Description: 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
Nowadays, it is seen that the rapid transformation of power systems from conventional with high natural damping, short-circuit current and natural inertia to power-electronic-based with limited damping, fault infeed and inertia may trigger unstable operation, if not investigated carefully. Moreover, the electrical infrastructure is becoming more complex due to the introduction of long high voltage alternating current (HVAC) cables, high voltage direct current (HVDC) connections, widespread penetration of renewable energy sources, e.g. photovoltaic (PV) plants, wind power plants (PPs), and offshore electrical network development. This power system transformation creates challenges such as operational coordination of grid-connected converters and small-signal stability assurance both in the sub-synchronous and harmonic (super-synchronous) frequency regions.
The increased use of power electronic converters in modern electrical systems creates challenges w.r.t. power system stability assurance but also simultaneously provides wide range of power system performance and stability enhancement solutions. Better understanding about the application of various instability mitigation methods, including impact on power system performance, use depending on instability root cause, implementation methodology, is needed. Power system operators, operators of renewable PPs, transmission solution developers, renewable generation developers, academic units and original equipment manufacturers expect coordinated effort to understand when and how to apply specific mitigation measures.
Therefore, the overview, status and outline of instability mitigation methods in converter-based modern power systems is needed. Thus, the CIGRE C4.49 working group entitled “Multi-frequency stability of converter-based modern power systems” was established. The instability phenomena, instability root cause and suggests optimal mitigation measures are investigated within the working group. Moreover, guidelines regarding the general approach how to choose optimal instability mitigation method will be suggested in the technical brochure.
Review of existing literature regarding subject related stability issues including state-of-the-art converter stability aspects.
Definition of stability phenomenon to be covered within the technical brochure.
Stability effects above the fundamental frequency, i.e. harmonic stability.
Small-signal stability below the fundamental frequency, i.e. sub-synchronous stability.
Clarification of definitions to avoid misinterpretation with steady-state harmonics and classical harmonic propagation analysis.
Symptoms and root causes of sub-synchronous and harmonic stability phenomenon.
Examples of sub-synchronous and harmonic stability phenomena observed and their impact on wider power systems.
The impact of grid-connected converter controllers on sub-synchronous and harmonic stability phenomenon.
Classification of typical controllers used in modern converters.
Evaluation of various control loops and techniques and their impact on stability, e.g. voltage control, current control, phase-locked loop.
Frequency range of interest and controller interactions/couplings.
Overview of linear modelling and analysis methods to perform small-signal stability studies, e.g.
Classical control theory approach of linear time-invariant systems, i.e. compensator and plant interactions, and possible general extension to linear time varying systems including e.g. linear time-varying periodic systems.
Impedance-based stability criterion.
Advantages and disadvantages of single-input single-output and multiple-input multiple-output representation.
Relevant stability evaluation methods, e.g. eigenvalue analysis, Nyquist criterion.
Other analysis techniques.
Time-domain numerical simulations of linear and non-linear systems.
Frequency and sequence coupling investigation.
Stability of non-linear dissipative dynamic systems including e.g. limit cycle and bifurcation theory investigation.
Description of mitigation methods to overcome sub-synchronous and harmonic stability issues, e. g.
Clear evaluation criteria and minimal requirements regarding the stability indices, e. g. stability margins, damping.
Recommendations to address plant resonance profile at early stage during the grid-connected converter controller design.
Converter coordination guidelines in modern power systems to avoid potential instability, e. g. passivity requirements.
Mitigation measures incorporated in the grid-connected converter control (e.g. active damping) or within the power system electrical infrastructure (e.g. passive damping), also at later stage of project development or during operation.
Guidelines on general approach to such studies and the availability as well as choice of tools. Identification of limitations with the available analysis tools and suggestion of possible areas for development.
Ł. Kocewiak, R. Blasco‐Giménez, C. Buchhagen, J. B. Kwon, M. Larsson, A. Schwanka Trevisan, Y. Sun, X. Wang, “Instability Mitigation Methods in Modern Converter-based Power Systems,” in Proc. The 20th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms, Energynautics GmbH, 29-30 September 2021.
