Powerin an electric circuit is the rate of flow of energy past a given point of the circuit. Inalternating currentcircuits, energy storage elements such asinductorsandcapacitorsmay result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as real power. The portion of power due to stored energy, which returns to the source in each cycle, is known as reactive power.Real, reactive, and apparent powerIn a simplealternating current(AC) circuit consisting of a source and a linear load, both the current and voltage aresinusoidal. If the load is purelyresistive, the two quantities reverse their polarity at the same time. At every instant the product of voltage and current is positive, indicating that the direction of energy flow does not reverse. In this case, only real power is transferred.If the loads are purelyreactive, then the voltage and current are 90 degrees out of phase. For half of each cycle, the product of voltage and current is positive, but on the other half of the cycle, the product is negative, indicating that on average, exactly as much energy flows toward the load as flows back. There is no net energy flow over one cycle. In this case, only reactive energy flowsthere is no net transfer of energy to the load.Practical loads have resistance, inductance, and capacitance, so both real and reactive power will flow to real loads. Power engineers measure apparent power as the magnitude of the vector sum of real and reactive power. Apparent power is the product of theroot-mean-squareof voltage and current.Engineers care about apparent power, because even though the current associated with reactive power does no work at the load, it heats the wires, wasting energy. Conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work.Another consequence is that adding the apparent power for two loads will not accurately give the total apparent power unless they have the same displacement between current and voltage (the samepower factor).Conventionally, capacitors are considered to generate reactive power and inductors to consume it. If a capacitor and an inductor are placed in parallel, then the currents flowing through the inductor and the capacitor tend to cancel rather than add. This is the fundamental mechanism for controlling the power factor in electric power transmission; capacitors (or inductors) are inserted in a circuit to partially cancel reactive power consumed by the load.

The complex power is the vector sum of real and reactive power. The apparent power is the magnitude of the complex power.Real power,PReactive power,QComplex power,SApparent power,|S|Phase of current,?Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them): Real power,P, oractive power:[1]watt(W) Reactive power,Q:volt-ampere reactive(var) Complex power,S:volt-ampere(VA) Apparent power, |S|: themagnitudeof complex powerS: volt-ampere (VA) Phase of voltage relative to current,?: the angle of difference (in degrees) between current and voltage; current lagging voltage (quadrant I vector), current leading voltage (quadrant IV vector)In the diagram,Pis the real power,Qis the reactive power (in this case positive),Sis the complex power and the length ofSis the apparent power. Reactive power does not do any work, so it is represented as theimaginary axisof the vector diagram. Real power does do work, so it is the real axis.The unit for all forms of power is thewatt(symbol: W), but this unit is generally reserved for real power. Apparent power is conventionally expressed involt-amperes(VA) since it is the product ofrmsvoltageand rmscurrent. The unit for reactive power is expressed as var, which stands forvolt-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 inelectrical gridsand its lack has been cited as a significant factor in theNortheast Blackout of 2003.[2]Understanding 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+ jQ(where j is theimaginary unit).Power factorMain article:Power factorThe ratio between real power and apparent power in a circuit is called thepower factor. Its a practical measure of the efficiency of a power distribution system. For two systems transmitting the same amount of real 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 a higher apparent power and higher losses for the same amount of real power.The power factor is unity (one) when the voltage and current are inphase. It is zero when the current leads or lags the voltage by 90 degrees. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle of current with respect to voltage.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 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.Where the waveforms are purely sinusoidal, the power factor is the cosine of the phase angle (?) between the current and voltage sinusoid waveforms. Equipment data sheets and nameplates often will abbreviate power factor as "" for this reason.Example: The real power is700 Wand the phase angle between voltage and current is 45.6. The power factor iscos(45.6) = 0.700. The apparent power is then:700 W / cos(45.6) = 1000 VA.[3]Reactive powerReactive power flow is needed in an alternating-current transmission system to support the transfer of real power over the network. In alternating current circuits, energy is stored temporarily in inductive and capacitive elements, which can result in the periodic reversal of the direction of energy flow. The portion of power flow remaining, after being averaged over a complete AC waveform, is the real power; that is, energy that can be used to do work (for example overcome friction in a motor, or heat an element). On the other hand, the portion of power flow that is temporarily stored in the form of magnetic or electric fields, due to inductive and capacitive network elements, and then returned to source, is known asreactive power.AC connected devices that store energy in the form of a magnetic field include devices called inductors, which consist of a large coil of wire. When a voltage is initially placed across the coil, a magnetic field builds up, and it takes a period of time for the current to reach full value. This causes the current to lag behind the voltage in phase; hence, these devices are said toabsorbreactive power.A capacitor is an AC device that stores energy in the form of an electric field. When current is driven through the capacitor, it takes a period of time for a charge to build up to produce the full voltage difference. On an AC network, the voltage across a capacitor is constantly changing the capacitor will oppose this change, causing the voltage to lag behind the current. In other words, the current leads the voltage in phase; hence, these devices are said togeneratereactive power.Energy stored in capacitive or inductive elements of the network give 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.Reactive power controlTransmission connected generators are generally required to support reactive power flow. For example on 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:Generator_MVARs + System_gain + Shunt_capacitors = MVAR_Demand + Reactive_losses + Shunt_reactorsThe System gain is an important source of reactive power in the above power balance equation, which is generated by the capacitive 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.Unbalanced polyphase systemsWhile real power and reactive power are well defined in any system, 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 toStanleysPhenomena of Retardation in the Induction Coil(1888) andSteinmetzsTheoretical Elements of Engineering(1915). However, with the development ofthree phasepower distribution, it became clear that the definition of apparent power and the power factor could not be applied to unbalancedpolyphase 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 quotient of the sums of the real powers for each phase over the sum of the apparent power for each phase.

that is, the quotient of the sums of the real powers for each phase over the magnitude of the sum of the complex powers for each phase.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 (Emanuel, 1993). Further resolution of this debate did not come until the late 1990s.Basic calculations using real numbersA perfect resistor stores no energy, so current and voltage are in phase. Therefore there is no reactive power and. Therefore for a perfect resistor

For a perfect capacitor or inductor there is no net power transfer, so all power is reactive. Therefore for a perfect capacitor or inductor:

WhereXis thereactanceof the capacitor or inductor.If X is defined as being positive for an inductor and negative for a capacitor then we can remove themodulussigns from S and X and get

Instantaneous power is defined as:

where v(t) and 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 nonsinusoidal waveforms are common.In general, we are interested in the real 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 real power regardless of harmonic content of the waveform. In practical applications, this would be done in the digital domain, where the calculation becomes trivial when compared to the use of rms and phase to determine real power.

Multiple frequency systemsSince an RMS value can be calculated for any waveform, apparent power can be calculated from this.For real power it would at first appear that we would have to calculate loads of product terms and average all of them. However if we look at one of these product terms in more detail we come to a very interesting result.

however the time average of a function of the form cos(?t+k) is zero provided that ? 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 real (average) power by simply treating each frequency separately and adding up the answers.Furthermore, if we assume the voltage of the mains supply is a single frequency (which it usually is), this shows thatharmonic currentsare 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 real power transferred. Hence, harmonic currents will reduce the power factor.Harmonic currents can be reduced by a filter placed at 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 activepower factor correctioncircuit at the input would generally reduce the harmonic currents further and maintain the power factor closer to unity.

