DC Connected Wind Farm

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DC Connected Wind Farm

Evaluation of Dynamic Performance

Elforsk rapport 08:44

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DC Connected Wind Farm

Evaluation of Dynamic Performance

Elforsk rapport 08:44

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Preface

The purpose of this project is to investigate dynamic properties and possible limitations when using a HVDC link, based on transistors (VSC HVDC) to control wind turbines in a park, instead of controlling each wind turbine individually.

The work was carried out by Andreas Petersson and Massimo Bongiorno at Gothia Power as a project within the Swedish wind energy research programme “Vindforsk – II”. The report is the final report for project V 138. Vindforsk – II is funded by ABB, the Norwegian based EBL-Kompetense, E.ON Sverige AB, Falkenberg Energi AB, Göteborg Energi, Jämtkraft AB, Karlstad Energi AB, Luleå Energi AB, Lunds Energi AB, Skellefteå Kraft AB, Svenska Kraftnät, Swedish Energy Agency, Tekniska Verken i Linköping AB, Umeå Energi AB, Varberg Energi, Vattenfall AB and Öresundskraft AB.

Comments on the work and the final report have been given by a reference group with the following members: Jörgen Svensson E.On and Lars Gertmar ABB.

Stockholm September 2008

Anders Björck

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Summary

Modern variable-speed wind turbines (WTs) which are connected to the grid by a voltage-source converter high-voltage direct current (VSC-HVDC) system may require several power-electronic components (PECs). Within the variable-speed turbines, there are normally PECs in order to control the turbine variable-speed and torque while the VSC-HVDC introduces additional conversions in order to achieve the grid connection. In this report, the possibility to the VSC-HVDC in order to control the WTs is studied, thus eliminating some of the PECs within the turbines. This means that there is a possibility to use simpler and cheaper types of WTs with less power-electronic equipment.

It has been found that a wind farm utilizing a VSC-HVDC rectifier in order to control the rotor speed of the wind turbine can utilize simper and cheaper type fixed-speed WTs and still produce the same amount of power. One drawback with these simpler type fixed-speed WTs is that they produce excess power, i.e., power above the rated. It is essential to determine the amount of excess power that can be expected from the WTs, since this will have an impact of the system design. However, these power variations will be less significant with the number of installed WTs in the wind farm.

Design of the control system of the wind-farm side VSC-HVDC must be done with care, since it is importance to ensure that the overall system is sufficiently damped at all critical frequencies.

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Sammanfattning

Moderna vindkraftverk med variabelt varvtal som kopplas till elnätet genom ett transistorbaserat HVDC system, består av många kraftelektroniska omvandlare. Vindkraftverk med variabelt varvtal har en kraftelektronisk omvandlare för att bl.a. reglera generatorns moment och varvtal samtidigt som HVDC systemet innebär ytterligare omvandlingar för nätanslutningen. I detta arbete har möjligheten att använda HVDC systemet för att även reglera vindkraftverket och därigenom minska mängden kraftelektronik i vindkraftverken studerats. Detta innebär att det finns en möjlighet att använda enklare och billigare typer av vindkraftverk som använder sig av färre kraftelektroniska komponenter.

Det har visats sig att en vindkraftspark som ansluts med ett transistorbaserat HVDC system kan utnyttja enklare och billigare fastvarvtalsvindkraftverk med i princip samma energi produktion. En nackdel med dessa enklare typer av vindkraftverk är att de producerar övereffekter, dvs. effekt över märkeffekt. Det är därför viktigt att bestämma hur stor övereffekten från en vindkraftspark kan bli eftersom detta kommer att påverka dimensioneringen av HVDC systemet. Dock så beror övereffekter på antalet vindkraftverk och övereffekten blir mindre signifikant med antalet vindkraftverk i parken.

Design av HVDC omformarens reglersystem mot vindkraftsparken måste göras noggrant, så att hela systemet är tillräckligt dämpat vid alla kritiska frekvenser.

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Introduction

Transporting electrical power over long distances using ac cables can be associated with very high costs. Therefore, grid connection of a wind farm by way of high-voltage direct current (HVDC) transmission may be cost effective alternative to ac transmission. See Figure 1 for a configuration example. Often, HVDC transmission based on VSC-technology, such as ABB’s HVDC Light and Siemens’s HVDC+, is considered. Such a HVDC system has many advantages compared to a thyristor-based classical HVDC configuration, such as lower harmonic pollution, higher controller bandwidth, possibility to interconnect weak systems. Furthermore, the VSC-based HVDC system enables the possibility to use induction generators within the wind farm. This can not easily be accomplished with a classical HVDC configuration, since both the thyristor-based HVDC converters and the induction generators require a strong grid for proper operation.

WT ≈ ₌ WT WT rectifier = ≈ inverter long distance

Figure 1: Wind farm with HVDC transmission.

Several offshore wind farms that rely upon VSC-HVDC for grid connection are already being planned. Outside (130 km) the German coast, a 400 MW off-shore wind farm will be constructed [3]. This wind farm constitutes of eighty 5 MW variable-speed WT with doubly-fed induction generators. The wind farm is connected to the mainland through a VSC-HVDC system [1]. The local wind farm grid has a voltage of 36 kV and is transformed up to 154 kV at the VSC-HVDC rectifier [3]. In contrast to the work in this report, though, it appears that mainly the PEC within each WT will be used in order to control the speed and torque.

Wind farms, based on modern variable-speed WTs, that are connected to the grid by a VSC-HVDC system, require several PECs. The main objective of the PECs in the WTs is to achieve variable-speed operation of the WT, while for the VSC-HVDC system the PEC main purposes are to convert ac to dc and vice-versa. The PEC topologies are similar in both the WT and the VSC-HVDC. Therefore, it may be possible to use the farm-side PEC in the VSC-HVDC in order to control the WTs. For instance, the VSC-HVDC can supply the wind farm with variable frequency. This means that there might be possibility to use simpler and cheaper types of WT with less power-electronic equipment.

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The main purpose of this report is to investigate a VSC-based HVDC system that simultaneously controls several WTs within a wind farm. The report gives an overview of different configuration of VSC-HVDC connected wind farms in order to have a cost-effective and reliable solution. Some of these configurations are investigated to provide an initial understanding of what such a system can achieve. The dynamic performance and possible limitations for each investigated configuration are also studied. The main focus of this study is the performance of the WTs and their impact of the VSC-HVDC.

This report is organized as follows. First, in Chapter 2, relevant background information is provided regarding, for instance, WT and HVDC. Then, in Chapter 3, the theory and modelling of the investigated WT are presented. In Chapter 4 the dynamical performance of the investigated wind farm is analyzed and, finally, in Chapter 5 the efficiency of the wind farm is determined.

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2

Background

This chapter describes the most common types of WTs and their operation, principles of HVDC transmission and presents possible layouts of a wind farm connected to a VSC-HVDC.

2.1

Wind turbines

For a fixed-speed WT, an induction generator (IG) is usually directly connected to the electrical grid, as depicted in Figure 2. The rotor speed of a fixed-speed WT is in principle determined by the grid frequency, the gearbox ratio and the pole-pair number of the generator. In order to limit the power input, the blades of a fixed-speed WT are normally designed to stall above a certain wind speed, which means that no pitch mechanism is necessary [4]. It is possible to further reduce the power output variations by way of active stall, which implies that the pitch angle can be increased towards stall. An advantage with stall control is that the power variations due to wind gusts are relatively small, however, the thrust forces that result from stall control are relatively large compared to pitch control.

