Busbar Size Calculation in Substation Design

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A busbar is nothing but the main conductor which connects the incoming/outgoing electric grid with the internal substation circuit. It is the main component of an electrical substation. A busbar is basically provided in a substation to carry a large amount of current that is received from the incoming feeders or the large amount of current that is distributed to the outgoing feeders.

In an electrical substation, it is important to choose the correct busbar size to ensure safety, thermal stability, mechanical strength, and compliance with regulatory standards. Read this chapter to learn the step-by-step process of how to calculate the busbar size in substation design.

Important Considerations for Busbar Sizing Calculation

While calculating the size of busbar in substation design, we need to consider the following key parameters −

• Continuous current carrying capacity − The busbar must be able to carry the rated load current without excessive temperature rise.
• Short-circuit withstand capacity − The busbar must be capable in withstanding thermal and mechanical stresses during short-circuit faults, typically 1s or 3s ratings.
• Material selection − If cheaper, lighter, and larger cross-sectional area is required, then we should select aluminum as the busbar material. On the other hand, if better conductivity and smaller size is desirable, then copper is one of the best choices.
• Standard compliance − The busbar must comply with regulatory standards such as IS 5082, IS8623/IEC61439, IEEE 605/IEC62271, etc.

Busbar Size Calculation

The step-by-step procedure for selecting correct busbar size in electrical substation design is explained below −

Step 1 - Calculate the Rated Current of Busbar

The busbar must be capable in carrying maximum load current in the substation, which can be estimated using the following formula −

$$\mathrm{I_{bb} \:=\: \frac{S}{\sqrt{3} \:\times\: V}}$$

Where, I_bb is the rated current of busbar, S is the kVA or MVA rating of transformer or feeder, and V is the system voltage.

Step 2 – Select Conductor Material for Busbar and Current Density

The current density depends on the material used, type of enclosure, cooling, and permissible temperature increase. Typical values for copper and aluminum are given here −

Step 3 - Calculate Required Area of Busbar

Then, calculate the area of cross-section required for busbar for the given material and current density. For this, we can use the following formula −

$$\mathrm{A \:=\: \frac{I_{bb}}{J}}$$

Here, A is the cross-sectional area and J is the current density.

Step 4 - Select Practical Busbar Dimensions

Now, select a practical busbar dimension depending on the area required as per the step-3. In general, busbar has a rectangular shape i.e., width x thickness. Where, width must be greater than or equal to 2 x thickness for better heat dissipation.

The following are some standard aluminum busbar dimensions as per the IS5082 standard −

• $\mathrm{50 \:\times\: 10\:mm \:=\: 500\: mm^{2}}$
• $\mathrm{60 \:\times\: 10\:mm \:=\: 600\: mm^{2}}$
• $\mathrm{80 \:\times\: 10\:mm \:=\: 800\: mm^{2}}$

Step 5 - Check Short-Circuit Withstand Capacity −

Busbars must be capable in handling peak and thermal stresses during short-circuit faults. The thermal withstand capacity of the busbar can be calculated by using the following formula −

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

Where, I_sc is the short-circuit withstand current in kA, K is the constant (for copper = 143 and for aluminum = 94), A is the cross-sectional area, and t is the fault duration in seconds, it is usually 1s or 3s.

Step 6 - Check Mechanical Stress

Now, we need to check mechanical stress or electrodynamic force that the busbar can withstand during short-circuit faults.

Here is the formula to calculate this electrodynamic force during short-circuits −

$$\mathrm{F \:=\: \frac{\mu_{0}}{2\pi} \:\times\: \frac{I_{m}^{2}}{d}}$$

Where,

$$\mathrm{I_{m} \:=\: \sqrt{2} \:\times\: I_{sc} \:\times\: k}$$

And d is the spacing between busbars.

Step 7 - Verify Temperature Increase

Finally, verify the temperature rise comply with the regulatory standards like for aluminum busbar it is $\mathrm{\:50^{\circ}\:C\:}$ over ambient as per the IS8623/IEC61439.

