Ga2510971106

Anitha Arumalla, M.Lokya, M.Tech / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1097-1106
A PMBLDCM Speed Control By Using A Buck DC-DC
Converter And Voltage Control

Anitha Arumalla, Student M.Lokya, M.Tech
Electrical Engineering Department, Mother Therisa Institute of Science and Technolgy, Sathupalli -507303,
India

Abstract
A buck half-bridge DC-DC converter is thereby poor efficiency and reduced life of the
used as a single-stage power factor correction motor. Moreover, the temperature of the air
(PFC) converter for feeding a voltage source conditioned zone is regulated in a hysteresis band.
inverter (VSI) based permanent magnet Therefore, improved efficiency of the Air-Con
brushless DC motor (PMBLDCM) drive. The system will certainly reduce the cost of living and
front end of this PFC converter is a diode bridge energy demand to cope-up with ever-increasing
rectifier (DBR) fed from single-phase AC mains. power crisis.
The PMBLDCM is used to drive a compressor A PMBLDCM which is a kind of three-
load of an air conditioner through a three-phase phase synchronous motor with permanent magnets
VSI fed from a controlled DC link voltage. The (PMs) on the rotor and trapezoidal back EMF
speed of the compressor is controlled to achieve waveform, operates on electronic commutation
energy conservation using a concept of the accomplished by solid state switches. It is powered
voltage control at DC link proportional to the through a three-phase voltage source inverter (VSI)
desired speed of the PMBLDCM. Therefore the which is fed from single-phase AC supply using a
VSI is operated only as an electronic commutator diode bridge rectifier (DBR) followed by
of the PMBLDCM. The stator current of the smoothening DC link capacitor. The compressor
PMBLDCM during step change of reference exerts constant torque (i.e. rated torque) on the
speed is controlled by a rate limiter for the PMBLDCM and is operated in speed control mode
reference voltage at DC link. The proposed to improve the efficiency of the Air-Con system.
PMBLDCM drive with voltage control based Since, the back-emf of the PMBLDCM is
PFC converter is designed, modeled and its proportional to the motor speed and the developed
performance is simulated in Matlab-Simulink torque is proportional to its phase current [1-4],
environment for an air conditioner compressor therefore, a constant torque is maintained by a
driven through a 1.5 kW, 1500 rpm PMBLDC constant current in the stator winding of the
motor. The evaluation results of the proposed PMBLDCM whereas the speed can be controlled by
speed control scheme are presented to varying the terminal voltage of the motor. Based on
demonstrate an improved efficiency of the this logic, a speed control scheme is proposed in this
proposed drive system with PFC feature in wide paper which uses a reference voltage at DC link
range of the speed and an input AC voltage. proportional to the desired speed of the PMBLDC
motor. However, the control of VSI is only for
Index Terms— PFC, PMBLDCM, Air electronic commutation which is based on the rotor
conditioner, Buck Half-bridge converter, Voltage position signals of the PMBLDC motor.
control, VSI. The PMBLDCM drive, fed from a single-
phase AC mains through a diode bridge rectifier
I. INTRODUCTION (DBR) followed by a DC link capacitor, suffers
from power quality (PQ) disturbances such as poor
PERMANENT magnet brushless DC motors power factor (PF), increased total harmonic
(PMBLDCMs) are preferred motors for a distortion (THD) of current at input AC mains and
compressor of an air-conditioning (Air-Con) system its high crest factor (CF). It is mainly due to
due to its features like high efficiency, wide speed uncontrolled charging of the DC link capacitor
range and low maintenance requirements [1-4]. The which results in a pulsed current waveform having a
operation of the compressor with the speed control peak value higher than the amplitude of the
results in an improved efficiency of the system while fundamental input current at AC mains. Moreover,
maintaining the temperature in the air-conditioned the PQ standards for low power equipments such as
zone at the set reference consistently. Whereas, the IEC 61000-3-2 [5], emphasize on low harmonic
existing air conditioners mostly have a single-phase contents and near unity power factor current to be
induction motor to drive the compressor in „on/off‟ drawn from AC mains by these motors. Therefore,
control mode. This results in increased losses due to use of a power factor correction (PFC) topology
frequent „on/off‟ operation with increased amongst various available topologies [6-14] is
mechanical and electrical stresses on the motor, almost inevitable for a PMBLDCM drive.

