# Relationship between phase angle and power factor show

### Power factor - Wikipedia

Power factor is nothing but cos ∆ where ∆ is the phase angle between voltage and current. Given power factor is That is, Cos ∆ = Hence the phase angle . Power factor is the ratio of real power to apparent power in an electrical system. is the phase angle of the current; we refer to φ as the power factor angle.1 We can show the relationships among real, apparent and reactive. least predictable amounts to the phase shift are important to allow Power factor (PF) expressed as a fraction is the ratio between the Chart 1 below shows the resulting calculated power factor as a result of the phase shift.

Reactive Power — the power that is constantly recycled through the non-resistive parts of the circuit i. Calculate the apparent power, the true power, the reactive power and the power factor. The sum is performed using the apparent power of each load. Example A single-phase load consists of: Calculate a the total Kw, b the total kVAr, c the total kVA, d the overall power factor, and e the total supply current at V.

The sum is shown in figure The angle of lag has a cosine of 0. This load is then added to the resultant A, and gives a total kVA of B, measured off as The in-phase horizontal component of this load is The quadrature vertical component is In DC systems it is easy to calculate the current that will flow through a piece of equipment since we would know the voltage of the supply and power rating of the equipment would probably be quoted.

The wave diagrams for the power in: Note that v, i and p are not plotted on the same scale. AC supplies are often rated in kVA to avoid confusion over the power factor.

If the load is inductive and resistive a motor for example the current will lag voltage and a smaller amount of active power is available although the same current can still be delivered, figure Therefore, a rating 30kVA will hold true for loads with any power factor whereas, a rating of 30kW really means that a maximum of 30kW can be delivered to a purely resistive load but to other loads, where the power factor is less than unity, the power delivered will be less.

To work out the active power delivered we need to know the power factor of the load.

AC machines are also often rated using kVA because they may work with different supply voltages. We have calculated this without knowing the power factor, and therefore without knowing the active power consumption of the motor. If the motor were rated in kW we would need to know the power factor to find out how much current it would draw.

• Practical Power Factor Correction
• Power factor
• Part 12: AC Power Factor

Example A single-phase 3. Another switched-mode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics, but permits cheaper and smaller passive components. It is frequently used in practice. For a three-phase SMPS, the Vienna rectifier configuration may be used to substantially improve the power factor. That feature is particularly welcome in power supplies for laptops.

Dynamic PFC[ edit ] Dynamic power factor correction DPFCsometimes referred to as "real-time power factor correction," is used for electrical stabilization in cases of rapid load changes e.

DPFC is useful when standard power factor correction would cause over or under correction. Importance of power factor in distribution systems[ edit ] 75 Mvar capacitor bank in a kV substation Power factors below 1. This increases generation and transmission costs. For example, if the load power factor were as low as 0.

Line current in the circuit would also be 1. Alternatively, all components of the system such as generators, conductors, transformers, and switchgear would be increased in size and cost to carry the extra current.

### Calculating Power Factor | Power Factor | Electronics Textbook

When the power factor is close to unity, for the same KVA rating of the transformer more load can be connected [27]. Utilities typically charge additional costs to commercial customers who have a power factor below some limit, which is typically 0. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.

With the rising cost of energy and concerns over the efficient delivery of power, active PFC has become more common in consumer electronics. According to a white paper authored by Intel and the U.

## Calculating Power Factor

Small customers, such as households, are not usually charged for reactive power and so power factor metering equipment for such customers will not be installed. Techniques for measuring the power factor[ edit ] The power factor in a single-phase circuit or balanced three-phase circuit can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current.

The power factor of a balanced polyphase circuit is the same as that of any phase. The power factor of an unbalanced poly phase circuit is not uniquely defined.

A direct reading power factor meter can be made with a moving coil meter of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument. The field of the instrument is energized by the circuit current flow. The two moving coils, A and B, are connected in parallel with the circuit load.

One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A.

At unity power factor, the current in A is in phase with the circuit current, and coil A provides maximum torque, driving the instrument pointer toward the 1. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torques provided by the two coils add and the pointer takes up intermediate positions.

The field coils are connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application.