School of Electrical Engineering
and Telecommunications
Term 2, 2023
ELEC 3105 - Electrical Energy
Assignment
INTRODUCTION
Requirements
• Assignments must be submitted as a single (either .doc, .docx or .pdf file) in a properly formatted
document.
• An appropriately prepared document (using Word, LaTeX etc) is strongly suggested. Handwritten
assignments are also acceptable but will have to be legible.
• All answers to questions should include explanations and justifications of your chosen approach.
• Figures and diagrams (when not explicitly requested) are strongly recommended.
• Late submission without prior approval will not be permitted under any circumstances.
• Submissions must be made in Moodle. An e-mail is not a valid submission.
Marks and Submissions
This assignment contributes 18% toward your final marks.
The last day of submitting the assignment is 11.59pm, Monday, 10th July 2023 via the Turnitin Assignment
submission link in Moodle: https://moodle.telt.unsw.edu.au/mod/turnitintooltwo/view.php?id=5746833.
Assessment and Plagiarism
Since this assignment counts towards your formal assessment for this subject, you are required to sign a
declaration and attach it as a cover sheet to the front of your submission. Without this signed declaration,
the assignment will not be considered for assessment. A fillable pdf file for signed declaration can be found
in Moodle.
Note that plagiarism (i.e. copying of assignment or pay someone to do your assignment) is an academic
offence. If suspected of plagiarism, you may be referred to disciplinary board and will be subjected to heavy
penalties.
Detailed information can be found in https://student.unsw.edu.au/plagiarism
LEARNING OUTCOMES AND GRADUATE ATTRIBUTES
This assignment covers the first three topics of ELEC3105; Energy generation, Three-phase systems and
Transformers.
The key learning outcomes of the activity are:
• Develop the capacity to select, design and justify important power engineering devices for real-life
applications,
• Be able to apply underlying theories and concepts in the design process.
The key graduate attributes linked to the activity are:
• Analytical skills, critical thinking and creative problem solving.
• Demonstration of the understanding of principles.
• Effective use and communication of relevant information.
1
TThe Great War of the Ring is behind us.
Dark Lord Sauron is no more and the One Ring has been cast into the fiery Mount Doom by Frodo Baggins.
The destruction of the Ring marks the end of the dark age of Sauron and the start of the Fourth Age, an age
of peace, prosperity and a time for rebuilding Middle Earth.
The descendants of Durin’s Folk, the long-bearded dwarves are amongst the first to spring into action. The
long abandoned Mines of Moria are now being rebuild. However, the ways of the old - fires, coal and hard
manual labour are no longer sustainable. The sun, the wind, water, the very same elements that stood
against the darkness are now the ones to mark the new era in dwarven industry and its electrification!!
This is, by no means, a small undertaking. The dwarves might be skilful masters of stone, metal and fire but
electricity is a new domain for them. They require guidance, leadership and great resolve. The call was sent
to all races around Middle Earth and this challenge has been accepted by you... (and your colleague, Bruce,
who has been sent by your engineering company to assist).
Good Lu†
Before You Begin
In order to complete your assignment, you need to receive your own set of parameters and values. To do so,
go to Moodle and start the quiz named "Assignment Parameters:
https://moodle.telt.unsw.edu.au/mod/quiz/view.php?id=5746835
Part 1 [28 marks]:
O
Upon arrival, you dust off three old single-phase transformers, that have no parameters on them except
their rated power (1 MVA) and the rated voltage at the low-voltage winding (6.6kV). You start conducting the
open-circuit and short-circuit test for the first transformer.
During your open-circuit test, you measure Ioc A at the low voltage winding and an active power of Poc kW.
1. [1 marks] What parameters can you calculate based on the above measurements?
2. [1 marks] How can you differentiate between the low-voltage and high-voltage windings of the trans-
former if no additional information is given to you?
3. [2 marks] Calculate the above parameters of your single-phase transformer.
4. [2 mark] Why is it important for all three transformers to have identical or very similar parameters if they
are to be used in a three-phase system?
During the short-circuit test, Bruce applies the rated voltage of the transformer across its high-voltage
windings.
1. [2 marks] Draw a diagram of the circuit in this test, including an appropriate equivalent transformer
circuit and explain what went wrong in this test.
2. [2 marks] Without any additional information, can you estimate how much current we would have
measured through the transformer (you can provide a range for your answers)? Explain how you
reached this conclusion.
As the other two transformers were damaged and rusty, you eventually choose to use the new transformer
that you brought with you. The nameplate of the transformer is as follows:
1. [3 marks] Calculate the parameters of the approximate equivalent transformer circuit in Ω. Explain the
steps in your calculation.
2
Nameplate: OPTIMUS PRIME
Primary Phases 3 Secondary Phases 3
Rated Power: 3 MVA
Primary Voltage 33 kV Secondary Voltage 6.6 kV
Frequency : 50 Hz
Impedance (%) XTx Series Resistance (%) RTx
Vector Symbol Yyn Oil Specs IEC-60296
2. [6 marks] Calculate the efficiency (in %) of the transformer at 30%, and 90% of its rated power for i)
unity power factor ii) 0.7 leading power factor.
3. [6 marks] Calculate the voltage regulation (%) of the transformer for any two of the operating conditions
of the previous question.
4. [3 marks] Draw the winding connections of the transformer clearly showing the phase and line voltages
of the primary and secondary windings. What is the rated voltage of the primary and the secondary of
the transformer windings?
Part 2 [26 marks]:
T
The transformer is used to electrify mining activities within the main mines of Mornia. Interestingly enough,
the Middle Earth power system is a 50 Hz power system.
