at 70°C = 35V × (1 - 0.18) = 28.7V
Max panels = Inverter max V ÷ Panel Vmp = 800V ÷ 28.7V = 27.9 panels
But need Vmp > 400V: 400V ÷ 28.7V = 13.9 panels minimum
Optimal is 22 panels: 22 × 28.7V = 631.4V (within 400-800V range)
Must check both minimum and maximum MPPT voltage limits at operating temperatures.
Question 7: Battery Runtime Calculation
Correct Answer: B. 12.3 hours
Usable capacity = 400Ah × 48V × 0.80 DoD = 15,360 Wh
AC output considering inverter efficiency = 15,360 Wh × 0.80 = 12,288 Wh
Runtime = 12,288 Wh ÷ 1,000W = 12.29 hours
Remember to account for both depth of discharge limits and inverter efficiency when calculating actual runtime.
Question 8: Location-Specific Sizing
Correct Answer: B. 23 panels
Daily production per panel = 350W × 4.5 hours × 0.85 (tilt/efficiency factor) = 1,338.75 Wh
Panels needed = 8,000W ÷ 1,338.75 Wh = 5.97 days worth
For monthly balance: 23 panels × 1.33875 kWh × 30 days = 923 kWh/month ≈ 8kW system
Location-specific factors (sun hours, tilt, temperature) significantly impact actual production.
Question 9: Inverter Current Output
Correct Answer: C. 30.1A
AC output power = 7,000W × 0.97 = 6,790W
Current = Power ÷ Voltage = 6,790W ÷ 240V = 28.29A
NEC continuous factor = 28.29A × 1.25 = 35.36A
But inverter max is 7,000W ÷ 240V = 29.17A × 1.25 = 36.46A
Lower value (inverter limit) governs: 29.17A × 1.25 = 36.46A circuit rating
Actual continuous current = 29.17A × 0.97 = 28.29A × 1.25 = 35.36A derated
Inverter output current is limited by both its power rating and efficiency.
Question 10: Charge Controller Sizing
Correct Answer: B. 65.1A
Controller current = Power ÷ Voltage = 2,500W ÷ 48V = 52.08A
With 25% oversizing = 52.08A × 1.25 = 65.1A
Charge controllers should be oversized by 25% to handle peak production and prevent clipping.
Question 11: Conductor Sizing per NEC
Correct Answer: A. 8 AWG
NEC Table 310.16: 8 AWG at 75°C has 50A ampacity
40A circuit requires minimum 50A-rated conductor
Next size down (10 AWG) is only 35A - insufficient
Conductors must have ampacity at least equal to circuit rating, with rounding up allowed.
Question 12: Capacity Factor Calculation
Correct Answer: B. 17.4%
Theoretical monthly production = 6kW × 24 hours × 30 days = 4,320 kWh
Actual production = 750 kWh
Capacity factor = (Actual ÷ Theoretical) × 100%
= (750 ÷ 4,320) × 100% = 17.36%
Capacity factor measures actual vs. theoretical maximum output. 15-25% is typical for solar PV systems.