Using sophisticated power electronics and communications systems to improve power system efficiency, flexibility and reliability is increasing interharmonic distortion and putting new equipment sensitive to that distortion on the system. Understanding interharmonics is necessary to prevent them from adversely affecting system operation.
IEEE Standard 519-2014, Recommended Practice and Requirements for Harmonic Control in Electric Power Systems, defines interharmonics as any “frequency component of a periodic quantity that is not an integer multiple of the frequency at which the supply system is operating.” IEC 61000-2-1 includes a similar definition. Mathematically, with f the supply (fundamental) frequency and m any positive non-integer, any signal with the frequency mf is an interharmonic of f. This is similar to the harmonic definition, nf, where f once again represents the fundamental frequency, but n represents any integer greater than zero.
While interharmonic and harmonic definitions are similar, their difference — that harmonics are periodic at the fundamental frequency and interharmonics are not — is important. All periodic waveforms can be represented by their fundamental component and a Fourier series of harmonics with various magnitudes, frequencies and angles. Interharmonics are not periodic at the fundamental frequency, so any waveform containing interharmonics is non-periodic and any non-periodic waveform includes interharmonics. The level of interharmonic distortion can be thought of as a measure of a waveform’s non-periodicity.
Interharmonics are usually created by one of three phenomena. The first is rapid non-periodic changes in current or voltage caused by temporary or permanent operation of load or generation in a transient state. Depending on the process and controls used, these changes can be quite random or fairly consistent. The second is communication signals sent on power lines to control or monitor system components. The third and increasingly common source of interharmonics is static converter switching not synchronized to the power system frequency.
Conventional thyristor switched converters are triggered into conducting mode and keep conducting until their current falls below their holding current. By turning off at the same point each cycle, these devices are synchronized to the power system frequency and do not produce interharmonics. Other high-power semiconductor devices — primarily insulated-gate bipolar transistors (IGBTs) that can be turned off as well as on — are replacing thyristors because their asynchronous switching, which produces interharmonics, enables reactive as well as real power regulation and power system oscillation damping. Two specific sources of interharmonics that deserve special attention are voltage source converters (VSCs) and power-line communications.
VSCs are increasingly being used for solar and wind generator power conversion, static synchronous compensators (STATCOMs) and high-voltage direct-current (HVDC) applications. The advantages of VSCs using IGBTs over converters using thyristors include the ability to regulate reactive power and operate under weak system conditions. The ability of IGBTs to turn off at any time also enables near-instantaneous control that can be used to improve system stability by damping oscillations.
One consequence of the increased control provided by VSCs is interharmonics. The level of interharmonics produced by a VSC device depends on its type, design and application. Early VSCs used pulse-width modulation (PWM) that produced much higher interharmonics than newer modular multilevel (MML) converters. The frequency and level of interharmonics produced by a specific VSC also depends on several design factors (for example, pulse number and levels) chosen for reasons unrelated to interharmonic generation. And, although designed to operate with a number of failed IGBTs, the failure of a single IGBT could significantly increase interharmonic distortion. System conditions such as strength and resonant frequencies also impact interharmonic levels.
Power-line communications are used to transmit system protection information to control certain loads or reactive resources, or for two-way communications with smart meters. All of these systems add non-periodic signals to the power system. Protection communications usually use frequencies in the hundreds-of-hertz range transmitted from one location to another and prevented from reaching the wider system by wave traps. Load or reactive resource control signals, sometimes called ripple control signals, are usually in the 100-Hz to 3000-Hz range and reach the wider system, but they are generally of short duration and used infrequently. Both protection and load-control signals usually communicate simple instructions (trip, block, turn on or turn off) using a minimal number of frequencies.
Smart meter communications over power lines are used for a variety of purposes with varying levels of data intensity. Generally, either the current, voltage or both are briefly shorted to send a step signal interpreted as a binary bit. Series of bits establish meter identity and communicate information. Multiple meters can send signals at the same time and can be quite reliable with multiple communications attempts and error checking.
