The document provides information about a course on power systems analysis and protection. It includes:
1. An overview of topics covered in the course including per-unit systems, power flow analysis, fault analysis, stability, and protection schemes.
2. Expected learning outcomes including analyzing balanced and unbalanced faults, demonstrating power flow software, and expressing suitable protection schemes.
3. A lecture plan outlining the contents to be covered each week.
4. Assessment details including oral exams, written tests, assignments, and a final exam.
This document discusses power system fault analysis. It begins by outlining the learning objectives and syllabus, which include power flow analysis, power system faults, and power system stability. It then provides an introduction to power system fault analysis, explaining that faults usually occur due to insulation failure, flashover, physical damage or human error. Faults can be three-phase symmetrical or asymmetrical, and involve short-circuits to earth, between phases, or open circuits. Fault analysis is carried out using per-unit quantities. The document goes on to discuss equivalent circuits for single-phase and three-phase systems, and revising per-unit quantities and conversions between different bases.
Three phase delta connection, Three phase delta connection,, how delta connection works, What is Delta Connection, WHY DELTA CONNECTION IS USED, DELTA ADVANTAGES
1) A three-phase power distribution system uses a balanced three-phase configuration to transmit power from generators to loads.
2) A balanced three-phase circuit can be analyzed as an equivalent single-phase circuit. This allows determining the unknown voltages and currents by solving for a single phase.
3) For a balanced Y-Y connected three-phase circuit, the line currents are equal and differ in phase by 120 degrees, while the line voltages are √3 times the phase voltages and differ in phase by 30 degrees.
The document provides information about a course on power systems analysis and protection. It includes:
1. An overview of topics covered in the course including per-unit systems, power flow analysis, fault analysis, stability, and protection schemes.
2. Expected learning outcomes including analyzing balanced and unbalanced faults, demonstrating power flow software, and expressing suitable protection schemes.
3. A lecture plan outlining the contents to be covered each week.
4. Assessment details including oral exams, written tests, assignments, and a final exam.
This document discusses power system fault analysis. It begins by outlining the learning objectives and syllabus, which include power flow analysis, power system faults, and power system stability. It then provides an introduction to power system fault analysis, explaining that faults usually occur due to insulation failure, flashover, physical damage or human error. Faults can be three-phase symmetrical or asymmetrical, and involve short-circuits to earth, between phases, or open circuits. Fault analysis is carried out using per-unit quantities. The document goes on to discuss equivalent circuits for single-phase and three-phase systems, and revising per-unit quantities and conversions between different bases.
Three phase delta connection, Three phase delta connection,, how delta connection works, What is Delta Connection, WHY DELTA CONNECTION IS USED, DELTA ADVANTAGES
1) A three-phase power distribution system uses a balanced three-phase configuration to transmit power from generators to loads.
2) A balanced three-phase circuit can be analyzed as an equivalent single-phase circuit. This allows determining the unknown voltages and currents by solving for a single phase.
3) For a balanced Y-Y connected three-phase circuit, the line currents are equal and differ in phase by 120 degrees, while the line voltages are √3 times the phase voltages and differ in phase by 30 degrees.
Ekeeda Provides Online Electrical and Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
Ekeeda Provides Online Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/streamdetails/stream/Electronics-Engineering
Omkar Dash is studying B.tech in CSE with registration number 220301120362 and section F. His topic is on three phase AC circuits. A three phase system has three voltage sources generated by rotating three coils separated by 120 degrees in a stationary magnetic field. The frequency of all three phases must be the same. Related terms include phase sequence, phase naming (RBY), subscript notation for voltages, balanced loads, star and delta connections. In a star connection, three similar ends are joined to a common point called the neutral. There is no neutral in a delta connection. Phase voltage is between a phase and neutral, line voltage is between two lines. Line current equals phase current in a star connection. Total power
Basic Electrical Engineering Module 1 Part 1Divya15121983
This document provides an overview of basic electrical engineering concepts including Ohm's Law, series and parallel circuits, and Kirchhoff's Laws. It defines Ohm's Law as stating that current is directly proportional to voltage and inversely proportional to resistance. Kirchhoff's Current Law and Voltage Law are introduced as the principles that the algebraic sum of currents at a junction is zero and the algebraic sum of voltages around a closed loop is also zero. An example circuit problem is worked through using these laws to solve for unknown currents.
