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LINEAR CIRCUIT ANALYSIS

SAJID HUSSAIN QAZI

MEHRAN U.E.T, KHAIRPUR CAMPUS

A.C POWERS AND POWER FACTOR

PRESENTATION FLOW

A.C POWERS

POWER FACTOR

CAUSES OF POWER FACTOR

CORRECTION OF POWER FACTOR

DE’MERITS OF LOW POWER FACTOR

A.C POWERS

Active Power: Measured in watts (normally shown as kW). Provides the “working” part

of the power system. Producing heat, light, motion etc.

Reactive Power: Measured in volt-ampere-reactive (normally show as kVAR). It only

Sustains the electromagnetic field and provides no “working” part of the power system.

Apparent Power: Measured in Volt-Ampere (normally shown as kVA). Provided both

working and nonworking parts of the power system.

A.C POWERS

Positive value of power waveform represents the real or working power which is delivered from the source to the load.Negative value of power waveform represents the reactive power which is returned from the load to the source.

From waveforms, 0 to t1, V and I are both positive; therefore, power is positive. At t=t1, Vis 0V and thus P is 0W. From t1 to t2, I is positive and V is negative; therefore, P is negative. From t2 to t3, both V and I are negative; therefore power is positive, and so on.

A.C POWERS - Power Comparison -

A.C POWERS

POWER FACTOR

Electrical energy is almost exclusively generated, transmitted and distributed in the form of alternating current, therefore the question of power factor comes immediately into picture.

Most loads (80%) in electrical distribution systems are inductive in nature and hence they have low P.F which is highly undesirable.

Low P.F causes an increase in reactive current, resulting in additional losses of active power in all elements of power system.

It is important to have power factor as close to unity as possible. Note that

leading power factor is also undesirable for power system.

POWER FACTOR

The cosine angle between the voltage and current is an a.c circuit is known as power factor.Power factor involves the relationship between two types of power, working power and reactive power.

Poor P.F 0.60 P.F >0.90

POWER FACTOR

If the circuit is inductive, the current lags behind the voltage by an angle Ѳ and power factor is referred to as lagging.

POWER FACTOR

If the circuit is capacitive, the current leads the voltage by an angle Ѳ and power factor is referred to as leading.

POWER FACTOR

If circuit is resistive, both current and voltage are in phase with each other and power factor is referred as unity.

POWER FACTOR -Power Triangle-

Working Power (kW)

Apparent Power (kVA)

Reactive Power (kVAR)

Ѳ

Working Power (kW)

Apparent Power (kVA)

Apparent power in a.c circuit has two components, active or working power and reactive power.From trigonometric relation,

Thus the power factor of a circuit may also be defined as the ratio of active power to the apparent power.For leading currents, the power triangle becomes reversed.

Ѳ

POWER FACTOR -Power Triangle-

Now the power factor can be defined in one of the following 3 ways:

1. Power factor = cosѲ = cosine angle between V and I.2. Power factor = cosѲ = Resistance/Impedance.3. Power factor = cosѲ = Active power/Apparent power.

Let us assume a circuit having current of 10 A at a voltage of 200 V and its power factor is 0.8 lagging.

S = VI = 200(10) = 2000VA = 2KVA P = VI cosѲ = 200(10)(0.8) = 1.6KW

Q = VI sinѲ = 200(10)(0.6) = 1.2kVARThe circuit receives an apparent power of 2KVA and is able to convert only 1.6KW into working or active power. Reactive power 1.2KVAR neither consumed nor it does any useful work, it flows back and forth in both direction periodically.

Ѳ

R

X Z

POWER FACTOR

Different types of electrical load have different Power Factors according to its nature.

