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Two overhead lines A and B, of length 75km, with an inductance of 2.1 mH/km and a capacitance of 0.02 μF/km are connected to each other by a 1.05km cable C with an inductance of 0.75 mH/km and a capacitance of 0.48 μF/km.  If a surge of 20 kV of rectangular waveform originates in line A and enters the cable, calculate the following:

a)Impedances of the lines and the cable per km
b)voltage and current in the cable
c)Transmission and Reflection operators for the lines into the cable
d)Transmission and reflection operators for the cable going into the line
e)Surge velocity in the cable
f)Using a Bewley Lattice Diagram, calculate the voltage at the junction of line A and the cable 40 μsec after the initial surge reaches this point?
g)Explain how this diagram relates to the transmission wave properties found in the Lab experiment using the Transmission Line Demonstrator.

## Surge Initiation on the Transmission Line by Switching Loads and Lightning Strikes

This particular diagram relates with the transmission wave properties such that any sudden change or disturbance in an overhead transmission line or underground cable will generate both backward and forwards TWs signals propagating away from disturbance point towards the bars bar.

Surge initiation on the transmission line by switching loads and lightning strikes

An electrical device is designed to handle a specific voltage but they damage in case the devices are subjected to a higher voltage than what they are designed for. The longer the period over the higher voltage is experienced, the greater the damage. The most common damage is triggered by the extreme voltage involving the quick heating and successive cooling of electrical wiring. In case the wiring in an office or home experiences brief jolts of high electrical voltage and the causes of the power surges may be as a result of overloading the circuits, damaged or exposed wiring which causes power surge since the electricity flowing through them is not being handled or directed the way it normally should. High power electrical devices such refrigerator, elevators, and conditioning in case they are powered on, they tend to draw an unusually large amount of electricity thus the extra power causes overpowering of the circuit and other appliances and other electronics in its path (Lu, 2015, p. 156).

When the switching on of no-load transmission line is suddenly done, then the voltage of the line becomes twice compared to the normal system’s voltage. This particular voltage is transient in nature thus in case of interruption or switching off of a loaded line causes the voltage across the lines to become high enough thus chopping in the system majorly during opening operations of the air blast circuit breaker which causes overvoltage in the system.

The alive conductor is earthed suddenly during insulation failure and this is also capable of causing overvoltage in the system and in case there is distortion in the emf wave produced by the alternator, it will result to the occurrence of the resonance (Kyamakya, 2017, p. 678).

Lightning originating from a charged cloud is an electric charge in form of flash or spark. The bottom area of the cloud is negatively charged and possesses a temperature of -50 degrees Celsius while the main positive charge center is situated numerous kilometers higher up, therefore, the energy dissipated in a lightning flash ranges from 1000 to 10000MJ. The problem on transmission line caused by the lightning strikes is experienced when the negatively charged charges from the bottom of the cloud induce charges possessing conflicting polarity on the transmission line. These are held in place of the in the capacitances between the cloud and the line, the line, and earth until discharging of the clouds occurs as a result of lightning stroke (Mazzanti, 2013, p. 322).

Methods of controlling disruption of surges

This method is mostly used compared to the electrical substation. In this method, a set of GI wire is mounted over the sub-station and they are used for earthing and they are grounded properly through different sub-stations structures. The grounding of GI wire offers a little resistance route to the ground for lightning strokes. This approach of high voltage protection is economic and simple but it has a disadvantage since the system cannot be protected from traveling wave which may reach the sub-station through dissimilar feeders (Rachid, 2008, p. 56).

1. Lightning Arrester

## Methods of Controlling Disruption of Surges

This type of device provides very low impedance path to the ground for traveling waves possessing high voltage and also behaves like a non-linear electrical resistance. As the voltage increases, the resistance also decreases and vice-versa.

The overhead earth wire is placed over an electrical sub-station whereby it is placed over the transmission network. The overhead earth wire or ground wires assist in diverting all the lightning strokes to the ground instead of permitting them to strike directly on the transmission conductors (Smeets, 2014, p. 79).

