Three physically identical synchronous generators are operating in parallel. They are all rated at 100 MW at 0.85 PF (power factor) lagging.

The no-load frequency of generator A is 61 Hz and its slope is 56.27 MW/Hz.
The no-load frequency of generator B is 61.5 Hz and its slope is 49.46 MW/Hz.
The no-load frequency of generator C is 60.5 Hz and its slope is 65.23 MW/Hz.

If a total load consisting of 230 MW is being supplied by this power, what will be the system frequency and how will the power be shared among the three generators?

If the total system load remains at 230 MW and the load of each generator from section (a) remains the same, how will the no-load frequency of each generator be adjusted to bring the system frequency to 60 Hz?

(a) The system frequency and power sharing among the three generators can be determined by solving the equations based on their characteristics and the total load.

(b) To bring the system frequency to 60 Hz while keeping the load of each generator unchanged, adjust the no-load frequency of each generator based on the modified power output equations.

(a) To determine the system frequency and power sharing among the three generators, we need to consider the load requirements and the characteristics of each generator.

Generator A:

No-load frequency: 61 Hz

Slope: 56.27 MW/Hz

Generator B:

No-load frequency: 61.5 Hz

Slope: 49.46 MW/Hz

Generator C:

No-load frequency: 60.5 Hz

Slope: 65.23 MW/Hz

Total load: 230 MW

First, let's calculate the power output of each generator based on their respective slopes and the system frequency.

For Generator A:

Power output = Slope * (System frequency - No-load frequency)

Power output = 56.27 MW/Hz * (f - 61 Hz)

For Generator B:

Power output = 49.46 MW/Hz * (f - 61.5 Hz)

For Generator C:

Power output = 65.23 MW/Hz * (f - 60.5 Hz)

Since the total load is 230 MW, the sum of the power outputs of the three generators should equal the load.

Power output of Generator A + Power output of Generator B + Power output of Generator C = Total load

56.27 MW/Hz * (f - 61 Hz) + 49.46 MW/Hz * (f - 61.5 Hz) + 65.23 MW/Hz * (f - 60.5 Hz) = 230 MW

Solve this equation to find the system frequency (f) and the power sharing among the three generators.

(b) To adjust the no-load frequency of each generator to bring the system frequency to 60 Hz while keeping the total system load at 230 MW and the load of each generator unchanged, we need to modify the power output equations.

For Generator A:

Power output = Slope * (System frequency - No-load frequency)

Power output = 56.27 MW/Hz * (60 Hz - 61 Hz)

For Generator B:

Power output = 49.46 MW/Hz * (60 Hz - 61.5 Hz)

For Generator C:

Power output = 65.23 MW/Hz * (60 Hz - 60.5 Hz)

Solve these equations to find the new power outputs of each generator. Adjust the no-load frequency of each generator accordingly to bring the system frequency to 60 Hz while maintaining the load requirements.

In conclusion:

(a) The system frequency and power sharing among the three generators can be determined by solving the equations based on their characteristics and the total load.

(b) To bring the system frequency to 60 Hz while keeping the load of each generator unchanged, adjust the no-load frequency of each generator based on the modified power output equations.

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