### What is Voltage Unbalance?

Differences in voltages are most often referred to as “unbalance in voltage”. Voltage Unbalance Factor (VUF) is a well-known engineering term. Strictly speaking, “asymmetrical voltages” qualifies the physical significance better as both the difference in amplitude and phase displacement is of concern. Most practical cases will be dominated by the difference in amplitude and not so much by the difference in phase displacement.

The VUF quantifies the unbalance between fundamental frequency phasors. It requires pre-processing of recorded data to calculate the VUF as a frequency analysis is first required to isolate the fundamental frequency phasors as harmonic distorted waveforms in modern power systems are common.

The Fourier transform is then followed by the Fortesque transform as the following mathematical expression of the VUF is based on sequence domain phasors:

is the absolute value of the fundamental frequency negative sequence phasor with  the fundamental frequency positive sequence phasor. Some publications will prefer the use of the term “voltage asymmetry factor” to VUF when the above formula is used.

It is possible to estimate to the VUF based on simple RMS measurements per phase, but the scientific basis of asymmetry requires the signal analysis discussed above.

The ImpedoDUO uses the scientific correct approach shown above in calculating VUF based on sequence domain phasors, but compliment VUF by also calculating the Current Unbalance Factor as is can be useful in the analysis of voltage unbalance. A practical case study is presented below.

### Why is voltage unbalance a concern?

Asymmetrical voltages can be a concern as it affects the apparent power loading of the supply system and degrade the performance of a rotating load. The concept of unbalance mostly refers to the difference in loading (current) per phase.

Most PQ standards set the compatibility level as 2% to the VUF. The reason is that if voltage unbalance in a 3-phase power system is maintained below this value, it contains the affect on rotating loads. A value of 2% is relatively high as values above 1% are reported in some literature to degrade the performance of energy efficient motors.

It does not make sense to drive a car on the open road with the handbrake engaged. Why then do we operate electrical motors with the handbrake on?

The reason is that practical power systems, especially at lower voltage levels, will not be perfectly balanced. The mathematical formula of VUF acknowledges the unbalance by a negative sequence voltage component.

The negative sequence impedance in rotating loads is 6 (or more) times less than the positive sequence impedance. The result is a negative sequence current being 6 (or more) times the value of the positive sequence current. A VUF of 1.5% can for example result in a negative sequence current of 9 – 15 % of the positive sequence current.

Positive sequence current sets up the magnetic field to generate torque in the positive direction of rotation. The negative sequence current will oppose this rotation by a torque component in the opposite direction, similar to that car being driven with the handbrake on!

It does not make sense, not even in the electrical world. Additional heat is generated in the motor, which could result in higher operating temperatures, and winding insulation degrades faster as temperature rise.

### Where does voltage unbalance comes from?

Incomplete transposition of transmission lines can cause significant enough asymmetrical phase impedances to result in different voltage drops per phase. Asymmetrical voltages at the receiving end of the line will result even with the loading between phases perfectly equal. Unbalanced load currents are the consequence.

Assume it is possible to build the perfect power system with supply impedances perfectly equal, loading per phase will not be perfects equal as it is not possible to arrange for example single-phase loads to be perfectly balanced at all times between phases in distribution systems. Loading per phase is normally better balanced at higher voltage levels as loading is mostly symmetrical. Unbalanced loading at higher voltages can be contributed by large industrial consumers such as arc-furnaces, which are inherently unbalanced.

Voltage unbalance is a reality in a modern power system and a practical case study is discussed next.

## Good wine requires perfectly symmetrical voltages!

Grapes have to ferment under controlled conditions. The cultivar of the grapes and the area where grown is important, but the temperature and the variation of the temperature during the fermentation process can ruin any cultivar!

A refrigeration cycle to maintain the temperature during the winemaking process requires a motor to drive a compressor. Energy-efficiency is one reason why modern cooling equipment makes use of motors that are optimized for the torque requirements of the compressor.