Figure 2: Fixed-speed wind turbine with an induction generator.

A “fixed-speed” WT system can in practice often operate at two different rotor speeds. This can be achieved with two generators that have different ratings and different number of pole pairs, or it can be implemented with a single dual-winding generator. A two-speed system provides increased aerodynamic efficiency as well as reduced magnetization losses at low wind speeds [12] compared to single-speed system.

A fixed-speed system normally uses a capacitor bank for compensation of the no-load reactive power consumption and a soft starter for smoother connection of the generator to the grid, as depicted in Figure 2.

Unfortunately, a standard fixed-speed pitch-controlled WT has relatively large variations in the active power output. Figure 3 shows an improved “fixed-speed” system, which uses transistor-controlled resistors connected to the rotor. This setup allows for the rotor resistance to be varied, which means

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that it is possible to temporarily vary the rotor speed and thereby decrease the active power variations due to wind gusts.

Modern variable-speed WTs more or less exclusively rely upon pitch control rather than stall control. With variable speed, the rotor is allowed to speed up during wind gusts, which considerably reduces variations in the active power output. This eliminates one of the main drawbacks of pitch control and due to lower thrust forces compared to stall control, pitch control is normally the preferred choice in modern variable-speed WTs.

In addition to less variation in the active power production, a variable-speed WT has several additional advantages compared to a fixed-speed system. For instance, a variable-speed WT can reduce the stresses placed on the mechanical structure, the acoustic noise at low wind speeds will be less severe and the reactive power can be controlled at the grid connection [4].

Figure 3: Fixed-speed wind turbine with an induction generator with variable slip by way of controllable rotor resistance.

Figure 4 shows a variable-speed WT with a full-power converter and a multiple-pole synchronous generator (SG).

Figure 4: Variable-speed wind turbine with a full-power converter.

Figure 5 shows a common variable-speed WT variant that uses a doubly-fed induction generator (DFIG). In a DFIG system, the stator is directly connected to the grid while the rotor winding is connected via slip rings to a converter.

Gear-box

IG

starter Soft

Capacitor bank

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Since a variable-speed WT typically operates within a limited speed range— ±30 % of synchronous speed is often sufficient—the DFIG can be an interesting solution, since the power electronic converter only has to handle a fraction (30%) of the total power. This reduces both the converter ratings and the initial system cost. In addition, the losses in the power-electronic converter can be reduced compared to a power configuration, since a full-power converter has to process the nominal full-power of the WT.

Figure 5: Variable-speed wind turbine with a doubly-fed induction generator.

The static and dynamic performances of the two above described variable-speed systems are more or less similar and most WT manufactures appear to prefer one of these variable variable-speed configurations when developing turbines in the 3-to-5-MW range [2]. Fixed-speed stall controlled WTs with IGs appear to gain less interest since they appear to be regarded as unfeasible for such large WTs [2].

2.2

HVDC transmission

When transmitting electrical power over long distances it may be beneficial to transmit the power as dc instead of ac. As already mentioned in the previous chapter, there are two main types of HVDC transmission, the traditional with line-commutated thyristors and the newer ones that use self-commutated transistors, where each converter station is used as a VSC.

A traditional thyristor-based HVDC system is capable of transmitting power up to 3000 MW over long distances [1]. By turning the thyristors on at different phase angles of the ac voltage, it is possible to control the transmitted power. However, the thyristors require a grid with a certain amount of short circuit power for proper operation [7]. Moreover, a thyristor converter consumes reactive power and the ac currents contain low-frequency harmonics. Therefore, phase compensation is normally used in order to improve the power factor and relatively large harmonic filter “traps” are required in order to reduce the current distortion.

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In a transistor-based (or VSC-based) HVDC system, on the other hand, the power transistors can be rapidly switched on and off independently of the ac voltage. This means that such a HVDC system can operate in island mode; hence a strong grid is not required for proper operation. Further, the use of transistors in place of thyristors allows a high control bandwidth for fast control of both active and reactive power. Moreover, thanks to the use of Pulse Width Modulation (PWM) technique, it is possible to select the switching frequency so that the ac currents will only contain high-frequency harmonics. These harmonics require much smaller filters compared to a traditional thyristor-based HVDC system. For these reasons, the VSC-HVDC is here considered as the most suitable solution for connection of a wind farm to the grid. It is of importance to consider that the control of the VSC-HVDC must be modified in order to control the WTs, as it will be explained later in this report.

2.3

Operation of wind turbines

The available power in the wind,

P

_W, depends on the air density,

ρ

, the wind

speed,

w

_s, and the swept rotor area with

R

being the radius of the swept area swept [4]:

( )

2 3

2

1

s W

R

w

P

=

ρ

π

. ₍₁₎

As seen in (1), the available power in the wind depends cubically on the wind speed. Above rated wind speed, defined as the lowest wind speed with nominal power production, the available power in the wind must be limited since the WT (turbine, gearbox, generator etc.) is designed according to rated power. There are three common methods in order to limit the power: stall, active stall control and pitch control. Figure 6 shows the output power for a stall-controlled WT that operates with a fixed pitch angle.

Figure 6: Power output from a WT. Solid line corresponds to a stalled controlled WT and dashed line to an active-stall controlled WT.

As seen in Figure 6 the output power of a stall-controlled WT tends to drop at higher wind speeds. By increasing the pitch angle towards stall, i.e., active stall control, the output power can be fine adjusted to the rated. This is

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illustrated with the dashed line in Figure 6. In Figure 7, the upper graphs shows the available power in the wind and the typical power output of a 2.3-MW turbine as a function of wind speed, while the lower graphs depict the corresponding pitch angles for active stall and pitch control.

5 10 15 20 25 30 0 2 4 6 Po w er [ M W ] Wind speed [m/s] Power output Available power 5 10 15 20 25 30 -10 0 10 20 30 P itc h ang le [ de g] Wind speed [m/s] Pitch control Active stall

Figure 7: Above: Power available in the wind and WT electrical power output as a function of wind speed. Below: Pitch angle during aerodynamic power limitation as a function of wind speed.

The output power, as depicted in Figure 7, can be limited to the rated, at least in the steady state, for both active-stall and pitch-controlled WTs by varying the pitch angle. It can also be seen that active stall requires negative values of the pitch angle in contrast to a pitch-controlled WT. Moreover, the range of pitch angles, in order to perform the aerodynamic power limitation, is much less for an active-stall WT compared to a pitch-controlled WT.

One advantage with pitch control is that the rotor thrust forces drop significantly above rated wind speed, while this is not the case for stall control, as illustrated in the right-hand side of Figure 8. In addition, the rotor blades of a pitch-controlled WT can be feathered completely at extremely high wind speed and, thus, greatly reduce the wind loading on the rotor blades [5]. Pitch control has been considered to be the preferred aerodynamic power control method since the blade loads can be predicted with more confidence compare to stall-controlled blades [4].

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0 5 10 15 20 25 Wind speed [m/s] R oto r th ru st [-] Stall control Pitch control

Figure 8: Rotor thrust force as a function of the wind speed for a stall- respectively a pitch-controlled WT. Source [5].

Figure 9 shows the power as a function wind speed for different negative pitch angles (towards stall) for an active-stall WT. In the same figure, the steady-state power output (thick blue line) for a typical 2.3-MW active-stall WT is also included. Dynamically, the power output will drop slightly when the wind speed increases before the pitch angle is increased and operation at the steady-state power curve is recovered. The variation in the power output will be rather small.

