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Lillgrund Wind Farm Modelling and Reactive Power Control
Isabelle Boulanger
Master Thesis Stockholm 2009
Electrical Machines and Power Electronics, Power Systems Royal Institute of Technology SWEDEN
Kungliga Tekniska Högskolan
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Abstract
The installation of wind power plant has significantly increased since several years due to the recent necessity of creating renewable and clean energy sources. Before the accomplishment of a wind power project many pre-studies are required in order to verify the possibility of integrating a wind power plant in the electrical network. The creation of models in different software and their simulation can bring the insurance of a secure operation that meets the numerous requirements imposed by the electrical system.
Hence, this Master thesis work consists in the creation of a wind turbine model. This model represents the turbines installed at Lillgrund wind farm, the biggest wind power plant in Sweden. The objectives of this project are to first develop an accurate model of the wind turbines installed at Lillgrund wind farm and further to use it in different kinds of simulations. Those simulations test the wind turbine operating according to different control modes. Also, a power quality analysis is carried out studying in particular two power quality phenomena, namely, the response to voltage sags and the harmonic distortion.
The model is created in the software PSCAD that enables the dynamic and static simulations of electromagnetic and electromechanical systems. The model of the wind turbine contains the electrical machine, the power electronics (converters), and the controls of the wind turbine. Especially, three different control modes, e.g., voltage control, reactive power control and power factor control, are implemented, tested and compared. The model is tested according to different cases of voltage sag and the study verifies the fault-ride through capability of the turbine. Moreover, a harmonics analysis is done. Eventually the work concludes about two power quality parameters.
Index Terms: Wind Power, Power Electronics, Induction Machine, Controls (Voltage Control, Active and Reactive Power Control, Current Control, DC Voltage Control), Voltage Source Converter (VSC), Power Quality, Voltage Sags, Harmonics, and Grid Code.
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Acknowledgements
This Master thesis was done at Vattenfall Research and Development AB and approved by the Division of Power Systems and the Division of Electrical Machines and Power Electronics belonging to the School of Electrical Engineering at KTH. Both divisions are engaged in this project since it treats different aspects within the whole electrical engineering area. The work was funded by Vattenfall Vindkraft.
My supervisors at KTH were Dr. Valerijs Knazkins and Professor Hans-Peter Nee and Dr. Fredrik Carlsson at Vattenfall Research and Development AB. My examiner at KTH was Assistant Professor Mehrdad Ghandhari.
I would like to thank some persons that played an important role during the 20 weeks of my Master thesis work.
I express my gratitude to Dr. Fredrik Carlsson, Dr. Valerijs Knazkins, and Professor Hans-Peter Nee for their help and guidance during the whole project. Thank to Mehrdad Ghandhari for accepting being my examiner for this Master thesis.
I am indebted to Evabritt, Urban Axelsson and Daniel Salomonsson for their help and support.
I absolutely want to thank Lovisa Stenberg and Laura Bergholz for being helpful, attentive and who always encouraged me. Especially I am very grateful to Lovisa Stenberg with whom I was sharing more than a room during these 20 weeks and who facilitated so much my integration in VRD.
I want to thank my parents for teaching me perseverance and rewards of work and also for encouraging me despite the 2000 km distance between us.
Finally I am thankful to Benjamin Boullanger who never gave up encouraging me and helping me. For the productive discussions we had and his relevant suggestions and advices.
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Table of Contents Page
1 Introduction 1 1.1 Background and prior studies 1 1.2 Lillgrund wind farm 2 1.3 Purpose 3 1.4 Report outline 4
2 Control theory 5 2.1 The control system of the wind turbine 5 2.2 Determination of the DC capacitor 5 2.3 Grid side control 7 2.3.1 The system 7 2.3.2 The inner current controller 9 2.3.3 The DC voltage controller 10 2.3.4 Three different control modes on turbine level and park pilot 11 2.3.5 Problems raised by the close bandwidth of the imbricate loops 13 2.4 Generator side control 15 2.4.1 Introduction to vector control 15 2.4.2 The induction generator 16 2.4.3 Current controller 16 2.4.4 Flux estimation for rotor flux orientation 17 2.4.5 Speed controller 19 2.4.6 Optimal speed control system 20 2.5 Siemens control system 21
3 Introduction to power quality analysis 22 3.1 Introduction to power quality – Grid Code 22 3.2 Voltage sags 23 3.2.1 Definition 23 3.2.2 Studied case 24 3.3 Harmonics 25 3.3.1 Measurements of harmonics 25 3.3.2 Induction machine harmonics 26 3.3.3 Power electronics harmonics 26 3.3.4 Transformer harmonics 27
4 Modelling and implementation in PSCAD 28 4.1 Wind turbine 28 4.1.1 Wind source 28
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4.1.2 Wind turbine 28 4.1.3 Governor 29 4.2 Induction generator 29 4.3 Voltage source converter 30 4.3.1 One module 30 4.3.2 The PWM inverter filter 31 4.4 Control system 31 4.4.1 Grid side control 32 4.4.2 Generator side converter 32 4.4.3 Pitch control in PSCAD 34 4.5 DC-link chopper 34
5 Simulation in PSCAD and analysis of results 35 5.1 Simulation on PSCAD – Introduction 35 5.2 Reactive Power Control and Voltage Control Modes 35 5.3 Results for one turbine – Compliance with IEC 61400-21 36 5.3.1 Voltage sags study 36 5.3.2 Harmonics analysis 39 5.4 Results concerning the voltage sag study for one or several turbines connected to the grid 40 5.4.1 Impact on the different voltages of the system 42 5.4.2 Impact on the wind turbine current 46 5.5 Results concerning the harmonics study for one or several turbines connected to the grid 47 5.6 Comparative analysis between two control modes 49 5.7 Comparison with the Siemens’ study 50 5.7.1 Harmonics study 50 5.7.2 Dynamic simulation study 51 5.8 Island Operation 53
6 Conclusions 55
7 Improvements and future works 56
References 58
Appendices 60
Simulations 65 SIMULATION A: Control mode test on the grid-side inverter connected to the grid 66 SIMULATION B: Test of the generator-side system 71 SIMULATION C: Test turbine with connexion IEC 73
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List of symbols
Symbol Quantity Unit
Vtri PWM triangular signal V
fs switching/triangular frequency Hz
Vcontrol PWM control/modulation signal V
f1 modulating frequency Hz
ma amplitude modulation ratio -
mf frequency modulation ratio ------C DC-link capacitance F
UDC DC-link voltage V
IDC DC-link current A
EDC energy stored in the DC-link capacitor J
PDC DC power W ------
Vabc 0.69/33 kV transformer input voltage V
Iabc converter output current A
Vabc_conv converter output voltage V
PAC AC active power W
QAC AC reactive power VAr
Vd,q Park coordinates of Vabc V
Vd,q_conv Park coordinates of Vabc_conv V Id,q Park coordinates of Iabc A R PWM filter resistance Ω L PWM filter inductance H X reactance corresponding to L (X = ω.L) Ω Ω angular frequency rad/s αβ axes defining the reference frame - dq axes defining the Park reference frame - θ Park transformation angle rad k Park transformation coefficient -
α1C bandwidth of a closed loop system rad/s
kp,1C proportional gain of the first current controller Ω
Ti,1C time constant of the first current controller s
tr,1C rise time corresponding to α s ------
Plosses losses in the converter W
Rvirtual virtual resistance in DC voltage control Ω
α1DC bandwidth of a closed loop system rad/s
kp,1DC proportional gain of the DC voltage controller Ω
Ti,1DC time constant of the DC voltage controller s
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tr,1DC rise time corresponding to α s ------
Us induction machine (IM) voltage V
Es IM internal voltage V
Is IM stator current A
ωm mechanical angular speed of the IM rad/s
ωr electrical angular speed of the IM rad/s
ψs rotor flux Wb
ψr stator flux Wb
Rs stator resistance Ω
Rr rotor resistance Ω
Lm magnetising inductance H
Lr rotor inductance H
Lls stator leakage inductance H
Llr rotor leakage inductance H ------ρ Park transformation angle for flux oriented frame rad
Lσ leakage inductance H
cT constant factor of the speed controller Nm/A
α2C bandwidth of a closed loop system rad/s
kp,2C proportional gain of the second current controller Ω
Ti,2C time constant of the second current controller s
tr,2C rise time corresponding to α s ------T torque N.m J inertia of the IM kg.m2 b damping constant of the IM Nm/s
α2ω bandwidth of the closed loop system rad/s
kp,2ω proportional gain of the speed controller Ω
Ti,2ω time constant of the speed controller s
tr,2ω rise time corresponding to α s ------cos(φ) power factor - H magnetic field intensity A/m s Laplace symbol 1/s
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Abbreviations
AC Alternating Current abc Three phase coordinates system DC Direct Current dq Park equivalent coordinates system d-axis direct axis in the Park representation q-axis quadrature axis in the Park representation DSO Distribution System Operator EMTDC ElectroMagnetic Transient including DC FFT Fast Fourier Transform FRT Fault Ride Through IEC International Electrotechnical Commission IGBT Insulated Gate Bipolar Transistor IHD Individual Harmonic Distortion IM Induction Machine IMC Internal Model Control (method) LVRT Low Voltage Ride Through mmf MagnetoMotive Force PCC Point of Common Coupling PE Power Electronics PI Proportional Integral PLL Phase Locked Loop PSCAD Power System Computer Aided Science pu per unit PWM Pulse Width Modulation RMS Root Mean Square THD Total Harmonic Distortion TSO Transmission System Operator VPC Vattenfall Power Consultant VRD Vattenfall R&D VSC Voltage Source Converter
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1 Introduction
1.1 Background and prior studies
Issues concerning electricity and energy generation have increased considerably over the last few decades. There exist many different ways of producing electrical energy. However, with the current concern about pollution, planet safety and oil reserve, the use of renewable energy sources has become much more systematic. Research and development in renewable energies such as wind power have increased since several decades. The wind power penetration is growing constantly over the world and especially the wind power production is increasing in Sweden [24][25].
The wind appears to be a perpetual source of power that can be used efficiently thanks to the development of new technologies. The wind industry meets different issues such as grid compatibility, acoustic performance, aerodynamic efficiency, visual impact, and wind farm location. All these issues constitute the main research and challenge of the wind industry these days. Important projects such as the Lillgrund wind farm are built up to give birth to a modern, reliable and clean source of energy.
The Lillgrund wind farm is the most important offshore wind power plant installed in Sweden with a total capacity of 110 MW, corresponding to 48 turbines. This large project sparked the interest of Vindforsk which decided to support a study principally by creating a PSCAD model of the farm. Vindforsk is a 3 years co-sponsored Swedish research program in the domain of wind power. The model of the wind farm was developed by VPC (Vattenfall Power Consultant) and studied especially the cables, transformers, breakers, and the grid. However the turbine power generation is represented by an AC current source connected to the turbine transformer, which is relatively simplistic. This model has been used to simulate some overvoltage cases, caused in particular by breaker switching . Siemens Erlangen has also performed different system studies for Lillgrund, which did not match exactly with the one of Vindforsk [26].
The objective of this project is to get a more elaborated representation of the turbine power generation. In the former model, the simple current source is not representative of the realistic turbine operation but the modelling of cables and transformers are good. Therefore, the Lillgrung wind farm model from VPC does not represent the wind turbine influence. The current project deals with the building of a turbine, which contains the electrical machine, the power electronics, and the control system of the turbine. With such a realistic model, some further simulations can be completed and compared with the former model. Vattenfall Vindkraft is the investigator and also funded the present project.
Thanks to the help of different tools, it is now possible to develop models and to simulate more or less accurately the real system of wind power. Now that the penetration of wind power is growing in the power system, the modelling of wind farms and wind turbines is more and more needed. The power system analysis is now often performed by means of different simulation tools. The modelling of the wind farm is performed in PSCAD/EMTDC [1]. PSCAD (Power System Computer Aided Design) is a graphical interface using the software EMTDC (ElectroMagnetic Transient including DC) that allows electromagnetic transients and electromechanical dynamic
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analysis [2]. The version used in this project is PSCAD 4.2.2 Professional. The software enables the creation of block diagram models and the simulation of them.
PSCAD/EMTDC allows the construction of models containing power electronics, machines, cables, transformers and breakers but also signal control process. PSCAD was chosen by Vattenfall to develop a model because it is suitable for steady state and transients simulation among others. Indeed a power quality study with analysis of voltage sags and harmonics will be carried out. Moreover, Vattenfall may start a two years project aiming at measuring and analysing the electrical transients and power quality parameters at Lillgrund wind farm. This study will try to correlate and compare the measurements with the simulation results from different models such as the one built in this Master thesis work.
1.2 Lillgrund wind farm
Figure 1: Lillgrund site
The Lillgrund offshore wind farm is situated 7 km south of the Öresund Bridge that connects Copenhagen in Denmark and Malmö in Sweden (Figure 1). The Lillgrund offshore wind farm consists of 48 wind turbines of type Siemens 2.3 MW Mk II. The wind farm plant includes: An EON’s 138 kV substation located at Bunkeflo near Malmö A 138 kV land and sea cable lines An offshore substation containing the main transformer 138/33 kV The 33 kV internal grid (Figure 2) 48 wind turbines in total The layout of the farm is seen on the Figure 2 and shows 5 feeders connected to the offshore substation each containing 9 or 10 turbines.
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Figure 2: Layout of the 33kV internal grid
Each 2.3MW wind turbine is then constituted as seen in Figure 3: 3-blades rotor Gear box Induction generator 4 quadrant Voltage Source Converter (VSC or full-power converter) 0.69/33kV transformer
Figure 3: Electrical system of one 2.3 MW turbine
1.3 Purpose
The aim of this project is to first develop an accurate model of one wind turbine. This model includes the induction generator, the power electronics, the turbine’s transformer, the filter situated at the VSC output, and the control system of the turbine. Further some power quality parameters, such as the turbine’s response to a voltage sag and the harmonics analysis, will be investigated for one, two and three turbines. Finally, a conclusion about the relevancy and the suitability of the model will be drawn.
