Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/we.1670
RESEARCH ARTICLE
A modular series connected converter structuresuitable for a high-voltage direct currenttransformerless offshore wind turbineS. Gjerde1, K. Ljøkelsøy2, R. Nilsen3 and T. Undeland1
1 Norwegian University of Science and Technology, 7491 Trondheim, Norway2 Sintef Energy Research, 7465 Trondheim, Norway3 Wartsila Norway, 7041 Trondheim
offshore wind power; modular power electronic converter; transformerless, DC grid
Correspondence
S. Gjerde, Ph.D.-student, Dep. of Electric Power Engineering, Norwegian University of Science and Technology.E-mail: [email protected]
Received 15 January 2013; Revised 28 June 2013; Accepted 21 August 2013
NOMENCLATURE
N number of modulesSubscript i ; j parameter related to module i ; j
Subscript n rated parameteric;i DC-capacitor current in moduleidc;i DC-current of moduleid ; iq d/q-axis current in one moduleiq ; bal DC-bus voltage control output
!e electrical, radial frequency i stator segment flux linkage
mem;ref torque referencemq;i q-axis modulation index for a converter unitn per unit speed
pac; i AC power in moduleptot total turbine output powerrs;i stator segment resistancexs;i synchronous reactance in one stator segment
Ul l;rms line RMS voltage of one moduleudc;i DC-bus voltage in module
udc;ref DC-voltage control referenceudc;tot total HVDC-grid voltageud ; uq stator voltages of one module, in the dq-reference frame
A modular series connected converter structure S. Gjerde et al.
1. INTRODUCTION
1.1. Motivation
Offshore wind power has emerged as one of the most promising renewable energy resources. In Europe, large areas in theNorth Sea have been identified as promising sites. There are already several offshore wind farms established in Denmark,Sweden, Germany and the UK, and more will come. Offshore wind power offers better, more stable wind conditions thanonshore, and less political issues in many places.
However, while onshore wind power technology is approaching maturity,1 offshore wind power emerges in the particularlocations mentioned previously because of good financial support schemes. Without these, taking the marginal profitablewind power business offshore would be difficult.
Wind turbines increased exponentially in size until the development stopped in 2003–2004,2 mainly because of logis-tics, but also visual impact. These limitations do not apply to the same extent offshore. Additionally, because increasing theturbine rating is believed to decrease the energy costs of offshore wind power,3 there is again a strong motivation presentfor developing turbines rated for 10 MW or even more. The background for the cost reduction is the nature of offshoreinstallations: Installation, and operation and maintenance (O&M) cost depends on number of units as much as the totalinstalled power. However, up-scaling of today’s turbine technology introduces new challenges, such as reliability of gearedconcepts4 and the weight of the nacelle. According to Zhang et al.,5 the weight of a state-of-the-art, 10 MW direct drivepermanent magnet synchronous generator alone will go beyond 300 tons.
The standard, low operating voltage (690 Vrms) introduces another issue when extrapolating today’s standard solutionsto 10 MW. At this voltage, the cables from the nacelle to ground will be bulky, heavy and stiff. Medium voltage solutionsare considered, but this will not make the distribution transformer superfluous. Therefore, it has been proposed to have thetransformer in the nacelle, which adds weight to the top mass. This results in a more demanding mechanical construction.Equally important is the O&M; when a transformer fails, a large offshore crane is necessary for maintenance. These cranesare both scarce and expensive today. It is therefore believed to be beneficial both for the turbine itself and O&M to omitthis transformer.
With this as background, this work focuses on analyzing a modular series connected converter suitable for the 100 kVdctransformerless concept intended for a large, offshore wind turbine.
1.2. Overview of research on transformerless concepts
A brief overview of the existing research on transformerless technologies is presented in the following: in the followingreferences,6,7 a special generator is used (concept 1 in Table I, Figure 1). The generator has multiple concentrated statorcoils that feeds single phase AC/DC-converters. The rectified output is fed to H-bridge modules. A distribution voltagelevel is synthesized with a cascaded H-bridge inverter. Module fault tolerant and distributed controllers for this concept areanalyzed in the following references.8,9 A similar converter concept is proposed in the following references10–12 (concept2). In the work of Dheng and Chen,13 a system with several six-phase PMSGs in parallel is proposed (concept 3). The con-verter solution is similar to concept 1 and 2. Another concept is built around three-phase converter units14,15 (concept 4).This system consists of four, three-level neutral point clamped converters. The output voltage is synthesized by connectingthe DC-buses in series, achieving 23:6 kVdc . A distinctively different approach is the series connection of turbines16–19
(concept 5): a PMSG is controlled by a (reduced) matrix converter, and the transmission voltage is increased by connectingturbines in series. The concept is not truly transformerless as it employs a compact, light weight, high-frequency trans-former to boost the output voltage from each turbine. The series connection of turbines has received considerable attention,and also other converter topologies have been proposed: cascaded pulse-width modulation current source converter,20
thyristor rectifier21 and diode bridges with compensation circuit.22 Small clusters of wind turbines with variable frequencyminigrids, interfaced to the series connection by one current source converter per cluster is proposed in the followingreference.23
Another solution, based on more unconventional generator technologies is concept 6, which provides high voltagedirectly from cable wound stator windings.24 A complete different approach is presented in the work of O’Donnell etal.:25 an electro static, variable-capacitance generator is proposed. The potential is 100–300 kVdc (concept 7).
