 Open Access
 Total Downloads : 65
 Authors : Huaqiang Zhang , Fengming Sun , Tong Yao , Xinsheng Wang, Xiujing Qin
 Paper ID : IJERTV8IS050332
 Volume & Issue : Volume 08, Issue 05 (May 2019)
 Published (First Online): 01062019
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Marine Hybrid Power Drive System Based on Model Predictive Control
Huaqiang Zhang1, Fengming Sun1, Tong Yao1,Xinsheng Wang1, Xiujing Qin1
1. Department of Electrical Engineering, Harbin Institute of Technology at Weihai,
Weihai Shandong 264209, China;
Abstract—Ship hybrid power drive is an energy saving ship power scheme, the redundant mechanical energy of the diesel main engine can be converted into electricity by the shaft motor. However, the stator current and electromagnetic torque of shaft motor have obvious pulsation, which leads to the instability of ship electrical power system. In this paper, the model predictive direct power and torque control (MPDPTC) for backtoback inverter is proposed based on the switch table direct power and torque control (STDPTC). The optimal voltage vector and optimal duty cycle can effectively reduce the pulsation of the stator current and electromagnetic torque, so the cost function is established to calculate them. The simulation results show the proposed method can effectively eliminate the pulsation of the stator current and electromagnetic torque. Finally, the MPDPTC was tested on a ship hybrid power experiment platform, and the surfacemounted permanent magnet synchronous motor is used as the shaft belt motor. The experimental results show pulsation of stator current and electromagnetic torque can be effectively eliminate when the shaft motor operates in the power generation or electric mod. The system achieves twoway flow of energy and has good static performance.
Key words: Hybrid power drive, energy feedback, model prediction control, optimal vector and duty cycle
. INTRODUCTION
With the onset of the oil crisis and the rise in international fuel prices, the requirements for energy saving of the marine power systems are becoming increasingly higher. The ship power types include mechanical propulsion and electric propulsion. For the
mechanical propulsion ship, the propulsion engines (gas turbines or diesel engines, etc.) directly drive the propeller through the shaft to power the ship. Due to the independence of the ship power and electric system, the fuel utilization rate is low. By contrast, the electric propulsion ships drive the motor via a frequency converter, and then the motor drives the propeller to power the ship. The operating efficiency and the energy efficiency are high due to the frequency drive method(1),(2). However, the cost of electric propulsion is high, and the capacity of the electric equipment is limited. The marine hybrid drive system has emerged owing to this situation, which combines the advantages of mechanical propulsion and electric propulsion. This system is composed of a marine shaft power generation system, reversible frequency conversion shaft motor, fourquadrant converter, propeller device, gearbox, clutch, marine power station and diesel engine unit. Because the fourquadrant converter can realise the twoway flow of energy, the system can meet multiple speed requirements. In the course of highspeed voyage, the propulsion host and the shaft motor propel jointly provide the maximum propulsion power to the ship. In the course of lowspeed voyage, the shaft motor is used separately to drive the ship. In the course of midspeed voyage, the shaft motor runs in the state of power generation to absorb the redundant power of the propulsion engine, in which the gridconnected operation is achieved through the gridside converter (3).
In order to ensure the grid stability, the early marine hybrid drive system uses the synchronous compensator to provide the reactive power compensation, which has high cost and large space. And then the power compensation shaft motor systems use the highpower thyristor converter
device; but the system harmonic content and power factor are not ideal. In this situation, the dual PWM backtoback inverter is applied to the marine hybrid drive system, which effectively improves the stability of the ship's power grid(4),(5). The traditional control strategy of the marine hybrid drive system includes the voltage vector directional control and the direct power torque control, the former has complex control algorithms and computations, and the latter significantly trembles during torque, active power and reactive power(6). In order to improve the system performance, (6) proposed a complex vector PI regulator for the the dual PWM backtoback inverter. Additionally,

proposed a variable frequency PWM rectifier scheme, which includes an inner current loop based on a complex vector PI controller and an outer voltage loop based on the instantaneous power balance. The method above renders a system that is robust to the frequency resonance transform. In addition to this, the new control strategies such as the sliding mode control and neural network control have the characteristics of fast tracking and antiinterference, which
effectively improves the performance of the shaft belt motor system(7)(9). Based on the switch table direct power and torque control (STDPTC), this paper proposes the model predictive direct power and torque control (MPDPTC), which effectively reduces the current ripple and torque ripple of the system, as well as improves the stability and robustness of the system.
. THE MATHEMATICAL MODLE OF BACKTOBACK INVERTER