Figure 10 shows the power output as a function of wind speed for different positive pitch angles (towards feather) for a typical 2.3-MW pitch-controlled WT. In contrast to an active-stall WT, a pitch-controlled WT produces rather high dynamic power-output variations when the wind speed varies. For example, if the WTs in Figure 9–10 operate at 17 m/s and the wind speed suddenly increases to 20 m/s (for simplicity the pitch angle is assumed to remain constant: –2° for the active-stall WT and 15° for the pitch controlled WT), then the power output of the active-stall WT will reduce to 2.14 MW, i.e., 93 % of the initial value. For the pitch-controlled WT, on the other hand, the power output increases to 3.0 MW, i.e., 130 % of the initial value. Hence, the pitch-controlled WT produces higher dynamic variations in the power output.

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5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 3 3.5 4 0_° -0.5_° -1_° -1.5_° -2_° Po w er [ M W ] Wind speed [m/s]

Figure 9: Power as a function wind speed for different pitch angles (pitch towards stall) for an active stall controlled turbine.

5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 3 3.5 4 0° 5_° 10_° 15_° 20_° 25_° Po w er [M W ] Wind speed [m/s]

Figure 10: Power as a function wind speed for different pitch angles for a pitch (towards feather) controlled turbine.

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The large power variations caused by pitch-controlled WTs can be reduced by way of variable-speed operation. With variable speed, the WT power variations are suppressed by either increasing or reducing the rotational kinetic energy of the rotor. This means that the power output of a pitch-controlled variable-speed WT can be made smoother above the rated wind speed. Other benefits with variable-speed operation are [4]:

• Below rated wind speed the rotor speed can vary with wind speed to maintain optimum aerodynamic efficiency.

• Acoustic noise reduction.

• Damping of drive line oscillations.

• Control of active and reactive power.

• Improved power quality.

Among other things, PECs are required in order to operate a generator with variable speed, see Section 2.1.

2.3.1 Possibilities with the dc transmission rectifier

Both variable-speed WT and VSC-HVDC use PECs for power conversion and control purposes. This means that, for a wind farm connected to a VSC-HVDC system, some of the features of the WT PECs may be transferred to the VSC-HVDC. The VSC-HVDC can then possibly used to control all WTs within the wind farm. Some of the features that can be transferred are:

• Below rated wind speed the rotor speed can vary with wind speed to maintain optimum aerodynamic efficiency.

• Control of active- and reactive power.

Other features, such as fully suppressing power variations with the variable rotor speed and damping of drive-line oscillations, may be difficult to accomplish when moving control functionality from the individual WTs to the VSC-HVDC system. This is due to that the VSC-HVDC cannot control each individual WT. Instead, all WTs will have to make do with a common voltage and frequency, which hopefully can be selected such that a reasonable performance is achieved for the entire wind farm.

Although the active power variations for each WT may increase when moving control functionality from the WTs to the VSC-HVDC, the power variations from the entire wind farm may remain at an acceptable level. One reason for this is that the relative power variation of a wind farm normally decreases with increasing number of WTs [16]. Another reason is that the VSC-HVDC system can be dimensioned to handle the power variation.

It might also be acceptable to allow larger variations in the active and the reactive power for a VSC-HVDC connected wind farm compared to an ac-connected wind farm. The power quality of an ordinary variable-speed WT has only a minor impact on the grid, i.e., the flicker contribution is low, the power factor can be controlled and soft start and stop is enabled [8]. For the VSC-HVDC connected wind farm, the transmission-side converter can provide similar benefits.

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2.4

Possible system layouts with dc transmission

In this section some of the possible system layouts for a dc connected system will be presented. The HVDC rectifier is used for controlling the WTs.

The simplest WT that is considered for a VSC-HVDC connected wind farm is the “fixed-speed” WT. The aerodynamic power limitation of the “fixed-speed” WT can be either active-stall or pitch controlled. The IG of the “fixed-speed” WT can use external rotor resistances, as illustrated in Figure 11, if individual control of each WT generator is required.

wind turbine IG = ≈ dc transmission VSC rectifier

more wind turbines

Figure 11: Block diagram of wind farm with IGs that have controllable rotor resistances, which are connected to the grid via transistor-based HVDC converters.

By varying the rotor resistance of the IG in Figure 11, it is possible to control the generator torque and speed and, thereby, achieve variable-speed operation, at least to some extent. If a higher degree of individual control of the WT generator is required (e.g. a larger variable-speed operating range or reactive power control) a DFIG system, as in Figure 12, can be used. In this case the size of the power-electronic converter of the DFIG system may be smaller than that of an ordinary DFIG system, since the power-electronic converter of a DFIG system need only to be rated for the maximum slip power. Therefore, the power-electronic converter of the DFIG system needs to be dimensioned for the maximum deviation of the WT rotor speed in relation to the reference rotor speed (or frequency) set by the VSC-HVDC. This means that the power-electronic converter has to be dimensioned for speed deviations required by the torque controller of the generator.

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= ≈ = ≈ wind turbine DFIG ≈ ₌ dc transmission VSC rectifier

more wind turbines

Figure 12: Block diagram of typical DFIG wind farm connected to the grid via transistor-based HVDC converters.

The last option presented here is shown in Figure 13. In this case, the dc is distributed directly into the WT. This means that all WT of the wind farm share the same dc-link voltage. As seen in Figure 13, the system may need a central or individual dc/dc converter to adjust the higher dc-link transmission voltage to a lower voltage level that is more suitable for the WT generator.

wind turbine

SG _{dc transmission}

more wind turbines = ≈ = = dc/dc converter

Figure 13: Block diagram of an SG wind farm with distributed dc.

System where dc is distributed directly to the WT, as in Figure 13, is under research; see for example References [9] and [10]. There are also other types of interesting configurations that, for instance, only need one single phase-leg of the VSC-HVDC rectifier compared to the three phase-legs of an ordinary VSC-HVDC converter [11]. These type of systems are very interesting solutions, however, it is not clear when such systems can be made commercially available.

When designing a VSC-HVDC connected wind farm it is also of interest to compare the cost of the different electrical system of the WTs. In Table 1, the relative cost of different electrical systems of WTs in the 0.5-3 MW range is presented [5]. Note that in the table the cost of the one-speed, fixed-speed WT is taken as reference (100% approximate cost ratio).

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Table 1. Approximate cost ratio of different electrical systems for geared WTs in the 0.5-3 MW range [5]. Note that mechanical systems are excluded.

System Approx. cost ratio

Fixed-speed WT, one-speed generator, phase

compensation 100 %

Fixed-speed WT, two-speed generator, phase

compensation 110 %

Variable-speed WT, DFIG 160 %

Variable-speed WT, SG, full-power converter 180 %

From Table 1 it can be seen that the cost of the electrical systems for fixed-speed WT is lower compared to variable-fixed-speed WT. However it should be kept in mind that a more complex electrical system may result in a cheaper overall solution, if it is associated with mechanical or operational advantages [5]. In Figure 14, the produced grid power together with the various loss components for an average wind speed of 6 m/s are presented for the various systems [12]. The systems are the DFIG system, the full variable-speed system (VSIG), one-speed system (FSIG 1), two-speed system (FSIG 2), and, a variable-speed system equipped with a permanent magnet synchronous generator (PMSG).

