Harmonic Study Analysis Guidelines for Industrial Power Systems

By Ali Mihirig, Ph.D., P.Eng.

Harmonic study analysis becomes an important and necessary task for consultants and engineers in almost every industrial project, primarily because of the fact that thyristor controlled equipment is widely and heavily used in most industrial plants.
This article provides step-by-step guidelines for engineers to conduct a proper harmonic study analysis for typical industrial power distribution systems in light of standards and good engineering practices. The task starts at the planning and design stage by laying down all the different options available concerning power factor correction capacitors -- sizing and location, advantages and disadvantages of each option and effects on the system performance.
This article introduces a practical method for system modelling. The method concludes that modelling of certain elements in the system have negligible or minimum effects on the study results.

Harmonic producing equipment represents a significant portion of the total connected load of modern industrial systems. The effect of harmonics can be noticeable in many ways such as voltage and current distortion, low voltage notching, communication systems interference and high voltages and currents in case of resonance.
Harmonics may cause relay misoperations, PLC interference, equipment failures, capacitor fuse interruptions and high overall system losses.
Harmonic study analysis must be conducted in the engineering design stage of all industrial systems that include harmonic producing equipment, alongside load flow and short circuit studies. The interaction between load flow and harmonic study should lead to the best system configuration design, optimal operating conditions and proper size and location of power factor correction capacitors.
When medium voltage capacitor banks are considered, it is also important to conduct transient analysis study to assess the possibility of switching problems.

Power Factor Correction Capacitors
Installation of power factor correction capacitors in industrial systems is one of the most effective ways to reduce energy consumption and utility bills. It also allows the usage of transformers and feeders full capacity. Although capacitors are easy to install and cheap to maintain, they can be the most troublesome element in the whole plant when installed in the presence of harmonics in the system.
Capacitors can be distributed all over the system at load locations or centralised in one location at the medium voltage level to correct power factor.

Distributed Capacitors
Usually medium and low voltage capacitors are distributed alongside loads at the 2.4kv and 600 volts or less. This method has the following advantages and disadvantages;

-   Power factor is corrected at load location where transformers and feeders can be utilised to full capacity.
-   Low possibility of harmonic resonance problems if proper size is selected.
-   Low possibility of switching transient problems.
-   Easier and less expensive to maintain.

-   Larger space is required and more expensive per Kvar compared to the centralised medium voltage banks.
-   Need to be tuned with reactors when connected in parallel with large harmonic producing loads.

Centralised Capacitors
Medium voltage capacitor banks at the 13.8kv or 6.6kv voltage levels are used to compensate the overall plant reactive power. Some advantages and disadvantages are;

-   Less space is required and less expensive per kvar compared to distributed capacitors.
-   Can be installed outdoors.

-   Series reactors are likely required to prevent harmonic and/or switching problems.
-   Loss of the bank for any reason subjects the plant to power factor penalties.
When tuning reactors are used with medium voltage capacitor banks, high magnetic fields are generated. They must be blocked by non-magnetic materials to prevent interaction with nearby sensitive equipment such as display systems and computers.

Power System Modelling
Power system modelling for harmonic studies still requires more improvements to achieve better accuracy and less complicated models. Improved models are specifically needed for transformers, loads, harmonic sources and utility equivalents.
In the real world, harmonic study must be conducted and accommodated within the electrical system study budget and time constraints. Therefore, system modelling should be as simple as practical that would provide reasonably accurate results for design purposes.
System flexibility is needed, however, for harmonic suppression after proper measurements are conducted to verify study results.
The resistance element of the following models must be frequency dependent to encounter for the skin effect and provide realistic harmonic damping in the system.

Harmonic Sources
Harmonic producing equipment such as variable speed and D.C. drives, arc furnaces and welders and any other non-linear loads are harmonic sources. Typically, harmonic sources are modelled as current source with magnitude and phase angle for each harmonic frequency. This model provides reasonable results for power systems with no resonance at or near generated harmonic frequencies.
When system impedance contains both inductive and capacitive elements, which is usually the case for industrial systems, the simple current source model produces unrealistically high estimates of harmonic voltages, current and distortion factor in case parallel or series resonance at or near one of the generated frequencies.
Simulating harmonic sources as current sources with an infinite shunt impedance means that harmonic parameters can reach any value without limitations. In fact every harmonic source is limited by its internal circuit. Therefore harmonic sources must be modelled by their Norton's or Thevinin's equivalents in order to limit harmonic voltage and current rises in case of resonance.
For power converter drive systems, the ratio of locked rotor current to rated current can be used to derive Norton or Thevinin equivalent impedance (ratio of 3 has been suggested [1]).
The harmonic producing equipment supplier must provide harmonic currents (magnitude and angle) to be used in simulation studies.
In most cases, measured harmonic currents are different from theoretical values given in text books or standards.