Capacitor vs InductorCapacitor and inductor are two electrical components used in circuit design. Both of them belong to passive elements category, which draw energy from the circuit, store, and then release. Both capacitor and inductor are widely used in AC (alternative current) and signal filtering applications.CapacitorCapacitor is made of two conductors separated by an insulating dielectric. When a potential difference is provided to these two conductors, an electric field is created and electric charges are stored. Once the potential difference is being removed and two conductors are connected, a current (stored charges) flows to neutralize that potential difference and electric field. The rate of discharge gets reduced with time and this is known as the capacitor discharging curve.In analysis, capacitor is considered as an insulator for DC (direct current) and conducting element for AC (alternating currents). Therefore, it is used as a DC blocking element in many circuit designs. Capacitance of a capacitor is known as the capability to store electric charges, and it is measured in the unit called Farad (F). However in practical circuits, capacitors are available in the ranges of micro Farads (F) to pico Farads (pF).InductorInductor is simply a coil and it stores energy as a magnetic field when an electric current passing through it. Inductance is a measure of an inductors capability to store energy. Inductance is measured in unit Henry (H). When an alternative current is passing through an inductor, a voltage across the device is observable due to changing magnetic field.Unlike capacitors, inductors act as conductors for DC, and the voltage drop on the element is almost zero, as there is no changing magnetic field. Transformers are made of coupled pair of inductors.What is the difference between Capacitor and Inductor?1. Capacitor stores an electric field, whereas inductor stores a magnetic field.2. Capacitor is open circuit for DC, and inductor is short circuit for DC.3. In an AC circuit, for capacitor, voltage lags current, whereas for inductor, current lags voltage.4. Energy stored in a capacitor is calculated in terms of voltage (1/2 x CV2), and this is done in terms of current for inductor (1/2 x LI2)

Key Difference:Capacitors and inductors are two passive energy storing devices. In capacitors, energy is stored in their electric field. However, in inductors energy is stored in their magnetic field.Capacitor is a device that is used to store an electric charge. It is basically an arrangement of conductors. Due to its characteristics, a capacitor is widely employed in the formation of electronic circuits. A capacitor stores electrical energy directly as an electrostatic field is created between two metal "plates". A capacitor is generally constructed using two metal plates or metal foils separated by an insulator called a dielectric material. Any non-conducting substance can be used as a dielectric material. However, porcelain, mylar, teflon, mica, cellulose are generally preferred. A capacitor is defined by the type of dielectric and electrode material selected. It also defines the application of the capacitor. The dielectric material is the main substance that helps in storing the electrical energy.The value of capacitance is determined by The size of the plates,The distance between them,The type of dielectric material used.Inductor is a passive electronic component that can store electrical energy in the form of magnetic energy. It uses a conductor that is wound into a coil. On the flow of electricity into the coil from the left to the right, a magnetic field gets generated in the clockwise direction. Whenever voltage is applied across an inductor, a current starts to flow. The current does not rise instantly. However, it increases gradually over time. The relationship of voltage to current vs. time gives rise to a property known as inductance. The current creates a magnetic field and due to this magnetic field, electric current is stored for a short interval of time. The electric current drops when the magnetic field around the coil collapses.Comparison between Capacitor and Inductor:CapacitorInductor

DefinitionIn capacitors, energy is stored in their electric field.In inductors, energy is stored in their magnetic field.

Uses High Voltage Electrolytic used in power supplies. Axial Electrolytic - lower voltage smaller size for general purpose where large capacitance values are needed. High Voltage disk ceramic - small size and capacitance value, excellent tolerance characteristics. Metalised Polypropylene - small size for values up to around 2F good reliability. Subminiature Multi layer ceramic chip (surface mount) capacitor. Relatively high capacitance for size achieved by multiple layers. Effectively several capacitors in parallel. Inductors are widely used in AC application like radio, TV, etc. Chokes The property of inductor is used in power supply circuits where AC mains supply needs to be converted to a DC supply. Energy store It is used to create the spark that ignites the petrol in automobile engines. Transformers Inductors with a sharing magnetic path can be combined to form a transformer.

Unit of measurementCapacitance is measured in units called farads (abbreviated F). It is equal to and is equal to a [Ampere-second/Volt]. Since an [Ampere] is a [Coulomb/second], we can also say that a [F]=[C/V].The value of an Inductor is called Inductance and is measured in Henries. It is actually the SI unit of Inductance. It is equal to a [Volt-second/Ampere].

TypesThree major types of capacitors are ceramic, electrolytic, and tantalum: Ceramic capacitors - They are quite smaller in size and value, ranging from a few Pico Farads to 1 F. Electrolytic capacitors - They resemble small cylinders and range in value from 1 F to several Farads. Tantalum capacitors They are quite similar in size to ceramic. However, they can hold more charge, up to several hundred F. They tend to be accurate and stable.Three major types of inductors are Coupled inductors, Multi-Layer Inductors, Ceramic Core Inductor and Molded Inductors: Coupled inductors- They show magnetic flux that is dependent on other conductors to which they are linked. Multi-Layer Inductors - This particular type of inductor consists of a layered coil, wound multiple times around the core. Due to these multiple layers and the insulation between them, multi-layer inductors have a comparatively high inductance level. Ceramic Core Inductors - a ceramic core inductor possess a dielectric ceramic core. It means that it is not capable of storing a lot a lot of energy but has very low distortion and hysteresis. Molded Inductors - These types of inductors are molded using a plastic or ceramic insulation.

Relationship between voltage and current in linear circuitVoltage lags behind Current by /2Current lags behind Voltage by /2

Short circuitA capacitor acts as a short circuit for Alternating Current.An Inductor is equivalent to a short circuit to Direct Current.

Characteristics Capacitors connected in parallel combine like resistors in series Capacitors in series combine like resistors in parallel Inductors in parallel combine like resistors in parallel Inductor in series combine like resistor in series

An inductor and capacitor are both devices that store energy. A capacitor stores charge electrical energy on two conductors separated by some insulating material. Charge collects on the conducting plates in an amount that is proportional to the areas of the conductors, how far they are apart, and the type of insulator used.

A inductor stores energy in a magnetic field. When current flows in a wire a magnetic field is set up circling the wire. Inductors use fact by making the core of the inductor a magnetic material to enhance the magnetic field around the inductor.

They both store energy.

However, inductors store energy in a magnetic field.Capacitors store the energy in an electric field.

Capacitors act as an open circuit to steady-state DCInductors act as a short circuit to steady-state DC

Likewise, capacitors do not allow abrupt changes in voltage.Inductors do not allow abrupt changes in current (this is the reason certain electronics spark as you unplug them)

Capacitors are cheaper and more 'ideal' in the sense that they have little resistance.Inductors have large resistances, and even some capacitance.

The basic electrical property of a capacitor is that the voltage across a capacitor cannot change instantaneously, whereas the basic property of inductance is that the current through an inductor cannot change instantaneously. Capacitors preserve voltage by storing energy in an electric field, whereas inductors preserve current by storing energy in a magnetic field.

in cap: i=C(dv/dt)-----> voltage varies with timein inductor: v=L(di/dt)-----> current varies with time

One result of this is that while capacitors conduct best at higher frequencies, inductors conduct best at lower frequencies. Another result is that if you put an AC current through a capacitor, the voltage will lag behind the current by some phase angle that depends on the capacitance and the frequency - capacitors inhibit changes in voltage. Meanwhile if you put an AC voltage across an inductor, the current will lag behind the voltage by a phase angle that depends on the inductance and the frequency - inductors inhibit changes in current.

We know that reactive loads such as inductors and capacitors dissipate zero power, yet the fact that they drop voltage and draw current gives the deceptive impression that they actuallydodissipate power. This phantom power is calledreactive power, and it is measured in a unit calledVolt-Amps-Reactive(VAR), rather than watts. The mathematical symbol for reactive power is (unfortunately) the capital letter Q. The actual amount of power being used, or dissipated, in a circuit is calledtrue power, and it is measured in watts (symbolized by the capital letter P, as always). The combination of reactive power and true power is calledapparent power, and it is the product of a circuits voltage and current, without reference to phase angle. Apparent power is measured in the unit ofVolt-Amps(VA) and is symbolized by the capital letter S.As a rule, true power is a function of a circuits dissipative elements, usually resistances (R). Reactive power is a function of a circuits reactance (X). Apparent power is a function of a circuits total impedance (Z). Since were dealing with scalar quantities for power calculation, any complex starting quantities such as voltage, current, and impedance must be represented by theirpolar magnitudes, not by real or imaginary rectangular components. For instance, if Im calculating true power from current and resistance, I must use the polar magnitude for current, and not merely the real or imaginary portion of the current. If Im calculating apparent power from voltage and impedance, both of these formerly complex quantities must be reduced to their polar magnitudes for the scalar arithmetic.There are several power equations relating the three types of power to resistance, reactance, and impedance (all using scalar quantities):

Please note that there are two equations each for the calculation of true and reactive power. There are three equations available for the calculation of apparent power, P=IE being usefulonlyfor that purpose. Examine the following circuits and see how these three types of power interrelate for: a purely resistive load in Figurebelow,a purely reactive load in Figurebelow,and a resistive/reactive load in Figurebelow.Resistive load only:

True power, reactive power, and apparent power for a purely resistive load.Reactive load only:

True power, reactive power, and apparent power for a purely reactive load.Resistive/reactive load:

True power, reactive power, and apparent power for a resistive/reactive load.

