Power quality: Beyond the fundamentals

Electrical Tester - 28 July 2017


In this article we explore some of the key practical aspects of measuring and assessing power quality. As the title suggests, we go well beyond the fundamentals, but in order to provide a sound foundation, we start with a brief review of some of basic concepts relating to power and power quality.

A few power basics

Instantaneous power in a circuit, according to IEEE1459 - and no doubt other similar standards around the world - is defined as the product of the instantaneous voltage and instantaneous current in the circuit. Instantaneous power is made up of two components: active power and the reactive power. Active power is produced by the component of the current that is in phase with the voltage, and it flows unidirectionally from the source to the load. Reactive power is produced by the component of the current that is out of phase with the voltage and, in effect, it oscillates between the source and the load. This means that the net transfer of energy from the source to the load due to reactive power is zero.

When making measurements, active power is the mean value of the instantaneous power during the observation time interval. This can be expressed mathematically by the formula:

where P = active power, T = 1/f in cycles, K = integer number, ԏ = the start of the measurement and p = instantaneous power.

Active power is a function of the circuit’s dissipative elements, which are often resistances. Active power, which is measured in Watts, is unidirectional and its value is always positive. In circuits that have sinusoidal current and voltage waveforms, active power can be expressed as

where θ is the phase angle between the voltage and the current.

Looking at reactive power in a similar way, it is a function of the amplitude of the oscillating instantaneous power measured over time, which can be expressed mathematically by the formula:

Reactive power is measured in VARs (volt-ampères reactive) and is a function of the circuit’s reactance. As already mentioned, as the energy associated with reactive power oscillates between the source and the load, there is no average net transfer of energy to the load. In circuits with sinusoidal current and voltage waveforms, reactive power can be expressed as 

where θ is the phase angle between the voltage and the current.

Another important quantity is apparent power. This is a function of the circuit’s total impedance, and is equal to the product of the root-mean-square (rms) current and the rms voltage. In a sinusoidal system with no harmonics, the relationship between reactive power (relating to reactance), active power (relating to resistance) and apparent power (relating to impedance) can be expressed graphically in the form of the “power triangle”.


Applying Pythagoras’s theorem to this triangle shows that apparent power squared is equal to the sum of the squares of the active and reactive powers or, to express this as a formula


Displacement power factor

Considering the power triangle, the cosine of the phase angle—that is, the angle between the voltage and current—is designated the displacement power factor (DPF). Note that DPF is valid only for sinusoidal waveforms and takes no account of harmonics. As reactance is added to a circuit, the phase angle increases and the DPF decreases. For example, in a purely resistive circuit, the phase angle is zero, and the DPF is 1. If reactance is added that increases the phase angle to 8º, the DPF drops to 0.992 and, if more reactance is added to further increase the phase angle to 26º, the DPF drops to 0.898.

Since reactive loads can be either inductive or capacitive, DPF values can be positive or negative, as inductive loads cause the current the lag the voltage, whereas capacitive loads cause the current to lead the voltage. When the current lags the voltage, the DPF is positive and when the current leads the voltage, the DPF is negative.

Low values of DPF are indicative of inefficiency in power systems, because the system has to support the delivery of reactive power that does no useful work. Improving the power factor of a system will allow it to deliver more energy to the load, while reducing the overall loading on components like cables and transformers. The improvements can be substantial, as this example shows. 

A system was delivering power to a load with a DPF of 0.829. The apparent power delivered (that is, the total load on the system) was 7030 kVA, which was 95% of the capacity of the system. The active power delivered was 5828 kW and the reactive power 3931 kVAR. Steps were taken to increase the DPF to 0.990, which reduced the apparent power delivered to 5960 kVA, equivalent to 80.5% of the capacity of the system. The active power delivered to the load remained almost unchanged at 5900 kW, while the reactive (wasted) power was reduced to 0.829 kVAR. In other words, improving the DPF from 0.829 to 0.990 freed up 15% of the capacity of the power system!

In practice, the loads on a power system are much more likely to be inductive than capacitive, so the DPF will be positive. In such cases, the DPF can be improved by adding a capacitor bank, which reduces reactive power and increases active power. Here’s an example of how this works:


It can be seen that when the reactance of the capacitor bank added to the circuit is equal to the inductive reactance of the loads in the circuit, the total reactance becomes zero and the circuit behaves as if it were a purely resistive load. In practice, such perfect power factor correction is unlikely to be achievable, but it can be closely approached.

Capacitor banks for power factor correction are usually rated in kVAR. The key nameplate values are voltage, frequency and kVAR. The impedance of the capacitor bank can be calculated using the formula


where Q is the kVAR rating of the capacitor bank. For example, if the bank is rated 10 kV and 150 kVAR, its impedance will be 667 ohms.

Total power factor

Returning now to the power triangle, it is important to remember that it works only with pure sinusoidal waveforms – the relationships it embodies do not hold true in the presence of harmonic distortion. This is because when harmonics are present, they do not shift the phase angle of the current as an inductive or capacitive load does, instead they distort the current waveform. 

