DIFFERENTIAL CALCULUS PLATES FOR 6:30 and 7:30 CLASSES


Please submit on or before 12:00 nn of January 6, 2013. Those submitted after the said date and time will be marked zero (0).

1. At what values of x does the graph of y = sec x have a horizontal tangent?

2. Find the derivate of Csc (3x - 5).

3. Find the first derivative of y = cos x / 1 - sin x.

4. Find an equation of the tangent line at the point P = (1, 1) on the curve y4 + xy = x3 − x + 2

5. Find y' if y = sin( cos x)

6. A person x inches tall has a pulse rate of y beats per minute, as given approximately by

y = 590x-1/2          30 X 75

What is the instantaneous rate of change of pulse rate at the
(A) 36-inch level?
(B) 64-inch level?

7. Suppose that a person learns y items in x hours, as given by y = 50x, 

 X ≤ 9

Find the rate of learning at the end of (A) 1 hour (B) 9 hours

GOOD LUCK.

MERRY CHRISTMAS AND HAPPY NEW YEAR

LEO


SYNCHRONOUS GENERATOR AS FAULT CURRENT SOURCE


If a short circuit is applied to the terminals of a synchronous generator, the short-circuit current starts out at a high value and decays to a steady-state value some time after the inception of the short circuit.

Since a synchronous generator continues to be driven by its prime mover and to have its field externally excited, the steady-state value of short-circuit current will persist unless interrupted by some switching means.

An equivalent circuit consisting of a constant driving voltage in series with an impedance that varies with time is used to represent this characteristic. The varying impedance consists primarily of reactance.

Xd"= subtransient reactance; determines current during Þrst cycle after fault occurs. In about 0.1 s reactance increases to

Xd'= transient reactance; assumed to determine current after several cycles at 60 Hz. In about 0.5 to 2 s reactance increases to

Xd = synchronous reactance; this is the value that determines the current ßow after a steadystate condition is reached.

Because most short-circuit interrupting devices, such as circuit breakers and fuses, operate well before steady-state conditions are reached, generator synchronous reactance is seldom used in calculating fault currents for application of these devices.

Synchronous generator data available from some manufacturers includes two values for direct axis subtransient reactanceÑfor example, subtransient reactances Xdv"(at rated voltage, saturated, smaller) and Xdi" (at rated current, unsaturated, larger).

Because a shortcircuited generator may be saturated, and for conservatism, the Xdv" value is used for short-circuit current calculations.

MEASUREMENT OF PHASE VOLTAGE UNBALANCE IN THREE PHASE SYSTEM

Causes of phase-voltage unbalance
Most utilities use four-wire grounded-wye primary distribution systems so that single-phase distribution transformers can be connected phase-to-neutral to supply single-phase loads, such as residences and street lights. Variations in single-phase loading cause the currents in the three-phase conductors to be different, \ producing different voltage drops and causing the phase voltages to become unbalanced.

Normally the maximum phase-voltage unbalance will occur at the end of the primary distribution system, but the actual amount will depend on how well the single-phase loads are balanced between the phases on the system.

Perfect balance can never be maintained because the loads are continually changing, causing the phase-voltage unbalance to vary continually. Blown fuses on three-phase capacitor banks will also unbalance the load and cause phase-voltage unbalance.

Industrial plants make extensive use of 480Y/277 V utilization voltage to supply lighting loads connected phase-to-neutral. Proper balancing of single-phase loads among the three phases on both branch circuits and feeders is necessary to keep the load unbalance and the corresponding phase-voltage unbalance within reasonable limits.

Measurement of phase-voltage unbalance
The simplest method of expressing the phase-voltage unbalance is to measure the voltages in each of the three phases:

The amount of voltage unbalance is better expressed in symmetrical components as the negative sequence component of the voltage:

percent unbalance = maximum deviation from average/ average X 100%

voltage unbalance factor = negative-sequence voltage/ positive-sequence voltage


BARE COPPER CONDUCTORS AMPACITY AND TABLE


Conductor current–carrying capacity, or ampacity, is determined by the maximum safe operating temperature of the insulation used on the conductor. Heat generated as a result of current flow is dissipated into the environment.

Thus, for a given installation context (open-air, buried in earth, or enclosed), ampacity increases with increasing conductor size and with maximum permissible insulation temperature.

If more than three conductors are placed in a conduit, the resultant increase in temperature requires that the conductors be derated to maintain safe operating conditions.

Because heat dissipation from a conductor in free air is much greater than that from the same conductor enclosed in conduit or directly buried, its corresponding allowable ampacity is also greater.

Conversely, if the ambient temperature around a conductor is higher than 30ºC (86ºF), the temperature upon which all standard ampacity tables are based, the permissible ampacity must be reduced.

Ampacity tables for conductors in free air, for cable types not shown in Table below, and derating factors for high ambient temperatures are all found in the NEC.

Physical Properties of Bare Copper Conductors



Source: Except for millimeter dimensions, this table was extracted from NFPA 70-1999, the National Electrical Code. © 1999, National Fire Protection Association, Quincy, MA 02269.

Note: This extracted material is not the complete and official position of the National Fire Protection Association on the referenced subject, which is represented only by the standard in its entirety.

COPPER CLAD ALUMINUM WIRE/ CONDUCTORS BASIC INFORMATION

What are copper clad aluminum conductors?

Copper-clad aluminum is the newest conductor material on the market. A copper-clad aluminum conductor is drawn from copper-clad aluminum rod, the copper being bonded metallurgically to an aluminum core. The copper forms a minimum of 10 percent of the cross-sectional area of the solid conductor or of that of each strand of a stranded conductor.

Although copper-clad aluminum contains only 10 percent of copper by volume (26.8 percent by weight), its electrical performance is equivalent to that of pure copper. It is lighter and easier to handle, and the price advantage, which reflects the value of the copper content, can be as much as 25 percent when copper peaks to one of its periodic highs. Detailed studies by Battelle Laboratories have shown that copper-clad aluminum and copper have the same connection reliability.

Because the electrical industry consumes 60 percent of all copper used in the United States, it is critically affected by copper’s fluctuating costs and uncertain supply. Until recently, however, aluminum was the only alternative to copper.

