AC Circuits

Topic includes

- Basic Definations 

- Power factor

- Cause and disadvantage of Power factor

- Improvement and it's importance 

- Network Topology

Some basic Definations

•  Alternating current

The current or voltage which alternates it's direction and magnitude every time. Now a days 95% of the total energy is produced, transmitted and distributed in AC supply.

• Form factor

The ratio of effective value or RMS value to the average value who is known as the form factor.

• Peak factor

The ratio of maximum value to The RMS value is the peak factor of the waveforms.

• Cycle

 One complete set of positive and negative values of an alternating quantity is called a cycle.

• Amplitude

the maximum value, positive or negative of an alternating quantity is known as its amplitude.

• Frequency

the number of cycles per second is known as frequency of an alternating quantity.

Its SI unit is Hertz.

•Time period

the time taken by an alternating quantity to complete the cycle is known its time period.

• Root mean square value

The RMS value of an alternating current is given by that steady current which when flowing through a given circuit for a given time, produces the same heat. 

same heat is produced by alternating current when flowing through the same circuit for the same time

RMS value is the value which is taken for our purpose of any description.

this value is obtained by finding the square root of the mean value of the square coordinates for a cycle or half cycle.

• Average or mean value

the average value of the voltage will be found to be 0.6 36 of the maximum value for a perfect sine wave.

• Active power 

the power which is actually consumed in an AC circuit is known as true or active power. Power is consumed only in resistance.

it is given by the product of circuit voltage, current and power factor which is expressed in watts.

• Reactive power

a pure inductor and a pure capacitor do not consume any power, as in a water cycle Power is drawn from the supply source by these components the same is returned to the supply source in the other quarter cycle. This power which flows back and fourth .

The reactive power of an AC circuit is given by the product of voltage, current and sine of the phase angle.

It is expressed in reactive voltage amperes.

• Q factor

It is define as the voltage magnification in the circuit at the time of resonance.

In series resonance, higher quality factor as well as higher selectivity of turning coil.

 POWER FACTOR

The cosine of angle between voltage and current is an AC circuit is known as power factor.

In an AC circuit there is generally a phase difference between voltage and current. The term cosine angle is gold the power factor of the circuit.

if a circuit is inductive, the current lags behind the voltage and power factor is referred to as lagging.

in a capacitive circuit, current leads the voltage and power factor is known as leading.

•Causes of low power factor

Low power factor is undesirable from economic point of view point normally, the power factor of the whole load on the supply system is lower than 0.8. The following are causes of low power factor

- most of AC motors are of induction type which have low lagging power factor. These motors work at a power factor which is extremely small on the light load and rises 0.8 or 0.9 at full load.

- Arc lamps, electric discharge lamps and industrial heating furnaces operate at low lagging power factor.

- the load on the power system is wearing between high during morning and evening and low at other times. During load period, supply voltage is increased which increases the magnetization current. This result in the degrees power factor.

- due to improper maintenance and repair of motor the power factor at which motors operate fall.

• Disadvantages of low power factor

- Large kVA rating of equipment.

it is clear that KVA rating of the equipment is inversely proportional to power factor. The smaller the power factor, the larger is KVA rating. Therefore, at low power factor, the KVA rating of equipment has to be made more, making the equipment larger and expensive.

- Greater conductor size 

to transmit aur distribute a fixed amount of power at constant voltage, the conductor will have to carry more current at low power factor. This necessities large conductor size.

- large copper losses

the large current at low power factor causes more iron losses in all the elements of the supply system. This results in poor efficiency.

- poor voltage regulation

the large current at low lagging power factor causes creative voltage drop in alternators, transformers, transmission line and distributors.

this results in the decrease voltage available at the supply end  thus impairing the performance of utilisation devices.

- 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 events of full utilisation of installed capacity.

• Power Factor Improvement

The low power factor is mainly due to the fact that most of the power loads are inductive and therefore taking lagging currents. In order to improve the power factor, some devices 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 completely neutralizes the lagging  reactive component of load current. This raises the power factor of the load.

• Importance of power factor improvement

the improvement of power factor is very important for both consumers and generating stations.

- For consumers

a consumer has to pay electricity charges for his maximum demand in KVA plus the units consumed.

if the consumer improve the power factor, then there is a reduction in his maximum KVA demand and consequently there will be annual saving due to maximum demand charges.

all the power factor improvement involves extra annual expenditure on account of power factor correction equipment, yet improvement of power factor to a proper value results in the net annual saving for the consumer.

- For generating stations

A generating station is as much concerned with power factor improvement as the consumer. The generators in a power station are rated in KVA but the useful output depends upon KW output point as station output is KW is equals to KVA multiplication of cosine angle therefore number of unit supplied by it depends upon the power factor.

 The greater the power factor of generating station, the higher is kwh to the system.

This leads to the conclusion that improve power factor increases the earning capacity of power station.

• Network Topology

- Graph of network

The diagram that gives the network configuration and uses line with very small circles at the ends of to represent a network element is known as graph network.

- Tree

Any connected open set of branches which includes all nodes of a given graph is known as a tree.

- Theorem of Topology

The basic theorem is

  

               b= n+l-1

where

b= number of branches

n = number of nodes 

l = number of independent loops

- Cut set 

Cutset is that set of elements that dissociates to main portions of network such that replacing any element will destroy this property.

each cut set contains One tree branch, the remaining element being tree links. Tree branches connected all the notes in the network.

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