PhD Course on  Harmonics in Power Electronics and Power Systems

This course provides a broad overview of power system harmonic problems, methods of analyzing, measuring and effectively mitigating them. Several extended simulation and data processing tools, among others DIgSILENT PowerFactory, Matlab/Simulink or LabVIEW are used to assess and study the harmonic distortion at different points of power networks.
The results of analytical investigation and simulations are validated against measurements applying sophisticated data processing techniques. Furthermore, deep understanding of hardware considerations regarding har- monic measurements in harsh industrial environment is given, using specialized equipment, for in- stance GPS-synchronized measuring instruments.

The course covers the following topics:

  • Power Quality definitions. Generation mechanism of power system harmonics. Harmonic indices.
  • Voltage vs. current distortion as well as parallel vs. series resonance in modern power systems. Point of Common Coupling (PCC).
  • Sources and effects of harmonic distortion.
  • Harmonic measuring instruments and measuring procedures in LV, MV and HV networks.
  • Mathematical tools and theories for analyzing distorted waveforms. Signal processing and uncertainty analysis.
  • Modelling of classical power system components. Harmonic analysis.
  • Modelling of grid-connected converters for harmonic analysis purposes and their application in modern power systems including e.g. offshore wind power plants.
  • Harmonic load-flow, frequency scan and time domain simulations. Linear and nonlinear analysis techniques.
  • Steady-state harmonics vs. harmonic stability. Small-signal representation, sequence and frequency coupling.
  • Software tools for harmonic analysis.
  • Precautionary (preventive) and corrective (remedial) harmonic mitigation techniques. Passive and active line filters. Filter design.

Organizer: Professor Claus Leth Bak
Lecturers: Christian Frank Flytkjær from Energinet and Łukasz H. Kocewiak from Ørsted

Harmonic current of 6-pulse rectifier supplying a resistive load
Figure 1 Harmonic current of 6-pulse rectifier supplying a resistive load.
Harmonics Wind Farms

Embedded Power Electronic Solutions in Offshore Wind Power Plants

There is a big potential of wide application of power electronic-based embedded converter systems (e.g. static synchronous compensator, battery energy storage system, active power filter). An optimized integration of aforementioned features can provide extensive functionality covering the following areas:

  1. Grid connection of renewable energy sources
    Wind power plants (especially offshore) are nowadays connected to the grid at remote locations, far from the main consumption centers. Active and reactive power control in battery energy storage systems assures robust operation and grid stability dynamically contributing to voltage and frequency control. It supports simultaneously the grid as well as the wind power plant, partially decoupling the dynamics of both.
  2. Wind fluctuation balancing and Load support
    Wind power is stochastic in nature. Active power from wind turbines, when set to maximum power point tracking, can therefore only be predicted subject to the accuracy of the forecasted wind. Likewise, there is continuous variation of the load demand. Any power system unbalance resulting from the variation of generation and/or load affects the system operation and leads as frequency variations. Battery energy storage systems can store energy from wind when there is excess generation and low demand and release the stored energy during periods of low generation and high demand. Moreover, battery energy storage systems can smoothen out fast ramping up/down of the wind power generation due to sudden fluctuations in the wind velocity. Thus, battery energy storage systems enable to optimize the mission profile and enable more predictable and reliable operation of the whole power system, including the wind power plant.
  3. Reserve capacity
    Battery energy storage systems can reduce the number of on-line generators in the system. It can provide the grid with the reserve capacity that is normally subject to limitations on power plant utilization. Battery energy storage systems serves as a dynamic power source. It can continuously support the grid with reactive power, and in the event of loss of generation, battery energy storage systems can supply active power into the grid until the grid is reconfigured (limited by the energy capacity and state of charge of the battery energy storage system).
  4. Ancillary services
    With higher and higher penetration of renewable energy sources, ancillary services to support the power system are becoming increasingly important, e.g. fast frequency response, virtual/synthetic inertia response, power oscillation damping. Frequency regulation service is often provided by generators having the spinning reserve when they are dispatched below their maximum output level. Battery energy storage system installation providing continuous grid support, such as for voltage control, supplies short-time real power at the lowest cost, thus making it the most attractive supplier.
  5. Emergency power
    In the event of a blackout, wind power plant internal/local loads and power system sensitive loads such as hospitals or power distribution areas, can be fed by a battery energy storage installation until emergency generators are started.
  6. Black start
    As the penetration of renewable energy sources increases, and as old thermal generation plants are phased out, there is an obvious need for new black start equipment in the power system grid. Battery energy storage systems can support generators that lack inherent black start capability. Battery energy storage systems can supply the power needed for safely controlled black starts. It keeps the frequency within range and controls the voltage throughout start-up.
  7. Active filtering
    Many modern industrial processes are, by nature, detrimental to power quality. At the same time, grid code requirements are becoming more stringent to address sensitive power electronic-based plants/loads. The modular multilevel converters have a high effective control bandwidth. This property can be used for active filtering of harmonics that are already present in the grid to compensate non-linear plants and improve the quality of power, as the power electronic interface in battery energy storage systems can inject harmonic currents into the grid with proper phase and amplitude to counteract the harmonic voltages. Furthermore, harmonic propagating through the system can be utilized to charge a battery energy storage system and consequently convert harmonics into the fundamental frequency.
Harmonics Wind Farms

Active Filtering Functionality in Wind Turbines Connected to Wind Power Plant Offhore Network

Active Filtering (AF) functionality can be understood very broadly. A number of technical solutions could be introduced in grid-tied converters functionality depending on the expected outcome.