Power Circuits and Transforers-Unit 6 Labvolt Student Manualphase3-120A
This document provides instruction on analyzing balanced three-phase AC circuits connected in wye and delta configurations. It discusses the differences between line and phase voltages and currents. Formulas are presented for calculating active, reactive, and apparent power in balanced three-phase circuits. Exercises are included to measure voltages and currents in wye- and delta-connected resistive loads to verify the theoretical calculations and relationships between line and phase values.
BEF 23803 - Lecture 9 - Three-Phase Power Calculations.pptLiewChiaPing
The document provides information about calculating power consumed by three-phase loads. It defines the formulas for calculating power consumed by star-connected and delta-connected loads. It states that for a balanced three-phase load, the total power is equal to 3 times the power per phase multiplied by the cosine of the phase angle. It also provides formulas for calculating total apparent power and reactive power for three-phase circuits. Worked examples are included to demonstrate calculating current, power, kVA, and power factor for some sample three-phase loads.
This document discusses power relationships in electrical systems. It begins by defining key terms like active power, reactive power, apparent power and power factor. It explains that active power is the rate of usable energy transfer while reactive power supplies stored energy in reactive elements. Apparent power is the product of voltage and current and comprises both active and reactive power. Power factor is the ratio of active to apparent power. Inductive loads cause current to lag voltage, lowering the power factor. The document then discusses power factor correction using capacitors and its benefits like increasing system capacity and reducing losses. It provides examples of calculating current, power and load impedance in wye-delta systems.
This document provides instruction on establishing three-phase circuits and measuring power in single-phase and three-phase circuits. It discusses the theory of three-phase circuits including line and phase voltages and currents. Formulas are given for calculating active, reactive, and apparent power in balanced wye- and delta-connected three-phase circuits using line voltages and currents. The document describes using a power meter to measure power in single-phase circuits and measuring total power in four-wire, three-phase circuits.
This document provides an introduction to power system calculations using the per unit method. It discusses calculating fault levels using a four step process involving representing the system as a single line diagram, developing an equivalent circuit in per unit values, applying circuit reduction techniques, and calculating the fault level and current. It also briefly discusses performing load flow calculations to determine power flows and voltages in an interconnected system. The overall document provides instruction on basic power system analysis techniques.
The document discusses three-phase circuits, including their advantages over single-phase circuits. It covers wye-connected and delta-connected systems, defining line and phase voltages and currents for each. It provides examples of calculating current, power, and power factor for loads in both wye and delta configurations. It also discusses power measurement using wattmeters and power factor correction by adding capacitance to an inductive load.
The document discusses three-phase circuits, including their advantages over single-phase circuits. It covers wye-connected and delta-connected systems, defining line and phase voltages and currents for each. It provides examples of calculating current, power, and power factor for three-phase loads. Power can be measured using two or three wattmeters depending on the system configuration. Power factor correction is also discussed as adding capacitance to counteract an inductive load.
- AC power transmission is more economical than DC transmission due to lower line losses and easier fault protection.
- In AC circuits, voltage and current can be represented as phasors to analyze the relationship between instantaneous and average power.
- Reactive power in inductive and capacitive circuits averages to zero over each cycle but increases apparent power. Power factor correction reduces reactive power.
- Three-phase systems are more efficient than single-phase as they transmit more power using three conductors with constant power output. Star and delta connections determine the relationship between phase and line voltages/currents.
1) A 3-phase system consists of a sending end transformer connected Y-Δ, feeding a cable connected to a receiving end transformer bank connected Δ-Δ.
2) A 3-phase short circuit occurs at the 240V secondary of the receiving end transformers.
3) To calculate the short circuit current, the equivalent impedances of the sending end transformer, cable, and receiving end transformers are determined and used to calculate the current through each component based on the 24kV source voltage. This gives the steady-state short circuit current in the different parts of the system.