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1.4 Report outline
Part 1 introduces the project by describing the context of the studied system, by explaining the main goal, and by giving an overview of the work.
Part 2 gives details about the theoretical study concerning the whole control system of the new wind turbine model.
Part 3 brings forth some informations about power quality and especially the parameters that will be further studied.
Part 4 presents the model created in PSCAD.
Finally Part 5 shows some simulation results that follows from the new model and analyses it.
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2 Control theory
2.1 The control system of the wind turbine
The wind turbine generator is an induction machine that is used as a variable speed machine thanks to the use of a full-power converter. The control system is based on two voltage source converters (VSC) as shown in Figure 3. The DC-link between the two converters consists of an energy storage device (capacitor); the choice of the capacitor is exposed in Section 2.2. One of the converters is connected to the turbine’s 0.69/33 kV transformer and controls the DC-link voltage across the capacitor as well as the active and reactive power flowing from the generator to the grid. The control of the DC-voltage and the control of the power flow are related and consist in one control (Section 2.3.3). It also permits a three-mode control, detailed in Section 2.3.4. From now on, this converter is referred to as the grid- side converter or inverter and the second one is referred to as the generator-side converter. The generator-side converter is connected to the generator and is used to control the speed and the electrical torque of the generator (Section 2.4). Upstream, a pitch control system governs the mechanical torque of the turbine. The vector control of induction machine turned out to be one of the most common and effective methods for ac-machines nowadays and especially for induction machines. This warrants the use of the vector control in this project. Since Vattenfall has no hint from Siemens, the control system supplier, it is assumed without any certainties that Siemens might use the vector control method. In total there are six controllers, displayed in Table 1, that compose the control system. In the table the controllers are ordered from the inner to the outer controller in the imbricate loop control system.
Table 1: List of the different controllers that compose the system
Grid-Side Generator-Side
Current controller: PI Current controller: PI DC-voltage controller including Speed and Torque controller: PI active power control: PI Reactive power, power factor and Pitch control (governor PSCAD) voltage control
2.2 Determination of the DC capacitor
The DC-link capacitor for such a system has a time constant of about 5 to 10 ms [17]. Given the impossibility to access the data of the Siemens’ control, the following model is used to guess a valuable value for the capacitor.
The cost of dc capacitor is relative to the cost of the voltage source converter (2.4 MW) that the capacitor is connected to. That is about 3.7 pu / (Energy Base). The power base in this case is 2.4 MVA. The energy base is 2.4 MJ that is the VSC power during 1 second. Therefore, the cost is 3.7 pu
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/2.4 MJ. Assume the cost of the VSC is 1 per unit. For a capacitor with a voltage rating equal to 1.754 kV and a time constant of 10 ms, the energy stored in the capacitor to get full power is 24 kJ. From these one can estimate the cost of the capacitor at 0.037 per unit that is 3.7 % of the whole VSC cost.
The capacitance of the capacitor is then calculated:
2 E 2 24 103 C (1) C 2 3 2 15.6 mF U DC (1.754 10 )
The cost figure is applicable to high power VSCs. This model is valid for high capacity converter [18].
A film capacitor of this size is generally made of several units in parallel. Typical units are found on the Internet web sites of different manufacturers. There are two different solutions to install the capacitor devise. Either it is composed by many small capacitors or by a few large capacitors in parallel. An example is drawn by examining the products of one manufacturer [19]. This manufacturer proposes a large choice of high power capacitor for power electronics.
Table 2 shows different possibilities to design the DC-link capacitor. Vn corresponds to the maximum operating peak voltage for which the capacitor has been designed for continuous operation.
Table 2: List of possible capacitor devices for the DC-link Capacitance Number of Total weight V [V] [uF] n devices [kg] 825 2000 20 210 1980 2000 8 152 1980 2000 8 168 3960 2000 4 144 3970 2000 4 142 8000 2000 2 120 8160 2000 2 117
The more devices, the heavier the capacitor is. Also, many small devices mean that more space is needed. The weight and size may be a factor to choose the design of the capacitor since the turbine must tolerate a certain maximum weight. However if one capacitor should fail, it is more ingenious to have small devices so that it is easier and cheaper to replace it. The case number 2 with 8 units of 1980 μF each seems to be a good compromise. A lot of other aspects as electrical and thermal characteristics and mechanical design of the devices are of interest for the user but are not part of the present study.
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2.3 Grid side control
2.3.1 The system
The purpose of the grid-side control is to regulate the DC voltage of the DC-link situated between the two converters. It also maintains the power balance between the DC-link and the AC side of the converter. The control strategy is studied in [2]. Also, the grid-side converter is equipped with a three- mode controller, which makes it possible for the grid-owner to choose either the reactive power control at the point of common coupling (PCC) or the power factor control at the PCC or the grid-side converter output voltage control. The controller of the grid-side converter is represented in Figure 4. The VSCs are constituted by six diodes and six IGBTs (isolated gate bipolar transistor) commanded by a PWM control (pulse width modulation).
Figure 4: Control model of the grid side converter
The equation connecting the converter AC voltage and the grid-side voltage is:
dI V R I L abc V (2) abc_ conv abc dt abc
where Vabc, Iabc and Vabc_conv represent the grid-side voltages, the grid currents and the converter output voltages. R and L are the three-phase resistance and inductance between the converter and the transformer. The PWM filter of the grid-side converter, which consists of R and L, is studied later in 4.3.2.
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In order to compute the VSC controller, it is more convenient to work in the dq- reference frame which is rotating at the grid speed = 2f [rad/s]. The transformation from the initial to the rotating reference frame is known as Park’s transformation and the rotating reference frame referred to as Park’s reference frame (or dq-reference frame). The angle θ (Figure 5) is the transformation angle for the Park transformation. The αβ- axis represents the initial reference frame corresponding to the three- phase vectors where Va is aligned on the α- axis. The choice is made to align the grid side voltage Vabc on the q-axis of the Park’s reference frame. This implies Vd = 0 and will simplify the equations. Figure 5 shows the old reference frame and the new reference frame in dq-coordinates defined by the grid-side voltage, which is aligned on the q-axis.
Figure 5: The initial reference frame and the dq-coordinates
Then equation (2) in the dq- reference frame becomes:
dI V R I L d I d _ conv d dt q (3) dI V R I L q I V q _ conv q dt d q
The power balance between the AC and DC side of the converter can be written in equation (4) and allows the control of the flowing power.
PDC U DC I DC PAC k Vq I q (4)
The factor k depends on the dq-transformation used and is equal to k = 3/2 in our case. It means that the Park’s transformation is amplitude invariant. k is determined by the abc to dq transformation made by the software PSCAD thanks to the block:
Figure 6: abc to dq transformation function on PSCAD
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The power control of a PWM converter is here achieved by using an inner current controller. To make it simple, the chosen controller is a proportional integral (PI) controller. It is calculated in details in Subsection 2.3.2. A PI controller is sufficient for this control since the grid-side electrical system is a first order with complex values. The DC voltage controller, which allows reasonable constant value of the voltage, is developed in Subsection 2.3.3.
2.3.2 The inner current controller
Figure 7: Block diagram representing the current control system
The inner current controller is obtained from equation (3):
Vd _ conv U'd I q (5) Vq _ conv U'q I d Vq
dI U ' R I L d d d dt (6) dI U ' R I L q q q dt
Thus by using the Laplace transform:
U'd (s) (R L s) id (s) (7) U'q (s) (R L s) iq (s)
And then, according to the block diagram in Figure 7 and the internal model control (IMC) design method [4], the coefficients of the PI controller are calculated. The results give the proportional gain and integral time constant of the PI function:
k L 1 p1C 1C F1C (s) k p1C 1 with L (8) T s i1C Ti1C R
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1C corresponds to the bandwidth of the closed loop system and is linked to the rise time of the closed loop system by the relation: 1C tr1C ln(9) . This relation is valuable for a first order system as has been designed in our case [5].
2.3.3 The DC voltage controller
It is necessary to control the DC-link voltage in order to ensure proper operation of the converters and thus of the whole wind turbine. Further, the grid-side VSC is used as the interface to the AC grid-side system and it allows the power balance between DC-side and grid-side. The control strategy used to regulate the DC link voltage is a simple PI controller, which regulates the energy stored in the DC side capacitor. This model is largely inspired by [4]. The power balance can be written as:
d P E P P (9) DC dt DC losses AC where:
PDC UDC IDC is the DC power 1 E C U 2 is the energy stored in the DC-capacitor DC 2 DC
Plosses are the losses in the converter 3 P V I is the AC power AC 2 q d
d Neglecting the losses, a linearity between I and W is implied by the equation (9). The power q dt C flowing from the DC side is modelled as the power from a virtual resistor Rvirtual, which gives:
2 U DC 2 EDC PDC U DC I DC (10) Rvirtual Rvirtual C
This resistor is calculated knowing the voltage and current values at the DC link. When the losses are neglected, the relation (9) becomes:
2 EDC d 3 EDC Vq I q (11) Rvirtual C dt 2
The Laplace transform leads to a transfer function defined by the following relation:
3 V E q F (s) DC (s) 2 (12a) 1DC I 2 q s R C
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A PI controller is designed using the IMC design method to get a closed-loop transfer function of order 1 in the following form:
EDC Fclosedloop(s) (s) (12b) I q s
1DC corresponds to the bandwidth of the closed loop system and is related to the rise time of this first order system by: 1DC tr1DC ln(9) . The PI controller is calculated according to:
k 1DC p1DC 3 1 Vq F1DC (s) k p1DC 1 with 2 (13) T s i1DC R C T virtual i1DC 2
2.3.4 Three different control modes on turbine level and park pilot
The grid-side converter allows the choice of three different control modes. Thanks to the use of the vector control method the reactive power, the power factor or the voltage can be regulated. The network owner requires the reactive power export to be zero at the point of common coupling (PCC) that corresponds to a unity power factor [6]. The voltage control aims at controlling the inverter output voltage amplitude. It is possible to switch from one control mode to another during operation. In fact, the voltage control mode is not implemented at Lillgrund. The only requirement is the unity power factor at Bunkeflo [6].
2.3.4.1 Reactive power control
As seen on Figure 4, the q-axis reference current is the output of the DC-voltage controller. Here, the d-axis current is used to control the reactive power, the power factor or the voltage. The expressions for the active and reactive power in the dq-reference frame are:
3 3 P V I and Q V I (14) AC 2 q q AC 2 q d
Thus, the d-axis current determines which quantity of reactive power is transmitted to the grid. Depending on which quantity of reactive power is needed at the PCC, a certain quantity of d-current is injected into the system. Figure 8 shows the vector representation of the system when the d-axis current is zero, i.e. no reactive power is flowing through the grid (the PWM filter resistance R is neglected).
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Figure 8: Vector representation of the system when Id=0, that is Q=0
If the reactive power needed is Qneeded, then the required current that must be injected becomes:
Q I needed (15) d required 3 V 2 q
2.3.4.2 Power factor control
The power factor control is close to the reactive power control since, from (14):
Q I tan() AC d (16) PAC I q
If the power factor needed is cos(φneeded), then the required current that must be injected becomes:
I d required I q tan() where arccos(cos(needed )) (17)
2.3.4.3 Voltage control
The aim of the voltage control is to regulate the voltage amplitude at a specific point in the wind farm, by adjusting the d-axis current to output reactive power. For instance, the desired voltage amplitude for the inverter output could either be the amplitude at the 0.69/33 kV transformer (node A between the transformer and the PWM filter) or at the offshore substation. Obviously, a new interaction between the turbines might appear when the voltage is controlled at the offshore substation. This will be discussed further in Chapter 5.
The desired voltage amplitude is measured and is equal to Udesired. This means that the inverter output amplitude has the form:
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2 2 2 2 U desired Vd _ conv Vq _ conv (X I q ) Vq _ conv (18)
From that, the required d-axis current is deduced:
2 2 V V Vq Udesired (X Iq ) I q q _ conv (19) d _ ref X X
Figure 9: Vector representation of the system when the voltage control mode is active
Figure 9 shows the process of the voltage control mode. Injecting some Id current in the system lowers the voltage amplitude of the inverter output. Meanwhile, the q-current Iq is maintained (the resistance R of the PWM filter is neglected).
2.3.5 Problems raised by the close bandwidth of the imbricate loops
The bandwidth must be appropriate for the different imbricate loops of the control system. In order to get a good operation of the system, the current loop bandwidth should be at least 10 times narrower than the switching angular speed of the PWM [17] that is
2 f s 1570.8rad / s (20) 1C 10
Then, the DC voltage controller should also be 10 times slower than the current controller in order to insure some good dynamic of the control system:
1DC 157.08rad / s (21)
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However, the DC voltage loop controls the voltage across the DC capacitor. The latter one has been chosen taking into account principally the price of this capacitor as seen previously in Section 2.2. This led us to the choice of a capacitor with a time constant of 10 ms. The DC voltage controller must be faster than the capacitor that is a bandwidth greater than 628 rad/s.
All these conditions can obviously not be fulfilled simultaneously. A compromise must be found. This is achieved by trying several bandwidths for the closed loop controllers during the simulation. The final bandwidth for the current controller and the DC-voltage controller are respectively equal to 1570.8 rad/s and 157 rad/s.
To conclude with this DC side control system, the final representation of the control is drawn on Figure 10. A phase locked loop (PLL) is used to compute the angle θ (Figure 5 ), which allows the abc to dq and dq to abc transformation. This PLL is a PSCAD library component and it generates a ramp signal that varies between 0 and 2π, locked in phase with the first input signal.
Figure 10: Detailed scheme of the Grid Side VSC Control
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2.4 Generator side control
2.4.1 Introduction to vector control
In order to control the speed and the torque of an induction machine (IM) tools such as vector control and speed regulation are needed. The following section aims at implementing a vector control for the induction generator. The vector control is one of the most common and effective modern methods used in the control of ac-machines. The induction machine will be forced to behave dynamically as the DC-machine thanks to the use of a feedback control. The machine is fed from the VSC, thus the frequency of the input signal can change. The frequency of the stator must not be seen as constant. Furthermore, the different values of current, voltage and flux are ac-values in the induction machine. Consequently, the rotating reference frame is needed to get DC-values under steady state.
