UPTEC E 20006

Examensarbete 30 hpJuni 2020

Modeling and comparative analysis of different grid-forming converter control concepts for very low inertia systems

Martin WestmanEllen Nordén

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Modeling and comparative analysis of differentgrid-forming converter control concepts for very lowinertia systemsMartin Westman & Ellen Nordén

As renewable power from DC sources are constantly increasing their power generation share compared to the high inertia generators that provide robustness to the grid, the overall stability of the grid decreases. Grid forming converter could be the solution to this problem.

This thesis includes a pre-study of grid forming control methods, implementation of the most promising and relevant methods in a generic PSCAD modeling environment for comparative analysis and for establishing pros and cons. Lastly, studying the system impact of each grid forming control method through small-signal stability and fault analysis.

Four methods of grid forming were implemented and evaluated during the course of the thesis, which were: Droop control, Virtual Synchronous Generator control, Power Synchronization control and Synchronous Power control. All methods fulfilled the criteria for successful implementation with good results. For further developments, we would recommend Synchronous Power control and Virtual Synchronous Generator control for their development potential and operational width.

Tryckt av: UppsalaISSN: 1654-7616, UPTEC E20006Examinator: Mats EkbergÄmnesgranskare: Cecilia BoströmHandledare: Pinaki Mitra

Popularvetenskaplig sammanfattning

Dagens elnat far idag sin stabilitet och robusthet av bland annat de synkrona maskinerna som tillforsvangmassa och effekt till natet. Ett stabilt elnat innebar att frekvensen pa natet halls konstant, kring detriktvardet varje land har. Ett instabilt nat skulle orsaka enorma problem for samhallet som helhet, pagrund av att vi idag ar beroende av en palitlig eltillforsel till samhallets alla delar.

Historiskt sett har elnatet over de flesta delar av varlden genererats av forbranning av fossila branslen somskapat energi fran roterande massor som i sin tur genererar elektricitet. En vanligt forekommandeenergikalla ar kolkraft, som bland annat orsakar massiva koldioxidutslapp som i sin tur bidrar till denglobala uppvarmningen. Detta har i sin tur lett till att forskning inom fornyelsebar elgenerering har okatenormt. Man har sett en stor uppgang for implementering av energikallor som vind- och solkraft pa senarear. Dessa kallor ar kopplade till natet via vaxelriktare och bidrar darfor inte idag till natstabilitet sasomroterande maskiner gor. Dessa fornyelsebara energikallor stodjer effekttillforseln och darmedfrekvensstabiliteten som de roterande maskinerna ger natet. Ett satt for att veta nar natet behover mereffekt ar via frekvensmatning som ges av de roterande maskinerna, och skulle dessa forsvinna maste andralosningar hittas.

En av dessa losningar ar ett koncept som kallas grid-forming converters. Tanken med dessa ar att uppfyllaelnatets effektbehov utan att mata den befintliga frekvensen. Detta gors da istallet via kontrollalgoritmersom kollar pa effektbehov och tillforsel pa natet. Detta gor det mojligt att styra natet istallet for att foljadet.

Malet med detta exjobb ar att utforska vilka metoder som forskats pa, implementera fyra av dessa somverkar visa goda egenskaper i ett simuleringsprogram. Simuleringsprogrammet heter PSCAD och ar ett avutvecklingsverktygen som anvands pa ABB for systemtester. Malet ar aven att utfora tester for att kunnajamfora dessa metoder mot varandra for att till sist gora en analys kring metodernas fordelar ochnackdelar.

Resultatet av arbetet ar fyra fullt fungerande implementerade grid-forming metoder. Dessa harimplementerats och testats i en forenklad elnatskonfiguration for att halla fokus pa metodernas generellabeteenden. Testerna som gjorts ar signalanalys samt kortslutningstester for att testa parameterbeteendenoch vad som hander vid ett stort fel. Samtliga metoder visar lovande resultat och uppfyller samtliga kravsom forvantas av dem. Framtida utvecklingsmojligheter inkluderar en mer omfattande matematisk analyssamt mer iterativ testning av metodernas beteende. Innan en storre analys kan goras pa de tester somgjorts skulle fler tester behova goras i en mer omfattad miljo.

Acknowledgments

Firstly, we would like to extend our gratitude to our supervisor Pinaki Mitra for his time invested inhelping and discussing problems and ideas during the entirety of the thesis project. We would also like tothank the department of System Design at ABB G&PQS for they warm welcome and support during thethesis.

Secondly, we want to thank our thesis supervisor at the university, Cecilia Bostrom as well as Sara Anttilafor guidance and support in keeping us on track and providing feedback on the report.

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Collaborators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Project goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Delimitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Work division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theory 32.1 Electrical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Voltage Source Converters (VSC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 PWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.3 SPWM control scheme for VSCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.4 Per Unit System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.5 Three-phase system representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.6 Clarke & Park Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.7 Electrical Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.8 Overcurrent protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.9 RMS Fault ride-through method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.10 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.11 Power grid system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Automatic Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 PID controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.3 Control system filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Grid Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Grid Following Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.2 Grid Forming Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.3 Control Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Grid forming control methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.1 Droop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.2 Virtual Synchronous Generator (with inertia) . . . . . . . . . . . . . . . . . . . . . . . 172.4.3 Virtual Synchronous Machine, without inertia (VSM0H) . . . . . . . . . . . . . . . . . 192.4.4 Power Synchronization Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.5 Synchronous Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.6 Virtual Oscillator Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Method 243.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.1 PSCAD modeling and testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.2 MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3

3.2 Pre-study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2.1 Choice of Grid Forming Converter-methods . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.1 Modeling of converters in PSCAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.2 Tuning of controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.3 Simulations in PSCAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.4 Small Signal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.5 Short Circuit analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Results 324.1 Final models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.1 General system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1.2 Inner Control loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.3 Droop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.4 Virtual Synchronous Generator Control . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.5 Power Synchronization Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.6 Synchronous Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.7 Fault detection and handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Small Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.1 Droop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.2 Virtual Synchronous Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.3 Power Synchronization Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.4 Synchronous Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.5 Inner loop performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2.6 Comparative result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.3 Fault behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.3.1 Droop Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.3.2 Virtual Synchronous Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.3.3 Power Synchronization Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3.4 Synchronous Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.3.5 Comparative result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5 Discussion 665.1 System analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.2 Test configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.3 Droop control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3.1 Model design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.3.2 Small Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.3.3 Fault analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.4 Virtual Synchronous Generator Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.1 Model design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.2 Small Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.3 Fault analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.5 Power Synchronization Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.5.1 Model design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.5.2 Small Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.5.3 Fault analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.6 Synchronous Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.6.1 Model design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.6.2 Small Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.6.3 Fault analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.7 Comparative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4

5.7.1 Small Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.7.2 Fault analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Conclusions 74

7 Appendix 797.1 MATLAB-code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2 Fault analysis - Droop control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.3 Fault analysis - VSG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.4 Fault analysis - PSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.5 Fault analysis - SPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Nomenclature

DC Direct Current

GFC Grid forming converter

HPF High pass filter

HVDC High-voltage direct current

IGBT Insulated-gate bipolar transistor

IPL Instantaneous Penetration Limit

LPF Low pass filter

p.u. Per Unit

PCC Point of Common Coupling

PLC Power loop controller

PLL Phase Locked Loop

PSC Power Synchronization Control

PSCAD Power System Computer Aided Design

PSL Power synchronization loop

PWM Pulse Width Modulation

SCR Short Circuit Ratio

SG Synchronous Generator

SM Synchronous Machine

SPC Synchronous Power Control

SPWM Sinusoidal Pulse Width Modulation

VA Virtual Admittance

VOC Virtual Oscillator Control

VSC Voltage Source Converter

VSG Virtual Synchronous Generator

VSM0H Virtual Synchronous Machine Zero Inertia

1. Introduction

1.1 Background

The electric power system over the world is currently going through an immense change - with the growingneed for electricity and the fact that greenhouse gas emissions globally need to be reduced. Over the past20 years the energy consumption of renewable sources as solar- and wind power has increased andconsidering modern renewables was the total share of the energy consumption globally in 2018 almost 11%, and the share is expected to grow over 15 % by 2030 [1].

This implies that the amount of installed non-synchronous based generation is increasing at a significantrate while the amount of installed synchronous generation relative to the non-synchronous generation,decrease. This entails challenges concerning the grid and its stability and the impact on the system isincreasing as the renewable penetration grows. Renewable sources like wind and solar power, are to a highextent connected to the grid via electronic power converters, which does not contribute to inertia in thesystem and it will cause a greater rate of change in the frequency, hence they cannot contribute to gridstability. Furthermore, the current power electronic converters struggle to operate under highly variableconditions. Therefore, the instantaneous penetration limit on the grid that can be achieved is constraineddue to the existing converter technology [2].

A possible solution to attain higher levels of renewable power generation while still preserving the gridstability, could be grid forming converters. Grid forming converters are voltage source converters that canreliably operate and maintain a stiff voltage even during highly variable conditions. The main mission of agrid forming converter is to replicate the behavior of the synchronous machine via different control strategies.Additionally, they can contribute to grid stability by providing voltage and frequency support [3].

1.1.1 Collaborators

This thesis has been done at ABB Power Grids Sweden - Grid & Power Quality Solutions. They haveprovided deep knowledge in the respective area, as well as guidance and some research materials.

1.2 Project goals

The goals of this project is to gain understanding of the grid-forming converter control concept and be able toidentify the most important and relevant grid-forming control methods and typologies. Further, the goal isto implement identified control methods in a generic PSCAD modeling environment for comparative analysisand then analytically compare pros and cons of different variations of the methods. Finally, studying thesystem impact of each grid-forming control method through frequency, transient and small-signal stabilityanalysis.

1

1.3 Delimitation

This Master thesis investigates six different grid forming converters that have been researched on, but thedevelopment of functioning models is limited to four converter control methods. The control methods areDroop control, Virtual Synchronous Generator, Power Synchronization Control and Synchronous PowerControl. The systems studies are limited to an average voltage source system and source harmonics aretherefore neglected. The average converter used are one where the six switches are replaced with threeideal ac voltage sources.

The control methods will be evaluated in the aspects of signal dynamics, transient behavior and fault ridethrough capabilities. The fault study will be limited to the symmetrical three phase fault. The study asa whole will be an empirical one, with no development of state space models as the thesis goal describes ageneral study of grid forming models.

1.4 Work division

The main work was to implement, test and analyze four different grid forming converters, and the workwas naturally divided for Martin and Ellen to be responsible for two methods each, includingimplementation, test, discussion and conclusion. Pre-study, comparison and conclusion were performedtogether, but the rest of the report and work was divided as follows;

Ellen was responsible for:

• Grid dimensioning

• Power Synchronization Control

• Synchronous Power Control

Martin was responsible for:

• Fault detection and handling

• Droop Control

• Virtual Synchronous Generator control

• (Block-diagrams)

2

2. Theory

2.1 Electrical Concepts

2.1.1 Voltage Source Converters (VSC)

A Voltage Source Converters’ basic principle is that it converts DC to AC voltage. The VSC consists of an namount of switches (IGBTs or Thyristors for example) which are oriented in an H-bridge configuration thatare switched on an off according to a predefined control scheme. This control flexibility allows for control ofvoltage magnitude, phase angle and frequency at its output [4].

2.1.2 PWM

Pulse Width Modulation (PWM) is a method that can adjust average voltage output signal. The PWMsignal is generally a control signal that enables switching of switches with varying duty cycle, which is theratio of on time of the switch. With a lower duty cycle, the switch is conducting a smaller fraction of theperiod, resulting in a decrease of voltage. [5]

2.1.3 SPWM control scheme for VSCs

The VSC:s are generally switched with a Sinusoidal-PWM switching scheme, which is a softer switchingscheme than pure PWM. It consists of a sinusoidal reference waveform with grid frequency and amplitudeVref . This sinusoidal is compared to a triangular carrier waveform with constant amplitude Vtri and frequencyftri, which also is the switching frequency of the VSC. There are also two modulation ratios connected toSPWM, frequency modulation ratio mf and amplitude modulation ratio ma, and they are calculated asstated in equation 2.1 and 2.2.

mf =ftrif1

(2.1)

ma =VrefVtri

(2.2)

Every leg of the VSC is controlled using the control scheme shown below in figure 2.1. The triangular carrierwave is compared to the sinusoidal reference wave and depending on when the triangular wave is larger orsmaller than the sinusoidal the switches in a VSC leg will open or close. Only one of the switches are openat any given time per leg.

3

Figure 2.1: The control scheme of bipolar SPWM.

If the amplitude modulation ratio exceeds 1 the system becomes over modulated, and the peaks of theoutput sinusoidal from the VSC becomes ”chopped off”, and we lose linearity as well as introduceunwanted low-frequency harmonics.

In order to increase the modulation ratio, and thereby increase the output voltage as well as decrease theTHD in the output current, Common-mode injection can be implemented [6].

2.1.4 Per Unit System

The Per Unit system is a way of expressing the system parameters in a normalized unit. This Per Unit (p.u.in short) normalization applies for power, voltage, current and impedance. The conversion between regularunits and p.u. is done by dividing the regular unit by the systems rated unit magnitude as seen in equation2.3.

per-unit quantity =actual quantity

base value of quantity(2.3)

The base value is calculated with Ohm’s law.

This conversion greatly simplifies the overview between systems by normalizing the system units, even thoughthey have different ratings. Since nominal values of systems parameters hover around 1, implementation ofregulators and its parameters are also kept around 1, which cuts down on regulator tuning complexity [7].

2.1.5 Three-phase system representations

The most usual three-phase representation is the ABC-frame, where phase A, B and C are placed 120

separate from each other. The A, B and C components can together represent any given phasor in a plane.Two other ways of representing the three phase system are the dq-frame and αβ-frame. Those frames arethe main classes of two-dimensional frames and are used to simplify analysis and control.

