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72-646: This original model of Compass lacked an internal battery compartment, requiring AC power from the wall. Grid sold the succeeding model, the Compass II, in 1984 with an optional external battery unit. Grid replaced the Compass with the GridCase line in 1985. Development of the Compass began in 1979, and the main buyer was the U.S. government. NASA used it on the Space Shuttle during the early 1980s, as it

144-467: A dielectric . Capacitive reactance is an opposition to the change of voltage across an element. Capacitive reactance X C {\displaystyle X_{C}} is inversely proportional to the signal frequency f {\displaystyle f} (or angular frequency ω {\displaystyle \omega } ) and the capacitance C {\displaystyle C} . There are two choices in

216-442: A short circuit . The application of a DC voltage across a capacitor causes positive charge to accumulate on one side and negative charge to accumulate on the other side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero. Driven by an AC supply (ideal AC current source),

288-509: A sinusoidal AC voltage source of RMS amplitude A {\displaystyle A} and frequency f {\displaystyle f} is equal to: Because a square wave has multiple amplitudes at sinusoidal harmonics , the average current flowing through an inductance L {\displaystyle L} in series with a square wave AC voltage source of RMS amplitude A {\displaystyle A} and frequency f {\displaystyle f}

360-608: A capacitor and an inductor are placed in series in a circuit, their contributions to the total circuit impedance are opposite. Capacitive reactance X C {\displaystyle X_{C}} and inductive reactance X L {\displaystyle X_{L}} contribute to the total reactance X {\displaystyle X} as follows: where: Hence: Note however that if X L {\displaystyle X_{L}} and X C {\displaystyle X_{C}} are assumed both positive by definition, then

432-401: A capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge is returned to the source. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current. Inductive reactance is a property exhibited by an inductor, and inductive reactance exists based on the fact that an electric current produces

504-405: A higher apparent power and higher losses for the same amount of active power. The power factor is 1.0 when the voltage and current are in phase . It is zero when the current leads or lags the voltage by 90 degrees. When the voltage and current are 180 degrees out of phase, the power factor is negative one, and the load is feeding energy into the source (an example would be a home with solar cells on

576-427: A magnetic field around it. In the context of an AC circuit (although this concept applies any time current is changing), this magnetic field is constantly changing as a result of current that oscillates back and forth. It is this change in magnetic field that induces another electric current to flow in the same wire (counter-EMF), in a direction such as to oppose the flow of the current originally responsible for producing

648-463: A measure of control to system operators over reactive power flow and thus voltage. Because these devices have opposite effects on the phase angle between voltage and current, they can be used to "cancel out" each other's effects. This usually takes the form of capacitor banks being used to counteract the lagging power factor caused by induction motors. Transmission connected generators are generally required to support reactive power flow. For example, on

720-452: A perfect capacitor or inductor, there is no net power transfer; so all power is reactive. Therefore, for a perfect capacitor or inductor: where X {\displaystyle X} is the reactance of the capacitor or inductor. If X {\displaystyle X} is defined as being positive for an inductor and negative for a capacitor, then the modulus signs can be removed from S and X and get Instantaneous power

792-484: A purely resistive load, real power can be simplified to: R denotes resistance (units in ohms, Ω) of the load. Reactive power (units in volts-amps-reactive, var) is derived as: For a purely reactive load, reactive power can be simplified to: where X denotes reactance (units in ohms, Ω) of the load. Combining, the complex power (units in volt-amps, VA) is back-derived as and the apparent power (units in volt-amps, VA) as These are simplified diagrammatically by

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864-417: A quantity that depends on the reference angle chosen for V or I, but defining S as V I* results in a quantity that doesn't depend on the reference angle and allows to relate S to P and Q. Other forms of complex power (units in volt-amps, VA) are derived from Z , the load impedance (units in ohms, Ω). Consequentially, with reference to the power triangle, real power (units in watts, W) is derived as: For

