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Chapter 4 Christianity

Course: RELI 1001 1001, Fall 2011
School: UGA
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4: Christian Chapter Traditions Origins The Life of Jesus We know very little about the early years of Jesus other than his birth in Bethlehem and that his childhood home was in Nazareth. His public years began at 30 Yrs old with his baptism by his older cousin, John the Baptist. Soon after, Jesus recruited twelve male disciples and a number of female followers. For the next year or more, Jesus travelled,...

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4: Christian Chapter Traditions Origins The Life of Jesus We know very little about the early years of Jesus other than his birth in Bethlehem and that his childhood home was in Nazareth. His public years began at 30 Yrs old with his baptism by his older cousin, John the Baptist. Soon after, Jesus recruited twelve male disciples and a number of female followers. For the next year or more, Jesus travelled, working miracles, teaching how to apply Jewish law to everyday life, and telling parables, many of which pointed to an impending apocalypse. A few days after entering Jerusalem for Passover, Jesus was arrested for perverting the people and claiming kingship over the Jews. He was condemned, nailed to a cross (crucified), and left to die. Two days later, some of his women followers claimed to find his tomb empty. It has become Christian belief that he had gone to sit at the right hand of God in heaven. Origins, contd. The Gospels The gospels, from the Greek evangel (good news), are accounts of Jesus life. The Christian message was crystallizing into recognizable form by the mid-fist century. When Christianity became the established religion of the Roman empire, church leaders made a list of the writings they acknowledged to be scripture, creating the New Testament. Marks account Lukes account Matthews account Johns gospel is very different in that his purpose is to set out not just the narrative but its cosmic significance. John proclaims Jesus as messiah and saviour Origins, contd. From Sect to Church The disciples were peasants and fishermen who expected the end of the age, and the glorious return of their teacher, to come at any moment. The principal influence on the early Church, however, was an educated and sophisticated convert who took the name Paul. According to Paul, it is not through observance of ritual laws or even correct moral conduct that salvation is attained, but rather through faith in Jesus and the divine grace that comes through him. Thanks to Pauls voyages, Christian communities were established in many of the port cities of the Roman Empire by the time he died. Crystallization Emerging Church Organization The Christian movement became formally organized during the early centuries. Before long, formal ordination was required to perform ritual and administrative functions. Sometime between the writing of the books of the New Testament and the early Christian councils, the priest emerged as the person in charge of ritual and instruction. The ranking priest in a particular political jurisdiction was known as a bishop. The hierarchy was further developed to include the role of archbishop. By the third century, four larger jurisdictions had gained prominence: Alexandria, Jerusalem, Antioch, and Rome. Crystallization, contd. Persecution and Martyrdom From the Roman perspective, early Christians were guilty of insubordination. In the 3rd century, the emperor Decius commanded public sacrifices to the Roman civic gods, with the penalty of death or imprisonment for anyone who would not comply. Christians were systematically persecuted as a matter of state policy. Imperial Christianity Constantine (r. 30637) gradually abandoned the persecution policy, issuing an edict in 313 that gave Christians liberty to practice their religion, and eventually granting them state support and patronage. It was only with Theodosius I (r. 37995) that the empire became officially Christian. Crystallization, contd. Creeds The Church began composing creedsstatements of the content of Christian faithvery early in its history. Because they define themselves as people who believe such-and-such about Jesus, Christians have expected other traditions to define themselves in terms of belief as well. Perhaps as early as 150, but certainly by the early 3rd century, a formulation known as the Apostles Creed was coming into use. The other well-known ancient formulation is the Nicene Creed, named for the Council of Nicaea in 325. The Nicene Creed is more specific about the Holy Spirit and more inclined to mention the Spirit along with God the father and Christ the son as part of a triadic