4

The dq-frame is a rotating frame which is rotating with the magnetic field, hence the magnitude of thephasors becomes constant. When synchronous the rotation is perpendicular to either the d or q axis, whichresults in one of the axes being around zero as the other changes in amplitude (as seen in figure 2.2). Thiscan be used for simplifying a sinusoidal problem to an equivalent DC-command problem. This entails thatPID-regulators can be used for the control.

The αβ-frame is a stationary frame where its magnitude has a sinusoidal behavior. The two phases areplaced perpendicular to each other and are in the same plane as the three-phase (ABC) reference frame [8].

Figure 2.2: Representation of the different reference frames [9].

2.1.6 Clarke & Park Transformations

The Clarke and Park transformations are used to change the representation of three phase phasors in orderto simplify the analysis and control of a three phase system. The Clarke and Park transformations arewidely used in control system because of their simplification of the three phase system.

The Clark transformation converts the three-phase quantities (ABC vectors) into balanced two-phasequadrature quantities (αβ). The αβ-frame is a stationary frame where its magnitude has a sinusoidalbehavior. The two phases are placed perpendicular to each other and are in the same plane as thethree-phase (ABC) reference frame[8]. The transformation from ABC-frame to the αβ-frame can be seen inequation 2.5. In order to transform from αβ-frame to ABC-frame the inverse of the Clarke transformationmatrix (eq.2.4) is multiplied with the αβ-frame.

Tαβ =2

3

1 − 12 − 1

2

0√32 −

√32

12

12

12

(2.4)

vαvβvγ

= Tαβ

vavbvc

(2.5)

This transformation can be utilized in some of the control systems that will be examined in this thesis, butis less used than its counterpart, the Park transformation.

The Park transformation changes the representation of the three phase sinusoidal to two DC-components,namely the d and q components. This embodies the αβ property of representing the system with two phasesbut rotates the reference frame at the ABC synchronous speed. This results in two DC-valued phases, thatcan be controlled using simple PID-control because of their linearity. To transform from ABC-frame to dq-frame the Park transformation has a transformation matrix, like the Clarke transformation, which is usedin the same way, as can be seen below in equation 2.6 and 2.7.

5

Tθ =2

3

cos(θ) cos(θ − 2π3 ) cos(θ + 2π

3 )−sin(θ) −sin(θ − 2π

3 ) −sin(θ + 2π3 )

12

12

12

(2.6)

vdvqv0

= Tθ

vavbvc

(2.7)

The Park transformation is the most common transformation used for grid control systems, which will beclear from the grid forming converter concepts below [9].

2.1.7 Electrical Faults

Electrical failures in an electrical system can arise because of various reasons, for example failure inequipment or environmental conditions such as lightning or earthquakes. These failures often lead to largefault currents (short circuit currents), which for instance can lead to arcing, mechanical stresses, heat, noiseor explosions. The resulting fault current is determined by the impedance between the machine voltageand the fault and by the internal voltages of the synchronous machines.

In order to avoid electrical faults, a fault analysis can be made, which reduces the risk of large losses in thesystem and increases the reliability and safety. Furthermore, it is possible to discover weak points, problemareas and identify solutions to existing problems. Also, one important purpose of doing a fault analysis isto determine the magnitude of the maximum currents generated by the fault, in order to ensure that theequipment in the system can survive a fault.

There are two main types of faults: symmetrical and asymmetrical faults. The main difference betweenthem is that when a symmetrical fault occurs the system will remain in balance, whilst the system becomesunbalanced if an asymmetrical fault arises. The symmetrical fault, being a fault across all phases presentsthe largest current surges but are relatively rare compared to an asymmetrical fault, but easier to analyze.

There are different types of faults, depending on where the fault occurs. The most common ones are:one phase to ground, phase to phase, two phases to ground and balanced three phase. When doing a faultanalysis on an unbalanced fault, a balanced three-phase network can be divided into three sequence networks;positive, negative and zero sequence. These network circuits can then be connected in different ways basedon which fault it is, to continue the fault analysis and establish the fault current [10] [11].

Three-phase fault

A three-phase fault is a balanced symmetrical fault, which means that only the positive sequence networkneeds to be considered. In this type of fault, all three phases are shorted together. It is the least commonfault but the one that can cause largest fault current and is therefore a good representation of theworst-case scenario considering faults.

When calculating the fault current, the following assumptions can be made [10]:

• Transformers can be represented by their leakage reactances

• Transmission lines are defined by their equivalent series reactances

• Synchronous machines (and often induction motors) are represented by a constant-voltage sourcebehind a subtransient reactance

• All non-rotating impedance loads are neglected

6

The three phase fault can be divided into four segments as seen in figure 2.3 and 2.4. Segment 1 showsthe nominal voltage/current operation, segment 2; the three phase fault, segment 3; the recovery phase andlastly the system returns to nominal voltage/current operation in segment 4. The current shown in figure2.4 is the current on the converter side, hence not were the fault occurs on the grid side.

Figure 2.3: The voltage during a three phase fault, with the sequences: (1) nominal operation, (2) the fault,(3) recovery and (4) nominal operation again.

Figure 2.4: The current (on the converter side) during a three phase fault, with the sequences: (1) nominaloperation, (2) the fault, (3) recovery and (4) nominal operation again.

To calculate the fault current for a three phase fault, a line diagram is used and only the positive networksequence is needed. To calculate, Ohm’s law is used, with a voltage of 1 p.u. and the total impedance inp.u, hence the fault current is dependent on how big the total impedance is. The per unit and base valuesare calculated as in section 2.1.4.

7

2.1.8 Overcurrent protection

In a system with a VSC and control loops, the inner control loop is responsible for the overcurrentprojection of the system, since the converters are prone to break upon too high currents. Transients, are acommon occurrence on the grid which happen due to unexpected load changes or short circuits forexample.

Synchronous generators can handle current spikes of about six times their rating for shorter periods of time,compared to the VSC:s that run nominally closer to their power ratings in order to not over dimension theswitches, and are therefore more prone to breaking during these events. Thus, a control system with thecapabilities to prevent the destruction of the VSC:s is crucial. This is usually done in the inner control loopswhich measure current and voltage, and limits these quantities inside their acceptable boundaries. [12]

2.1.9 RMS Fault ride-through method

As power ratings on connected systems increase, so does the electrical faults during power variations.Traditionally synchronous generator-based systems handle variations better because of its physicaldampening behavior and the resilience to high current spikes, while VSC-based solutions do not. Thesesystems need smart fault detection methods in order to dampen the power spikes to protect the hardware.

A commonly used fault detection method is by examining the RMS voltage or current at the Point ofCommon Coupling (PCC), hence at the grid-side, as the RMS value will either drop below or rise abovea chosen threshold [13]. This method does however have the downside of needing one cycle to reach thecorrect RMS value [14]. The reason for this delay being the analytical calculation of RMS values seen belowin equation 2.8.

VRMS =

√1

T

∫ T

0

V 2cos2(ωt)dt (2.8)

VRMS is the RMS voltage, V is the sinusoidal voltage and T equals to the period time, and the computationis done continuously on all phases, on the outlook for deviating behavior.

2.1.10 Inertia

Inertia refers to the resistance to change. In an electricity grid, inertia represents large rotating masseswhich are the large synchronous generators that are directly connected to the grid. These rotating masseshold a kinetic energy which provides stability. Since their rotating speed is connected to the grid and itsfrequency, they counteract the change in frequency. This contributes to a mechanical inertia in the system,which helps preventing instability and disturbance.

The frequency in a system shows how well-balanced electricity production and consumption are at everygiven moment. If the consumption increases, the frequency will decrease (or the opposite if theconsumption decreases), but the inertia in the system will make the decrease happen slower. The moreinertia in the system, the smaller will the impact between consumption and production have on thefrequency [15].

The relationship between the frequency and power balance is described by the Swing equation:

Jω · dωdt

= ∆P (2.9)

where J is the inertia [kgm2], ω is the rotational speed [rad/s] and ∆P is the difference between currentproduction and consumption [W].

8

H =Jω2

0

2Sbase(2.10)

The inertia of the synchronous generator is also defined as equation 2.10, where H is the synchronousgenerators inertial constant, Sbase is the base power rating and ω0 is the generators rotational speed [16].

2.1.11 Power grid system

An electrical grid system is generally consisting of a type of generating station which provides electricity, atransformer, transmission lines and a type of load. A transmission line is generally represented as a seriesimpedance (consisting of an inductance and a resistance), often together with some shunt admittance [17].

When discussing the power grid and different sources of generation, one often used concept is theInstantaneous Penetration Limit (IPL), which can be described by following equation:

IPL =PV SCPdemand

· 100% (2.11)

which means that the IPL describes how much of the total demand can be delivered by the power from theVSC [18].

Weak vs Strong grid

A grid can either be described as a ’strong’ or a ’weak grid’ and is represented with the Short Circuit Ratio(SCR). A strong grid is more stable and has less impact from disturbances. How strong a grid is can bedefined by the capability to maintain a constant voltage independently of the load. In general, a higher valueof the inductance and resistance means a higher grid impedance, i.e. a weaker grid. The SCR is defined by:

SCR =SacSrated

(2.12)

and

SCR =Xgrid

Rgrid(2.13)

where Sac is the capacity of ac-short circuit and Srated is the rated capacity. A general guideline to knowthe strength of a grid described by the SCR is that SCR ≤ 3 describes a weak grid and SCR greater than 3describes a strong/stiff grid [19] [20].

9

2.2 Automatic Control

Control theory is based around the concept of controlling physical phenomena, this encapsulates everythingfrom electrical grid stability to the operation and stability of an aircraft [21]. For this Master thesis control,theory will be used for ensuring fast and stable performance of the systems.

2.2.1 PID controllers

The PID regulator is the most common regulator used in the industry [22]. PID stands for ProportionalIntegral Derivative and is generally defined as in equation 2.14. Regulators are used to control an outputsignal according to a signal values, by continuously trying to minimize the error between them. Theminimization of the error can be realized in different ways, namely using proportional (P), integral (I ) andderivative (D) terms of the error which will result in different response of the regulator system.

u(t) = Kpe(t) +Ki

∫e(t)dt+Kd

d

dte(t) (2.14)

The error e(t) is defined as the error between the reference signal and the output signal:

e(t) = r(t) − y(t) (2.15)

The goal of the PID controller is to follow a set reference value (r) as fast and accurately as possible. Thedifferent components of the regulator Proportional, Integral and Derivative has different ways ofeliminating the control error (e).

The proportional (P) regulator has an output that is proportional to the error (u(t) = Kp(r(t) − y(t))).This results in a controller that never reaches steady state and often has a steady state error, which is anoffset compared to the reference value.

The proportional integral (PI) controller adds the integral action on the error. This will eliminate thesteady state error but results in the regulation of the system taking longer to settle.

The last type of regulator is the proportional, integral and derivative (PID) regulator and has the benefitsof the PI regulator, with the added benefit of also taking the derivative of the error into account. This candecrease overshoot, decrease settling time and somewhat improve stability of the system [22].

2.2.2 Transient Response

The transient response of a system describes how it behaves under sudden change of input [22]. Theunderstanding of an electrical systems transient response is of utmost importance, in order to be able topredict how the system will behave under unpredictable situations such as sudden disturbances to steadystate operations. For the case of grid converters these transient quantities can be instabilities in the gridthat is compensated for. The transient properties of a system are often determined by its control loops, asthey can control how properties such as rise time, overshoot and settling time are managed. Transientresponse can also be determined by a mechanical factor.

10

Figure 2.5: Transient response [23].

The main parameters regarded in transient response is as mentioned above; rise time, overshoot and settlingtime. The rise time is defined as the time it takes for the system to reach 90% of the set point value. Theovershoot of a transient is by how much the control signal misses the reference signal as it tries to settle,this quantity is given in percent. The cause of an overshoot is that the system is not dampened enoughor that the rise time is too high (slow) for the system to slow down before reaching its set point, thereforeovershooting its target. The settling time determines how long it takes for the signal to settle within a errormargin to the set point value [24].

2.2.3 Control system filtering

When designing a control system, noisy measurement signals has to be taken into account. If the inputsignals to the controllers are too noisy, that might result in unstable regulatory conditions. To combat this,filtering can be implemented at the inputs, to ensure a more stable operation. The low-pass filter, whichattenuates frequency components above a certain frequency level, as seen in Laplace form in equation 2.16.

H(s) =ωc

s+ ωc=

1

1 + sωc

=1

1 + τs(2.16)

The high-pass filter has the same function as the low-pass filter, only inverted, as it attenuates frequencycomponents below a selected frequency. The Laplace domain representation can be seen in equation 2.17

H(s) =s

s+ ωc=

sωc

1 + sωc

=τs

1 + τs(2.17)

The transfer functions for the given filters consist of controllable parameters, were ωc is the given cutofffrequency and τ (τ = 1

2πf ) being the corresponding time constant for the cutoff frequency [25].

11

2.3 Grid Converters

As the grid inertia decrease and the steady flow of power to the grid becomes more variable as more renewableenergy sources are being deployed, the grid will start using more grid converters in order to control the flowof power to the grid. In table 2.1 a general comparison between two grid converters that will be discussedfurther in the report is presented [26].

Table 2.1: General comparison between Grid Forming and Grid Following converters.

Grid Following Converter Grid Forming ConverterControls Current and phase angle Controls Voltage magnitude and frequencyCannot operate in standalone-mode Can operate in standalone-mode

Cannot achieve 100% grid penetration Can achieve 100% grid penetration

For the definition of what 100 % grid penetration means, see equation 2.11.

2.3.1 Grid Following Converter

Grid Following Converters mimic the instantaneous inertial response of Synchronous Machines. This typeof converter can only operate under grid connected mode which follow the grids behavior and injects powerwhen needed. The Grid Following Converter can be modeled as a current source connected in parallel tothe grid. The converter synchronizes with the grid frequency utilizing a phase locked loop (PLL), as wellas measure phase and voltage amplitude, which is used as the reference to the control system. The controlsystem translates the measurements to inverters control signals, which compensates for possible errors inactive and reactive power on the grid. This type of converter is the dominant type present on the grid as ofnow.