936-480: A shunt capacitor is installed close to the load itself. This allows all reactive power needed by the load to be supplied by the capacitor and not have to be transferred over the transmission lines. This practice saves energy because it reduces the amount of energy that is required to be produced by the utility to do the same amount of work. Additionally, it allows for more efficient transmission line designs using smaller conductors or fewer bundled conductors and optimizing

1008-424: A very interesting result. However, the time average of a function of the form cos( ωt + k ) is zero provided that ω is nonzero. Therefore, the only product terms that have a nonzero average are those where the frequency of voltage and current match. In other words, it is possible to calculate active (average) power by simply treating each frequency separately and adding up the answers. Furthermore, if voltage of

1080-546: A zero rate-of-change, and sees an inductor as a short-circuit (it is typically made from a material with a low resistivity ). An alternating current has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency. Both reactance X {\displaystyle {X}} and resistance R {\displaystyle {R}} are components of impedance Z {\displaystyle {\mathbf {Z} }} . where: When both

1152-475: Is proportional to the sinusoidal signal frequency f {\displaystyle f} and the inductance L {\displaystyle L} , which depends on the physical shape of the inductor: X L = ω L = 2 π f L {\displaystyle X_{L}=\omega L=2\pi fL} . The average current flowing through an inductance L {\displaystyle L} in series with

1224-449: Is 45.6°. The power factor is cos(45.6°) = 0.700 . The apparent power is then: 700 W / cos(45.6°) = 1000 VA . The concept of power dissipation in AC circuit is explained and illustrated with the example. For instance, a power factor of 0.68 means that only 68 percent of the total current supplied (in magnitude) is actually doing work; the remaining current does no work at the load. Power Factor

1296-642: Is an important source of reactive power in the above power balance equation, which is generated by the capacitative nature of the transmission network itself. By making decisive switching actions in the early morning before the demand increases, the system gain can be maximized early on, helping to secure the system for the whole day. To balance the equation some pre-fault reactive generator use will be required. Other sources of reactive power that will also be used include shunt capacitors, shunt reactors, static VAR compensators and voltage control circuits. While active power and reactive power are well defined in any system,

1368-442: Is defined as: where v ( t ) {\displaystyle v(t)} and i ( t ) {\displaystyle i(t)} are the time-varying voltage and current waveforms. This definition is useful because it applies to all waveforms, whether they are sinusoidal or not. This is particularly useful in power electronics, where non-sinusoidal waveforms are common. In general, engineers are interested in

1440-450: Is equal to: making it appear as if the inductive reactance to a square wave was about 19% smaller X L = 16 π f L {\displaystyle X_{L}={16 \over \pi }fL} than the reactance to the AC sine wave. Any conductor of finite dimensions has inductance; the inductance is made larger by the multiple turns in an electromagnetic coil . Faraday's law of electromagnetic induction gives

1512-409: Is positive while instantaneous voltage is negative, or vice versa, implying negative power transfer. Hence, real work is not performed when power transfer is "negative". However, current still flows even when a system is out-of-phase, which causes transmission lines to heat up due to current flow. Consequently, transmission lines can only heat up so much (or else they would physically sag too much, due to

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1584-478: Is positive, but for the other two quarters, the product is negative, indicating that on average, exactly as much energy flows into the load as flows back out. There is no net energy flow over each half cycle. In this case, only reactive power flows: There is no net transfer of energy to the load; however, electrical power does flow along the wires and returns by flowing in reverse along the same wires. The current required for this reactive power flow dissipates energy in

1656-419: Is similar to resistance in that larger reactance leads to smaller currents for the same applied voltage. Further, a circuit made entirely of elements that have only reactance (and no resistance) can be treated the same way as a circuit made entirely of resistances. These same techniques can also be used to combine elements with reactance with elements with resistance but complex numbers are typically needed. This

1728-411: Is the active power, Q is the reactive power (in this case positive), S is the complex power and the length of S is the apparent power. Reactive power does not do any work, so it is represented as the imaginary axis of the vector diagram. Active power does do work, so it is the real axis. The unit for power is the watt (symbol: W). Apparent power is often expressed in volt-amperes (VA) since it