The surges on the transmission line can be caused by three possible discharge path which includes

1. The primary route is from the lightning stroke to the earth whereby the capacitance between the earth and the leader is promptly discharged while the phase conductor is discharged ultimately by traveling wave action resulting when the capacitance from the leader moves to the earth wire. This causes induced voltage caused by the lightning stroke to nearby ground(Jensen, 2014, p. 111).
2. The following discharge route is amid the earth conductor and the lightning head where the capacitance is discharged between the two. The resulting traveling wave comes down the tower, acting through its effective impedance and raises the potential of the lower top to a point where the differences in voltage are enough to cause the flashover to the conductor(Humpage, 2011, p. 561).
3. The third discharge is between the phase conductor and the lead core where the capacitance is charged between these two and the main discharge current is injected into the phase conductor, so developing a surge impedance voltage across the insulator string(Rajput, 2008, p. 98).

The overvoltage can be produced by lightning when it smashes the line conductors (direct stroke) or a point in the locality of the supply network (indirect stroke). The impressing of the overvoltage can be done by atmospheric discharge and the magnitudes of lightning surges appearing on the transmission lines which are mostly affected by the designing of the line.

Explaining the use of lamps and electrical test meters during synchronization

Synchronization is simply the procedure of matching elements for example frequency, phase sequence, voltage, waveform alternator, phase sequence and extra sources with running or efficient power system. The power cannot be delivered by the generator unless the frequency, voltage and other parameters and the networks are matching.

The actual synchronization process involves the following procedures;

• Considering that the bus bar is supplied with power at rated frequency and voltage.
• Secondly, the alternator -2 and alternator-1 to be connected parallel to each other. The frequency is increased as a result of increasing the alternator speed and this also causes an adjustment in speed till it matches with the frequency of the bus bar.
• The generation of three voltages by the alternator-2must be in phase with the specific voltage of the bus bar and this can be attained by upholding the same frequency and phase sequence of alternator-2 with the alternator-1 bus bar(Hossain, 2014, p. 12).

One of the methods used for synchronizing the machine include; Three Dark Lamps Method and Synchroscope.

The connection of the three lamps takes place across the switches of the alternator-2. The alternator is synchronizing by driving the alternator prime mover at a velocity adjacent to the synchronous speed decided by the frequency of the bus bar and the number of poles of the alternator. On and off rate of the lamp is decided based on the difference in frequency between the bus bar voltage and alternator-2 voltage (Glover, 2016, p. 333).

When all the parameters are put in order then the lamp becomes darker and then the synchronizing switch can be closed to synchronize alternator-2 with alternator-1. The major demerit of this approach is that the flickering rate only shows the difference between the bus bar and the alternator-2. Lamps and bright technique is not a correct method since it needs a correct sense of judgment, therefore, personal judgment should be avoided (Diesendorf, 2015, p. 321).

In synchronization of three-phase alternators, there is a connection of three lamps so as to assist in indicating whether the incoming machine is running fast or low. The lamps would glow up or dark out in case of symmetrical connections so long as the phase sequence for base bar and the incoming machine is similar. In synchronization of alternators, there are conditions that should be met which include;

• The voltage of the bus bar of the entering machine must be similar to the terminal voltage.
• The frequency of the bus bar must be similar to that of the incoming machine and this indicates that there must be a proper adjustment of speed.
• Phase sequence for the two voltages must be similar with respect to the external load.

This is an accurate device comprising a rotary pointer which assists in showing the accurate moment of closing the synchronizing switch. In a situation where the rotation of the pointer takes place in an anticlockwise route, therefore, it shows that the entering machine is running low whereas an indication that the mechanism is operating quicker is when the pointer is rotating in the clockwise direction. The turning of the pointer is relational to the difference in the two frequencies (Humpage, 2011, p. 75). The rotation of the pointer should take place at a very low speed in the marked direction in the figure

## Explaining the Use of Lamps and Electrical Test Meters During Synchronization

When the pointer rotating attains the perpendicular point at slow speed, the switch must be closed. The oscillation of the pointer will take place at about some mean position instead of rotating if the difference in frequencies is large. In such cases, adjustment of the speed of the incoming machine should be done appropriately (Hossain, 2014, p. 453).

During connection, the two bus bar is connected to its terminals while the terminal remaining is linked to the conforming lines of the incoming machine and both the phase sequence from the machine and from the bus bar should be similar. The phase sequence indicator can be used to check if they are similar. The checking if the voltage of the incoming machine and the bus bar if they are equal then voltmeter can be used. Using this method, an error of a few electrical degrees between the generator and the system will lead into a momentary inrush and sudden change in speed of the generator (Christian, 2009, p. 234).