As the number of power-electronic-based power generation units (PGUs) and the power system infrastructure complexity are rapidly increasing, there is a need for carefully investing the system stability to assure robust and reliable operation. However, no commonly agreed methods are available for the analysis of potential sub-synchronous and harmonic (or super-synchronous) stability problems.
Hence, there is a need to provide a general overview of the topic, highlighting the root-cause of sub-synchronous and harmonic stability issues of grid-connected power electronic devices supported by state-of-the-art literature survey as well as industrial experience.
Instability in modern power systems
Several instability incidents related to control system in PGUs have been seen until know. Some of them are briefly summarized below.
1. Oscillations in PV systems with harmonic resonances 
Measurements of unstable PV PPs are documented in . The paper takes a model-based approach to predict instability within the harmonic frequency range and improve robustness in a PV PP. The measurements showing instability are obtained from a commercially operating PV PP and are presented in Figure 1.
Furthermore, the studies clearly show that increase of power-electronic-based PGUs in electrical grids characterized by weak conditions increase the need for power converter controllers able to adapt to wide range of grid conditions. The need to change from classical current-controlled VSCs to a more adaptive approach is acknowledged.
2. Oscillations in wind PP with HVDC and harmonic resonances 
The paper  shows measurements and analysis of one instability incident that happened in German North Sea at an offshore wind PP, connected to onshore by a VSC HVDC system. After a switching operation of a cable an oscillatory behavior could be seen on the voltage waveform as shown in Figure 2. The instability was caused by a control interaction, most likely due to the WTs being sensitive to a grid resonance.
The time domain and impedance-based analysis showed that the WT controllers in use had stability problems with a very poorly damped resonance at the frequency around the 9th harmonic. Due to the switching operation the resonance frequency drops from 600 Hz to around 450 Hz which caused the instability.
3. Oscillations in systems with Type 3 WTs and series compensation 
The paper  describes a sub-synchronous resonance observed in a wind PP in North China. The measured oscillations were around 6-8 Hz (see Figure 3) and driven by interaction between double-fed induction generators and series-compensated transmission lines.
The system vulnerable to sub-synchronous oscillations was investigated using time-domain simulations and supported by eigenvalue-based analysis to understand the impact of grid parameters on the instability.
4. Oscillations in Type 4 WTs in weak grids 
The publication  presents the need to perform eigenvalue-based stability analysis to investigate sub-synchronous oscillations in an offshore wind PP. It is reported that the instability happened during PP contingency operation due to one export HVAC cable outage. Excessive power oscillations were measured as presented in Figure 4.
The paper shows that the effective short-circuit ratio (SCR) at the MV terminal of the WT transformer dropped due to the contingency to 1.2-1.5. Such extreme weak grid conditions triggered WT controller instability.
Instability mitigation methods
Following the investigations and discussions of previous sections on instabilities and their root-causes, this section outlines recommended practices for risk mitigation. The following methods have been identified :
Power grid operational measures
Passive filter placement
Converter setpoint adjustment
 F. Ackermann et al., “Stability prediction and stability enhancement for large-scale PV Power plants,” in Proc. 7th International Symposium on Power Electronics for Distributed Generation Systems, 2016.  C. Buchhagen et al, “Harmonic Stability – Practical Experience of a TSO,” in Proc. The 15th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms, 2016.  L. Wang et al., “Investigation of SSR in Practical DFIG-Based Wind Farms Connected to a Series-Compensated Power System,” IEEE Transactions on Power Systems, 2015.  L. Shuai et al, “Eigenvalue-based Stability Analysis of Sub-synchronous Oscillation in an Offshore Wind Power Plant,” in Proc. The 17th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms, 2018.  Ł. Kocewiak, R. Blasco‐Giménez, C. Buchhagen, J. B. Kwon, Y. Sun, A. Schwanka Trevisan, M. Larsson, X. Wang, “Overview, Status and Outline of Stability Analysis in Converter‐based Power Systems,” in Proc. The 19th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as Transmission Networks for Offshore Wind Farms, Energynautics GmbH, 11-12 November 2020.
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:
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.
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.
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).
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.
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.
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.
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.
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.