These three types of powertrue, reactive, and apparentrelate to one another in trigonometric form. We call this thepower triangle: (Figurebelow).

Power triangle relating appearant power to true power and reactive power.Using the laws of trigonometry, we can solve for the length of any side (amount of any type of power), given the lengths of the other two sides, or the length of one side and an angle. REVIEW: Power dissipated by a load is referred to astrue power. True power is symbolized by the letter P and is measured in the unit of Watts (W). Power merely absorbed and returned in load due to its reactive properties is referred to asreactive power. Reactive power is symbolized by the letter Q and is measured in the unit of Volt-Amps-Reactive (VAR). Total power in an AC circuit, both dissipated and absorbed/returned is referred to asapparent power. Apparent power is symbolized by the letter S and is measured in the unit of Volt-Amps (VA). These three types of power are trigonometrically related to one another. In a right triangle, P = adjacent length, Q = opposite length, and S = hypotenuse length. The opposite angle is equal to the circuits impedance (Z) phase angle. Active, Reactive, Apparent and Complex Power. Simple explanation with formulas. (1)Real Power: (P) Alternative words used for Real Power (Actual Power, True Power, Watt-full Power, Useful Power, Real Power, and Active Power) In a DC Circuit, power supply to the DC load is simply the product of Voltage across the load and Current flowing through it i.e., P = V I. because in DC Circuits, there is no concept of phase angle between current and voltage. In other words, there is noPower factorin DC Circuits. But the situation is Sinusoidal or AC Circuits is more complex because of phase difference between Current and Voltage. Therefore average value of power (Real Power) is P = VI Cos is in fact supplied to the load. In AC circuits, When circuit is pure resistive, then the same formula used for power as used in DC as P = V I. You may also read aboutPower Formulas in DC, AC Single Phase and and AC Three Phase Circuits. Real Power formulas: P = V I(In DC circuits) P = VI Cos(in Single phase AC Circuits) P = 3 VLILCosor(in Three Phase AC Circuits) P = 3 VPhIPhCos P = (S2 Q2)or P = (VA2 VAR2) or Real or True power = (Apparent Power2 Reactive Power2) or kW = (kVA2 kVAR2) (2)Reactive Power: (Q) Also known as (Use-less Power, Watt less Power) The powers that continuously bounce back and forth between source and load is known as reactive Power (Q) Power merely absorbed and returned in load due to its reactive properties is referred to asreactive power The unit of Active or Real power is Watt where 1W = 1V x 1 A. Reactive power represent that the energy is first stored and then released in the form of magnetic field or electrostatic field in case of inductor and capacitor respectively. Reactive power is given by Q = V I Sin which can be positive (+ve) for inductive, negative (-Ve) for capacitive load. The unit of reactive power is Volt-Ampere reactive. I.e. VAR where 1 VAR = 1V x 1A. In more simple words, in Inductor or Capacitor, how much magnetic or electric field made by 1A x 1V is called the unit of reactive power. Reactive power formulas: Q = V I Sin Reactive Power= (Apparent Power2 True power2) VAR = (VA2 P2) kVAR = (kVA2 kW2) (3)Apparent Power: (S) The product of voltage and current if and only if the phase angle differences between current and voltage are ignored. Total power in an AC circuit, both dissipated and absorbed/returned is referred to asapparent power The combination of reactive power and true power is calledapparent power In an AC circuit, the product of the r.m.s voltage and the r.m.s current is calledapparent power. It is the product of Voltage and Current without phase angle The unit of Apparent power (S) VA i.e. 1VA = 1V x 1A. When the circuit is pure resistive, then apparent power is equal to real or true power, but in inductive or capacitive circuit, (when Reactances exist) then apparent power is greater than real or true power. Apparent power formulas: S = V I Apparent Power = (True power2+ Reactive Power2) kVA = kW2+ kVAR2 AlsoNote that; Resistor absorbs the real power and dissipates in the form of heat and light. Inductor absorbs the reactive power and dissipates in the form of magnetic field Capacitor absorbs the reactive power and dissipates in the form of electric or electrostatic filed These all quantities trigonometrically related to each other as shown in below figure. Click image to enlarge For more Clearance andexplanation., i used Lays Chips and Beer Analogy for Real or True Power, Reactive Power , Apparent power andpower factorLays Chips Analogy of Real or True Power, Reactive Power, Apparent power &power factor Click image to enlarge Beer Analogy of Active or True power, Reactive power, Apparent Power and Power factor.

If you want to gain an intuitive understanding of how this can be true, let's consider first an inductor, because this makes a better physical analogy. In an AC circuit with an inductive load, voltage leads current by 90 degrees. It's the opposite of a capacitive load.Why? Well, an inductor is like a flywheel that gives inertia to current. The proper name for voltage is electromotive force. That is, it's aforcethat causeselectricityto move. When electricity moves, we call it a current.Imagine a flywheel. The angular inertia (size and weight) of the flywheel is the value of the inductor. The voltage is a force you apply to the flywheel. The current is the speed the flywheel is spinning. Now, say you apply a force to this flywheel. It does not begin spinning instantly. Rather, the force you apply accelerates it. Now, you apply force in the other direction. It does not immediately reverse direction. First it must slow, and eventually it will turn the other way. But by the time it has done this, you have moved on and have changed your direction of force yet again.If the force you apply is sinusoidal, and there is no friction (resistance) in the spinning of the flywheel, then the speed of the flywheel will be 90 degrees out of phase with the force that's being applied to it.Now, go develop agood mental model of a capacitor, and consider the same sort of thing. It should make more sense, just with current and voltage reversed, or the phase shift in the other direction.The formula for current through a capacitor is:I = C * (dV / dt)The small d stands for a tiny change, known as delta()This means the faster the voltage change, the higher the current through the capacitor. The capacitor acts as a differentiator.Now if we connect a sine wave voltage across a capacitor, the calculation for the current is the derivative of this voltage.From calculus, we know that the derivative of sin(t) is cos(t):

If we plot these values:

You can see that when the voltage is changing fastest (at it's zero crossing), the current is at the maximum, and when the voltage is not changing (at the peak of the sine wave) the current is zero. We can see the 90 phase shift clearly.This also explains why a capacitor blocks DC but passes AC.In an inductor, voltage leads current, because in an inductor, there is drag on the current flow. You could call it inertia, but basically it is the electromagnetic field the inductor produces as it energizes. This field gives current "momentum" because when the supply voltage changes, the magnetic field which has already established itself will attempt to maintain the same current flow, slowing down the "response time" of the current. The field also resists initial power up, due to the same "inertia". Imagine a guy with a steel ball chained to his leg - he is the voltage and the ball is the current he's dragging around with him. Once he can get the ball rolling, it does not want to stop.Capacitors on the other hand work by loading up one side of a dielectric medium with electrons. This time we can imagine the same guy only plowing snow with a snow shovel. The snow (current) is leading by 90 degrees out of phase because the applied voltage is directly proportional to how much excess electrons (current) are stacked up one side of the capacitor. As the snow shovel gets full, there comes a point where we can't push any more - voltage between the capacitor and supply is zero, however measuring across the cap terminals will equal supply voltage. The electrons flowing is the catalyst that changes the voltage as it passes through the capacitor, thus current leads phase.The phase shift idea can be understood and explained intuitively by means of the water analogy. Imagine you fill (sinusoidally) a vessel with water and you picture graphically this process (choose the half of the maximum water height as a zero level - the ground).Analogy.So, you first open and then close (sinusoidally) the supply faucet. But note no matter you close the faucet (in the second part of the process) the level of the water continues rising... it is strange that you close the faucet but the water still continue rising... Finally, the faucet completely closed (zero current), but the level of the water (the voltage) is maximum.Now, at this point, you have to change the flow (current) direction to make the water level decrease. For this purpose, you open (and later close) another faucet at the bottom to draw the water (now you draw a current from the capacitor). But again, no matter you close the faucet the level of water continues falling... and it is strange again that you close the faucet but the water still continues falling. Finally, you have completely closed the faucet (zero current), but the level of the water will be maximum negative (maximum negative voltage).So, the basic idea behind all kind of such elements storing pressure-like quantities (water, air, sand, money, data...) namedintegratorsis:The sign of the output pressure-like quantitty can be changed only by changing the direction of the input flow-like quantity (current, water flow, air flow, etc.); it cannot be changed by changing the magnitude of the flow-like quantity.Capacitor.Let's now explain this phenomenon fully electrically. Imagine we drive a capacitor by a sinusoidal current source ("current source" means that it produces and passes a sinusoidal current in spite of all). No matter what the voltage (drop) across the capacitor is - zero (empty capacitor), positive (charged capacitor) or even negative (reverse charged capacitor), our current source will pass the desired current with desired direction through the capacitor. The voltage across the capacitor does not impede the current (it impedes but the current source compensates it).So, until the input current is positive (imagine the positive half-sine wave) it enters the capacitor and its voltage continously increases in spite of the current's magnitude (only the rate of change varies)... Imagine... the current rapidly increases -> slows down -> rapidly decreases... and finally becomes zero. At this moment there is a maximum voltage (drop) across the capacitor.Thus, at the maximum voltage across the capacitor, there is no current through it... Now the current changes its direction and begins rapidly increasing again -> slows down -> rapidly decreases... and becomes zero again... and again and again and again...So, in this arrangement, the phase shift is constant and exactly 90 degree because of the ideal input current source that compensates somehow the voltage drop (losses) across the capacitor.RC circuit.Let's now consider the ubiquitous RC circuit. First, let's build it. Since it is incorrect to drive a capacitor directly by a voltage source, we have to drive it by a current source. For this purpose, let's connect a resistor between the voltage source and the capacitor to convert the input voltage to a current; so, the resistor acts here as avoltage-to-current converter.Imagine how the input voltage VIN changes in a sinusoidal manner. In the beginning, the voltage rapidly increases and a current I = (VIN - VC)/R flows from the input source through the resistor and enters the capacitor; the output voltage begins increasing lazy. After some time, the input voltage approaches the sine peak and then begins decreasing. But until the input voltage is higher than the voltage across the capacitor the current continues flowing in the same direction. As above, it is strange that the input voltage decreases but the capacitor voltage continues increasing. Figuratively speaking, the two voltages move against each other and finally meet. At this instant, the two voltages become equal; the current is zero and the capacitor voltage is maximum. The input voltage continues decreasing and becomes less than the capacitor voltage. The current changes its direction, begins flowing from the capacitor through the resistor and enters the input voltage source.It is very interesting that the capacitor acts as a voltage source that "pushes" a current into the input voltage source acting as a load. Before the source was a source and the capacitor was a load; now, the source is a load and the capacitor is a source...So, the moment where the two voltages become equal and the current changes its direction is the moment of the maximum output voltage. Note it depends on the rate of changing (the frequency) of the input voltage: as higher the frequency is, as low the maximum voltage across the capacitor is... as later the moment is... as bigger the phase shift between the two voltages is... At the maximum frequency, the voltage across the capacitor cannot move from the ground and the moment of the current direction change is when the input voltage crosses the zero (the situation is similar to the arrangement of a current-supplied capacitor).The conclusion is that,in this arrangement, the phase shift varies from zero to 90 degree when the frequency varies from zero to infinity because of the imperfect input current source that cannot compensate the voltage drop (losses) across the capacitor.Consider a circuit for a single-phase AC power system, where a 120 volt, 60 Hz AC voltage source is delivering power to a resistive load: (Figurebelow)

Ac source drives a purely resistive load.

In this example, the current to the load would be 2 amps, RMS. The power dissipated at the load would be 240 watts. Because this load is purely resistive (no reactance), the current is in phase with the voltage, and calculations look similar to that in an equivalent DC circuit. If we were to plot the voltage, current, and power waveforms for this circuit, it would look like Figurebelow.

Current is in phase with voltage in a resistive circuit.Note that the waveform for power is always positive, never negative for this resistive circuit. This means that power is always being dissipated by the resistive load, and never returned to the source as it is with reactive loads. If the source were a mechanical generator, it would take 240 watts worth of mechanical energy (about 1/3 horsepower) to turn the shaft.Also note that the waveform for power is not at the same frequency as the voltage or current! Rather, its frequency isdoublethat of either the voltage or current waveforms. This different frequency prohibits our expression of power in an AC circuit using the same complex (rectangular or polar) notation as used for voltage, current, and impedance, because this form of mathematical symbolism implies unchanging phase relationships. When frequencies are not the same, phase relationships constantly change.As strange as it may seem, the best way to proceed with AC power calculations is to usescalarnotation, and to handle any relevant phase relationships with trigonometry.For comparison, lets consider a simple AC circuit with a purely reactive load in Figurebelow.

AC circuit with a purely reactive (inductive) load.

Power is not dissipated in a purely reactive load. Though it is alternately absorbed from and returned to the source.Note that the power alternates equally between cycles of positive and negative. (Figureabove) This means that power is being alternately absorbed from and returned to the source. If the source were a mechanical generator, it would take (practically) no net mechanical energy to turn the shaft, because no power would be used by the load. The generator shaft would be easy to spin, and the inductor would not become warm as a resistor would.Now, lets consider an AC circuit with a load consisting of both inductance and resistance in Figurebelow.

AC circuit with both reactance and resistance.

At a frequency of 60 Hz, the 160 millihenrys of inductance gives us 60.319 of inductive reactance. This reactance combines with the 60 of resistance to form a total load impedance of 60 + j60.319 , or 85.078 45.152o. If were not concerned with phase angles (which were not at this point), we may calculate current in the circuit by taking the polar magnitude of the voltage source (120 volts) and dividing it by the polar magnitude of the impedance (85.078 ). With a power supply voltage of 120 volts RMS, our load current is 1.410 amps. This is the figure an RMS ammeter would indicate if connected in series with the resistor and inductor.We already know that reactive components dissipate zero power, as they equally absorb power from, and return power to, the rest of the circuit. Therefore, any inductive reactance in this load will likewise dissipate zero power. The only thing left to dissipate power here is the resistive portion of the load impedance. If we look at the waveform plot of voltage, current, and total power for this circuit, we see how this combination works in Figurebelow.

A combined resistive/reactive circuit dissipates more power than it returns to the source. The reactance dissipates no power; though, the resistor does.As with any reactive circuit, the power alternates between positive and negative instantaneous values over time. In a purely reactive circuit that alternation between positive and negative power is equally divided, resulting in a net power dissipation of zero. However, in circuits with mixed resistance and reactance like this one, the power waveform will still alternate between positive and negative, but the amount of positive power will exceed the amount of negative power. In other words, the combined inductive/resistive load will consume more power than it returns back to the source.Looking at the waveform plot for power, it should be evident that the wave spends more time on the positive side of the center line than on the negative, indicating that there is more power absorbed by the load than there is returned to the circuit. What little returning of power that occurs is due to the reactance; the imbalance of positive versus negative power is due to the resistance as it dissipates energy outside of the circuit (usually in the form of heat). If the source were a mechanical generator, the amount of mechanical energy needed to turn the shaft would be the amount of power averaged between the positive and negative power cycles.

