Title: Optimal design of a 1 kW switched reluctance generator for wind power systems using a genetic algorithm
Abstract: IET Electric Power ApplicationsVolume 10, Issue 8 p. 807-817 Research ArticlesFree Access Optimal design of a 1 kW switched reluctance generator for wind power systems using a genetic algorithm Hye-Ung Shin, Hye-Ung Shin Department of Electrical and Computer Engineering, Ajou University, San5, Woncheon-dong, Yeongtong-gu, Suwon, 443-749 KoreaSearch for more papers by this authorKyo-Beum Lee, Corresponding Author Kyo-Beum Lee [email protected] Department of Electrical and Computer Engineering, Ajou University, San5, Woncheon-dong, Yeongtong-gu, Suwon, 443-749 KoreaSearch for more papers by this author Hye-Ung Shin, Hye-Ung Shin Department of Electrical and Computer Engineering, Ajou University, San5, Woncheon-dong, Yeongtong-gu, Suwon, 443-749 KoreaSearch for more papers by this authorKyo-Beum Lee, Corresponding Author Kyo-Beum Lee [email protected] Department of Electrical and Computer Engineering, Ajou University, San5, Woncheon-dong, Yeongtong-gu, Suwon, 443-749 KoreaSearch for more papers by this author First published: 01 September 2016 https://doi.org/10.1049/iet-epa.2015.0582Citations: 22AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study presents an optimal design for a 1 kW switched reluctance generator (SRG) for wind-power applications. The design of the SRG is optimised to increase efficiency and reduce the volume of the generator compared with a basic model designed using the D2L method. To begin the optimisation, Latin hypercube sampling is employed to extract samples of the design variables for the design of experiment. The Kriging method of approximation modelling is used to interpolate the non-linear characteristics for the optimal design. Finally, a genetic algorithm is utilised to optimise the original design model for efficiency and reduced volume. The optimal design of the SRG uses the shape parameters of the basic model. Design variables are selected to be at their maxima. The designed optimal model is compared with the basic model and prototype to verify the results. 1 Introduction Wind-power generator systems typically use doubly fed induction and permanent magnet (PM) machines for ∼100 kW or higher capacities owing to their numerous advantages in terms of efficiency and the wide range of operation strategies available for their control [1-4]. Doubly fed induction machines, however, suffer from relatively low efficiency issues. PM machines are expensive because of the type of rare earth magnets used in the rotor. To address these drawbacks, a switched reluctance generator (SRG) utilising a rotor core without rare earth magnets [5] is investigated in this paper. Skyscrapers continue to be constructed in major cities. These buildings cause problems including greenhouse gas emissions and increased energy loss compared with smaller buildings. However, skyscrapers can be used as bases to install small wind turbines because of the buildings' significant height. Further, small wind-power systems can be installed in mountainous villages and on small islands [6]. The proposed SRG can be used to replace induction and PM machines in small-scale wind-power generator systems. To implement the proposed generator in skyscrapers, mountainous villages, or small islands, the load portion of the SRG can be connected to a battery that stores the electrical energy produced by the generator. The major advantages of SRGs include high-efficiency, high-speed response, low spin loss, heat resistance, durability, and low production cost [7]. Recently, technological advances in power semiconductors have increased owing to their extensive utilisation in machine drive applications. Moreover, power semiconductors used in power conversion systems can be reduced in terms of the number of elements, resulting in low-cost, robust wind-power generator systems. These machines are also a focus of research because of their advantages in variable speed operation over a wide range [8]. There are different methods with regards to the design and control level to increase the efficiency of low-cost SRGs. There are several optimisation techniques that can be used to obtain an optimal design that improves the efficiency of the machine. Evolutionary algorithms such as genetic algorithm (GA) and immune algorithm can be used in a broader sense compared with sensitivity-based methods [9-11] because they only require objective function values. Sensitivity analysis has attracted considerable interest because of its ability to address a large