The Mathematical Model of Voltage Source Rectifier
The grid side of the backtoback inverter adopts the threephase voltage source PWM rectifier (VSR) which conducts rectifier function, and the voltage source inverter (VSI) is used to drive the Permanent Magnet Synchronous Motor (PMSM) in the machine side.(The functions of VSR and VSI are interchanged to achieve energy feedback when the PMSM is working in the state of power generation) Fig. 1 shows the topology of the backtoback inverter(10).
VSR VSI
G11 G21 G31 G41 G51 G61
ua L11 R1 A
ub L12 R2
N
uc L13 R3
C1 U
B
Udc
C V
C2 W
PMSM
G12
G22
G32
G42
G52
G62
Fig. 1. The topology of backtoback inverter
The circuit of a threephase ac/dc converter studied in this paper is illustrated in Fig. 1 and its mathematical
S p jq 3 (i * u)
2
(2)
model in two phase stationary – frame is expressed as:
u Ri L di u (1)
dt VSR
where i* is the conjugate complex number of i, p and q represent the active power and reactive power, respectively. The following equations holds true for balanced
where uVSR, u, and i are rectifier voltage vector, grid voltage vector, and grid current vector, respectively; R and L are the equivalent series resistance and inductance of
threephase grid voltages:
du j u e jt
dt
(3)
grid filter. The complex power is introduced in order to immediately control the active and reactive powers. The complex power S at the grid side can be calculated from instantaneous theory as:
where is the grid frequency, u is the modulus of the grid voltage vector, The differentiation of grid current can be obtained from (1) as
di 1 (u Ri u )
The Motor movement equation is as follows:
dt L
VSR
(4)
T T
J dr R (9)
From (2) to (4), the differentiation of complex power S
can be obtained as:
dS 3 ( du i * di * u)
dt 2 dt dt
e L dt r
where sd, sq are stator flux dq axis component respectively, isd, isq are stator current dq axis component respectively, TL is motor load torque, Te is motor
3 1 (u* u*
 p>Ri* )u
i* ju
electromagnetic torque, J is motor inertia, r is motor rotor
2 L VSR
3 2
(5)
mechanical angular velocity, r is electrical motor speed,

u

u
( u
( u
2
2
*
VSR

(R jL)S
L
R is damping coefficient.

The Mathematical Model of PMSM
These assumptions are listed to facilitate the analysis:

Ignore the eddy current effect and hysteresis effect of motor.

Ignore the effect of the magnetic saturation.

The threephase stator winding is symmetrical and there are 120 electrical angle differences between two adjacent winding.

The magnetic field presents a sine distribution in the air gap between stator and rotor.

The permanent magnet in the rotor adopts the patch structure ,furthermore, the distribution of the magnetic circuit is symmetrical.
Under the threephase stationary coordinate system, the mathematical model of PMSM is nonlinear and close coupling. After transforming the mathematical model by Clark and Park transforms, the dq axis mathematical model of PMSM can be obtained(11),(12).
The motor voltage equation are as follows:
. THE CONTROL STRATEGY OF BACKTOBACK
INVERTER

