Countries all around the world are setting new targets, on renewable energy, to be achieved in the coming years. Europe is proceeding in line with its 2020 targets, and current discussion within EU indicate that the overall renewable targets could be raised to 35% by 2030. Due to this there is still a great need around the world for new power generation, which is clean, affordable, reliable and quick to install. Wind power is leading the transition away from fossil fuels and continues to blow away the competition on price, performance and reliability. The industry is maturing really fast, especially the offshore sector. Offshore prices for projects to be completed in the next five years or so are half of what they were for the last five years, installations in 2017 almost doubled the one in 2016 marking a record year for the offshore wind industry.
This thesis, developed in collaboration with the ABB Corporate Research Center in Ladenburg (Germany), deals with the analysis of an innovative offshore wind farm configuration based on a DC grid. First the state of art and the different offshore wind farm topologies were introduced, then the system analysed in the thesis was presented and discussed in details through software modelling and simulations.
Chapter 2 shows how the main components of the system were modelled using the PLECS software. A detailed description of all components was provided, with equations and models.
The control system was designed and modelled using the reference feedforward technique because it has several advantages compare to the classical feedback configuration. It was implemented in Matlab/Simulink how shown in Chapter 3. The cable length was designed to avoid resonances in the interconnection cable between the wind turbine and the offshore substation. Investigating the influence of the control parameters a new way to avoid resonances was found, which is changing the gains of the PI controller.
In the end, simulations results are shown and discussed in details to demon-strate the effectiveness of the analysed system and of the adopted designing method.
Acronyms iv
List of Figures vi
List of Tables viii
1 Introduction 1
1.1 Wind Energy Trend Development . . . 1
1.2 Offshore Wind Farm Configurations . . . 5
1.2.1 Doubly Fed Induction Generator System with AC Grid . . 6
1.2.2 Full-Scale Converter System with AC Grid . . . 6
1.2.3 Full-Scale Converter System with DC Grid . . . 7
1.2.4 Full-Scale Converter System with DC Distribution and DC Transmission Grid . . . 8
1.3 DC Wind Turbines . . . 11
1.4 Wind Turbines Connection . . . 11
1.5 The Thesis . . . 12
2 Modelling of the Main Components of the System 14 2.1 Wind Turbine . . . 14 2.2 Generator . . . 16 2.3 Converter . . . 19 2.4 Cable . . . 24 2.5 Offshore Substation . . . 24 2.6 Conclusions . . . 24 3 Control System 25 3.1 Reference Feedforward Control Strategy . . . 26
3.2 Current Control . . . 28
3.3 Generator Operational Region . . . 31
3.4 Speed Control . . . 34
4.2 Simulation Results . . . 42 4.3 Influence of Control Parameters . . . 45 4.4 Conclusions . . . 46
5 Conclusions 54
Bibliography 56
A Coordinate Transformations 57
B Control Strategies Comparison 60
C Simulink and PLECS Models 65
C.1 Transfer Functions Calculation . . . 65 C.2 Simulation Model . . . 65
D Matlab Scripts 71
D.1 Space Vector Modulation . . . 71 D.2 Generator Operational Region . . . 74
AC Alternating Current
DC Direct Current
HVAC High Voltage Alternating Current MVAC Medium Voltage Alternating Current HVDC High Voltage Direct Current
MVDC Medium Voltage Direct Current DFIG Doubly Fed Induction Generator
PMSG Permanent Magnet Synchronous Generator m.m.f. magneto motive force
SVM Space Vector Modulator PWM Pulse Width Modulation THD Total Harmonic Distortion PI Proportional Integral
1.1 Global cumulative installed wind capacity 2010-2017 . . . 2
1.2 Cumulative offshore wind capacity 2011-2017 . . . 4
1.3 Global cumulative offshore wind capacity in 2017 . . . 5
1.4 Doubly fed induction generator system with AC grid . . . 6
1.5 Full-scale converter system with AC grid . . . 7
1.6 Full-scale converter system with DC grid . . . 8
1.7 Full-scale converter system with DC distribution and transmission grid . . . 8
1.8 DC wind farm configurations with multiple conversion stages . . . 10
1.9 DC wind turbine configurations . . . 11
1.10 Wind turbines connection . . . 12
1.11 Block diagram of the system . . . 13
2.1 System configuration . . . 15
2.2 Wind turbine PLECS model . . . 16
2.3 PMSG PLECS model . . . 18
2.4 PMSG electric model . . . 19
2.5 PMSG mechanical model . . . 19
2.6 PLECS model of the converter block . . . 20
2.7 Simplified converter scheme for the space vector modulation . . . 21
2.8 Available switching vectors and sectors definition . . . 22
2.9 Reference vector and converter vectors that delimit the sector ”i” 22 2.10 Reference vector and converter vectors that delimit the sector ”i” in αβ reference frame . . . 23
2.11 Symmetrical commutation sequence pattern for the first sector . . 24
3.1 Block diagram of the control system . . . 25
3.2 Control scheme . . . 26
3.3 Control system configuration to tune the PI controller . . . 27
3.4 Tuning of PI controller with root locus technique . . . 27
3.5 Current control system . . . 29
3.6 Root locus of Id/Iref,d . . . 30
3.7 Root locus of Iq/Iref,q . . . 31
3.8 Example of PMSG operational region . . . 33
3.9 Comparison between control system with and without anti-windup 35 3.10 Speed control system . . . 35
4.1 Idc current of the converter . . . 38
4.2 Bode plot of the Idc for all the generator operational regions . . . 39
4.3 Pole-Zero plot of the Idc for all the generator operational regions . 40 4.4 Model used to calculate the cable transfer function . . . 40
4.5 Simplified model used to calculate the cable transfer function . . . 41
4.6 Bode plot of the cable transfer function . . . 42
4.7 Pole-Zero plot of the cable transfer function . . . 43
4.8 Bode plot comparison between Idc and cable . . . 44
4.9 Pole-Zero plot comparison between Idcand cable for different cable length . . . 45
4.10 Generator speed . . . 46
4.11 Generator speed oscillation due to the square wave disturbances, first in the speed and then in the torque . . . 47
4.12 Generator torque . . . 48
4.13 Generator current in the dq frame . . . 48
4.14 Generator current in the abc frame . . . 49
4.15 Generator current in the abc frame at steady state . . . 49
4.16 Idc current . . . 50
4.17 Idc current at steady state . . . 50
4.18 DC link voltage . . . 51
4.19 Cable current . . . 51
4.20 Electrical power produced by the generator . . . 52
4.21 Pole-Zero plot comparison of Idc transfer function for different val-ues of the gains of the speed PI controller . . . 52
4.22 Pole-Zero plot comparison of Idc transfer function for different val-ues of the gains of the current PI controller . . . 53
A.1 Spatial vector in αβ frame . . . 58
A.2 Spatial vector in rotating dq frame . . . 58
B.1 Reference feedforward control scheme . . . 60
B.2 Feedback control scheme . . . 60
B.3 Output signal trend for both control strategy . . . 61
B.4 Output signal trend, of feedback control strategy, for different val-ues of the PI controller parameters . . . 61
B.5 Output signal trend, of reference feedforward control strategy, for different values of the PI controller parameters . . . 62
B.6 Input signal trend, of feedback control strategy, for different values of the PI controller parameters . . . 62
B.7 Input signal trend, of reference feedforward control strategy, for different values of the PI controller parameters . . . 63
B.8 Output signal trend, of reference feedforward control strategy, for different values of the prefilter time constant . . . 64
C.1 Model used to calculate the Idc transfer function . . . 65
C.2 Model of the complete system . . . 66
C.3 Control system . . . 67
C.4 Speed control system . . . 67
C.5 Generator operational region . . . 67
C.6 Current control system . . . 68
C.7 PLECS model of the power system . . . 68
C.8 PMSG PLECS model . . . 69
C.9 PMSG electric model . . . 69
C.10 PMSG mechanical model . . . 70
C.11 PLECS model of the converter block . . . 70
C.12 PLECS model of the cable . . . 70
E.1 Generator speed (region AB) . . . 78
E.2 Generator torque (region AB) . . . 79
E.3 Generator current in the dq frame (region AB) . . . 79
E.4 Generator current in the abc frame (region AB) . . . 81
E.5 Idc current (region AB) . . . 81
E.6 DC link voltage (region AB) . . . 82
E.7 Cable current (region AB) . . . 82
E.8 Electrical power produced by the generator (region AB) . . . 83
E.9 Generator speed (region CD) . . . 83
E.10 Generator torque (region CD) . . . 84
E.11 Generator current in the dq frame (region CD) . . . 84
E.12 Generator current in the abc frame (region CD) . . . 85
E.13 Idc current (region CD) . . . 85
E.14 DC link voltage (region CD) . . . 86
E.15 Cable current (region CD) . . . 86
E.16 Electrical power produced by the generator (region CD) . . . 87
E.17 Generator speed (region DE) . . . 87
E.18 Generator torque (region DE) . . . 88
E.19 Generator current in the dq frame (region DE) . . . 88
E.20 Generator current in the abc frame (region DE) . . . 89
E.21 Idc current (region DE) . . . 89
E.22 DC link voltage (region DE) . . . 90
E.23 Cable current (region DE) . . . 90
1.1 Top ten cumulative installed wind capacity at the end of December
2017 . . . 3
1.2 HVDC systems in Germany . . . 9
2.1 Wind turbine parameters . . . 15
2.2 PMSG parameters . . . 17
2.3 Output voltage vectors of a two-level converter . . . 21
Introduction
In this chapter, the trend development of wind energy, its state of art in 2017 and the future trends, are introduced. Different offshore wind farm configurations are presented. Existing and new topologies, with AC and DC distribution/transmis-sion, are described and compared together with new wind turbine layouts. Fur-thermore, the possible wind turbine connections, series and parallel, are shown. Then the thesis, with its purpose and contents, are introduced.
