Comparison of electrical collection topologies for multi-rotor wind turbines

Multi-rotor wind turbines (MRWT) have been suggested in literature as a solution to achieving wind turbine systems with capacities greater than 10 MW. MWRT’s utilise a large number of small rotors connected to one support structure instead of one large rotor, with the aim of circumventing the square cube law. Potential benefits of MRWT’s include cost and material savings, standardisation of parts, increased control possibilities and improved logistics for assembly and maintenance. Almost all previous work has focused on mechanical and aerodynamic feasibility, with almost no attention being paid to the electrical 5 systems. In this research eight different topologies of the electrical collection network for MRWT’s are analysed to assess which are the most economically and practically viable options. AC and DC collection networks are presented in radial, star, cluster and DC series topologies. Mass, capital cost and losses are estimated based on scaling relationships from academic literature and up to date commercial data. The focus of this study is the assessment of the type of electrical collector topology so component type and voltage level are kept consistent between topology designs in order to facilitate a fair comparison. 10 Topologies are compared in terms of four main criteria; capital cost, cost effectiveness, total mass, and reliability. The most suitable collection topology for MRWT’s is shown to be of the star type, in which each turbine is connected to the step up transformer via its own cable. DC topologies are generally found to be more expensive when compared to their AC counterparts due to the high cost of DC-DC converters and DC switchgear.

. Proposed layout of a 45 rotor MRWT system. is used in various studies such as (Jamieson and Branney, 2012) and (Jamieson et al., 2015). The Innwind study provides a conceptual design for such a system and also makes comparisons to an equivalent system consisting of two 10MW RWT's 90 from DTU to highlight the reduction in LCOE that could be realised by the MRWT concept. It is therefore desirable to use a similar system in this study to allow for easy comparison to both systems. Each rotor has a diameter of 41 m which results in the same total swept area as the two 10 MW RWT's. Using examples of commercial wind turbines of this approximate size of rotor, a representative rated power of 500 kW was selected for each turbine, giving the system a total rated power of 22.5 MW.

