Do-Kwan Hong, Byung-Chul Woo, Dae-Hyun Koo, and Un-Jae Seo
Electric Motor Research Center, Korea Electro technology Research Institute, Changwon, 641-120, Korea
Energy Conversion Engineering, University of Science & Technology, Changwon, 641-120, Korea
IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011, Page(s) : 4250 ~ 4253
 Adviser :Ming–Shyan Wang
 Student :Ming- Yi Chiou
 Student ID: Ma120122
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• This research deals with the optimization of a single-phase brushless DC motor (BLDCM) by substituting a commercial single-phase BLDCM for pump application in order to satisfactorily improve its efficiency regarding the required performance of a motor for pump systems (pump load 1,800 rpm, at 2 Nm m). The reliability of the results is verified between simulation and experiment using performance tests.
• (GA) is implemented to search for optimum solutions on the constructed meta model which consists of two objective functions. With the optimal design set, predicted results of the
GA are better than the generalized reduced gradient (GRG) algorithm. Nevertheless, verification results of the GRG are better than the GA. This result has an error within 1%.Index
Terms—Equivalent magnetic circuit (EMC), generalized reduced gradient (GRG), genetic algorithm (GA), meta model, multi objective evolutionary algorithm (MOEA), multi objective problem (MOP), response surface methodology (RSM), singlephase brushless DC motor (BLDCM).
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I.
• This paper deals with the optimum design of a single-phase BLDCM in order to maximize efficiency and torque per current
(TPC) due to the necessity for high efficiency BLDCMs to take into consideration water cooling pump loads.
• For the first step, the sampling process is applied to the table of orthogonal array to minimize the experimental process. NSGA-
II can lead to multiple Pareto-optimal solutions while only one solution can be acquired by the generalized reduced gradient(GRG).
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II.
• Fig. 1. Single-phase BLDCM for pump application. (a) Pump system. (b)
• Outer rotor. (c) Stator, winding, driver with hole IC. (d) Performance testing.
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Fig. 2. Performance curve of single-phase BLDCM (simulation(EMC)& test).
Fig. 1 shows a single-phase BLDCM for pump application with four poles and four slots, the performances of a commercial motor are analyzed. The simulation results using EMC are compared with the experiment, and are within a 5% deviation of each other as shown in Fig. 2. The reliability of the results is verified between the simulation and experiment, and maximum efficiency is about
35% as seen .
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Fig. 3. Design variables of a single-phase BLDCM.
TABLE I. DESIGN VARIABLES OF
SINGLE-PHASE BLDCM
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A. Design Variables, Levels and Sampling
Fig. 3 shows an initially designed single-phase BLDCM.
It is an outer rotor type and consists of four poles and four slots.
To solve the optimum problem, effective design variables capable of significantly influencing the objective function need to be chosen. The basic properties of electrical circuits including inductance, back EMF voltage, and the actual condition of the motor operated at a constant speed are simulated by EMC
In the first step, eight design variables and their levels are selected as shown in Table I. The level value is repeatedly selected considering the magnetic density of the stator and rotor yoke, he gross slot fill and current density.
In the next step, the orthogonal array is determined by considering the number of design variables and each of their levels.
The orthogonal array is selected as it can minimize the number of simulations required for the purposes of sampling. Having to repeat the experimental process poses serious burdens in terms of time and cost. The magnetic field is analyzed for each experiment
.
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B. Response Surface Methodology
The RSM can be well adapted to develop an analytical model for complex problems. With this analytical model, an objective function can be easily created and evaluated, and the computation time can be saved. A polynomial approximation model is commonly used for a second-order fitted response and can be written as follows: egression coefficients, : design variables; random error, : number of design variables.
The least squares method is used to estimate unknown coefficients.
Matrix notations of the fitted coefficients and the fitted response model should be as shown below: where, is a vector of the unknown coefficients which are estimated to minimize the sum of the squares of the error term.
It should be evaluated at the data points. RSM can be applied in connection with Equivalent Magnetic Circuit (EMC) and the response actually represents EMC output values.
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C ‧Multi objective Problem
A general MOP consists of a number of objective functions.
Optimized solutions for MOP are non dominated points compared to whole obtained solutions. The superiority of only one solution over the all solutions cannot be established using MOP.
Dominance relation to maximize the objective is defined below: x is said to dominate , denoted as
If X is partially larger than Y , we say that solution dominates
Y. Any member of such vectors which is not dominated by any other member is said to be non dominated. The optimal solutions to MOP are non dominated solutions.
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TABLE II TABLE OF
ORTHOGONAL ARRAY
TABLE III SIMULATION RESULT OF SINGLE-PHASE
BLDCM
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A. Sampling and Meta model
Table II and Table III represent the tables of orthogonal array for the selected effective design variables and simulation results for each experiment. Based on these experimental data, a function to draw a response surface should be extracted. In this paper, two fitted second order polynomials having eight design variables for each objective function, TPC and efficiency, are determined as shown in (6) and (7). The adjusted coefficients of multiple determinations are 100% and 100% for each objective function, TPC and efficiency, respectively. The reliability of the optimum design depends on the of the proposed meta model in (6) and (7).
At the sampling step, the meta model is determined and the influence of each design variable on the objective function can be obtained as below:
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B
. Optimization Using GRG Algorithm
Fig. 4. Predicted optimum solution by RSM and GRG algorithm
Fig. 4 shows each response of the objective function with the variation of the design variables to find the optimal solution. Each slope shows the sensitivity of the design variables on the objective function. The determined optimum solution set for efficiency and TPC is shown for each design variable. The optimization formulation is shown below.
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C. Optimization Using GA
Fig. 5. All obtained solutions that are considered as first rank solutions.
For solving MOP containing (6) and (7), the GA runs ten times with 100,000 function evolutions for each run. Therefore, the total function evolution is one million. After the number of total function evolution reaches one million, all obtained optimal solutions are resorted. The non nominated solutions over resorted solutions are considered as Pareto-optimal solutions as shown in Fig. 5. Only one appropriate solution is chosen and verified by EMC. The optimum set of design parameters is determined to be
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D. Comparison Optimum Result
Fig. 6. Performance curve of GA result for verification (pump load: 2 , at 1,800 rpm).
TABLE IV COMPARISON OF
COMMERCIAL AND OPTIMUM MODEL
With these optimized design values, the performance curve of a single-phase
BLDCM is evaluated by EMC as shown in Fig. 6. Comparing existing commercial single-phase BLDCMs, optimized single-phase BLDCMs have better performance in terms of efficiency by 80.7% for the required motor performance for pump systems. The predicted performance by GRG algorithm and GA is also in good agreement with the simulation results for verification within a maximum of 0.38% as shown in Table IV. The optimum model which satisfies the required performance is superior to existing commercial single-phase BLDCMs.
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• This paper deals with the optimization of a single-phase
BLDCM by substituting a commercial single-phase BLDCM for pump application to improve the efficiency with satisfaction to the required performance of motors for pump systems. We used RSM and GA method for the present optimization because those are the methods that have shown the most promise in the field of electric machinery optimization. In the sampling process, latin hyper cubic sampling (LHS), the subject of many experiments, is usually used, although it requires a great deal of time and expense. In addition, a meta model with second approximation polynomials is made using
RSM. The adjusted coefficients of multiple determinations which shows the reliability of the meta model (multi objective functions) is 100%. This result shows that the table of orthogonal array with the smallest number of experiments is suitable for sampling. With the optimal design set, the efficiency of the optimum designed model using GA is 80.7% and is better than GRG (80.47%). Nevertheless, verification results of the GR Gare better than the GA. This result has an error within maximum 1%.
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