1.1
Wind Energy Trend Development
In 2017, the global wind industry continued with installations above 50 GW. After five years of essentially flat markets from 2009-2013 due to the global financial crisis, installations crossed the 50 GW mark in 2014, and have stayed over 50 GW for the last four years, with the anomalous Chinese market in 2015 pushing the total over 60 GW. Globally, cumulative installations passed 500 GW in 2017, Figure 1.1, with Europe, India and the offshore sector having a record year. Chinese installations were down but the rest of the world made up for most of that. Total installations in 2017 were 52.492 MW, bringing the global total to 539.123 MW, an increasing of 11% over 2016’s year-end total of 487.279 MW [1]. Cratering prices for both onshore and offshore wind continue to surprise. Overall, offshore prices for projects to be completed in the next five years or so are half of what they were for the last five years; and this trend is likely to continue. The reasons for this are many: the maturing of the industry, the im-provement and maturation of the technology and management that cause growing investor confidence and the introduction and deployment of a new generation of turbines, with enormous swept area and output power.
The technology continues to improve, opening up many areas for onshore wind development which were previously not commercial. More sophisticated power electronics, better planning and overall management have contributed to increased reliability as well as price reductions. About offshore, the size of the machines continues to grow. On 1 March GE announced its long-awaited next-gen design, the 12 MW Haliade-X, with a rotor diameter of 220 m, which could
Figure 1.1: Global cumulative installed wind capacity 2010-2017
come into commercial operation as early as 2021.
China, the largest overall market for wind power since 2009, retained the top spot in 2017, Table 1.1. Installations in Asia once again lead the global markets, with Europe in the second spot, and North America after them. By the end of 2017 there were 30 countries with more than 1.000 MW installed: 18 in Europe, 5 in Asia-Pacific, 3 in North America, 3 in Latin America and 1 in Africa. Nine countries have more than 10.000 MW of installed capacity, including China, the US, Germany, India, Spain, the UK, France, Brazil and Canada.
In terms of annual installations China maintained its leadership position, al-though the annual market dropped about 16% compared to last year, adding 19,7 GW of new capacity. In 2017, wind power generation reached 305,7 TWh, an increase of more than 26% compared with 2016, and accounts for about 4,75% of total Chinese power generation. In Asia, India had a record year in 2017, with 4.148 MW being added to the grid, the first time the country has broken 4 GW in a single year.
Also Europe set new records in 2017, with new record high installations for the offshore sector. 16,8 GW of new wind power capacity was installed in the Europe during 2017, 3.148 MW of that was offshore. Annual onshore installations increased by 14%, while offshore installations doubled. Germany lead all markets with 6.581 MW (a 15% increase on 2016); 19% (1.247 MW) of Germany’s installed capacity was offshore. The UK was second with 4.270 MW, five times more than installations in 2016, with more than a third (1.680 MW) offshore. France came third with 1.694 MW (9% growth on the previous year). The new cumulative total at the end of 2017 in Europe is 177,5 GW of wind power capacity, 153 GW onshore and 15,8 GW offshore, making wind energy second only to gas in the European market. Germany retains the number one spot with a cumulative total of 56,1 GW, followed by Spain (23,2 GW), the UK (18,9 GW), France (13,8 GW) and Italy (9,5 GW), Figure 1.1. In total, wind energy generated about 336 TWh
Table 1.1: Top ten cumulative installed wind capacity at the end of December 2017
Country Power (MW) % Share
PR China 188.392 35 USA 89.077 17 Germany 56.132 10 India 32.848 6 Spain 23.170 4 United Kingdom 18.872 4 France 13.759 3 Brazil 12.763 2 Canada 12.239 2 Italy 9.479 2
Rest of the world 82.391 85
Total top 10 456.732 85
World Total 539.123 100
in 2017, representing about 11,6% of the Europe electricity demand.
2017 was also a great year for the offshore wind sector: the cratering prices with first zero bids for offshore in Germany, a full ‘zero subsidy’ tender in the Netherlands, larger and larger turbines, Europe’s first floating offshore wind farm came online, a plan for building an offshore wind island with more than twice today’s total installed offshore wind power in Europe and the number of markets expanding rapidly, including newcomers India, Australia, Brazil and Turkey. The rapid maturing of the technology has meant that offshore wind is taking shape as a mainstream energy source. A historical record of 4.334 MW of new offshore wind power was installed in 2017. This represents a 95% increase on the 2016 market. Overall, there are now 18.814 MW of installed offshore wind capacity around the world, Figure 1.2. The 84% of the offshore installations are in Europe, the remaining 16% is located largely in China, followed by Vietnam, Japan, South Korea, the United States and Taiwan.
The UK is the world’s largest offshore wind market and accounts for just over 36% of installed capacity, including the commissioning of the first floating offshore wind farm in Scotland, followed by Germany in the second spot with 28,5%. China comes third in the global offshore rankings with just under 15%, Figure 1.3. The average installed offshore wind turbine grid-connected in 2017 was 5,9 MW, a 23% increase over 2016. The average size of a grid-connected offshore wind farm in 2017 was 493 MW, 34% larger than the previous year.
Figure 1.2: Cumulative offshore wind capacity 2011-2017
targets, and current discussions within the EU indicate that the overall renew-able targets could be raised to 35% by 2030, which would put the industry in a much stronger position for the post-2020 market. Overall, the expectation is that Europe will install about 76 GW of new wind power by the end of 2022, reaching a cumulative total of 254 GW. Compare to the last year the growth will be not so fast but will be balanced by increases in North America, Middle East, Africa and Latin America. The annual market will return to growth in 2019 and 2020, breaching the 60 GW barrier. The expectation is to reach a cumulative installations of 840 GW by the end of 2022.
