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In this article we will discuss about:- 1. Methods of Power Factor Improvement 2. Advantages of Power Factor Improvement 3. Economics 4. Economical Comparison of the Two Methods of Increasing the Power Supplied.

**Methods of Power Factor Improvement:**

The low power factor is almost invariably due to inductive nature of load and, therefore, the logical corrective is to connect such devices across the load, which takes leading reactive power such as static capacitors, synchronous machines or synchronous condensers.

The leading reactive component of current drawn by power factor correcting device neutralises the lagging reactive component of current drawn by the load partly or completely. Power factor of the system will become unity when lagging reactive component of load current is completely neutralised by the leading reactive component of current drawn by power factor correcting device.

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Let the current drawn by an inductive circuit be I lagging behind the applied voltage by an angle ɸ. The leading current required to neutralize the lagging reactive component of current drawn by the inductive circuit (equipment) to give unity power factor.

**By Use of Static Capacitors****: **

Power factor can be improved by connecting the capacitors in parallel with the equipment operating at lagging power factor such as induction motors, fluorescent tubes. Static capacitors have the advantages of small losses (less than ½ per cent) or higher efficiency (say 99.6%), low initial cost, little maintenance owing to absence of rotating parts, easy installation being lighter in weight and capability to operate under ordinary atmospheric conditions.

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However, they have drawbacks of short service life (8 to 10 years), getting damaged on over-voltages and uneconomical repair. The current drawn by induction motors or fluorescent tubes can be resolved into two components; the active component, which is in phase with the supply voltage and the quadrature or wattless component of constant magnitude.

The capacitors draw current leading the supply voltage by 90° approximately and neutralise the quadrature or wattless component of current drawn by the equipment across which these are connected. These capacitors remain connected permanently across the equipment and are across the supply mains, whenever the equipment is switched on.

**The value of the static capacitors for the improvement of the power factor can be determined as follows: **

**The leading current required to neutralise the lagging reactive component of the current drawn by the equipment to give unity power factor is expressed as: **

**The value of capacitance in star bank is given by: **

Where V is the phase voltage, I is the phase current and / is supply frequency.

For given kVAR and line voltage the delta value will be one-third of star value.

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Power factor can also be improved by connecting static capacitors in series with the line, as shown in Fig. 15.10. Capacitors connected in series with the line neutralize the line reactance. The capacitors, when connected in series with the line, are called the series capacitors, and when connected in parallel with the equipment, are called the shunt capacitors.

Shunt capacitors are used in factories, plants and also on transmission lines.

Series capacitors are used on long transmission lines as they provide automatic compensation with the variations in load.

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**The capacity of the capacitors to neutralize the line reactance is given by: **

Where f is the supply frequency and L is the inductance of the line per phase.

The value of reactance required is usually very large but reduced to reasonable value by use of a transformer, as shown in Fig. 15.11.

Shunt capacitors are used in ratings from 15 kVAR to 10,000 kVAR. Small capacitors, up to a few hundred rating are used on individual distribution circuits of customers. Capacitors banks of 500 – 3,000 kVAR ratings are employed in small distribution substations and those with larger rating at big substations.

Three phase capacitor banks can be connected in star earthed, star unearthed or in delta arrangements. Ungrounded star connection is preferred because of easier protection. In this method, the fault current in case of a fault in any unit in one of the phases is restricted by the capacitors in the sound phases. This results in the use of smaller fuses and less protection materials.

The capacitor must be provided with a suitable discharge device to dissipate the stored energy, and to reduce the residual voltage to a safer value within a short period (50 V or less within one minute in case of medium voltage capacitors and within five minutes in case of high voltage capacitors as per ISS 2834-1963).

The discharge resistance is usually incorporated within the ‘unit’ itself in the case of medium voltage capacitors and in case of high voltage capacitors, potential transformers of the circuit breakers are generally utilised as a discharge device.

**The reactive output of the capacitors in kVAR is given by: **

Where V_{L} is the line voltage, f is the supply frequency in Hz and C is the capacitance in µF between the line terminals.

Thus we see that the corrective capacity of the capacitors is a function of the line voltage and supply frequency, varying in accordance with the square of the voltage and directly with the supply frequency. The units as manufactured are designed for a variation of voltage of ±10% of normal voltage. It is, therefore, impossible to overload these units so long as normal voltage and frequency are maintained.

The characteristics of capacitors, in general, are similar to those of synchronous condensers except that the corrective kVAR of the synchronous condenser is adjustable and may be controlled automatically whereas that of the capacitor is fixed unless there is a possibility of change in the number of units connected.

**By Use of Synchronous or High Power Factor Machines****: **

Synchronous machines are excited by dc, and the power factor may be controlled by controlling the field excitation. The various synchronous machines available for power factor correction comprise synchronous motors, synchronous condensers, synchronous converters, synchronous phase modifiers, phase advancers, and synchronous-induction motors.

