Regarding the calculation of the power factor of switching power supplies , the calculation still follows the definition of power factor, which is the ratio of active power to apparent power, based on its input terminal. However, in practice, switching power supply manufacturers use measurement methods, employing specialized instruments to measure various parameters of the switching power supply, including its power factor value. Due to historical reasons, many people believe the formula for calculating the power factor is: PF = cosφ. In reality, this formula only applies under specific conditions, namely: the load is a non-purely resistive linear load. The true definition of power factor is: PF = Active Power / Apparent Power.
What is active power? Active power is the power actually consumed by the load, calculated as: P<sub>active</sub> = ∫u·i. This is essentially the average of the product of instantaneous voltage and instantaneous current. Apparent power, on the other hand, is defined as: P<sub>apparent</sub> = URMS·IRMS. Unlike active power, the current and voltage here are measured separately. So, how does the formula PF = cosφ come about? For inductive loads such as AC motors (and in practice, capacitive loads are similar, though less common), the current and voltage waveforms are the same, but with a phase difference.
Regarding the current I with a phase difference φ: it can be decomposed into a weight that is in phase with the voltage, with a fluctuation of I·cosφ; and a weight that is orthogonal to the voltage (90° out of phase), with a fluctuation of I·sinφ. The average of these two weights multiplied by the voltage is calculated. The average of the product of the orthogonal weight and the voltage is zero. The remaining value is P<sub>active</sub> = P<sub>apparent</sub>·cosφ. Here, the reactive current is: I<sub>reactive</sub> = IRMS·sinφ.
For loads like switching power supplies, there is no significant phase difference between the current and voltage waveforms, but the current waveform is not sinusoidal; such loads are, in practice, typical nonlinear loads. Similar to the previous example, the average value of the product of a non-sinusoidal current and a sinusoidal voltage can be calculated by decomposing the current into components with the same frequency and phase as the voltage, and components with different frequencies or phases. Here, the current waveform has virtually no phase difference, but contains a large number of harmonic components. Performing a Fourier transform on the current waveform yields a series of harmonic components. Among these: as long as the average of the product of the fundamental frequency component and the voltage is not zero, this portion of the current is active current; while the average of the product of all higher harmonic components and the voltage is zero, so all higher harmonic currents are reactive currents. Since they are independent of the actual power consumed, the total value of the reactive current is the square root of the sum of the squares of all higher harmonic currents.
Disclaimer: This article is a reprint. If it involves copyright issues, please contact us promptly for deletion (QQ: 2737591964). We apologize for any inconvenience.
