Control design and validation of voltage source converters

Treball de Fi de Grau Grau en enginyeria en tecnologies industrials Control design and validation of Voltage Source Converters Report June 25, 2024 Author: Amanda Gener Alarcón Supervisor: Oriol Gomis-Bellmunt Co-supervisor: Jaume Badia Girona Call: Spring 2024 Escola Tècnica Superior d’Enginyeria Industrial de Barcelona page 2 Report Control design and validation of Voltage Source Converters page 3 Resum 1 Pàgina. L’objectiu d’aquest treball és dissenyar i validar un model Simulink d’un convertidor de font de tensió (VSC) en el context dels sistemes de generació d’energia eòlica. La primera part de l’informe ofereix una visió general de les principals característiques dels VSC, la seva aplicació als sistemes de generació d’energia eòlica i els seus principis operatius específics. S’analitzen diferents tipus d’aerogeneradors i es selecciona una part específica del sistema d’un d’ells per a estudiar-la més a fons. A partir d’aquí, s’exploren alguns conceptes i dispositius clau d’electrònica de potència amb la finalitat de comprendre els principis bàsics del funcionament d’un VSC (necessaris per al disseny del model realitzat en la segona part). La segona part de l’informe ofereix una explicació detallada dels subsistemes del model dissenyat del VSC. S’aborden les seves configuracions específiques, models matemàtics subjacents, esquemes de control i interaccions amb altres subsistemes. Els resultats finals de la simulació no s’inclouen en aquesta part. A la tercera part de l’informe, s’assigna un valor a totes les variables i s’executen dues simulacions amb l’objectiu d’explorar la resposta del VSC davant diferents escenaris. Els resultats al final d’aquest informe validen amb èxit el model dissenyat i serveixen com a prova del seu impacte en els sistemes de generació de turbines eòliques. page 4 Report Resumen 1 Página. El objetivo de este trabajo es diseñar y validar un modelo Simulink de un convertidor de fuente de tensión (VSC) en el contexto de los sistemas de generación de energía eólica. La primera parte del informe ofrece una visión general de las principales características de los VSC, su aplicación a los sistemas de generación de energía eólica y sus principios operativos específicos. Se analizan distintos tipos de aerogeneradores y se selecciona una parte específica del sistema de uno de ellos para estudiarla más a fondo. A partir de ahí, se exploran algunos conceptos y dispositivos clave de electrónica de potencia con el fin de comprender los principios básicos del funcionamiento de un VSC (necesarios para el diseño del modelo realizado en la segunda parte). La segunda parte del informe ofrece una explicación detallada de los subsistemas del modelo diseñado del VSC. Se abordan sus configuraciones específicas, modelos matemáticos subyacentes, esquemas de control e interacciones con otros subsistemas. Los resultados finales de la simulación no se incluyen en esta parte. En la tercera parte del informe, se asigna un valor a todas las variables y se ejecutan dos simulaciones con el objetivo de explorar la respuesta de los VSCs ante diferentes escenarios. Los resultados al final de este informe validan con éxito el modelo diseñado y sirven como prueba de su impacto en los sistemas de generación de turbinas eólicas. Control design and validation of Voltage Source Converters page 5 Abstract 1 Page. The aim of this report is to design and validate a Simulink model of a Voltage Source Converter (VSC) in the context of wind power generation systems. The first part of the report provides an extensive overview of VSCs main assets, how do they apply to wind power generation systems and their specific operative principles. Different types of wind turbines are debriefed and an specific part of the system of one of them is selected for further study. Built on the latter, some key power electronics concepts and devices are then explored with the purpose of understanding the basic principles of how does a VSC work (necessary for the model design carried out in part two). The second part of the report provides a detailed explanation of the subsystems in the designed model of the VSC. Their specific configuration, underlying mathematical models, control schemes and interactions with other subsystems are addressed. Final simulation results are not included in this part. In the third part of the report, all variables are assigned to a value and two simulations are executed with the aim to explore the VSC’s response to different scenarios. The results at the end of this report successfully validate the designed model and serve as evidence of their impact in Wind Turbine Generation systems. page 6 Report Control design and validation of Voltage Source Converters page 7 Contents 1 Introduction to the project 14 1.1 Motivation ......................................... 14 1.2 Scope ............................................ 14 1.3 Prerequisites ........................................ 15 1.4 Objectives ......................................... 15 2 Voltage-Source Converters: A debrief 16 2.1 Smart grids and why Voltage Source Converters are essential ............ 16 2.2 Technical definition .................................... 17 2.3 Practical scenario: Wind turbine generated power transmission systems ..... 18 2.3.1 An introduction to wind turbine power generation .............. 