Reference no: EM132205264

Questions -

Question 1: The block diagram in Figure 1 is a control schematic for a single area, controlled system where ΔP_L is the change in the load demand and ΔF is resultant change in frequency

(a) Derive the expression for the transfer function of this system.

(b) If the turbine time constant T_t→0 this transfer function has the following form

ΔF/ΔP_L = Ks/(s²+2ζωs+ω²)

Derive the overall gain, damping factor and natural frequency of the system.

(c) In the system shown in Figure 1, the gain of the power system shown is 100 and its time constant is 20 seconds. The droop of overall system is 4% on 50Hz. The integral controller gain is set at 0.3. Calculate the gain, natural frequency and the damping factor of the system.

Question 2: An interconnected system is shown Figure 2 ΔP_LA(s) and ΔP_LB(s) are the changes in the load demand in areas A and B respectively and Δ_FA(s) and Δ_FB(s) are the resultant changes in the frequency in each area.

(a) The power transfer, ΔP_AB(s) between area A and area B can be shown to be:

Show that the two areas settle to the same frequency deviation after the step changes in demand of M_A p.u. MW in area A and M_B p.u. MW in area B.

(b) Table 2 lists the parameters of the interconnected power system shown:

Parameter		Area A	Area B
Power system time constant	Tp	15s	25s
Power system gain	Kp	100	120
Turbine time consonant	TT	0.2s	0.1s
Droop [Hz/p.u. MW]	R	2	3
Table 2

Calculate the final frequency deviation in response to a step increases in demand of 0.01 p.u MW in Area A and 0.006 p.u. MW in Area B.

Question 3:

(a) Derive an expression for the power transfer ΔP_AB, in the Laplace domain in terms of f_A(s), f_B(s), the interconnector gain K_IC and the load changes ΔP_LA and ΔP_LB.

(b) Show that the two areas settle to the same frequency deviation after step disturbances occur in each area.