1800-413: Is the cosine of the phase angle ( φ {\displaystyle \varphi } ) between the current and voltage sinusoidal waveforms. Equipment data sheets and nameplates will often abbreviate power factor as " cos ⁡ ϕ {\displaystyle \cos \phi } " for this reason. Example: The active power is 700 W and the phase angle between voltage and current

1872-441: Is the opposition presented to alternating current by inductance and capacitance . Along with resistance, it is one of two elements of impedance ; however, while both elements involve transfer of electrical energy, no dissipation of electrical energy as heat occurs in reactance; instead, the reactance stores energy until a quarter-cycle later when the energy is returned to the circuit. Greater reactance gives smaller current for

1944-456: Is the product of RMS voltage and RMS current . The unit for reactive power is var, which stands for volt-ampere reactive . Since reactive power transfers no net energy to the load, it is sometimes called "wattless" power. It does, however, serve an important function in electrical grids and its lack has been cited as a significant factor in the Northeast blackout of 2003 . Understanding

2016-475: Is treated below in the section on impedance . There are several important differences between reactance and resistance, though. First, reactance changes the phase so that the current through the element is shifted by a quarter of a cycle relative to the phase of the voltage applied across the element. Second, power is not dissipated in a purely reactive element but is stored instead. Third, reactances can be negative so that they can 'cancel' each other out. Finally,

2088-470: Is very important in Power sector substations. Form the national grid the sub sectors are required to have minimum amount of power factor. Otherwise there are many loss. Mainly the required vary around 0.90 to 0.96 or more. Better the power factor less the loss. In a direct current circuit, the power flowing to the load is proportional to the product of the current through the load and the potential drop across

2160-545: The United Kingdom transmission system, generators are required by the Grid Code Requirements to supply their rated power between the limits of 0.85 power factor lagging and 0.90 power factor leading at the designated terminals. The system operator will perform switching actions to maintain a secure and economical voltage profile while maintaining a reactive power balance equation: The " system gain "

2232-430: The active power averaged over a period of time, whether it is a low frequency line cycle or a high frequency power converter switching period. The simplest way to get that result is to take the integral of the instantaneous calculation over the desired period: This method of calculating the average power gives the active power regardless of harmonic content of the waveform. In practical applications, this would be done in

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2304-488: The addressable device bus. It weighed 5 kg ( 11 lb ). The power input is ~ 110/220 V AC, 47–66 Hz , 75 W . The Compass II was released in 1984; known as 1121, 1129, 1131 and 1139 models. AC power In an electric circuit, instantaneous power is the time rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of

2376-430: The amplitude as RMS , and I denotes current in phasor form, with the amplitude as RMS. Also by convention, the complex conjugate of I is used, which is denoted I ∗ {\displaystyle I^{*}} (or I ¯ {\displaystyle {\overline {I}}} ), rather than I itself. This is done because otherwise using the product V I to define S would result in

2448-446: The capacitor structure. In an AC network, the voltage across a capacitor is constantly changing. The capacitor opposes this change, causing the current to lead the voltage in phase. Capacitors are said to "source" reactive power, and thus to cause a leading power factor. Induction machines are some of the most common types of loads in the electric power system today. These machines use inductors , or large coils of wire to store energy in

2520-463: The counter- emf E {\displaystyle {\mathcal {E}}} (voltage opposing current) due to a rate-of-change of magnetic flux density B {\displaystyle \scriptstyle {B}} through a current loop. For an inductor consisting of a coil with N {\displaystyle N} loops this gives: The counter-emf is the source of the opposition to current flow. A constant direct current has

2592-412: The current waveform lagging the voltage waveform by 90 degrees. The result of this is that capacitive and inductive circuit elements tend to cancel each other out. Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them): These are all denoted in the adjacent diagram (called a power triangle). In the diagram, P