list. Crystallization, contd. The differences between the two creeds reflect the emergence of the explicit doctrine of the Trinity. At stake was the relationship among the three divine persons or manifestations: God as heavenly father and creator, Jesus as son and redeemer, and the Holy Spirit as a continuing source of inspiration, guidance, and comfort. No sooner had the dust settled on the debate over the Trinity in 381 than the doctrine of Christology came into debate. Was Christ two separate persons, one divine and one human (as believed by the Nestorian churches)? Was Christ one person, with only a divine nature (as believed by the Monophysite churches)? Was Christ one person, with both a divine and a human nature (as believed by the Greek and Roman churches)? Differentiation Alexandrian vs. Antiochene Christianity The Alexandrians, such as Cyril, understood Christ as the eternal Word incarnated in the human person of Jesus. The Antiochenes, such as Nestorius, argued that the Word was an entity distinct from the human Jesus, over whom it exercised a controlling influence. Despite the victory of the Alexandrians at the Council of Ephesus in 431, Nestorian Christianity persisted, eventually spreading from its centre in Northeastern Syria across Central Asia to western China and the southwestern coast of India. Differentiation, contd. Eutyches, who headed a large monastery near Constantinople, taught that in terms of the union of the divine and the human in Jesus, the human was fully absorbed into or replaced by the divine. The Council of Chalcedon in 451 steered a middle course between the Nestorians, who compromised the eternal deity of Jesus, and the Monophysites, who compromised his humanity, asserting that the incarnate Christ was one person with both a divine and human nature. After this, three Eastern regional groups separated themselves from Constantinople: The Coptic Christians of Egypt and Ethiopia, the Jacobites of Syria, and the Armenians. Differentiation, contd. The Greek Orthodox Tradition After the Council of Chalcedon, Greek and Latin Christianity grew further apart. The final break between Rome and Constantinople came in 1054. Formally tolerated under Islam, the Byzantine (Greek) Church became a self-governing religious community under the Ottoman Turks, with the patriarch as its civil ruler. Eastern Orthodoxy is the name used to refer to the form of Christianity that was carried from Byzantium to various peoples in eastern Europe. Language played an important part in their success, for they used local vernaculars rather than Greek, and this encouraged the development of independent local churches with a strong sense of national identity based on language. The Orthodox Church also venerated icons and permitted its clergy to marry. Differentiation, contd. The Latin Tradition The Church centred in Rome thought of itself as catholic, that is, universal The bishop of Rome had unchallenged ecclesiastical authority in the Latin-speaking West. A landmark figure in the issue of human sinfulness and the possibility of divine redemption was Aurelius Augustine (354.430). Differentiation, contd. Medieval Christianity The Middle Ages are generally considered to stretch from the collapse of the Western Roman Empire, around 500, to the beginning of the Renaissance, around 1500. Monastic communities developed a highly structured discipline in the medieval period. The medieval monasteries played a crucial role as cultural custodians, for their scholars and libraries preserved much ancient learning that might have otherwise been lost. By the 10th century, however, many monasteries were attracting criticism for their worldliness. To respond to the needs of the urban poor, a new type of religious order emerged. The mendicant orders, such as the Franciscans, dedicated themselves to serving the people. In 121617 the preaching order of the Dominicans was formed. Differentiation, contd. Popes and Princes From the 9th century onward, popes and princes competed for supremacy. In the 10th century ecclesiastical appointments could be bought and sold. In 1059, Pope Nicholas II took advantage of a fluid political situation to decree that the selection of popes should be decided by an assembly of cardinals. Institutionally, the Church grew to resemble the secular states with which it competed. It depended on tax revenues and was subject to coups both from within the Church and from outside. Differentiation, contd. The Crusades The Crusades were a series of military campaigns spanning two centuries, in which Western Christians attempted to recover Jerusalem from Muslim control. Arab Muslims had captured Jerusalem in 637. The Muslims were generally tolerant of the Christian locals and pilgrims until the 11th century. In 