© 2014 IJIRT | Volume 1 Issue 6 | ISSN: 2349-6002
COMPLEX POWER
Akshay Rohilla, Harish Chand Joshi, Anurag Negi
Electronics & Communication Department,
Dronacharya College of Engineering
complex power. Real power, P Reactive power, Q Complex
Abstract-Power in an electric circuit is the rate of flow of
power, S Apparent power, |S| Phase of current, φ Engineers use
energy past a given point of the circuit. In alternating current
the following terms to describe energy flow in a system (and
circuits, energy storage elements such as inductors and
assign each of them a different unit to differentiate between them):
capacitors may result in periodic reversals of the direction of
Real power, P, or active power: watt (W) Reactive power, Q: voltenergy flow. The portion of power that, averaged over a
ampere reactive (var) Complex power, S: volt-ampere (VA)
complete cycle of the AC waveform, results in net transfer of
Apparent power, |S|: the magnitude of complex power S: voltenergy in one direction is known as real or active power. The
ampere (VA) Phase of voltage relative to current, φ: the angle of
portion of power due to stored energy, which returns to the
difference (in degrees) between current and voltage; current
source in each cycle, is known as reactive power .The sum of
lagging voltage (quadrant I vector), current leading voltage
the two results in complex power.
(quadrant IV vector) In the diagram, P is the real power, Q is the
reactive power (in this case positive), S is the complex power and
INTRODUCTION
In a simple alternating current (AC) circuit consisting of a source
the length of S is the apparent power. Reactive power does not do
and a linear load, both the current and voltage are sinusoidal. If
any work, so it is represented as the imaginary axis of the vector
the load is purely resistive, the two quantities reverse their polarity
diagram. Real power does do work, so it is the real axis. The unit
at the same time. At every instant the product of voltage and
for all forms of power is the watt (symbol: W), but this unit is
current is positive, indicating that the direction of energy flow
generally reserved for real power. Apparent power is
does not reverse. In this case, only real power is transferred. If the
conventionally expressed in volt-amperes (VA) since it is the
loads are purely reactive, then the voltage and current are 90
product of rms voltage and rms current. The unit for reactive
degrees out of phase. For half of each cycle, the product of voltage
power is expressed as var, which stands for volt-ampere reactive.
and current is positive, but on the other half of the cycle, the
Since reactive power transfers no net energy to the load, it is
product is negative, indicating that on average, exactly as much
sometimes called "wattless" power. It does, however, serve an
energy flows toward the load as flows back. There is no net energy
important function in electrical grids and its lack has been cited as
flow over one cycle. In this case, only reactive energy flows—
a significant factor in the Northeast Blackout of 2003.[2]
there is no net transfer of energy to the load. Practical loads have
Understanding the relationship among these three quantities lies
resistance, inductance, and capacitance, so both real and reactive
at the heart of understanding power engineering. The
power will flow to real loads. Power engineers measure apparent
mathematical relationship among them can be represented by
power as the magnitude of the vector sum of real and reactive
vectors or expressed using complex numbers, S = P + jQ (where j
power. Apparent power is the product of the root-mean-square of
is the imaginary unit).
voltage and current. Engineers care about apparent power,
because even though the current associated with reactive power
does no work at the load, it heats the wires, wasting energy.
Conductors, transformers and generators must be sized to carry
the total current, not just the current that does useful work.
Another consequence is that adding the apparent power for two
loads will not accurately give the total apparent power unless they
have the same displacement between current and voltage (the
same power factor). Conventionally, capacitors are considered to
generate reactive power and inductors to consume it. If a capacitor
and an inductor are placed in parallel, then the currents flowing
The complex power is the vector sum of real and reactive power.
through the inductor and the capacitor tend to cancel rather than
The apparent power is the magnitude of the complex power.
