Electric Power
AC versus DC
Warning: Alternating currents (AC) pose significant dangers and are primarily suited for applications like the electric chair The only commonality between AC and direct current (DC) lighting systems is their origin from the same coal source.
And thus did Thomas Edison try to discourage the growing use of alternating-current electric power that was competing with his DC
Edison established the first true central generating station at Pearl Street, New York City, utilizing direct current (DC) to manage generators and maintain a battery supply during low demand However, the limited voltage of DC restricted the geographic expansion of electric utilities, despite its suitability for local generation, which led to a rapid increase in electric power usage Direct current motors began to replace steam engines in various industries, allowing individual machines to operate independently without relying on belting to a line shaft Early generators primarily used low-speed reciprocating steam engines, particularly double-expansion designs, which enhanced efficiency by exhausting steam from a high-pressure cylinder to a low-pressure cylinder.
Generators operating at 7500 hp and 75 rpm were driven at higher speeds than the engine using pulleys and belts Typically, storage batteries supplied excitation to the generators and were charged by a smaller generator DC machines could be easily paralleled by aligning the incoming machine's voltage with the bus voltage before switching it in, while load sharing was managed through field control.
For several years, alternating-current (AC) generators were developed, but the advancement of AC power was hindered by the absence of effective AC motors While low-frequency AC could operate commutator motors, which were essentially direct current (DC) machines, attempts to utilize higher AC frequencies to reduce lamp flicker proved unsuccessful Additionally, early AC generators faced challenges in being paralleled, necessitating that each generator be connected to a specific load and remain online continuously, eliminating the possibility of battery backup or operation at light loads Moreover, the generation and utilization voltages of AC systems were comparable to those of DC systems.
AC offered no advantage in this regard.
Pivotal Inventions
The invention of the transformer by George Westinghouse, who acquired the patent rights from Gaulard and Gibbs, marked a pivotal moment in the adoption of alternating current (AC) power This technology enabled AC electricity to be transmitted at high voltages and then transformed for safe low-voltage use, significantly reducing power losses and allowing generation at remote locations This advancement facilitated hydroelectric power to reach industries and households far from the generation site An early example of AC generation and distribution was implemented by Westinghouse expert William Stanley in Great Barrington, MA, in 1886, where a Siemens generator supplied power to 200 lamps at a distribution voltage of 500 V.
Nikola Tesla, a talented engineer working for Westinghouse, invented the induction motor, which initially featured two-phase power designs before advancing to three-phase systems Three-phase transmission became the preferred method due to its efficiency in reducing copper usage for power transmission The robust and straightforward design of the induction motor facilitated its rapid production and played a crucial role in the adoption of alternating current (AC) technology.
The induction motor revolutionized electric power in the industry by eliminating the need for complex starting mechanisms, being cost-effective, and performing reliably in challenging environments Coupled with transformers, these innovations significantly contributed to the swift expansion of alternating current (AC) power systems.
In 1893, Westinghouse showcased the superiority of AC power by illuminating the Columbian Exposition in Chicago with a two-phase system, transforming night into day To work around Edison's patents on the glass-sealed incandescent lamp, Westinghouse created a stopper lamp using sealing wax, which, while not commercially successful, effectively demonstrated the potential of electric lighting This stunning display captivated visitors, many of whom experienced electric light for the first time.
A significant breakthrough in AC generation and transmission occurred with the installation at Niagara Falls, where the immense power potential had long been acknowledged Various methods, including compressed air and mechanical systems, were proposed to harness this energy Ultimately, a comprehensive study led to the successful installation by Westinghouse, marking a pivotal moment in the utilization of hydropower.
In 1895, AC generators utilizing a 25-Hz two-phase system were developed, incorporating transformers and transmission lines to power multiple factories The decision to use a 25-Hz frequency, rather than the increasingly popular 60 Hz, was driven by the needs of various process industries that required substantial amounts of DC power, which rotary converters at the time could not efficiently handle at 60 Hz.
In the 1890s, frequencies of 40, 50, and 133 Hz were commonly utilized, with 50 Hz remaining in use on the Southern California Edison System until the mid-20th century Additionally, several utilities continued to supply 25-Hz power well into the late 20th century.
Generation
Slow-speed reciprocating steam engines increased in size to meet rising power demands, reaching a peak of approximately 7500 horsepower While some high-speed steam engines were utilized in England, a significant disparity often existed between the optimal speeds for the engines and those required for generators By the early twentieth century, the large steam engines in operation exemplified this trend.
Electric Traction
The introduction of steam turbines directly connected to generators addressed the disturbances caused by earlier systems, significantly improving energy generation The pivotal moment came in 1901 with the installation of a 2000-kW, 1200-rpm, 60-Hz turbine generator set in Hartford, CT, which catalyzed the transition to steam turbine technology This advancement led to the development of steam turbine generators capable of producing over 1500 MW, marking a significant evolution in power generation.
Hydroelectric generation has seen significant growth, with Hoover Dam generators initially rated at 87 MVA each, later upgraded to 114 MVA The Grand Coulee Third Powerhouse boasts massive generators rated at 700 MW each, contributing to a total generation capacity of 6480 MW This concentration of hydroelectric power has enabled economies of scale, leading to reduced generation costs and attracting energy-intensive industries, such as large-scale aluminum reduction plants, to remote areas.
Siemens developed a DC motor in Germany for powering trams, replacing horses on surface lines and enabling the expansion of extensive subway systems While DC distribution challenges arose, they were less severe than in residential applications due to the higher voltage of 600 V used in traction systems Initially, these systems relied on DC generation and distribution, but by the turn of the century, the trend shifted towards AC generation and high-voltage distribution, with rotary converters at local substations converting to DC for trolley wires and subway third rails In 1903, the Interborough Rapid Transit Company in New York implemented a system utilizing 11,000-V, 25-Hz, three-phase power for distribution alongside a 600-Vdc system.
The new subway cars utilize an electric power third rail pickup system Notably, the directors opted for reciprocating steam engines instead of turbines for power generation, although they did incorporate several small turbine sets for lighting and excitation purposes.
The advent of electric power revolutionized transit by enabling the establishment of interurban trolley lines, leading to the expansion of extensive trolley networks that connected numerous small communities By the early 1900s, these systems offered a more cost-effective alternative to steam trains, significantly enhancing regional connectivity.
AC generation and distribution utilized rotary converters to provide DC power to trolley wires The rise of well-constructed roads and dependable automobiles led to the decline of interurban transit lines, with many disappearing by the mid-20th century.
The New York New Haven and Hartford Railroad utilized 11,000-V, 25-Hz three-phase power for main-line traction, employing transformers on locomotives to power traction motors at 250 Vac, which then operated on a 600 Vdc third-rail for underground travel into Manhattan This power distribution system is still in use today by Amtrak on the Northeast Corridor, where catenary is supplied at 25 Hz via solid-state cycloconverters connected to a 60-Hz utility system Various pioneering electric railroads in the USA also implemented 3000 Vdc catenary and three-phase 25-Hz AC systems, showcasing a wide range of AC and DC power configurations, including 16-2/3 Hz, for traction worldwide However, most electric locomotives have been replaced by diesel electrics, which provide lower operating costs and reduced overhead, except for commuter lines and specialized installations.