Mathematically representing power in an AC circuit is a challenge, because the power wave isnt at the same frequency as voltage or current. Furthermore, the phase angle for power means something quite different from the phase angle for either voltage or current. Whereas the angle for voltage or current represents a relativeshift in timingbetween two waves, the phase angle for power represents aratiobetween power dissipated and power returned. Because of this way in which AC power differs from AC voltage or current, it is actually easier to arrive at figures for power by calculating withscalarquantities of voltage, current, resistance, and reactance than it is to try to derive it fromvector, orcomplexquantities of voltage, current, and impedance that weve worked with so far. REVIEW: In a purely resistive circuit, all circuit power is dissipated by the resistor(s). Voltage and current are in phase with each other. In a purely reactive circuit, no circuit power is dissipated by the load(s). Rather, power is alternately absorbed from and returned to the AC source. Voltage and current are 90oout of phase with each other. In a circuit consisting of resistance and reactance mixed, there will be more power dissipated by the load(s) than returned, but some power will definitely be dissipated and some will merely be absorbed and returned. Voltage and current in such a circuit will be out of phase by a value somewhere between 0oand 90o.The AC WaveformDirect CurrentorD.C.as it is more commonly called, is a form of current or voltage that flows around an electrical circuit in one direction only, making it a Uni-directional supply. Generally, both DC currents and voltages are produced by power supplies, batteries, dynamos and solar cells to name a few. A DC voltage or current has a fixed magnitude (amplitude) and a definite direction associated with it. For example,+12Vrepresents 12 volts in the positive direction, or-5Vrepresents 5 volts in the negative direction.We also know that DC power supplies do not change their value with regards to time, they are a constant value flowing in a continuous steady state direction. In other words, DC maintains the same value for all times and a constant uni-directional DC supply never changes or becomes negative unless its connections are physically reversed. An example of a simple DC or direct current circuit is shown below.DC Circuit and Waveform

An alternating function orAC Waveformon the other hand is defined as one that varies in both magnitude and direction in more or less an even manner with respect to time making it a Bi-directional waveform. An AC function can represent either a power source or a signal source with the shape of anAC waveformgenerally following that of a mathematical sinusoid as defined by:-A(t)=Amaxxsin(2t).The term AC or to give it its full description ofAlternating Current, generally refers to a time-varying waveform with the most common of all being called aSinusoidbetter known as aSinusoidal Waveform. Sinusoidal waveforms are more generally called by their short description asSine Waves. Sine waves are by far one of the most important types of AC waveform used in electrical engineering.The shape obtained by plotting the instantaneous ordinate values of either voltage or current against time is called anAC Waveform. An AC waveform is constantly changing its polarity every half cycle alternating between a positive maximum value and a negative maximum value respectively with regards to time with a common example of this being the domestic mains voltage supply we use in our homes.This means then that theAC Waveformis a time-dependent signal with the most common type of time-dependant signal being that of thePeriodic Waveform. The periodic or AC waveform is the resulting product of a rotating electrical generator. Generally, the shape of any periodic waveform can be generated using a fundamental frequency and superimposing it with harmonic signals of varying frequencies and amplitudes but thats for another tutorial.Alternating voltages and currents can not be stored in batteries or cells like direct current (DC) can, it is much easier and cheaper to generate these quantities using alternators or waveform generators when they are needed. The type and shape of an AC waveform depends upon the generator or device producing them, but all AC waveforms consist of a zero voltage line that divides the waveform into two symmetrical halves. The main characteristics of anAC Waveformare defined as:AC Waveform Characteristics The Period, (T)is the length of time in seconds that the waveform takes to repeat itself from start to finish. This can also be called thePeriodic Timeof the waveform for sine waves, or thePulse Widthfor square waves. The Frequency, ()is the number of times the waveform repeats itself within a one second time period. Frequency is the reciprocal of the time period, (=1/T) with the unit of frequency being theHertz, (Hz). The Amplitude (A)is the magnitude or intensity of the signal waveform measured in volts or amps.In our tutorial aboutWaveforms,we looked at different types of waveforms and said that Waveformsare basically a visual representation of the variation of a voltage or current plotted to a base of time. Generally, for AC waveforms this horizontal base line represents a zero condition of either voltage or current. Any part of an AC type waveform which lies above the horizontal zero axis represents a voltage or current flowing in one direction.Likewise, any part of the waveform which lies below the horizontal zero axis represents a voltage or current flowing in the opposite direction to the first. Generally for sinusoidal AC waveforms the shape of the waveform above the zero axis is the same as the shape below it. However, for most non-power AC signals including audio waveforms this is not always the case.The most common periodic signal waveforms that are used in Electrical and Electronic Engineering are theSinusoidal Waveforms. However, an alternating AC waveform may not always take the shape of a smooth shape based around the trigonometric sine or cosine function. AC waveforms can also take the shape of eitherComplex Waves,Square WavesorTriangular Wavesand these are shown below.Types of Periodic Waveform

The time taken for anAC Waveformto complete one full pattern from its positive half to its negative half and back to its zero baseline again is called aCycleand one complete cycle contains both a positive half-cycle and a negative half-cycle. The time taken by the waveform to complete one full cycle is called thePeriodic Timeof the waveform, and is given the symbolT.The number of complete cycles that are produced within one second (cycles/second) is called theFrequency, symbolof the alternating waveform. Frequency is measured inHertz, (Hz) named after the German physicist Heinrich Hertz.Then we can see that a relationship exists between cycles (oscillations), periodic time and frequency (cycles per second), so if there arenumber of cycles in one second, each individual cycle must take1/seconds to complete.Relationship Between Frequency and Periodic Time

AC Waveform Example No11. What will be the periodic time of a 50Hz waveform and 2. what is the frequency of an AC waveform that has a periodic time of 10mS.1).

2).

Frequency used to be expressed in cycles per second abbreviated to cps, but today it is more commonly specified in units called Hertz. For a domestic mains supply the frequency will be either 50Hz or 60Hz depending upon the country and is fixed by the speed of rotation of the generator. But one hertz is a very small unit so prefixes are used that denote the order of magnitude of the waveform at higher frequencies such askHz,MHzand evenGHz.Definition of Frequency PrefixesPrefixDefinitionWritten asPeriodic Time

KiloThousandkHz1ms

MegaMillionMHz1us

GigaBillionGHz1ns

TerraTrillionTHz1ps

Amplitude of an AC WaveformAs well as knowing either the periodic time or the frequency of the alternating quantity, another important parameter of the AC waveform isAmplitude, better known as its Maximum or Peak value represented by the terms,Vmaxfor voltage orImaxfor current.The peak value is the greatest value of either voltage or current that the waveform reaches during each half cycle measured from the zero baseline. Unlike a DC voltage or current which has a steady state that can be measured or calculated usingOhms Law, an alternating quantity is constantly changing its value over time.For pure sinusoidal waveforms this peak value will always be the same for both half cycles (+Vm=-Vm) but for non-sinusoidal or complex waveforms the maximum peak value can be very different for each half cycle. Sometimes, alternating waveforms are given apeak-to-peak,Vp-pvalue and this is simply the distance or the sum in voltage between the maximum peak value,+Vmaxand the minimum peak value,-Vmaxduring one complete cycle.The Average Value of an AC WaveformThe average or mean value of a continuous DC voltage will always be equal to its maximum peak value as a DC voltage is constant. This average value will only change if the duty cycle of the DC voltage changes. In a pure sine wave if the average value is calculated over the full cycle, the average value would be equal to zero as the positive and negative halves will cancel each other out. So the average or mean value of an AC waveform is calculated or measured over a half cycle only and this is shown below.Average Value of a Non-sinusoidal Waveform

To find the average value of the waveform we need to calculate the area underneath the waveform using the mid-ordinate rule, trapezoidal rule or the Simpsons rule found commonly in mathematics. The approximate area under any irregular waveform can easily be found by simply using the mid-ordinate rule.The zero axis base line is divided up into any number of equal parts and in our simple example above this value was nine, (V1to V9). The more ordinate lines that are drawn the more accurate will be the final average or mean value. The average value will be the addition of all the instantaneous values added together and then divided by the total number. This is given as.Average Value of an AC Waveform

Where:nequals the actual number of mid-ordinates used.For a pure sinusoidal waveform this average or mean value will always be equal to0.637xVmaxand this relationship also holds true for average values of current.The RMS Value of an AC WaveformThe average value of an AC waveform is NOT the same value as that for a DC waveforms average value. This is because the AC waveform is constantly changing with time and the heating effect given by the formula (P=I2.R), will also be changing producing a positive power consumption. The equivalent average value for an alternating current system that provides the same power to the load as a DC equivalent circuit is called the effective value.This effective power in an alternating current system is therefore equal to: (I2.R.Average). As power is proportional to current squared, the effective current,Iwill be equal toI squaredAve. Therefore, the effective current in an AC system is called theRoot Mean SquaredorR.M.S.value and RMS values are the DC equivalent values that provide the same power to the load.The effective or RMS value of an alternating current is measured in terms of the direct current value that produces the same heating effect in the same value resistance. The RMS value for any AC waveform can be found from the following modified average value formula.RMS Value of an AC Waveform

Where:nequals the number of mid-ordinates.

