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Active and reactive power and its equations

The document discusses active, reactive, and apparent power, emphasizing the importance of power factor in AC circuits. It explains how reactive power is exchanged between inductors and capacitors, detailing the disadvantages of low power factor, including increased line losses, equipment size, and penalties from power companies. The text also outlines the causes of low power factor and the roles of resistance, inductance, and capacitance in electrical circuits.

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Active, Reactive, Apparent power and Power factor
Active power or real power or useful power The Active power is the power that is dissipated in the resistance of the load. The REAL Power is the only useful power delivered to the load. Reactive power or useless power The reactive power is the power that is exchanged between reactive components (inductors and capacitors) i.e it is being transferred back and forth between the load and the source. Example: AC Motor loads and other loads require reactive power
Utility meters in home measure…………….. And power company will charge for it. Residential customers do not pay for……….. and utility meters in homes cannot perform work. By using multimeter we can measure current and voltage and then multiply the readings together we…………. Power.
Ratios of active and reactive power
POWER FACTOR The power factor of a circuit can be defined in one of the following three ways: a)Power factor = cosØ= cosine of the angle between voltage and current. b)Power factor = R/Z = Resistance/ Impedance c)Power factor = VIcosØ /VI = =Active power/Apparent power
WHERE DOES THIS REACTIVE POWER COME FROM Reactive power is mainly present when the voltage and current are not in phase 1. One Waveform leads the other 2. Phase angle not equal to zero
POWER FACTOR  If the circuit is inductive, the current lags behind the voltage and the power factor is to as lagging.  However in capacitive circuit , current leads the voltage and the power factor is said to be leading. UNITS Active power = watts or kW Reactive Power = VAR or kVAR Apparent power = VA or kVA
Let us illustrate the power relations in an a.c circuit with an example. 1. Suppose a circuit of 10A at a voltage of 200V and its p.f is 0.8 lagging. Find Apparent power, active power and reactive power.
Apparent power =2000VA Active power = 1600W Reactive power = 1200VAR  The circuit receives an apparent power of 2000VA and is able to convert only 1600watts into active power.  The reactive power is 1200VAR and does no useful work. It merely flows into and out of the circuit periodically.  In fact, reactive power factor is a liability on the source because the source has to supply the additional current(i.e IsinØ).
DISADVANTAGES OF LOW POWER FACTOR Power factor play an important role in AC circuits and power dissipation depends on this factor. WKT Power in a Three Phase AC Circuit P = √3 V x I CosФ And Current in a Three Phase AC Circuits i.e I 1 /CosФ….… (1) ∝ Also, Power in a Single Phase AC Circuits P = V x I CosФ And Current in a Three phase AC Circuits I = P / (V x CosФ) •I 1/CosФ……… (2) ∝
It is clear from both equations (1) an (2) that Current “I” is inversely proportional to CosФ i.e. Power Factor. I 1/CosФ ∝  In other words, When Power Factor increases, Current Decreases, and when Power Factor decreases, Current Increases. Now, in case of Low Power Factor, Current will be increased, and this high current will cause to the following disadvantages.
1) LARGE LINE LOSSES (COPPER LOSSES) We know that Line Losses is directly proportional to the square of Current “I2 ” . Power Loss = I2 xR i.e., the larger the current, the greater the line losses i.e. I >> Line Losses. In other words, Power Loss = I2 xR = 1/CosФ2 ….. Refer to Equation “I 1/CosФ”….… (1) ∝ Thus, if Power factor = 0.8, then losses on this power factor =1/CosФ2 = 1/ 0.82 = 1.56 times will be greater than losses on Unity power factor.
2) Large kVA rating and Size of Electrical Equipments: • As we know that almost all Electrical Machinery (Transformer, Alternator, Switchgears etc) rated in kVA. But, it is clear from the following formula that Power factor is inversely proportional to the kVA i.e. CosФ = kW / kVA • Therefore, The Lower the Power factor, the larger the kVA rating of Machines also, the larger the kVA rating of Machines, The larger the Size of Machines and The Larger the size of Machines, the Larger the Cost of machines.
3) Greater Conductor Size and Cost In case of low power factor, current will be increased, thus, to transmit this high current, we need the larger size of conductor. Also, the cost of large size of conductor will be increased.
4) Poor Voltage Regulation and Large Voltage Drop Voltage Drop = V = IZ Now in case of Low Power factor, Current will be increased. So the Larger the current, the Larger the Voltage Drop. Also Voltage Regulation V.R = (VNo Load – VFull Load)/ VFull Load In case of Low Power Factor (lagging Power factor) there would be large voltage drop which cause low voltage regulation. Therefore, keeping Voltage drop in the particular limit, we need to install Extra regulation equipments i.e. Voltage regulators.
5) Low Efficiency In case of low Power Factor, there would be large voltage drop and large line losses and this will cause the system or equipments efficiency too low. For instant, due to low power factor, there would be large line losses; therefore, alternator needs high excitation, thus, generation efficiency would be low. 6) Penalty from Electric Power Supply Company on Low Power factor Electrical Power supply Company imposes a penalty of power factor below 0.95 lagging in Electric power bill. So you must improve Pf above 0.95.
CAUSES OF LOW POWER FACTOR Low power factor is undesirable from economic point of view. Normally, the power factor of the whole load on the supply system in lower than 0·8. The following are the causes of low power factor: (i)Most of the a.c. motors are of induction type (1φ and 3φ induction motors) which have low lagging power factor. These motors work at a power factor which is extremely small on light load (0·2 to 0·3) and rises to 0·8 or 0·9 at full load.
(ii) Arc lamps, electric discharge lamps and industrial heating furnaces operate at low lagging power factor. (iii) The load on the power system is varying; being high during morning and evening and low at other times. During low load period, supply voltage is increased which increases the magnetisation current. This results in the decreased power factor.
A current flowing around an electric circuit may meet with three different kinds of opposition or impedance They are caused by 1.Resistance (R), 2. inductance (L), and 3. capacitance (C).
Resistance Of these, resistance is the easiest to understand, because it has the same effect on both direct currents and alternating currents. When the voltage across the two terminals of a resistance changes, the current changes immediately. If the voltage rises, the current rises; and if the voltage falls, the current falls, and so on. Current and voltage are said to be in phase.
Inductor Inductors (L) and capacitors (C) behave quite differently, In "L" circuits a rise in voltage is accompanied by a rise in current, but this rise is delayed by a back e.m.f. (see reactance) generated by the inductor. As the voltage rises and falls, the current rises and falls, but a fraction of a second later. So the current flowing through the inductor is always lagging behind the voltage, and current and voltage are said to be out of phase.
capacitor In "C" circuits, on the other hand, the current in the circuit must first flow to the two plates of the capacitor (round the circuit from plate to plate and not across the gap between the plates) to make potential difference across them. As the current rises, the voltage between the two plates rises; and as the current falls, the voltage falls, but the voltage follows the current's lead a fraction of a second later. Current and voltage are again out of phase, only in "C" circuits the current is always leading the voltage.
Active and reactive power and its equations
Active and reactive power and its equations
Active and reactive power and its equations
Active and reactive power and its equations