**1. By Use of Synchronous Motors:**

These motors have characteristics that make them adaptable for a wide range of applications. The speed is constant, the efficiency is high and uniform from light loads up to considerable overloads, and the starting characteristics compare favourably with those of induction motors.

Another desirable characteristic of the synchronous motor is its tendency to maintain a constant load voltage even if there are variations in the supply voltage. When the line voltage increases, the leading reactive kVA falls and when the line voltage falls, the leading reactive kVA increases.

The usual practice is to keep the field excitation constant at a value corresponding to normal full-load rating as regards output and power factor. Synchronous motors are designed for 1.0 – 0.8 leading power factors at full load. The unity power factor motor costs less and has a higher efficiency, but if fully loaded, it cannot furnish leading reactive kVA to compensate for lagging reactive kVA in the system.

**2. By Use of Synchronous Condensers:**

An overexcited synchronous motor running on no load is called the synchronous condenser or synchronous phase advancer and behaves like a capacitor, the capacitive reactance of which depends upon the motor excitation. Power factor can be improved by using synchronous condensers like shunt capacitors connected across the supply.

In phasor diagram (Fig. 15.12), phasor I_{L} represents the current drawn by the industrial load, lagging behind the applied voltage V by a large angle ɸ_{L} and phasor I_{M} represents the current drawn by the synchronous condenser leading the applied voltage V by the angle ɸ_{M}. The resultant current I is the phasor sum of I_{L} and I_{M} and now angle of lag ɸ is much smaller than ɸ_{L}. Thus overall power factor is improved from cos ɸ_{L} to cos ɸ by the use of the synchronous condenser. In this way the power factor can be made unity even.

Synchronous condensers are usually built in large units and are employed where a large quantity of corrective kVAR (say 5,000 kVAR or more) is required.

**The advantages of synchronous condensers over static capacitors as a power factor correction devices are:**

(i) A finer control can be obtained by variation of field excitation;

(ii) Inherent characteristic of synchronous condensers of stabilizing variations in the line voltage and thereby automatically aid in regulation,

(iii) Possibility of overloading a synchronous condenser for short periods, and

(iv) Improvement in the system stability and reduction of the effect of sudden changes in load owing to inertia of synchronous condenser.

By use of synchronous condensers at intermediate stations, the voltage of the line can be kept constant at various points along its length, thereby, increasing the current carrying capacity of the line and improvement of power factor.

**The disadvantages of synchronous condensers over static capacitors as power factor correcting devices are: **

(i) Except in size above about 5,000 kVAR, the cost is higher than that of static capacitors of the same rating;

(ii) Comparatively higher maintenance and operating costs;

(iii) Comparatively lower efficiency (say 97%) due to losses in rotating parts and heat losses,

(vi) Noise is produced in operation,

(v) An auxiliary equipment is required for starting synchronous condensers;

(vi) Possibility of synchronous condensers falling out of synchronism causing in interruption of supply; and

(vii) Increase of short-circuit currents when the fault occurs near the synchronous condenser.

Synchronous condensers are largely employed by utilities at large substations for improving the power factor and voltage regulation. Machines up to 100 MVAR rating or even higher have been used. The excitation current is regulated automatically to give a desired voltage level.

**3. By Use of Phase Advancers:**

The power factor of an induction motor falls mainly due to its exciting current drawn from the ac supply mains, because exciting current lags behind the voltage by π/2. It may be improved by equipping the set with an ac exciter or phase advancer which supplies this exciting current to the rotor circuit at slip frequency. Such an exciter may be mounted on the same shaft as the main motor or may be suitably driven from it.

Use of phase advancer is not generally economical in connection with motors below 150 kW output but above this size, phase advancers are frequently employed. Shunt and series type of phase advancers are available according to whether the exciting winding of the advancer is connected in parallel or series with the rotor winding of the induction motor.

**There are two main advantages of phase advancers:**

(i) Lagging kVAR drawn by the motor are considerably reduced due to supply of exciting ampere-turns at slip frequency, and

(ii) The phase advancers can be conveniently employed where the use of synchronous motor is inadmissible.

**4. By Use of Synchronous-Induction Motors:**

These are special types of motors which operate at certain loads as synchronous motors and at other loads as induction motors.

**5. By Use of High Power Factor Motors:**

Besides synchronous motors or synchronous-induction motors there are other several types of motors which operate at a power factor of approximately unity such as compensated induction motors, and Schrage motors. These motors are more expensive and have higher maintenance cost than ordinary induction motors.

