Design and Performance of a 20kW, 100rpm

Design and Performance of a 20kW, 100rpm, Switched Reluctance Generator for a Direct Drive Wind Energy Converter M. A. Mueller School of Engineering & Electronics University of Edinburgh The King’s Buildings Edinburgh EH9 3JL Abstract-The application of switched reluctance generators for use in direct drive wind turbines is discussed in the paper. A 20kW prototype machine operating at a rated speed in the region of 100rpm was designed, built and tested. Experimental results verified the design procedures and also illustrated the suitability of switched reluctance machines for wind energy converters. From full load to ¼ load the efficiency of the machine and converter varied from 88% to 80% respectively. I. INTRODUCTION The trend for the power rating of wind turbines has increased significantly in the last 10 years from 100kW to existing commercial prototypes at 5MW. On average the most common installed unit is rated at 1.3MW and is principally for onshore use [1]. However, wind energy developers are now exploiting the offshore wind resource, where average wind speeds are greater than on land and visual impact is less of an issue. Going offshore creates technical and economic challenges to the developer in terms of installation, operation and maintenance. In order to improve the economics there is a trend to increase the unit rating of turbine units, with 5MW prototypes being tested onshore at present, and 10MW units in the design stage. The economics are linked to operation and maintenance issues, which are very different in the offshore environment compared to onshore. Access for maintenance is more limited and costly relying on access to boats and a decent weather window. Robustness and reliability are vital to the economic operation of large multi-MW wind turbines in the offshore environment. Recent events at Horns Rev highlight that onshore technology needs to be more robust in order to operate effectively in the offshore environment. The reliability of gearbox drivetrains is being questioned particularly at the proposed ratings in excess of 5MW. Some manufacturers are pursuing direct drive systems using permanent magnet (PM) [2] or field wound synchronous generators [3]. PM machines will have a better torque density than the field wound version, but the presence of PMs will make assembly more difficult. In the field wound synchronous machine brushes, required to excite the field winding, demand maintenance at regular intervals. The switched reluctance machine consists of a very robust and simple construction with no rotor windings and concentrated coils on the stator. The mechanical engineering challenges of building large diameter machines are the same for switched reluctance machines and field or PM excited machines, but the lack of permanent magnets will simplify assembly and no brushes on the rotor eliminates a maintenance requirement. The switched reluctance machine is an inherently variable speed machine that can be easily controlled and matched to its load by controlling the instants of energising and de-energising the stator phases, whether it is operating in motoring or generating mode. Switched reluctance machines have been proposed for wind power in the past, but only results from paper design studies have been presented [4,5,6]. The reader is referred to these papers and additional references [7-11] in order to understand the principles of operation of the switched reluctance machine in generation mode. The main points are summarised in this paper for completeness sake. In this paper the author presents the design and build of a low speed (100rpm) 20 kW machine chosen for a commercial wind turbine. Experimental tests of the prototype verify the design procedures used and demonstrate the high performance of the machine in terms of efficiency. II. WIND ENERGY Equation 1 gives the power converted by a wind turbine, where R (m) is the blade radius, V (m/s) is the wind speed, ρ (kg/m3) is the air density, Cp(λ) represents the aerodynamic conversion factor for the wind turbine, which is a function of the tip speed ratio λ, given in (2) )( 2 1 32 λρpi pCVRP = (1) V Rωλ = (2) 0-7803-8987-5/05/$20.00 ©2005 IEEE. 56 The prototype 20kW generator was designed for a commercially available wind turbine manufactured by Gazelle Wind Turbines in the UK [12]. Fig. 1 shows the Cp-λ curve for this turbine, which has a maximum conversion coefficient of 0.42 at a tip-speed ratio equal to 9. A typical wind profile has been calculated using expressions in [13] and is shown in Fig 2. Naturally the user has no control over the wind speed, and hence the only way to ensure that the turbine is always operating at its optimum value of Cp is to control the rotational