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Guide to transformer harmonics and k-factor

Harmonics can be harmful for a transformer's operation. However, they can be mitigated by K-Factor rated transformers, Zigzag transformers, and other options.

August 9, 2022

AC power supply wave with harmonics

Electronic innovation has opened the door for more efficient technology in today’s economy, such as renewable energy devices for wind and solar farms, large variable frequency drives (VFDs) for running motors, and the advanced electronic equipment used for mining cryptocurrency. Whether directly or indirectly, these devices are designed with optimal efficiency and performance in mind for the systems where they are used. This means lower power consumption and lower equipment operation costs, but this gain in efficiency comes with a unique set of challenges.

Most high-efficiency electronic devices produce what are known as harmonics. Left unchecked, harmonics can cause overloading, overheating, and loss of power in an electrical system—particularly at the transformer. In this article, we’ll take a look at four main questions about harmonics and transformers:

  • What are harmonics?
  • What causes harmonics?
  • How do harmonics affect transformers?
  • Which transformer design should you choose for systems with harmonics?

What Are Harmonics?

In a standard AC power supply, an electrical signal takes the shape of a sine wave. This is what the electric equipment at the end of the line consumes and uses to do work (powering lights, running motors, printing, running computer programs, etc.). Notice the even shape of the wave in the image below; each peak and crest has the same amplitude. In a 60-Hz system, this wave cycles up and down 60 times per second.

AC power supply wave

Now let’s take a look at the AC power supply from above (shown in orange below and referred to as the fundamental frequency) with harmonics added in.

Comparison of AC fundamental frequency to 3rd and 5th harmonic waves

The orange sine wave represents the AC power signal at 60 Hz moving through a transformer to a load (such as a motor). The two blue waves are harmonics. Notice that these harmonic waves are not congruent with the fundamental one at 60 Hz; they appear at higher frequencies. At 180 Hz, the 3rd harmonic is three times greater than the 60-Hz fundamental frequency, and at 300 Hz, the 5th harmonic is five times greater, meaning they cycle up and down 180 and 300 times per second respectively. Since harmonics are integer multiples of the fundamental frequency, they always appear at significantly higher frequencies in an electrical system.

What Causes Harmonics?

Linear and non-linear loads

In an electrical system, equipment consumes power linearly or nonlinearly. With linear loads, the consumption of power follows the same shape as the AC sine wave. If you think of the power supply like a sandwich, a linear load would eat the whole sandwich. Non-linear loads consume power in a way that does not follow the sinusoidal shape of the AC power supply (consuming certain portions of the wave shape at designated intervals). To use the sandwich analogy, non-linear loads may only consume a part of the sandwich, like the bun. Examples of linear loads would be motors or incandescent lighting. Examples of non-linear loads would be computers, electronic lighting ballasts, variable frequency drives, and fluorescent lighting. These non-linear loads and the particular manner in which they consume power produce harmonics.

As we discussed in the beginning, modern electronic equipment is designed to operate at a higher efficiency (meaning less power is wasted during operation). This is accomplished by what is known as use-based power consumption––the equipment automatically switches on for operation and then off again when it is not doing work. This on/off switching function introduces harmonics into the electrical circuit. Again, if we think of the AC power supply like a sandwich, electronic devices designed to operate only while in use will consume only parts of the sandwich. A lower amount of the total power supply is consumed, but the process required to do this produces a higher amount of harmonic content.

As the figures below show, any harmonic (3rd, 5th, 7th, etc.) present in the electrical system will become superimposed upon the fundamental 60-Hz frequency, creating a complex, non-sinusoidal waveform. This non-sinusoidal component must be accounted for when estimating load requirements and sizing transformers that supply power to large nonlinear devices. The more harmonic distortion present in the system, the more non-sinusoidal the load current.

Interaction of fundamental frequency and harmonics creates resultant non-sinusoidal waveform

How Do Harmonics Affect Transformers

Transformers are typically built for usual service conditions unless specified otherwise by the customer. Applications with a significant amount of non-sinusoidal load current (or harmonic distortion), fall into the category of unusual service conditions. This non-sinusoidal component puts greater stress on conductor insulation and increases winding and core losses at the transformer, resulting in excessive heat levels and loss of power. The overheating effects of high-frequency harmonics are observed mainly at the coils, core, and neutral conductor of the transformer.

