08_chapter 2.pdf

20

CHAPTER 2 DESIGN AND MODELLING OF THE SOLAR WATER PUMPING SYSTEM

There are many factors to be considered while designing a solar pumping system. This chapter provides the information to select a pump, controller, sensors, solar array, wiring, and piping for the solar pumping system. A simple solar water-pumping system that is installed for a pumping operation includes the PV array, the controller, the pump, and accessories. The size of the array and the pump will be determined by several factors. In this chapter, the methodology used to determine the size of the system is described. 2.1

DESIGN PROCESS OF THE SYSTEM The design process of the SPVWPS is broken down into various

steps. The necessary steps and key components needed to design and build a pump using photovoltaic system was examined by Abu-Aligah (2011). First, the design has to begin with the water required for different crops over a period of time and the water source where the pump can be installed. Second, if necessary, designing a water storage system to store the water to supply during insufficient delivery of water by the SPVWPS. Third, analyzing the solar insolation level in the particular location and the placing of the solar panels in the direction of the direct sunlight for the maximum time possible, in the case of a fixed tracking system. Fourth, calculating the daily flow rate of the pump to deliver water for irrigation over a period of time. Fifth,

21 calculating the total dynamic head for the pump to operate. Sixth, selecting the pump to meet the daily flow rate and to deliver the required water for the period of time (Martin & Gilley 1993). Seventh, selecting the solar array size of the WPS based on the power requirement of the pump. The description of different components of solar-powered water pump systems, their important planning considerations and general guidance on designing a solar-powered water pump system was reviewed by Morales & Busch (2010). Figure 2.1 shows the layout of the SPVWPS, which indicates the different parameters required for sizing the solar PV array and the pump. The technical design procedure on photovoltaic water pumping system for irrigation of GORGAN’s farm fields was analysed by Alireza & Asghar (2013).

Courtesy: http://www.hydratelife.org

Figure 2.1 Layout of the solar water pump

22 2.1.1

Selection of the Water Source The type of water source and its location relative to the places

where the water is to be provided defines the configuration of the watering system. The water source will either be subsurface (well) or surface (pond, stream, or spring). Wells are preferable because of the improved water quality and consistency. However, wells are expensive to drill, particularly where water tables are deep. Surface water sources may vary seasonally, such that the amount and quality of the water is low during the summer when it is needed most. For wells, the following needs to be determined: Static water level Seasonal depth variations Recovery rate and Water quality This information may be obtained by the well driller for a new well. For most wells, water quality is not an issue if not used for human consumption. For surface water sources, the following needs to be determined: Seasonal variations and Water quality, including presence of silt, organic debris, etc. 2.1.2

Water Storage The size and cost of the water storage system will depend on the

amount of water required per day. AC pumping systems connected to a utility

23 power grid are generally designed to run on demand with a specified flow rate. Unlike grid-tied systems, solar pumping systems are designed to provide a certain quantity of water per day. Water is pumped during sunlight hours and stored in a tank. The daily requirement is simply the total of all water required during a 24-hour period. Tanks are used to store water for use during the night or periods of cloudy weather and are usually large enough to hold three to five days of daily water output. For agricultural use, a large amount of water has to be supplied on a periodic basis. Hence, the system should have a tank large enough to hold at least one and half times the required limit. 2.1.3

Solar Insolation and Panel Installation The site of the water source must be evaluated for its suitability in

installing the solar-powered water pumping system. The following are the specific issues to be addressed: The solar panels require a south facing location with no significant shading, Locations must be found for the water pump (surface), controllers, storage tank and other system components, The solar array should be as close to the pump as possible to minimize the wire size and installation cost, If batteries are to be used, they must be placed in a reasonably dry/temperature controlled location with proper venting, and If year-round water is required, freeze-proofing issues must be addressed. A heated area is preferred for water storage and pressure tanks. It is not economical to use PV to run a resistance heater in the winter.