speed, ω. Both the torque and speed of the turbine need to be matched in order to optimise the performance of the overall system. The switched reluctance machine is very suited to such a prime-mover because the torque and the speed can be controlled by varying the instants of energisation, ie. the firing angles. In a direct drive power take off system the generator rotates at the same speed as the turbine, which is considerably less than an induction machine in a geared drive-train. For the 20kW turbine used in this study a direct drive generator operates in the region of 100rpm. Table 1 summarises the turbine speeds for a range of machines manufactured by Enercon in Germany [3]. The speed of rotation has a significant impact on the design of the switched reluctance machine in terms of the topology, ie. the stator/rotor pole combination, which will be discussed in the paper. 0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 tip speed ratio C p Fig. 1 Cp-λ curve of the 20kW Gazelle Wind Turbine. 0 5 10 15 20 25 30 -5 0 5 10 15 20 25 30 35 time (s) w in d s pe e d (m /s ) Fig. 2 Typical wind profile. TABLE 1 TURBINE SPEED FOR RANGE OF TURBINES Power (kW) N (rpm) Device 300 46 E30 600 34 E40 1000 24 E58 1800 22 E66 4500 13 E112 III. MODELLING SWITCHED RELUCTANCE GENERATORS Fig. 3 shows a typical current waveform for a switched reluctance machine operating in generation mode. If a phase is energised so that the turn-on angle falls in the rising part of the inductance profile and the turn off angle falls after the fully aligned position, the machine will generate power back into the supply. During the conduction period from θon to θoff, current flows from the supply and energy is stored in the machine. This period of energisation is known as the excitation period and is necessary because the switched reluctance machine is a singly excited machine. The energy stored during this period is referred to as the excitation energy. After commutation, at θoff, the excitation energy is returned to the supply and at the same time the mechanical energy provided by the prime mover, the wind turbine, is converted to electrical energy. At θend all the flux from the excitation period has been supressed, and no more electrical energy is returned to the supply. The period from θoff to θend is referred to as the active period. Liu and Stiebler [9] define an excitation current, Ie, and an active current, Ia in each of these periods. In order for generation to be sustained the net electrical output energy must exceed the excitation energy. In order to calculate the performance of the machine the flux-linkage current position map must be determined. This is obtained using algorithms in [14 & 15] and involves the following aspects. A. Inductance Profile To calculate the flux-linkage position current map the inductance profile is first estimated from the aligned and mis-aligned inductances. From the unaligned position to θ I L θ e n dθ o ffθ o n Fig. 3. Typical inductance and current waveforms. 57 Fig. 4 Inductance profile. the onset of overlap it is assumed that the inductance remains constant. Between overlap and the fully aligned position it was assumed that the inductance increased linearly, resulting in a distribution similar to that shown in Fig. 4. The flux-linkage current position map is determined from the inductance profile using the relationship, Li=Ψ . Calculation of Lmax The maximum inductance is calculated by modelling the flux paths using a magnetic equivalent circuit, and including the effect of the material properties. Due to symmetry only a pole pitch needs to be modelled. Fig. 5 shows the magnetic equivalent circuit for a single pole pitch. Each reluctance in the circuit represents a separate flux path. The relative permeability of the iron paths are modelled using the B-H curve for mild steel, the material used in the stator and rotor laminations. The flux flowing in the circuit is found from (4), which is solved for a range of current levels, so that the effect of saturation on the inductance is taken into account. The first term in the brackets represents the airgap flux paths and the remaining terms represent the flux paths in the stator/rotor poles and the stator/rotor core-backs (yokes). NI is the mmf driving flux around the circuit. � � � � � ��� ++++= −−−− A l A l A l A l A l NI r yoker r yokes r poler r polesg µµµµµµµµµ φ 00000 222 4 The model was verified using a 2D finite element model [16]. Calculation of Lmin The flux paths in the un-aligned position are not so well defined as in the fully aligned position. Hence a 2D finite element model was used to determine the un- aligned inductance. Fig. 6 shows a finite element model for a 3-phase 12/8 machine with flux paths highlighted. The minimum inductance