Figure 2.6: The model representation of the Grid Following Converter [27].

These types of converters do however work under the assumption that there is a stable voltage referenceto synchronize to (usually from SGs) and will therefore never achieve 100 % penetration on the grid. Thisposes the largest problem with Grid Following Converters, that if (when) the number of SGs decrease as aconsequence of the rise of renewable energy sources, Grid Following converters will not be suitable for use[28].

Phase Locked Loop

Phase Locked Loop, or PLL for short is a control system for synchronizing the phase of the input to theoutput. This is implemented in some grid solutions where an easy way of measuring frequency is soughtafter. The control system is fed with voltage measurements and outputs the corresponding frequency neededto synchronize the rotational speed of the rotating dq-reference system [29].

12

Figure 2.7: The general design of the PLL [30].

In figure 2.7 the basic block diagram of the PLL is presented. It inputs the voltage in dq-domain and outputscorresponding phase angle of the grid in dq-form.

2.3.2 Grid Forming Converter

Grid forming converters are much like Grid Following Converters when it comes to the basic hardwareconcept. However, the major thing that differentiates the two is their manner of operation. The gridforming converter does, opposed to the Grid Following Converter not use the reference frequency of thegrid into account, but rather sets its frequency reference to the local grid frequency and outputs the neededactive and reactive power in order to stabilize the grid. The grid forming converter proposes to ’lead ’ thegrids behavior, rather than to follow it. The grid forming converter can therefore be modeled as a lowimpedance voltage source with the main goal of enforcing an amplitude and frequency at its output, ratherthan conforming to the grid’s behavior [31].

Figure 2.8: The general design of the Grid Forming Converter.

13

The grid forming converter also offers some advantages over the grid following converter, such as atheoretical 100 % penetration level, since the operation of the converter is not dependent on a stablevoltage reference since that is set in the converter. Good theoretical black start capability (restoring a partof a grid or an electrical power station without being dependent of the external electric power transmissionnetwork) is also a benefit [32].

Grid forming converter do however have some downsides. Since they act as voltage sources overcurrentprotection is needed for situations when transients occur (fast load change, short circuit etc...). Somecontroller-based safety features can however be implemented in order to ameliorate these current spikes [28].

Figure 2.9: The model representation of the Grid Forming Converter [27].

2.3.3 Control Loops

For grid forming and following converters to behave in a sought-after way, different constellations of controlloops are needed. These control loops translate measured quantities and reference values to signals thatcan be used to control the inverter in order to achieve a reference output. Depending on the converter typedifferent amount of control layers will be implemented in order to limit the output current or regulate certainfeedback parameters. [27]

Figure 2.10: The general design of the control loops [27].

14

Outer Control Loop

The outer-most control loop is commonly the placeholder for the high system level control, which is wherethe control methods are implemented, which will be discussed further below. The inputs to this controllayer often consist of measurements from the PCC and the output of the converter in order to determinepower levels as well as sought-after quantities of voltage, current and frequency. The power measurementsare calculated using the voltage and current in dq-form as seen below [27].

P = vdid + vqiq (2.18)

Q = vqid − vdiq (2.19)

The outer control loop will in most control methods output control signals to the inner loop.

Inner Control Loop

As the inner control loop receives reference data from the outer control loop it acts on this information bycontrolling the VSC:s to achieve the wanted output from the converter. This could include regulating thevoltage, current or frequency of the converter. The inner control loop is generally comprised of a voltagecontrol loop and a current control loop. The sampling frequency of the inner loop is much higher than thatof the outer control loop (at least 10x). This is to ensure decoupling of the signals.

The voltage control loop typically receives voltage references in dq-form from the outer control loop and issubtracted from the actual d and q component of the output filter to generate the difference between thereference and actual value. The delta is then PI-regulated to reach a stable output [27].

Figure 2.11: The general design of the voltage control loop.

The references generated from the voltage control loop is then fed into the current control loop which hasa similar layout to that of the voltage control loop, with the addition of a filter compensation component(ωL).

15

Figure 2.12: The general design of the current control loop.

The current control loop output is fed into a dq to abc transformer, which generates three sinusoidals (ma,mb

and mc) which are used to control the switching generation shown in figure 2.13.

Figure 2.13: The general design of the SPWM switching generation.

The switching traditionally is done according to the SPWM switching scheme seen in figure 2.1, where thegenerated sinusoidals are compared to a triangle wave in order to switch the inverters switches (S1 to S6) inthe correct order.

2.4 Grid forming control methods

2.4.1 Droop Control

Droop control is one of the more widely studied control methods for grid forming converters and its controlphilosophy is quite simple. The controller regulates the output voltage frequency and magnitude by alteringthe set-points for active and reactive power, which are computed using equation 2.20 and 2.21. The computedactive and reactive power is then used for calculating the reference values of the output frequency and voltagethat corresponds to these set-points. According to these parameters the modulation of the inverter is changedto accommodate the correct output.

16

Figure 2.14: The general Droop Control scheme [33].

P = vdid + vqiq (2.20)

Q = vqid − vdiq (2.21)

Equation 2.22 and 2.23 is generally referred to as P-f droop and Q-V droop respectively.

ω = ωref −KpωcP

s+ ωcP(P − Pref ) (2.22)

V = Vref − (Kqp +Kqi

s)

ωcQs+ ωcQ

(Q−Qref ) (2.23)

The final control algorithms for frequency (eq.2.22) and voltage (eq.2.23) use the active and reactive powerto control the two parameters. A low-pass filter is implemented into both equations in order to avoid highfrequency disturbances, which could destabilize the control method [28]. The independent droop gains Kp

and Kqp act as damping factors for the frequency deviations of the system as well as Kqi which is theintegrator term gain.

2.4.2 Virtual Synchronous Generator (with inertia)

The Virtual Synchronous Generator (VSG) is designed to mimic the behavior of a synchronous generator,most importantly its inertial properties. Its working principle is similar to that of the droop controlmethod with P-f and Q-V droop, but with additional control components added to the P-f droop such asvirtual inertia and damping factors. There are two main versions of the Virtual Synchronous Generatorthat is reoccurring in research articles [34][31], which both show promise.

The outputs from the QDroop and the swing equations are utilized to generate control signals (eq. 2.24) tothe voltage loop.

V1 = VDrcos(θ) (2.24a)

V2 = VDrcos(θ +2π

3) (2.24b)

V3 = VDrcos(θ −2π

3) (2.24c)

17

The VSG:s frequency computation is designed having the swing equation in focus (eq. 2.9), as well as thevirtual synchronous generator governor, which is the virtual equivalent to a speed controller. In figure 2.15the general frequency computation is presented. The governor operated by computing the frequency delta,as well as the rate of change of the active power, which has the purpose of damping system overshoot. Inthe final stage of the governor the frequency delta is subtracted by the active power reference, as well asthe rate of change damper to form the output of the governor.

The governor control signal is fed into the swing equation where it is compared to the active power,frequency reference and fed through the virtual inertial block to finally result in an output frequency andphase angle θ. Furthermore, the active power is used to regulate the frequency for simulating the inertia(J ) for resemble the swing equation (eq. 2.9). Q-V droop is implemented by altering the reactive powerreference according to the voltage difference. The output reactive power error is then integrated to obtainoutput V.

Figure 2.15: VSG - Active Power loop version 1[34].

There are two recurring versions of VSG, where the other method can be seen in figure 2.16.

Figure 2.16: VSG - Active Power loop version 2 [31].

θ = 2π

∫ (Kp(f − fref ) + Pref − P −Dfref (f − fref )

Jfref

)dt (2.25)

θ = 2π

∫ (1

Js(Pref − P + (f − fref ))D

)dt (2.26)

V = Vref +Kq(Qref −Q) (2.27)

18

The control equations for frequency and voltage can be seen in equation 2.25, 2.26 and 2.27. Theassumption can be made that fref and Vref are constant, J is the inertia of the VSG, as defined inequation 2.10.

The inertial constant H which determines the magnitude of the virtual inertia is calculated using equation2.10, as a higher inertial constant equals more virtual inertia.

2.4.3 Virtual Synchronous Machine, without inertia (VSM0H)

The Virtual Synchronous Machine with zero inertia is a control method closely related to the VirtualSynchronous Generator, with the main difference between the methods being that the VSM0H introducesno virtual inertia. The benefit with this being fast dynamic response of the system [35]. In fact, VSM0Halso discards the inner current loop to generate balanced switching signals, but uses an averaging filterapplied to the measured active and reactive power, to get stable measurements even in scenarios of systemunbalance [35]. As system speed is prioritized, it is assumed that sufficient power can be delivered from theDC bus.

Figure 2.17: The general schematic of the VSM0H.

The main control block as seen in figure 2.17 as Droop controllers are computed as described in equation2.28 and 2.29, with its corresponding reference values and damping parameters (Df and DV ).

f = fref +Df (Pref − P )(1 +kDs

1 + τkDs) (2.28)

V = Vref +DV (Qref −Q) (2.29)

It can also be observed that the VSM0H is similar to Droop control, with the modification of implementinga boxcar filter, that encapsulates one period of the fundamental frequency as well as the removal of the innercurrent control loop. This would theoretically enable the elimination of harmonics, and faster system.

2.4.4 Power Synchronization Control

The Power Synchronization Control (PSC) was first developed to be applied and work in very weak HVDCgrids. In PSC the phase angle and the voltage magnitude are utilized for directly control the active andreactive power [36].

19

Figure 2.18: General design of the Power synchronization loop [37].

The active power output from the VSC is controlled by a Power Synchronization Loop (PSL) (figure 2.18),which is converting the power control error to a frequency deviation between the grid and the VSC. Thecontrol law is according to:

∆θ + ωref =kps

(Pref − P ) (2.30)

to get the phase angle. Kp is proportional gain, P is the measured power output from the VSC and Pref isthe reference value.

The output θ from the PSL gives the angle for converting the voltage reference from dq-frame toABC-frame, which then supplies the reference for the VSC. This implies that the PSL is used both forcontrolling the active power and for maintaining grid synchronization.

The reactive power is controlled by adjusting the voltage magnitude. This entails that an inner currentcontrol loop is not necessary. Although, in case of ac-faults, a current control system must be used forpreventing over currents. In most solutions is a current-limiter control used together with a back-up PLLto maintain synchronization with the grid. If the converter current is exceeding its maximum current ratingis a current limitation controller used to enable switching to the vector-current control and the use of theback-up PLL [37] [38]. To enable the switching between the regular synchronization of PSL and the back-upPLL can be set-up according to figure 2.19.

Figure 2.19: PSL and back-up PLL [36].

20

The angle correction and the feedback part from θv has the function to make it smoother to switchbetween the synchronization methods. It causes them to follow whichever one that is active, hence thefrequency of the system.

During normal operation, there is a mechanism of limiting current and controlling the voltage output (withoutthe back-up PLL) which could be realized as a standard inner control loop described in section 2.3.3, butoften with an added high pass filter to prevent instability and eliminate noise [36].

2.4.5 Synchronous Power Control

The Synchronous Power Control (SPC) utilizes the main working principle of the PSC, but with addeddamping and inertial characteristics.

Figure 2.20: The general schematic of the SPC [39].

The control of the SPC is multi-layered, as it takes inspiration from several other grid forming controlmethods. It is based on the synchronous generator with both an electric and a mechanical part with inertiaand damping characteristics.

The main design used can be seen in figure 2.20, which is based on reactive and active power control,described as:

ω∗r = (P − Pref ) · PLC + ωref (2.31)

and

E∗ = (Q−Qref )(Kp +Ki

s) + Vref (2.32)

where PLC stands for the power loop controller.

The current and voltage are measured at the PCC. The reactive and active power is calculated and is fedinto a Droop controller. The voltage and the frequency angle from the power loops are then fed into avoltage controlled oscillator which is generating a sinus voltage signal. The signal, which is supposed tosimulate the electromotive force is then fed through the virtual admittance (VA), further to the currentcontroller [39].

There are two main methods used in the active power control loop as the PLC. One where the control isbased on the synchronous generator swing equation:

ω = ωref +Kps+Ki

s+KG(2.33)

21

Ki, Kp and KG describes the inertia, damping and droop characteristics. Ki is expressed as:

Ki =ωs

2H · SN(2.34)

Kp is expressed as:

Kp = 2ζ ·√

ωs2H · SN · Pmax

− 1

2H ·Rd · Pmax(2.35)

and KG is expressed as:

KG =1

2H ·Rd(2.36)

where ζ is the damping factor (normal range: 0.1-1.1), H is the inertia constant (normal range: 1-10), SNis the nominal power, ωS is the nominal angular speed and Rd is the value of the P-f droop slope thatdescribes the variance of the frequency in percentage (normal range: 2-5%) [40].

Its control scheme is shown in the figure below.

Figure 2.21: One method of constructing the PLC [40].

The other method which is also often used is a simpler method where the PLC is constructed as in figure2.22 [40].

Figure 2.22: Another method of constructing the PLC [39].

Where GPLC is:

22

GPLC(s) =1

ωs(Js+D)(2.37)

Here, J is the inertia constant and D represent the damping.

J can be calculated as in 2.10, and D is calculated as:

D =2ζ

ωs

√2H · SN · Pmax

ωs(2.38)

The VA is included because of its capacity to ensure a high X/R ratio (SCR) in the system. It is representedas a low pass filter-block with a resistance and inductance as the constants [39]:

V A =1

Rv + Lvs(2.39)

2.4.6 Virtual Oscillator Control

The Virtual Oscillator Control (VOC) differs from the other grid forming methods because of its use of anoscillator to control the VSC parameters, also since it is based on instantaneous time signals, using neitherdq nor αβ. The oscillator used can for example be a dead zone or a Van der Pool oscillator and it isdesigned to perform as a voltage dependent current source, and it is connected to an LCR-filter. L and Care designed to tune the oscillator and the resistance is chosen to ensure a stable operation. Because of itssimple design, without conversion between ABC and dq-frame and without regulation parameters, it is fastand acts directly on disturbances [41]. The overall system of the VOC can be seen in figure 2.23.