Even if the offshore is only 3,5% of global installed capacity, those numbers will increase substantially in the coming five years. In 2019 Europe expects to see another record year for offshore wind power. This is mainly due to the delay of some projects in the UK in 2016, then remain stable for the rest of the period and approximately doubling existing offshore installations by the end of 2022. Countries like China and Japan, set target of 5 GW by 2020 while Taiwan set the target of 5,5 GW by 2025. Then other countries, South Korea and US, are ready for the wind expansion. The offshore will have a great growth in the next years, it should also be noted that those offshore MW will generate significantly more electricity than their onshore counterparts.
There is still a great need around the world for new power generation, which is clean, affordable, reliable and quick to install. Wind power is leading the transition away from fossil fuels and continues to blow away the competition on price, performance and reliability.
Figure 1.3: Global cumulative offshore wind capacity in 2017
1.2
Offshore Wind Farm Configurations
The main offshore wind farm configurations can be classified in three groups: Medium voltage alternating current (MVAC) grid within the park and
transmission to the shore via high voltage alternating current (HVAC). Medium voltage alternating current (MVAC) grid within the park and
transmission to the shore via high voltage direct current (HVDC).
Medium voltage direct current (MVDC) grid within the park and transmis-sion to the shore via high voltage direct current (HVDC).
1.2.1
Doubly Fed Induction Generator System with AC
Grid
The induction generator is connected via transformer to a MVAC grid, then via another transformer the voltage is stepped up to HVAC transmission level to deliver the power to the shore. The stator of the induction generator is directly connected to the grid while the rotor is connected via converter. Thanks to this the converter rating is around 25% of the total system power, so the converter cost and losses are reduced. But the range speed is limited to ±33% of the synchronous speed. Because of the limitation of reactive power capability, a reactive power compensator such as a static synchronous compensator (STATCOM) may be needed in this configuration to fully satisfy some emerging grid requirements.
A typical wind farm equipped with a doubly fed induction generator (DFIG) is shown in Figure 1.4. This configuration is in operations in Horns Rev offshore wind farm in Denmark with a capacity of 160 MW, which is composed of 80 wind turbines rated at 2 MW [2].
Figure 1.4: Doubly fed induction generator system with AC grid
1.2.2
Full-Scale Converter System with AC Grid
It is similar to the previous configuration, with MVAC grid within the park and HVAC transmission to the shore, but the induction generator is replaced by a permanent magnet synchronous generator (PMSG) with a full-scale converter [2]. This configuration has become the dominant choice in the established offshore wind farms since 2010. This because the PMSG has several advantages compare to DFIG: higher efficiency and reliability, it allows to decouple the generator from the grid, the reactive power capability is significantly extended, full speed range, possibility to avoid the gearbox (or to use low ratio gearbox), lower maintenance and construction simplicity. The main drawbacks are: cost, large size and the converter has to be rated for the full system power.
The voltage level for the MVAC grid is between 33÷66 kV, the most used levels are 33 and 34 kV, 66 kV is the new standard because there are transformers able to reach this level and meet the wind farms requirements but there are no practical realization yet. For the HVAC the voltage level is between 120÷220 kV. A typical wind farm equipped with a full-scale converter system and AC grid is shown in Figure 1.5. An example is the London Array in United Kingdom, which is the biggest offshore wind farm with 175 wind turbines of 3,6 MW each, for a nominal capacity of 630 MW. The power is collected at 33 kV and then transmitted to the onshore substation via HVAC at 150 kV.
Figure 1.5: Full-scale converter system with AC grid
1.2.3
Full-Scale Converter System with DC Grid
The generator is a PMSG with full-scale converter and is connected to the MVAC grid by a transformer. Then there is another step up transformer before the HVDC offshore substation that convert the AC in DC for the transmission to the shore [2]. This configuration, Figure 1.6, particularly fitted in the wind parks where the distance from the shore is very big, above 80 km, because for these distances the transmission via HVDC is in general more economic than the HVAC transmission. Even if the cost for the DC terminals is higher than the one for the AC terminals, with DC there are no need for reactive power compensator which is a great advantage because the transmission is made via submarine cables.
In Germany there are several wind farms located more than 80 km from the coast. Thanks to the last developments in HVDC technologies, HVDC offshore converter substations have been installed to connect one or more wind farms to the shore, as shown in Table 1.2 .
Figure 1.6: Full-scale converter system with DC grid
1.2.4
Full-Scale Converter System with DC Distribution
and DC Transmission Grid
This is the most recent configuration, there is no wind farm based on this topology. The wind turbines are connected to a MVDC grid, via converter, then a DC/DC transformer step up the voltage to the HVDC transmission level as shown in Figure 1.7 [2].
Figure 1.7: Full-scale converter system with DC distribution and transmission grid
The benefits of a DC distribution systems compare to one in AC are: 2 terminals instead of 3.
No skin and proximity effects in the cables (only resistive losses).
No reactive power compensator are needed (great advantage because the transmission is via submarine cables).
Table 1.2: HVDC systems in Germany
HVDC System Wind Farm Capacity (MW) Voltage Levels
BorWin1 BARD Offshore 1 400 155 kV AC offshore
± 150 kV DC
BorWin2 Veja Mate 800 155 kV AC offshore
Global Tech 1 ± 300 kV DC DolWin1 Borkum West II 800 155 kV AC offshore Borkum Riffgrund ± 320 kV DC MEG Offshore 1
HelWin1 Nordsee Ost 557 155 kV AC offshore
Meerwind ± 250 kV DC
HelWin2 Amrumbank and 670 155 kV AC offshore
future wind farms ± 320 kV DC
SylWin1 Dan Tysk 833 155 kV AC offshore Butendiek ± 320 kV DC Sandbank
Medium frequency transformers used in the isolated DC/DC converters can reduce size, space and weight of the converters (they can be placed inside the nacelle).
The modular design of the DC/DC converters increase the reliability and flexibility of the system.
The weight and size of DC collection cable are smaller than those of AC cables for the same rating.
The main drawbacks of a MVDC grid are:
Technology is untested on large scale MW applications. Challenges arise with medium frequency transformers. Fast DC breakers to limit short-circuit current are essential.
Reduced power conversion stages is possible only with generators of high ratings and high output voltage.
There are no standard DC voltage levels yet.
A MVDC grid can be economically feasible for large wind farms with high rating generators, in this way the power conversion stages can be reduced and
the overall efficiency of the system increase. Otherwise more DC/DC converters are needed [3]. The new conversion stages can be placed in different positions within the system as shown in Figure 1.8.
Figure 1.8: DC wind farm configurations with multiple conversion stages If the DC/DC converter is placed inside the nacelle after the wind turbine rectifier each wind turbine can works independently at different speed (voltage). Whatever is the output voltage of the rectifier (depending on wind speed) the DC/DC converter will keep the voltage of each wind turbine in the string constant. The DC/DC converter can also be placed at the end of the wind turbine string, usually a string is composed by 3÷5 wind turbines. In this case less converters are needed (one for each string instead of one for each wind turbine) so the losses in power electronics are reduced, but the transmission between the wind turbines is at lower voltage compare to the previous solution and the converters need to be located on their own platform. All wind turbines are connected to the same DC/DC converter, so they will all work at the same operational speed. This operational speed can vary over time. Large offshore wind farms, however, will cover such large area that only a few turbines will be exposed to the same wind speed at any given time. If the rectifier is a diode-bridge the operational speed of most wind turbines will not lead to optimal aerodynamic efficiency. The wind turbines of a string will operate at the same speed, which can vary over time. As the wind speed can also vary between those wind turbines, the overall aerodynamic efficiency of this solution will still be lower than in the case of individual variable speeds at each turbine. The idea, however, is that the cost benefits of using strings are larger than the drawbacks of the lower aerodynamic efficiency.