Name of Equipment Power Factor Percent

Lightly loaded induction motor 0.20 Lagging

Full Loaded induction motor 0.80 Lagging

Neon-lighting equipment 0.30 - 0.70 Lagging

Incandescent lamps 1.0 Unity

All types of resistance heating devices (e.g. toaster, heater)

1.0 Unity

CAUSES OF POWER LOW FACTOR

MOST LOADS (80%) IN ELECTRICAL DISTRIBUTION SYSTEM ARE INDUCTIVE INNATURE. THE CAUSE OF LOW POWER FACTOR IS ONLY DUE TO INDUCTIVELOADS. INDUCTIVE LOADS RESPONSIBLE FOR LOW P.F ARE AS FOLLOWS:

Most of a.c motors are induction type motors (1Φ and 3 Φ). At light load these motors work at extremely low P.F of the order of 0.2 to 0.3 and rises to 0.8 or 0.9 at full load.

Arc lamps, electric discharge lamps, welding equipment and industrial heating furnaces operated at low lagging power factor.

Transformers draws a magnetizing current from the supply. At normal load this current does not affect the P.F, but they draws larger amount of magnetizing current at light load, causes low primary current P.F.

POWER FACTOR CORRECTION

The process of supplying reactive power (lagging or leading) to bring the P.F closer to unity is known as power factor correction.

This can be done by following equipments, should be connected in parallel with the load.

RESISTOR INDUCTOR CAPACITOR SYNCHRONOUS CONDENSER

DE’MERITS OF POWER FACTOR

LOW POWER FACTOR RESULTS IN THE FOLLOWING DISADVANTAGES

LARGER KVA RATING: Electric machines (alternators, transformers, switchgears) are always rated in KVA. KVA rating of any equipment varies inversely with the P.F, therefore low P.F increases the KVA rating, as a result KVA rating making the equipment larger and expensive.

GREATER CONDUCTOR SIZE: To transmit a fixed amount of power at constant voltage, the conductor will have to carry more current a low factor.

DE’MERITS OF POWER FACTOR

LARGE COPPER LOSSES: The larger amount of current at low power factor causes more I R losses in all the elements of the system.

POOR VOLTAGE REGULATION: Larger amount of current produces large voltage drops in alternators, transformers, transmission lines and distributors. This results in poor voltage regulation.

PAYED EXTRA UTILITY CHARGES: System operated at low P.F is uneconomical from supplier`s point of view. Suppliers usually takes extra charges from consumers who operated their load at low power factor.

2

If the generator is rated in KW instead of KVA, then generator greatly overloaded by extra reactive current and damage may result as indicated.

DE’MERITS OF POWER FACTOR

If the P.F is not improved, then larger conductor, larger transformer, larger switchgears are required to handle extra reactive current, which is not economical from supplier point of view.

IMPEDANCE AND ADMITTANCE

A sinusoidal voltage or current when applied to a passive or RLC circuit produces sinusoidal response.

With time function such as v(t) or i(t), circuit is said to be in time domain, and when analyzing by using phasor is said to be in frequency domain.

Voltage and current can be written as

IMPEDANCE AND ADMITTANCE

The ratio of phase voltage and current is called as Impedance (Z);

The reciprocal of Impedance is Admittance (Y)

Basically Impedance and Admittance are complex numbers.

IMPEDANCE AND ADMITTANCE

Real part of Impedance is Resistance (R) and Imaginary part is Reactance (X).

When reactance is inductive in nature (+ve) sign will be written and when capacitive in nature (-ve) sign will be written.

IMPEDANCE AND ADMITTANCE

Real part of Admittance is Conductance (G) and Imaginary part is Susceptance (B).

When Susceptance is inductive in nature (-ve) sign will be written and when capacitive in nature (+ve) sign will be written.

COMBINATION OF IMPEDANCE

The relation V=IZ is formally identical to Ohm’s Law V=IR. Therefore impedance combine like resistance.

IMPEDANCE IN PARALLEL

IMPEDANCE IN SERIES+.....

IMPEDANCE

Impedance can be written in two forms,i. Rectangular Formii. Polar Form

Rectangular Form= Polar Form=

We can convert both these forms by using,