This document discusses per unit systems and symmetrical components for power system analysis. It defines a per unit system as expressing quantities as fractions of a defined base unit to simplify calculations when referring values across transformers. Advantages of per unit systems include similar impedances for similar apparatus and improved numerical stability. The document also defines symmetrical components as representing unbalanced three-phase quantities as the sum of three balanced components to analyze unbalanced faults.
This document provides an overview and summary of key concepts from a lecture on three-phase power system operations and analysis:
1) It introduces the per-phase analysis method which allows analysis of a balanced three-phase system as if it were a single phase by representing loads and sources as wye-connected equivalents and assuming phases are decoupled.
2) It provides an example of using the per-phase analysis method to solve a circuit and determine real and reactive power flows between generators supplying a delta-connected load.
3) It discusses basic power system components and operations including generation, load, transmission, distribution of power, and the goal of maintaining real and reactive power balance at all buses.
Ekeeda Provides Online Electrical and Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
Ekeeda Provides Online Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/streamdetails/stream/Electronics-Engineering
Omkar Dash is studying B.tech in CSE with registration number 220301120362 and section F. His topic is on three phase AC circuits. A three phase system has three voltage sources generated by rotating three coils separated by 120 degrees in a stationary magnetic field. The frequency of all three phases must be the same. Related terms include phase sequence, phase naming (RBY), subscript notation for voltages, balanced loads, star and delta connections. In a star connection, three similar ends are joined to a common point called the neutral. There is no neutral in a delta connection. Phase voltage is between a phase and neutral, line voltage is between two lines. Line current equals phase current in a star connection. Total power
Basic Electrical Engineering Module 1 Part 1Divya15121983
This document provides an overview of basic electrical engineering concepts including Ohm's Law, series and parallel circuits, and Kirchhoff's Laws. It defines Ohm's Law as stating that current is directly proportional to voltage and inversely proportional to resistance. Kirchhoff's Current Law and Voltage Law are introduced as the principles that the algebraic sum of currents at a junction is zero and the algebraic sum of voltages around a closed loop is also zero. An example circuit problem is worked through using these laws to solve for unknown currents.
Power Circuits and Transforers-Unit 6 Labvolt Student Manualphase3-120A
This document provides instruction on analyzing balanced three-phase AC circuits connected in wye and delta configurations. It discusses the differences between line and phase voltages and currents. Formulas are presented for calculating active, reactive, and apparent power in balanced three-phase circuits. Exercises are included to measure voltages and currents in wye- and delta-connected resistive loads to verify the theoretical calculations and relationships between line and phase values.
BEF 23803 - Lecture 9 - Three-Phase Power Calculations.pptLiewChiaPing
The document provides information about calculating power consumed by three-phase loads. It defines the formulas for calculating power consumed by star-connected and delta-connected loads. It states that for a balanced three-phase load, the total power is equal to 3 times the power per phase multiplied by the cosine of the phase angle. It also provides formulas for calculating total apparent power and reactive power for three-phase circuits. Worked examples are included to demonstrate calculating current, power, kVA, and power factor for some sample three-phase loads.
This document discusses power relationships in electrical systems. It begins by defining key terms like active power, reactive power, apparent power and power factor. It explains that active power is the rate of usable energy transfer while reactive power supplies stored energy in reactive elements. Apparent power is the product of voltage and current and comprises both active and reactive power. Power factor is the ratio of active to apparent power. Inductive loads cause current to lag voltage, lowering the power factor. The document then discusses power factor correction using capacitors and its benefits like increasing system capacity and reducing losses. It provides examples of calculating current, power and load impedance in wye-delta systems.
This document provides instruction on establishing three-phase circuits and measuring power in single-phase and three-phase circuits. It discusses the theory of three-phase circuits including line and phase voltages and currents. Formulas are given for calculating active, reactive, and apparent power in balanced wye- and delta-connected three-phase circuits using line voltages and currents. The document describes using a power meter to measure power in single-phase circuits and measuring total power in four-wire, three-phase circuits.
This document provides an introduction to power system calculations using the per unit method. It discusses calculating fault levels using a four step process involving representing the system as a single line diagram, developing an equivalent circuit in per unit values, applying circuit reduction techniques, and calculating the fault level and current. It also briefly discusses performing load flow calculations to determine power flows and voltages in an interconnected system. The overall document provides instruction on basic power system analysis techniques.