The generators used in the wind turbines have a rated voltage between 690÷3300 V. High speed generators have high voltage but they require more complex gear box, which implies more cost and maintenance.
1.3
DC Wind Turbines
The name DC wind turbine refers to a wind turbine with a classical AC generator (PMSG) and a conversion stage from AC to DC. Figure 1.9 shows three wind turbine configurations with DC output.
(a) Low frequency transformer configura-tion
(b) Transformerless configuration
(c) 2 stage converter configuration Figure 1.9: DC wind turbine configurations
The first solution, Figure 1.9a, has a low frequency transformer (big size and weight) and an AC/DC converter. The transformerless configuration, Figure 1.9b, has just one conversion stage and it is characterized by simple structure (no transformer, small size and light weight) and low losses, but if the output generator voltage is not high enough another conversion stage is needed as shown in Figure 1.9c. The DC/DC converter can be a double active bridge (DAB) with a medium frequency transformer to reduce size and weight. The second conversion stage introduces more losses but it is necessary to have a voltage high enough to reduce the losses during the distribution. The best solution is the second one, with just one conversion stage, low losses, simple structure and small size. This configuration can be feasible only with high rating wind turbine components (generator, converter).
1.4
Wind Turbines Connection
Nowadays wind turbines are usually connected in parallel to each other, but in the past years a lot of studies have been done on wind turbines series connection. Series connection can bring some advantages compare to the parallel connection but it still has several important challenges. The term series connection, for large wind farms, refers to a parallel of several wind turbines connected in series as shown in Figure 1.10b.
(a) Parallel connection (b) Series connection Figure 1.10: Wind turbines connection
In the parallel connection, Figure 1.10a, voltage control is needed because each wind turbine needs to have the same output voltage. This configuration has a high reliability because in case of failure or maintenance, one or more wind turbine can be isolated from the system.
The great advantage of the series connection is that the voltage can be increase by connecting several wind turbines in series. Is possible to avoid the use of step up converters and also the HVDC converter, which means less foundations and platform costs. Also the length and size of the cables can be reduced. Compare to the parallel connection, cable losses are lower but the power losses in the converters are higher. Since the wind turbines are connected in series, they will be crossed by the same current, so a current control, which is more difficult than a voltage control, is needed. Then the sum of the output wind turbines voltage connected in series needs to stay constant and equal to the sum of the others wind turbines output voltage connected in parallel, which is the transmission voltage in the example of Figure 1.10b. In case of failure or maintenance of one or more wind turbines, the rest of the series wind turbines need to keep the voltage constant, so some wind turbine and electrical components need to be overrated to handle the overvoltage due to this condition. Also a bypass link is needed to isolate the faulty turbine. If a lot of wind turbines are connected in series there are insulation issues because the wind turbines far away from the electrical ground need to handle a really high voltage (total series voltage).
The series connection presents less cable losses and requires less conversion stages and investment cost. But control, overvoltage and insulation are still great challenges.
1.5
The Thesis
The thesis was developed in collaboration with the ABB Corporate Research Center in Ladenburg, Germany. The purpose is to model and analyse an offshore
wind farm with DC distribution grid. The system taken into account is shown in Figure 1.11. Only the distribution part of a wind farm is considered.
Figure 1.11: Block diagram of the system The system is composed by:
Wind turbine Generator
AC/DC converter Submarine cable Offshore substation
From the mathematical equations each component was modelled in PLECS. The control system of the generator was designed using Matlab and implemented in Simulink, the reference feedforward technique was adopted because it has sev-eral advantages compare to the classical feedback control technique. By transfer functions comparison the cable length of the submarine cable was design to avoid resonances and then, for the same purpose, other solutions were investigated act-ing on the controller parameters. Trough simulations the stability and robustness of the system were analysed together with the behaviour of each element of the wind farm. For the analysis, a step signal with a square wave disturbance was introduced as input to highlight the behaviour in the worst case scenario from the control point of view.
Modelling of the Main
Components of the System
This chapter describes how the main components of the system were modelled in PLECS. The models and equations used to build them are presented. Figure 2.1 shows the system configuration and its components:
Wind turbine Generator
AC/DC converter Submarine cable Offshore substation
In this analysis only the distribution part of a wind farm was considered, from the wind turbine to the offshore substation.
2.1
Wind Turbine
The wind turbine has a rated power of 5 MW and a diameter of 126 m for a swept area of 12.467 m2. The other wind turbine parameters are listed in Table 2.1.
The inertia was calculated according to [4], Jwt = 14.500 9 P 1,2 ratedR 2 (2.1)
Where Prated is the rated power of the wind turbine (M W ) and R is the wind
turbine radius (m).
The PLECS model of the wind turbine, represented in Figure 2.2, is based on the steady state power characteristics of the turbine. The output power is given by,
Pwt =
1
2ρ Cp(λ, β) π R
Figure 2.1: System configuration Table 2.1: Wind turbine parameters
Rated power 5 MW
Diameter 126 m
Swept area 12.467 m2
Cut-in wind speed 3 m/s
Rated wind speed 11,4 m/s
Cut-out wind speed 25 m/s
Rated rotor speed 12 rpm
Inertia 4,4 × 107kg m2
where ρ is the air density (kg/m3), R is the radius of the wind turbine (m), v
is the wind speed (m/s) and Cp(λ, β) is the power coefficient and is a measure of
the efficiency at which the wind turbine converts the wind power into mechanical power. Cp is a function of the pitch angle of rotor blades β (degree) and the
tip-speed ratio λ that is given by,
λ = ΩwtR
v (2.3)
where Ωwt is the rotor mechanical speed of the wind turbine (rad/s).
The turbine power conversion coefficient is defined by the following equations [5], Cp(λ, β) = 0, 73 151 λi − 0, 58β − 0, 002β−2,14− 13, 2 exp −18, 4 λi (2.4)
Figure 2.2: Wind turbine PLECS model 1 λi = 1 λi− 0, 02β + 0, 003 β3+ 1 (2.5)
The torque produced by the wind turbine can be expressed by, Twt=
Pwt
Ωwt
(2.6) Since the rated rotor speed of the wind turbine is different from the rated electric generator speed, a gearbox is needed. The gearbox ratio is,
N = Ωwt
Ωgenerator
(2.7) So the wind turbine rotor speed can be calculated from the electric generator speed as,
Ωwt = N Ωgenerator (2.8)
2.2
Generator
The electric machine is a Permanent Magnet Synchronous Generator (PMSG). The machine is anisotropic composed of a three-phase wound stator Y-connected and a permanent magnet rotor. The machine parameters are listed in Table 2.2. To implement the PMSG model the following simplified hypotheses are intro-duced:
the machine magnetic circuit does not work in saturation conditions, hys-teresis and eddy currents are neglected (linear behaviour of the machine); permeability of permanent magnets is equal to air;
Table 2.2: PMSG parameters
Active power 5.500 kW
Apparent power 5.900 kVA
Frequency at nominal speed 27 Hz Operational speed range 50÷160 rpm
Voltage 3.300 V
Current 1.000 A
Torque 400 kN m
Inertia 6.000 kg m2
iron permeability is much higher than air, permitting to neglect magneto motive force (m.m.f.) drops inside it;
the extremity effects are neglected, in this way it can be considered that the trend of the various quantities repeats itself identically in all the planes orthogonal to the machine axis;
the structure of windings is symmetrical;
the stator surface facing the air gap is considered to be perfectly smooth and free of slot openings and the conductors constituting each winding side are concentrated on the inner surface of the stator in correspondence of the centre slot opening;
the trend of the magnetic field is considered radial inside the air gap and the magnets;
the fundamental component of the m.m.f. and the air gap flux is dominant. Figure 2.3 shows the PLECS model inside the PMSG block. The generator model is composed of the electric and mechanical block, that represent the electric and mechanical behaviour of the machine, respectively, and the transformation blocks between the different reference frames. The electric model of the machine is implemented in the dq frame (see Apppendix A), the Park transformation parameter is chosen as usual to be proportional to the angle between the magnetic axes of the rotor and of stator phase A.