add. This is the fundamental mechanism for controlling the power
Real power, P
factor in electric power transmission; capacitors (or inductors) are
Reactive power, Q
inserted in a circuit to partially cancel reactive power 'consumed'
Complex power, S
by the load. The complex power is the vector sum of real and
Apparent power, |S|
reactive power. The apparent power is the magnitude of the
Phase of current, φ
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EXPLANATION
1) Real Power: (P) Alternative words used for Real Power
(Actual Power, True Power, Watt-full Power, Useful
Power, Real Power, and Active Power) In a DC Circuit,
power supply to the DC load is simply the product of
Voltage across the load and Current flowing through it
i.e., P = V I. because in DC Circuits, there is no concept
of phase angle between current and voltage. In other
words, there is no Power factor in DC Circuits. But the
situation is Sinusoidal or AC Circuits is more complex
because of phase difference between Current and
Voltage. Therefore average value of power (Real Power)
is P = VI Cosθ is in fact supplied to the load. In AC
circuits, When circuit is pure resistive, then the same
formula used for power as used in DC as P = V I. Real
Power formulas: P = V I (In DC circuits) P = VI Cosθ (in
Single phase AC Circuits) P = √3 VL IL Cosθ or (in
Three Phase AC Circuits) P = 3 VPh IPh Cosθ P = √ (S2
– Q2)or P =√ (VA2 – VAR2) or Real or True power = √
(Apparent Power2– Reactive Power2) or kW = √ (kVA2
– kVAR2)
(2) Reactive Power: (Q) Also known as (Use-less Power, Watt
less Power) The powers that continuously bounce back and forth
between source and load is known as reactive Power (Q) Power
merely absorbed and returned in load due to its reactive properties
is referred to as reactive power The unit of Active or Real power
is Watt where 1W = 1V x 1 A. Reactive power represent that the
energy is first stored and then released in the form of magnetic
field or electrostatic field in case of inductor and capacitor
respectively. Reactive power is given by Q = V I Sinθ which can
be positive (+ve) for inductive, negative (-Ve) for capacitive load.
The unit of reactive power is Volt-Ampere reactive. I.e. VAR
where 1 VAR = 1V x 1A. In more simple words, in Inductor or
Capacitor, how much magnetic or electric field made by 1A x 1V
is called the unit of reactive power. Reactive power formulas: Q
= V I Sinθ Reactive Power=√ (Apparent Power2- True power2)
VAR =√ (VA2 – P2) kVAR = √ (kVA2 – kW2) (3) Apparent
Power: (S) The product of voltage and current if and only if the
phase angle differences between current and voltage are ignored.
Total power in an AC circuit, both dissipated and
absorbed/returned is referred to as apparent power The
combination of reactive power and true power is called apparent
power In an AC circuit, the product of the r.m.s voltage and the
r.m.s current is called apparent power. It is the product of Voltage
and Current without phase angle The unit of Apparent power (S)
VA i.e. 1VA = 1V x 1A. When the circuit is pure resistive, then
apparent power is equal to real or true power, but in inductive or
capacitive circuit, (when Reactances exist) then apparent power is
greater than real or true power. Apparent power formulas: S = V
I Apparent Power = √ (True power2 + Reactive Power2) kVA =
√kW2 + kVAR2
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POWER FACTOR
1). The Cosine of angle between Current and Voltage is called
Power Factor. P = VI Cosθ OR Cosθ = P / V I OR Cosθ = kW /
kVA Cosθ = True Power/ Apparent Power
2). The ratio between resistance and Impedance is Called Power
Factor. Cosθ = R/Z
3). The ratio between Actual Power and Apparent Power is called
power factor. Cosθ = kW / Kva
Causes of low Power Factor
The main cause of low Power factor is Inductive Load. As in pure
inductive circuit, Current lags 90° from Voltage, this large
difference of phase angle between current and voltage causes zero
power factor. Basically, all those circuit having Capacitance and
inductance (except resonance circuit (or Tune Circuit) where
inductive reactance = capacitive reactance (XL = Xc), so the
circuit becomes a resistive circuit), power factor would be exist
over there because Capacitance and inductance causes in
difference of phase angle (θ) between current and voltage. there
are a lot of disadvantages of low Pf and we must improve Pf .
Following are the causes of low Power factor:
1. Single phase and three phase induction Motors(Usually,
Induction motor works at poor power factor i.e. at: Full load, Pf =
0.8 -0.9 Small load, Pf = 0.2 -0.3 No Load, Pf may come to Zero
(0).
2. Varying Load in Power System(As we know that load on
power system is varying. During low load period, supply voltage
is increased which increase the magnetizing current which cause
the decreased power factor)
3. Industrial heating furnaces
4. Electrical discharge lamps (High intensity discharge lighting)
Arc lamps (operate a very low power factor)
5. Transformers
6. Harmonic Currents
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Methods for Power Factor Improvement
The following devices and equipments are used for Power Factor
Improvement.
-Static Capacitor
-Synchronous Condenser
-Phase Advancer
1. Static Capacitor
We know that most of the industries and power system loads are
inductive that take lagging current which decrease the system
power factor (See Disadvantages of Low Power factor) . For
Power factor improvement purpose, Static capacitors are
connected in parallel with those devices which work on low power
factor. These static capacitors provides leading current which
neutralize (totally or approximately) the lagging inductive
component of load current (i.e. leading component neutralize or
eliminate the lagging component of load current) thus power
factor of the load circuit is improved. These capacitors are
installed in Vicinity of large inductive load e.g Induction motors
and transformers etc, and improve the load circuit power factor to
improve the system or devises efficiency. Suppose,here is a single
phase inductive load which is taking lagging current (I) and the
load power factor is Cosθ as shown in fig-1. In fig-2, a Capacitor
(C) has been connected in parallel with load. Now a current (Ic)
is flowing through Capacitor which lead 90° from the supply
voltage ( Note that Capacitor provides leading Current i.e., In a
pure capacitive circuit, Current leading 90° from the supply
Voltage, in other words, Voltage are 90° lagging from Current).