18 2.3.2 High Voltage Direct Current transmission and the role of Voltage Sourced Converters ..................................... 21 2.3.3 WTG power generation and model simplifications .............. 22 2.4 Operating principles: How to go from DC to AC and viceversa ........... 26 2.4.1 The role of half bridge converters ........................ 26 2.4.2 About PWM technique .............................. 29 2.4.3 Clarke and Park transformations ........................ 30 3 The model 33 3.1 General Scheme and model simplifications ...................... 33 3.2 Subsystems ......................................... 35 3.2.1 AC Grid Simulation ............................... 35 3.2.2 Phase Locked Loop controller .......................... 36 3.2.3 Voltage and active power control ........................ 38 3.2.4 Current Loop Control .............................. 42 4 Results and discussion 46 4.1 Results ........................................... 46 4.2 Analysis of the results .................................. 53 5 Planning 54 6 Economic assessment 55 7 Environmental assessment 57 8 Social and gender equality assessment 58 9 Conclusions 59 Bibliography 60 page 8 Report Abbreviations and Symbols Symbol/Abbreviation Parameter AC Alternating Current B2B-converter Back to Back converter BJT Bipolar Junction Transistor CLC Current Loop Control DC Direct Current DFIG Doubly Fed Induction Generator HVDC High Voltage Direct Current IGBT Insular-Gate Bipolar Transistor MMC Multilevel Modular Converter MOSFET Metal-Oxide-Semiconductor Field-Effect Transistor PLL Phase Locked Loop PSMG Permanent Magnet Syncronous Generator PWM Pulse Width Modulation SCIG Squirell Cage Induction Generator SDG Sustainable Development Goals STATCOM Static Synchronous Compensator VSC Voltage Source Converter WRIG Wound Rotor Inductor Generator WTG Wind Turbine Generator ASwept area of the wind turbine generator CCapacitance CpPower coefficient ExVoltage of circuit x fxFrequency of circuit x Gcx Controller transfer function of system x KxConstant of controller x LlInductance PxActive power injection of circuit x PtTurbine power QxReactive power injection of circuit x RRadius RlResistance SxApparent power of circuit x Tqd0Park transformation matrix Vpeak Peak voltage Xil Magnitude of phase i X∗ iReference magnitude for Xi XiPhasor expression of Xi xi(t)Time domain expression of Xi Xerror Error magnitude of a system Xα, XβClarke transformed magnitudes Xq, XdPark transformed magnitudes Control design and validation of Voltage Source Converters page 9 Symbol/Abbreviation Parameter αβ-frame Reference frame related to Clarke transformation qd-frame Reference frame related to Park transformation βWind turbine generator pitch angle ΓTorque of the wind turbine ˆ θAngular position of the grid λWind turbine generator tip-speed ratio ρAir density τxTime constant of system x vwWind speed ξiDamping ratio of system x z−1Control time delay ωxAngular speed of system x page 16 Report 2 Voltage-Source Converters: A debrief 2.1 Smart grids and why Voltage Source Converters are essential Some challenges that motivated this paper are related to the traditional power grid, that while long useful, presents several limitations[33]: •At capacity: Power plant is allocated to too many sources and demand exceeds supply. •Aging infrastructure: Inefficiencies and increased risk of failure. • Relies on a single source: On the power plant itself, which means that, in case of a failure, without a secondary source, blackouts/voltage peaks/etc. will inevitably occur. • Lack of real-time report: In the event of a failure, identifying where the failure has occurred and why is a large time consuming activity. Only by executing an inspection of the power grid in person will you find the source of the problem and solve it. To address these limitations, throughout the years, more power plants have been built. This, in addition to only addressing the first drawback, implies a greater negative impact on the planet: more power plants, more burning of fossil fuels. As a counter proposal, smart power grids tackle this issues head on with features such as [33]: • Real time system monitoring: Accurate detection and location of faults by integrating sensors throughout the grid. Possibility of controlling the grid remotely to solve certain faults, redistributing electric flux, etc. • Efficient energy management: Optimized distribution, cost management and fault prevention. • Renewable energy integration: Wind, hydro, solar additional cleaner power plants as complementary sources, reducing the electric power plant’s load and acting as backup in the event of failure. Key functionalities of VSC converters that support the implementation of all these features are[4]: • Mitigating energy fluctuations: VSC’s are able to compensate the sources’ ups and downs, thus ensuring a steady flow of electricity to the grid. • More efficient energy transmission: VSC’s harness renewable energy sources that are located in far, remote areas and delivers the needed electricity with minimal losses compared to traditional AC transmission lines. • Better reliability of the grid: With its features, VSC converters help to prevent blackouts and power surges, enhancing grid stability. Control design and validation of Voltage Source Converters page 17 2.2 Technical definition It has been stated in previous chapters of this paper that the main function of a VSC is to act as a bridge between renewable energy sourced electricity and the power grid. Yet its specific components and how does it work are still to be debriefed. When it comes to power electronics context, Amirnaser Yazdani and Reza Iravani provide the following definition [4] for power-electronic converters: "...a multiport circuit that is composed of semiconductor (electronic) switches and can also include auxiliary components and apparatus, for example, capacitors, inductors, and transformers. The main function of a converter is to facilitate the exchange of energy between two (or more) subsystems, in a desired manner, based on prespecified performance specifications."