number of design variables rapidly and effectively [12, 13]; however, it has the problem that a solution may converge on a local minimum. Therefore, the approach to determine an optimal design should include GA, Latin hypercube sampling (LHS), the response surface method (RSM) of design of experiment (DOE), Kriging method of approximation modelling for non-linear characteristics, and Taguchi method [14-16]. LHS is an integration of stratified and random sampling. It samples states from the entire distributions of random variables and produces more stable and precise estimates than Monte Carlo (MC) sampling with the same sample size [17]. Therefore, LHS can obtain more accurate reliability indices than MC sampling. In order to approximate the optimal model, the RSM is generally used in the electric machine. [18]. However, this model is not adequate to approximate a non-linear function such as inductance parameters because of the low-order polynominal regression of RSM. For reducing this drawback, the Kriging method can be applied to the optimal design of electric machine for the global optimisation. This paper addresses the optimal design of a 1 kW SRG for a small wind-power generator system. The optimal design is based on the specifications for a basic model designed using the D2L method. The results of the basic model are validated using finite element analysis (FEA). LHS is used to extract samples of the design variables. The design variables are distributed evenly in the design variable range. Samples are extracted among these evenly distributed design variables using LHS. Owing to its suitability for non-linear data, the Kriging method is used to approximate the extracted variables. The optimal design is finalised using a GA and the extracted samples [19-21]. Optimal design results are compared with a basic design model to demonstrate the improved performance of the optimised model using FEA. A prototype of the optimised model is built and tested to validate the design results. 2 Design of basic model 2.1 Design procedure of basic model The design specification of the SRG is 8/6 four-phase, 1 kW, 1000 rpm. To satisfy the electrical output of 1 kW, the basic model is determined considering the rated torque and rated speed. Once the design specifications are determined, the design is performed in accordance with the design process illustrated in Fig. 1. Fig. 1Open in figure viewerPowerPoint Design process of the basic model The D2L method is proportional to the volume of rotor. The dimension of the generator is determined by the torque. The dimension of the generator can be obtained as follows (1)where T is the torque, k is the output coefficient, Dr is the outer diameter of the rotor, and Lstk is the stack length. The output coefficient k is set to 1.3 for a small machine [22]. Dr and Lstk are calculated from (1) and Ds is calculated by applying Dr/Ds = 0.53, which is decided based on Table 1 considering the number of phases of the generator, because Ds should be considered to maximise the output power in the basic design. In addition, Table 1 can be generalised based upon the number of phases using Table 1 [21]. Table 1. General ratio according to number of phase and pole Phase Ns Nr Dr/Ds 3 6 4 0.50 3 12 8 0.57 4 8 6 0.53 The air gap is determined from the outer diameter of the rotor and stack lengths. When the gap is small, the leakage magnetic flux is reduced. However, when fabricating a generator, it is difficult to reduce the air-gap length below 0.2 mm because of the manufacturing constraints for the prototype. Therefore, the air-gap length is set to 0.2 mm. Once the pole arcs are determined in accordance with the outer diameter of the stator, the stator pole width and rotor pole width can be expressed as follows (2) (3)where ts is the stator pole width, tr is the rotor pole width, βs is the stator pole arc, βr is the rotor pole arc, and r1 is the radius of the rotor. Since the stator and rotor yoke thickness must be designed without saturating the core, the stator yoke thickness must be ts/2 or greater. In a practical design, the stator yoke thickness is normally calculated to be 1.1 times larger than the stator pole width, because the stiffness of SRG can be increased in accordance with the stator yoke thickness and can reduce the noise of SRG. However, the weight of the machine increases and the slot area is not sufficiently large for a winding. Therefore, the stator yoke thickness properly should be selected by the situation of the application. The rotor pole width should be higher compared with the rotor yoke thickness by a factor