Protection of the motor contains the adverse affect of negative sequence currents by shutting it down if above it rises too high. The protection is needed, as the optimized motor will not be able to drive the compressor if that motor is operated with the “handbrake” resulting in less torque output.

More than often, these wineries are located within rural distribution networks. These distribution lines normally service a high number of single-phase loads all over an agricultural area, as not all loads can be 3-phase. This unbalanced loading can be aggravated by incomplete transposition of the rural distribution lines. This is a recipe for unbalanced voltages.

Wineries that cannot maintain a constant fermentation temperature because the cooling equipment regularly trips will not bottle the wine of the year. Good wine requires voltage unbalance to be contained.

An assessment of voltage unbalance resulting in a highest VUF value of 1.8% can be a concern. It complies to the 2% compatibility statement, then why is this a problem? Let’s explain:

• The compatibility level assessment is based on 10-min values for VUF. This value is an aggregation of what “happened” during the past 10 minutes. It could be that some VUF values during that 10 minutes were even above 2% but the 10-min VUF value could be calculated as 1.4% for example due to the principle of aggregation. Incidents of high voltage unbalance can occur without reflected in the 10-min VUF value. But, that is the process to be followed as stipulated by the PQ standard pertaining.
• An incident of higher VUF during the 10-min period will not necessarily trip the cooling compressor as some hysteresis is normally based on an approximation of the thermal consequence. It can be based on exceeding the VUF level for a minimum period of time.
• The compatibility statement requires that voltage unbalance remains below the compatibility level of 2% (the NRS 048 part 2-2007 value), for 95% of the total time. It literally means that 95% of the 10-min VUF values have to be less than 2%.
• A number of incidents above a VUF value of 2% could occur during the 5% period of time.
• The user (our winery in this case) could have had a number of incidents distributed all over a 24-hour period where the winemaking process was compromised by the cooling equipment not able to maintain temperature as the protection equipment has shut down the compressor.
• Based on the principle of incidents rather than simple compliance to a PQ standard, observe the graph below depicting the number of incidents recorded where a single VUF was above 1.5% (figure 1) and above 1.7% (figure 2).

Figure 1: Number of incidents per day; Vunb exceeding 1.5%

Figure 2: umber of incidents per day; Vunb exceeding 1.7%

The number of incidents per day requiring a physical restart of the compressor manifest as a variation in temperature in the fermentation tank. Good wine clearly requires voltage unbalance to be contained so that temperature in the tanks remains constant.

Observe that the above is based on the number of incidents per day when the VUF was relatively high, not even above 2%. Practical experience with modern energy efficient cooling equipment in use at a winery has shown that the built-in protection will indeed shut down the machine if unbalance in current rise beyond 10%.

A VUF value of 1.7% can result in current unbalance factors of above 10% due to the ratio (6, it can be up to about 10) between positive and negative sequence impedance in an induction machine.

The winemaking is at risk. A PQ complaint to the supply authority will not change the situation easily:

• The utility cannot change the distribution of the single-phase loads and/or the transposition of lines in the short term. It can even proof to be ineffective as it can be impossible to mitigate the voltage unbalance well enough in the lines under the control of the local supply authority. It can be that the contribution to voltage unbalance from an upstream supply network requires involvement from other energy utilities or departments, complicating an effective solution.
• The utility at hand is in compliance to the minimum standards of the PQ standard, at least in South Africa if the NRS 048 part 2 of 2007 is applied. Observe the display of a 7-day sliding assessment of VUF values recorded over a period of time shown in Figure 3:

Figure 3: NRS 048 part 2-2007 7-day sliding assessment of voltage unbalance

The highest VUF value based on the 95% highest value is 1.8. It literally means that for 95% of the time, the highest value recorded was 1.8.

Strictly speaking, the supply authority is in compliance to the compatibility requirement. A PQ complaint filed can thus be rejected on this basis.

But we want good wine! What now?

### Compensate for voltage unbalance: the easy way

Voltage unbalance mitigation can be done locally. It is possible to install active compensating equipment at the point of supply to continuously compensate for the variation in levels of voltage unbalance.

