Two generators operate in parallel to supply a load. G1 has 4 poles and \(s_{p1}=5MW/Hz\). G2 has 16 poles and \(s_{p2}=4MW/Hz\) (This is the case shown on the similar sized generators page.)

1. If the load is 1.4MW, \(f_{nl1}=60.1Hz\), \(f_{nl2}=60.05Hz\), calculate:
   1. System frequency, \(f_{sys}\)
   2. Rotational speed of each generator \(n_{s1}\), \(n_{s2}\)
   3. Power supplied by each generator
2. If the power is constant at 1.4MW \(f_{nl1}=60.1Hz\), what value of \(n_{nl2}\) is required to adjust system freqeuncy to 60Hz?

1. 1. The output power is the sum of the power from each generator:
      \[ \begin{aligned} P_{load} & =s_{p1}\left(f_{nl1}-f_{sys}\right) +s_{p2}\left(f_{nl2}-f_{sys}\right) \\ 1.4 & = 5\left(60.1-f_{sys}\right) + 4\left(60.05-f_{sys}\right) \end{aligned} \]
      re-arranging gives \(f_{sys}=59.922Hz\).
   2. For all synchronous machines \(n_s=\frac{120f}{p}\).

      \(n_{s1} = 1797.67rpm\), \(n_{s2} = 449.42rpm\)

   3. Substituting into \(P =s_{p}\left(f_{nl}-f_{sys}\right)\) gives \(P_1 = 888.89kW\), \(P_1 = 511.11kW\)
2. At 60Hz, \(P_1 =s_{p1}\left(60.1-60 = 500kW\right)\).

   Therefore \(P_2=P_{load}-P_1 = 900kW\). \(P_2 =s_{p2}\left(f_{nl2}-60 \right)\) gives \(f_{nl2}=60.225Hz\).

   Therefore \(n_{nl2}=\frac{120 \times 60.225Hz} {16} = 451.688 rpm\)