Page 1 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine Load V E E t x a x l r a I Et Ixa Ixl Ira V I A E s (a) (b)phasor diagram for R load x s r a I Load Z s E t V Et IZs IXs V ? f (c) (d)phasor diagram for R-L load Figure 30: Equivalent circuits The synchronous generator, under the assumption of constant synchronous reactance, may be considered as representable by an equivalent circuit comprising an ideal winding in which an e.m.f. E t proportional to the ?eld excitation is developed, the winding being connected to the terminals of the machine through a resistance r a and reactance 43 Page 2 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine Load V E E t x a x l r a I Et Ixa Ixl Ira V I A E s (a) (b)phasor diagram for R load x s r a I Load Z s E t V Et IZs IXs V ? f (c) (d)phasor diagram for R-L load Figure 30: Equivalent circuits The synchronous generator, under the assumption of constant synchronous reactance, may be considered as representable by an equivalent circuit comprising an ideal winding in which an e.m.f. E t proportional to the ?eld excitation is developed, the winding being connected to the terminals of the machine through a resistance r a and reactance 43 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras (X l +X a ) = X s all per phase. This is shown in Fig. 30. The principal characteristics of the synchronous generator will be obtained qualitatively from this circuit. 3.1.1 Generator Load Characteristics Consider a synchronous generator driven at constant speed and with constant exci- tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E t . Suppose a unity-power-factor load be connected to the machine. The ?ow of load current produces a voltage drop IZ s in the synchronous impedance, and terminal voltage V is re- duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that the angle s between E t and V increases with load, indicating a shift of the ?ux across the pole faces due to cross- magnetization. The terminal voltage is obtained from the complex summation V +Z s =E t or V = E t -IZ s (24) Algebraically this can be written V = q (E 2 t -I 2 X 2 s )-I r (25) for non-reactive loads. Since normally r is small compared with X s V 2 +I 2 X 2 s ˜ E 2 t = constant (26) so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E t and I sc . The current I sc is that which ?ows when the load resistance is reduced to zero. The voltage V falls to zero also and the machine is on short-circuit with V = 0 and I =I sc = E t /Z s ˜ E t /X s (27) Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage is given as before and since the resistance in normal machines is small compared with the synchronous reactance, the voltage is given approximately by V ˜ E t -IX s (28) 44 Page 3 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine Load V E E t x a x l r a I Et Ixa Ixl Ira V I A E s (a) (b)phasor diagram for R load x s r a I Load Z s E t V Et IZs IXs V ? f (c) (d)phasor diagram for R-L load Figure 30: Equivalent circuits The synchronous generator, under the assumption of constant synchronous reactance, may be considered as representable by an equivalent circuit comprising an ideal winding in which an e.m.f. E t proportional to the ?eld excitation is developed, the winding being connected to the terminals of the machine through a resistance r a and reactance 43 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras (X l +X a ) = X s all per phase. This is shown in Fig. 30. The principal characteristics of the synchronous generator will be obtained qualitatively from this circuit. 3.1.1 Generator Load Characteristics Consider a synchronous generator driven at constant speed and with constant exci- tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E t . Suppose a unity-power-factor load be connected to the machine. The ?ow of load current produces a voltage drop IZ s in the synchronous impedance, and terminal voltage V is re- duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that the angle s between E t and V increases with load, indicating a shift of the ?ux across the pole faces due to cross- magnetization. The terminal voltage is obtained from the complex summation V +Z s =E t or V = E t -IZ s (24) Algebraically this can be written V = q (E 2 t -I 2 X 2 s )-I r (25) for non-reactive loads. Since normally r is small compared with X s V 2 +I 2 X 2 s ˜ E 2 t = constant (26) so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E t and I sc . The current I sc is that which ?ows when the load resistance is reduced to zero. The voltage V falls to zero also and the machine is on short-circuit with V = 0 and I =I sc = E t /Z s ˜ E t /X s (27) Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage is given as before and