24 2.1.4

Design of the Flow Rate of the Pump Most of the crops cultivated in India use 3000 m3/ha to

20000 m3/ha of water. Table 2.1 shows the water requirement of the various seasonal crops in India. In this chapter, the water needs for rice cultivation in an area of 1 ha (2.47 acres) for 120 days is considered, which is 46 m3/ha/day. Hence, the water required for an average of 120 days is 5,600 m3/ha/day (120×5600 m3/ha) or 56,00,000 L/ha for the entire cultivating period. Table 2.1 Water requirement of seasonal crops

Crop

Growing period Water needed for the growing period (mm) (days)

Range (m3/ha)

Rice

90-150

450-700

4,800-6,500

Barley/Oats/Wheat

120-150

450-650

3,300-5,800

Maize grain

125-180

500-800

3,200-4,100

Onion

150-210

350-550

3,500-5,000

Potato

105-145

500-700

3,500-4,500

Cabbage

120-140

350-500

3,500-4,800

Sugarcane

270-365

1500-2500

10,000-18,000

Banana

300-365

1200-2200

10,000-16,000

The water required is for the complete growing period = 5600 × 1000 L/ha per 120 days Daily flow rate

= 5600 × 1000 / 120 = 46667 L/ha/day

Flow rate per minute = 46667 / (5.3 × 60) = 146 L/ha/min Flow rate per second = 146 / 60 = 2.44 L/ha/s

25 2.1.5

Total Dynamic Head (TDH) for the Pump Figure 2.2 depicts the head pressure that a well pump works

against, which is called the total dynamic head (TDH).

Courtesy: http://www.siliconsolar.com

Figure 2.2 Total dynamic head for the pump The two factors required for calculating the TDH are the desired flow rate and the total amount of lift required. Flow Rate It is the volume of fluid, which passes per unit time. Vertical Lift Submersible well pumps provide lift to overcome head pressure. TDH = Pumping Level + Vertical Rise + Friction Loss

26 For a deep well, The static water level (SWL) to ground level is 45 m. The height from the well ground level to the inlet of the storage tank is 1.2 m. The height from ground to storage tank is 1 m. Equation (2.1) gives the Darcy-Weisbach equation for calculating the head loss, l d h

h

v2 2g

(2.1)

where, h is the head loss due to friction (m), l is the length of the pipe (m), and dh is the hydraulic diameter of the pipe (for a pipe of circular section, this is the internal diameter of the pipe) (m), v is the average flow velocity, experimentally measured as the volumetric flow rate per unit cross-sectional wetted area (m/s), g is the local acceleration due to gravity (m/s2), and f is a dimensionless parameter called the Darcy friction factor. For laminar flow,

f

64 ; Re is the Reynolds Number R e

(2.2)

For Turbulent flow, Re > 3000 Darcy friction loss calculation for a 1 inch pipe is 40.76 m.

(2.3)

27 Darcy friction loss calculation for a 1.25 inch pipe is 14.18 m. Therefore, the TDH of the SPVWPS (for a 1 inch pipe) = 45 + 1.2 + 1 + 40.76

88 m, and the TDH of the SPVWPS (for a 1.25 inch pipe) = 45

+ 1.2 + 1 + 14.18 2.1.6

60 m.

Pump Selection and Associated Power Requirement The pump is selected considering the induction motor and BLDC

motor pump to deliver the water. Table 2.2 gives the rating selected for operating the solar pump to deliver 47000 L/day. Table 2.2 Selection of power rating of the solar pump Type of motor

Phase

Power

Voltage

Current

PV array

Induction Motor

3 Ph

1 HP

300 V

5A

900 Wp

BLDC Motor

3 Ph

1 HP

300 V

4.3 A

900 Wp

2.1.7

Sizing of the PV Array PV arrays are installed so that they maximize the amount of direct

exposure to the sun. This means placing the array in an area clear of shading from buildings and trees, in a southward direction, and at an angle equal to the latitude of the location. The PV array is specified in terms of wattage and voltage. It is a standard procedure to increase the specified wattage by 25% (multiply by 1.25) to compensate for power losses due to high heat, dust, aging, etc.

28 The total power of the PV array is (300 × 4.3) = 1290 Wp for the BLDC water pumping system. For this work, SOLKAR make panels are used. Table 2.3 provides the specifications of this panel at standard test conditions (STC), that is, irradiation level G = 1000 W/m2; temperature T = 25oC; air mass AM = 1.5 are given in Appendix A1.1 and Appendix A1.2. Table 2.3 Specifications of SOLKAR PV Panel at STC Parameters

2.2

Values

Rated Power (Pmax)

37.08 W

Voltage at Maximum power (Vmax)

16.56 V

Current at Maximum power (Imax)

2.25 A

Open circuit voltage (Voc)

21.24 V

Short circuit current (Isc)

2.55 A

No. of series cells (Ns)

36

Array Size (Nss × Npp)

20 × 2

SYSTEM DESCRIPTION Figure 2.3 shows the various components of the system, which

includes the solar PV array, a boost converter that acts as the MPPT, a threephase full bridge inverter and the AC motor, which drives the centrifugal water pump. A unique step-by-step procedure for the simulation of photovoltaic modules with Matlab/Simulink was presented by Pandiarajan & Ranganath Muthu (2011).

29

Figure 2.3 Block diagram of the solar photovoltaic water pumping system A solar photovoltaic (SPV) water pumping system consists of the following components (Pandiarajan et al 2011): a.

PV Array: Selecting a suitable array size based on the load requirement, here in this case an AC motor operating a centrifugal or helical pump. Should be mounted on a suitable structure with a provision of tracking the sun or with a fixed tilted position to obtain the optimum incidence of sunlight over the array panels.

b.

Controllers: Selecting power converters to convert the electrical power from the SPV array to the load effectively. To convert and obtain the maximum power, the Maximum Power Point Tracker (MPPT) is used.

30 Selecting the appropriate power converters such as the DC-AC converter (inverters) to transfer the power from the MPPT to the AC motor. Control unit to track the PV voltage and current to meet the reference value and to have a simplified control of the AC motor to deliver constant throughput. c.

Motor Pump Set (surface or submersible): D.C. motor pump set (with brushes or brushless D.C.) A.C. motor pump set with a suitable inverter. Here the AC motor that can be used are the induction motor, synchronous motor, or a BLDC motor.

2.3

MODELLING OF THE PV ARRAY Figure 2.4 shows the electrical equivalent model of a PV cell

(Pandiarajan et al 2012). A group of SPV cells forms the PV power generation system (Sko il & Donsión 2004). There are different sizes of PV modules commercially available typically sized at different wattage levels. Usually, a number of PV modules are combined as an array to meet energy demands. Easy and accurate method of modeling photovoltaic arrays was presented by (Villalva et al 2009). The method proposed by them was used to obtain the parameters of the array model. The size of system selected for the proposed system is 740 W. Each module provides a maximum power of 37 W. Therefore, the proposed system requires 20 PV panels. The following equations are used for the mathematical modelling of a single PV panel (Keshavani et al 2014). Equation (2.4) gives the output current from PV panel.

31 I pv

I

ph

ID

I

(2.4)

sh

Rse

I

Ish

Isc D

Rsh

V

RL

Figure 2.4 Equivalent circuit model of the PV cell Equation (2.5) gives the photon generated current of the PV panel, Iph.

I

K T Tn i

ph

I pvn

G Gn

(2.5)

Equation (2.6) gives the calculated current through the diode.

ID

Vpv IpvRse V 1 ta Ir e

(2.6)

K T Tn I scn i K v T Tn Vocn Vta 1

(2.7)

Ir e

The above equations are used for modelling of a single PV panel. For modelling an array consisting of Nss number of panels in series, as shown in Figure 2.5 and Npp number of panels in parallel, as shown in Figure 2.6 is used, Equation (2.7) can be rewritten as Equation (2.8).

32

Vpv IpvRse IPV I Npp Ir Npp exp ph

Nss Npp

Vt Nss

1

N Vpv IPVRse ss Npp

(2.8)

Nss R sh N pp

I

Figure 2.5

V3

V2

V1

V...

V20

SPV panels connected in series to meet the voltage requirement

V1

V2

V3

V…

V20

I1 I=I1+I2 V1

V2

V3

V…

V20

I2

Figure 2.6

Solar PV panels connected in series and in parallel to meet both current and voltage requirements

For the control of speed, the electric motor rating is selected to have a DC voltage of 400 V. To supply the required power to the motor from the PV system, 20 PV panels are connected in series to provide (16.5 V × 20) 330 V to the MPPT. The MPPT provides the rated supply voltage for the

33 motor to operate (Abdulkadir et al 2012). Figure 2.7 shows the characteristics of the PV array. The MATLAB models are given in the Appendix A1.3, Appendix A1.4 and Appendix A1.5.

Figure 2.7 Simulated characteristics of the PV array 2.4

DESIGN OF THE MPP TRACKER Figure 2.8 shows a boost converter with a switching period of T

and a duty cycle of D (Amrani 2013). Hua and Shen (1998) investigated the maximum power tracking algorithms on different DC/DC converter and formulated a simple method which combines a discrete time control and a PI compensator to track the maximum power points (MPPs) of the solar array. Assuming continuous conduction mode of operation, Equation (2.9) gives the operation of the converter when the main switch is ON. di L dt dv o dt

1 (V ) L in ,0 1 Vo ( ) C R

t

dT, Q : ON

(2.9)

34

iin

+ vL – iL

Iout

iD

L + Vin

S

–

C

+ V iC o –

Figure 2.8 MPP Tracker or DC – DC boost converter Equation (2.10) gives the operation of the converter when the main switch is OFF. diL 1 (V Vo ) dt L in , dT t T, Q : OFF Vo ) dVo 1 (i C L R dt

(2.10)

Equation (2.11) gives the duty cycle of the boost converter, which is varied by the MPPT algorithm by comparing the PV cell voltage and current.

D 1

V in(min) Vo

(2.11)

where, D is the duty cycle, Vin(min) is the minimum input voltage (this will lead to the maximum switch current), Vo is the desired output voltage, and

is the

efficiency of the converter. Selecting the inductor is one of the most crucial components in designing the MPPT. The higher the inductor value, the higher is the

35 maximum possible output current because of the reduced ripple current. Equation (2.12) gives the formula for calculating the value of the inductor of the boost converter, V (Vo V in in) IL f Vo s

L

(2.12)

where, L is the inductance (H), V in is the typical input voltage, fs is the minimum switching frequency of the converter, and

IL is the estimated

inductor ripple current A good estimation of the inductor ripple current is 20% to 40% of the output current. A smaller ripple reduces the magnetic hysteresis losses in the inductor, as well as output voltage ripple and EMI, but the regulation time increases as the load changes. In addition, a larger inductor increases the total system costs (Rashid et al 2011). Equations (2.13) and (2.14) give the calculation of the inductor current,

IL

I

(0.2 to 0.4) I

out(max)

I

Vo out(max) V in IL

LIM(min)

2

(1 D)

(2.13)

(2.14)

where, ILIM(min) is the minimum value of the current limit of the switch. The minimum value of the output capacitor of the converter is calculated by Equation (2.15), I Cout(min)

out(max) fs Vo

D

(2.15)

36 where, Cout(min) is the minimum output capacitance required, Iout(max) is the maximum output current for the desired application, and

Vo is the desired

output voltage ripple. 2.5

SELECTION OF THE MPPT ALGORITHM A typical solar panel converts only 30 to 40 percent of the incident

solar irradiation into electrical energy. Maximum power point tracking technique improves the efficiency of the solar panel. Kim & Krein (2010) examined a variety of configurations using photovoltaic (PV) boost converter modules for maximum power point operation. The modules were locally controlled with maximum power point tracking to provide a good solution with simple control of the PV converter module. According to the Maximum Power Transfer theorem, the power output of a circuit is maximum when the Thevenin impedance of the circuit (source impedance) matches with the load impedance. Hence, our problem of tracking the maximum power point reduces to an impedance matching problem. A detailed comparative study between two most popular algorithms technique, which is incremental conductance algorithm and perturb and observe algorithm was performed by Zainudin & Mekhilef (2010). The method was tested studied and tested on three different converter buck, boost and Cuk converter. The boost converter shown in Figure 2.9 is chosen as the MPPT converter to match the load resistance with the source resistance, as seen by the source, by varying its duty cycle for the changes in environmental conditions. The change in irradiance levels causes the change in the internal resistance of the PV panel. Hence, for every change, the duty cycle of the MPPT has to be chosen properly to adjust the resistance of the converter.

37

Figure 2.9 Block diagram of the MPPT controller The MPPT controller generates the reference voltage from the PV voltage and PV current (Masoum et al 2002). This reference voltage is compared with the actual PV voltage and the error signal is given as the input to the PI controller to minimize the error within the limits of control. The output of the PI controller gives the reference DC voltage (Durgadevi & Arulselvi 2012). The generated DC voltage is then given to the PWM modulator, which compares the controller error with a high frequency triangular carrier wave (Jiang et al 2005). a)

Perturb and Observe (P&O) Algorithm A slight perturbation is introduced in this algorithm. The

perturbation causes the power of the solar module to change. If the power increases due to the perturbation, the perturbations continue in the same direction. The power at the next instant decreases after the peak power is reached, and after that, the perturbation reverses. The algorithm, as shown in Figure 2.10, oscillates around the peak point when the steady state is reached. The magnitude of the perturbation is kept very small in order to keep the power variation small.

38

Figure 2.10 MPPT algorithm for perturb and observe (P&O) technique The algorithm is developed in such a manner that it sets a reference voltage for the module corresponding to the peak voltage of the module. A PI controller is used to move the operating point of the module to that particular voltage level. It is observed that there is some power loss due to the perturbation and the MPPT controller fails to track the power under highly varying atmospheric conditions. Still, this algorithm is very popular because of its simplicity. b)

Incremental Conductance (INC) Algorithm The Incremental Conductance (IC) method, shown in Figure 2.11,

overcomes the disadvantage of the perturb and observe method for tracking

39 the peak power under highly varying atmospheric conditions. This method can determine whether the MPPT has reached the MPP and stops perturbing the operating point. If this condition is not met, the direction in which the MPPT operating point must be perturbed is calculated using the relationship between dI/dV and –I/V.

Figure 2.11 MPPT algorithm for the incremental conductance (INC) MPPT technique This relationship is derived from the fact that dP/dV is negative when the MPPT is to the right of the MPP and positive when it is to the left of the MPP. This algorithm determines when the MPPT has reached the MPP, whereas P&O oscillates around the MPP. This is clearly an advantage over P&O. In addition, INC algorithm can track rapidly increasing and decreasing irradiance conditions with a higher accuracy than the P&O method. The

40 disadvantage of this algorithm is that it is more complex when compared to P&O algorithm. 2.6

SELECTION

OF

THE

MPPT

ALGORITHM

FOR

IMPLEMENTATION The choice of the algorithm depends on the complexity the algorithm takes to track the MPP, implementation cost and the ease of implementation. Table 2.4 Characteristics of MPPT techniques MPPT technique Perturb and Observe Incremental Conductance

Convergence Speed

Implementation Complexity

Periodic Sensed Turning Parameters

Varies

Low

No

Varies

Medium

No

Voltage Voltage, Current

The advantages of the IC method over the P&O method are: Incremental method can calculate the direction, for which the array’s point changes for reaching the MPP, Incremental method determines precisely when the MPP is reached, Incremental method does not oscillate about the MPP once it reaches it, Incremental method does not go in the wrong direction when conditions in the system changes rapidly.

41 However, the P&O method does not take account of the rapid change of irradiation level (due to which MPPT changes). It considers it as a change in MPP due to perturbation, and ends up calculating the wrong MPP. To avoid this problem, the incremental conductance method was used as MPPT algorithm. 2.7

MATHEMATICAL MODELLING OF THE INDUCTION

MOTOR The voltage and torque equations that describe the dynamic behavior of an induction motor are time-varying. It is successfully used to solve such differential equations and it may involve some complexity. A change of variables can be used to reduce the complexity of these equations by eliminating all time-varying inductances, due to electric circuits in relative motion, from the voltage equations of the machine (Batool & Ahmad 2013). By this approach, a polyphase winding can be reduced to a set of two-phase windings (q-d) with their magnetic axes formed in quadrature, as shown in Figure 2.12. Filho & Souza (1997) presented a more comprehensive three-phase induction motor dynamic mathematical model mainly those including fast motor speed changes, intermittent loading and in case of motors fed from nonsinusoidal voltages contributing to the energy conservation and power quality subjects. Also a step-by-step Matlab/Simulink implementation of an induction machine using dq0 axis transformations of the stator and rotor variables in the arbitrary reference frame was formulated by Ratnani & Thosar (2014). The stator and the rotor variables (voltages, currents and flux linkages) of an induction machine are transferred to a reference frame, which may rotate at any angular velocity or remain stationary. Such a frame of reference is commonly known in the generalized machine analysis as an arbitrary reference frame.

42

Figure 2.12 The dq0 equivalent circuit of an induction motor The dynamic analysis of symmetrical induction machines in the arbitrary reference frame has been intensively used as a standard simulation approach. From this approach, any particular mode of operation may then be developed. The model equations are derived from the dq0 equivalent circuit of the induction machine shown in Figure 2.12. The flux linkages equations associated

with

this

circuit

can

be

found

by

Equations (2.16) to (2.19). V

+

V

+

V V Where,

(

)

(

)

(2.16)

(

)

(2.17)

+

(2.18)

+

(2.19)

43

X

=X

+

(2.20)

=X

+

(2.21)

=

(2.22)

Substituting the values of the flux linkages from Equation (2.16) to Equation (2.19), the currents can be found by Equations (2.23) to Equation (2.26). I

=

I

=

I

=

I

=

(2.23) [

]

(2.24)

(2.25) [

]

(2.26)

Based on the Equations (2.23) to (2.26), the torque and rotor speed can be determined Equation (2.27) and Equation (2.28) respectively, T = =

I (T

I

T)

(2.27)

(2.28)

where, p is the number of poles and J is the moment of inertia (Kg/m2) For a squirrel cage induction motor, the rotor voltages Vqr and Vdr in the flux equations are set to zero since the rotor cage bars are shorted. After

44 deriving the torque and speed equations in term of d-q flux linkages and currents of the stator, the d-q axis transformation should be applied to the machine input (stator) voltages. Equations (2.29), (2.30) and (2.31) express the three-phase stator voltages of an induction machine under balanced conditions. V = 2V

V = 2V V = 2V

sin

t)

sin

sin

(2.29)

t+

)

(2.30)

)

(2.31)

These three-phase voltages are transferred to the synchronously rotating reference frame with only two phases (d-q axis transformation) by using Equation (2.32).

V V

=

1

0

1

2

3

1

2

V V 3 2 V

2

(2.32)

Then, the direct and quadrature axes voltages are given by Equation (2.33), V V

=

cos sin

sin cos

V V

(2.33)

The instantaneous values of the stator and rotor currents in the three-phase system are ultimately calculated using the transformation in Equations (2.34) and (2.35). I I

=

cos sin

sin cos

I I

(2.34)

45

I I I 2.8

=

1 1 1

2

2

0 3

3

2

(2.35)

2

MATHEMATICAL MODELLING OF THE BLDC MOTOR Modelling of a BLDC motor, shown in Figure 2.13, can be

developed in a similar manner as a three-phase synchronous machine (Immaneni 2013). Since there is a permanent magnet mounted on the rotor, some dynamic characteristics are different. Mondal et al (2015) presented a mathematical model of a three-phase Brushless DC motor based on precise speed control methodology with ideal Back EMF on MATLAB/Simulink platform which are based on phase voltage and electromagnetic torque equation (Shivraj et al 2014).

Figure 2.13 Circuit diagram of the BLDC drive system

46 A cylindrical rotor and the stator having three-phase windings a, b, and c are considered. The rotor is a permanent magnet rotor, and hence the air gap is uniform. The stator has three phases with distributed winding structure and star connected. Equations (2.36) to (2.38) give the dynamic equations of phases a, b, and c,

Van

Rs

L

V bn

Rs

L

Vcn

Rs

L

di a dt

di M

b dt

M

di c dt

ea

(2.36)

b dt

M

di c dt

M

di a dt

e

(2.37)

di c dt

M

di a dt

M

di

b

di

b dt

(2.38)

ec

where, L is armature self-inductance (H), M is armature mutual inductance (H), R is armature resistance ( ); Van, Vbn and Vcn are the terminal phase voltages (V); ia, ib and ic are motor input current [A]; and ea, eb and ec are motor back emfs (V). These are stator three equations, the rotor is a permanent magnet, and hence does not have any winding. Therefore, the rotor structure not having any equation. Equations (2.36) – (2.38) can be represented in the form of a matrix given in Equation (2.39). Van V bn Vcn

Rs 0 0

0 Rs 0

0 ia 0 i b R s ic

L M M ia M L M P i b ic M M L

ea e b ec

(2.39)

In the BLDC motor, the back emfs are a function of the rotor position and are at 120° phase angle difference. Hence, Equation (2.39) is modified to Equations (2.40) - (2.48).

47

ea

e r' b

Ka fa

k f b b

d(i

Van

Rs

L

di a dt

M

Van

Rs

L

di a dt

M

Van

Rs

( L - M)

di a dt

Van

Rs

L

V bn

Rs

L

Vcn

Rs

L

e r' c

3

i ) b c dt

k cf c

3

r'

(2.41)

ea

di

di a s dt

a dt

(2.40)

(2.42)

ea

(2.43)

ea

ea

(2.44)

b s dt

e

(2.45)

di c s dt

ec

di

b

(2.46) di

Van Vbn Vcn

Rs 0 0

0 Rs 0

a dt di b L s dt di c dt

0 ia 0 ib R s ic

ea eb ec

(2.47)

di

a dt di b dt di c dt

The

V an V bn V cn

three

R

s 0 0

0 R s 0

0

i

e

a 0 i - e b b e R i c s c

simultaneous

a

differential

1 L s

(2.48)

equations

namely,

Equation (2.47) can be solved by any numerical technique. For example,

48 using the Runga-Kutta fourth order, the the values of ia, ib and ic are obtained from Equations (2.51) - (2.53). ea

(2.49)

Ka r

Pm (ea i a e i ecic ) bb Te

Te

Te

Pm rm

ea ia

e i bb r

K a ia

K i bb

(2.50) e ci c ) P

K cic

r

P(K a i a

K i bb 2

2 r P 2

K cic )

(2.51)

(2.52)

(2.53)

Equations (2.54) - (2.56) give the equations for the mechanical sub-system.

Te

TL

Jd rm dt

Te

TL

Jd r P dt 2

r dt

2.9

P T T L 2J e

rm

(2.54)

r

(2.55)

2B P r

(2.56)

P 2

SOLAR WATER PUMPS A solar water pump has a mini powerhouse as a major component

and consists of a designed solar array to meet the power requirement of the pump for a particular application. This system is capable of running all types of electrical water pumps with applications varying from irrigation to

49 household demands. Irrigation pumps such as submersible, surface or deep well can also be coupled with the drip irrigation systems. A typical solar water pumping system is known by the solar array size that is required to run the attached pump. A 1000 Wp solar water pump is capable of drawing and pumping approximately 40,000 litres of water per day from a source that is up to 10 meters deep. This is sufficient to irrigate about 2 acres of land with regular crops. A 1000 Wp solar water pump helps save up to Rs. 45,000 in a year, when compared to the use of the diesel-operated pump. 2.9.1

Selection of Solar Pump Motors There are currently three pumping configurations commonly

utilized: i.

DC drive with positive displacement pumps: This consists of four pump technologies: a)

Diaphragm pump driven by a brushed DC motor: Submersible motor/pump:

Example:

Shurflo,

DivWatt,

All

Power

Watermax. b)

Helical rotor pump driven by a brushless DC motor: Submersible motor/pump: Example: Total Energie TSP 1000.

c)

Helical rotor pump driven by surface mounted brushed DC motor: Example: Mono/Orbit pump with DC motor

d)

Piston pump driven by surface mounted brushed DC motor: Example: Reciprocating piston pump.

50 ii.

AC drive powering a submersible induction motor/centrifugal pump unit: This category consists of ac motor pumps, which are of submersible induction type Example: Total Energie TSP 2000, 4000 & 6000 range; Grundfos SA 1500 and SA 400 which has been utilized extensively in South Africa but may be phased out in the near future.

iii.

Powering the AC drive with a three-phase permanent magnet synchronous motor: This category consists of: a)

Positive displacement helical rotor pump: Example: Grundfos SQ Flex, Lorentz HR range.

b)

Centrifugal pump: Example: Grundfos SQ Flex, Lorentz C range.

iv.

Powering the AC drive with a three-phase Brushless DC motor: This category of motors operates with helical rotor and centrifugal

pumps to deliver water for domestic and agriculture use. They have high efficiency, low maintenance, longer period of operation over a day and long life compared to the other motors. 2.9.2

Diesel Pumps The diesel pumps under review are in the power range of 2 to

12 kW. The diesel pumping systems is based on a helical rotor and a positive displacement pump (Mono and Orbit elements). The most common diesel engine configuration is the progressive cavity pump. The diesel engine in conjunction with a reciprocating pump is a configuration that is used in a

51 hybrid pumping setup with a wind pump, where the diesel acts as a backup for the wind pump during periods of low wind or during maintenance work on the wind tower. A similar configuration is encountered where the wind pump is backed-up with an electric submersible pump (fitted underneath the cylinder) which is powered by a diesel or petrol generator. The submersible pump remains in the bore-hole and when there is a need for additional water pumping, then the diesel/petrol generator is taken to site for pumping. The diesel pumping configuration, which is used as the comparative case for the PV pumping system, is the progressive cavity pump, which is a standalone single energy source pumping system and presents the most efficient diesel pumping configuration. The survey on diesel engines in the local market identified four different makes of diesel engines. These are Hatz, Lister (South African manufacture), Kia (India), and Kirloskar (India). The most common progressive cavity pump elements on the market are Mono and Orbit. There is a range of elements, which cover the 0 to 200 m head adequately. The diesel engine system is capable of operating anywhere for the hydraulic load. For example, a diesel engine system can be designed to pump over a head of 200 m and deliver 6 m3/h (60 m3 over ten hours). Diesel pumps are suitable for remote off-grid pumping applications in places where the water requirement is more than 1,500 m3/day. The ability of a diesel pump to pump large volumes of water against high heads makes a diesel pump suitable for large village supplies. 2.10

SUMMARY

52 The design process explained in this chapter provides the design of the PV WPS for agriculture use. The TDH is calculated based on the water source for the irrigation of a rice field. With the calculation of the water demand and the power rating of the motor selected, PV array sizing was done. In addition, the design of the MPP Tracker and selection of the MPPT algorithm for the rapidly changing irradiance level was carried out. The inverter controlling the power input to the motor was selected based on the motor rating. The study of the existing diesel system is also provided for the comparison of the SPV WPS and diesel operated system in the forthcoming chapters.