In our last blog, we described how balanced three-phase AC systems act like three independent single-phase systems. There’s no neutral current, and the total active and reactive powers are just the sum of the active and reactive phase powers. That holds for the apparent power, too, which is what the utility sees. In the fourth part of this five-part blog, we will look at unbalanced power.

For a start, when there is any phase unbalance or harmonics, this Classical (arithmetic) approach doesn’t hold for apparent power. You need either IEEE 1459 or the Unified Power Measurement method to calculate it. If your (useful) real power differs substantially from your apparent power, your utility will start adding expensive penalty charges.

Unbalanced systems

Phasor diagram for an unbalanced system
Phasor diagram for an unbalanced system

The magnitudes and/or phase angles in the vector diagram can all differ for unbalanced currents.

Unbalance effects can be severe when equipment is improperly installed or fails. They can be severe, too, where PV solar power systems are connected to a single phase. Current (load) unbalance is normally far greater than voltage (source) unbalance. So, we’ll assume a balanced voltage U to which we connect unbalanced loads.

With an unbalanced system, or where you have harmonics, you can no longer calculate apparent power by simply adding the power in the three phases. Active power P = PA + PB + PC while reactive power Q = QA + QB + QC but in general apparent power S ≠ SA + SB + SC.

Unbalanced currents don’t add up to zero, so they produce a neutral current. Neutral current into the impedance of the neutral conductor generates neutral power. Unbalance and harmonic components can cause active power loss because voltages can be associated with them.

With current unbalance, we can no longer say that apparent power S is simply the arithmetic sum of the different phases.
With current unbalance, we can no longer say that apparent power S is simply the arithmetic sum of the different phases.

The actual values of S (and fundamental apparent power S1) are larger than the Classical arithmetic or vectorial calculations.


The IEEE 1459 and Unified methods calculate apparent power for systems with significant unbalance and harmonic effects. The difference between IEEE 1459 and Unified results lies in what is included in apparent power. In general, UPM produces lower and more realistic numbers for apparent power than IEEE 1459 with large neutral currents. Under conditions of significant unbalance and distortion, working to UPM saves money by not over-specifying the system.

Decomposing unbalanced systems

In an unbalanced system, some of the alternating current will tend to drive the motor forwards (sequence A-B-C). Some will drive it backwards to act as a brake (sequence B-A-C), and some will just generate heat. We can call these the positive sequence currents, negative sequence currents, and zero sequence currents respectively.

UPM converts an unbalanced system into three balanced positive/negative/zero sequence systems. These can therefore simply be added using the Classical method again.

Only the positive-sequence active current generates useful work. The ratio of the positive and negative sequence currents indicates the amount of unbalance in the system.

Our final Electrical Power Explained blog will give a practical example of unbalance. We’ll show how our 430 Series II Power Quality Analyzers estimate the waste and calculate the savings. And we’ll outline the simple measures to improve the safety and reliability of your power network and avoid utility penalties.



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