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Power Systems
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Power Factor | It's Calculation, Power Factor Improvement Methods

Power Factor | Calculation and Power Factor Improvement Methods


What Is Electrical Power Factor ?

The cosine of angle between voltage and current in an a.c. circuit is known as power factor. In an a.c. circuit, there is generally a phase difference φ between voltage and current. The term cos φ is called the power factor of the circuit. If the circuit is inductive, the current lags behind the voltage and the power factor is referred to as lagging. However, in a capacitive circuit, current leads the voltage and power factor is said to be leading.



Consider an inductive circuit taking a lagging current I from supply voltage V; the angle of lag being φ. The phasor diagram of the circuit is shown in fig. The circuit current I can be resolved into two perpendicular components, namely ;

(a) I cos φ in phase with V
(b) I sin φ 90°  out of phase with V

The component I cos φ is known as active or wattful component, whereas component I sin φ is called the reactive or wattless component. The reactive component is a measure of the power factor. If the reactive component is small, the phase angle φ is small and hence power factor cos φ will be high. Therefore, a circuit having small reactive current (i.e., I sin φ) will have high power factor and vice-versa. It may be noted that value of power factor can never be more than unity.

(i) It is a usual practice to attach the word ‘lagging’ or ‘leading’ with the numerical value of power factor to signify whether the current lags or leads the voltage. Thus if the circuit has a p.f. of 0·5 and the current lags the voltage, we generally write p.f. as 0·5 lagging.

(ii) Sometimes power factor is expressed as a percentage. Thus 0·8 lagging power factor may be expressed as 80% lagging.

Power Triangle 

The analysis of power factor can also be made in terms of power drawn by the a.c. circuit. If each side of the current triangle oab of below figure is multiplied by voltage V, then we get the power triangle OAB shown in figure where
OA = VI cos φ and represents the active power in watts or kW
AB = VI sin φ and represents the reactive power in VAR or kVAR
OB = VI and represents the apparent power in VA or kVA
The following points may be noted form the power triangle :



(i) The apparent power in an a.c. circuit has two components viz., active and reactive power at right angles to each other.
OB² = OA² + AB²
or (apparent power)² = (active power)² + (reactive power)²
or (kVA)²= (kW)² + (kVAR)²

(ii) Power factor, cos φ = OA/OB = active power/apparent power = kW/kVA
Thus the power factor of a circuit may also be defined as the ratio of active power to the apparent power. This is a perfectly general definition and can be applied to all cases, whatever be the waveform.

(iii) The lagging reactive power is responsible for the low power factor. It is clear from the power triangle that smaller the reactive power component, the higher is the power factor of the circuit.
kVAR = kVA sin φ = (kW * sin φ)/cos φ
∴ kVAR = kW tan φ

(iv) For leading currents, the power triangle becomes reversed. This fact provides a key to the power factor improvement. If a device taking leading reactive power (e.g. capacitor) is connected in parallel with the load, then the lagging reactive power of the load will be partly neutralized, thus improving the power factor of the load.

(v) The power factor of a circuit can be defined in one of the following three ways :

(a) Power factor = cos φ = cosine of angle between V and I

(b) Power factor = R/Z= Resistance/Impedance

(c) Power factor = VI/(VI * cosφ) = Active power/Apparent Power

(vi) The reactive power is neither consumed in the circuit nor it does any useful work. It merely flows back and forth in both directions in the circuit. A wattmeter does not measure reactive power.

Disadvantages of Low Power Factor

The power factor plays an importance role in a.c. circuits since power consumed depends upon this
factor.

P = VL IL cos φ

It is clear from above that for fixed power and voltage, the load current is inversely proportional to the power factor. Lower the power factor, higher is the load current and vice-versa. A power factor less than unity results in the following disadvantages :

(i) Large kVA rating of equipment. The electrical machinery (e.g., alternators, transformers, switchgear) is always rated in kVA.
Now, kVA = kW/cos φ
It is clear that kVA rating of the equipment is inversely proportional to power factor. The smaller the power factor, the larger is the kVA rating. Therefore, at low power factor, the kVA rating of the equipment has to be made more, making the equipment larger and expensive.

(ii) Greater conductor size. To transmit or distribute a fixed amount of power at constant voltage, the conductor will have to carry more current at low power factor. This necessitates large conductor size. 

(iii) Large copper losses. The large current at low power factor causes more I²R losses in all the elements of the supply system. This results in poor efficiency.

(iv) Poor voltage regulation. The large current at low lagging power factor causes greater voltage drops in alternators, transformers, transmission lines and distributors. This results in the decreased voltage available at the supply end, thus impairing the performance of utilization devices. In order to keep the receiving end voltage within permissible limits, extra equipment (i.e., voltage regulators) is required.

(v) Reduced handling capacity of system. The lagging power factor reduces the handling capacity of all the elements of the system. It is because the reactive component of current prevents the full utilisation of installed capacity. The above discussion leads to the conclusion that low power factor is an objectionable feature in the supply system.

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 magnetization current. This results in the decreased power factor.

Power Factor Improvement Methods 


The low power factor is mainly due to the fact that most of the power loads are inductive and, therefore, take lagging currents. In order to improve the power factor, some device taking leading power should be connected in parallel with the load. One of such devices can be a capacitor. The capacitor draws a leading current and partly or completely neutralists the lagging reactive component of load current. This raises the power factor of the load.
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Insulators | Types of Electrical Insulators in Overhead Lines

The overhead line insulators provide insulation between the overhead line conductors and the earthed cross-arm to which they are connected and also provide support to the conductors.An ideal insulator should not allow leakage of current from the line conductor to the earthed cross-arm besides providing adequate clearance between the line conductors and metal work.