Aluminum, in the more than 70 years since its introduction as an electrical conductor, has significantly penetrated such areas as electric power transmission lines, transformer windings, and telephone communications cables. On the other hand, it has received relatively limited acceptance in nonmetallic-sheathed cable and other small-gage building wires. The reason has been a lack of acceptable means of connecting or terminating aluminum conductors of 6 AWG or smaller cross-sectional areas.

Connector manufacturers, the National Electrical Manufacturers Association (NEMA), Underwriters Laboratories (UL), and aluminum companies have devoted much attention to this connection problem. The most significant advance in aluminum termination has been the institution of UL’s new requirements and testing procedures for wiring devices for use in branch-circuit-size aluminum conductors. Devices which meet the revised UL requirements are marked CO/ALR and carry that mark on the mounting strap. Only CO/ALR switches and receptacles should be used in aluminum 15- and 20-A branchcircuit wiring.

Copper-clad aluminum is now available to counter the disadvantages of high price and lack of availability of copper and the problems of connection reliability of aluminum. It is a product of a metallurgical material system, i.e., a system in which two or more metals are inseparably bonded in a design that utilizes the benefits of each component metal while minimizing their deficiencies. In copper-clad aluminum conductors, the electrical reliability of copper is combined with the abundant supply, stable price, and light weight of aluminum.

Copper-clad aluminum is already being used for building wire, battery cable, magnet wire, and radio-frequency (rf ) coaxial cable.

The ampacity (current-carrying capacity) of copper-clad aluminum conductors is the same as that of aluminum conductors. It is required that the wire connectors used with copper-clad aluminum conductors be recognized for use with copper and copper-clad aluminum conductors and be marked CC-CU or CU-AL, except that 12-10 AWG solid copper-clad aluminum conductors may be used with wire-binding screws and in pressureplate connecting mechanisms that are recognized for use for copper conductors.

Copperclad aluminum conductors are suitable for intermixing with copper and aluminum conductors in terminals for splicing connections only when the wire connectors are specifically recognized for such use. Such intermixed connections are limited to dry locations.

METAL-ENCLOSED INTERRUPTER SWITCHGEAR PRODUCTION TESTS

Production Tests
Unless otherwise specified, all production tests shall be made by the manufacturer at the factory on the complete MEI switchgear or its component for the purpose of checking the correctness of manufacturing operations and materials. (See ANSI/IEEE C37.20.3-1987.)
Production tests shall include the following:
1) Low-frequency withstand voltage tests
2) Mechanical operation tests
3) Grounding of instrument transformer cases test
4) Electrical operation and wiring tests
Low-Frequency Withstand Voltage Tests
Low-frequency withstand tests shall be made at the factory on each switchgear assembly in the same manner as described in 4.5.2 with the exception that tests across the open gap(s) (see 4.5.1(2)) are not required. Tests shall be made in accordance with 4.5.1(1) and 4.5.2.2.

Drawout interrupter switch removable elements need not be tested in the assembly if they are tested separately. Control devices, potential transformers, and control power transformers, which are connected to the primary circuit, may be disconnected during the test.

Mechanical Operation Tests
Mechanical operation tests shall be performed to ensure the proper functioning of removable element operating mechanisms, shutter, mechanical interlocks, and the like. These tests shall ensure the interchangeability of removable elements designed to be interchangeable.

Grounding of Instrument Transformer Cases Test
The effectiveness of grounding of each instrument transformer case or frame shall be checked with a low-potential source, such as 10 volts or less, using bells, buzzers, or lights. This test is required only when instrument transformers are of metal case design.
Electrical Operation and Wiring Tests
Control Wiring Continuity
The correctness of the control wiring of MEI switchgear shall be verified by (1) actual electrical operation of the component control devices, or (2) individual circuit continuity checks by electrical circuit testers, or by both (1) and (2).
Control Wiring Insulation Test
A 60-Hz test voltage, 1500 volts to ground, shall be applied for 1 minute after all circuit grounds have been disconnected and all circuits wired together with small bare wire to short-circuit coil windings. The duration of the test shall be 1 second if a voltage of 1800 volts is applied. At the option of the manufacturer, switchgear-mounted devices that have been individually tested may be disconnected during this test.

Polarity Verification
Tests or inspections shall be made to ensure that connections between instrument transformers and meters or relays or similar devices are connected with proper polarities. Instruments shall be checked to ensure that pointers move in the proper direction. This does not require tests using primary voltage and current.
Sequence Tests
MEI switchgear involving the sequential operation of devices shall be tested to ensure that the devices in the sequence function properly and in the order intended. This sequence test need not include remote equipment controlled by the MEI switchgear; however, this equipment may be simulated where necessary.

SWITCHGEAR ASSEMBLIES FOR NUCLEAR GENERATING PLANTS SERVICE CONDITIONS

The service conditions below are significant to the qualification of switchgear assemblies and included components.
 
Usual Service Conditions
The values given as usual service conditions represent the anticipated average conditions for switchgear assemblies in nuclear power generating stations. These values are recommended for use in generic qualification programs and do not imply a derating of the equipment.
 
Ambient Temperature
A yearly average ambient temperature of 30 °C with temperature excursions to 10 °C and 40 °C is considered usual.
 
Relative Humidity
Relative humidity variations between 10% and 90% are considered usual.
 
Altitude
Altitudes of up to 6600 ft (2000 m) above sea level for metal-enclosed low-voltage power circuit breaker switchgear and up to 3300 ft (1000 m) for metal-clad switchgear and metal-enclosed interrupter switchgear are considered usual.
 
Radiation
Radiation exposure of up to 104 rads equivalent gamma total integrated dose over the qualified life is considered usual.
 
Line Voltage
The line voltage shall be specified for the application. Voltage ratings as specified in ANSI/IEEE C37.20.1-1987 [12], ANSI/IEEE C37.20.2-1987 [13], ANSI/IEEE C37.20.3-1987 [14], and ANSI/IEEE C37.23-1987 [15] are considered usual. Switching surges of up to twice peak line-to neutral voltage may occur occasionally, but Class 1E switchgear installations are usually not exposed to lightning surges.
 
