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Though in practice 3-phase 3-wire ac system is universally used for power transmission and 3-phase 4-wire ac system is used for distribution of electric power but for special purposes other systems may also be used.

#### Various Systems of Power Transmission:

**The various systems of power transmission are: **

**(a) ****DC Systems: **

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(i) DC two-wire system.

(ii) DC two-wire system with mid-point earthed.

(iii) DC three wire-system.

**(b) ****Single Phase AC Systems: **

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(i) Single phase two-wire system.

(ii) Single phase two-wire system with mid-point earthed.

(iii) Single phase three-wire system.

**(c) ****Two-Phase AC Systems: **

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(i) Two-phase four-wire system.

(ii) Two-phase three-wire system.

**(d) Three Phase AC Systems: **

(i) Three-phase 3-wire system.

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(ii) Three-phase 4-wire system.

From such a big list of possible systems of transmission it is difficult to decide the best system without making comparison. The basis for comparison between the various systems of power transmission is usually economy. Since in a transmission system, the cost of the conductor material accounts for a major part of the total cost, the best system for transmission of electrical power is that for which the volume of conductor materials required is minimum. Thus the requirement of volume of conductor material forms the basis of comparison between various systems.

In making comparison of the volume of conductor material required for various transmission systems, the basis will be the equal maximum stress on the dielectric. This is because the voltage is only limited by the problem of insulating the conductors against disruptive discharge.

**For comparing the amount of conductor material required for different systems two cases arise: **

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(i) When overhead system is employed for transmission of power. In overhead system the conductors are insulated from the x-arms and supporting towers and as the towers and x-arms are earthed so the maximum voltage between each conductor and earth forms the basis of comparison of volume of conductor material required.

(ii) When underground cables are employed for transmission of power. In underground cables the maximum disruptive stress is between the two conductors of the cable; so the maximum voltage between conductors forms the basis of comparison of volume of conductor material required.

**Comparison of Cost of Conductors-Overhead Systems****: **

**The assumptions made for comparison are: **

(i) In all cases power to be transmitted is same (say, P watts).

(ii) The distance over which the power is to be transmitted is same (say I).

(iii) The line losses are same (say, W watts).

(iv) The maximum voltage to earth is same (say, V_{m} volts).

**(a) DC Systems: **

**(i) DC 2-Wire System with One Conductor Earthed [Fig. 2.3 (i)]: **

Maximum voltage between conductors = V_{m} volts

Power to be transmitted = P watts

Load current, I_{1} = P/V_{m}

This system is usually formed the basis, for comparison with other systems. Thus the volume of conductor material required in this system shall be taken as the basic quantity i.e.

**(ii) DC Two-Wire System with Mid-Point Earthed: **

This system is shown in Fig. 2.3 (ii).

The maximum voltage between any conductor and earth is V_{m} volts so,

Maximum voltage between conductors = 2 V_{m} volts

Hence volume of conductor material required is one-fourth of that required in two-wire dc System with one conductor earthed.

**(iii) DC Three-Wire System: **

In a 3-wire d c system, there are two outers and one middle wire, called the neutral wire which is grounded at the generator end, as illustrated in Fig. 2.3 (iii). For balanced load on the system, the middle wire carries no current.

Assuming load balanced,

Maximum voltage between the outer and earth = V_{m} volts

Assuming area of x-section of neutral wire as half of that of any of the outers,

Hence volume of conductor material required is 0.3125 times of that required in two-wire dc system with one conductor earthed.

**(b) Single Phase AC Systems****: **

**(i) AC Single Phase Two-Wire System with One Conductor Earthed Fig. 2.3 (iv): **

Peak value of voltage between conductors = V_{m} volts

RMS value of voltage between conductors = V_{m}/√2 volts

where cos ɸ is the power factor of the load

Hence volume of conductor material required in this system is 2/cos^{2} ɸ times of that required in 2-wire dc system with one conductor earthed.

**(ii) AC Single Phase Two-Wire System with Mid-Point Earthed [Fig. 2.3 (v)]: **

Peak value of voltage between conductors = 2 V_{m} volts

RMS value of voltage between conductors = 2 V_{m}/√2 = √2 V_{m} volts

Hence volume of conductor material required in this system is 0.5/cos^{2} ɸ times of that required in 2-wire dc system with one conductor earthed.

**(iii) AC Single Phase Three-Wire System [Fig. 2.3 (vi)]: **

Maximum voltage between outer conductors = 2 V_{m} volts

RMS value of voltage between outer and earth = V_{m}/√2 volts

Assuming x-section of neutral wire half of that of any of the outers,

Volume of conductor material required

Hence volume of conductor material required in this system is 0.625/cos^{2} ɸ times of that required in 2-wire dc system with one conductor earthed.

**(c) Two-Phase AC Systems: **

**(i) AC Two-Phase Four-Wire System [Fig. 2.3 (vii)]: **

RMS value of voltage between the outers = 2 V_{m}/√2 = √2 V_{m}

Load supplied by each phase = P/2

Hence volume of conductor material required in this system is 0.5/cos^{2} ɸ times of that required in two-wire dc system with one conductor earthed.

**(ii) AC Two-Phase Three-Wire System [Fig. 2.3 (viii)]: **

Considering balanced load, RMS value of voltage between any outer and neutral = V_{m}/√2

Assuming current density constant, area of x-section of neutral wire is √2 times of that of either of the outers.

