Vector Control Of An Induction Motor For Photovoltaic Pumping Imene Yahyaoui 1,2, Souhir Sallem2, Maher Chaabene 2 and Fernando Tadeo1 1
Industrial Engineering school, University of Valladolid, Spain e-mail:
[email protected], e-mail:
[email protected] 2 Unité de Commande de Machines et Réseaux de Puissance CMERP-ENIS, University of Sfax, Tunisia e-mail:
[email protected],
[email protected] Abstract -The PhotoVoltaic water Pumping Systems (PVPS) constitute a potential option to extract water in remote locations for agriculture. This technique requires an efficient control of the system components. The aim of this work is to study the efficiency of the vector method in controlling an asynchronous machine used for water pumping. With a maximum power extracted from the photovoltaic panel, the control method is studied from the point of view of pumped water volume. For this, a typical situation is considered: A pumping system composed of a 4500 W pump driven by an asynchronous machine which is powered by a 5000 W photovoltaic array. Using measured data of irradiation and temperature, a comparison has been carried out using a detailed simulation for a medium season under the outdoor conditions of Sfax site. Through the comparison of the obtained results of different parameters as power, daily cumulative water, it has been proved that the vector control gives maximum of pumped water volume. Keywords - photovoltaic pumping, vector control, water volume
1. Introduction In Tunisian remote areas, the agriculture uses traditional systems, as the diesel engine pumps, to extract water from wells. These systems are easy to install, however, they present some major inconvenient, since they involve frequent repairs, refueling and often the diesel is not available in these areas. Furthermore, the use of fossil fuels causes environmental problems as the emission of the Carbon Dioxide ( ) into the atmosphere. On the other hand, there is a great potential of both solar energy source and underground water reserve, which is encouraging for an off-grid Photovoltaic Water Pumping system. This paper presents a continuation of previous published works [1], in which the authors established an algorithm that manages the instantaneous PVPG and the existing energy in the battery to be used for water pumping purpose. The main purpose of our study is to provide water for agricultural applications using clean energy. Over the last few years, in this area, research interests are essentially related to the modeling [2] and the optimization [3]. According to equipment needs, many others researches were focused on PV pumping from sizing points, based on the potential of solar energy and water demand [4]. The same works of different PV pumping systems were studied in different sites [5]. Other investigators established strategies to insure optimum energy management of PV systems [6–7]. Therefore, numerous algorithms are advanced to predict climatic parameters performance throughout daylight.
DC motors were firstly used since they provide easy operation with low-cost power conversion [8, 9]. Operational pumping systems have revealed that this type of pump needs regular maintenance. To overcome this weakness, brushless permanent magnet motors have been suggested [10]. Nevertheless, this solution is restricted for low power PV systems. The induction motor based PV pumping systems offer an alternative for a more efficient and maintenance free system [11]. Different optimization strategies have been proposed to improve the overall system efficiency. This paper presents a study for the pump yield resulted with the use of the vector control method for controlling an asynchronous motor. The pump is supplied by a photovoltaic panel that provides maximum power thanks to the MPPT algorithm. The system components are modeled in section 2. The control strategy is detailed in section 3. Section 4 illustrates the results and discussion. Finally, we conclude our paper in section 5 by a conclusion and some perspectives. 2. System modeling The studied structure is constituted by a 5000 W photovoltaic array, a DC / DC converter operating in MPPT, an inverter and a 4.5 kW induction motor coupled to a centrifugal pump as shown in figure 1. The proposed approach consists in tracking the maximum panel power during the pump function, in order to collect the maximum of pumped water. In fact, from the measured values of the temperature and radiation, the system fixes the references speed
of the asynchronous machine. In this sense, we should take into account the motor losses. The DC–DC converter, introduced between the panel and the load, adjusts the dynamic equivalent impedance of the inverter and the induction motor. Thus, the MPPT can be ensured. The inverter is controlled by the application of the field-oriented control method to the IM, permitting then to avoid the magnetic saturation problems in the machine. This strategy benefits from the measured speed, the nominal magnetic flux and the torque reference values to determine the frequency and the current references necessary to control the PWM inverter. The following section details the system components modeling.