Interharmonics can be generated at and transferred to any voltage level. Although a relatively limited number of interharmonic measurements are available, low levels of voltage interharmonics (<0.1%) have been measured at transmission levels with no known large interharmonic sources. Even with known interharmonic sources, voltage interharmonic levels rarely exceed 0.5%, except under resonance conditions.
IGBTs used for power conversion, such as these in the Mackinac voltage source converter HVDC valve hall, can be a significant source of interharmonic distortion.
Three Categories of Effects
Interharmonics, like harmonics, are an additional signal on the power system that can cause a number of effects, particularly if magnified by resonance. The wider the range of frequencies present, the greater the risk of resonance. Many of the effects of interharmonics are similar to those of harmonics, but some are unique because of the non-periodic nature of interharmonics.
Like harmonic effects, interharmonic effects can be separated into three categories: overloads, oscillations and distortion.
Overload effects include additional energy losses that can contribute to heating, overloading filters or other system components, and current transformer saturation. Depending on frequency, interharmonics can cause oscillations in mechanical systems, acoustic disturbances or interfere with telecommunications signals. Distortion of the fundamental frequency can interfere with the operation of equipment synchronized with system zero crossings or dependent on a consistent crest voltage, such as fluorescent lights, timing devices and some electronic equipment. In general, interharmonic levels have been lower than harmonic levels, making issues with the effects of interharmonics that are similar to the effects of harmonics unusual.
Two of the most common and impactful effects of interharmonics — but not with harmonic distortion — are light flicker and power-line communications interference.
Light flicker is caused by variations in root-mean-square (rms) voltage magnitude. The perceptibility of flicker varies with frequency and magnitude. The effect of interharmonics on rms voltage variation is frequency dependent such that interharmoncis above 120 Hz have a minimal impact on flicker.
Power-line communications are not only a source of interharmonics but also can be affected by interharmonics. Protection and ripple control signals often consist of a single interharmonic frequency and are usually not affected by interharmonics of other frequencies. Two-way smart meter communications use step changes in voltage or current to send bits of information that consist of multiple interharmonic frequencies. If interharmonics from other sources are in the same magnitude and frequency range, they can interfere with communications. For instance, interharmonics produced by a VSC HVDC installation can cause communication problems with a local automatic meter reading system. Increasing power-line communication signal strength to overcome interharmonic distortion may not be possible because it could cause flicker.
The voltages produced by a voltage source converter will be dramatically different depending on if a pulse-width modulation (A) or modular multilevel (B) design is used.
The effect of a 0.2% interharmonic distortion on rms voltage varies with frequency and has little impact above the second harmonic (50-Hz system example shown).
Simplify the Measurement
To simplify interharmonic measurement and produce repeatable results, IEC 61000-4-7 defines a measurement methodology based on the concept of grouping. For a 60-Hz system, its basis is Fourier analysis with a 12-fundamental-cycle basis that uses a phase locked loop synchronized with the fundamental frequency. This produces harmonics at frequencies that are multiples of the fundamental and interharmonics every 5 Hz between the harmonic frequencies.
These harmonic and interharmonic components then can be grouped into harmonic groups, interharmonic groups, harmonic subgroups and interharmonic subgroups. The magnitude of each group or subgroup is calculated by taking the square root of the sum of the squares of the components of each group or subgroup. A total interharmonic distortion can be calculated by taking the square root of the sum of the squares of all interharmonic groups of significant value.
To simplify interharmonic measurement and analysis, signals are measured every 5 Hz and combined into groups and subgroups.
Standards, Guidelines and Limits
Interharmonics effects include the following:
- Those related to flicker
- Those similar to harmonics
- Those affecting power-line communications.
Because these phenomena are different, the limits required to prevent issues related to each of them also are different.
IEEE Standard 519-2014 contains informative interharmonic limits designed to prevent flicker. IEC 61000-2-2: 2002 contains similar standard compatibility levels. Both standards limit the interharmonics of concern for flicker to frequencies below the second harmonic. The IEEE limits are as high as 5% below 16 Hz, above 104 Hz and very close to 60 Hz for voltages less than or equal to 1 kV. The limit is as low as 0.23% at 51 Hz and 69 Hz for all voltages.
