5.1 Frequency sensitive loads. The total load connected to a power system is found to increase by D% due to a 1% increase in the frequency. For a particular operating condition the system load at the nominal system frequency, f0, is PL(f0) = PL0. (a) Derive the following equation for the system load, PL(f), as a function system frequency f = f0 + Δf. PL(f) = PL0(1 + D(Δf/f0)) (1) (b) Sketch a graph of the relationship you derived in (a) assuming that D > 0. (c) The system is initially operating with a load of PL10 at nominal frequency f0. As above, the load increases by D% due to a 1% increase in frequency. An additional load is then connected to the system which consumes ΔPL0 at the nominal frequency. Thus, the final load at the nominal frequency is PL20 = PL10 + ΔPL0. Assume that the frequency sensitivity of the initial and final values of the load are the same. Show that: PL2(f) = PL1(f) + ΔPL0 (2) (d) Sketch a graph showing PL1(f) and PL2(f). (e) For a particular system the load increases by 2% due to a 1% increase in frequency. The initial system load is 2000 MW at the nominal frequency of 50 Hz. An additional load of 50 MW (as measured at 50Hz) is connected to the system. The connection of this load causes a decrease in frequency of 0.2 Hz. What is the total system load taking into account the decrease in system frequency?