Star-Delta Calculation: Formulas and Worked Examples
Short version: in star the current is three times smaller than in delta. That single relation is the reason Y-Δ exists as a reduced-voltage start. In practice you calculate four numbers: motor rated current, DOL starting current, reduced Y-Δ starting current, and the current in the cable between the Y-Δ cabinet and the motor — that one is below rated current. Miss the last point and you will oversize the cable by 50%, making the customer pay for copper they never needed.
Rated Current Formula
Rated phase current for a three-phase induction motor:
In = P / (√3 · UL · cos φ · η)
P in watts, UL is line voltage (380 V here), cos φ is power factor (0.82-0.86 for induction motors), η is efficiency (0.86-0.93 for IE2 standard motors). √3 ≈ 1.732.
Rule of thumb: for IE2/IE3 motors with cos φ·η ≈ 0.75, rated current approximately equals In ≈ P(kW) × 2. So 11 kW → ~22 A, 22 kW → ~43 A. Error ±10%, which is fine for preliminary breaker and cable sizing.
Rated Current Table for Standard Power Ratings
| P, kW | cos φ | η | In, A (exact) | In, A (×2) |
|---|---|---|---|---|
| 5.5 | 0.84 | 0.87 | 11.5 | 11 |
| 7.5 | 0.85 | 0.88 | 15.2 | 15 |
| 11 | 0.85 | 0.89 | 22.0 | 22 |
| 15 | 0.85 | 0.90 | 29.8 | 30 |
| 18.5 | 0.86 | 0.91 | 35.9 | 37 |
| 22 | 0.86 | 0.92 | 42.2 | 44 |
| 30 | 0.87 | 0.93 | 56.4 | 60 |
| 37 | 0.87 | 0.93 | 69.5 | 74 |
| 45 | 0.88 | 0.94 | 82.6 | 90 |
ABB motors with EU 400/690 V markings use the same numbers with a small voltage correction: on a 380 V grid the current sits within 5% of the table value.
Starting Current: Direct Online
Connected straight to the line (DOL, direct online), the motor pulls Istart = (5÷8) · In at the instant of start. The exact ratio depends on the rotor class. Nameplates often show Istart/In = Ki — for IE2/IE3 motors that is typically 6.5-7.2.
Example for 11 kW with Ki = 7: Istart = 22 × 7 = 154 A. That is a 0.1-0.5 second spike until the rotor reaches working speed. If the grid holds the spike, the start goes through. If not — lights flicker in the next bay, the fridge drops out, the substation breaker walks toward its limit.
Why 6-7× and Not 10-20×
Old handbooks list "10-20 In". That was real for 1960-70s motors with high-resistance rotors. Modern IE2/IE3 motors with improved rotor design show Ki = 5-8. Calculations today use that range, not the old figure.
Reduced Starting Current Under Y-Δ
The math trick: when the windings are wired in star, each winding sees UL/√3 = 380/1.73 = 220 V instead of 380. Winding current drops proportionally, and because star line current equals winding current — line current in the grid drops too. Net result:
Istart(Y) = Istart(Δ) / 3
So starting current in star is three times smaller than starting current in delta. For 11 kW with 154 A DOL start → around 51 A in star. That is roughly 2.3 In, a level a class D breaker absorbs without trouble.
Starting torque drops in parallel. Delta gives 100% of rated torque (typically 180-220% during inrush); star gives 33% of that. Loaded machines cannot start under Y because the torque never exceeds the load torque.
Side-by-Side Numbers for a Few Power Levels
| P, kW | In, A | Istart DOL, A | Istart Y-Δ, A | Breaker savings |
|---|---|---|---|---|
| 5.5 | 11 | 77 | 26 | from C100 to C32 |
| 11 | 22 | 154 | 51 | from C160 to C50 |
| 15 | 30 | 210 | 70 | from C250 to C63 |
| 22 | 43 | 301 | 100 | from C400 to C100 |
| 30 | 60 | 420 | 140 | from C630 to C160 |
The breaker itself is always sized against the running current in delta, not the start. The point is that a class D breaker (magnetic element up to 10 In) swallows a Y-Δ spike without tripping, while DOL spikes trip even D breakers at higher power.
Current in the Cable Between Cabinet and Motor
This is the most common mistake we see on sites. The cable from a Y-Δ cabinet to the motor terminal box carries six conductors, not three. Each conductor handles the current of one winding. In delta mode that is:
Iwinding = Iline / √3 = In / √3
For 11 kW: Iwinding = 22 / 1.73 = 12.7 A. Each of the six conductors carries 12.7 A, not 22. That means the cross-section is well below the line cable.
Cabinet-to-Motor Cable Sizing Table
| P, kW | In, A | Iwinding, A | Cross-section (6-core), mm² | Nearest standard |
|---|---|---|---|---|
| 5.5 | 11 | 6.4 | 1.0 | 6×1.5 |
| 11 | 22 | 12.7 | 1.5 | 6×2.5 |
| 15 | 30 | 17.3 | 2.5 | 6×2.5 |
| 22 | 43 | 24.9 | 4.0 | 6×4 |
| 30 | 60 | 34.6 | 6.0 | 6×6 |
Real mistake from a recent site visit: the installer ran 6×4 mm² for an 11 kW motor (sized for the 22 A rated value per the wiring code). That is over 50% oversize. The customer paid around 1,200 UAH extra for 40 meters of cable. Correct size — 6×2.5 with margin.
