Offshore wind farm cluster-based DC collection network: operation and design considerations
A direct current (DC) cluster-based wind farm collection network with permanent magnet generators and passive rectifiers is described and modelled. The ability of the generator speed to ‘slip’ from the cluster synchronous speed is discussed along with the relationship between the slip and generator stator inductances. An investigation of the harmonics present in the system highlights the presence of sixth harmonic torque and DC current components.
Author(s): Douglas W. Elliott; Catherine E. Jones; Stephen Jon Finney
Abstract
Modelling of two and five turbine clusters indicates that the super position of the sixth harmonics produced by adjacent turbines, introduces a lower frequency harmonic components to both the DC current and generator torques. Modelling also highlights the presence of circulating current components flowing between the turbines, which give rise to both transient and steady-state interactions. Finally, the impact of increasing the branch inductances is studied and shown to affect the response of the machines following changes of wind speed.
Introduction
Power-electronic converters within wind turbines have proven themselves to be particularly susceptible to failure and indeed one of the most failure-prone components within a wind farm electrical system [1]. By dividing a wind farm into groups of five turbines and aggregating the outputs before feeding them into a central power converter, the number of failure-prone power-electronic converters can be reduced. This small group of turbines forms a cluster where the converter exercises control over them all and couples them to a wider collection network.
By operating a wind farm as a set of smaller clusters, the number of converters required is reduced fivefold. Therefore, the number of failures that is attributed to the power converters can also be reduced fivefold, which in the context of a large offshore wind farm operating, for example, in the middle of the North Sea provides a significant reduction in the number of visits required to carry out maintenance and repairs. Where a clustered approach is used, the potential consequences of a converter failure would be greater; this could be mitigated, however, by the co-location of the converters for multiple clusters on a single substation platform and the provision of redundancy. The benefit of taking a clustered approach is improved availability of the wind farm and also a significant reduction in the number of maintenance visits required, along with cost savings this would allow.
Electrical clusters of wind turbines could be implemented using three different technologies: parallel connected induction generators with a variable frequency cluster network, parallel connected permanent magnet (PM) generators with a variable frequency cluster network and PM generators with passively rectified outputs connected with a multi-terminal DC cluster network [2]. There are various pros and cons to each technology; the aim of this paper is to discuss the design and operational aspects of the third technology.
Modern wind turbines use power converters to provide active torque control and also to improve energy capture by allowing the turbine rotational speed to vary. In a clustered case, the single power converter must regulate the torque and speed of all of the wind turbines in a cluster, posing challenges to the operation of the turbines and the design of the cluster electrical network.
To investigate these challenges, dynamic models of the wind turbine rotor, PM generators, rectifiers, DC link and cluster controller have been developed in the Simulink environment.
System modelling
The basic outline of the five-turbine model developed is shown in Fig 1 There are four major parts: the wind turbine, generator, rectifier and DC electrical system.
Fig 1: Five-machine cluster model outline
Wind turbine model
The wind turbine model is based around a power coefficient, Cp, against tip-speed ratio, λ, curve describing the relationship of the power capture efficiency of the turbine rotor and the ratio of the rotor tip speed, to the incident wind speed. The turbine gearbox is represented by a ratio, stepping up the rotational speed of the rotor to drive the PM generator. The Cp– λ curve, rotor diameter (63 m) and gearbox ratio (97) of the NREL 5 MW reference turbine have been used [3].
PM generator model
A two-axis model of a PM generator is used, where the rotor of the PM generator is assumed to be non-salient [4]. The generator model takes the mechanical torque input from the wind turbine model and outputs the winding currents and measurements of the generated electromechanical (machine) torque and rotational speed. The model is configured so that the rated phase terminal voltage is 3.5 kV at a rated rotational speed of 137 rad/s. The machine windings comprise two pairs of poles.
Rectifier model
The rectifier consists of a three-phase full-wave diode rectifier, giving a peak DC-side voltage equal to the PM generator line-to-line terminal voltage magnitude of ∼6.2 kV. The system voltage and power level used will inherently lead to very high output currents, which are not practical. This fact is recognised and it is anticipated that a step-up transformer would be included to step the voltage up to ∼33 kV prior to rectification, but is not considered any further here.