The knowledge of the parameters of the IM is needed. During the description of the vector control, several reference frames (stator reference frame, synchronous reference frame and field oriented reference frame) are used. A current controller and a speed regulation system are built. Both controllers use PI-controllers, which is suitable since the systems are defined only by first order equations.
Figure 11: Scheme of the generator-side VSC control system
All this part is almost exclusively inspired by [5]. The control system is drawn on Figure 11.
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2.4.2 The induction generator
Figure 12 depicts the equivalent circuit of the induction machine. Unlike the traditional model of the IM, this dynamic model from [5] is even correct during transients; it is not limited to steady-state cases.
Figure 12: Dynamic equivalent circuit for the induction machine
The parameters of the machine are deduced from the no-load and rotor-blocked tests performed by the manufacturer (Appendix 4). This model is used later to determine part of the control system and some simplifying assumptions will be made (see next section 2.4.3).
2.4.3 Current controller
Assumption: The induction machine, as a three-phase device, can be represented according to the Figure 13. Because of the very fast dynamic of the magnetizing current, the magnetizing inductance is disregarded and in our case:
L Ll Lls Lrl (22) R Rs Rr
The voltage Us is the rectifier voltage vector, es the voltage is the internal voltage of the machine, φr is the rotor flux and ωr is the rotor electrical speed. They are linked by equation (23):
es j r r (23)
The differential equation governing the system is in the synchronous reference frame:
di U e (R jL)i L s (24) s s s dt
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Figure 13: Load/Generator model
By dropping the equation in the d- and q-axis, one gets two interacting systems that leads to the cross coupling between the d- and q-axis currents (as for the grid-side controller in Subsection 2.3.2).
The current-controller system is represented on Figure 14 where G2C(s) represents the machine and F(s) the controller.
1 I(s) G (s) (25) 2C (s j)L R U(s) E(s)
Figure 14: Current controller loop
The IMC method is used to design a PI controller and make the closed loop system responding as a first order system.
k L 1 p2C 2C F2C (s) k p2C 1 with L (26) T s i2C Ti2C R
This controller has the same shape as the one defined in Subsection 2.3.2 for the grid side control.
2.4.4 Flux estimation for rotor flux orientation
That step makes the necessary calculations that will allow working in the new coordinates system. The new frame is the so-called “field-oriented reference frame”. It is more natural and also simpler to use this one instead of the synchronous reference frame since the field-oriented reference frame rotates synchronously during steady state operation. On the contrary, the synchronous reference frame
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depends on the stator frequency that can be affected by transients. The new frame is field-oriented, that is the d-axis is aligned with the rotor flux.
Consequently, one needs to know the rotor flux. Since there is no cheap and reliable way to measure the rotor flux, it will be estimated. The estimation can be made according to different methods described in [5]. However, given that the rotor will not operate at low speeds (not under 40%); one decides to estimate the flux by using the “Voltage Model”. Indeed, at low speed the voltage drop due to the stator resistance cannot be neglected anymore and the model would not be valid. The induction machine can be described by the following differential equations linking the rotor and stator flux ψ, currents I and voltages U:
d s d s s U s R I s (stator) and r j s R 'I s (rotor) (27) dt s s s dt r r r r
s s s s s s s Lm I r Ls I s and r Lm I s Lr I r (28)
Combining these equations in a proper way leads to the following expression of the rotor flux:
s Lr s s r s L I s (29) Lm where: 2 Lm L Ls represents an equivalent inductance Lr
That corresponds to the voltage model for rotor flux estimation. All these equations are written in the synchronous rotating reference frame denoted by the superscript “s” and rotating with the stator currents. The subscripts “s” and “r” means respectively the stator and rotor values.
Figure 15: Stator reference frame and rotor flux reference frame
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Figure 15 shows the old reference frame and the new reference frame in dq-coordinates defined by the rotor flux φr, which is aligned on the d-axis. The transformation from the initial to the rotating reference frame use Park’s transformation and the new dq-reference frame corresponds to the field- oriented reference frame. The angle ρ is the transformation angle that allows working in the field- oriented reference frame. The αβ-axis represents the initial reference frame corresponding to the synchronous reference frame.
Knowing the rotor flux, it is from now on possible to work with the flux coordinates that will be denoted by a subscript “ρ”. Figure 15 illustrates the transformation from the stator reference frame to the field-oriented reference frame. The new rotating reference frame “flux-oriented” will be used to determine the speed controller.
2.4.5 Speed controller
In the flux-oriented reference frame, the relation between the electrical torque T and the current I is:
3 Lm I sq_ T p rd _ I sq_ (30) 2 Lr cT
where:
rd _ is the rotor flux in the “ρ” reference frame
Isq_ is the d-axis current in the “ρ” reference frame p is the number of pole pair of the IM cT defines a variable that will be used later
The speed controller will force the machine to turn at a certain reference speed by providing a reference value to the torque that is for the q-axis current. The reference q-axis current input in the current controller is the output of the speed controller. In the flux-oriented reference frame, the relation (31) defines the reference d-axis current input in the current controller:
ref r I sd _ (31) Lm where: ref r is the desired flux
Isd _ is the q-axis current in the “ρ” reference frame
Figure 16 shows the block diagram of the speed control loop including the controller and the system. It describes the mechanical relation between the speed and the torques (load torque TL and electrical
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torque Te). The factor cT is defined by the equation (30) and describes the relation between the electrical torque and the q-axis current.
Figure 16: Speed control loop
Again, the PI control is determined by using the IMC method and its expression is found as:
k J 1 p2 2 with (32) F2 (s) k p2 1 J Ti2 s Ti2 b
ln(9) where 2 is the bandwidth of the closed loop system, b is the coefficient corresponding to tr2 the frictions and J is the inertia of the induction machine. The choice of the bandwidth is also critical for the speed controller; a too high bandwidth could lead to very high current peaks when a change in the speed occurs [5]. It will be discussed further in section 4.4.2.
2.4.6 Optimal speed control system
Equations (33) and (34) defines the power coefficient Cp and the tip speed ratio λ.
rotor power P C rotor (33) p available power in the wind 1 A.v 3 2 where: ρ is the air density A is the rotor blade area v is the wind speed
blade tip speed R (34) wind speed v where:
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R is the rotor radius ω is the angular speed of the rotor
Figure 17: Power coefficient versus tip speed ratio [22]
To increase the aerodynamic efficiency of the wind turbine, it is possible to control the mechanical torque in order to get the optimal speed operation. The power coefficient Cp of the wind turbine depends on the tip ratio λ as illustrated on the Figure 17. The maximum power coefficient corresponds to a certain tip speed ratio λopt from which an optimum speed can be deduced according to equation (35). From this, a reference value for the speed is input in the speed controller defined in section 2.4.5.
v opt (35) opt R
The speed tracking for optimum efficiency is a practical tool and several strategies exist. The knowledge of the power coefficient versus the tip speed ratio is needed to employ this method. The turbine manufacturer Siemens can provide it. However, it is not implemented in the PSCAD model since it is not defined in the project initial purpose.
2.5 Siemens control system
Siemens is the provider of the control system of the turbines and the offshore substation of Lillgrund wind farm. Vattenfall did not succeed in obtaining any information from Siemens concerning the control system of Lillgrund. Therefore, the whole project is based on some assumptions of what Siemens might use as control. In particular, the most common methods for controlling such a wind farm are used in this project. For example, the vector control of the induction machine, and the whole grid-side converter control correspond to common tools for such a system. The only known information about the wind farm control is the unity power factor at the PCC (Bunkeflo) and that the grid codes are fulfilled.
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3 Introduction to power quality analysis
3.1 Introduction to power quality – Grid Code
Nowadays with the increasing penetration of wind power generation in the power system, the necessity of defining the so-called grid code appeared. This code corresponds to technical requirements insuring a secure and safe operation of the electrical system. Especially, it defines in which extent and under which conditions a wind power plant can be connected to the network and power quality requirements has to be satisfied. Indeed, the transmission system operator (TSO) and the distribution system operator (DSO) must deliver high quality energy to the consumer. Thus the connection of Lillgrund wind farm, being the biggest wind power production in Sweden, has raised the interest of studying the power quality carefully. A two years project will be launch by Vattenfall aiming at a power quality and transient measurements study which will lead to a secure and high performance operation of Lillgrund offshore wind farm [7]. The electrical system must fulfil the grid codes and some specific devices are installed as for example the PWM filter studied previously. The power quality concerns several phenomena as listed in Table 3 below. In general, power quality concerns any possible divergence of the voltage from the ideal sinusoidal waveform, with constant and unique frequency, constant amplitude, and power factor. This work focuses on the study of harmonics and voltage sags (see Section 1.3).
Table 3: Power quality variation categories
Example of power Symptom Main cause quality category
Flicker Voltage fluctuation Large fluctuating load
rms voltage reduction or Faulted power line, Voltage sags and swells increase during a certain starting of large load duration
Distortion in the current or Harmonics Non linear load voltage waveform
rms voltage reduction or Undervoltage and Motor starting, load increase for more than 1 Overvoltage variations, load dropping minute
Total loss of electric power System protection, Interruption during a certain duration maintenance
Sudden increase in the Switching (load, capacitor, Transient Voltage voltage during a short time line), lightning
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Besides the grid codes, there exists some voltage tolerance for information technology (IT) equipment and control systems [26]. The ITI curves represent the AC voltage envelope that can be tolerated by most of the IT equipment and control systems [28].
A Danish project, dealing with the power quality study of wind farms, was carried out lately. Vattenfall participated to this Master thesis work, which deeply investigates the measurement methods for harmonics and flicker [9].
The IEC standard 61400-21 stipulates the methods to assess and measure the power quality parameters of grid-connected wind turbines [12]. In the simulation part of the project, an attempt is made to measure two power quality parameters (response to a voltage sag and harmonics study) according to this standard (see Section 5.3). Obviously, if the results obtained during simulations are within the limits; the conclusion will be drawn that the system has good power quality reliability.
3.2 Voltage sags
One requirement of the grid-code is the fault ride-through (FRT) capability and also low-voltage ride through (LVRT) capability. It means that the wind turbine or the wind park must endure voltage sags without disconnecting from the grid. The LVRT is a more recent concept. The LVRT is a type of FRT where the voltage reduction that the system must handle is limited. Indeed, the most common voltage sags present between 70 and 90 % remaining voltage (see Figure 18 in Subsection 3.2.2).
3.2.1 Definition
A voltage sag is a reduction down to 90-10% of the RMS voltage magnitude during a period from half a cycle (10 ms at 50 Hz) to one minute [16]. The voltage sag mainly origins from motor starting, transformer energizing, and faults [19]. The latter provokes the most important damage and for this reason, the study principally focuses on this type of fault. The different types of voltage sags are summarized in Table 4.
Table 4: Voltage sag - origins and characteristics
Origin Characteristics Impact on 3 phases
Motor Starting Sudden drop in the voltage and Balanced progressive recovery
Transformer Energizing Sudden drop in the voltage and Unbalanced progressive recovery
Usually constant voltage sag with immediate recovery (can contain Fault Depends on the type of fault different stages if several events happens)
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The duration of the sag that origins from failures, is the time it takes for the protections to disconnect the faulted power line that is the fault clearing time. Mostly it takes 100 ms. There are different types of voltage sags depending on the nature of the short circuit, which provoked it. That can be line-to- line, line-to-ground or two or three phases.
The effects of voltage sag are stated in [11] as well as some solution to ride-through voltage sags. An induction machine may trip and disconnect under voltage sag, there are also impacts on wind turbines, line-connected synchronous machine and DC-link voltage stability.
3.2.2 Studied case
The model has not been implemented for asymmetrical cases. The simulation of asymmetrical cases would need some further considerations (positive and negative sequences modelling) and consequently a more complex model. Thus, symmetrical fault will be considered more carefully.
Voltage sag ride through is one of the requirements of the grid code for a wind power plant. The wind power plant must remain connected to the grid when a voltage sag occurs that is when a fault happens in a power line.
Figure 18: Voltage sags recorded during March-August 1999 at SSAB Oxelösund AB, Sweden
Figure 18 shows the 6 months measurements results of voltage sags at SSAB Oxelösund [10]. Most of the voltage sags have a short duration of 100-150 ms and a magnitude of 70-90 %.
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Thus the project essentially focuses on symmetrical voltage sags on the magnitude range of 70-90 % and a duration of 100 ms. Furthermore, such a voltage sag can be simply simulated on the software.
3.3 Harmonics
Every integrable function and among it every periodical function sT(t) can be factorized according to the Fourier analysis (equation (36)). The signal is then composed by a fundamental component and several harmonic components. Each is characterized by amplitude and a frequency. The harmonics frequencies are multiple of the fundamental frequency. A perfect sinusoidal signal contains only the fundamental component.
s(t) an cos(n..t) bn sin(n..t) sDC s f (t) sn (t) (36) n0 n2 where:
sDC is the DC component of the signal
s f (t) is the fundamental component of the signal, frequency f0 = 50 Hz
sn (t) is the harmonic of order n, frequency fn = n. f0
The presence of harmonics in a signal provokes the distortion of the signal. In this project, harmonics are due to the switching power electronics devices and the variable speed induction machine among others.
Among voltage and current harmonics, the later has the most important impact in the power installations. The consequences of harmonics are significant on the distribution network since the transformers, the cables and the overhead lines bear it. Partly because transformers must endure more than under good conditions, they are oversized by 40% rated power to handle that. Moreover, harmonics current provokes overheating of the transformers that is losses. That also reduces the lifetime of the transformer. All these facts lead to non-negligible costs. Presence of harmonics in the power system raises costs and must be limited. Some codes and regulations exist that defines the maximum tolerable harmonic quantity. For wind power generation these limitations are defined in the grid-code. Harmonics causes and effects are studied in [13] and [14].
