Background and Motivation

The global demand for electricity has grown rapidly as the global economy has developed over the last decades, and according to the International Energy Agency (IEA), the demand rose to 25606 TWh annually in 2017[1]. The rising demand for energy has been followed by an increased focus on the environmental challenges related to CO₂ emissions, where electricity production is a key driver. The energy industry has therefore been forced into an energy transition where renewables are at the centre of technological development. This transition is clearly visible when looking at the global energy mix, where the share of global electricity generation in 2018 coming from renewables was26%, with an estimated increase to49%in 2030[2].

To ensure the transition into a sustainable future, both the European Union (EU) and the United Nations (UN) have enacted different policy frameworks describing climate and energy policies and targets going forward. The EU passed a framework containing EU-wide targets for the year 2030 stating that the EU as a whole should achieve at least 32% share of renewable energy, and be climate neutral in 2050[3]. In 2016 the UN also came to a new agreement meant to replace the Kyoto Protocol from 1997. The Paris Climate Agreement, ratified by 187 party-members of the UN, sets a target of keeping the global temperature increase below 2°C and pursue efforts to keep it to 1.5°C within the current century[4]. These two accords, as well as other national climate policy frameworks, have led to the need for significant changes in the power system, integrating even more Renewable Energy Sources (RES). Here, wind power is highlighted as one of the primary solutions to reduce the environmental footprint, as well as emissions of greenhouse gases, coming from power generation.

The increased focus on RES has also made an impact on the economical landscape governing the investments of energy companies. Technologies such as wind and solar have now matured enough to be able to compete with conventional energy sources such as coal and gas without the

need of heavy subsidies[5], making them more attractive to the energy companies. Combining this with stricter policies related to the quotas for the EU Emission Trading System (EU ETS) and short gestation times from investment decision to full operation, the Levelized Cost of Electricity (LCOE) for wind energy has become lower than coal-fired electricity[6]. Based on this, wind power was presumed to pass natural gas in 2019, becoming the leading energy technology in Europe measured by installed capacity[7].

However, Renewable Energy Sources (RES) like wind and solar are intermittent and not neces-sarily generating electricity that is directly compatible with the parameters of the grid. This is especially true for Photo Voltaic (PV) systems which generate Direct Current (DC), and wind power which often generate variable frequency Alternating Current (AC). Thus, these intermittent sources have to be connected to the grid using power electronic converters which effectively decouples the properties of the electric machine from the grid properties such as frequency and voltage. In addition, the system will to a large degree transition from having centralised generation to distributed generation[8].

This new system topology dominated by converter connected generation may bring challenges to the conventional operation of the power system when the share of RES becomes significantly large. Challenges may include problems related to the security of supply, capacity adequacy, power system stability and reliability. The conventional operation of the grid has until now been based on highly controllable rotating machines using either thermal energy from fossil fuels or hydropower to drive a turbine that in turns drive a generator that is directly coupled to the grid at the synchronous speed/frequency, i.e. the generator stator frequency is equal to the grid frequency. This topology has made it relatively easy to adjust and balance the grid in case of contingencies, in addition to being able to support the grid with an inertial response and ancillary services such as voltage support and frequency support.

However, as the frequency of the converter connected generation is effectively decoupled from the grid, so is the available inertia of the generator/turbine. In addition, converter connected generation is often controlled to inject all power available from the source, and is less likely to be able to participate in frequency control such as Frequency Containment Reserves (FCR) and Frequency Restoration Reserves (FRR)[9], which may be a threat to the secure system operation.

Transmission System Operators (TSOs) have therefore implemented new grid code requirements that power generation connected through converters must comply with to be allowed to connect to the grid. Notable requirements include the ability to provide frequency- and voltage support, have adequately fault ride-through (FRT) capabilities, and easy determination of stability limits and operating range[10]. It is therefore of interest to develop technologies that equip also converter connected generation with these abilities, and a method that has been shown to be very promising is the Virtual Synchronous Machine (VSM) control technology. A Virtual Synchronous Machine is a control method used to control converters in such a way that many of the attributes of the conventional Synchronous generator (SG) are preserved, i.e. the converter can be seen as an SG by the grid. Thus, VSMs are designed to possess many of the characteristics inherently found in conventional SGs, and are therefore also, to a certain degree, capable of providing the grid with ancillary services. This is vital to facilitate an accelerated integration of renewables. It is therefore of academic interest to study different aspects related to the VSM, and to validate its performance under different operating conditions. Through this research, the academic society can motivate utilities and energy companies to increase their investments in renewables and to trust that the new technologies introduced, such as the VSM, does not put system integrity at risk.