Frequency
A nominal frequency of 60 Hz is considered usual for ac equipment.
 
Control Voltages
The nominal control voltages shall be specified for the application. Control voltage variations within the ranges given in the standards below are considered usual:
ANSI C37.06-1979 [1] — high-voltage circuit breakers.
ANSI C37.16-1980 [2] — low-voltage circuit breakers.
ANSI C37.33-1970 [5] — high-voltage interrupter switches.
 
Control Currents
The maximum control auxiliary circuit currents to be made, carried, and interrupted by auxiliary contacts of breakers and other components shall be as specified for the application.
 
Continuous Current
The average loading shall be estimated for the application. The qualified life of switchgear components is dependent on the average loading. Considering duty and available power distribution options in nuclear Class 1E systems, the average loading rarely, if ever, approaches the continuous current rating of the equipment.
 
Short-Circuit Current
The maximum short-circuit current shall be specified for the application.
 
Mechanical Operations
In order to provide a basis for qualified life demonstration, circuit breaker mechanical operations shall be specified. A cumulative number of mechanical operations not greater than that corresponding to two maintenance intervals, as defined in applicable circuit breaker standards, is considered usual.
 
Mechanical Interface Loading
It is considered usual that the mechanical loads from incoming cables, conduits, other interfacing hardware, or equipment such as transformers are separately supported or isolated so as not to impose significant mechanical loading on the switchgear assembly structure.
 
Unusual Service Conditions
When switchgear assemblies are applied where the service conditions are not within the range given as usual service conditions, the applicable service conditions shall be specified and the switchgear assemblies shall be qualified for these conditions. Where qualification to unusual conditions becomes impractical, improvement of the service conditions may be necessary.
 
Design Basis Events (DBEs)
The DBE that usually applies to switchgear assemblies is a seismic event. Other DBEs, such as the severe environmental conditions associated with a loss-of-coolant accident and high-energy line break, are not normally applicable.
 
Seismic Excitation
Due to the seismic variations between sites and building structural differences, seismic loading in the form of required response spectra shall be specified for each switchgear assembly application. The switchgear assemblies shall be qualified in accordance with ANSI/IEEE Std 344-1975 [20].
 
Other Design Basis Events (DBEs)
If DBEs or unusual requirements in addition to the seismic event are applicable to switchgear assemblies, detailed conditions shall be specified and considered.

DISTRIBUTION AUTOMATION - A GUEST POST BY DARYLL VALDEZ

Today's post is brought to us by our guest. He is Daryll Valdez, a student from the University of Mindanao, in the Philippines. Darryl is currently finishing his Bachelor's Degree in Electrical Engineering. 

Distribution Automation
Daryll Valdez

A Distribution Automation (DA) System enhances the efficiency and productivity of a utility. It also provides intangible benefits such as improved public image and market advantages. A utility should evaluate the benefits and costs of such a system before committing funds. The expenditure for distribution automation is economical when justified by the deferral of a capacity increase, a decrease in peak power demand, or a reduction in O&M requirements. Distribution Automation Systems have been defined by the Institute of Electrical and Electronic Engineers (IEEE) as systems that enable an electric utility to monitor, coordinate, and operate distribution components in a real-time mode from remote locations. 

The DA System is modular and may be implemented in phases to include remote monitoring and control of substation, feeder and consumer devices, and loads. The overall goals of distribution automation are to reduce costs, improve service, reliability, provide better consumer service, and enhance government relations. The successful implementation of the DA System results in deferred capital expenditures, reduced operations and maintenance expenses, improved outage response and restoration, enhanced system efficiencies, enhanced consumer satisfaction, improved data and information, positive public Image.

Fundamentally, there are three components of a system-wide distribution automation system. These include control centre-based control and monitoring systems, including distribution SCADA or distribution management systems; the data communications infrastructure and methodology required to acquire and transmit operating data to and from various network points in addition to substations; and the various distribution automation field equipment, ranging from remote terminal units to intelligent electronic devices required to measure, monitor, control and meter power flow. Taken together, expenditures for this wide range of electric power grid distribution automation activity exceed $1 billion dollars each year.
  
Distribution Automation functions can provide both benefits and challenges. Often these benefits and the challenges are closely intertwined, with the real and complete benefits not achievable until some of the challenges (including the financial challenges) have been overcome. Yet waiting for these challenges to be overcome or ameliorated often means missing out on some of the benefits – not doing anything can often be worse than doing something. Therefore the key to distribution automation is assessing the balance of benefits versus challenges, including the “lost opportunity” risks of doing nothing. 

The distribution automation functions can in general be divided into two main categories, namely customer level functions and system level functions. The customer level functions are those functions which require installation of some device with communication capability at the customers’ premises. These include load control, remote meter reading, time-of-use rates, and remote connect/disconnect the system level functions are those functions which relate to system operations. The control and communications devices for these functions are installed at different locations in the system, such as substations and feeders. These functions include fault detection and service restoration, feeder reconfiguration, voltage/var control etc. In addition to system operation type functions, digital protection of substations and feeders is considered part of distribution automation in some situations.

Reference:
http://www.scribd.com/doc/36666306/Distribution-Automation-Doc
http://www.energy.siemens.com/hq/en/automation/power-transmission-distribution/eneas/distribution-automation/
http://www.silverspringnet.com/solutions/distribution-automation/#.Ue07dqJHJJs
http://energycentral.fileburst.com/Sourcebooks/gsbk0106.pdf

TRANSMISSION LINE MATERIALS HANDLING AND STORAGE

In the unloading, handling, and storage of structures, care should be exercised so as not to damage the surface or surface coating, or deform the members. Bare wire rope or steel chains should not be used for handling without adequate protection of the surface. Structural members should not be dumped, dragged, rolled, dropped, nor used as loading or unloading skids or blocking.
 