The difference between the two control strategies
The traditional backtoback inverter adopts the STDPTC, which selects the voltage vector through the hysteresis comparator state and location of the magnetic chain, and the voltage vector of the STDPTC is discontinuous. Therefore, the insulatedgate bipolar transistor (IGBT) switching frequency is not fixed and this phenomenon leads to performance deterioration in switching losses, active power pulsations, and the total harmonic distortion (THD) of the gridside current(13),(14). In order to solve the problems existing in traditional controllers, MPDPTC is proposed in this section. Based on the figure 2, the voltage vectors is selected based on the hysteresis comparator and switch table in the traditional control strategy, which cannot match the system state very well. As well as the hysteresis also causes a certain error in the switching of the voltage vector. In contrast, the voltage vector is selected by the cost function in the improved
u R i d sd
control strategy, which can better match the system state,
sd s sd dt
d
r sq
(6)
and the system runs more smoothly. In the model
u R i sq
predictive direct power control (MPDPC), the selection
sq s sq dt
r sd
method of optimal voltage vector is proposed to optimize
where Rs is stator resistance, np is pole pairs, Ld, Lq are stator inductance dq axis component respectively. Motor is patch type. Thus, Ld is equal to Lq. The electromagnetic torque equation is as follows:
the vectors selection. On the other hand, in the model predictive direct torque control (MPDTC), the selection method of optimal duty cycle is proposed to select an appropriate operating time of the optimal voltage
T 2 n i
(7)
vector(15),(16). All these methods ensure the stability of the
e 3 p f sq
system.
The stator flux equation are as follows:
sd Ldisd f
(8)
sq Lqisq
Udc L
Power and
k
k
Delay
pk+1
p Active and
u
U
xy L
q virtual flux R
compensation
reactive power
i
I R
STDPC
qref=0 –
+
U
estimator IL
p
n1
G1
Switch table
G1
n1
G1
Switch table
G1
VSR
Model prediction
Model prediction
pk+2
qk+2
qk+1
calculator
Optimal goal evaluation function
uopt
Optimal goal evaluation function
uopt
qk
SVPWM
–
VSR
dcref
+ – PI
+ –
pref
MPDPC
qref =0
pref
Hysteresis comparator
Dq
Dp
Hysteresis comparator
Dq
Dp
Reference power
udc
Udc
Power forward feedback
calculation
PI udcref + –
VSI
mref
sref
+ –
PI
D
Hysteresis comparator
DT
Switch G2 table
VSI
+
rref
– PI
sref
Teref
Optimal goal u
evaluation function
opt
,topt
SVPWM
Te
+
m –
Teref + –
G2 n2
r Tek
+2
sk+
Model prediction
+2
sk+
Model prediction
2
ui,t
ref i
Optimal duty
Voltage vector
cycle control ui selection
Te Torque and
Udc
k+1
k+1 s
Tek+1
STDTC
s Stator Flux
Estimator Is
m
PMSM
MPDTC
s
isk+1
Torque and flux estimation & Delay compensation control
r
is
us
PMSM

The structure of the STDPTC (b) The structure of the MPDPTC
Fig. 2. The structure of control strategy


