This document discusses balanced three-phase delta-connected loads. It covers calculating voltages, currents, and power in delta-connected circuits. The key learning goals are understanding basic delta connections, calculating voltages and currents in balanced delta loads, and calculating complex power. Examples are provided to demonstrate calculating phase and line currents and drawing phasor diagrams for delta loads.
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.
1) The document discusses balanced three-phase systems where the loads have the same impedance in each phase.
2) It provides examples of calculating currents in star-connected and delta-connected balanced three-phase load systems. The phase currents are equal but offset by 120 degrees, while the line currents are calculated using Kirchhoff's laws.
3) Power calculations for a star-connected balanced load show that total power is three times the power measured in one phase using a wattmeter.
The calculation of a Triangle Voltage Stability Index (TVSI) for monitored alternating-current circuits using voltage data from a PSSE load flow study. The analysis provides TVSI values for monitored transmission circuits in the Bulk Electric System under varying power transfers and contingencies.
TVSI provides an indication of the closeness of the load voltage to potential voltage collapse. To provide situational awareness to system operators, AEP proposes monitoring the phase angle across a low loss EHV overhead circuit operating in a system environment and comparing the angle to an established phase angle loci as a proxy for TVSI.
This monitoring could be independent of the line loading or the associated line impedance.
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 discusses balanced three-phase delta-connected loads. It covers calculating voltages, currents, and power in delta-connected circuits. The key learning goals are understanding basic delta connections, calculating voltages and currents in balanced delta loads, and calculating complex power. Examples are provided to demonstrate calculating phase and line currents and drawing phasor diagrams for delta loads.
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.
1) The document discusses balanced three-phase systems where the loads have the same impedance in each phase.
2) It provides examples of calculating currents in star-connected and delta-connected balanced three-phase load systems. The phase currents are equal but offset by 120 degrees, while the line currents are calculated using Kirchhoff's laws.
3) Power calculations for a star-connected balanced load show that total power is three times the power measured in one phase using a wattmeter.
The calculation of a Triangle Voltage Stability Index (TVSI) for monitored alternating-current circuits using voltage data from a PSSE load flow study. The analysis provides TVSI values for monitored transmission circuits in the Bulk Electric System under varying power transfers and contingencies.
TVSI provides an indication of the closeness of the load voltage to potential voltage collapse. To provide situational awareness to system operators, AEP proposes monitoring the phase angle across a low loss EHV overhead circuit operating in a system environment and comparing the angle to an established phase angle loci as a proxy for TVSI.
This monitoring could be independent of the line loading or the associated line impedance.
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.
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
This document discusses different types of polyphase systems for generating and supplying alternating current (AC). It describes single phase, two phase, and three phase systems. In a three phase system, a generator contains three coils placed 120 degrees apart that generate three voltages equal in magnitude but out of phase by 120 degrees. Common connections of three phase systems include wye-wye, wye-delta, delta-delta, and delta-wye. Phase and line quantities are also defined.
The document discusses three-phase AC circuits with balanced and unbalanced star-connected and delta-connected loads. It covers topics such as phase and line voltage/current relations, neutral shift, and circulating currents with unbalanced loads. Examples are provided to calculate line currents, phase voltages, and neutral shift voltage for a three-phase system with a star-connected balanced load. Similar concepts are described for a delta-connected load connected to a three-wire balanced source.
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 and their analysis. It covers balanced and unbalanced three-phase configurations, power in balanced systems, and analyzing unbalanced systems using PSpice. The objectives are to understand different three-phase connections, distinguish balanced and unbalanced circuits, calculate power in balanced systems, analyze unbalanced systems, and apply the concepts to measurement and residential wiring. Key points covered include wye-wye, wye-delta, delta-delta, and delta-wye connections for both sources and loads.
The document discusses three-phase circuits. It begins by defining single-phase and three-phase generators. It then explains that three-phase systems are preferred for power transmission due to using thinner conductors and having more even power flow. The document outlines different three-phase connections including wye-wye, wye-delta, delta-delta, and delta-wye. It provides diagrams and explanations of how to analyze balanced configurations of each connection type. The objectives are to learn how to analyze different three-phase configurations, understand balanced and unbalanced circuits, and use PSpice software to simulate three-phase circuits.