of at least 0.7 (tr ≥ 0.7yr) in order to avoid magnetic saturation in the rotor [21]. The shaft diameter can be determined in accordance with the depth of the rotor yoke and the rotor slot (4)where Dsh is the shaft diameter, dr is the slot depth of the rotor, and yr is the rotor yoke thickness. The number of turns can be obtained as follows (5)where Np is the number of turns, Vs is the rated voltage, rpm is the rated speed, m is the number of phases, and Bs is the magnetic flux density. Table 2 is the design result for the basic model. The parameters of the basic model are calculated using the above design process. The design results of the basic model are validated using FEA. The FEA results are explained by comparing the basic and optimal models in Section 4. Table 2. Design result of basic model Parameters Basic model Unit stator outer diameter Ds 161 mm pole arc βs 16 deg. pole width ts 12 mm yoke thickness ys 10 mm rotor outer diameter Dr 85 mm pole arc Βr 17 deg. pole width tr 12.6 mm yoke thickness yr 9 mm air gap Gair 0.2 mm shaft diameter Dsh 37.3 mm stack length Lstk 100 mm number of turns Np 98 turns 3 Optimal design of basic model 3.1 Design procedure of optimal design Fig. 2 presents the design process of the optimal SRG using a GA. First, the design variables and design ranges are determined to achieve the optimum performance of the SRG. LHS is executed based on the DOE to distribute evenly in the range of the design variables [17, 23]. To verify the property of the sampling points, FEA is performed on the sampling points; it is important to analyse the sampling points using FEA. Then, these results are used to approximate the modelling using the Kriging method for the suitability of the non-linear characteristics. The optimisation is performed within these constraints until the optimal design is achieved. If the solution converges to the desired specifications, the optimisation process is successful. Otherwise, the variables are adjusted to achieve the targeted optimised values within the given constraints. Fig. 2Open in figure viewerPowerPoint Design process of the optimal SRG Table 3 displays the optimal design parameters of the proposed generator. The design variables from k1 to k7 are used to increase the efficiency and power density of this optimal design. The range of the design parameters is selected based on the basic model parameters. To avoid magnetic saturation, k1 is properly determined using the median of the stator yoke thickness of the basic model parameter. In a similar manner, k2, k3, and k4 are determined from the median of the basic model parameters. The power density performance of the generator improves by reducing the size of k5 and is limited to 0.2 mm considering the manufacturing constraints for the prototype. The optimal design variables k6 and k7 are selected in the indicated range to increase the output power density. When the outer diameter of the stator is changed, the outer diameter of the rotor can be changed. In that case, the output power of the SRG is changed in accordance with (1). In addition, the result of the exact optimal design cannot be obtained compared with the basic model. Therefore, to obtain the same output power, the outer diameter of the stator has not been changed. Table 3. Optimal design variables of SRG Parameter Design variable Range Unit stator yoke thickness k1 8–12 mm stator pole arc k2 13–20 deg. rotor yoke thickness k3 8–11 mm rotor pole arc k4 14–21 deg. air gap k5 0.2–0.3 mm shaft diameter k6 37.5–43.5 mm stack length k7 80–100 mm When the machine has a thin stator yoke, the core is saturated owing to high magnetic flux. To avoid flux saturation, the slot area must be designed to be wider. Furthermore, because the stack length is directly related to the output power of the generator, the stack length is selected appropriately to maintain the power of the machine at ∼1 kW. The LHS is used to replace each value of a variable with the samples, no matter which value might turn out to be more important. For each sample [k1, k2], the sample values of X, Y are determined by the following equation (6)where n is the sample size, ξX and ξY are the random numbers (ξX, ξY ∈ [0, 1]), and FX and FY are the cumulative probability distribution functions of X and Y, respectively. A valid LHS can be generated by starting with a sequence of n number 1, 2,…, n and taking various permutations of this sequence. In this paper, LHS [24] is used and it can be easily accessed through 'Toolboxes' in Matlab. After determining the range of the optimal design variables, the number of samples to