Please allow me to answer several posts at once.

First, we can't confuse phase rotation and phase synchronization. Before paralleling generators, during installation, one must do a phase rotation check and be sure the line side of all generator breakers are phase A, B, C with a phase rotation meter and physically switch cables accordingly until all are alike. Then we can begin the paralleling explanation:

First, synchronizing:

Sync scopes and lamps do not guarantee voltage level differences, they only guarantee phase alignment by using potential differences between phases as a means of looking at the two generators NOT YET connected to each other (a way of looking in advance of combining them before doing so). Phase alignment comes with 2 things, speed and simple alignment. Imagine 2 children, each with their own drum in separate rooms, with a closed connecting door separating them momentarily, beating their drums independently. One is beating boom . . . boom . . . boom at a certain speed. The other, boom,boom,boom at a different speed. First we must get them BOTH on the same speed. Boom .. boom .. boom. But if we want alignment for a concert, speed is one 'must' but alignment is the other 'must' so both children hit the first beat and subsequent beats together, same speed, in sync.

How it works is you have one unit on line (one child in one room), and the other unit is started and producing voltage and frequency (the other child in the other room) but the tie breaker (the door) is not connecting the two units yet. So we can put a voltmeter (listen) across the tie breaker with leads on the same phase of the breaker, such as both leads on phase A. An old analog voltmeter is more visual. Put the leads across the breaker, one lead on the line side and one lead on the load side of the same phase. When the phases of one machine cross by the phases of the other, there is potential difference. So on a 400 volt system, when the phases criss-cross and momentarily line up, the difference is zero (the voltmeter goes to zero or the sync lamps go dark), but when the phases are at the maximum out of alignment the difference is 800 volts (the voltmeter goes to 800 volts and the lamps would glow very bright). If the phases are criss-crossing fast, the lamps blink very fast (speeds are very different); and if using a voltmeter the needle is going from zero to 800 VAC very fast. So we must get the speeds closer, so you adjust the speed of the oncoming machine and you will notice the lamps slow down in blinking as the phases become aligned and leave alignment. The idea with sync lamps is to get them to blink 3-4 times a minute. If the speed matches exactly, the lamps will stay in a steady state wherever they are, glowing bright, glowing half bright, glowing dim or not glowing. If there is any sign of glowing, but they are steady state, then the speeds match, but they are out of phase by the amount that represents a potential difference equal to the brightness. If they are steady, but dark, you are in sync (no potential difference with phases so you must be aligned one on top of the other (you have the two children lined up on each other when they hit the drum . . . . same speed . . . same timing). Then you can close the tie circuit breaker (open the central door in the children's rooms to connect the two drummers together in concert).

If the lamps are blinking too fast, it is difficult to time closing the tie breaker precisely when they are dark.

If there is voltage difference between two machines, let's say one at 400 VAC and the other at 390, then this would make the lamps not as bright (790) as they would be if they were at 400 VAC and 400 (800), but they would still blink with a speed difference, and still go dark when phases were lined up.

The sync scope is a fancy device like lights but tells you which machine is going too fast (CW or CCW needle movement) and also tell you the phase angle difference by where the needle is. So you connect the two generators when the needle is no more than 5* of zenith and moving slow enough you have time to close the breaker.

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Load sharing:

In Ovide Brudo example, they all will share load automatically the same. The electronic governors 'talk' to each other and adjust the amount of power (throttle) to each engine, and it is this available extra torque that causes one machine to take additional load even though the bus frequency remains constant. To explain this scientifically requires vector diagrams of torque vs active power and Andy might can explain it, but I too dumb actually

The voltage droop is taken care of by the regulator automatically adjusting the field current against the target line voltage. Due to the reactive capacity of generators, they have inherent voltage droop under load, so we must compensate for that with a precision voltage regulator. For about 20+ years, the newer analog regulators can hold 1/2%. The new digital ones are also about ½% or maybe even a bit better, but they are very fast, sometimes too fast.

Once paralleled, the bus voltage is constant, but individual generators can be slightly different voltage and then current will flow between units. A protective relay will not allow paralleling unless the voltage is within the limits of the cross current compensation CT circuit. Normally a difference of 5% voltage between machines will lock out the permissive voltage segment of the "Sync Check" relay. So modern regulators have the cross current compensation design, when cross currents (actually recirculating currents) are detected between machines it produces backwards current flow only on the one phase where you mounted the CCCT . . . . then voltage is adjusted (field current is increased by the regulator) until there is no reverse current flow. How we did this manually in the old days was to adjust each generator's voltage until the lowest amount of amps was indicated on each generator ammeter. And like above with speed droop, we would use a slide resistor to get the voltage droop the same in a manual paralleling system

When a large amount of current is detected on all phases, we have a reverse power situation meaning we are motoring one unit from the other unit due to one governor giving more fuel to a unit (more torque) faster than the bus load can accept it. Then the reverse power relay trips the breakers.

Reactance assists with voltage dip, waveform distortion and recovery time for different types of loads. The problem with going with low sub transient reactance (<12% x"d), which is good for motor starting and reactive loads, is that the short circuit current is very high and you may need more expensive switchgear bus and bus bracing. Higher x"d reactances of 20% or so limit short circuit capacity and you can use smaller bus bars and less bus bracing since short circuit amps are significantly reduced (they literally wind the generator with special high resistance wire that has more impedance under load and limits ampacity).

I hope this clears up some misunderstandings and keep in mind I am an idiot so only above half of the above is technically accurate.