Heavy members should not be stacked on top of lighter members. The maximum weight of material bundles should not exceed a specified weight, typically 1600–1800 kg (3500–4000 lb), to facilitate handling and unloading. Components with dissimilar finishes should not be stored over one another to minimize discoloration of the lower members.
Care should be taken to ensure proper blocking, stacking, and handling of concrete members. Refer to the structure drawings and instructions to verify correct lifting methods, replacement of support blocking, and stacking limitations.
 
It is very common for concrete poles to require a two-point pickup due to the weight and possible long lengths. Identifying the correct blocking locations is important to eliminate the potential of overstressing the member. The constructor should verify correct blocking and number of possible layers for stacking to avoid damage to concrete members lower in the stack.
 
All members should be placed on wood blocking or other suitable material to ensure that the material to be stored is not in contact with the ground. Blocking should also be used to separate layers of stacked material.
It should be noted that oak wood blocking or oil-treated timbers can bleed and stain a structure finish. Members should be supported in such a manner as to prevent bending and distortion as well as to allow water to drain from the material.

Failure to provide for proper drainage of stacked, galvanized steel components could result in the formation of “white rust.” White rust (zinc oxide) forms when two galvanized surfaces are closely nested for an extended time without adequate ventilation. Ingress of water between the surfaces forms an electrolytic cell which may, in time, erode some of the zinc layer.
 
The white rusting action will stop after exposure to air. When extended transport or storage is anticipated, either of the following two methods can be used to prevent oxide formation:
a) Spacers may be placed between the nested pieces to ensure adequate ventilation.
b) Galvanized members may be treated with a solution which will inhibit oxide formation for six months to one year.

Weathering steel fasteners, though rarely used on concrete poles, and other materials subject to deterioration should be protected from the elements during storage.

During the course of the project, the material yard should be kept relatively neat and clean and the growth of vegetation kept to a minimum. Good housekeeping minimizes damage and loss of material in the yard, facilitates material handling and periodic physical inventories, and complies with environmental considerations.

If delivery of material is made initially to the structure site for storage, care should be taken to avoid interference with foundation construction, access roads, or drainage. Truck delivery of complete structures from the manufacturer directly to the structure site can be advantageous since it eliminates at least one unloading and loading cycle.
 
However, security of material stored at a structure site is minimal and the subsequent loss of time due to missing items can result in significant construction cost increases.

ELECTRIC BUS WAYS CURRENT RATING BASIC INFORMATION

To apply busways properly in an electric power distribution system, some of the more important items to consider are the following.

Current-carrying capacity
Busways should be rated on a temperature-rise basis to provide safe operation, long life, and reliable service.

Conductor size (cross-sectional area) should not be used as the sole criterion for specifying busway. Busway may have seemingly adequate cross-sectional area and yet have a dangerously high temperature rise.

The UL requirement for temperature rise (55 deg C) (see ANSI/UL 857-1989) should be used to specify the maximum temperature rise permitted. Larger crosssectional areas can be used to provide lower voltage drop and temperature rise.

Although the temperature rise will not vary significantly with changes in ambient temperature, it may be a significant factor in the life of the busway. The limiting factor in most busway designs is the insulation life, and there is a wide range of types of insulating materials used by various manufacturers. If the ambient temperature exceeds 40 deg C or a total temperature in excess of 95 deg C is expected, then the manufacturer should be consulted.

Short-circuit current rating
The bus bars in busways may be subject to electromagnetic forces of considerable magnitude by a short-circuit current. The generated force per unit length of bus bar is directly proportional to the square of the short-circuit current and is inversely proportional to the spacing between bus bars.

Short-circuit current ratings are generally assigned in accordance with ANSI/NEMA BU1-1988 and tested in accordance with ANSI/UL 857-1989. The ratings are based on (1) the use of an adequately rated protective device ahead of the busway that will clear the short circuit in 3 cycles and (2) application in a system with short-circuit power factor not less than that given in table 13-1.


If the system on which the busway is to be applied has a lower short-circuit power factor (larger
X/R ratio), the short-circuit current rating of the bus may have to be increased. The manufacturer should then be consulted.
The required short-circuit current rating should be determined by calculating the available short-circuit current and X/R ratio at the point where the input end of the busway is to be connected. The short-circuit current rating of the busway must equal or exceed the available short-circuit current.
The short-circuit current may be reduced by using a current- limiting fuse or circuit breaker at the supply end of the busway to cut it off before it reaches maximum value. Short-circuit current ratings are dependent on many factors, such as bus bar center line spacing, size, strength of bus bars, and mechanical supports.

Since the ratings are different for each design of busway, the manufacturer should be consulted for speciÞc ratings. Short-circuit current ratings should include the ability of the ground return path (housing and ground bar if provided) to carry the rated short-circuit current.
Failure of the ground return path to adequately carry this current can result in arcing at joints, creating a fire hazard. The ground-fault current can also be reduced to the point that the overcurrent protective device does not operate. Bus plugs and attachment accessories also should have adequate short-circuit interrupting and/or withstand ratings.

FAULT ARC PATH OF TRANSMISSION LINE BASIC INFORMATION

When lightning strikes a transmission line the field intensity stressing the insulation may exceed the ionization field intensity level (roughly 30kV/cm) and create an arc from the line to ground. A path now exists for current flow.

The resulting discharge current flow from the lightning stroke is usually over within a few milliseconds but the ionized path has been established and a 60Hz “follow” current flows. This current must be detected and interrupted by deenergizing the line with circuit breakers.

For the ionization path to dissipate, the voltage must be absent for a sufficient duration. The time during which the voltage is absent is commonly called “dead” time.

For transient faults to be successfully cleared, an adequate time for deionization must be afforded. Table 1 shows the minimum time required by voltage level and by probability of successfully reclosing and energizing the line.

Table 1. Minimum De-Ionization Time for Reclosing Breakers

System Voltage                                                         Cycles on 60-Cycle Basis
(line-line kV)                                                       95% probability    75% probability
23                                                                                    4
46                                                                                    5                             3.5
69                                                                                    6                              4
115                                                                                 8.5                            6
138                                                                                 10                            7.5
161                                                                                 13                            10
230                                                                                 18                            14

If sufficient motor load is still connected during the dead time the ionization path can/will be kept intact and a fault reignition will result when the utility breakers reclose. This occurs even though the fault is phase-ground and there is an interposing delta winding between the motor load and the fault.