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The following design constraints have been used to design the electrical topologies: 1. The system in question must have 45 rotors: to facilitate fair comparison with results in the Innwind project.
2. Each turbine must have a rating of 500 kW , diameter or 41 m, rated wind speed of 11.5 m/s, maximum coefficient of power (C P ) of 0.45, and rated rotor speed of 30 rpm: these values have been selected as representative values from available wind turbines of this scale used within the industry. 3. Each turbine must have independent speed control: This is required in order to maximise energy capture and minimise loading on blades and drive train components. 4. It is assumed that each turbine operates in a maximum C P tracking mode below rated wind speed, and then power is held constant at rated power above rated wind speed via pitch control. 5. Each topology must connect to an AC collection network at 33kV : this is a common voltage level used within the wind 105 industry for collection networks. DC collection networks have been discussed in literature, but there is still no real world applications.
A total of eight topologies were designed and each are described in this section. Each topology is based on commonly discussed collection network topologies for offshore wind farms.
The AC star and DC star topologies are shown in Fig. 2 and Fig. 3 respectively. In both the AC and DC star topologies each turbine is connected via its own cable to the converter or transformer situated at the base of the structure. The AC star uses a 3.3kV permanent magnet synchronous generator (PMSG) with a fully rated back-to-back IGBT based voltage source 115 converter (VSC). The DC star uses a 1.5 kV PMSG with controlled IGBT based VSC. Various types of DC output wind turbines have been suggested in the literature with some utilising diode rectifiers to reduce weight and cost, and others utilising controlled IGBT based rectifiers. The advantage of using an IGBT based VSC is that it is able to easily control both the torque of the generator as well as the reactive power to the generator. This allows for independent speed control of each turbine while maintaining a constant DC output voltage, and also allows the use of any type of generator. A controlled rectifier has been 120 selected for these reasons for each DC topology in this study. To allow for a fair comparison between topologies, all use a PMSG. The DC star topology uses a lower rated generator in order to have the DC cable voltage directly comparable to the AC star topology, which facilitates a fair comparison between the two and keeps the emphasis on the type of system rather than system voltage. Medium voltage (MV) generators are required to avoid high conduction losses in low voltage (LV) cables and also to remove the need for a transformer within the nacelle. The star topologies benefit from excellent redundancy as a fault 125 in any one component within the array only results in the loss of 1/45th the total rated power. The disadvantage is that there is a large total cable distance, but cables with a smaller cross sectional area (CSA) can be used compared to other topologies.
The DC star topology also may benefit from greater efficiency and lower mass due to fewer conversion steps and the use of DC cables (DC cables are known to be lighter and smaller compared to AC cables (Lakshmanan et al., 2015)).
The AC and DC cluster topologies are shown in Fig. 4 and Fig. 5 respectively. The cluster topologies gather power from a 130 number of rotors, step up the voltage using either an AC transformer or a DC-DC converter and then transmit the power to the converter/transformer at the base of the structure. This allows for the use of industry standard 690 V generators as the cable distance between each rotor and the transformer or DC-DC converter is very small. Cluster topologies use much smaller cable distances compared to the star topologies, but require cables with larger CSA to handle higher currents. DC-DC converters are used in the DC topology and a 50/60 Hz transformer is used in the AC topology. DC-DC converters are smaller and lighter 135 compared to AC transformers (Lakshmanan et al., 2015) but are also significantly more expensive, so it is expected that the DC cluster topology be more expensive but lighter than the AC cluster topology. The main disadvantage of the cluster topologies is the failure of the cluster transformer/DC-DC converter would result in the loss of the entire cluster of turbines.
The AC and DC radial topologies are shown in Fig. 6 and Fig. 7 respectively. These are based on the most common type of offshore collection network; the AC radial collection network (Bahirat et al., 2012). As it is the most common configuration,    the AC radial topology will be used as the base topology throughout this study. In the radial topologies, a number of turbines are connected to a feeder cable which transmits the power to the transformer/converter at the base of the support structure. The 6 https://doi.org/10.5194/wes-2020-19 Preprint. Discussion started: 25 February 2020 c Author(s) 2020. CC BY 4.0 License.  amount of turbines connected to a feeder cable is determined by the current carrying capacity of the cable and the power output of the turbines. For simplicity, both AC and DC radial topologies use non tapered cables in each string. Use of a 3.3kV feeder cable in the DC radial design was originally used, but after initial assessment it was deemed unrealistic due to the large CSA 145 of cables required so the next standard voltage level of 6.6 kV was selected. Radial designs benefit from short cable distances, simple design and operational experience. The main drawback is poor reliability as a fault in a feeder cable would result in the loss of the entire string. It should be noted that failure rates for cables are significantly lower than that of power electronic converters or generators.
DC series and DC series/parallel connected wind farm collection networks have been discussed in the literature and show 150 enough promise to be included in this study (Bahirat et al., 2012;Ng and Ran, 2016;Lundberg, 2003). The main idea behind the DC series topology is to connect DC output turbines together in series to increase the voltage of the string without the use of AC transformers or large DC-DC converters, resulting in a very lightweight system. Figure 8 shows the DC series topology and Fig. 9 shows the DC series/parallel topology. In the DC series topology, a standard 690V AC PMSG is used with a controlled rectifier to produce a DC output of 1.5 kV. Each string contains five turbines connected in series to produce a string voltage 155 of 7.5 kV. Generator torque control is performed by the controlled rectifier and the string DC-DC converter maintains the DC voltage of the string. A fault in one turbine can be isolated by using a circuit breaker that operates in short circuit, maintaining a path for the DC current within the string. In the case of a fault within the string, the DC-DC converter at the end of the sting can vary its duty ratio to maintain the 11kV bus voltage. This system should have a low mass due to the small number of converters used, but may be expensive due to the use of DC-DC converters and more expensive DC protection devices. There may also  be issues regarding insulation as some components will require an insulation level high enough to withstand the whole string voltage to ground. This will be explored further if the topology shows promise.
The DC series/parallel topology is similar to the DC series topology in that is utilises DC output turbines connected in series to produce a high voltage within strings. It utilises a variable voltage output DC wind turbine where the generator is connected to a controlled rectifier and a DC-DC converter. As multiple strings of DC series turbines are connected together in parallel, 165 the voltage of each sting must be kept the same as the others. This is achieved by the use of the DC-DC converter at the turbine level. If one turbine within a string fails, the voltage is maintained by the other turbines in the string increasing their output voltage. This topology is designed to reduce the cable distance, but will undoubtedly require heavier and more expensive cables to utilise. Disadvantages of this topology are similar to those of the DC series topology.