Chopper
Inverter
IM
Pump
PV-Panel Figure 1 The proposed photovoltaic water pumping system 2.1 Photovoltaic panel modeling The conversion of the solar radiation into electrical power is ensured by photovoltaic cells. A photovoltaic generator is composed by many strings of solar cells in series, connected in parallel, in order to deliver the desired values of photovoltaic voltage and current. The photovoltaic power is expressed as following [12]:
G PPV 20 I pv, STC scT GSTC G 1 I SC , STC VPV GSTC Tc Tc TSTC Ta
Tc (1)
G NOCT Ta ,ref TSTC (2) 800
where: PPV is the estimated photovoltaic power (W), G is the measured radiation (W/ ), Ta is the ambient temperature (°C). 2.2 Moto-pump modeling The motor adopted is an asynchronous machine. The motor mode and vectors transformation in the asynchronous machine circuits provide the dynamic model of the asynchronous motor in the d–q reference frame (equations (3)) [13]:
(3)
where: Vs is the stator voltage (V),
Vr is the rotor voltage (V). In addition, the machine fluxes are expressed as following: s l s I s m I r r lr I r m I s
(4)
where: s is the stator flux (Wb), r is the rotor flux (Wb). The associated motion equation is given by equation (5) [14]: d p (5) Cem Cl dt
~
d Vs Vds jVqs rs I s dt s jws s V V jV r I d jw dr qr r r r g r r dt
J
where: is the mechanical speed (rad/s). Cem is the electromagnetic torque, given by equation (6) [14]: m Cem p dr iqs qr ids l r
C l is the torque motion, expressed by [15]: Cl kl 2 where: Cem nom kl 2 nom
(6)
(7)
(8)
3. The control strategy The asynchronous motor is controlled by the vector control with a rotor flux orientation. In fact, the torque control is ensured by calculating the desired components of the stator current. It is maximum for a given current if we impose qr =0. Thus, the rotor flux is positioned to coincide with the d-axis component (i.e, dr = r and qr = 0). Acting on the q-axis stator current, the control of the torque is ensured. Whereas, the rotor flux can be monitored with the d-axis stator current. Then, its expression is given by: m (9) dr ids 1 r s where: r : The time constant of the rotor (s). Hence, the electromagnetic torque Cem is proportional to the quadratic stator current iqs . Consequently, the torque can be expressed by [16]:
Cem p
m r iqs lr
(10)
Figure 2 presents the rotor field-oriented vector control principle [17]. Compensation of Vds Flux regulator
+-
r ref
H1(s)
- +-
𝑉𝑑𝑠
𝑤𝑚𝑒𝑠
+-
Torque regulator
Speed Regulator
Photovoltaic panel
+-
𝑤𝑠 𝑑𝑡
𝑤𝑟𝑒𝑓
H2(s)
+- +
𝜃𝑠 𝑉𝑞𝑠
Inverter
𝑒 −𝑗
rd est
𝑖𝑠1,
,3
IM
Compensation of 𝑉𝑞𝑠
𝐶𝑒𝑚 𝑒𝑠𝑡
Figure 2 The block-diagram of a rotor field-oriented control of the induction machine The regulators used are PI type whose transfer functions are given by: K p 1 ps (11) Rs ps
where: K p is the proportional gain of the regulator,
p is the time constant of the proportional regulator
function relating the electromagnetic torque variation to the electric speed variation must be done around a functional point. This transfer function is given by equation (14): 1 2 kl 0 s (14) H s J Cem s 1 s 2 kl 0 To calculate the speed reference, we took in consideration losses in the stator. In fact, the power balance of the asynchronous machine is given by equation (15) [17]: 3 (15) Pl PPV rs I 2 s 2 Consequently, for the vector control, the rotor pulsation can be evaluated from: w (16) Pl C em s C em s p where: (17) Cem kl 2 thus, equation (16) becomes: k Pl l w w g w 2 p3
I s ids 2 iqs 2
(12)
Using equation (10), the torque regulation ensures the regulation of the quadrature stator current iqs . The transfer function relating the current to the voltage of the quadrature stator component is given by equation 13. 1 2 rs m lr r iqs s H 2 s ks vqs s 1 s 2 rs m lr r
ids
dr
(20)
m
2 l r kl w2 3 p 3m r using equation (22) [17]: m 1 wg i qs r r iqs
(21)
(22)
equation (18) may be written as following:
a w4 b w3 c 0
(23)
where:
a
l k 12 rs r l 18 p 6 m r
b
(13)
The pump resistive torque is function of the squared speed. Thus, the elaboration of the transfer
(19)
where:
1 2 rs m lr r i s H 1 s ds* ks vds s 1 s 2 rs m lr r
(18)
Moreover, the stator current is function of the direct and quadrature current:
(s). The transfer function relating the current to the voltage of the direct stator component is given by equation 12.