Electric Utilities
Utility operations are usually considered in the three classes of gen- eration, transmission, and distribution, although recent deregulation
1.5 Electric Utilities 7 has separated generation from the latter two Figure 1.2 shows a typ- ical hierarchy of voltages and loads Transmission lines carry the power over the longer distances to substations that step the transmis- sion voltage down to a sub-transmission level Some high-voltage transmission lines are also the interconnect points between utilities in a regional grid High-power loads, such as electric arc furnaces and electrochemical plants, may be fed directly from the transmis- sion system Others are fed from the subtransmission system or from distribution feeders that supply small industries as well as commer- cial and residential loads The electric utility systems in this country have grown to a generation capacity of more than 1000 GW at this date Steam turbines, coal or nuclear powered, and hydraulic tur- bines supply the vast majority of the motive power for generators, but natural gas fired combustion turbines are growing rapidly as environmental concerns limit additional coal and nuclear power. Much lower levels of power are produced by wind farms, although this area is expanding as the art progresses Still lesser amounts of power are produced by reciprocating diesel engines in small munici- pal utilities.
F IGURE 1.2 Typical section of a utility.
The national transmission system operates through regional power pools of interconnected utilities, while generation is now managed by numerous independent operators due to government regulation Over the years, transmission voltages have increased, reaching around 230 kV, but the construction of the Hoover Dam significantly enhanced Los Angeles' energy supply with hydroelectric power When completed in the late 1930s, the transmission line from the dam was the longest and highest voltage line in the country at 287 kV Extensive research focused on the insulation system and conductor design to reduce corona losses, leading to the introduction of progressively higher transmission voltages and the development of switchgear standards.
Extra high voltage (EHV) transmission lines, defined as those operating at or above 500 kV, play a crucial role in power distribution A significant EHV project in the U.S is the 905-mile Pacific Intertie, which connects the Bonneville Power Administration in Washington to the Los Angeles area, utilizing two 500-kV transmission lines to deliver approximately 2500 MW of hydroelectric power from the Columbia River Additionally, Hydro-Québec manages an extensive network of 765-kV transmission lines that transport hydroelectric power from northern Québec to various load centers across Canada and the U.S.
Transmission lines are typically identified by their nominal voltage, but they are engineered to withstand a specific basic insulation level (BIL) to account for lightning strikes and switching transients Lightning strikes can reach voltages of 5 MV and currents of 220 kA, with a maximum rate of change of 50 kA/µs, posing a significant risk of damage For protection against such events, lightning arresters are utilized, as detailed in Chapter 2.
High-voltage DC (HVDC) transmission lines have emerged due to advancements in power electronics, offering significant advantages over traditional AC lines Unlike AC systems, HVDC lines are not affected by capacitive effects or phase shifts, which can lead to regulation issues and compromise system stability during faults One of the first HVDC transmission lines was established between BPA sites in Washington and Sylmar, California, just north of Los Angeles.
1.5 Electric Utilities 9 les, to supplement the AC Pacific Intertie It is rated 1200 MW at ±400 kVdc The converter station at Sylmar was originally built with mercury vapor controlled rectifiers but was destroyed by an earth- quake It was rebuilt as one of the early silicon controlled rectifier (SCR) converters used in HVDC service Some other large HVDC installations are in Japan from Honshu to Hokkaido; in Italy from the mainland to Sardinia; and between North Island and South Island in New Zealand Hydro-Québec operates an HVDC system, ±450 kV,
The 2250 MW power transmission begins at the Radisson station near James Bay and travels 640 miles to a 1200-MVA converter station in Nicolet From there, it continues for 66 miles to a 400-MVA converter station at Des Cantons, which serves as an interchange point to the New England Power Pool in Vermont The route then proceeds through Comerford, NH, before reaching its final destination at the Ayer (Sandy Pond) converter station in Massachusetts, located northwest of Boston This journey illustrates the full cycle of DC power transmission.
Residential electric utility customers are typically charged based on kilowatt hours without considering their power factor, while industrial customers face a two-part billing system They are billed for energy consumption measured in kilowatt hours, currently costing around 3 to 5 cents per kilowatt hour, which covers the utility's fuel costs for coal, gas, or oil, as well as some infrastructure expenses It's important to note that even hydroelectric power incurs costs.
Demand charges on utility bills are typically based on the maximum half-hour average kilowatt load during the billing period, as recorded by a demand register on the kWh meter This demand is then adjusted upward according to the average power factor for the month, with typical charges ranging from $5 to $15 per month for each power factor adjusted peak kilowatt demand These charges are essential for maintaining the transformers, transmission lines, and distribution systems that facilitate power delivery, emphasizing the importance of amperes in the delivery process Additionally, demand charges serve as a significant incentive for industrial users to manage their power consumption effectively.
Improving power factor can lead to significant savings for Electric Power customers, as the installation of capacitors often results in a quick return on investment However, billing practices vary widely among electric utilities across the country Utility representatives are typically willing to offer guidance on strategies to reduce power bills For more detailed information, refer to Chapter 14.
The U.S is facing a significant challenge with the increasing demands on its transmission system, exacerbated by the deregulation of the energy market Previously, utilities managed their own power generation and transmission, ensuring stability through interconnections However, the current market dynamics have led to remote power generation, overloading transmission lines and compromising system stability Public opposition, known as NIMBY (Not In My Backyard), has made it difficult to construct new transmission lines, and utilities lack incentives to build lines for power they cannot charge customers for Despite these hurdles, enhancing transmission capacity is essential for ensuring reliable interconnected systems.
On August 14, 2003, a significant power outage affected the entire northeastern U.S., leading to billions in lost production and revenue The outage was primarily due to inadequate maintenance of transmission line rights of way by an Ohio utility While concerns were raised about the outdated transmission system, it's important to note that the electric utility industry has maintained a commendable reliability record despite the challenges posed by deregulation Moving forward, the industry faces the critical challenge of improving this reliability even further.
The development of FACTS (Flexible AC Transmission Systems) converter systems has significantly enhanced system stability These power electronics control systems enable rapid adjustments in system voltages and phase angles, ensuring that voltages are stabilized during fault conditions.
In-Plant Distribution
Damping oscillations is possible, ensuring system stability even under increased transmission line loadings FACTS installations can help avoid or postpone the necessity for additional transmission lines, which are often challenging to install due to environmental issues, permitting processes, and right-of-way expenses.
Power distribution systems in industrial plants exhibit significant diversity, with several common configurations At the lower end, 120/240-V single-phase systems are used for lighting loads at 120 V and small motors at 240 V The 120/208-V three-phase distribution is popular for lighting and can also power three-phase motors rated at 208 V, as many induction motors are dual-rated for 208/240 V For safety, the 120/208-V neutral is typically solidly grounded The 277/480-V distribution system is favored in medium-sized industrial plants, with a solidly grounded wye secondary neutral, although resistance or reactance grounding may be employed In Canada, the most prevalent distribution voltage is 600 V.
Many older plants utilize a 2300-V three-phase delta-connected system, typically without grounding, though some may ground one corner of the delta For the next higher power level, the 2400/4160 V distribution system is the most commonly used At even higher power levels, older plants frequently adopt different configurations.
The trend in electrical distribution systems is shifting towards 13.8 kV in newer plants, moving away from the traditional 6900 V or 7200 V options For lower power applications, utilities typically install fused distribution transformers, while higher power installations often employ padmount transformers equipped with circuit breakers and protective relays for enhanced safety and efficiency.
A medium-sized plant typically organizes its power distribution by routing incoming electricity to various distribution centers, referred to as load centers or motor control centers These centers feature multiple circuit breakers or load break switches housed in metal cabinets, with some sections including controls for motor circuits.