be obtained using LHS is set to 20. Overlapping samples are discarded while selecting these 20 samples. The results from LHS are provided in Table 4. Fig. 3 shows a sample distribution map of the variables determined using LHS. Sample points (k1, k2, and k3) are confirmed to be distributed in two-dimensional (2D) space. Consequently, the seven design variables do not overlap in the range of the design parameters. Table 4. Sample distribution using LHS Number of samples k1 k2 k3 k4 k5 k6 k7 1 8.8 13.4 8.9 20.3 0.221 42.6 81.1 2 10.3 14.8 8.5 20.6 0.232 41.6 93.7 3 11.8 17.1 9.7 18.4 0.295 37.5 87.4 4 9.1 16.3 9.1 17.7 0.226 38.1 96.8 5 8.6 17.8 9.6 18.8 0.247 41.0 88.4 6 10.5 14.1 8.0 18.1 0.237 37.8 80.0 7 12.0 15.6 10.8 19.2 0.284 41.3 90.5 8 10.7 14.5 8.3 15.5 0.289 40.3 82.1 9 10.1 19.3 10.2 21.0 0.242 38.8 85.3 10 11.6 13.0 8.6 19.9 0.300 39.1 95.8 11 8.4 20.0 10.4 15.1 0.200 41.9 84.2 12 9.9 13.7 8.8 14.0 0.258 42.2 94.7 13 9.3 18.5 10.7 19.5 0.211 40.7 97.9 14 8.0 17.4 8.2 15.8 0.216 39.7 89.5 15 9.5 18.9 11.0 16.9 0.263 43.2 100.0 16 11.4 15.2 9.4 16.2 0.253 40.0 91.6 17 10.9 16.7 9.9 17.3 0.274 42.9 83.2 18 8.2 15.9 9.3 16.6 0.205 43.5 92.6 19 9.7 18.2 10.5 14.4 0.268 39.4 86.3 20 11.2 19.6 10.1 14.7 0.279 38.4 98.9 Fig. 3Open in figure viewerPowerPoint Sample distribution map using LHS a k1 and k2 b k1 and k3 To verify the characteristics of each sample model, the 20 samples obtained using LHS are simulated using 2D FEA that is used to reduce the solution time [25]. After performing LHS based on the DOE, Kriging approximation modelling is performed to approximate the non-linear points within the distributed sample points [16, 17]. To calculate the Kriging approximation model, the Gaussian correlation function and exponential function can express the linear and non-linear characteristics (7)where ndv is the number of design parameters, θk and Pk are the unknown correlation parameters used to fit the model, and and are the kth components of sample points and . The average and variance of the Kriging approximation model can be summarised as follows (8) (9)where is the best linear unbiased predictor, yx is the reactivity value, F is the set of the global model function, is the mean square predictor of the regression coefficient, r(x) is equal to the correlation between a random point x and the experimental data, and f(x) is the distribution of design parameter. By selecting the correlation elements, and , the Kriging modelling is determined. The correlation elements are obtained by maximising the likelihood function as follows (10) (11)where σ2 is the maximum-likelihood predictor value. The Kriging technique is performed using the above formula. The objective functions and constraint functions are approximated using the Kriging method. 3.2 Genetic algorithm A GA is used to optimise the machine model by applying the Kriging approximation model result based on LHS. In addition, GA can be accessed through the optimal design tool 'Piano'. The objective function and constraints are considered to increase the efficiency and power density. The maximum efficiency is selected as the objective function to be optimised. Further, the constraints cannot violate the optimal design area. Equation (12) expresses the objective function and constraints of the optimisation problem (12)The efficiency of the generator in the optimal model is set to be higher than that of the basic design model, which is selected as the objective function of the problem. The torque and the output power are constrained to satisfy the capacity of 1 kW. An iterative method is used to obtain the optimal solution for the problem using the values of the design variables. 4 Simulation results 4.1 Optimal design simulation Fig. 4 illustrates the convergence progress to the optimal point using a GA. The stack length decreased from 100 to 81.2 mm. Although the stack length of the SRG decreased compared with that of the basic model, the output power remained constant. The efficiency of the optimal model increased to ∼83%. Therefore, the result satisfied the optimum design conditions. Fig. 4Open in figure viewerPowerPoint Convergence progress of optimal point using GA a Efficiency b Stack length c Output power Fig. 5 shows a comparison of the design parameter results for the basic and optimal models; these parameters are listed in Table 5. Seven (k1–k7) variable values contributed to the cases in the optimal design range using LHS. Table 5. Comparison results of basic model and optimal model Parameters Design variable Basic model Optimal model Unit stator outer diameter Ds – 161 161 mm