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The cost, mass and loss performance of each component used in the proposed topologies must be estimated in order to determine each topologies suitability. A variety of academic literature and commercial information has been used to accurately estimate the properties of each component used. Information regarding cost and mass of components is rarely available in the public domain for the exact power rating and size of components required. It is therefore necessary to rely on scaling relationships from the academic literature that estimate the cost and mass of generic components based on parameters like 175 component power rating, P , or torque rating. Within this study, these scaling relationships have been adapted where possible to include th most up to date commercial information in order to reflect realistic components used within the wind industry. A summary of the relationships used to estimate mass and cost of components in this study is presented in Table 1. The cost of components can often be difficult to estimate as component producers will vary prices depending on market pressures, location 8 https://doi.org/10.5194/wes-2020-19 Preprint. Discussion started: 25 February 2020 c Author(s) 2020. CC BY 4.0 License.
of projects, availability of materials etc. It is therefore necessary to rely on the academic literature in order to estimate the price of each component. Although the estimated prices may not be exact, they are sufficient to compare the cost effectiveness of each topology. All cost estimates used within this study are presented in 2019 GBP.

Generators
NREL provide a mass estimation relationship for medium speed PMSG's in (Fingersh et al., 2006). However this relationship was produced in 2006 and does not reflect any of the recent developments in generator design made over the last decade.

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Information is available from ABB about mass of generators in (ABB, 2012), which provides an up to date and industrial comparison point to check the NREL relationships against. Table 2 shows a comparison between actual mass given by ABB and the estimated mass using the NREL relationships from the 2006 study, as well as a correction factor required so that the two agree. It is clear that the original relationships overestimate the mass of PMSG's significantly, which reflects the advancement in this technology in recent years. The most conservative correction factor has been applied to the relationship. This results

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in the relationship shown in Table 1, which also closely agrees with data given by The Switch in (The Switch, 2013). The cost of the PMSG's are also estimated using relationships provided by NREL in (Fingersh et al., 2006). Both mass and cost relationships are calculated based on the rated power of the machine in kW .

Gearboxes
All generators in this study are assumed to be used in connection with a three stage gearbox. This assumption is based on a 195 typical rated speed of a medium speed PMSG of 1500 rpm and rated speed of the wind turbine rotors. This results in a required gearbox ratio of 1:50, which is easily achievable with a three stage gearbox. The cost and mass estimation relationship for a three stage gearbox is taken from the same NREL study as the generator relationships. It is assumed that the mass of gearboxes has not decreased considerably since the publication of this report as the gearbox was considered a mature technology in 2006. The mass of the gearbox is calculated based on the low speed shaft torque (LSST) and the cost is based on the rated power of 200 the gearbox in kW