Electrical Engineering is the Branch of Engineering. Electrical Engineering field requires an understanding of core areas including Thermal and Hydraulics Prime Movers, Analog Electronic Circuits, Network Analysis and Synthesis, DC Machines and Transformers, Digital Electronic Circuits, Fundamentals of Power Electronics, Control System Engineering, Engineering Electromagnetics, Microprocessor and Microcontroller. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus.
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.
The document contains 10 practice questions related to symmetrical components for electrical circuits:
1. Find symmetrical components of line currents for an unbalanced star-connected load.
2. Determine symmetrical components of given line voltages and draw the vector diagram.
3. Calculate symmetrical components of phase currents for a delta-connected balanced load.
4. Use symmetrical components to calculate active and reactive power for a delta-connected circuit.
5. Use symmetrical components to calculate active and reactive power for another delta-connected circuit.
6. Build line currents vectors for a transformer circuit given symmetrical components.
7. Determine line currents and symmetrical components before and after a line fault in a delta load.
8. Calculate branch currents
The document contains 10 problems related to symmetrical components analysis of three-phase electrical circuits:
1. Compute polar forms of complex expressions.
2. Determine line voltages and currents for a Y-connected resistor bank connected to a Δ-Y transformer.
3. Find symmetrical components of three phase voltages.
The problems involve calculating symmetrical components of voltages and currents, determining line quantities from symmetrical components, drawing sequence networks, and solving circuits using symmetrical components analysis.
This document discusses unbalanced three-phase systems and loads. It begins by defining unbalanced loads as those where impedances differ between phases, resulting in unequal and displaced currents. It then discusses various types of unbalanced loads including four-wire star-connected, three-wire star-connected, and delta-connected loads. Methods for analyzing unbalanced loads are presented, including using star-delta conversions to solve unbalanced star-connected loads by converting them to an equivalent delta connection. Worked examples calculate currents and voltages for specific unbalanced load configurations.
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.
This document describes a proposed unified power quality conditioner (UPQC) topology that can compensate for voltage sags, swells and current harmonics with a reduced DC-link voltage without compromising performance. The UPQC uses a capacitor in series with the interfacing inductor of the shunt active filter and connects the system neutral to the negative DC-link terminal. This allows the DC-link voltage requirements of the series and shunt active filters to be matched with a common DC-link capacitor. The performance of the proposed topology is evaluated through MATLAB/Simulink simulation.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A step-by-step approach to prepare fault studies of electrical power systemsH. Kheir
The following are covered: the classification of faults, sources of fault currents, sequence impedance networks, the calculation of the fault currents for different types of shunt faults, the preparation of coordination studies and the inclusion of the different current time characteristics curves, damage curves/points and inrush (energization) currents.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
This document provides an overview of basic electrical and electronics engineering concepts. It begins by defining common units like the meter, kilogram, second, and ampere. It then discusses electric circuits, electromagnetism, and various instruments. Key concepts covered include Ohm's law, Kirchhoff's laws, series and parallel circuits, and the different characteristics of common circuit elements like resistors, voltage sources, and current sources. Measurement instruments are also introduced.
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.
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
This document discusses different types of polyphase systems for generating and supplying alternating current (AC). It describes single phase, two phase, and three phase systems. In a three phase system, a generator contains three coils placed 120 degrees apart that generate three voltages equal in magnitude but out of phase by 120 degrees. Common connections of three phase systems include wye-wye, wye-delta, delta-delta, and delta-wye. Phase and line quantities are also defined.
The document discusses three-phase AC circuits with balanced and unbalanced star-connected and delta-connected loads. It covers topics such as phase and line voltage/current relations, neutral shift, and circulating currents with unbalanced loads. Examples are provided to calculate line currents, phase voltages, and neutral shift voltage for a three-phase system with a star-connected balanced load. Similar concepts are described for a delta-connected load connected to a three-wire balanced source.