Figure 14: The produced average grid power and generator, converter and gearbox losses for an average wind speed of 6 m/s. 100% correspond to the input turbine power at optimal, with respect to the rotor speed, aerodynamic efficiency. FSIG 1: speed WT (one-speed generator), FSIG 2: Fixed-speed WT (two-Fixed-speed generator), VSIG: Variable-Fixed-speed WT with IG, PMSG: Variable-Speed direct-drive PMSG and DFIG: Variable-speed WT with DFIG. Source [12].

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In the figure it can be seen that the one-speed system (FSIG 1) has the disadvantage of poor aerodynamic efficiency. However, with the two-speed system (FSIG 2) the aerodynamic efficiency is improved and similar to that of the variable-speed systems (VSIG, PMSG and DFIG). The losses in the power-electronic equipment counteract the gain in aerodynamic efficiency of the variable-speed turbines. Worth stressing is that the main reason for using a variable-speed turbine instead of a fixed-speed turbine is not the energy efficiency, instead it is the possibility of lowering the mechanical stresses [6] and also improving the power quality [8].

2.4.1 Investigated system

In order to investigate the dynamic performance of a system where the rectifier of the dc transmission is used to control the WTs, the “fixed speed” WT, with and without slip control (rotor resistance control), is considered for further investigation. The main reasons for choosing this type of turbine are:

• Simple and well proven WT technology.

• Low cost electrical system.

• With slip control the “fixed speed” WT behaves almost as a variable-speed WT, although the variable-variable-speed range will be smaller.

Another reason for choosing this system is that the main components, such as the WT and the VSC-HVDC, already exist, it merely a matter of merging two existing technologies. Wind farm where dc is distributed to all WT, such as in Figure 13, is beyond the scope of this project.

2.5

Requirements

In a VSC-HVDC connected wind farm, the WTs are operated in a separated ac grid. This local ac grid can be designed with different requirements compared to that of a conventional ac connection, which, for instance, must be designed according to the requirements of the transmission system operator (TSO), see Figure 15 for a requirement example.

With a VSC-HVDC connection, on the other hand, the TSO requirements are mainly an issue for the transmission-side converter. Therefore, the local ac grid can be designed according to, possibly, less demanding requirements. For example, the VSC-HVDC system can be designed to take care of low-voltage ride-through requirements. This means that a "braking" chopper, acting as a load dump, may have to be installed at the dc link. Observe that a dc-chopper may already be installed in a VSC-HVDC system in order to protect the dc-link capacitors against overvoltages. Other requirements, such as voltage and reactive power control, can also be handled by the VSC-HVDC converters. Off course, adding features to the VSC-HVDC system will increase cost. However, this cost increment must be compared to the cost of fulfilling the TSO requirements using other methods.

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Figure 15: Example of requirements from Svenska Kraftnät (SvK) [13]. Left: Voltage and frequency tolerances. Right: Low-voltage ride through require-ment.

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3

Theory and modelling

This chapter presents the theory and the models of the investigated system. In order to evaluate the dynamic performance of the investigated wind power system, the simulation package PSCAD/EMTDC is used. PSCAD/EMTDC is a powerful tool in evaluating dynamic performances of electrical power systems. The investigated WTs are rated 2.3 MW and use similar electrical systems as that of a conventional fixed-speed WT. A general model for this type of turbine is modelled according to Figure 16. The model consists of two IGs with a two-mass model for the mechanical system. Dual-speed “fixed-speed” WTs is modelled with a “large machine” and a “small machine”, as depicted in Figure 16. e1r TL N I M Te W #1 #2 P = 1.071 Q = -1.562 V = 28.31 V A Te w 4 .5e 3 [u F ] BLM TL N I M Te W TeSM wSM 1 .1e 3 [u F ] BSM 1 BSM * TL 1 BLM * "Large machine" "Small machine" BLM BSM TLSM 32.0 [ohm ] 32.0 [ohm ] 32.0 [ohm ] 15 4.0 [oh m ] 15 4.0 [oh m ] 15 4.0 [oh m ] Ir Re xt + Re xt + Re xt + vs M u ltim a ss Te W p u ( IndM /c ) TL Mu lti m a ss Te W p u ( IndM /c ) TL

Figure 16: Electrical configuration of the WTs simulation model.

The WT model is equipped with capacitor banks that compensate for the no-load reactive power consumption of the IGs. The shunt resistors, connected to the IG stators, model the magnetization losses of the IGs since these are not included in the built-in PSCAD/EMTDC model. Moreover, the “larger machine” in Figure 16 is equipped with external rotor resistors. By controlling the external rotor resistances, it is possible to control the slip of the IG and

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thereby the speed of the rotor to some extent. In order to configure the model to the desired WT the model also includes four breakers. This means that the model presented in Figure 16 can be used to model several types of “fixed-speed” WTs connected both directly to an ac transmission or to a dc transmission with VSC-HVDC depending on the how the model is configured. The model can be used for the following simulations:

• One speed or two speed generator.

• Stall, active stall or pitch control.

• With or without variable slip (controllable rotor resistances).

3.1

Wind

The wind speeds in the simulation model are pre-generated and imported into the simulation model. The pre-generated wind speed has a turbulence intensity of 10% and is calculated in one point over the rotor disc. The spatial effect of the rotor disc is accounted for by feeding the wind speed model through a first-order low-pass filter [15]. An example of a pre-generated wind speed is shown in Figure 17.

0 10 20 30 40 50 60 0 2 4 6 8 10 12 Time [s] W in d s pee d [m /s ]

Wind speed in one point Wind speed after spatial filter

Figure 17: Wind speed in one point of the rotor disc and the corresponding wind speed after spatial filtering. The average wind speed is 9 m/s.

In order to account for the rotational sampling of the wind by the turbine rotor, a so called rotational sampling filter is implemented in the simulation model. This filter amplifies the variations at a frequency region around the blade passing frequency. In other regions this filter has a gain of nearly one [15]. The rotational sampling filter acts on the wind speed.

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3.2

Turbine

Some of the available power in the wind is converted by the rotor blades to mechanical power acting on the rotor shaft of the WT. For steady-state calculations, the so called

C

_p

( )

λ

,

β

-curve can be used to model this WT power conversion. The mechanical power of the turbine,

P

_T, equals:

( )

3

( )

2 3

,

2

1

,

2

1

s p s r p T

C

A

w

C

R

w

P

=

λ

β

ρ

=

λ

β

ρ

π

(2) s

w

R

Ω

=

λ

(3)

In the above equations,

C

_p

( )

λ

,

β

is the power coefficient,

β

is the pitch angle,

λ

is the tip speed ratio,

w

_s is the wind speed,

Ω

is the rotor speed

(on the low-speed side of the gearbox),

R

is the rotor-plane radius,

ρ

is the air density and

A

_r is the area swept by the rotor. The power coefficient

( )

λ

,

β

p

C

describes the aerodynamic efficiency, i.e., how much of the available power in the wind that is converted to mechanical power. The mechanical torque,

T

_T, from the turbine that acts on the drive line can be further expressed as

( )

λ

π

ρ

β

λ

2 2

,

2

1

p s T T

Rw

R

C

P

T

=

Ω

=

(4)

In the simulation model, (4) is implemented as a model of the turbine and the power coefficient

C

p

( )

λ

,

β

is determined from a look-up table. In Figure 9 and Figure 10 the characteristics of the implemented turbine model are shown.