DC network model
The DC network is a series of cables running from each turbine to a point of common coupling (PCC) and from there on to the active front end (AFE) converter. Cable lengths of 10 km are assumed for all connections and they are modelled as inductances with resistive components. The cables are assumed to have equal cross-sections of 800 mm ^{2} and the per km inductance of the cables, L_{l} , is 0.83 mH/km and resistance, R _{l} , 0.0221 Ω/km [5]. The AFE converter is modelled as an ideal controllable voltage source, and the power flowing into the AFE is measured at its terminals. Fig 2 shows the layout of the electrical model with a single generator.
Fig 2: Layout of the electrical model, where only a single generator is present
System control and operation principles
The system controller acts to regulate the voltage at the PCC; by doing so, it indirectly regulates the rotational speed of the generators, as they are proportional to the generator emf. A maximum power point tracking approach is used to regulate the DC voltage against the power flow through the AFE, to give an optimised ‘synchronous speed’ for the cluster to maximise energy capture efficiency. The branch cable impedances, between the PCC and the terminals of the rectifiers and the internal generator voltage drop, produce voltage differences, which are reflected as differences of rotational speed; allowing for varying aerodynamic torques, owing to wind speed changes, to be absorbed by the variation in the rotational speeds of each turbine. Drawing an analogy with induction generators, the variations in rotational speed are achieved by allowing the generators to slip from the cluster synchronous speed.
The proportionality between the rotational speed and the emf of the generators requires the slip to be achieved by allowing the machine terminal voltages to vary with reference to the PCC voltage. Adding resistance to the circuit in order to facilitate this is not preferred, because it will reduce the energy transfer efficiency; however, the distortion of the machine terminal voltages because of the commutation overlap of the output current in the phase windings by the rectifiers introduces a voltage drop that is of use [6]. During commutation there is an effective short circuit between the two phase windings involved, clamping them at the same voltage. This transfer of current between the inductances of the two windings forces the line-to-line voltage between them to zero for the duration of the commutation. This subsequent distortion of the phase terminal voltages of the generators is reflected through the rectifier, causing a reduction in the average terminal voltage over the conduction period of each winding, π/3 radians. The output current from the rectifier is driven by the average rectifier terminal voltage; therefore this reduction acts like a resistive voltage drop, but without the energy loss. The relationship between the stator winding inductance, L _{s}, of the machine, the output current and the frequency of the generator output with the magnitude of the commutation voltage drop is given in (1) [6]. The magnitude of this voltage drop is shown in Fig 3 for different output currents. The amount of slip that is achievable in the system is a function of the commutation voltage drop and the resistive voltage drop across the branch cable, given by (2).
Fig 3: Voltage difference between the generator and the PCC with output current and for different generator-side inductances
To allow the best operation of the system, the amount of slip that each turbine can achieve from the cluster synchronous speed should be maximised. The loss-free commutation voltage drop can be exploited for this by increasing the inductance on the generator side of the rectifier. Fig 4 shows the slip achievable between the rotational speed of the generators and the cluster synchronous speed with output current and for different machine-side inductances; the values for slip provided here take into account commutation voltage drop and also the voltage drop owing to the resistive elements in the cables. It is therefore evident that approximately 13% slip can be achieved at full load, which could be increased to ∼17% by increasing the generator-side inductance to 2.2 mH.
Fig 4: Generator slip with output current for different generator-side inductances
Fig 5 shows the change in the rotational speed of each of the five turbines in the cluster in response to varying and different wind speeds on each turbine, along with the cluster synchronous speed. It can be observed that all of the turbines operate with rotational speeds greater than the synchronous speed and that the slip in the system allows each turbine to refine its speed to the local wind conditions, although the general behaviour of each of the turbines follows the change in the synchronous speed, driven by the cluster controller.
