Power Factor (In Detail) #3

Related Posts
Power Factor #1
Power Factor #2

From our previous discussion we saw that Power Factor can be defined in 3 definitions. ie

• The cosine of an angle between Voltage (V) and Current (I)
• True Power / Apparent Power
• Resistance / Impedance

Please note that in the above expressions, the value of Power Factor can never be greater than 1. A good power factor is always 0.9 or 0.89

In this post we are going to look into detail the Power Factor of angle between Voltage(V) and Current (I)


The power factor PF is mathematically defined as the cosine of the phase angle between voltage and current. True power is defined by the equation . The graphical representation produces a product of the voltage and current. This product is represented as a sine wave, which is twice the frequency of the voltage and current and represents the instantaneous power and its direction. If the power sine wave is completely on the positive side of the axis, it shows that the power in the system is traveling only in one direction, toward the load.

The area under this power sine wave curve represents the amount of energy delivered to the load. If the power sine wave is shifted, the difference in area between the positive and the negative sides represents the power delivered to the load. The negative side of the power sine wave represents the reflected power from a reactive load.

A lagging power factor is one in which the current is lagging behind the voltage and is characteristic of an inductive load.

A leading power factor is one in which the current is leading the voltage and is characteristic of a capacitive load. If the phase angle were to be shifted to be greater than 90 degrees in either direction, the load would effectively become the source.

Power Factor Correction
A power factor of one (1) or "unity power factor" is the goal of any electric utility company since if the power factor is less than one (<1) , they have to supply more current to the user for a given amount of power use. In so doing, they incur more line losses. They also must have larger capacity equipment in place than would be otherwise necessary. As a result, an industrial facility will be charged a penalty if its power factor is much different from 1.

Industrial facilities tend to have a "lagging power factor", where the current lags the voltage (like an inductor). This is primarily the result of having a lot of electric induction motors - the windings of motors act as inductors as seen by the power supply. Capacitors have the opposite effect and can compensate for the inductive motor windings. Some industrial sites will have large banks of capacitors strictly for the purpose of correcting the power factor back toward one to save on utility company charges.

Kenya to build local power transformer plant

Kenya is set to construct the first electricity transformers manufacturing plant in the region to boost electricity distribution in the country.
According to the Kenya Power and Lighting Company the plant will manufacture and assemble transformer for local as well as regional market.

In a paid up advert in local dailies the company is calling interested firms to help in carrying out a study on the viability of such a project.

Late last year the company raised 9.8 billion shillings through a rights issue, which KPLC says was meant for upgrading its systems in the country.

KPLC has invited prequalification bids for a viability study on building a local transformer manufacturing plant to help meet the country's growing demand for power.

 Kenya suffers regular power failure owing to insufficient electricity generation capacity and a dilapidated transmission network which have been largely blamed on investor flights and high power bills.....

The Star-Delta 3-phase Motor Starting Method

The Star Delta starting method is a motor starting mechanism that minimizes the large amount of starting current that motors draw in. The Star Delta, as the name suggests basically involves feeding the motor with 1/sq.root3 (58%) of the full load current until it attains speed then applying the full load current. This method is commonly referred to as "Soft Starting" the motor, For this to work the whole set-up requires 3 contactor i.e The Star Contactor, The Delta Contactor & The Main Contactor.However for the motor to be started in Star Delta, its internal connection at the terminal box has to be wired in Delta-giving it capability of receiving the full-load current at any instant.

Traditionally, in many regions there was a requirement that all motor connections be fitted with a reduced voltage starter for motors greater than 4KW 5HP.This was to curb the high inrush of starting currents associated with starting induction motors.
Advantages of this method is low or reduced cost as compared to other methods...

Community Power Centers (CPC) : UNIDO

United Nations Industrial Development Organization (UNIDO), in partnership with other stakeholders has been working on a project of lighting up Kenya using electricity generated from renewable sources. The energy generated is taken to a village power center that acts as a community development center.Once electricity is at the center, it is used for different applications. Presently, unto 2Billion people lack access to modern energy mainly those living in of-grid areas.

The Community Power Centers Project
The community power project is a source of energy powered by zero-emission hybrid renewable energy sources such as:
 Micro-hydro, Mini-hydro
 Bio-gas

Extra High Voltage Systems - 400kV Lines

Nominal Voltage                      400kV
Cicuits per phase                     1
Sub-conductors per phase        2
Span                                      400m
Conductor Name and Size       Moose,54/3.53mm Alluminium  7/3.53mm Steel
Sub-conductor Diameter          3.177cm
Bundle Configuration                Horizontal
Bundle Spacing                       450mm
Interphase Spacing                   11m
Condutor Configuration            Horizontal
Resistance per phase per km at 20degrees 0.0274Ohm
Inductive Reactance per phase per km              0.3321Ohm
Shunt Admittance per phase per km                  3.2983*10-6
Surge Impedance                    282Ohm
Surge Impedance Loading        505MW
Current Carying capacity at 40degrees ambient temperature 900A
Ground Wire                           2Number,7/3.66mm Galvanised Steel
Ground wire height at tower                30.4m
Tower height                           30.4m
Conductor Height at tower           20.75m
Conductor sag at 0degrees           8.39m
Ground wire sag at 0degrees               6.654m
Shielding angle                           10degrees
Suspension string                   23dics,225*145mm
Impulse Flashover voltage                   1550kV

Examples:Sultanpur-Lucknow Line, Obra-kanput Line, Kanpur-Maradnagar Line.

Power Factor #2

Power factor in Relation to Power

Power is consumed only in resistance since neither pure inductor nor the capacitor consumes any power. The power consumed (True Power) in Inductor (L) and Capacitor (C) is zero. There is a circulating power that moves from the source to the load back and forth and does not do any useful work in the circuit. Current and voltage are in phase in a Resistance while they are 90 Degrees out of phase in (L) and (C). When current is in phase with voltage it produces active or True Power while it produces Reactive Power when 90 Degrees out of phase with voltage.