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Most of the existing systems use a boost required only at the commutation points, e.g.,
converter for PFC as the front-end converter every 60°electrical in the three-phase [1-4]. The
and an isolated DC-DC converter to produce rotor position of PMBLDCM is sensed using
desired output voltage constituting a two-stage Hall effect position sensors and used to
PFC drive [7-8]. The DC-DC converter used in generate switching sequence for the VSI as
the second stage is usually a flyback or forward shown in Table-I.
converter for low power applications and a full-
bridge converter for higher power applications. The DC link voltage is controlled by a
However, these two stage PFC converters have half-bridge buck DC-DC converter based on the
high cost and complexity in implementing two duty ratio (D) of the converter. For a fast and
separate switch-mode converters, therefore a effective control with reduced size of magnetics
single stage converter combining the PFC and and filters, a high switching frequency is used;
voltage regulation at DC link is more in however, the switching frequency (fs) is limited
demand. The single-stage PFC converters by the switching device used, operating power
operate with only one controller to regulate the level and switching losses of the device. Metal
DC link voltage along with the power factor oxide field effect transistors (MOSFETs) are
correction. The absence of a second controller used as the switching device for high switching
has a greater impact on the performance of frequency in the proposed PFC converter.
single-stage PFC converters and requires a However, insulated gate bipolar transistors
design to operate over a much wider range of (IGBTs) are used in VSI bridge feeding
operating conditions. PMBLDCM, to reduce the switching stress, as
it operates at lower frequency compared to PFC
For the proposed voltage controlled drive, a switches.
half-bridge buck DC-DC converter is selected
because of its high power handling capacity as The PFC control scheme uses a current
compared to the single switch converters. control loop inside the speed control loop with
Moreover, it has switching losses comparable to current multiplier approach which operates in
the single switch converters as only one switch continuous conduction mode (CCM) with
is in operation at any instant of time. It can be average current control. The control loop begins
operated as a single-stage power factor with the comparison of sensed DC link voltage
corrected (PFC) converter when connected with a voltage equivalent to the reference
between the VSI and the DBR fed from single- speed. The resultant voltage error is passed
phase AC mains, besides controlling the voltage through a proportional -integral (PI) controller
at DC link for the desired speed of the Air-Con to give the modulating current signal. This
compressor. A detailed modeling, design and signal is multiplied with a unit template of input
performance evaluation of the proposed drive AC voltage and compared with DC current
are presented for an air conditioner compressor sensed after the DBR. The resultant current
driven by a PMBLDC motor of 1.5 kW, 1500 error is amplified and compared with saw-tooth
rpm rating. carrier wave of fixed frequency (fs) in unipolar
scheme (as shown in Fig.2) to generate the
II. PROPOSED SPEED CONTROL PWM pulses for the half-bridge converter. For
SCHEME OF PMBLDC the current control of the PMBLDCM during
MOTOR FOR AIR CONDITIONER step change of the reference voltage due to the
The proposed speed control scheme (as change in the reference speed, a voltage
shown in Fig. 1) controls reference voltage at gradient less than 800 V/s is introduced for the
DC link as an equivalent reference speed, change of DC link voltage, which ensures the
thereby replaces the conventional control of the stator current of the PMBLDCM within the
motor speed and a stator current involving specified limits (i.e. double the rated current).
various sensors for voltage and current signals.
Moreover, the rotor position signals are used to
generate the switching sequence for the VSI as
an electronic commutator of the PMBLDC
motor. Therefore, rotor-position information is

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filter restricts the inductor peak to peak ripple
current ( ILo) within specified value for the given
switching frequency (fs), whereas, the capacitance
(Cd) is calculated for a specified ripple in the
output voltage ( VCd) [7-8]. The output filter
inductor and capacitor are given as

Lo= (0.5-D)Vdc/{fs( ILo) } (3)
Cd=Io/(2ωΔVCd) (4)