is determined from the stored energy. Fig. 5 Magnetic Equivalent Circuit for a pole pitch. Fig. 6 Finite element model in the un-aligned position. B. Calculation of Current and Torque In order to deduce the instantaneous current (5) is solved numerically to give the flux linkage, where V is the voltage applied to the windings and R is the phase winding resistance. iRV dt d −= Ψ (5) The position is determined by solving the equation of motion, (6) (mechanical losses have been neglected), where Tm is the input mechanical torque of the wind turbine, Te is the electrical torque of the generator, J is the inertia and ω is the rotational speed. dt dJTT em ω =− (6) With this information the new current can be deduced from the flux-linkage current position map, and the instantaneous electrical torque is calculated from (7). θd dLITe 2 2 1 = (7) The new value of current and electrical torque is then used in the next time step in (5) & (6) from which the new flux-linkage and position are determined. The 58 whole process then repeats itself. The average torque, eT , is determined from the area enclosed within the flux-linkage current trajectory for a particular conduction period. During generator operation the enclosed area is proportional to the prime mover mechanical energy input. If this area is equal to E (J) the mean electrical torque for a machine with m phases, Nr rotor poles is given by : Nm 2 E mN T re pi = (8) IV. 20 kW PROTOTYPE DESIGN STUDY The model was used to investigate switched reluctance machine topologies for the Gazelle Wind turbine [12], which is rated at 20kW at a wind speed of 12m/s. Assuming the turbine is operating at its maximum value of Cp, 0.4 from Fig. 1, then the turbine rotates at 114.6 rpm. The main challenge in switched reluctance machine design is in the choice of numbers of poles on the stator and rotor. There are two options available: 1. Choose the number of stator and rotor poles for a particular number of poles per phase. 2. Fix the stator poles and number of phases and vary the number of rotor poles. For this study the number of phases was set to 3, and the number of poles per phase was varied from 4 to 8 in steps of 2. Pole combinations used include 12/8 (stator poles/ rotor poles), 18/12 & 24/16, which correspond to 4,6 and 8 poles per phase respectively. In addition designs were obtained for 12/16, 12/20 & 12/40, all of which only have 4 poles per phase, but have an increasing value of so-called magnetic gear ratio, which will be discussed later. As a starting point to the design study the outside diameter of the machine is limited to 10% of the turbine rotor diameter in order to minimise any disturbance to the airflow through the turbine. The airgap radius and core-length were chosen for a specific torque per unit of rotor volume, which for an industrial machine is typically 13 kNm/m3 [11]. An airgap diameter of 650mm was chosen to define the radial envelope, and hence the core-length could be determined. The airgap and the current density were set to 0.5mm and 3A/mm2 respectively for all designs. The remaining dimensions and turns per coil were varied until it was felt that the best design had been found. Initially the geometrical dimensions were chosen so that the pole flux density at commutation was 1.4-1.5T and the core-back flux density was 1.0T. The machines were therefore not operating hard into saturation. Designs were optimised for efficiency, and weight. Unless otherwise stated it is assumed that the generator is operating in single pulse mode at a supply voltage of 400 V. These simple assumptions provide the designer with some physical geometrical dimensions as the starting point in the more detailed design stage. In the design study a number of parameters were compared: torque per unit mass, excitation penalty, VA requirements and efficiency. These parameters have been defined in [9 & 11], but are stated here for completeness sake. A. Definitions Equivalent of Power Factor The net dc output current is the difference between the active current and the excitation current (Io=Ia-Ie). If the voltage remains constant during the entire conduction period then the electrical output power can be found. Liu and Stiebler defined an equivalent term to power factor for the switched reluctance generator as : r o I I =λ (9) where, Ir is the rms phase current. This power factor term can be used as a measure of the VA requirements of the converter. Excitation Penalty Without the excitation period the SR machine would not be able to generate. Ideally the mean excitation current should be very small in comparison to the mean active current so that the net output current is maximised. Miller defines the excitation penalty as: o e I I e = (10) Converter VA Requirement. A summary