功率因数计算器

计算功率因数、视在功率、无功功率，并估算校正电容器容量以提高电气效率。

Calculate Power Factor

Enter values and click Calculate to see results

About Power Factor

What is Power Factor?

Power factor is a dimensionless number between 0 and 1 that represents how efficiently electrical power is being used in a circuit. It is defined as the ratio of real power (P) to apparent power (S) in an AC electrical system.

A power factor of 1 (or 100%) indicates that all power is being used efficiently to perform work (purely resistive load). A power factor less than 1 means that some power is being wasted, with energy flowing back and forth in the circuit without producing useful work.

Power Components

Real Power (P)

The actual power consumed to do useful work, measured in watts (W). This is the power that performs actual work like producing heat, light, or motion.

$$P = V \times I \times \cos\phi \text{ (W)}$$

Reactive Power (Q)

Power that flows back and forth in the circuit without performing work, measured in volt-amperes reactive (VAR). It is used by inductive loads like motors to create and maintain magnetic fields.

$$Q = V \times I \times \sin\phi \text{ (VAR)}$$

Apparent Power (S)

The total power supplied to the circuit, measured in volt-amperes (VA). It is the vector sum of real power and reactive power.

$$S = V \times I \text{ (VA)}$$

What is Power Factor?

Power Components

Real Power (P)

The actual power consumed to do useful work, measured in watts (W). This is the power that performs actual work like producing heat, light, or motion.

$$P = V \times I \times \cos\phi \text{ (W)}$$

Reactive Power (Q)

Power that flows back and forth in the circuit without performing work, measured in volt-amperes reactive (VAR). It is used by inductive loads like motors to create and maintain magnetic fields.

$$Q = V \times I \times \sin\phi \text{ (VAR)}$$

Apparent Power (S)

The total power supplied to the circuit, measured in volt-amperes (VA). It is the vector sum of real power and reactive power.

$$S = V \times I \text{ (VA)}$$

How to Use This Calculator

This power factor calculator allows you to determine power factor and related values using three different calculation methods, based on the available measurements.

Select the calculation method based on available measurements
Choose single phase or three phase system
Enter values for frequency and available measurements
For power factor correction, enter existing and target power factors
Click Calculate to see results

For the most accurate results, ensure all measurements are in compatible units and are taken from the same circuit under identical conditions.

Calculation Methods

Power & Current Method

Uses measurements of real power, current, and voltage. Useful when you have direct measurements from a wattmeter and ammeter.

Power & Voltage Method with Power Factor Correction

Calculates apparent and reactive power based on measured real power and existing power factor. Also estimates the capacitance required to improve to a target power factor.

Apparent & Reactive Power Method

Directly calculates power factor from measured real, apparent, and reactive power values. Useful when you have readings from a power analyzer.

Power Triangle Explained

The power triangle is a graphical representation of the relationship between real power (P), reactive power (Q), and apparent power (S) in an AC circuit. It helps visualize the power factor as the cosine of the angle between apparent power and real power.

$$\text{功率三角形关系：} S^2 = P^2 + Q^2$$

Key Relationships

The hypotenuse of the triangle represents apparent power (S)
The horizontal side represents real power (P)
The vertical side represents reactive power (Q)
The angle between S and P is the phase angle φ, whose cosine is the power factor

Power Triangle Formulas

$$\text{功率因数} = \cos \phi = \frac{P}{S} = \frac{P}{\sqrt{P^2 + Q^2}}$$

$$\text{相位角} = \phi = \cos^{-1}(\text{功率因数}) = \tan^{-1}\left(\frac{Q}{P}\right)$$

$$\text{视在功率} = S = \sqrt{P^2 + Q^2} = \frac{P}{\cos \phi}$$

$$\text{无功功率} = Q = S \times \sin \phi = P \times \tan \phi$$

Power Factor Correction

Power factor correction is the process of improving the power factor of an electrical system by adding capacitors to the circuit. This reduces reactive power, resulting in more efficient power usage and potentially lower electricity bills.

Low power factors (below 0.9) often lead to increased electrical costs, as utilities may charge penalties for systems with poor power factors. Improving power factor also reduces losses in electrical distribution systems and increases system capacity.

Capacitance Formula

$$C = \frac{P(\tan \phi_1 - \tan \phi_2)}{2\pi f U^2} \times 10^6 \text{ (μF)}$$

Where P is real power (watts), φ₁ is the existing phase angle, φ₂ is the target phase angle, f is the frequency (Hz), and U is the voltage (volts).

Benefits of Power Factor Correction

Reduction in utility bills (many utilities charge penalties for low power factor)
Increased electrical system capacity
Reduced power losses in distribution systems
Improved voltage regulation and reduced voltage drops

Applications and Typical Values

Power factor is an important consideration in various electrical systems, particularly in industrial and commercial settings where large motors and other inductive loads are common.

Industrial Applications

Factories with numerous motors, transformers, and inductive equipment often have power factors between 0.7 and 0.85 without correction. Improving these can significantly reduce operating costs.

Commercial Applications

Office buildings, shopping centers, and hospitals typically have power factors ranging from 0.8 to 0.95, depending on the types of lighting and HVAC equipment installed.

Common Load Types

Different electrical devices have different inherent power factors. Resistive loads like heating elements have near-perfect power factors, while inductive loads like motors and fluorescent lighting without correction have lower power factors.

Typical Power Factor Values

Load Type	Typical Power Factor
Resistive heating elements	1.0
Incandescent lighting	1.0
Fluorescent lighting (without correction)	0.5-0.7
Electric motors (at full load)	0.7-0.9
Transformers (at full load)	0.8-0.9

Frequently Asked Questions

Why is a low power factor problematic?

A low power factor means that electrical equipment is drawing more current than necessary for the actual work being done. This excess current causes additional losses in the distribution system, can overload transformers and conductors, and often results in additional charges from utility companies.

How do I know if I need power factor correction?

You may need power factor correction if you have higher than expected electricity bills (especially with power factor penalties), your electrical equipment is overheating, you experience voltage drops, or circuit breakers trip frequently. Measuring the power factor with a power analyzer can confirm if correction is needed.

What is a good target power factor?

Most utilities consider a power factor of 0.95 or higher to be acceptable. Many industrial facilities aim for a power factor between 0.95 and 0.98, as the cost of achieving power factors closer to 1.0 often exceeds the additional benefits.

Can power factor ever be greater than 1?

No, power factor cannot exceed 1 (or 100%). A power factor of 1 represents perfect efficiency where all power drawn from the source is converted into useful work.

How are power factor correction capacitors sized and installed?

Capacitors are sized based on the amount of reactive power (kVAR) needed to achieve the desired power factor. They can be installed at individual equipment (decentralized), at distribution panels (group compensation), or at main service entrance (centralized compensation). Installation should be performed by qualified electricians who understand the electrical system and potential resonance issues.

功率因数计算器

Calculate Power Factor

About Power Factor

What is Power Factor?

Power Components

Real Power (P)

Reactive Power (Q)

Apparent Power (S)

相关计算器推荐