The PFC converter is designed for a base DC link
voltage of V dc = 400 V at Vin = 198 V from Vs =
220 Vrms. The turns ratio of the high frequency
transformer (N2/N 1) is taken as 6:1 to maintain the
desired DC link voltage at low input AC voltages
typically at 170V. Other design data are fs = 40
Figure 1. Control schematic of Proposed Bridge- kHz, Io = 4 A, VCd= 4 V (1% of Vdc), ILo= 0.8 A
buck PFC converter fed PMBLDCM drive (20% of Io). The design parameters are calculated
as Lo=2.0 mH, Cd=1600 µF.
III.DESIGN OF PFC BUCK HALF- TABL VSI SWITCHING SEQUENCE BASED
E I. ON THE HALL EFFECT
BRIDGE CONVERTER
SENSOR
BASED PMBLDCM DRIVE
The proposed PFC buck half-bridge SIGNALS
converter is designed for a PMBLDCM drive with
main considerations on PQ constraints at AC H E E E
mains and allowable ripple in DC link voltage. Ha b Hc a b c S1 S2 S3 S4 S5 S6
The DC link voltage of the PFC converter is given 0 0 0 0 0 0 0 0 0 0 0 0
as, 0 0 1 0 -1 +1 0 0 0 1 1 0
Vdc = 2 (N2/N1) Vin D and N2= N21=N22 (1) where 0 1 0 -1 +1 0 0 1 1 0 0 0
N1, N21, N22 are number of turns in primary, 0 1 1 -1 0 +1 0 1 0 0 1 0
secondary upper and lower windings of the high 1 0 0 +1 0 -1 1 0 0 0 0 1
frequency (HF) isolation transformer, respectively. 1 0 1 +1 -1 0 1 0 0 1 0 0
1 1 0 0 +1 -1 0 0 1 0 0 1
1 1 1 0 0 0 0 0 0 0 0 0
I MODELING OF THE PROPOSED PMBLDCM
V. DRIVE

The main components of the proposed PMBLDCM
drive are the PFC converter and PMBLDCM drive,
which are modeled by mathematical equations and
the complete drive is represented as a combination
of these models.

A. PFC Converter
The modeling of the PFC converter
consists of the modeling of a speed controller, a
Figure 2. PWM control of the buck half-bridge reference current generator and a PWM controller
converter as given below.
Vin is the average output of the DBR for a given
AC input voltage (Vs) related as, 1) Speed Controller: The speed controller, the
prime component of this control scheme, is a
Vin = 2√2Vs/π (2) proportional-integral (PI) controller which closely
tracks the reference speed as an equivalent
A ripple filter is designed to reduce the ripples reference voltage. If at kth instant of time, V*dc(k) is
introduced in the output voltage due to high reference DC link voltage, Vdc(k) is sensed DC link
switching frequency for constant of the buck half- voltage then the voltage error Ve(k) is calculated
bridge converter. The inductance (Lo) of the ripple as,

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Ve(k) =V*dc(k)-Vdc(k) (5) as „o‟ in Fig. 3. The voltages van, vbn, vcn are
voltages of three-phases with respect to neutral
The PI controller gives desired control point (n) and Vdc is the DC link voltage. S= 1 and
signal after processing this voltage error. The 0 represent „on‟ and „off‟ position of respective
output of the controller Ic(k) at kth instant is given IGBTs of the VSI and considered in a similar way
as, for other IGBTs of the VSI i.e. S3- S6.
Ic (k) = Ic (k-1) + Kp{Ve(k) – Ve(k-1)} + KiVe(k) Using similar logic vbo, vco, vbn, vcn are
(6) where Kp and Ki are the proportional and generated for other two phases of the VSI feeding
integral gains of the PI controller. PMBLDC motor.

2) Reference Current Generator: The reference 3) PMBLDC Motor:The PMBLDCM is
input current of the PFC converter is denoted by represented in the form of a set of differential
idc* and given as, i*dc = Ic (k) uVs (7) where uVs is equations [3] given as,
the unit template of the voltage at input AC mains, van = Ria + pλa +ean (15)
calculated as, uVs = vd/Vsm; vd = |vs|; vs= Vsm sin ωt
(8) where Vsm is the amplitude of the voltage and vbn = Rib + pλb +ebn (16)
ω is frequency in rad/sec at AC mains. vcn = Ric + pλc +ecn (17)