1.3. Grid connection
Offshore, it has generally become accepted that high-voltage direct current (HVDC)-transmission is the only reasonablechoice beyond a certain distance from the shore.26 The wind farm internal collection grid has so far been AC based.However, recent years have shown a growing interest in DC-distribution grids.27–31 An increased system efficiency isthe main motivation,27 in addition to reduced investment costs, i.e., the DC/AC-conversion stage in each turbine can be
VSC, voltage source converter; CHB, cascade H-bridge.
Figure 1. Different converter topologies proposed for transformerless wind turbine concepts. The figures are taken from therespective references.
avoided, and only two conductors are needed for the connecting cables. The transformerless solution is analyzed assuminga DC-collection grid with central grid voltage control.
1.4. Contribution and outline of the paper
The modular series connected converter of concept 4 has earlier been identified as a promising solution for the systemaddressed in this work.32 The control system was proposed in the work of Carmelli et al.14 and further analyzed anddeveloped in the following references.32–34 In this work, the properties and limitations of the generator/converter systemare analyzed for different control strategies. Because of the dimensions of the machine design, parameter deviations canoccur between the stator segments, especially concerning the stator flux linkage. Therefore, a steady-state model relatingthe DC-bus voltage imbalance and these parameter deviations is developed. The findings are further investigated throughdynamic simulations in EMDTC/PSCAD, where emphasis is on differences in the stator segment flux linkage. Impacts ofthe control strategy are also evaluated by simulation. Finally, experimental results from a 45 kW laboratory model of thesystem are used to verify the theoretical results.
2. SYSTEM DESCRIPTION
2.1. The generator
An axial flux, ironless stator PMSG (AF-IL-PMSG)35 is the base for this work. The ironless stator concept is chosenbecause it has a higher power-to-weight ratio than conventional PMSGs.36,37 The AF-IL-PMSG possesses also severalother interesting features that will be discussed in this section.
The AF-IL-PMSG was initially designed for a low weight, three-phase medium voltage system in a direct drive offshorewind turbine. However, a modular stator, with N three-phase groups can easily be made by reconfiguring the windings like
A modular series connected converter structure S. Gjerde et al.
(a) (b)
Figure 2. (a) Overview of the analyzed generator/converter system, with N system were modules and (b) the detailed view of oneconverter unit (upper part) and a principal sketch of stator/rotor alignment with two rotor disks (lower part).
illustrated in Figure 2(a). The absence of iron in the stator, and the concentrated coils results in a weak magnetic couplingbetween the machine sections. This simplifies the control system.32
The generator considered here has a large diameter and large air gap. Combined with axial rotor displacement,Figure 2(b), this can result in notable parameter differences between the stator segments. The stator segment flux linkage( i ) could therefore vary substantially between the segment, resulting in different power produced in the modules.
Other generator designs have not been able to insulate for high voltages in an efficient way, to the authors knowledge.As a result, high voltage electrical machines have been large and heavy, making them unsuitable for wind turbines. How-ever, a solution for efficient high-voltage machine insulation based on the AF-IL-PMSG presented previously is proposedin the work of Olsen et al.38 The basic principle is to divide the voltage into several levels and insulate between these.Arranging the generator/converter as in Figure 2(a) results in splitting the electric field as required. The voltage imposedon each winding set is a DC-field (phase–ground) with a superimposed AC-field (phase–phase). The amplitude of thisAC-field, and hence module voltage, is directly linked to the insulation levels in the machine and the level to which it canbe optimized.
2.2. Converter topology
The series-connected modular converter adapted in this work14 is based on three-phase voltage source converter (VSC)-units that are series connected on the DC-side. This allows for a partitioning of the DC-voltage as required by the insulationsystem, resulting in a high DC-voltage to ground with a superimposed medium AC-voltage (phase–phase).
From an insulation perspective, the lower the amplitude of the line voltage, the better. Therefore, the number of VSC-units is increased from 414 to N to exploit the full potential of the idea. In38, N D 9 was found to yield a suitable trade-offbetween insulation thickness and complexity. This results in several floating modules, as opposed to that in the work ofCarmeli et al.14 where all the modules are connected to a fixed potential, i.e., DC+/ground/DC-. The floating modulesresults, potentially in a more challenging control coordination.
Based on N D 9 modules,39 showed that a multilevel converter unit would be beneficial for the system overall design.However, for the work presented here, there is no practical difference between a multilevel converter and two-level VSC.To simplify, the latter is used for this analysis. A complete optimization of the generator and converter system could alsoresult in N¤ 9, especially taking into account the possibility of a simpler, robust converter structure. The presented resultsare valid for any value of N .
The converter and segment parameters used in the simulations are based on N D 9. But since the generator prototypeused for experimental verification only consists of three stator segments, the system simulations were also limited to threemodules.
S. Gjerde et al. A modular series connected converter structure
3. STEADY STATE CHARACTERISTICS
3.1. Steady state model
It was in the previous sections argued that the dimensions of the generator can cause parameter deviations between the dif-ferent segments, leading to different power in the different modules, if not controlled. Therefore, a model which describesthe consequences on the operation of the converter chain of such a parameter deviation is developed. The model describesthe power in each stator segment’s impact on the distribution of module DC-bus voltages. A different power would leadto deviations in the DC-bus voltages of the modules since the series connection imposes equal DC-current for all the con-verter units, in quasi-steady state. The relation between the system parameter deviations and the DC-bus voltage imbalanceis investigated in this section.
