Relationship between Real Power, Apparent Power and Power Factor
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Electric power expressed as watts in d-c circuits is the
product of the voltage and current (voltage times
current). In a-c circuits the calculation is complicated by
the need to take into account the shape of the voltage
and current waveforms and their relative phase angle.
Real power is mathematically determined by dividing
time into a very large number of small segments and
multiplying the instantaneous voltage present in each
time segment by the instantaneous current flowing and
averaging the results.
FIGURE 14 -
Relationship between real and apparent power in a sinusoidal system
A wattmeter gives the same result in a real world circuit
because the instrument reacts to the simultaneous effects
of the voltage and current present from instant to
instant. When separate measurements are made of
voltage and current, the product is NOT a-c power since
each meter reads an average or rms value of the voltage
or current over time without reflecting the phase shift
that may be present. If there is a difference in phase
between the voltage and current waveforms, the peak
current may not be present when the voltage reaches its
peak. The apparent power will be the vector sum of the
real power and the imaginary power.
The angle is the phase shift. In a non-reactive circuit,
the voltage and current will be in phase, the imaginary
power is zero and the real power will equal the apparent
power. Their ratio is expressed as power factor (PF) and
when they are equal, the power factor is unity (1).
Waveform distortion, of the type caused by capacitor
input filter circuits following rectifiers, is another source
of low power factor. It results from the creation of
discontinuous waveforms as the current to the load flows
for just the part of the cycle where the voltage from the
rectifier exceeds the d-c level across the capacitor. In
terms of rms values, there are an infinite number of
waveforms that can yield the same rms value. If the
current is not sinusoidal, a narrow spike, for example,
the rms value may remain the same even though the
average value can be quite different. Although the voltage
and current are in phase with each other, the power
factor can differ from the unity value that two sinusoidal
waveforms would produce. A Fourier analysis would show
that changing the shape of either the voltage or current
waveform reduces the power factor from the unity value
that you might expect from the in-phase relationship.
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The input off-line capacitors of switch mode power
supplies do significantly change the current waveform.
As the voltage reaches the stored level in the capacitor,
the rectifier diode switches on, forcing the current to
flow for a shorter time interval than the voltage.
While the load current is drawn from the capacitor
continuously, or at the high switching frequency of the
converter, the capacitor is recharged only during the
interval when the input rectifiers conduct. No current
flows into the capacitor from any point along the voltage
waveform where its amplitude falls below the capacitor's
d-c voltage. Current only flows when it again rises above
the d-c value during the next mains half cycle.
Low power factor results when the load current is drawn
over only a part of each mains cycle. This is a common
result in off-line rectifiers where the input diode does not
conduct until the peak of the rectified mains waveform
exceeds the d-c level across the input capacitors.
FIGURE 15 -
A capacitor-input filter as used in off-line power supplies produces
discontinuous current flow. a-c current flows only when the
a-c voltage exceeds the d-c change in the capacitor
The period of time during which no current flows into
the capacitor, expressed in terms of degrees along the
voltage waveform, is the rectifier's dead angle.
Conversely, the period during which current does flow
into the capacitor is the rectifier's conduction angle. The
ratio of these angles depends upon the filter's capacitance
and how much energy is being withdrawn by the power
converter which is the capacitor's load. This, in turn,
depends on the amount of power demanded by the
output load on the converter. With a light load, the
conduction angle may be just a few degrees. At full rated
load, the conduction angle will be larger, but even with
heavy loads, conduction is not continuous. The current has
the form of relatively large, short-duration pulses. Because
the a-c mains exhibit a non-zero source impedance,
the high current peaks cause some clipping distortion on
the peaks of the voltage sinusoid. Fourier analysis would
show that this lowers the power factor significantly.
Since power factor represents the ratio of real to apparent
power, the high apparent power that yields a low power
factor translates into a higher current than the load
actually needs to satisfy its real power requirement.
The difference between the current that produces
the real power consumed by the load and the
current measured on an ammeter is known as the
circulating current. It is so called because even though it
does no real work, it continuously flows back and forth
between the mains and the load.
FIGURE 16 -
Waveforms illustrating the peak flattening effect that the
narrow current pulses impose on the mains voltage
A switching converter with 80 percent efficiency and an
uncorrected power factor of 0.65 can produce only 717
watts of real power to a load with 12 amperes from a
115V a-c utility mains. (12 amperes is the maximum
continuous rating of a standard 15 ampere branch
circuit.) Equipping this power supply with power factor
correction, despite lower conversion efficiency, allows
it to use the full 12 amperes to produce real power for
its load. With an overall efficiency of 67.5%the 12
amperes from the 115V a-c branch circuit produces
932 watts to the load, an increase of 30%.