1071, Jerusalem was captured by the Seljuq Turks, who as recent converts to Islam, were less accommodating than the Arabs had been. In 1095, Pope Urban II declared it Gods will that Western Christians go to the aid of the Eastern Christians and liberate the holy places of Palestine. The crusaders won some bloody victories, but were driven out again. Differentiation, contd. Sainthood Saints came to be regarded as a kind of heavenly senate or honour society. By praying to a saint or making a pilgrimage to his/her shrine, one might win release from punishment in the next existence and from guilt in this one. Certain saints came to be associated with specific conditions, occupations, or symbols. In some places, the traditions of particular saints include elements of pre-Christian customs and symbolism. Pre-eminent among the Christian saints was Mary, the mother of Jesus. Though she is largely in the background in the biblical accounts of Jesus life, she became a figure of intense popular devotion, both as the principal feminine point of access to the Trinity and as a model of sorrow-enduring love. Differentiation, contd. Evil, Devil, and Angels In the biblical tradition, the term angel can also mean messenger. A view common since early Christian writers is that the devil started as an angel, but that through pride he tried to take over Gods role and so fell from grace. The devil presides over the realm of hell, which is the destiny of the wicked after their earthly life. In 1252, Pope Innocent IV rules that torture could be used and that heretics handed over to the secular authorities should be executed within five days. Peasant superstition contributed to the medieval tendency to identify certain individuals as witches or agents of the devil. Societys efforts to hunt down, prosecute, and execute such individuals by burning demonstrates how devastating the fear of non-conforming behaviour can be. Differentiation, contd. Sin, Heresy, and the Inquisition Humans were considered originally sinful owing to their pride and self-will, but specific actions were also objectified as sins. In the Middle Ages, European society was dominated by the Church, and those who were not baptized into the faith, notably Jews and Muslims, lacked the rights and privileges of the mainstream society. There were also, occasionally, Christianswhether dissenting intellectuals or ill-informed peasantswhose differences from the mainstream marked them as heretics. During the 11th century, increasing numbers of heretics were burned at the stake. In 1184, Pope Lucius III instructed bishops to investigate allegations of heretical activity, examine the suspects, and turn over any resisters to secular authorities for punishment. Those accused of heresy were presumed guilty unless they could prove their innocence. Differentiation, contd. Scholastic Philosophy The dominant expression of thought in Western Europe in the Middle Ages is known as scholasticism. Faith and reason, for scholastics, are mutually confirming. Early scholastic teaching was based on the reading of scripture. Anselm (c. 10331109) moved away from the principle of scriptural authority, asserting that faith itself has a kind of rationality. It was in the 12th century that Western Christianity discovered the thoughts of Aristotle, which gave more scope for practical considerations and examination of the material world. Thomas Aquinas (c. 122574) identified five ways of proving Gods existence Differentiation, contd. Medieval Mystics The late Middle Ages saw a remarkable flowering of mysticism. Mysticism is a specific tradition that emphasizes the certainty of profound personal experience . The most formidable systematizer of mystical thought was the German Dominican Johannes (Meister) Eckhart (c. 12601327). Whereas Eckhart, and others, sought to identify the self with the image of God, others saw God in all the nearness of humanity. A striking feature of late medieval mysticism was the scope it afforded for women. Differentiation, contd. The Protestant Reformation In the 15th century, Christianity was essentially a European phenomenon. The fall of Constantinople to the Ottoman Turks in 1453 sealed the victory of the Muslims over Byzantine Christians after seven centuries of rivalry. A generation after the fall of Constantinople, Christendom s horizons were vastly broadened when the Portuguese sailed around southern Africa, outflanking the Turks who had controlled the overland routes to Asia. Ironically, just as European Christianity was poised for global expansion, it was fragmented by a crisis of intuitional and spiritual authority: the challenge of Protestantism. It was the stubborn personality of Martin Luther (14831546) that made it possible for the Protestant Reformation to erupt as