Voltage and current distortion is a major problem in nowadays power systems due to nonlinear loads such as variable frequency drives, arc furnaces or inverters of renewable energy power plants. Harmonics can cause equipment failure, high temperatures of transformer windings, erratic operation of protection relays and additional active power losses. Because of this, active and passive filters are used to mitigate harmonics related negative effects.

Harmonic distortion is highest closer to the load, therefore, at this study we will analyze industrial power network.

Calculations will be proceeded with power system modeling software EA-PSM, which also allows to select power factor correction and harmonics mitigation equipment. The calculations are done to find steady-state operation conditions of the network.

#### Nonlinear load as harmonic currents source

In accordance to Ref.[1], nonlinear devices (inverters, VFDs, arc furnaces, resistance welding and etc.) can be represented as current sources of harmonics in a power network. The assumption that permits this representation is that the system voltage is not distorted, and is quite accurate up to harmonic voltage distortion levels of 10%.

To specify nonlinear load, current harmonics at the connection point of that load should be known either form measurements or from manufacturer provided data.

Injected current harmonics will create voltage distortion, which will depend on the magnitude of currents as well as on the resistance and reactance of the network. Reactance will have bigger influence as it will be higher for higher order harmonics. This means, that by measuring voltage and current harmonics, it is possible to validate if network parameters where specified correctly in EA-PSM. This can be done by connecting nonlinear load to the network. Measured current harmonics should be specified in the nonlinear load as explained in section “3.9 Defining parameters of the Inverter” of EA-PSM manual. After the load is specified, calculation of harmonic load flows should be done. Voltage harmonics at inverter connection bus should be the same as measured with the power analyzer. If there is any difference, parameters of cables, transformers, power system and other loads should be checked for compliance with a physical system.

Order of harmonics generated by semiconductor converter equipment, depends on its pulse number. The pulse number itself shows how many commutations occur during each cycle in the converter. For harmonics order calculation, the equation is used:

ℎ=𝑘𝑞±1

where k – any integer number, q – pulse number of the converter. According to this formula, 6-pulse inverter should generate only 5th,7th,11th,13th and etc. harmonics. For example, 3rd harmonics are generated by 4-pulse rectifiers that are commonly used in light bulbs and computers. Presence of other harmonics than calculated with Eq.1, mean abnormal operation conditions for the converter, like high imbalance in the ac power system or asymmetrical delay angle.

Typical current harmonics of a 6-pulse inverter are provided in the EA-PSM according to Ref.[1] data. In Fig. 1 these harmonics are compared to ones measured near to the transformer in random industrial network. Because there are different types of nonlinear loads connected to the network, for example, 2-pulse inverters, there is a slight difference between measured and standard harmonics. However, IEEE519 provided values are good for practical estimation of harmonic load flows in the network.

**Fig. 1** Standard harmonics for a 6-pulse inverter comparison to measurements in a real network

#### One-line network diagram development

In order to make calculations, mathematical model of the physical network has to be created. Software EA-PSM has built-in models of the most common equipment in industrial, distribution and transmission networks, therefore, user just need to specify parameters of the equipment. It is also important to understand, how specific parameters affect harmonic load flows.

One-line network diagram development is one of the most important part of the study, because reliability and accuracy of calculated result depends on the accuracy of specified equipment parameters. It is recommended to rely on the manufacturer specified data from the equipment catalogue.

Harmonic currents flow from nonlinear loads toward the lowest impedance path. Usually this path is the utility source, which impedance is much lower than parallel paths provided by loads, however, harmonic currents will split depending on the impedance ratios. These effects will be taken into consideration by EA-PSM software. In Fig. 2 harmonic currents paths are depicted. The important conclusion can be made, that in order to reduce harmonic currents to system, low impedance path should be constructed for them.

**Fig. 2** Harmonic currents paths in the one-line network diagram

One-line network diagram development begins from the specification of the system bus. In EA-PSM select bus elementand place on the workspace. The first bus placed on the workspace is considered as system bus, for more information refer to section “3.3 Creating the Infinite Busbar” in EA-PSM manual. The harmonic load flows will be affected by system short-circuit capacity, which indicates system impedance for the fundamental harmonic. EA-PSM will automatically calculate system impedance for higher harmonics, according to this data.

Systems with higher short-circuit capacities will have lower voltage distortion for the same size harmonic current source than weaker system. Because of this, it is important to conduct measurements at various supply network states or alternately to do calculations with EA-PSM and save your time.

Capacitor banks will also have major influence on the harmonics, because connection of capacitors can cause series and parallel resonance conditions. In some case capacitor can help to mitigate harmonics, however, most commonly if capacitor is sized improperly, it will cause extremely high harmonic distortion. Cables and overhead lines also have distributed capacitance between wire and ground. This capacitance is in parallel with the network, therefore, can also cause resonance conditions.

Other network loads like heating elements, induction motors will also have influence on the harmonics. The resistive portion of the load will reduce harmonic currents magnitudes near resonance frequencies, what is more the inductive reactance of loads (mainly induction motors) will shift the frequencies at which resonances occur. It is important to evaluate, that variation of loading will affect harmonic magnitudes and can shift resonance frequencies. In the typical industrial network, there is often very little resistive type loads to provide damping near the resonant frequencies, however, induction motors play a more important role as they shift resonant frequencies.

Accurate parameters of the step-down transformer are also important. For higher order harmonics, transformer impedance becomes high if compared to loads impedance, therefore, transformer isolates higher harmonics from the network, in that case harmonic currents will choose lower impedance path. Also, there is possibility, that harmonics will cancel each other at transformer windings, thus it is important to accurately specify phase shifting angles.

#### References

[1] Young-Sik Cho, Hanju Cha, Single-tuned Passive Harmonic Filter Design Considering Variances of Tuning and Quality Factors, Journal of International Council on Electrical Engineering, 2014

[2] IEC 61642 Industrial a.c. networks affected by harmonic – Application of filters and shunt capacitors

#### Harmonics Mitigation Study:

Part 1. Single line diagram development

Part 2. Parallel and series resonance. Triple harmonics. Solutions to avoid resonances

Part 3. Passive harmonic filters selection. Short circuit protection and commutation