Power Electronic Converters
The mass of low voltage (690V AC), IGBT based back-to-back VSC's designed specifically for wind turbines are given for units of different power ratings in a data sheet provided by ABB (ABB, 2018). The mass is given for complete units and includes the converters, filters, circuit breakers, casings, cooling systems and any other auxiliary systems that are required for 205 the converters to operate. This information has been plotted and a linear approximation has been used to develop a scaling relationship that can estimate the mass of the back-to-back converter with power rating required for the MRWT system. Figure   10 shows that the linear approximation achieves a reasonable estimation of converter mass, particularly at lower power ratings.
Some topologies also use medium voltage converters, but little information is available on the mass of commercially available MV converters, particularly at low power ratings. Wind turbines have traditionally used LV generators of 690V until recently 210 when power ratings of wind turbines have increased significantly and it became more appropriate to use MV machines. It can be assumed that the same relationship holds for both low and medium voltage back-to-back converters. Comparing the mass of LV and MV back-to-back converter units of similar power ratings, both produced by ABB, it is seen that the MV converter mass is lower compared to its LV counterpart (ABB, 2019), suggesting that the mass estimation for low power medium voltage converters may be conservative. Mass for controlled rectifiers or inverters will be taken as half of the back-to-back converter 215 mass. Costs used in two recent studies (Parker and Anaya-Lara, 2013;Lakshmanan et al., 2015) have been converted to 2019 GBP to give a cost of a back-to-back converter (regardless of type) of £132/kV A and a controlled rectifier of £66/kV A.

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DC-DC converter price estimates vary significantly in the literature due to the lack of commercially available converters for wind applications and the variety of designs suggested. It is therefore most appropriate to take a range of prices available in the literature for suitable DC-DC converters and take an average of this price. The studies used for this are: (Lakshmanan et al., 2015;Fingersh et al., 2006;Max et al., 2007;Lundberg, 2003;Georgios and Wheeler, 2010). This gives an average cost of £110/kV A.

Cables
Mass of cables can be easily assessed using mass per km values given in data sheets of cables from a variety of cable manufacturers.
Cable costs are estimated from (Dicorato et al., 2011) which provides a cost function for a kilometre of cable based on the CSA of the cables. The study uses available costs from numerous sources and averages them for each CSA then uses a 240 least square linear regression to produce the relationship. The paper states that this relationship is valid for medium voltage copper conductor XLPE insulated cables. Although not stated, most offshore installations use three core cable, so it will be assumed that this is the cost for three core cable. Suitable cables have been selected for each topology based on the required current carrying capacity of the cables. Cable distances have been estimated for each topology based on realistic cable layout designs that follow the triangular lattice support structure beams as closely as possible to avoid loose hanging cables within the 245 structure.

Transformers
Mass of transformers has been estimated by using information given in (Declercq, 2003) regarding the 'SLIM' range of transformers for wind turbines manufactured by Pauwels International (now 'CG'). The mass of transformers from different information from (Islam et al., 2014) was used to develop the relationship shown in Table 1, which estimates the given masses of transformers very well. It also generally agrees with other information from data sheets for ABB distribution step down transformers. The mass of transformers is estimated based on the power rating of the transformer in kV A.
Lundberg (Lundberg, 2003) provides a formula for estimating the cost of MV/HV transformers rated between 6.3 and 150 MVA, with low side voltage rating between 10.5 and 77 kV and high side rating between 47kV and 140kV. The transformers 255 required in this study do not quite fall into this category, but will be assumed to follow this cost model. This cost model provides the base for many cost estimates of transformers in the literature, with (Parker and Anaya-Lara, 2013;Dicorato et al., 2011;Lakshmanan et al., 2015) all using this relationship and scaling it to present day value in the currency of the paper. The cost estimates for transformers in this study are based on the rated power of the transformer in V A.

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Lundberg (Lundberg, 2003) also provides a cost model for AC switchgear based on the voltage rating in V , which is commonly used within academic literature. The cost of DC switchgear is also required for this study, which is more difficult to estimate due to the lack of commercially available DC switchgear. It is suggested in (Lakshmanan et al., 2015) that the cost of DC switchgear could be as much as four times that of AC switchgear, but this figure is based on a study from 2007. Since then advancements in DC switchgear have been made, so a relationship of two times the cost of AC switchgear will be used here 265 to reflect advancements in technology. The mass of switchgear is assumed to be negligible in this study as the VSC mass estimations includes some switchgear masses.