The electric model of the machine in Figure 2.4 is based on the following equations. Vd= RId+ Ld dId dt − ωeΨq (2.9) Vq = RIq+ Lq dIq dt + ωeΨd (2.10)
Figure 2.3: PMSG PLECS model ωe= p Ωm= p dθ dt (2.11) Ψd= LdId+ Ψpm (2.12) Ψq = LqIq (2.13) Tem = 3 2p [ΨpmIq+ (Ld− Lq)IdIq] (2.14) Where Vdand Vq are the d and q components of the stator voltage vector (V ),
Id and Iq are the dq components of the stator current vector (A), R is the stator
windings resistance (Ω), Ld and Lq are the stator windings inductance (H) on d
and q axis, Ψd, Ψq and Ψpm are the dq flux linkages and the permanent magnet
flux linkage respectively (W b), Tem is the electromagnetic torque produced by the
machine (kN m), ωe is the synchronous speed that is the rotating speed of the dq
reference frame (rad/s).
The mechanical behaviour is described by a one-mass model with damping coefficient through the following equation and the relative model in Figure 2.5.
Tem− Twt = Jeq
dΩm
Figure 2.4: PMSG electric model
Where Ωm is the rotational mechanical speed of the generator (rad/s), Deq is
the damping coefficient (kg m2/s) and J
eq is the equivalent inertia of the system
(kg m2) that takes into account the inertia of wind turbine Jwt and generator Jg.
Jeq= JwtN2 + Jg (2.16)
Figure 2.5: PMSG mechanical model
2.3
Converter
The converter is a two-level converter with IGBT (Insulated Gate Bipolar Tran-sistor) and anti-parallel diode. The PLECS model of the converter block is shown
in Figure 2.6. The gate signal is produced by a space vector modulator (SVM) with symmetric commutation sequence and the switching frequency is 1.200 Hz. The switching frequency is related to the control frequency. As lower as better for the losses, but worse for the dynamic. Due to the high power of the system the switching frequency can not be too high. Then in big motor applications the dynamic is anyway limited by the dynamics of the motor. Even with fast control/switching the reaction of the machine would not change much.
Figure 2.6: PLECS model of the converter block
A space vector modulation technique was chosen because it has several ad-vantages compare to the classical PWM (Pulse Width Modulation) technique: it directly uses the control variable given by the control system, better utilization of DC link, lower THD (Total Harmonic Distortion) and commutation losses, it is suitable for digital signal processing (DSP) implementation and optimization of switching patterns as well [6].
To implement the space vector technique is useful to represent the inverter as shown in the Figure 2.7, in which cell voltages are evaluated with respect to the negative pole of the DC bus (Point N).
The variables d1, d2, d3 can assume two different states, 1 or 0. When the
state is 1 the upper cell of the leg is active and the bottom one is off, while if the state is 0 the bottom cell of the leg is active and the upper one is off. The two-level converter can produce eight output voltage vectors, six non-zero vectors (U1− U6) with an amplitude of 23Vdc and two zero vectors (U0, U7), as shown in
Table 2.3. The non-zero vectors divide the space into six sectors, Figure 2.8. The reference voltage is produced by the current control system as a spatial vector in dq frame. It is converted into αβ coordinates and then it is produced by a proper combination of the eight converter vectors during the switching period
Figure 2.7: Simplified converter scheme for the space vector modulation Table 2.3: Output voltage vectors of a two-level converter
d1 d2 d3 |U| arg(U) vector
0 0 0 0 U0 1 0 0 23Vdc 0° U1 1 1 0 23Vdc 60° U2 0 1 0 23Vdc 120° U3 0 1 1 23Vdc 180° U4 0 0 1 23Vdc 240° U5 1 0 1 23Vdc 300° U6 1 1 1 0 U7 Tsw. Tsw = 1 fsw (2.17) Where fsw is the switching frequency.
The first step consists in detecting the sector on which the reference vector lies. The reference is produced by the application of the two nearest non-zero vectors, which delimit the sector, and one or both zero vectors. Each vector is applied for a certain time in order to have the average vector on the time Tsw
equal to the reference voltage vector.
If the reference voltage vector is ~U∗and it is in the sector ”i” the two non-zero vectors will be ~Ui and ~Ui+1 as in Figure 2.9 [7].
The vector ~U∗ is obtained by the average value, on the switching period Tsw,
of the following vector sequence: ~Ui applied for a time T1;
Figure 2.8: Available switching vectors and sectors definition
Figure 2.9: Reference vector and converter vectors that delimit the sector ”i” zero vector applied for a time T0 = Tsw− (T1+ T2).
In the αβ reference system, Figure 2.10, the relationship is as follow. Uα∗+ jUβ∗ = 1 T sw Z T1 0 (Uαi+ jUβi) dt + Z T1+T2 T1 Uα(i+1)+ jUβ(i+1) dt (2.18) Where the subscripts α and β indicate the components of the corresponding vector.
Breaking into the real and imaginary part, Uα∗ = 1 T sw h RT1 0 Uαidt + RT1+T2 T1 Uα(i+1)) dt i Uβ∗ = T sw1 hRT1 0 Uβidt + RT1+T2 T1 Uβ(i+1)) dt i (2.19)
Figure 2.10: Reference vector and converter vectors that delimit the sector ”i” in αβ reference frame UαiT1+ Uα(i+1)T2 = Uα∗Tsw UβiT1+ Uβ(i+1)T2 = Uβ∗Tsw (2.20)
Knowing the application time of the non-zero vectors T1 and T2 is possible to
calculate the application time of the zero vector T0.
The two most popular modulation strategy are: alternating zero vector strat-egy and symmetrical modulation stratstrat-egy. In the first one only one of the two available zero vectors is used during a switching sequence, this modulation strat-egy therefore minimizes the number of switch transitions that occur during a single switching period. In the second one both zero vectors are applied during a single switching sequence. In this case the symmetrical modulation strategy was implemented because even if it has a lower efficiency (higher number of commu-tations) the THD is lower than the alternating zero vector strategy.
In the symmetrical modulation strategy one zero vector is applied at the start and the end of the switching cycle and the other zero vector is applied during the middle of the switching cycle. The resultant switching sequence is symmetrical and comprises seven time slices, as shown in Figure 2.11 for the first sector.
The Simulink model and the Matlab script implemented are shown,respectively, in Appendix C and D.
Figure 2.11: Symmetrical commutation sequence pattern for the first sector
2.4
Cable
The submarine connection cable between the converter and the offshore substa-tion is a MVDC cable with copper conductor and XLPE (cross-linked polyethy-lene) insulation. It was implemented in the system as a π − model. In chapter 4 more details about design and cable parameters are given.
2.5
Offshore Substation
The offshore substation has been modelled assuming that several lines, so several wind turbines, are connected to the substation. In this case the capacitor bank of the substation is really big comparing to the DC capacitor of the wind turbine, so the offshore substation can be modelled as a constant voltage generator. Then this allows to decouple the behaviour of the different lines connected to the substation.
