AC DISTRIBUTIONAC DISTRIBUTION

PROBLEMSPROBLEMS

Fed at One End –Fed at One End –

Equal & Unequal VoltagesEqual & Unequal Voltages

A single phase distributor 2 A single phase distributor 2 kilometres long supplies a load of kilometres long supplies a load of 120 A at 0·8 p.f. lagging at its far 120 A at 0·8 p.f. lagging at its far end and a load of 80 A at 0·9 p.f. end and a load of 80 A at 0·9 p.f. lagging at its mid-point. Both lagging at its mid-point. Both power factors arepower factors are referred to the referred to the voltage at the far end. The resistance voltage at the far end. The resistance and reactance per km (go and return) and reactance per km (go and return) are 0·05 Ω and 0· 1 Ω respectively. If are 0·05 Ω and 0· 1 Ω respectively. If the voltage at the far end is the voltage at the far end is maintained at 230 V, maintained at 230 V,

calculate : calculate : (i) voltage at the sending end (ii) (i) voltage at the sending end (ii)

phase angle between voltages at the phase angle between voltages at the two ends. two ends.

Fig. shows the distributor AB with C as Fig. shows the distributor AB with C as the mid-point the mid-point

Impedance of distributor/ km= Impedance of distributor/ km=

(0·05+j 0·1) Ω(0·05+j 0·1) Ω

Impedance of section ACImpedance of section AC,,

Z Z ACAC = (0·05 + j 0·1) × 1000/1000 = = (0·05 + j 0·1) × 1000/1000 =

(0·05 + j 0·1) Ω(0·05 + j 0·1) Ω

Impedance of section CBImpedance of section CB,,

ZZCBCB = (0·05 + j 0·1) × 1000/1000 = = (0·05 + j 0·1) × 1000/1000 =

(0·05 + j 0·1) Ω(0·05 + j 0·1) Ω

Let the voltage VLet the voltage VBB at point B be taken as at point B be taken as the reference vector.the reference vector.

VVBB = 230 + j 0 = 230 + j 0

A single phase distributor one km long A single phase distributor one km long has resistance and reactance per con-has resistance and reactance per con-ductor of 0·1 Ω and 0·15 Ω ductor of 0·1 Ω and 0·15 Ω respectively. At the far end, the respectively. At the far end, the voltage VB = 200 V and the current is voltage VB = 200 V and the current is 100A at a p.f. of 0·8 lagging. At the 100A at a p.f. of 0·8 lagging. At the mid-point M of the distributor, a mid-point M of the distributor, a current of 100 A is tapped at a p.f. of current of 100 A is tapped at a p.f. of 0·6 lagging with reference to the 0·6 lagging with reference to the voltage VM at the mid-point. voltage VM at the mid-point.

Calculate : (i) voltage at mid-point Calculate : (i) voltage at mid-point (ii) sending end voltage VA (iii) (ii) sending end voltage VA (iii) phase angle between Vphase angle between VAA and V and VBB

Fig. shows the single line diagram of the Fig. shows the single line diagram of the distributor AB with M as the mid-point. distributor AB with M as the mid-point.

EHV AC & HVDC TransmissionEHV AC & HVDC Transmission Advantages.Advantages. The high voltage d.c. transmission has the The high voltage d.c. transmission has the

following advantages over high voltage a.c. following advantages over high voltage a.c. transmission :transmission :

(i) It requires only two conductors as compared to (i) It requires only two conductors as compared to three for a.c. transmission.three for a.c. transmission.

(ii) There is no inductance, capacitance, phase (ii) There is no inductance, capacitance, phase displacement and surge problems in d.c. displacement and surge problems in d.c. transmission.transmission.

(iii) Due to the absence of inductance, the voltage (iii) Due to the absence of inductance, the voltage drop in a d.c. transmission line is less than the drop in a d.c. transmission line is less than the a.c. line for the same load and sending end a.c. line for the same load and sending end voltage. For this reason, a d.c. transmission line voltage. For this reason, a d.c. transmission line has better voltage regulation.has better voltage regulation.

(iv) There is no skin effect in a d.c. system. (iv) There is no skin effect in a d.c. system. Therefore, entire cross-section of the line Therefore, entire cross-section of the line conductor is utilised.conductor is utilised.

v) For the same working voltage, the v) For the same working voltage, the potential stress on the insulation is potential stress on the insulation is less in case of d.c. system than that less in case of d.c. system than that in a.c. system. Therefore, a d.c. line in a.c. system. Therefore, a d.c. line requires less insulation.requires less insulation.

