Lesson Three-Phase Power · Loads and alternator
Three-phase load calculations
Real systems stack loads. Delmar’s Unit 27 works Load 1, Load 2, Load 3 style problems by calculating each load’s current and power, then combining them back toward the source. Work from the loads toward the alternator, keeping wye/delta rules and √3 power formulas straight at every step.
Why stepwise loads matter
A feeder may supply:
- A pure resistive heater bank
- An inductive motor load
- A mixed or capacitive section
Each has its own PF and connection. Line segments between loads carry the vector sum of everything downstream — not a simple arithmetic amp add when angles differ.
General method
- Identify each load: connection (wye/delta), EL, P or Z, PF or R/XL/XC.
- Find each load’s line current and phase angle.
- At each junction, combine currents as phasors (or use power: sum kW, sum kVAR, then rebuild VA and I).
- Move upstream and repeat until you reach the source.
- Check source current, PF, and voltages against ratings.
Power summing trick (balanced case)
For multiple balanced loads on the same bus:
P_total = P1 + P2 + P3 VARs_total = VARs1 + VARs2 + VARs3 (signs: lagging positive or per your convention) VA_total = √(P_total² + VARs_total²) I_line = VA_total / (√3 × ELine) PF = P_total / VA_total
This often beats wrestling every current angle by hand.
Load 3 → Load 2 → Load 1 mindset
Textbook problems label the farthest load as Load 3 and the nearest as Load 1. Start at Load 3 because nothing downstream complicates it. Then fold Load 2’s demand onto that feeder current, then Load 1.
Watch connection types
A delta motor and a wye heater on the same 480 V bus both use ELine = 480 V in the √3 formulas, but internal phase voltages differ. Do not convert one load with the wrong identity mid-problem.
Field translation
You may not solve full textbook multi-load sets daily, but you do decide whether a feeder can take another motor: add estimated kW and kVAR to existing measured load, recompute amps, compare to conductor and breaker ratings.
Numbers you should be able to work cold
Two balanced loads on 480 V:
Load A: 20 kW at 0.8 lag → VARsA = 15 kVAR lag, S_A=25 kVA Load B: 10 kW at 1.0 → VARsB=0, S_B=10 kVA
Totals: P=30 kW, VARs=15 kVAR, S=√(30²+15²)=33.5 kVA I=S/(√3×480)≈40.3 A PF=30/33.5≈0.89 lag
Adding a third capacitive load subtracts VARs and can raise PF further.
Diversity vs arithmetic
Code and engineering apply diversity factors; textbook Load 1–3 problems often assume simultaneous demand. In the field, ask whether loads run together before declaring a feeder dead on paper.
Documentation
Write P, VAR, I assumptions on the job sheet. Future you will thank present you.
Field case
Situation. A panel already runs near 80% of breaker rating. Someone wants to add a 20 HP motor. A helper adds “20 A” by rule of thumb without PF or √3.
What happened. Using nameplate FLA (which already is three-phase line current) is better than inventing numbers. Summing with existing clamp readings plus diversity/engineering rules keeps the breaker honest.
Applied lesson. Multi-load thinking is load addition with PF awareness — not random amp guesses.
### Teaching pause — say this out loud
Before you leave this lesson, explain the main idea to an imaginary first-month helper in under one minute. If you need the book open to do it, reread How it works once more. Field diagnosis only helps after the concept is yours.
Also sketch the key diagram from memory (triangle, wye/delta, filter shape, or charge curve — whichever this lesson used). Labels beat artistic skill.
### Why this lesson matters on Monday morning
Three-phase load calculations is not trivia. You will meet it when a meter reading looks “impossible,” when a replacement part is almost right, or when a helper asks why the book uses √3 or lead/lag. Master the model here so the next call is pattern recognition, not panic.
Common Monday uses: verify a nameplate against clamps, explain a PF or capacitor change to a customer, or catch a miswired series/parallel or wye/delta assumption before energizing.
In the field
Symptom
Breaker trips after adding equipment; unexplained feeder heating
Where to look
Diversity of loads, PF, continuous vs noncontinuous
Likely causes
- Arithmetic amp add ignored angles
- ignored continuous load factors
What to measure
- Existing kW/kVAR/I
- new load nameplate
- recalculate
What not to do
- Add nameplate FLAs as if PF and diversity were irrelevant without checking code rules
Checklist
- I work from farthest load toward the source
- I can sum P and VARs then rebuild I
- I keep wye/delta conversions consistent
- I use √3 with line quantities
- I apply the method to “can this feeder take another motor?”
- I remeasure after energizing new loads