# What is the power factor of an independent power supply system?

Of further concern in AC systems are the reactive elements (inductive and capacitive elements in sinusoidal AC circuits). Reactance can be either capacitive or inductive, but no work is done by current flowing through either type of reactance. The electrical power in a DC circuit is equal to the product of the voltage and the current, i.e.
P=UI

The power meter measures the average power over a short period of time, and then continuously accumulates the power measurements to obtain the total power (w*h).

In an AC circuit, the reactance of the load causes a phase shift between the current waveform and the applied voltage. The phase difference θ between the voltage and current makes the amount of power supplied to the load greater than that measured by the power meter. The electrical power supplied to the load is called apparent power, and its unit of measurement is volt-ampere (VA).
Apparent power = UI

The phase difference between voltage and current is measured by the power factor (PF), which is equal to the cosine of the phase angle between the voltage and current. The phase difference caused by all reactive loads depends on their inductance or capacitance value.
PF=cosθ

Purely resistive loads (such as heaters, incandescent lamps) do not cause a phase difference between voltage and current, at which point the active power is equal to the apparent power. Because there is no phase difference between voltage and current, the power factor is equal to 1 (cos0°=1).

In an AC circuit, the electrical power consumed by the load is measured in unit W, which is called active power. The relationship between active power and apparent power is shown in Figure 1. Its calculation formula is
Active power=UI×PF

Generally speaking, inductive (or lagging) power factor in power systems is caused by motors, transformers and ballasts. In particular, AC motors, whose active power measured by a wattmeter may be small, but whose apparent power is high leads to additional heat dissipation in AC power distribution equipment, such as transformers and cables.

In order to calculate the power factor of the electrical equipment, it is necessary to measure the effective value of the alternating current and voltage, and then calculate the product between the two effective values ​​to obtain the apparent power (VA), and then use the alternating current power meter to measure its active power, power The factor can be calculated using the following formula
PE=active power/apparent power
Note: The power factor can only take the value of 0~1.

Low power factor electrical equipment (PF<0.7) often brings trouble to the power supply department, and high apparent power will lead to additional electrical losses in the power distribution system. Therefore, industrial users usually need to install a compensation device on site to correct the power factor according to the regulations of the power supply department. The desired effect of this measure is to adjust the power factor close to the ideal value of 1.

Table 1 shows the main types of loads commonly found in stand-alone power supply systems. The following sections discuss inverters for different types of loads. Only sine wave inverters are currently available in Australia, so some of the discussion in this book that only applies to square wave inverters applies only to situations where a square wave inverter is installed and used.

[Example] A row of 36W fluorescent lighting equipment with 5 single tubes uses traditional iron core ballasts, and an AC power meter is used to measure the average active power of the load. The alternating current is measured by an ammeter, the degree of the meter is: the degree of the power meter is 243W, and the effective value of the alternating current is 2.25A.

Such loads include ovens, irons, hair dryers (appliances with heating elements), and incandescent lamps, and are the most inverter-friendly of all load types.

A power factor equal to 1 means that the apparent power is equal to the active power. The simplest load for an inverter is one whose voltage and current are in phase.

The low power factor of this type of load means that the inverter (or generator set) must be loaded to make the apparent current in the 240V circuit larger. This is why AS4509.2 requires the inverter to be rated according to the apparent power rather than the active power, which is also the rated power value of the device.

All motors can be classified as inductive loads, including DC motors, AC/DC motors, and AC induction motors. Portable power tools and some kitchen appliances use DC motors. Such appliances can be powered by square wave and pure sine wave inverters, but additional consideration should be given to the considerable starting current of such tools, especially when they are operated at low loads. The lowest power factor of all motors is the induction motor. Induction motors for refrigerators and water pumps have the largest inrush currents at low load startup.

For iron core ballast fluorescent lamps, the continuous operation rated power value can be increased by 30%~40%.

3. Inductive loads with power factor correction
From the point of view of using DC power, the configuration of reactive power compensation capacitors for inductive electrical equipment does not necessarily guarantee that the efficiency will be improved. The result of the efficiency improvement caused by the power factor correction depends on the type of inverter (such as sine wave type or corrected sine wave type, etc.) and the type of inductive load, and the specific situation should be analyzed in detail.