The basic, steady-state relation between udc;i and the total DC-link voltage, 1 in per unit, is found by combiningidc;i D igrid (quasi-steady state), and that igrid D ptot /udc;tot :
udc;i � idc;i D pdc;i
) udc;i Dpdc;i
idc;iDpdc;i
igrid
) udc;i Dpdc;i
ptot� udc;tot
(1)
The total power equals the sum of the power extracted from each module, pdc;i . As a consequence, if all converter unitsdeliver the same power to the DC-link, all bus voltages will have the same value.If the converter efficiencies are neglected, the power in each module is given by 2, where n is the per unit speed, commonfor all segments, and i is the stator segment flux linkage.From 1, it can further be concluded that the DC-bus voltage in a a specific module depends on the relation between themodule power and average power extracted from all modules.The total power in the turbine can, if neglecting losses, be expressed as
ptot D p1C p2C : : :C pN
pi DmemnD i � n � iq;i
) ptot D n � . 1iq;1C : : :C N iq;N /
(2)
1 and 2 combined show that the DC-bus voltage is directly depending on the ratio between the q-axis currents in the statorsegments. As a direct consequence, the DC-bus voltage of a module can be adjusted by adjusting the corresponding currentwith respect to the average current.
An additional, important observation is that if one segment/module experiences problems that leads to constrains in thecurrent, the power in that module is reduced. Following from this, the corresponding DC-bus voltage is also reduced, sincethe DC-current is constant. This voltage reduction will continue until the bus voltage is equal to the generator voltage, whenthe freewheeling diodes start to conduct uncontrolled. Control of the converter module is then lost, and the bus-voltage willbe given by 3 for low current, and 4 for high loading:
Udc;i Dp2 �Ul l;rms;i (3)
Udc;i D3p2
��Ul l;rms;i (4)
A more detailed model, taking into account module physical system parameter deviations, is presented in 5. id=0 andcurrent control are pre-requisites for the development. It is assumed that all converter modules are operated with the sametorque reference, and no compensation for parameter differences is implemented. Hence, all three-phase stator segmentscarry the same current. The variables are defined in Figure 2(a). A detailed derivation is given in Appendix A.
udc;i D�i � .�rs;i iq C n i /PN
jD1 �j � .�rs;j iq C n j /� udc;tot (5)
From 5, it can be observed that the DC-bus voltage in one module depends on the relation between a parameter of thatspecific module and the average of all the modules. Additionally, differences in stator flux of the segments will only impactthe imbalance when the machine is rotating. Equally, stator losses will only affect the imbalance when there is currentflowing.
A modular series connected converter structure S. Gjerde et al.
3.2. Impact of the parameter variations on DC-bus voltages
The variations in the converter unit DC-bus voltage as function of parameter deviations (From the nominal values, Table II)was assessed for different turbine operating points. This was carried out by solving 5 for a range of variations in oneparameter for one module at the time. The results are presented in Figure 3(a)–(f).
At cut-in speed (0.3 pu), the parameter that has the largest impact is the converter unit efficiency, �i , Figure 3(e), whilethe stator segment resistance rs;i has a small impact, Figure 3(a). At nominal speed, the stator flux linkage, i has asubstantial effect, Figure 3(d) while the impact of the module efficiency is unchanged, Figure 3(f). At nominal speed, theimpact of the stator resistance can be neglected Figure 3(b).
4. CONTROL SYSTEM
4.1. Control system design
A suitable control system (Figure 4(a)) that complies with the basic demands of the system was first proposed in the work ofCarmeli et al.,14 and further analyzed and developed in the following references.32–34 A brief description is given here forthe completeness of the text. The control is a modular system, where each module is a standard three-phase VSC-controlsystem, operating asynchronous with respect to the other modules, Figure 4(b). For torque control is the indirect speedcontrol maximum power point tracker40 implemented. The interface between the main- and module control is the torquereference mem;ref and DC-voltage reference, udc;ref .
It was stressed in Section 2 that control of the DC-bus voltage amplitude is essential for the insulation system design.This control takes the form of a cascaded controller, with the converter unit DC-voltage control in cascade with the q-axiscurrent control in each module. A voltage droop control in the master regulates the udc;ref set-point on the basis of the sumof the balance contributions. The sum of the balance control outputs should be zero under normal operating conditions33.
The sum of the turbine torque reference, mem;ref , and DC-voltage control output, iq;bal;i , is limited by the modulemaximum current level.
4.2. Control strategies
4.2.1. Constant power control of converter units.In the following, the stability of the converter chain operation is assessed without the DC-bus voltage control imple-
mented, to characterize the basic dynamics of the system. The small-signal stability for the DC-bus voltage of the converterunit in the series connection is discussed with respect to perturbations in the bus voltage. For the completeness of the anal-ysis, both generator and motor operation of the system are addressed. In wind turbines, motor operation of the machine canoccur during special operating conditions, for instance under start-up.
Without DC-bus voltage control, the quasi-steady state characteristic of a converter unit is that of a constant-powerload.41 That is, assuming the power reference set-point is constant for a period, changes in the rotor speed will be compen-sated with changes in the torque to maintain constant power. Also, the DC-bus voltage will be given as function of the DCcurrent, and therefore the torque, Figure 5.
In generator mode, the power balance for one module with pac;i Dconstant can be expressed by 6:
udc;i � idc;i D pac;i
idc;i D ic;i C igrid
) udc;i � .ic;i C igrid /D pac;i
(6)
Table II. Nominal parameters for theoretical calculation ofDC-voltage imbalance.