(vi) A d.c. line has less corona loss and (vi) A d.c. line has less corona loss and reduced interference with reduced interference with communication circuits.communication circuits.

(vii) The high voltage d.c. transmission (vii) The high voltage d.c. transmission is free from the dielectric losses, is free from the dielectric losses, particularly in the case of cables.particularly in the case of cables.

(viii) In d.c. transmission, there are no (viii) In d.c. transmission, there are no stability problems and synchronising stability problems and synchronising difficulties.difficulties.

DisadvantagesDisadvantages

(i) Electric power cannot be (i) Electric power cannot be generated at high d.c. voltage due generated at high d.c. voltage due to commutation problems.to commutation problems.

(ii) The d.c. voltage cannot be (ii) The d.c. voltage cannot be stepped up for transmission of stepped up for transmission of power at high voltages.power at high voltages.

(iii) The d.c. switches and circuit (iii) The d.c. switches and circuit breakers have their own limitations breakers have their own limitations

EHV AC TransmissionEHV AC Transmission Now-a-days, electrical energy is almost Now-a-days, electrical energy is almost

exclusively generated, transmitted and exclusively generated, transmitted and distributed in the form of a.c.distributed in the form of a.c.

AdvantagesAdvantages

(i) The power can be generated at high (i) The power can be generated at high voltages.voltages.

(ii) The maintenance of a.c. sub-stations is (ii) The maintenance of a.c. sub-stations is easy and cheaper.easy and cheaper.

(iii) The a.c. voltage can be stepped up or (iii) The a.c. voltage can be stepped up or stepped down by transformers with ease stepped down by transformers with ease and effi-and effi-

ciency. This permits to transmit power at ciency. This permits to transmit power at high voltages and distribute it at safe high voltages and distribute it at safe potentials.potentials.

DisadvantagesDisadvantages

((i) An a.c. line requires more copper i) An a.c. line requires more copper than a d.c. line.than a d.c. line.

(ii) The construction of a.c. (ii) The construction of a.c. transmission line is more transmission line is more complicated than a d.c. transmission complicated than a d.c. transmission line.line.

(iii) Due to skin effect in the a.c. (iii) Due to skin effect in the a.c. system, the effective resistance of system, the effective resistance of the line is increased.the line is increased.

(iv) An a.c. line has capacitance. (iv) An a.c. line has capacitance. Therefore, there is a continuous loss Therefore, there is a continuous loss of power due to charging current of power due to charging current even when theeven when the line is open. line is open.

From the above comparison, it is clear that From the above comparison, it is clear that high voltage d.c. transmission is superior high voltage d.c. transmission is superior to high voltage a.c. transmission. Although to high voltage a.c. transmission. Although at present, transmission of electric power at present, transmission of electric power is carried by a.c., there is an increasing is carried by a.c., there is an increasing interest in d.c. transmission. interest in d.c. transmission.

The introduction of mercury arc rectifiers The introduction of mercury arc rectifiers and thyratrons have made it possible to and thyratrons have made it possible to convert a.c. into d.c. and vice-versa easily convert a.c. into d.c. and vice-versa easily and efficiently. Such devices can operate and efficiently. Such devices can operate upto 30 MW at 400 kV in single units. The upto 30 MW at 400 kV in single units. The present day trend is towards a.c. for present day trend is towards a.c. for generation and distribution and high generation and distribution and high voltage d.c. for transmission.voltage d.c. for transmission.

Fig. 7.3 shows the single line diagram of Fig. 7.3 shows the single line diagram of high voltage d.c. transmission. The high voltage d.c. transmission. The electric power is generated as a.c. and is electric power is generated as a.c. and is stepped up to high voltage by the stepped up to high voltage by the sending end transformer TS. sending end transformer TS.

The a.c. power at high voltage is fed to the The a.c. power at high voltage is fed to the mercury arc rectifiers which convert a.c. mercury arc rectifiers which convert a.c. into d.c. into d.c.

The transmission of electric power is The transmission of electric power is carried at high d.c. voltage. At the carried at high d.c. voltage. At the receiving end, d.c. is converted into a.c. receiving end, d.c. is converted into a.c. with the help of thyratrons. The a.c. with the help of thyratrons. The a.c. supply is stepped down to low voltage by supply is stepped down to low voltage by receiving end transformer TR for receiving end transformer TR for distribution.distribution.