There are three main loads that are supplied by your main 33kV supply and through the transformer of Part
1 which is included in underground mining substation. These three loads are :
1. Drilling equipment: PL1 kW at a p f1 lagging power factor.
2. Conveyor belts: SL2 MVA at p f2 lagging power factor.
3. Pumps, fans and blowers: PL3 kW, QL3 kVAr.
The voltage at your loads under any operating conditions should be constant and equal to 6.6 kV. Initially,
your substation operates at the very entrance of the mines directly next to the 33 kV supply substation (any
impedance on the lines between the two can be ignored at this stage).
1. [2 marks] Calculate the power factor at the load terminals when all loads are connected and operating.
2. [3 marks] Calculate the current at the low-voltage and the high-voltage side of your transformer when
all loads are connected and operating.
3. [5 marks] Calculate the voltage at the supply side of the transformer in order for the load voltage to be
equal to 6.6kV when all loads are connected and operating. What is the power factor at the high-voltage
side?
Eventually your substation moves down the mines so that mining activities can begin. Your mining location is
3 km deep within the mines, at which point your transformer / substation is located 2 km from your main
supply and 1 km from your mining location.
Your 33 kV feeder cables have a resistance of 0.494 Ω/km and an inductance of 0.515 mH/km.
Your 6.6 kV feeder cables have a a resistance of R6.6kV Ω/km and an inductance of L6.6kV mH/km.
If the voltage at the loads is equal to 6.6 kV and all three loads are connected:
1. [2 marks] Draw your per-phase equivalent circuit in per-unit.
2. [2 marks] Calculate the voltage at the low-voltage terminals of the transformer in per-unit.
3
3. [2 marks] Calculate the voltage at the high-voltage terminals of the transformer in per-unit.
4. [2 marks] Calculate the voltage at the supply substation in per-unit.
5. [4 marks] Draw the phasor diagram of including all voltages and currents in your system.
6. [4 marks] What is the value of the capacitors that need to be connected in each phase at the load side
to make the total power factor when all loads are connected equal to unity? What are the differences
between the possible connections of the capacitors?
Part 3 [36 marks]:
T
1. [3 marks] The average wind-speed above the mines of Moria is 7 m/s and follows a Weibull distribution,
specifically Rayleigh statistics. What is the specific power of this wind?
2. [6 marks] What is the cross-sectional area of a wind-turbine that can capture the same power as that
required by the loads? How much of this power might eventually make it into electricity?
Unfortunately, logistic issues and the collapse of the Bridge of Khazad-Dum (Cause of the collapse here:
https://www.youtube.com/watch?v=3xYXUeSmb-Y) means that your are not able to install a wind turbine and
instead a solar PV system will be built. This system needs to be able, on average generate throughout the
day the same amount of energy required by your mining loads. For unexplained reasons, the only available
solar PV module that you can purchase and ship to the mines of Moria is the CanadianSolar TOPHiKu6
N-type TOPCon module.
Datasheet available in Moodle: https://moodle.telt.unsw.edu.au/mod/resource/view.php?id=5746834
1. [2 marks] Calculate the total energy consumption of the mine over one day.
2. [5 marks] While you were trying to figure out the wind turbine, Bruce has back from scouting a location
to install your solar farm. It is easy to get to, next to the road but the average temperature is 85◦. What
is the fill factor of your PV panel when operating at a temperature of 85◦1?
3. [2 marks] Eventually, you choose a better site for your system, with conditions much closer to the STC
ones. What is the fill factor of your PV module?
4. [2 marks] Your datasheet includes a value "Module efficiency". Explain its meaning.
5. [8 marks] Assume that the power output of each solar panel is directly proportional to irradiance and
that the solar irradiance in the location where you plan to install your solar farm is given in the following
table2
Table 1 Daily Solar Irradiance
Time Irradiance (W/m2)
6 am - 9 am 200
9 am - 11 am 400
11 am - 7 pm 1000
7 pm - 9 pm 200
Calculate the number of panels that you need generate throughout the day the same amount of energy
required by your mining loads. Assume an efficiency in your inverter of 97%, and 2% losses in your
1You can choose any of the 5 modules available in the datasheet. They all share the same temperature characteristics also
provided in the datasheet.
2Note that the eye of Sauron keeps solar irradiance constant from 11am to 7pm. Don’t ask how!
4
transformer (that connects your PV system to your 33kV supply) and the cables from the PV system to
your 33 kV feeder in the mine.
6. [4 marks] Your datasheet allows for two configurations for your modules, one with a maximum voltage
of 1000V and ones for 1500V. Choose one of the two and calculate the number of panels in series and
in parallel for your system.
7. [4 marks] Draw a single line of the whole system, including the supply, mining substation, cables, PV
system (and all its components) when you are mining 3 km deep in the mines.
Bonus Questions:
B
1. [3 marks] In part 2, question 6 you calculated the required capacitance to achieve unity power factor.
Are there other options to improve the efficiency of your system without including capacitors? Explain
your answers.
2. [4 marks] In part 3, question 6, you have the choice of 1000 V or 1500 V. Are there any advantages in
choosing a higher voltage over a lower voltage? Any disadvantages to consider?
3. [2 marks] Is ELEC3105 memeable? Have a go, class of 2023! Not power, not electrical engineering,
but ELEC3105!
Extra Notes:
Mining substations for underground applications are, in fact a real thing. They are actually placed in tracks
and move along the mine to supply all electrical equipment. Similar substations are also used to power
drilling equipment for tunnel excavations like the new harbour metro tunnel. Transformers and everything
else has to follow very strict regulations due to the explosive nature of the locations they are being used.
They look like this: