Emergency Generator Sizing

The PG1–PG3 method: running load, voltage dip on motor starting, and instantaneous engine load.

1. What this check does

Takes the loads a generator must carry, including motors and how they start, and computes three required capacities. PG1 covers the running load; PG2 keeps the terminal voltage dip within the allowed value when the motor with the largest starting kVA starts; PG3 keeps the engine within its short-time overload while that start happens with everything else running. The generator must meet the largest of the three.

2. Inputs used

Each load: kW (shaft output for motors, input for other loads), quantity, demand factor, efficiency, power factor.
Motors: starting method (across-the-line, star-delta, autotransformer tap, soft starter or VFD current limit), locked-rotor multiple and starting power factor.
Generator: transient reactance Xd′, allowable transient voltage dip, engine short-time overload capability K, rated power factor; optionally the subtransient reactance Xd″ for the non-linear load check.

3. Formulas and assumptions

Running load (PG1)

Input kW

P = \sum \dfrac{\mathrm{kW}_i\,\mathrm{qty}_i\,\mathrm{DF}_i}{\eta_i} \qquad Q = \sum P_i \tan(\arccos \mathrm{PF}_i)

PG1

PG_1 = \max\left(\sqrt{P^2 + Q^2},\ \dfrac{P}{\cos\theta_G}\right)

Voltage dip on motor starting (PG2)

Starting kVA

Q_L = k_{\text{start}}\,\dfrac{\mathrm{kW}}{\eta\,\mathrm{PF}}

k_start = LR (DOL), LR/3 (star-delta), LR·tap² (autotransformer), current limit (soft starter, VFD).

Dip

\Delta V = \dfrac{X_d'\,q}{1 + X_d'\,q}, \qquad q = \dfrac{Q_L}{PG}

Xd′ = transient reactance. Xd″ governs only the first one or two cycles and would understate the dip.

PG2

PG_2 = Q_L\, X_d'\,\dfrac{1 - \Delta V}{\Delta V}

Instantaneous load (PG3) and result

PG3

PG_3 = \dfrac{P - P_{\text{run},m} + Q_{L,m}\cos\theta_s}{K \cos\theta_G}

m = the motor whose start adds the most kW.

Fire pump

PG_{fp} = Q_{L,fp}\, X_d'\,\dfrac{0.85}{0.15}

Dip ≤ 15% when a fire pump is marked.

Required

\mathrm{kVA} = \max\bigl(PG_1,\ PG_2,\ PG_3,\ PG_{fp}\bigr), \qquad \mathrm{kW} = \mathrm{kVA}\cos\theta_G

Rounded up to the next listed rating.

Step loading

\Delta V_k = \dfrac{X_d'\,q_k}{1 + X_d'\,q_k}, \quad q_k = \dfrac{\sum_{\text{step } k} S_{\text{start}}}{\mathrm{kVA}_{\text{gen}}} \qquad \text{engine}_k = \dfrac{P_{<k} + \sum_{\text{step } k} P_{\text{start}}}{\mathrm{kW}_{\text{gen}}}

Loads with the same step number start together, with all earlier steps running.

Symbols

$\mathrm{kW}_i,\ \mathrm{qty}_i,\ \mathrm{DF}_i$	Load rating, quantity and demand factor	kW, —, —
$\eta_i,\ \mathrm{PF}_i$	Load efficiency and power factor
$P,\ Q$	Total input real and reactive power	kW, kVAR
$\cos\theta_G$	Generator rated power factor (usually 0.8)
$Q_L,\ k_{\text{start}}$	Starting kVA of the motor; starting multiple for the starter type	kVA, —
$X_d'$	Generator transient reactance (sets the starting dip)	per unit
$X_d''$	Generator subtransient reactance (non-linear load check only)	per unit
$q,\ \Delta V$	Starting kVA over generator kVA; instantaneous voltage dip	per unit
$\cos\theta_s$	Motor power factor during starting
$K$	Engine short-time overload capability (e.g. 1.2)
$PG_1,\ PG_2,\ PG_3$	Generator kVA for running load, voltage dip, instantaneous load	kVA

Bar chart comparing PG1, PG2 and PG3 in kVA with the largest one highlighted as the required size. — **Figure 1.** Three checks, the largest wins: PG1 running load, PG2 voltage dip, PG3 instantaneous load.

