In a balanced three-phase system, the constancy of total power is an important principle that arises from the nature of sinusoidal waveforms and the symmetrical arrangement of phases. This principle is a result of the cancellation of instantaneous power variations due to the phase differences between the three phases.
In a three-phase system, there are three conductors, often labeled as phases A, B, and C, carrying alternating currents that are 120 degrees out of phase with each other. The voltage and current waveforms for each phase are sinusoidal in nature.
The instantaneous power
P in an AC circuit is given by the product of instantaneous voltage
V and current
I at any given point in time:
(
)
=
(
)
×
(
)
P(t)=V(t)×I(t)
For a balanced three-phase system, the key points to note are:
Equal Amplitude: The magnitudes of the voltages and currents in each phase are equal.
120-degree Phase Shift: The three phases are 120 degrees out of phase with each other. This phase shift is maintained consistently over time.
Due to the equal amplitudes and the 120-degree phase shift, the instantaneous powers in the three phases have the same magnitude but are 120 degrees apart in terms of phase. This leads to power fluctuations in each phase, but these fluctuations cancel each other out over time. When you sum the powers of the three phases, the variations in power cancel each other due to the phase offset.
Mathematically, if
(
)
P
A
(t),
(
)
P
B
(t), and
(
)
P
C
(t) are the instantaneous powers of phases A, B, and C respectively, then the total instantaneous power
total
(
)
P
total
(t) is given by:
total
(
)
=
(
)
+
(
)
+
(
)
P
total
(t)=P
A
(t)+P
B
(t)+P
C
(t)
Because of the phase shift between the phases, the sum
(
)
+
(
)
+
(
)
P
A
(t)+P
B
(t)+P
C
(t) remains relatively constant over time, resulting in a nearly constant total power.
This constancy of total power is a fundamental property of balanced three-phase systems and is utilized in various applications, including power generation, transmission, and distribution. It allows for efficient utilization of power resources and stable operation of electrical networks.