Comparison of Volume of Copper in Underground System

Comparison of Volume of Copper in Underground System

In case of underground system, the maximum stress exists between the line conductors. Hence the various assumptions for such comparison are,

1. The maximum voltage (V_m), between the conductors is same.

2. The power (P) transmitted in all the systems is same.

3. The distance (l) over which the power is transmitted is same.

4. The copper losses (W) are same in all the systems.

1. Two Wire D.C. System

The system is represented in the Fig. 7.17.1.

The voltage between the two conductors is V_m. It can be seen that there are no changes in the condition which we have discussed for two wire d.c. system for overhead system earlier in the section 7.16.1.

So     I = P / V_m  = Load current

This is the base of comparison of other systems.

2. Two Wire D.C. System with Midpoint Earthed

The system is shown in the Fig. 7.17.2.

It can be noted that the maximum voltage V_m exists between the two lines.

So I = P / V_m = Load current

The total copper loss is,

Key Point Thus the volume of copper required in this system is same as that required for two wire d.c. system.

3.  Three Wire D.C. System

The system is represented in the Fig. 7.17.3.

Again the voltage between the two lines is maximum which is V_m.

I = P / V_m = Load current

Assume balanced load so there is no current through the neutral and there are no copper losses in neutral. So total copper loss is,

W = 2I²R = 2 P² / V²m . ρ l / A

where A = Area of cross-section of each line conductor

2 P² / V²m . ρ l / W

Let area of cross-section of neutral wire is half of the area of cross-section of each conductor i.e. 0.5 A.

Hence the total volume of copper required is

Key Point Thus the volume of copper required for this system is 1.25 times than that required for 2 wire d.c. system. So 25% more copper is required in this system.

4. Three Phase Three Wire A.C. System

Consider a star connected three phase three wire a.c. system as shown in the Fig. 7.17.4. Note that the voltage between the line conductors is V_m Thus the line voltage is V_m

The r.m.s. value of the phase voltage is,

The power transmitted per phase is,

P_ph = P/3

Let cos ϕ be the load power factor.

Key Point Thus the volume of copper required in this system depends on the load power factor and it is 1.5/cos² ϕ times than that required for two wire d.c. system.

The result remains same whether the system is star or delta connected.

5. Three Phase Four Wire A.C. System

The system is shown in the Fig. 7.17.5. The neutral is available for the load connection. As the load is assumed to be balanced, the neutral current is zero and the copper losses in neutral are zero. Note that the voltage between the lines is V_m

Hence the r.m.s. value of the phase voltage is,

The power per phase is given by

This is same as obtained for three phase three wire system. The total copper loss is,

Let the cross-section of the neutral wire be half of the cross-section of each line conductor i.e. 0.5 A.

Hence the total volume of copper required is

Key Point Thus the volume of copper required, in this system is 1.75/cos²ϕ times the volume of copper required for two wire d.c. system.

Review Questions

1. Compare the various underground a.c. and d.c. systems based on the volume of copper required. State the assumptions used.

2. Assuming delta connected three phase three wire system and underground transmission, prove that the amount of copper required is 1.5/cos²ϕ times the copper required by two wire d.c. system.