In this paper, characteristics of blushless direct current (BLDC) motor including core loss are analyzed considering pulse width modulation (PWM) of inverter. Input voltage of BLDC motor due to PWM is calculated considering duty ratio and carrier frequency of inverter in order to control torque or speed of BLDC motor. For the calculation of core loss, the input current with harmonics due to PWM voltage is calculated by using equivalent circuit model of BLDC motor according to switching pattern and carrier frequency. Next, core loss is analyzed by inputting the currents as a source of BLDC motor for FEM. Characteristics including core loss are compared with ones without PWM waveform according to reference speed.
1. Introduction
Nowadays, it is important to analyze the losses such as core loss, copper loss and stray load loss in order to assess exact efficiency on the design stage of the motor. These losses are the main sources of heat generation. For the compact design and low operating cost of the system, these should be decreased when designing motor. Especially, core loss is increased remarkably at high speed. A lot of studies on the core loss of motor have been conducted by engineers
[1

4]
. However, these are based on ideal input voltage or current without inverter switching. In case of inverter driven motor, input voltage to the motor has harmonics due to switch pattern of inverter for pulse width modulation (PWM). The voltage with PWM waveform makes the current with harmonics. Therefore, core loss as well as copper loss is remarkably increased due to magnetic flux fluctuation in the core by current harmonics
[5
,
7]
. Therefore, the analysis methodology for core loss considering PWM switching pattern of inverter is necessary in order for the exact assessment of system efficiency. K. Yamazaki researched analysis method for eddy current loss in the permanent magnets of motor by inputting ideal PWM waveform to FEM model
[8]
. However, it is difficult to consider the PWM voltage waveform due to control algorithm and carrier frequency.
The speed of blushless DC (BLDC) motor is generally controlled by PWM by changing duty ratio of switch at certain carrier frequency. In case of inverter driven motor such as BLDC, its efficiency is vary depending on carrier frequency, duty ratio, reactance of motor, etc. Therefore, loss analysis considering inverter parameters is necessary.
In this paper, inverter model including duty ratio control strategy is introduced in order to make PWM voltage waveform and BLDC motor model with equivalent circuit is used for the calculation of current waveform with harmonics from the PWM voltage waveform. Next, the characteristics of BLDC motor are analyzed by using FEM in which current waveform is a source of magnetomotive force. And then the core loss by proposed method is compared with that by ideal current waveform without PWM switching strategy. Finally the core loss is also compared with experimental one.
2. Analysis Model of Inverter Driven BDLC Motor
The application of the inverter driven BLDC motor introduced in the paper is for electric compressor.
Fig. 1
shows the analysis model of BLDC motor. It has 6 poles and 9 slots combination. For the compact design, it is wound with concentrated winding. The material of permanent magnet is ferrite. The inverter makes controllable voltage for speed reference by using duty ratio parameter.
Table 1
shows the brief specification of BLDC motor and inverter for the analysis.
Analysis model of BDLC motor
Specification of the BLDC motor and inverter
Specification of the BLDC motor and inverter
3. Cosimulation Model of Inverter Driven BLDCM
For the exact loss analysis, the cosimulation model for inverter driven BLDC motor including PWM switching algorithm based on ANSYS Simplorer software is introduced as shown in
Fig. 2
. The cosimulation model has inverter with 6 MOSFET switches which can be turn on and off by PWM subcontroller and BLDC motor model with equivalent circuit. Each of switching devices has 120° electric conduction region in which PWM with duty ratio is applied. For the simplicity of analysis, dead time of them against arm short is not considered in the model.
Cosimulation model of inverter driven BLDC motor
 3.1 Analysis model of BLDC motor
The equivalent circuit is configured based on the voltage equation of the BLDC motor as shown in (1)
where
v_{a}
,
v_{b}
,
v_{c}
are phase voltages;
R_{s}
is winding resistance;
i_{a}
,
i_{b}
,
i_{c}
are phase currents of each stator winding;
E_{a}
,
E_{b}
,
E_{c}
are phase back EMFs;
L_{s}
is selfinductance;
M
is mutualinductance;
L_{end}
is leakageinductance of end winding.