Many studies have been performed to prove the effectiveness and the functioning of the VSM concept for providing ancillary services to the grid, but very few studies look into the subjects related to VSM and transient power system stability. Furthermore, one of the main challenges with VSM controlled voltage source converters is that they lack the ability to limit the current, possibly leading to excessively high currents both during- and after a fault has occurred. This can be extremely harmful to the converters, which in most cases disconnect to minimise damage.

As such, converters are known to have very poor Fault Ride Through (FRT) capabilities.

In this thesis, a transient stability analysis will be carried out using classical power system stability tools for a system consisting of a VSM. The study will assess the applicability of classical stability analysis methods, known from conventional SG, when analysing VSM-controlled converters.

If the classical analysis is shown to be unfeasible, a modified analysis method also applicable to the VSM should be outlined, thus drastically simplifying their introduction to the grid.

Furthermore, the thesis will look into how modifications to the VSM control system can enhance system stability using very little effort and without changes to the power system topology. These modifications to the control system will aim at both improving the transient stability and reducing the possibility of operating at too high converter currents.

This is motivated by the ongoing energy transition described above, where VSMs are considered a key solution to the successful integration of renewables. In addition, easy determination of stability limits is specifically mentioned as a key characteristic of the VSM to comply with new grid codes, and it is therefore of interest to investigate whether methods known from the SG can be applied also to the VSM. Also, it will be of importance to demonstrate that VSMs can be analysed analytically when investigating their stability, and that they can actually increase stability limits without adding the large costs normally required when enhancing the stability of a system consisting of conventional SGs.

1.2 Objectives

The objectives of this master’s thesis are to investigate the transient stability of a power system consisting of a Virtual Synchronous Machine (VSM) based Wind Energy Conversion System (WECS), propose methods of improving the stability of the system if possible, and to simulate both the original system, as well as the improved system, in the MATLAB/Simulink environment to verify the functioning of both the stability analysis and the proposed enhanced system controls.

As such, the thesis consists of two main research objectives plus some add-on objectives, where the two main objectives are; perform a stability analysis of the original system, and improve the control structure to achieve enhanced stability. The stability analysis aims at investigating the applicability of well-known analytical stability assessment methods from the conventional synchronous generator when analysing thevirtualsynchronous generator, and comparing the analytical results with simulation results. The objective of improving the system stability revolves around adding new control loops to the VSM control algorithm to improve the dynamic response when subjected to large disturbances, thus improving the transient stability and mitigating high converter currents.

These objectives are largely motivated by the factors outlined in Section 1.1 and are thus seen in the context of the technological advancements and state-of-art of the energy system. In addition, the thesis objectives are motivated by the recommendations for future work pointed out in the preliminary study preceding this thesis, and the fundamental drive behind any research, which is to advance on the state-of-art within a given field of study.

More specifically, the objectives can be divided into five parts listed as follows:

• Acquire sufficient knowledge on the complex theory related to power system stability and associated methods of stability assessments.

• Perform an investigation into the transient stability of a given VSM system using related theory known from classical stability analysis. The objective aims at investigating whether classical stability analysis known from the conventional synchronous generator is also applicable to the VSM. If this is not the case, a method also applicable to the Synchronverter should be derived for easy identification of stability limits.

• Propose new control loops that can be added to the Synchronverter VSM to enhance the system stability and improve the dynamic response of the Synchronverter control system, with a special focus on mitigating the converter current without affecting the steady-state characteristics.

• Construct a test-bed in the MATLAB/Simulink environment to test- and validate the theoretical concepts and analytical results, and to verify the effectiveness of the proposed enhanced control structure.

• Put forward well-judged tasks that should be further investigated in future research based on the experience and results obtained from the thesis work.

1.3 Contribution

This thesis’s contribution to the already established research on the topic will be to create an analytical model that can be used to investigate the Synchronverter dynamical response, and provide a detailed comparison between the simulated system and the obtained analytical model.

The analytical model will further be utilised in a modified Lyapunov method for investigating the transient stability of the VSM.

Furthermore, a novel, enhanced Synchronverter control structure will be proposed, drastically improving the dynamic response of the Synchronverter control system when subjected to a contingency and thus advancing the transient stability of a power system consisting of a VSM-connected wind turbine. More precisely, the use of a virtual resistor and artificial damper windings will be adapted to the Synchronverter control system, yielding both a dynamical response and stability limits far superior to the original system.

The proposed control structure will require a minimum amount of both tuning and increase in controller complexity. Furthermore, it will be easily implemented, and thus make the VSM an even more attractive solution in the energy transition by simplifying the adaption of the VSM to systems that dictate high demands related to power system stability and security.

In addition, parallel to the thesis work, a scientific paper has been written and submitted for publication based on the results of the specialisation project. The paper, having the title Small-signal Modelling and Tuning of Synchronverter-based wind energy conversion systems, is currently in major revision, and is attached in Appendix E for the completeness of the contribution of the specialisation project and the master’s thesis as a whole.