Parameter Value
Stator resistance, rs 0.02 [pu]Rated efficiency, �n 98 %Stator rated flux, n 1.0 [pu]Number of modules, N 9
S. Gjerde et al. A modular series connected converter structure
0.010.02
0.030.5
10.9
1
1.1
r s,i [pu] r s,i [pu]
i q,i [pu]
i q,i [pu] i q,i [pu]
i q,i [pu]
i q,i [pu]i q,i [pu]
u dc
,i [p
u]
u dc
,i [p
u]u
dc,i
[pu]
u dc
,i [p
u]
u dc
,i [p
u]u
dc,i
[pu]
(a)
0.010.02
0.030.5
10.9
1
1.1
(b)
0.90.95
1.10.5
10.8
1
1.2
ψ i [pu] ψ i [pu]
(c)
0.90.95
1.10.5
10.8
1
1.2
(d)
0.90.950.5
10.8
0.9
1
1.1
η i [pu] η i [pu]
(e)
0.90.950.5
10.8
0.9
1
1.1
(f)
Figure 3. The DC-bus voltage in one module as function of its varying parameters from the nominal parameter in a system withnine modules. (a) Stator resistance at 0.3 pu speed, (b) stator resistance at nominal speed, (c) Magnetization at 0.3 pu speed, (d)
magnetization at nominal speed, (e) efficiency at 0.3 pu speed and (f) efficiency at nominal speed.
(a) (b)
Figure 4. (a) Main control system structure for the modular converter system. (b)Structure of the control system associated witheach module in the converter chain.
A modular series connected converter structure S. Gjerde et al.
−1.5 −1 −0.5 0 0.5 1 1.50.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
idc [pu]
u dc [p
u]
pac,g
= 1.0 pu
pac,g
= 0.7 pu
pac,m
= 1.0 pu
pac,m
= 0.7 pu
udc
= 1.0 pu
udc0
,idc0
1audc0
,idc0
1b
2b
2a
generator modemotormode
3a
pac
=1.0u
dc,maxpac
=1.0
current limit
udc,min
Constant voltagecontrol strategy
current limit
pac
=0.7p
ac=0.7
3b
Figure 5. Constant power load, voltage-current curve for generator (positive idc) and motor mode (negative idc), given for power of0.7 and 1.0 pu. Voltage and current limits are marked. The DC-voltage small-signal stability is indicated by the numbered points, as
described in the text.
Where
dudc;i
dtDic;i
c(7)
And igrid is constant due to the series connection. By combining these, 8 is obtained:
udc;i � .igrid C ic;i /D pac;i
udc;i �
�igrid C c
dudc;i
dt
�D pac;i
(8)
From 8 (Figure 5), it can be seen that a small positive disturbance �udc (point 1a) will lead to an absolute increase in the
current (2a) and a negative dudcdt
(3a). The DC-bus voltage converges towards a stable value, and it can be concluded thatthe generator mode is self stabilizing.
The motoring mode can be explained by the same reasoning as for the generator mode but changing the signs of thecurrents according to motor operation. This results in 9:
udc;i � .igrid � ic;i /D pac;i
udc;i �
�igrid � c
dudc;i
dt
�D pac;i
(9)
A small negative voltage disturbance (point 1b, Figure 5) results in an increase in current (2b) that is followed by a
negative dudcdt
(3b). This causes the DC-bus voltages to diverge in time, and the operation is unstable. Since there is nonatural border between motor and generator mode with active converter units, the system can end up in motoring mode,and DC-voltage control is necessary to guarantee stable operation.
4.2.2. Natural equalization of bus-voltages without DC-voltage control.In Section 4.2.1, it was demonstrated that when operating in generator mode, the system is naturally stable. Additionally,
the system is naturally balanced with respect to DC-voltage disturbances when all modules are identical.This can be explained as follows: the current in a module is described by 10.
S. Gjerde et al. A modular series connected converter structure
The capacitor current is proportional to dudcdt
, and steady state demands
idc;i .t/D igrid .t/
) idc;i .t/Duq;i � iq;i
udc;i
)uq;1 � iq;1
udc;1Duq;2 � iq;2
udc;2: : :D
uq;N � iq;N
udc;N
(11)
Assuming an ideal current control with identical reference simplifies 11. Introducing uq;i D mq;i � udc;i leads to thefollowing condition for steady state:
mq;1.t/Dmq;2.t/ : : :Dmq;N .t/ (12)
The modulation index, mq;i is a function of udc;i , xs;i , i and rs . If the latter three parameters are identical for allmodules, the only situation that can fulfill 12 is when
udc;1 D udc;2 : : :Dudc;tot
N(13)
4.2.3. Feasible control strategies.The control strategy implemented in this work is balanced DC-bus module voltages for minimal insulation stress. The
consequences of this strategy are treated in detail in the following sections of the paper. However, with the implementedcontrol structure, several other strategies can be executed. This can be carried out by generating different set points forudc;ref for the different modules, depending on the state of the system. Possible strategies are the following:
� Equal AC current: The DC voltage is adjusted so that the AC current is equal in all converters. This ensures even lossdistribution in the winding.
� Winding temperature: Uneven losses and uneven cooling may result in uneven temperature distribution among thegenerator winding or converter modules, even with equal AC currents. The segment with the highest temperature willlimit the maximum power, so by reducing the DC voltage for this section, its power and AC current can be reduced.This leads to lower losses, which reduces its temperature.
� Mechanical stress: A mechanical model of the generator may be utilized to estimate the the forces and deformations inthe construction caused by the torque. This can be used to adjust the torque in the modules independently to improvethe force distribution and to counteract imbalances in the generator assembly.
