Three-Phase Power

Three-phase power is a type of electrical power distribution system that uses three alternating currents (phases) that are offset in time to each other by one-third of the total cycle. It is commonly used in industrial and commercial applications.

Real Power Calculation √3
Reactive Power (Q) Calculation √3
Apparent Power Calculation √3
Power Factor Calculation √3
Voltage Drop Calculation √3

Key Characteristics of Three-Phase Power:

Three-phase power systems provide a more balanced and efficient distribution of electrical power compared to single-phase systems.
Each phase in a three-phase system carries a sinusoidal waveform, and the three phases are typically denoted as phase A, phase B, and phase C.
The voltage and current waveforms of the three phases are 120 degrees out of phase with each other.
The combination of the three phases results in a smoother and more constant power delivery, reducing voltage drops and improving overall power quality.
Three-phase power allows for higher power transmission with less current compared to single-phase systems, making it suitable for high-power applications.
Three-phase power is widely used in industrial machinery, motors, large-scale electrical systems, and power distribution grids.

Real Power Calculation (Three-Phase)

Real power is the actual power transferred to a load and is measured in watts (W).

Formula:

P = √3 * V_L-L * I_L * PF

Real power represents the useful power consumed by resistive and reactive loads.

Formula Breakdown:

P is the power in watts (W).
√3 is the square root of 3, approximately equal to 1.732.
VL-L is the line-to-line voltage in volts (V).
IL is the line current in amperes (A).
PF is the power factor, which is a dimensionless quantity.

Reactive Power (Q) Calculation

Reactive power is the power used by inductive or capacitive loads and is measured in volt-amperes reactive (VAR).

Formula:

Q = √3 * V_L-L * I_L * sin(θ)

Reactive power is required for the magnetizing of equipment such as motors and transformers.

Formula Breakdown:

Q is the reactive power in volt-amperes reactive (VAR).
√3 is the square root of 3, approximately equal to 1.732.
VL-L is the line-to-line voltage in volts (V).
IL is the line current in amperes (A).
θ is the phase angle or power factor angle, measured in radians (rad).

Apparent Power Calculation (Three-Phase)

Apparent power is the vector sum of real power and reactive power and is measured in volt-amperes (VA).

Formula:

S = √3 * V_L-L * I_L

Apparent power represents the total power supplied or consumed by a three-phase system.

Formula Breakdown:

S is the apparent power in volt-amperes (VA).
√3 is the square root of 3, approximately equal to 1.732.
VL-L is the line-to-line voltage in volts (V).
IL is the line current in amperes (A).

Power Factor Calculation (Three-Phase)

Power factor is the ratio of real power to apparent power and is a measure of how effectively electrical power is utilized.To calculate the power factor, divide the active power by the product of the square root of 3, line-to-line voltage, and line current. A power factor of 1 (or close to 1) indicates a highly efficient system where the active power is fully utilized. A power factor below 1 indicates reactive power consumption, which can lead to inefficiencies in the system.

Formula:

PF = P / (√3 * VL-L * IL)

Formula Breakdown:

PF is the power factor (a value between 0 and 1)
P is the active power in watts (W)
√3 is the square root of 3, approximately equal to 1.732
VL-L is the line-to-line voltage in volts (V)
IL is the line current in amperes (A)

Voltage Drop Calculation for Three-Phase System

Formula:

Voltage Drop = (2 * Current * Length * 0.3048 * 12.9) / (Conductor Size * Power Factor^1.5)

Formula Breakdown:

Current: The current in amperes flowing through the wire.
Length: The length of the wire in feet.
Conductor Size: The size of the conductor (wire) in AWG (American Wire Gauge).
Power Factor: The power factor of the electrical system.