The Optimal Voltage Vector of Model Predictive Direct Power Control
From Equation (9), the prediction of p and q at (k + 1)th can be obtained as
In model predictive direct power control(MPDPC), the
pk 1 pk 3T uk Re(conj(uk
)uk )
S
VSR
minimum power error is the basis for voltage vector
VSR
VSR
selection in the next control period, so the cost function is
qk 1 qk
2L
Im(conj(uk
)uk )
(12)
RT pk qk
S TS
set which takes both the power errors and selection of each voltage vector. And the optimal voltage vector is applied in the next control period which has the minimum cost result. Due to the control input of the system is finite, and
L qk pk
The formula of the active power and reactive power at (k)th are as follows:
combined with the characteristics of the finite control set
pk 3 uk uk ik
(13)
model predictive control(FCSMPC), the cost function and
the predictive model are as follows:
qk 2 uk uk ik
g Sk 1 Sk 1 2 S k 1 S k Sk 1 2
where u ,u are grid voltage axis component
1 ref ref
(10)
respectively, i ,i
are grid current axis component
ref
ref
( pk 1 pk 1 )2 (qk 1 )2
The (k) or (k+1) in the superscript represents the sampled value of the parameter at (k)th or (k+1)th, Sk+1 is the change in complex power at (k+1)th. The complex power at (k + 1)th instant should be predicted for the aim of cost function evaluation for each voltage vector. By decomposing the real and imaginary components of Equation (9), the differentiations of active and reactive powers are as follows
dp
respectively. Based on the Equation (10), the selection is cumbersome, which needs to check the voltage vector one by one. To simplify the process of vector selection, an optimal voltage vector selection method is described in this section. In the process of vector selection by Equation (10), it is found that the Sk+1 is the most complicated part. Combined with the Equation (5), Sk+1 includes the timevarying parameter u* and u, which increases the complexity of the vector selection. Where u* is the conjugate coefficient of converter voltage and u is the grid
dt
3 u 2 Re(u* u)
R p q
VSR
VSR
VSR
VSR
voltage vector. In order to get the optimal voltage vector
dq
2L Im(u*
VSR
u)
L q p
L q p
(11)
faster, the way of the vector selection will be transformed
dt
VSR
to an appropriate coordinate system(17)
. In synchronous dq
coordinate system with the daxis attached to the position
of grid voltage vector, the grid voltage becomes
v1*
c
1<2
 = 
udq=u=U, where U is the amplitude of grid voltagev *
1 2
d v6*
vector. Firstly, the timevarying term in Equation (5) can be eliminated in dq coordinate system, the new equation is as follows:
2
b
1 2
1
2
b= X(k+1)0,7S(k+1)dqref
*
*
1=3UTs/2Lv1
*
*
=S
=S
2=3UTs/2Lv6 c=(S1(k+1)dq)
dS 3 (U 2 u* U ) (R jL)S
VSR dq
VSR dq
(k+1)
dqref
X(k+1)
0,7
+1
dq 2 dq
dt L
(14)
v *
=1b
(k+1)
(k+1)
d=(S2 dq)
where
u
u
*
VSRdq
3
is the conjugate rectifier voltage vector in
v4*
v5*
(k+1)
=S
=S
dqref
=2b
X(k+1)
0,7
+2
synchronous dq frame. It can be obtained from the
conjugate rectifiers voltage vector
*
u
u
VSR
in stationary frame
using Park transformation as follows:
Fig. 3. Voltage vector selection method
u
u
*
VSRdq
u* .e j
(15)
According to the formula in Fig. 3, 1 is equal to 2 because of v * is equal to v *, the complex power error c
VSR
VSR
1 6
where = u is the angle of grid voltage vector. After discretization processing, the new dqaxis mathematical equation of the complex power is as follows:
and d can be calculated base on the Equation (17): c=1b,d=2b. The size of c and d can be obtained by the cosine theorem: c2=12+b221bcos2,
S
S
k1 dq
3 (U 2 u*
2S
2S
VSR
VSR
dq
k
dq
U ) (R jL)S k T
dq s
L
(16)
d2=22+b222bcos1 and 1>1. Clearly, d<c, and v6 is more suitable than v1 in Fig. 3. This selection process is much simpler than searching the optimal voltage vector
According to Equation (12) and the characteristics of the effective and zero voltage vectors, the influence of the
one by one. Thus, the cost function of the optimal voltage vector is as follows:
zero vector is expressed
g Sk 1 Sk 1 2
2
Sk 1 Sk 1
(18)
3U 2 (R jL)S k T
1 ref dqref dq
as S 2
as S 2
k
dq L
dq s
X
X
k 0,7
and the influence of
Under ideal conditions, the controller exerts the grid voltage vector at the k moment, subsequently, the active
the effective vector is expressed as
3UTS u*
. Thus, the
and reactive powers can quickly reach the given value at
2 VSRdq
mathematical equation of the complex power at (k+1)th is as follows:
(S k 1 ) S k 1 S k 1
(k+1)th. Owing to the system hysteresis, the control reaches the given value at (k+2)th, clearly, the system lag time has to be compensated(18). Thus, the improved EF of
the optimal voltage vector is as follows:
dq dqref
dq
3UT
ref
ref
k 2
k 2 2
k 2
k 2 2
S k 1 X k 1 s u*
(17)
g1 Sref

S Sdq Sdq
(19)
dqref
0,7
2L VSRdq
( X k 1 ) 3UTs u*
0,7 2L VSRdq
Fig. 3 shows the selection method of voltage vector.
b X (k 1) S (k 1) ( X k 1) is in the sector shown in Fig. 3,
Based on the model prediction, the MPDPC controls the active and reactive powers in real time during each sampling period in order to control the grid current. For a
minimum error, cost function is set to obtain the optimal
0,7
dqref
0,7
voltage vector, so that the system can quickly control the
where is the influence of the effective voltage vector, c and d respectively represent the complex power error of the effective voltages v6 and v1.
rectifier to meet the dynamic performance index.
C. The Optimal Duty Cycle of Model Predictive Direct Torque Control
Fig. 3 shows that the model predictive direct torque
system at (k+2)th,
T /
en s
en s
ref
represents the weight
control (MPDTC) is adopted by the inverter. According to the characteristics of the system, the system prediction model and cost function are established based on FCSMPC. Firstly, the PMSM mathematical model in synchronous dq frame is known, by the Park inverse transformation, the formula of stator flux and electromagnetic torque at (k)th are as follows:
coefficient of stator flux and electromagnetic torque.
The torque ripple is the toughest challenge of the direct torque control, this is because the voltage vector remains constant in each sampling period. Although this problem can be improved by shortening the sampling time, the performance requirements of the power component are very high and the switching losses are larger. Therefore,
k
k (u

R i
)dt 0
the zero vector is introduced to match the action time of
s 0 s
s s
s
(20)
k k
the optimal voltage vector to reduce the motor torque
s
s
s
0
(us