pole arc βs k2 16 18.2 deg. pole width Ts – 12 13.6 mm yoke thickness ys k1 10 11.8 mm rotor outer diameter Dr – 85 85 mm pole arc Βr k4 17 17.5 deg. pole width Tr – 12.6 13 mm yoke thickness yr k3 9 9.7 mm air gap Gair k5 0.2 0.2 mm shaft diameter Dsh k6 37.3 42.5 mm stack length Lstk k7 100 81.2 mm Fig. 5Open in figure viewerPowerPoint Comparison of design parameters a Optimal design parameters b Basic model c Optimal model The outer diameter of the rotor did not change to maintain the same output power at the same speed. Moreover, the outer diameter did not change. However, the pole arc and the pole width of the rotor and stator did change. Since the stator pole arc increased from 16° to 18.2°, the magnetic flux was not saturated in the stator pole arc. In addition, when the stator pole arc increases, the static torque becomes wider, due to the longer duration of alignment of stator and rotor pole. By proper choice of the stator and rotor pole arcs for a given machine, more average torque with reduced ripple can be achieved [26]. Further, the stator pole width increased from 12 to 13.6 mm. As a result, the basic model is optimised for the efficiency of the generator. Although the optimal model resulted in βs > βr, the windings of the generator for the optimal design have sufficient place. It is worth noting that unnecessary winding area and stack length decreased completely through the optimal design. The efficiency of the SRG increased to ∼83% by optimising the basic model of the SRG. 4.2 Power losses To compare the power losses of the basic design and the optimal design models, the losses were calculated using a loss equation and FEA. The power losses of the SRG include stator losses and rotor losses. The stator of the generator produces both iron losses and copper losses owing to the stator windings. However, the rotor of the generator does not contain any windings and contributes only to the iron losses of the machine. The electric power output and power losses from the SRG can be computed as follows [27] (13) (14) (15)where ωr is the angular velocity of the rotor, Pcu is the copper loss, Pi is the iron loss, irms is the root mean square (rms) value of the phase current, rph is the phase resistance, km is the loss factor, and Wm is the weights of the iron segments. The copper losses of the generator are directly calculated in each stator winding, whereas the iron losses are obtained using the J-MAG FEA tool based on the electromagnetic analysis by considering its operation at the base frequency of the SRG. 4.3 Finite element analysis Fig. 6 presents the system configuration for the simulation and experiment. To validate the design results of the basic and optimal models, 2D FEA was performed. 3D FEA considers the contribution of motor end windings to the overall inductance of the machine. Although the end effects and axial fringing field are not considered in 2D FEA, it is similar with 3D FEA [28]. The entire system consisted of a 1 kW SRG, asymmetric bridge converter, prime mover, and load, which was a battery for the actual application. When the prime mover was rotating at 1000 rpm, the power generation characteristics of the SRG confirmed the simulation. The SRG was controlled by a hard-chopping control. The hard-chopping scheme was driven by turn-on and turn-off of the two switches of each phase simultaneously. This control scheme was used in the simulation and the experiment to compare the generation characteristics of the basic and optimal models. The turn-on angle was 30.5° and the turn-off angle was 45°. The energy generated by the SRG can be stored in a battery for practical applications of a skyscraper, mountainous village, or small island. Fig. 6Open in figure viewerPowerPoint System configuration for simulation and experiment Fig. 7 shows a distribution comparison of the magnetic flux density of the basic and optimal models. The mesh of the basic model consisted of 10,592 elements that were used to simulate the entire model. The mesh of the optimal model consisted of 10,072 elements that were used to simulate the entire model. The material of the SRG core was s18. When the magnetic flux density of s18 was >2.1 T, the stator core became fully saturated based on the B–H curve of s18. As indicated in Fig. 7, the magnetic flux density was not saturated when the rotor rotated at 1000 rpm. Moreover, the optimal model generated a greater magnetic flux than the basic model. Consequently, higher electromagnetic torque is predictable. Fig. 7Open in figure viewerPowerPoint Distribution comparison of magnetic flux density a Basic model