Transformer power is measured in VA, not in Watts. This is because the simple Watts = Volts x Amps equivalence cannot be used if the voltage and current are not aligned and are out of phase. For AC circuits, the reactance of any capacitive or inductive load elements shifts the phase of the current to the voltage. For mainly capacitive loads, the current waveform lags the voltage and for mainly inductive loads, the current leads the voltage. A simple way to remember which way the phase difference goes is the word CIVIL:
Fig. 3.1: AC voltage, current and apparent power for a mainly inductive load. The current lags the voltage and the reactive power can go negative (the load is supplying power back into the source)
If the AC current is out of alignment with the AC input voltage, then the shift can be described as a phase angle. A phase angle of 0° means that the current and voltage are perfectly aligned (in other words, the load is purely resistive). A phase angle of 90° means that the load is purely reactive (either +90° = purely inductive or -90° = purely capacitive). With no resistive element, a purely reactive load consumes no power: for two quarters of the cycle the sum of the current and voltage is positive but for the other two quarters of the cycle the sum is negative and the two balance out.
Fig. 3.2: Waveforms and apparent power for a purely inductive load
In practice purely reactive loads do not exist as there are always some resistive losses in the wiring. In a power supply circuit, there will be a mix of both reactive and resistive losses leading to a power factor (the ratio of active power to reactive power) somewhere between 1 and 0 (a power factor of 1 corresponds to a phase angle of zero and a power factor of 0 corresponds to a phase angle of 90°)
Fig. 3.3: Apparent power vector diagram. Reactive power does no useful work - like the head in a beer glass
By convention, capacitive loads generate reactive power and inductive loads consume reactive power. This is very useful, as a capacitor can be used to bring the power factor closer to 1 for a mainly inductive load such as a motor or an inductor can be used to bring the power factor closer to 1 for a mainly capacitive load. Adding such reactive components to adjust the power factor is called passive power factor correction.
But why bother correcting the power factor? The purely reactive element of the load consumes no power overall as energy absorbed in one part of the cycle is returned in another part, so most electricity meters only measure the active power consumed and ignore the reactive power. The main problem is that the electricity company has to supply enough power to cope with the peak power demand which is the combination of active and reactive powers. Even if some of this energy is returned in other parts of the cycle, the distribution system has to cope with the worst case instantaneous power consumption. Also, the reactive power circulating current and therefore the cable losses in a system with “poor” power factor will be higher than one with a “good” power factor (closer to 1). By encouraging customers to power-factor-correct their energy consumption (by either charging more for poor power factor loads or by lobbying governments to force customers to add power factor correction), the power companies can save money.
It is a common mistake to think that, for example, an LED driver with power factor correction is somehow “greener” and consumes less power. The additional power factor correction circuitry actually reduces overall efficiency by adding additional power stages to the design.
A more serious issue is the problem of electromagnetic interference if the power supply is not properly power factor corrected. Take the example shown in figure 3.4 of a linear power supply. The input current is in phase with the input voltage, but severely distorted. Using the relationship shown in figure 3.3 might give the impression that the power factor = 1 as Cos φ = 1.
Fig. 3.4: Linear power supply input current vs voltage
However, looking at the harmonics generated by the distorted input current reveals a different story:
Fig. 3.5: Harmonics generated by the input current shown in figure 3.4
The fundamental harmonic (number 1) is the input frequency (50Hz or 60Hz). This represents the real power supplied to the converter. The remaining odd harmonics 3, 5, 7, 9, etc. represent the apparent power. As the current waveform is almost perfectly symmetrical, the even harmonics hardly show. As can be seen from this diagram, there is a considerable amount of energy present in the higher harmonics and therefore the power factor is not 1 but in fact closer to 0.6, even though the current is in phase with the voltage. The problem lies in that the input voltage is a pure sine wave but the current is a much-distorted waveform. This distortion factor can be added to the basic Cos φ relationship to give the true real power/apparent-power relationship:
In comparison, a near-perfect power factor corrected circuit where the current is not only in phase with the input, but also a sine wave gives an ideal harmonic graph with almost all of the input power in the fundamental harmonic only:
The sum of the unwanted harmonics (2nd harmonic and higher) is called the total harmonic distortion (THD) and its relationship to power factor, PF, is given by:
CIVIL
For capacitance, C, current I leads voltage V.
