PV-POWERED DC MOTORS
Mohammad S. Widyan
Electrical Engineering Department
The Hashemite University
13115 Zaqrq
JORDAN
ABSTRACT
This paper presents one of the application of Photovoltaic cells. It includes the dynamical and steady-state
charateristics of PV-powered DC shunt, series and permanent-magnet motors. The study comprises the two cases when
the motors are directly connected to the PV cells as compared with the case of supplying the motors with fixed terminal
voltage and the case when the motors are connected via DC-DC buck-boost switch mode converter with the aim of
keeping constant voltage at the terminals of the motors irrespective of the load current for all realistic solar
illuminations. In all cases the PV cells are designed such that their maximum power point are at the rated conditions of
the motors. The study has extended to include the simulations at different solar illuminations.
I.
INTRODUCTION
DC motors are electrical machines that consume DC electrical power and produce mechanical power.
Historically, DC machines are classified according to the connection of the field circuit with respect to the armature
circuit. In shunt machines, the field circuit is connected in parallel with the armature circuit while DC series machines
have their field circuit in series with the armature where both field and armature currents are identical. Permanentmagnet machines, on the other hand, have only one circuit (armature winding) and the flux generated by the magnets is
constant. Compared with conventional electrical machines, permanent-magnet machines exhibit higher efficiency,
higher power to weight ratio and simpler construction.
The use of photovoltaic systems as a power source for electrical machines is considered a promising area in
photovoltaic applications due to the ongoing growth of PV-market [1]. The dynamical and steady-state characteristics
of PV-powered DC motors at different solar intensities, different loading conditions and different system controllers &
configurations have been proposed [2]-[8]. Similar studies for permanent-magnet and AC machines are presented [9][14]. In this study, the photovoltaic cells are designed to provide their maximum power at the rated conditions of the
DC motors when the PV array is fully illuminated. The nonlinearity of the magnetization curve of the ferromagnetic
materials of the machines and that of the I/V characteristics of the photovoltaic cells are included. The average value of
the output voltage of the DC-DC converter is controlled by its duty ratio with an aim of keeping fixed voltage across the
terminals of the motors at all realistic loading conditions and solar illuminations.
II.
SYSTEM DESCRIPTION:
Fig. 1 shows the first system under study which is a PV array directly connected to a DC motor. Fig. 2 shows
the same PV array feeding a DC motor via DC-DC buck-boost switch mode converter.
Fig. 1: A photovoltaic array consisting of
N s series- and N p
parallel-connected modules loaded by DC motor
Fig. 2: Block diagram for the system under study
The circuit of the DC-DC Buck/Boost switch mode converter is:
Fig. 3: Buck-boost converter circuit
III.
MATHEMATICAL MODEL AND CHARACTERISTICS:
The dynamical model of DC shunt, series and permanent-magnet motors are presented in this section.
a) DC Shunt Motor
In shunt motor, the field circuit is connected in parallel with the armature. Adjustable resistor R adj is normally
connected in series with the field circuit for speed control. DC shunt motor has the following dynamical model:
LF
La
di F
 VT  ( RF  Radj )i F
dt
(1)
dia
 VT  Ra ia  K
dt
(2)
d
 Kia  TL
dt
J
where
(3)
LF : field winding inductance, i F : field current, VT : terminal voltage and R F  Radj : total field resistance,
La : armature winding inductance, i a : armature current, Ra : armature resistance, K : constant related to the design of
the machine,
 : flux per pole,  : rotational speed of the rotor, J : rotor and load moment of inertia and TL : load
torque. Eqs. (1), (2) and (3) represent the nonlinear dynamical behavior of a DC shunt motor including the nonlinearity
of the magnetization curve of the ferromagnetic material of the machine.
b) DC Series Motor
DC series motor, with its own characteristics of high starting torque which makes it suitable for high inertia as
well as traction systems, has a nonlinear dynamical model. As its name indicates, the field circuit is connected in series
with the armature and therefore the armature and field currents are identical. It has the following nonlinear dynamical
mathematical model:
( LF  La )
dia
 VT  ( Ra  RF )ia  K
dt
J
d
 Kia  TL
dt
(4)
(5)
Eqs. (4) and (5) represent the nonlinear dynamical behavior of a DC series motor including the nonlinearity of the
ferromagnetic material of the machine.
c) Permanent-Magnet DC Motor
Due to absence of the field current and field winding, permanent magnet machines exhibit high efficiency in
operation, simple and robust structure in construction and high power to weight ratio. The attractiveness of the
permanent-magnet machines is further enhanced by the availability of high-energy rare-earth permanent-magnet
materials like SmCo and NdFeB [15]. However, the speed control of permanent-magnet DC motor via changing the
field current is not possible. Its dynamical model can be summarized as:
La
dia
 VT  Ra ia  K m
dt
J
d
 K m i a  TL
dt
(6)
(7)
Eqs. (6) and (7) represent the dynamical model of permanent-magnet DC motor. The output charateristics of the
designed PV array are given in Fig. 4 at different solar illuminations:
180
160
0.75 of Full Illumination
Full Illumination
140
120
Voltage (V)
0.6 of Full Illumination
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
Current (A)
Fig. 4: Output charateristics of the designed PV array at different illuminations
IV.