3.3.1 Measurements of harmonics
Several ways exists to depict the harmonics impact and importance on a signal. The Fast Fourier Transform (FFT) is a powerful algorithm that decomposes a signal into its different harmonic components. The on-line frequency scanner of the PSCAD’s master library uses the FFT algorithm to measure the amplitude and phase of a signal harmonics (till a certain order n). This tool is used in the harmonic measurement part of the project. Also a common tool remains the individual harmonic distortion (IHD) and the total harmonic distortion (THD) defined by equations (37) and (38). These two quantities represent the part of harmonics contained in a periodical signal compared to its fundamental part.
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The current and voltage harmonic measurements are made at the output of the 0.69/33 kV transformer that is at the output of the turbine.
1 T 2 sn (t) dt T 0 IHDn (37) 1 T 2 s f (t) dt T 0
1 T 2 sn (t) dt T 0 THD n2 (38) 1 T 2 s f (t) dt T 0
3.3.2 Induction machine harmonics
In a real induction machine several types of harmonics exists as space and time harmonics. Times harmonics are mainly due to the presence of harmonics in the supplying source, but can also be a consequence of space harmonics. Space harmonics are due to the winding distribution in the stator. In reality it is not perfectly sinusoidal. The slots in the stator may also influence the magnetomotive force (mmf). Mostly when studying an induction machine, these harmonics are neglected since the mmf is supposed to be perfectly sinusoidal.
3.3.3 Power electronics harmonics
A PWM signal is defined by its amplitude and frequency modulation ratio that are respectively:
^ V control ma ^ (39) V triangle
f s m f (40) f1 where: ^ V control is the peak amplitude of the control signal that oscillates at the frequency of the line 50 Hz. ^ V triangle is the peak value of the triangle signal which has a high frequency (2.5 kHz for the grid-side converter).
From [15], the harmonics in the inverter output voltage waveform are centred on the switching frequency fs and its multiples. The harmonic orders are: n i m f k (i and k integers). The harmonics only exist when i is even and k is odd, or vice versa. The amplitude of the harmonic depends on the amplitude modulation ratio ma and an example is shown in the following table.
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Table 5: Harmonics in the voltage for a large mf [15]
order n fn (Hz) Amplitude for ma=0.6 1 50 0.6
m f 2500 1.006
m f 2 2400/2600 0.131
m f 4 2300/2700
2 m f 1 4950/5050 0.37
2 m f 3 4850/5150 0.071
2 m f 5 4750/5250 …
3 m f 7500 0.083
3 m f 2 7400/7600 0.203
3 m f 4 7300/7700 0.047 …
4 m f 1 9950/10050 0.008
4 m f 3 9850/10150 0.132 …
As seen previously, a PWM filter is installed behind the inverter to comply with the grid code. This powerful filter removes the harmonics of high order (Appendix 3).
3.3.4 Transformer harmonics
The magnetic material that composes the transformer is almost linear when operating under low value of magnetic field intensity H. Nevertheless, when working in the saturation zone of the material, i.e. under high H, the transformer is not linear and it induces harmonics.
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4 Modelling and implementation in PSCAD
4.1 Wind turbine
4.1.1 Wind source Wind Source Mean ES Vw
Figure 19: PSCAD wind source component
This component simulates the wind speed available for the turbine. It can be a simple constant wind speed source. It allows the simulation of gusts, ramp and noise in the wind speed.
4.1.2 Wind turbine
Figure 20: PSCAD wind turbine component
This model simulates a wind turbine when entering the wind speed and the mechanical speed of the electrical generator connected to it. The angle beta is the angle of the pitch that can be controlled by a governor (see section 4.1.3 and simulation B in the appendices). The parameters defining the model are: -The machine rated power: 2.7 MVA -The machine rated speed: 162.42 rad/s -The rotor radius: 46.5 m -The rotor blade area: 6800 m2 -The air density: 1.225 kg/m3 -The gearbox ratio and its efficiency 97 % Finally, the user chooses a mode “MOD2” that corresponds to a horizontal axis turbine with 3 blades. The wind turbine component gives the torque and the power produced.
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4.1.3 Governor Beta
Wind Turbine Governor MOD 2 Type Pg
Figure 21: PSCAD wind governor – pitch control component
The governor needs the mechanical power produced by the generator “Pg” in order to compute the pitch angle “Beta”. The dynamic pitch control means that the blades can turn around their longitudinal axis. A power reference of the regulation system is given and according to that reference, the system turns the blades in order to regulate the output power.
4.2 Induction generator
Squirrel cage induction generator is a good solution in the field of wind power generation since it appears to be robust, cheap compared with other solution and it needs less maintenance. The model used first in PSCAD is shown on the following figure. It can be either speed or torque controlled. The starting of the machine is made with speed control and then a control signal permit to switch to the torque control mode. When the machine is torque controlled, the speed is calculated based on the machine inertia, the damping factor among others. W A
I M S B
T C
Figure 22: PSCAD induction machine
The motor has a nominal power of 2.7 MVA. In the reality the stator windings are Delta-connected, but in PSCAD the IM model is Y-connected.
Delta Connection: Y Connection: I 2.07 kA I 1.195kA LL LL U 0.75kV LL U LL 3 0.75 kV
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Figure 23: Delta and Star Connexion
The typical data generation model in PSCAD defines the machine thanks to the nominal voltage, power and current. The others parameters are calculated by the software. However, to create the vector control of the machine, these parameters are needed. In consequence, the parameters of the machines are determined thanks to the rotor-locked and the no-load tests simulated in PSCAD (see Appendix 4).
4.3 Voltage source converter
The full-power converter used in the turbine is constituted by a parallel connection of six IGBT- modules: three for the generator-side converter (fs = 1250 Hz) and three for the grid-side inverter (fs = 2500 Hz). It is manufactured by Alstom and represents an essential part of the turbine since it allows the main control of the wind farm that is the reactive power control [6].
4.3.1 One module
One module of the VSC is constituted by a diode and an IGBT (Figure 24). The latter is commanded by the PWM signal. This PWM signal is calculated by the controllers defined in the Chapter 2.
I I 2
Figure 24: PSCAD module of the VSC composed by a diode and an IGBT in parallel
The configuration of the IGBT and diode is studied in order to get a model matching with the reality. The main parameters are the on-resistance, the off-resistance and the forward voltage drop. All these parameters will affect the converter losses. Indeed the losses in the power electronics switch corresponds to (the off- losses are neglected):
Plosses_ switch Pswitching Pconduction (41)
2 Plosses_ switch f s (EON EOFF ) V0 I average RON I rms (42)
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1 I average I cond (t) dt T tcond (43) 1 2 I rms I cond (t) dt T tcond
where:
Plosses_ switch are the total losses in the devices [W]
Pswitchingare the losses due to switching [W]
Pconductionare the conduction losses [W]
EON is the turn-on switching energy [J]
EOFF is the turn-off switching energy [J]
V0 is the forward voltage drop [V]
RON is the conduction resistance [Ω]
f s is the switching frequency [Hz]
4.3.2 The PWM inverter filter
In order to satisfy the grid code and to decrease the harmonics caused by the PWM inverter (2,5 kHz), a PWM filter is installed between the 0.69/33 kV transformer and the inverter.
Figure 25: PWM filter installed at the output of the grid-side converter
There are several ways to construct such a filter. However one easy way is to use a RL series filter. The model used comes from [8] and it is represented on Figure 25. A frequency analysis of this filter is made in the Appendix 3 and shows the efficiency of the RL series filter. Nevertheless a RL filter is a simple filter and does not represent the most powerful filter. In [4] a more complex and powerful filter is developed that could be adapted to the wind turbine model in an eventual future work.
4.4 Control system
The control system in PSCAD could be implemented in two different ways: by writing a FORTRAN code which describes the systems thanks to equations or by using the graphical interface and the library pre-defined functions. The second has been chosen for a question of simplicity and rapidity as well as for a friendly use of the software (the author was not familiar with the FORTRAN language).
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Coding the whole system in FORTRAN may have led to a more accurate and quicker model but SYSTEM would also consist of a heavy code.
Current source + DC-link Capacitor Grid-Side PWM filter : R and L Converter 4.4.1 Grid side control
Figure 26 shows the grid-side system. A DC-current source is connected in parallel to the DC- capacitor and to the grid-side converter, which is connected to the PWM filter. I I I I I I 2 2 2
PWM1 PWM2 PWM3 A
V A 15607 [uF] 15607 Uab_conv 0.007406[ohm] B Vdcc A A V 2.3574e-4 [H] V
C
B A
Power Q P measurements I I I I I I NODE A 2 2 2 PWM1inv PWM2inv PWM3inv Q
Figure 26: Grid-Side Converter System
The grid-side converter is controlled as described in Section 2.3. A switch has been installed which allows the choice between constant reactive power, power factor control, and constant power factor control. Depending on the chosen control, the d-axis reference current is computed and input to the control system (see Subsection 2.3.4). Appendix 1 contains the PSCAD schemes of the control system and Figure A 1 in SIMULATION A shows the PSCAD scheme that allows the different control modes.
4.4.2 Generator side converter
As explained in Section 4.2 the IM data generation is made by PSCAD. Some of the parameters of the IM are calculated thanks to the results of several tests (see section 2.4.2 and Appendix 4). Nevertheless, the inertia J and the damping constant b of the IM remain unknown. These two parameters are the key for the speed loop controller since they allow computing the PI controller time constant and gain. That fact made the implementation of the speed loop control complicated and long. Moreover the bandwidth must be chosen with care in order not to reach high peak currents whe a speed change occurs (see Subsection 2.4.5). Thanks to perseverance and some simulation tests, the PI controller is finally tuned correctly.
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Figure 27 shows the IM connected to the generator-side controller and to a DC-voltage source that was A used to tune the control of the generator-sideVdcc converter.V The control scheme appears in Appendix 2.
Rated speed in pu Figure 28 shows the wind turbine which blade pitch is controlled by the wind governor, and the wind I I I I I I 2 2 2 PWM3_rec PWM2_rec PWM1_rec 1.034 W source Athat input the wind speed to the turbine. The mechanical torque produced by the turbine is input I M Uab_gene StoT S to the IM. This one obviously operates with the torque control mode (see Section 4.2).
TIME 1 A B R=0 ABB Gene V T C Switch to Torque TS input at 0.1 Second measuremen...
I I I I I I 2 2 2 PWM3inv_rec PWM2inv_rec PWM1inv_rec
Generator-Side Converter + DC voltage source
Cut-in/out StoT * TS Min speed D -1 Ctrl Main ... Main ... limits 999.0 E GR Es Wind Source Wind Turbine B Mean MOD 2 Type 400 30 ES Vw Tm Gust Vw Ctrl = 1 Es Ramp Vw A W P
0 0 Sample & Hold Tm 100 5 when switched from Beta constant Speed to GR constant Torque Pi * N 100 N/D * 3.07 GR - Gear Ratio D Figure 27: Generator-side system – IM and converter Es - External signal for wind 2.0 A 4 Pole Machine pole pairs speed Mechanical speed = W(pu)*2*pi*f/(pole paris) A Ctrl = 1 Wg B 1.034 Ctrl
CNT
Beta Initial Pitch angle and the Power When w>13.5 m/s, for a demand of reference (demand) are inputs to TIME CNT Wind Turbine this module. Power demand = 2.3 MW Ctrl Governor For this example : -1 MOD 2 Type w=13.5 m/s Then, the blades has to pitch in Pg * B Pg Initial pitch angle =3.07 deg order to produce a maximum of 2.3 Signal CNT enables the Ctrl = 0 Power demand = 2.3 MW MW pitch angle dynamics at t=1s 1.0 A P_init Main ... P_demand 2.3 P_demand
MW
0 2.3
Figure 28: Generator-side system – Wind source and pitch control
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4.4.3 Pitch control in PSCAD
The wind turbine governor component regulates the pitch angle β of the blades. The governor compares the power reference that corresponds to the power that we want to output from the turbine and the current power output of the induction generator. Then, according to certain characteristic defined on the FORTRAN code, the pitch angle is calculated to produce the desired power.
4.5 DC-link chopper
In parallel to the DC-link capacitor, a chopper resistance is installed. It permits to waste the excess of energy produced during fault in order to comply with the current limits of the different components of the system. During voltage sags for example, the current transmitted becomes higher, which can cause the damage of some components if it is not limited. Thanks to the DC-chopper, there will be less abrupt changes in the power output from the induction generator. Another solution would be to reduce the induction generator output power thanks to a control. However it depends on how the IM responds to a sudden voltage variation. The DC chopper appears to be a robust and reliable solution that is easy to implement both in the software model and the reality. It remains one of the most common contemporary solutions.
In our project, the VSCs (voltage source converters) are water cooled and not so compact. The IGBT can approximately handle currents up to 1.5 or even 2 pu during a short time of a few hundred milliseconds. For the same duration, diodes handle currents up to 7 pu [8].
It is chosen that the breaker in series with the chopper resistance closes when the DC-link voltage exceed 1.08 pu. However this maximum value must be inferior to the voltage ripple across the capacitor. Thus, the ripple in the DC-link voltage was first measured: UDC varies between +/- 1.94 % of its reference value. To ensure safe operation of the turbine, the control of the breaker is separated from the main control of the turbine.
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5 Simulation in PSCAD and analysis of results
5.1 Simulation on PSCAD – Introduction
One of the biggest issues in the simulation of such a project is the runtime settings that play a decisive role in the results computed by the software. The runtime, the solution time step and also the channel plot step are parameters that must be chosen with care in order to obtain coherent and correct results. With the introduction of very fast switching power electronics components (2500 and 1250 Hz), the solution time step should be at the most 1 μs [8]; unless the calculations will accumulate errors that lead to incorrect and illogical results. However, it appears that a solution time step of 1 μs conducts to false computations of the model. It induces a very high amount of losses in the system. The switching frequency of the PWM inverter (2500 Hz) corresponds to a 400 μs period, thus the solution time step must be very short. Furthermore, all the calculations induced by the control system increase the total amount of errors. In fact, the control system uses block components defined in the master library of PSCAD and the whole connected system is then encoded in FORTRAN language to make the calculations. The control system being complex and weighty brings error accumulation in the system that provokes a huge amount of losses. An example of some aberration that can happen when the time step is not adapted is quoted in Table 6.