[4] This definition and function can of course be applied to VSC. In the context of this paper, it will exchange the power output of a wind turbine generator (modelled as DC in this report, detailed in 2.3.3) with an AC distribution grid. Its specific tasks will entail [5]: • Bidirectional conversion: In this case, from DC (wind power generation) to AC (transmission to the grid), detailed in 2.3.3. •Active and Reactive power control: Regulating these magnitudes to ensure grid stability. page 18 Report 2.3 Practical scenario: Wind turbine generated power transmission systems 2.3.1 An introduction to wind turbine power generation The basic principle of electrical power generation through wind energy conversion relies on capturing the kinetic energy of the turning windmills and transforming it into electricity[34]. Figure 1: Scheme of the interior of a wind turbine [36] The turbine’s blades, which specific shape and orientation are crucial for efficient wind capture, rotate by the force of wind, imparting a torque on the rotor shaft[ 34 ]. This movement’s speed is then increased by a gearbox (not in all types of generators, detailed later in this section), which steps up the rotational velocity to a level suitable enough for efficient electricity generation[ 34 ]. This rotational movement activates the electric generator that converts the high-speed rotational kinetic energy from the gearbox shaft into electrical alternating current (AC)[34]. The basic function of a generator like the one just mentioned is to provoke movement of electrons (flow of electric current) by using electromagnetic induction[35]: Figure 2: Generator scheme, modified from [38] Control design and validation of Voltage Source Converters page 19 The rotor is equipped with magnets that, in spinning in presence of a metallic coverage (coil), create an electromagnetic field that causes the electrons to move. Since the rotor varies its relative position passing through the same angular coordinates over and over again with each spin, the electrons find themselves periodically switching their direction of motion, creating an alternating flow of electric current (AC)[35]. Wind Turbine generators can be asynchronous or synchronous, and communicate with the grid through numerous configurations [6]: Type 1 Wind Turbine Generator: A type 1 turbine is mainly characterized for rotating at a fixed speed that follows the frequency of the electrical grid[ 6 ]. It can act as a motor (sub-synchronous speed) or a generator (supersynchronous speed) and presents a rigid torque-speed curve (its optimal performance is achieved at a single wind speed), reducing its operating speed range[ 35 ]. A Squirrel Cage Induction Generator (SCIG) converts motion into electricity and is directly connected to the transformer, eliminating the need for a converter and synchronization system[ 35 ]. Nonetheless, the absence of a converter increases the turbine’s sensitivity to voltage dips and grid faults when fluctuations in wind speed occur[ 35 ]. Simply put, Type 1 WTGs offer simplicity at the expense of an inflexible operative range and significant susceptibility to grid disturbances. Figure 3: Scheme of a Type 1 Wind Turbine Generator[6] Type 2 Wind Turbine Generator: Type 2 WTGs are very similar to Type 1, the main difference is that this type rotates at variable, but limited speed[ 35 ]. They include a variable resistor in the rotor so that the power curve can be shifted to higher rotational speeds[ 35 ]. They operate with a Wound Rotor Inductor Generator (WRIG) and are also connected directly to the transformer[ 35 ]. Similarly to Type 1, the main drawback comes from the direct connection to the grid, which exposes the system to grid disturbances[35]. page 20 Report Figure 4: Scheme of a Type 2 Wind Turbine Generator[6] Type 3 Wind Turbine Generator: Instead of the resistors mentioned in Type 2, Type 3 applies variable frequency alternating excitation, which allows to adjust the rotor speed and phase almost instantaneously, resulting in much better control of the stator circuit[ 6 ]. In addition, this type of turbine pioneered in power control systems by adding a low power VSC back-to-back converter (functionality later explained in 2.3.2) in between its generation system (which operates using a Doubly Fed Induction Generator or DFIG) and the grid[ 6 ]. This feature allows control over both active and reactive power, while being able to rotate at asynchronous speeds (acts as a motor when sub-synchronous and as a generator when super-synchronous)[ 15 ]. Hence, Type 3 WTGs are more capable of mitigating voltage dips and grid faults because of the converter[ 35 ]. However, since not all energy flows through the VSC converter, the operational flexibility and control design of this generator can