The document discusses three-phase circuits, including their advantages over single-phase circuits. It covers wye-connected and delta-connected systems, defining line and phase voltages and currents for each. It provides examples of calculating current, power, and power factor for loads in both wye and delta configurations. It also discusses power measurement using wattmeters and power factor correction by adding capacitance to an inductive load.
The document discusses three-phase circuits, including their advantages over single-phase circuits. It covers wye-connected and delta-connected systems, defining line and phase voltages and currents for each. It provides examples of calculating current, power, and power factor for three-phase loads. Power can be measured using two or three wattmeters depending on the system configuration. Power factor correction is also discussed as adding capacitance to counteract an inductive load.
- AC power transmission is more economical than DC transmission due to lower line losses and easier fault protection.
- In AC circuits, voltage and current can be represented as phasors to analyze the relationship between instantaneous and average power.
- Reactive power in inductive and capacitive circuits averages to zero over each cycle but increases apparent power. Power factor correction reduces reactive power.
- Three-phase systems are more efficient than single-phase as they transmit more power using three conductors with constant power output. Star and delta connections determine the relationship between phase and line voltages/currents.
1) A 3-phase system consists of a sending end transformer connected Y-Δ, feeding a cable connected to a receiving end transformer bank connected Δ-Δ.
2) A 3-phase short circuit occurs at the 240V secondary of the receiving end transformers.
3) To calculate the short circuit current, the equivalent impedances of the sending end transformer, cable, and receiving end transformers are determined and used to calculate the current through each component based on the 24kV source voltage. This gives the steady-state short circuit current in the different parts of the system.
This document discusses per unit systems and symmetrical components for power system analysis. It defines a per unit system as expressing quantities as fractions of a defined base unit to simplify calculations when referring values across transformers. Advantages of per unit systems include similar impedances for similar apparatus and improved numerical stability. The document also defines symmetrical components as representing unbalanced three-phase quantities as the sum of three balanced components to analyze unbalanced faults.
This document provides an overview and summary of key concepts from a lecture on three-phase power system operations and analysis:
1) It introduces the per-phase analysis method which allows analysis of a balanced three-phase system as if it were a single phase by representing loads and sources as wye-connected equivalents and assuming phases are decoupled.
2) It provides an example of using the per-phase analysis method to solve a circuit and determine real and reactive power flows between generators supplying a delta-connected load.
3) It discusses basic power system components and operations including generation, load, transmission, distribution of power, and the goal of maintaining real and reactive power balance at all buses.
Similar to class notes of electrical & electronics.pptx (20)
The document proposes two uses of AI technology for town planning:
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This document outlines the Dowry Prohibition Act of 1961 in India, which aims to prohibit the practice of dowry. Some key points:
- It defines dowry as any property or valuable security given by one party or their relatives to the other party around the time of marriage.
- It establishes penalties for both giving/taking dowry as well as demanding dowry, including imprisonment and fines.
- Any dowry received must be transferred to the wife within a few months, and failure to do so is also punishable.
- It gives powers to Dowry Prohibition Officers to enforce the act and collect evidence of offenses.
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This document provides an introduction to the Women's Empowerment Principles (WEPs), a set of principles for business on promoting gender equality and women's empowerment. It outlines that gender equality is a fundamental human right, and discusses how empowering women drives sustainable development and economic growth. It then presents the business case for gender equality, facts on the current barriers facing women, and an overview of the seven WEPs and how companies can implement them. Finally, it encourages engagement with UN Global Compact Local Networks to promote the WEPs.
This document introduces linear time-varying (LTV) systems and the computation of the state transition matrix (STM) for LTV systems. It discusses:
1) The definition and properties of the STM for LTV systems.
2) Conditions under which the system matrix A(t) commutes with the integral of A(t), which is required to compute the STM.
3) Examples of computing the STM for different time-varying system matrices.
4) How to obtain the overall state solution for an LTV system given its STM.
5) An introduction to discretizing continuous-time systems.