Higher frequency currents (like harmonics) naturally move toward the outside of the winding conductor, which causes an increase in resistance and heat. This principle is known as the skin effect. The densely packed construction of the coils also adds to heat build-up at the windings, and the end result is a reduction in the total current-carrying capacity of the transformer’s conductors.

Higher frequency harmonics can have adverse effects on a transformer’s core as well. In an AC circuit, the polarity of the magnetizing current in the core switches back and forth with the direction of the applied current. In other words, the rate at which the magnetizing current in the core changes polarity is driven by the frequency of the applied current. If the frequency of a standard AC power supply is doubled from 60 Hz to 120 Hz, then the magnetizing current in the core will go from switching polarity 60 times per second to 120 times per second. The higher the rate of change in the magnetizing current, the greater the amount of heat loss in the core. These additional losses are known as hysteresis losses.

Some losses in the core are inherent to the design of the transformer. Small pockets of swirling current, known as eddy currents, are another source of heat loss in transformers. Efficient laminated core designs (like those produced today) will minimize eddy currents as much as possible. While these undesirable phenomena are not a byproduct of harmonics, their negative effects are increased exponentially with the introduction of such higher frequency currents. The presence of higher harmonic frequencies multiplies an eddy current’s adverse heating effects several times that of the normal 60 Hz frequency. If a transformer’s core is not designed for such conditions, the resulting increase in the unit’s operating temperature could be detrimental.

The third most common area of overheating in the transformer is the neutral conductor on wye-connected windings. With wye-connected systems, triplen harmonics (3rd, 9th, 15th, and so on) will be present. These particular frequencies are most often seen where transformers serve large single-phase loads. Any triplen harmonics present in one or more phases of the system will add together at the neutral conductor. These harmonics crowd together in the neutral and reduce its current-carrying capacity. If the amount of triplen harmonics is high enough, the neutral conductor will overheat and its insulation system will fail. For such cases, an oversized neutral is generally used.

Which Transformer Design Should You Choose for Systems with Harmonics?

Determining the level of harmonic content in an electrical system is the first step in selecting the correct transformer for a project where harmonics may pose a significant concern. There are electrical industry guides that define the maximum level of harmonic content (or distortion) allowed for transformers designed for usual service conditions (see IEEE 519). As a general rule of thumb, if the total harmonic distortion (THD) in the system is above 5%, you will need 1) a transformer built to handle the harmonic content or 2) a means of mitigating the presence of harmonics at the transformer. Below, we’ve outlined the available options for both solutions.

1. K-factor rated transformers

Most often referred to as drive-isolation transformers (because they’re used in applications with motor drives like VFDs), K-factor rated transformers are built to handle the additional stress imposed by harmonics. K-factor rated transformers do not filter or mitigate harmonic distortion, they simply withstand it. Think of a transformer with a K-factor like a punching bag—the bigger and heavier the bag, the more hits it will be able to withstand. In a similar way, the higher the K-factor rating on a transformer, the more harmonic distortion it will be able to handle.

A transformer built for usual service conditions has a K-1 rating (a K-factor of 1 means there is no harmonic distortion in the system). K-factor ratings go all the way up to 50, but it’s rare to see anything above K-20 in the commercial and industrial market. For most harmonic profiles, a K-4 rated unit is sufficient. K-factor rated units include a 200% rated neutral conductor for handling the addition of triplen harmonics (see page 3 of this paper for a more detailed description of triplen harmonics), as well as an electrostatic shield between the HV and LV windings. In addition to harmonics, the switching function of non-linear devices also produces potential switching transients (common in solar inverters), which can lead to voltage distortion on the load side and high-voltage spikes on the supply side of the transformer. An electrostatic shield reduces these power quality issues.