3) PWM Controller:The reference input current where p is a differential operator (d/dt),
of the buck half-bridge converter (idc*) is ia, ib, ic are three-phase currents, λa, λb, λc are flux
compared with its sensed current (idc) to generate linkages and ean, ebn, ecn are phase to neutral back
the current error idc=(idc* - idc). This current error emfs of PMBLDCM, in respective phases, R is
is amplified by gain kdc and compared with fixed resistance of motor windings/phase.
frequency (fs) saw-tooth carrier waveform md(t)
(as shown in Fig.2) in unipolar switching mode [7] Therefore, the electromagnetic torque is expressed
to get the switching signals for the MOSFETs of as,
the PFC buck half-bridge converter as, Te = Kb{fa(θ) ia + fb(θ) ib+ fc(θ) ic} (31)
id md The mechanical equation of motion in speed
If kdc c > (t) then SA = 1 else SA = 0 (9) derivative form is given as,
i pω = (P/2) (Te-TL-Bω)/(J) (32)
d md
If -kdc c > (t) then SB = 1 else SB = 0 (10) The derivative of the rotor position angle is given as,
pθ = ω (33)
where SA, SB are upper and lower
switches of the half-bridge converter as shown in where P is no. poles, TL is load torque in
Fig. 1 and their values „1‟ and „0‟ represent „on‟ Nm, J is moment of inertia in kg-m2 and B is
and „off‟ position of the respective MOSFET of friction coefficient in Nms/Rad.
the PFC converter.
These equations (15-33) represent the dynamic
B. PMBLDCM Drive model of the PMBLDC motor.
The PMBLDCM drive consists of an electronic
commutator, a VSI and a PMBLDC motor.
1) Electronic Commutator: The electronic
commutator uses signals from Hall effect position
sensors to generate the switching sequence for the
voltage source inverter based on the logic given in
Table I.
2) Voltage Source Inverter: Fig. 3 shows an
equivalent circuit of a VSI fed PMBLDCM. The
output of VSI to be fed
to phase „a‟ of the PMBLDC motor is given as,
fo S
vao = (Vdc/2) r 1 =1 (11)
fo S Figure 3. Equivalent Circuit of a VSI fed
vao = (-Vdc/2) r 2 =1 (12) PMBLDCM Drive
The flux linkages are represented as,
vao = 0 for S1 = 0, and S2 = 0 (13)
van = vao – vno (14) λa = Lia - M (ib + ic) (18)
where vao, vbo, vco, and vno are voltages of λb = Lib - M (ia + ic) (19)
the three-phases and neutral point (n) with respect
to virtual mid-point of the DC link voltage shown λc = Lic - M (ib + ia) (20)

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where L is self-inductance/phase, M is The compressor load is considered as a constant
mutual inductance of motor winding/phase. Since torque load equal to rated torque with the speed
the PMBLDCM has no neutral connection, control required by air conditioning system. A 1.5
therefore, kW rating PMBLDCM is used to drive the air
ia + ib + ic = 0 (21) conditioner compressor, speed of which is
From Eqs. (14-21) the voltage between controlled effectively by controlling the DC link
neutral terminal (n) and mid-point of the DC link voltage. The detailed data of the motor and
(o) is given as, simulation parameters are given in Appendix. The
performance of the proposed PFC drive is
vno = {vao +vbo + vco – (ean +ebn +ecn)}/3 (22)
evaluated on the basis of various parameters such
From Eqs. (18-21), the flux linkages are given as, as total harmonic distortion (THDi) and the crest
λa = (L+M) i a, λb = (L+M) ib, λc = (L+M) ic, (23) factor (CF) of the current at input AC mains,
From Eqs. (15-17 and 23), the current derivatives displacement power factor (DPF), power factor
in generalized state space form is given as, (PF) and efficiency of the drive system (ηdrive) at
different speeds of the motor. Moreover, these
parameters are also evaluated for variable input
pix = (vxn - ix R – exn)/(L+M) (24) AC voltage at DC link voltage of 416 V which is
where x represents phase a, b or c. equivalent to the rated speed (1500 rpm) of the
PMBLDCM. The results are shown in Figs. 4-9
V. PERFORMANCE EVALUATION and Tables II-III to demonstrate the effectiveness
OF PROPOSED PFC DRIVE of the proposed PMBLDCM drive in a wide range
The proposed PMBLDCM drive is of speed and input AC voltage.
modeled in Matlab-Simulink environment and
evaluated for an air conditioning compressor load.