2
2 k 2 rr 3 p 6 r 2
kl p3
(24) (25)
2
c
3 r rs PPV 2 m
(26)
The resolution of equation (23) allows deducing the reference electric speed. The results are given in section 4.
4. Results and discussion Powers (W)
10000 Ppv
Pm
5000
Electric speed (rad/s)
0 0 400
5
10
15
20
25 w ref w mes
200
Flux (Wb)
0 0 1
5
10
15
20
25 phi rd phi rq
0 -1 0
5
10
Time (h)
15
20
25
Figure 4 Evolution using the vector control for October 22 nd , 2011 30 20 10 Current (A)
With the aim of evaluating the proposed fieldoriented control rule for the vector control approach, simulations were carried out using data measured from the target location. We selected the nominal values for the rotor fluxes references. Figures 3 (a) and (b) demonstrate the evolution of the radiance and the ambient temperature corresponding to a typical sunny day (October 22 nd , 2011). With the aim of testing the effectiveness of the suggested method, we performed the simulation for three days corresponding to three seasons: moderate, cold and hot seasons, permitting then the radiance and temperature change. Figures 4, 7 and 8 show the characteristics of the mechanical power, electric speed and the rotor flux responses, using the vector control, respectively to the dates October , December and August , in 2011. It is clear that in rapid changing in atmospheric conditions, the panel is able to operate around the optimal value. The obtained curves demonstrate the viability of the suggested structure shown in figure 2. In fact, the flux magnitude is retained at its nominal value of -0.36 Wb. Moreover, these figures show that the rotor pulsation meets to its reference. Figures 5 and 6 demonstrate that the proposed approach respect the nominal values of the IM.
0 -10 -20
(a) 900
-30 0
5
10
Time (h)
15
20
25
700 600
20
500 400
15
300
10
200
5
100 0 6
8
10
12 Time (h)
14
16
18
Current (A)
Solar radiation W/m
2
800
0 -5 -10
(b)
-15
35
-20 11.145
Temperature (°C)
30
11.155
11.16
11.165 Time (h)
11.17
11.175
11.18
Figure 5 The current curve corresponding to October 22 nd , 2011
25
20
15 6
11.15
8
10
12 Time (h)
14
16
18
Figure 3 Photovoltaic characteristics for October 22 nd , 2011 (a) Solar radiation, (b) Ambient temperature
300 Vsd
Vsq
200
where ρ is the density (Kg/ 3); g is the acceleration of gravity ( /s), H is the height of rise (m), q(t) is the flow ( 3/s), is the shaft power, which is the mechanical power on the shaft coupled to the pump, and η is the pump efficiency. The pumped volume is given by equation (28): (28) V qt * T
Voltage (V)
100 0 -100 -200 -300 0
The useful power of the centrifugal pump is expressed by equation (27) [1]: (27) Pu t Pl g H qt
5
10
15
20
25
Time (h)
Figure 6 The stator voltage curves corresponding to October 22 nd , 2011
where T is the pumping duration (s) . Figure 9 illustrates the pumped water obtained without control, and with vector control. Table 1 contains the values of the pumped volume. 350
Ppv
with control
Pm
0
Electric speed (rad/s)
-5000 0 500
5
10
15
20
25 wref
250 200 150 100 50
5
10
15
20
25 0
phi rd
Flux (Wb)
wmes
0 -500 0 1
8
phi rq
10
15
20
25
Season
Figure 7 Evolution using the vector control for December 6 th 2011 6000 Powers (W)
12
Table 1. Water volume obtained 5
Time (h)
4000 2000 0 0
10 Time (h)