still be optimized. Figure 5: Scheme of a Type 3 Wind Turbine Generator[6] Type 4 Wind Turbine Generator: Type 4 wind turbines are the most commonly used for offshore power generation and, in fact, the ones modelled in this project. This is due to the power electronics technology included in their configuration, that, in contrast with Type 3, flows all energy through the VSC back-to-back. This configuration decouples the turbine from the grid’s frequency, enabling full regulation of its velocity to achieve aerodynamic efficiency (this allows full variable rotational speed) without compromising the grid’s needs[ 6 ]. In addition, they are capable of controlling the flow of reactive power and act similarly to a STATCOM (Static Synchronous Compensator), a device used to maintain voltage stability in the grid[ 6 ]. They usually operate with a permanent magnet Control design and validation of Voltage Source Converters page 21 synchronous generator (PMSG)[ 6 ], which functionality has been previously explained in this chapter and eliminates the need of a gearbox[35]. Figure 6: Scheme of a Type 4 Wind Turbine Generator[6] 2.3.2 High Voltage Direct Current transmission and the role of Voltage Sourced Converters In the previous section, it was explained that Type 3 and 4 WTG contain a VSC back-to-back converter which objective is to achieve full control over the system’s active and reactive power distribution and protect the circuit from grid unsteadiness. The aim of this chapter is to explain exactly how is this device integrated in the WTG and which specific part of it is simulated in this project. Figure 6is a pretty good scheme to pinpoint where the VSC is located in the system, however, it must be considered that this type of turbine is mostly used for offshore wind generation because of its great ride-trough capabilities[ 16 ]. Hence, a more realistic scheme of WTG 4 supply system is provided: Figure 7: Diagram of a WTG 4 integration system[17] To understand the following explanation, the essential terms stated in the image are MMC (Multilevel Modular Converter), HDVC (High Voltage Direct Current), PMSG (Permanent Magnet Synchronous Generator) and B2B-Converter (VSC back-to-back converter). From observing figure 7, it can be noted that two sets of VSC back-to-back converters are present (since a VSC can be considered, in essence, a type of MMC). The first set (left side of the image, encapsulated as "B2B-Converter") is incorporated inside the WTG’s configuration, and the second set (right side of the image, encapsulated as "HVDC system") communicates the offshore supply with the onshore grid. Located in the B2B-Converter system, the left converter is the one modeled in this paper, given that VSCs are bidirectional, it is now clarified that the simulation will perform specifically a DC-AC conversion, hence, the simulated VSC will act as an inverter. page 22 Report 2.3.3 WTG power generation and model simplifications As discussed in 2.3.1, the wind turbine model designated for this report is type 4, illustrated in Figure 6. This specific model utilizes a Permanent Magnet Synchronous Generator (PMSG) for electricity generation, the principles behind the functionality of which were also covered in section 2.3.1. WTG 4 integrated VSC back-to-back converter uses an anti-parallel IGBT+diode assembly as switching device, the justification for this decision is explained in 2.4.1. A scheme of the WTG integrated in the VSC is provided: Figure 8: WTG integrated with VSC back to back[18] Notice how the WTG is followed by two sets of VSCs in figure 8, this assembly is known as VSC Back-to-Back. It serves two primary purposes: • AC-DC conversion: The first VSC converts the variable AC output voltage from the PMSG into a regulated DC voltage. • DC-AC conversion: The second VSC then transforms the regulated DC voltage into a controllable AC voltage. The AC output of this converter, as can be seen in figure 7, flows through a tranformer and enters the HVDC transmission system, which is composed by another VSC back-to-back. Since the VSC modeled in the report corresponds to the inverter noted as "Grid side converter" in Figure 8, for simplification issues, its connection to the turbine will be through direct generated power transmission. This implies that all the power generated by the WTG’s torque is directly injected into the DC side of the simulated inverter, this is detailed in 3.2.3. An scheme is provided for further understanding: Control design and validation of Voltage Source Converters page 23 Figure 9: Scheme of simplified model[39] In order to simulate power extraction from the WTG, three key concepts are to be introduced: • Power (P): The instantaneous energy that the turbine produces and is transferred to the PMSG using torque.[18] • Torque ( Γ ): The rotational force acting on the wind turbine shaft. It’s the twisting force that causes the shaft to rotate, which is transferred to the PMSG. It is calculated by dividing the power of the turbine by the angular velocity of the rotor ωm.[18] • Power Coefficient ( Cp ): A dimensionless parameter that measures the efficiency of the energy that is captured by the WTG. It depends on the pitch angle ( β ) and the tip speed ratio of the wind turbine (λ).[18] The power output (Pt) of the wind turbine can be calculated using the following formula[18]: Pt=1 2Cp(λ, β)ρAv3 w(1) Where: •ρ : Air density ( kg/m3 ), this parameter depends on factors like altitude and temperature. At sea level its value is 1.225 kg/m3[18], which will be the value used for the simulation. •A: Swept area of the wind turbine blades (m2), depends on their radius, R.[18] page 24 Report •Cp: Power coefficient •vw: Wind speed (m/s) As every efficiency parameter, Cp is calculated as the ratio between the real (actual power provided by the rotating shaft) and the nominal power (total wind power)[ 18 ]. While Betz limit defines its maximum theoretical value as 0.5925[ 19 ], its real value can be computed as the following nonlinear function of λand β[20]: Cp(λ, β)=0.5(116 1 λi−0.4β−5)e−21 λi(2) Where: λ=ωmR vw (3) 1 λi =1 λ+ 0.08β− 0.035 1 + β3(4) To add realism to the simulation, the optimal Cp will be calculated using a Matlab script that applies expression 2through various values of both λ and β . The results are plotted in the following figure: Figure 10: Graph of Cpvs λfor several values of β[39] The maximum power coefficient ( Cp1 ) can ve observed along with its specific parameters ( λ1 and β1 ). Once these values have been determined, and considering expression 3, the parameters needed to calculate Pt that remain undefined are R and ωm or vw . Given the power ranges that a Type 4 WTG entails (>4MW)[ 15 ], a radius ( R ) of 75 meters (extracted from an existing WTG Control design and validation of Voltage Source Converters page 25 model called V150-4.2MW [ 21 ]) and a wind speed of 35 km/h[ 22 ] = 9.72 m/s is assumed in order to keep proportionality. In order to observe how does the model react to power variations, Cp2 , λ2 and β2 will also be simulated in 4, the corresponding wind speed along with all of the other values are later grouped in table 1. page 32 Report Figure 20: Three-phase voltages in the αβ0 frame[39] The Park transformation presents an additional advantage in comparison to Clarke: it transforms these oscillations into constants, with this, controlling a sinusoidal magnitude now becomes equivalent to controlling a constant magnitude, simplifying the process. Its main equations to carry a Park transformation are the following: [xqd0]=[Tqd0]·[xabc](7) Tqd0(θ) = 2 3·   cos(θ) cos(θ−2π 3) cos(θ+2π 3) sin(θ) sin(θ−2π 3) sin(θ+2π 3 1 2 1 2 1 2   (8) In a nutshell, controlling a three-phase VSC with fluctuating AC signals is more complex than controlling constant magnitudes. To address this, αβ and dq-frames will be implemented: 1. Creating two separate magnitudes with different values to replace xa , xb and xc for them: reduction of the number of controlled parameters. 2. Eliminating oscillations: constant position of the voltages will be controlled. 3. Ultimately, simplifying the overall control process Control design and validation of Voltage Source Converters page 33 3 The model 3.1 General Scheme and model simplifications The proposed model for the VSC will be composed of 3 main control schemes and a reference computation that is based on the instantaneous power theory. A scheme of the system is provided for further understanding: Figure 21: General scheme of the subsystems present in the model of the VSC[39] Everything that is explained now is detailed during chapter, all given information should be taken as a mere introduction of the following subsections. The DC side of the VSC is composed by a current source and a shunt capacitor (detailed in 3.2.3). The power generated by the turbine is directly injected as PDC and gives place to a corresponding current ( IDC ) and voltage ( EDC ). The latter is controlled by using the an active power reference (P∗) that is directly related in magnitude to E2 DC (detailed in 3.2.3). The AC side attached to the VSC is composed by a three phase grid ( Va, Vb, Vc , generated in 3.2.1), its angle ( θgrid ) is used as control input for the Phase Loop Controller (which aim is to synchronize the grid to the converter for control purposes). The controlled angle is used to transform these alternating three phase voltages into two constant magnitudes ( Vq and Vd ) in page 34 Report order to simplify the control process (Park Transformation, detailed in 2.4.3). So far, a controlled DC voltage magnitude ( EDC ) and two simplified magnitudes originated from the AC grid ( Vq and Vd ) have been obtained. By applying the instantaneous power theory (detailed at the end of 3.2.3) to Vq , P∗ and Q∗ (a reactive power reference not yet explained), two reference currents are obtained ( I∗ q and I∗ d ). By decoupling and controlling this currents with a Current Loop Controller (detailed in 3.2.4), two new controlled voltages are obtained ( Vql and Vdl ). Both of them are now anti-transformed and a fully controlled three phase AC grid ( Val, Vbl, Vcl ) is achieved. This grid conforms the AC side of the VSC, it is connected to the real AC grid through a low pass filter (detailed in 3.2.1) that smooths the interaction between them. Control design and validation of Voltage Source Converters page 35 3.2 Subsystems 3.2.1 AC Grid Simulation To model the VSC, it is previously required to implement both AC and DC sides of the system. The AC side is related to the distribution grid mentioned in 2.3.1), while the DC side is connected to the energy transmission system described in 2.3.2. To simulate the AC grid in Simulink, the first step was to implement all three voltages ( VA , VB and VC ). This was achieved by using three Voltage Source Controlled Blocks, which use cosinusoidal waveforms as input and generate the expected magnitudes. The waves were generated by implementing the following system: Figure 22: System that generates three cosinus wave with specific parameters[39] The values of the variables observed in the graph are calculated as so: ω0= 2 ·π·f0(9) Vpeak =r2 3·Em(10) The obtained voltage phasors are: VA= 2300V VB= 2302π 3V VC= 230− 2π 3V (11) The three phases of the grid have been implemented by individual blocks of constant values 0, page 36 Report 2π 3 and − 2π 3 radians respectively. The output signals (Phase A, Phase B and Phase C) are used as input for three Controlled Voltage Source Blocks (one for each phase): Figure 23: Scheme of the three cosines waves entering the controlled voltage source blocks[ 39 ] The resulting magnitudes ( VA , VB and VC ) are connected to the converter by means of a non ideal inductive filter shown below: Figure 24: AC voltages and low pass filter[39] Where VAl , VBl and VCl are originated by several control systems (such as Current Loop Control) that will be later explained. Current measurement devices were included for further calculations. 3.2.2 Phase Locked Loop controller A Phase Locked Loop (PLL) controller’s role in the VSC structure is to determine the angle and the angular velocity of the electrical network[ 5 ] and ensure that all the system’s controlled voltages are in sync with it. This is achieved by minimizing Vd(mentioned in 2.4.3). When V d approaches zero, the angle of the grid voltage ( θabc ) aligns with the d-axis of the dq reference frame, indicating successful voltage synchronization between the grid and VSC controlled voltage[5]. Control design and validation of Voltage Source Converters page 37 Figure 25: Graphic representation of Park transformation[39] The control process goes as so[5]: 1. Vd is compared to a reference (zero in this case), providing the error of the system ( θerror ). 2. θerror is controlled by a PI controller, obtaining the angular velocity of the system (ˆω) 3. ˆωis integrated to obtain angular position (ˆ θ) 4. ˆ θ is fed-back into a Park transformation block, which delivers Vd (that is compared to zero) and Vqvalues. Figure 26: Scheme of a PLL control system[39] The equation[5] of the PI controller is: page 38 Report Kf(s) = KpP LL     1 τP LL +s s    (12) Where KpP LL stands for the proportional gain that determines the strength of the control action of Kf(s). Its value is determined by the following expressions[5]: ωn=rKpP LL ·Em τP LL (13) ξ=pτP LL ·KpP LL ·Em 2(14) The controller has been implemented via Simulink: Figure 27: Scheme of a PLL controller simulated with Matlab Simulink[39] All magnitudes have been previously explained and the Park transformation block has ˆ θ as input as well as Va , Vb and Vc (labeled as A, B and C in Figure 27), which have been extracted from a simulated electric grid that is not shown in the image but can be found in Figure 23. This process is validated in 4. 3.2.3 Voltage and active power control In grid-connected converters, controlling the injected or extracted power is crucial for maintaining stability and proper operation of the power system. While AC grid has been modelled using sinusoidal waves, the DC side of the converter can be modelled as a voltage source or current source with a shunt capacitor[5]. Control design and validation of Voltage Source Converters page 39 It is intended to ensure that the DC side feeds the grid using the power extracted from the turbine ( PDC ) whilst maintaining a stable voltage ( EDC ). To ensure this, the latter approach is used and applied with the next expression: EDC =PDC IDC (15) Now, the power generated by the wind turbine ( PDC ) flows into the DC side of the VSC in form of current (IDC). The circuit can be observed in the next images1: Figure 28: Scheme of both AC and DC side interconnected by the VSC[39] Figure 29: Simulink model of active power extraction and calculation of EDC using a controlled current source[39] In order to properly model the VSC, a constant DC voltage flow is needed, this is addressed by the capacitor, C . Regulating EDC ’s value is possible thanks to its ability to store (charge) and release (discharge) energy when convenient. Whenever the AC grid’s demand differs from the power generated by the turbine (DC side), EDC fluctuates in value during the transient state. To 1 In Figure 29 a delay ( z−1 ) can be observed, this was included in order to agilize the iterative calculation process of EDC using equation 15 page 40 Report mitigate this, the capacitor either stores or releases IDC so that EDC ’s value presents no variation when steady state is achieved. Consequently, if the grid consumes less power than the turbine generates, EDC tends to increase in the transient state and IDC is stored by C in the form of an electrostatic field. Conversely, if the grid requires more power than the wind turbine provides, the capacitor releases the stored electrostatic field energy, providing the required additional current (and therefore power) to the circuit, without varying EDC ’s value. By continuously cycling between charging and discharging based on the power flow conditions, the capacitor acts as a buffer, absorbing excess energy and releasing it when needed. This ensures a stable voltage in the DC side. The active power reference ( P∗ ) can then be obtained as the sum of the active power generated by the turbine ( PDC ) and the active power of the capacitor, P∗ C , which can be expressed in the Laplace domain as: P∗ C(s) = 1 2·s·C·(EDC)2(16) Considering 16, in order to maintain P∗ C ’s magnitude, (EDC)2 will be the controlled variable (referred to as E2 from now on) instead of EDC . The model requires a defined reference value E2∗ , which will be compared to E2 .The outcome of this comparison (error of the system) will enter a PI controller to finally determine P∗ C . Notice that when the system’s error is zero E2=E2∗ , EDC =Eref , voltage can be considered stable and controlled. The resulting control scheme of this process is: Figure 30: Control scheme for active power[39] P∗ now serves as a setpoint, it determines the desired amount of power to be exchanged with the grid. This magnitude will now be used to determine the currents I∗ q and I∗ d using instantaneous power theory, which is defined by Akagi, Watanabe, and Aredes (2007)[7] as so: "The p-q Theory is based on a set of instantaneous powers defined in the time domain. No restrictions are imposed on the voltage or current waveforms, and it can be applied to three-phase systems with or without a neutral wire for three-phase generic voltage and current waveforms. Thus, it is valid not only in the steady state, but also in the transient state. As will be seen in the following chapters, this theory is very efficient and flexible in designing controllers for power conditioners based on power electronics devices...." (Akagi, Watanabe, and Aredes, 2007, page 41)[7] It is fair to say that this theory is an adequate approach for the context described in this paper. Applying Park’s transformation 7to the expressions for three phase voltages in 5, the expressions of Vqd0and Iqd0are obtained: Control design and validation of Voltage Source Converters page 41 Vqd0=Vq−jVd √2 Iqd0=Iq−jId √2 (17) The power of a three phase balanced voltage system can be calculated as [8]: S=P+jQ = 3 ·Vqd0·(Iqd0)∗= 3 · Vq−jVd √2· Iq+jId √2(18) The equation for both active and reactive power can be then obtained: P∗=3 2·(VqI∗ q+VdI∗ d) Q∗=3 2·(VqI∗ d−VdI∗ q) (19) As explained in 3.2.2, the PLL system makes sure that Vdis reduced to zero, this applied to the expressions in 19 allows currents to be computed as: I∗ q=2 3· P∗ Vq I∗ d=2 3· Q∗ Vq (20) In the following figure, the Simulink model of Figure 30 is included and it presents Iq∗ as output of the system by appyling this last equation: Figure 31: Model of voltage and active power control[39] page 48 Report Figure 38: Comparative overview of the grid’s angular speed and position to the system’s angular grid and position[39] Figure 39: Simulated magnitudes Vqand Vd[39] It can be observed that the all values are controlled ( ωP LL =ω0 , θP LL =θ0 , Vd= 0 ) in a matter of approximately milliseconds, validating the PLL functionality in synchronizing the controlled system to the grid’s frequency and minimizing Vd. Validation of simulated DC Voltage regulation system Control design and validation of Voltage Source Converters page 49 Figure 40: Comparative overview of EDC and Eref [39] It can be observed how the system successfully controls EDC for both power inputs detailed in Figure 36. Validation of simulated Current Loop Control system Figure 41: Comparative graph of Iqand I∗ q[39] Figure 42: Comparative graph of Idand I∗ d[39] Both Iq and Id stick to their reference values for different power inputs. From the instantaneous page 50 Report power theory described in 3.2.3, given that Q∗= 0 in this simulation, I∗ d should remain zero as well, which can be observed in the graph. Active and Reactive power control system validation Figure 43: Active Power and Active Power reference overlapped[39] Figure 44: Siulation 2: Reactive power and reactive power reference[39] Both previous figures validate that both active and reactive power of the system are controlled. However, in order to fully validate the model, another simulation is carried out with the following new values2: 2Values not included in this table have stayed the same Control design and validation of Voltage Source Converters page 51 Parameter Symbol Value Unit Tip speed ratio λ7.954 - Pitch angle β0degrees Power coefficient Cp0.411 - Wind speed vw9.72 m/s Wind Turbine Power Pt4.09 MW Reference reactive power Q∗4MW Table 2: Values changed/added in the second simulation In this simulation, no wind power input change will be applied, but a Q∗ step perturbation in the current control loop system in t= 1s. The graphs are yet again presented3: Validation of simulated DC Voltage regulation system Figure 45: Second comparative overview of EDC and Eref [39] Validation of simulated Current Loop Control system 3 the systems not included in this second simulation have stayed the same, since Q∗ has been injected to the Current Loop Control and does not impact all magnitudes of the system page 52 Report Figure 46: Second comparative graph of Iqand I∗ q[39] Figure 47: Second comparative graph of Idand I∗ d[39] Active and Reactive power control system validation Figure 48: Active Power and Active Power reference overlapped for simulation 2[39] Control design and validation of Voltage Source Converters page 53 Figure 49: Reactive power and reactive power reference for simulation 2[39] All previous figures show that the model is robust, validating the functionality of the VSC. 4.2 Analysis of the results The first simulation performed in 4.1 evaluated the system’s response to a change in power injection (the power generated by the wind turbine became higher at t= 1s ). The results clearly indicate that all controllers are functioning properly, since all magnitudes appear controlled in shape and value. In this simulation, reactive power was not injected in the system so a second simulation has been executed in order to observe the system’s response to another perturbation signal, in this case ( Q∗ ). The results exposed in the second simulation also suggest that all subsystems are correctly designed and modeled, given that all changes in the magnitudes are again controlled and present coherent in values. In the beginning of this report, it was adressed that VSCs are able to mitigate energy fluctuations that can happen due to several scenarios (variability of a renewable energy source, power drops or surges, blackouts,...). This protects both devices that are connected to the ends of the VSC, in this case, the DC side is connected to a Wind Turbine Generator (with ideal simplifications) and the AC is connected to a distribution grid-line that conducts this energy to the offshore VSC back-to-back converter that can be observed in Figure 7. The simulations have provided two examples of power variation and proved how the VSC is capable of stabilizing all affected magnitudes, fulfilling its purpose in the Wind Generation System. page 54 Report 5 Planning Figure 50: Gantt Diagram 10/02/2024-29/03/2024[39] Figure 51: Gantt Diagram 30/03/2024-17/05/2024[39] Figure 52: Gantt Diagram 18/05/2024-23/06/2024[39] Control design and validation of Voltage Source Converters page 55 6 Economic assessment As per the economical resources required in the making of this project, four main areas will be entailed: Human Resources All hours implied in investigating, writing and developing the simulation will be accounted for a value of 15 €per hour (an estimation based on the usual payroll of a junior Industrial Engineer in Spain). Task Hourly price Hours Price General research and academic background 15 €/h 60 h 1200 € Simulation development 15 €/h 160 h 2250 € Writing and editing 15 €/h 100 h 1200 € Total - 320 h 4650 € Table 3: Human resources related cost Tools and programs To run the simulation, both a MATLAB and Simulink student license permit were used. The price plan is detailed in source [12]: License Yearly price Duration of project Price MATLAB 262 €/year 6 months 131 € Total - - 131 € Table 4: Tools and programs related cost Machinery Considering the approximate price of the computer that was used to carry out the simulation (900 €) and a depreciation period of 5 years. The monthly cost can be calculated as: 900 AC 5years ·12 months = 15 AC/month (31) Object Monthly price Duration of project Price Computer 15 €/month 5 months 75 € Total - - 75 € Table 5: Machinery related cost Electrical consumption Given that the price of 1 kWh is 0.1519 €[13]: page 56 Report Equipment Power (W) Usage (h) Consumption (kWh) (€/kWh) Total Cost (€) Laptop 100 320 32 0.1519 4.56 Table 6: Electrical consumption related costs The total cost of the project can then be calculated as: Total cost without taxes = 4650 + 131 + 75 + 4.56 = 4856.56 AC(32) The total cost of the work amounts to 4856.56 euros, adding the corresponding local taxes (21%), it would be 5876.4376 €. Control design and validation of Voltage Source Converters page 57 7 Environmental assessment This chapter analyzes the environmental impact associated with the making of this report, specifically the carbon dioxide ( CO2 ) emissions generated due to computer usage detailes in 6. The estimated electric consumption ( ec ) has been determined in 6and its value is 0.1519 kWh. The emission factor ( ef ) used to compute the emissions, which can vary depending on the electricity source and location, is 273 gCO2eq/kWh [ 37 ]. The equation to calculate the emissions is then provided as: CO2[kg] = efec 1000 (33) Based on the formula and provided values, the following table shows the results: Electric consumption (ec) Emission factor (ef)CO2emissions 0.1519 kWh 273 gCO2eq/kWh 0.0414687 kg Table 7: kg of CO2generated in the making of this paper This result represents a small environmental impact. However, its accuracy presents limitations. It has been assumed an average emission factor of 2022, and the actual emissions might vary depending on the specific electricity source used and on the actual date. Additionally, the assessment only considers the electricity consumption during computer usage, other factors like lights, printing of material, transportation and so on also present an impact that has not been considered. page 64 Report Retrieved from: Wind Power in Power Systems [36] Dehghanimadvar, Mohammad, Ahmadi, Farzin, Shirmohammadi, Reza, Aslani and Alireza. (2019). Forecasting of wind energy technology domains based on the technology life cycle approach. In: Energy Reports Journal pp (1236–1248) DOI:10.1016/j.egyr.2019.08.069 Retrieved from: Forecasting of wind energy technology domains based on the technology life cycle approach. [37] Gencat (2022) Factor d’emissió de l’energia elèctrica: el mix elèctric Date of consultation: June 18th, 2024 Retrieved from: Factor d’emissió de l’energia elèctrica: el mix elèctric [38] DOB-Academy. (2018). Wind Turbine Generators, HOW DO THEY WORK? YouTube video Date of consultation: May 15th, 2024 Retrieved from: Wind Turbine Generators, HOW DO THEY WORK? [39] Image of own creation