close

Вход

Забыли?

вход по аккаунту

код для вставкиСкачать
A Single-Phase Brushless DC Motor With
Improved High Efficiency for Water Cooling
Pump Systems
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
Student ID:
Chiou
Ma120122
Renewable & Intelligent Power System Lab.
Outline
• I. INTRODUCTION
• II. PERFORMANCE MEASUREMENT OF
A COMMERCIAL SINGLE-PHASE
BLDCM
• III. METAMODEL & OPTIMUM DESIGN
THEORY
• IV. OPTIMUM DESIGN
• V. CONCLUSION
Renewable & Intelligent Power System Lab.
2
Preface
• 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).
Renewable & Intelligent Power System Lab.
3
I. INTRODUCTION
• 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. NSGAII can lead to multiple Pareto-optimal
solutions while only one solution can be
acquired by the generalized reduced
gradient(GRG).
Renewable & Intelligent Power System Lab.
4
•
•
II. PERFORMANCE
MEASUREMENT OF A
COMMERCIAL SINGLEPHASE BLDCM
Fig. 1. Single-phase BLDCM for pump application. (a) Pump system. (b)
Outer rotor. (c) Stator, winding, driver with hole IC. (d) Performance testing.
Renewable & Intelligent Power System Lab.
5
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 .
Renewable & Intelligent Power System Lab.
6
III. METAMODEL & OPTIMUM
DESIGN THEORY
Fig. 3. Design variables of a
single-phase BLDCM.
Renewable & Intelligent Power System Lab.
TABLE I. DESIGN VARIABLES OF
SINGLE-PHASE BLDCM
7
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.
Renewable & Intelligent Power System Lab.
8
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.
Renewable & Intelligent Power System Lab.
9
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.
Renewable & Intelligent Power System Lab.
10
IV. OPTIMUM DESIGN
TABLE II TABLE OF
ORTHOGONAL ARRAY
Renewable & Intelligent Power System Lab.
TABLE III SIMULATION RESULT OF SINGLE-PHASE
BLDCM
11
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:
Renewable & Intelligent Power System Lab.
12
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.
Renewable & Intelligent Power System Lab.
13
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
Renewable & Intelligent Power System Lab.
14
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.
Renewable & Intelligent Power System Lab.
15
V. CONCLUSION
• 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%.
Renewable & Intelligent Power System Lab.
16
REFERENCES
•
•
•
•
•
•
•
•
•
•
•
•
•
[1] P. Pillay and R. Krishnan, IEEE Trans. Ind. Appl., vol. 27, no. 5, pp.
986–996, Sep.–Oct. 1991.
[2] D. Hanselman, Brushless Permanent Magnet Motor Design, 2nd ed.
Cranston, RI: Writers’ Collective, 2003.
[3] C.-L. Chiu, Y.-T. Chen, and W.-S. Jhang, IEEE Trans. Magn., vol. 44,
no. 10, pp. 2317–2323, Oct. 2008.
[4] D. K. Hong, B. C. Woo, J. H. Chang, and D. H. Kang, IEEE Trans.
Magn., vol. 43, no. 4, pp. 1613–1616, Apr. 2007.
[5] J. H. Lee, IEEE Trans. Magn., vol. 45, no. 3, pp. 1578–1581, Mar. 2009.
[6] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, IEEE Trans. Evol.
Comput., vol. 6, pp. 182–197, Apr. 2002.
[7] K. Deb, A. Anand, and D. Joshi, Evol. Comput., vol. 10, no. 4, pp.
371–395, Winter, 2002.
Renewable & Intelligent Power System Lab.
17
THE END THANKS
Renewable & Intelligent Power System Lab.
18
1/--страниц
Пожаловаться на содержимое документа