3.2.1 Rotor speed reference

When a “fixed-speed” WT is connected to a VSC-HVDC converter, the VSC can be used to achieve variable-speed operation. At low and medium wind speeds, the rotor speed reference should be selected such that the aerodynamic efficiency is maximized. This can be achieved by operating the WT at the peak of the power coefficient curve in Figure 18. As shown, the power coefficient peaks at the “optimal” tip-speed ratio,

λ

_opt, and operation at

opt

λ

can, according to (3), be achieved by varying the rotor speed reference proportionally to the wind speed.

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0 5 10 15 20 25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 P ow er c oe ffi ci en t [-]

Tip speed ratio [-]

λ_opt

Figure 18: Power coefficient as a function of the tip-speed ratio with constant rotor speed.

Figure 19 shows the power output and the rotor speed for a variable-speed WT that operates at the optimal tip-speed ratio. In this figure, the rotor speed of the investigated WT reaches the rated rotor speed at approximately 9 m/s. This means that the rotor speed reference remains constant for wind speeds that exceed 9 m/s.

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5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 Po w er [ M W ] Wind speed [m/s] 5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 R ot or s pee d [r ad /s ] Wind speed [m/s]

Figure 19: Power output and rotor speed (low-speed side of the gearbox) for the investigated turbine when operated as a variable-speed WT.

3.2.2 Pitch control

In the model there are two options for the pitch (blade) angle controller, i.e., active stall or pitch control, see Figure 20. In order to simplify the model of the pitch-angle controller, the pitch angle is determined from the wind speed by way of a look-up table. The look-up table is set according to the steady state characteristics shown in Figure 7.

ws Table G 1 + sT Active stall _A B Ctrl Ctrl = 0 Table

Pitch control _{[Setup] PitchControl} d/dt

beta

Figure 20: Simulation model of the pitch angle control.

The low-pass filter after the look-up table in Figure 20 is used to model the closed-loop bandwidth of the pitch-angle controller. The last block in the

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figure is a rate limiter that limits the rate of change of the pitch angle to a maximum of 10 deg/s.

3.3

Mechanical dynamics

The gearbox and drive line are represented as a two-mass system with a spring constant and a mutual damping. The inertia constant of the turbine is set to 2.7 s while the generators inertia constant is set to 0.3 s. The spring constant is selected such that the un-damped system has a resonance frequency at 1.7 Hz. The damping constant is tuned such that the logarithmic decrement, due to a step response, between two adjacent amplitude peaks equals 7.5 %.

3.4

Generator and step-up transformer

The generator is modelled as a wound-rotor induction generator from the PSCAD/EMTDC standard library. The IG is a 2.6 MVA four-pole generator and phase compensated for the no-load reactive power consumption. Moreover, the model also consists of a smaller 0.52 MVA six-pole IG for modelling of fixed-speed WT with two different “fixed speeds.” The rated voltage and frequency of the generators are 690 V and 50 Hz respectively. The IG reactive power consumption as a function of the active power is shown in Figure 21. In the figure, both the uncompensated and the phase compensated for the no-load reactive power consumption are presented. As expected, the IG reactive power consumption has a dependency on the active power production.

0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 Active power [MW] R ea cti ve p ow er [M va r] Uncompensated No-load compensated

Figure 21: Reactive power as a function of the active power for the induction generator both for an uncompensated and no-load compensated generator.

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The 0.69/33.0 kV step-up transformer is rated for 2.5 MVA and has a leakage inductance of 7.0 %. The transformer model is, similarly to the IG, selected from the PSCAD/EMTDC standard library.

3.4.1 Control of rotor resistance

The model of the 2.6 MVA IG also has variable external rotor resistances. If the variable external rotor resistance is set to a very small constant value, the IG behaves as an ordinary IG. It is also possible to control the slip by the variable external rotor resistances, which means that the same model can also be used for variable-slip systems. By varying the slip and thereby the rotor speed, it is possible to “store” the power variations caused by wind gusts as rotational energy. This means that the output power from the turbine can be smoother with the variable slip system.

The output power is controlled through a fast inner current control loop. The power reference is proportional to the slip (low-pass filtered) up to rated power where it is kept constant.

3.5

Coordinated control of main VSC

In Figure 22 the wind farm VSC (the rectifier), point of common connection (PCC), filter inductance and the wind farms WTs are shown. The VSC-HVDC rectifier is used to control the voltage at PCC. Steady-state compensation of the voltage drop over the filter reactor is also included in the controller.

WT ≈ ₌ WT WT rectifier

V

_pcc

L

_filter

Figure 22: VSC-HVDC rectifier and filter inductance.

In this study the reference voltage is determined from the desired electric frequency within the wind farm. For simplicity and in order to maintain the speed-torque characteristics of the IG, the ratio between the voltage and frequency is kept constant, see Figure 23 (left), which is referred to as V/Hz control. In Figure 23 (right) the speed-torque characteristics of the IG are shown for different rotor speeds when the ratio between the voltage and frequency is kept constant. Note that the speed-torque characteristics are given with motor references, so negative torque implies generator operation.

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0 10 20 30 40 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Frequency [Hz] S tat or v ol tag e [ kV ] 0 500 1000 1500 2000 -3 -2 -1 0 1 2 3 4 5 Speed [rpm] T or que [ pu] U=U_N, f=f_N U=0.7U_N, f=0.7f_N U=0.5U_N, f=0.5f_N

Figure 23: Open-loop control of V/Hz characteristics (left) and speed-torque characteristic of an induction motor (right).

As mentioned in Section 3.2.1, the power output is proportional to the cube of the rotor speed. By inversing this relation, it is possible to determine the reference frequency, which essentially equals the rotor speed in steady state if the slip is neglected, Figure 24 illustrates the algorithm for calculating the frequency set-point. The low-pass filter determines how fast the VSC-HVDC converter tracks the optimal tip-speed ratio.

Figure 24: Determination of reference frequency.

3.6

Wind farm configuration

The wind farm can in the simulation model either be connected to the power system by a dc or an ac transmission system, as seen in Figure 25.

Wind Park E DC Transm. EW EG AC Grid EG BDC BAC AC connection DC connection

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This means the wind farm can be studied with either an ordinary ac connection or with a dc connection. In Figure 26 the layout of the wind farm with five WTs in one radial is shown. The WTs are connected with PI-sections that represent the cables between the turbines. The electrical configuration of the WTs was presented in Chapter 3. As previously discussed, the WTs can be operated as several different types of “fixed-speed” WTs.

E [Setup] ws1 PI COUPLED SECTION PI CO UP LE D SEC T IO N PI CO U P L E D SEC T IO N PI CO UP LE D SEC T IO N PI CO U P L E D SEC T IO N IniSpd [Setup] ws2 [Setup] ws3 [Setup] ws4 [Setup] ws5 Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM RelSM RelLM BLM Wind Turbine 3 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 4 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 5 ws RelSM e1r IniSpd RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM Wind Turbine 2 ws RelSM e1r IniSpd RelLM BLM IniSpd RelSM RelLM BLM P = 1.857 Q = -1.032 V = 23.66 V A

Figure 26: Wind farm with five WTs connected with cables.

In order to compare, some simulations will also be performed with a larger wind farm with 25 WTs, as illustrated in Figure 27. The large wind farm is implemented as five clusters, which each contains five WTs. Each cluster is modelled as the smaller wind farm presented in Figure 26. However, the WTs are supplied with individual uncorrelated wind speed signals.