Rsis
)dt 0
ripple. By combining the MPDTC with the optimal duty
T k 3 n ( k ik
k ik )
(21)
cycle control, the action time of effective voltage vector
e 2 p s s
s s
can be controlled. The inverter outputs two voltage vectors
Subsequently, the prediction model of the stator flux is obtained by discretization of the motor voltage formula in stationary frame.
in each sampling cycle. Under this premise, the zero vector mainly reduces the electromagnetic torque, however the effective voltage vector is used to increase the electromagnetic torque, so that the effective voltage vector
k 1 k uk R ik
s
s T s
s s
(22)
needs to be selected specifically.
k 1 k s uk

R ik
s s s
s s
Table1. The switching lookup table
s in sector i
Te
s
ui+1
u0, u7
ui+2
u0, u7
s in sector i
Te
s
ui+1
u0, u7
ui+2
u0, u7
The predicted value of stator current is necessary to the torque prediction model. According to Equation (6) and (8), the prediction model of stator current in synchronous dq frame is as follows:
ik 1 ik T
uk k L ik R ik
The voltage vector selection table is as follows:In the
d
d
sq s sq r d sd r f
sq s sq r d sd r f
sd sd s
sd r q sd s sq
(23)
sq sq
sq sq
ik 1
ik
L uk R ik k L ik k
Table1, where i is the stator flux sector position, the
According to the Equation (23), the current predicted value in synchronous dq frame is obtained. Subsequently, the current predicted value is inverse Park transformed, combined with the predicted value of the stator flux, the prediction formula of the motor torque is as follows:
selection of effective voltage vectors form a cycle from u1 to u6, () indicates that the voltage vector can increase (reduce) the value of the corresponding item. To obtain the optimal duty cycle of the effective voltage vector, the mathematical model of the electromagnetic torque under
the influence of the effective and zero voltage vectors must
T k 1 3 n k 1ik 1 k 1ik 1
(24)
e 2 p s s s s
be constructed. According to this model, the minimum
Owing to the system hysteresis, the expected control effect is achieved at (k+2)th when the motor controller applies the stator voltage vector at (k)th. Thus, the system requires a time delay compensation. The cost function of the optimal voltage vector is as follows:
error between the actual value and the reference value of the electromagnetic torque in each sampling period must be ensured(19). Through Equations (6), (7) and (8), the mathematical expression of electromagnetic torque under the influence of the effective voltage vector is as follows:
T T
T T
dTe
3np Rs
k 2 k 2 2 2 k2 k2 2
g
g
2 e ref e sref s
(25)
(Im(us f ) Im(sf ) r Re(sf )) dt 2Ld Ld
(26)
where
eref
eref
T k+2 is the preset electromagnetic torque of the
Similarly, the mathematical expression of the electromagnetic torque under the influence of the zero voltage vector is as follows:
system at (k+2)th,
k+2 is the preset stator flux of the
dTe 3np ( Rs Im( ) Re( ))
sref
sref
(27)
dt 2Ld Ld
s f r s f
According to Equations (23) and (24), the
2(T