In the simulation model in
Fig. 2
, the back EMF
E_{a}
,
E_{b}
,
E_{c}
generated by 2D FEM of BLDC motor is directly used as lookup table. Because equivalent circuit parameters are derived from 2D FEM, the leakage inductance of end winding should be included in the model.
For the calculation of output torque,
T_{e}
for the feedback control, output power,
P_{e}
is divided by angular velocity of rotor,
ω_{m}
as shown in (2) and (3).
Fig. 3
shows the position sensing subcircuit of the simulation model in order to determine rotor position. When speed reference of controller is given, the rotor position angle is calculated as theta through the position sensing subcircuit. The parameter of rotor position angle is used for two parts in the cosimulation model. First, theta is needed to select back EMFs from the lookup table in the equivalent circuit of BLDC motor. Second, it is needed to decide the switching sequence of the inverter in the controller subcircuit.
Position sensing subcircuit of the simulation model
 3.2 Analysis model of inverter considering PWM control
For the exact loss assessment, inverter model considering PWM voltage waveform should be adopted in the cosimulation model. In the paper, in order to make control voltage from battery voltage, duty ratio technique is used. As shown in
Fig. 4
, On and Off states of switch control signal are determined through the comparison between saw tooth voltage,
v_{st}
with a certain carrier frequency and control voltage,
v_{control}
. When the control voltage is greater than the saw tooth voltage, the switch is ‘Turn On’. Inverse case, it is ‘Turn Off’.
PWM duty ratio control technique of BLDC motor
The interval time of ‘Turn On’ and ‘Turn Off’ could be changed by the ratio of the amplitude of the saw tooth voltage,
v^{′}_{st}
and control voltage,
v_{control}
.
T_{s}
is sum of the switch On and Off time. The switching frequency is also represented by the reciprocal of the cycle in (4). The switching duty ratio,
D
is the ratio of turn on time,
t_{on}
and
T_{s}
in (5)
Conditional block of state equation for determining the switching operation as shown in
Fig. 6
is represented by
PWM Control subcircuit in the cosimulation
The PWM technique is classified as the bipolar and unipolar switching patterns according to the conduction and switching patterns as shown in
Fig. 5
. In case of unipolar switching pattern, it can reduce switching loss. It also has the advantage of a smaller current ripple. For this reason, unipolar switching pattern is usually used to control the BLDC motor. In the paper, unipolar H_PWML_ ON pattern in
Fig. 5 (c)
is used to make PWM voltage waveforms for the loss analysis of inverter driven BLDC motor. Next, it is compared with the result of ideal case without switching pattern in order to verify the loss difference due to PWM voltage waveforms.
Switching patterns of PWM in the inverter
Fig. 6
shows control subcircuit for PWM voltage waveforms based on duty ratio in the cosimulation model. The state of 6 MOSFET switch control signal can be decided through comparison between saw tooth voltage,
v_{st}
and control voltage,
v_{control}
due to duty ratio. Reference voltage,
v_{ref}
has a 120° flatted waveform with amplitude of 1 as shown in
Fig. 5 (a)
. Multiplying these two parameters of the switch control signal and reference voltage,
v_{ref}
, the final PWM output signal can be generated.
 3.3 The comparison of current and voltage waveforms between simulation and experiment
Through the cosimulation model for inverter driven BLDC motor in
Fig. 2
, the current and voltage waveforms can be extracted in
Figs. 7 (a)
and
(c)
. The simulation results are similar to experiment results with prototype having same carrier frequency and PWM duty ratio.
Current and voltage waveforms between the simulation and the experiment
4. Comparison Results on Core Loss
 4.1 Comparison according to switching patterns
Figs. 8
and
Fig. 9
show analysis results by inputting current waveforms generated from cosimulation model to 2D FEM as a current source. The analysis results in
Fig. 8
are derived from ideal switch pattern of inverter without PWM control. On the other hand, the results in
Fig. 9
show the waveforms with harmonics because of unipolar H_PWML_ON switch pattern.
Analysis results of ideal pattern (@1,500rpm)
Analysis results of PWM pattern (@1,500rpm)
Fig. 10
shows harmonics on phase current by FFT analysis. As a result of FFT analysis of phase current with ideal switch pattern, harmonics over 45
^{th}
nearly does not included. However, in case of PWM switch pattern, there are harmonics over 60
^{th}
harmonics due to carrier frequency for duty ratio control.