Passive loads are modelled by their equivalent impedance based on MW, Mvar and rated voltage. Motor loads are represented by their subtransient and locked rotor impedance for synchronous and asynchronous motors respectively.
Several detailed motor models are proposed for harmonic studies. In practice, when detailed models are used in a typical industrial system of several hundred motors, the task of harmonic study analysis become unbearable due to budget and time constraints. Furthermore, the effect of low voltage loads on the system impedance-frequency response is only marginal and falls within 10-15 per cent. e.g. Typical 3 MVA transformer with 5.75 per cent impedance supplying full load and 750 Kvar capacitor bank at 600v, the resultant parallel resonance at the 600v bus is largely dominated by the transformer and capacitor reactance regardless of the load models being used. Therefore, loads can be generally neglected at low voltage levels (<600v). Only in special cases when filters are considered at low voltages, should loads be included to size filter elements.
When medium voltage capacitors (2.4kv-13.8kv) are considered, load modelling becomes more significant and may be included. Here again, the simple model of sub-transient and locked rotor impedance models are acceptable for motors.

Transformers, Transmission Lines and Cables
For low frequency harmonics up to 1.5KH, transformers, transmission lines and cables can be safely represented by their equivalent short circuit impedance. For higher harmonic calculations such as I.T. product, these models become inaccurate and may produce misleading results.
Detailed models were proposed but again with so many transformers in industrial systems it becomes impractical to use detailed models unless studying the performance of a few or a single transformer in the system. This situation arises when calculating the telephone influence I.T product at the point of service with utility. It is important in this case to model tie transformers and associated cables in more detail including their internal capacitance which becomes effective with higher harmonic frequencies.
Using simple short circuit impedance model for utility tie transformers, lines and cables to calculate the I.T product at the point of service with utility would generally produce higher results than the measured ones.

Utility Equivalent
The utility equivalent short circuit impedance is usually used to represent the utility system at the point of service. This model can be used with a good degree of accuracy in the following cases:
-   No series or shunt capacitors are connected to the transmission line or nearby substation serving the system under study.
-   Calculation of low frequency harmonics up to 1.5KH.
-   No other customers closeby producing harmonics and sharing the same line with the studied system.
In most cases, the above conditions are not satisfied because of the fact that most North American utilities are now in the process of implementing the IEEE standard 519 which recommends specific limits for harmonic distortion and telephone interference.
For the telephone interference calculation, higher harmonics must be included because of their large weighting factor in the I.T product. It is important in this case to model the utility by its frequency dependent equivalent up to the 49th harmonic. Closeby capacitor banks and other harmonic producing customers must also be included in the model.
It is important that both utilities and their customers share responsibilities and join efforts to meet the specific limits of the standard. In some cases, the customer operates very well below the standard voltage distortion and telephone interference levels but as soon as the utility switches on their capacitor bank in the nearby substation, the harmonic distortion or interference rises above the standard limits. This case requires joint effort by both parties to satisfy the standard. In another case, two industrial customers share the same transmission line, one of them is injecting harmonics into the line such that the distortion factor is already up to the limit (e.g. 1.5 per cent at 220Kv). Later the new customer will face a zero tolerance situation where any additional harmonic injections will push the harmonic distortion higher and therefore exceed the standard limit. In this case the three parties should share the cost of reducing the harmonic distortion.

Impedance Calculation
After system modelling is completed, the first step in the harmonic study is to explore resonance points through impedance versus frequency calculations. These calculations can be simplified in the case where only one capacitor bank exists in the system. Impedance versus frequency can be calculated for a quick scan of the system to determine resonance frequencies. A typical industrial system with distributed capacitors and various harmonic sources requires computer calculations.
Generally, if the system exhibits resonance at or near any of the system potential harmonics, mainly at the 5th, 7,11 or 13th harmonic, in the presence of harmonics and medium voltage capacitor banks (2.4Kv-13.8Kv), then the safest thing to do is to tune the capacitor banks to the 5th harmonic to eliminate any possibility of resonance above the 5th harmonic. The tuned capacitor bank size is usually capable of absorbing all 5th harmonic currents as it is sized for power factor correction purposes not as a harmonic filter.
In case of distributed capacitors at load locations (480v-2.4kv), impedance versus frequency calculations should be performed at each capacitor location. The size of these capacitors must be selected such that it does not resonate with its area transformer impedance.
Where the load is a harmonic source, the capacitor bank can be de-tuned at a much lower frequency (2nd-3rd harmonics) to reduce reactive losses and force harmonics to flow upstream. This can be done as far as the harmonic distortion at the higher voltage level is kept within acceptable limits.
Impedance-frequency plots are very helpful to visualise potential resonance for different system configuration and corrective measures. Frequency steps should be small enough to detect sharp resonance (.1 to .5 pu).