2.6
Conclusions
This chapter presented how the main components of the system were modelled using the PLECS software. A detailed description of all components was pro-vided, with equations and models, except for the cable. It was briefly introduced, further details about its design and parameters will be presented in chapter 4. The electrical and mechanical model of the generator were described with the hypothesis adopted to model them. The same was done for the converter, where also the space vector modulation technique used to control it was introduced.
Control System
This chapter describes how the control system was designed and implemented us-ing Matlab/Simulink. It was designed to not exceed the electrical and mechanical constraints of the generator at any time. The control system, shown in Figure 3.1, is composed by:
Space vector modulator Current controller
Generator operational region Speed controller
Figure 3.1: Block diagram of the control system
The space vector modulator was introduced in the previous chapter, in this chapter the current controller, generator operational region and speed controller will be introduced, but first the control strategy adopted is exposed.
3.1
Reference Feedforward Control Strategy
The control scheme used in the current and speed control is shown in Figure 3.2. The layout is characterized by the reference feedforward, a prefilter and a PI (Proportional Integral) controller.
Figure 3.2: Control scheme
The prefilter is the reference model that gives the desired response. For exam-ple, in a classical feedback control scheme, if the reference is a step the regulation action at the beginning will be high because the output will not change instantly, so the input might be over the limit set by the plant. In this case if the prefilter is a low pass filter the reference is more smooth, the regulation action is less and the input will be lower than the maximum input value of the plant.
Usually the feedforward block has the following transfer function, F eedf orward(s) = 1
P lant(s)∗ (3.1)
where P lant(s)∗ is the minimum-phase part of the plant transfer function. With this choice the reference tracking is perfect, but it has to be feasible.
The great advantage of this control configuration, compared to the classical feedback, is that the tuning for the reference tracking and the disturbance rejec-tion can be done independently. The reference tracking can be tune by adjusting the prefilter and feedforward parameters while the disturbance rejection can be achieved by tuning the PI controller. This means that if the PI controller param-eters change, only the disturbance rejection will vary while the reference tracking will remain the same. In the classical feedback control a change in the PI con-troller parameters affects both, disturbance rejection and reference tracking, so a good trade off is needed. A comparison between the two control strategy is presented in Appendix B.
The PI controller was tuned with the root locus technique. Since the PI controller affects only the disturbance rejection the control system can be rep-resented as in Figure 3.3. Considering a unitary integral gain of the controller (Ki) the system is equivalent to the one in Figure 3.4a. Opening the loop before
the integrator, Figure 3.4b, and performing the root locus we obtain the system in Figure 3.4c, which is equivalent to the initial control configuration in Figure 3.3. The tuning was done in Matlab. The rlocus command in Matlab shows the
Figure 3.3: Control system configuration to tune the PI controller
(a) Equivalent system with Ki = 1
(b) System with open loop
(c) Equivalent system with root locus
Figure 3.4: Tuning of PI controller with root locus technique
closed-loop poles trajectory as a function of the feedback gain K = Ki (assuming
negative feedback), as shown by the red part of Figure 3.4c. So for each value of the proportional gain (Kp) is possible to see how the poles of the system vary for
different values of Ki. The values of the controller parameters (Kp and Ki) are
chosen by assuming constraints such as overshoot and maximum pole frequency. After the tuning of the PI controller, the time constant of prefilter and feed-forward transfer function is chosen to not have the input beyond the limit value imposed by the plant for any reference value.
3.2
Current Control
The current control system has the dq components of the reference current, ing from the generator operational region, as input and as output the dq com-ponents of the reference voltage that after the transformation to αβ coordinates, become the reference voltage for the space vector modulator.
From equations (2.9) and (2.10) the dynamic of the dq components of the stator current can be evaluated.
RId+ Ld dId dt = Vd+ ωeΨq (3.2) RIq+ Lq dIq dt = Vq− ωeΨd (3.3)
Substituting equations (2.12) and (2.13) above, in laplace domain the Id and
Iq components are, Id= 1 R + sLd (Vd+ ωeLqIq) (3.4) Iq = 1 R + sLq (Vq− ωeLdId− ωeΨpm) (3.5)
The two dynamics are not independent. It is necessary to decouple the two equations to have an advanced control of the two components. To do that an external signal needs to be injected in both voltage components.
Vd∗ = Vd− ˆωeLˆqIˆq (3.6)
Vq∗ = Vq+ ˆωeLˆdIˆd+ ˆωeΨˆpm (3.7)
where the hat symbol means that those parameters are estimated, but in this case a perfect estimation is considered, so the symbol can be deleted. Replacing Vd,q in (3.4) and (3.5) with Vd,q∗ the following equations are obtained.
Id= 1 R + sLd Vd (3.8) Iq = 1 R + sLq Vq (3.9)
Now the dq components of the stator current are decoupled.
The current control has been done in the dq reference system adopting the control configuration explained previously, as shown in Figure 3.5. It is composed of one control system for each axis and the decoupling signals.
The PI controller was tuned using the root locus technique, as shown in section 3.1, with the following constraints:
Figure 3.5: Current control system overshoot ≤ 5%
ωmax =
2πfsw
k = 1.256, 6rad/s
where fsw = 1.200Hz is the switching frequency and k = 6 is a scale coefficient
used to not have a dynamic behaviour of the control system faster than the update speed of the SVM and to have a margin for the control.
In this case the plant block is represented by the electrical machine and since the cross coupling has been neglected,to tune the PI controllers, the plant transfer function on d and q axes are,
P lantd(s) = 1 R + sLd (3.10) P lantq(s) = 1 R + sLq (3.11) The root locus are shown in Figure 3.6 and 3.7 for d and q axes respectively. They are plotted for six different value of Kp from 10 to 15. Respecting the
constraints, the PI controllers parameters are: Kpd= 13
Kid= 11.200
Kpq = 14
Kiq = 12.100
Figure 3.6: Root locus of Id/Iref,d
As a prefilter a simple low-pass filter was chosen, the transfer function is the same on both axes. While for the feedforward the reverse of the plant transfer function was chosen (to have a perfect tracking), so they will be different for d and q axes. Since the the reverse plant transfer function is not feasible it was multiplied by the prefilter transfer transfer function to make it feasible.
P ref ilter(s) = 1 s τf i+ 1 (3.12) F eedf orwardd(s) = sLd+ R s τf i+ 1 (3.13) F eedf orwardq(s) = sLq+ R s τf i+ 1 (3.14) The parameter τf iwas chosen to not have a reference voltage for the generator
higher than its maximum phase rated value when the reference dq current is a step with an amplitude equal the maximum rated current of the generator. Assuming this constraint τf i = 0, 006 s.
Figure 3.7: Root locus of Iq/Iref,q
3.3
Generator Operational Region
Based on the reference torque and the generator speed, the block of the genera-tor operational region produces the reference dq current to respect the machine constraints and don’t go beyond its limits. The following constraints were con-sidered:
thermal constraint voltage constraint
demagnetization constraint
To identify the d and q component of the stator current the constraints have to be represented on the Id, Iq plane. Each constraint will be represent as a
region and the operational region will be the intersection of all of them, while the operating point will be a point (Id, Iq) within that region.
