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Power Factor Correction

Basic Concepts
In every industrial, commercial or residential installation, equipment transforms some kind of energy into work and the
determined quantity of energy granted by an energy source per time unit is called Power.

In electric systems, the energy provided by a particular source can be divided into:
• Active Power: the power that is transformed into work, generating heat, light, movement, etc. It is measured in kW.
• Reactive Power: the power used only to create and maintain the magnetic field in inductive loads. It is measured in kVAr.
• Apparent Power: the vector sum of the Active and Reactive Power, representing the total power delivered by the power
source (electric generator, utility company, etc) or the total power consumed by a load/system. It is measured in kVA.

A rectangle triangle is frequently used to represent the relation between Active, Reactive and Apparent Power.

The relation between Active Power (the one that does work) and Apparent Power (the total power delivered by the power
source) can be used to indicate the usage “efficiency” of electric energy, and is defined as Power Factor.

A high Power Factor indicates a high efficiency or a better usage of energy, while a low Power Factor indicates low efficiency,
or a worse energy use.

For purely linear loads, the Power Factor can be defined as the displacement factor cos φ, which is the time discrepancy
between the voltage and current waveforms:

Causes and Consequences of a Low Power Factor

Losses in Installation
The electric losses occur in the form of heat and are proportional to the square of the total current (I² x R). As this current
grows with the increase of reactive power, a relation between the loss increase and low power factor is established causing
the heating up on cables and equipment.

Voltage Drops
The increase of current due to the excess of reactive power results in large voltage drops, and may even cause the interruption of the energy supply and overloads in some equipment. Above all, this risk is increased during the periods where the power line is highly required. The voltage drops can also cause the reduction in luminous intensity of lamps and the increase of current in electric motors.

Underuse of Installed Capacity
The overload on the electric installation caused by the reactive energy unables its full use. So, for new loads, further
investments have to be made which could be avoided if the power factor had higher levels. The “space” occupied by the
reactive energy could be then used for the new loads. The investments on expansion of the electric installation are mainly
related to transformers and conductors. The installed transformer must attend the total power of the installed equipment but,
due to the presence of reactive power, its capacity must be calculated taking the apparent power into consideration. The table below shows the total power that a transformer must have to attend a load of 800 kW for increasing power factors.

The cost of the switch and control gear of the equipment grows with the increase of the reactive power. Likewise, to conduct the same active power without the increase of losses, the section of the conductors increases as the power factor decreases. Table 2 shows the variation of the section of the conductor with the power factor. Tit also demnostrates that the required section, supposing a power factor of 0.70, is double the section for a power factor of 1.00.

The power factor correction alone can increase the capacity for installing new equipment without the need of investing in new
transformers or replacing the cables. Besides this, it may also increase the voltage levels. The example below shows the
increase of capacity of the installation.

It is evident, then that, in this case, after the correction of the power factor, the installation may have load increases up to 41% without additional high investments, such as new transformers and/or cables.

Main Consequences of Low Power Factor
• Increase of energy bill due to the low power factor
• Limitation of capacity of power transformers
• Voltage drops and fluctuations on distribution circuits
• Overload on switch gear, limiting useful life
• Electrical losses increase on distribution line due to Joule effect
• Need of increasing the conductors section
• Need of increasing capacity of the switch and control gear

Main Causes of Low Power Factor
• Induction motors running without load
• Oversized motors
• Transformers without load or with low loads
• Low power factor Reactors on lighting system
• Induction or Arc furnaces
• Thermal treatment machines
• Welding machines
• Voltage level above rated, resulting in higher reactive power consumption

Power Factor Correction in Low Voltages
Types of Power Factor Correction
Correction can be made by installing the capacitors in four different ways resulting in energy conservation and cost/
benefit relation.

a) Correction on the low voltage energy input: allows a significant correction normally with automatic capacitor banks. This
type of correction may be used on electrical installations with a high number of loads with different power and utilization
regimes with little uniformity. The main disadvantage is not to have a sensitive relief of the feeders of each equipment.

b) Correction by load groups: the capacitors are installed to correct a specific area or a set of small machines (< 7.5 kW / 10 HP). They are installed along with the distribution board that supplies this equipment. The disadvantage is it does not lower the current on the feeding circuits of each equipment.

c) Local correction: is obtained by installing the capacitors next to the equipment where the reduction of the power factor is
required. This kind of correction represents, from the technical point of view, the best solution with the following advantages:
• Reduces energy losses in installation;
• Lowers load on feeding circuits;
• A single system can de used for controlling and switching load and capacitors sparing one set of equipment;
• Generates reactive power only where it is necessary;

d) Mixed correction: from the “Energy Conservation” point of view, considering the technical, practical and financial aspects, it
is the best solution. The following criteria are used for mixed correction:

1. A fixed capacitor is installed next to secondary of transformer;
2. Motors of 7.5 kW (10 HP) or more are locally corrected (be careful with high inertia motors because use of contactors for
switching of capacitors should always be used when rated current of these motors is higher than 90% of excitation current
of motor)
3. Motors with less than 7.5 kW (10 HP) are corrected by groups
4. Lighting lines with discharge lamps, with low power factor reactors, are corrected on line input
5. Automatic capacitor bank is installed on input for final equalization.

The diagram below shows all of the installation types explained earlier:

Example: Correction of the PF of a W22 motor, 55 kW, IV poles, 50 Hz, 380-415 V operating in a power supply of
400 V / 50 Hz and at 75% of the rated load.

For power factor correction of electric motors, the following equation is used:

%load = Factor related to operational power of motor:
%load = 0.50 means motor operating at 50% load;
%load = 0.75 means motor operating at 75% load;
%load = 1.00 means motor operating at 100% load;
P = Active Power in kW;
F = Multiplication Factor, according to table below;
η = Motor efficiency according to percentage of load it is operating;
Qcapm = Required reactive power on motor in kVAr.