## Relationship between Real Power, Apparent Power and Power Factor |

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. |

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

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 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).

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.

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