Table 6: Example of the aberration caused by a wrong solution time step Solution time step (μs) Losses in the converter (%) 10 120 1 45 0.1 18 0.05 9
Then the problem raised by having a very short solution time step is that the sample density and the storage needs become very high. This can provoke instability when solving the system. Moreover, the simulation time increases when decreasing the solution time step especially for a so complex system. The simulation can be very long depending on which runtime parameters are chosen.
Concerning the channel plot step, an inappropriate one may also be the cause of some errors in the practical results. Indeed, if it is not short enough, the observed curves may be distorted. The channel plot step must remain consistent especially with the different frequencies of the system.
5.2 Reactive Power Control and Voltage Control Modes
From now on, only two control modes are considered and tested: reactive power and voltage control. Indeed, the power factor control mode uses the same principle as the reactive power control mode. Furthermore, it gives the same results since unity power factor at Bunkeflo corresponds to zero reactive power at the same node.
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It is chosen that the voltage level of the grid-side converter is regulated compared to the offshore substation voltage level. The offshore substation connects every wind turbines through five feeders.
The simulations using the voltage control mode and the reactive power control mode give coherent results. These are detailed and compared in SIMULATION C in the appendices. The simulation tests the turbine both during normal condition and when a voltage sag (50% remaining voltage during 500 ms) occurs.
5.3 Results for one turbine – Compliance with IEC 61400-21
5.3.1 Voltage sags study
Reference [12] specifies the conditions under which the turbine must be tested for a voltage sag event as well as the measurement settings. The test is made for a non-connected turbine and it checks the wind turbine response to voltage sags. Four different tests are made on the turbine, that are 50% symmetrical three-phase and two-phase voltage sags with a duration of 500 ms and 20% symmetrical three-phase and two-phase voltage sags with a duration of 200 ms (see Figure 30). The simulation of the voltage drop is made according to [12] that is according to Figure 29.
Figure 29: System for testing wind turbine under voltage sag
These four tests are made on the new model with the voltage control mode or the reactive power control mode active. Moreover, the former model (current source + transformer) is also tested. This leads to some comparative analysis between the two modes of control and the former model of turbine that is not equipped with control. The new model with power factor control is not tested since it is quite the same principle of control as for the reactive power control. Indeed, instead of measuring the reactive power to deduce the Id current necessary to compensate it, the power factor is measured and then the Id current is deduced (Subsection 2.3.4).
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Symmetrical three-phase fault Asymmetrical two-phase fault
Main : Graphs Main : Graphs Ea Ea 30 30
20 20 50 % 10 10
0 0
y y remaining -10 -10 voltage -20 -20 -30 -30 ... 0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ......
Main : Graphs Main : Graphs Ea Ea 30 30
20 20 20 % 10 10
0 0
y y remaining -10 -10 voltage -20 -20 -30 -30 0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ... 0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 ......
Figure 30: Type of fault applied to the voltage at node A
In each case, the turbine rides through the voltage sag. However, the consequences of the fault are more or less significants depending on the voltage sag type. With the reactive power control active, the reactive power is adjusted to zero at node A (Figure 29) whereas it is not when the voltage control mode is active.
Symmetrical voltage sag with 20% remaining voltage represents the worst case. Some severe changes and peaks in the DC-link voltage, the speed of the IM and the output voltage and current of the turbines occur right after the fault is cleared. The limits for current and voltage defined by the hard limiters and the chopper are reached. The chopper operates almost during the entire sag.
For voltage sags with 50% remaining voltage, either two- or three-phase fault, the amplitude of the DC-link voltage does not exceed 1.05 pu. For voltage sags with 20% remaining voltage, either two- or three-phase fault, the amplitude of the DC-link voltage does not exceed 1.1 pu (see Figure 31).The chopper resistance is only used when the sag is more severe that is 20% remaining voltage in this case. Concerning the negative overflow, it can reach some high values especially in the case of the 20% three-phase voltage sag.
Also the voltage control implies an important variation of the reactive power right after the voltage sag due to the brutal change in the voltage. Because of that, it will be essential to verify if the grid owner will accept this transfer of reactive power when the turbine is connected to the grid. However since it is a large and short variation (about 100 ms) that should not be a problem.
During two-phase voltage sag the turbine rides through. Though an amplified oscillating phenomenon appears. The reactive power oscillates with large amplitude during the sag. Consequently, the Id current shows also some oscillations during the sag. This phenomenon is due to the fact that the fault
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is not symmetrical. As explained previously in Section 3.2.2, it is also important to remind that the control system has not been designed for asymmetrical cases.
Figure 31: Maximum and minimum peak values reached by the DC-link voltage UDC at the beginning and right after the voltage sag
In general it is seen that the impact of the voltage sag is more important when the voltage control mode is active than when the reactive power control mode is active. The peak values reached by the DC-link voltage (see Figure 31) are larger with the voltage control mode. This result was expected. The voltage regulation depends on the voltage at the node where the sag is applied. When the sag happens, it implies an abrupt change in the rms voltage, which reflects in the regulation of the voltage.
Impact of a sag on the turbine current two control modes - IEC connection
2,5 reactive power control 2
1,5 voltage control
1 Former model 0,5
0 of theof turbine [pu] 0 20 40 60 80 100 120
peak current at the output remaining voltage during the sag [%]
Figure 32: Peak current caused by a three-phase voltage sag at the output of the turbine
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The most noticeable fact from Figure 32 is that the former wind turbine model withstands a very low variation of the current due to the voltage sag compared to the new model equipped either with voltage or reactive power control. It was observed previously that the peak currents due to a voltage sag are more severe in the reality than the one simulated with the former model of VPC (Vattenfall Power Consultant) [23]. The former turbine model from VPC is composed of an ideal current source and a transformer. The impacts of the voltage sags are different for the two control modes of the new model. The turbine operating with voltage control has to face higher peak current. The current peak is roughly proportional to the voltage change, especially when the reactive power control is active. But for the voltage control, beyond a 50% remaining voltage sag the peak currents rises. Furthermore, beyond a certain amplitude of the voltage sag, the limits imposed by the DC-chopper and the current hard- limiters are reached and the curves of Figure 32 become flat.
With the IEC standard connection (Figure 29) the reactive power at the node A is about zero. Consequently the d-axis current injected by the wind turbine is also close to zero. However, it will not be the case in the next section where the wind turbine is connected to the grid through different cables and transformer. Thus, the d-axis current injected will be quite high and the wind turbine will output a higher current during normal conditions (no sag). It is thus expected that the red curve in Figure 32 will be translated upward.
5.3.2 Harmonics analysis
The harmonic measurement described in the IEC 61400-21 is tedious because it is long and heavy. Current harmonics, interharmonics and high frequency harmonics are considered. Furthermore, the measurements are made for 11 sets of operation (active power bins). Consequently and because of the long simulation time implied, the measurements of harmonics will not be carried out according to the IEC 61400-21.
However, the harmonics are calculated thanks to the software Matlab that use the fast Fourier transform (FFT). Matlab computes the discrete Fourier transform of a discrete signal output from the PSCAD simulations. The following table shows the results obtained in the scope of the IEC61400-21 connection defined previously. The harmonics are measured in the output voltage and current of the grid-side converter.
Table 7: Harmonic content of the grid-side converter output current and voltage Amplitude Amplitude order n f (Hz) n Measured Ivsc (pu) Measured Evsc (pu) 1 50 1 1 Harmonics due to PWM
m f 2500 0 0.01
m f 2 2400/2600 0.015 0.03
m f 4 2300/2700 ~ 0 0.01
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… …. ~ 0
2 m f 1 4950/5050 0.02 0.06
2 m f 3 4850/5150 ~ 0 0.02
2 m f 5 4750/5250 ~ 0 0.01 … … ~ 0
3 m f 7500 0 ~ 0
3 m f 2 7400/7600 0.006 0.03
3 m f 4 7300/7700 0.006 0.01 …
4 m f 1 9950/10050 ~ 0 0.02
4 m f 3 9850/10150 ~ 0 ~ 0 … Other order 112.5 0.03 0 215 0.02 0
3 f1 150 0.01 0.01
5 f1 250 0.02 0.005
7 f1 350 0.01 0.02
The orders of the PWM harmonics correspond to the one in Section 3.3 Table 5 and some other harmonic orders are observed. The third, fifth and seventh harmonics especially appear in the converter output voltage and current. However, neither the current nor the voltage contains harmonics with an amplitude superior to 6%. Compared to the values quoted in the Table 5 the harmonics content is very low which partly proves the efficiency of the PWM filter.
5.4 Results concerning the voltage sag study for one or several turbines connected to the grid
Figure 33: Connection of the turbine to the grid via cables and offshore substation transformer
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As stipulated in Section 3.2.2, the simulation test is a 75% symmetrical three-phase voltage sag during 100 ms. The wind speed is constant, equal to 13.5 m/s to get the maximum power output from the wind turbine. Also, to observe the response of the turbine facing a larger disturbance, it was decided that a simulation test with 25% symmetrical three-phase voltage sag during 100 ms would be studied. The wind turbine is tested according to Figure 33 in this section.
Main : Graphs Main : Graphs Bunkeflo Voltage Bunkeflo Voltage 200 200
150 150
100 100
50 50
0 0
y y -50 -50
-100 -100
-150 -150
-200 -200 ... 0.900 0.950 1.000 1.050 1.100 1.150 1.200 ... 0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 ...... Figure 34: Voltage sag at Bunkeflo: 75% Figure 35: Voltage sag at Bunkeflo: 25% remaining voltage during 100 ms remaining voltage during 100 ms
The simulation time of two turbines connected to the grid is almost equal to twice the simulation time for one turbine. The turbine model is heavy and induces a lot of calculations. Many signals are registered, plotted and then analyzed. This provokes a quite long simulation time. Moreover the time step has to be short to obtain a plausible and more accurate response as explained in Section 5.1.
During the simulations, the time step is not so short because it could then increase the simulation time a lot. The solution time step is 0.5 μs that induces losses in the converter (see Section 5.1). So one turbine output about 1.2 MW of active power and output different amount of reactive power depending on the control mode active. It output almost 2 MVAr when the reactive power control is active, which thus means that the wind turbine runs at about 2.3 MVA.
At the end of the voltage sag, some disturbance in the Bunkeflo voltage occurs (see Figure 34 and Figure 35). Figure 36 zooms on this phenomenon, which appears to be some kind of resonance in the Bunkeflo voltage. The oscillations starts when the phase voltage reaches zero and disappear after 150 ms. The resonance might come from a resonant circuit formed by the capacitance (cable) and inductance (grid) of the upstream circuit.
Main : Graphs Bunkeflo Voltage 200
150
100
50
0 y -50
-100
-150
-200 1.090 1.100 1.110 1.120 1.130 ...... Figure 36: Zoom on the oscillation occurring after the fault is cleared
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5.4.1 Impact on the different voltages of the system
The two following figures show the results obtained when simulating two different voltage sags, with two different control modes and with one, two turbines and three turbines.
Voltage Sag 100 ms 75 % remaining voltage
10
[%] DC DC 5
0 Turbine 1 1 2 3 4 5 6 Turbine 2 -5 Turbine 3
-10
Maxima and Minima in U Maximain and Minima Reactive Pow er Voltage Control causedby the voltage sag -15 Control Mode & Number of Turbine running
Figure 37: Results for two control modes and one, two or several turbines – 75 % voltage sag
Voltage Sag 100 ms 25 % remaining voltage
10
5
0 Turbine 1 1 2 3 4 5 6 -5 Turbine 2
[%] Turbine 3 -10
-15
caused by the voltage sag sag voltage the by caused -20 Maxima and Minimaand Maxima in UDC Control Mode & Number of Turbines
Figure 38: Results for two control modes and one, two or several turbines – 25 % voltage sag
The same conclusion as in Section 5.3 cannot be drawn by analyzing Figure 37 and Figure 38. The impact on the DC-link voltage appears to be larger in the case when the reactive power control mode is active. In this case, the turbine is connected to the grid (Figure 33) and partly compensates the amount of reactive power at Bunkeflo. This generates larger currents and can explain a larger impact
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on the whole turbine electrical system than in the case of the IEC connection where quite no reactive power is transferred from the turbine (see Figure 42).
The general tendency consists in a decrease of the peaks in the DC-link voltage when more turbines are operating. The voltage sag effect is damped when more turbines are running. One can expect that a whole feeder of nine turbines could handle the same voltage sag more easily.
The following figures (Figure 39 to Figure 41) show the rms voltages in per unit at different nodes in the system, namely at the PCC (Bunkeflo), at the offshore substation and at the wind turbine output (output of the turbine transformer) for two control modes when a 100 ms voltage sag with 25% remaining voltage occurs. As stated previously, the voltage level of the grid-side converter output (behind the wind turbine transformer) is regulated according to the offshore substation level. The three following figures illustrate the voltage regulation (blue curves); the regulated and reference voltages are close by 0.5%. In the case of reactive power control, the wind turbine voltage level differs from the substation voltage level by about 4%. The voltage control mode is therefore quite efficient according to the results obtained during the simulation.
The number of turbine operating does not affect the voltage control at each turbine output; the turbine voltage it differs from the offshore substation voltage by maximum 0.5 % in each case (one, two or three turbines running). However, a small difference appears at the moment when the voltage sag occurs. With three turbines running, a peak is observed at the time of the sag and during the voltage sag, the voltage regulation is less fast and accurate when two or three turbines are running.
Figure 39: Voltage response at different nodes for one turbine for different control modes
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Figure 40: Voltage response at different nodes for two turbines for different control modes
Figure 41: Voltage response at different nodes for three turbines for different control modes
For each case (one, two or three turbines running) the voltage response is the same for each turbine. This result is expected since the control implemented in the PSCAD model is exactly the same for every turbine.
It would be interesting to simulate one feeder containing ten wind turbines and even more in order to observe an eventual interaction between the wind turbines when the voltage control mode is active. In fact, the voltage control is regulated according to the reference voltage at the offshore substation that connects the five feeders together (description in Section 1.2). This might imply an interaction between the turbines operating with voltage control.