Losses
Losses of each individual component were estimated at each 0.5 m/s wind speed increment between cut-in and cut-out wind speed. Mechanical power is calculated as follows where P mech is the mechanical power produced by the turbine, ρ is the density of air, A is the swept area, v is the wind speed and C P is the coefficient of performance. Loss profiles that describe the losses of each component over the entire operating range of wind speeds were used in order to account for varying efficiencies of components when operating at part load. For each topology, the mechanical power was calculated using Eq (1) and losses for each component subtracted at each wind speed.

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The output power of each component was used as the input power of the next component. For example, the input power of the generator is the mechanical power produced by the turbine minus the gearbox losses. Matlab scripts were created to calculate the total losses at each wind speed of each collection topology.
An equation is presented for gearbox efficiency in (Jamieson, 2011), which was developed by GL Garrad Hassan. It comprises of a loss that varies in proportion to the operating power level, and a constant loss that is related to the rated power and 280 number of stages: where L gear is the losses in the gearbox in kW, N is the number of stages, P r is the rated power of the gearbox in kW (constant) and P i is the input power of the gearbox in kW (variable). This equation is used to estimate losses of gearboxes in this study.
Losses for generators, power converters and DC-DC converters were estimated by using a combination of data presented in 285 a Lundberg study (Lundberg, 2003) and various data sheets from commercial suppliers. The Lundberg study presents losses of various components as a percentage of rated power over a full range of wind speeds, so can be applied to a variety of different power ratings while the commercial data is used to ensure up to date losses at rated power of the different components are used.
This allows for a simple method suitable for early stage analysis, while allowing the loss characteristics of different components at part load to be included. Loss data for each component was produced based on the Lundberg study and reconfigured to 290 reflect commercial rated efficiencies and a different rated wind speed, while maintaining the below rated characteristics of the components.
Medium speed PMSG efficiency at rated power is listed as over 98% by ABB (ABB, 2012). Back-to-back converter efficiency at rated power for LV converter unit is given as 97% in (ABB, 2018). Back-to-back converter efficiency at rated power for MV converter unit is given as 98% in (ABB, 2019). These efficiencies include back-to-back converters, filtering, cooling 295 systems etc. and is used in this study. For controlled rectifiers, an efficiency at rated power of 99% for MV and 98.5% for LV has been be used.
There are a huge amount of DC-DC converters proposed and studied in the literature in recent years. The advancement of power electronic devices and the increasing need to minimise mass in offshore applications has led to an increased interest in DC-DC converter topologies that are suitable for use in offshore wind farms. In (Parastar et al., 2015) a multilevel modular 300 DC-DC converter for high voltage DC wind farm is suggested and reports efficiencies of around 97% at rated power for a small scale prototype. In (Chen et al., 2013) various types of converters are compared in terms of mass, number of components, efficiency and volume. The two best candidates are a buck/boost converter based on IGBT's with a rated efficiency of 97.5% and a resonant switched capacitor converter with a very high efficiency of over 99%. In (Max and Lundberg, 2008) three converter types are analysed and compared, with the author concluding that the most suited type of converter for use in a DC 305 wind farm is a full bridge converter based on IGBT switches. The study presents efficiencies of both a turbine level and group level converter as 97.08% and 97.97% respectively. Finally, various topologies of DC turbine configurations are also shown in Lundberg's 2003 comprehensive study which all are approximately 97% efficiency (Lundberg, 2003). The conclusion reached is that a rated efficiency of 97% will be used for the DC-DC converters in this study, with below rated efficiencies capturing the characteristics of the converters presented in (Lundberg, 2003). This provides a realistic and slightly conservative estimate 310 of losses within a DC-DC converter suitable for the MRWT application.
Losses in cables can be approximated by where L cable_3Φ is the losses in the three phase AC cables in W, I RM S is the rms AC current in each phase in A, R AC is the 315 resistance of the AC cable in Ω, L cable_DC is the losses in the DC cable in W, I DC is the DC current in A and R DC is the resistance of the DC cable in Ω (Starke et al., 2008). Resistances of the cables can be calculated by considering the total length of cables within the topology and the given resistance per length for the cables CSA.
Transformer efficiencies are estimated using a combination of the loss profile presented by Lundberg in (Lundberg, 2003) and full load efficiencies presented in (Islam et al., 2014). Losses in switchgear are considered negligible.