**Location of Power Factor Correction Equipment****: **

The best location for the power factor correction equipment to be installed is where the apparatus or equipment responsible for low power factor is operating. Synchronous condensers are used at load centres where considerable corrective kVAR is required whereas static capacitors are justifiably used in smaller units and may be placed closer to the point where the load of inductive nature is installed and thereby relieving the distributors and feeders from carrying excessive currents owing to low power factor.

In cases of transmission system, if synchronous condensers are to be employed for power factor improvement then these should be installed at the receiving end so that not only the generators but also the transmission lines are relieved of carrying excessive current due to poor power factor. However, if synchronous condensers are installed near the generators then only generators will be relieved from the excessive current component and the transmission lines will have to carry it.

**Advantages of Power Factor Improvement****: **

Modern alternators are designed to have high reactance in order that alternators may not get damaged at the time of short circuit and normally reactance is 20 times of resistance. Any change in current and power factor causes the change in terminal voltage, so voltage can be kept fairly constant by power factor control.

If the power factor of the supply or power station is raised to unity, the current for the same amount of power to be supplied is reduced to minimum. This results in reduction of transmission line copper losses, and reduction of voltage drop in transmission line and in alternator windings, as copper losses are directly proportional to the square of supply current and voltage drop is directly proportional to the current.

The terminal voltage of an alternator is given by the phasor difference of induced emf and voltage drop in synchronous impedance. Neglecting the resistance as compared to synchronous reactance, the synchronous impedance can be considered purely inductive, so synchronous impedance voltage drop leads the load current by π/2.

From the phasor diagrams shown in Figs. 15.13 (a), 15.13 (b) and 15.13 (c) for lagging, unity and leading power factor respectively it is obvious that as the power factor is raised from lagging to unity, the difference of terminal voltage and induced emf is reduced and this difference can be reduced to zero by making the power factor, leading and less than unity. Hence to have zero regulation the power factor should be made leading one, so that no other regulating equipment is required.

**It is not economical to raise the power to unity or leading one due to the following reasons: **

1. In case the power factor is improved to unity for full- load conditions, it would become leading for loads less than full load (unless some capacitors are switched off which is usually difficult). At power factors lower than unity (lagging or leading) the current for the same amount of power to be supplied is increased and thereby energy losses in generators, transformers, transmission lines and distribution lines will be increased.

2. As the power factor approaches unity, the capacity of power factor correction device increases more rapidly i.e., the power factor of an installation can be improved from 0.7 or 0.8 to 0.8 or 0.9 by a much smaller capacitive kVAR than that required for raising the power factor from 0.9 to unity.

**The advantages of good (or improved) power factor are:**

(i) Reduction in load current;

(ii) Increase in voltage level across the load;

(iii) Reduction in energy losses in the system (generators. transformers. transmission lines and distributors) due to reduction in load current;

(iv) Reduction in kVA loading of the generators and transformers which may relieve an overloaded system or release capacity for additional growth of load, and

(v) Reduction in kVA demand charge for large consumers.

**Economics of Power Factor Improvement****: **

When the power factor is improved it involves an expenditure on account of the power factor correcting equipment. Improvement of power factor will result in reduction of maximum demand and thus affect an annual saving over the maximum demand charge but on the other hand an expenditure is to be incurred every year in the shape of interest and depreciation on account of the investment made over the power factor correcting equipment.

The limit of the power factor at which the net saving (saving in annual maximum demand charges less annual expenditure incurred on power factor correcting equipment) is maximum is known as economical limit of power factor correcting. It will be seen that the economical limit of power factor correction is governed by the relative costs of the supply and power factor correcting equipment.

Consider a consumer taking a peak load of P kW at a power factor of cos ɸ_{1}, and charged at the rate of Rs x per kVA of maximum demand per annum. Let the expenditure per kVAR per annum of the power factor correction equipment be Rs y.

From, the above expression, value of most economical power factor cos ɸ_{2} can be determined which is independent of original factor cos ɸ_{1} and is governed by the relative costs of supply and power factor correction equipment.

**Example 1:**

**Calculate the value of the new power factor when the tariff is Rs 1,350 per kVA of maximum demand plus a flat rate paise 80 per kWh. Assume additional cost of condensers etc. at Rs 1,050 per kVA of such plant. Rate of interest and depreciation together is taken as 10%. **

**Solution: **

Maximum demand charges,

x = Rs 1,350 per kVA/annum

Cost of phase advancing plant = Rs 1,050 per kVA

Expenditure on phase advancing plant,

y = Annual interest and depreciation

= Rs 1,050 × (10/100) = Rs 105/kVAR/annum

Most economical power factor.