Voltage versus time curve showing a sudden dip when a motor starts and recovery by the voltage regulator; the dip depth is Delta V. — **Figure 2.** Generator voltage when the largest motor starts.

Figure 3. Starting kVA by starting method.

Equivalent circuit: generator EMF behind transient reactance Xd′ feeding a motor starting impedance. — **Figure 4.** The dip comes from the starting current flowing through the generator transient reactance.

PG1–PG3 take one motor starting at a time with all other loads already running (worst case for PG3). The step table takes the loads you give the same step number as starting together, with the earlier steps running, and reports each step's dip and engine load at the selected rating.
Motor efficiency left blank defaults to the US federal minimum for a 4-pole enclosed motor of that rating (10 CFR 431.25, 2016 levels; fire pumps use the fire pump motor table), with ratings between table values rounded as the regulation specifies.
The starting load is treated as a sudden impedance behind the transient reactance Xd′, the value that sets the dip seen over the first few cycles until the voltage regulator responds; regulator and governor action are not modeled, which is conservative. The subtransient Xd″ is smaller and lasts only one or two cycles, so using it here would understate the dip.
The listed generator ratings are common standby kW sizes; manufacturers differ, so enter your own list if needed.
PG1–PG3 is the Korean building-code form of the same checks that US manufacturer sizing programs make (running kVA, transient voltage dip on the largest start, engine kW with the start in progress). Use the manufacturer program for the final selection; NFPA 110 type, class and level and NEC 700/701/702 govern the installation.
Xd′, allowable dip and K are entered by you from the generator and load data. No public table gives reactances by rating; standby alternators typically show Xd′ around 20–30% and Xd″ around 12–20%. UFC 3-540-01 D-2.3 limits Xd″ to 0.12 when non-linear loads are 25% or more of the load; enter Xd″ to have that checked.
At the selected rating the tool reports the starting dip and the running loading; UFC 3-540-01 H-3.2.3.1 asks for at least 35% of rated kW (without the fire pump) to avoid wet stacking.

4. What is NOT checked

Altitude and ambient temperature derating.
Frequency dip and governor response during step loading; block-load acceptance limits of the engine.
Harmonic heating from non-linear loads (flagged, not computed).
Fuel, run time and paralleling controls.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

NFPA 110 — emergency and standby power systems
IEEE Std 446 — emergency and standby power (Orange Book)
Korean building electrical design criteria — PG1–PG3 generator capacity method
NEC 2023 Articles 700, 701, 702 (context); Article 695 (fire pumps)
UFC 3-540-01 Engine-Driven Generator Systems for Prime and Standby Power (Change 3, 2023) — U.S. DoD, approved for public release

6. Validation cases

These worked examples run through the engine on every change; the expected values come from the cited source. All cases: Validation.

Emergency generator: pump (DOL), lighting, two fans (star-delta) generator/sizing · Hand calculation

Pass

Source: Hand calculation of the PG1–PG3 method (running load, voltage dip on largest start, instantaneous load) — PG2 = 717.7 kVA × 0.20 × 0.8 / 0.2 = 574.2 kVA governs.

Quantity	Expected	RokBench	Error	Result
pg1Kva	275.6	275.6	0%	Pass
pg2Kva	574.16	574.2	0.007%	Pass
pg3Kva	344.3	344.3	0%	Pass
requiredKw	459.3	459.3	0%	Pass

7. Known issues and changes

See the Engineering Notes. Try the tool: Emergency Generator Sizing.