Figure 2.23: Virtual Oscillator Control of an inverter [41].

23

3. Method

The method used can be divided into different segments. Firstly, a literature study was completed, readingand gaining knowledge about grid-forming control principles and concepts. Furthermore, studying variouscontrol methods including advantages, disadvantages, similarities and differences among them. Thereafter,the four most interesting and most applicable ones out of ABBs point of view were selected and modeled inPSCAD for further study, analysis and comparison.

3.1 Software

Investigating the behavior and prototyping power systems is mainly done by software simulations in powersystem analysis software. This will, besides the pre-study serve as the majority of the master thesis, as itwill be done in software.

3.1.1 PSCAD modeling and testing

The main software that will be used for implementing and modeling the grid forming control methods isPSCAD (Power System Computer Aided Design). PSCAD is used to design and simulate power systemsof various sorts. PSCAD has a predefined library of system models and electrical components that enablesfaster model creation [42]. PSCAD allows for continuous time simulations with great accuracy.

3.1.2 MATLAB

MATLAB will be used for mathematical computations and for final plotting and comparison of the controlmethods signals. Calculations that are to be made are network parameters, SCR:s and DC voltages.

ABB has developed an in-house MATLAB tool called TSPLOT, which enables comparative plotting fromthe PSCAD output files.

24

3.2 Pre-study

3.2.1 Choice of Grid Forming Converter-methods

During this master thesis’ pre-study six grid forming control methods were evaluated at a deep level, aspresented in the previous chapter. At the end of the pre-study these control methods were compared witheach other on aspects such as performance, complexity and applicability for ABB:s current hardwaresystems in order to choose which control methods that were to be further investigated. The followingsection will summarize the considerations that were made for each of the control methods and why theywere chosen or not.

Droop Control

The principle of Droop control is based on basic Droop equations which were discussed in the theory section.It turned out that a lot of the control methods that were evaluated were based on, or similar to Droopcontrol. Besides being a method that is similar to others, it also showed promising behavior, despite itssimplicity in the articles examined in the pre-study. These factors led to including Droop control in thefurther investigation and modeling.

Virtual Synchronous Generator (VSG)

The Virtual Synchronous Generator is one of the control methods that mimics the inertial-like behavior ofthe synchronous generators. As seen in the theory chapter, the VSG has some similarities to Droop control,as the voltage amplitude reference algorithm is identical between the models as well as the rest of the system.The differing factor is the frequency generation, were the VSG is more complex, but also adds more featuressuch as the virtual inertia. The performance of the VSG also shows promise in the stability aspect as wellas fault-ride through capabilities in several articles. Being similar to the Droop control method, as well asthe performance promise made the VSG the second control method that was to be implemented in PSCAD.

Virtual Synchronous Machine, without inertia (VSM0H)

The Virtual Synchronous Machine without inertia (VSM0H) was a control method whose main advantagewas supposed to be fast response and regulation. The main concept of this control method being that ofthe Virtual Synchronous Generator, but with no virtual inertia as well as the removal of the inner currentcontrol. This would in theory make the control system response faster. The conclusion made in the pre-studyhowever is that this system would give a similar behavior to the Droop Control method, as their models aresimilar, as well as the lack of research that had been made on the control method. Based on these factors,the decision not to move forward with this control was made.

Power Synchronization Control

The main advantage with the PSC is its simplicity and its ability to work well in HVDC-applications. Themethod is a variant of droop-control but it has also been further studied and regulated to work well in weaksystems. What also differs the PSC from the other control methods and the fact that it needs to use aback-up PLL in case of faults. Since the further analysis is supposed to be in a HVDC-environment withstability studies in weak systems, and because of the comparisons that can be made based on the similaritiesand differences of the control methods, the PSC is the third method that is chosen for further studies.

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Synchronous Power Control

The SPC can be seen as a development of PSC, but with elements of other control methods such as VSG andDroop. However, compared to PSC it has been less tested in weak HVDC systems, but has the advantagesof the added damping and inertia characteristics. With that in mind, plus the fact that a back-up PLL isnot needed, it is chosen to be implemented for further studies.

Virtual Oscillator Control

The primary advantage with the VOC is its simple design without conversion between the different frame-representations, which makes it fast. The downside of the method is that the parameters of R, L and C aretuned for specific power ratings, which makes it less flexible. Also, regarding further studies and the fact thatthe methods chosen must be applicable for ABB, which considering current and future implementations, theVOC will not be chosen for further modeling or analysis.

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3.3 Implementation

The pre-study main purpose was to gain knowledge in the relatively new and cutting-edge technology thatgrid forming converters are. As a consequence, to this technology being new, and not implemented on alarge scale, as well as generally only studied on a microgrid level, some generalizations have been done. Asa standard does not exist for any of these converters, the decision to change and experiment with theimplementations in order to tailor the systems to ABBs needs. The converters as described in the theoryare a general or average interpretation of the numerous variants that have been researched in the academicpapers that form the base of the theory section.

The performance of the grid forming models are to achieve predetermined criteria in order for implementationof the model to be considered as successful and complete. These are the following criteria:

• The model is able to reach the entire power span of P and Q (-1 to 1 p.u) during nominal operation(IPL=100%)

• All signals of interest follow the control signals with minimal steady-state error

• The model has good fault-ride through capabilities

• The model exhibits stable frequency characteristics

The criteria above are specified for very weak grids with an Short Circuit Ratio of 1, but will be evaluatedfor stronger grids as well to benchmark their operational span.

3.3.1 Modeling of converters in PSCAD

Average inverter model

As one of the goals of the master thesis was to implement generic control method models in PSCAD forcomparative analysis the decision to implement an average inverter model was made. The average invertermodel is a simplification of the inverter control model, as it is represented with three ideal ac voltage sourceswith a phase difference of 120 degrees between them, instead of the standard six-switch inverter model. Thiseliminates harmonics generated from the inverter, thus creating a cleaner output to analyze. The averageinverter model can also be seen as an infinite bus, meaning that the available power delivery is infinite. Thisdecision could also enable a more direct comparison between the general behavior of the control methods,putting their dynamics in focus. It has to be noted however that harmonics do matter, but ABB did notfeel as this was the main goal of the thesis, as a general behavioral test were to be executed.

Figure 3.1: The general design of the average model switching generation.

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The design of the average model can be seen in figure 3.1 and when compared to the standard inverterswitching model, as seen in figure 2.13 some simplifications can be seen. The main difference being that theaverage model controls three voltage sources, and the full model switches the inverters switches in order togenerate three voltages.

Grid modeling

The type of grid that the grid forming converter was to be connected to was of great importance in ananalytical perspective, as different grid types corresponds to a different system response. The system wastherefore altered with respect to the SCR.

The grid voltage across all tests was set to 400kV L-L RMS, as was the converter side voltage. This wasdone to simplify the analysis, as it meant that the transformer ratio was 1:1. The transformer is in a Y-Yconfiguration, 50 Hz base frequency, 0.15 p.u. leakage reactance and a power rating of 600 MVA. Thesevalues were chosen in cooporation with the supervisor at ABB.

The resistive and inductive components corresponding to a specific SCR was derived and computed inMATLAB using equations 2.12 and 2.13 with respect to the given grid parameters.

The output value of the ac voltage sources in the average model described above, were generated by a DC-voltage multiplied with three generated switching signals. The system was rated for 600 MVA, and sincethe system had to be able to reach Q = 600 MVAr on the grid side was the DC-voltage required to be acertain value in order to generate large enough ac-voltage. The DC voltage was therefore calculated to bebig enough for the system to be able to inject the rated power. The calculations were done in MATLAB.

General system

The general structure of the control system for all the converter methods is the same, regarding conversionbetween the grid and control parameters and the switching part. Firstly, as described above is the averageinverter model used, where the output values were transformed to grid voltage via a transformer. Thethree phase (abc) voltages and currents were measured after the transformer, at the PCC. All themeasured values were converted into p.u. and then converted to dq-frame, according to the equations 2.3and 2.6. Furthermore, was the active and reactive power at the PCC calculated with equation 2.18 and2.19. The calculated grid powers were then used for realizing the control of the angle and voltage, whichtakes place in the outer control loop.

All the grid forming control methods covered in this thesis utilizes some variant of the inner control loops’voltage and current control. These control loops see to that voltage and current levels are regulatedaccording to the desired behavior. From this inner control the average inverter model as mentioned aboveis controlled to output the correct voltage and current levels.

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3.3.2 Tuning of controllers

All the grid forming control methods consist of cascaded regulators in different control loops. For the majorityof the models P (proportional) or PI (proportional and integrating) regulators have been implemented. Asthe regulators are in series a proper tuning methodology had to be applied. This procedure involved startingto implement the last regulator in the regulator chain, the current control loops PI regulators. This entailedinputting test values into the input and tuning the parameters until precise output tracking was achieved.This method is applied to the voltage control loop as well, this ensures correct behavior throughout thecontrol loops. How the outer and inner control loops is coupled with P and PI-controllers can be seen infigure 3.2.

Figure 3.2: Cascaded Control loop structure.

Once the inner control loop is tuned, the outer loop has to be tuned. As it proved the inner loop tuningremained the same, with some minor changes done between the different control methods.

3.3.3 Simulations in PSCAD

During the time that the control models were developed, simulations were used to verify their behavior.Subsystems could with ease be individually tested and debugged block-wise, in order to minimize errorswhen putting all of the subsystems together.

Debugging simulations would include running everything from shorter simulations in order to verify thatspecific system parameters were behaving as expected to longer stability centered simulations. However,the primary type of simulation that were initially run were tuning simulations, were the developer’s mainobjective was to try to get the entire system running at a basic level. Because of the systems complexity,small changes could lead to the system not functioning properly, an area were the quick simulation tools ofPSCAD came in handy.

When functioning on a fundamental level, the models were given a reference power, to examine what theresponse to a power order was. Why changing the power reference as a validator to if the system isbehaving properly is based on the fact that changing the power (active and reactive) will impact all systemparameters which then can be verified to be working properly or not.

Post to the system working properly is when the performance test could begin. This included step tests,stability analysis and fault-ride through capabilities. These tests will be repeated for different scenariossuch as SCR 1 and 5 and different amounts of virtual inertia for the grid forming models that consist ofvirtual inertia. All simulations were considered completed when the powers in the individual test hadreached a steady value.

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When doing the simulations of the grid converter control methods that contained a virtual inertia, both theparameters J and H are mentioned in the theory. How they correlate can be seen in table 3.1.

Table 3.1: Value of J that were utilized and the corresponding H.

J 0.0005 0.004 0.005 0.01 1H 0.63 5 6.3 12.5 1250

3.3.4 Small Signal Analysis

To investigate impact of individual and impactful parameters in a control system, a small signal analysisought to be performed. In the case of the control methods implemented in this thesis the focus was put onthe outer loop parameters (i.e. the control method specific parameters) in order to collect as much data aspossible on stability regions and how parameters impact the systems response, which is what will be shownin the small signal analysis result section below.

One of the properties that the grid forming models comparison is based on is their transient behavior, inother words how they behave in sudden operational change. The fundamental way that this is going to beperformed is through a step change from 0.95 p.u. to 1 p.u., solely on the active power, seen in table 3.2.

Table 3.2: Step test scenario.

Test scenario Start p.u. Stop p.u.

Active power step 0.95 1

The reason to not execute the step test on negative steps (-0.95 p.u. to -1 p.u.) as well as reactive power isbased on ABB:s guidance, as it can be presumed that the step response is similar on both ends of thespectrum. As mentioned above this impacts all system parameters, and therefore can be used to analyzeand compare how systems behave during this change.

The response of the parameters during an active power step will be evaluated based on their; rise time,overshoot and settling time, as being the main parameters discussed in the Transient Response sectionof the theory. The tuned optimal parameter values will be marked as bold. The sections will also bestructured by the presentation of a table that summarizes the tests that have been done, followed by graphicalrepresentations of the same tests.

3.3.5 Short Circuit analysis

The models are tested for short circuit resilience using the built in three-phase timed fault logic in PSCAD.The three phase fault duration set to 200 ms for a substantial fault period. The models will be tested underdifferent test environments, as the transient behavior analysis. The following short circuit tests are to beexecuted:

Table 3.3: Short circuit test scenariosTest scenario Active Power (P) Reactive power (Q)

1 - Maximum active power 1 02 - Minimum active power -1 0

3 - Maximum reactive power 0 14 - Minimum reactive power 0 -1

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The short circuits tests are designed to stress test the models as they operate at their limit at the time ofthe three-phase fault. Successful short circuits tests at the extremes will ensure good performance across thepower spectrum for other scenarios that are not tested here. This results in four tests for the non-inertialmodels and eight for the ones that have. The main parameters that will be examined in the fault tests are isthe power (active and reactive, depending on the test scenario), converter-side current (to monitor recoveryand current levels over switches) as well as the grid frequency.

RMS fault-ride through method

To improve the system impact during a fault a fault-ride through method is designed to be used for all gridforming models. The chosen fault-ride through method is the RMS method discussed in the theory section.This was chosen because if its relationship between simplicity and effectiveness, with the major drawbackbeing the delay of half a period (10 milliseconds) due to the nature of the RMS calculation.

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4. Results

4.1 Final models

This section will cover the final implementation of the different systems. This will include parameter choices,model design as well as model specific descriptions.

4.1.1 General system model

The four implemented control methods have different control models implemented. However, their generalsystem models are identical, in order to make a comparative analysis. The following description of the gridand converter model will be done from left to right in figure 4.1. At the very left the converter outputresides and is represented with three AC voltage sources (Va, Vb, Vc), which have a variable amplitude thatis controlled according to the implemented control method and are electrically phase-shifted by 120degrees. This is what the implementation defined as the ’Average Switching model ’ as it does not rely onactual switches but generated the sinusoidals expected from the regular switching model, apart from theharmonics generated.