**Example 2:**

**A factory operates at 0.8 pf lagging and has a monthly demand of 750 kVA. The monthly power rate is Rs 8.50 per kVA. To improve the power factor, 250 kVA capacitors are installed in which there is negligible loss. The installed cost of equipment is Rs 20,000 and fixed charges are estimated as 10% per year. Calculate the annual savings affected by the use of capacitors. **

**Solution: **

Maximum demand = 750 kVA

Load power factor, cos ɸ = 0.8

Power factor angle ɸ = cos^{-1} 0.8 = 36.87°

kW component of load, P = kVA cos ɸ = 750 x 0.8 = 600 kW

kVAR component of load, Q_{1} = kVA sin ɸ = 750 sin 36.87° = 450 (lagging)

Leading kVAR supplied after pf improvement,

Q = Q_{1} – kVAR supplied by capacitors = 450 – 250 = 200

kVA demand after pf improvement,

Reduction in kVA demand = 750 – 632.45 = 117.55

Annual savings on kVA charge = Rs 8.50 × 12 × 117.55 = Rs 11,990

Fixed charges per annum on the capacitors = Rs 20,000 × (10/100) = Rs × 2,000

Annual savings = Rs 11,990 – Rs 2,000 = Rs 9,900 Ans.

**Economical Comparison of the Two Methods of Increasing the Power Supplied****: **

The increase in power demand on the generating station can be met either by increasing the capacity of the generating plant working at the same pf or by raising the power factor of the system by installation of phase advancers.

Owing to improvement of power factor in the beginning the saving in the generating and distributing plant outweighs the extra cost of the pf correction equipment in most of the cases but as the power factor is raised further its cost begins to approximate to the saving and finally any saving over the plant is obtained by incurring a greater expenditure on the pf correcting equipment.

Thus there is a limit beyond which it is not economical still further to improve the power factor. The maximum value to which the power factor can be economically raised entirely depends upon the relative costs of the generating plant and phase advancing plant.

Let the rating of generating station be S in kVA, supplying load at power factor cos ɸ_{2}.

Assume new demand can be met by improving the power factor from cos ɸ_{1} to cos ɸ_{2} with the same capacity of the plant.

Existing load in kW, P_{1} = S cos ɸ_{1}

New load in kW, P_{2} = S cos ɸ_{2}

**(i) Cost by increasing the capacity of the generating station: **

Increase in load = P_{2} – P_{1} = S (cos ɸ_{2} – cos ɸ_{1})

Increase in the capacity of the generating plant operating at pf cos ɸ_{1}

Increase in annual cost due to increase in capacity of the plant-

where x is the annual cost per kVA of generating plant

**(ii) Cost on power factor correction equipment: **

Reactive power drawn by load operating at the old power factor, cos ɸ_{1} = P_{2} tan ɸ_{1} = S cos ɸ_{2} tan ɸ_{1}

Reactive power supplied by the plant = Capacity of the plant in kVA sin ɸ_{2} = S sin ɸ_{2 }since kVA rating of the plant remains the same

kVAR rating of the pf correction equipment = Reactive power drawn by load – reactive power supplied by the plant = S cos ɸ_{2} tan ɸ_{1} – S sin ɸ_{2} = S (cos ɸ_{2} tan ɸ_{1} – sin ɸ_{2})

Annual cost on pf correction equipment-

= Rs y S (cos ɸ_{2} tan ɸ_{1} – sin ɸ_{2}) …(15.9)

where y is the annual cost per kVAR rating of power factor correction equipment.

Power factor correction equipment will be cheaper if annual cost on it is less than annual cost on account of increasing the generating capacity.

In the limiting case, the maximum cost of pf correction equipment, which would justify its installation, should be equal to cost on account of increasing the generating plant capacity.

**Example 3:**

**A power plant is working at its maximum kVA capacity with a lagging pf of 0.7. It is now required to increase its kW capacity to meet the demand of additional load. **

**This can be done: **

**(i) By increasing the pf to 0.85 (lagging) by pf correction equipment. **

**Or **

**(ii) By installing additional generation plant costing Rs 800 per kVA.**

**What is the maximum cost per kVA of pf correction equipment to make its use more economical than the additional plant? **

**Solution: **

Let the rating of the power plant be S kVA Increase in load

= P_{2} – P_{1} = S(cos ɸ_{2} – cos ɸ_{1}) = S(0.85 – 0.7) = 0.15 S

Increase in capacity of the generating plant-

Cost of additional plant = Rs 800 × 0.2143 S = Rs 171.43 S

Let the rate of interest and depreciation be m per cent per annum Increase in annual cost due to increase in capacity of power plant-

**Alternative Method:**

Annual cost per kVA of generating plant-

where m is the rate of interest and depreciation per annum.

Original power factor,

cos ɸ_{1} = 0.707 and therefore ɸ_{1} = Cos^{-1} 0.7 = 45.573°

Improved power factor,

cos ɸ_{2} = 0.87 and therefore ɸ_{2} = Cos^{-1} 085 = 31.788˚

Annual cost per kVAR of pf correction equipment-