Tapped motor load holds up the voltage as it decays. At the time of the reclose the voltage is roughly 50% of nominal. Oscillographic data has been obtained in the past showing transmission line voltage being maintained by tapped motor load during reclosing dead time.

Effect on Motors
Unsupervised high-speed reclosing on islanded motors (induction or synchronous machines) before their “residual” voltage has subsided below 25% may subject the motors and other equipment to damage. The motor should not be subjected to a reclose when the phasor difference between the source volts/Hz and the motor residual volts/Hz exceeds 1.33 per unit volts/Hz.

The available literature clearly indicates that reclosing on motor load should be delayed long enough for their residual voltage to decay to acceptable levels (or their contactors drop out) to prevent damage which may be immediate or cumulative. Alternatively, some means to ensure the two voltages are in-phase would be needed.

Damage may include shifting of stator coils, loosening of rotor bars, distortion of coil ends, shaft damage etc. In some cases torsional resonance can be established with resulting torques as high as 20
times normal.

When a motor is disconnected from its power supply it starts to slow down depending on its inertia and the characteristics of its connected load. For an open circuited induction (asynchronous) motor the voltage at its terminals will be a product of its speed, open circuit time constant, and its trapped rotor flux.

For a synchronous machine with field forcing it may take much longer for its voltage to decay. If not open circuited, the motors will experience an electrical interaction with other motors bussed with them as well (an electrical to-and-fro of energy).
From the moment the motors are disconnected from the power system they begin to slip out-of-phase with the power system and their voltage magnitude begins to decay. The voltage impressed across them at reclose will be a function of this internal residual voltage and the power system voltage at time of reclosing. If the two voltages were equal in magnitude and 180° out-of-phase the resulting voltage difference would be 2.0 per unit.

SERIES COMPENSATED TRANSMISSION LINES BASIC INFORMATION

Series compensation of long high-voltage and extra-high-voltage lines has become almost standard practice. The presence of series compensation affects the X0/X1 ratios of the system, with the reactance of the series capacitor appearing in all three sequence networks.

Therefore, temporary and transient overvoltages as a result of faults, as well as circuitbreaker recovery voltages and surge arrester operation, are different than those that would appear in the uncompensated system.

There have also been concerns about ferroresonant TOVs in series-compensation systems , but few if any cases of ferroresonance have been reported for operating transmission or subtransmission systems.

However, because of this concern, some utilities buying series capacitors have specified special subharmonic detection devices as part of the series capacitor bank. There are also concerns about subsynchronous resonance (SSR) of rotating machine mechanical systems with the series compensated electrical system.

Additional concerns have centered on fundamental-frequency resonance conditions during faults at critical locations in the transmission systems. But economical applications of series capacitors dictate that some means be supplied to limit the overvoltage appearing across the series capacitor during faults to voltages no higher than economical design levels.

Limiting this overvoltage virtually eliminates the possibility of high temporary fundamental resonant overvoltages.
The overvoltage protection for series capacitors applied to transmission systems has taken two forms. The earliest forms of overvoltage protection were spark-gap systems that limited voltage to the sparkover voltage of the gap setting, which was generally no more than 3.5 times the rated voltage across the series capacitor bank, but often less.

More recently, the protection has been achieved by metal-oxide varistors, somewhat similar to surge arresters but applied across the series capacitor and limiting the voltage to about two times the rated voltage across the series capacitor bank.

Both forms, when acting during a fault, can reduce temporary and transient overvoltages, the spark gap by electrically bypassing the capacitor during its arcing time, and the metaloxide varistors by limiting the overvoltage, inherently reducing the capacitive reactance, and inserting some value of equivalent resistance into the circuit until the fault is cleared.

The effect on temporary and transient overvoltages (and the possibility of SSR) as a result\ of using of series compensation with its overvoltage protection should be carefully studied.

CONNECTION AND TERMINATIONS OF METAL CLAD SWITCHGEARS BASIC INFORMATION

Bus connections
When the MC switchgear consists of several shipping sections, the main bus is necessarily disconnected before shipping. The main bus should be reconnected, with particular attention paid to the cleanliness of and pressure between the contact surfaces.

It is essential that the connections be securely bolted because the conductivity of the joints is dependent on the applied pressure. Refer to the manufacturer’s torque recommendations and any other special instructions.
Cable connections
Before the cable connections are made, the phasing of each cable should be determined in accordance with the connection diagram, and the cables should be tagged accordingly. The cable manufacturer’s instructions should be followed in forming cable terminations and during the installation of the cable.

It is essential that the connections be clean and torqued to manufacturer’s recommendations since the conductivity of the joints is proportional to the applied pressure. The terminating devices (where required) should be installed pursuant to the terminator manufacturer’s instructions.
Control connections
Control wires between shipping sections should be reconnected as marked by the manufacturer. Connections that are to be connected to terminals in apparatuses remote from the switchgear should be checked carefully against the connection diagram.

In making connections to terminals, care should be exercised to ensure that the connections are made properly.
Grounding
Sections of ground bus previously disconnected at shipping sections must be reconnected when the units are installed. It should be ensured that all secondary wiring is connected to the switchgear ground bus as indicated on the drawings.

The ground bus should be connected to the system ground with as direct a connection as possible and should not be run in metal conduit unless the conduit is adequately bonded to the circuit. The grounding conductor should be capable of carrying the maximum line-to-ground short-circuit current for the duration of a fault.

A reliable ground connection is necessary for every switchgear installation. It should be of sufficient capacity to handle any abnormal condition that might occur in the system and should be independent of the grounds used for other apparatuses.

A permanent low-resistance ground is essential for adequate protection and safety.

PAD MOUNTED FUSED SWITCHGEAR RATING INFORMATION

Overall ratings
The overall ratings of PMFSG shall include the following:
a) Rated power frequency;
b) Rated maximum voltage;
c) Rated lightning-impulse withstand voltage;
d) Rated power-frequency withstand voltage;
e) Rated short-circuit current.
Rated power frequencyThe rated power frequency shall be the frequency at which the PMFSG and its components are designed to operate. The preferred rated power frequency is 50 Hz or 60 Hz.

