Technical Article

# Motor Starters Part 4: Selecting and Sizing Star-Delta Parts

December 02, 2022 by Simon Mugo

## This article makes the selection and sizing of the star-delta motor starter parts very easy. Here you will learn how to select and size the fuse, circuit breaker, thermal overload relay, and contactor.

Part 3 of the series discussed the basic theories of the star-delta motor stater, noting the composition of contactors, fuses, circuit breakers, and overload relays. These components come in different sizes and create challenges in selection and sizing. This article will address how to select and size the fuse, circuit breaker, thermal overload relay, and contactor.

### A Sample Motor Challenge to Solve

In this article we will walk through the design of a star-delta motor starter to meet the following requirements:

• 415 V 3-phase motor
• 10 HP
• Code A
• Efficiency of 80%
• PF of 0.8
• Rotating at 600 RPM.

Motor Torque and Current

#### The 5252 Conversion Factor

When calculating the motor-rated torque or the Full Load Torque (FLT) of the motor, use the constant 5252. The number 5252 represents the point during the revolution range of the motor where the torque and the horsepower cross paths. It is derived from the relationship between the motor speed, power, and torque as follows:

$$1 \text{ HP} = 33000 \text{ ft-lb/min}$$

Given that:

$$1 \text{ revolution} = 360° = 2\pi$$

The crossing path factor will be determined by:

$$\frac{33000}{2\pi} = 5252.113 ≈ 5252$$

#### Formula for the Motor Full Load Torque (FLT)

Let's now caluclate the value of the motor's full load torque:

$$\text{FLT} = \frac{5252\cdot\text{HP}}{\text{RPM}}$$

Let's now input the values from our sample motor design challenge:

$$\text{FLT} = \frac{5252×10}{600} = 88 \text{ lb-ft}$$

#### We can now converting FLT from lb-ft to Nm using the folloowing:

$$1 \text{ lb-ft} = 1.356 \text{ Nm}$$

Therefore,

$$\text{FLT} = 88 \times 1.356 = 119 \text{ Nm}$$

#### Calculating the Starting Torque of the Motor

For motors of capacity below 30 kW, then the induction motor starting torque is 3 times the motor full load torque. We can plug in our previously calculated value for the FLT to derive the starting torque:

$$\text{Starting Torque of the Motor} = 3 \times \text{Full Load Torque}$$

$$\text{Starting Torque of the Motor} = 3 \times 119 = 357 \text{ Nm}$$

#### Calculating the Lock Rotor Current of the Motor

The Lock Rotor Current is in the form of a range that can be attained from the standard table of Locked Rotor Current given the code of the motor as shown below in Table 1. Note that the full table runs from code A to code V. For our sample motor problem, the moder is code A.

##### Table 1. Locked Rotor Currents
 CODE MIN MAX A 1 3.14 B 3.15 3.54 C 3.55 3.99 D 4 4.49

The formula for calculating the locked rotor current (LRC) of the motor is given by:

$$\text{LRC} =\frac{1000 \times \text{ HP} \times \text{ Locked Rotor Current Code Value}}{1.732 \times V}$$

Now, we can calculate the minimum and maximum motor LRC using the horsepower and voltage of the motor:

$\text{LRC}_{min} =\frac{1000 \times 10 \times 1}{1.732 \times 415} = 13.91 \text{ A}$

\$\text{LRC}_{max} =\frac{1000 \times 10 \times 3.14}{1.732 \times 415} = 43.69 \text{ A}$

#### Calculating the Full Load Current of the Motor

The formulas for the line and phase full load currents are given by equals:

$$FLC_{LINE}=\frac{1000 \times P}{1.732×PF}$$

$$FLC_{phase}=\frac{FLC_{Line}}{1.732}$$

Using those equations and plugging in the values for our sample motor:

$$FLC_{LINE}=\frac{1000×10×0.746}{1.732×415×0.8}=12.97 \text{ A}$$

$$FLC_{phase}=\frac{12.97}{1.732}=7.49 \text{ A}$$

#### Calculating the Star-delta Starter Motor Starting Current

Finally, the formula for the star-delta starter motor starting current equals:

$$\text{Motor Starting Current} = 3 \times FLC = 3 \times 12.97 = 38.91 \text{ A}$$

After calculating all the basic required values, it becomes easy for engineers and technicians to size the components of the star-delta starter.