b Optimal model Fig. 8 compares the magnetisation characteristics of the basic and optimal models in terms of the flux linkage and the inductance of the machine obtained using FEA. It is evident that the basic model produced higher flux linkage compared with the optimal model. However, the optimal model could operate effectively owing to its evenly distributed inductance profile. Although the stack length was reduced, the optimal model generated a similar magnetic flux to the basic model. When a 20 A or greater current was energised to the generator, the magnetic flux was saturated. Although a greater current was energised to the SRG, the inductance decreased because magnetic flux was not generated. Since the inductance of Fig. 8b shows low at a mechanical angle of 30°, the overlap region of the flux linkage is produced by the inductance in the low current range. Fig. 8Open in figure viewerPowerPoint Magnetisation characteristics a Flux linkage of basic model b Inductance of basic model c Flux linkage of optimal model d Inductance of optimal model However, the inductance of the optimal model was 66% higher than the inductance of the basic model at the mechanical angle of 30°. Therefore, the overlap region of the flux linkage is reduced in comparing with the flux linkage of the basic model as shown in Fig. 8c. Fig. 9 shows a comparison of the FEA results of the basic and optimal models. Fig. 9a illustrates the simulation results of the basic and optimal models. The output power and output voltage in the optimal model were confirmed to be 1005.9 Wrms and 77.4 Vrms, respectively. Fig. 9b displays the phase-A current of the basic and optimised models. The generation current of the optimised model was determined to be greater than that of the basic model. Fig. 9c compares the torques of the basic and optimal models. When comparing the torque pulsation of the basic and optimal models, the torque pulsation of the optimal model was reduced. Fig. 9Open in figure viewerPowerPoint Comparison of FEA results of basic model and optimal model a Simulation results b Phase-A current c Torque A torque ripple comparison of the basic and optimal models of the SRG is presented in Table 6. It can be observed that the optimal design model exhibited 14% reduced torque ripple compared with the basic model. This torque ripple can be further reduced by applying torque ripple reduction methods. If a torque ripple reduction method is applied to the SRG, the torque ripple can be further reduced. Table 6. Torque ripple comparison of basic model and optimal model Parameters Basic design model Optimal design model average value, Nm 9.6 9.4 minimum value, Nm 3.4 3.1 maximum value, Nm 23.5 20.4 torque ripple, Nm 20.1 17.3 torque ripple decrease 14% Table 7 presents the performance results of the basic and optimal models of the SRG. The efficiency was calculated using the rated output power and input power. The input power was the supply source and mechanical energy. The rated output power was obtained from the output voltage and output current. The efficiency increased from 82 to 83% compared with the efficiency of the basic design model. Further, because the stack length decreased by 81.2 mm, the output power density improved by ∼11.4%. Table 7. FEA results of basic model and optimal model of SRG Parameters Basic design model Optimal design model rated output power, Wrms 1062.5 1005.9 input power, Wrms 1295.9 1212.9 rated torque, Nm 9.6 9.4 copper loss, W 102.5 86.7 iron loss, W 14.5 14.3 rated speed, rpm 1000 1000 rated voltage, Vrms 79.6 77.4 Efficiency, % 82 83 output power density, W/kg 126.8 143.2 5 Experiment results Fig. 10 illustrates the experiment configuration of the SRG. Fig. 10a shows the motor-generator (MG) set with the optimal model of the SRG. The MG set consists of a prime mover, inverter, and the SRG. The 3.75 kW three-phase squirrel-cage induction motor replaces the prime mover. The prime mover rotates the SRG at a constant speed of 1000 rpm during the experiment. Fig. 10Open in figure viewerPowerPoint Experiment set of the SRG a MG set b Control set Fig. 10b shows the control set of the SRG. The control set consists of a control board and an asymmetric bridge converter. The capacitor and resistance are used to address the generation energy. The resistance is set at 6.15 Ω to fulfil the output voltage requirements. A hard-chopping control is used to confirm the generation characteristics. The switch on angle is 30° and the off angle is 45°. Fig. 11 displays the characteristics of the SRG based on the speed. When the SRG rotated at 1000 rpm, the SRG drive