Rated maximum voltage
The rated maximum voltage of PMFSG shall be that of the way with the lowest rating. A three-phase PMFSG containing one or more ways with components, such as fuses, single-phase switches, or fused-loadbreak devices rated for phase-to-ground voltage (maximum voltage divided by 1.732), shall have the designation “Grd-Y” (grounded-wye) added to the rated maximum voltage.

The application of Grd-Y rated PMFSG should be limited to those three-phase applications where the recovery voltage, during switching or fault clearing across any Grd-Y rated way, does not exceed the phase-to-ground rating of components, and the three-phase system voltage does not exceed the rated maximum voltage of the PMFSG.
Rated lightning-impulse withstand voltage
The rated lightning-impulse withstand voltage shall be that of the way with the lowest rating.
Rated power-frequency withstand voltage
The rated power-frequency withstand voltage shall be that of the way with the lowest rating.
Rated short-circuit current
The rated short-circuit current shall be the lowest of the following ratings of any of the ways, and shall be expressed in both symmetrical (sym) and asymmetrical (asym) rms amperes (peak amperes may also be included or substituted for asymmetrical amperes):

a) The rated interrupting current of the fuses, if applicable (see IEEE Std C37.41-1994);
b) The rated momentary and short-time current of the switches, loadbreak devices (if applicable), and bus;

c) The rated fault-closing current of the switches and loadbreak devices.
NOTES
1—A PMFSG consisting of only a single switched way and ways containing fuses may have a rated short-circuit current equal to that of the fuses, if it can be demonstrated that the switch can withstand the fault-closing and momentary duty, as limited by the fuses.
2—Bushings, separable connectors, terminators, or cables may not have short-circuit capabilities as high as the rating of the gear, and could limit the application.

SUBSTATION SHIELDING AND GROUNDING PRACTICES BASIC INFORMATION

The following are recommendation based on IEEE STD 525-1992

Shielding practices
a) The cable for computer or high-speed data logging applications, using low-level analog signals, should be made up of twisted and shielded pairs. For noncomputer type applications, such as annunciators, shielding may not be required.
b) Twisting and shielding requirements for both digital input and digital output signals vary among different manufacturers of computerized instrumentation systems. Separation of digital input cables and digital output cables from each other and from power cables may be required.

Where digital inputs originate in proximity to each other, twisted pair multiple conductor cables with overall shield should be used or multiple conductor cable with common return may be permitted, and overall shielding may not be required.

Digital output cables of similar constructions may also be permitted. Individual twisted and shielded pairs should be considered for pulse-type circuits.
c) Cable shields should be electrically continuous except when specific reasons otherwise dictate. When two lengths of shielded cable are connected together at a terminal block, an insulated point on the terminal block should be used for connecting the shields.
d) Shields should be isolated and insulated except at their selected grounding point to prevent stray and multiple grounds to the shield.
e) At the point of termination, the shield should not be stripped back any further than necessary from the terminal block.
f) The shield should not be used as an electrical conductor except for neutralizing transformer excitation.
g) For signal circuits, the shield must not be part of the signal circuit. Furthermore, the use of shielded, twisted pairs into balanced terminations greatly improves transient suppression. It is never acceptable to use a common line return both for a low-voltage signal and a power circuit.
Grounding practices
a) All shields should be grounded in accordance with provisions above.
b) Signal circuits, if grounded, should be grounded at only one point.
c) Digital signal circuits should be grounded only at the power supply.
d) The shields of all grounded junction thermocouple circuits and the shields of thermocouple circuits intentionally grounded at the thermocouple should be grounded at or near the thermocouple well.
e) Multipair cables used with thermocouples should have twisted pairs with individually insulated shields so that each shield may be maintained at the particular thermocouple ground potential.
f) Each resistance temperature detector (RTD) system consisting of one power supply and one or more ungrounded RTDs should be grounded only at the power supply.
g) Each grounded RTD should be on a separate ungrounded power supply except as follows:
h) Groups of RTDs embedded in the windings of transformers and rotating machines should be grounded at the frame of the respective equipment for safety. A separate ungrounded power supply should be furnished for the group of RTDs installed in each piece of equipment.
i) When a signal circuit is grounded, the low or negative voltage lead and the shield should be grounded at the same point.

TYPES OF SHUNT REACTOR BASIC INFORMATION


The two general types of construction used for shunt reactors are dry-type and oil-immersed. The construction features of each type, along with variations in design, are discussed under the headings which follow.

Dry Type
Dry-type shunt reactors generally are limited to voltages through 34.5 kV and are usually applied on the tertiary of a transformer which is connected to the transmission line being compensated. The reactors are of the air-core (coreless) type, open to the atmosphere, suitable for indoor or outdoor application. Natural convection of ambient air is generally used for cooling the unit by arranging the windings so as to permit free circulation of air between layers and turns.

The layers and turns are supported mechanically by bracing members or supports made from materials such as ceramics, glass polyester, and concrete. The reactors are constructed as single-phase units and are mounted on base insulators or insulating pedestals which provide the insulation to ground and the support for the reactor.

Because the dry-type shunt reactor has no housing or shielding, a high-intensity external magnetic field is produced when the reactor is energized. Care is thus required in specifying the clearances and arrangement of the reactor units, mounting pad, station structure, and any metal enclosure around the reactor or in the proximity of the reactor.

A closed metallic loop in the vicinity of the reactor produces losses, heating, and arcing at poor joints; therefore, it is important to avoid these loops and to maintain sufficient separation distances. Shielding may be required when it is not possible to arrange dry-type units in an equilateral-triangle configuration isolated from external magnetic influences. This shielding is required to limit the impedance deviation between phases. Deviation from impedance values for reactors will result in a deviation from the actual MVAR rating.

For the same range of applications, the primary advantages of dry-type air-core reactors, compared to oil-immersed types, are lower initial and operating costs, lower weight, lower losses, and the absence of insulating oil and its maintenance. The main disadvantages of dry-type reactors are limitations on voltage and kVA ratings and the high intensity external magnetic field mentioned above. Because these reactors do not have an iron core, there is no magnetizing inrush current when the reactor is energized.