Fig 5: Generator rotational speeds in response to varying wind speed, along with the cluster synchronous speed for comparison
System harmonics
The use of a passive rectifier to convert the generator output to DC introduces harmonic components to the rectifier DC output voltage and current, machine winding currents and machine torque. The harmonics on the DC-link voltage are present, owing to the sampling of the AC line-to-line voltage by the rectifier, which, during the conduction period of each pair of windings, rises to its peak and falls again. The rectifier changes between windings six times per cycle and therefore the harmonic present is the sixth harmonic component of the fundamental AC frequency. This harmonic component also produces the DC current harmonic, the magnitude and phase of which are proportional to the impedance in the DC-link.
The harmonics present on the machine winding currents have two origins: the DC current harmonic and the shift of the output current between generator windings by the rectifier. The individual winding currents possess a generally trapezoidal shape, with the DC current harmonic superimposed on top during their conduction periods. The trapezoidal currents consist of significant fifth and seventh harmonic components in addition to the fundamental component; the sixth DC current harmonic is reflected at the same frequencies onto the winding currents. The winding current harmonic components are reflected as a sixth harmonic onto the generator torque.
The relationship between the DC and the AC current harmonic components has been derived using Fourier analysis. Equation (3) gives the DC-link current, which consists of DC and sixth harmonic components, and the resulting harmonic coefficients are given in Table 1. For the purposes of this analysis, it is assumed that the resistive component of the DC-link impedance is negligible and therefore the sixth DC current harmonic lags the DC voltage harmonic by π/2 radians and is therefore a sine component, where the DC voltage harmonic is cosine.
Table 1
First, fifth and seventh harmonic component coefficients of the machine winding currents determined by Fourier analysis
a _{1} | a _{5} | a _{7} |
I123√πI123π | −I123√5π−I1235π | I123√7πI1237π |
b _{1} | b _{5} | b _{7} |
−123√I635π−123I635π | 123√I611π123I611π | 123√I613π |
The torque harmonic components are determined by transforming the winding currents to the rotating reference frame of the machine model and applying the machine torque equation, given in [4]. Substituting the coefficients from Table 1 gives the torque as a function of the DC current components (4).
where p is the number of pole pairs, K is the machine constant, ω is the fundamental frequency (rad/s), t is the time (s) and T is the machine torque (Nm).
Table 1 shows that the sixth DC current harmonic, I _{6}, introduces the b _{n} components to the windings currents and the a _{n }components result from the shift in the average DC output current, I _{0}, between the machine windings. Equation (4) shows that the sixth torque harmonic has components related to I _{0} and I _{6}. If the DC current was ideal, I _{6} = 0, significant sixth harmonic torque components would remain, owing to the presence of the I _{0} components. Applying (4), with the values for I _{0} and I _{6} taken from the model output when the wind turbine is operating at rated power, indicates that the torque ripple is 5.74%, which is a peak-to-peak average torque produced by the machine. By reducing I _{6} to zero, the torque harmonic is reduced to 5.71%, which indicates that the majority of the harmonic content results from the shifting of the output current between the generator windings.
The presence of these harmonics is felt by the drivetrain of the wind turbine, where they introduce vibration and create audible noise. The harmonics could also excite the resonant frequency of the cable impendences. The DC current harmonics could be reduced in magnitude by the increase of the DC-side inductance; however, this will have limited impact on the torque harmonics.
Multiple machine operation
To investigate the operation of the cluster network when there are multiple machines connected in parallel, two- and five-machine models have been used. The basic outline of the five-machine model is shown in Fig 1. The cluster controller applied in either case is very similar; only the power reference is scaled by the number of turbines present, two and five, respectively.
Cluster operation with two wind turbines
The following test scenarios are applied to the two-machine model: constant and equal wind speeds, constant but different wind speeds and initially equal wind speeds with a step increase on machine 1.