7 Cost effectiveness
In order to analyse the cost effectiveness of each topology a levelised cost of energy (LCOE) calculation was performed that considered the capital cost of the drive train and electrical components and the total electricity produced by each topology over a 20 year lifetime of the project in net present value (NPV). Equation 5 was used to calculate this LCOE and the NPV of electricity produced was calculated according to Eq (6) where AEC is the annual energy capture, i is the discount rate which 325 is equal to 10% and n is the lifetime of the project in years. No costs associated with operations and maintenance or loss of power due to failures were included in this calculation.
LCOE elec = Capital cost of electrical components and gearbox sum of electricity produced over lifetime (5) Figure 13. Total losses at rated power of electrical topologies with breakdown by component. The LCOE of the electrical system and gearbox of each topology is shown in A comparison of each topology can be seen in Table 4. The AC radial is considered the base topology as it is the most 365 commonly used collection network in offshore wind farms. Base levels are marked with 'O' in Table 4  each topology, but a first pass attempt has been made here to at least indicate which topologies will benefit the most from this characteristic. Although cable failure rates are significantly lower than other components used in wind turbines, cable failures have still been included in this analysis. Cables in MRWT arrays will have less physical protection than sub sea cables used in wind farms so failure rates may be higher than stated in wind farm collection network failure studies.
The AC star topology is the best solution overall as it only performs slightly worse than the base case in the category of 380 efficiency and performs very well in each of the other categories, specifically reliability and mass per nacelle. The DC star topology also performs well overall and could see an improvement in reliability compared to the AC star topology due to its lower component count. It is recommended that more detailed design and analysis work are carried out for these two topologies.
The basic cost estimation of electrical components made in the Innwind project (Jamieson et al., 2015) totals to £4.6 million.
This cost estimation was lacking detail and significantly underestimated the cost of electrical systems required for a MRWT,385 with this study showing the cheapest system to cost in the region of £8.9 million. The capital cost of electrical components (as well as gearbox cost) in the Innwind project is 13.3% of the capital cost of the entire system, and LCOE of the electrical system and gearbox is estimated to be 10. to a large single rotor turbine. Combined with the savings in material costs for blades, improvements in O&M costs, reduced installation and transport costs and power increases due to clustering of turbines it is still expected that the MWRT concept will achieve a much improved overall LCOE regardless of the increase in cost of electrical components.
The cost estimates presented here are highly sensitive to the cost of DC-DC converters and DC switchgear. Although these costs may fall in the future, the reductions would have to be significant for the DC systems to be comparable in price to the AC 395 systems in the context of MRWT electrical systems. DC systems may be more attractive if the MRWT would connect to a DC collection network, however there is currently no DC collection networks in operation, and the feasibility of their existence  within the near future is still low. DC systems could also reduce cost and mass significantly by using diode rectifier in place of controlled rectifiers, but this would jeopardise the controllability of the entire system and in most cases lose the ability to control the speed of the turbines individually. From the systems analysed, the most promising type of system is the AC star topology; it performs well in a large range of categories, and has very good reliability compared to other systems. The high reliability is due to the design of the system which has no shared equipment between turbines. The DC star topology also performs well overall and could have even higher reliability than the AC star topology due to its lower component count. Both topologies should be considered for more detailed 415 design and analysis in future work.
Author contributions. PP carried out all design and analysis work under supervision and guidance from DC and OA.
Competing interests. The authors declare that they have no conflict of interest