Figure 9 Water volume comparison
0 -1 0
without control
300 Pumped water volume 3 (m per day )
Powers (W)
5000
5
10
15
20
25
Volume obtained without control
Volume obtained with vector
( m 3 /day)
control ( m 3 /day)
Moderate season
103
275.6
Cold season
59.42
127.5
Hot season
257.4
317.9
Speed (rad/s)
400 200 0 0
5. Conclusion 5
10
5
10
15
20
25
15
20
25
Fluxes (Wb)
0.5 0 -0.5 -1 0
Time (h)
Figure 8 Evolution using the vector control for August 22 nd , 2011
An optimal process of a photovoltaic pumping system based on an induction machine was detailed. The goal was to ensure maximum motor efficiency after extracting maximum photovoltaic power with MPPT method. The study was carried out on the vector control. The simulation results show the increase of the daily pumped quantity reached by the vector control. The investigation of the vector control with cheap available electronic instruments still is an objective for generalizing and spreading the use of pumping photovoltaic systems.
Acknowledgements This work is done thanks to the support of ISA department from the Industrial Engineering School of Valladolid University (Spain) and CMERP unity from the National School for Engineering of Sfax University (Tunisia). It was funded by MiCInn project DPI2010-21589-c05. Nomenclature PVPS PVPG
Photovoltaic Water Pumping Systems Generated Photovoltaic Power
Vqs
Quadratic component of the stator voltage (V)
rs
Stator phase resistance (Ω)
ls
Cyclic stator reluctance (H)
s
Stator flux (Wb)
ws
Stator pulsation (rad/s)
is
Stator current (A)
Vr
Rotor voltage (V) Direct component of the rotor voltage (V) Quadratic component of the rotor voltage (V) Rotor phase resistance (Ω)
PV
PhotoVoltaic
Vdr
MPPT
Maximum Power Point
Vqr
IM
Induction machine
rr
PWM
Pulse Width Modulation
PPV
Photovoltaic power (W)
I pv,STC
The module current in normal condition (A)
scT
The temperature coefficient of the short circuit current (mA/ °C)
G
The measured radiation (W/ )
GSTC
r
Rotor flux (Wb) Slip pulsation (rad/s)
m
Mutual inductance (H)
Ω
Mechanical speed (rad/s)
p
Number of poles pairs
J
Inertia moment (Kg.
)
Cem
Electromagnetic torque (N.m)
The radiation in normal condition (W/m²)
Cl
Resistive torque (N.m)
Tc
The temperature difference (°C)
dr
The short circuit current in standard condition (A)
i qs
I SC,STC
Direct component of the rotor flux (Wb) Quadratic component of the stator current (A)
qr
Quadratic component of the rotor flux (Wb)
i ds
Direct component of the stator current (A)
kl
Torque constant (Nm. s 2 . rad 2 )
r
Rotor constant time (s)
VPV Tc TSTC Ta
NOCT
The photovoltaic voltage (V) Contact temperature (°C) Standard condition temperature (°C) Ambient temperature (°C) Normal Operating Cell Temperature (°C)
Ta ,ref
The reference ambient temperature (°C)
TSTC
Standard condition temperature (°C)
Vs
Stator voltage (V)
Vds
Direct component of the stator voltage (V)
p
Proportional gain of the PI regulator Proportional regulator constant time (s)
Pu
Useful pump power
Water density (Kg/ m )
g
Gravity acceleration ( m /s)
H
Height of rise (m)
q(t)
Water flow ( m /s)
kp
3
2
3
Pl
Shaft power (W)
Pump efficiency
V
Volume of the pumped water ( 3)
T
Pumping time duration (s)
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