What is the approximate relationship between active power and reactive power in a balanced three-phase system?

In a balanced three-phase system, the relationship between active power and reactive power can indeed be described using the Pythagorean theorem. This relationship is depicted in a power triangle, where the horizontal axis represents active power (measured in watts) and the vertical axis represents reactive power (measured in volt-amperes reactive, or VAR). The hypotenuse of the triangle represents apparent power (measured in volt-amperes).

The Pythagorean theorem helps to illustrate that the total apparent power is the square root of the sum of the squares of active and reactive power. Mathematically, this can be expressed as:

[

S^2 = P^2 + Q^2

]

where (S) is the apparent power, (P) is the active power, and (Q) is the reactive power. This relationship emphasizes how active and reactive powers combine to form the total power being handled in the system, showing that they are not only related but that their values can be calculated in relation to one another using this mathematical principle.

By using the Pythagorean theorem, one can also determine the power factor of the system, which indicates how effectively the electrical power is being converted into useful work