2.4.1 Basic Operation Principle
Due to the flux distribution varies with rotor positions, the magnetic field produced from stator winding should synchronize with rotor field. Fig. 2.9(a) shows the schematic of the commutation control circuit for the single-phase BLDC fan motor with Hall sensor feedback [1]-[3]. The full-bridge inverter consists of four switches S1 to S4 which were controlled to supply required direction of driving current. Each switch connects with anti-parallel diode to remain driving current during the current commutation. Each winding terminal is connected to a pair of switches as shown. When both switches in the same phase are on, the bus voltage is short circuit. This condition should be inhibited at all times. To eliminate short circuit during switching transients, a small dead-time is introduced in between turn-off of one switch and turn-on of the other switch in the same phase.
A linear Hall sensor is fixed to a on drive PCB of the single-phase motor, and biased by a constant voltage. The linear Hall sensor produces an output signal which is proportional to the intensity of the induced rotor field, so it is used to provide rotor position and velocity feedback information via signal processing technique. Fig. 2.9(b) shows the operation waveform based on open-loop voltage-mode control of hard-commutation scheme. The control system accepts the Hall sensor feedback and determines the switching status to commutate the phase current. The phase winding will be conducted 180 electrical degrees for both positive and negative driving current. When the Hall sensor waveform goes through zero from negative to positive transistors S1 and S4 are switched ON and switches S2 and S3 are switched OFF, while when the Hall sensor waveform goes through zero from positive to negative switches S2 and S3 are switched ON and switches S1 and S4 are switched OFF. In other words, transistors S1, S4 and the transistors S2, S3 are complementarily turned ON/OFF to change the directions of the driving current whereby the single-phase motor is revolved.
S1 S3 BLDC Fan motor
Commutation Logic
180° 360° 180° 360°
Commutation signal
(b)
Fig. 2.9. The open-loop voltage-mode control of hard-commutation scheme (a) the schematic of commutation control circuit and (b) operation waveform.
2.4.2 Analyses of Steady-State Response
Fig. 2.10 is the steady-state current response when using open-loop voltage-mode of hard-commutation scheme. There is a significant current spike at commutation boundary. The dynamic behavior of current response is given as follow
)
Phase current (A)
Back-EMF (V)
Torque (N.m)
Current spike
Diode conduction interval
Negative torque
Fig. 2.10. Steady-state current response when using open-loop voltage-mode control of hard-commutation scheme.
where v is the input voltage of phase winding. Rs and Ls are the series resistance and the series inductance of stator winding, respectively. vemf is the back-EMF induced by rotor flux variation. Owing to the back-EMF seriously drops at commutation boundary, and it results in a great rising slope of current response, that is the current spike. Moreover, due to the winding inductance, the polarity of the phase current cannot be changed instantaneously, so the current will pass through the anti-parallel diode and decrease to zero at commutation boundary. It results in the driving current out of phase with back-EMF and a negative torque is generated, and consequently the overall efficiency is seriously degraded in wide speed control applications for single-phase BLDC fan motors.
Because of non-linear flux distribution, there are obvious torque ripples during motor revolution [20]. This will result in undesirable effects such as speed ripple and acoustic noise.
As commonly known, it is better to achieve constant torque for smooth revolution, which requires very high current to compensate the weak magnetic field at commutation boundary.
However, such high current will reduce the overall efficiency and increase the power circuit
rating. Fig. 2.11 shows the steady-state torque response at 4000 RPM. From (2-4) and (2-5), the developed torque can be revised as
L r m r m e
av B T
dt J d T
T +Δ = ω + ω +
(2-18)
where Tav is the average torque and ΔTe is the torque ripple. So, the corresponding speed ripple can be calculated by
m r e
J t T ⋅Δ
= Δ
Δω . (2-19)
From (2-19), the speed ripple is proportional to the torque ripple which is related to the flux distribution and phase current waveform. For the same model of single-phase BLDC fan motor, a suitable current shaping will reduce the torque ripple as well as speed ripple.