T k+1) s
D eref e 2
(29)
mathematical expression of the electromagnetic torque
(2s1 s2 )Ts 2s1 s2
under the influence of the voltage vector can be obtained. As s1 is the rate of change under the effective voltage vector, s2 is the rate of change under the zero voltage vector. In fact, the sampling time set by the experimental platform and the simulation is 5 105 s. As the sampling time of the system is very short, s1 and s2 can be considered constant. The evaluation method of the optimal duty cycle is shown in Fig. 4, where te is the instantaneous value of the electromagnetic torque in the whole process, and Te(k+1) is the electromagnetic torque obtained after the delay compensation, S1, S2, and S3 are the area of shadow.
By combining the MPDTC algorithm with optimal duty cycle control, the system effectively reduces the torque ripple and improves the system stability.
. THE SIMULATION OF MPDPTC
In order to verify the correctness and validity of the MPDPTC, the STDPTC and MPDPTC are
experimented respectively in Matlab environment. Table 2 shows the system parameters.
Parameter
Value
Parameter
Value
Rated Power PN
5.5kW
qaxis inductance Lq
8.5mH
Rated Speed nN
1500r/min
daxis inductance Ld
8.5mH
Rated Current IN
10A
Permanent flux f
0.175Wb
Rated Voltage UN
380V
Stator Resistance Rs
2.875
Pole pairs np
2
Rotational Inertia J
0.045kgm2
Parameter
Value
Parameter
Value
Rated Power PN
5.5kW
qaxis inductance Lq
8.5mH
Rated Speed nN
1500r/min
daxis inductance Ld
8.5mH
Rated Current IN
10A
Permanent flux f
0.175Wb
Rated Voltage UN
380V
Stator Resistance Rs
2.875
Pole pairs np
2
Rotational Inertia J
0.045kgm2
Table 2. PMSM Parameters
Teref
S1
DTs te
S2
S3
Setting the simulation conditions: the preset speed is equal to 1200 r/min before 0.3s, after that, the preset speed turn into 800 r/min to realize the power generation
Tek+1 the slope is s1
Teref
the slope is s2
operation of the system. Fig. 5 shows the simulation results of the speed, Udc, active power, reactive power,
S1+S3+S2 min
(k+1)Ts (k+2)Ts
Fig. 4. The evaluation method of optimal duty cycle
In order to ensure the stable operation of the system, it is necessary to select an optimal duty cycle D to match the voltage vector. According to Fig. 4, the deviation degree of electromagnetic torque te from the given value Teref can be expressed by the shadow in a sampling period. The shadow area formula is as follows:
electromagnetic torque, stator current and current harmonic analysis. Firstly, the system speed is stable about 0.05s, then the motor switches to the power generation mode at 0.3s, the speed has an instantaneous overshoot about 0.34s, finally the speed stable at 800r/min. Based on the speed results, there is no significant difference in the speed control capability of the two control strategies. And then, both MPDPTC and STDPTC ensure Udc stability in the two work modes in the result.
Act
ual spe
ed
Re
ference
speed
Act
ual spe
ed
Re
ference
speed
1500
n(r/min)
n(r/min)
1000
1 (k 2)Ts
1 (k D)Ts
500
T e
eref
T e e 0
1
1
(t T
s (k+1)Ts
)2 dt
(t
s (k+1)Ts
1 (k 2)Ts


T k 1 s t)2 dt
500
T e e 12
0 0.1 0.2 0.3 0.4 0.5 0.6
(t
s (k+D)Ts

T k 1 s D s t)2 dt
(28)
1000
t(s)

The speed simulation of MPDPTC

To reduce the electromagnetic torque ripple, the state when the integral value is minimum must be obtained, and then the optimal duty cycle is obtained. The derivative of integral value with respect to duty cycle D is set to zero(20). According to the geometric relationship in the Fig. 5, the optimal duty cycle of the effective voltage is obtained:
600
Udc(V)
Udc(V)
400
200
0
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)

the MPDPTC Udc
4
1200
1700
2200
0
.4 0.
45 0.5
3000
2500
2000
0.
1 0.15
0.2
1200
1700
2200
0
.4 0.
45 0.5
3000
2500
2000
0.
1 0.15
0.2
x 10
P(W)
P(W)
1
0
1
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
600
Udc(V)
Udc(V)
400
200
0
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
(i) the STDPTC Udc
5
x 10
4

the active power of MPDPTC
1000
4
x 10
1
1200
1700
P(W)
P(W)
0
0
2200
Q(Var)
Q(Var)
2 0
1000
0 0.4 0.45
0.5
0.4 0.45 0.5
3000
2500
1 2000
0.1 0.15 0.2
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)

the reactive power of MPDPTC
100
4
x 10
10
Q(Var)
Q(Var)
5

the active power of STDPTC
1000
0
1000
Te(N.m)
Te(N.m)
0
100
23
20
17
0.1 0.15 0.2
23
20
17
0.4 0.45 0.5
0.4 0.45 0.5
0
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)

the reactive power of STDPTC
(e) The electromagnetic torque of MPDPTC
50
ia,b,c (A)
ia,b,c (A)
0
100
Te(N.m)
Te(N.m)
0
100
23
20
17
0.1 0.15 0.2
23
20
17
0.4 0.45 0.5
50
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
(f) The stator current of MPDPTC
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
(l) The electromagnetic torque of STDPTC
ia,b,c(A)
ia,b,c(A)
50
Fundamental (27Hz) = 8.17 , THD= 1.29% Fundamental (40Hz) = 8.21 , THD= 0.53%
Mag (% of Fundamental)
Mag (% of Fundamental)
100
50
0
0
500
Frequency (Hz)
1000
100
50
0
0 500 1000
Frequency (Hz)
0
50
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
(m) The stator current of STDPTC
(g) The stator current of STDPTC
Mag (% of Fundamental)
Mag (% of Fundamental)
Fundamental (27Hz) = 8.9 , THD= 8.12% Fundamental (40Hz) = 8.4 , THD= 12.97%
A 
ctual sp 
eed 