1           Local resonance damping

The Wind Turbine (WT) is connected to an offshore array cable system within Wind Power Plant (WPP) electrical infrastructure. The aim of AF is to mitigate or damp internal resonances within the WT Low-Voltage (LV) circuit. It could be mainly resonances caused by shunt-connected Pulse Width Modulation (PWM) filters in connection to series inductance. That would allow other converters (e.g. WTs) in the same power system not to be affected by undamped resonances. In this case the WT is acting as virtual damping circuit.

2           Local harmonic current compensation

It can be seen that WTs inject harmonics into the system to which are connected. The amount of injected current is of course dependent on the system impedance. In that case even small voltage distortion imposed by the Voltage Source Converter (VSC) can cause unacceptable excessive distortion level caused by a resonance circuit within the offshore electrical infrastructure. Furthermore due to already existing harmonic voltage distortion in the system where the WT is connected harmonic current can also flow into the WT internal circuit from the network. The task of AF would be to control the current flow between the WT converter and the external network and e.g. reduce it to minimum.

3           Local voltage distortion mitigation

As mentioned above even small voltage distortion introduced by WT’s grid-tied converter can lead to excessive harmonic current flow in the resonant network to which the WT is connected. The goal of AF would be to improve and minimise as much as possible the voltage distortion level at the converter terminals caused by the power electronics non-linarites as well as limited harmonic rejection capability of the controller. The equivalent voltage source of the VSC would tend to be as less distorted as possible.

4           Unity amplification factor

In many cases when a new plant (e.g. STATCOM) is connected to already existing power systems it is strongly desired that the new plant will not change the harmonic profile after the connection of the existing before system. This can be obtained fulfilling two objectives (i) no harmonic contribution/injection, (ii) no changes in the system impedance at the Point of Connection (POC). The second objective is related to unity amplification factor at POC which can be achieved by AF so the newly connected impedance in not visible to the existing network. Such requirement can be put also to WTs.

5           Resonance damping at the remote bus

Having a number of WTs in WPPs allows also looking on AF in more global way. WTs could be programmed to mitigate prominent resonances in the WPP offshore network, e.g. Offshore Grid Entry Point (OGEP) in the UK or Point of Common Coupling (PCC) in Germany. This would optimize the overall system damping leading to robustness increase of grid-tied converters as well as lower harmonic voltage distortion level. The WTs would operate in groups or clusters and could be understood from electrical infrastructure perspective as an equivalent damped filter.

6           Harmonic compensation at the remote bus

Nowadays it is more and more challenging to meet demanding grid-code requirements, especially in resonant offshore networks with low damping. Therefore the AF functionality in WTs leading to keep the harmonic voltage distortion level at e.g. PCC as specified in the grid-code is critical to assure continuous WPP active power production. WTs could act in groups or individually to achieve that objective, e.g. the 7th harmonic equal or lower than 0.5% at OGEP in the UK or harmonic current injection from all WTs cannot cause higher voltage distortion incremental higher than 0.1% in Germany.

7           Converter controller passivity

In modern WPPs the industry is facing more and more diversification in utilized power electronic devices and their controls. One of examples would be HVDC-connected WPP with multi-vendor WT configuration or HVAC-connected system employed simultaneously with WTs and STATCOMs. That creates even more challenges considering grid-tied converter interaction issues such as stability. Furthermore more complex control structures imposed by AF functionality application requires more focus at the early stage of the WPP system design. Therefore one of potential requirements to the suppliers would be to assure converter passivity within specified frequency range where e.g. where AF is applied. This would secure the robustness of the overall system operation.

Harmonics Wind Farms

Active Filtering Functionality in Wind Turbines - Motivation

The offshore AC electrical infrastructure in Wind Power Plants (WPPs) connected via either HVAC transmission cable (e.g. Hornsea Wind Farm) or HVDC link (e.g. Gode Wind Farm) is a sensitive network because of its low damping caused by the design focused on low transmission losses. The combination of transformers and cables with low equivalent resistance within the electrical infrastructure makes very good resonance circuits due to the low damping. There are many possible resonance frequencies in the offshore grid with a large amount of cables and transformers connected. Such complex configuration as well as low active power dissipation (due to low resistance to reduce active power losses) creates challenges by means of harmonic performance, grid code compliance, power transmission, stability of grid-tied converters etc.

The presence of undamped resonances means that whenever an oscillation is excited (e.g. by non-linear components such as transformers, power electronics etc.) it takes long time for it to be damped out. The problem becomes even more severe when the system is unloaded, e.g. during energization or when some Wind Turbines (WTs) are out of service and the cable network is unloaded. When the system is loaded (active power is transmitted), the overall damping is higher and the harmonics are reduced faster than with an unloaded scenario.