Simulations with the large wind-farm model are much more time consuming compared to the wind farm with only five WTs. Therefore, only a few simulations have been made with the large wind farm. The ratings of the VSC-HVDC, and other components, are of course increased in order to match 25 WTs instead of 5 WTs.

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E [Setup] ws 1 PI COUPL E D SE CTIO N PI CO UP LED SECT ION PI CO UP LED SE CTIO N PI CO UP L ED SEC TION PI COUPL ED SEC TIO N IniSpd [Setup] ws2 [Setup] ws 3 [Setup] ws4 [Setup] ws 5 Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM RelSM RelLM BLM Wind Turbine 3 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 4 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 5 ws RelSM e1r IniSpd RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM Wind Turbine 2 ws RelSM e1r IniSpd RelLM BLM IniSpd RelSM RelLM BLM Q = -9.347 V = 32.5 V A PI CO UP LED SE CTIO N PI CO UP LED SECT IO N PI CO UP LE D SE C TION PI CO UP LED SEC TIO N PI COUPL E D SEC TION IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM PI CO UP LED SE CTIO N PI CO UP LE D SECT IO N PI CO UP LED SE CTIO N PI CO UP LE D SEC TIO N PI COUPL ED SEC TIO N IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM PI CO UP LED SEC TIO N PI CO UP LED SE CTIO N PI COUPL ED SEC TIO N PI COUPL ED SECTI ON PI COUPL ED SECTI O N IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM PI CO UP LED SEC TION PI CO UP LED SE CTIO N PI COUPL ED SEC TION PI COUPL ED SECTI O N PI COUPL ED SECTI ON IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM IniSpd RelSM RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM Wind Turbine 1 ws RelSM e1r IniSpd RelLM BLM [Setup] ws6 [Setup] ws 7 [Setup] ws8 [Setup] ws 9 [Setup] ws10 [Setup] ws11 [Setup] ws12 [Setup] ws13 [Setup] ws14 [Setup] ws15 [Setup] ws 16 [Setup] ws17 [Setup] ws 18 [Setup] ws19 [Setup] ws 20 [Setup] ws21 [Setup] ws 22 [Setup] ws23 [Setup] ws 24 [Setup] ws25

Figure 27: Wind farm with 25 WTs connected with cables. Note that this configuration is only used in a small number of simulations and for comparison to the smaller wind farm with five WT.

3.6.1 Simulation setup

In this report several types of “fixed-speed” WTs and configuration will be investigated. In Table 2, an overview of these different basic wind-farm configurations are presented.

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Table 2. Description of wind farm configuration.

No. Description

1 Wind farm ac connected. The small IG is connected and WT are limited aerodynamically by active stall. This setup is intended for lower wind speeds.

2 Wind farm ac connected. The large IG is connected and WT are limited aerodynamically by active stall. This setup is intended for higher wind speeds.

3 Wind farm dc connected. The large IG is connected and WT are limited aerodynamically by active stall. This setup is intended for both low and high wind speeds.

13 Wind farm dc connected. The large IG is connected and WT are limited aerodynamically by pitch control. This setup is intended for both low and high wind speeds.

23 Wind farm dc connected. The large IG is connected and WT are limited aerodynamically by pitch control. Moreover, the slip of the WTs IG is controlled in order to minimize power variations. This setup is intended for both low and high wind speeds.

All simulations are dynamic and last for 300 s (5 minutes) unless otherwise stated. Moreover, all WTs are subjected to the same average wind speed but the “transients”, such as the turbulence, are individual for each WT and uncorrelated. The basic configuration of the wind farm is given in Table 2 and other parameters that vary between the different simulations will be explained where appropriate.

3.7

Example simulations

In the coming chapter the results from several simulations will be put together and presented in figures. However, to make it clearer to the reader some examples of single simulations are provided here. An example of one single simulation is given in Figure 28. In the figure the wind speed, wind farm voltage, frequency, active and reactive power of the wind farm are presented as a function of time. In the figure only 60 s is presented, instead of 300 s that is simulated, in order to make the figure clearer. In this case wind farm configuration 13 (VSC-HVDC and pitch control) is used and an average wind speed of 6 m/s.

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0 10 20 30 40 50 60 0 10 20 W ind s pee d [m /s ] Simulation name: 13_6_40_30 WT1 WT2 WT3 WT4 WT5 0 10 20 30 40 50 60 0 20 40 V ol tag e [ kV ] 0 10 20 30 40 50 60 0 20 40 60 F re que nc y [ H z] 0 10 20 30 40 50 60 0 1 2 Ac tiv e p ow er [ M W ] 0 10 20 30 40 50 60 -1.5 -1 -0.5 0 R eac tiv e p ow er [ M va r] Time [s]

Figure 28: Simulation example with wind farm no. 13 and an average wind speed of 6 m/s.

As seen in Figure 28, the wind farm operates at a low average wind speed and the electric frequency within the wind farm is therefore less than the nominal 50 Hz. This results in that the WT operates at nearly maximum aerodynamic efficiency. To maintain constant V/Hz ratio, the voltage within the wind farm must consequently be less than the rated 33 kV. It can also be seen that both

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the average wind speed slowly reduces. The wind farm controller senses the wind-speed reduction from the measured electric power and reduces both the electric frequency and the voltage in order to track the optimal aerodynamic operating point and meanwhile preserve the V/Hz ratio. A similar simulation with a higher average wind speed is presented in Figure 29.

0 10 20 30 40 50 60 0 10 20 Wi nd s pee d [m /s ] Simulation name: 13_15_40_30 WT1 WT2 WT3 WT4 WT5 0 10 20 30 40 50 60 0 20 40 V ol tag e [ kV ] 0 10 20 30 40 50 60 0 20 40 60 F requ en cy [ H z] 0 10 20 30 40 50 60 0 5 10 15 A cti ve p ow er [M W ] 0 10 20 30 40 50 60 -4 -2 0 Re ac tiv e p owe r [M va r] Time [s]

Figure 29: Simulation example with wind farm no. 13 and an average wind speed of 15 m/s.

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When operating at a high average wind speed the available power in the wind is aerodynamically limited to the rated value. In this case (configuration 13) the WT power is controlled aerodynamically by pitch control. When this occurs, there is no need to run the IGs at variable speed, which can be seen from the frequency being constant at 50 Hz in Figure 29.

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4

Evaluation of dynamic performance

The dynamic performance of a wind farm connected to a VSC-HVDC system will be investigated. Different types of “fixed-speed” type WT will be investigated and compared.

4.1

Produced power

The average wind farm electric power output during a 300 s (5 minutes) simulation as a function of the average wind speed is shown in Figure 26. The average power is measured at the wind farm side, which means that the losses of the connection (ac or dc) to the grid are neglected. In the figure, results from wind farm configuration 1, 2 and 3 are presented, i.e., ac connection with a small IG with lower synchronous speed, ac connection with a large IG and normal synchronous speed and dc connection with a large IG and variable speed from the HVDC-VSC. For all of these three configurations the WTs are limited aerodynamically by active stall. Moreover, in this case the blade angle is controlled with a time constant of 2.0 s.

5 10 15 20 0 2 4 6 8 10 12 P rod uc ed po w er [ M W] Wind speed [m/s]

Wind farm no. 1 Wind farm no. 2 Wind farm no. 3

Figure 30: Produced power for three configurations of the wind farm as a function of the wind speed. The produced power is the average power of a 300 s (5 minutes) simulation at the corresponding average wind speed.