2664-471: The definition of apparent power for unbalanced polyphase systems is considered to be one of the most controversial topics in power engineering. Originally, apparent power arose merely as a figure of merit. Major delineations of the concept are attributed to Stanley 's Phenomena of Retardation in the Induction Coil (1888) and Steinmetz 's Theoretical Elements of Engineering (1915). However, with

2736-448: The design of transmission towers. Stored energy in the magnetic or electric field of a load device, such as a motor or capacitor, causes an offset between the current and the voltage waveforms. A capacitor is a device that stores energy in the form of an electric field. As current is driven through the capacitor, charge build-up causes an opposing voltage to develop across the capacitor. This voltage increases until some maximum dictated by

2808-557: The development of three phase power distribution, it became clear that the definition of apparent power and the power factor could not be applied to unbalanced polyphase systems . In 1920, a "Special Joint Committee of the AIEE and the National Electric Light Association" met to resolve the issue. They considered two definitions. that is, the arithmetic sum of the phase apparent powers; and that is,

2880-424: The digital domain, where the calculation becomes trivial when compared to the use of rms and phase to determine active power: Since an RMS value can be calculated for any waveform, apparent power can be calculated from this. For active power it would at first appear that it would be necessary to calculate many product terms and average all of them. However, looking at one of these product terms in more detail produces

2952-466: The direction of energy flow. Its SI unit is the watt . The portion of instantaneous power that, averaged over a complete cycle of the AC waveform , results in net transfer of energy in one direction is known as instantaneous active power, and its time average is known as active power or real power . The portion of instantaneous power that results in no net transfer of energy but instead oscillates between

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3024-443: The form of a magnetic field. When a voltage is initially placed across the coil, the inductor strongly resists this change in a current and magnetic field, which causes a time delay for the current to reach its maximum value. This causes the current to lag behind the voltage in phase. Inductors are said to "sink" reactive power, and thus to cause a lagging power factor. Induction generators can source or sink reactive power, and provide

3096-406: The fundamental mechanism for controlling the power factor in electric power transmission; capacitors (or inductors) are inserted in a circuit to partially compensate for reactive power 'consumed' ('generated') by the load. Purely capacitive circuits supply reactive power with the current waveform leading the voltage waveform by 90 degrees, while purely inductive circuits absorb reactive power with

3168-413: The heat expanding the metal transmission lines), so transmission line operators have a "ceiling" on the amount of current that can flow through a given line, and excessive inductive reactance can limit the power capacity of a line. Power providers utilize capacitors to shift the phase and minimize the losses, based on usage patterns. Inductive reactance X L {\displaystyle X_{L}}

3240-399: The input of the device. Typically this will consist of either just a capacitor (relying on parasitic resistance and inductance in the supply) or a capacitor-inductor network. An active power factor correction circuit at the input would generally reduce the harmonic currents further and maintain the power factor closer to unity. Electrical reactance In electrical circuits, reactance

3312-509: The intermediary formula changes to a difference: but the ultimate value is the same. The phase of the voltage across a purely reactive device (i.e. with zero parasitic resistance ) lags the current by π 2 {\displaystyle {\tfrac {\pi }{2}}} radians for a capacitive reactance and leads the current by π 2 {\displaystyle {\tfrac {\pi }{2}}} radians for an inductive reactance. Without knowledge of both

3384-645: The late 1960s. GRiD Systems Corporation subsequently earned significant returns on its patent rights as its innovations became commonplace. The portable Osborne 1 computer sold at around the same time as the GRiD, was more affordable and more popular, and ran the popular CP/M operating system. But, unlike the Compass, the Osborne was not a laptop and lacked the Compass's refinement and small size. The Compass ran its own operating system, GRiD-OS. Its specialized software and high price ( US$ 8,000 – $ 10,000 ) meant that it

3456-491: The line resistance, even if the ideal load device consumes no energy itself. Practical loads have resistance as well as inductance, or capacitance, so both active and reactive powers will flow to normal loads. Apparent power is the product of the RMS values of voltage and current. Apparent power is taken into account when designing and operating power systems, because although the current associated with reactive power does no work at