This means that in circuits with harmonics present, DPF is not an accurate measure of power factor, since it takes into account only phase shift and not waveform distortion. For this reason, a different measure of power factor is needed in circuits that have significant levels of harmonics. This is total power factor (TPF, or sometimes just PF) and it takes into account distortion as well as phase shift. 


TPF is defined as power divided by apparent power (P/S). If no harmonics are present in a circuit, TPF is equal to DPF. As the level of harmonics increases, however, so does the difference between TPF and DPF. A related parameter that is sometimes encountered is distortion power factor (dPF), which is defined as the ratio between TPF and DPF (TPF/DPF).

Power systems and measuring arrangements

Let’s now move on to look at the configurations and characteristics of some practical power distribution systems, and the way in which power measurements can be made on these systems. The first is the four-wire wye (star) system shown here:

The benefits of this arrangement are that the neutral connection provides additional safety, insulation stresses are lower than with most other power distribution arrangements, and it is possible to connect loads either phase-to-phase or phase-to-neutral, effectively offering a choice of two different supply voltages. Disadvantages are that faults can lead to loss of voltage on one phase, and the arrangement is susceptible to zero-sequence harmonics. In addition, the phases can be unbalanced and this, together with zero-sequence harmonics, can give rise to high neutral currents. Neutral conductors of adequate rating must, therefore, be provided, which significantly increases costs. 

An alternative arrangement is the three-wire delta configuration, shown here:

The benefits of this arrangement are that zero-sequence harmonics are automatically suppressed, and that a fault will not lead to the loss of a phase. In addition, the system will remain balanced in the presence of unbalanced single-phase loads, although it should be noted that unbalance can be produced by phase shifts. Costs are lower than the four-wire wye-connected system, as no neutral conductor is needed. The disadvantages are that loss of a phase will increase the current in the remaining phases, which means that a higher grade of insulation is needed. In addition, the absence of a neutral reduces safety.

The next arrangement to be considered goes by various names—red-leg delta, wild-leg delta, high-leg delta and others. Whatever the name, this arrangement uses a centre-tapped delta transformer to provide two 120 V sources. Details are shown in the following diagram; note particularly that the angle between the phases is 90º and not 120º as is usual in three-phase systems.

The benefits of the three-phase red-leg delta arrangement are that it can provide three different supply voltages—240 V, 208 V and 120 V—and that, where the three-phase load is small, it is possible to use two individual transformers instead of three, which reduces costs. The disadvantages are that this arrangement can lead to unbalance due to unbalanced single-phase loads, and that only a limited load can be connected between the high leg and the neutral. This arrangement also makes network design more complicated.

The last arrangement we will consider is split-phase power, which is most often used to deliver single-phase supplies to residential properties.


The main benefits of this arrangement are simplicity and low cost. In addition, it provides two supply voltages—240 V and 120 V. The shortcomings here are that it can become unbalanced, it is susceptible to zero-sequence harmonics, and these harmonics, together with unbalanced loads, can lead to high neutral currents.

Blondel’s theorem and delta-wye conversions

For each of the arrangements we have considered, the diagrams have included wattmeter connections. It is however useful to know that Blondel’s theorem states the total power in a system of N conductors can be properly measured by using N wattmeters or watt-measuring elements. The N wattmeters are separately connected such that each one measures the current level in one of the N conductors and the potential level between that conductor and a common point. If, however, the common point is one of the conductors, the wattmeter on that conductor can be removed, which means that only N-1 wattmeters or watt-measuring elements are needed.

It is also useful to know that phase voltages measured line-to-line in a delta-connected system can easily be converted to a “virtual” line-to-neutral voltage simply by dividing the line-to-line values by √3. This allows power values to be viewed per channel, but it is important to remember that this calculation is valid only if the delta system on which the measurements are being made is balanced. Fortunately, delta systems usually remain balanced even in the presence of unbalanced loads, but they can become unbalanced when phase shifts are introduced.

Reviewing energy data

When reviewing energy data collected by power quality instruments or, indeed, viewing that data in real time, one of the first things to verify that the active power is positive. Reversal of active power can occur when power is fed back into a supply system when sources such as renewables and distributed generation systems come on line. Negative active power is problematic as it can lead to frequent transformer tap changing, resulting in excessive wear on the tap changers.

Histograms showing hourly power usage over the test interval also provide invaluable information. It is worth noting the times when energy usage is at its peak, and also reviewing the total apparent, active and reactive energy usage over the test interval. 

Data relating to neutral currents is worthy of attention, as high neutral currents are indicative either of poorly balanced loads or harmonic issues, both of which indicate a need for further investigation. 

A significant difference between TPF and DPF is usually a reliable indicator of the presence of harmonics, but a word of caution is necessary. If very small loads appear to have high harmonics, this may be due to poor signal-to-noise ratio in the measuring system. This problem can be avoided by appropriate choice of the CTs used to make the measurements. Don't use for instance a 6000 A CT to monitor a circuit with a load current of 60 A!