it did. The development of the technology of printing from movable type allowed Luthers ideas to be quickly disseminated. Luther effectively took the priesthood off the pedestal of status and authority that it and the institutional Church had enjoyed since the time of Constantine. Differentiation, contd. The Reformation marked was by division and diversity. A denominationally fragmented Church has been the legacy of the Protestant Reformation down to the present day. Three main establishments emerged from the 16th century: Lutheran, Anglican, and Calvinist. The followers of Martin Luther flourished in Germany and Scandinavia. Lutheranism allowed ample scope for rational and intellectual argument in the exposition of scripture, but it also encouraged a deep sense of personal piety. They retained a Eucharist-like sacrament, but they celebrated it in the vernacular and held that Christs body was present along with the bread and wine, but was not produced out of them. Differentiation, contd. In Germany the Reformation was a popular movement, but in England it was royal policy. In 1534, the English parliament passed an Act of Supremacy, which proclaimed the king as supreme head of the Church of England. The Church of England is known in most parts of the world as Anglican, although in the United States it is called Episcopalian. The dominant intellectual leader of the Reformation was John Calvin (150964) who imposed rigorous norms of doctrine and conduct on the city of Geneva. For Calvin, God was absolutely sovereign, initiating all actions. This teaching implies that humans are so sinful that they are utterly dependent on divine grace for salvation, and that the sovereign God has predestined every person to either salvation or damnation. In the Netherlands and Hungary, the Calvinist churches have been known as Reformed churches. In England and Differentiation, contd. Another group, the Anabaptists, emphasized adult rather than infant baptism, as well as the separation of political institutions and religion. A former Dutch priest called Menno Simons led this movement into a largely otherworldly and non-violent path: his followers are called Mennonites. Unitarianism rejects the doctrine of the Trinity. Puritanism was not a denomination in itself, but a movement in English and colonial American Protestant Churches. The Puritans held firmly to Calvinist theology, committing themselves to a rigorous view of human sinfulness and divine predestination. Differentiation, contd. 17th-century Denominations Like the Anabaptists in continental Europe, the English Baptists practiced the baptism of mature believers, but they were much more connected with the Puritan movement than with the Anabaptists. George Fox was an English dissenter who, in 1646, began to preach that moral and spiritual peace was not to be had in the institutional churches but in the experience of the inner light of the living Christ. 18th-century Denominations Pietism, a movement rather than a denomination, was about seeking spontaneous renewal of faith accompanied by a feeling of the certainty of divine forgiveness and acceptance. In the late 1720s, a number of Anglican students at Oxford University formed a group to study the Bible: they were called the Methodists. Efforts to promote a reawakening of spiritual enthusiasm resulted in a wave of revivals, especially in America, such as the Great Awakening of 17403. Differentiation, contd. Roman Catholicism after 1500 The Roman Church recognized the need to correct the abuses of ecclesiastical power that Luther had condemned. The Council of Trent (154563) acted to enforce discipline and end the abuses, though it reaffirmed the authority of institutional tradition alongside scripture and upheld the idea of a priesthood of celibate intermediaries. Founded shortly before the Council of Trent, in 1540, the Society of Jesus, or Jesuit order, exemplified three of the principle areas of renewal in the Catholic Church: spiritual discipline, education, and missionary expansion. Differentiation, contd. Once the Portuguese had opened a trade route to India, the king of Portugal sent Jesuits to evangelize the East Indies. In Japan and China, assimilation to the local culture produced remarkable success, at first. Overall, European Christianity had failed to displace the religious traditions, social institutions, and sophisticated intellectual heritages of the Eastern civilizations. Barely a year after Columbus landed at Santo Domingo in 1492, the pope effectively divided the non-European world between Spain and Portugal. When Hernan Cortes reached Mexico in 1519 and Francisco Pizarro reached Peru in 15323, they encountered highly sophisticated social and religious institutions. Practice Christian prayer is a reverent