system determined the pulses of the encoder (A-pulse and B-pulse) as indicated in Fig. 11a. At the generation mode, phase-A current was produced by the excitation source. Fig. 11b indicates the results of the noise measurement as the SRG accelerated to its rated speed of 1000 rpm. A digital noise meter (TES-1350A) was used for the noise measurement of the SRG. While changing the speed, the noise of the SRG was measured at the same distance. The vibration of the machine is directly related to the torque ripples; torque ripples reduce as the speed of the machine increases. Therefore, Fig. 11b indicates a reduction in vibration as the SRG accelerated towards its rated speed. Fig. 11Open in figure viewerPowerPoint Characteristic of the SRG a Phase-A current and pulses of encoder b Noise of the SRG based on speed Fig. 12 displays the experiment results for the SRG. Fig. 12a shows the phase-A current and inductance of the SRG according to the on and off switching signals. The simulation results of Fig. 9b can be compared with these experiment results. Fig. 12b shows the phase-A current and excitation current of the source according to the on and off switching signals at the rated speed of the generator. The excitation current of phase-A increased when the switch was turned on and continued increasing until the switch was turned off. A similar explanation is true for the sequentially energised phase-B as indicated in Fig. 12b. Fig. 12Open in figure viewerPowerPoint Experiment results for the SRG a On and off switching signals b Excitation current c Three-phase currents d Output voltage and output current The output voltage was ∼77.6 V and the phase current was ∼18.4 A as indicated in Fig. 12c. Fig. 12d displays the output voltage and output current of the SRG, which were ∼77.6 V and 12.9 A. The simulated results for the optimised model were confirmed by these experiment results. Further, the efficiency of the SRG was determined to be ∼82.6%, as was expected from the simulation results. 6 Conclusion This paper proposed an optimal design for a small, 1 kW SRG. A basic model of the SRG was developed to satisfy the basic specifications. An optimisation was performed on the basic model to obtain higher efficiency and power density. LHS was used to extract samples of the design variables. After extracting the samples, the optimal design was obtained using the Kriging method and a GA. FEA was used to compare the basic and optimal models. A prototype model with the optimised design was built and tested for the desired performance. The optimally designed SRG demonstrated superior performance in terms of efficiency and power density. 7 References 1Chwa, D.K., Lee, K.B.: 'Variable structure control of the active and reactive powers for a DFIG in wind turbines', IEEE Trans. Ind. Appl., 2010, 46, (6), pp. 2545– 2555 (doi: https://doi.org/10.1109/TIA.2010.2073674) 2Valenciaga, F., Puleston, P.F.: 'High-order sliding control for a wind energy conversion system based on a permanent magnet synchronous generator', IEEE Trans. Energy Convers., 2008, 23, (3), pp. 860– 867 (doi: https://doi.org/10.1109/TEC.2008.922013) 3Lee, S.B., Lee, K.B., Lee, D.C., et al: 'An improved control method for a DFIG in a wind turbine under an unbalanced grid voltage condition', J. Electr. Eng. Technol., 2010, 5, (4), pp. 614– 622 (doi: https://doi.org/10.5370/JEET.2010.5.4.614) 4Kang, Y.K., Jeong, H.G., Lee, K.B., et al: 'Simple estimation scheme for initial rotor position and inductances for effective MTPA-operation in wind-power systems using an IPMSM', J. Power Electron., 2010, 10, (4), pp. 396– 404 (doi: https://doi.org/10.6113/JPE.2010.10.4.396) 5Mendez, S., Martinez, A., Millan, W., et al: 'Design, characterization, and validation of a 1 kW AC self-excited switched reluctance generator', IEEE Trans. Ind. Electron., 2014, 61, (2), pp. 846– 855 (doi: https://doi.org/10.1109/TIE.2013.2254098) 6Chen, J., Nayar, C.V., Xu, L.: 'Design and finite-element analysis of an outer-rotor permanent-magnet generator for directly coupled wind turbines', IEEE Trans. Magn., 2000, 36, (5), pp. 3802– 3809 (doi: https://doi.org/10.1109/20.908378) 7Cardenas, R., Pena, R., Perez, M., et al: 'Control of a switched reluctance generator for variable-speed wind energy applications', IEEE Trans. Energy Convers., 2005, 20, (4), pp. 781– 791 (doi: https://doi.org/10.1109/TEC.2005.853733) 8Xue, X.D.K., Cheng, W.E., Bao, Y.J., et al: 'Switched reluctance generators with hybrid magnetic paths for wind power generation', IEEE Trans. Magn., 2012, 48, (11), pp. 3863– 3866 (doi: https://doi.org/10.1109/TMAG.2012.2202094) 