High levels of reactive power are another call to action, as big cost savings can often be made by providing capacitive compensation for large inductive loads, especially as many supply utilities impose penalties for poor power factor. Nevertheless, over-compensation can also be problematic, and it is always important to verify that the power factor is lagging rather than leading.

One reason is that loads with a leading power factor can adversely affect the operation of generators. The voltage regulator in a generator is designed to maintain the output voltage at a predetermined value. As the lagging out-of-phase current is increased, it decreases to the strength of the field of the rotor. The voltage regulator compensates by increasing the current to the rotor. 

If, however, the generator is supplying a load with a leading power factor, as the leading out-of-phase current is increased, this adds to the strength of the field of the rotor. The voltage regulator decreases the current supplied to the electromagnet to compensate. And, if the leading out-of-phase current becomes large enough the regulator supplies no current at all, which can lead to over-voltage tripping.

Loads with a leading power factor can also cause problems for uninterruptible power supplies (UPSs). These have a DC system that rectifies AC to DC, and an AC system that inverts DC to AC. Some inverter designs have large capacitive output filters. The capacitive reactance of these filters offsets the reactance of loads with a lagging power factor, allowing the UPS to deliver almost all of its rated power. If the load has a leading power factor, however, the reactance of the filters adds to the reactance of the loads, severely limiting the power that the UPS can deliver.

Performing energy tests

There are four essential steps in performing energy tests on an installation: benchmarking, auditing, recommending changes and retesting. We will look at each of these in turn.

The benchmarking stage should start by collecting between one and three years of energy bills and by carefully reviewing historical energy consumption. Yearly trends should be identified—is energy usage steadily increasing, decreasing or remaining about the same? Seasonal trends should also be considered. These are normal and to be expected, but large changes could point to issues relating to heating, air-conditioning or process control systems, or to a need for better building insulation. The utility rate schedules should also be scrutinised carefully in case there is a possibility of cutting energy costs by, for example, rescheduling energy-consuming operations.

Benchmarking should also include listing all the primary energy consuming equipment on the site and noting the hours of operation of each item of equipment. Particular attention should be given to the lighting, as the influence of this on overall energy consumption is frequently underestimated. The type of lighting should be considered, as well as whether the light levels provided in the building are adequate.

The next step is auditing; but before proceeding, safety must be given very careful thought and attention. Check the site for safety hazards, ensure that all of the systems meet the relevant codes and standards and check for bad connections—a thermal imaging camera may be useful for this. Remember that bad connections mean higher resistances, which are not only a safety hazard, but also represent energy wastage.

The audit will involve recording the energy usage of the entire facility over a period of time, but it is also essential to record individually the energy usage of the primary energy-consuming items of equipment. Before recording can start however, it’s necessary to select the appropriate current transducers. 

Choose transducers with the proper range: if the range is too low, the CT may saturate, but if it’s too high it will give poor resolution. Also consider whether a flexible or split-core transducer will be needed: will it fit the location where it needs to installed, and does it need batteries? If you’re working in an area with high EMF, then a split-core transducer will be the best option, and if you’re recording DC, you must use a Hall-effect CT.

When programming the instrument that will make the recordings for the audit, first of all verify that the proper power configuration is selected, then set the demand rate to the same rate as the revenue meter, paying attention to whether it is a fixed or sliding rate and whether it is a demand interval or demand rate tariff. Be sure to enable harmonic recording!

With the preliminaries completed, the monitoring phase of the audit can begin. When connecting the PQ analyser, always use appropriate personal protective equipment (PPE). Verify that the voltage leads are connected correctly in line with the instructions provided by the manufacturer of the analyser, that the CT ranges are set correctly and that the CTs are connected in the proper direction. Next, verify that the power (kW) is positive and check the phase angles. 

It’s a big benefit to use an instrument that automatically verifies that it is correctly configured before starting a long-term recording. It’s annoying and costly to return to an instrument after a week only to find recording was aborted because of a simple error. When all is ready, make sure the instrument is grounded, make one final check that it really is recording, then lock it up and leave it to its work. The recordings of the total facility power consumption and the consumption of the key items of equipment should continue for at least one full week.

At the end of this time, analyse the data, paying particular attention to reviewing power consumption, reviewing the energy usage histogram, as well as looking at the reactive power, displacement power factor, true power factor, unbalance and harmonics. Carry out this analysis not only for the whole facility but also for the each of the primary items of energy-consuming equipment.

Using the information provided by this analysis, it will almost always be possible to recommend changes that will improve the energy efficiency and reduce the energy costs of the facility. Typical examples include reducing loads, shifting loads to off-peak hours, installing lighting that’s more energy efficient, reducing heating and cooling requirements and improving thermal insulation. In almost every case, the savings will quickly cover the cost of the audit and the necessary improvements many times over. 

There now remains one further task. After the recommended improvements have been made, go back the facility and repeat the audit! This way, the effectiveness of the improvements will be confirmed and it may even prove possible to suggest further enhancements. Energy efficiency is, after all, about continual improvement rather than a one-time fix!