Thermal Constraint
The thermal limit identifies the set of working points for which the corresponding losses determine a regime temperature lower than the limit temperature allowed by the isolation class. The thermal limit is identified by the rated current of the generator (Irated). On Id, Iq plane the thermal constraint can be represent as,
~ I ≤ √ 2 Irated (3.15)
where ~I is the vector of the stator current. In terms of its components it can be written as, q I2 d + Iq2 ≤ √ 2 Irated (3.16)
that is a circle with the centre in the origin of the axes and a radius R = √
2 Irated.
Voltage Constraint
The voltage on the DC bus determines the maximum value Vmax of the stator
voltage vector ~V . ~ V ≤ Vmax (3.17)
Considering the space vector modulation the maximum voltage can be calcu-lated as [8],
Vmax =
Vdc
√
3η (3.18)
where η is a coefficient equal 0,9÷0,95 that is used to have a control margin, in this case η = 0, 9 was chosen. Substituting (2.9) and (2.10) in (3.17) and neglecting the resistive voltage drops, on Id, Iq plane the voltage constraint can
be represent as, L2d Id+ Ψpm Ld 2 + L2qIq2 ≤ Vmax ωe 2 (3.19) Id+ Ψpm Ld 2 Vmax ωe 2 1 L2 d + I 2 q Vmax ωe 2 1 L2 q ≤ 1 (3.20)
that is the equation of an ellipse with centre in −Ψpm Ld , 0 and semiaxes equal Vmax ωeLd and Vmax ωeLq
. From 3.20 is possible to see that greater the machine speed is, smaller the ellipse is.
Demagnetization Constraint
In order to protect the machine from the demagnetization of the permanent magnets, it is necessary to ensure that the direct axis component of the current Id
does not produce a magnetic flux that weakens the magnetic flux and therefore the magnetic field produced by the permanent magnets, above the value of permanent demagnetization. The flux on d axis is,
The demagnetization constraint can be represent as, Id≥ −k
Ψpm
Ld
(3.22) where k ∈ [0, 1] is a coefficient that takes into account the intrinsic charac-teristics of permanent magnets. When it is 1, the magnetic field produced by the permanent magnet is cancelled while when it is 0, the demagnetization is not allowed. In this case k = 0, 5 was chosen. On the Id, Iq plane the constraint is
represented by a line parallel to the Iq axis.
Figure 3.8 shows an example of the generator operational, where the voltage constraint is represented for the maximum speed, the torque curve is referred to the rated electromagnetic torque and for the demagnetization constraint the coefficient k was chosen to take into account all the possible operational regions of the generator.
Figure 3.8: Example of PMSG operational region There are four operational regions:
AB: in this region the losses due to joule effect are minimized
BC: in this region the operating point is on the constant torque curve CD: in this region the operating point is on the maximum current circle DE: in this region the operating point is on the demagnetization limit
At low speed the losses in the iron were not considered and only the losses in the copper were optimized (AB region) following the MTPA (Maximum Torque per Ampere) strategy, because at low speed losses are mainly due to losses in copper. The operating point will be, at any time, in one of these regions based on the reference torque and the measured speed.
The MTPA control strategy assures that for a required torque level the min-imum stator current magnitude is applied, because for a given torque there are multiple choices of the Id and Iq currents. By doing this the copper losses are
minimized, and the overall efficiency of the motor can be increased. The dq stator current can be expressed as,
Id= I cos(δ) (3.23)
Iq = I sin(δ) (3.24)
where I and δ are respectively, the amplitude and the phase of the stator current vector. Replacing (3.23) and (3.24) in (2.14) the torque equations is,
Tem =
3
2p [ΨpmI sin(δ) + (Ld− Lq)I
2cos(δ) sin(δ)] (3.25)
by calculating the maximum of the torque function, that is deriving it respect to the current phase,
∂Tem
∂δ =
3
2p [ΨpmI cos(δ) + (Ld− Lq)I
2(cos2(δ) − sin2(δ)] (3.26)
and imposing it equal to zero,
ΨpmI cos(δ) − (Lq− Ld)I2(cos2(δ) − sin2(δ) = 0 (3.27)
The (3.27) expresses the condition for which, whatever is the value I of the current, the maximum torque is obtained, ie the condition for which the torque per unit of current is maximized. Introducing now the (3.23) and (3.24) in (3.27), this condition can be rewritten in terms of the dq components of the current,
Id2− Ψpm Lq− Ld
Id− Iq2 = 0 (3.28)
the MTPA equation in the Id, Iq plane is a parabola with vertex in the origin and
it has as axis the Id axis. For a given torque the MTPA curve gives the minimum
stator current.
3.4
Speed Control
The speed control system has the reference speed of the generator as input and the reference torque as output. The control system configuration, shown in Figure
3.10, is the same to the one shown in section 3.1, the only difference is that the PI controller has also an anti-windup system. It’s purpose is to avoid that the reference torque goes beyond the maximum torque allowed by the machine. So at any time the reference torque will be equal to or less than the maximum torque for any input. The impact of the anti-windup is on the integrator of the PI controller. When the output of the PI is saturated, the integration effect of the PI is lowered. Figure 3.9 shows the trend of the reference torque, produced by the control system, with and without the anti-windup system. At the beginning the torque reaches really high values, so the current, dangerous for the machine and converter. Instead with the anti-windup system, the torque is limited to its maximum value at the beginning and then it decreases and the trend is the same as in the case without the anti-windup.
Figure 3.9: Comparison between control system with and without anti-windup
The PI controller was tuned with the root locus technique, as shown in section 3.1, with the following constraints:
overshoot ≤ 5% ωmax =
2πfsw
k = 6, 28rad/s
where fsw = 1.200Hz is the switching frequency and k = 1.200 is a scale
coefficient used to not have a dynamic behaviour of the control system faster than the update speed of the SVM and to have a margin for the control.
The plant transfer function is represented by the mechanical model of the system,
P lant(s) = 1
s Jeq+ Deq
(3.29) The PI controller parameters for the speed control are:
Kp = 3,1 × 106
Ki = 1,39 × 107
The root locus is shown in Figure 3.11.
Figure 3.11: Root locus of Ωm/Ωref
The gain of the anti-windup system was chosen according to [9], Kaw−up=
1
The prefilter is a simple low-pass filter with a time constant τf s. The
feed-forward transfer function is the reverse of the plant transfer function, to have a perfect tracking, multiplied by the low-pass filter transfer function to have a feasible system. P ref ilter(s) = 1 s τf s+ 1 (3.31) F eedf orward(s) = s Jeq+ Deq s τf s+ 1 (3.32) The time constant of the prefilter should be chosen to not have a reference torque greater than the maximum torque of the machine. Because of the anti-windup system is possible to tune harder the prefilter, so choose a lower time constant to have a faster system. But lower the time constant is, higher the oscillations, due to the anti-windup operation, are. So it needs to find a good trade off to not have high oscillations in the speed of the generator that might destabilize the system. In this case with τf s = 10 s the oscillations in the speed
are really low.
3.5
Conclusions
The control system and all its elements were presented. It was implemented in Matlab/Simulink and not in PLECS like the power system. First the reference feedforward control strategy and its characteristics were introduced. Then each block shown in Figure 3.1 was presented. In particular, the control strategy was applied to the current and speed controller, then the methods adopted to tune each parameter were explained. The operational region of the generator was also presented, with all its constraints and the equations used to implement it.
Preliminary Design of the
System and Simulation Results
In this chapter the overall system is analysed. First a strategy to choose the cable length ,by comparing two transfer functions to avoid resonances in the cable, is presented. Then the whole system is simulated and the influence of the parameters are investigated.4.1
Cable Design
The cable length was chosen by comparing two transfer functions. The Idctransfer
function and the cable transfer function. The comparison is useful to avoid that the poles of the two transfer functions match each other, in this way is possible to avoid resonances in the connection cable between the wind turbine and the offshore substation.
The Idc current is the output current of the converter before the DC link
capacitor, as shown in Figure 4.1.