since the resistance in normal machines is small compared with the synchronous reactance, the voltage is given approximately by V ˜ E t -IX s (28) 44 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras s Ixs Et I V Ir s I Et V v s IXs Et I Ir V1 (a)phasor diagram for di?erent R loads (b) Et Ea v I Et Ea v Ir Ixs I (c) (d) Figure 31: Variation of voltage with load at constant Excitation 45 Page 4 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine Load V E E t x a x l r a I Et Ixa Ixl Ira V I A E s (a) (b)phasor diagram for R load x s r a I Load Z s E t V Et IZs IXs V ? f (c) (d)phasor diagram for R-L load Figure 30: Equivalent circuits The synchronous generator, under the assumption of constant synchronous reactance, may be considered as representable by an equivalent circuit comprising an ideal winding in which an e.m.f. E t proportional to the ?eld excitation is developed, the winding being connected to the terminals of the machine through a resistance r a and reactance 43 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras (X l +X a ) = X s all per phase. This is shown in Fig. 30. The principal characteristics of the synchronous generator will be obtained qualitatively from this circuit. 3.1.1 Generator Load Characteristics Consider a synchronous generator driven at constant speed and with constant exci- tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E t . Suppose a unity-power-factor load be connected to the machine. The ?ow of load current produces a voltage drop IZ s in the synchronous impedance, and terminal voltage V is re- duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that the angle s between E t and V increases with load, indicating a shift of the ?ux across the pole faces due to cross- magnetization. The terminal voltage is obtained from the complex summation V +Z s =E t or V = E t -IZ s (24) Algebraically this can be written V = q (E 2 t -I 2 X 2 s )-I r (25) for non-reactive loads. Since normally r is small compared with X s V 2 +I 2 X 2 s ˜ E 2 t = constant (26) so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E t and I sc . The current I sc is that which ?ows when the load resistance is reduced to zero. The voltage V falls to zero also and the machine is on short-circuit with V = 0 and I =I sc = E t /Z s ˜ E t /X s (27) Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage is given as before and since the resistance in normal machines is small compared with the synchronous reactance, the voltage is given approximately by V ˜ E t -IX s (28) 44 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras s Ixs Et I V Ir s I Et V v s IXs Et I Ir V1 (a)phasor diagram for di?erent R loads (b) Et Ea v I Et Ea v Ir Ixs I (c) (d) Figure 31: Variation of voltage with load at constant Excitation 45 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 0.0 Leading 0.8 Leading 0.9 Leading 1.0 0.9 Lagging 0.0 Lagging 100 100 0 Perfect of full -load current Perfect of no-load voltage Isc Figure 32: Generator Load characteristics which is the straight line marked for cosf = 0 lagging in Fig. 32. A leading load of zero power factor Fig. 31. will have the voltage V ˜ E t +IX s (29) another straight line for which, by reason of the direct magnetizing e?ect of leading currents, the voltage increases with load. Intermediate load power factors produce voltage/current characteristics resembling those in Fig. 32. The voltage-drop with load (i.e. the regulation) is clearly dependent upon the power factor of the load. The short-circuit current I sc at which the load terminal voltage falls to zero may be about 150 per cent (1.5 per unit) of normal current in large modern machines. 3.1.2 Generator Voltage-Regulation The voltage-regulation of a synchronous generator is the voltage rise at the terminals when a given load is thrown o?, the excitation and speed remaining constant. The voltage- rise is clearly the numerical di?erence between E t and V, where V is the terminal voltage for a given load and E t is the open-circuit voltage for the same ?eld excitation. Expressed 46 Page 5 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 3 Synchronous Generator Operation 3.1 Cylindrical Rotor Machine Load V E E t x a x l r a I Et Ixa Ixl Ira V I A E s (a) (b)phasor diagram for R load x s r a I Load Z s E t V Et IZs IXs V ? f (c) (d)phasor diagram for R-L load Figure 30: Equivalent circuits The synchronous generator, under the assumption of constant synchronous reactance, may be considered as representable by an equivalent circuit comprising an ideal winding in which an e.m.f. E t proportional to the ?eld excitation is developed, the winding being connected to the terminals of the machine through a resistance r a and reactance 43 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras (X l +X a ) = X s all per phase. This is shown in Fig. 30. The principal characteristics of the synchronous generator will be obtained qualitatively from this circuit. 