Cable Size Calculation in Substation Design

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In electrical substation design, Cable Sizing is an important concept that design engineers must understand. It plays an important role because a properly selected cable size ensures safe, reliable, and efficient operation. It also complies with regulatory standards.

In substation design, if an undersized cable is selected, then it may overheat and fail prematurely; while if an oversized cable is chosen, then it may result in increased cost unnecessarily.

Read this chapter to learn a fundamental and practical method for selecting proper cable size.

What is Cable Sizing?

Cable Sizing is nothing but a method of selecting the proper area of cross-section of conductors used in substations for carrying rated electric current safely and efficiently under both normal and faulty operating conditions.

A correctly sized cable used in substations must be able to −

• Carry the rated full load current continuously without getting overheated.
• Handle short-circuit currents for a specific duration such as 1 sec or 3 sec.
• Maintain voltage drop within an acceptable limit.
• Withstand installation and environmental conditions like buried, tray, ducts, ambient temperature, etc.

Important Parameters for Cable Sizing

The following table highlights some of the key parameters required for calculating size of cable in substation design −

Standards Related to Cable Sizing in Substation Design

The following table provides a list of important Indian and international standards related to cable sizing calculation in substation design −

Cable Sizing Calculation in Substation Design

This section explains the step-by-step procedure for calculation cable size in substation design with the help of numerical example.

Step 1 - First of all, calculate the design/rated current of the load to be connected to the cable

$$\mathrm{I_{rated} \:=\: \frac{P}{\sqrt{3} \:\times\: V \:\times\: \cos\phi}}$$

Where, P is the rated power of load device, V is the system voltage, and cos φ is the load power factor.

For example, we have to connect a 3-phase electric motor of 200 kW at 11 kV and power factor equals to 0.87. Then, the design load current will be,

$$\mathrm{I_{rated} \:=\: \frac{200 \:\times\: 1000}{\sqrt{3} \:\times\: 11000 \:\times\: 0.87} \:=\: 12.07\:A}$$

Step 2 - Select the type of cable −

Next, we need to select the right cable based on the following parameters −

• Voltage class − for 11 kV, we generally select XLPE, armoured, aluminum conductor cable.
• Installation type − buried or tray or trench.
• Mechanical protection provided − steel wire or tape armoured.
• Environmental condition − moisture, chemicals, and ambient temperature.

Step 3 - Determine the base current carrying capacity of the cable

After knowing about the parameters mentioned in the above step, find the current rating or base current carrying capacity (I_b) of the cable from the IS 3961 or manufacturer's catalog. The cable must be selected for which current rating is greater than or equal to design current after applying the correction factors.

For example, from the manufacturer catalog −

• 3C × 25 sq mm AL XLPE 11 kV has a current rating of 87 A.
• 3C × 50 sq mm AL XLPE 11 kV has a current rating of 115 A.

Let's we are selecting 115 A cable.

Step 4 - Apply derating factors −

As we know, cables do not operate under standard conditions, hence we need to apply correction factors as follows −

$$\mathrm{I_{b} \:=\: I_{rated} \:\times\: C_{T} \:\times\: C_{G} \:\times\: C_{D}}$$

Here, C_T is the ambient temperature factor which has typical value equals to 0.94 at 45° C.

C_G is the grouping or number of circuits connected, its typical value is 0.9 for two circuits.

C_D is the soil thermal resistivity applicable to buried cables and it has a typical value equal to 0.85.

Hence, the current rating of cable after considering derating will be,

$$\mathrm{I_{b} \:=\: 115 \:\times\: 0.94 \:\times\: 0.9 \:\times\: 0.85 \:=\: 82.69 \:A}$$

Since our rated load current is only 12.07 A and the current rating of cable is 82.69 A. Thus, the 50 sq mm cable is adequate for our load.

Step 5 - Verify cable voltage drop limit

According to IS1255 and design specifications, the voltage drop in cable must be within acceptable limits. It can be calculated as follows −

$$\mathrm{\Delta V \:=\: \sqrt{3} \:\times\: I \:\times\: l \:\times\: (R\cos\phi \:+\: X\sin\phi)}$$

Here, L is the length of cable in km, R is the resistance per km, and X is the reactance per km.

For example, for our 50 sq mm aluminum cable, R = 0.642 Ω/km, X = 0.083 Ω/km, and l = 0.15 km, then voltage drop will be,

$$\mathrm{\Delta V \:=\: \sqrt{3} \:\times\: 12.07 \:\times\: 0.15 \:\times\: (0.642 \:\times\: 0.9 \:+\: 0.083 \:\times\: 0.435) \:=\: 1.92\:V}$$

Then, percentage voltage drop will be,

$$\mathrm{\%\Delta V \:=\: \frac{1.92}{11000} \:\times\: 100 \:=\: 0.017\:\%}$$

As per standards the permissible limit of voltage drop is 3 to 5 %. In our case, it is 0.017% which is acceptable.

Step 6 - Verify short-circuit current handling capability

The selected cable must be capable in withstand against short-circuit current for a specified time like 1 sec or 3 sec.

As per IEC 60949 standard, we can determine cross-section area for a specified short-circuit current and time as follows −

$$\mathrm{A \:=\: \frac{I_{sc} \:\times\: \sqrt{t}}{k}}$$

Here, A is the cross-sectional area in sq mm, I_sc is the short circuit current, t is the time duration, and k is the material constant which is 73 for aluminum and 115 for copper.

For example, let I_sc = 25 kA for 1 sec, we get,

$$\mathrm{A \:=\: \frac{25 \:\times\: 1}{73} \:=\: 342.46\:mm^{2}}$$

As we selected a 50 sq mm cable, but 25 kA for 1 sec requires 342.46 sq mm area. Thus, our cable cannot withstand the 25 kA short circuit current. Hence, we need to provide fault protection or multiple parallel cables for high-current circuits.

Practical Recommendation for Cable Sizing

The following table highlights the practical recommendations for cable sizing in substation design −

Voltage Drop Limits in Cables

Cables used in substations must fulfill the following voltage drop limits −

• For low voltage power circuit cables, the maximum voltage drop must not exceed 3% of rated voltage.
• For low voltage lighting circuit cables, the maximum voltage drop must not exceed 5% of rated voltage.
• For high voltage circuits, the maximum voltage drop must not exceed 2% of rated voltage.

Conclusion

Cable sizing is one of the fundamental concepts in substation design and engineering. Proper cable sizing and selection ensure safe, efficient, and economical operation of electrical system within a substation. We can calculate the cable size by understanding the fundamental principles such as current carrying capacity, derating factors, voltage drop, and short-circuit withstand capability of the cable.