and contemplative conversation with the divine. In Latin Christianity a list of seven sacraments emerged: baptism, confirmation, the Eucharist, penance, anointing the seriously ill, ordination, and marriage. The Eucharist is common to all branches of Christianity, although it is referred to by different names, such as Communion. It re-enacts the Passover supper that was Jesus last meal with his disciples, when he distributed the bread and wine, declaring them to be his body and blood. Baptism is the Christian ritual in which a person is admitted into participation in the community. Protestant Worship Different Protestant forms of worship express varying degrees of departure from the Roman model. Most Protestant churches emphasize the reading of scripture and the interpretation of it in the ministers sermon. Practice, contd. The Christian Year The liturgical year begins with Advent, the series of four Sundays that precede Christmas. Christmas (Dec. 25 in the Gregorian calendar) The time of year when Jesus was actually born is not known. The celebration of his birth is set around the midwinter solstice as the Christian idea of a birth that would bring new blessings was easily associated with the annual renewal of the suns radiance. The feast of Epiphany comes twelve days after Christmas and celebrates both the visit of the wise men to the infant Jesus and his baptism as an adult. Practice, contd. Easter Easter, in the Gregorian calendar, takes place on the first Sunday after the first full moon after the spring equinox.( around the same time as Jewish passover.) It is the feast of Jesus resurrection and comes as the conclusion of Lent, a period of 6 weeks of solemnity, reflection, and discipline. The Friday before Easter is known as Good Friday and is marked by services recalling Jesus Passionhis suffering on the cross. The fiftieth day after Easter is Pentecost, marking the emergence of the Church. Cultural Expressions The cross is the central symbol of Christianity. Other important symbols are the fish and the first and last letters of the Greek alphabet (alpha and omega). Many see the fish as code, since the Greek word for fish, ichthus, is made up of the initial letters of the Greek phrase Iesous Christos, Theou huios, soter (Jesus Christ, son of God, saviour). Others see it as reference to Jesus description of his disciples as fishers of humanity. Jesus In early representations he is portrayed as a simple shepherd. After Constantine made Christianity respectable, Jesus began to be represented as an older, bearded man, a king or a judge, attired in robes reflecting the dignity of his office. By the 6th century, Byzantine mosaics were depicting Christ enthroned in heaven as the ruler of creation. Cultural Expressions, contd. Church Architecture With imperial patronage, Christians began to build ambitious large-scale sanctuaries in the 4th century. In northern Europe, a new style of arch came into fashion around the 12th century. A feature unique to Roman Catholic churches is a sequence of fourteen images representing the Stations of the Cross: the sequence of events from Jesus trial to the placing of this body in the tomb. Protestant churches rearranged the furniture of the church to suit their theology. Instead of an altar that the priest faced with his back to the worshippers, Protestants adopted a communion table behind which the minister stood, facing the congregation. Interaction and Adaptation The Enlightenment By the end of the 18th century, Christianity was no longer at the centre of Western civilization. At the heart of the Enlightenment was a growing confidence in human reason. The growing importance of science was reflected in the rise of Deism, which envisioned God as a divine clockmaker, who assembles or shapes the universe and then leaves it to run on its own. The 18th century was also a period of philosophical skepticism about claims of the transcendent. The 19th century brought a tendency to look at religion in a social context. The 20th century revised our view of the way the self functions. Religions was seen by some, such as Freud and Jung, as a product of psychological processes. Interaction and Adaptation, contd. Evolution Darwin proposed that new types of organisms were not created by a deity but developed over time through a process he called natural selection. Thanks to Darwin, modern Christian theologians assessing the place of human life in the universe have tended to locate human distinctiveness not in a special physical creation, but in a unique intellectual and spiritual capacity for transcendence. Interaction and Adaptation, contd. New American Denominations Seventh-Day Adventists was founded by William Miller, who argued that the second coming of Christ the adventwas