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 and their analysis. It covers balanced and unbalanced three-phase configurations, power in balanced systems, and analyzing unbalanced systems using PSpice. The objectives are to understand different three-phase connections, distinguish balanced and unbalanced circuits, calculate power in balanced systems, analyze unbalanced systems, and apply the concepts to measurement and residential wiring. Key points covered include wye-wye, wye-delta, delta-delta, and delta-wye connections for both sources and loads.
The document discusses three-phase circuits. It begins by defining single-phase and three-phase generators. It then explains that three-phase systems are preferred for power transmission due to using thinner conductors and having more even power flow. The document outlines different three-phase connections including wye-wye, wye-delta, delta-delta, and delta-wye. It provides diagrams and explanations of how to analyze balanced configurations of each connection type. The objectives are to learn how to analyze different three-phase configurations, understand balanced and unbalanced circuits, and use PSpice software to simulate three-phase circuits.
Electrical Engineering is the Branch of Engineering. Electrical Engineering field requires an understanding of core areas including Thermal and Hydraulics Prime Movers, Analog Electronic Circuits, Network Analysis and Synthesis, DC Machines and Transformers, Digital Electronic Circuits, Fundamentals of Power Electronics, Control System Engineering, Engineering Electromagnetics, Microprocessor and Microcontroller. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus.
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.
The document contains 10 practice questions related to symmetrical components for electrical circuits:
1. Find symmetrical components of line currents for an unbalanced star-connected load.
2. Determine symmetrical components of given line voltages and draw the vector diagram.
3. Calculate symmetrical components of phase currents for a delta-connected balanced load.
4. Use symmetrical components to calculate active and reactive power for a delta-connected circuit.
5. Use symmetrical components to calculate active and reactive power for another delta-connected circuit.
6. Build line currents vectors for a transformer circuit given symmetrical components.
7. Determine line currents and symmetrical components before and after a line fault in a delta load.
8. Calculate branch currents
The document contains 10 problems related to symmetrical components analysis of three-phase electrical circuits:
1. Compute polar forms of complex expressions.
2. Determine line voltages and currents for a Y-connected resistor bank connected to a Δ-Y transformer.
3. Find symmetrical components of three phase voltages.
The problems involve calculating symmetrical components of voltages and currents, determining line quantities from symmetrical components, drawing sequence networks, and solving circuits using symmetrical components analysis.
This document discusses unbalanced three-phase systems and loads. It begins by defining unbalanced loads as those where impedances differ between phases, resulting in unequal and displaced currents. It then discusses various types of unbalanced loads including four-wire star-connected, three-wire star-connected, and delta-connected loads. Methods for analyzing unbalanced loads are presented, including using star-delta conversions to solve unbalanced star-connected loads by converting them to an equivalent delta connection. Worked examples calculate currents and voltages for specific unbalanced load configurations.
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.
This document describes a proposed unified power quality conditioner (UPQC) topology that can compensate for voltage sags, swells and current harmonics with a reduced DC-link voltage without compromising performance. The UPQC uses a capacitor in series with the interfacing inductor of the shunt active filter and connects the system neutral to the negative DC-link terminal. This allows the DC-link voltage requirements of the series and shunt active filters to be matched with a common DC-link capacitor. The performance of the proposed topology is evaluated through MATLAB/Simulink simulation.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A step-by-step approach to prepare fault studies of electrical power systemsH. Kheir
The following are covered: the classification of faults, sources of fault currents, sequence impedance networks, the calculation of the fault currents for different types of shunt faults, the preparation of coordination studies and the inclusion of the different current time characteristics curves, damage curves/points and inrush (energization) currents.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
This document provides an overview of basic electrical and electronics engineering concepts. It begins by defining common units like the meter, kilogram, second, and ampere. It then discusses electric circuits, electromagnetism, and various instruments. Key concepts covered include Ohm's law, Kirchhoff's laws, series and parallel circuits, and the different characteristics of common circuit elements like resistors, voltage sources, and current sources. Measurement instruments are also introduced.