� Oscillation damping: A large mechanical system such as a wind turbine may be exposed to poorly damped oscilla-tions in the generator itself, the turbine blades, the shaft or the tower. These oscillations may be detected by straingauges, displacement measurements or other methods. The generator control system can be used for active damp-ing by adding frequency components to the reference signals that makes the generator windings create forces thatcounters the oscillations. Internal oscillations in the generator and its support structures may be handled by individualdamping signals for each section, without affecting the total power flow.
� Diode rectifier mode: This operation mode may occur when the converters transistors are disabled so the free-wheelingdiodes of the VSC carry the current. The generator current waveform will now be is trapezoidal, and is determinedby the DC link current. The module DC-bus voltage is given by the generator speed and the voltage drop in the statorinductance. In this mode, variations in induced voltage are directly translated into power differences. As the DC linkvoltage varies with load and speed the DC voltage across the insulation will vary. The diode rectifier mode voltagecorresponds to the minimum DC-bus voltage for controlled converter operation.
� Over voltage protection: This operation mode should have priority over the other modes and alters the set points forthe module DC-bus controllers to save the converter modules from dangerous operating conditions.
5. SIMULATIONS
5.1. Simulation model
The turbine was simulated using EMTDC/PSCAD. To implement the system, one synchronous generator model with fixedexcitation was used for modeling each segment33, and ideal switches were used to model the insulated gate bipolar transis-tors (IGBT). The grid was considered to be a stiff DC voltage, and a pitch controller was implemented for power control.A three-module version of the system was used to reduce the computational effort. The scaling parameters were DC-linkvoltage and total system power. The simulation parameters are given in Table III.
A modular series connected converter structure S. Gjerde et al.
Table III. Simulation parameters.
Turbine/generator parameter Value Converter parameter Value
Rotor swept area 17683 m2 DC-link voltage Udc 11.11 kVMechanical time constant �m 3.5 s DC-link capacitor Cbus 340 �FTurbine rated wind speed 13 m/s Nominal modulation index mn 0.95Generator segment nominal power 1.11 MVA Switching frequency fsw 1.0 kHzNominal voltage Ull;rms 6.46 kV DC-bus controller gain, Kp;dc 2.14Stator resistance rs 0.02 pu DC-bus integral gain, Ki;dc 1.56Synchronous reactance xd = xq 0.33 puGenerator nominal frequency fn 29.6 Hz
15 20 25 308
9
10
11
12
13
14
Udc
[kV
]
Time [s]
Udc,1
Udc,2
Udc,3
(a)
15 20 25 30−0.5
0
0.5
q−ax
is c
urre
nt [p
u]
Time [s]
iq,1
iq,2
iq,3
(b)
Figure 6. Transition from generator mode to motor mode, at t D 20 s, without DC-voltage control. (a) DC-bus voltage. (b) Statorsegment q-axis current.
5.2. Instability of motor mode without DC-bus voltage control
In Figure 6, the bus-voltages are simulated for a transition from generator mode to motor mode. The bus system is operatedin current control (i.e., no DC-voltage control), and the transition starts at t D 20 s. From the figure, it can be seen thatthe system is stable as long as it is in generator mode. However, as soon as the motor mode is entered, the bus-voltagesstarts to diverge, and consequently, the control is lost. This is in accordance with the discussion on small-signal stability inSection 4.2.
5.3. Impact of control strategy and parameter deviations
In the simulation results presented in Sections 5.3.1–5.3.3, parameter variations are according to Table IV. The turbine isinitiated at a wind speed of 6 m/s and then ramped up to 13 m/s.
5.3.1. Turbine operation in current control mode (no DC-bus voltage control).First, the system was simulated without any DC-bus control (i.e, current controlled), Figure 7. The deviation in voltages
is increasing with the turbine speed and power, which is in accordance with 5. At 13 m/s, voltage deviation from the aver-age is 8%. This deviation would be higher with more modules, since the parameter sensitivity increases with number ofmodules. Another consequence is that the torque in segments 2 and 3 will be 5% above the rated torque, while in module 1,
S. Gjerde et al. A modular series connected converter structure
10 20 30 400
5
10
Win
d sp
eed
[m/s
]
Time [s]
10 20 30 40
0
0.5
1
Pow
er/s
peed
[pu]
Time [s]
pturbine
nturbine
10 20 30 40
0
0.5
1
q−ax
is c
urre
nt [p
u]
Time [s]
iq,1
iq,2
iq,3
10 20 30 40
6
8
10
12
Time [s]
Udc
[kV
]
Udc,1
Udc,2
Udc,3
Figure 7. Turbine response with current control strategy, when ramped from start up to nominal wind speed. (a) Wind speed pattern,(b) Turbine power/speed c) iq;i for the modules and (d) Udc;i in the modules. The parameter variations were according to Table IV.
it will be 5% less. This will create unbalance in the mechanical forces and hence impose additional stress on the supportstructure.
5.3.2. DC-bus voltage balance with limitation in the module current.In Figure 8, the simulation results with DC-bus balance control strategy are presented. However, converter unit voltage
balancing is only prioritized up to the current limit is reached in one of the modules, after that, the power capture is priori-tized. When the torque reference approaches 1.0 pu, current limitation occurs in module 1 because of the contribution fromits DC-voltage control. Consequently, control of the DC-bus module voltages is lost, and the system ends up in currentcontrol mode. Such a strategy is the least desirable, since the loss of balance is handled passively, which makes it diffi-cult to take into account in the system design phase. However, the long term stress on the generator insulation is reducedcompared with the completely uncontrolled case, since balanced buses are achieved up to approximately 92% of the powerrange.
