Chapter 21, Problem 9RQ

To determine

The conductor sizes, overload heater size, circuit breaker size, fuse size, minimum NEMA and IEC starter sizes, and the upper and lower range of starting current for this motor.

Explanation of Solution

Given:

Horsepower of the motor $\left(\text{P}\right)$ is $75\text{hp}$.

Line voltage $\left(\text{V}\right)$ is $230\text{V}$.

Power factor $\left(\text{F}\right)$ is $80\%$.

Full-load current $\left(\text{I}\right)$ is $185\text{A}$.

A temperature rise $\left(\Delta \text{T}\right)$ is $40°\text{C}$.

Three phase synchronous motor.

Code letter is $\text{A}$.

Conductor is copper wire with THHN insulation.

Transformer ratio $\left(\text{T}\right)$ is $300:5$.

Calculate the maximum ampacity $\left({\text{I}}_{\text{i}}\right)$ using the relation.

  ${\text{I}}_{\text{i}}=\frac{\text{I}}{\text{F}}$

  $\begin{array}{c}{\text{I}}_{\text{i}}=\frac{185\text{A}}{80\%\times \left(\frac{1}{100\%}\right)}\\ =1.25\times 185\text{A}\\ =231.25\text{A}\end{array}$

Refer to Table 310.15(B)(16), “Conductor sizes” to obtain the size of conductor as $4/0\text{AWG}$ corresponding to copper conductor with THHN insulation and $260\text{A}$ nearest value to $231.25\text{A}$.

Refer to Table 430.52, “Percentage of full load current” to obtain the percentage full-load current as $300\text{A}$ corresponding to inverse time breaker and synchronous type motor.

Refer to Figure 21-19, “Fuse size” to obtain the fuse size as $300\text{A}$ nearest to percentage of full-load current $300\text{A}$.

Refer to Figure 21-21, “IEC motor starter by size, horsepower” to obtain the size of IEC starter as $\text{S}$ corresponding to $75\text{hp}$ and $230\text{V}$.

Refer to Figure 21-20, “NEMA motor starter sizes” to obtain the size of IEC starter as $4$ corresponding to $75\text{hp}$ and $230\text{V}$.

Refer to Table 430.7(B) “Locked-Rotor indicating code” to obtain the upper and lower range of starting current as $0\frac{\text{kV}\cdot \text{A}}{\text{hp}}-3.14\frac{\text{kV}\cdot \text{A}}{\text{hp}}$ corresponding to code letter $\text{A}$.

Calculate the upper limit $\left({\text{I}}_1\right)$ using the relation.

  ${\text{I}}_1=\frac{\text{P}\times {\text{C}}_1}{\text{V}\left(\sqrt{3}\right)}$

  $\begin{array}{c}{\text{I}}_1=\frac{75\text{hp}\times 0\frac{\text{kV}\cdot \text{A}}{\text{hp}}}{230\text{V}\left(\sqrt{3}\right)}\\ =0\text{A}\end{array}$

Calculate the lower limit $\left({\text{I}}_2\right)$ using the relation.

  ${\text{I}}_2=\frac{\text{P}\times {\text{C}}_2}{\text{V}\left(\sqrt{3}\right)}$

  $\begin{array}{c}{\text{I}}_2=\frac{75\text{hp}\times 3.14\frac{\text{kV}\cdot \text{A}}{\text{hp}}}{230\text{V}\left(\sqrt{3}\right)}\\ =0.5911\text{kA}\times \left(\frac{{10}^3\text{A}}{1\text{kA}}\right)\\ =591.1\text{A}\end{array}$

Thus, the conductor size is $\underset{\_}{4/0\text{AWG}}$, fuse size is $\underset{\_}{300\text{A}}$, minimum NEMA motor starter size is $\underset{\_}{4}$ and IEC starter size is $\underset{\_}{\text{S}}$, and the upper range of starting current is $\underset{\_}{0\text{A}}$ and lower range of starting current is $\underset{\_}{591.1\text{A}}$.