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.
Similar to class notes for electronics and electrical.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:
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class notes for electronics and electrical.pptx
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. 2.7 Star and Delta Connections
Dr.S.ALBERTALEXANDER-SELECT-
VIT 3
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
A balanced delta-connected load is more common than a
balanced wye-connected load
It is due to the ease with which loads may be added or
removed from each phase of a delta-connected load
It is very difficult with a wye-connected load because the
neutral may not be accessible
On the other hand, delta-connected sources are not
common in practice because of the circulating current that
will result in the delta-mesh if the three-phase voltages are
slightly unbalanced
4. (i) Balanced Star-Star Connection
A balanced Y-Y system is a three-phase system with a
balanced Y-connected source and a balanced Y-connected
load
A Y-connected load is connected to a Y-connected source
Dr.S.ALBERTALEXANDER-SELECT-
VIT 4
5. Balanced Star-Star Connection
Dr.S.ALBERTALEXANDER-SELECT-
VIT 5
Assume a balanced load so that load impedances are
equal
Although the impedance ZY is the total load impedance per
phase, it may also be regarded as the sum of the source
impedance ZS, line impedance Zl and load impedance ZL
for each phase, since these impedances are in series
ZS denotes the internal impedance of the phase winding of
the generator
Zl is the impedance of the line joining a phase of the source
with a phase of the load
ZL is the impedance of each phase of the load
Zn is the impedance of the neutral line.
ZY = ZS +Zl +ZL
6. Balanced Star-Star Connection
ZS and Zl are often very small compared with ZL so assume
that ZY = ZL if no source or line impedance is given
In any event, by lumping the impedances together, the Y-Y
can be simplified as shown below:
Dr.S.ALBERTALEXANDER-SELECT-
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7. Analysis
Assuming the positive sequence, the phase voltages (or
line-to neutral voltages) are Van= Vp00; Vbn= Vp-1200 and
Vcn= Vp-2400
The line-to-line voltages or simply line voltages Vab, Vbc
and Vca are related to the phase voltages
Vab= Van+Vnb=Van-Vbn = Vp00 - Vp-1200
ab p 2 2 p
V = V (1 + 1
+j 3
)= 3 V 300
Similarly, Vbc= Vbn-Vcn = 3 Vp-900
Vca= Vcn-Van = 3 Vp-2100
Magnitude of the line voltages is times the magnitude of
the phase voltages Vp or VL= 𝟑 Vp
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8. Analysis
VL= 𝟑 Vp
Vp= │
V
an│=│
Vbn│
=│
Vcn│
VL= │
V
ab│=│
Vbc│
=│
Vca│
Line voltages lead their corresponding phase voltages by
1200
Vab leads Vbc by 1200 and Vbc leads Vca by 1200 so that the line
voltages sum up to zero as do the phase voltages
Dr.S.ALBERTALEXANDER-SELECT-
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9. Analysis
Apply KVL to each phase, we obtain the line currents as,
Van
Ia= ZY
Vbn
Ib= ZY
=
Van−1200
ZY
= Ia−120 0
Vcn
Ic= Z =
Van−2400
Z
Y Y
= Ia−240 0
We can readily infer that the line currents add up to zero,
Ia+Ib+Ic=0
In=-(Ia+Ib+Ic)
Vn= ZnIn=0
The voltage across the neutral wire is zero
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10. Analysis
Dr.S.ALBERTALEXANDER-SELECT-
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Vn= ZnIn=0
The voltage across the neutral wire is zero
The neutral line can thus be removed without affecting the
system
In fact, in long distance power transmission, conductors in
multiples of three are used with the earth itself acting as
the neutral conductor
Power systems designed in this way are well grounded at
all critical points to ensure safety
While the line current is the current in each line, the phase
current is the current in each phase of the source or load
In the Y-Y system, the line current is the same as the
phase current
11. Exercise-1
Calculate the line currents in the three-wire Y-Y system.