Electric power protective relays and instrumentation are essential for managing lighting circuits within a building These circuits, operating at 120/208 V, are organized in panel boards, each featuring a master breaker that controls multiple molded case circuit breakers Lighting panelboards typically range from 100 to 400 A, accommodating individual lighting circuits of 20 to 30 A, while air conditioning and similar loads require higher current ratings.
Internal wiring practices utilize plastic or metal conduits and cable trays for effective conductor management Conduits are ideal for lower power levels, offering protection against water and mechanical damage by housing conductors in rigid tubing In contrast, cable trays are preferred for higher power levels, accommodating a wide range of conductor sizes secured to prevent movement during faults These trays feature open construction with simple angles and cross braces, promoting ventilation When running high- and low-voltage circuits together in either conduits or cable trays, it's essential that all conductors are rated for the highest voltage present.
Emergency Power
When planning for emergency power, it's crucial to consider three levels of reliability, starting with the essential power needed for emergency exit signs and interior lighting during outages Typically, this power is provided by an automatic natural gas engine generator set that activates during an external power failure, although battery backups can also be utilized For larger facilities, diesel engine-generator sets may be employed A brief power interruption is generally acceptable for these systems, but regular testing is vital to ensure they function properly when required.
The second reliability level of emergency power ensures continuous operations in industrial plants, where production losses can be costly This is typically achieved by supplying two distinct power feeders from separate utility lines To facilitate a seamless transition between power sources, transfer breakers are employed to switch from a failing circuit to an operational one, minimizing any momentary power interruptions.
1.7 Emergency Power 13 ruption may be acceptable with only a minor inconvenience to pro- duction Diesel engines or combustion turbines and generators may also be used for plant generation where warranted If a momentary outage cannot be tolerated, solid-state transfer switches can be used for subcycle switching.
Critical operations, such as data processing centers and semiconductor fabrication plants, demand the highest level of reliability, as even brief power interruptions can lead to significant financial losses To ensure uninterrupted power supply, fuel cells powered by natural gas are increasingly being utilized to generate DC power, which can be converted to AC using power electronics for plant operations This system allows for critical loads to receive power from dual sources, including utility supply, managed by solid-state transfer switches Additionally, any surplus power generated by the fuel cells can potentially be sold back to the utility, making this approach a versatile and efficient solution for maintaining continuous operations.
Power Apparatus
Switchgear
Switchgear refers to the equipment used to connect and disconnect power circuits, encompassing a wide range of devices from small molded-case circuit breakers found in household panelboards to large air break units.
Power apparatus switches for 750-kV transmission lines are categorized into four main groups: disconnect or isolator switches, load break switches, circuit breakers, and contactors Disconnect or isolator switches are specifically designed to connect or disconnect circuits under no load or very light loads, possessing minimal arc-quenching capability These switches primarily interrupt transmission line charging currents or transformer exciting currents and are typically the most cost-effective option Mechanically, they are engineered to maintain sufficient contact pressure during fault currents, counteracting the high mechanical forces involved Various designs exist, including simple knife switches with multiple leaves for contact, over-center latches, and clamping locks that engage at the end of the closing cycle All types operate in air, feature visible contacts for safety, and include lockout provisions, while low-voltage safety switches depend on handle position for safety.
Medium- and high-voltage disconnect switches are available as indoor designs that are typically mounted in metal switchgear enclo-
2.1 Switchgear 17 sures or as outdoor switches incorporated into elevated structures. Both horizontally and vertically operating switches are available in outdoor designs, and most are available with motor operators Some have optional pneumatic operators.
Load break switches are similar in design to disconnect switches but include arc chutes that allow them to interrupt the designated current Unlike circuit breakers, they are not intended to interrupt fault currents and must stay closed during such events Many designs offer motor operators, making motor-operated load break switches a cost-effective solution for applications that require remote control.
Circuit breakers are robust components of switchgear, designed to handle both continuous load currents and maximum fault currents Smaller breakers utilize arcing contacts in air, while larger models operate in vacuum or oil environments, and high-voltage utility breakers may use sulfur hexafluoride (SF6) gas Most circuit breakers feature a stored energy operating mechanism that employs a motor to wind a heavy spring, which is then quickly released to separate the contacts during a trip operation This process typically clears the circuit within 3 to 5 cycles to effectively reduce arc heating and contact erosion Indoor circuit breakers are generally housed in metal cabinets as part of a switchgear assembly, while outdoor breakers can function as standalone units.
When specifying vacuum circuit breakers, caution is essential due to the behavior of the chop current, which can reach levels of 3 to 5 A Initially, the voltage across the contacts is low, but as the current diminishes, it is abruptly extinguished with a high di/dt If the breaker is positioned before a transformer, this high di/dt can induce a significant voltage through the transformer's exciting inductance, potentially affecting secondary circuits To manage this voltage, implementing arresters on the primary side or utilizing metal oxide varistors is advisable.
To ensure optimal performance, power apparatus varistors (MOVs) should be installed on the secondary side of the transformer These MOVs need to be rated to handle the transformed chop current at their specified clamping voltage Additionally, they must be capable of repeated operations while dissipating half of the LI² energy from the primary inductance, where I represents the chop current.
Molded case breakers feature self-contained thermal and magnetic overload elements, rated by maximum load current and interrupt capacity Thermal breakers utilize selectable heaters for overload protection, while larger breakers rely on external protective relays for both overload and short circuit protection through time over-current and instantaneous elements, typically operated by solid-state current transformers Due to their heavy operating mechanisms, circuit breakers are not designed for frequent use and have a maximum number of recommended operations before requiring inspection and potential repairs Additionally, after clearing a fault, it is essential to inspect breakers for arc damage or mechanical issues.
Contactors are essential components of switchgear, functioning as electromagnetically operated switches for motor starting and general control, capable of enduring thousands of operations They utilize air breaks for low voltages and vacuum contacts for medium voltages, typically featuring continuously energized operating coils that disengage when control power is lost Motor starters can manage overloads exceeding five times their rated capacity, while lighting contactors are designed with overload ratings for incandescent lamps The operating coils possess a magnetic circuit characterized by a large air gap when open and a minimal gap when closed, often experiencing a high inrush current upon activation It is crucial for the control power source to accommodate this current without significant voltage drops, and some contactors offer optional DC coils that incorporate a current-reducing resistor into the control circuit during closure.
Surge Suppression
Electrically operated switchgear, including breakers and contactors, can generate high voltages in control circuits when interrupted, necessitating the use of R/C transient suppressors for effective design While MOVs can limit the voltage during operation, they do not mitigate the di/dt that could disrupt other circuits Contactors can be installed either within equipment cabinets or as standalone units.
Transient overvoltages can originate from various sources, primarily due to power disturbances caused by lightning strikes or switching operations on transmission and distribution lines A significant contributor to these switching transients is the operation of power factor correction capacitors aimed at voltage control Utility lines are engineered with a specific basic insulation level (BIL), which defines the maximum surge voltage that can be tolerated without damaging utility equipment, although this voltage may still affect customers When dealing with high-power electronics that are directly connected to medium-voltage utility lines, it is crucial to consider the supply system's BIL, with relevant information typically obtainable from utility representatives The standard test waveform used to determine BIL capability features a voltage that rises to the instantaneous BIL value in 1.2 microseconds and then decays to half that value in an additional 50 microseconds.
Transient overvoltages can originate from power electronics equipment, including interruptions in contactor coils and reverse recovery current transients from diodes and SCRs Additionally, arcing loads may necessitate shielding for control circuits Overall, implementing a robust grounding system can significantly reduce these issues.