This is an option available to the winemaker, as risk has to be mitigated and the user has to participate in containing the risk. Equipment costs for mitigation voltage unbalance are not high and can be recovered in less than one season based on experience.

Two approaches are known to be effective. The first approach, the cheapest, is a compensator with in-line reactors with motorized mechanisms to actively control the voltage to the load similar to a continuously changing resistive voltage divider.

The second approach is to compensate simultaneously for voltage unbalance and voltage sags. A process of parallel rectification and injecting the compensating voltage value by means of a transformer winding in series with the supply line was found to be the best cost-for-benefit solution by far if both voltage sags and unbalance is to be compensated.

Omniverter is a reputable company who can supply (www.omniverter.com) the mitigation products discussed above.

### How can we make voltage unbalance visible?

The metrology and methodology on how to measure PQ parameters was made comparable internationally if the instrument in use is accredited as being of a certain class. International definition of the class is found in the IEC 61000-4-30 PQ standard. The performance of CT Lab’s ImpedoDUO is certified as being Class A, the highest class. Voltage unbalance measurements are not based on an approximation when this instrument is used.

Frequency (Fourier) analysis extract the fundamental frequency phasors needed by the subsequent Fortesque transform to calculate the sequence domain phasors needed for the VUF (ratio of negative to positive sequence voltage phasor). The current unbalance factor is also calculated, as it could be useful in the analysis of root cause. Data input to the signal analysis is based on 16-bit signal acquisition. In the case at hand, data was acquired for 2 months and pushed continuously over the Internet to an Oracle data server at CT Lab. Internet access at the remote location was possible due to cell phone coverage.

A PQ investigation mostly, requires no premium to Internet bandwidth and data volume as parameters are based on 10-min values. Additional data can be acquired based on a trigger to be set to retain detail waveform data if a pre-defined event condition occurs.

### Is it possible to tell where the voltage unbalance is coming from?

The electrical interconnection of a power system creates unique scientific challenges to apportion the contribution of a specific source to the voltage unbalance measured at a point of interest. Supply conditions and loading conditions all over contributes.

It is possible to estimate the contribution of the upstream and the downstream network. Detail knowledge on the transposition of lines, transformer impedances, and other sources of voltage unbalance upstream may not be available. The challenge to understand how much of the voltage unbalance is from the upstream network and how much from the downstream network can benefit from simple data analysis methods. Observe the scatterplots shown in Figure 4 and Figure 5.

Figure 4: Voltage unbalance against current unbalance during a 2-month period

Figure 5: Current unbalance against apparent power loading during the same 2-month period

Assuming that the load is causing the voltage unbalance, some correlation between current unbalance and voltage is to be expected. Ohm’s law dictate that a significant change in voltage unbalance will require an even more significant change in current unbalance as the supply impedance should be relatively low (at least on a per unit basis). If such measurement results are obtained indicating that current unbalance is “driving” voltage unbalance, it makes sense to declare the load a culprit.

Figure 4 indicates that a significant change in voltage unbalance relate to very little change in current unbalance. It is therefore not possible to conclude that current unbalance is dictating voltage unbalance. But, what is missing in Figure 4, is the level of loading! Current unbalance being high cannot cause voltage unbalance when the loading is very low, consult Mr Ohm on this principle.

That is why Figure 5 depicts the variation in loading on current unbalance. If high levels in loading coincides with high levels in current unbalance, and high levels in current unbalance coincide with voltage unbalance, then the loading can be accused as “driving” the voltage unbalance. Unfortunately, Figure 5 show that during all times, current unbalance remain fairly low regardless of loading. The supply side is clearly “driving” the voltage unbalance. Loading of the point under investigation cannot be blamed.

Reason remains unknown. It can be that the local transformer have unequal phase impedances, the transmission line to this transformer have unequal phase impedances due to incomplete transposition, or that a large user (arc furnace for example) somewhere upstream is withdrawing unequal phase currents.

Take note that the above is merely a qualitative analysis as information on the exact contribution to voltage unbalance by the supply and load side cannot be extracted by such an approach.