2. Zigzag transformers

Harmonic-mitigating (or zigzag) transformers (HMTs) do exactly what their name suggests: reduce the presence of harmonic currents in an electrical system. Unlike units designed with a K-factor rating, HMTs filter a portion of the harmonic content. The installation of a stand-alone HMT will reduce the amount of triplen harmonics (3rd, 9th, 15, etc.) present in a circuit. Installing an additional HMT on the same circuit with a -30 degree phase shift (when the first unit has a 0-degree phase shift, or vice versa) can further reduce the amount of 5th and 7th harmonics. This dual-unit phase shift method can also be accomplished with standard delta-wye transformers, but a zigzag winding offers a more economic solution. HMTs are generally used for systems that operate several non-linear loads.

3. Passive Harmonic Filters

In addition to K-factor rated and harmonic-mitigating transformers, Maddox also offers a passive harmonic filter, a combination of capacitors and reactors. A passive harmonic filter is used to reduce the harmonic current flowing through the main circuit pathway. It accomplishes this by providing a lower impedance path for the harmonic current to travel—the harmonic current is diverted away from the system’s bus, which, in turn, lowers the circuit impedance. Passive harmonic filters can be tuned for one or more particular harmonic frequencies in a given system, making them a more versatile solution than the HMT. Higher K-ratings for larger transformers can significantly increase the cost of a unit, so the passive harmonic filter may provide a more cost-effective solution. Diverting the harmonic current in the system away from the main current-carrying pathway allows for the installation of standard equipment throughout the circuit (including the distribution transformer).

4. Delta-wye transformers

For systems where only triplen harmonics are present, a standard delta-wye transformer may be a sufficient solution. As mentioned earlier, triplen harmonics often cause problems for the neutral conductor, but when a delta winding is present on the primary side of a two-winding transformer, the triplen harmonics will circulate inside the delta winding instead of the neutral conductor. If a study of the harmonic profile of a system shows that only 3rd, 9th, or 15th harmonics are significantly present, a standard delta-wye transformer will be a sufficient solution. A delta-wye transformer also eliminates the problem of zero sequence currents, which are characteristic of wye-wye connected windings. For this reason, delta-wye winding configurations are often favored for applications where the load may be unbalanced.

5. Oversizing standard distribution transformers

Another way to account for harmonic distortion in a system is to simply oversize the kVA of a standard transformer design. This is a quick and easy solution when it is not feasible to wait for a custom-built transformer from the factory with a designated K rating. For applications where the THD is minimal (K-4, for instance), a simple oversizing of the kVA—or establishing a derating factor—may work just fine.

Oversizing the transformer kVA will increase the size of the core, windings, and neutral conductor. If the harmonic content in a system reduces the capacity of the transformer by 20%, then the unit will need to be oversized accordingly. For example, if a 1,000 kVA transformer is only good for 80% of its nameplate rating, the derating factor would require oversizing the unit to at least 1,200 kVA. Applying a derating factor is more common with liquid-filled transformers, which are naturally better suited for handling harmonic distortion than dry-types. It’s more common to see harmonic distortion handled with K-factor ratings in dry-type transformers.

It is key to note there are certain special design considerations made when building K-rated transformers which are not included with standard designs, such as the electrostatic shield and 200% rated neutral. Also, K-rated transformers sometimes include specially shaped winding conductors to reduce the increase in heat and resistance from harmonics. If triplen harmonics can be effectively mitigated at the transformer with a delta winding (negating the need for the larger 200% rated neutral), and if there is no need for electrostatic shielding, applying a derating factor and oversizing the distribution transformer can be a simple and effective solution. For more information on this method, take a look at this article on sizing transformers for crypto mining.

We’re Here to Help

The topic of harmonics will continue to require attention wherever electronic innovation and non-linear loads make up a significant portion of the demand in electrical circuits. Without proper counter-measures, harmonic distortion can lead to costly repairs and replacement. Our goal at Maddox is to meet these growing demands in the electrical industry with transformers designed and built for such applications, ensuring peak performance and longevity of service on every project.

Maddox offers all five of the above solutions to ensure that you have access to the equipment you need, when you need it. If you have questions about harmonics or want to request a quote for a Maddox transformer, fill out the form below or give us a call at 1-800-270-2011.

Maddox padmount transformer loaded on truck

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