The document summarizes key findings from the Institute for Economics and Peace's 2021 Global Peace Index report. It finds that 73 countries deteriorated in peacefulness while 87 improved. Deteriorations were primarily driven by increases in militarization, military spending, and declines in safety and security, while improvements stemmed from reductions in conflicts and terrorism impacts. Iceland remains the most peaceful country while Afghanistan is the least peaceful. The economic cost of violence amounts to $1.496 trillion, or 11.6% of world GDP.
The document provides information about the Electrical and Electronics Engineering department at Chandil Polytechnic. The department was established in 2017 and offers 3-year diploma programs in electrical and electronics engineering. It aims to impart quality teaching and provide hands-on experience to produce skilled engineers. The department offers bachelor's and master's degrees and has laboratories for electronics, instrumentation, digital circuits, and power electronics. Graduates have good job prospects in industries like Siemens, Bosch, and BHEL.
This chapter discusses entrepreneurship and the process of starting a new business venture. It defines entrepreneurs as individuals who take on the risk of starting a business to pursue opportunities. It identifies different types of entrepreneurs and common personality traits they possess, such as high energy, self-confidence, and creativity. The chapter also explains why people choose to become entrepreneurs, factors supporting entrepreneurship, and outlines the typical process of selecting an idea, writing a business plan, and obtaining financing to launch a new company.
This document outlines the course objectives, expected outcomes, student learning outcomes, and modules of the MEE2022 Power Plant Engineering course. The course aims to discuss various power generation units and steam cycles, introduce concepts of steam generators and combustion methods, and discuss nuclear, gas turbine, hydro, and diesel power plants. Students will understand basic power generation types and steam cycles, learn about different boiler types, solve problems related to gas turbine and Rankine cycles, distinguish power generation units based on economic and environmental factors, and gain knowledge on contemporary issues. The course contains 7 modules covering topics like steam power plants, combustion and firing methods, nuclear power plants, gas turbine power plants, hydroelectric power plants, and diesel engine power plants.
This document contains a 50 question quiz on power plant engineering concepts. The questions cover topics like fuels used in nuclear power plants, the purpose of moderators and coolants, types of reactors (e.g. pressurized water, boiling water, gas cooled), and materials used. Multiple choice answers are provided for each question.
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This document discusses solar dryers, which use solar energy to dry substances like food. It describes the two main types - direct and indirect dryers - and explains their construction and working principles. Solar dryers are needed to prevent spoilage of foods in rainy seasons and address other issues like spreading harvests. Key advantages are less drying time than sun drying, protection from pests and weather, and hygienic drying. The document also reviews improvements possible in solar dryers and their limitations, concluding that India should make more use of this renewable energy source to address food waste problems.
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it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
1. BEEE102L BASIC ELECTRICAL
AND ELECTRONICS
ENGINEERING
Dr.S.ALBERT ALEXANDER
SCHOOL OF ELECTRICAL ENGINEERING
albert.alexander@vit.ac.in
1
Dr.S.ALBERTALEXANDER-
SELECT-VIT
2. Module 2
Dr.S.ALBERTALEXANDER-SELECT-
VIT 2
Alternating voltages and currents
RMS, average, maximum values
Single Phase RL, RC, RLC series circuits
Power in AC circuits
Power Factor
Three phase balanced systems
Star and delta Connections
Electrical Safety, Fuses and Earthing
3. 2.6 Three phase systems
Dr.S.ALBERTALEXANDER-SELECT-
VIT 3