Surge protection devices vary widely, from small discs in 120-V power strips for computers to large lightning arresters used on 765-kV transmission lines Many of these devices incorporate the nonlinear properties of metal oxide varistors (MOVs), which are made from zinc oxide (ZnO) ceramic materials and offer effective surge protection.
As the applied voltage to power apparatus increases, the leakage current rises until it reaches a threshold, causing a rapid increase at higher voltages The operating voltage is determined by the thickness of the ceramic disk and the processing methods used To achieve higher voltages, metal oxide varistors (MOVs) can be stacked in series, while stacking them in parallel allows for handling higher currents.
Lightning arresters are categorized based on their current rating at specific clamping voltages, with station-class arresters managing the highest currents for utility transmission and subtransmission lines Intermediate-class arresters, featuring lower clamping abilities, are utilized in substations and certain power electronics connected to them, while distribution-class arresters, with the lowest clamping currents, are employed on distribution feeders and smaller power electronics The cost of arresters correlates with their clamping current ratings, which are designated by class and maximum continuous operating voltage (MCOV) Typically connected line-to-ground, lightning arresters are essential for protecting dry-type transformers in power electronic equipment, especially when these transformers have a lower Basic Insulation Level (BIL) rating compared to the supply switchgear For instance, in 15-kV-class equipment, switchgear may be rated for BIL levels of 95 or 110 kV, while the transformer could be rated at only 60 kV.
MOVs are essential for protecting power electronics by limiting peak voltage transients to 2.5 times their maximum continuous rated RMS voltage In three-phase circuits, they can be connected line-to-line or line-to-ground; line-to-line connections effectively limit switching voltage transients but fail to guard against common-mode transients Conversely, line-to-ground connections protect against common-mode transients but are less effective against applied line transients For optimal protection in environments prone to severe lightning or switching transients, employing both connection types may be necessary It's crucial to verify the volt-ampere curves of the MOV to ensure it can handle sufficient current at the maximum tolerable circuit voltage for the expected transient energies.
Conductors
MOVs come in various sizes and diameters to meet diverse design requirements Smaller units feature wire leads, while larger models are housed in molded cases equipped with mounting feet and screw terminals for easy connections.
Surge capacitors are essential components in protecting transformers and motor windings from transient voltages with rapid rise times, which can cause uneven voltage distribution due to turn-to-turn and turn-to-ground capacitance effects By slowing the dv/dt, surge capacitors help minimize overvoltages at the winding ends, typically ranging from 0.5 to 1.0 µF for medium-voltage applications However, caution is necessary when using them with SCR circuits, as they may lead to significant overvoltages from ringing, potentially requiring the addition of damping resistors.
Current-carrying conductors vary from small household wires to large bus bars capable of handling several hundred kiloamperes Copper is the primary choice for conductors, while aluminum is frequently utilized for bus bars and transformer windings The cross-sectional areas of smaller conductors are indicated by the American Wire Gauge (AWG) number, where a decrease of three numbers signifies a doubling of the cross-sectional area, with sizes reaching up to #0000 (four aught) For larger conductors, cross sections are measured in circular mils, calculated as D², where D represents the conductor diameter in thousandths of an inch; for instance, a conductor with a diameter of 1/2 inch equates to 250,000 circular mils.
250 kcm, although older tables may use 250 mcm For noncircular conductors, the area in circular mils is the area in square inches times (4/π) × 10 6
High-current conductors are usually divided into a number of spaced parallel bus bars to facilitate cooling A rough guide to current
The power apparatus capacity under standard conditions is rated at 1000 A/in² of cross-section To prevent issues from differential expansion between conductors and fastening bolts, connections between bus bar sections must be carefully designed, considering the thermal effects of current and ambient temperature Silicon bronze bolts are ideal due to their compatible temperature expansion with copper and adequate strength for secure connections Alternatively, reliable joints can be achieved using steel bolts paired with heavy Belleville washers and larger-diameter steel flat washers, ensuring the Belleville washer is flattened during tightening Ordinary split washers are not advisable While stainless steel hardware is recommended for high magnetic fields, it is typically unnecessary for the bus's own magnetic field, though environmental conditions may warrant its use.
To ensure optimal performance, all joints in buswork should be thoroughly cleaned and free of grease Utilize fine steel wool for cleaning and apply a commercial joint compound before bolting For aluminum bus, it is essential to remove all oxide and promptly protect the surface with an aluminum-rated joint compound to prevent further oxide formation.
Control wiring typically consists of bare copper stranded conductors with 300- or 600-V insulation, predominantly made from polyvinyl chloride (PVC) These conductors are usually certified by Underwriter’s Laboratories or the Canadian Standards Association, and equipment standards mandate that labeled wire display a UL or CSA listing number, along with the AWG gauge and insulation temperature rating Adhering to the National Electric Code is essential for determining the appropriate current rating of these conductors While power wiring shares similarities with control wiring, it is generally larger in size Additionally, cabinet wiring is often restricted to approximately 250 kcm due to the required bending radii, although specific regulations may vary.
The article outlines essential specifications for appliance wire, including vendor identification, wire size, voltage rating, fire retardant class, insulation temperature, and relevant listing agencies such as Underwriters Laboratories (UL) and the Canadian Standards Association (CSA) It also highlights the appliance wire listing number, its potential use as control circuit wire, maximum operating temperature, and listing identification.
Stranded conductors must be terminated using pressure-swaged crimp connectors, which can then be securely bolted to bus work or terminal blocks For circuit breakers and other power devices, it's important to utilize fastening provisions like clamp plates or pressure bolts with rounded ends, while avoiding the use of swaged connectors on these terminals Additionally, fine-strand, extra-flexible welding cables should not be paired with clamp plates; instead, pressure-crimped connectors are essential for reliable connections.
Medium-voltage conductors rated for 7.5 kV can be either shielded or unshielded, while higher-voltage cables must be shielded unless adequately spaced from other conductors and ground, adhering to established standards Shielded conductors consist of a central current-carrying conductor, an insulating layer, and a conductive shield, all covered by an insulated protective layer, with the shield grounded to ensure a uniform radial electrostatic field and prevent insulation voids that could lead to corona deterioration Terminations utilize stress cones, which gradually increase the insulation radius to the shield while maintaining void-free conditions; once the radius sufficiently reduces voltage stress, the shield can be terminated, allowing for the attachment of conventional terminal lugs Some stress cones incorporate shrink-fit tubing or silicone grease to further eliminate voids.
The forces acting between current-carrying conductors increase with the square of the current, making it crucial to brace against fault currents in high-power equipment Electronic systems, like motor starters directly linked to power lines, are particularly vulnerable to elevated fault currents Additionally, circuit breakers can take several cycles to trip, rendering them ineffective in immediate fault scenarios.
Power apparatus plays a crucial role in limiting initial fault currents, as traditional fuses often have prolonged melting times and are ineffective in this regard In contrast, semiconductor-type fuses can melt within a subcycle, effectively limiting fault current levels that would otherwise depend on the prospective fault current without a fuse Additionally, the force generated between two parallel round conductors, spaced d inches apart, can be measured in pounds per linear foot.
The force (F) acting on conductors is calculated using the formula F = 5.41 I² × 10⁻⁷ /d, where I represents the rms fault current in each conductor This force is influenced by the geometry of the conductors, with attractive forces occurring when currents flow in the same direction and repulsive forces arising when the currents have opposite polarities.