For a pure sinusoidal waveform this effective or R.M.S. value will always be equal to1/2xVmaxwhich is equal to0.707xVmaxand this relationship holds true for RMS values of current. The RMS value for a sinusoidal waveform is always greater than the average value except for a rectangular waveform. In this case the heating effect remains constant so the average and the RMS values will be the same.One final comment about R.M.S. values. Most multimeters, either digital or analogue unless otherwise stated only measure the R.M.S. values of voltage and current and not the average. Therefore when using a multimeter on a direct current system the reading will be equal toI=V/Rand for an alternating current system the reading will be equal toIrms=Vrms/R.Also, except for average power calculations, when calculating RMS or peak voltages, only use VRMSto find IRMSvalues, or peak voltage, Vp to find peak current, Ip values. Do not mix the two together average, RMS or peak values as they are completely different and your results will be incorrect.Form Factor and Crest FactorAlthough little used these days, bothForm FactorandCrest Factorcan be used to give information about the actual shape of the AC waveform. Form Factor is the ratio between the average value and the RMS value and is given as.

For a pure sinusoidal waveform the Form Factor will always be equal to1.11. Crest Factor is the ratio between the R.M.S. value and the Peak value of the waveform and is given as.

For a pure sinusoidal waveform the Crest Factor will always be equal to1.414.AC Waveform Example No2A sinusoidal alternating current of 6 amps is flowing through a resistance of 40. Calculate the average voltage and the peak voltage of the supply.The R.M.S. Voltage value is calculated as:

The Average Voltage value is calculated as:

The Peak Voltage value is calculated as:

The use and calculation of Average, R.M.S, Form factor and Crest Factor can also be use with any type of periodic waveform including Triangular, Square, Sawtoothed or any other irregular or complex voltage/current waveform shape. Conversion between the various sinusoidal values can sometimes be confusing so the following table gives a convenient way of converting one sine wave value to another.Sinusoidal Waveform Conversion TableConvert FromMultipy ByOr ByTo Get Value

Peak2(2)2Peak-to-Peak

Peak-to-Peak0.51/2Peak

Peak0.70711/(2)RMS

Peak0.6372/Average

Average1.570/2Peak

Average1.111/(22)RMS

RMS1.4142Peak

RMS0.901(22)/Average

In the next tutorial aboutSinusoidal Waveformswe will look at the principal of generating a sinusoidal AC waveform (a sinusoid) along with its angular velocity representation.

Reactive Power CompensationReactive Powercan best be described as the quantity of unused power that is developed by reactive components, such as inductors or capacitors in an AC circuit or system. In a DC circuit, the product of volts x amps gives the power consumed in watts by the circuit. However, while this formula is also true for purely resistive AC circuits, the situation is slightly more complex in an AC circuits containing reactive components as this volt-amp product can change with frequency.In an AC circuit, the product of voltage and current is expressed as volt-amperes (VA) or kilo volt-amperes (kVA) and is known asApparent power, symbolS. In a non-inductive purely resistive circuit such as heaters, irons, kettles and filament bulbs, etc. their reactance is practically zero, and the impedance of the circuit is composed almost entirely of just resistance.For an AC resistive circuit, the current and voltage are in-phase and the power at any instant can be found by multiplying the voltage by the current at that instant, and because of this in-phase relationship, the rms values can be used to find the equivalent DC power or heating effect.However, if the circuit contains reactive components, the voltage and current waveforms will be out-of-phase by some amount determined by the circuits phase angle. If the phase angle between the voltage and the current is at its maximum of 90o, the volt-amp product will have equal positive and negative values.In other words, the reactive circuit returns as much power to the supply as it consumes resulting in the average power consumed by the circuit being zero, as the same amount of energy keeps flowing alternately from source to the load and back from load to source.Since we have a voltage and a current but no power dissipated, the expression of P = IV (rms) is no longer valid and it therefore follows that the volt-amp product in an AC circuit does not necessarily give the power consumed. Then in order to determine the real power, also calledActive power, symbolPconsumed by an AC circuit, we need to account for not only the volt-amp product but also the phase angle difference between the voltage and the current waveforms given by the equation:VI.cos.Then we can write the relationship between the apparent power and active or real power as:

Note that power factor (PF) is defined as the ratio between the active power in watts and the apparent power in volt-amperes and indicates how effectively electrical power is being used. In a non-inductive resistive AC circuit, the active power will be equal to the apparent power as the fraction ofP/Sbecomes equal to one or unity. A circuits power factor can be expressed either as a decimal value or as a percentage.But as well as the active and apparent powers in AC circuits, there is also another power component that is present whenever there is a phase angle. This component is calledReactive Power(sometimes referred to as imaginary power) and is expressed in a unit called volt-amperes reactive, (VAr), symbolQand is given by the equation:VI.sin.Reactive power, or VAr, is not really power at all but represents the product of volts and amperes that are out-of-phase with each other. The amount of reactive power present in an AC circuit will depend upon the phase shift or phase angle between the voltage and the current and just like active power, reactive power is positive when it is supplied and negative when it is consumed.The relationship of the three elements of power, active power, (watts) apparent power, (VA) and reactive power, (VAr) in an AC circuit can be represented by the three sides of right-angled triangle. This representation is called aPower Triangleas shown:Power in an AC Circuit

From the above power triangle we can see that AC circuits supply or consume two kinds of power: active power and reactive power. Also, active power is never negative, whereas reactive power can be either positive or negative in value so it is always advantageous to reduce reactive power in order to improve system efficiency.The main advantage of using AC electrical power distribution is that the supply voltage level can be changed using transformers, but transformers and induction motors of household appliances, air conditioners and industrial equipment all consume reactive power which takes up space on the transmission lines since larger conductors and transformers are required to handle the larger currents which you need to pay for.

Reactive Power Analogy with BeerIn many ways, reactive power can be thought of like the foam head on a pint or glass of beer. You pay the barman for a full glass of beer but only drink the actual liquid beer which is always less than a full glass.This is because the head (or froth) of the beer takes up additional wasted space in the glass leaving less room for the real beer that you consume, and the same idea is true for reactive power.But for many industrial power applications, reactive power is often useful for an electrical circuit to have. While the real or active power is the energy supplied to run a motor, heat a home, or illuminate an electric light bulb, reactive power provides the important function of regulating the voltage thereby helping to move power effectively through the utility grid and transmission lines to where it is required by the load.While reducing reactive power to help improve the power factor and system efficiency is a good thing, one of the disadvantages of reactive power is that a sufficient quantity of it is required to control the voltage and overcome the losses in a transmission network. This is because if the electrical network voltage is not high enough, active power cannot be supplied. But having too much reactive power flowing around in the network can cause excess heating (I2Rlosses) and undesirable voltage drops and loss of power along the transmission lines.Power Factor Correction of Reactive PowerOne way to avoid reactive power charges, is to install power factor correction capacitors. Normally residential customers are charged only for the active power consumed in kilo-watt hours (kWhr) because nearly all residential and single phase power factor values are essentially the same due to power factor correction capacitors being built into most domestic appliances by the manufacturer.Industrial customers, on the other hand, which use 3-phase supplies have widely different power factors, and for this reason, the electrical utility may have to take the power factors of these industrial customers into account paying a penalty if their power factor drops below a prescribed value because it costs the utility companies more to supply industrial customers since larger conductors, larger transformers, larger switchgear, etc, is required to handle the larger currents.Generally, for a load with a power factor of less than 0.95 more reactive power is required. For a load with a power factor value higher than 0.95 is considered good as the power is being consumed more effectively, and a load with a power factor of 1.0 or unity is considered perfect and does not use any reactive power.Then we have seen that apparent power is a combination of both reactive power and active power. Active or real power is a result of a circuit containing resistive components only, while reactive power results from a circuit containing either capacitive and inductive components. Almost all AC circuits will contain a combination of theseR, LandCcomponents.Since reactive power takes away from the active power, it must be considered in an electrical system to ensure that the apparent power supplied is sufficient to supply the load. This is a critical aspect of understanding AC power sources because the power source must be capable of supplying the necessary volt-amp (VA) power for any given load.MVA is the aparant power, MW is the real power and, MVAR is reactive power. If you remember your Circuit II course MVA is the Square Root of MW^2+MVAR^2. Just like a right triangle. It is actually called the power triangle. You adjust the MW of a plant based on the load on the grid. Generation = Load at all times. You adjust the MVAR of the machine to adjust grid voltage in the local area. MVARs are the result of the magnetic coupling needed to produce work with a machine. They are not exportable therefor you either have local generation or capacitor banks provide them. You adjust the MW of the machine with the amount of torque you apply to the input shaft of the machine. This usually means more steam to the turbine. This tries to speed up the machine against the grid and produces more power. You adjust the MVAR output of the machine by adjusting the exciter of the machine. That is to raise MVAR output you excite the machine more by increasing the current in the field (rotor). This increases the magnetic coupling of the rotor to the stator and increases the MVAR output.BEPC13 explained it correctly however, it may be clearer to simply state that an MVAR meter in a power plant is a center zero device. By raising the machine volts the generator will export VARs to the system and conversely by decreasing the machine volts VARs will be imported to the generator. When I was working as a power plant operator shortly after graduating in the early 60s. Each power station on the grid had to maintain its voltage within given parameters. This generally mean't that the voltage on the outgoing line was had to be kept at its nominal kV. The power plant I operated, was on the end of a 132kV spur line some 120 miles from the main 330kV interconnected system, and the voltage used to vary substantially over 24hrs. During the night on light system loads, the voltage would rise and we would have to import VARs by lowering the generator volts and during peak periods on high system loads, raise the generator volts and export VARs to maintain nominal voltage on the 132kV feeder. I guess these days the system controllers spread the VAR loads around much better than we did in the old days.....