The following figure (Figure 42) shows the reactive power measured at Bunkeflo (PCC) for one, two or three turbines withstanding a 100 ms 25 % remaining voltage sag. On the right figure, the voltage control is active and on the left figure the reactive power control is active. It is observed that one turbine output about 1.8 MVAr of reactive power at the maximum when the reactive power control is
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active. We can guess that with a fourth wind turbine the whole reactive power at Bunkeflo would be compensated. On the contrary, the reactive power at Bunkeflo remains high when the voltage control is active. During the voltage sag, the reactive power at Bunkeflo drops due to the decrease of the rms voltage.
Figure 42: Reactive power measured at Bunkeflo in the cases of one, two, and three turbines operating and withstanding a 100 ms 25% remaining voltage
Figure 43 shows the generator electrical speed for one wind turbine with two control modes withstanding a 100 ms 25 % remaining voltage sag. The speed variation due to the voltage sag is at the most 0.5%. Also when the reactive power control is active, the speed suffers the impact of the voltage sag faster than when the voltage is controlled. Moreover the peaks values of the speed right after the voltage sag are higher with the reactive power control. The impact is more important on the speed when the reactive power is controlled.
Figure 43: IM electrical speed for two control modes
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The same comments can be formulated for the rotor flux shown in Figure 44 and Figure 45. The later shows the rotor flux angle that varies between -π and π. The influence of the sag is not obvious on this figure but it is in the left side figure. It represents the dq-axis rotor flux. The q-axis rotor flux is zero since the field oriented reference frame is used (see Section 2.4). The d-axis withstands the voltage sag quite well. Its oscillations amplitude decreases but some noise appears in it. After the voltage sag, the oscillations show greater amplitude, that are then damped with the time.
Figure 44: dq-axis flux angle for two control Figure 45: rotor flux angle for two control modes mode
The impact of the voltage sag on the induction machine is thus of no consequences. The effects are far from large and are damped quite immediately. The induction machine is protected by the VSCs control system.
5.4.2 Impact on the wind turbine current
Figure 46 shows the results expected in Section 5.3.1.
The former wind turbine model from VPC (current source + transformer) is not realistic; there is quite no impact of the voltage sag on the turbine output current.
Since the reactive power at Bunkeflo is high due to the cables in particular, the wind turbine injects quite a high amount of reactive power to the grid in order to compensate it (about 1.8 MVAr). It means that the d-axis current injected is high. Thus the wind turbine operates with larger currents than when the voltage control mode is active. The wind turbine output almost 1 pu during normal conditions (no voltage sag) when the reactive power is controlled although it output 0.6 pu when the voltage is controlled (See Figure 46).
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Therefore the impact of a voltage sag on the turbine output current is less significant when the voltage control mode is active
The overcurrents increase with the amplitude of the voltage sag for the new wind turbine model.
Beyond certain remaining amplitude of the sag, the overcurrents keep the same value (for the red curve): the limits imposed by the currents hard limiters that are the maximum allowed values are reached.
The maximum overcurrents are about 2 pu that is acceptable during a few hundred ms as stated in 4.5
Impact of a voltage sag on the turbine current for two control modes Connection to the grid
2,5
2
1,5 voltage control
1 former model
0,5 Reactive power control the turbine [pu] 0
peak current of at the output 0 20 40 60 80 100 120 remaining voltage during the voltage sag [%]
Figure 46: Peak current caused by a three-phase voltage sag at the output of the turbine
5.5 Results concerning the harmonics study for one or several turbines connected to the grid
The Matlab program (in Appendix 5) gives the following results concerning the harmonics content of the current measured at the offshore substation. The computation of the FFT in Matlab is made on a finite interval and that can might affect the accuracy of the results.
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Table 8: Amplitude of harmonics in the offshore substation current for one, two or three turbines operating Amplitude (pu) Amplitude (pu) Amplitude (pu) order n f (Hz) n 1 turbine 2 turbines 3 turbines 1 50 1 1 1 Harmonics
due to PWM
m f 2500 ~ 0 ~ 0 0
m f 2 2400/2600 0.02 0.02 ~ 0
m f 4 2300/2700 0.01 ~ 0.005 0 … ….
2 m f 1 4950/5050 0.04 0.05 0.04
2 m f 3 4850/5150 ~ 0 ~ 0 0
2 m f 5 4750/5250 0.005 ~ 0.005 0 … …
3 m f 7500 ~ 0 ~ 0 0
3 m f 2 7400/7600 0.02 0.03 ~ 0
3 m f 4 7300/7700 0.01 0.02 0 …
4 m f 1 9950/10050 0.015 ~ 0 0
4 m f 3 9850/10150 ~ 0 ~ 0 0
Other order 112.5 0.03 0.03 0.01 215 0.03 0.03 0.03
5 f1 250 0.02 0.01 ~ 0.008
7 f1 350 0.01 ~ 0.005 ~ 0.005
Harmonic Analysis of the turbine output current
0,06 0,05 0,04 1 turbine
0,03 2 turbines [pu] 0,02 3 turbines 0,01
0 Amplitude of theharmonic of Amplitude 250 112.5 2500 7500
2300/27004850/5150 7300/7700 9850/10150 frequency [Hz]
Figure 47: Amplitude of harmonics in the offshore substation current for one, two or three turbines operating
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Table 9: Amplitude of harmonics in the offshore substation voltage for one, two or three turbines operating Amplitude (pu) Amplitude (pu) Amplitude (pu) order n f (Hz) n 1 turbine 2 turbines 3 turbines 1 50 1 Harmonics
due to PWM
m f 2500 0 0 0
m f 2 2400/2600 ~ 0 ~ 0 ~ 0
m f 4 2300/2700 ~ 0 ~ 0 ~ 0 … ….
2 m f 1 4950/5050 ~ 0 0.01 0.03
2 m f 3 4850/5150 ~ 0 ~ 0 ~ 0
2 m f 5 4750/5250 ~ 0 ~ 0 ~ 0 … …
3 m f 7500 0 0 0
3 m f 2 7400/7600 ~ 0 0.01 0.015
3 m f 4 7300/7700 ~ 0 ~ 0.005 ~ 0 …
4 m f 1 9950/10050 ~ 0 ~ 0 ~ 0
4 m f 3 9850/10150 ~ 0 ~ 0 ~ 0 … Other order 112.5 - - 0.03 215 - - 0.01
5 f1 250 - - 0.01
7 f1 350 - - ~ 0
The harmonics content for current and voltage is the same as in the previous section (Section 5.3.2 in Table 7). With one two or three turbines, the harmonics content changes. Either some harmonics are cancelled or reduced; some others do not change and some increases. With several turbines operating, the harmonics can be added to each other or cancel each other. This clearly appears on Figure 47.
5.6 Comparative analysis between two control modes
From the previous results in Section 5.3, 5.4, and 5.5 some conclusions comparing the two control modes studied can already be done. Table 10 summarizes the results obtained from the simulations of the new wind turbine model. It concerns the characteristics of each control mode and the short power quality analysis (response to a voltage sag and harmonics study).
From the electrical network point of view the reactive power control mode is more advantageous because it allows fulfilling the requirement of zero reactive power at Bunkeflo. This is also wanted by
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the wind farm owner, that has to meet the requirement. However, it induces higher currents which also means that the wind turbine run at higher apparent power. So the wind turbine is fully used unlike with the voltage control mode. The high overcurrents are a drawback for the turbine manufacturer that must invest in adapted equipment. Therefore, for the turbine manufacturer the voltage control is profitable. Moreover, the voltage is maintained stable at the turbines output. One other advantage is that the impact of voltage sags on the internal DC-link voltage is less important with the voltage control mode (for voltage sag with remaining amplitude superior to 30% of the initial voltage). The harmonics content of currents and voltage does not depends on the control mode and we know that the requirements concerning the harmonic distortion are fulfilled at Lillgrund.
Table 10: Comparative analysis between reactive power and voltage control
Reactive power Voltage control control
Constant and stable value for the voltage - + even during events
Reactive power compensation + -
Impact of a sag on the turbine output current + -
Impact of a sag on the DC-link voltage Depends on the type of Depends on the type of fault fault
Harmonics = =
In Table 10, + corresponds to positive and – to negative points.
5.7 Comparison with the Siemens’ study
This section compares the results obtained by Siemens and summarized in [6] with the one obtained during the simulations of the new model. The results might differ because of different causes: The control system is built with no hint from Siemens, the control system supplier. The simulation on a software always induces errors, e.g. the losses explained in Section 5.1. We are not sure that the measurements are carried out in the same way.
5.7.1 Harmonics study
Table 11 compares the harmonics results obtained in this study and the results from Siemens study. A quite important difference is observed that could mainly comes from the two following facts.
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For one turbine, the harmonic content of the current mainly depends on the PWM filter installed at the output of the inverter. Siemens stipulates that the IHD (individual harmonic distortion) of the current varies within the range indicated in Table 11 depending on the filter concept. The filter adopted in the PSCAD model was described and justified in section 4.3.2 and Appendix 3. However, it was seen that a more adapted filter (from [4]) could be studied in the new turbine model to improve its efficiency (Section 4.3.2).
In the case of the entire wind farm, the phenomenon of random mitigation occurs. That induces the cancellation or the decrease of many harmonics in the current. This was shown in the previous Section 5.5 when comparing the harmonic content of one, two or three turbines connected to the main grid. In the Siemens study, control mitigation is implemented. By the mean of probabilistic methods, it decreases considerably the quantity of harmonics by cancellation. The random mitigation is more significant for many turbines. However, the results of the random mitigation cannot be observed in the present case since the 48 wind turbines are not simulated.
Table 11: Comparison of the THD and IHD from Siemens and from simulating the new model THD (%) IHD (%)
Siemens PSCAD Model Siemens PSCAD Model One Unknown THD < 3 0.125 < IHD < 0.5 IHD < 2 turbine PCC at THD < 0.9 THD < 4.5 (3 turbines) IHD < 0.025 IHD < 2 (3 turbines) Bunkeflo
In Table 11, the last row shows the IHD (individual harmonic distortion) and THD (total harmonic distortion) for 48 wind turbines in the case of Siemens study but only of 3 turbines in the case of the new model. This must be taken into consideration when reading the table.
5.7.2 Dynamic simulation study
Siemens carried out a study to check some dynamic response of the wind farm.
Siemens: For a voltage sag defined by the TSO and occurring at the PCC, the wind turbines rides through. The voltage sag curve is defined by Svenska Kraftnät and is shown on Figure 48. Figure 48 corresponds to the most severe voltage sag that might happen at PCC and that is one of the requirements of the grid code. The wind farm or wind turbine must withstand it [21]. New model simulation: The simulation of similar voltage sag is made on PSCAD with a duration of 250 ms and no remaining voltage. The turbine rides through this sag.
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Figure 48: Ride-through requirement for Svenska Kraftnät grid code [21]
Siemens: When the voltage sag occurs at the PCC, the voltage drop at the output of the wind turbine is limited to 0.3 pu by the FRT system. Maximum reactive power is brought in to the grid. New model simulation: The next three tests shows that the voltage drop at the output of the wind turbine is limited to 0.15 pu by the FRT system for the present model (see Figure 49 and Table 12). This limit is induced by the current limits. The maximum reactive power is also brought in to the grid when the reactive power control is active.
The voltage sags tests are 250 ms voltage sags with 75% (green curves), 25% (red curves) and 0% (blue curves) remaining voltage (Figure 49).
Figure 49: Rms voltages at the output of the turbines and at Bunkeflo during different voltage sag occurring at the PCC (Bunkeflo) for two control modes (reactive power on the left and voltage on the right)
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Table 12: Remaining voltage level at the turbine output foe three types of voltage sag Duration of the sag [ms] 100 100 250 Remaining voltage during the voltage sag at 0.75 0.25 0 Bunkeflo [pu] Remaining voltage during the voltage sag at the 0.71 ~0.25 ~0.15 output of the turbine [pu]
Figure 50 shows the reactive power at Bunkeflo for these three different voltage sags. When running one turbine with reactive power control, the maximum possible reactive power is transmitted in to the grid during normal condition (Figure 50 before the sag happens). Nevertheless, only one turbine cannot compensate the whole reactive power induced at Bunkeflo. With voltage control there is no reactive power compensation. However, the turbine voltage level is regulated (see Figure 50, graph on the right).
Figure 50: Bunkeflo reactive power during different voltage sags occurring at the PCC (Bunkeflo) for two control modes (reactive power on the left and voltage on the right)
5.8 Island Operation
It might happen in the future that wind power plant becomes disconnected from the grid but must still supply some loads. This might only be possible if the wind park is able to operate within a certain range of frequencies and voltage level when disconnected from the grid. Indeed, the customers supplied by the wind power plant still need the same quality of energy. If the requirements are not respected, the wind power plant must also disconnect from the remaining loads.
This part concerns the island operation of the wind turbine or farm. What are the consequences of the disconnection of the turbine from the grid? How the present model of turbine handles this event? The island operation has no time limit. However, 1 s of island operation is sufficient to draw some conclusions. The connection of the wind turbine is the same as described in Figure 33.
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The three following figures (Figure 48 to Figure 50) illustrate the response of the turbine when it is disconnected from the grid at t = 1 s. Particularly, the frequency and the voltage at the offshore substation are observed. The wind turbine could not be connected to a load to supply it energy. The frequency decreases and varies between 0.65 and 0.8 pu with the reactive power control mode. With the voltage control mode, it first drops and then stabilizes at a constant value of 0.88 pu which is quite good but not high enough to satisfy the TSO requirements. The rms voltage oscillates largely (between 0.6 and 1.3 pu) with the reactive power control. No stability is reached. With the voltage control, the voltage level reaches a stable value of about 0.5 pu. However the signal is not sinusoidal at all. It contains a large amount of harmonics. The island operation does not fulfil the necessary requirements concerning the voltage quality in order to supply a potential customer.
Figure 51: Voltage at the offshore Figure 52: rms voltage at the offshore substation substation
Figure 53: Island operation at t = 1 s – Impact on the frequency
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6 Conclusions
The master thesis work gives an overview of one possible control system for a wind turbine installed at Lillgrund wind farm. The corresponding model has been implemented in PSCAD in order to simulate and verify the operation of such a turbine. Reactive power control is installed at Lillgrund wind farm and is implemented in the PSCAD model. Moreover, a voltage control has also been implemented in the project in order to compare the results for different control modes of the turbine.