As already mentioned a typical (ac connected) fixed-speed WT has often two different synchronous speeds. This means that the WT can operate with a

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lower rotor speed at lower wind speeds and thereby increase the aerodynamic efficiency. This type of WT constitutes of a mixture of wind farm configuration 1 and 2, i.e. configuration 1 is used at low wind speeds and configuration 2 at higher wind speeds. For the WT investigated here an average wind speed of approximately 8 m/s determines which IG (or the number of poles) that should be connected.

In Figure 26 it can be seen that wind farm configuration 3 (dc connected wind farm) where the variable speed is achieved with the VSC-HVDC produces the same amount of power as the combination of wind farm configuration 1 and 2. Although it might be obvious, Figure 26 shows that a wind farm that utilize a VSC-HVDC rectifier in order to control the wind farm grid frequency (and thereby also the rotor speed of the WT) can utilize simpler “fixed speed” WT without, for instance, any pole-changing mechanism, and still produce the same amount of power (excluding the transmission of the power to the grid). This means that the cost of the electrical system of the WT can be reduced with approximately 10 % in comparison to a generator with a pole-changing mechanism [5]. According to [5] the generator system of a 750-kW stall-controlled WT costs 7.5 % of the total WT.

4.2

Power variations

As described in Section 2.3 different aerodynamic power limitation methods causes different amount of power variations due to wind gusts. In this section the average, maximum, minimum and the standard deviation of the produced power for different configurations of the wind farm will be investigated for certain cases. The average, maximum, minimum and the standard deviation of power are determined from 300 s (or five minutes) long simulations of the wind farm with five WT, as the ones presented earlier, unless otherwise stated.

Figure 31 shows the average, maximum, minimum and the standard deviation of the produced power as a function of the blade (pitch) angle time constant. Three different wind farm configurations have been simulated, each simulation lasts for 300 s, each WT receives the same uncorrelated wind during each simulation and the average wind speed equals 20 m/s. The presented power variations are the total power produced by all WTs.

It can be seen in the figure that the average power production of all simulations are approximately equal. The small differences are within the error margin of the wind-farm model. For the turbines utilizing active stall (configuration 3) the blade (pitch) angle time constant has been simulated up to 5 s, since the main objective with active stall is to adjust output power to the rated (for stall controlled WT the power output tends to slightly drop at higher wind speeds). For the pitch-controlled WT (configuration 13 and 23), on the other hand, the blade (pitch) angle time constant is shorter since the power variations (due to wind gusts) are relatively large. Hence, it is important to limit the power variations and therefore the time constant is naturally shorter for pitch-controlled WT.

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 A ve rag e ac tiv e po w er [ M W ] Wind speed: 20 m/s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 Ma xi mu m ac tiv e pow er [ M W] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 Mi ni m um ac tiv e po w er [ M W ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 S ta nd ar d de vi at io n ac tiv e po w er [ M W]

Pitch control time constant [s]

Figure 31: Power variations for three configurations of the wind farm as a function of the pitch angle control time constant for an average wind speed of 20 m/s.

As expected, Figure 31 shows that the WT with pitch control (configuration 13) has the largest power variations. The maximum power for configuration 13 is 15 MW, which corresponds to 130 % of the rated power of all WTs. If the pitch-controlled WT is equipped with variable speed, such as slip control as in configuration 23, the power variations can be significantly reduced. This can be seen in the figure as well. The reactive power consumed by the IG

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depends on the operating condition, see Section 3.4. Therefore, the maximum apparent power is of interest, since it will determine the size of the VSC-HVDC system. The corresponding average, maximum, minimum and standard deviation of the apparent power are shown in Figure 32.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 5 10 15 A verag e ap pa re nt po w er [ M V A ] Wind speed: 20 m/s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 10 12 14 16 18 Ma xi mu m ap pa re nt p ow er [ M V A ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 4 6 8 10 Mi ni mu m ap pa re nt p ow er [ M V A ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 S tan da rd d ev ia tio n ap pa re nt p ow er [ M V A ]

Figure 32: Apparent power variations for three configurations of the wind farm as a function of the pitch angle control time constant for an average wind speed of 20 m/s.

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As seen in Figure 32, the maximum apparent power depends on the pitch control time constant for wind farm configuration 13. For configuration 3 and 23 the maximum apparent power is not to that extent dependent on the pitch control time constant. For comparison reasons, the average, maximum, minimum and standard deviation of the power on a single WT, in the wind farm, are shown in Figure 33. The average output power of the WTs is approximately 2.3 MW. 0 0.5 1 1.5 0 1 2 3 A ve rag e ac tiv e po w er [ M W ] Wind speed: 20 m/s

0 0.5 1 1.5 0 1 2 3 4 Ma xi mu m ac tiv e p ow er [MW ] 0 0.5 1 1.5 0 1 2 3 Mi ni mu m ac tiv e p ow er [ M W] 0 0.5 1 1.5 0 0.5 1 S tan da rd de vi at io n ac tiv e p ow er [ M W]

Figure 33: Power variations from a single WT for three configurations of the wind farm as a function of the pitch angle control time constant for an average wind speed of 20 m/s.

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From Figure 33 it is seen that the maximum power of the active stall WT (configuration 3) is 135% of the WT rated power (2.3 MW) while for the pitch controlled WT (configuration 13) it is up to 175 % of the rated power. If the pitch controlled WT have variable slip IG (configuration 23), then the maximum power can be very close to the rated power if the pitch control time constant is short. These power variations are larger compared to above results for an entire wind farm, which is due to that the individual WTs do not produce maximum power at the same time instant, so the power variations decrease with increasing number of WTs. This phenomenon is further illustrated in Figure 34, were the wind farm has been increased from 5 to 25 WTs. Otherwise the conditions are as in Figure 31. Here the maximum power of the active stall WT (configuration 3) is close to the rated power of the wind farm (57.5 MW) while for the pitch controlled WT (configuration 13) the maximum power is 110 % of the rated power of the wind farm.

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 25 50 75 A verag e ac tiv e po w er [ M W ] Wind speed: 20 m/s

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 25 50 75 Ma xi mu m ac tiv e p ow er [ M W ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 25 50 75 Mi ni mu m ac tiv e pow er [M W] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 S tan da rd de vi at io n ac tiv e p ow er [M W ]

Figure 34: Power variations for three configurations of a large wind farm as a function of the pitch angle control time constant. The average wind speed equals 20 m/s and the wind farm contains 25 WTs.

In Figure 35 the frequency spectrum of the power variations in percentage of the average produced power are shown for 1, 5 and 25 WTs. The wind farm configuration 13 is used and the WTs operate at an average wind speed of 20 m/s.

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10-3 10-2 10-1 100 101 102 10-5 10-4 10-3 10-2 10-1 100 101 P owe r v ari at io n [ % ] Frequency [Hz] 1 WT 5 WTs 25 WTs

Figure 35: Frequency spectrum of the power variations for one, five and twenty five WTs in percentage of average produced power. The WT:s operates at an average wind speed of 20 m/s.