Oil-Immersed
The two design configurations of oil-immersed shunt reactors are coreless type and gapped iron-core type. Both designs are subject to low-frequency longtime constant currents during de-energizing, determined by the parallel combination of the reactor's inductance and line capacitance. However, the gapped iron-core design is subject to more severe energizing inrush than the coreless type.

Most coreless shunt reactor designs have a magnetic circuit (magnetic shield) which surrounds the coil to contain the flux within the reactor tank. The steel core-leg that normally provides a magnetic flux path through the coil of a power transformer is replaced (when constructing coreless reactors) by insulating support structures. This type of construction results in an inductor that is linear with respect to voltage.

The magnetic circuit of a gapped iron-core reactor is constructed in a manner very similar to that used for power transformers with the exception that small gaps are introduced in the iron core to improve the linearity of inductance of the reactor and to reduce residual or remanent flux when compared to a reactor without a gapped core.

Oil-immersed shunt reactors can be constructed as single-phase or three-phase units and are very similar in external appearance to that of conventional power transformers. They are designed for either self cooling or forced cooling.

AUTO RECLOSING OF TURBINE-GENERATOR CONSIDERATIONS


Manual closing or autoreclosing without synchronization supervision at line terminals that are in close electrical proximity to turbine-generators can subject them to excessive shaft torques and winding stresses with resultant loss of life of the turbine-generator system.

These effects should be studied and evaluated before autoreclosing is initiated by tripping. It is preferable to re-energize a line at a terminal remote from the generator bus, check synchronism between the generator bus and line, and then close the breaker at the generator end.

In past years, considerable research and analysis focused on the stresses in the shafts and components of turbine-generators due to switching operations. There is little documentation of actual damage to, or failure of, turbine-generators resulting from autoreclosing or switching.

The effects of these stresses induced are cumulative and can be caused by normal switching operations or system faults. Therefore, autoreclosing can be a contributing factor to machine failure, but not necessarily the sole contributor.

An unsuccessful autoreclose attempt (particularly three-phase faults) close in to a generating plant can contribute to accelerated torsional fatigue on the turbine-generator shafts (ANSI C30.13-1977 [B1], IEEE Committee Report [B8], and Jackson et al. [B12]). This can be dealt with by not autoreclosing near generating plants or by blocking the autoreclose for close-in faults or three-phase faults.

Consideration should be given as well to the natural oscillatory frequency of the transmission line as autoreclosing can result in a resonance condition, which could contribute to other system problems. The operation of closing a breaker in the power system can result in the creation of power transients and current oscillations, which can stress or damage generating units located electrically close to that breaker.

These transients effect various components of the turbine-generator. The concern is the average initial power, dP, which occurs when the breaker is closed, and its effect in producing torsional stresses, primarily in the rotational members of the turbine-generator.

For this condition, the permissible limit for dP or dI at the generator terminals are 0.5 per unit based on the rated load and power factor. Regardless of the cause of initial disturbance, autoreclosing times in excess of 10 s appear long enough to allow the oscillations from the initial disturbance to die out.

Turbine-generators when subjected to high-speed autoreclosing can resonate at the natural frequencies of the turbine and shaft. These transient torques will cause cyclic stress variations in the generator shaft resulting in cumulative fatigue damage when they exceed material fatigue limits.

This results in reduced component life of shafts, retaining rings, and rotors. In extreme cases, these torsional vibrations have led to growing oscillations resulting in shaft damage. Some of the more recent papers on the subject of shaft fatigue as a result of high-speed autoreclosing (ANSI C30.13-1977 [B1]) suggest that simple measures such as dP or dI cannot be correlated directly.

Transient torque studies that quantify the impact of high-speed autoreclosing can be performed to calculate the impact on the turbine-generators. This study would require a detailed turbine-mass representation and is generally performed using the Electro Magnetic Transient Program (EMTP). This study can then provide a basis for evaluating the need for torsional monitors/relays on the turbine-generators.

The torsional monitoring devices monitor the turbine-generator shaft for torsional oscillations by providing torsional mechanical response evaluation, shaft torsional stress, and fatigue evaluation, and can be used by the operator to assess torsional impact of an event on a unit. The torsional protective devices continuously monitor the turbine-generator shaft and provide trip output contacts when shaft fatigue reaches predetermined levels.
As a result of the apparent risk to turbine-generator life, most utilities have modified their autoreclosing practices to some form of the following:

a) Autoreclose by synchronism check only
b) Allow a minimum of a 10-s delay prior to any autoreclose attempt
c) Use single pole tripping and allow autoreclose on single phase faults only
d) Autoreclose lines with tapped generation only under dead-line conditions
e) Use no autoreclosing near generation

TRANSMISSION SYSTEM GROUNDING TEMPORARY OVERVOLTAGE (TOV) AND ARRESTER RATING


The ultimate surge voltage protection is obtained through arrester voltage ratings as low as system grounding conditions will permit during normal and abnormal system conditions. Initially, however, when the surge arrester was adopted as the basic protection device, the equipment design (coordination of major insulating structures) assumed that an “ungrounded neutral” or “100% rated” arrester would be used, unless otherwise specified.

In time, after successful service experience with 100% rated arresters (100% of maximum line-line voltage), it was reasoned that lower rated arresters would be suitable on grounded neutral systems. On these systems, the TOV on the unfaulted phases during a line-to-ground fault would bear the same relationship to arrester rating as “maximum line-line voltage” in an ungrounded system.

An “effectively grounded” system was then defined in terms of the symmetrical-component sequence resistances and reactances, for which the TOV on an unfaulted phase does not exceed 80% of the maximum line-to-line voltage. Under this condition, an arrester rated at 80% of maximum line-to-line voltage was deemed applicable, and it was classified as a “grounded neutral” arrester.