5.3.3. DC-bus voltage control with turbine-level compensation of limitation inmodule current.
The last case was simulated with priority given to maintaining the modules balanced (Figure 9). That is, when the currentin module 1 reaches its limit, the torque limit of the indirect speed control is reduced to reserve sufficient amount of currentcapacity to comply with the balance demands. As a consequence, the power reference of the pitch controller will have tobe reduced accordingly to keep the turbine speed within its nominal value in steady state.
5.3.4. Comparison of captured power from the three control strategies.A significant power capture difference can be observed when comparing the three different operation strategies,
Figures 7–9. An uncompensated strategy provides almost 10% more power at rated wind than the strictly balancedapproach, at the cost of higher system stresses. However, the trend is clear: the overall gain in system efficiency claimed inthe work of Olsen et al.38 can easily be lost with poor accuracy in the manufacturing of the system.
A modular series connected converter structure S. Gjerde et al.
10 20 30 400
5
10
Win
d sp
eed
[m/s
]
Time [s]
10 20 30 40
0
0.5
1
Pow
er/s
peed
[pu]
Time [s]
pturbine
nturbine
10 20 30 40
0
0.5
1
q−ax
is c
urre
nt [p
u]
Time [s]
iq,1
iq,2
iq,3
10 20 30 40
6
8
10
12
Time [s]
U dc
[kV
]
Udc,1
Udc,2
Udc,3
Figure 8. Turbine response with DC-bus balance control up to limitation of the current, and current control after the limitation occurs.(a) Wind speed pattern, (b) turbine power/speed, (c) iq;i for the modules and (d) Udc;i in the modules. The parameter variations were
according to Table IV.
10 20 30 400
5
10
Win
d sp
eed
[m/s
]
Time [s]
10 20 30 40
0
0.5
1
Pow
er/s
peed
[pu]
Time [s]
pturbine
nturbine
10 20 30 40
0
0.5
1
q−ax
is c
urre
nt [p
u]
Time [s]
iq,1
iq,2
iq,3
10 20 30 40
6
8
10
12
Time [s]
Udc
[kV
]
Udc,1
Udc,2
Udc,3
Figure 9. Simulation of the turbine with balance control up to limitation of the current reference. (a) Wind speed pattern, (b) turbineresponse, (c) q-axis current and (d) DC-bus voltage.
S. Gjerde et al. A modular series connected converter structure
5 10 150
0.2
0.4
0.6
0.8
1
Pow
er [p
u]
Vindspeed [m/s]
IdealCase1Case2Case3Case4
(a)
5 10 150
0.2
0.4
0.6
0.8
1
Pow
er [p
u]
Vindspeed [m/s]
IdealCase1Case2Case3Case4
(b)
Figure 10. Turbine captured power as function of the wind speed, and with generator stator segment flux linkage variations accord-ing to Table V. The captured power is calculated from measured DC and DC voltage (a) series connection, (b) parallel connection for
comparison, on the basis of the same modules as for the series connection.
Table V. Definition of cases of different magnetization.
5.4. Impact of parameter deviations on power capture
In the previous section, different strategies for control of the DC-bus power of the modules were investigated. It becameobvious that the preferred strategy seen from the generator design is unfavorable considering power capture at nominalpower. The effect was investigated further by simulating the system for wind speed of 5, 7 ,9, 11, 13 and 15 m/s, calculatingthe steady-state power production, Figure 10(a). The parameters were varied according to Table V.
In steady state, the turbine control was restricted by the following demands:
� DC-bus voltage balance maintained� Current reference � nominal generator current� nturbine � nominal speed
Cases 1 and 3 yield lower power than the nominal turbine power, as expected. What does also become clear from thesimulations is that the series connection is not stronger than its weakest link. A high excitation of the other segments donot compensate for one with weak excitation.
When comparing with a parallel connection of the converter modules (Figure 10(b)), it is observed that the series con-nection introduces additional ‘losses’ (in this, both actual losses and loss in energy capture is included). In a parallelconnection, only the segment with low flux linkage would provide less power, leading to less energy capture. However, afull efficiency analysis including the transmission would decrease the observed difference. To perform such an analysis isoutside the scope of this work.
6. EXPERIMENTAL VERIFICATION
Earlier work14 has experimentally proven the feasibility of controlling two series connected converters in a modular way.These converter units were connected to two machines mounted on the same shaft, and yielded limited information whenit comes to the magnetic decoupling and converter units operating on a floating potential. It was therefore necessary forthis work to extend the results to include three converter units (one floating) connected to the same physical machine. Theimpact of parameter deviation in the modules has been demonstrated by circuit manipulation to support the results fromtheory/simulations.
Due to limitations in the laboratory equipment, the verification is limited to control and operation of the seriesconnection. Verification of the generator HVDC insulation is outside the scope of this paper.
A modular series connected converter structure S. Gjerde et al.
6.1. Laboratory set-up
The 45 kW axial flux ironless stator PMSG prototype produced by SmartMotor42 used in the tests was originally designedas a three-phase machine. The stator windings were reconfigured into three three-phase groups. A nominal current limitedto 35 Arms was necessary due to challenges with the stator water cooling. A speed limitation of 40 rpm was imposedbecause of restrictions in the gear box. Three two-level, 20 kW laboratory VSCs (43) were used as converter units on thebasis of Semikron IGBTs.44 In Figure 11, a schematic shows the main components in the laboratory setup.
Three control boards based on Xilinx Virtex-5 FPGAs with PowerPC440 processor were used for control systemrealization, one for each module. One of the boards was also used to emulate turbine main control.