The results show that the requirements concerning the reactive power are fulfilled. That is the power factor at the PCC at Bunkeflo is maintained at the unity or the reactive power at zero. Four turbines are necessary to manage it that is to compensate the reactive power created by the cables in particular. Only one turbine can produce a limited amount of reactive power because of its electrical design.
The comparison between the reactive power control and the voltage control leads to the conclusion that the impact of voltage sags on the turbine differ a little. The peak currents reached by the turbine bearing voltage sags are larger in the case when the turbine is reactive power controlled. This is partly due to the fact that the reactive power control induces higher current even during normal conditions of operation. The comparison between the two control modes is summarized in Table 10 in Section 5.6.
The new model implemented in PSCAD is closer to the reality since it includes almost all the components and controls of the turbine. Also, the simulations give coherent results that approach the reality. Especially, it was seen that the former turbine model (current source + transformer) does not show large overcurrents when a voltage sag occurs although it happens in the real case. Also, the harmonics study of the former wind turbine model is obviously not representative of the real case since nor power electronics neither generator are implemented in the model.
The power quality study of the model shows first of all that the wind turbine rides through voltage sags independently of its amplitude and duration. Secondly the harmonics content of the output currents and voltages changes with the number of turbines. The main advantage is the harmonics cancellation that results from this random mitigation.
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7 Improvements and future works
Improvements for the model:
The data generation for the induction machine is the typical method defined on PSCAD. It is also possible to use the explicit method, which would give an IM model close to the real machine. This explicit method needs the knowledge of the machine parameters and also a good understanding of the machine theory and model of PSCAD.
The model has not been equipped by some protections. A study could be carried out in order to include protective equipment in the model.
Optimal speed control system could be implemented to increase the efficiency of the turbine (see Section 2.4.6).
To make the model less heavy, it could be possible to encode some of the control in FORTRAN that could decrease the simulation time and in the same time the errors.
Field weakening control could be implemented in the PSCAD model to allow the induction machine operating at low torque. At low torque, the variable speed induction generator runs at higher speed and the power is kept approximately constant. This is done by reducing the flux (“flux weakening”) which is controlled by the d-axis current Isd control the flux (equation 31). A reduced flux corresponds to an increased speed since the inverter voltage is kept constant (equation 23). However this possibility would not increase the efficiency of the wind turbine significantly since the power from the low wind speed is low.
Future works:
First of all, the results obtained with this new model developed by PSCAD might be compared with some measurements. So far, no measurements allowing a potential comparison were available at Lillgrund. However, some on-coming project might lead to the achievement of such a comparison and a verification of the present model.
The simulation of the whole farm equipped with the new turbine model could lead to some possible studies. However, the simulation time of this would become huge (more than a day, maybe one week).
The suggestion of using wind farm for power quality improvement might lead to a possible future project applicable in the national grid (proposal by F. Carlsson).
The model developed in the project might also be used to simulate another wind farm. The future project of a 23 wind turbines power plant at Hjuleberg could be simulated. However, the present model should be simplified or reduced in order to simulate the 23 turbines. One possible simplification
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would be to represents the part upstream the capacitor by a controllable current source. Then the reactive power control is still possible and the size of the model is almost divided by two. Another possibility would be to encode some of the control in FORTRAN so that the model is less heavy and more accurate.
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References
[1] PSCAD/EMTDC, Manitoba HVDC Research Centre, https://pscad.com/index.cfm [2] T. Lund, J. Eek, S. Uski, A. Perdana, “Dynamic Fault Simulation of Wind Turbines using Commercial Simulation Tools ” 5th International Workshop on Large-Scale Integration of Wind Power and Transmission Networks for Offshore Wind Farms, pages 238-246, Glasgow, April 2005. [3] M. Molina, B. Naess, W. Gullvik, T. Undeland, “Control of Wind Turbine with Induction Generators interfaced to the Grid with Power Electronics Converters” Presented at the International Power Electronics Conference IPEC 05, Niigata, Japan. [4] H. Xie, “Voltage Source Converter with Energy Storage Capability”. KTH, Stockholm, Sweden. Licentiate Thesis in Power Electronics. 2006. [5] ”Electrical Machines and Drives”. KTH Electrical Machines and Power Electronics. Stockholm, 2008. [6] Å. Larsson “Lillgrund Wind Power Plant – Documentation of electrical system”, April 2008, Vattenfall Power Consultant AB. [7] F Carlsson, U Axelsson, M. Lindgren, H. K. Nielsen ”Assignment Specification for Simulation Studies and Measurements of Electrical Transients and Power Quality Parameters at Lillgrund Wind Power Farm”, October 2008, Vattenfall Research and Development AB. [8] Private communication with D. Salomonsson, Vattenfall research and development AB, 2008-2009. [9] B. B. Garzon, “Power quality of wind farm – Validation of standard methods for assessing flicker and harmonics” Technical University of Denmark DTU, Copenhagen, Denmark. Master thesis. July 2008. [10] F. Carlsson “On impact and Ride Through of Voltage Sags Exposing Line-Operated AC-Machines and Metal Processes”. KTH Electrical Engineering, Stockholm, Sweden. Doctoral Thesis. 2003. [11] K. Pietiläinen “Voltage Sag Ride-Through of AC drives: Control and Analysis”. KTH Electrical Engineering, Stockholm, Sweden. Doctoral Thesis. 2005. [12] IEC 61400-21 “Wind Turbines – Part 21: Measurement and assessment of power quality characteristics of grid connected wind turbines” [13] F. Carlsson, A. Badano “Elektronisk last - Omvärldsanalys”, Elforsk rapport 08:51, June 2008, Elforsk. [14] ”Harmonics – Causes and Effects” Power Quality Application Guide, http://www.copperinfo.co.uk/power-quality/downloads/pqug/31-causes-and- effects.pdf [15] N. Mohan, T M. Undeland, W P. Robbins “Power Electronics – Converters, Applications, and Design”, third edition, John Wiley & Sons. USA. 2003.
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[16] IEEE recommended Practice for Monitoring Electrical Power Quality, IEEE Std.1159-1995, New-York, IEEE, 1995. [17] Private communication with H-P. Nee, KTH Electrical Engineering, division Power Electronics and Electrical Machines, 2008-2009. [18] Private communication with H. Xie, KTH Electrical Engineering, division Power Electronics and Electrical Machines, 2008-2009. [19] M.H.J. Bollen “Voltage Sags in Three-Phase Systems”, IEEE Power Engineering Review. Volume 21, September 2001. [20] AVX Corporation, Kyocera group company, http://www.avx.com [21] Ackermann, Thomas (editor) (2005). Wind Power in Power Systems. Chichester, West Sussex: John Wiley & Sons, Ltd. [22] R. Pena, R. Cardenas, R. Blasco, G. Asher, J. Clare, “A Cage Induction Generator Using Back to Back PWM Converters for Variable Speed Grid Connected Wind Energy System” the 27th Annual Conference of the IEEE Industrial Electronics Society, 2001. [23] Private communication with U. Axelsson, Vattenfall Research and Development AB, 2008-2009. [24] F. Carlsson, V. Neimane, “A massive introduction of wind power - changed market conditions? ”, Elforsk report 08:41 June 2008. [25] Energimyndigheten: “Nytt planeringsmål för vinkraften år 2020”. ER 2008:45, ISSN 1403-1892. 2007. [26] “Syftet med förstudiens simuleringar” [27] Angelo Baggini, "Handbook of Power Quality", John Wiley & Sons, 2008 [28] “ITI (CBEMA) Curves Application Note” Technical Committee 3 (TC3) of the Information Technology Industry Council (ITI, formerly known as the Computer & Business Equipment Manufacturers Association). http://www.itic.org/
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Kungliga Tekniska Högskolan pwm1 PWM1 fs pwm1_in PWM 2500.0 PWM1inv fs [Hz] ua_ctrl pwm2 PWM2 ub_ctrl pwm2_in Appendices PWM2inv uc_ctrl pwm3 PWM3 Appendix 1: Grid-side control systempwm3_in - PSCAD model PWM3inv
ua_ctrl ub_ctrl uc_ctrl
I_line I_line Vdcc Vdc_mea U_net U_net VSC_Controller * Vdc_ref TIME 1.7537 ctrl Q_needed U_desired cosphi_needed ctrl
pwm1 PWM1_rec fs [Hz] fs pwm1_in 1250.0 PWM Current Controller PWM1inv_rec I_gene ua_ctrl ua_ctrl pwm2 PWM2_rec Rotor Flux Estimator ub_ctrl ub_ctrl pwm2_in I_gene PWM2inv_rec I_gene rho rho uc_ctrl uc_ctrl pwm3 V_gene Appendix 2: Generator side-control - PSCADPWM3_rec model V_gene id_ref iq_ref pwm3_in PWM3inv_rec
0.918665
Speed Controller Wg_ref 1.034 Iq_ref Wg Wg
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Appendix 3: PWM filter frequency analysis Figure x in the report shows the PWM filter installed at the output of the grid-side converter. The transfer function F(s) linking the current through the filter I and the voltage across it Vconv is expressed as: I(s) 1 F(s) (43) Vconv(s) R L s
Written in the normalized way:
I(s) K F(s) (44) V (s) conv 1 j c
1 R The constant K represents the gain of the low pass-filter and f c 5Hz is the R c 2 2 L cut-off frequency of the filter, which is the frequency, corresponding to the point at which the filter attenuates the signal by 3dB. Figure 54 shows the bode diagram of the filter transfer function and proves the efficiency of the filter. The filter attenuates the frequency above 1000 Hz by more than 45dB that is the amplitude is attenuated by more than 99 %.
Figure 54: Bode diagram of the PWM filter transfer function
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Appendix 4: Rotor-locked test and no-load test for the induction machine (IM)
By simulating the PSCAD IM model, the induction machine parameters can be identified.
Figure 55: Equivalent circuit of the IM The parameters of the IM shown on Figure 55are:
Rs the stator resistance
Lls the stator leakage inductance
Llr the rotor leakage inductance
Lm the magnetizing inductance
Rr’ the rotor resistance (s is the slip)
The active power of the IM is
P 3 U s I s cos() (45)
The no-load test is simulated by setting the input value of the electrical torque equal to zero, which signify no load torque. The slip is very close to zero, which means a very high equivalent resistance on the rotor side. Thus, the equivalent resistance is:
U s Z eq0 Rs j X m X ls (46) 3 I s
U s Rs cos() (47) 3 I s
U s X m X ls sin() (48) 3 I s
The rotor-blocked test is imitated by inputting the nominal current but reduced voltage. The IM is used under speed control mode with the speed equal to zero, that is the rotor does not move. The magnetizing reactance is much bigger than the other impedance, thus it is approximated as an open circuit. Consequently the equivalent impedance is:
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U s Z eq0 Rs Rr ' j X ls X lr (49) 3 I s
U s Rs Rr ' cos() (50) 3 I s
U s X ls X lr sin() (51) 3 I s
The IM parameters are deduced as follows.
Rs 0.0507 R ' 0.0352 r (52) X m 0.8164
X ls X ls 0.0726
Appendix 5: Matlab code used to compute the harmonics of a signal saved from PSCAD in a data file
%------% COMPUTATION OF THE HARMONICS % The data are loaded from PSCAD and the function FFT is used on % matlab to compute and observ the harmonics. %------clear all; format long; %------%Parameters ts = 5e-5; % [s] channel plot step fs = 1/ts; t0 = 0.8; % [s] initial time tf = 1; % [s] end time T = [t0 : ts : tf]; % calculation period L0 = t0/ts + 1; LF = tf/ts + 1; L = L0-LF; %------%Loading the data from a data file load channels_01.dat; % load the file containing the data of load channels_02.dat; % PSCAD channels output load channels_04.dat;
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%------%Plot the curves that we want the FFT n = 10; % column n in the data file corresponding to the current values X1 = channels_01 (:,n); % Vector of which the FFT will be computed figure (1) plot (T,X1(L0:LF)) title('Current at node A - IA') xlabel('time s') ylabel('amplitude kA') %------%Calculate the FFT NFFT = 2^nextpow2(L); % returns the first NFFT such that 2^NFFT >= abs(L)
Y1 = fft(X1(L0:LF),NFFT)/L; % calculate the FFT of the vector X1 f = fs/2*linspace(0,1,NFFT/2); figure (4) plot(f,2*abs(Y1(1:NFFT/2))); % plot the single sided amplitude spectrum of the signal title('Spectrum of IA and Ivsc') xlabel('Frequency (Hz)') ylabel('|IA(f)|')
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Simulations
SIMULATION A: Control mode test on the grid-side inverter connected to the grid. SIMULATION B: Test of the Generator-Side system SIMULATION C: Test new model with IEC-connexion SIMULATION D: Comparison of the control modes for different amplitude of the sag
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SIMULATION A: Control mode test on the grid-side inverter connected to the grid
Here, the voltage control and the reactive power control mode are tested on a simulation. The power factor control mode is not tested since it is very similar to the reactive power mode. The voltage control maintains the voltage amplitude of the inverter output at the offshore sub-station level. The reactive power is controlled to be zero at Bunkeflo. The turbine operate at 2,25 MW power and the reactive power depends on the control modes but the maximum amount that can be produced or consumed is 0,5 MVAr (S=2,3 MVA).
The table above describes the different stages of a simulation made on the grid side converter system connected to the grid via the two transformers and two different cables.