Practical Guidelines for Substations in India

Listed below are some important practical guidelines for substation design in India −

• Aluminum busbars are used in 11 kV and 33 kV distribution substations due to their cost-effectiveness.
• Copper busbars are to be used in 132 kV and above substations and in those having space constraints.
• Always provide sliver or tin plating at joints to reduce resistance.
• Follow the specifications defined by regulatory compliances.

Recommended Busbar Sizes

The following table provides the recommended sections of aluminum busbars for some rated currents, indoor installation, and 1 A/mm² current density −

Numerical Example

Calculate the busbar size for a substation having a transformer of 20 MVA/33 kV.

Solution– Given data,

• Rating of transformer in substation, S = 20 MVA = 20000 kVA
• Rated busbar voltage, V = 33 kV = 33000 V

Let us select an aluminum busbar with indoor installation, and current density J = 0.8 A/mm²

Let us consider fault level at bus I_sc = 25 kA with fault clearing time t = 1 s

Let us take phase-to-phase bus spacing d = 0.20 m, then the size of busbar can be calculated as follows −

Step 1 - Continuous rated current of busbar −

$$\mathrm{I_{bb} \:=\: \frac{S}{\sqrt{3} \:\times\: V} \:=\: \frac{20000}{\sqrt{3} \:\times\: 33}}$$

$$\mathrm{\therefore\: I_{bb} \:=\: 349.9\:A \:=\: 350\:A}$$

Step 2 - Required area of cross-section −

$$\mathrm{A \:=\: \frac{I_{bb}}{J} \:=\: \frac{350}{0.8}}$$

$$\mathrm{\therefore\: A \:=\: 437.5\: mm^{2}}$$

We will select next standard size of aluminum busbar which is greater than or equal to required area (A). Practically, we will select 60 × 10 mm = 600 mm² including safety margin.

Step 3 - Verify short-circuit thermal withstand capacity

In this step, we have to verify that the selected size of busbar can handle thermal energy of a short-circuit fault.

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

Here K = 148 for bare aluminum, then minimum area required for the assumed fault level i.e., I_sc = 25 kA, t = 1s is

$$\mathrm{A_{min} \:=\: \frac{I_{sc} \:\times\: \sqrt{t}}{K} \:=\: \frac{25000 \:\times\: \sqrt{1}}{148} \:=\: 169\:mm^{2}}$$

As we selected 600 mm² which is much higher than 169 mm².

Step 4 - Verify permissible short-circuit current for selected busbar size

$$\mathrm{I_{sc} \:=\: \frac{148 \:\times\: 600}{\sqrt{1}} \:=\: 88.8 \:kA}$$

Thus, selected 600 mm² aluminum busbar can withstand 88.8 kA, 1s (theoretically).

Step 5 - Verify mechanical stress/electrodynamic force

$$\mathrm{F \:=\: \frac{\mu_{0}}{2\pi} \:\times\: \frac{I_{m}^{2}}{d} \:=\: \frac{\mu_{0}}{2\pi} \:\times\: \frac{(\sqrt{2} \:\times\: I_{sc})^{2}}{d}}$$

$$\mathrm{\Rightarrow\: F \:=\: 2 \:\times\: 10^{-7} \:\times\: \frac{(\sqrt{2} \:\times\: 25000)^{2}}{0.20}}$$

$$\mathrm{\therefore\: F \:=\: 1250\: Nm^{-1}}$$

We need to design supports and clamps to withstand this mechanical stress.

Hence, we will select an aluminum busbar for the given substation having 600 mm² with 88.8 kA, 1s thermal stress and 1250 N/m mechanical stress.

Conclusion

In conclusion, the busbar is one of the crucial components in a substation and selecting its correct size plays an important role in safe and efficient power evacuation. In this chapter, we explained the practical method for designing the busbar system in electrical substations.