develope electromagneti i The performance of the proposed PMBLDCM drive
The d c torque Te n the fed
from 220 V AC mains during starting at rated torque and
PMBLDCM is given as, 900
rpm speed is shown in Fig. 4a. A rate limiter of 800 V/s
is
Te = (ean ia + ebn ib +ecn ic)/ ω (25) introduced in the reference voltage to limit the starting
current
where ω is motor speed in rad/sec, of the motor as well as the charging current of the DC
link
capacitor. The PI controller closely tracks the reference
The back emfs may be expressed as a function of speed
rotor so that the motor attains reference speed smoothly within
0.35
position (θ) as, sec while keeping the stator current within the desired
limits
exn= Kb fx(θ) ω (26) i.e. double the rated value. The current (is) waveform at
input
where x can be phase a, b or c and accordingly fx(θ) A main i phas wit suppl voltag
represents C s is n e h the y e (vs)
function of rotor position with a maximum value ±1,
identical demonstrating nearly unity power factor during the
starting.
to trapezoidal induced emf given as, Performance under Speed
B. Control
fa(θ) = 1 for 0 < θ < 2π/3 (27) Figs. 4-6 show the performance of the
proposed
fa(θ) = {(6/ π)( π- θ)}- PMBLDCM drive under the speed control at constant
1 for 2π/3 < θ < π (28) rated
torque (9.55 Nm) and 220 V AC mains supply voltage.
These
fa(θ) = -1 for π < θ < 5π/3 (29) results are categorized as performance during transient
fa(θ) = {(6/π)(θ - and
2π)}+1 for 5π/3 < θ < 2π (30) steady state conditions.

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The functions fb(θ) and fc(θ) are similar to fa(θ)
with a phase difference of 120º and 240º
respectively.
1) Transient Condition: Figs. 4b-c show the
performance of the drive during the speed
control of the compressor. The

Fig. 4a: Starting performance of the PMBLDCM drive at 900 rpm.

Fig. 4b: PMBLDCM drive under speed variation from 900 rpm to 1500 rpm.

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Anitha Arumalla, M.Lokya, M.Tech / International Journal of Engineering Research
and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Fig. 4c: PMBLDCM drive under speed variation from 900 rpm to 300 rpm.
Figure 4. Performance of the Proposed PMBLDCM drive under speed variation at 220 VAC
input.

Fig. 5a: Performance of the PMBLDCM drive at 300 rpm.

Fig. 5b: Performance of the PMBLDCM drive at 900 rpm.

Fig. 5c: Performance of the PMBLDCM drive at rated speed (1500 rpm).
Figure 5. Performance of the PMBLDCM drive under steady state condition at 220 VAC input.

1103 | P a g e

reference speed is changed from 900 rpm to 1500
rpm for the rated load performance of the
compressor; from 900 rpm to 300 rpm for
performance of the compressor at light load. It is
observed that the speed control is fast and smooth
in either direction i.e. acceleration or retardation
with power factor maintained at nearly unity Figure 7. PQ parameters of PMBLDCM drive
value. Moreover, the stator current of PMBLDCM under speed control at rated torque and 220 VAC
is within the allowed limit (twice the rated current) input
due to the introduction of a rate limiter in the
reference voltage.