imminent. Jehovahs Witnesses are another millenarian group centred on the belief that the Advent is imminent. They reject the doctrine of the Trinity and regard Jesus Christ as a created being, although they believe that in dying he gave humanity a second chance to choose righteousness and escape the punishment expected at the end. The Church of Christ, Scientist was founded by Mary Baker Eddy who advocated non-medical healing. She believed that the material world and its evils of sickness, suffering, and death could be transcended, and that spiritual existence was possible in the here and now. Interaction and Adaptation, contd. The Church of Jesus Christ of Latter-day Saints (Mormons) was founded by Joseph Smith who claimed to have experienced a vision of God and Jesus. The textual basis for Smiths new faith was an account of Gods activity in the Western hemisphere entitled The Book of Mormon. Protestant congregations that cultivate the practice of speaking in tongues call themselves Pentecostal after the feast during which the apostles received the miraculous gift of speaking in foreign languages. With its emphasis on immediate personal experience, rather than textual or doctrinal tradition, Pentecostalism is more accessible to people with little formal education and has also had remarkable success in Latin American and Africa. Interaction and Adaptation, contd. Contextualizing the Bible Until the 19th century, most Christians believed that the Bible was the word of God, a factual account of the creation of the world, the origins of the human race, and the emergence of the Israelite nation. By the end of the 19th century, historians were able to situate the Bible in a specific cultural context. The Hebrews, it now appeared, were a minor group on the receiving end of ideas and technology from the major centres of empire, such as Mesopotamia and Egypt. During the 19th century many scholars had argued that Jesus was a great moral teacher. In 1906, Albert Schweitzer suggested that the Jesus presented in the gospel accounts was more an apocalyptic fanatic who believed the current world order would come to a dramatic end within the lifetime of his listeners. Interaction and Adaptation, contd. Evangelicalism Protestant evangelicalism draws on earlier themes, notably the assurance of Gods grace and acceptance, which they refer to as being born again. Committed to the literal authority of the Bible, evangelicals fought a rearguard battle against both modern biblical criticism and the Darwinian theory of human evolution. By 1920, some were beginning to label the most deeply conservative advocates of the inerrancy of scripture fundamentalists. Radio was the first medium to make it possible to preach to a widely dispersed, unseen audience. This lead into the use of television which gave rise to televangelism. Interaction and Adaptation, contd. Modern Roman Catholicism For Roman Catholics, modernity has posed challenges to, among others, the status of Mary and the saints, clerical celibacy, and rules around reproduction. The authority of the institutional church is a common focus. In 196265, pope John XXIII convened the Second Vatican Council to address some of these issues. In 1968, pope Paul VI, in his encyclical Humanae Vitae (On Human Life) prohibited the use of artificial birth control. The gap between the Churchs official stand on sexuality and the actual practices of Catholics has only widened in the intervening decades. Interaction and Adaptation, contd. Ecumenism In 1948, the Word Council of Churches was formed with representation from most major Protestant and Orthodox bodies. Ecumenism (from the Greek meaning inhabited world) offered a climate of mutual acceptance and common purpose, an emphasis on unity within diversity. A number of denominational mergers also took place in the 20th century, such as the 1925 formation of the United Church of Canada by the Methodists, Congregationalists, and a majority of the Presbyterians. In 1960, Roman Catholic pope John XXIII created the Secretariat for the Promotion of Christian Unity which was designed to bring about a rapprochement with Interaction and Adaptation, contd. Reforming Society The denominations influenced by Puritanism emphasized personal morality, which they expected to bear fruit in society. Social issues such as slavery and race-relations have divided churches. In the decade before WWI, Christian critics of the civic and corporate order in North America called for the Christianization of the economy, leading to the social gospel movement. South American liberation theology makes use of Christian biblical and theological resources that parallel Marxist thought. The 20th century brought dramatic changes in the cultural expectations of women in society.