Each of the slaves were operated as an isolated, sensorless converter control. The time critical tasks, such as currentcontrol and measurement acquisition were performed in the FPGA to increase the controller bandwidth. Flux estimation,45
phase locked loop46 and DC-bus voltage control were implemented in the fast interrupt of the processor. The system statemachine and torque reference were handled in the slow interrupt routine (10 ms).
For feedback loops, the phase currents were measured using LEM current transducers,47 and DC-bus voltages weremeasured with LEM voltage transducers.48
In this work, the DC load was emulated using a resistor and a diode bridge that charged the link up to approximately0.9 pu voltage at no load. The resistor is controlled manually in large steps. As a result, the grid connection model was aconstant DC source for low power and resistive for high power. The asynchronous drive machine was speed controlled.
A simulation model of the laboratory setup is used for comparison between the simulation results and the experimentalresults. The model is in principle equal to that utilized for the system simulations in Section 5 but with module parametersaccording to Table VI. The diode bridge and variable transformer in Figure 11 are modeled as ideal components.
Figure 11. Schematic of the laboratory setup for verification of the operation and control of the modular generator/converter sys-tem. The DC load, diode bridge and Rload , results in a DC-grid voltage with small variations around the nominal value, depending on
generator power output.
Table VI. Laboratory setup essential parameters.
Machine parameter Value Converter parameter Value
AF-IL-PMSG rated power 45 kW VSC-module rated power 20 kWGenerator rated voltage 240 Vll VSC-module switching frequency fsw 2 kHzGenerator rated current with water cooling 35 Arms VSC-module bus capacitor Cbus 3300 �FGenerator rated current without water cooling 110 Arms Totalt DC-voltage Udc;tot 225 VGenerator rated speed 74 rpmMax generator speed due to gearbox 40 rpmPole pairs 24Number of stator segments 3
AF-IL-PMSG, axial flux, ironless stator PMSG; VSC, voltage source converter; DC, direct current.
S. Gjerde et al. A modular series connected converter structure
(a) (b)
2 4 6 8 10 1260
65
70
75
80
85
90
95
100
Time [s]
2 4 6 8 10 12
0
2
4
6
8
10
Cur
rent
[A]
Udc,3
Udc,2
Udc,1
Idc
(c)
2 4 6 8 10 1260
65
70
75
80
85
90
95
100
Udc
[V]
Udc
[V]
Time [s]
2 4 6 8 10 12
0
1
2
3
4
5
Cur
rent
[A]
Udc,3
Udc,2
Udc,1
Idc
(d)
Figure 12. Power ramps without the DC bus voltage control activated (a) torque ramp from 0 to 0.5 pu, constant speed (20 rpm) and(b) speed ramp 20–40 rpm, constant torque (0.1 pu). (c) Simulation corresponding to (a). (d) Simulation corresponding to (b). (Ch.1:
Udc;1, Ch.2: Udc;2,Ch.3: Udc;3,Ch.4: Idc).
6.2. Results
6.2.1. Current control, no DC bus voltage control.The response to a torque reference ramp at constant speed is shown in Figure 12(a) and the opposite (constant torque,
variable speed) in Figure 12(b). A DC voltage difference, almost identical, independent of loading, is found from Fig-ure 12(a) by inspecting the minimum and maximum voltages. This indicates that stator resistance is not the only cause ofthe initial imbalance, since there should then be zero voltage deviation at no load. The second figure shows a slightly largervoltage deviation between maximum speed and minimum speed. This indicates an effect of differences in the stator fluxlinkage between the segments.
The oscillations in bus voltages have the same frequency as the mechanical speed. These oscillations originates from dif-ferences in the stator segment flux linkages, which depend on the rotor disk position. The oscillations provides an additionalargument for implementing the DC-bus voltage control with the turbine tied to a DC grid.
In Figure 12(c) and 12(d), results from corresponding simulations are presented. In general, a good resemblance betweenthe experimental and simulation results was obtained for both the variable torque and speed cases. The differences in DCvoltage at low power, in the beginning of each sequence, is due to ideal model of the diode bridge in the simulations.
6.2.2. Inserted phase resistance without DC-voltage control.The setup was manipulated by inserting a three-phase resistor in series with the stator. It was first connected to converter
unit 1 (Figure 13(a)), which has the highest DC voltage in the non-manipulated case (Figure 13(a)), and then converter unitthree, which has the lowest power production (Figure 13(b)). The same torque reference wave form as earlier was applied.The impact of the added 30 m�dc resistance can be seen in the figures. In the first case, module 1 goes from the highestcontribution at low load, to the least contribution at high system loading. In case 2, the contribution from module 3 dropssignificantly compared with Figure 12(a). With phase resistance (Rs + Rf ilter )D 70 m�dc , the added resistance was43%.
A modular series connected converter structure S. Gjerde et al.
(a) (b)
Figure 13. Same case as in Figure 12(a), with added phase resistance in series with the filter to one module at the time (a) theresistors is added to module 1, which has the highest power production in the original setup. (b) The resistors added to module two,
which has the lowest power production. (Ch.1: Udc;1, Ch.2: Udc;2,Ch.3: Udc;3,Ch.4: Idc).
(a)
13 23 33 43 53 63 73 83 93 103 11360
70
80
90
100
Udc
[V]
Time [s]
−5.5
−2
5
9.5
I dc
[A]
Udc,3
Udc,2
Udc,1
Idc
(b)
Figure 14. Balanced operation of the three converter modules at constant speed and varying torque. (a) Experimental results. (b)Simulated results. Ch.1: (Udc;1, Ch.2: Udc;2,Ch.3: Udc;3,Ch.4: Idc).