2) Steady State Condition:The speed control of
the PMBLDCM driven compressor under steady
state condition is carried out for different speeds
and the results are shown in Figs. 5-6 and Table-II
to demonstrate the effectiveness of the proposed
drive in wide speed range. Figs.5a-c show voltage
(vs) and current (is) waveforms at AC mains, DC
link voltage (Vdc), speed of the motor (N), Fig. 8a. At 300 rpm Fig. 8b. At 900 rpm Fig.
developed electromagnetic torque of the motor 8c. At 1500 rpm
(Te), the stator current of the PMBLDC motor for Figure 8. Current waveform at AC mains and its
phase „a‟ (Ia), and shaft power output (Po) at 300 harmonic spectra of the PMBLDCM drive under
rpm, 900 rpm and 1500 rpm speeds. Fig. 6a shows steady state condition at rated torque and 220 VAC
linear relation between motor speed and DC link
voltage. Since the reference speed is decided by TABLE II. PERFORMANCE OF DRIVE
the reference voltage at DC link, it is observed that UNDER SPEED CONTROL AT 220 V AC
the control of the reference DC link voltage INPUT
controls the speed of the motor instantaneously. Spee TH ηdriv
Fig.6b shows the improved efficiency of the drive d VDC Di DPF PF e Load
system (ηdrive) in wide range of the motor speed. (rpm (%
) (V) ) (%) (%)
C. Power Quality Performance 4.8
The performance of the proposed 300 100 4 0.9999 0.9987 74.2 20.0
PMBLDCM drive in terms of various PQ 3.9
parameters such as THDi, CF, DPF, PF is 400 126 4 0.9999 0.9991 79.1 26.7
summarized in Table-II and shown in Figs. 7-8.
3.3
Nearly unity power factor (PF) and reduced THD
500 153 3 0.9999 0.9993 81.8 33.3
of AC mains current are observed in wide speed
2.9
range of the PMBLDCM as shown in Figs. 7a-b.
600 179 2 0.9999 0.9995 83.8 40.0
The THD of AC mains current remains less than
5% along with nearly unity PF in wide range of 2.6
speed as well as load as shown in Table-II and 700 205 3 0.9999 0.9996 85.3 46.6
Figs. 8a-c. 2.4
800 232 0 0.9999 0.9996 86.1 53.3
2.2
900 258 4 0.9999 0.9996 87.0 60.0
2.1
1000 284 6 0.9999 0.9997 87.6 66.6
2.0
1100 310 9 0.9999 0.9997 88.1 73.3
2.0
1200 337 3 0.9999 0.9997 88.1 80.0
2.0
1300 363 5 0.9999 0.9997 88.2 86.6
Fig. 6a. DC link voltage with speed Fig. 6b.
Efficiency with load 2.0
1400 390 7 0.9999 0.9997 88.1 93.3
Figure 6. Performance of the proposed PFC drive 2.0
under speed control at rated torque and 220 VAC 1500 416 9 0.9999 0.9997 88.1 100.0

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D. Performance under Variable Input AC VI. CONCLUSION
Voltage A new speed control strategy of a
Performance evaluation of the proposed PMBLDCM drive is validated for a compressor
PMBLDCM drive is carried out under varying load of an air conditioner which uses the reference
input AC voltage at rated load (i.e. rated torque speed as an equivalent reference voltage at DC
and rated speed) to demonstrate the operation of link. The speed control is directly proportional to
proposed PMBLDCM drive for air conditioning the voltage control at DC link. The rate limiter
system in various practical situations as introduced in the reference voltage at DC link
summarized in Table-III. effectively limits the motor current within the
desired value during the transient condition
Figs. 9a-b show variation of input current (starting and speed control). The additional PFC
and its THD at AC mains, DPF and PF with AC feature to the proposed drive ensures nearly unity
input voltage. The THD of current at AC mains is PF in wide range of speed and input AC voltage.
within specified limits of international norms [5] Moreover, power quality parameters of the
along with nearly unity power factor in wide range proposed PMBLDCM drive are in conformity to an
of AC input voltage. International standard IEC 61000-3-2 [5]. The
proposed drive has demonstrated good speed
control with energy efficient operation of the drive
system in the wide range of speed and input AC
voltage. The proposed drive has been found as a
promising candidate for a PMBLDCM driving Air-
Con load in 1-2 kW power range.

APPENDIX
Rated Power: 1.5 kW, rated speed: 1500
rpm, rated current: 4.0 A, rated torque: 9.55 Nm,
number of poles: 4, stator resistance (R): 2.8 Ω/ph.,
Fig. 9a. Current at AC mains and its THD Fig. 9b. inductance (L+M): 5.21 mH/ph., back EMF
DPF and PF Figure 9. PQ parameters with input constant (Kb): 0.615 Vsec/rad, inertia (J): 0.013
AC voltage at 416 VDC (1500 rpm) Kg-m2. Source impedance (Zs): 0.03 pu, switching
frequency of PFC switch (fs) = 40 kHz, capacitors
TABLE III. VARIATION OF PQ (C1= C2): 15nF, PI speed controller gains (Kp):
PARAMETERS WITH INPUT AC VOLTAGE 0.145, (Ki): 1.45.
(VS) AT 1500 RPM (416 VDC)
VA TH Is ηdri REFERENCES
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