A three-phase system is produced by a generator
consisting of three sources having the same amplitude and
frequency but out of phase with each other by 1200
All electric power is generated and distributed in three-
phase, at the operating frequency of 60 Hz in the USA or
50 Hz in India
When one-phase or two-phase inputs are required, they
are taken from the three-phase system rather than
generated independently
The instantaneous power in a three-phase system can be
constant (not pulsating) resulting in uniform power
transmission and less vibration of three-phase machines
4. Three phase systems
For the same amount of power, the three-phase system is
more economical than the single phase
The amount of wire required for a three-phase system is
less than that required for an equivalent single-phase
system
Dr.S.ALBERTALEXANDER-SELECT-
VIT 4
5. Three phase balanced systems
Three-phase voltages are often produced with a three-
phase ac generator (or alternator)
The generator basically consists of a rotating magnet
(rotor) surrounded by a stationary winding (stator)
Dr.S.ALBERTALEXANDER-SELECT-
VIT 5
6. Three phase balanced systems
Three separate windings or coils with terminals a-a’, b-b’
and c-c’ are physically placed 1200 apart around the stator
Terminals a and a’ for example, stand for one of the ends
of coils going into and the other end coming out
As the rotor rotates, its magnetic field “cuts” the flux from
the three coils and induces voltages in the coils
Because the coils are placed apart, the induced voltages in
the coils are equal in magnitude but out of phase by 1200
Since each coil can be regarded as a single-phase
generator by itself, the three-phase generator can supply
power to both single-phase and three-phase loads
Dr.S.ALBERTALEXANDER-SELECT-
VIT 6
7. Three phase balanced systems
A typical three-phase system consists of three voltage
sources connected to loads by three or four wires (or
transmission lines)
Three phase current sources are very scarce
A three-phase system is equivalent to three single-phase
circuits
The voltage sources can be either wye (Y)-connected or
delta ()-connected
Dr.S.ALBERTALEXANDER-SELECT-
VIT 7
8. Analysis
Let Van, Vbn and Vcn be the voltages between lines a, b, and
c, and the neutral line n “phase voltages”
If the voltage sources have the same amplitude and
frequency and are out of phase with each other by the
voltages are said to be balanced
Van+Vbn+Vcn=0
│
V
an│=│
Vbn│
=│
Vcn│
Balanced phase voltages are equal in magnitude and are
out of phase with each other by 1200
Dr.S.ALBERTALEXANDER-SELECT-
VIT 8
9. Analysis
Since the three-phase voltages are out of phase with each
other, there are two possible combinations
Van= Vp00
Vbn= Vp-1200
Vcn= Vp-2400 or Vcn= Vp+1200
+ve sequence
Rotor rotates counter clockwise
Dr.S.ALBERTALEXANDER-SELECT-
VIT 9
Van= Vp00
Vcn= Vp-1200
Vbn= Vp-2400 or Vcn= Vp+1200
-ve sequence
Rotor rotates clockwise
10. Analysis
Dr.S.ALBERTALEXANDER-SELECT-
VIT 10
The phase sequence is the time order in which the
voltages pass through their respective maximum values
A balanced load is one in which the phase impedances are
equal in magnitude and in phase
For a balanced wye-connected load, Z1=Z2=Z3=ZY
ZY is the load impedance per phase
For a balanced delta connected load, Za=Zb=Zc=Z
Z is the load impedance per phase
Wye-connected load can be transformed into a delta
connected load, or vice versa, using Z=3ZY
Since both the 3 source and 3 load can be either wye or
delta connected, we have four possible connections: Y-Y,
Y-, - and -Y
11. Exercise 1
Dr.S.ALBERTALEXANDER-SELECT-
VIT 11
Determine the phase sequence of the set of voltages:
van= 200 cos(t+100)
vbn= 200 cos(t-2300)
vcn= 200 cos(t-1100)
SOLUTION
The voltages can be expressed in phasor form as,
Van = 200100
Vbn = 200-2300
Vcn = 200-1100
Van leads Vcn by 1200 and in turn Vcn leads Vbn by 1200
Hence, the sequence is a-c-b
12. Power in a balanced system
For a Y-connected load, the phase voltages are
vAN= 2 Vp cost
vBN= 2 Vp cos (t-1200)
vCN= 2 Vp cos (t+1200)
The factor 2 is necessary because Vp has been defined
as the rms value of the phase voltage
behind their
If ZY=Z, the phase currents lag
corresponding phase voltages by .