3528-564: The literature for defining reactance for a capacitor. One is to use a uniform notion of reactance as the imaginary part of impedance, in which case the reactance of a capacitor is the negative number, Another choice is to define capacitive reactance as a positive number, In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e. Z c = − j X c {\displaystyle Z_{c}=-jX_{c}} . At f = 0 {\displaystyle f=0} ,

3600-432: The load, it still must be supplied by the power source. Conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work. Insufficient reactive power can depress voltage levels on an electrical grid and, under certain operating conditions, collapse the network (a blackout ). Another consequence is that adding the apparent power for two loads will not accurately give

3672-523: The load. The power that happens because of a capacitor or inductor is called reactive power. It happens because of the AC nature of elements like inductors and capacitors. Energy flows in one direction from the source to the load. In AC power, the voltage and current both vary approximately sinusoidally. When there is inductance or capacitance in the circuit, the voltage and current waveforms do not line up perfectly. The power flow has two components – one component flows from source to load and can perform work at

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3744-530: The load; the other portion, known as "reactive power", is due to the delay between voltage and current, known as phase angle, and cannot do useful work at the load. It can be thought of as current that is arriving at the wrong time (too late or too early). To distinguish reactive power from active power, it is measured in units of " volt-amperes reactive ", or var. These units can simplify to watts but are left as var to denote that they represent no actual work output. Energy stored in capacitive or inductive elements of

3816-407: The magnetic field (known as Lenz's Law). Hence, inductive reactance is an opposition to the change of current through an element. For an ideal inductor in an AC circuit, the inhibitive effect on change in current flow results in a delay, or a phase shift, of the alternating current with respect to alternating voltage. Specifically, an ideal inductor (with no resistance) will cause the current to lag

3888-464: The magnitude of the capacitor's reactance is infinite, behaving like an open circuit (preventing any current from flowing through the dielectric). As frequency increases, the magnitude of reactance decreases, allowing more current to flow. As f {\displaystyle f} approaches ∞ {\displaystyle \infty } , the capacitor's reactance approaches 0 {\displaystyle 0} , behaving like

3960-459: The magnitude of total three-phase complex power. The 1920 committee found no consensus and the topic continued to dominate discussions. In 1930, another committee formed and once again failed to resolve the question. The transcripts of their discussions are the lengthiest and most controversial ever published by the AIEE. Further resolution of this debate did not come until the late 1990s. A new definition based on symmetrical components theory

4032-624: The main circuit elements that have reactance (capacitors and inductors) have a frequency dependent reactance, unlike resistors which have the same resistance for all frequencies, at least in the ideal case. The term reactance was first suggested by French engineer M. Hospitalier in L'Industrie Electrique on 10 May 1893. It was officially adopted by the American Institute of Electrical Engineers in May 1894. A capacitor consists of two conductors separated by an insulator , also known as

4104-457: The mains supply is assumed to be a single frequency (which it usually is), this shows that harmonic currents are a bad thing. They will increase the RMS current (since there will be non-zero terms added) and therefore apparent power, but they will have no effect on the active power transferred. Hence, harmonic currents will reduce the power factor. Harmonic currents can be reduced by a filter placed at

4176-483: The network gives rise to reactive power flow. Reactive power flow strongly influences the voltage levels across the network. Voltage levels and reactive power flow must be carefully controlled to allow a power system to be operated within acceptable limits. A technique known as reactive compensation is used to reduce apparent power flow to a load by reducing reactive power supplied from transmission lines and providing it locally. For example, to compensate an inductive load,

4248-406: The positive sequence voltage phasor, and I + {\displaystyle I^{+}} denotes the positive sequence current phasor. A perfect resistor stores no energy; so current and voltage are in phase. Therefore, there is no reactive power and P = S {\displaystyle P=S} (using the passive sign convention ). Therefore, for a perfect resistor For

4320-449: The power triangle. The ratio of active power to apparent power in a circuit is called the power factor . For two systems transmitting the same amount of active power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. These higher currents produce higher losses and reduce overall transmission efficiency. A lower power factor circuit will have