When equipment is powered by an internal transformer rated for the load current, the steady-state fault current typically does not exceed twenty times the rated current However, an inductive source can produce an asymmetric fault current that may theoretically reach up to twice the steady-state peak value Due to L/R current decay, a peak of approximately 1.5 times the steady-state peak is more probable, yet this still permits a fault current exceeding twice the steady-state peak, as the force is proportional to the square of the current Circuit breakers are designed to handle these variations effectively.
F IGURE 2.3 Stress cone termination for shielded cable.
2.3 Capacitors 25 a maximum peak current that will allow them to close and latch the mechanism
High-current conductors often employ liquid cooling, featuring copper tubing soldered or brazed into grooves along the bus edge This method effectively transfers heat to water, reducing air temperature within power electronics cabinets Additionally, liquid cooling contributes to cost savings on copper materials.
High levels of AC currents in buswork, particularly those with significant harmonic content, can lead to parasitic heating in nearby steel cabinet components due to induced eddy currents To mitigate this issue, one effective approach is to substitute cabinet sections with materials such as stainless steel, aluminum, or fiberglass Alternatively, placing a copper plate between the bus and the problematic cabinet member can also help; while the copper will experience high eddy currents, its low resistance will reduce losses This setup allows the eddy currents in the copper to produce a counteracting flux, effectively shielding the steel cabinet from heating.
Capacitors
The three main types of capacitors are film dielectrics, electrolytics, and ceramics Film capacitors are primarily used for power factor correction and R/C snubbers, while electrolytic capacitors are favored for filters due to their high energy storage capacity in a compact size However, electrolytics are limited to about 500 V and are typically rated for DC applications, with drawbacks such as leakage currents and restricted ripple current ratings Their longevity is also a concern, as the electrolyte can evaporate over time, particularly under high ripple currents or elevated temperatures, necessitating careful design considerations for ventilation or heat sinking.
Film dielectric power factor correction capacitors have largely supplanted older paper dielectric types and are rated in kilovars (kvar) at their specified voltage They come in both single units and three-phase assemblies within a single can These capacitors are always equipped with fuses, which can be standard medium-voltage fuses or expulsion fuses for outdoor use Expulsion fuses release a plume of water vapor when the fuse clears a fault, as the ablative material in the fuse tube evaporates.
Capacitors in power systems can lead to issues when harmonics from nonlinear loads are present, as they may create parallel resonance with the utility supply's source inductance This resonance can coincide with harmonic frequencies, potentially causing significant overvoltages or overcurrents To mitigate these risks, it is essential to conduct a harmonic voltage survey prior to the installation of power factor correction capacitors.
Power factor capacitor ratings are detailed in IEEE 18-2002, which specifies that these capacitors can operate at maximum conditions of 110% of the rated rms voltage, 120% of the rated peak voltage, 135% of the rated kvar, and 180% of the rated rms current It is essential to account for any harmonic voltages or currents in these ratings Additionally, when capacitors are paired with a series inductor to create a series resonant harmonic current trap, the voltage increase at power frequency due to the inductor must be taken into consideration Consequently, many third-harmonic filters and certain fifth-harmonic filters may necessitate capacitors with ratings exceeding the nominal circuit voltage.
Energizing a section of a capacitor bank while the rest is operational can lead to harmful transient currents When a single capacitor connects to a power line, surge current is mitigated by the source's impedance However, in a capacitor bank, the only impedance that restricts switching current comes from the minimal inductance and resistance of the buswork between sections, allowing charged capacitors to discharge into the incoming capacitor with minimal current limitation Therefore, it is essential to protect each switched section within a capacitor bank.
2.3 Capacitors 27 with a current-limiting reactor Surge currents should be kept within the instantaneous ratings of the capacitors and switchgear.
Certain capacitors intended for DC applications feature a lengthy cylindrical design, consisting of alternating conductive and dielectric strips rolled together Connections are established at one end of the two conductive strips.
Tab foil capacitors feature a design that includes a dielectric strip with a metal foil or deposited film on one side, allowing for self-healing capabilities in case of internal failures For R/C snubber circuits, capacitors must be rated to handle high RMS currents, typically constructed from aluminum foil strips and film dielectric rolled into a cylinder with axially offset foil layers This extended foil arrangement reduces inductance and minimizes resistive losses by allowing current to flow more efficiently along the edges of the windings It is crucial to note that DC-rated capacitors should not be used for AC applications or R/C snubbers unless they have appropriate AC voltage and current ratings, as snubber capacitors experience repetitive charge and discharge cycles.
28 2 ◊ Power Apparatus results in much higher rms currents than would be expected from their capacitance and applied voltage.
Capacitors can be connected in series or parallel to achieve higher voltages or capacitances, with parallel connections being straightforward However, series connections often necessitate voltage-sharing resistors in parallel with each capacitor, especially when DC voltage components are involved, as these resistors help manage the uneven distribution of voltage caused by varying leakage resistances For film capacitors used in AC circuits, sharing resistors may not be needed To ensure uniform voltage distribution, sharing resistors should have a low resistance to effectively counteract leakage resistance variations, and design guidance is available from manufacturers.
Ceramic capacitors, made from high dielectric constant materials, typically feature smaller capacitances while supporting high voltage ratings These capacitors are known for their low self-inductance, making them suitable for specific applications like snubbers.
Resistors
Power electronic systems utilize various types of resistors, particularly in low-power applications such as R/C snubber circuits, voltage dividers, and damping elements for resonant circuits The primary resistor classes in this range include wirewound and metallized film resistors Wirewound resistors consist of resistance alloy wire wound around a cylindrical ceramic core, with terminal connections welded at both ends Non-inductive wirewound resistors feature two parallel windings in opposite directions to cancel out their magnetic fields Additionally, another construction method involves using an elongated hairpin design, where the loop is anchored at one end and the leads are extended from the other end.
2.3 Resistors 29 being insulated from each other There are many variations on these basic construction techniques Resistors for snubber use, especially with fast switching semiconductors, must have an inductance as low as possible to minimize transient voltages Metallized film resistors utilize a vacuum deposited resistance metal film on a ceramic sub- strate Such metal film resistors have little transient heat storage capacity and are not generally recommended for snubber use The same is true for carbon film resistors Carbon composition types are preferred for low-power snubbers These are made from a bulk carbon cylinder within a ceramic tube.
Ceramic resistors are created in different designs using various conductive ceramics, featuring metallized areas that enable terminal connections through a sprayed conductive metal Their low inherent inductance makes them ideal for snubber applications Additionally, some ceramic resistors are encased in cast metal bodies, which serve as insulated heat sinks to effectively dissipate power.
High-power resistors are designed for efficient cooling and come in various forms, including rectangular conductors of resistance alloy wound into air core cylinders for lower power ranges and stamped sheet metal alloys for higher ratings, often referred to as grid resistors These resistors have historical significance, as iron grid castings were used to start DC motors in trolley cars Additionally, water-cooled resistors, commonly made from stainless steel or Monel tubing, are ideal for applications involving water-cooled semiconductors and compact testing loads in power electronic systems When water flows through these resistors, it can experience a temperature rise of 3.8°C for every 1 kW of power dissipation at a flow rate of 1 gallon per minute, and it is crucial to keep the exit water temperature below 70°C to prevent material leaching from the resistor's interior wall.
Resistors play a crucial role in heating applications across various process industries Globar® silicon carbide resistors, designed as long cylindrical elements, operate at several hundred volts and can achieve temperatures exceeding 1200°C Additionally, sheathed wires, resembling electric stove elements with grounded surfaces, are utilized for processes such as annealing and drying While not classified as resistors, molten glass is highly conductive and is electrically maintained at high temperatures in melters for fiberglass nozzles, bottling lines, float glass, and other glass fabrication processes, with connections established using silicon carbide rods.