Next comes the filter inductance, which filters the output of the converter. This is also where the filtercurrent and voltages are measured, which are parameters used in the control methods. Next comes thesystem transformer which has a transformation ratio of 1 for added simplicity in the comparison. Thesecondary side of the transformer is where the PCC is located, which is where the converter connects to thegrid. The grid naturally has a grid impedance and the grid voltage is represented with an AC-source to thevery right in figure 4.1.

Figure 4.1: Grid and converter model.

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The table 4.1 represents different grid configurations, namely different ’grid strengths’, which represents thegrid impedance. A SCR of 1 represents the weakest grid model (and also the highest impedance) and 5 thestrongest in the test setup.

Table 4.1: Different grid parameters.

Grid SCR Resistive component [Ω] Inductive component [H]

5 2.9527 0.11284 3.6909 0.14103 4.9212 0.18802 7.3818 0.28201 14.7636 0.5639

The system grid shown in figure 4.1 has the set parameters as shown in table 4.2. These parameters areused during the entirety of the grid forming analysis.

Table 4.2: System parameters.

Component location Parameter name Value

DC voltage source Vdc 850 [kV]AC voltage source Vabc Variable [V]

VResistance 0 [Ω]Filter inductance 0.041 [H]

Y-Y transformer Power rating 600 [MVA]Frequency rating 50 [Hz]Primary voltage 400 [kV]Secondary voltage 400 [kV]Leakage reacteance 0.15 [pu]Other losses None

Grid Grid inductance Table 4.1Grid resistance Table 4.1Grid voltage 400 [kV]

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On a control-based level figure 4.2 shows the generalized picture of what the control methods consist of.Figure 4.2 comprises of ”black boxes” in order to get a better overview of how the models are interconnected,both on the control and grid side.

Figure 4.2: Full developed and generalized grid forming model.

The computational cycle of the grid forming converters that were implemented can be seen in figure 4.3,starting from the top and going clockwise around the figure.

Figure 4.3: Computational cycle of the grid forming converter.

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When examining figure 4.2 the first step is the measurement of filter and PCC voltage and currents, as thisis converted into dq-domain and the power quantities are computed. Passing the measured powers into the’Active Power loop’ and ’Reactive Power loops’ to calculate the voltage sinusoidals that are to be passedinto the inner control loops. These loops make sure that the voltage and current levels are kept within thespecified limits as well as outputting the control parameters needed to feed or absorb the grid with energy.As this cycle repeats, the system continuously controls that the output values are equal to the referencevalues that are set at any given time.

4.1.2 Inner Control loop

The inner control loop shown in figure 4.4 is the general set-up in all the control methods, although somesmall changes can occur in the different methods.

Figure 4.4: Inner control loops of the grid forming model.

4.1.3 Droop Control

The Droop control method was implemented as figures 4.5 and 4.6 show below. The model differ somewhatfrom how the theory defines it. Firstly, both the active and reactive power controls are controlled by a PIcontroller, compared to that of the P controller in the theory.

Figure 4.5: Droop Control - Active Power loop.

Secondly, the reactive power loop does not have a low pass filter as the theory states and does have acontroller feedback.

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Figure 4.6: Droop Control - Reactive Power loop.

4.1.4 Virtual Synchronous Generator Control

The Virtual Synchronous Generator control model had two versions of the model brought up in the theorysection. However, after implementation of both models one of them showed more promise than the other,this is the control scheme shown in figure 4.7. The model is simpler and consists of a virtual inertia block’1/Js’ and a damping factor ’D ’.

Figure 4.7: Virtual Synchronous Generator Control - Active Power loop.

The reactive power control was implemented in the same way as that of the Droop control, as can be seenbelow in figure 4.8.

Figure 4.8: Virtual Synchronous Generator Control - Reactive Power loop.

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4.1.5 Power Synchronization Control

The power synchronization control was implemented almost as described in the theory as in figure 2.19.What differs was the feedback part in the PSL where the γ was implemented on both sides, instead of oneside. Also, a PI-controller was used instead of a P-control. The final active and reactive power loop can beseen in 4.9 and 4.10.

Figure 4.9: Power Synchronization Control - Power synchronization loop.

Figure 4.10: Power Synchronization Control - Reactive Power loop.

The inner loop control was implemented as in 4.4 but with a HPF instead of a LPF when IfD and IfQ areadded at the voltage control loop. Also, a LPF was implemented when UfD and UfQ are subtracted.

4.1.6 Synchronous Power Control

The two methods of the power loop control described in the theory section were both implemented at first.It was seen early that one of the methods had an advantage regarding performance, and it was the methodseen in figure 2.21. The final result is seen in 4.11 and 4.12.

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Figure 4.11: Synchronous Power Control - Power Loop Controller.

Figure 4.12: Synchronous Power Control - Reactive Power Control.

The overall system was modeled as in figure 2.20 with the current controller implemented as in figure 4.4.

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4.1.7 Fault detection and handling

The fault detection and handling implementation is nothing but standard, and is therefore not included inthe theory section, other than the fact that faults can be detected utilizing the RMS voltage and athreshold value to monitor the state of the system. This is what can be seen in the ’Fault Detection’ box infigure 4.13. This box consists of RMS measurement of all phases and compares these to a set thresholdvalue, that if crossed will output a digital high from the comparator. All of the phase comparators areconnected to an AND-gate which outputs a fault detection high if any of the phases fall below theirthreshold values.

Figure 4.13: Fault detection and recovery handling model. Left: Fault detection for all phases coupled withan AND-gate for minimum detection time. Middle: Selectors for power reference as well as ramp for differentfault scenarios. Right: Sign comparator and output for power reference.

The second box in figure 4.13 describes part of the fault handling algorithm. The top of the controllers is forthe active power handling, and the bottom one is for the reactive power. This algorithm sets the referencevalue for the active and reactive power to zero if a fault occurs and ramps the power references back to theirprevious values after the fault has been cleared. The speed of the ramp is adjustable to the users needs.The final block in the figure selects which of the four power reference outputs in block two to output to thesystem.

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4.2 Small Signal analysis

If nothing else is stated, all graphs are showing values in per unit.

4.2.1 Droop Control

The parameters that were deemed to have a significant enough impact (meaning that the parameter impactis non-negligible) on the system behavior on the Droop control method were; Kpp, Kpq, Kip, ωc. Theirresponse can be seen in table 4.3.

Table 4.3: Droop Control - small signal analysis performance.

Parameter Value Rise Time [ms] Overshoot [%] Settling Time [ms]

Kpp 1.2 144 15.6 6852.2 113 16.9 5163.2 101 36.9 435

Kpq 0.02 76 30.5 3810.12 70 16.5 4430.22 63 9.2 458

Kiq 0.1 49 36.8 3660.7 67 16.7 4431.3 70 12.4 535

ωc 5 122 100.2 363025 65 10.7 44445 69 16.5 440

The proportional gain of the active power loop Kpp shows significant impact on the system performance.With a higher gain the rise time decreases, but with the cost of a much larger overshoot than the optimalvalue as well as having more oscillations. The settling time for the higher proportional gain was howeversimilar to that of the optimal parameter. The lower Kpp exhibits slow overall response, as it has a slower risetime, equal overshoot and much longer settling time than the optimally tuned parameter, and can thereforenot be seen as favorable.

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Figure 4.14: Small signal analysis of Kpp. Blue: Active power reference, Red: Proportional gain, activepower loop (1.2), Yellow: Proportional gain, active power loop (2.2), Purple: Proportional gain, active powerloop (3.2).

The proportional gain of the reactive power loop Kpq, showed some impact on the system. As can beobserved the tuned parameter value and the higher parameter value showed similar responses during thetest, with what looks like a favorable result for the larger value. A Kpq of 0.02 resulted in a response thatwas slower, had more overshoot and took longer to settle.

Figure 4.15: Small signal analysis of Kpq. Blue: Reactive power reference, Red: Proportional gain, reactivepower loop (0.02), Yellow: Proportional gain, reactive power loop (0.12), Purple: Proportional gain, reactivepower loop (0.22).

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The integral gain of the reactive power loop Kiq, presented dynamic change in system response dependingon the chosen parameter. With a small integral gain the step response became oscillative, but did settle inthe end. The response of the optimal parameter value compared to the higher value in the interval had afaster rise time, lower overshoot and a faster settling time as shown in figure 4.16.

Figure 4.16: Small signal analysis of Kiq. Blue: Active power reference, Red: Integral gain, reactive powerloop (0.1), Yellow: Integral gain, reactive power loop (0.7), Purple: Integral gain, reactive power loop (1.3).

The cutoff frequency of the active power control low-pass filter showed some varying results. With a lowcutoff frequency the system became very oscillative, with great overshoot and a long settling time. Theoptimal value of 25 Hz and the highest value of 45 Hz showed similar results, with the optimal value beingmarginally better in all comparative aspects.

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Figure 4.17: Small signal analysis of ωc. Blue: Active power reference, Red: Cutoff frequency (5 Hz), Yellow:Cutoff frequency (25 Hz), Purple: Cutoff frequency (45 Hz).

4.2.2 Virtual Synchronous Generator

The parameters that displayed a significant impact on the system dynamics of the Virtual SynchronousGenerator control method were; Kpp(D), J, Kpq, Kip. The summarized results of the tests are seen in table4.4.

Table 4.4: VSG Control - small signal analysis performance.

Parameter Value Rise Time [ms] Overshoot [%] Settling Time [ms]

kpp (D) 0.1 - - -2 375 2.6 435

3.9 862 0.9 1658J 0.0005 389 0.5 468

0.01 382 0.6 4591 359 5 1194

kpq 0.06 358 1.3 11780.26 389 0.4 4660.46 420 0.3 533

kiq 0.1 467 0.5 7600.6 397 1.6 4701.1 397 1.7 464

The damping factor of the VSG presented the system with interesting dynamics, such as a damping factorof 0.01 placed the system outside the stability region, as the system showed an ever increasingly oscillatingbehavior. A larger damping factor did however stabilize the system and returned a slower system with lessovershoot and longer settling time for larger values of the damping factor.

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Figure 4.18: Small signal analysis of D. Blue: Active power reference, Red: Damping, active power loop(0.1), Yellow: Damping, active power loop (2.0), Purple: Damping, active power loop (3.9).

The virtual inertia was one of the more defining variables of the VSG, therefore its impact on the systemdynamics had to be examined. For larger virtual inertias (larger J) the system became slower and moreoscillative, whereas for the smaller magnitudes of the inertia, the system response was very similar, with aalmost non existing overshoot and reasonably fast rise and settling time.

Figure 4.19: Small signal analysis of J. Blue: Active power reference, Red: Virtual inertia (0.0005), Yellow:Virtual inertia (0.01), Purple: Virtual inertia (1).

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The proportional gain of the reactive power loop showed fast rise time , and long settling time for smallervalues as well as slower rise times and still slower settling times than the optimal parameter choice. As theoptimal had a comparable rise time to that of the lower parameter value, and overshoot to that of the highervalue, while remaining the fastest iteration to settle of the three.

Figure 4.20: Small signal analysis of Kiq. Blue: Active power reference, Red: Integral gain, reactive powerloop (0.06), Yellow: Integral gain, reactive power loop (0.26), Purple: Integral gain, reactive power loop(0.45).

The final parameter to be closer examined on the VSG was Kiq, the integral term of reactive power loop.When at low values the system became slower, both in the respects of rise time and settling time, with adampened overshoot. Values around and above the tuned one seemed to display a similar rise time, a slightincrease in overshoot and faster settling time, which was amplified at higher parameter values.

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Figure 4.21: Small signal analysis of Kpq. Blue: Active power reference, Red: Proportional gain, reactivepower loop (0.1), Yellow: Proportional gain, reactive power loop (0.6), Purple: Proportional gain, reactivepower loop (1.1).

4.2.3 Power Synchronization Control

The parameters that had the most impact of the system were Kpq and Kiq, and the parameters with smallerimpact were Kpp, as seen in the table 4.5.

Table 4.5: PSC Control - small signal analysis performance.

Parameter Value Rise Time [ms] Overshoot [%] Settling Time [ms]

Kip 0.1 94 8.1 3610.2 97 8.1 2380.4 97 8 356

Kpq 0.2 77 7.1 3270.4 102 7.8 3510.6 105 8.1 375

Kiq 0.1 102 9.1 4100.3 102 13.8 4530.5 105 15.8 500

As seen in the table 4.5, different values of Kip had no greater impact in the system step response, thesame result applied for Kpp as well.

The proportional gain of the reactive power loop Kpq had some impact of the step response of P, but hada greater impact of the step response of Q. As seen in the figure 4.23, a greater value of Kpq gives a fasterresponse with a smaller settling time. An important note is that Kpq = 0.6 has an IPL of less than 100%.

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Figure 4.22: Small signal analysis of Kpq. The top plot representing a step response of active power andthe lower reactive power. Blue: Proportional gain, reactive power loop (0.2), Red: Proportional gain,reactive power loop (0.4), Yellow: Proportional gain, reactive power loop (0.6), Purple: Active/reactivepower reference.

The integral gain of the reactive control loop Kiq gives a slower system the greater value. When doing thestep response of P, a smaller value gives a damped overshoot, compared to the step response of Q where asmaller value gives a higher overshoot.

Figure 4.23: Small signal analysis of Kiq. The top plot representing a step response of active power and thelower reactive power. Blue: Integral gain, reactive power loop (0.1), Red: Integral gain, reactive power loop(0.3), Yellow: Integral gain, reactive power loop (0.5), Purple: Active/reactive power reference.

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When changing the SCR to 5, these parameters required a re-tuning: Kpp, Kip, Kiq and Kp in thevoltage control loop.

Comparing the step response of SCR=1 and SCR=5, SCR=5 gives a faster system but with a greaterovershoot. Also, the signal of SCR=5 provides a more oscillating system, seen in figure 4.24.