of converter requirements is treated by Miller. It is expressed in terms of the excitation penalty, the converter VA requirement as follows : VA 12 � � � � + = k eP N Q o rδ pi (11) where Nr is the number of rotor poles, δ is the conduction angle (θoff - θon) and k is the utilisation factor. Utilisation Factor The utilisation factor is a measure of how much energy actually flows compared to the product of the peak flux linkage )ˆ(Ψ and the peak current )ˆ(I . The peak flux linkage occurs at commutation, but the peak current does not necessarily occur at the same instant. It is given by (12). ( ) ˆˆ 1 I eWk Ψ + = (12) 59 B. Design Study Results TABLE 2 Lamination data for different designs 12/8 18/12 24/16 12/16 12/20 12/40 Od (mm) 810 810 786 775 760 727.5 Gd (mm) 650 650 650 650 650 650 Sc (mm) 35 35 23 30 25 25 Rc (mm) 35 35 23 30 25 25 Sd (mm) 410 410 434 450 450 550 Clen(mm) 350 350 400 350 450 800 Table 2 gives the main lamination data for each of the topologies designed, which satisfy the constraints outlined above, where Od is the stator outside diameter, Gd is the airgap diameter, Sc & Rc are the stator and rotor core-back depths, Sd is the shaft diameter & Clen is the core length. Fig. 7 shows the flux-linkage trajectory for all the topologies considered and Table 3 summarises the main performance data. Compared to the 12/8 topology the area enclosed decreases as the number of rotor poles increase. The area enclosed by the loop is proportional to the energy converted per stroke. In going from 12/8 to 18/12, E has decreased by a factor of 1.5, and for 12/20 it has decreased by a factor of 2.6 times. The effect of the increased number of rotor poles has been to increase the number of energisations per revolution, and hence compensate for the reduction in E. All machines exhibit high efficiency, but the 12/8 appears to be the best in terms of power factor and excitation penalty. In a wind energy system machine weight is very important. The results in Table 3 do show that some benefit is to be gained in terms of torque per unit weight from going to higher pole number machines. Fig. 7: Flux-linkage map for the different topologies. TABLE 3 Performance data. λ e Lmax Lmin % T/kg kVA rating 12/8 0.44 0.18 27.3 91.0 2.5 58 18/12 0.42 0.20 18.1 91.8 2.6 100 24/16 0.4 0.24 13.8 92.7 2.7 104 12/16 0.43 0.32 12.2 91.4 3.1 80 12/20 0.35 0.50 9.8 90.6 2.8 102 12/40 0.33 0.65 5.5 91.8 2.3 115 The 12/16 & 12/20 topologies offer the best torque per unit weight ratio. If the number of stator poles is fixed, but the rotor poles increased, more circumferential space is available for copper. This allows the radial dimensions such as outside diameter and core-back to be reduced. However for very high rotor pole numbers the decrease in pole-width results in high pole flux densities. This is evident in the 12/40, in which the core length has had to be increased to 800mm to ensure a reasonable flux density level in the poles. The torque per unit weight for the 12/40 is therefore not so good. As the excitation penalty increases, so does the VA requirements of the converter. However, it is of interest to note that the 12/16 is better than the 24/16 even though the excitation penalty is worse for the former compared to the latter. In the case of the 24/16 the space available for coils is considerably less than that in the 12/16. In order to achieve low copper loss, fewer turns are used in the 24/16 compared to the 12/16. The inductances are therefore lower, although the ratio of unaligned to fully aligned are comparable in the case of the 12/16. Lower inductance leads to higher peak currents, which results in a higher converter requirement. The designs presented in Table 2 are conservative such that the iron was not driven into saturation. In order to see how the different topologies performed when driven harder, the geometry was changed so that the pole flux density was in the region of 1.8T, and the core-back flux density was in the region of 1.5 T. The main reason for doing this was to see if any more gains in torque per unit weight could be achieved, without a reduction in performance. Table 4 gives the modified lamination data and Table 5 the performance data. TABLE 4 MODIFIED LAMINATION DATA 12/8 18/12 24/16 12/16 12/20 Od (mm) 800 800 786 755 750 Gd (mm) 650 650 650 650 650 Sc (mm) 30 23 23 25 25 Rc (mm) 30 23 23 25 25 Sd (mm) 550 550 550 550 550 Clen(mm) 500 350 400 350 400 Flux-linkage against phase current 0 2 4 6 8 10 12 0 50 100 150 phase current (A) flu x lin ka ge (W b tu rn s ) 12/8 18/12 24/16 12/16 12/20 12/40 60 TABLE 5 PERFORMANCE DATA λ e kVA T/kg % 12/8 0.33 0.52 122.2 2.26 84.8 18/12 0.36 0.35 107.7 2.94 88.9 24/16 0.40 0.26 112.0 3.19 91.2 12/16 0.37 0.43 110.6 4.22 90.5 12/20 0.33 0.50 137.6 3