Besides in case of widespread array cable system in the offshore electrical infrastructure resonance frequencies can shift due to changes in the system topology, e.g. number of WTs is varying, transformer or transmission cable disconnection, interlink operation etc. This furthermore creates challenges to introduce robust harmonic resonance mitigation measure. Typically one can recognize two ways of mitigating unwanted harmonics in modern power systems (i) passive filtering, (ii) Active Filtering (AF) by grid-tied converters. Variation of resonance frequencies caused by topology change requires large passive filters (e.g. damped high-pass filters such as C-type) which are not feasible, in many cases, to be installed offshore. Therefore, for optimization of offshore electrical infrastructure in WPPs AF (or a combination of active and passive filters) seems to be solution that is more appropriate.

The density of power in modern WTs is increasing meaning that they contribute more to the system’s quality of power. It could be either by higher harmonic pollution or by improved technical solutions leading to almost undistorted networks. In case of resonance networks, it is critical that the harmonic injection by WTs is very small and controlled. Therefore, utilization AF in WTs is a natural step forward to improve the overall distortion level of offshore networks in WPPs.

Harmonics Wind Farms

Active filtering vs. passive filtering

Let us think about various sources of harmonic problems in large wind power plants (WPPs) and different ways of optimized harmonic mitigation methods. We discussed previously about harmonic problems such as sources of harmonic emission and amplification as well as harmonic stability which are commonly seen in large WPPs. Fortunately a significant variety of modern preventive and remedial harmonic mitigation methods in terms of passive and active filtering are possible.

Passive filtering

Three-phase harmonic filters utilized in the WPPs nowadays are shunt elements. They are intended to decrease the voltage distortions at the point of interest. From the grid code requirements point of view, a WPP voltage distortion is evaluated at the point of common coupling (PCC).
Nonlinear elements such as the power electronic converters, transformers, etc. generate harmonic currents or harmonic voltages inside the WPP as well as in the external network. The resultant harmonic current flows throughout system impedance. Passive harmonic filters reduce distortion by providing low impedance to the harmonic currents.
Typical shunt harmonic filters are presented in Fig. 1. Such filtering depending on the harmonic emission source can be installed either in the wind turbine circuit or somewhere at the WPP level (e.g. onshore substation, offshore substation, etc.).


  • Known state-of-the-art technology,
  • Relatively cheap solution,
  • High reliability due to simplicity in the build,
  • Effective if designed correctly.


  • Significant size especially for lower frequencies (for large WPPs the tuned frequencies are getting lower),
  • Additional losses,
  • Can cause some over-voltages during switching operations (e.g. energization),
  • Tuned only for specific frequencies (i.e. limited bandwidth),
  • Affected by uncertainties during the WPP design phase,
  • Cannot be easily re-tuned in the case of changing grid conditions during the operation of the WPP,
  • Uncertainties in terms of sizing due to lack of information from wind turbine manufacturers and TSOs during the design phase,
  • Size limitations during design due to e.g. limited space at offshore substation,
  • Long lead-time because of custom-made reactors.

Active filtering

All active filtering solutions employ power electronic converters for the absorption (e.g. harmonic compensation) or suppression (e.g. active damping) of harmonics. Nowadays large WPPs are already equipped with a number of grid connected converters either as a part of the wind turbines or as some sort of FACTS devices. In that case, the implementation of active filtering technique would only mean the retuning of the converter controller in order to meet with controlled harmonic levels.
The converter might be controlled adaptively or otherwise to suppress the selected critical harmonic components. From this perspective there is no need to interfere with the WPP design but it entails to providing additional control features. Such issues could be specified on a contractual level and required to be provided as an add-on together with the product.
Connecting all possible active filtering methods together with state-of-the-art passive filtering methods an optimized hybrid solution can be obtained.


  • Already existing technologies such as STATCOMS can be utilized for the active filtering at the PCC,
  • Active tuning might be permissible even during the operation,
  • Almost unlimited control potential (e.g. selective harmonic compensation, wide band high-pass active filtering, etc.),
  • Network impedance changes during operation could be addressed,
  • Control method can be tuned for each of WPPs independently taking into consideration grid code issues as well as WPP structure,
  • Negligible losses for series connected active filters such as wind turbines,
  • Reduces risk due to uncertainties related with lack of information from manufacturers (e.g. models) and TSOs (e.g. harmonic background, models, etc.).


  • Recent technology; not commonly applied in WPPs,
  • May suffer from harmonic stability problems,
  • Improved bandwidth and increased switching frequency is needed,
  • Component sizing issues and limited DC-link voltage utilization.

[1] Ł. H. Kocewiak, "Harmonics in Large Offshore Wind Farms," PhD Thesis, Aalborg University, Aalborg, 2012.
[2] Ł. H. Kocewiak, S. K. Chaudhary, B. Hesselbæk, "Harmonic Mitigation Methods in Large Offshore Wind Power Plants," in Proc. of The 12th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms, Energynautics GmbH, London, UK, 22-24 October 2013, 443-448.