With regards to"What happens when all those workers turn off their motor driven machines at the end of the work day and go home and turn on their electric space heaters, coffee pots, toasters, ovens, and lights.You get the picture, purely resistive load, approaching unity power factor" as aked by the previous thread, the following happens.First of all as the overall system MW decrease, the systemvoltage tends to rise. To control the volts, inductive MVARs have to be generated by either switching in reactors or reducing MVARs by reducing volts on the generators supplying MVARs to the system.With regards to Utility companies charging for MVARs. as it wattless current (except for I2R losses)utility companies do not have fuel costs generating VARs. So should only charge for generator losses etc. which would be very small.Reactive power supply is essential for reliably operating the electric transmission system. Inadequate reactive power has led to voltage collapses and has been a major cause of several recent major power outages worldwide

One source for supply or absolve reactive power is a generator. For instance, when a generator is operating at certain limits, a generator can increase its dynamic reactive power is produced from equipment that can quickly change the Mvar level independent of the voltage level. Thus, the equipment can increase its reactive power production level when voltage drops and prevent a voltage collapse.By convention, reactive power, like real power, is positive when it is supplied and negative when it is consumed. Consuming reactive power lowers voltage magnitudes, while supplying reactive power increases voltage magnitudes.

We should keep in mind that a production or consumption of reactive power by a generator only could be done by reducing its production of real power. As a result, producing additional reactive power results in reduced revenues associated with reduced real-power production. This may be seen in the generator capability curve similar to the one enclose below.Reactive power must be produced by the utility to compensate for reactive power consumed in its own systems and for that consumed by customers. It utilizes T&D capacity and it wastes real power due to the I^2R losses it creates.

Generators, capacitors, synchronous condensers and static VAR compensators are all used to produce reactive power. Capacitors are usually distributed around the network for voltage control and to get VAR production as close to the VAR consumption as possible to minimize I^2R losses and capacity utilization. Switched capacitors are used to help stabilize voltage as reactive loads fluctuate.The generator is a voltage source, when it is considered as an electrical component in a network.The parameters of a voltage source, or, in this case, a generator in a large ("infinite") network are the magnitude and the phase of the internal voltage. This internal voltage is induced in the stator windings by the rotating magnetic field of the rotor. The voltage source, i.e. the generator has also an internal impedance. The induced voltage can be thought to be behind this fixed internal impedance.A generator has several variables that one wants to control: The magnitude and phase angle of the internal voltage,the power, and the reactive power, at least. There are two control variables: the throttle position of the prime mover and the magnetisation current. How do you control those four variables with these two control variables? Well, you don't, at least not at the same time.

The effects of the throttle and the magnetisation current are not quite simple. When one opens the throttle a little from the present position, the generator attempts to increase the rotating speed, i.e. the frequency.But if the generator is a part of a large network containing several generators, it cannot increase the speed, because it has not enough power to force all the other generators to accept the same speed. The result is that the relative position of the rotor only advances a little. This means that the phase angle (the "power angle")of the induced voltage changes in the positive direction, because it is determined by the relative rotor position.

When the magnetisation current is increased, the magnet of the rotor becomes stronger and the magnitude of the induced voltage in the stator windings increases. But a larger voltage means a larger current and a larger power and a larger loading of the prime mover. This loading attempts to slow down the prime mover and the rotor. Again, it is not possible to reduce the rotating speed because of the large network. If the throttle position and thus power are kept constant, the relative position of the rotor retards a little, so that the "power angle" becomes smaller.

In a summary: The magnetisation current controls both the magnitude and phase of the internal voltage. The throttle position controls the phase of the internal voltage. These controls must be used together in practice, as rcwilson writes.

The change in the power and the reactive power depends on how these two control variables are operated. The analysis is fortunately simplified by the assumption that the generator sits in a large network containing several generators. This means that the voltage at the terminals of the generator can be assumed to be constant. The reason is the same as that for the constant frequency: One generator cannot do much about the voltage at the terminals, it can only adjust the internal voltage.

The internal impedance Zsof a generator is typically almost purely inductive, the resistance is very small, Zs = jXs. If Ef is the induced internal voltage, and V is the voltage at the terminals, then the generator current is simply Is = (Ef V)/jXs=-j(Ef V)/Xs. This current is 90 degrees behind the voltage difference Ef V, but it may lead or lag the voltage V at the terminals.

It is known that 1) the voltage V is given, 2) the reactance Xs is given and fixed, 3) the magnitude and phase of the voltage Ef are controlled by the magnetisation current, and 4) the phase of Ef is controlled by the throttle position. It should now be possible (but not necessarily easy) to see what happens to the real and reactive power in different control operations. (Remember, the complex power P + jQ = voltage times the complex conjugate of current.)

So, what happens, when the power is increased, but the magnetisation current is kept constant, as rmw asks? See figure 2.6b in the above reference. The induced voltage vector Ef turns counter-clockwise, with a constant magnitudes, i.e. the phase moves in the positive direction. As a consequence, the phase of the current moves also in the positive direction and its magnitude increases. The reactive power Qbecomes less negative first, then zero, and eventually positive.See figure 2.8 in the link above for the opposite case of a constant power and varying magnetisation current.

That was a lengthyexplanation, and I hope that I got it right.

To explain it simply:Apparent power is measured in Volt-Amps (usually kVA)Apparent Power = Voltage x Current

Real Power is measured in Watts and takes into account power factor.Real Power = Apparent Power x power factor.jghrist(Electrical)28 Oct 05 08:32Seehttp://www.kilowattclassroom.com/Archive/PWR.pdffor a basic explanation.cuky2000(Electrical)28 Oct 05 10:30To explain the physical meaning of real (active) and apparent (reactive) power, consider an engine couple to a generator:

-The power delivered in the shaft of the engine can be converted to active power by the generator witch is consumed by the load (ex. Motors, heating, lighting, etc).-The engine does not produce reactive power; however, the generator does. This power is used to magnetize the inductive components of circuits (ex. Motors, capacitor, line, ballast & transformers, etc.).This power keeps circulating in the system without requiring extra active power from the engine.

The additional current produced by the demand of reactive power will increase the size and capacity of the electrical components such as cable, generators, transformer, etc.

Fro additioanl reference see the enclose sitehttp://www.ibiblio.org/obp/electricCircuits/AC/AC_11.htmlunclebob(Electrical)28 Oct 05 11:16Here is a nice exemple:

Suppose you have a glass of beer.The liquid represent real power because it quench your thirst!The suds or brew (or wathever you call it) on the topis reactive power, it takes places and does nothing to you.