4392-402: The relationship among these three quantities lies at the heart of understanding power engineering. The mathematical relationship among them can be represented by vectors or expressed using complex numbers , S  =  P  +  j Q (where j is the imaginary unit ). The formula for complex power (units: VA) in phasor form is: where V denotes voltage in phasor form, with

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4464-403: The resistance and reactance the relationship between voltage and current cannot be determined. The origin of the different signs for capacitive and inductive reactance is the phase factor e ± j π 2 {\displaystyle e^{\pm \mathbf {j} {\frac {\pi }{2}}}} in the impedance. For a reactive component the sinusoidal voltage across

4536-408: The roof that feed power into the power grid when the sun is shining). Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle of current with respect to voltage. Voltage is designated as the base to which current angle is compared, meaning that current is thought of as either "leading" or "lagging" voltage. Where the waveforms are purely sinusoidal, the power factor

4608-607: The same applied voltage . Reactance is used to compute amplitude and phase changes of sinusoidal alternating current going through a circuit element. Like resistance, reactance is measured in ohms , with positive values indicating inductive reactance and negative indicating capacitive reactance. It is denoted by the symbol X {\displaystyle X} . An ideal resistor has zero reactance, whereas ideal reactors have no shunt conductance and no series resistance. As frequency increases, inductive reactance increases and capacitive reactance decreases. Reactance

4680-418: The same time. Hence, the instantaneous power, given by the product of voltage and current, is always positive, such that the direction of energy flow does not reverse and always is toward the resistor. In this case, only active power is transferred. If the load is purely reactive , then the voltage and current are 90 degrees out of phase. For two quarters of each cycle, the product of voltage and current

4752-420: The source and load in each cycle due to stored energy is known as instantaneous reactive power, and its amplitude is the absolute value of reactive power . In a simple alternating current (AC) circuit consisting of a source and a linear time-invariant load, both the current and voltage are sinusoidal at the same frequency. If the load is purely resistive , the two quantities reverse their polarity at

4824-399: The total power unless they have the same phase difference between current and voltage (the same power factor ). Conventionally, capacitors are treated as if they generate reactive power, and inductors are treated as if they consume it. If a capacitor and an inductor are placed in parallel, then the currents flowing through the capacitor and the inductor tend to cancel rather than add. This is

4896-500: The voltage by a quarter cycle, or 90°. In electric power systems, inductive reactance (and capacitive reactance, however inductive reactance is more common) can limit the power capacity of an AC transmission line, because power is not completely transferred when voltage and current are out-of-phase (detailed above). That is, current will flow for an out-of-phase system, however real power at certain times will not be transferred, because there will be points during which instantaneous current

4968-460: Was limited to specialized applications. The initial model, the 1101, was introduced in April 1982; The 1100 model designation were never released commercially, but featured in some pre-release marketing material. The computer was designed by British industrial designer Bill Moggridge . The design used a clamshell case (where the screen folds flat to the rest of the computer when closed), which

5040-473: Was made from a magnesium alloy. The computer featured an Intel 8086 processor , a 320 × 240-pixel electroluminescent display , 340- kilobyte magnetic bubble memory , and a 1200  bit/s modem . Devices such as hard drives and floppy drives could be connected via the IEEE-488 I/O (also known as GPIB or General Purpose Interface Bus). This port made it possible to connect multiple devices to

5112-583: Was powerful, lightweight, and compact. The military Special Forces also purchased the machine, as it could be used by paratroopers in combat. Along with the Gavilan SC and Sharp PC-5000 released the following year, the GRiD Compass established much of the basic design of subsequent laptop computers, although the laptop concept itself owed much to the Dynabook project developed at Xerox PARC from

5184-400: Was proposed in 1993 by Alexander Emanuel for unbalanced linear load supplied with asymmetrical sinusoidal voltages: that is, the root of squared sums of line voltages multiplied by the root of squared sums of line currents. P + {\displaystyle P^{+}} denotes the positive sequence power: V + {\displaystyle V^{+}} denotes

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