Fuses
Electric melters are more environmentally friendly than gas-fired units.
Protective elements are essential in power electronics design, including various types of fuses tailored for specific applications From small glass cartridge fuses for control circuits to medium-voltage options, each type has unique characteristics Control fuses should be rated at approximately 125% of the expected load current, while standard fuses suffice for most control circuits However, slo-blo fuses are recommended for loads like small motors and contactor coils that experience inrush currents.
Semiconductor fuses are specialized devices designed to limit fault currents by clearing them in subcycle time, effectively protecting power semiconductors from load faults Constructed with multiple thin silver links embedded in sand and a binder, these fuses melt rapidly during faults, extinguishing arcs by evaporating the binder and melting the sand They come in various currents, voltages, and case styles, with most featuring a ceramic casing and many designed for direct integration into buswork High-current models are often available as matched units from vendors In pulsed applications, it is crucial not to exceed an rms pulse current of 60 to 70% of the melting current for the pulse duration, while steady-state currents should remain below 80% of the rated capacity.
To ensure the protection of semiconductors, it is crucial that the fuse I²t rating is significantly lower than that of the semiconductor itself Improved coordination in SCR converters can be achieved by fusing each SCR path individually instead of the supply lines This method also provides added protection against internal bus-to-bus faults, especially when the load is capable of sourcing power.
Medium-voltage fuses are categorized into "E" rated fuses, suitable for transformers and general-purpose applications, and "R" rated fuses, designed for high starting current applications like motors These fuses typically mount in clips for easy installation.
32 2 ◊ Power Apparatus assemblies These fuses may be matched in resistance and paralleled by the vendor for higher currents
To ensure optimal performance, all high-current fuses must be securely bolted into sanded buswork using joint compound and adequate pressure to minimize resistance It is essential to note that fuse ratings are based on the expectation that the buswork will dissipate heat from the fuse rather than transfer heat back into it.
Supply Voltages
Power electronics primarily operate at two voltage classes: low-voltage (600 V or less) and medium-voltage (601 V to 34.5 kV) In the U.S., most power electronics are utilized with 600-V, 5-kV, or 15-kV-class supplies, although there are additional applications for other voltage levels.
2400 V and 6900 V, especially in older plants Overseas, many other voltages may be encountered, with 400 V, 3300 V, and 11 kV being popular, all at 50 Hz.
Enclosures
According to NEMA standard ICS 1-110, equipment enclosures are categorized primarily into Type 1, Type 4, and Type 12 Type 1 enclosures serve as general-purpose indoor, ventilated options that safeguard personnel from high voltage exposure and shield equipment from dripping water Type 4 enclosures are watertight and dusttight, suitable for both indoor and outdoor use, while Type 12 enclosures are designed to be dusttight and driptight for indoor settings, with some sections being nonventilated and others potentially ventilated.
Most enclosures are made with 10 to 12 ga steel, although smaller wall mount cabinets may be 14 ga Corners and seams are welded,
Hipot, Corona, and BIL
Free-standing enclosures feature three-point door latches for enhanced security and safety They are designed with welded studs on the rear wall to support a removable panel, allowing for convenient component assembly outside the cabinet To ensure safety, all doors must be connected to the enclosure frame using flexible grounding straps The standard height for free-standing enclosures in the industry is 90 inches.
An effective insulation system must withstand continuous voltage, transient overvoltage, and surge voltage while remaining free of partial discharge under extreme operating conditions The hipot test, usually conducted for one minute at a frequency of 50 or 60 Hz, involves applying voltage between all conductors and ground, ensuring no short circuits or fluctuating leakage currents occur While displacement currents may arise from capacitance to ground, the insulation system must maintain its integrity throughout the testing process.
In the absence of a specific high-potential test specification, a general guideline suggests applying a 1-minute, 60-Hz sinusoidal voltage that is twice the rated RMS voltage plus 1000 V for equipment rated at 600 V or less, and 2.25 times the rated voltage plus 2000 V for equipment rated at 601 V and above.
The capacity to endure surge voltages is characterized by a test wave featuring a 1.2 microsecond rise time to peak and a 50 microsecond fall to half voltage, which helps establish the basic insulation level (BIL) of the system This test involves a single application of the wave, with the primary criterion for success being the absence of breakdown.
The voltage at which corona discharge initiates is identified by observing impulse discharge currents on an oscilloscope as the voltage is gradually increased This threshold is known as the inception level, while the point at which these impulses cease during voltage reduction is referred to as the extinction voltage Commercial corona testers utilize standardized metering circuits to quantify these impulse currents in micro-coulombs of current-time integral.
A simple corona tester can be constructed using a hipot tester, a noise filter, and a coupling circuit The noise filter, made from a high-voltage resistor and capacitor, must maintain current below the hipot tester's maximum rating An RF choke, which can be a small inductor ranging from 1 to 100 mH, along with a low-pass R/C filter, helps eliminate fundamental current interference on the oscilloscope As the voltage increases, corona discharge is indicated by noise spikes Testing can be conducted using twisted hookup wire.
Spacings
Even the lowest-voltage systems require some consideration for the electrical clearances between conductors of different voltage Stan- dards have been developed by the Canadian Standards Association
(CSA), Institute of Electrical and Electronics Engineers (IEEE),
National Electrical Manufacturers Association (NEMA), and Under- writer’s Laboratories (UL) These standards cover everything from PC boards to high-voltage switchgear.
Spacings are generally considered in two classes: strike, the clear- ance through air paths, and creep, the clearance along insulating sur-
Metal Oxide Varistors
The strike capability of an air path between spherical conductors can significantly exceed established standards; however, these standards take into account the realities of sharp-edged conductors, conductor movement during faults, voltage transients, and necessary safety margins.
Similarly, the creep standards recognize that insulating surfaces may become contaminated by conductive dust or moisture
Understanding the standards for medium-voltage transformers connected to customer switchgear is crucial, as the switchgear serves as the first line of defense against lightning and switching transient voltages These transients can affect connected equipment unless it is safeguarded by auxiliary arresters or surge capacitors Therefore, any equipment linked to customer switchgear must adhere to the same standards to ensure proper protection.
Table 2.1 is taken from the Westinghouse document, “Electrical
Clearances for Switchgear,” and, although some years old, it is typical of the several extant standards.
The insulated conductors include extruded insulations, insulating boots, and high-voltage taping The standards recognize that these insulating materials may degrade with continued exposure to high voltages
Metal oxide varistors (MOVs) are components that have a nonlinear
V/I characteristic In the case of varistors used for voltage protection,
T ABLE 2.1 Switchgear Electrical Clearance Standards
Power apparatus designed for power electronics maintains a stable voltage across a broad current range These devices are crafted by pressing and sintering zinc oxide ceramic wafers, with their characteristics influenced by the manufacturing process, diameter, and thickness Available in various sizes, they cater to applications from surface mounting on PC boards to large station-type lightning arresters, with diameters ranging from a few millimeters up to 90 mm.
The V/I curve for a 60-mm diameter, 480-V rated Metal Oxide Varistor (MOV) indicates that the current is only 1 A at a peak voltage of 1000 V and nearly zero at 680 V in a 480-V circuit Importantly, the MOV can limit the peak voltage to approximately 1200 V while handling transient currents up to 1000 A, thereby protecting devices like 1200-V Silicon Controlled Rectifiers (SCRs) from high peak transient currents Typically, MOVs are utilized at their nominal RMS voltage rating and are designed to clamp transients to a peak voltage of 2.5 times their RMS rating.