FIGURE 17 -
Waveforms illustrating the reduced peak current when the current
waveform is made to conduct continuously by power factor correction
PROTECTING SENSITIVE EQUIPMENT FROM ELECTRO-MAGNETIC INTERFERENCE
The EMI produced by the high-frequency switching of
a switch-mode converter is well recognized and may be
dealt with through special filters built into nearly all such
power supplies. The discontinuous current pulses created
by the charging action of a power supply's input circuit
is another form of EMI. As such it can affect the
operation of sensitive equipment operated in close
proximity to the a-c mains. This interference takes two
forms. First, the high amplitude of the current pulses
generate electromagnetic fields strong enough to be
detected by sensitive amplifiers. Second, as the current
pulses occur around the peaks of the voltage waveform,
the IR drop in the wiring flattens the voltage waveform
producing harmonic distortion. This may adversely
affect instruments that depend upon the presence of a
normal a-c sinusoid. When more than one power supply
operates from such distorted mains, the problem is
compounded as each power supply tries to charge its
input capacitor from the same peak of the a-c voltage.
THE EUROPEAN VIEW OF POWER FACTOR: EN 61000-3-2
The European electrical system distributes power at 240
volts. This means that the current is half what it would
be in the USA for an equivalent load. Because of this,
European distribution systems use smaller gauge wire
and lower amperage fuses. As a result, they are more
sensitive to circulating current than their USA
counterparts. With the goal of minimizing circulating current,
the International Electrotechnical Committee (IEC)
took a look at the discontinuous currents produced by
switch mode power converters and other electrical
equipment. Any discontinuous waveform consists of a
pure sine wave at the fundamental frequency plus sine
waves of various amplitudes occurring at each of the
fundamental's harmonic frequencies. The IEC codified
its findings in IEC 555-2, setting limits for currents at
each harmonic frequency through the 40th harmonic.
The IEC divided equipment into four classes, each with
its own set of harmonic current limits. These limits have
been codified into a "European norm," EN61000-3-2.
To meet these limits various power factor correcting
(PFC) circuits are employed to actively force the main
rectifier(s) to conduct over the whole of each half cycle
of the ac power mains. These sometimes take the form
of a high frequency boost converter that preceeds the
input filter capacitor.
At some sacrifice in efficiency and some loss of
simplicity, the PFC boost converter reduces the power
factor to something between 0.95 and 0.99 (sufficient
to meet the harmonic current limits). Additionally,
PFC enhances the energy storing function of the input
capacitor. A boost converter can also provide a relatively
stable output over a wide range of input voltages. The
power factor correcting boost converter produces a
constantly high voltage across its input capacitor
regardless of the input mains voltage. Thus the
hold-up time becomes independent of the mains voltage.
Power supplies with active power factor correction
(PFC) include the Kepco ABC (100W), MST (200W),
RCW (350, 750 and 1500W), RKW (50, 100, 150, 300,
600 and 1500W), HSP (1000 and 1500W), BOP High
Power (1000 and 2000W) and HSM (1000 and 1500W).
Model ABC 10-10DM
Model BOP High Power 10-75MG
Model RKW Programmable - 1500W size
THE CE MARK AND SAFETY AGENCY MONOGRAMS
The CE mark is required by the European Community
on certain products. Since January 1, 1997, there are two
requirements for the CE mark:Electromagnetic
compatibility (EMC) and the Low Voltage Directive
(LVD). The EMC standards address both emitted EMI
and the susceptibility to RF and electrostatic discharge.
The low voltage directive addresses safety issues.
Kepco produces both instrumentation power supplies,
which are self-contained products, and modular power
supplies which are considered components of a larger
assembly. They have different rules. The Low Voltage
Directive applicable for our instrumentation power
supplies is EN61010-1. The standard currently applicable
for component power supplies is EN60950. (The UL
standard for the USA is based on the same recommenda-
tion of the International Electrotechnical Commission
(IEC): IEC 950 and is known as UL60950.)
All component power supplies intended for sale overseas
have been CE marked per the Low Voltage Directive
(LVD) EN60950. They are NOT certified to the
EMC/EMI standards because as components they are
intended to obtain their shielding from the larger assembly
into which they are mounted. Kepco's component power
supplies do, of course, contain input EMI filters
designed to reduce conducted EMI below the limits of
Class A or B emissions depending on the product. Such
filters, however, do not guarantee that the end product
into which the power supply is installed will meet all of its
EMC/EMI requirements. That remains the responsibility
of the end item producer.
Instrumentation power supplies designed to mount within
another enclosure or rack are similarly CE marked per the
Low Voltage Directive (LVD) EN61010-1, but not the
EMC/EMI directives. Those instrumentation power
supplies designed for stand-alone bench use are CE
marked for both the EMC/EMI directives and the LVD.
Kepco uses the services of Underwriters Laboratories,
(UL), the Canadian Standards Association, (CSA), TÜV
Rheinland and VDE to perform safety certifications on
our products. The LVD test data is on file at Kepco and
is available for review by authorized EC port inspectors
on request. We can provide, upon request, copies of our
certifications by these independent safety agencies or
declarations of conformity which indicate the directives
for which compliance is declared.
Kepco's facility in Flushing, New York, has
received ISO 9001 certificate, number 109592,
from Lloyd's Register of Quality Assurance.
