Example for Coordination of Cascaded Circuit Breakers

Inputs for Coordination Calculation

A 440 V 60 Hz switchboard feeds a 4-wire distribution board for small loads such as socket outlets. The switchboard has a fault making capacity of 100kA rms. After applying diversity factors to the loads the total load current is 90 A. Moulded case circuit breakers (MCCBs) rated at 16 A and 32 A are to be used for the loads.

The installation will use cables having copper conductors and XLPE insulation. The cable from the switchboard to the distribution board is 20 metres in length.

A typical load cable is 15 metres in length and will carry a current of 29 A at a power factor of 0.85 lagging.

Let’s dive into solution!

1. Choose the upstream MCCB at the switchboard and its settings

From a manufacturer’s data sheet a 125 A MCCB with an adjustable 100 A thermal release is chosen. The thermal release is set to 90 A to match the total load.

2. Choose the incoming feeder cable

From a manufacturer’s data sheet several cables can be compared for the same ambient conditions and laying arrangements. Their details are:

• 50 mm² cable, maximum current 124 A, R = 0.492, X = 0.110 ohms/km.
• 70 mm² cable, maximum current 159 A, R = 0.340, X = 0.106 ohms/km.
• 95 mm² cable, maximum current 193 A, R = 0.247, X = 0.093 ohms/km.

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3. Choose the downstream load MCCB and its settings

From a manufacturer’s data sheet a 32 A MCCB with an adjustable 32 A thermal release is chosen. The thermal release is set to 29 A to match its load.

4. Find the upstream fault source impedance

For a prospective symmetrical fault current of 100 kA rms the upstream fault source impedance Z_up is:

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5. Find the cut-off, or let-through, current from the switchboard

From a manufacturer’s data sheet a 125 A MCCB has a let-through current I_p of 25 kA peak for a prospective fault current I_s of 100 kArms.

6.  Find the impedance of the incoming cable

The impedance Z_c1 of the incoming cable is:

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7. Find the impedance of the load cable

The impedance Z_c2 of the incoming cable is:

From a manufacturer’s data sheet several cables can be compared for the same ambient conditions and laying arrangements. Their details are:

• 6 mm² cable, maximum current 33.8 A, R = 3.91, X = 0.130 ohms/km.
• 10 mm² cable, maximum current 46.7 A, R = 2.31, X = 0.126 ohms/km.

The impedance Z_c2 of the load cable is:

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8. Find the fault current at the distribution board, point B

From a manufacturer’s data sheet the contact impedance data for low voltage MCCBs are:

Hence the upstream MCCB impedance Z_m1 is 0.0008 + j 0.0001 ohms. Therefore the fault impedance Z_fb is:

The fault making current I_fb is:

Where V_p is the line-to-neutral voltage. Locate the point R for 26,195 A on the prospective curve in Figure 1.

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9. Find the fault current at the beginning of the load cable, point C

Hence the downstream MCCB impedance Z_m2 is 0.005+j0.000009 ohms. Add this to Z_fb to give the fault impedance Z_fc as:

The fault making current I_fc is:

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10. Find the fault current at the end of the load cable, point D

Add Z_c2 to Z_fc to give the fault impedance Z_fd as:

The fault making current I_fd is:

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11. Check the peak making capacity and peak let-through capacity of the MCCBs chosen above

The following manufacturer’s data are typical for 125 A and 32 A MCCBs:

*** Approximate values of the doubling factor taken to be 2.2

Hence the peak making capacity of the 32 A MCCB is well in excess of the let-through peak current of the 125 A MCCB.

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12. Find the highest I²t value for the upstream MCCB

Locate two points P and Q on the curve of the upstream MCCB as follows,

Hence I²t at P exceeds that at Q.

13. Calculate a suitable size for the load cable to satisfy the I²t duty

For XLPE cables the ‘k factor’ for the I²t is 143. The cross-sectional area A is:

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14. Calculate the volt-drop in the load cable

The usual limit to volt-drop in three-phase cables feeding static loads is 2.5% at full load.

Where, I_flc = 29 A, L = 15 m and φ = 54.5495 degrees. For a 6 mm² cable the volt-drop is found to be:

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15. Select the largest conductor size from the above calculations

Comparing the conductor sizes found in 13. and 14. gives the larger as 10 mm², and this size should be used. Revise the calculation of the fault current I_fd. The impedance Z_c2 of the load cable is:

Add Z_c2 to Z_fc to give the fault impedance Z_fd as:

The fault making current I_fd is:

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16. Plot the results

The results are plotted in Figure 1.

Refrence // Switchgear and Motor Control Centres – Handbook of Electrical Engineering: For Practitioners in the Oil, Gas and Petrochemical Industry by Alan L. Sheldrake (Download here)