Figure 4.24: Step response comparing of PSC in SCR=1 and SCR=5. Blue: active power SCR=1, red:active power SCR=5, green: active power reference.

4.2.4 Synchronous Power Control

The table 4.6 shows the different parameters and their impact of the system.

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Table 4.6: SPC Control - small signal analysis performance.

Parameter Value Rise Time Overshoot Settling Time

Kpq (P-step) 0.4 154 15.9 5600.5 154 14.9 5790.6 153 14.2 598

Kpq (Q-step) 0.4 114.2 2.7 208.40.5 106.4 2.3 202.20.6 117 2.2 234

Kiq (P-step) 0.2 115 13.4 5480.3 155 15.6 6010.4 154 15.6 635

Kiq (Q-step) 0.2 85.8 3.4 161.40.3 115.8 2.5 212.40.4 124.4 2.2 260

Rv 0.65 161 10.1 5270.82 152 13.8 5730.84 157.4 14.7 581

Lv 0.003 155.6 14.7 5980.005 153.2 13.8 5750.007 157.8 13.7 551

J 0.004 145 18.1 5900.005 148 15.3 5920.006 152 14 5960.008 161 12.5 6080.01 160 11.8 603

The values of J changed the values of Kp, KG and KI according to equations 2.34, 2.35 and 2.36. Forcalculating those constants, the following values were chosen:

Table 4.7: Parameter values for calculating Kp, KG and KI .

Parameter ξ SN Rd Pmax ωsValue 0.7 1 5% 1 50

When altering the value of Kpq, it can be seen that the change does not has a great impact. Although, alower value gives a more damped system but with a greater settling time. The result also shows that theparameter has a greater impact on the step response of Q.

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Figure 4.25: Small signal analysis of Kpq. The top plot representing a step response of active power andthe lower reactive power. Blue: Proportional gain, reactive power loop (0.4), Red: Proportional gain,reactive power loop (0.5), Yellow: Proportional gain, reactive power loop (0.6), Purple: Active/reactivepower reference.

When altering the integral gain of the reactive power loop, it is clearly observed that a greater valuecorresponds to a greater rise and settling time. The impact of the integral gain on the overshoot dependson whether the step response of P or Q is of interest.

Figure 4.26: Small signal analysis of Kiq. The top plot representing a step response of active power and thelower reactive power. Blue: Integral gain, reactive power loop (0.2), Red: Integral gain, reactive power loop(0.3), Yellow: Integral gain, reactive power loop (0.4), Purple: Active/reactive power reference.

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The parameters Rv and Lv are part of the VA, which is a low pass filter. When varying Rv, a smaller valuecorresponds to a smaller overshoot, hence a more damped system. It also contributes to a slower systembut with a shorter settling time. One important note is that Rv below 0.7 has an IPL beneath 100%.

A greater value of Lv gives a shorter settling time, but otherwise has a small impact on the overshoot andthe rise time.

Figure 4.27: Small signal analysis of Rv (virtual admittance). Blue: Active power (Rv=0.65), Red: Activepower (Rv=0.82), Green: Active power (Rv=0.84), Purple: Active power reference.

Figure 4.28: Small signal analysis of Lv (virtual admittance). Blue: Active power (Lv=0.0.003), Red: Activepower (Lv=0.005), Green: Active power (Lv=0.007), Purple: Active power reference.

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The value of J, hence the virtual inertia does has an impact, but a rather small one since the span of whichit can perform properly is limited (see table 4.10). A greater value of J implies a slower but a more dampedsystem.

Figure 4.29: Small signal analysis of different values of J. Blue: Active power (J=0.004), Red: Active power(J=0.005), Yellow: Active power (J=0.006), Purple: Active power (J=0.008), Green: Active power (J=0.01),Turquoise: Active power reference.

In the figure 4.30 the behavior with and without the VA is seen, implying that the system without the VAis oscillating more in general.

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Figure 4.30: Step response of P with and without the virtual admittance. Blue: Active power, no VA, Red:Active power, with VA, Yellow: Active power reference.

Comparing the step response with SCR=5 and SCR=1, in figure 4.31, the system with a higher SCR isfaster but less damped.

Figure 4.31: Step response comparing of PSC in SCR=1 and SCR=5, with J=0.004. Blue: Active power(SCR=1), Red: Active power (SCR=5), Green: Active power reference.

The figure 4.32 shows how different values of ξ in equation 2.35 is affecting the step response. Clearly, agreater value of ξ is resulting in a faster and more damped system. An important note is that for whenusing the values in table 4.7, a value greater than ξ = 0.7 imply a system that could not be kept stable forall fault scenarios.

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Figure 4.32: Step response for different values of ξ. Blue: Active power reference, Red: Active power (ξ=0.7),Green: Active power (ξ=0.9), Purple: Active power (ξ=1), Yellow: Active power (ξ=1.2), Turquoise: Activepower (ξ=1.8) Dark red: Active power (ξ=2.2).

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4.2.5 Inner loop performance

Throughout all of the tests in the small signal analysis section the tuning parameters of the inner loop(voltage and current loop) have been kept the same. The reason for this was that the inner loop wasdeemed well-tuned, regardless of control method or change of parameters in the outer loop. As mentionedin the method, the inner loop is tuned from end to beginning, meaning that the tuning starts from theoutput and works its way back through the system, and will after tuning perform in the same mannerregardless of input. The performance of the inner loop could be measured by latency and ability to followdrastic change in the system demands.

The first performance index to be examined was the latency of the system. At any given moment, duringany operation the lag of the actual outputted filter current for example was around 1 millisecond, as shownin figure 4.33.

Figure 4.33: Delta of control signal and the actual current. Blue: Filter current (actual), Red: Controlcurrent.

The second performance index was how well the actual signal would follow the reference generated in theinner control loop. As can be seen in figure 4.34, the actual signal did follow the reference even during largersystem transients.

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Figure 4.34: Following capabilities of the inner control loop. Blue: Filter current (actual), Red: Controlcurrent.

4.2.6 Comparative result

Seen in the table 4.8 is the general behaviour of all the models when doing a step response of P from 0.95to 1 p.u. What can be seen clearly is that Droop Control is the fastest method and VSG is the slowest one.Droop control has on the other hand most overshoot together with SPC which is in the same span, andVSG has the lowest overshoot. Considering rise time, PSC also quite fast and SPC is somewhere in themiddle.

Table 4.8: Step response and the general behaviour of all the methodsMethod Rise time [ms ] Overshoot [%] Settling time [ms]

Droop Control 65 12 440VSG 380 1 440SPC 150 13 550PSC 100 8 340

The grid forming models were compared to each-other in several aspects. The first one being their flexibilityto work on a range of different types of grids, ranging from very weak grids at SCR = 1 to very strong grids.As the thesis was centered around the analysis of how the grid forming converter work in very weak grids,they are therefore tuned to this type of grid. Their compatibility towards other network types was thenexamined, and table 4.9 tells the result of this inquiry.

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Table 4.9: Table showing if the models are stable at different SCR.

Model SCR=1 SCR=2 SCR=3 SCR=4 SCR=5

Droop Ok Ok Ok if re-tuned Ok if re-tuned Ok if re-tunedVSG Ok Ok Ok if re-tuned Ok if re-tuned Ok if re-tunedPSC Ok Ok Ok if re-tuned Ok if re-tuned Ok if re-tunedSPC Ok Ok Ok Ok Ok

In table 4.9, ’Ok’ implies that the models achieve full penetration and good fault-ride through capabilitywithout change, and ’Ok if re-tuned implies changing one or several parameters in order to achieve thesame result.

Another aspect that was worth investigating was mapping of the stability regions of the parameters thatwere looked at with extra care. Table 4.10 defines the stability region for all analyzed parameters in whichthe system achieves full penetration and good fault-ride through capability. The sign ’<>’ in table 4.10indicates the lower stability region on the left of the sign, and higher on the right side.

Table 4.10: Stability interval for the models at SCR=1.

Model / Param Kpp Kip Kpq Kiq J ωc [Hz] D

Droop 0.05 <> 2.8 - 0 <> 0.85 0 <> inf(3) - 5 <> inf(45) -VSG 1.5 <> 20 - 0 <> 1.2 0 <> inf(10) 0.0005 <> 2.6 - -PSC 1.3 <> 2.1 0.2 <> 0.8 0.1 <> 0.4 0 <> inf - - 1 <> 7SPC - - 0.2 <> 0.5 0 <> inf 0.004 <> 0.016 - -

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4.3 Fault behavior

When doing the following three phase fault scenarios, the settling time, overshoot, recovery and overallperformance and stability is investigated for the power, current and frequency for all models. If nothing elseis stated, the fault is executed at SCR=1 and for the optimal (bold) values in the tables 4.3, 4.4, 4.5 and4.6. For all models, the first scenario will be presented in the result section and the other scenarios will bepresented in the appendix.

4.3.1 Droop Control

When running fault scenario 1 (4.35) on the Droop control the total fault recovery time was from thebeginning of the fault to nominal behavior approximately 0.6 seconds. This included a power transient thatpeaked at +1 and -0.2 p.u. during the recovery. The output current had its peak at around 1.45 p.u., butwith dampened oscillations during the later phase of recovery. The grid frequency had its largest deviationat 47.8 Hz with some smaller ripples above 50 Hz during the recovery ramp.

Figure 4.35: Three phase fault scenario 1. First graph: Blue: Active power reference and Red: Actual activepower. Second graph: Blue: Filter current (phase A), Red: filter current (phase B), Yellow: filter current(phase C). Third graph: Frequency [Hz].

4.3.2 Virtual Synchronous Generator

In this section the Virtual Synchronous Generators’ fault behavior is evaluated, with the addition ofdirectly comparing the impact of the virtual inertial impact. The inertial values compared are J = 1, 0.01and 0.0005, ranging from high inertia to low.

When examining scenario and the impacts of the different inertias it can be observed in figure 4.36 that thepower curve with the highest inertia also has the largest overshoot of 1.35 p.u., as well as settling time ofover 3 seconds. For J = 0.01 and 0.0005 the overshoot was a comparable 1.2 p.u., with the lowest inertialtest having a smaller second overshoot than that of the test with J = 0.01. The recovery time of the lowestand next to lowest inertia tests had a similar recovery time of around 1.8 seconds.

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The primary current peak of the three tests is identical and peaks at 1.6 p.u. for a short amount of time.In the ramp back to the nominal power reference the highest inertia test also resulted in the higher of thetransient peaks as the lower J tests display a smaller current transient the lower the inertia becomes.

As for the frequency, the system shows a smaller frequency deviation for higher virtual inertias, but withthe cost of longer settling times. When comparing the lower inertia tests to each other the smallest inertiahas somewhat lower overshoot but equal settling time to that of J = 0.01.

Figure 4.36: Three phase fault scenario 1. First graph: Blue: Active power reference, Red: Actual activepower (J=0.005), Green: Actual active power (J=01), Purple: Actual active power (J=1). Second graph:Blue: Filter current (J=0.005), Red: filter current (J=0.01), Yellow: filter current (J=1). Third graph:Blue: Frequency [Hz] (J=0.005), Red: Frequency [Hz] (J=0.01), Green: Frequency [Hz] (J=1).

4.3.3 Power Synchronization Control

For scenario 1 and 2 were the synchronization switched from PSL to the back-up PLL when the RMS-valueof Upcc reached a threshold of less than 0.5 p.u. As seen in the figure 4.37, the power turned 0 when thePLL was implemented.

For scenario 1 (figure 4.37) , the total recovery time was approximately 0.8 s before it became completelystable after the fault occurrence. The overshoot of the frequency was during the recovery maximum near50.5 Hz, with a transient of 51.7 Hz at the fault occurrence. The maximum fault current peak was around1.7 p.u.

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Figure 4.37: Three phase fault scenario 1. First graph: Blue: Active power reference, Red: Actual activepower. Second graph: Blue: Filter current (phase A), Red: filter current (phase B), Yellow: filter current(phase C). Third graph: Frequency [Hz]

Figure 4.38 shows a three phase fault with different values of the damping constant (γ). With a greatervalue of γ, the overshoot got smaller but the undershoot became greater.

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Figure 4.38: Fault analysis of different values of the damping (different values of γ). First graph: Blue:Active power (γ=1), Red: Active power (γ=2), Green: Active power (γ=3), Purple: Active power (γ=4),Yellow: Active power (γ=5). Second graph: Blue: Filter current (γ=1), Red: Filter current (γ=2), Green:Filter current (γ=3), Purple: Filter current (γ=4), Yellow: Filter current (γ=5). Third graph: Frequency[Hz] (γ=1), Red: Frequency [Hz] (γ=2), Green: Frequency [Hz] (γ=3), Purple: Frequency [Hz] (γ=4),Yellow: Frequency [Hz] (γ=5).

It can be seen in figure 4.39) that for SCR=5, the settling time for the power was greater, the overshoot forthe power and current were slightly smaller whilst the overshoot for the frequency was greater, compared toSCR=1.

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Figure 4.39: Fault - comparing of PSC in SCR=1 and SCR=5. First graph: Blue: Active power (SCR=5),Red: Active power (SCR=1). Second graph: Blue: Filter current (SCR=5), Red: filter current (SCR=1).Third graph: Blue: Frequency [Hz] (SCR=5), Red: Frequency [Hz] (SCR=1).

4.3.4 Synchronous Power Control

The synchronous power control different fault scenarios will be evaluated considering the same aspects asfor Droop and PSC, but also considering two different values of the virtual inertia (J=0.01 and J=0.004).

For the first scenario (figure 4.40), the difference between J=0.01 and J=0.004 is that the system has moredamping characteristics considering the power at J=0.01. Otherwise the system is alike regarding overshoot,settling time and transients. The total recovery time was around 1.2 s, the maximum current transient peakwas 1.6 p.u. and the frequency had its peak at ± 1.2 Hz.

