Engineering guides
One question, one worked model.
Each guide answers a different search question from a formula already in the calculator. Numbers come from the unit-test fixtures. They are not new field measurements.
Transformer turns ratio and voltage regulation
TOPIC-01Ideal Transformer Turns and Voltage RatioIn this ideal model, winding-phase voltages are in the same ratio as the turns. With N1 = 100, N2 = 10 and V1 = 230 V, V2 = 23 V and N1/N2 = 10.TOPIC-01Transformer Voltage Regulation PercentFor load fraction 1, power factor 0.8 lagging, R = 2% and X = 4%, the no-load equivalent voltage magnitude is sqrt(1.082) per unit. Regulation percent is (sqrt(1.082) − 1) × 100.
Balanced three-phase power and power factor
TOPIC-02Balanced Three-Phase Power and CurrentFor a balanced three-phase load, apparent power is √3 × line voltage × line current. At 400 V, 10 A and 0.8 lagging, active power is 5542.56258422 W, apparent power is 6928.203230276 VA, and lagging reactive power is 4156.921938165 var.TOPIC-02Lagging Load Power Factor CorrectionThe required capacitive vars are P times the drop in tan(acos pf). For 10000 W from 0.8 to 1.0, that is 7500 var. Leading loads are rejected.
Cable voltage drop and thermal current
TOPIC-03DC Voltage Drop on a Two-Wire CableDC drop on a two-wire run is 2 × I × L × r. At 20 A, 50 m and 0.003 Ω/m the drop is 6 V, the end voltage is 224 V, and 100 × 6 / 230 is 2.609% when rounded to three decimals.TOPIC-03Steady-State Cable Thermal Current EstimateThe estimate is the current whose I²R heat matches the entered temperature rise across one thermal resistance. For the base fixture, resistance at the maximum temperature is 0.0128 Ω/m and the current is sqrt(60 / (0.0128 × 0.5)).
Battery runtime and UPS sizing
TOPIC-04UPS Sizing Versus Battery RuntimeUPS sizing and runtime answer different questions. This fixture needs 1080 W and 1200 VA. Usable energy is 3840 Wh, battery-side power is 1000 W, and runtime is 3.84 hours.TOPIC-04Battery Runtime from Watt-HoursDeliverable energy is voltage × ampere-hours × state-of-charge window × health × discharge efficiency. The locked fixture delivers 864 Wh and runs 8.64 hours at 100 W.
Solar payback and string voltage
TOPIC-05Simple Solar Payback from Monthly GenerationWith those zeros, simple payback is capital divided by the constant net cash flow. 6000 kWh produces 960 of annual benefit, 860 after maintenance, and 5000 / 860 = 5.814 years to three decimals.TOPIC-05PV String Voltage at Entered TemperaturesCold string Voc is module Voc times the linear temperature factor times the series count. The teaching inputs produce 431.7058 V at −8 °C, 342.583 V at 70 °C, 325 V at the reference Vmp, 20 modules and 8000 Wdc.