Refe 
rence s 
peed 

A 
ctual sp 
eed 

Refe 
rence s 
peed 

1500
1000
n(r/min)
n(r/min)
500
0
500
1000
100
50
0
0 500 1000
Frequency (Hz)
100
50
0
0 500 1000
Frequency (Hz)
0 0.1 0.2 0.3 0.4 0.5 0.6
t(s)
(h) the speed simulation of STDPTC
(n) The stator current of STDPTC
Fig.5 The simulink result of MPDPTC and STDPTC
According to Fig. 5, the simulation result of the active power, reactive power, electromagnetic torque, stator current and current harmonic is as follows: Firstly, the system status is stable about 0.05s, the active power of motor reaches to 2.5kW and reactive power reaches to 0 Var, as well as the value of the electromagnetic torque is 20N.m at this time. Subsequently, the motor switches to the power generation mode when the time is 0.3s, the electromagnetic torque reaches the limit value and the system transits to steady state quickly. Finally, the state of the system reaches stability about 0.34s. At this point, the value of active power is
1.7kW and reactive power is 0 Var. By comparing the simulation results of MPDPTC and STDPTC, the following conclusions can be obtained: although both strategies can achieve the control purpose, the active power ripple, reactive power ripple, stator flux ripple, stator current ripple, and electromagnetic torque ripple of the MPDPTC are smaller than those of STDPTC, and the stator current of the MPDPTC is more similar to the sinusoidal waveform,
furthermore the stability and robustness of the system are significantly improved.
. EXPERIMENT OF MARINE HYBRID DRIVE SYSTEM
MPDPTC is applied to marine hybrid drive system, TMS320F28335 chip is used as experiment platform in the system, 3kW asynchronous motor is simulated as marine main diesel engines, 2.2kW PMSM is used as Shaft motor, these two motors are connected with power shaft of the ship through the magnetic powder clutch. Power mode can be switched by the magnetic powder clutch. The Normal converter and backtoback inverter respectively control asynchronous motor and PMSM. All experimental devices of marine hybrid drive system are controlled by S7200 PLC, and network switch control is achieved by bus RS485. The whole experimental device is shown in the Fig. 6.
Encoder speed Shaft motor speed 

Encoder speed Shaft motor speed 

Fig. 6. The experiment platform
There are four working modes of the system, the main motor drives the ship separately; the shaft motor drives the ship separately; the main motor and shaft belt motor synchronously drive the ship; and the shaft motor works in the power generation mode when the main motor drives the ship. Owing to the output shaft diameter of two motors, the working frequency ratio of shaft motor and main motor is set to 1.017 when system works in the compound drive mode.
1500
1350
1200
1050
n(r/min)
n(r/min)
900
750
600
450
300
150
0
0 10 20
f(Hz)
30 40 50
The partial operating status of the system are given as follows:

The operating speed at shaft motor drive
20
Shaft motor torque
18
Te(N.m)
Te(N.m)
16
14
12
Based on Fig. a and Fig. b, It can be found that both motors can independently guarantee the normal operation of marine power system. At the compound drive mode, the operating conditions of the system are shown in fig. c. Under high speed, the torque of the two motors is relatively
balanced, the main motor speed is consistent with the shaft
10
0 10 20
f(Hz)
30 40 50
motor speed after scaling, and the combined drive is
1500
1350
1200
1050
n(r/min)
n(r/min)
900
750
600
450
300
150

The operating torque at shaft motor drive
basically realized. One of the operating conditions is selected to measure the electrical parameters. the system operating conditions are shown in Fig. 8. Note: All the test items in the figure are Aphase parameters. A and B in the figure respectively represent two channels of A phase.
Encoder speed Main motor speed
Encoder speed Main motor speed
0
0 10 20
f(Hz)
30 40 50

The operating speed at main motor drive
Main motor torque
Main motor torque
25
22.5
20
17.5
Te(N.m)
Te(N.m)
15
12.5
10
7.5
5
2.5
0
0 10 20
f(Hz)
a b
30 40 50