SOLUTION
Van
Ia= ZY
11000 11000 11000
= (5−j2)(10+j8)= 15+j6 = 16.15521.80
0
= 6.81−
21.8 A
Source voltages are in +ve sequence
Ib= Ia−1200= 6.81−141.80 A
Ic= Ia−2400 = 6.81−261.80 A = 6.8198.20 A
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12. Exercise 2
A three phase star connected supply system delivering power
to three phase star connected load. The voltage in star
connected supply system between lines is 415 V, 50 Hz ac
supply. The load is balanced load and its load impedance per
phase is (8+j20) Ω. For the given load, calculate (i) Line and
phase currents (ii) active power (iii) Reactive power (iv) power
factor (v) Apparent power.
SOLUTION
(i) Phase current, Iph = Vph
Z
I 338.8 338.800
ph = 8+j20 = 21.5468.20
0
ph L
I =15.72 −
68.2 A and I =
Iph
2
=
15.72
2
=11.12 A
VL (rms)=415 V
ph (rms) 3
V =415 = 239.6
Vph-R= 239.6 2 00 =338.0 00
Vph-Y= 338.0 −1200
Vph-B= =338.0 1200
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13. Exercise 2 (Contd..)
(ii) Active power: 3 VLIL cos = 3 (415)(11.12) cos(68.2)
= 2969 W
(iii) Reactive power: 3 VLILsin= 3 (415)(11.12) sin (68.2)
= 7421 VAR
(iv) power factor: cos(68.2) = 0.371 (lagging)
(v) Apparent power= 3 VLIL= 3 (415)(11.12)= 7993 VA
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14. (ii) Balanced Delta-Delta Connection
A balanced system - is one in which both the balanced
source and balanced load are -connected
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15. Analysis
Assuming the positive sequence, the phase voltages Vab=
Vp00; Vbc= Vp-1200 and Vca= Vp-2400 or Vp+1200
The line voltages are same as the phase voltages
Assuming there is no line impedances, the phase voltages
of the delta connected source are equal to the voltages
,
across the impedances: Vab=VAB , Vbc=VBC and Vca= VCA
The phase currents are:
IAB=VAB= Vab
Z Z
IBC=VBC = Vbc
Z Z
ICA
=VCA = Vca
Z Z
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16. Analysis
Apply KCL at nodes A,B,C, we obtain the line currents as,
Ia=IAB-ICA, Ib=IBC-IAB, Ic=ICA-IBC
Each line current lags the corresponding phase current by
300
Magnitude of the line current is 3 times the magnitude of
the phase current or IL= 𝟑 Ip
An alternative way of analyzing the - circuit is to convert
both the source and the load to their Y equivalents
Y
Z =Z
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3
17. Exercise-4
A balanced -connected load having an impedance 20-j15
is connected to a -connected, positive-sequence generator
having Vab=33000 V. Calculate the phase currents of the
load and the line currents.
SOLUTION
Phase currents:
VAB
IAB= Z
=
33000
20−j15
=
33000
25−36.87 0
0
= 13.236.87 A
IBC= IAB−1200 = 13.2-83.130 A
ICA= IAB−2400 = 13.2156.870 A
Line currents:
3-30 = 22.86 6.87 A
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Ia= IAB 3-30= (13.236.870 )
Ib= Ia−1200= 22.86 -113.13 A
Ic= Ia−2400= 22.86 126.87 A
18. SUMMARY
Type Phase
voltages
Phase currents Line voltages Line currents
Y-Y Van= Vp00
Vbn= Vp-1200
Vcn= Vp-2400
Same as line
currents
Vab = 3Vp300
Vbc= Vab -1200
Vca= Vab +1200
I =Van
a ZY
Ib=Ia−1200
Ic=Ia+1200
- Vab= Vp00
Vbc= Vp-1200
Vca= Vp-2400
I = Vab
AB Z
I= Vbc
BCZ
I= Vca
CA Z
Same as phase
voltage
Ia=IAB 3-300
Ia=Ib-1200
Ia=Ic+1200
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