The main method of controlling voltage frequency and power factor

The main technique of controlling voltage frequency in the synchronous machine is the use of Automatic Voltage Regulator. The AVR takes the voltage fluctuating then changes them into a constant voltage. Voltage fluctuation usually comes as a result of load variation in the supply system (Pansini, 2009, p. 456).  The power system equipment is destroyed because of voltage fluctuation and they can be controlled by installation of the voltage regulator in numerous sectors near the generators, transformers, and feeders. The provision of the voltage regulator is done in many places in the power system to assist in controlling variations in voltage. In AC systems, controlling voltage can be done by employing methods such as shunt condenser, booster transformers, and induction regulators while controlling voltage in DC supply system is done by using over compound generators in case equal length of feeders and use of feeder booster in case the feeders vary in length (Chakrabati, 2013, p. 123).

The AVR works on the principle of detention of errors. The output voltage of an AC generator acquired through a potential transformer and then rectified, filtered and compared with a reference.  The error voltage is simply the variation between the actual voltage and the reference voltage and it is amplified by an amplifier then supplied to the pilot exciter or the main exciter (Bakshi, 2009, p. 45).

The amplified error signals regulate the excitation of the pilot or main exciter through a boost or a buck action. The main alternator terminal voltage s controlled by the exciter output control. Apart from controlling the voltage of the system, the Automatic Voltage Regulator performs various functions such as;

• It assists in the reduction of overvoltage which occurs as a result of sudden loss of the load on the system(Perker, 2008, p. 89).
• It increases the excitation of the system under fault condition leading to the existence of synchronizing power at the time of clearance of the fault(Wang, 2010, p. 543).
• It assists in dividing the reactive load between the alternators operating in parallel

There should be a change in excitation system in case of a sudden change in load in the alternator so as provide similar voltage based on the new load condition. Automatic Voltage Regulator equipment operates in the exciter field and changes the output voltage of the exciter and the field current. The ARV usually does not offer a quick response in case there is a violent fluctuation (Baba, 2016, p. 123).

Baba, Y., 2016. Electromagnetic Computation Method for Lightning Surge Protection. s.l.: Hachette Livre.

Bakshi, U., 2009. Transmission and Distribution of Electrical Power. s.l. Cambridge University Press.

Chakrabarti, A., 2013. Power System Dynamics And Simulation. s.l. OLMA Media Group.

Christian, I., 2009. Advances in Power System Control, Operations, and Management. s.l.:HarperCollins.

Diesendorf, W., 2015. Insulation Co-ordination in High-voltage Electric Power System. s.l.: McGraw-Hill Education.

Glover, D., 2016. Power System Analysis and Design. s.l. Adventure Works Press.

Hossain, J., 2014. Robust Control for Grid Voltage Stability. s.l. Sanoma.

Humpage, D., 2011. Z- Transform Electromagnetic Transient Analysis in High Voltage. s.l. Haufe Gruppe.

Jensen, C., 2014. Online Location of Faults on AC Cables in Underground Transmission. s.l.:Simon & Schuster.

Kyamakya, K., 2017. Recent Advances in Nonlinear Synchronization. s.l.: Thomson-Reuters.

Lu, Z., 2015. Protective Relaying of Power Systems Using Mathematical Morphology. s.l.: China Publishing Company.

Mazzanti, G., 2013. Extruded Cables for High-Voltage Direct-Current Transmission. s.l.: Reed Elsevier.

Monro, R., 2012. The History of Electric Wires and Cables. s.l.: Wolters Kluwer.

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Parker, K., 2008. High Voltage Direct Current Transmission and Annotated. s.l.: Houghton Mifflin Harcourt.

Rachid, F., 2008. electromagnetic Field Interaction with Transmission. s.l. Media Participation.

Rajput, E., 2008. The utilization of Electrical Power. s.l. Gakken.

Smeets, R., 2014. Switching in Electrical Transmission and Distribution Systems. s.l.: Random House.

Uman, M., 2008. The Art and Science of Lightning Protection. s.l.: Wiley.

Wang, X.-F., 2010. Modern Power System Analysis. s.l.: China Publishing Company.

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