The operating torque at main motor drive
1500
1350
1200
n(r/min)
n(r/min)
1050
900
750
600
450
300
150
0
Encoder speed Main motor speed Shaft motor speed
Encoder speed Main motor speed Shaft motor speed
0 10 20
f(Hz)
30 40 50
c d
Fig. 8.The system conditions at the compound drive mode: (a) A phase

The operating speed at compound drive mode
Main motor torque
Shaft motor torque
Main motor torque
Shaft motor torque
30
27
24
Te(N.m)
Te(N.m)
21
18
15
12
9
6
3
voltage and A phase current of main motor, (b) A phase current spectrum of main motor, (c) A phase voltage and A phase current of shaft motor, (d) A phase current spectrum of shaft motor.
Fig. 8 shows system operating conditions: When the
system works in the compound drive mode, Aphase current frequency of the main motor is equal to 42.01Hz, and the THD of the main motor current is equal to 8.31%, Aphase
current frequency of the shaft motor is equal to 45.04Hz, the
0
0 10 20
f(Hz)
30 40 50
THD of the shaft motor current is equal to 6.32%. Obviously

The operating torque at the compound drive mode Fig. 7. The operating conditions of experimental platform
the THD of current and torque ripple are effectively reduced and the steady state performance of system is improved.
In order to examine the bidirectional motor flow characteristic of the marine drive system when the system adopts the MPDPTC, the main motor is set in electric mode and the shaft motor is set in power generation mode. In order to feedback the redundant energy of main motor, the working frequency ratio of shaft motor and main motor is set to 1, and then the operating conditions of the system are shown in Fig. 9.
Encoder speed Main motor speed Shaft motor speed 

Encoder speed Main motor speed Shaft motor speed 

1500
1350 c d
1200
n(r/min)
n(r/min)
1050
900
750
600
450
300
150
0
0 10 20
Feedback power 

Feedback power 

3
2.7
2.4
2.1
P(kW)
P(kW)
1.8
1.5
1.2
0.9
0.6
0.3
0
0 10 20
f(Hz)
a
f(Hz)
b
30 40 50
e f
30 40 50
Fig. 9. The operating conditions at the power generation mode: (a) The speed results of experimental platform, (b) The feedback power of
experimental platform
Based on Fig. 9, it is learned that the speed of main motor and shaft belt motor are basically consistent, and the system can realize the energy feedback. One of the operating conditions is selected to measure the electrical parameters. the system operating conditions are shown in Fig. 10(16).
a b
g h
Fig. 10. The operating conditions under the shaft motor power generation mode: (a) A phase voltage and A phase current of shaft motor, (b)
A phase current spectrum of shaft motor, (c) The feedback voltage and current of A phase, (d) The spectrum of feedback A phase voltage, (e) The spectrum of feedback A phase current, (f) The feedback active power of A phase, (g) The spectrum of feedback A phase active power, (h) The DC bus voltage.
Fig. 10 shows that, under the power generation mode, the
THD of the shaft motor A phase stator current reach 3.77%, the stator current is approximately sinusoidal and the shaft motor runs smoothly. The system feeds back the motor to the grid by the backtoback inverter, the feedback voltage frequency and current frequency of A phase are equal to
49.97 Hz, the THD of voltage and current respectively reach 2.1% and 11.5%,furthermore, the power factor reaches 0.99
and the feedback active power ripple is ideal. The operating conditions show the system can feed back motor to the grid under the MPDPTC strategy, the voltage of DC bus is stable, moreover,compared to the power grid of 50Hz, the frequency error of feedback voltage and current is 0.06%. The feedback power quality and THD of feedback voltage reach the desired state. Although the THD of current needs to be improved, the design goal is basically realized.
. CONCLUSIONS
The MPDPTC is adopted in the marine hybrid drive system. In order to obtain the optimal voltage vector quickly, the complexity of the MPDPC is simplified by an additional control algorithm. Similarly, the optimal duty cycle is introduced in the MPDTC to reduce flux ripple and torque ripple. According to the comparison of simulation results between the STDPTC and MPDPTC, the MPDPTC effectively reduces the active power ripple, reactive power ripple, stator flux ripple, stator current ripple, and electromagnetic torque ripple of the system, furthermore, the stability and robustness of the system are significantly improved. Based on the experiment results: The operating mode of shaft motor is switched smoothly in the power generation and electric state. On the one hand when main
motor is combined with shaft motor, the THD of the shaft
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