MOVs have limited power dissipation capabilities and are vulnerable to damage from repetitive transients, such as those generated by SCR commutation Catalogs for MOVs provide lifetime characteristics based on the magnitude and duration of the current When utilized for surge protection, it is crucial to consider these factors to ensure their effectiveness and longevity.
2.11 Protective Relays 37 pressing breaker chop, for example, the maximum lifetime exposure should be calculated so that a suitably sized MOV can be specified.
Protective Relays
Utilities and large industrial plants rely on various types of relays to safeguard their systems and components from fault currents The fundamental type is the overcurrent relay, which comes in multiple styles While all overcurrent relays are designed to trip a breaker when an overcurrent occurs, their timing varies significantly across different models These relays range from inverse to extremely inverse in design, typically tripping with a delay for low-current faults but responding more rapidly as the fault current increases.
Many modern circuit breakers feature an auxiliary instantaneous element that triggers during subcycle events Most of these devices are electronic, drawing power from the protected circuit They are typically arranged in a cascading manner with progressively lower trip current settings as the system extends from the source to the load through various buses and breakers This design enables quick clearing of overcurrents near the fault, minimizing disruption to other connected loads.
A differential relay is an essential device featuring two sets of current coils that activate when there is a current imbalance between them By utilizing appropriate current transformer ratios, this relay effectively safeguards transformers or generators from internal faults while differentiating these faults from external ones Additionally, most differential relays incorporate delay elements to accommodate inrush currents in transformers.
Electric utilities utilize impedance or distance relays for the protection of transmission and distribution circuits Despite the increasing reliance on computers for these tasks, the fundamental principles of operation remain unchanged An impedance relay consists of both current and voltage coils, where the voltage coils act as restraint elements When voltage levels are sufficiently high, the current coils are prevented from tripping the associated breaker Essentially, this relay measures impedance to determine the distance to a fault.
38 2 ◊ Power Apparatus it can decide whether a downstream breaker can clear the fault with less disturbance to the system
In system single-line diagrams, relays are designated by specific types: 50 for instantaneous overcurrent relays, 51 for time overcurrent relays, 64 for ground fault relays, 87 for differential relays, and 21 for impedance or distance relays These designations are typically placed next to the circuit breaker they control, with instantaneous and time overcurrent relays represented as 50/51 Additionally, there are various other relay types, including undervoltage, phase balance, phase sequence, directional power, and frequency relays.
In power systems, impedance is frequently treated as reactance due to the minimal impact of resistive losses on fault currents and regulation This simplification also applies to commutation in converters, where resistance has a minor influence.
Analytical Tools
Symmetrical Components
Analyzing unbalanced currents or voltages in a three-phase AC circuit often leads to complex calculations In 1918, Dr C L Fortesque presented a pivotal paper to the AIEE, which introduced the concept of symmetrical components This method allows for the representation of unbalanced voltage or current phasors using symmetrical sets of phasors, including positive-sequence and negative-sequence three-phase components, as well as a zero-sequence single-phase component, particularly relevant in four-wire systems involving ground circuits The network can be effectively solved using the standard approaches applied to these symmetrical components.
40 3 ◊ Analytical Tools components, and then the individual solutions combined to represent the unbalanced system Symmetrical components are universally used by power company engineers for system parameters.
Symmetrical component analysis employs a complex operator, denoted as a, where a = –0.5 + j 0.866 represents a unit phasor at 120° The subsequent values are a² = –0.5 – j 0.866 and a³ = 1.0 When dealing with a set of asymmetric phasors x, y, and z, all quantities are treated as phasors The components Ex0, Ex1, and Ex2 correspond to the zero-sequence, positive-sequence, and negative-sequence components of x, respectively Notably, Ex0 equals Ey0 and Ez0, while Ey1 is equal to a² Ex1.
Ez1 = aEx1, Ey2 = aEx2 and Ez2 = a 2 Ex2
This process is shown in Fig 3.8 where a (very) unbalanced set of phasors are x = 6.0, y = –j2.0 and z = –0.707 + j0.707 The sequence networks are shown at the right In this case,
Ex2 = 1.337 + j0.011 The original asymmetric phasors may then be reconstituted as x = Ex0 + Ex1 + Ex2 y = Ey0 + Ey1 + Ey2 = Ex0 + a 2 Ex1 + aEx2 z = Ez0 + Ez1 + Ez2 = Ex0 + aEx1 + a 2 Ex2
Per Unit Constants
To determine line currents from a set of phasors representing load impedances, apply the balanced line voltages to the three sequence networks individually and then sum the three components of each line current.
Symmetrical components are essential for analyzing overhead transmission lines, as they help describe the unique characteristics of a set of three conductors arranged in a horizontal row While the outer conductors exhibit equal coupling to the center conductor, they have varying couplings to each other, leading to distinct mutual inductances and capacitances By utilizing symmetrical components of these impedances, the transmission line can be effectively analyzed as two balanced positive- and negative-sequence networks, allowing for the combination of resultant currents.
Absent a grounded circuit, the zero-sequence network is not present
Modern circuit simulation software significantly minimizes the reliance on symmetrical components for circuit solutions; however, these components remain essential for accurately defining the performance of synchronous machines under unbalanced loading and fault conditions.
The per unit system simplifies the comparison of power apparatus by normalizing the characteristics of elements in a power electronics system, allowing for analysis independent of specific voltage levels This method aids in fault calculations and enhances the understanding of system components.
42 3 ◊ Analytical Tools translated relative to a common base so that extended calculations can be made easily
In its simplest form, a per unit quantity is merely the percent quan- tity divided by 100 It spares one the nonsense of 50% voltage times
50% current equals 2500% power In per unit notation, 0.5 pu voltage times 0.5 pu current equals 0.25 pu power as it should be A trans- former with 6% impedance would have a per unit impedance of
0.06 pu Although not described as such, this impedance is based on the rated voltage and current of the transformer It accommodates the differences in primary and secondary voltages by describing the per- cent rated voltage in either winding required to produce rated current in that winding with the other winding shorted The regulation charac- teristics of the transformer are completely described by this figure.
When additional components are integrated into a system, the ratings of these elements can vary significantly For instance, a 500-kVA transformer operating at 4160 V with a 6% reactance can support a 50-kVA transformer at 480 V with a 4% reactance, which in turn supplies a 5-kVA lighting transformer at 120 V with a 3% reactance Tracking down the different voltages and currents to determine the short circuit current at the final transformer can be cumbersome However, using per unit quantities simplifies this process.
First, one must choose a particular power level as a base quantity.
The selection of components in a system is typically arbitrary but often linked to the rating of one of the items For instance, using a 50-kVA transformer as the base with a leakage impedance of 4% (0.04 pu), we can relate a 5-kVA lighting transformer by multiplying its impedance of 0.03 pu by the power ratio of 50 kVA to 5 kVA, which equals 10 When these two transformers are connected in cascade, the total impedance is calculated as 0.04 + (0.03 × 10), resulting in 0.34 pu.
