A couple of comments concerning paralleling generators and the angle between the vectors at the instant of closure.
Let's take a system which is operating at 13,200 volts and it is desired to bring another generator on line with the existing unit. As mention by several others, the incoming machine should be running at a slightly higher speed and a slightly higher terminal voltage than the machine which is on the bus. The higher speed is indicated by the synchroscope rotating in the fast direction and the voltage is indicated on their respective maters. Two posts have indicated different closure angles.
The higher speed of the incoming speed is desired because the incoming machine will immediately assume some of the bus KW load. The slighly higher incoming voltage will cause this machine to assume some of the KVAR bus loading.
Let's assume you have a bus voltage of 1 per unit voltage(13,200 volts) and the incoming machine has a voltage of 1.02 per unit ( 13,464 volts). If the paralleling circuit breaker is closed when the closure angle is 10 degrees, the voltage across the breaker contacts is .1772 per unit. When the closure angle is 45 degrees, the voltage across the circuit breaker contacts is .773 per unit-a very large value. Converting this information into actual voltages for a system operating at 13,200 volts phase to phase results in the following voltages on this system.
10 degrees closure. The line to neutral voltage is 1,350 volts across the breaker contacts.
45 degrees closure. The line to neutral voltage is 5,891 volts across the breaker contacts.
The instant the breaker contacts are closed the voltage difference must instantaneously become zero. This is accomplished by a rapid change of vars between the generators. This change of vars should be controlled to avoid upsets on the electrical system. The smaller the closing angle, the less the effects on the system. The voltage across the breaker contacts can be determined by using the law of cosines. It can be seen that the voltage across the breaker contacts is a function of the cosine of angle between the two vectors. It can be demonstrated that the closing angle has much more impact on the voltage across the contacts than the magnitudes of the inoming and bus voltages.
In summary the smaller the angle of closure, the less the effects on the system. I only discussed the effects on the systems voltages and there is another part of the story and that is the mechanical effects associated by lagre closure angles. The mechanical shock is also proportional to the closing angle and the smaller the angle, the less the shock. If the closure angle is excessively large and the prime movers are steam turbines, you had better have spare thrust bearings available and an alternate source of power.
One other note concerning power flow into a machine. Power flow into a generator can create a serious condition for the prime mover (steam and diesel) but generally this is only a concern when the steam rack or fuel rack is in a closed position. A closed steam rack deprives the turbine from the cooling effects of the steam and the unit tries to act as an air pump which will overheat the turbine blading and causes distortion. In a diesel unit there is a risk that some unburned fuel remains in the diesel and this creats an explosion hazard. To prevent these conditions for extended periods of time ( ~ > 10 seconds), a directional power relay is installed on each unit capable of being operated in parallel. Some refer to this device as an anti-motoring relay.