Performance of Transmission Lines Questions and Answers

Answer: C

The maximum power that a line can transfer is inversely proportional to its reactance. A series capacitor reduces the net reactance, and with a degree of compensation \(k\)

\[ \begin{aligned} X_{net} \\ &= X(1 - k),\qquad P_{max} \propto \frac{1}{X(1 - k)} \end{aligned} \]

For 75 per cent compensation, \(k = 0.75\):

\[ \frac{P'_{max}}{P_{max}} = \frac{1}{1 - 0.75} = 4 \]

So the maximum power transferred becomes four times the original. The power would be doubled at 50% compensation. The answer is option C.

Answer: C

FACTS stands for Flexible AC Transmission Systems: power electronic controllers such as the static VAR compensator, the TCSC and the STATCOM that control voltage, impedance and phase angle so that a line can carry more power in a controllable way. The letter F is for Flexible, not for forward, fixed or finite. The answer is option C.

Answer: D

FACTS devices are power electronic controllers for AC transmission systems: shunt compensators (the static VAR compensator and STATCOM), series compensators (TCSC and SSSC), and combined controllers such as the unified power flow controller (UPFC). A DC-DC converter changes one DC voltage level to another, and it is used in drives and power supplies, not as a FACTS controller of an AC line. The answer is option D.

Answer: A

The key gives \(60^\circ\). For a thyristor controlled reactor the fundamental susceptance depends on the firing angle \(\alpha\) through

\[ \begin{aligned} B(\alpha) \\ &= \frac{1}{X}\left(\frac{2(\pi - \alpha) + \sin 2\alpha}{\pi}\right) \end{aligned} \]

The full reactor at 220 V and 1 ohm would absorb \(220^2/1 = 48.4\) kVA, and the stated power of 48.4 kW is that full value, which corresponds to full conduction. The conduction angle in the item is given in a different convention from the one used here, so I could not reproduce the \(60^\circ\) independently. The explanation follows the key, option A.

Answer: C

The unified power flow controller (UPFC) combines a shunt converter (a STATCOM) and a series converter (an SSSC) joined by a common DC link. The series converter can inject a voltage in series with the line, controlling both active and reactive power flow, and the shunt converter can supply or absorb reactive power and provide the real power for the DC link. So a UPFC can supply both active and reactive power, and it also controls the voltage. The answer is option C.

Answer: A

A shunt controller of the FACTS family (such as a STATCOM or a static VAR compensator) is connected in parallel with the line and injects current into it at the point of connection, so it acts like a controllable current source. A series controller, in contrast, injects a voltage in series with the line and so acts like a voltage source. The power source and phase angle source options do not describe the way the shunt device acts on the network. The answer is option A.

Answer: B

The power transferred through a line is \(P = \dfrac{V_1V_2}{X}\sin\delta\), and for the same level of compensation a series compensator, a capacitor in series with the line, reduces the effective reactance \(X\) directly and so raises the power limit most effectively. A shunt compensator mainly keeps the mid point voltage near its rated value, which also helps but gives less increase for the same size, and a phase angle regulator changes the angle \(\delta\) rather than the reactance. A voltage source inverter is a building block, not a compensator type. The answer is the series compensator, option B.

Answer: C

On a long, lightly loaded or open ended transmission line the charging current of the line capacitance flows through the line inductance and raises the voltage along the line, so that the receiving end voltage is greater than the sending end voltage at no load. This is called the Ferranti effect. The thermal effect is the heating of conductors by current, the induction effect is the induced voltage on neighbouring circuits, and humidity effect is not a line effect. The answer is option C.

Answer: A

The steady state power limit between two sources is \(P_{max} = \dfrac{E_gE_m}{X_{total}}\). Without the reactor the total reactance is the sum of the series parts.

\[ X = 1.0 + 0.1 + 0.25 + 0.1 + 1.0 = 2.45\ \text{pu} \]

\[ P_{max} = \frac{1.2 \times 1}{2.45} = 0.49\ \text{pu} \]

This is option A, and it is the value without the reactor switch closed. The item asks for the limit with and without the reactor, but the options give a single number, so the key is read as the without reactor figure. With the shunt capacitor switched in at the motor bus, the transfer reactance changes and the limit rises above this value.

Answer: C

The Ferranti effect is the rise in voltage at the receiving end of a long, lightly loaded or open-circuited transmission line, so that the receiving end voltage is greater than the sending end voltage. It is caused by the charging current flowing through the inductance of the line.

The effect does not make either voltage zero, and the sending end voltage is not the greater of the two, since the receiving end is the one that rises. So the third option is correct.