At the risk of fomenting brouhaha I’ve taken the liberty of addressing the challenge (?) by CSA. First my "claimer"... the following discussion is excerpted from the text* I used to teach an Electrical Technology course in Staten Island Community College, a Division of City University of New York! Copies of the pertinent Section(s) are available on request!
A) Fundamentals
Before paralleling two alternators (or an alternator and a bus) several requirements are necessary. Some of them were mentioned by other posters:
1. Their voltages must have the same waveform (sinusoidal.)
2. Their voltage waveforms must be exactly opposite in phase.
3. The product of their poles and speeds must be the same.
4. Their effective (rms) values of generated voltages should be closely matched
5. Their combined over-all alternator voltage and the prime-mover characteristic should be drooping (whether introduced naturally or electronically) with application of load.
6. Their rotational speeds (frequency), at the time they are switched together, should be closely matched.
7. For polyphase machines only, the phase-sequence must be the same as that of the bus.
In effect all of the requirements above (excluding #5) can be met with the single statement that "the polarities of the two sources of voltage must be equal, but opposite at all times." Also note the term "closely matched" in items #4 and #5. If the terms 'equal', 'identical', 'same', and 'zero' were used then Gurpreet's "floating generator" phenomenon would exist, but no current will flow and therefore synchronism cannot be accomplished.
B) The Mechanics of Synchronizing Single-Ph Alternators.
Consider alternator A, the running machine and alternator B the incoming machine. Their generated voltages are Ea and Eb, respectively. Finally, assume there is a means of "observing" the synchronization procedure. In the olden days lamps were used (please no arguments about whether the dark-method or light-method is superior!) Another observation method is to use a two-channel oscilloscope. A third method could consist of a single-channel scope synched to machine A. Today, of course, a synchroscope is used. But, for this discussion, consider two lamps, one across each contact of the switch or breaker connecting the two machines:
Case 1: Machine A's voltage is 220V, and its frequency is 60Hz, while machine B's voltage is 200V, and its frequency 59.5Hz. Then:
a) The maximum resultant voltage, Er, across each lamp is (Ea+Eb)/2 or 221V.
b) The minimum Er is (Ea-Eb)/2 or 1V.
c) The frequency is 60-59.5 or 0.5Hz.
d) The number of light pulsations = 0.5Hz x 60sec/min or 30 lamp-on pulsations per minute.
Case 2: Machine A’s voltage is 220V, and its frequency is 60Hz, while machine B’s voltage is 230V, and its frequency 61Hz. Then:
a) The maximum Er is (Ea+Eb)/2 or 225V.
b) The minimum Er is (Ea-Eb)/2 or 5V.
c) The frequency is 60-61 or 1.0Hz.
d) The number of light pulsations = 1.0Hz x 60sec/min or 60 lamp-on pulsations per minute.
C) Development of Synchronizing-Power
At the instant the switch is closed when the voltages are closely matched so that Er exists, a circulating or synchronizing-current, Is, will flow in both armatures, limited only by the synchronous-impedance, Zs, of the two machines (neglecting intervening impedances such as leads, bus bar, breakers, etc) in parallel. Because of the inductive nature of Zs, synchronizing-current lags, Er. The actual angle by which it lags is Theta = Arctan (Xs/Rs), where Xs and Rs are the synchronous-reactance and synchronous-resistance, respectively. Expressing it mathematically,
Is=(Ea-Eb)/(Zsa+Zsb)= Er/(Rsa+Rsb+j(Xsa+Xsb)
D) Effects of Synchronizing-Power
The synchronous-current, hence synchronizing-power, is circulating in the armatures of both machines. Assume that the excitation of B is such that Eb > Ea. Then, for B,
Psb = Eb x Is x Cos (Theta), while for A,
Psa = Ea x Is x Cos (180 - Theta) = - Psba.
Note that generator-action (+) is produced in machine B, but motor-action (-) is produced in machine A.
In closing, this discussion covers the very simplistic case of synchronizing like-machines, both of which are unloaded. If there is sufficient interest I will produce Part Deux, covering more advanced topics like the influence of Armature-Reaction and Load, and their effect on Torque- or Power-Angle!