Harmonic Parameters Calculation
Harmonic parameters usually calculated in typical harmonic study are:
-   Harmonic Voltages at buses of concern.
-   Harmonic Currents at branches of concern.
-   Total harmonic distortion factors (THD for voltage and current)
-   Telephone interference factor and I.T product.
-   Residual telephone interference and I.T product.
Harmonic analysis computer programs are needed to calculate the above parameters for mid-size and large industrial systems. Results of computer programs must be taken with caution for the obvious modelling limitation reasons mentioned in section 4 above. Field measurements are necessary to verify the theoretical computer simulation results.
Various system equipment ratings must be checked for possible overload and/or over stress due to excessive harmonic currents and voltages. Power factor correction capacitors are particularly vulnerable to high harmonic voltages and currents due to system resonance. Capacitor total rms voltages and currents, including harmonics, must be checked against standard maximum rated parameters [4].
The total voltage harmonic distortion factor THD% is a very significant measure to ensure proper overall performance of system equipment. Acceptable limits for harmonic distortion are given in the IEEE standard 519-1992 for different voltage levels [5].
Total harmonic distortion factor is defined by:
THD% = SQRT( Vh2 / V12 ) % [1]
Vh is harmonic voltage for h = 5, 7, 11, 13......etc.
V1 is the fundamental voltage, h=1
Also the maximum THD% for a known drive characteristic is given by:
THD% = 100 x SQRT((4.24 x 10-6 x An x F1)/(V1)) [2]
An = Notch area in volt-microseconds.
F1 = Fundamental frequency
· = Ratio of the total inductance to the common system inductance
Although equation 2 is derived from equation 1, two different results have been reported [6] when using an oscilloscope to measure the notching for equation 2 and spectrum analyser which uses equation 1. It is recommended, therefore, to use an oscilloscope to measure notching and equation 2 to calculate the harmonic distortion at the harmonic source supply bus.
The I.T. product calculation can be estimated by calculating all harmonic currents injected into the utility system at the point of service, then multiplying each by its TIF weighting values. The utility system, in this case, must be represented as a frequency dependent equivalent impedance in order to get reasonable results.

Harmonic Measurements
Simulation results could be far from reality and therefore must be verified by field measurements to ensure proper system performance. Measurements of harmonic voltages and currents through typical system voltage and current transformers are subject to limitations and can only be trusted up to 1.5-2 KHz. This may be enough to identify potential harmonic problems due to system resonance in the range of 5th to 13th harmonics. For the purpose of telephone interference measurements which highly depend on the higher harmonic frequencies, special measurement devices are required.
Voltage harmonic distortion measurements using spectrum analyser may be misleading in the presence of deep short notching in the system, especially at the harmonic source bus.
Measurements can be confirmed by careful analysis of the notching spikes as mentioned in section 3 above and reference [6].
It is important that harmonic currents injected into the system from all harmonic sources be measured and compared with theoretical values used in the simulation. Harmonic filters and capacitor banks should also be targeted for harmonic current measurements to ensure proper performance.
The basic equipment required for harmonic measurements is spectrum analyser and/or oscilloscope with data recorder. This equipment is enough for industrial plant harmonic measurement purposes. High frequency harmonic filters are required for telephone interference and I.T. product measurements.

1-   John Cuffman "power factor correction capacitors and their side effects"
2-   Roger Dugan, "Electric power system harmonic design guide" report for the US department of energy.
3-   A. Roeper, "Short circuit currents in three phase systems", Siemens publications.
4-   ANSI/IEEE Standard 18-1980, "IEEE standard for shunt power capacitors"
5-   IEEE Standard 519-1992, "IEEE recommended practice and requirements for harmonic control in electrical power systems"
6-   "Vendor contracts must specify noise limits", Electrical World Magazine, pp 75-76, May 1988.