Types of insulators in overhead Lines

Depending on the applications and the operating voltage levels ,the overhead line insulators are divided into three types.They are, 

(i) Pin type insulators 
(ii) Suspension type insulators and
(iii) Strain type insulators 

(i) Pin type insulators- Electrical Insulators 

Pin type insulators are used for supporting line conductors.For low voltages up to and including 11 KV one piece insulators can be used and two piece insulators are commonly used for 25 KV and for 44 KV up to and including 66 KV three and four piece insulators can be employed.The pin type insulator figure shown in fig.



Pin type insulator consists of single or multiple shells arranged in parallel and mounted on a cross-arm of the pole or tower.The designing of sheds or petticoats should be such that even when the outer surface is wet due to rain,the inner dry surface provides sufficient leakage resistance.On the top of the insulator the conductor bound into a groove,which is cemented on to a galvanized steel pin.A soft metal thimble is used to avoid the direct contact between the porcelain and the metal pin.The potential difference between the sheds can be increased by increasing distance between the sheds.

Advantages Of Pin type insulators :

1.Pin type insulators  are simple in construction and cheap in cost.
2.It provides economic and most efficient method of supporting conductors.
3.In many cases on pin type insulator is used instead of two suspension type insulators.

Disadvantages Of Pin type insulators :

For voltages below 50 KV,they give satisfactory performance ,beyond that,they become bulky and uneconomical.

(ii) Suspension type insulators- Electrical Insulators

At high voltages pin type insulators becomes more bulky,cumbersome and uneconomical.In this case,suspension type insulators are used to insulate the high voltage transmission lines.Normally,these are used up to and including 400 KV .The suspension type insulators shown in fig.



Suspension type insulators consists of porcelain discs arranged in series as shown fig.,by metal links to form a string.The conductor is suspected at its lower end  and it's other end hangs from cross-arm of the supporting structure tower.Thw whole arrangement of a suspension type insulators are called as string(String Efficiency).The number of insulators in a string depends upon the working voltage,weather condition,size of insulation etc.,and if necessary,the discs to that string can be added easily.

Advantages of Suspension type insulators:

1.If any one of the insulator in the string fails, only that insulator can be replaced instead of whole string. 
2.These are much cheaper in cost and used for operating voltages above 50 kV.
3. It gives more flexible operation and by this arrangement the mechanical stresses are reduced.
4. In suspension type insulator, additional insulation can be obtained by adding one or more discs to that string. 
5.When these are used in conjunction with the steel towers, provides protection against lightening. 

(iii) Strain type insulator- Electrical Insulators 

Strain type insulators are used when the line is subjected to greater tension such as dead ends,river crossings,sharp curves and when there is a change in the direction of line.The main function of this insulator is to reduce excessive tension on the line. It is basically an assembly of suspension insulator used in horizontal position as shown in figure.



A strain insulator are designed with considerable good strength and with necessary dielectric properties. In case, when the tension is exceedingly high, two or more strings of insulator can be used in parallel.For voltages up to 11 KV,Shackle type insulator can be used.But for high voltages,strain type insulators should be used.strain type insulators also called as tension insulators. 


In addition to that there are other two types of electrical insulator available mainly for low voltage application, e.i. Stay Insulator and Shackle Insulator.

Tags: what is an insulator of electricity,different types of electrical insulators pdf,types of insulators wikipedia
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String Efficiency & It's Significance In Overhead Transmission Lines

String Efficiency & It's Significance In Overhead Transmission Lines 

Efficiency is a factor that defines the performance of any device or equipment. Generally, it is specified as the ratio of the output obtained to the input fed to a device. It suggests to what extent a device is utilized. 



In an overhead transmission line (OHTL) insulator, a number of insulator discs are arranged in a string in accordance with the operating voltage. The lowest disc or unit which is i near the power conductor experiences maximum stress or it is fully utilized. But, as we move towards the top most unit, the units are not heavily stressed and hence not fully utilized. Hence, the measure of utilization of the string gives string efficiency. Definition The string efficiency of an over head transmission line insulator is defined as the ratio of the voltage across the complete string to that of the product the number of units and the voltage across the unit nearest to the power conductor. 
It is given as, 

η=Voltage across the string/{ n x Voltage across the unit nearest to the conductor}

n= No.of units in the string.

 It can also be defined as the ratio of the spark over voltage of the complete string to that of the product of the number of discs and the spark over voltage of one disc. 

Significance of String efficiency 

String efficiency is an important factor as it suggests the overall potential distribution along the string of insulators. For obtaining uniform voltage distribution, the string efficiency should be as good as possible. if the distribution of voltage is uniform, then each disc will be fully and equally utilized. This also implies that, the discs in the string will experience equal stress so that the life of the string is enhanced.

In ideal case, the string efficiency is maximum and the voltage distribution across each disc will be exactly the same. But in real time situation, it is impossible to achieve 100% string efficiency. Efforts' can be made to improve string efficiency. If the value of 'V (i.e., ratio of mutual capacitance to self capacitance) is decreased then the potential distribution is more uniform and string efficiency is increased. The non-uniformity in voltage distribution increases with the increase in number of discs in the string. Therefore, shorter string has more efficiency than the larger one.

Tags:string efficiency in power system,string efficiency formula,string efficiency of suspension insulators,string efficiency in power system pdf,string efficiency transmission line improving methods
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