What is unbalance?
Any deviation in voltage and current waveform from perfect sinusoidal, in terms of magnitude or phase shift is termed as unbalance. In ideal conditions i.e. with only linear loads connected to the system, the phases of power supply are 120 degree apart in terms of phase angle and magnitude of their peaks should be same. On distribution level, the load imperfections cause current unbalance which travel to transformer and cause unbalance in the three phase voltage. Even minor unbalance in the voltage at transformer level disturbs the current waveform significantly on all the loads connected to it. Not only in the distribution side but through the transformer, voltage unbalances disturbs the high voltage power system as well.
Causes of unbalance
Practical imperfections which can result in unbalances are:-
1. A three phase equipment such as induction motor with unbalance in its windings. If the reactance of three phases is not same, it will result in varying current flowing in three phases and give out system unbalance.
– With continuous operation, motor’s physical environment cause degradation of rotor and stator windings. This degradation is usually different in different phases, affecting both, the magnitude and phase angel of current waveform.
– A current leakage from any phase through bearings or motor body provides floating earth at times, causing fluctuating current.
2. Any large single phase load, or a number of small loads connected to only one phase cause more current to flow from that particular phase causing voltage drop on line.
3. Switching of three phase heavy loads results in current and voltage surges which cause unbalance in the system.
4. Unequal impedances in the power transmission or distribution system cause differentiating current in three phases.
How to calculate unbalance –
Unbalance is calculated in terms of maximum deviation of current in a phase from the mean of three phases. To calculate the percentage deviation- 
Where- Im is mean of currents in three phases (i.e. Im= (Ir+Iy+Ib)/3
Ir, Iy, Ib are phase currents.
Besides, an unbalance can also be quantified by comparing the intensity of negative sequence currents in comparison to the positive sequence currents. The permissible limit in terms of percentage of negative phase sequence current over positive sequence current is 1.3% ideally but acceptable upto 2%.
Effects of unbalance:
1. The unbalance decreases the motor efficiency by causing extra heating in the motor. Heat generated also effect the equipment life by increasing the operating temperature, which decompose the grease or oil in the bearing and de-rate the motor windings.
2. In induction motors connected to unbalanced supply, the negative sequence currents flow along with positive sequence current resulting in decreased percentage of productive current and poor motor efficiency. Any unbalance above 3% hampers the motor efficiency.
3. Torque (and thus the speed) produced by the motor becomes fluctuating. These sudden changes in torque cause more vibration in the gear box or the equipment connected to it. The vibration and noise produced damages the equipment and also reduces the efficiency of equipment.
4. The variable frequency or speed drives connected to an unbalanced system can trip off. VFD treats high level unbalances as phase fault and can trip on earth fault or missing phase fault.
5. Unbalances cause de-rating of power cables and thus increase I2R losses in the cable. For distribution cables de-rating factor represents the part of total current giving fruitful outcomes.
6. UPS or inverter supplies also perform with poor efficiency and inject more harmonic currents in case of unbalances in the system.
7. Negative phase sequence current flowing due to unbalance can cause faults in the motor, resulting in, tripping or permanent damage of the electrical equipment.
Quantifying the losses-
An unbalance of 1% is acceptable as it doesn’t affect the cable. But above 1% it increases linearly and at 4% the de-rating is 20%.  This implies that- 20% of the current flowing in the cable will be unproductive and thus the copper losses in the cable will increase by 25% at 4% unbalance.
1. For motors, an unbalance of 5% will result in capacity reduction by 25%.  That means, the motor current will increase to match the equipment’s torque needs which will result in proportional copper losses in motor. The voltage unbalance of 3% increase the heating by 20% for an induction motor.
2. The resistance for negative sequence current is 1/6th of the positive sequence current which means a small unbalance in voltage waveform will give more current and thus losses.
Effects on the distribution Transformer-
Transformer offers high reactance to negative phase sequence currents and thus reduces the level of unbalance on the other side of the system.
– Ideally any distribution transformer gives best performance at 50% loading and every electrical distribution system is designed for it. But in case of unbalance the loading goes over 50% as the equipments draw more current.
– Following data represents the efficiency of transformer under different loading conditions-
1. Full Load- 98.1%
2. Half Load- 98.64%
3. Unbalanced loads- 96.5%
For a distribution transformer of 200KVA rating, the eddy currents accounts for 200W but in case of 5% voltage unbalance they can rise upto 720W.
1. All the single phase loads should be distributed on the three phase system such that they put equal load on three phases.
2. Replacing the disturbing equipments i.e. with unbalanced three phase reactance.
3. Reducing the harmonics also reduces the unbalance, which can be done by installing reactive or active filters. These filters reduce the negative phase sequence currents by injecting a compensating current wave.
4. In case the disturbing loads cannot be replaced or repaired, connect them with high voltage side this reduces the effects in terms of percentage and even controlled disturbance in low voltage side.
5. Motors with unbalanced phase reactance should be replaced and re-winded.
To identify the exact reasons for unbalance, Zenatix recommends metering at different loads in the distribution. Zenatix can collect high resolution data from these metering locations and analyze it to identify the exact causes and control measures that can result in improvement in the unbalance. Further, such detailed metering will provide data that can be used to identify other wastages that happen in the day to day operations of a facility thus providing further benefits of the installed solution.
For further clarification on the voltage and current unbalance, three phase currents of two of the zenatix’s customers were analyzed. For the purpose of case study, we can name the two clients as client1 & client2.
First, the readings of three phase currents were taken at the frequency of 15 minutes for a month. Then we need to remove the readings during non-working hours too, as during such times load current will be quite low and thus a current unbalance of only 2-3 amps can shown very high percentage unbalance. After refining the data, percentage of unbalance was calculated by running simulation on R-software. As all the readings mentioned are taken at the duration of 15 minutes, we got percentage unbalance readings for the whole month with the frequency of 15 minutes. These continuous readings were then plotted.
It is clear by only looking at the plot that for client1’s system is more balanced as compared to client2’s. Further analysis was done for getting consolidated data on what is maximum unbalance, what is the average unbalance and which phase is causing it.
Following data was tabulated based on the results obtained after analysis.
Fig.1 – Shows the plot of percentage unbalance with time for zenatix’s client with balanced system.
Fig.2 – Shows the plot of percentage unbalance with time for zenatix’s client with balanced system.
Fig.3 -Shows the comparison between the system of two clients.