AC/DC Circuit Theorems, Electromagnetic Principles, and Properties

This report provides a comprehensive analysis of AC/DC circuit theorems, electromagnetic principles, and their application in flywheel energy storage systems. It begins with an introduction to the operation of motor/generators in flywheel systems, detailing their function as both motors and generators. The report then applies Kirchhoff's laws to determine the magnitude and direction of currents through resistors in a DC circuit, calculating voltage drops across each resistor. Furthermore, it analyzes AC circuits, calculating impedance, current, voltage, phase angle, and power factor for various configurations, including series circuits with resistors, inductors, and capacitors. The report concludes with a bibliography of cited sources.

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
AC/DC CIRCUIT THEOREMS, ELECTROMAGNETIC PRINCIPLES AND
PROPERTIES
A Research Paper on Energy By
Student’s Name
Name of the Professor
Institutional Affiliation
City/State
Year/Month/Day

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
INTRODUCTION
As a junior engineer in a global engineering consultancy firm and then transferred to
the Electrical Power team where there is need of contributing a broad understanding of
AD/DC circuit theorems, electromagnetics principles, and properties. There is need of
provision of information on the characteristics of circuits connected to either the AC or DC
buses from the flywheel-based energy storage system shown below:
Task 1.1
Operation of Motor/Generator in flywheel energy storage system
The motor/generator forms the electrical machines in the flywheel by working as a
motor to transfer electrical energy to this energy storage device and as a generator to restore
the energy stored into the flywheel. When acting as a generator, kinetic energy stored in the
rotor is transformed into electrical energy (Hans, 2014).
Figure 1: Basics of Motor/Generator in Flywheel

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
When performing as a motor, the supplied electrical energy to the windings of stator
is changed into mechanical energy leading to an increase in the velocity of the flywheel. It is
important to build a generator which generates high voltage that is greater than 10kV and low
current, which would lead to low power losses and high power supply. The electrical energy
input accelerates the mass to velocity through an integrated motor-generator. The energy is
discharged through reducing the kinetic energy by the use of the same motor-generator
(Kerry, 2013).
Low rotor losses, robust rotor structure, and high efficiency are the major
requirements for the motor/generator of the flywheel system. The figure below shows the rate
of radiated heat loss against rotor temperature:
The quantity of transfer of heat through radiation is minute except at high temperatures, and
high path of thermal through the bearings is minimal hence controlling the losses of the rotor
is important to prevent the rotor from overheating (Hans, 2014).
Task 1.2
Using Kirchhoff’s laws determine the magnitude and direction of the currents through each
resistor in the circuit below where the V1 and V2 of 12 V are connected to the DC pick- off
shown from the AC/DC/AC Power Converter above. From these currents determine the
voltage drops across each resistor:

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
By the use of the Kirchhoff’s voltage law which states that the algebraic sum of all the
voltages around any closed loop in a circuit is equal to zero, the figure above can be divided
into two loops: (Strasik, 2012)
Loop 1
V1 + Rload I1 + R1I1 = 0
V1 + 30I1 + 10I1 = 0
12 + 30I1 + 10I1 = 0
12 + 40I1 = 0
40I1 = -12
I1 = -0.3A
Loop 2

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
V2 + I2R2 + I2Rload = 0
12V + 20 I2 + 30I2 = 0
12 + 50I2 = 0
50I2 = -12
I2 = -0.24A
The current 11 whose magnitude is 0.3A passes through resistant R1 and R load in the
negative direction to the voltage V1 in the first loop while current I2 whose magnitude is
0.24A passes through resistant R2 and Rload in the opposite direction to the voltage V2 in the
second loop.
Task 1.4.1
1.4.1. The first is connected to one of the AC supplies when it’s set to 24 V(RMS), 800 Hz
and consists of a resistor of 500  in series with an inductor of 10mH and a capacitor of
800nF. You are required to determine the:
a. Impedance of the circuit.
XL = 2ΠfL
= 2*22/7*800*10*10-3
= 50.286 Ω
Xc = 1
2 Π fc =
1
2∗22
7 ∗800∗800∗10−9
= 248.58 Ω

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
X = Xc - Xl
= 248.58-50.286
= 198.29 Ω
Z = Sqr(198.292*5002)
= 537.885 Ω
b. Current flowing and the reading expected on an ammeter connected in the circuit.
V average = 24rms*sqr2
=33.941V
Z = 537.885 Ω
I = 33.941/537.885
= 0.0631A
The reading expected on an ammeter connected in the circuit = 0.0631A
c. Voltage across the inductor and the reading expected on a voltmeter connected across
the inductor.
Voltage across inductor = IXl
= 0.0631*2*Π*800*10*10-3
= 3.173V
The reading expected on a voltmeter connected across the inductor = 3.173V
d. Circuit phase angle and its power factor.

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
Tan ϴ = 198.29/500
= 21.63o
Circuit phase angle = 21.63o
Power factor = Cos ϴ
= 0.9296
Task 1.4.2
The second consists of a coil of resistance 4Ω and inductance 33mH is connected in series
with a resistor of 20Ω and a capacitor of 150μF. The circuit is then connected to a 15V,
50Hz supply. Determine:
a. The impedance of the coil.
XL = 2ΠfL
= 2*22/7*50*33*10-3
= 10.371 Ω

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
Impedance, Z = Sqr(42 + 10.3712)
= 11.116 Ω
b. The impedance of the whole circuit and the current flowing in it.
Xc = 1
2 Π fc =
1
2∗22
7 ∗50∗150∗10−6
= 21.212 Ω
X = Xc – XL
= 21.212 – 10.371
= 10.841 Ω
Z = Sqr(242*10.8412)
= 26.335 Ω

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
Current flowing in the whole circuit
I = V/R
= 15/26.335 = 0.57A
c. The voltage across the coil (resistance and inductance).
V = IR
= IXl
= 0.57*10.371
= 5.71V

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AC/DC Circuit Theorems, Electromagnetic Principles and Properties
Bibliography
Hans, B., 2014. Flywheel Energy and Power. London: Renewable and Sustainable Energy Reviews.
Kerry, M., 2013. NASA Flywheel System Development. Colorado: Space Power Workshop.
Strasik, M., 2012. Design, Fabrication, and Test of a 5-kWh/100-kW Flywheel Energy Storage Utilizing
a High-Temperature Superconducting Bearing. Michigan: IEEE.