Main control Time period (s) Control mode Control place Event signal
Phase 1 0 - 0.5 4 No control Substation -
Reactive Phase 2 0.5 – 1 1 Bunkeflo - power
Phase 3 1 – 1.5 3 Voltage Substation -
Voltage sag Phase 4 1.5 – 1.6 3 Voltage Substation in the grid Choice of Control Table A 1: Description of the Simulations Stages
Main : Controls Choice of The COntrol Mode : Choice Control ModeA control interface of PSCAD is used to make the choice of the control mode. The value of the control 4 1 Reactive POwer can change during the simulation2 Power (see Factor Figure A 1). 3 ctrl_choice 3 Voltage 2 4 Default Mode (no Id injected) 1 4
Qbunk phibunk Measurement needed : * E_offsub_rms 0.8165 ctrl_choice Reactive Power at Bunkeflo Pbunk Power Factor at Bunkeflo Voltage at the offshore substation (low voltage)
Control
Figure A 1: Control Implementation in the Model – Possibility to Switch during the Simulation
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The voltage sag that occurs at 1,5 s at Bunkeflo has duration of 100 ms and the remaining voltage is 75% of the normal voltage (Figure A 2).
Main : Graphs Bunkeflo Voltage 200
150
100
50
0 y -50
-100
-150
-200 1.400 1.450 1.500 1.550 1.600 1.650 1.700 ...... Figure A 2: Voltage sag in Bunkeflo: 75 % remaining voltage, duration = 200 ms
First no control is active. By default, it means that no d-axis current is injected. That also means that the reactive power injected by the turbine is zero.
At the second stage, the control is switched on reactive power control mode. The device is supposed to supply a certain amount of reactive power, which will partly compensate the reactive power at Bunkeflo. The objective is that the whole wind farm compensate the reactive power at Bunkeflo in order to get no reactive power at that node. Indeed, it is required to have a unity power factor at Bunkeflo that is no reactive power. However, it is not possible with only one turbine. So a d-axis current is estimated and then injected to remedy the reactive power; the maximum possible reactive power is injected by the turbine (Q = 0,5 MVAr). It is seen on Figure A 3 that 0,6 kA are supplied during this second step. However, it only allows to decrease the reactive power at Bunkeflo by 0,5 MVAr (Figure A 4). Only one device cannot handle the whole compensation of the Bunkeflo reactive power.
VSC_Controller : Graphs Iq_net Id_net Iq_ref Id_ref 4.0
3.0
2.0
1.0
0.0 y
-1.0
-2.0
-3.0
-4.0
0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...... Figure A 3: dq-axis current at the converter output¨
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Main : Graphs Main : Graphs Bunkeflo reactive pow er turbine reactive pow er 8.0 0.20
7.0 0.10
6.0 0.00
5.0 -0.10 -0.20
4.0 y y -0.30 3.0 -0.40 2.0 -0.50
1.0 -0.60
0.0 -0.70 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 ... 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...... Figure A 4: Bunkeflo and turbine output reactive power
During the two last stages, the voltage control mode is active. As it is seen on the Figure A 5, the voltage amplitude is maintained to the desired level, which is the amplitude of the substation voltage (readjusted to the 0,69 kV base voltage on this side of the transformer). It is especially well shown during the voltage sag event.
VSC_Controller : Graphs Amplitude output converter voltage Amplitude desired 1.40
1.20
1.00
0.80 y
0.60
0.40
0.20 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...... Figure A 5: Converter output voltage amplitude and the desired amplitude for voltage control
During the whole simulation the DC-link voltage is regulated at the required level and reasonably constant value, even during the voltage sag (Figure A 6). This allows good operation of the turbine.
Main : Graphs Vdcc
1.800
1.780
1.760
1.740
y (kV) 1.720
1.700
1.680
1.660 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ......
Figure A 6: DC-link voltage UDC
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Main : Graphs Main : Graphs Ia_conv Ua_conv 5.0 1.00
4.0 0.80
3.0 0.60 2.0 0.40 1.0 0.20
0.0 y y 0.00 -1.0 -0.20 -2.0 -3.0 -0.40 -4.0 -0.60 -5.0 -0.80 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ... 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 ...... Figure A 7: Output current of the converter Figure A 8: Ouput voltage of the converter
Figure A 7 and Figure A 8 show the current and voltage at the output of the converter. The voltage is observed and the current variation commented previously can also be seen.
Main : Graphs Turbine Voltage [pu] Offshore Substation Voltage [pu]
1.050
1.000
0.950 y 0.900
0.850
0.800
0.750
0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...... Figure A 9: Amplitude if the voltage in per unit at the output of the converter and at the offshore substation
Figure A 9 shows the amplitude of the voltages at the offshore substation and at the output of the converter. From t = 1 s, the voltage control mode is activated and the two voltage amplitudes corresponds. In the contrary during the two first stages, the two voltage amplitudes are different by 5 and 4 % respectively.
Main : Graphs I offshore substation 0.150
0.100
0.050
0.000 y
-0.050
-0.100
-0.150 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ...... Figure A 10: Current at the offshore substation
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During the stage 2, some d-axis current is injected to compensate the reactive power at Bunkeflo. Consequently, there is an increase of the current amplitude as seen in Figure A 10. Also, during the voltage sag the amplitude of the current increases due to two reasons. First, during the sag, the voltage decreases; some q-axis current is injected to maintain the power balance. Secondly, some d-axis current is injected to maintain the voltage level of the converter output. Conclusion:
The simulation was carried out with a time step of 0,5 us. This time step is a good compromise since then the simulation last only a few minutes and the losses induced by the calculation are not so important (12 %).
The dq-axis currents are limited by a hard limiter that keeps them within a certain range of value (+/- 2 pu). Indeed, the material must be protected from overcurrents.
The reactive power at the PCC (point of common coupling, Bunkeflo) is high (7.5 MVar) because of the cables. When using the reactive power control mode, the d-axis current Id that would theoretically compensate this reactive power at Bunkeflo is unfeasible, so compensation is not achievable with one turbine. However, the hard limiter limits the current. Because of that, the reactive power at Bunkeflo is only partially compensated. To compensate the reactive power induced by the source and cables, at least 15 wind turbines are necessary (with this set of operation).
If we assume that there is no limits for the currents, then the d-axis current Id would reach a high value in order to compensate the reactive power. Nevertheless, it would imply a decrease of the active power transmitted from the converter as it is shown on Figure A 11 and equation (14).
Figure A 11: Park representation of the voltages and current at the converter output
One possibility is to set the different controls at different nodes. For example, the voltage can be regulated to follow any voltage of the system. For example the reference voltage could be the voltage at the output of the 0.69/33 kV transformer.
For the farm or for a radian, we can expect some interactions between the turbines if the voltage controller reference is the offshore substation voltage. However if the voltage controller reference were the output of each 0.69/33 kV transformers, then these would disappear.
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SIMULATION B: Test of the generator-side system
The system is composed of the wind source, the wind turbine, the pitch governor, the IM and the inverter. Also it includes the control system of the machine described in section 2.4. The system PSCAD scheme consists in Figure 11 in section 2.4.1.
The test is a simulation during a runtime of 75 s with the occurrence of several events described in Table B 1.
Table B 1: Description of the simulation stages Time Event Switch the generator from speed control to torque Step 1 0.1 s control mode Step 2 1 s Switch ON the Pitch control 3 gusts with a period of 0.2 s and an amplitude of Step 3 25 s 2 m/s Step 4 35 – 45 s Wind ramp during 10 s
The IM is started in speed control mode, which means that the speed reference is imposed. After the initial transients, it operates in torque control mode and the input torque of the IM is the output torque of the wind turbine component. At t = 1 s, the pitch control is activated. The governor regulates the pitch angle by knowing the power demand (set to 2.3 MW) and the generator active power. Normally it takes more than 100 s for the pitch to reach its steady state value under good conditions (wind speed constant). When the gusts occurs at t = 25 s, a zoom on the pitch angle shows that it is recalculated. Also, the impact on the torque and the speed of the IM is seen on Figure B 1 and Figure B 4. When the wind speed ramp occurs at t = 35 s, the pitch angle is regulated. As soon as the wind speed increase, the pitch angle starts increasing. Since the power demand remains 2.3 MW, but the wind increases, the blades must pitch to control the output power produced by the generator.
Speed_Controller : Graphs Wg
1.240
1.220
1.200
1.180 y 1.160
1.140
1.120
1.100 0 20 40 60 ...... Figure B 1: IM mechanical speed in pu
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Main : Graphs Beta 11.0
10.0
9.0
8.0
7.0 y 6.0
5.0
4.0
3.0 w ind speed 15.50
15.25
15.00
14.75
14.50 y 14.25
14.00
13.75
13.50
0 10 20 30 40 50 60 70 80 ...... Figure B 2: Pitch Angle of the Blades and Wind Speed
The dynamic of the mechanical system induced by the pitch control is very slow. However the solution time step must be kept short because of the power electronics of the VSC. Thus, the simulations time increases.
Main : Graphs Main : Graphs Tel mechanical torque machine P_gene P_turbine [MW] 0.00
-0.20 2.80
2.60 -0.40
2.40 -0.60 y
2.20 -0.80 y (MW ) 2.00 -1.00
1.80 -1.20 1.60 0 10 20 30 40 50 60 70 ... 0 10 20 30 40 50 60 70 ...... Figure B 3: Generator Electrical Power and Figure B 4: Electrical Torque of the Machine Turbine Mechanical Power and Mechanical Torque
The mechanical torque of the IM and the turbine torque are the same since the IM operates at torque control mode. Thus, the input of the IM is the mechanical torque that corresponds to the turbine torque.
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SIMULATION C: Test turbine with connexion IEC
Timed This appendixFault shows the results obtained for different tests made on one turbine connected according Fault Logic to Figure 29 in 5.3.1 and Figure C 1 below. It details the section 5.3.1 that only gives a summary of the
whole simulation results.
2.0 2.0 [nF]
Fault Fault Fault
2.0 2.0 [nF] At t = 1 s, the 500 ms voltage sag is applied at the output of the transformer thanks to the short-circuit 2.0 2.0 [nF] emulator (Figure50 % R C = 0.11). ohm The voltage supports a three-phase symmetrical voltage sag with 50%
remaining amplitude.20 % R = 0.4 ohm
0.1 [ohm]0.1 [ohm]0.1 0.1[ohm]
umec A A 2.55 [MVA]
B B #2 #1 A V 0.1[ohm] Ek R=0 C 33 [kV] C V f 0.69 [kV] 26.94 50.0
U [kV] 0.5 0.5 [ohm]
Figure C 1: Connexion of one turbine to test it according the IEC standard
C1 - Comparison of the reactive power flowing for different cases
The four following figures show the reactive power measured at the node where the sag occurs for the former model and the new model with different control mode active.
Main : Graphs Qa Main : Graphs 0.050 Qa 0.050 0.040 0.000 0.030 -0.050 0.020
y -0.100
0.010 y -0.150 0.000 -0.200 -0.010 -0.250 -0.020 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 ... -0.030 ... 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 ...... Figure C 3: New Model – No control active Figure C 2: Former model of the wind (no Id is injected) turbine – No control
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Main : Graphs Main : Graphs Qa Qa 0.200 0.20 0.150 0.00 0.100 -0.20 0.050 -0.40 -0.60
y 0.000 y -0.80 -0.050 -1.00 -0.100 -1.20 -0.150 -1.40 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 ...... 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 ...... Figure C 4: New model – Reactive Power Figure C 5: New Model – Voltage Control Control Mode active Mode active
The former turbine model is an ideal current source connected to the 0.69/33 kV transformer. The reactive power is not regulated and oscillates around its average value. The sag induces a small change in the reactive power flowing. This is due to the change in the rms voltage level at the output of the turbine and the impedances of the circuit. When there is no d-axis current injected, it means that the reactive power at the output of the converter is zero (equation (14)). It also means that the reactive power at the output of the transformer is not exactly zero (Figure C 3). During the sag, a small decrease of the reactive power is seen. The reactive power controller is quite efficient and regulates the reactive power to zero at the output of the turbine. When the voltage sag occurs, it takes 150 ms for the reactive power to be cancelled. The control is fast. The voltage control mode is also efficient since the voltage level at the output of the grid-side converter follows the desired voltage (defined in equation (18)). Figure C 6 shows it.
VSC_Controller : Graphs U_conv_module U_desired 1.00 0.90 0.80 0.70 0.60
0.50 y 0.40 0.30 0.20 0.10 0.00 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 ...... Figure C 6: Output Voltage at the output of the converter and desired voltage
The injection of d-axis current at the output of the grid-side converter is the mean for both reactive power and voltage control. The dq-axis currents are analysed for each mode in the following section.
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Kungliga Tekniska Högskolan
C2- Comparison of the dq-axis current for each control mode
The three following figures illustrate the dq-axis current of the grid-side converter output before, during and after the voltage sag.
VSC_Controller : Graphs Iq_net Iq_ref Id_net Id_ref 4.00
3.50
3.00
2.50
2.00
1.50 y
1.00
0.50
0.00
-0.50
-1.00
0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ......
Figure C 7: New Model – No control active (no Id is injected)
VSC_Controller : Graphs VSC_Controller : Graphs Iq_net Iq_ref Id_net Id_ref Iq_net Iq_ref Id_net Id_ref 3.50 4.0
3.00 3.0
2.50
2.0 2.00
1.50 1.0 y
1.00 y 0.0 0.50 -1.0 0.00
-0.50 -2.0
-1.00 -3.0 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 ...... 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 ...... Figure C 8: New model – Reactive Power Figure C 9: New Model – Voltage Control Control Mode active Mode active
q-axis current analysis
In the case observed on Figure C 7, the reference of the d-axis current is zero, no control is active (Id = 0 constitute the default mode). During the voltage sag, the q-axis current is increased. Indeed, the control has been designed to control the power balance between the DC- and AC- side of the controller. During the voltage sag, the voltage decreases by 25 % in this case. Thus, the DC-link voltage controller output a q-axis reference current higher in order to maintain the relation defined by equation (9). For any control mode, the q-axis current has the same shape during the sag (see also Figure C 9 and Figure C 9).
d-axis current analysis When the reactive power mode is active, some d-axis current is injected as well to regulate the quantity of reactive power. During the voltage sag, the reactive power change since the voltage amplitude changes. Thus some d-axis current is injected to cancel this reactive power (see Figure C 9). When the voltage control mode is active, some d-axis current is injected in order to regulate the amplitude of the converter output voltage. This is especially obvious during the sag (see Figure C 9) since the converter voltage amplitude must decrease by 25 %.
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