So, the glass contains both the liquid and the foam, that isapparent power!!

rmw(Mechanical)28 Oct 05 12:04I love unclebob's analogy. LOL.However, I have a question (also asked as an ME for whom reactive power is black art).

Since the beer foam occupies space in the glass, doesn't that also require a larger glass?

Asked on topic, since reactive power produces heat in the conductors rather than output in the driven motors, isn't the energy required to produce that heating of the conductors produced by the engine driving the generator?

So, if you had a zero PF system (if there is such a thing) wouldn't the engine still have to produce the same HP to drive the generator to put all the power into heating conductors?More realistically asked, a system that had a highly inductive load of 50% PF wouldn't require half the engine to pull it as compared to a system with a purely resistive load at a PF of 1.0 would it?

rmwjghrist(Electrical)28 Oct 05 13:44The amount of beer left in the glass after downing it (losses) is small in comparison to the total volume of the glass, even though it is real beer, not useless foam.rbulsara(Electrical)28 Oct 05 14:22rmw:

On a sober note, the energy used in the heating will constitute part of the 'real' power part of the total (apparent power). I^2R losses. Reactive current in 'ideal' (zero resistance conductor) will not create heating.

And yes, the engine only provides real (kW) power and noreactive power. So a system with 0.5 pf system and 100kVA of load, for example, will only require a 50kW (plus losses) rated engine.

That is why, you can start a motor of kW rating same as an engine (after accounting for efficiecny losses), as long the alternater kVA rating is adequate to accomodate the starting kVA of the motor within acceptable voltage dip.

abcd3286(Electrical)29 Oct 05 00:21OKsupposedly there is no cost for reactive power ie what is required for magnetizing fields (motors etc).Several people said this is not developed by the engine (or other prime mover of an alternator).

WHY then doesSeattle city light (a utility with a few alternators) tell me they have to open the throttle if reactive load changes.ALSO if it is free why do they go thru the expense of power factor correction?AND why do they bill you for it if is free.

To the bear and foamgranted the foam is uselessBUT are you able to make it for free?itsmoked(Electrical)29 Oct 05 00:30Everything in the magnetic realm has to be built larger to carry the magnetizing currents.Hence the adder.edison123(Electrical)29 Oct 05 00:46Reactive power is a necessary evil - like beer froth

* Why is the time of day with the slowest traffic called "rush hour"? *2ijl(Electrical)29 Oct 05 05:27One more attempt to explain the apparent power:

The momentary power at a given time in an electric circuit is equal to the momentary voltage times the momentary current. This is not a definition, but follows from the definition of power, voltage and current. The momentary power is of little practical use in an AC-network, because the current and voltage are functions of time. It is better to calculate the average power over one cycle. It is equal to the rms voltage times the rms current times the cosinus of the phase difference between the voltage and current. That is, P = U I cos(fii), where P is the power, U is the rms voltage and I is the rms current, and fii is the phase difference. The cos(fii) is also called the power factor, pf.

Because cos(fii) appears in the expression of the power P, it is tempting :) to define another quantity, Q = U I sin(fii). This is the reactive power. The apparent powerS is then the vector sum of the power P and the reactive power Q,S = sqrt(P*P + Q*Q).

The reactive power and the apparent power do not have a direct physical interpretation. (I am afraid that the colleagues here might not agree with this view?)A load can generally be described as a resistance and an inductance in parallel. The power P is then the real, physical or proper power consumed in the resistance. It can be seen and felt as heat, mechanical power, etc. The reactive power is the powerlike quantity consumed in the inductance. It is related to the power that is oscillating between the load and the source.

The apparent power can be seen as the requirement for the maximum capacity of a transmission line. This can be seen in the following way:The voltage U in a network is more or less constant. Thus, if the power factor is low, then the current must be high in order to get the same power as with load having a higher power factor. The transmission lines must be capable of passing this current. The losses in the transmission lines are equal to the resistance times the current squared. (Again ,this is not a definition, but can be derived using Ohms law and the expression for power.) Because the losses depend on the resistance of the wires, not on the reactance, they do not know about the power factor. This means that the wires can be considered (and dimensioned for) to transmit a real power equal to the apparent power, but with a power factor equal to one.

The losses are apparently one of the reasons why the utilities do not like a low power factor, and why the power of the source must go up, when the power factor goes down.rmw(Mechanical)29 Oct 05 12:54ijl,

As a ME, I am hanging on by my fingernails trying to stay with you, but I think I understand what you said in your post.

Here is what I specifically remember from an EE class (for non EE majors) during my university days.

First, here is some background as to why I might have remembered this comment.

I returned to college after a stint in the US Navy where had worked in the machinery spaces of warships.While I was obviously more interested as a future ME (a lot of what propelled me into the power side of Mechanical Engineering) in the boilers, pumps, and turbines, we did generate and distribute the ships electrical power, too.

Upon returning to the University, I worked in the campus power house as a student utility worker, and while I had no significant operating responsibility, I was around the daily operations of the central power station, which included interactions with other utilities on the grid to which parts of the campus was connected.

I said all that to say that I had some small limited amount of working knowledge of power generation, transmission, and distribution systems when I later attended my obligatory EE courses.

I assume that when we are discussing reactive power, we are talking about the term I learned as VAR's?????

I still see VAR meters on power company power panels.

The way the professor described VARs to us, and yes, this was complete with vector diagrams, was to use the analogy of a freezing rainy winter day (in our part of the world, we get a lot of ice hanging on electrical lines during freezing rain events-often causing major system wide damage and outages) of the power company dispatcher calling up such and such a plant across the system and saying 'ship me some VARs.'Purpose being to get the ice off of the transmission wires.

Based on your detailed and excellent post, I assume that this analogy he used would be a manner of speaking that would really mean 'lower the power factor so that the line losses pick up, heating the wires, and melting the ice off of them'.

Am I anywhere near close in my understanding?

I was about to dig into my personal library to see if I couldn't clear myself up on this, as I am in and out of a lot of power stations, and while power factor and VARs rarely interact with my work, often, such as in measuring pump work or generator output, it enters in.So, it is a peripheral issue to me.

Thanks for the time you took in your above post.I give it a star.

rmwitsmoked(Electrical)29 Oct 05 14:48I think you have it.

With respect to ijl's post which is nice. I would replace "momentary" with "instantaneous" but that may just be a USA semantic difference.ITSTOAST(Electrical)30 Oct 05 11:29Itsmoked,I agree, the utility has to size its distribution system according to amperage and low P.F. costs them money.In return they charge my facilities $100K's per year for any percentage above or below unity.Yes, any.Its "Coming soon to your local provider" --start planning a strategy now.ijl(Electrical)31 Oct 05 07:53itsmoked,My instantaneous reaction to your comment was a momentaryconfusion (or the other way round, or neither? :)RudyL54(Electrical)31 Oct 05 11:44In the example, the glass is the cable capacity. So the glass should be taller to accomodate the beer suds.

Easy to remember. Apparent power equals real power if the unit is perfect. No losses due to reactive impedance.

However, in real life, there is no perfect system. So, it is well accepted that the apparent power should be slightly higher than real power. The factor added in the equation is known as the power factor (PF).

Power (VA) = Power (watts) x PFSources of power are rated in KVA or VA (Volts-Ampere)( ex. transformers, generators) while machines or equipment (ex. motors) that use power are rated in WATTS.

Some times they are in HP (Horse Power)(=746 watts).

coconutalley(Electrical)31 Oct 05 12:25Can't resist -- already lot's of good answers at different views:Seattle City light wants you to get your Power Factor up because the more VA [apparent power] means to them that they have to generate more current [Amps] capacity--physically this means bigger generator and bigger wires.itsmoked(Electrical)31 Oct 05 13:00Rudy's addition to the beer analogy is outstandingly correct! Wow... I am humbled...

RudyL54(Electrical)31 Oct 05 13:47My apology. I mistyped X instead of /.

So it should be Apparent Power (VA) = Real Power (in watts)/PF(power factor).

Power factor is normally less than one.

Thanks itsmoked for your comment.