9Byun, J.K., Park, I.H., Hahn, S.Y.: 'Topology optimization of electrostatic actuator using design sensitivity', IEEE Trans. Magn., 2002, 38, (2), pp. 1053– 1056 (doi: https://doi.org/10.1109/20.996270) 10Dyck, D.N., Lowther, D.A.: 'Automated design of magnetic devices by optimizing material distribution', IEEE Trans. Magn., 1996, 32, (3), pp. 1188– 1193 (doi: https://doi.org/10.1109/20.497456) 11Mirzaeian, B., Moallem, M., Tahani, V., et al: 'Multi objective optimization method based on a genetic algorithm for switched reluctance motor design', IEEE Trans. Magn., 2002, 38, (3), pp. 1524– 1527 (doi: https://doi.org/10.1109/20.999126) 12Byun, J.K., Hahn, S.Y., Park, I.H.: 'Topology optimization of electrical devices using mutual energy and sensitivity', IEEE Trans. Magn., 1999, 35, (5), pp. 3718– 3720 (doi: https://doi.org/10.1109/20.800642) 13Byun, J.K., Lee, J.H., Park, I.H., et al: 'Inverse problem application of topology optimization method with mutual energy concept and design sensitivity', IEEE Trans. Magn., 2000, 36, (4), pp. 1144– 1147 (doi: https://doi.org/10.1109/20.877643) 14Kim, J.B., Hwang, K.Y., Kwon, B.I.: 'Optimization of two-phase in-wheel IPMSM for wide speed range by using the Kriging model based on Latin hypercube sampling', IEEE Trans. Magn., 2011, 47, (5), pp. 1078– 1081 (doi: https://doi.org/10.1109/TMAG.2010.2096409) 15Hwang, C.C., Lyu, L.Y., Liu, C.T., et al: 'Optimal design of an SPM motor using genetic algorithms and Taguchi method', IEEE Trans. Magn., 2008, 44, (11), pp. 4325– 4328 (doi: https://doi.org/10.1109/TMAG.2008.2001526) 16Simpson, T.W., Mauery, T.M., Korte, J., et al: 'Kriging models for global approximation in simulation-based multidisciplinary design optimization', AIAA, 2001, 39, (12), pp. 2233– 2241 (doi: https://doi.org/10.2514/2.1234) 17Davey, K.R.: 'Latin hypercube sampling and pattern search in magnetic field optimization problems', IEEE Trans. Magn., 2008, 44, (6), pp. 974– 977 (doi: https://doi.org/10.1109/TMAG.2007.916292) 18Kim, S., Bhan, J.H., Hong, J.P., et al: ' Optimization technique for improving torque performance of concentrated winding interior PM synchronous motor with wide speed range'. Proc. 41st IAS Annual Meeting, Tampa, USA, October 2006, pp. 1933– 1940 19Kobetski, A., Coulomb, J.L., Costa, M.C., et al: 'Comparison of radial basis function approximation techniques', COMPEL, 2003, 22, (3), pp. 616– 629 (doi: https://doi.org/10.1108/03321640310475074) 20Mahmoudi, A., Kahourzade, S., Rahim, N.A., et al: 'Design, analysis, and prototyping of an axial-flux permanent magnet motor based on genetic algorithm and finite-element analysis', IEEE Trans. Magn., 2013, 49, (4), pp. 1479– 1492 (doi: https://doi.org/10.1109/TMAG.2012.2228213) 21Krishnan, R.: ' Switched reluctance motor drives: modeling, simulation, analysis, design, and applications' ( CRC Press, Boca Raton, FL, USA, 2001), pp. 82– 83 22Krishnan, R., Arumugam, R., Lindsay, J.F.: 'Design procedure for switched-reluctance motors', IEEE Trans. Ind. Appl., 1988, 24, (3), pp. 456– 461 (doi: https://doi.org/10.1109/28.2896) 23Shin, P.S., Woo, S.H., Koh, C.S.: 'An optimal design of large scale permanent magnet pole shape using adaptive response surface method with Latin hypercube sampling strategy', IEEE Trans. Magn., 2009, 45, (3), pp. 1214– 1217 (doi: https://doi.org/10.1109/TMAG.2009.2012565) 24Cheng, J., Druzdzel, M.J.: ' Latin hypercube sampling in Bayesian networks'. Proc. Int. Conf. on FLAIRS, Austin, USA, July/August 2000, pp. 287– 292 25Widmer, J.D., Mecrow, B.C.: 'Optimized segmental rotor switched reluctance machines with a greater number of rotor segments than stator slots', IEEE Trans. Ind. Appl., 2013, 49, (4), pp. 1491– 1498 (doi: https://doi.org/10.1109/TIA.2013.2255574) 26Sheth, N.K., Rajagopal, K.R.: 'Optimum pole arcs for a switched reluctance motor for higher torque with reduced ripple', IEEE Trans. Magn., 2003, 39, (5), pp. 3214– 3216 (doi: https://doi.org/10.1109/TMAG.2003.816151) 27Materu, P.N., Krishnan, R.: 'Estimation of switched reluctance motor losses', IEEE Trans. Ind. Appl., 1992, 28, (3), pp. 668– 679 (doi: https://doi.org/10.1109/28.137456) 28Torkaman, H., Ebrahim, A.: 'Comprehensive study of 2-D and 3-D finite element analysis of a switched reluctance motor', J. Appl. Sci., 2008, 8, (15), pp. 2758– 2763 (doi: https://doi.org/10.3923/jas.2008.2758.2763) Citing Literature Volume10, Issue8September 2016Pages 807-817 FiguresReferencesRelatedInformation
Publication Year: 2016
Publication Date: 2016-09-01
Language: en
Type: article
Indexed In: ['crossref']
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