Harmonics of phase current according to switching patterns (@1,500rpm)
The harmonics on PWM voltage waveform by duty ratio control based on carrier frequency generate current ripple and affects the ripple of back EMF waveform. The torque of BLDC motor is occurred by multiplying the current and the back EMF. Therefore, the torque ripple is increased due to harmonics. In addition, the core loss between ideal and PWM switching patterns show distinct difference in the waveform. The core loss density by current harmonics is increased remarkably.
For the analysis of coreloss including harmonic effect, ANSYS Maxwell software is used by inputting several magnetic flux density vs. coreloss curves according to frequencies from 30 Hz to 2,000 Hz as shown in
Fig. 11
.
BP curves for the finite element analysis
Fig. 12
shows the core loss distributions in the core of BLDC motor according to PWM switch patterns. The inside region of dotted line indicates region having core loss over 30kW/m
^{3}
. Due to the current harmonics by PWM switch pattern, the region of core loss is also expanded.
Core loss distribution according to switching patterns (@1,500rpm)
 4.2 Comparison according to motor speed without changing carrier frequency
In general, core loss increases rapidly according to motor speed. However, harmonics of phase current are changed with motor speed due to fixed carrier frequency, it is necessary to analyze the core loss according to motor speed.
Fig. 13
shows the analysis results with current waveform of the PWM switch pattern at 2,700rpm. The carrier frequency of 5 kHz is same with 1,500rpm. In
Fig. 14
, phase current with ideal switch pattern almost does not include harmonics over 30
^{th}
. On the other hand, in case of PWM switch pattern, there are harmonics above 30
^{th}
harmonics due to carrier frequency. The harmonics is also varied according to motor speed. The region of core loss generation is expanded at high speed operation in
Fig. 15
.
Analysis results of PWM switch pattern (@2,700 rpm)
Harmonics of phase current according to switching patterns (@2,700rpm)
Core loss distribution according to motor speed
Analysis results of total harmonic distortion (THD) on phase current according to PWM switching patterns are shown in
Table 2
. Although fundamental component of phase current is about 0.27A regardless of switch patterns, THD is different because of the harmonics by carrier frequency for PWM control. Finally, analysis results of inverter driven BLDC motor is showed in
Table 3
.
THD results according to switching patterns
THD results according to switching patterns
Characteristics of inverter driven BLDC motor
Characteristics of inverter driven BLDC motor
Because THD of current waveform by PWM is 7% larger than that of ideal switch pattern at 1,500rpm, the torque ripple of the analysis model with PWM control considering carrier frequency increases about 70%. Both iron loss and copper loss also increase about 119mW and 12.7mW respectively. For this reason, the efficiency is approximately decreased about 0.5%.
For the validity of the simulation results, coreloss is measured on the dynamometer by subtracting mechanical loss and copper loss out of total loss which can be derived from input power and output power of BLDC motor. Coreloss is measured as 1,080 mW at 1,500 rpm and 2,020 mW at 2,700 rpm respectively.
In case of different carrier frequency at fixed rated operating point, the higher the carrier frequency is induced, the lower the coreloss is occurred.
5. Conclusion
The analysis method for the characteristics of inverter driven BLDC motor is proposed by using cosimulation model of inverter and motor in the paper. In general, ideal switch pattern of inverter is used at design stage of BLDC motor. However, it is difficult to assess core loss as well as copper loss due to harmonics of voltage and current. Especially characteristics of motor are affected by inverter parameters such as carrier frequency, duty ratio and frequency of voltage, etc. By using the proposed method, increase on core loss of inverter driven BLDC motor can be assessed qualitively rather than exact quantitive core loss and effective motor design can be realized considering these inverter parameters.
Acknowledgements
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning(2014R1A1A1006069)
BIO
KiChan Kim was born in Korea on August 8, 1972. He received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 1996, 1998 and 2005, respectively. He worked for Hyundai Heavy Industries Co., Ltd. from 1998 to 2005. Currently, he is an Assistant Professor in Electrical Engineering at Hanbat National University, Daejeon, Korea. His special area of interest includes the design and analysis of electrical motor and sensors.
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