Neglecting the losses, the current can be calculated from the power balance, Pdc = Pac (4.1) VdcIdc = 3 2(VdId+ VqIq) (4.2) Idc = 3 2Vdc (VdId+ VqIq) (4.3)
where Pac is the active power produced by the generator. The Idc transfer
function must to be calculated in all the four operational regions of the generator. It can be obtained substituting in (4.3) the transfer function from Ωref to Vd, Id,
Vq and Iq, calculated in each region. These transfer functions were obtained
using the LinearAnalysisT oolbox of Matlab. The model used for the calculation is represented in Figure C.1 in Appendix C. There is no converter, therefore no SVM and the DC link is replaced by a constant voltage source equal Vdc. Acting
on the two inputs, reference speed of the generator and wind turbine torque, the operational region was chosen and after the steady state was reached, the model was linearised. Figure 4.2 and Figure 4.3 show the bode plot and the pole-zero plot of Idc for each operational region of the generator.
Figure 4.3: Pole-Zero plot of the Idc for all the generator operational regions
The roots at low frequencies are due to the speed control that is slow while the roots at higher frequencies are due to the current control. They all have a good damping factor, around 70% for the roots at high frequencies and higher than 95% for the roots at low frequencies.
To calculate the cable transfer function the model in Figure 4.4 was used. In addition to the π − model of the cable there are the current generator that represents the Idc, the DC link capacitor Cdcbecause it was not taken into account
in the calculation of the Idc transfer function and then, to represent the offshore
substation, a DC capacitor and a constant voltage generator.
Figure 4.4: Model used to calculate the cable transfer function
The DC link capacitor is needed to maintain the DC link voltage Vdc constant,
its variations are generally due to power unbalance. Cdccan be calculated as [10],
Cdc =
Pn
V2
dc( + 0, 5 2) fsw
(4.4) where fsw is the switching frequency, Pn is the nominal power that is the
nominal apparent power of the generator Sn =
√
3VnIn in (V A) and is the
voltage ripple that was chosen equal to 1% of Vdc.
The connection cable was designed based on its rated current, that can be expressed as,
Icable,rated =
Sn
Vdc
(4.5) where Sn is nominal apparent power of the generator (V A). From the
cata-logue [11] the type of cable, its parameters per unit length (Rcable, Lcable, Ccable)
and the number of cables in parallel (Ncable) can be chosen. After the rated
current is known, considering Ncable in parallel, the parameters of the equivalent
π − model of the cable can be calculated as, Req= Rcable Ncable (4.6) Leq = Lcable Ncable (4.7) Ceq = NcableCcable (4.8)
Since the offshore substation is modelled as a constant voltage source the model in Figure 4.4 can be simplified as in Figure 4.5. The cable transfer function is, Icable Idc = 1 s2LC + s RC + 1 (4.9) where R = Req, L = Leq and C = Cdc+ Ceq 2 .
Figure 4.5: Simplified model used to calculate the cable transfer function The parameters R, L and C depend on the cable length, so for different lengths there are different transfer functions and different poles. Figure 4.6 and Figure 4.7 show the bode plot and the pole-zero plot of the cable transfer function for a length of 1 km. It has two complex poles at a frequency of 99,5 Hz with a low damping coefficient, 25%.
Figure 4.6: Bode plot of the cable transfer function
Comparing the transfer functions (4.3) and (4.9) is possible to check if for some frequencies the poles match each others and try to avoid resonances by changing the cable length. For a cable length of 1 km there are no resonances, as shown in Figure 4.8 and Figure 4.9. Increasing the length, the poles of the cable approach the Idc poles. For a cable length of about 10 km resonances may
occur but the damping factor is high, around 95%, so an eventual resonance is very well damped.
4.2
Simulation Results
The overall system was simulated using Matlab/Simulink for the control system and PLECS for the power system. The whole system model is represented in Figure C.2 in Appendix C. The simulation parameters are listed in Table E.1 in Appendix E.
The stability of the system was checked introducing two steps as input and adding a square wave disturbance in both of them, reference speed and wind turbine torque. This is the worst case scenario from a control point of view. The square wave has a frequency equal to the frequency of the poles of the cable transfer function, 99,5 Hz, and an amplitude equal to 10% of the input step amplitude. Only in the DE operational region of the machine the amplitude of the square wave disturbance in the reference speed is 3%, because adding the
Figure 4.7: Pole-Zero plot of the cable transfer function
10%, the speed exceeds the limit of the generator. The disturbance is injected first in the reference speed and then in the wind turbine torque.
Here the simulation results for steps input equal the rated values are shown. For a step from zero to rated generator speed and from zero to rated wind turbine torque, the generator works in the operational region BC. The results shown in this chapter are valid only for this region, the results for the other operational regions are shown in Appendix E.
The trend of the generator speed is shown in Figure 4.10. The green line is the reference speed, equal the rated generator speed, the red one is the reference filtered speed, that is the reference produced by the prefilter of the speed control system. The blue one is the measured speed of the generator, that is equal the reference filtered speed except at the beginning where there is a little oscillation due to the anti-windup system that limits the torque to its maximum value. Bigger is the step amplitude of the reference speed and greater are the oscillations due to the anti-windup, as can be seen in Figure E.17 in Appendix E for the DE region. These oscillations can be reduced by changing the prefilter, for example by choosing a larger value for the time constant τf s, but the response of the system
will be slower. The settling time is 29 seconds and there is no overshoot in the response. The system is stable even after the injection of the two square wave disturbances. Due to them there are oscillations in the speed but their amplitudes are very little, as shown in Figure 4.11. A disturbance in the reference torque
Figure 4.8: Bode plot comparison between Idc and cable
has a lower impact than a disturbance in the reference speed, so the torque can change more quickly compare to the speed, because the speed is the integral of the torque.
Due to the step from zero to the rated wind turbine torque the generator torque, at the beginning, is limited to its maximum value by the anti-windup system, Figure 4.12. Then the torque decreases to reach the reference value, the red one is the reference torque while the green one is the generator torque. After 60 seconds the disturbance injection in the reference speed signal is visible.
Figure 4.13 shows the trend of the dq stator current. It can be seen how the limitation on the current is then reflected in the electromagnetic torque plotted in Figure 4.12 and how the trend of the Iq is very similar to the torque trend,
this shows that the q component of the current affects more the electromagnetic torque. The oscillations in the current, at the end, are due to the disturbance in the reference speed while the disturbance in reference torque has basically a null effect on the current.
The generator current in abc frame is shown in Figure 4.14. It increases then at steady state it remains constant and always lower than the maximum generator current. It is stable even after the disturbances injection and it has a sinusoidal waveform with a small ripple, as shown in Figure 4.15.
Figure 4.9: Pole-Zero plot comparison between Idc and cable for different cable
length
vector modulation. In Figure 4.17 can be seen that when the current is zero, the applied vector is (111) or (000), all the upper switches are on and all the bottom ones are off or vice versa. The average value is not zero, so there is power transmission to the DC link.
Figure 4.18 shows the DC link voltage. It starts from 4.500 V and then at steady state it reaches 4.537,5 V, an increasing of about 0,83%. It is stable even after the injection of the square wave disturbance in the reference speed signal. The ripple is 0,05% which is much smaller than the maximum ripple (1%) hypothesized to calculate Cdc.
The current in the cable is represented in Figure 4.19. Also here the most influential disturbance is the one in the speed, but after some oscillations the current remains stable with very low ripple.
The power produced by the generator, with rated input values, and delivered to the DC link is shown in Figure 4.20.
4.3
Influence of Control Parameters
As seen before the Idctransfer function depends on the gains of the PI controllers.
These parameters can be modified, for example they can be increased or decreased by 20% respect to their rated values. Four different cases were investigated:
