Smart Grid and Renewable Energy, 2013, 4, 409-418
http://dx.doi.org/10.4236/sgre.2013.45047 Published Online August 2013 (http://www.scirp.org/journal/sgre)
409
PV-Grid Tie System Energizing Water Pump
Sameer Khader, Abdel-Karim Daud
Electrical Engineering Department, Palestine Polytechnic University (PPU), Hebron, Palestine.
Received June 27th, 2013; revised July 27th, 2013; accepted August 4th, 2013
Copyright © 2013 Sameer Khader, Abdel-Karim Daud. This is an open access article distributed under the Creative Commons At-
tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop-
erly cited.
ABSTRACT
This paper presents the behaviours of three-phase induction motor driving centrifugal pump under various solar irradia-
tion levels, where the motor speed and torque depend on the source voltage and frequency, while the water-flow rate
depends on the motor speed, density, and static head according to affinity flow. Matlab/Simulink model is proposed for
studying the behaviours of these machines with respect to water flow capacity, motor current, electro-magnetic torque,
and motor efficiency. The proposed photovoltaic with maximum power point tracking model based on observation and
perturbation (O&P) maximum power tracking model is applied. The output voltage is regulated throughout Buck-Boost
converter with purpose maintaining the output voltage at predetermined values. Since Induction motors are widely used
in pump systems, the electromagnetic torque, water-flow rate are studied for various source frequencies. Comparison
analysis is conducted for both motors with respect to water flow-rate, heads elevation, and motor current. In addition to
that, the proposed system presents Photovoltaic-Grid (PV-Grid) Integrated model, where the power shortage required
for normally operation of the pump is drawn from the electrical grid.
Keywords: Photovoltaic; Induction Motor; Centrifugal Pumps; Electrical Grids; Matlab/Simulink
1. Introduction
Photovoltaic energy resources presents alternative and
friendly to the environment sources. It presents unique
solution for providing remote area with clean and sus-
tainable energy during the daytime in heating, lighting,
refrigeration and water pumps systems [1-3] without the
need of battery system, while during the night time the
accumulated energy can be fully or partially used to
cover the energy domain. The output circuit connected to
the photovoltaic system is usually dc-dc converters main-
ly boost choppers in order to boost the voltage to the
predetermined levels.
The DC/DC converters are widely used in regulated
switch mode power supplies, where the input voltage to
these converters varies in wide range especially in the
case of Photovoltaic (PV) supply source due to unpre-
dictable and sudden change in the solar irradiation level
as well as the cell operating temperature. Several con-
nection topologies concerning the switching systems
have been proposed [4-8] aiming at realizing the required
voltage level during different periods of day for certain
applications such as pumps, motors in general and power
supplies.
On the other hand water flow consumption determines
the rate of motor speed according to affinity law [6,7]
which in turn determines the elevation (static head) and
consumed power. Variable Frequency Drive (VFD) can
be applied to achieve up mentioned facts.
The proposed model consists of several modules as
shown in Figure 1 with the following functions:
 PV Photovoltaic Array (PV) that converts the solar
irradiation into voltage Vpv and current Ipv.
 Buck-Boost DC Chopper Module that boosts up the
PV voltage to the predetermined levels. Conversely in
case of high Vpv the output voltage is reduced.
 MPPT, maximum power point tracking unit that
tracks the optimized operation point for power extrac-
tion by controlling the chopper duty cycle.
 Variable Frequency Drive that controls the speed
and torque of three-phase induction motor driving
centrifugal pump by controlling the voltage and fre-
quency.
 Speed-Flow Control Unit that determines the requir-
ed voltage and frequency aiming at regulating the
motor speed and torque according to actual water
flow consumption.

PV-Grid Tie System Energizing Water Pump 410
PV Array Buck-Boost
Chopper
Power
Estimator
AC-DC
Converter
PV-Grid
Integrator
Va ri abl e
Frequency
Drive
3-phase
IM
Speed-Flow
Control Unit
Pump
MPPT
AC Grid
P
G
P
PV
Q
act
P
L
Q
ref
P
mech
P
in
p
Figure 1. Functional block diagram of proposed model.
 Power Estimator that detects the available Ppv power,
the consumed motor power PL and the amount of
power shortage PG that should be supplied from AC-
grid.
 PV-Grid Integrator that provides the load with nec-
essary power taken from either one of the sources PV
or AC grid, or from both.
 Amount of power shortage PG that should be supplied
from AC-grid.
 AC-DC Converter that converts the grid voltage into
smoothed DC voltage that should be easily tied to the
PV output terminal aiming at avoiding synchronizing
procedures.
The proposed model differs from other models, where
the system is consumed energy from the grid in case of
energy shortages and night time operation. It is fully
simulated using Matlab/Simulink, where the system pa-
rameters can be changed and investigated.
2. Modeling of Proposed Electrical Model
2.1. PV Performances
The application of Photovoltaic solar energy in energiz-
ing electrical load on-grid connected, where the pump
power is controlled based on the extracted from the PV
module power.
2.1.1. Phot ov o l tai c Mo del In terpretation
Basically, PV cell is a P-N semiconductor junction that
directly converts light energy into electricity. It has the
equivalent circuit shown in Figure 2 [9,10].
The following are the simplified equations describing
Figure 2. Equivalent circuit for PV cell.
the cell output voltage and current:
ln ph do
c
oso
o
III
AKT
VRI
qI







(1)
e1
os
c
qV N
AKT
op phd
INI I





  




(2)
311
e
g
rc
qE
B
KT T
c
dor
r
T
II
T








 (3)




; t
p
hpscncr nr
I
NI ITTGG    (4)
The idealistic diode idealistic factors A & B are with
values vary between 1 and 2 depending on I-V perform-
ance shaping and approximations.
2.1.2. Photovoltaic I-V Performance
In order to study the I-V performance of the PV circuit
and to look for appropriate dc chopper for boosting up
the output voltage to predetermined value it is necessary
to illustrate the obtained PV voltage and current for boost
chopper according to specifications given in Table 1 at

PV-Grid Tie System Energizing Water Pump 411
reference irradiation (Gr = 1000 W/m2). The PV Array
voltage can be obtained by multiplying the module volt-
age and current by Nsm and Npm. Figure 3 illustrates the
proposed PV array built in Matlab/Simulink [11] with
R-L load, where the obtained results for different varia-
tion levels are presented. From these performances it is
shown that the total output PV voltage and current varies
according to irradiation level with approximated 65 W
maximum power at G = 1000 W/m2.
Table 1. Data specification for PV Array.
q K Iph I
d R S R P
1.602e - 19 C1.38e - 23J/˚K4 A 0.2 mA 1 m10 k
NS N
P V O V OC I SC V MPP
38 4 0.6 V 21.5 V 4 A 17.5 V
IMPP N
Sm N Pm V pv R load T C
3.7 A 6 1 130 V 44 25˚C
powergui
C
ontinuous
V2
v
+
-
V1
v
+
-
T_ var
11.2903
T
1
Rf- Cf
R-L
PV Array
T
G
Ns
Np
GND
+V pv
Output
Nsm
6
Npm
1
Lo
I
i
+-
G_var2
G_T
(a)
05 10 15 20 25
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Ipv,A
I-V performance
Vpv, V
1200W/m2
1000W/m2
800W/m2
600W/m2
400W/m2
(b)
Figure 3. PV model with I-V performances. (a) Proposed model for PV array in Simulink environment; (b) I-V performance
of PV module.

PV-Grid Tie System Energizing Water Pump 412
2.2. The Integration of PV with Water Pumping
System
A centrifugal pumps are used as electrical load [6],
where the pump power, speed and torque are directly
affected by either load-side parameters in form of water
flow-rate, static head, water pressure, and line side in
form of solar irradiation, weather conditions, and ex-
tracted power. Figure 4 illustrates PV solar system ener-
gized water pump installation, where the water pumping
system can be directly energized from the PV or indi-
rectly throughout battery bank [10]. Both configurations
have their advantages and disadvantages.
Direct-coupled pumping systems illustrated in Figure
4(a) are sized to store extra water on sunny days so it is
available on cloudy days and at night. Water can be stor-
ed in a larger-than-needed watering tank or in a separate
storage tank and then gravity-fed to smaller watering
tanks. Water-storage capacity is important in this pump-
ing system.
While Figure 4(b) illustrates battery-coupled water
pumping systems which consist of photovoltaic (PV)
panels, charge control regulator, batteries, pump control-
ler, pressure switch, tank, and AC water pump. The elec-
tric current produced by PV panels during daylight hours
charges the batteries, and the batteries in turn supply
power to the pump anytime water is needed. The use of
batteries spreads the pumping over a longer period of
time by providing a variable voltage and frequency de-
pending on the water-consumption rate, which in turn
reduces the pump losses and increases the battery dis-
charging time which is an important factor during the
night and low light periods, the system can still deliver a
needed rate of water for livestock.
2.2.1. Centrifugal Pump Performances
According to [8] the power demand of the water pump is
expressed using the following expression:
p
p
g
QH
P



 (5)
The pump operational performance which presents the
relationships between total head including static head and
friction head, water flow-rate, and pump efficiency are
illustrated in Figure 5 for certain commercial pump.
By applying the principle of motor-pump power bal-
ance, Equation (5) can be integrated with motor speed-
torque performance as:
pm
gQH T

    (6)
Now referring to Figure 5 where the pump (H-Q)
curve is illustrated, which normally used to locate the
pump’s operation point. For exact determining the men-
tioned operation point there is a need to determine the
total head of the installation HA, which is the sum of the
(a)
(b)
Figure 4. PV system energizing water-pumping systems. (a)
Direct-coupled water-pumping systems; (b) Battery-cou-
pled water-pumping systems.
Figure 5. Water pump operational characteristic.
static head HS known as elevation difference, and the
network hydraulic losses HL, thus :
2
AsL
H
HH hQ 

 (7)
The friction coefficient  depends on the system in-
stallation, pipes section, and liquid viscosity. The opera-
tion point results by the application of the following
equation:
A
H
H

(8)
This condition can be obtained by intersecting of the
corresponding curves of Figure 5.
2.2.2. Electrical Motor Performances
Centrifugal pumps can be driven by either direct current
motors [9] or alternating current motors, mainly induc-

PV-Grid Tie System Energizing Water Pump 413
tion motors [12]. Due to massive exploitation of induc-
tion motors in water pump system, the electromagnetic
performances of induction motor are going to be de-
scribed in the following sections.
2.2.2.1. M at h ematical Model
Utilizing the induction motor as prime mover source for
providing the pump machine with needed energy. Three-
phase induction motor is going to be describes as follows
[13].
The stator winding is supplied with balanced three-
phase ac voltages, which produces induced voltages in
the rotor windings due to transformer action. The distri-
bution of stator windings is arranged, so that there is an
effect of multiple poles, producing several cycles of
magneto motive force (or field) around the air gap. This
field establishes a spatial distribution sinusoidal flux den-
sity in the air gap. The synchronous speed of the rotating
filed is defined by [14]:
4π and 120
sn nsnn
f
pn fp

 (9)
A very useful quantity in studying induction machines
is the slip s:
ss
nn
sn




(10)
Per-phase equivalent circuit of a three-phase induction
motor is shown in Figure 6(a) [15]. An expression for
the torque of an induction machine as a function of its
slip may be obtained by application of Thevenin’s theo-
rem to the circuit model to the circuit model (Figure
6(b)). The rotor circuit, as referred to the stator, may be
considered as being attached to an equivalent Thevenin
generator, as shown in Figure 6(b).
As well known for electrical machines theory in order
to maintain constant maximum torque and to avoid motor
saturation and to minimize the losses the (volt/hertz) ra-
tion must be kept constant for speeds less than the syn-
chronous speed, while for speeds over the synchronous
the voltage is maintained at its rated value and the fre-
quency is increased over the rated limits.
(a) (b)
Figure 6. Equivalent circuit of 3-phase inducti on motor. (a)
Equivalent circuit for one phase; (b) Application of Theve-
nin’s theorem.
According to [13] if the frequency is increased above
rated value, the flux and torque would decrease. If the
synchronous speed corresponding to the rated frequency
fn is called base speed

sn, or nsn, the synchronous speed
at any other frequency becomes:
or
s
osnsosn
K
nKn



 (11)
where on
K
ff

.
Substituting Equation (11) in Equation (17) the elec-
tromagnetic torque can be expressed as:
2
2
2
1 1
2
22
22
2
v
em p
m
n
th
th
n
K
Tk
XX R
ff
Rsf
sR RXX
sff f
 
 





  
 
 


(12)
where 22
pmsn
K
Xw.
According to [15] vLn
K
Vf for n
f
f; and


max 11
, , , , , ,.
vthth
KfTRXfXR for n
f
f

.
The electromagnetic power Pem and the losses can be
defined as follow:


1
ememo snemmechconst
PTK sTPP    (13)
Varying the frequency of the motor causes significant
change in the drawn by the motor current, and in turn the
consumed power. According to Figure 6, the power and
current can be given as follows:

1
11
11
22
; 3 cos; tan
ph inp
LinpLLL
in inp
in inpinpo
om
VX
IPVI
ZR
ZR jXRjKX
jKXRsjKo X






 
  
(14)
2.2.2.2. Simulation Resul ts
Considering the rated parameter values of the selected
induction motor [15]:
n = 2835 rpm; Pn = 1100 W; Vn = 127 Vac; R1 = R’2 =
1.27 ; X1 = X’2 = 3.860 ; Xm = 60 .
Substituting the outlined motor parameters in the de-
veloped mathematical model, we obtain through simula-
tion the motor torque as a function of speed (and slip) for
different supply frequencies as shown in Figure 7. For a
constant (V/F) ratio, the motor develops a constant ma-
ximum torque, except at low speeds (or frequencies).
From this curve the motor develops two operation modes:
constant torque modes for frequencies less than the rated
where the torque is maintained constant; and constant
power mode for frequencies greater than the rated where
the speed exceeds the synchronous and the torque falls
down keeping the power at constant value.

PV-Grid Tie System Energizing Water Pump 414
0 1 2 345 6 78
0
500
1000
1500
2000
2500
3000
3500
4000 s peed n(T)
T, N.m
n,rpm f=30Hz
f=40Hz
f=50Hz
f=60Hz
Figure 7. Simulation results of the mechanical performance
of three-phase induction motor.
Having the mechanical performance of the motor at
various frequencies, where two operation mode can be
applied constant torque (V/F = const) & constant power
(V = const, f > fn) throughout VFD inverter we can build
the pump performance. Way out from the natural curve
of the pump at rated motor speed, where f, H & Q are
nominal values, and known from the pump data sheet.
Taking into consideration the affinity law and derived
equation stated in [16,17] for various motor speeds the
water flow-rate changes at various elevations (static head)
as follows:
223
; & mech
nn
n nmechn
P
H
nf f
H
nfP f
  
 
  
 
 (15)
Applying Equation (15) in presented model requires to
select the whether the pump operates at maximum effi-
ciency where the water-flow rate has optimized value
(Q
 max), thus:
2
max
max max
max
; for
22
1;for
n
n
n
fQQ
f
H
HQQ fQQ
Qf



























(16)
where

max max
max max
;
@ 50 Hz &
and
n
n
n
nn
f
QQ f
QQfn
f
or ffff








 
(17)
The simulated results are displayed in Figure 8, where
the pump flow-rate and static heads changed at different
frequencies. According to pump data sheet the value of
(Q
 max = 9.5 m3/hr) is taken as a reference value obtained
at maximum efficiency and 50 Hz frequency. Also it’s
shown that regulating the source frequency directly af-
fects the static head and water-flow rate.
On other hand regulating the frequency causes signifi-
cant change in motor current as shown in Figure 9,
where at low frequency the drawn by the motor current is
the highest comparing with others at both operation
modes, starting and rated operation.
At different frequencies there is a stable operation
points where the motor operates at its rated slip (sn)
where the amount of pumped water depends on the me-
chanical torque developed at these frequencies and given
head. Referring to Equation (6) and substituting the value
of rated slip in Equations (12) and (14), the water flow-
rate can be written as:


4π1n
p
em n
fs
QTss
gHP



  (18)
0 24 6810 12 1416
0
5
10
15
20
25
30
35
40
H=f(Q)
Q m3/hr
H,m
f=50Hz
f=40Hz
f=30Hz
Q m
3
/h
r
Figure 8. Simulation results of the pump performance H =
f(Q).
05001000 1500 2000 2500 3000 3500 4000
0
5
10
15
20
25
30
35 Curren t I(n )
n
I
30Hz
40Hz
50Hz60Hz
Figure 9. Simulation results of the motor current at various
frequencies Iph = f(n).

PV-Grid Tie System Energizing Water Pump 415
The obtained simulation results at rated motor opera-
tion for various frequencies and elevation are givenin
Figure 10 for water flow-rates at three heads (10 m, 25
m and 40 m) where it can be seen that for frequencies
below the rated (f < 50 Hz) Q has quadratic relation with
speed.
3. SIMULINK Model of Described Pump
System
3.1. Simulation Model
A Matlab/Simulink for proposed mathematical model is
presented for induction motor pump, taking into account
that varying the motor voltage and frequency in accor-
dance with water flow-rate level saves energy and oper-
ates the motor at maximum pump efficiency.
Figure 11 presents the whole Simulink model includ-
ing solar PVmodel, Variable voltage-variable frequency
inverter system, Pump system, and water flow-rate sys-
tem, that predicts the water flow-rate and regulates both
voltage and frequency by using the variable voltage-
variable frequency (VFD) technology in order to keep
the motor operating at constant torque.
3.2. Simulation Results
The obtained simulation results from above mentioned
model are displayed in Figure 12 for various water flow-
rate and corresponding reference and actual speed, where
it’s shown that the motor adjusts its speed in accordance
with the needed flow-rate, which in turn significantly
reduces the power consumption.
While Figure 13 illustrates the generated by PV gen-
erator effective power at various radiations and con-
sumed by the pump effective power at water elevation of
05001000 1500 2000 2500 3000 3500
0
5
10
15
20
25
30
35
40
45
50 Q= f(N)
n, rpm
Q, m3/hr
H=10m
H=25m
H=40m
Q, m
3
/hr
Figure 10. Simulation results for pump performance at dif-
ferent heads (elevations).
T
(N. m)
1500
rpm
Discrete,
Ts = 2e-05 s.
-K -
n/wm1
-K -
n/wm
Q
Head
Vph
Eff_pump
Qref
Pinp
IL
Qnet
Tmech
Nrpm
Water
Water Pump
Vpv
v
+
-speedpulses
Vector control
v
+
-
Vab
z
1
20
TDH, m
298
T,[K]
Sg2
Sg1
Scope3
+
Ro
RT
Ra te2
RT
Ra te1
Radiation
Running
RMS
RMS
Q, m3/hr
T
G
Ipv
+Vout
-Vout
PV-MPPT
Outpu t
4
Max flow
s -+
Ir
i
+-
IO
m
A
B
C
Tm
IM
1.5 HP / 380
g
A
B
C
+
-
IGBT In verter
380
Grid, V
Iabc
Speed
Q, m3/hr
Flow diagram
0.65
Eta_pump
0.5
+
C2
1
<Rot or s peed (wm)>
Iabc (A)
Iabc (A)
Vab (V)
Vab (V)
<Elect rom agnet ic t orque Te (N* m )>
<Elect rom agnet ic t orque Te (N* m )>
Figure 11. Matlab/Simulink model of induction-motor pump.

PV-Grid Tie System Energizing Water Pump 416
00.5 11.5 22.5 3
x 10
5
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
time,s
Q, m3/hr
Water flow-rate di agram
Q, m
3
/hr
(a)
00.5 11.5 22.5 3
x 10
5
-200
0
200
400
600
800
1000
1200
1400
time
Speed, rpm
VF D of IM-Pum p
Nref
Nact
(b)
Figure 12. Simulation results of water flow-rate and ob-
tained speed. (a) Water flow-rate diagram; (b) Pump actual
& reference speed at 20 m elevation.
20 m. It can be seen that at various water consumption
the PV system is capable to energize the pump system
and the excess of power at light consumption rate can be
used for energizing another loads. Furthermore applying
(VFD) saves energy and gives the pump system the abil-
ity for normally operation even at light irradiations or
cloudy weather.
3.3. Grid-Integrated Simulation Model
The proposed pump system is mainly energized from the
PV source, while the AC utility serves to recover the ener-
gy shortages [17]. Figure 14 illustrates the complete si-
mulation model including power estimator module, grid
compensation module, grid-tie module, etc.
Avoiding synchronizing procedure when two AC sources
are parallel connected, the AC utility is converted into
DC and connected to the load based on switching com-
mands sent by power estimator module to switch Q4 by
mean of the logic depicted in Equation (19).
The total power in form of voltage and current are
0246810 12 1416
x 10
4
0
100
200
300
400
500
time,s
Prms
RMS PV & Pump Power
Ppump
PpvG=1000W/m2
(a)
0 2 4 6810 12 14 16
x 10
4
0
50
100
150
200
250
300
350
time, s
Prms,W
RMS PV & Pump Power
Ppv
G= 400..800W/m 2
Ppump
(b)
Figure 13. Generated and consumed power at various irra-
diations. (a) Power diagram at constant irradiation; (b)
Power diagram at various irradiations.
converted into AC through out inverter circuit.
4
if Pure Source
/ if Combined
for Night time.
pv L
pv L
OFF PPPV
QONOFFPP
ON







 (19)
Figure 15 illustrates the results obtained from the
mentioned simulation model, and proposed logic in Equa-
tion (19) where it’s shown that the grid will be switched
on only when there are a power shortages (Ppv < PLoad)
and the load needs to be fully energized. Meanwhile,
on-off grid connection can be realized in cases of load
level fluctuation or cloudy weather. During the night
time the load is energized from the AC utility. The pro-
posed circuit can be applied for either AC load or pump
system, single or three phase pumps.
4. Conclusions
A complete mathematical model has been developed for
studying the pump behaviours at various elevations, wa-
ter consumption rate and source voltage frequencies.
The proposed PV model consists of variable tracking
module and voltage drop compensating module that can
be used for either dc or ac loads with precise voltage
tracking procedure.
The proposed Simulink model for induction motor

PV-Grid Tie System Energizing Water Pump 417
Ipv
Vact_rms
V grid_rms
Q4
Grid
PV
Continuous
powergui
RMS
(
discrete)
Vrms+dv
220
Vref_var
1
Vref1
RMS
d
iscrete
Vpv_rms
RMS
d
iscrete
Vout_ rms
v
+
-
Vout3
v
+
-
Vout2
v
+
-
Vout-ac
v
+
-
Vout
110
Vac_grid_rms
Vact
Vref Gate
VVT
GVg_Q1
VGT
110.1
A
B
+
-
UB
20
T_var
1
T
Sv
Sg
Scope1
R-L
R
g
CE
Q3
g C
E
Q2
g C
E
Q1
Ppv_rms
current
Voltage
Max current
PV-Power
P_status
Pulse_G
Ptot
Power Status Estimater
T
G
Ns
Np
Ipv
GND
+Vpv
PV Array
Output chopper
Vg
DCi DCO
OCP
6
Ns
1
Npm
Ls
Lf
Lb7
Lb4
Lb3
Lb2
Lb1
Irms_load
RMS
(discrete)
Iout_rms1
RMS
(discrete)
Iout_rms
i
+-
Io2
i
+-
Io1
i
+-
Io
DC
AC2
AC1
Inverter
20
Igrid-max1
g
CE
Grid_co nnector
[Vg_p]
Goto
821.1984
G_var1
G_var
1
G
[Vg_p]
From
D7
D5
D4
D3
D2
D1
AC Grid Voltage
12
1:1
.-
Vpv
Iload_r ms/Ipv
Vac_grid_rms
Vout_boost
VG_ch
Vgrid+DV
PV-Grid Compensation
Output inverter
v
+
-
NOT
Figure 14. Matlab/Simulink for grid-integrated configuration.
00.5 11.5 22.5 3
0
1000
2000
G, W/ m2
00.5 11.5 22.5 3
0
100
200
300
Ppv, Pload, W
00.5 11.5 22.5 3
-200
0
200
dp, W
00.5 11.5 22.5 3
0
0. 5
1
Pulse-Q4
Tim e, S
PV-Grid Contribution .. . .
Grid-off
Grid-on
Ppv
Pload
Figure 15. Power diagram at various irradiations & loading
status.
pumps shows the effect of applying VFD control on the
speed and water-flow rate. The added power-status esti-
mator module creates new aspect to this model, where
the power shortages can be measured and delivered from
alternative sources or main ac-grid.
The saved energy due to applying VFD control may
reaches 30% of consumed power, therefore being more
suitable to be energized from PV generator.
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Nomenclature
A,B diode idealistic factors
Eg band gap energy of the semiconductor
fn rated supply voltage frequency
g gravity acceleration (9.8 m/s2)
G solar irradiation
Gr reference solar irradiation
h reservoir elevation (m)
H total head (m)
HA total installation head (m)
HS static head (m)
HL network hydraulic losses (m)
 water density (1000 kg/m3)
ηp pump efficiency (%)
Id diode saturation current
IMPP PV module current at maximum power
Io cell current
Iph cell photo current
Ipv Photovoltaic current
Isc short circuit current
Ior,It constants given at standard conditions
IL1 motor line current
K Boltzman constant
n rotor speed in rpm
ns motor synchronous speed in rpm
Np number of parallel connected cells
Npm number of parallel connected PV modules
Ns number of series connected cells
Nsm number of series connected PV modules
p number of motor poles
PG grid power
Pconst constant losses power
PL load consumed power
Pem electromagnetic power
Pmech net mechanical power
RLoad load resistance
Rp PV intersinc shunt resistance
Rs PV intersinc series resistance
R1 stator resistance of induction motor
R’2 rotor resistance motor referred to stator
R’th Thevinen resistance referred to stator
Rinp total input stator resistance
Q electric charge (Coulomb)
Q water flow-rate (m3/hr)
Ppv Photovoltaic generated power
PV Photovoltaic
Pinp motor input power
Tc cell temperature in Kelvin
Tem electromagnetic torque (N·m)
Tm motor net mechanical torque (Nm)
Tr reference temperature in Kelvin
VFD Variable Frequency Drive
VMPP PV module voltage at maximum power
VO cell output voltage
VOC PV module open circuit voltage
Vph terminal phase voltage
Vpv array photovoltaic voltage
Vth Thevinen voltage
Xm magnetic reactance
X1 stator reactance of induction mptor
X’2 rotor reactance of induction motor referred to stator
X’th Thevinen reactance referred to stator
Xinp total input stator reactance
Zth Thevinen impedance
Zinp total input stator impedance
n normalized insulation
 motor phase shift angle
 rotor speed in rad/s
 friction coefficient