500-kVA transformer by the same procedure becomes 0.06 50/500 0.006 pu on the 50-kVA base The series string impedance is then
0.006 + 0.04 + 0.30 = 0.346 pu on the 50 kVA base This total series impedance is 0.0346 pu on a 5-kVA base, and a fault on the secondary of the 5-kVA transformer will result in 1/0.0346 = 28.9 times rated
3.2 Circuit Simulation 43 current, 28.9 pu on the 5-kVA base At the 50-kVA transformer, this fault will result in 1/0.346 pu = 2.89 pu current on a 50 kVA base, and at the 500-kVA transformer the fault is 1/3.46 = 0.289 pu on a
500-kVA base At any point in the system, one can define a base impedance as Zbase = V LL 2 /VA or Zbase = V LL 2 /(1000 × kVA) where
VA or kVA represents a three-phase rating, where the base impedance (Zbase) is defined as the impedance that, when connected to each line of a three-phase system at its rated voltage, will draw the rated load current and generate the specified voltamperes (Zohms = ZbaseZpu).
Familiarizing yourself with the per unit system is essential, as it simplifies discussions with utility engineers, motor designers, transformer designers, and other professionals in power electronics This system is widely adopted and recognized across the industry.
Circuit Simulation
Power electronics circuits can be effectively simulated using straightforward computer programs Although many engineers opt for commercial circuit simulation software, there are advantages to writing simple code for analyzing circuit behavior during transient conditions The following example illustrates this approach.
BASIC, but it can be easily translated to C or any other preferred pro- gramming language It is the concepts of handling the circuit that count
The circuit depicted in Fig 3.2 is an arc heater designed by the author, featuring a current regulator aimed at managing current overshoot during arc ignition from applied voltage This 24-pulse converter allows for a rapid current loop of 2000 rad/s and includes a nonlinear output inductor, a feedback filter, transport lag from SCRs and serial optical links, a negative slew rate limit, and an arc strike voltage The accompanying BASIC program is well-documented to clarify the methodology As shown in Fig 3.3, the output waveform indicates an initial current transient reaching 270% of the set-point, which is deemed acceptable, with a slight undershoot followed by an overshoot as the current stabilizes at the command level after arc ignition.
F IGURE 3.3 Circuit voltage and current waveforms.
Initial voltage: 0 – current integrator enabled at t = 0
Initial current: 0.01 A (to get a finite inductance)
Inductor: Inductance inversely proportional to current to
1.1 power, bounded by 10 mH maximum and 1.1 mH minimum
Feedback: Three cascaded filter poles at 2000 rad/s Filter will handle both feedback and anti-aliasing in the digital system.
In the simulation, a transport lag of 1 ms is introduced in the SCRs and digital system to reflect real-world delays The regulator is set to lead at 250 rad/s to align with a load time constant of 4 ms To closely mimic a 50-Hz sine wave, a negative slew rate of –10%/ms is implemented The commanded current is initially set to 100 A, ensuring a low starting point to reduce overshoot.
This program will run in BASIC 4.5 or higher as well as QuickBASIC.
PALETTE 0,4144959 ' set reverse palette colors
DIM ed(10000) td = 100 'delay in 10 às increments dt = 00001 ' time increment 10 às icom = 100 ' current command level ecom = icom / 300 ' current command = 33 v for 100A rL = 25 ' load resistance r3 = 40000 ' lead resistor r4 = 10000 ' input resistor
46 3 ◊ Analytical Tools ra = 500 ' filter resistors rb = 500 rc = 500 ca = 000001 ' filter capacitors cb = 000001 cc = 000001 cd = 000001 c3 = 000001 ' integrator capacitor i = 01 ' initial current again:
IF L > 01 THEN L = 01 ' maximum inductance 10 mH
In a digital system, if the inductance (L) is less than 0.0011, it is set to a minimum value of 0.0011 H to ensure saturated inductance at 1.1 mH The error signal (ee) is calculated by subtracting feedback (ef) from the command (ecom) The filter capacitor current (ia) is determined using Euler integration, where ia equals the difference between the input error (ei) and the output error (ea) divided by the resistance (ra) Similarly, the current for the next stage (ib) is calculated as the difference between the output error (ea) and the next stage error (eb) divided by the resistance (rb), while the final stage current (ic) follows the same formula Finally, the digital system transport lag (p) is derived by subtracting the time delay (td) from the number of samples (n).
To initialize the filter voltage, set p to 1 if it is less than 1, and assign ed(n) to ec The last stage filter voltage ef is determined by ed(p) The delay is calculated as td/100 ms, while ec is updated by adding the product of ic and dt divided by cc The filter consists of three cascaded poles located at 2000 rad/s Each section of the filter is isolated, with eb updated by ib multiplied by dt over cb, and ea updated by ia multiplied by dt over ca Euler integration is applied with ei equal to 0.0033 times i, where 1500 A corresponds to a feedback voltage of 5 V from the shunt Finally, the converter gain is calculated with econ equal to 240 times eo, equating 5 V to 1200 V.
IF econ < 0 THEN econ = 0 ' commutating diode prevents negative voltage
IF econ > 1200 THEN econ = 1200 ' voltage ceiling
IF (i < icom) AND (econ > 650) THEN econ = 650 ' starting voltage limit
IF econx - econ > 1 THEN econ = econx - 1 ' negative slew rate limit 10%/ms i = i + (econ - eL) * dt / L ' load current
IF econ > 600 THEN k = 1 ' flag to detect first current above isetpoint
IF k = 0 THEN i = 0 ' no current until econ> 600 V arc ignition voltage eL = i * rL ' load voltage eo = ee * ( r3 / r4 ) + ecap ' output voltage of opamp
IF eo > 10 THEN eo = 10 ' opamp limit ecap = ecap + (eo - ecap ) / r3 * dt / c3 ' voltage on integrator cap
IF n > 10000 GOTO quit: ' end of display econx = econ ' set econx for prior voltage to set negative slew rate maximum
LOCATE 27 , 15: PRINT “ Horizontal 20 ms/div, V 0 V/ div, I0 A/div”
LOCATE 28 , 20: PRINT “ ARC HEATER STARTING
Various software packages are now accessible for simulating the operation of nearly any power electronic circuit, featuring included component characteristics and user-friendly circuit representation Detailed descriptions of these programs can be found online, with many offering student versions, limited-capability options, or introductory packages It’s important to note that the information provided reflects a specific timeframe, as the software continues to evolve rapidly.
MATLAB is an interactive software used for numerical computation and data visualization, primarily by control engineers for analysis and design It offers various toolboxes, including SIMULINK, which is a differential equation solver for simulating dynamic systems The program features an interactive graphical environment and customizable block libraries, enabling the design, simulation, and implementation of control systems, signal processing, communications, and other time-varying applications.
MATHCAD is an equation-based software that enables users to document, execute, and share their calculations and design projects efficiently It seamlessly integrates mathematical notation, text, and graphics within a single worksheet, making it an essential tool for capturing critical methods and values in engineering projects.
Spice is one of the pioneering simulation programs that enables users to construct circuits in schematic form directly on the display screen It offers libraries for various circuit elements and allows for the analysis of both steady-state and transient behavior Additionally, there are several related programs, such as PSpice, Saber, and Micro-Cap, which are either compatible with Spice or provide similar functionalities.
The ElectroMagnetic Transients Program (EMTP) focuses on addressing transient effects in electric power systems, offering various options for circuit analysis Developed and maintained by a consortium of international power companies and organizations, the core program is publicly available.
There are various popular software options available for circuit analysis, many of which can be purchased online Additionally, some packages offer free student versions that can be easily downloaded.
Simulation Software
Feedback control systems are essential for the operation of nearly all power electronics systems This chapter focuses on basic analog analysis, as it provides a more intuitive understanding of system behavior compared to modern control theory and digital techniques.
Figure 4.1 illustrates the basic structure of a feedback control system, where a command signal is processed at a summing junction and compared against a feedback signal of opposing polarity The resulting difference signal is then transmitted to an amplifier for further action.