The feed cable from the main panel to the cabinet input breaker is sized the normal way, for full motor rated current. 11 kW needs 4×4 mm² (three phases + PE). No shortcut there because that line carries full motor current once the motor is in delta.
Breaker and Contactor Selection
Overload breaker rating:
- Ibrk = 1.15 · In for a standard thermal element.
- Curve D (magnetic up to 10 In) — mandatory for motor loads.
- Round to the standard series: 16, 20, 25, 32, 40, 50, 63, 80, 100, 125, 160 A.
Ready numbers:
- 5.5 kW (In 11 A) → 16A D breaker
- 11 kW (In 22 A) → 32A D breaker
- 15 kW (In 30 A) → 40A D breaker
- 22 kW (In 43 A) → 63A D breaker
- 30 kW (In 60 A) → 80A D breaker
Contactors are sized for the winding current In/√3. For 11 kW (Iwinding = 12.7 A) pick three 16-18 A contactors: ABB AF16-30 or Schneider LC1D18 (~800-1,000 UAH each). Installing three 25-32 A contactors "for margin" wastes money and grows the cabinet enclosure by 20%.
Timer Delay Calculation
The timer delay depends on the load inertia. Star acceleration time:
t = (J · ω) / (Mstart - Mload)
J is inertia in kg·m², ω is angular speed (≈157 rad/s for 1500 rpm), Mstart is star starting torque (33% of rated), Mload is the mechanism resistance torque.
In practice the formula gets replaced by a clamp ammeter: run three or four starts at different delays (2 s, 5 s, 8 s, 12 s) and pick the one where the current spike after the switch is smallest.
Ballpark Values for Typical Loads
- Axial fan up to 15 kW — 4-6 s
- Radial fan with flywheel — 8-12 s
- Centrifugal pump — 3-5 s
- Empty belt conveyor — 5-8 s
- Machine tool with flywheel — 10-15 s
- Screw conveyor for bulk material — 6-10 s
Thermal Check: Will the Motor Hold
Frequent start-stop cycles load the windings thermally. Working rule for Y-Δ: no more than 6 starts per hour at full acceleration time. Class F insulation (155°C) handles that easily. Class B insulation (130°C) tolerates only 3-4 starts per hour.
If the process needs more, only a VFD fits. A drive starts the motor with no current spike, the thermal load on windings is minimal, and 50-100 starts per hour run without damage.
Frequently Asked Questions
How do I estimate cos φ if the nameplate is missing?
Standard IE2 asynchronous motors from 5.5 to 45 kW fall in the 0.82-0.88 range. Use 0.85 as the average. IE3 motors run 0.84-0.90, 0.85 still works. The exact figure matters only for energy audits; for breaker sizing the ±2% error is irrelevant.
Why is current in star three times smaller, not √3 times?
Winding voltage in star is √3 times smaller (220 V vs 380 V). Winding current drops √3 times. But in star line current equals winding current. In delta line current is √3 times larger than winding current. Multiply the two factors and you get 3. So line current in star is genuinely three times smaller than line current in delta, even though each individual factor is √3.
Do I need to calculate the PE conductor current?
The protective earth conductor carries no working current in normal operation — only during a fault. Code sizing: S_PE = 16 mm² if S_phase ≤ 16, or half of phase cross-section if the phase is larger. For 11 kW with a 4 mm² phase, the PE is also 4 mm² (not half, because the phase is below 16).
How do I calculate for a 400/690 V motor instead of 380/660?
Modern European motors (ABB, Siemens) carry 400/690 V markings. On a Ukrainian 380 V grid they run with about 5% reduced current. Same formula, just 5% below the 400 V table value. Code margins of 10% cover the difference with room to spare.
When does the Y-Δ calculation stop making sense?
Below 5.5 kW the DOL inrush is only 55-77 A for half a second. Any feeder behind a 400 A transformer takes it without a visible dip. Building a three-contactor cabinet plus a timer for that job wastes money. A soft starter for 7-8k UAH or a 2.2 kW VFD for 10-12k delivers the same result and saves energy along the way.
Wrap-Up
The Y-Δ calculation lives in four numbers: rated current from P×2 (fast) or the full cos φ·η formula (accurate), DOL starting current = 6-7 In, Y-Δ starting current = 2-2.3 In, cabinet-to-motor cable current = In/√3. With those you pick a 1.15 In class D breaker, contactors rated at In/√3, a feed cable for full In, and a branch cable for In/√3. If the numbers feel off, share the motor data with a Chastotnik.ua engineer — we recalculate within 15 minutes and send back a ready parts list. Related reading: the full Y-Δ scheme, Y-Δ timer relay wiring, Y-Δ vs soft starter vs VFD, motor with a VFD, how a soft starter works.
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