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Figure 4.40: Three phase fault scenario 1. First graph: Blue: Active power reference, Red: Actual activepower (J=0.004), Green: Actual active power (J=0.01). Second graph: Blue: Filter current (J=0.004), Red:filter current (J=0.01). Third graph: Blue: Frequency [Hz] (J=0.004), Red: Frequency [Hz] (J=0.01).

As seen in figure 4.41, the system with SCR=1 was somewhat more damped but had a greater settling time,considering all signals.

Figure 4.41: Fault - comparing of SPC in SCR=1 and SCR=5, with J=0.004. First graph: Blue: Active powerreference. Red: Active power (SCR=1), Green: Active power (SCR=5). Second graph: Blue: Filter current(SCR=1), Red: filter current (SCR=5). Third graph: Blue: Frequency [Hz] (SCR=1), Red: Frequency [Hz](SCR=5).

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4.3.5 Comparative result

In figure 4.42 all methods are compared regarding the three phase fault scenario 1.

Overall, VSG has the greatest settling time considering all signals and Droop control has the smallestsettling time. PSC is almost as fast as Droop and has an overall more damped system compared to theothers. VSG also has an overall damped system, whereas Droop has a greater overshoot looking at the powerand frequency. Moreover, Droop and SPC have a large frequency transient at the fault occurrence, wherePSC and VSG have a more damped transient.

Figure 4.42: Fault - comparing all models. SPC and VSG with J=0.01. First graph: Blue: Active powerVSG, Red: Actual active power SPC, Green: Actual active power PSC, Purple: Active power Droop, Yellow:Active power reference, Second graph: Blue: Filter current VSG, Red: filter current SPC, Green: Filtercurrent PSC, Purple: filter current Droop. Third graph: Blue: Frequency [Hz] VSG, Red: Frequency [Hz]SPC, Green: [Hz] PSC, Purple: [Hz] Droop.

Comparing the two models which have virtual inertia, VSG and SPC, the general behavior is that VSG hasmore damping characteristics but has a greater settling and recovery time, as seen in figure 4.43.

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Figure 4.43: Fault - comparing VSG and SPC. Both with J=0.01. First graph: Blue: Active power VSG,Red: Actual active power SPC, Green: Active power reference, Second graph: Blue: Filter current VSG,Red: filter current SPC, Third graph: Blue: Frequency [Hz] VSG, Red: Frequency [Hz] SPC.

Comparing Droop and PSC, Droop is somewhat faster but has a greater overshoot in general, seen in figure4.44.

Figure 4.44: Fault - comparing Droop and PSC. First graph: Blue: Active power PSC, Red: Actual activepower Droop, Green: Active power reference, Second graph: Blue: Filter current PSC, Red: filter currentDroop, Third graph: Blue: Frequency [Hz] PSC, Red: Frequency [Hz] Droop.

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5. Discussion

Before performing analysis, comparative or not of the grid forming models it should be made clear that theresults that were presented in the result section can not be analyzed whether they perform good or bad ina real, practical implementation. A comparison towards the research articles is also difficult, because of thelack of research on the particular setup that has been implemented in this report.

5.1 System analysis

One can discuss the control methods and the classification of grid forming versus grid following converters.Considering table 2.1, there are some objectives that must be fulfilled for the methods to be consideredgrid forming converters. The first one, being ”controls voltage magnitude and frequency”, it is clearlyobserved in the result chapter that all the methods are controlling the frequency and the voltage. Anoverview how this is made can be seen in figure 4.2. The second objective being ”can operate in standalonemode” can also be clarified because of the generated frequency in all models. Instead of following the gridfrequency all models are generating its own. The last objective is ”can achieve 100 % penetration” and itwas proven for all models by testing if they were stable for the whole power span.

The final general grid model seen in figure 4.1 had for all models the parameter values seen in table 4.2.Almost all of them were given parameters to make the system somewhat uncomplicated and to be able toonly focus on the performance of the different control methods. For example, the choice of having a Y-Ytransformer with 1:1 ratio, made it simpler to analyze the system without considering the transformer orthe difference of primary and secondary side, the only thing to consider was the transformer (leakage) losswhich was constant. The value of the filter inductance was given from ABB to suit the system and thevalues of the power rating, frequency, grid voltage and primary and secondary voltage were chosen becauseof the fact that it was supposed to be a high voltage system with standard values. The values of VDC , gridinductance and resistance were calculated according to requested performance of the general system.

The filter dimension can be seen as an important factor, as it is shown in all fault tests they display thesimilar output filter transient during faults regardless of control method. To ameliorate this transient aproper dimension investigation could be executed to protect the hardware from breaking, if and when aphysical implementation is done.

The fault detection and ramping function did during the faults tests prove to function quite well. As thedetection of faults was done in a timely manner according to theory and that the ramping function after afault had been cleared proved effective in damping the transients that could follow when returning tonominal operations, without the ramping algorithm in place.

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As three phase fault was the only type of fault that was considered in this thesis the fault detection is mainlyfocused on monitoring positive sequence RMS voltages, and not negative and zero sequences that do occurin asymmetrical faults. However, the implemented detection algorithm is designed to monitor all phasevoltages, to trigger if one of the phases drops, enabling it to better detect one phase faults, even though itis not designed for it. This would ease the further development and implementation of asymmetrical faulthandling.

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5.2 Test configuration

The result section in this report roots itself in tests, tests that are designed to encapsulate as muchcomparative results as possible between the grid forming models, as well as to satisfy ABB:s needs andinterests in the topic. As described in the introduction of the report some of the goals of this project is to’studying the system impact of each grid-forming control method through frequency, transient andsmall-signal stability analysis’, which is exactly what we strode for when designing the tests.

The transient and small-signal stability test were limited to only performing an active power step from 0.95to 1 pu, as it proved to be representative of the behavior of step tests in other power regions. ABB alsoexpressed the same opinion when consulting with them regarding the design of tests. Having the gridforming converter deliver power would also be more common than it absorbing it (meaning setting thepower reference to a negative value), which made the small-signal test scenario resemble nominaloperations.

Moreover, the decision to not include all parameters in the small-signal analysis was a logical one. As themodels are built from the ground up, the thesis authors were well aware of which parameters made asignificant impact on the systems dynamic behavior, and which parameters were needed but did not makemuch of a difference when altered. Therefore, to make the results more graspable and primarily focused onrelevance all parameters variations were not included.

The decision to only examine three phase faults was done by our thesis supervisor at ABB, as the threephase fault is a worst case scenario and would stress the grid forming converters as well as keep theresources on developing the actual models, and not algorithms to handle asymmetrical faults such as theone phase fault. However, the only thing missing in order for the models to properly handle all other typesof faults is a fault detection algorithm suited for these, as the models proved effective in the worst casescenario. The configuration of the three phase fault having a total fault duration of 200 ms was also donein conjunction with ABB and reviewing of statistical grid fault duration from several national gridagencies. As could be seen in the results the current measurement was done at the converter instead of thePCC, because of the fragile nature of inverter switches when experiencing currents above the switch rating.Therefore, the current levels may seem lower than expected during a fault. This was the case at the PCC.

It was also discussed if a mix of active and reactive power respectively should be present in test scenarios,but in this regard both our initial tests and discussions with ABB led to running the tests with either activepower or reactive power only.

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5.3 Droop control

5.3.1 Model design

As mentioned in the result section the model differs somewhat from what is generally stated in researcharticles, the main difference being the replacement of the P controller with a PI for both the P andQ-droop control loops. The motivation behind this change was to avoid steady state errors, especially inthe θ that was to be used to synchronize and control the entire system. The feed-forward term on theQ-Droop was also implemented to better handle unexpected transients such as faults, as the feed-forward’pre-charges’ the PI controller with values from its output, enabling faster reaction times.

Droop control is a control method that has been around for quite some time and is not purposely designedfor grid forming control. Therefore, we believe that the steady state error that the original P controllerbrought with it was up to standards for earlier applications, but not as one of the defining factors in gridforming Droop control. Adding the integral term does have an effect on how fast the controller can adjust,but it was understood that the stability benefits of using a PI controller outweighed that of the speed anderror of the P controller.

5.3.2 Small Signal analysis

When the control method was evaluated in the small-signal analysis it did show some promise. Droopcontrols main benefit is its fast system response time, especially when looking at step response rise timesthe results are below 100 ms. As a consequence to its fast response, the Droop control is also accompaniedby a characteristic of having some overshoot, ranges from 10 to 17 %, which is not catastrophic, butoptimally that behavior would be some percentage lower.

One conclusion that can be made when looking at table 4.3 is that the system is well tuned, as the performanceof the optimal values can be verified as being ’optimal ’ when compared to its neighboring parameter variants.One goal of executing a small-signal analysis is coming to the conclusion of proper parameter choices, whichwas the case here.

5.3.3 Fault analysis

As discussed earlier, Droop control is a fast control method, which also applies for fault recovery, with afast recovery of around 0.55 seconds regardless of fault scenario. What could be noted however is that thefast recovery and relatively great damping of the converters output current during this phase comes at thecost of high grid frequency variations, with a variance up to 2.25 Hz from the nominal value. Even thoughthis deviation only lasts for a short while, it is quite substantial. What can be done to remedy this is tolower the proportional gain of the active power loop, and therefore sacrificing performance, but keeping thefrequency regulation within a lower span during faults.

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5.4 Virtual Synchronous Generator Control

5.4.1 Model design

During the literature study to this thesis two reoccurring VSG models were identified, which both showedpromise. As described in the theory section the models had some similarities, and as soon as one of themethods was designed the other one could be derived from it. Both methods were fully implemented andtested, until it could be determined that the model now seen in the result was chosen based on its generallybetter performance and simplicity. The alternative method did have a more stable behavior, but exhibitedslow tendencies, and was therefore discarded for this report, but will still be delivered to ABB.

The implemented model is very similar to what was described in articles. However there was no indicationon how tuning or implementation should be approached, which became part of the literature study. In figure4.7 it can be observed that the model only has a damping factor, which resembles that of the P regulator, asthe inertial block provides integral action (as 1/s in Laplace domain is an integral). Which gives the model aPI-regulated behavior with the benefit of no steady state error. The reactive power loop is likewise, identicalto what was described in the theory.

5.4.2 Small Signal analysis

The results of the small-signal analysis of the VSG presented a robust response, as it was in the slower endof the spectrum, but proved to be solid with dampened overshoot and minimal steady state error. Asparameters changed during the analysis the response of the system changed in some aspects, such asovershoot and settling time, but retained a somewhat reasonable rise time. This tells us that the model canoperate in a large span of parameter tuning, without showing signs of instability.

The parameter that had the largest impact on the systems rise time was the proportional gain of the activepower loop, also known as the damping of the system. This parameter should probably be kept at itsoptimum. The virtual inertia of the system was a parameter of great interest when executing the test as wellas during the literature study. It proved to have similar behavior in the system response for test iterationswith lower inertia, but displayed more swing for the higher inertia test, which could be expected according tothe theory of swing equations. Otherwise the tuning parameters of the reactive power droop had a pervadingeffect on system response as seen in the small-signal analysis for Droop control for example, which couldhint to that they have the same impact on the system in both models.

5.4.3 Fault analysis

The area that the VSG should have presented good results is in the fault handling, which was also thecase. In fact, the grid forming model was so robust that it managed to ride through faults before the faultdetection and handling algorithm was implemented. The full recovery time was in the higher spectrum, butis a behavior to be expect from the swing equations that the model is based upon. It also showed greatability to keep the grid frequency stable during the faults with minor overshoots. The increased inertia diddampen the frequency deviation compared to that of the tests with lower inertia. The question at hand ishowever what is preferred, a faster recovery, with larger current and frequency deviations, or a more robustrecovery that has the side-effect of being somewhat slower?

It can be argued that after the comprehensive study of this model a variable virtual inertia should beconsidered for future work in this area. This could enable optimal behavior in fault scenarios as well asnominal operation.

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5.5 Power Synchronization Control

5.5.1 Model design

The final result of the PSC differed from the theory at some aspects. The decision of having the feedbackdamping part on both the PSL and the PLL was made after testing the method as in the theory with thefeedback only on one side, resulting in a better performance than having it on both sides. The resultshowed that the synchronization had a smoother transition and it was also more difficult to findsatisfactory values for the angle correction described in the theory.

The decision of having a PI instead of a P controller was made also after testing the method with andwithout the integrating part, and it was realized that the system performed better in steady state, withoutan error, with a PI controller.

The inner loop was implemented as in the theory, although different articles presented some design differencesregarding the inner loop. Overall, many of the decisions made were based on what gave a satisfactory resultin the overall system that was used.

5.5.2 Small Signal analysis

The results of doing a small signal analysis showed that the PSC overall is a fast method with rather smallrise and settling time. When altering the parameters Kip, Kpq and Kiq, they did not have a great impacton the step response of P and it can also be seen in table 4.10 that they have rather big operation span aswell. The PI controller in the reactive power loop naturally has a bigger impact on the step response of Qthan on P, which is also seen in the figures 4.22 and 4.23. When analyzing the table 4.5, the optimal valuesfor the step response of P may not correspond to the optimal values for the step response of Q, which mustbe considered when tuning and choosing values for all methods.

The results when comparing SCR=1 and SCR=5 is showing that the SCR=5 results in a faster systembut with a more oscillating behavior. One reason for the oscillations is probably the filtering that is notoptimally tuned for the system. It is expected that the system with a higher SCR is faster because of itsstrong stability characteristics.

5.5.3 Fault analysis

Because of the back-up PLL was implemented, it was difficult to implement some sort of rampingtechnique for when P was 1 or -1, which resulted in a less smooth transition for the recovery. Otherwiseshowed the method overall a quite stable response with a general fast recovery time and a reasonableovershoot. Although, for scenario 2 the recovery time was greater with some oscillations before it becamestable. This was a general response for when P was negative.

One important parameter considering the fault recovery and damping was the damping parameter γ whichcan be altered dependent on which system is requested, since it affected both the settling time and theovershoot.

When comparing two different SCRs when applying a fault, the system with a greater SCR became slowerconsidering the power recovery and with a more unstable result considering the frequency. This resultcompared with the step response with different SCRs is strengthening the result of a greater overshoot whenSCR=5, but regarding the recovery time the two results are dissimilar.