The load current is (I). The Vectors combination of (I) and (Ic) is
(I’) which is lagging from voltage at θ2 as shown in fig 3. It can
be seen from fig 3 that angle of θ2 < θ1 i.e. angle of θ2 is less than
from angle of θ2. Therefore Cosθ2 is less than from Cosθ1
(Cosθ2> Cosθ1). Hence the load power factor is improved by
capacitor. Also note that after the power factor improvement, the
circuit current would be less than from the low power factor
circuit current. Also, before and after the power factor
improvement, the active component of current would be same in
that circuit because capacitor eliminates only the re-active
component of current. Also, the Active power (in Watts) would
be same after and before power factor improvement. Advantages:
Capacitor bank offers several advantages over other methods of
power factor improvement. Losses are low in static capacitors
There is no moving part, therefore need low maintenance Itcan
work innormalairconditions (i.e. ordinary atmospheric
conditions) Do not require a foundation for installation They are
lightweight so it is can be easy to installed
Disadvantages: The age of static capacitor bank is less (8 – 10
years) With changing load, we have to ON or OFF the
capacitorbank, which causes switching surges on the system If the
rated voltage increases, then it causes damage it Once the
capacitors spoiled, then repairing is costly
2. Synchronous Condenser When a Synchronous
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motor operates at No-Load and over-exited then it’s
called a synchronous Condenser. Whenever a
Synchronous motor is over-exited then it provides
leading current and works like a capacitor. When a
synchronous condenser is connected across supply
voltage (in parallel) then it draws leading current and
partially eliminates the re-active component and this
way, power factor is improved. Generally,
synchronous condenser is used to improve the power
factor in large industries.
Advantages: Long life (almost 25 years) High Reliability
Step-less adjustment of power factor. No generation of harmonics
of maintenance The faults can be removed easily It’s not affected
by harmonics. Require Low maintenance (only periodic bearing
greasing is necessary) Disadvantages: It is expensive
(maintenance cost is also high) and therefore mostly used by large
power users. An auxiliary device has to be used for this operation
because synchronous motor has no self starting torque It produces
noise
3. Phase Advancer
Phase advancer is a simple AC exciter which is connected on the
main shaft of the motor and operates with the motor’s rotor circuit
for power factor improvement. Phase advancer is used to improve
the power factor of induction motor in industries. As the stator
windings of induction motor takes lagging current 90° out of
phase with Voltage, therefore the power factor of induction motor
is low. If the exciting ampere-turns are excited by external AC
source, then there would be no effect of exciting current on stator
windings. Therefore the power factor of induction motor will be
improved. This process is done by Phase advancer.
Advantages: Lagging kVAR (Reactive component of Power or
reactive power) drawn by the motor is sufficiently reduced
because the exciting ampere turns are supplied at slip frequency
(fs). The phase advancer can be easily used where the use of
synchronous motors is Unacceptable
Disadvantage: Using Phase advancer is not economical for
motors
below
200
H.P.
(about
150kW)
RESULT
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A complex number raised to the zero power is equal
to 1. It's not exactly an axiom, but it comes about due to the way
exponentiation is defined. For integer exponents, exponentiation
of complex numbers is defined in just the same way as
exponentiation of real numbers. One way to look at it is that the
integer exponent specifies how many times to multiply the base
number. If you multiply the number zero times, you are left with
the multiplicative identity, which is 1. Similarly, a number times
0 is 0 because multiplication by an integer can be thought of as
repeated addition, and adding the number zero times leaves you
with the additive identity, which is 0.
CONCLUSION
In power engineering, the power-flow study, or load-flow study,
is a numerical analysis of the flow of electric power in an
interconnected system. A power-flow study usually uses
simplified notation such as a one-line diagram and per-unit
system, and focuses on various aspects of AC power parameters,
such as voltages, voltage angles, real power and reactive power.
It analyzes the power systems in normal steady-state operation.
Power-flow or load-flow studies are important for planning future
expansion of power systems as well as in determining the best
operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of
the voltage at each bus, and the real and reactive power flowing
in each line.
REFERENCE
Internet and power system book,J.P navani and Sonal Sapra
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