When subject to equal wind speeds the operation of the machines is identical and both achieve maximum energy capture efficiency. When the wind speeds are constant but different on each turbine (turbine 1 = 7 m/s and turbine 2 = 8 m/s) the turbines rotate at different speeds. Close inspection of the machine torques and branch currents reveals a lower frequency component, in addition to the sixth harmonic components discussed above, shown in Fig 6. The difference between the rotational speeds results in different sixth harmonic current frequencies. The superposition of the different frequency harmonic currents in the main cluster cable produces the lower frequency ‘beat’ on the aggregated current, which causes the potential difference across the cluster output cable impedance and the PCC voltage to fluctuate at the same frequency. This causes the potential difference across the branch cable to also fluctuate, affecting the output current and torque produced by each generator, shown in Fig 7. The frequency of this ‘beat’ is equal to the difference between the sixth harmonic frequencies produced by each rectifier and is therefore likely to be small in comparison, if the turbines are operating at similar speeds. The impact could excite mechanical resonances in the turbine drivetrain and structure, which are of the order 0.8–2.6 Hz [7].
Fig 6: Machine 1 DC branch current showing high-frequency sixth harmonic component and lower frequency component
Fig 7: Electromechanical torque produced by machine 1, exhibiting the low-frequency harmonic component
When a wind speed step change is applied to turbine 1, it is also observed that a circulating component of current flows from turbine 1 to turbine 2. The response of the turbine output currents to this step can be separated into transient and steady-state responses; the transient response is driven by the sharp increase of the output current from turbine 1, which develops an increased voltage across the cluster output impedance raising the PCC voltage. This will reduce the potential difference across turbine 2's branch cable, reducing the output current, as shown in Fig 8, reducing the machine torque and allowing it to speed up, shown in Fig 9. The reduction of the current in turbine 2 is effectively caused by a circulating current component from turbine 1 (to demonstrate this, the AFE voltage is held constant). The increased speed of the generator that results drives an increased machine terminal voltage, thereby increasing the potential difference across the branch impedance, forcing the current output of machine 2 to rise once again, counteracting the initial change and returning the system to a steady state. The system reaches a new steady state following the change where machine 2 is now rotating at a higher speed in order for it to output the same power, shown in Fig 9. This is regarded as the steady-state response of the currents in the system.
Fig 8: Change of turbine 1 (M1), turbine 2 (M2) and cluster output currents in response to a step increase of the wind speed on M1 from 7 to 8 m/s
(Note: the high-frequency harmonics present in previous figures have been removed by averaging for clarity)
Fig 9: Rotational speeds of generator 1 (M1) and generator 2 (M2) in response to the step change of wind speed on turbine 1
Cluster operation with five wind turbines
The five wind turbine model allows the response of each turbine in the cluster to be observed when changes in wind speed are applied, when the initial wind speeds on each machine are different. This is of interest because it allows the impact of different initial wind speeds to be determined on circulating current components. The initial wind speeds on each turbine are spread from 5 to 7 m/s in 0.5 m/s intervals; a step increase of wind speed from 7 to 7.25 m/s is then applied to turbine 1. To clearly demonstrate the presence of the circulating current component, the AFE voltage is once again held constant. Fig 10 shows that the output currents from turbines 2, 3, 4 and 5 fall initially in response to the increased output of turbine 1; plotted as percentages of their initial output current magnitudes prior to the step change. These reductions are caused by the circulating current components flowing from turbine 1.
Fig 10: Percentage change of the output currents from machines 2, 3, 4 and 5, in response to a step increase of wind speed on machine 1 of 7–7.25 m/s
It can be observed from Fig 10 that the percentage change of the currents is greatest for the machine that possesses the lowest initial wind speed, machine 5. Therefore, the severity of the response of these machines to a change in wind speed on machine 1 is a function of the difference between the wind speeds on each machine and on machine 1. The machine that has the greatest wind speed difference will subsequently exhibit the largest response.
Impact of the ratio of the DC-side impedances
So far the discussion has focused on the system where the DC-side impedances between the machines and the PCC and the PCC and the AFE are equal, with a ratio of 1:1; making the assumption that this will always be the case is not wise, because these impedances are a function of the cable lengths between the turbines. Therefore, the impact of changing the ratio of the impedances is investigated, in particular looking at the effect of increasing the branch inductances.