6.3. Balanced DC-bus voltage under torque variation
A torque waveform identical to the previous cases was applied to the system with the DC-voltage balance control activated.A DC-bus control limit of 0.85 pu (lower), and 1.2 pu (upper) was set. The first 30 s (Figure 14(a)), the torque set-pointsresults in lower power than what is required to maintain a minimum voltage. Hence, the DC-bus voltage controllers ends upcontrolling the DC-bus voltage level, in addition to the voltage balance. The two voltage transients are due to small, quickincreases in the torque reference, with the slow response in the droop control eliminating the DC-bus voltage controlleroffset. At t D 30 s, the power drawn from the generator is sufficient to eliminate the contribution from the diode rectifiercompletely. The control system is capable of maintaining balanced buses both for constant and varying grid voltage. Inaddition, the average DC voltage (and therefore also grid current) matches the unbalanced cases. This verifies the droop inthe DC-bus voltage balance control system. Yet another observation is that the DC-bus voltage control is able to eliminatethe oscillations observed in the unbalanced cases. The same load profile was simulated, and the results are presented inFigure 14(b). There is a good correspondence between the simulation results and the experimental results, with only minordifferences observed between the simulated and experimentally obtained DC-bus voltages.
7. CONCLUSIONS
In this work, a modular converter system suitable for an HVDC transformerless offshore wind turbine system has been ana-lyzed. Due to a large diameter machine and mechanical tolerances, the power production in each module can vary notably.Therefore, first the relation between power extraction from the segments and the corresponding DC voltages was discussed.This was followed up by developing a mathematical expression relating the steady state DC-bus voltage imbalance to thesystem parameter deviations between different parts of the system. A qualitative, small-signal stability analysis revealedthat the series connection renders a natural stable system in generator mode, while it is naturally instable in motor mode.
S. Gjerde et al. A modular series connected converter structure
This, together with the need to balance the DC-bus module voltages to comply with insulation requirements demonstratedthe necessity of the DC-bus voltage control. Although only the balanced-module-DC-voltage strategy has been studied indetail in this paper, also the possibility for other control strategies were discussed. Dynamic simulations were performed inEMTDC/PSCAD to support the conclusions from the theoretical parts, including the impact of the DC-bus voltage balancestrategy on system operation. From the simulation results, a strong relation between tolerances in machine construction(stator segment flux linkage), control strategy and the power capture capability of the turbine was identified. If such param-eter variations are detected during operation, a minor derating of the turbine may be necessary to preserve control reservefor the DC-bus voltage balance.
Finally, a 45 kW laboratory set-up with a prototype of the machine with three stator segments and three converter unitshas been built for experimental verification of the system. And although there were limitations in the possibility to manip-ulate the system, a clear indication on the relations found by theoretical investigations was obtained. The effectiveness, andnecessity, of a DC-bus voltage control to eliminate output power oscillations caused by imperfect generator constructionwas also demonstrated. The experimental results compare well with the simulation results, and hence, the simulation modelis validated.
ACKNOWLEDGMENTS
The authors acknowledge the support from SmartMotor AS for the possibility to use the ironless, Axial Flux-PMSGprototype for the experiments. This work has been co-founded by The Norwegian Research Centre for Offshore WindTechnology, NOWITECH.
APPENDIX A. DETAILED DERIVATION OF THE STEADY STATE MODEL
The variable names for the following derivation are all defined in Figure 2(b).The power produced by segment i can be expressed by 14 with id;i D 0:
pac;i D Eudq;i �Ei�dq;i) pac;i D uq;i � iq;i (14)
And the power on the DC bus of one VSC-module by (15):
pdc;i D udc;i � idc;i (15)
Where, in general idc;i D igrid for stationary operation. Due to the series connection, igrid is common for all modules.Hence, the DC-bus voltage in a VSC-module can be expressed by 16.
pdc;i D �i � pac;i ) udc;i D�i � uq;i iq;i
igrid(16)
The dynamic model of a generator segment can be expressed by 17 (49):
uds;i D�
�rs;i id;i C ls;i �
did;i
dt
�C!els;i iq;i
uqs;i D�
�rs;i iq;i C ls;i �
diq;i
dt
��!els;i id;i C!e‰i
(17)
Eliminating all transient terms, acknowledging that !e � ls D n � xs and setting id;i to zero results in the following:
uds;i D nxs;i iq;i
uqs;i D�rs;i iq;i C n i(18)
Inserting 18 into 16 yields the following:
udc;i D�i � .�rs;i iq;i C n i / � iq;i
igrid(19)
From the grid side, the power that is transferred to the grid can be expressed in two ways (20 and 21):
A modular series connected converter structure S. Gjerde et al.
pdc;tot D .�1 � uq;1iq;1/C .�2 � uq;2iq;2/ (21)
Where iq;1 = iq;2 = iq . igrid can then be expressed by Equations 20 and 21:
igrid � .udc;1C udc;2/D iq � .�1uq;1C �2uq;2/) igrid D iq�1uq;1C �2uq;2
udc;1C udc;2(22)
Generalizing 22 for N modules, and combining with 18 results in 23
igrid D iq �
PNiD1.�rs;i iq;i C n i /
udc;tot(23)
And, by combining 19 with 23, the bus steady state voltage across one module can be described by 24
udc;i D�i � .�rs;i iq C n i /PN
jD1 �j � .�rs;j iq;j C n j /� udc;tot (24)
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