ωr
Δ
i (A)
KT(N.m/A)
Torque (N.m)
Fig. 2.11. Steady-state torque response when using open-loop voltage-mode control of hard-commutation scheme.
On the other hand, the ideal voltage sources VDC at the input usually accompany with a suitable sized capacitor. The capacitor normally large enough to store a considerable amount of energy and their purpose is to deliver it to the load, rapidly enough not to cause the circulation of high-frequency currents through the primary source. Fig. 2.12 shows the equivalent model of dc-bus circuit. The current idcm passes through the inverter to the motor winding, so there exists high-frequency current due to current commutation.
When the motor is operated at predefined speed, the corresponding current idcm is served as independence current source which can be expressed as
cap dcr
dcm i i
i = + (2-20)
where idcr is the average current and icap is current ripple which is composed of twice angular frequency and switching frequency of current ripple. Because the operation speed and required input power have been determined, the average current will be derived as
DC dcr in
V
i = P (2-21)
where Pin is the required input power at operation speed and VDC is dc-link voltage source.
The average current will pass through the dc-link voltage source, so the equivalent circuit is a resistor Rdc which can be given as
dcr dc DC
i
R =V . (2-22)
After properly modeling of dc-bus circuit, the transfer function from idcr to idcm can be expressed as
1
which is a typical first-order low-pass filter. Therefore, the addition of capacitor will filter the
high-frequency current idcm. In order to reduce the twice angular frequency of current ripple, the bandwidth of low-pass filter should be low enough which will require a very large dc-link capacitor. Fig. 2.13 shows the simulation results of above discussion. If the capacitor is large enough to absorb the high-frequency current icap, the current idcm will be filtered to an average value idcr which is convenient to calculate the input power of motor drives.
VDC
Cdc
idcr idcm
icap i
idcr idcm
icap
Rdc Cdc t
Fig. 2.12. Equivalent dc-bus model of power stage.
idcr(A) idcm(A) i (A)
icap(A)
2.4.3 Verification of Proposed Model
According to previous description, a simple modeling method with an illustrated parameter identification scheme for single-phase BLDC fan motor has been proposed. The parameters of Table I substitute the proposed model and verify with a real single-phase BLDC fan motor by computer simulation and experiment measurement. Using the open-loop voltage-mode of hard-commutation scheme, Fig. 2.14 shows the simulation results of steady-state response under duty ratio 100 %, 80 %, and 50 %, respectively. Fig. 2.15 shows the consistency of the proposed model and the real fan motor, it can be seen that simulation results are close to experiment measurements under different duty ratio. Fig. 2.16 shows the RMS value of phase current and rotor speed curves under different duty ratio, the simulation result is also close to experiment measurement. That is, above of all confirm the validity of the proposed model.
Speed (RPM)
Phase current
(A)
Hall sensor
Rotor position (degree)
(a)
Speed (RPM)
Phase current
(A)
Hall sensor
Rotor position (degree)
(b)
Speed (RPM)
Phase current
(A)
Hall sensor
Rotor position (degree)
(c)
Fig. 2.14. Simulation result with open-loop voltage-mode control of hard-commutation scheme under (a) duty = 100 %, (b) duty = 80 %, and (c) duty = 50 %.
0 2 4 6 8
Phase current (A)
Experiment Result Simulation Result
0 0.002 0.004 0.006 0.008 0.01
-0.8
Phase currnet (A)
Experiment Result Simulation Result
(a) (b)
0 0.002 0.004 0.006 0.008 0.01 0.012 -0.4
Phase current (A)
Experiment Result
Phase current (A)
Experiment Result Simulation Result
(c) (d)
Fig. 2.15. Phase current comparison between simulation result and experiment measurement (a) duty = 100 %, (b) duty = 80 %, (c) duty = 50 %, and (d) duty = 20 %.
0 20 40 60 80 100 0
50 100 150 200 250 300 350 400 450 500
Duty (%)
RMS current (mA)
Experiment results Simulation results
(a)
0 20 40 60 80 100
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Duty (%)
Speed (RPM)
Experiment results Simulation results
(b)
Fig. 2.16. The RMS value of phase current and rotor speed curves under different duty ratios.