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Steady State StabilityllllThe ability of the power system to remain in synchronismwhen subject to small disturbancesStability is assured if the system returns to its originaloperating state (voltage magnitude and angle profile)The behavior can be
FSU - EEL - 4213
Transient StabilityThe ability of the power system to remain in synchronismwhen subject to large disturbancesLyapunov energy functionsLarge power and voltage angle oscillations do not permitlinearization of the generator swing equationssimplified en
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Solving Non-linear ODEObjectiveTime domain solution of a system of differential equations Given a function or a system of functions: f(x) or F(x) Seek a time domain solution x(t) or x(t) which satisfy f(x) or F(x)Integration of the differential equat
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Multi-machine SystemsEach synchronous machine is represented by a constantvoltage source behind the direct axis transient reactanceThe input powers are assumed to remain constantUsing the pre-fault voltage, all loads are converted toequivalent admitt
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EEL 3216 Introduction to Power SystemsHomework # 2CHAPTER 1.8 and 21. A three phase wye-connected unbalanced load is supplied by a balanced three-phasedelta connected source. The three source voltages and two of the line currents are:Vab = 13.2 kV 90
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EEL 3216 Introduction to Power SystemsHomework # 3CHAPTER 3(Problems 3-1, 3-2, 3-3, 3-4, 3-6, 3-7, 3-8, pp 154-157 in Textbook)1. The secondary winding of a transformer has a terminal voltage ofvs(t) = 282.8 sin 377t V. The turns ratio of the transfo
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Life Long LearningProfessional development: seminars, workshops, conferences,summer courses, PE licenseLiterature resourcesReference books, i.e. McGraw Hill Standard Handbook for ElectricalEngineersMagazines, i.e. IEEE Power & Energy, CIGRE Electra
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Transmission LinesOverhead ConductorOverhead Spacer CableUnderground CableThree-Conductor CableService CablesFundamentals of Power SystemsLecture 141Overhead ConductorsACSRAluminum Conductor withinner Steel ReinforcedstrandsACARAluminum Con
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Induced Voltage in Stator Coil P-PolesFor a P-pole machine the flux per pole remains the same(integrating d =rlBmcos(P/2 )d over one pole pitch - /P to + /P )2rlBMThe electrical frequency becomesP2elmTherefore, the induced voltage per pole-pair (
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EEL 3216 Introduction to Power SystemsHomework # 1SOLUTIONS1. In the 60Hz circuit shown in Figure 1, VS = 240.0VR1 = 2.530 and I1 = 38.8A-36.2.L1 = 0.015 Ha) Determine the phasor currents, IS and I2, and the impedance Z2.b) Calculate the apparent
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EEL 3216 Introduction to Power SystemsHomework # 2SOLUTIONS1. A three phase wye-connected unbalanced load is supplied by a balanced three-phasedelta connected source. The source voltages and load impedances are:Vab = 13.2 kV 90Vbc = 13.2 kV 210Vca
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EEL 3216 Introduction to Power SystemsHomework # 3SolutionsCHAPTER 3(Problems 3-1, 3-2, 3-3, 3-4, 3-6, 3-7, 3-8, pp 154-157 in Textbook)1. The secondary winding of a transformer has a terminal voltage ofvs(t) = 282.8 sin 377t V. The turns ratio of t
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EEL 3216 Introduction to Power SystemsHomework # 4SOLUTIONS1. A Y-connected bank of three identical 100-kVA, 7967/480-V transformers is suppliedwith power directly from a large constant-voltage bus. In the short-circuit test, therecorded values on th
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EEL 3216 Introduction to Power SystemsHomework # 5, SOLUTIONS4-2. A three-phase four-pole winding is installed in 12 slots on a stator. There are 40turns of wire in each slot of the windings. All coils in each phase are connected inseries, and the thr
