Novel Pumping System based on Micro-Hydro Turbine and Centrifugal

Pump coupled using EVT Induction Machine.

Application in Rural Area Irrigation.

MARCELO G. CENDOYA, SANTIAGO A. VERNE, PEDRO E. BATTAIOTTO

Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales (LEICI)

UNLP - CONICET - CIC PBA

Departamento de Electrotecnia, Facultad de Ingeniería

Universidad Nacional de La Plata

Calle 1 y 47, La Plata (B1900TAG, Buenos Aires

ARGENTINA

Abstract: - In this article, a topology for energy conversion oriented to water pumping for irrigation in remote

areas is proposed. A micro-hydraulic turbine working at fixed speed, in a "run-off-river" configuration, drives a

centrifugal pump through a variable electric transmission (EVT). An EVT based on induction machines was

selected, with the stator directly connected to a weak AC grid but the internal rotor fed by a variable frequency

drive, allowing an adjustable pump speed. The grid supplies a base power for residential consumption, while

the hydro turbine increases the available power for irrigation and thus augmenting productivity of the land

uphill and beyond the vicinity of the watercourse. The grid also provides an assistance function,

absorbing/delivering a reduced amount of power in case the hydraulic resource is excessive/insufficient for the

requested water pumping.

As the turbine delivery is constant, the water pumping requirement establishes the power exchanged between

turbine, AC grid and pump. For this reason, an analysis to quantify the power flow in the system components

for different pump speeds has been carried out. The system modeling is described and computer simulations,

using a specific pump speed profile, are presented to validate the performed theoretical analysis.

Key-Words: - Electric Variable Transmission; Micro-hydro Turbines; Water Pumping; Weak Grids.

Received: September 23, 2022. Revised: February 19, 2023. Accepted: March 18, 2023. Published: May 8, 2023.

1 Introduction

The availability of water and renewable energy in

rural areas far from cities is vital for the economic

and productive development of a region.

Fortunately, Argentina has many water resources,

especially in the adjacent area near to Los Andes

Mountains and in the northern region. Additionally,

the territory is suitable for growing various species

such as grapevines, olives, and fruits, which are the

stronger productive industries in that region [1] [2].

Moreover, these crops increase their productivity by

optimizing the irrigation regime, especially

considering the scarce rainfall and low humidity

levels. For this reason, the exploitable territory is

close to watercourses. However, the traditional

runoff irrigation method presents a low efficiency of

water usage, about 65%, and it is highly restricted

by the characteristic land conditions. In this sense,

drip or micro-sprinkler irrigation is a promising

technology to increase both water usage in rational

form and land productivity, since it allows for the

exploitation of lands in higher elevations with

uneven surfaces, and relatively far from water

resources [3]-[6].

The infrastructure of such an irrigation system

consists of a pressurized water distribution network

through pipes, pumping systems, and a power

supply. Frequently, productive areas are not reached

by the electrical utility grid, and a significant part of

the energy requirements are supplied by diesel fuel.

However, due to the constant decrease in costs,

renewable energies tend to provide viable solutions

[7] [8]. Sometimes, a weak grid reaches the site, but

its power capacity is limited in quantity and/or

quality. However, areas that have surface water

resources, such as waterfalls or small streams, can

be used to convert the energy of water into another

type of energy, typically electricity. In the power

range of less than 100 kW, such facilities are called

micro-hydropower plants and constitute a very

attractive energy conversion technology that allows

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

for the supply of reliable and constant energy in an

isolated form or interconnected to a grid [9] [10].

Many primary energy sources come in the form of

mechanical power. Then, equipment usually

converts it into electricity which is easily distributed

among loads. In water pumping systems, the

electrical energy from the renewable sources is used

to power the variable speed pumps through electric

motors fed by variable frequency drives (VFD’s)

[11] [12]. However, this topology involves a double

conversion (mechanical-electrical-mechanical) of

the entire power which lowers the overall efficiency,

due to losses in each conversion stage. A variable

electrical transmission (EVT) is an electromagnetic

conversion device based on an electric machine with

two mechanically decoupled shafts and two electric

ports [13]. EVT integrates a driving machine and a

load machine into a single machine that allows the

conversion of mechanical energy between both

shafts. On the other hand, although electronic

converters are required to control the power flow, it

is possible to undersize them to a fraction of the

power in EVT`s mechanical ports [14]. Therefore,

an EVT is a promising device for mechanical

conversion applications such as electric vehicle

propulsion and even as a gearbox in wind turbines

[15][16].

This paper proposes a hydraulic energy conversion

system, connected to a weak grid, that is oriented to

irrigation purposes. The local generation source is

based on a propeller type (also known as semi-

Kaplan due to the fixed pitch angle) micro-hydraulic

turbine, whose main function is to provide a power

increase (above the power level available from the

weak grid) needed to augment the capacity of the

water pumping system. The turbine is linked to a

centrifugal pump through an EVT. As the stator of

the EVT input shaft is connected to the grid, the

turbine operates at fixed speed. On the other hand,

the internal rotor of the EVT is fed by a VFD,

allowing an adjustable output shaft speed, where

there is the centrifugal pump.

Section 2 describes the architecture of the irrigation

system under study and presents the mathematical

model of each component. In Section 3 is carried

out an analysis of the power distribution in different

working conditions, which are determined by the

pumping requirements. Section 4 shows computer

simulations made to validate the foregoing analysis,

accompanied by a discussion of the obtained results.