Beyond the interharmonic limits based on flicker, IEEE 519 states “the effects of interharmonics on other equipment and systems” should be given “due consideration” and “appropriate interharmonic current limits should be developed on a case-by-case basis.” IEC 6100-2-2 states there is not enough knowledge of interharmonics for there to be agreement on compatibility limits beyond those for flicker, but for addressing interharmonic issues that are similar to harmonic issues, the standard suggests interharmonic and harmonic limits should be similar.
The IEC standard states ripple control receivers can be expected to respond correctly to voltages as low as 0.3% of the supply voltage and suggests limiting interharmonics near the ripple control frequency to 0.2% of the supply voltage. The IEC suggests limiting any frequency, harmonic or interharmonic, from the 50th harmonic to 9 kHz, to 0.2% and any 200-Hz band in this range to 0.3%.
None of these limits are enforceable, and there is no consensus on their appropriateness. Unfortunately, without accepted limits, equipment and system design is difficult. One thing becoming clear is the limits necessary to enable power-line communications could be about an order of magnitude lower than the limits necessary to prevent flicker or harmonic-related issues.
Measurements show that under certain conditions, interharmonic distortion during HVDC operation can exceed the interharmonic distortion that is produced by automatic meter reading (AMR) communications.
The effects of interharmonic distortion can be mitigated by reducing emission levels, reducing load sensitivity or reducing the coupling between distortion generating equipment and sensitive loads.
The wide-band nature and variability of the interharmonic distortion emitted from certain types of loads can make all three mitigation methods difficult.
Reducing interharmonic emission levels is difficult without also reducing interharmonic-producing equipment benefits, although new MML VSC designs seem to produce lower levels of interharmonics than previous VSC designs. Reducing the sensitivity of loads to interharmonics is possible in some cases. If current overloads or voltage peaks are an issue, higher-rated equipment can be used. Timing issues created by distorted voltage waveforms or zero crossing may be addressed by using equipment not synchronized to the power system.
Power-line communications issues are more difficult to address. Signal strength usually cannot be significantly increased without the risk of creating flicker. While single-frequency signals can be modified to avoid certain sensitive frequencies, wide-spectrum signals cannot. Often, the most practical solution is to remove wide-spectrum communications from power lines.
Filters can reduce coupling between interharmonic-producing devices and sensitive loads, but they may not be practical unless there is a single or minimal number of interharmonic frequencies of concern. When multiple interharmonics are an issue, filtering may not be practical because filters, especially lower-loss undamped filters, can amplify non-targeted frequencies. Designing filters to avoid amplifying critical frequencies may not be possible when a wide range of interharmonics are present.
Another concern is filter megavolt-ampere-reactive (MVAR) size. Power-line communications require a low level of interharmonics to function as designed, which means larger (on a MVAR basis) filtering is necessary. These large filters may create unacceptable voltage regulation and cost issues.
Coming to Conclusions
The level of interharmonic distortion is generally low because, presently, there are few large interharmonic sources. This has kept interharmonic-related problems and the need to measure or mitigate interharmonics rare. As the benefits and use of interharmonic-generating equipment increases, this may change. Other than for flicker, there are few guidelines and no mandatory standards for limiting interharmonics. Without additional guidelines, the potential for interharmonic-producing equipment and equipment sensitive to interharmonics being incompatible with each other is increasing. ♦
Michael B. Marz is a principal transmission planning engineer at American Transmission Co. Prior to joining ATC in May 2001, he spent 12 years with Cooper Power Systems’ systems engineering group and five years with Minnesota Power’s system control and performance group. He holds a BSEE degree from the University of Notre Dame, an MSEE degree from Purdue University and an MBA degree from the University of Minnesota. He is a senior member of IEEE and a professional engineer in Minnesota and Wisconsin.