ia= 2 Ip cos (t-)
ib= 2 Ip cos (t--1200)
ic= 2 Ip cos (t-+1200)
Ip is the rms value of phase current
Dr.S.ALBERTALEXANDER-SELECT-
VIT 12
13. Power in a balanced system
The total instantaneous power in the load is the sum of
the instantaneous powers in the three phases
p=pa+pb+pc= vANia+vBNib+vCNic =3VpIp cos
The total instantaneous power is independent of time
The average power per phase Pp for -connected load or
Y-connected load is p/3 or Pp =VpIp cos
The reactive power per phase is: Qp =VpIp sin
The apparent power per phase is: Sp= VpIp
The complex power per phase is: Sp= Pp +jQp =VpIp*
Vp and Ip are the phase voltage and phase current with
magnitudes Vp and Ip respectively
The total
=3VpIp cos=
average power is: P=Pa+Pb+Pc=3Pp
3 VLIL cos
Dr.S.ALBERTALEXANDER-SELECT-
VIT 13
14. Power in a balanced system
For a Y-connected load, IL=IP, VL= 3 Vp
For a -connected load, IL= 3 Ip, VL=Vp
For both Y and -connected loads:
Total Average Power: P= 3 VLIL cos
Total Reactive Power: Q= 3 VLIL sin
Total Complex Power: S= 3 VLIL
Vp, Ip, VL and IL are rms values and is the angle of the
load impedance or the angle between the phase voltage
and the phase current
Dr.S.ALBERTALEXANDER-SELECT-
VIT 14
15. Exercise 2
A balanced ∆-connected load having an impedance 20−j15 Ω is
connected to a ∆- connected, positive-sequence generator
having Vab = 330∠0° V. Calculate a) Phase currents of the
load, b) Line currents, c) Total real power d) Total reactive
power.
SOLUTION
Vab = 330∠0°, Vbc= 330∠-120° and Vca = 330∠120°
Z1=Z2=Z3=Z = 20−
j15 Ω= 25∠-36.87°
a) Phase currents of the load:
Iab
1
Z 25∠−36.87°
=Vab = 330∠0° = 13.2∠36.87°A
bc Z2 25∠−36.87°
I =Vbc = 330∠−
120°= 13.2∠-83.13° A
ca Z3 25∠−36.87°
I =Vca = 330∠120° = 13.2∠156.87° A
In connection, line currents are
300 lagging with phase current and
magnitude is 3 times the phase
current.
Dr.S.ALBERTALEXANDER-SELECT-
VIT 15
16. Exercise 2 (Contd..)
b) Line currents:
IL= 3 Ip (-300)
Ia= 3 × 13.2(36.870-300)= 22.866.80 A
Ib= 3 × 13.2(-83.130-300)= 22.86-113.130 A
Ic= 3 × 13.2(156.870-300)= 22.86126.870 A
c) Total real power:
P= 3 VLIL cos = 3 × 330 × 22.86 ×cos (-36.87)= 10.452 kW
d) Total reactive power.
P= 3 VLIL sin = 3 × 330 × 22.86 × sin (-36.87)= -7840 VAR
Dr.S.ALBERTALEXANDER-SELECT-
VIT 16
17. Exercise 3
Determine the total average power, reactive
complex power at the source and at the load.
power, and
SOLUTION
It is sufficient to consider one phase, as the system is
balanced. For phase a,
Van
Ia= ZY
= 11000 11000 11000
(5−
j2)+(10+j8)= 15+j6 = 16.15521.80
0
= 6.81−
21.8 A
Dr.S.ALBERTALEXANDER-SELECT-
VIT 17
18. Exercise 3 (Contd..)
Dr.S.ALBERTALEXANDER-SELECT-
VIT 18
At the source, the complex power absorbed is,
SS=-3VpIp*= -3(11000)(6.81−21.80) =-224721.80
=-(2087+j834.6) VA
The real or average power absorbed is -2087 W
The reactive power is -834.6 VAR
At the load, the complex power absorbed is,
SL=3│Ip│2 Zp= 3(6.81)2(10+j8)= 3(6.81)2(12.8138.660)
=1782 38.660 = (1392+j1113.3) VA
The real power absorbed is 1392 W
The reactive power absorbed is 1113.3 VAR
19. Exercise 4
A three-phase motor can be regarded as a balanced Y-load.
A three phase motor draws 5.6 kW when the line voltage is
220 V and the line current is 18.2 A. Determine the power
factor of the motor.
SOLUTION
The apparent power is, S= 3 VLIL
3 (220)(18.2)= 6935.13 VA
Since the real power is, P = 5600 W
Power factor is, cos = P/S = 5600/ 6935.13 =0.8075
Dr.S.ALBERTALEXANDER-SELECT-
VIT 19