As seen in Figure 35 the there is a peak at approximately 0.5 Hz. This peak arises from the mechanical system of the WTs. The influence of the mechanical system is further investigated in Section 4.3. It is also realized from the figure that the relative variation in power will be smaller with number of installed WTs. Finally in Figure 36 the average, maximum, minimum and standard deviation of the power from several 300 s long simulations are shown as a function of the average wind speed. Here the pitch control time constant set constant, 2 s for the configuration 3 (active stall) and 0.25 s for configuration 13 and 23 (pitch control).

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5 10 15 20 0 5 10 15 A ver ag e a ct iv e po w er [ M W ]

5 10 15 20 0 5 10 15 Ma xi mu m ac tiv e p ow er [M W ] 5 10 15 20 0 5 10 15 Mi ni mu m ac tiv e p ow er [M W ] 5 10 15 20 0 0.5 1 1.5 S tan da rd de vi at io n ac tiv e p ow er [M W ]

Average wind speed [m/s]

Figure 36: Power variations for three configurations of the wind farm as a function of average wind speed. The pitch control time constant is equals 2 s for the configuration 3 (active stall) and 0.25 s for configuration 13 and 23 (pitch control).

In Figure 36 it is seen, as before, that configuration 13 has the highest maximum power and the largest standard deviation of the power.

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4.2.1 Influence of the phase compensation

In this section the influence of the phase compensation (capacitor bank) at the individual WT will be investigated. This means that similar simulations will be performed here but the phase compensation (capacitor bank) at the individual WTs will be removed. In Figure 37 a comparison of the average, maximum, minimum and standard deviation of the apparent power for configuration 13 (pitch control) with and without phase compensation is presented. The differences between average, maximum and minimum value of the apparent power, for the case with and without phase compensation, are rather constant as seen in Figure 37. The capacitor banks at the WTs produce in total 3.4 Mvar, at rated voltage and frequency, which explains the difference. Please note that in Figure 37 the apparent power is shown and not the reactive power. The standard deviation of the apparent power is however the same with or without phase compensation. This is also true for configuration 3 (active stall) and 23 (pitch and slip control) even though it is not presented here. This means, at least from a power variation point of view, that the phase compensation is a design issue. Either phase-compensation capacitors are used or the VSC-HVDC rectifier has to compensate for the total reactive power. If the VSC-HVDC rectifier compensates for the reactive power, the current rating of the VSC-HVDC rectifier has to be increased accordingly. Further, the losses in the VSC-HVDC system will increase due to the increased amount of reactive power output of the VSC.

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 A ve rag e a ppa re nt pow er [ M V A ] Wind speed: 20 m/s Phase compensation No phase compensation 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 12 14 16 18 Ma xi mu m app ar ent po w er [ M V A ] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4 6 8 10 12 Mi ni mu m ap par ent po w er [ M V A ] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 S ta nda rd dev ia tion ap par ent po w er [ M V A ]

Figure 37: Apparent power variations for configuration 13 (pitch control), with and without phase compensation at the individual WTs, as a function of the pitch angle control time constant. The average wind speed equals 20 m/s. 4.2.2 Influence of the IG flux level

By reducing the flux level in the IG the efficiency of the IG can be improved [14]. Therefore, the flux levels of the IG influence on the power variations will be investigated. If the flux level is decreased by reducing the stator voltage

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the damping of the IG is increased [14]. This can also be realised from Figure 38 were the torque-speed characteristics of the IG is shown for different flux levels. 0 500 1000 1500 2000 -3 -2 -1 0 1 2 3 Speed [rpm] T or que [ pu] 1500 1505 1510 1515 1520 1525 -2.5 -2 -1.5 -1 -0.5 0 Speed [rpm] T or que [ pu] ψ=_ψ_N ψ=1.1_ψ_N ψ=0.95_ψ_N

Figure 38: Torque-speed characteristics for an induction machine at different flux levels. Right figure is a close up of the left figure. The flux level is

adjusted with the stator voltage. Note that motor reference is used.

If the flux level is increased the pull-out torque will be higher and the torque-speed characteristic will be stiffer (a torque-speed change results in a larger change in torque) as seen in Figure 38. On the other hand if the flux level is decreased the pull-out torque will be lower and the torque-speed characteristic will be softer (a speed change results in a smaller change in torque).

In Figure 39 a comparison of the average, maximum, minimum and standard deviation of the apparent power for configuration 13 (pitch control) at different flux levels is depicted. Even though the difference in average, maximum, minimum and standard deviation of the apparent power is small, it can, as expected, be seen in the figure that the power variations is increased with the flux level. However, decreasing the flux level in order to increase the efficiency of the IG must be done with care since the pull-out torque also is reduced.

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 5 10 15 A ver ag e a ppa re nt po w er [ M VA] Wind speed: 20 m/s 100 % flux 110 % flux 95 % flux 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 10 12 14 16 18 Ma xi mu m ap pa ren t po w er [ M V A ] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 4 6 8 10 12 Mi ni m um appa re nt po w er [ M V A ] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.5 1 1.5 2 S tan da rd de vi at io n app ar ent p ow er [ M V A ]

Figure 39: Apparent power variations for configuration 13 (pitch control), at different flux levels, as a function of the pitch angle control time constant. The average wind speed equals 20 m/s.

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4.3

Impact of V/Hz controller time constant on system

stability

As already mentioned in Chapter 3, in this report the mechanical system of the induction generator in the WT is represented as a two mass model. The model is depicted in Figure 40. As shown, the two rotating masses (representing the turbine mass, JT, and the generator mass, JG) are connected by an elastic shaft section, represented in the figure by a spring coefficient KTG, and a mutual damping term DTG. Further, to take into account the braking torque due to windage and friction that is naturally present in a rotating mass, a self damping term (denoted in the figure as DT and DG for the turbine and the generator, respectively) has also been introduced.

Figure 40: Mechanical model of induction generator.

Figure 41 shows the frequency response of the mechanical system depicted in the figure above. The transfer function considered in the figure is from the electrical torque Te to the rotor speed ωr. From the figure, it is possible to observe that the mechanical system is characterized by a resonant peak having characteristic frequency of 1.7 Hz, as expected from the parameters selection described in Section 3.3. Further, the frequency response presents a notch at 0.55 Hz, due to a zero in the investigated transfer function. With the selected parameters, it has been found that this zero is poorly damped, characterized by a damping factor of 0.0045 (which leads to an overshoot of 98.6%). This is due to the fact that the real part of the zero is constituted by the damping terms only (typically very small in an actual system), while its imaginary part is mainly dependent on the inertia of the turbine (high for wind power units) and on the elastic spring constant:

N Nm T N TG T TG T TG T

S

J

H

K

H

D

z

2 2 2 , 1

2

1

,

4

8

)

(

ω

=

−

+

±

−

=

The presence of the zero in the transfer function for the mechanical system has a big impact on the stability of the investigated system. With the wind farm connected to the VSC-HVDC, it has been found through dynamical simulations that, when low values of the V/Hz controller time constant were selected, the simulated system was unstable. From a more detailed analysis,

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it was observed that the system was self-excited and that the electrical torque in the generator units was affected by growing oscillations having characteristic frequency of 0.55 Hz. These oscillations built up from a steady-state condition and the rate of change in their amplitude was dependent on the operating conditions and on the V/Hz control setting. In particular, the system resulted unstable for time constants for the V/Hz controller below 30 s. As an example, Figure 42 shows the electrical torque for one of the generation units. The system simulated here is the DC connected wind farm case with active stall; the average wind speed of the site is 5 m/s, while the time constant for the V

DC Connected Wind Farm