SIMULATION RESULTS
1) The case of Direct Connection with Photovoltaic Cells
This section presents some dynamical and steady-state simulation results for the DC motors that are directly powered by
PV cells.
a) DC Shunt Motor
Fig. 5 shows the armature current and motor rotational speed at different solar illuminations as compared with
the case of supplying the motor by fixed terminal voltage. Fig. 6 shows the steady-state charateristics of DC shunt
motor at different solar illuminations as compared with the case of supplying it by fixed terminal voltage.
16
with fixed terminal voltage
15
with photovoltaic cells at full illumination
14
with photovoltaic cells at 0.75 of full illumination
Armature Current (A)
13
12
11
10
9
8
7
6
0
5
10
15
20
25
Time (Sec)
(a)
30
35
40
45
50
1900
1800
with photovoltaic cells at full illumination
Rotational Speed (rpm)
1700
with fixed terminal voltage
1600
1500
1400
with photovoltaic cells at 0.75 of full illumination
1300
1200
0
5
10
15
20
25
30
35
40
45
50
Time (Sec)
(b)
Fig. 5: (a) armature current and (b) rotational speed of DC shunt motor after a step change on the load torque from 5Nm to 10.4Nm
2000
with photovoltaic cells at full illumination
with fixed terminal voltage
1800
1600
with photovoltaic cells at 0.75 illumination
Rotational Speed (rpm)
1400
1200
1000
800
600
400
200
0
0
2
4
6
8
10
12
Torque (Nm)
Fig. 6: Torque-speed characteristics of DC shunt motor with photovoltaic cells at different illuminations and fixed terminal voltage
b) DC Series Motor
Fig. 7 shows the armature current and motor rotational speed at different solar illuminations as compared with
the case of supplying the motor by fixed terminal voltage.
18
with photovoltaic cells at full illumination
16
with photovoltaic cells at 0.75 illumination
Armature Current (A)
14
with fixed terminal voltage
12
10
8
6
4
2
0
5
10
15
20
25
30
35
40
45
50
45
50
Time (Sec)
(a)
2000
1800
1600
Rotational Speed (rpm)
1400
with photovoltaic cells at full illumination
1200
with fixed terminal voltage
1000
800
with photovoltaic cells at 0.75 illumination
600
400
200
0
0
5
10
15
20
25
30
35
40
Time (Sec)
(b)
Fig. 7: (a) Armature current and (b) rotational speed of the DC series motor after a step increase in the load torque from 5Nm to 17Nm
c)
Permanent-Magnet DC Motor
Fig. 8 shows the armature current and motor rotational speed at different solar illuminations as compared with
the case of supplying the motor by fixed terminal voltage.
18
with fixed terminal voltage
16
Armature Current (A)
with photovoltaic cells at 0.75 of full illumination
14
with photovoltaic cells at full illumination
12
10
8
6
0
5
10
15
20
25
30
35
40
45
50
Time (Sec)
(a)
2200
Rotational Speed (rpm)
2000
1800
with fixed
terminal voltage
with photovoltaic cells at full illumination
1600
1400
with photovoltaic cells at 0.75 illumination
1200
1000
0
5
10
15
20
25
30
35
40
45
50
Time (Sec)
(b)Fig. 8: (a) Armature current and (b) rotational speed of the permanent-magnet DC motor after a step increase in the load torque from
5Nm to 11.9Nm
2) The case of Connection via DC-DC Buck/Boost Switch Mode Converter
This section presents some dynamical and steady-state charateristics of DC motors powered by PV cells via DCDC Buck-Boost switch mode converter.
a) DC Shunt Motor
165
Photovoltaic Cells Terminal Voltage (V)
160
155
at full illumination
150
145
140
at 0.75 of full illumination
135
130
125
0
2
4
6
8
10
12
14
12
14
16
18
20
Time (Sec)
(a)
Motor Terminal Voltage (Converter Terminal Voltage) (V)
125.5
at 0.75 of full illumination
at full illumination
125
124.5
124
0
2
4
6
8
10
16
18
20
Time (Sec)
(b)
Fig. 9: Photovoltaic cells terminal voltage at full illumination and 0.75 of full illumination after step increase in the load torque from 5Nm to
10.4Nm and (b) the corresponding DC shunt motor terminal voltage
300
Line: at full illumination
o: at 0.75 of full illumination
280
Rotational Speed (Rad/Sec)
260
DC Series Motor
240
220
200
Permanent-Magnet DC Motor
180
160
DC Shunt Motor
140
120
100
0
2
4
6
8
10
12
14
16
18
Load Torque (Nm)
Fig. 10: Torque-speed characteristics of DC shunt, series and permanent-magnet motors fed by photovoltaic cells via DC-DC buck-boost
switch mode converter at full solar illumination and 0.75 of full illumination
CONCLUSIONS
The dynamical and steady-state charateristics of DC shunt, series and permanent-magnet motors are presented. The case
of supplying the motors directly from PV cells as compared with the case of supplying them from fixed terminal voltage
is presented. Additionally, the case of powering the DC motors by PV cells via DC-DC Buck-Boost switch mode
converters is addressed.
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