3.1.1 Generator Load Characteristics Consider a synchronous generator driven at constant speed and with constant exci- tation. On open circuit the terminal voltage V is the same as the open circuit e.m.f. E t . Suppose a unity-power-factor load be connected to the machine. The ?ow of load current produces a voltage drop IZ s in the synchronous impedance, and terminal voltage V is re- duced. Fig. 31 shows the complexor diagram for three types of load. It will be seen that the angle s between E t and V increases with load, indicating a shift of the ?ux across the pole faces due to cross- magnetization. The terminal voltage is obtained from the complex summation V +Z s =E t or V = E t -IZ s (24) Algebraically this can be written V = q (E 2 t -I 2 X 2 s )-I r (25) for non-reactive loads. Since normally r is small compared with X s V 2 +I 2 X 2 s ˜ E 2 t = constant (26) so that the V/I curve, Fig. 32, is nearly an ellipse with semi-axes E t and I sc . The current I sc is that which ?ows when the load resistance is reduced to zero. The voltage V falls to zero also and the machine is on short-circuit with V = 0 and I =I sc = E t /Z s ˜ E t /X s (27) Fora laggingloadofzero power-factor, diagramisgiven in Fig.31The voltage is given as before and since the resistance in normal machines is small compared with the synchronous reactance, the voltage is given approximately by V ˜ E t -IX s (28) 44 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras s Ixs Et I V Ir s I Et V v s IXs Et I Ir V1 (a)phasor diagram for di?erent R loads (b) Et Ea v I Et Ea v Ir Ixs I (c) (d) Figure 31: Variation of voltage with load at constant Excitation 45 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras 0.0 Leading 0.8 Leading 0.9 Leading 1.0 0.9 Lagging 0.0 Lagging 100 100 0 Perfect of full -load current Perfect of no-load voltage Isc Figure 32: Generator Load characteristics which is the straight line marked for cosf = 0 lagging in Fig. 32. A leading load of zero power factor Fig. 31. will have the voltage V ˜ E t +IX s (29) another straight line for which, by reason of the direct magnetizing e?ect of leading currents, the voltage increases with load. Intermediate load power factors produce voltage/current characteristics resembling those in Fig. 32. The voltage-drop with load (i.e. the regulation) is clearly dependent upon the power factor of the load. The short-circuit current I sc at which the load terminal voltage falls to zero may be about 150 per cent (1.5 per unit) of normal current in large modern machines. 3.1.2 Generator Voltage-Regulation The voltage-regulation of a synchronous generator is the voltage rise at the terminals when a given load is thrown o?, the excitation and speed remaining constant. The voltage- rise is clearly the numerical di?erence between E t and V, where V is the terminal voltage for a given load and E t is the open-circuit voltage for the same ?eld excitation. Expressed 46 Electrical Machines II Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao Indian Institute of Technology Madras as a fraction, the regulation is e = (E t -V)/V perunit (30) Comparing the voltages on full load (1.0 per unit normal current) in Fig. 32, it will be seen that much depends on the power factor of the load. For unity and lagging power factors there is always a voltage drop with increase of load, but for a certain leading power factor the full-load regulation is zero, i.e. the terminal voltage is the same for both full and no-load conditions. At lower leading power factors the voltage rises with increase of load, and the regulation is negative. From Fig. 30, the regulation for a load current I at power factor cosf is obtained from the equality E 2 t = (V cosf+Ir) 2 +(V sinf+IX s ) 2 (31) from which the regulation is calculated, when both E t and V are known or found. 3.1.3 Generator excitation for constant voltage 200 100 0 0 100 0.9 Leading 0.0 Lagging 0.8 Lagging 0.9 Lagging 0.8 Leading 0.0 Leading Percent of full -load current per phase Percent of no -load field excitation upf Figure 33: Generator Excitation for constant Voltage Since the e.m.f. E t is proportional to the excitation when the synchronous reactance is constant, the Eqn. 31 can be applied directly to obtain the excitation necessary to maintain constant output voltage for all loads. All unity-and lagging power-factor loads will require an increase of excitation with increase of load current, as a corollary of Fig. 32. 47Read More

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