A generating station comprises four 125 MVA, 22 kV, 0.84 pf lagging synchronous generators with a frequency drop of 5 Hz from no-load to full. At a frequency of 50 Hz, three generators supply a steady load of 75 MW each while the balance is shared by the fourth generator (called swing generator)

Question

(a) For a total load of 260 MW at 50 Hz, find the no-load frequency setting of the generators.

(b) With no change in governor setting as in part (a), find the system frequency if the system load rises to 310 MW

(c) Find the no-load frequency of the swing generator for the system frequency to be restored to 50 Hz for the load in part (b).

(d) If the swing generator trips off what will be system frequency

Accepted Answer

(a) Total load = 260 MW; full load each generator [latex] =125 imes 0.84=105 MW[/latex]

3 generators can supply a load of each 75 MW at 50 Hz

So load shared by swing generator [latex] =260-3 imes 75=260-225=35 MW[/latex]

Slope [latex] m=-\frac{5}{105}=.0476 Hz / MW =m[/latex]

At 75 MW fall in frequency for first three generators [latex] =75 imes .0476=3.57 Hz[/latex]

The system frequency = 50 Hz. By applying straight line equation [latex] y=m x+c ; y=[/latex] system frequency, m = slope, x = load share and c = set frequency.

So set frequency of [latex] G_{1}, G_{2}[/latex] and [latex] G_{3}[/latex] c = y – mx = 50 + 3.57 = 53.57 Hz = 53.6 Hz

For 35 MW load supplied from swing generator, the set frequency [latex] =50-35 imes(-0.0476)=51.7 Hz[/latex]

(b) Since all the four generator are having same slope, the load will be shared equally.

[latex] herefore[/latex] New load sharing of each [latex] (G_{1}, G_{2}[/latex] and [latex] G_{3}) =75+\frac{50}{4}=87.5 MW [/latex]

So new system frequency [latex] =53.6+(-0.0476) imes 87.5=49.43 Hz[/latex]

(c) If the system frequency is 50 Hz, then the three generators can supply only 75 MW each. So the remaining power is shared by swing generator

New load of swing generator [latex] =310-3 imes 75=310-225=85 MW[/latex]

So set frequency of swing generator [latex] = 50-(-0.0476) imes 85=54.04 Hz[/latex]

(d) The new system frequency after the swing generator trips off.

New load sharing [latex] =\frac{310}{3}=103.33 MW[/latex]

New system frequency [latex] =53.6+(-0.0476) imes 103.33=48.68 Hz[/latex]

Question 8.49: A generating station comprises four 125 MVA, 22 kV, 0.84 pf ...

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