### Selecting and Sizing the Fuse

Table 2 contains data on standard fuse current ratings as per NEC 430-52, which will make fuse selection and sizing easy.

##### Table 2. Sizes of fuses per NEC 430-52
 MOTOR TYPE TIME DELAY FUSE (% OF FLC) NON-TIME DELAY FUSE (% OF FLC) Single phase 300 175 3-phase 300 175 Synchronous 300 175 Wound rotor 150 150 Direct current 150 150

The motor being powered is a 3-phase motor. The fuse time delay will be 300% of FLC and the non-time delay will be 175% of the FLC.

Time delay fuse maximum size = 300%×FLC = 300%×13 = 39A

Non - time delay fuse maximum size = 175%×FLC = 175%×13 = 22.75A≅23A

### Selecting and Sizing the Circuit Breaker

The table below represents NEC 430-52 circuit breaker sizes.

##### Table 3. Sizes of Circuit Breakers
 CIRCUIT BREAKERS AS PER NEC 430-52 MOTOR TYPE INSTANTANEOUS TRIP IN % INVERSE TIME IN % Single Phase 800 250 Three-Phase 800 250 Synchronous 800 250 Wound Rotor 800 150 Direct Current 200 150

Calculate the instantaneous trip circuit breaker using the formula below:

Instantaneous Circuit Breaker Maximum Size = 800%×FLC = 800%×13 = 104A

Now calculate the size of the inverse trip circuit breaker as shown below:

Inverse Trip Circuit Breaker Size = 250%×FLC = 250%×13 = 32.5A≅32A

### Selecting and Sizing of Thermal Overload Relay

As the sizing of the DOL starter demonstrated, the thermal overload relay has an upper and lower value.

#### The Phase Thermal Overload Relay

Lower Limit of the Range = 70%×FLCphase = 70%×7 = 4.9A≅5A

Upper Limit of the Range = 120%×FLCphase = 120%×7 = 8.4A≅9A

#### The Line Thermal Overload Relay

For the start-delta starter, the thermal overload can be placed in the windings or the line.

When placed in line

Supply > O/L  > Main Contactor

Thermal Overload Relay = 100%×FLCLINE = 100%×13 = 13A

When placing O/L Relay in windings

Main Supply > Main - Contactor - Delta Contactor > Overload Relay

Thermal Overload Relay = 58×FLCLINE = 58%×13 = 7.54A≅8A

### Selecting and Sizing the Contactor Type

#### Main and Delta Contactor

Here the contactors are smaller as compared to the one used in DOL Starter. This is because the contractor here is only used to control the currents in the winding only.

The winding current = 1.723×58%×Line current

They are rated at 58% of the motor current rating.

#### Star Contactor

This is the third contactor and it only carries the star current. The current here is 58 % of the current in the delta contactor, which is 33% of the motor rating currents.

As in the DOL calculation, the same types of contractors exist. From the chart of standard types, the type of contactor is AC1.

Breaking Contactor Capacity = Value in the Chart×FLCLINE = 1.5×13 = 19.5A≅19A

Main Contactor Size = 58%FLCLINE= 58%×13 = 7.54A≅8A

Star Contactor Size =3 3%× FLCLINE = 33%×13 = 4.29A≅4A

Delta Contactor Size = 58 % FLCLINE = 58%×13 = 7.54A≅8A

### Key Takeaways of Selecting and Sizing Star-Delta Motor Starter Parts

In brief:

• Torque conversion factor is 5252
• The size of the fuse is 39 A for maximum and 23 A for the minimum size
• Instantaneous circuit breaker size is 104 A and the inverse trip circuit breaker size is 32 A
• The lower limit current of the thermal overload relay is 5 A and the upper limit is 9 A
• The line thermal overload relay is 13 A while the windings thermal overload relay is 8 A
• Main contactor is rated 8 A, star contactor 4 A while the delta contactor 8 A

Featured image used courtesy of Adobe Stock