Concept of Power Factor Improvement

Concept of Power Factor Improvement

The electrical energy is exclusively generated and transmitted in the form of alternating current. And hence the question of power factor immediately arises. The low power factor is undesirable and for better engineering and economical conditions of supply system, it is necessary to have power factor as close as unity. Let us see, why it is so and how to improve it if it is very low.

1. Power Factor

In a.c. circuits the cosine of angle between voltage and current is called as power factor.

We have seen that the angle between voltage and current is called as power factor angle ϕ and it affects the active power consumption. For inductive circuits ϕ is lagging while for capacitive circuits it is leading in nature.

From the Fig. 7.19.1 it can be seen that the current I in the circuit can be resolved into two components

i) I cos ϕ which is in phase with V

ii) I sin ϕ which is out of phase with V by an angle of 90°

I cos ϕ is called active component or wattful component while I sin ϕ  is reactive or wattless component. Lesser the value of this reactive component, smaller is the power factor angle or phase angle ϕ and power factor cos ϕ will be high. Thus the circuit with lesser reactive current component I sin ϕ will result in higher power factor. Power factor always lies between zero and one never exceeds unity.

The words lagging or leading are used along with numerical value of power factor to indicate whether current is lagging or leading with respect to voltage. The power factor can also be expressed as a percentage. A power factor of 0.5 lagging can also be expressed as 50 %.

So power consumption in a.c. circuits is the product of voltage and the component of the current which is in phase with the voltage. So if current is lagging with respect to voltage by angle ( then active power consumption gets decided by the component Icos( , which is in phase with the voltage, as shown in the Fig. 7.19.1

So for single phase circuits, the active power is given by,

P = VI cos ϕ W

While for three phase circuits, the active power is given by

P = √3 V_L I_L cos ϕ w 

In the three phase circuits, ϕ  is the angle between phase voltage and the phase current. We have seen the power triangle for three phase circuit which is as shown in the Fig. 7.19.2.

So power factor can be defined as the ratio of active power to apparent power. If the lagging reactive power component is shown downwards then the leading reactive power component is shown upwards. So lagging reactive power tries to lower the power factor while compensating leading reactive power can increase the power factor. Hence leading power factor loads is the key of power factor improvement.

2. Power Triangle

The power triangle is obtained by multiplying each side of current triangle by voltage V. This is shown the Fig. 7.19.3.

The active power in watts or kW is represented by OX which is VI cos ϕ . The reactive power in VAR or kVAR is represented by XY which is VI sin ϕ . The apparent power in VA or kVA represented by or is given by VI.

The apparent power (VI) has two components viz. active and reactive which are perpendicular to each other.

By Pythagorous Theorem,

Lagging reactive power is drawn by the circuit when current lags behind voltage while reactive power drawn is leading when current leads voltage .

The power factor can also be given by,

Power factor, cos ϕ  = R/ Z = Resistance / Impedance

The power triangle for capacitive circuit is as shown in the Fig. 7.19.4.

This triangle is opposite to that in case of lagging load. Thus if capacitor is connected in parallel with the load which has lagging power factor in order to improve overall power factor of the circuit then the lagging reactive power of the load is partly neutralized.

The reactive power is never actually consumed in the circuit. It is not doing any useful work. It is taken from the supply in some part of alternating cycle while returned back to the supply in another part of cycle thus merely flowing back and forth in both directions in the circuit. The reactive power is not indicated on wattmeter if connected in the circuit.

3. Disadvantages of Low Power Factor

We have seen that the single phase power is given by,

Now supply voltage is generally constant and hence for supplying fixed power to the load, the current is inversely proportional to the power factor cos ϕ . Let a load of 5 kW is to be supplied from 230 V, single phase supply. Let power factor of the system be 0.8 lagging then the current drawn becomes,

I = 5 × 10³ / 230 × 0.8 = 27.17 A

Now if the same load of 5 kW is to be supplied with power factor of 0.6 lagging then the current becomes,

I = 5 × 10³ / 230 × 0.6 = 36.23 A

So as power factor decreases, current drawn from the supply increases to supply the same load power. As against this if power factor is improved to unity in this case, the current becomes,

I = 5 × 10³ / 230 × 1 = 21.73 A

This is minimum current drawn to supply the load. In general, lower is the power factor, higher is the load current and viceversa. Such higher current results into the following disadvantages :

i) If the fixed amount of power is to be transmitted or distributed at constant supply voltage then conductor with lower power factor has to carry more current as the current is inversely proportional to the power factor if other quantities are constant as seen from the expression I = P / V cos ϕ This requires greater conductor size which also increases its cost.

To understand this point clearly, let us consider an example. Let a particular electrical appliance has a rating of 5 kW on full load and rated at 230 V. At unity p.f. the current drawn from supply is,

If the same equipment is operated at 0.7 lagging power factor then current drawn is,

With increase in current at low power factor, the cross-sectional are of cables is to be selected based on current of 32 A and not on 22 A which would be obviously greater than that required for unity power factor.

ii) We have seen that,

cos ϕ = Active power / Apparent power = kW/ kVA 

Now kVA is nothing but the rating of various machines, like alternators, transformers and other swithgear elements. For low power factor values, to supply fixed active power, large kVA rating alternators and transformers are required. This makes the equipments larger in size. Thus overall cost of the system increases.

iii) Large current at lower power factor causes more copper losses which results into poor efficiency.

iv) Large current with low power factor causes large voltage drop (IZ) in transmission lines, alternators and transformers. This reduces the voltage available at supply or receiving end. Thus the performance of various devices is greatly affected due to poor regulation. To compensate such voltage drop and to keep the voltage within permissible limits, extra regulating equipment is necessary which further increases the cost.

v) The lagging power factor reduces the power handling capacity as the reactive component of current restricts the complete utilization of installed capacity.

Thus for a given power, lower is the power factor, the greater is the cost of generation, transmission and distribution. Therefore supply authorities encourage the consumers to increase their power factor.

4. Causes of Low Power Factor

As seen from previous section, lower value of power factor is undesirable from economic point of view and efficient operation of the system. Normally the power factor of the supply system is around 0.8.

The causes of low power factor are listed below

a) Electric discharge lamps, heating furnaces in industries, are lamps operate at low lagging factors.

b) Majority of the motors used in industrial applications or in pumping applications are of induction type either single or three phase. These motors work at low lagging power factor as their stator windings takes exciting current from supply which lags behind the voltage by 90°. The power factor of these motors at no load or light load condition is very small at 0.2 to 0.3 lagging which improves to 0.8 at full load condition.

c) The load on the power system is never constant but keeps on varying all the time. The peak load hours are during morning and evening while at other time the load is low. During low load period, the supply voltage being more, the magnetisation current is increased lowering the power factor. 

Review Questions

1. Define power factor. State the causes of low power factor.

2. Explain the disadvantages of low power factor.