The use of a “grounded neutral” arrester with lower protective levels enabled designs in some electrical equipment, such as transformers, to have reduced insulation levels with adequate protection. Reduced insulation allowed reduction in size, weight, and cost. Subsequently, still lower rated arresters were commonly applied whenever the grounding was significantly better than “effective,” particularly at system voltages where these reductions were significant (above 230 kV).

Usually the TOV produced by a system ground fault is greater than that produced by other causes (generator overspeed, ferroresonance, harmonics, etc.). An exception to this might occur on systems where the coefficient of grounding is less than 80%. The rating of gapped silicon-carbide surge arresters generally exceeded the TOV due to a phase-to-ground fault on the system where it was applied.

This criterion was based on the assumptions that the maximum TOV is produced by a ground fault and that the arrester might operate due to a surge while there was a ground fault on another phase. The arrester had then to seal off against the TOV, which was sustained until the fault was interrupted.

There were some arresters that sealed off against voltages higher than their rating. Overvoltage characteristics for these arresters were published in the late 1960s or early 1970s. This feature has sometimes been utilized to provide lower protective levels.

An important consideration for selecting a metal-oxide arrester is the maximum continuous operating voltage (MCOV); however, the arrester will also be subjected to TOVs. A conservative criterion is that the TOV should not exceed the duty cycle voltage rating of the arrester. However, metal-oxide arresters can have thermal capability for TOVs in excess of the duty-cycle rating for specified times, and data and curves of TOV versus allowable time of the overvoltage are available.

EXTERNAL FUSE SELECTION AND OPERATION OF SHUNT CAPACITOR BANKS


IEEE Std C37.48-1997 covers in detail the application guidelines for high-voltage external capacitor fuses.

The energy stored in the healthy capacitors of one series group of parallel-connected capacitors will discharge into the failed capacitor unit of that group and its fuse. The fuse shall be able to interrupt the energy supplied by the parallel group of capacitor units when they are charged to their peak voltage.

If the capacitor bank design has an available discharge energy higher than the capacitor units or expulsion fuses can withstand, current-limiting fuses with adequate energy rating should be considered. When ungrounded wye capacitor banks are supplied in an enclosure, current-limiting fuses shall be used to eliminate the arc products that occur with the use of an expulsion fuse.

These arc products in the confined enclosure could cause further evolution of the fault. Current-limiting fuses may also be required on enclosed single-group ungrounded wye banks that are designed with two bushing units. In this design, the first bushing is used for the phase connection, the second bushing used for the neutral connection, and the case connected to ground.

This arrangement requires the capacitor fuses to interrupt system fault current in the event of a failure of the unit insulation near the phase bushing. NEMA CP1-1988 [B11] suggests a parallel energy limit of 15 kJ (4650 kvar) for all film dielectric capacitors.

Expulsion fuses are frequently applied with higher parallel energy (to 30 kJ) (Mendis et al. [B9]). This higher energy application is acceptable if the total available discharge energy of the bank does not exceed the discharge energy rating of the fuse or the capability of the faulted capacitor unit.

To determine proper fuse selection, the capacitor unit case rupture curve shall be available from the manufacturer.

Case rupture curves are different for different capacitor unit constructions and designs. The total clearing curve of the fuse or fuse link is then compared to the case rupture curve; adequate protection is assured if the total clearing curve of the fuse is to the left of and below the rupture curve of the capacitor unit.

Other important considerations for external fuse selection and operation include the following:

— Fuses should be designed and rated for the externally fused capacitor bank application.
— Fuses should provide for the fast isolation of a faulted capacitor unit.
— Voltage interruption capability of the fuse shall be coordinated with the voltage withstand capability of the capacitor unit.
— Fuses shall handle the transient inrush and outrush current.
— Fuses shall be designed for the current loadability requirements, including harmonics and adequate allowance factors.
— Fuses shall be designed for the inductive and capacitive current interruption capability.
— Fuse characteristics shall coordinate between the different shunt bank protection schemes and the characteristics of the fuses (that is, expulsion, current-limiting, or a combination of both).

NEUTRAL GROUNDING OF CAPACITOR BANKS – AN INTRODUCTION


The application of large shunt capacitor banks with switched parallel banks in high-voltage transmission systems involves a number of considerations, one of which is grounding. It is generally recommended that the neutral of capacitor banks be grounded only to systems that are effectively grounded.

In the event of a phase-to-ground fault, a grounded capacitor bank neutral in an otherwise ungrounded system may lead to high transient overvoltages in the system and capacitor bank as a result of restriking of the arcing fault to ground.

One of the main advantages associated with neutral grounding concerns the severity of the recovery voltage across the first pole of the switch to clear, interrupting the charging current of the capacitor bank.

The recovery voltage across the first pole to open consists of trapped charges on the capacitors and the variation in the 60 Hz voltage of the system. Due to system parameters and capacitor bank size, the recovery voltage can be approximately two times normal peak voltage when the bank is grounded.

On an ungrounded bank, the magnitude of the first peak of the recovery voltage can be as high as three times the peak system line-to-ground voltage when the bank is switched. Because recovery voltage is a critical factor in determining the capability of a switching device to switch capacitive reactive power, it may be desirable (in terms of switch performance) to ground the neutral of shunt capacitor banks.

IEEE Std C37.04-1979 and ANSI C37.06-1997 recommend that both the shunt capacitor bank and the system be grounded at voltage levels of 121 kV and above. Many capacitor banks of higher voltage are installed ungrounded, but the circuit breaker manufacturer should be consulted for the application of a breaker if these conditions are not met.

While many shunt capacitor banks are directly connected to a high-voltage substation bus, switched capacitor banks may be applied to tertiaries of power transformers that are connected to the line or possibly to the bus. Grounding the neutral of the wye-connected capacitor bank should be done only on an effectively grounded system.

For instance, the delta tertiary of the auto transformer represents an isolated source; grounding the capacitor bank neutral makes this side of the transformer capacitively grounded. Overvoltages may be experienced during line-to-ground faults for certain ratios of X0/X1, depending on system, transformer, and capacitor bank parameters.

If the neutral is to be grounded on a system that is not effectively grounded, the application should be thoroughly analyzed for proper application of surge arresters, bank configuration, bank switching devices, etc.
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