When synchronous motor is over excited it takes leading p.f. current. If synchronous motor is on no load, where load angle δ is very small and it is over excited (Eb >  V) then power factor angle increases almost upto 90o. And motor runs with almost zero leading power factor condition. This is shown in the phasor diagram Fig. 1.
2. The p.f. is given by
cosΦ = Active power/ Apparent = (P in KW)/ (S i.e. KVA rating)
       This is how the synchronous motor as a synchronous condenser is used to improve power factor of the combined load.
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| Fig. 1 Synchronous condenser | 
        This characteristics is similar to a normal capacitor which takes  leading power factor current. Hence over excited synchronous motor  operating on no load condition is called as synchronous condenser or  synchronous capacitor. This is the property due to which synchronous  motor is used as a phase advancer or as power improvement device.
1.1 Disadvantage of Low Power Factor
        In various industries, many machines are of induction motor type. The  lighting and heating loads are supplied through transformers. The  induction motors and transformers draw lagging current from the supply.  Hence the overall power factor is very low and lagging in nature.
       The power is given by,
                       P = VI cosΦ                                         .............. single phase 
...                     I = P/(VcosΦ)
        The supply voltage is constant and hence for supplying a fixed power P,  the current is inversely proportional to the p.f. cosΦ. Let P = KW is  to be supplied with a voltage of 230 V then,
Case i) cosΦ = 0.8,
                   I = (5 x103)/(230 x 0.8) = 27.17 A
Case ii) cos = 0.6,
Case ii) cos = 0.6,
                   I = (5 x103)/(230 x 0.6) = 36.23 A
        Thus as p.f. decreases, becomes low, the current drawn from the supply  increases to supply same power to the load. But if p.f. maintained high,  the current drawn from supply is less.
The high current due to low p.f. has following disadvantages :
1. For higher current, conductor size required is more which increases the cost.The high current due to low p.f. has following disadvantages :
2. The p.f. is given by
cosΦ = Active power/ Apparent = (P in KW)/ (S i.e. KVA rating)
       Thus for fixed active power P, low p.f. demands large KVA rating alternators and transformers. This increases the cost.
3. Large current means more copper losses and poor efficiency.4. Large current causes large voltage  drops in transmission lines, alternators and other equipments. This  results into poor regulation. To compensate such drop extra equipments  is necessary which further increases the cost.
Note : Hence power factor improvement is must practice. Hence the supply authorities encourage consumers to improve the p.f.
1.1 Use of Synchronous Condenser in Power Factor Improvement
        The low power factor increases the cost of generation, distribution and  transmission of the electrical energy. Hence such low power factor  needs to be corrected. Such power factor correction is possible by  connecting synchronous motor across the supply and operating it on no  load with over excitation.
       Now let Vph  is the voltage applied and I1ph   is the current lagging Vph   by angle Φ1. This power factor Φ1 is very low, lagging.
        The synchronous motor acting as a synchronous condenser is now  connected across the same supply. This draws a leading current of I2ph.
       The total current drawn from the supply is now phasor of Iph and I2ph. This total current IT   now lags Vph   by smaller angle Φ due to which effective power factor gets improved. This is shown in the Fig. 2.
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| Fig. 2 Power factor correction by synchronous condenser | 


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