For inductance, L, current I lags voltage V.
For capacitance, C, current I leads voltage V.
For inductance, L, current I lags voltage V.
Fig. 3.1: AC voltage, current and apparent power for a mainly inductive load. The current lags the voltage and the reactive power can go negative (the load is supplying power back into the source)
If the AC current is out of alignment with the AC input voltage, then the shift can be described as a phase angle. A phase angle of 0° means that the current and voltage are perfectly aligned (in other words, the load is purely resistive). A phase angle of 90° means that the load is purely reactive (either +90° = purely inductive or -90° = purely capacitive). With no resistive element, a purely reactive load consumes no power: for two quarters of the cycle the sum of the current and voltage is positive but for the other two quarters of the cycle the sum is negative and the two balance out.
Fig. 3.2: Waveforms and apparent power for a purely inductive load
In practice purely reactive loads do not exist as there are always some resistive losses in the wiring. In a power supply circuit, there will be a mix of both reactive and resistive losses leading to a power factor (the ratio of active power to reactive power) somewhere between 1 and 0 (a power factor of 1 corresponds to a phase angle of zero and a power factor of 0 corresponds to a phase angle of 90°)
Fig. 3.3: Apparent power vector diagram. Reactive power does no useful work - like the head in a beer glass
By convention, capacitive loads generate reactive power and inductive loads consume reactive power. This is very useful, as a capacitor can be used to bring the power factor closer to 1 for a mainly inductive load such as a motor or an inductor can be used to bring the power factor closer to 1 for a mainly capacitive load. Adding such reactive components to adjust the power factor is called passive power factor correction.
But why bother correcting the power factor? The purely reactive element of the load consumes no power overall as energy absorbed in one part of the cycle is returned in another part, so most electricity meters only measure the active power consumed and ignore the reactive power. The main problem is that the electricity company has to supply enough power to cope with the peak power demand which is the combination of active and reactive powers. Even if some of this energy is returned in other parts of the cycle, the distribution system has to cope with the worst case instantaneous power consumption. Also, the reactive power circulating current and therefore the cable losses in a system with “poor” power factor will be higher than one with a “good” power factor (closer to 1). By encouraging customers to power-factor-correct their energy consumption (by either charging more for poor power factor loads or by lobbying governments to force customers to add power factor correction), the power companies can save money.
It is a common mistake to think that, for example, an LED driver with power factor correction is somehow “greener” and consumes less power. The additional power factor correction circuitry actually reduces overall efficiency by adding additional power stages to the design.
A more serious issue is the problem of electromagnetic interference if the power supply is not properly power factor corrected. Take the example shown in figure 3.4 of a linear power supply. The input current is in phase with the input voltage, but severely distorted. Using the relationship shown in figure 3.3 might give the impression that the power factor = 1 as Cos φ = 1.
Fig. 3.4: Linear power supply input current vs voltage
However, looking at the harmonics generated by the distorted input current reveals a different story:
Fig. 3.5: Harmonics generated by the input current shown in figure 3.4
The fundamental harmonic (number 1) is the input frequency (50Hz or 60Hz). This represents the real power supplied to the converter. The remaining odd harmonics 3, 5, 7, 9, etc. represent the apparent power. As the current waveform is almost perfectly symmetrical, the even harmonics hardly show. As can be seen from this diagram, there is a considerable amount of energy present in the higher harmonics and therefore the power factor is not 1 but in fact closer to 0.6, even though the current is in phase with the voltage. The problem lies in that the input voltage is a pure sine wave but the current is a much-distorted waveform. This distortion factor can be added to the basic Cos φ relationship to give the true real power/apparent-power relationship:
| Eq. 3.1: |  |
|---|
In comparison, a near-perfect power factor corrected circuit where the current is not only in phase with the input, but also a sine wave gives an ideal harmonic graph with almost all of the input power in the fundamental harmonic only:
Fig. 3.6: Near-ideal power factor and its harmonics
The sum of the unwanted harmonics (2nd harmonic and higher) is called the total harmonic distortion (THD) and its relationship to power factor, PF, is given by:
| Eq. 3.2: |  |
|---|