ELEMENTS OF
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`Power System Analysis
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`WILLIAM D. STEVENSON, Jr.
`
`Professor of Electrical Engineering
`North Carolina State College
`
`SECOND EDITION
`
` McGRAW-HILL BOOK COMPANY, INC.
`
`ewYork
`Bas
`okey
`
`San Francisco
`
`Toronto
`
`1962
`
`London
`
`GE2015
`Vestas v. GE
`IPR2018-01015
`
`GE 2015
`Vestas v. GE
`IPR2018-01015
`
`i
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`

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`GENERAL BACKGROUND
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`13
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`made to determine the best operating procedure in the event of the loss of
`one or more generating stations or transmission lines.
`1.4. Economical Load Distribution. On first thought, the power indus-
`try may seem to lack competition. This idea arises because each power
`company operates in a geographic area not served by other companies.
`Competition is present, however, in attracting new industries to an area
`and in the possibility of local generation by a large consumer. Favorable
`electric rates are a very compelling factor in the location of industry.
`Power companies compete heavily to attract industrial customers to their
`territories. This competition for the heavy consumer demands that each
`company keep its rates as low as possible. Regulation of rates by state
`utility commissions also puts great pressure on companies to achieve
`maximum economy and earn a profit while maintaining fixed rates in the
`face of advancing costs. Economical operation is very important to all
`power companies.
`Advances in engineering mean that the most modern generating unit on
`a power system is the most economical, but loading the most economical
`units to capacity before operating less efficient units does not necessarily
`result in the lowest delivered cost of power. We shall consider this prob-
`lem in some detail in Chap. 11. We can see immediately, however, that
`transmission losses must be correlated with production costs at the gener-
`ator to solve the problem of the most economical loading of each generat-
`ing plant. For example, to have a very economic plant supply a load
`over a long line might make the delivered cost of power more than the cost
`of supplying a large part of the load from nearby butless efficient plants.
`Weshall see that all plants on a system can be controlled continuously
`:
`_. by a computer as load changes occur so that the generation is allocated
`_ for the most economical operation.
`In Chap. 11 we shall examine some
`_
`features of an analog computer which accomplishes this objective.
`1.5 Fault Calculations. The American Institute of Electrical Engi-
`_ neers defines a fault in a wire or cable as follows:
`‘‘A wire or cable fault
`is a partial or total failure in the insulation or continuity of a conductor.’’!
`Most faults on transmission lines of 115 kv and higher are caused by
`lightning which results in the flashover of insulators. The high voltage
`_between a conductor and the grounded supporting tower causes ionization
`which provides a path to groundfor the charge induced by the lightning
`‘Stroke. Once the ionized path to groundis established, the resultant low
`impedanceto groundallows the flow of power currentfrom. the conductor
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`to ground and through the ground to the grounded neutral of a trans-
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`former or generator, thus completing the circuit. Line-to-line faults not
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`Involving ground are less common. The opening of circuit breakers to
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`a ‘“‘American Standard Definitions of Electrical Terms,” 35.40.213, American Insti~
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`_tute of Electrical Engineers, New York, 1942.
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`14
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`ELEMENTS OF POWER SYSTEM ANALYSIS
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`isolate the faulted portion of the line from the rest-of the system interrupts
`the flow of current in the ionized path and allows deionization to take
`piace. After an interval of about 20 cycles to allow deionization, breakers
`can usually be reclosed without the reestablishment of the arc. Experi-
`ence in the operation of transmission lines has shown that ultra-high-
`speed reclosing breakers successfully reclose after most faults. Of those
`cases where reclosure is not successful, an appreciable number are caused
`by permanent faults where reclosure would be impossible regardless of the
`interval between opening and reclosing. Permanent faults are caused by
`lines being on the ground, by insulator strings breaking because of ice
`loads, by permanent damage to towers, and by lightning-arrester failures.
`Experience has shown that between 70 and 80% of transmission-line
`faults are single line-to-ground faults, which arise from the flashover of
`only one line to the tower and ground. The smallest number of faults,
`roughly 5%, involve all three phases and are called three-phase faults.
`Other types of transmission-line faults are line-to-line faults, which do not
`involve ground, and double lne-to-ground faults. All the above faults
`except the three-phase type are unsymmetrical and cause an unbalance
`between the phases.
`The current which flows in different parts of a power system immedi-
`ately after the occurrence of a fault differs from that flowing a few cycles
`later just before circuit breakers are called upon to open the line on both
`sides of the fault, and both these currents differ widely from the current
`which would flow under steady-state conditions if the fault were not
`isolated from the rest of the system by the operation of circuit breakers.
`Two of the factors upon which the proper selection of circuit breakers
`depends are the current flowing immediately after the fault occurs and
`the current which the breaker must interrupt. Fault calculations con-
`sist in determining these currents for various types of faults at various
`locations in the system. The data obtained from fault calculations also
`serve to determinethe settings of relays which control the circuit breakers.
`For simple systems, analytic calculations of fault currents are practical,
`but for the more complex systems the engineer must call upon the digital
`computer or the calculating board.
`If great accuracy is not required and
`the system can be assumed to be composed of purely inductive reactances
`or of impedances of nearly equal phase angles only, a d-c calculating board
`with resistances replacing the inductive reactances can be used instead of
`the more costly a-c board.
`Analysis by symmetrical components is a powerful tool which we shall
`study Jater and which makes the calculation of unsymmetrical faults
`almost as easy as the calculation of three-phase faults. A knowledge of
`symmetrical components is necessary whether the fault calculations are |
`carried out analytically or on a calculating board.
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