Electrical ELEC5204 Power Systems - Tutorial Questions 2/3/09
1) A 132 kV (nominal) three-phase supply to a distribution company supplies 200 MW with a lagging power factor of 0.9, when the voltage at the supply point is V = 1.03 0 per unit. a) What is the apparent power, S that is supplied into the load, in per unit on 100 MVA? Find the magnitude I of the current phasor, I = I into the load in per unit on 100 MVA; Find the phase angle to then find the supplied current I as a phasor in per unit on 100 MVA ; Find the complex power supplied, S (in per unit on 100 MVA); Find the reactive power supplied, Q in per unit on 100 MVA; Find the base current IB at 132 kV on 100 MVA ; Use this value of IB to find the rms current magnitude in A (i.e. in amperes) in each phase of the supply to the load; and
B
b)
c)
d) e) f) g)
h)
Write an expression that defines the c-phase current waveform into the load as a function of time in A (i.e. in amperes).
2)
Figure 1 shows the single-phase equivalent circuit of a 250 km, 330 kV three-phase transmission line connected between Locations A and B.
Location A
Zser = R + j X
Location B
Y sh = j
BC 2
Ysh = j
BC 2
Figure 1. A single-phase equivalent of a 250 km, 330 kV transmission line
The equivalent pi model (a type that is commonly used in load flow studies) of Figure 1 has: The series resistance and reactance of the line lumped into one series impedance equal to Zser = R + j X = 0.015 j + 0.116 pu on 100 MVA; and
The shunt susceptance of the line (BC = 1.41 pu on 100 MVA) due to its capacitance (that is actually uniformly distributed along the length of the line) is split into two halves, which are connected at the two ends of the line model.
B
Location A is connected to the rest of the 330 kV system, and its voltage is
VA = 1.00 0 pu on 330kV.
The only connection to Location B is the 330 kV line shown in Figure 1. Questions: a) Convert the shunt admittance ( j BC /2) into a shunt impedance Zsh that is connected at each end of the line shown in Figure 1;
B
b)
Consider that the series impedance of the line (Zser = R + j X) and the shunt impedance Zsh at the Location B end of the line act as a voltage divider, to find the phasor voltage (in pu) at Location B; and
c)
A 330 kV, 60 MVAr shunt reactor (i.e. a fixed-value three-phase shunt inductance that absorbs 60 MVAr when a balanced threephase voltage of 330 kV is applied to it) is now connected to the open end of the line at Location B, while the voltage at Location A remains at: i)
VA =1.00 0 pu:
Find the (shunt) impedance of the shunt reactor in per unit on 100 MVA; Combine the shunt reactor impedance with the shunt capacitive impedance Zsh calculated above, to produce an effective total shunt impedance connected at the Location B end of the line; and
ii)
iii)
Find the phasor voltage at Location B when the shunt reactor is connected there.