Impact of ratio increase on machine responses
To clearly demonstrate the impacts of changing the ratio, a ratio of 10:1 (turbine branch inductance:cluster cable inductance) has been applied. The impedance ratio of 1:1 has been used as a base case for comparison and the branch inductances for each turbine have been increased equally, although only the currents of turbines 1 and 5 are shown for clarity. A change in the ratio impacts on the rates at which the turbines in the cluster react to a change of wind speed and input torque on one turbine, restricting the change of the output current and torque produced by the generators. When a step increase in wind speed is applied to turbine 1, the restriction to the rate of change of current allows the turbine rotor to accelerate quicker, leading to a higher rotational speed early on, compared to the base case, as shown in Fig 11. This results in a higher potential difference between the generator terminals and the PCC, acting to force up the output currents, shown in Fig 12.
Fig 11: Change in rotational speed of M1 and M5 for the base case and the ratio of 10:1, in response to a wind speed step change on M1 of 7–7.25 m/s
Fig 12: Percentage change of the output currents of M1 and M5 for the base case impedance ratio of 1:1 and the ratio of 10:1, in response to a wind speed increase on M1 of 7–7.25 m/s
It is shown that the acceleration of turbine 1, in Fig 12, is checked and reversed for a period as the machine torque surpasses the input mechanical torque, which is shown by the output current from turbine 1 becoming larger than the base case current. This occurs because of the restriction applied to the change in the rate of current increase by the larger inductance. By studying the rate of change of the output currents from the other turbines in the cluster, in particular turbine 5 in Fig 11, it is observed that the initial rate of decrease of the current is slower compared with the base case; the magnitude of the current also surpasses the base case current. Therefore, the initial acceleration of turbine 5 is restricted, but the rotational speed eventually catches up and exceeds the base case for a short period, as with turbine 1.
It can be concluded that changing the impedance ratio to 10:1 introduces a slight delay before the turbine output currents and torques respond to the change in wind speed; allowing turbine 1 to accelerate quicker and slowing the initial acceleration of the other turbines. The slower initial acceleration of the other machines is compensated for by larger peak circulating current components and the subsequent greater peak reduction of the machine torques which allows their rotational speeds to accelerate further to catch up with the base case.
The careful design of the DC side impedances is required so that the delay of the machine torque responses is not sufficient to allow the turbines to accelerate beyond their operating range. The impedance ratio should also be large enough to prevent large shock torques being applied to the drivetrain by the generators when acting to control the accelerations; which may have a detrimental effect on the mechanical drivetrain of the wind turbine.
Conclusion
The investigations presented here into the operation of a cluster of wind turbines highlight three major effects of interest. The use of passive rectifiers introduces sixth harmonic components to the torques applied by the generators onto the turbine drivetrains, the peak-to-peak value of which is ∼5.74% of the average torque output, at the rated power output from the wind turbine. The source of this harmonic has been traced to two places: the voltage ripple introduced to the DC voltage at the rectifier terminals by the sampling of the line-to-line generator terminal voltages, and the shifting of the DC output current between the generator windings. Fourier analysis has allowed the influence of each effect on the machine torque harmonic magnitude to be determined, highlighting that the second effect is dominant.
The two-machine model highlighted the presence of a lower frequency ‘beat’ harmonic component on the torque when the machines are rotating at different speeds. This component is the result of the superposition of the DC-side harmonic currents when they are aggregated in the cluster output cable, the effects of which are reflected on the generator torques and are applied to the turbine drivetrain.
Both the two-machine and five-machine models highlight the presence of circulating current components passing between the turbines when they are subject to different wind speeds and are rotating at different speeds. Changing the DC-link inductance ratio affects these circulating components changing the accelerations of the turbines, requiring greater peak torques to control them. Therefore, careful selection of the cable lengths between the turbines and the PCC and the PCC and the AFE is required to keep rates of acceleration and the maximum torque within limits.
Acknowledgments
This work is funded by the EPSRC through the CDT in Wind Energy Systems at the University of Strathclyde, UK, Project reference no. EP/G037728/1.
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