Volume of conductor material required =

Hence volume of conductor material required in this system is 1.457/cos^{2} ɸ times of that required in 2-wire dc system with one conductor earthed.

**(d) 3-Phase**** AC Systems: **

**(i) AC 3-Phase 3-Wire System [Fig. 2.3 (ix)]: **

Hence, volume of conductor material required in this system is 0.5/cos^{2} ɸ times of that required in two-wire dc system with one conductor earthed.

**(ii) AC 3-Phase 4-Wire System [Fig. 2.3 (x)]: **

Assuming balanced load, there will be no current in neutral wire and copper losses will be same as in 3-phase 3-wire system,

Taking x-section of neutral wire as half of either outer,

Hence volume of conductor material required in this case is 0.583/cos^{2} ɸ times of that required in case of two-wire dc system with one conductor earthed.

**Comparison of Cost of Conductors-Underground Systems****: **

**The assumptions made for comparison are: **

(i) In all cases the power to be transmitted is same (say, P watts).

(ii) The distance over which the power is to be transmitted is same (say, l).

(iii) The line losses are same (say, W watts).

(iv) The maximum voltage between two conductors is same (say, V_{m} volts).

**(a) DC Systems: **

**(i) DC Two-Wire System [Fig. 2.4 (i)]: **

Voltage between two conductors = V_{m} volts

**(ii) DC Two-Wire System with Mid-Point Earthed [Fig. 2.4 (ii): **

This system is the same as a 2-wire dc system, so volume of conductor material required for this system is the same as that in a 2-wire dc system.

**(iii) DC Three-Wire System [Fig. 2.4 (iii)]: **

Assuming balanced load, the current through the neutral or mid wire is zero.

Maximum voltage between outers = V_{m} volts

Assuming x-section of neutral as half of that of either outer Volume of conductor material required

Hence volume of conductor material required in this system is 1.25 times of that required in a two-wire dc system.

**(b) Single Phase AC Systems****: **

**(i) AC Single Phase Two-Wire System [Fig 2.4 (iv)]: **

Maximum value of voltage between outers = V_{m} volts

RMS value of voltage between outers = V_{m}/√2 volts

where cos ɸ is the power factor of the load

Hence volume of conductor material required in this system is 2/cos^{2} ɸ times of that required for a two-wire dc system.

**(ii) AC Single Phase Two-Wire System with Mid-Point Earthed [Fig. 2.4 (v)]: **

This system is the same as a 2-wire single phase ac system, so volume of conductor material required in this case is also 2/cos^{2} ɸ times of that required in a two-wire dc system.

**(iii) AC Single Phase Three-Wire System [Fig. 2.4 (vi)]: **

Assuming balanced load, the system reduces to a single phase, 2-wire ac system except that a neutral conductor of half the x-section is provided in addition.

So volume of conductor material required

Hence volume of conductor material required in this case is 2.5/cos^{2} ɸ times of that required in a two-wire dc system.

**(c) Two-Phase AC Systems****: **

**(i) ****AC Two Phase 4-Wire System [Fig. 2.4 (vii)]: **

In this system each phase shares the half of the total load. This system is equivalent to two-wire ac system. In this case cross-section area of each conductor is taken half of that of single phase two-wire ac system but four wires are required in place of two wires, so the same volume of conductor material is required i.e. 2/cos^{2} ɸ times of that required in case of two-wire dc system.

**(ii) ****AC Two-Phase Three-Wire System [Fig. 2.4 (viii)]: **

RMS value of voltage between outers = V_{m}/√2

RMS value of voltage per phase = V_{m}/ (√2 √2) = V_{m}/2

The current in middle wire = √2 I_{8 }

The x-section of middle wire is taken √2 times of either outer so that current density may remain the same.

Volume of conductor material required = 2 a_{8 }l + √2 a_{8} l

Hence conductor material required in this system is 2.914/cos^{2} ɸ times of that required in a 2-wire dc system.

**(d) 3-Phase AC Systems****: **

**(i) AC Three-Phase Three-Wire System [Fig. 2.4 (ix)]: **

Maximum value of voltage between the conductors = V_{m}

RMS value of voltage between the conductors = V_{m}/√2

Hence volume of conductor material required in this case is 1.5/cos^{2} ɸ times of that required in case of a two-wire dc system.

**(ii) AC Three-Phase Four-Wire System [Fig. 2.4 (x)]: **

Assuming balanced load, this system is reduced to a 3-ɸ, ac system except that an additional wire, called the neutral wire, is provided of the half the cross-section of that either outer

So volume of conductor material required = 3.5 a_{9} l

Hence volume of conductor material required in this system is 1.75/cos^{2} ɸ times of that required in case of a 2-wire dc system.

**Results of Comparison of Transmission Systems****: **

**The results obtained above are summarised as below: **

From the above table it is obvious that for transmission dc system is an ideal one from economic point of view, particularly when it is remembered that the power factor of an ac system is usually considerably less than unity.

Two-phase three-wire system is obviously quite unsuitable for long distance transmission and needs no further consideration.

Among the remaining ac systems for overhead systems there is no difference in single phase, 2-wire and three-phase 3-wire systems and for underground systems there is a decided saving in conductor material with the three phase system. Considering other factors such as efficiency of operation and convenience three-phase three-wire system is usually adopted.