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EEL 3216 Introduction to Power SystemsHomework # 6SOLUTIONS4-6. The flux density distribution over the surface of a two-pole stator of radius r andlength l is given by)B BM cos( m tProve that the flux density under each pole face is2rlBMSolve fir
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EEL 3216 Introduction to Power SystemsHomework # 7 Solution1. A 3-phase, 4-pole synchronous machine rotates CCW with 1500 rpm and produces arated torque of 668.45 Nm at the shaft in CW direction. The total rated losses are5 kW and the rated stator (co
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EEL 3216 Introduction to Power SystemsHomework # 8A balanced 3-phase impedance type load is rated 3 MVA at 4.16 kV, with a laggingpower factor of 0.75. It is supplied by a generator via a 2 km long overhead transmissionline. The GMD of the conductors
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EEL 3216 Introduction to Power SystemsHomework # 8A balanced 3-phase impedance type load is rated 3 MVA at 4.16 kV, with a laggingpower factor of 0.75. It is supplied by a generator via a 2 km long overhead transmissionline. The GMD of the conductors
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EEL 3216 Introduction to Power SystemsHomework # 9Problems from book 9-6, 9-11, and 9-15 as shown below.Problem 9-6 refers to a single-phase, 8 kV, 50 Hz, 50 km long transmission line consisting of twoaluminum conductors with a 3 cm diameter separated
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EEL 3216 Introduction to Power SystemsHomework # 9Problems from book 9-6, 9-11, and 9-15 as shown below.Problem 9-6 refers to a single-phase, 8 kV, 50 Hz, 50 km long transmission line consisting of twoaluminum conductors with a 3 cm diameter separated
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EEL 3216 Introduction to Power SystemsHomework # 10Problem from book 5-29 as shown below.
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EEL 3216 Introduction to Power SystemsHomework # 10SOLUTION
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EEL 3216 Introduction to Power SystemsHomework # 11Problem from book 7-5, 7-7, 7-11 as shown below.7-57-77-11
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EEL 3216 Introduction to Power SystemsHomework # 11 SOLUTIONSProblem from book 7-5, 7-7, 7-11 as shown below.7-5Attention: this solution, as provided by the author of the book, is inconsistent with the text of thebook. The core losses are supplied by
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EEL 3216 Fundamentals of Power SystemsHomework # 12You are encouraged to solve the two problems below in a group effort. Therefore, amaximum of 5 students may submit one assignment together. If you do so, clearly writethe names of the 5 students who h
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Electric MotorsThree basic types of motorsSynchronous, SMInduction (asynchronous), IMDC motorsIn the past: preferred for variable speed applicationsDecreasing in popularity; replaced by combination of IM and powerelectronic variable speed drive (VS
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U.S. Electric Power Industry ExistingNet Summer Capacity by State, 2003Fundamentals of Power SystemsLecture 11U.S. Electric Power TransmissionSystem in 2000Fundamentals of Power SystemsLecture 1Page 12Power Systems ComponentsPrimary power sour
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Electric Powersingle-phase (1~) systemsOne sourceTwo energy-carrying wiresPulsating instantaneous power (2f)three-phase (3~) systemsThree sources, 120 phase shiftedLecture 2Fundamentals of Power Systems1Single Phase Powerptv, i, pPVvtptDe
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Notes on Phasor Notation andDiagramsMathematically correctComplex quantity(underlined)VmMagnitudeV Vm e jvttVm cos( t )Re(V) Vm cosvtorjVm sin( t )tIm(V) Vm sintPractical notation and usageComplex quantity, butI = 10 Aunderlining omitt
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Ideal 1~ Transformer ModelFlux linkages (winding flux)Ideali1i2N1N1 ,1N22N2SourceV2av1e1 , v2e2aV1N1N2e1e2ZLN1N2Loadv1v2i2i1Dot conventionCurrent into doted end produces positive MMF (NI) orampere-turnsTherefore, orientat