*Text: Electrical Machinery and Control, 1964
Author: Irving L. Kosow
Publisher: Prentice-Hall
LofC Card:64-22802
Regards, Phil Corso (cepsicon [at] aol [dot] com)
A) Fundamentals
Before paralleling two alternators (or an alternator and a bus) several requirements are necessary. Some of them were mentioned by other posters:
1. Their voltages must have the same waveform (sinusoidal.)
2. Their voltage waveforms must be exactly opposite in phase.
3. The product of their poles and speeds must be the same.
4. Their effective (rms) values of generated voltages should be closely matched
5. Their combined over-all alternator voltage and the prime-mover characteristic should be drooping (whether introduced naturally or electronically) with application of load.
6. Their rotational speeds (frequency), at the time they are switched together, should be closely matched.
7. For polyphase machines only, the phase-sequence must be the same as that of the bus.
In effect all of the requirements above (excluding #5) can be met with the single statement that "the polarities of the two sources of voltage must be equal, but opposite at all times." Also note the term "closely matched" in items #4 and #5. If the terms 'equal', 'identical', 'same', and 'zero' were used then Gurpreet's "floating generator" phenomenon would exist, but no current will flow and therefore synchronism cannot be accomplished.
B) The Mechanics of Synchronizing Single-Ph Alternators.
Consider alternator A, the running machine and alternator B the incoming machine. Their generated voltages are Ea and Eb, respectively. Finally, assume there is a means of "observing" the synchronization procedure. In the olden days lamps were used (please no arguments about whether the dark-method or light-method is superior!) Another observation method is to use a two-channel oscilloscope. A third method could consist of a single-channel scope synched to machine A. Today, of course, a synchroscope is used. But, for this discussion, consider two lamps, one across each contact of the switch or breaker connecting the two machines:
Case 1: Machine A's voltage is 220V, and its frequency is 60Hz, while machine B's voltage is 200V, and its frequency 59.5Hz. Then:
a) The maximum resultant voltage, Er, across each lamp is (Ea+Eb)/2 or 221V.
b) The minimum Er is (Ea-Eb)/2 or 1V.
c) The frequency is 60-59.5 or 0.5Hz.
d) The number of light pulsations = 0.5Hz x 60sec/min or 30 lamp-on pulsations per minute.
Case 2: Machine A’s voltage is 220V, and its frequency is 60Hz, while machine B’s voltage is 230V, and its frequency 61Hz. Then:
a) The maximum Er is (Ea+Eb)/2 or 225V.
b) The minimum Er is (Ea-Eb)/2 or 5V.
c) The frequency is 60-61 or 1.0Hz.
d) The number of light pulsations = 1.0Hz x 60sec/min or 60 lamp-on pulsations per minute.
C) Development of Synchronizing-Power
At the instant the switch is closed when the voltages are closely matched so that Er exists, a circulating or synchronizing-current, Is, will flow in both armatures, limited only by the synchronous-impedance, Zs, of the two machines (neglecting intervening impedances such as leads, bus bar, breakers, etc) in parallel. Because of the inductive nature of Zs, synchronizing-current lags, Er. The actual angle by which it lags is Theta = Arctan (Xs/Rs), where Xs and Rs are the synchronous-reactance and synchronous-resistance, respectively. Expressing it mathematically,
Is=(Ea-Eb)/(Zsa+Zsb)= Er/(Rsa+Rsb+j(Xsa+Xsb)
D) Effects of Synchronizing-Power
The synchronous-current, hence synchronizing-power, is circulating in the armatures of both machines. Assume that the excitation of B is such that Eb > Ea. Then, for B,
Psb = Eb x Is x Cos (Theta), while for A,
Psa = Ea x Is x Cos (180 - Theta) = - Psba.
Note that generator-action (+) is produced in machine B, but motor-action (-) is produced in machine A.
In closing, this discussion covers the very simplistic case of synchronizing like-machines, both of which are unloaded. If there is sufficient interest I will produce Part Deux, covering more advanced topics like the influence of Armature-Reaction and Load, and their effect on Torque- or Power-Angle!
*Text: Electrical Machinery and Control, 1964
Author: Irving L. Kosow
Publisher: Prentice-Hall
LofC Card:64-22802
Regards, Phil Corso (cepsicon [at] aol [dot] com)