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5.6 Synchronous Power Control

5.6.1 Model design

The first decision made when implementing the SPC was which method to do further analysis on, and itwas early seen that the method that was chosen performed better regarding stability and flexibility. It wasbecause of the ease of implementing the method and the greater span of which the parameters made thesystem stable. The difficult part was to choose reasonable parameters when altering Kp, KG and KI , sincethey were dependent on several parameter each.

5.6.2 Small Signal analysis

Overall, you can see in table 4.6 that the overshoot is in the upper region of what is preferable, although afast system is also desirable. The result of doing a small signal analysis is indicating that when altering theparameters, one has to compromise regarding getting the fastest system but with most damping. Since allparameters are dependent on each other, one can re-tune and analyze the system even more than what hasbeen made, but without doing a mathematical analysis, it would not be time efficient.

Regarding the values of the VA, the impact of when altering the values was quite small, although the mostimportant result was the figure 4.30 where the system was tested with and without the VA. The result wasexpected since the VA is a LPF and it should provide a system with less noise.

What is most interesting with the SPC is the parameters Kp, KG and KI since they are dependent on 5other parameters in the equations 2.34, 2.35 and 2.36. For this thesis, it was decided to focus mostly on theimpact of J and some impact of ξ keeping the other parameters constant. This decision was made becauseof the reason to keep the scope of the thesis at a reasonable level.

When analyzing the response of different virtual inertia’s (J), firstly is the span of which the system isfunctioning expected (table 4.10), since it was clearly stated in the theory that a reasonable span of H isbetween 1 and 10. The result of the step response with varying J was expected and a higher value gave amore damped system but a slower one, and what is preferable is dependent on what system is desired

A really interesting parameter is the damping coefficient ξ, which from one test (figure 4.32) showed a greatimpact regarding both damping and settling time. In the system with the parameters chosen (table 4.7),only a value of 0.7 and smaller was able to perform for all the fault scenarios. If there had been more timeto investigate a higher value of ξ but with alternating values of the other parameters, one could maybe finda solution and a way of making it work for all scenarios, with the advantages of a higher value of ξ.

One major advantage with SPC is that it was stable for all SCR up to SCR=5 without the need of retuning.This implies that the method is stable and could have a greater span of in which situations it could besuitable to be applied in.

5.6.3 Fault analysis

When comparing J=0.01 and J=0.004, the fault analysis was really similar, but J=0.01 had overall somebetter damping performance. The scenarios when P and Q were positive, the system was overall stablewith quite fast settling time, compared to the scenarios where P and Q were negative. Some scenarios hada substantial peak for both frequency and the power, although only for a short moment. For it to be morecompetitive and work for all systems regarding safety and stability, this peak would have to decrease.

Because of its origin in the swing equation, it is expected for it to be somewhat slower than the methodswithout the inertia characteristics.

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5.7 Comparative analysis

Directly comparing performance, the grid forming models that will be discussed in this section is onlyrepresentable for the test environment that has been setup in this thesis. The system that has been setup isa compressed and simplified one, and conclusions regarding other scenarios cannot be done.

5.7.1 Small Signal analysis

The first thing that can be done is dividing the models into two categories. That being the slower but morerobust models that include virtual inertia (SPC and VSG) and the faster ones which are less robust (Droopand PSC). When examining the respective small-signal analysis tables (tables 4.3, 4.4, 4.5 and 4.6) thiscategorization can quickly be identified.

Comparing the two methods containing virtual inertia, we see that VSG is the slower one but with aoverall more damped system. As can be observed, the SPC has a rise time of 2 times smaller than the VSGbut also a overshoot that is substantially larger. The final comparison of settling time, we can see thatthey are quite similar but VSG is around 150 ms faster.

When examining the two methods without inertia both show fast performance, but with the cost of generallyovershooting the target reference. The reason for this could possibly be a result of their shared heritage ofbeing based on similar philosophies, as they are quite similar in the design aspect. As Droop control exhibitsgenerally faster response time, it also has a larger overshoot, which is natural. Even though the settlingtimes differ somewhat, they can be deemed as similar.

5.7.2 Fault analysis

Comparing all methods, the general behavior as for the small signal analysis stands for the fault analysis aswell, with Droop and PSC having the faster recovery than that of SPC and VSG. Also, regarding theovershoot, where the Droop control has the largest overshoot concerning both power and frequency.

In figure 4.42 it can be observed that the models that allow a larger amount of grid frequency deviationalso seem to recover faster from the fault than those who has smaller variance in the frequency generation.This fact is especially clear when comparing the VSG to Droop control, as the VSG has a very conservativefrequency deviation but has a longer recovery time. This would give the hardware in an actual hardwareimplementation to recover. These are important factors to consider when choosing appropriate convertersfor applications.

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6. Conclusions

Before this thesis project was started several project goals were set up which where declared in theintroduction of this report. As the project came to a close, the success of the goals was to be evaluated. Torecapitulatilze, the goals were the following:

• Gain understanding of grid forming converter concepts, including identifying the most important andrelevant control methods and typologies

• Implementation of the relevant grid forming models in PSCAD

• Perform analytical and comparative tests of the implemented models and its system dynamics

When reviewing the goals stated above, all of them have been fulfilled during the project. The first monthof the thesis was spent in a literature study, reviewing over a hundred different academic articles ondifferent grid forming models, summarizing and discussing the topic. This provided the basis of which thechoice of the four grid forming models to implement, and provided the support needed to implement themodels in PSCAD. When the implementations were close to complete, a secondary literature study wasdone with the focus on electrical faults and transient behavior of systems. The gained knowledge in thearea and in discussions with ABB to the formulatation of test scenarios for the analytical and comparativepart of the thesis, which were fully implemented and reviewed in the result and discussion sections above.

The system and general model that have been utilized for all methods has been of great use, because of thesimplified model could the focus be on creating and developing the control methods. The fact that theinner loop for the all the methods were almost the same, simplified the general comparison and analysis ofthe outer loops.

The Droop control method proved being in the faster segment of grid forming converters, exactly asdescribed in academic articles. The model did however display less robust system dynamics compared tothe other evaluated methods. Droop control has the benefit of being a somewhat simple control method,but with a narrower parameter tuning window.

The Virtual Synchronous Generator control is probably the most robust control method evaluated in thisthesis project. The fact that the method has such a large parameter span in which it is stable is a greatbenefit and has great prerequisites for further developments and improvement.

To conclude the performance of the PSC, it is a fast method with a rather low overshoot in general,considering both step response and fault analysis. What would be interesting to see in future work, is if itcan improve its performance in case of fault, considering removing the back-up PLL.

The SPC, is in general a stable method with potential good prospects, since it has a great span of workingareas considering strong/weak grids. Its damping properties in this study were found to be limited,although we believe that with more studies involving all the parameters for calculating Kp, KI and KG,the outcome could be improved further.

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We believe that all these methods have their pros and cons, and with more time for studies, all of themcould be further adjusted and improved. However, the two most interesting methods for future work wouldbe the Synchronous Power Control and Virtual Synchronous Generator control. It is because of theirdevelopment potential and width. We are convinced that the current future grid demands stability andreliability, which these control methods have a high probability of delivering.

Suggestions for future studies would be to develop a general state space model which could be modified tosuit all the models. The purpose of the state space model would be to more efficiently examine the gridforming models behavior on a larger scale, as well as properly place poles and zeros for optimalperformance. The possibilities if a state space model would be implemented could also help automate thetuning parameters for different grid scenarios, this thesis proved that they do function for a large range ofgrid types (very weak to strong) with no or little adjustment of control parameters.

Further development in the physical appearance of the grid forming models is something that also shouldbe taken into consideration. The general theme in the academic studies is that similar models and scenariosare researched, therefore making less progress and improvement. The study that has been conducted in thisthesis looked at parameters that are rarely seen in the articles, such as different grid configurations, highvoltage applications and model flexibility in regard to changing scenarios. For further investigation in thearea one should explore the possibility to mix the performance promoting behaviors of one control methodto another. This could potentially eliminate shortcomings of some grid forming models to ensure reliabilityas well as performance on the future electrical grid.

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7. Appendix

7.1 MATLAB-code

MATLAB-code of calculating the grid parameters VDC , R and L.

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7.2 Fault analysis - Droop control

Scenario 2 (figure 7.1) presented a recovery time of around the same as scenario 1 of 0.6 seconds includingthe fault period of 0.2 seconds. During the recovery ramp the power peaks at -1.7 p.u. with some rippleon the swing-back from the peak, to finally settle at the nominal power reference. The current exhibiteda multistage variation consisting of nominal, smaller ripple, filter transient to then ramp down to nominalbehavior around the 11.1 second mark. The grid frequency overshot its nominal value by 3.5 Hz during thefault recovery.

Figure 7.1: Three phase fault scenario 2.

Scenario 3 (figure 7.2) was when the reactive power reference was set to 1 p.u., and displayed an oscillativefault response in the power domain, as the overshoot peaks at 2.5 p.u., and gradually dampens from thereon, until reaching steady state some 0.8 seconds later. As in scenario 1 the output current peaks at 1.5 p.u.during the filter phase, as it then was attenuated to reach its nominal value. The grid frequency mimickedthe ringing of the reactive power during recovery, with a maximum overshoot of 1.5 Hz.

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Figure 7.2: Three phase fault scenario 3.

The final fault scenario for the Droop control method is scenario 4 (figure 7.3) . The power stays within thespan of operation (± 1 p.u.) during its transients and recovers in around 1 second after the fault has begun.The current flowing out of the converter peaked at approximately 1.2 p.u. for the duration of around 0.15seconds to later quickly dampen and return to nominal levels. The frequency dips down to 48.6 Hz duringthe recovery, and maxes out at 51 Hz before returning to its nominal value of 50 Hz.

Figure 7.3: Three phase fault scenario 4.

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7.3 Fault analysis - VSG

Scenario 2 initially displays similar behavior for all of the inertial cases with a slight overshoot duringrecovery of + 0.4 p.u./- 1.6 p.u.. At the 12.8 second mark in figure 7.4 the higher inertia test scenarioinitially shows the most dampened tertiary overshoot, but later takes longer to recover than both J = 0.01and 0.0005. The output current magnitudes follow the same trend as seen in scenario 1, where the higherinertia exhibits a higher recovery current than the two lower ones, which are similar, with the slight edge ofthe lower inertia setups.

The grid frequency response also showed resemblance to that of fault scenario 1, with the lower inertia testsshowing similar behavior to one another, with a maximum frequency deviation of 0.75 Hz to quickly recoverto operating frequency. The higher of the inertias show very little deviation but took some time settling.

Figure 7.4: Three phase fault scenario 2.

For fault scenario 3 7.5) all of the inertial tests show similar behaviors, with a recovery time of around 2seconds, Q overshoot of 1.65 p.u. and an almost identical output current waveform. The tests differ in thefrequency response, as the lower inertias show similar results as in scenario 1 and 2 and the higher inertiahaving a more dampened overshoot and longer recovery time.

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Figure 7.5: Three phase fault scenario 3.

Fault scenario 4 (figure 7.6) presents results similar to that of scenario 3 with the difference being themagnitudes of all overshoots are dampened, otherwise the results are the same.

Figure 7.6: Three phase fault scenario 4.

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7.4 Fault analysis - PSC

For scenario 2 (figure 7.7) , the overall transition between the PSL and PLL was more unstable and the totalrecovery time was approximately 2 s from the fault occurrence. The overshoot of the frequency was duringthe recovery maximum approximately 1.8 Hz and the maximum fault current peak was around 1.5 p.u.

Figure 7.7: Three phase fault scenario 2.

For scenario 3 and 4, Q was set to 0 when the RMS-value of Upcc reached the threshold of less than 0.5 p.u.and was then ramped to 1 or -1. For scenario 3, the ramping time was set to 0.2 s and for scenario 4 wasthe ramping time set to 0.5 s, because of the fact that it became unstable for any ramping time below 0.5 s.

For scenario 3 (7.8) the total recovery time was approximately 1 s, the overshoot of the frequency reached amaximum of 50.7 Hz and the maximum fault current peak was around 1.8 p.u.

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Figure 7.8: Three phase fault scenario 3.

For scenario 4 (figure 7.9) was the total recovery time around 1 s from the occurrence of the fault. Theovershoot of the frequency was during the recovery maximum ± 0.5 Hz and the fault current peak reacheda maximum of 1.4 p.u.

Figure 7.9: Three phase fault scenario 4.

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7.5 Fault analysis - SPC

For scenario 2 (figure 7.10), the overall system was more unstable and the recovery time was around total4 s, regardless the value of J. But similar to scenario 1, the was damping greater at J=0.01. The currentpeak was a bit smaller than for scenario 1 with a peak of 1.5 p.u. The frequency had a transient peak atmaximum 51.8 Hz.

Figure 7.10: Three phase fault scenario 2.

For scenario 3 (figure 7.11), the power had a peak at +2.1 p.u. compared with scenario 1 and 2 were thepower peaked -0.6 and +0.1 from its original value. The total recovery time was around 1.5 s, the currentpeaked at 1.6 p.u. and the frequency had a maximum peak at -48.9 Hz. The difference in the overall behaviorfor J=0.004 and J=0.01 were almost non-existence.

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Figure 7.11: Three phase fault scenario 3.

For scenario 4 (figure 7.12), the recovery time was approximately 1.2 s, the maximum current peak was at1.2 p.u. and the frequency had the same peak as for scenario 3. Also, it showed the same behavior for J=0.01and J=0.04, except for a small difference in the damping characteristics for the frequency, where J=0.01 wasslightly more damped.

Figure 7.12: Three phase fault scenario 4.

Comparing fault performance for the system with and without a VA, it is clearly seen in figure 7.13 that thesystem with VA is more damped and less oscillative.

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Figure 7.13: Three phase fault scenario 1 with and without virtual admittance.

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