Finally, the conclusions of the work done are

outlined.

2 System Description

Figure 1 shows the geographical scenario for the

irrigation system. At a certain height, part of the

flow is diverted from the main channel of the

watercourse. The civil works for the diversion

channel could be carried out ad-hoc or even be

previously existing [9][17][18]. In both cases, the

micro-hydro power plant is located inside the

powerhouse, at the bottom of the channel. The water

intake may include a natural or built reservoir in the

upper part of the turbine feeding pipe (penstock).

Subsequently, a desanding/load chamber removes

particles which could damage the turbine and

eliminates possible turbulences prior to the

discharge through the penstock. The outlet of the

penstock supplies the water flow for the turbine,

which is attached to the EVT input shaft, whilst the

turbine discharge returns to the watercourse. The

centrifugal pump is linked to the EVT output shaft,

and its outlet supplies the necessary filling flow

(through the main pipe) to maintain an adequate

level in the irrigation water reservoir, which is

located at a higher height than the powerhouse. To

not disturb the water flowing through the turbine,

the inlet of the centrifugal pump is fed from the

turbine discharge. This is possible since the pump

must supply a relatively low flow to a water

reservoir located at a considerable height, contrary

to the turbine that operates at a low head and a

higher flow (remember that the hydraulic power

depends on the product of the head times the flow;

furthermore, the hydraulic power of the turbine and

the pump are comparable in this case).

Fig.1: Geographical distribution of the irrigation system.

Figure 2 shows the mechanical coupling between

the turbine and the pump through the EVT, and its

electrical connections. A weak AC distribution grid

is supplying the residential loads. A link (ACN)

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

connects the EVT to the weak grid. As mentioned in

the Introduction, the micro turbine is coupled to the

input shaft of the EVT (external rotor), whose stator

is directly connected to ACN without any electronic

conversion, which is possible because this part of

the EVT behaves like a conventional squirrel cage

induction generator (a more detailed description of

the EVT will be given in the following section).

This causes the turbine speed to remain in a small

interval around the synchronous speed, which is set

by the weak grid electrical frequency. In this typical

situation (ignoring the small speed slip), the turbine

is said to be operating at "fixed speed". The

centrifugal pump is coupled to the output shaft of

the EVT (internal rotor), whose winding is fed by a

VFD, also connected to ACN. The use of a VFD

allows adjusting the speed of the centrifugal pump

in an ample range. The speed reference signal for

the VFD is generated from an external control loop

that regulates the water level in the irrigation water

reservoir at some desired value.

Fig.2: Turbine and pump mechanical coupling and EVT

electrical connections.

2.1 Micro Hydro Turbine

In this work it is considered the use of a semi-

Kaplan micro-hydro turbine, also known as a

"propeller" turbine because (unlike the standard

Kaplan turbine) the blades have a fixed pitch angle.

This is an axial flow turbine that, due to its design

features, is well-suited for low to moderate heads

(less than 40m), where water flow is relatively high

[19]. The turbine is located inside the powerhouse at

a low level of the terrain, to establish a sufficient

head. The hydraulic power PH of a water flow Q

falling from a net head H (which is the actual static

head minus the dynamic head that represents the

friction losses in the penstock) can be calculated as:

  (1)

In (1) ρ is the water density (1000 kg/m3) and g is

the acceleration due to gravity (9.8m/s2). A

hydraulic turbine converts only a fraction of the

total hydraulic power PH into mechanical power PT

on its shaft, that is the product of the turbine

mechanical torque TT and the shaft rotating speed

ωT. This fraction is called the turbine conversion

efficiency ηT:

   (2)

The mechanical power and the turbine efficiency are

variable depending on H, Q, and ωT. There is an

optimal operating point in which the mechanical

power reaches its maximum value [20]. The optimal

operating speed ωTopt of a semi-Kaplan turbine, for a

given values of H and Q, can be determined using

the following formula [21]:

  󰇛󰇜

 (3)

In (3), σ is a characteristic design parameter that

depends on H and whose typical value can be found

in [21].

To make approximate evaluations by computer

simulation in a preliminary project stage (for

example, to design and tuning a controller), it is

possible to use a simplified mathematical expression

for the torque developed by the turbine, such as the

one that can be found in [22]:

 󰇛  󰇜 (4)

In (4) To is the turbine starting torque (when ωT=0)

and ωTmax is the turbine runaway rotating speed

(when TT=0). The expression (4) is valid only when

the turbine operates with a constant head and a

constant flow rate. In our case, as the penstock is

usually fed from the discharge of a small reservoir

that has a relief duct, (which means that it stays

completely full most of the time), the head will be

constant. On the other hand, as the flow depends on

the head and the rotating speed of the turbine (both

constant quantities in our case), one can conclude

that the flow will also be a constant magnitude.

Therefore, the use of (4) is completely justified for

the situation under analysis. If (4) is assumed to be

valid, then the mechanical power delivered by the

turbine at is shaft is:

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

 󰇛 󰇜 (5)

From (5) the maximum power of the turbine can be

derived:

   (6)

which occurs at an optimal rotational speed ωopt:

   (7)

Equations (4) and (5) are depicted in Figure 3,

which shows the maximum mechanical power point,

defined by (6), and a selected operating point (A)

(PTA, nTA) slightly shifted to the left as in [22].

Fig.3: Torque/Power - speed characteristic of the turbine.

2.2 Electric Variable Transmission (EVT)

As already mentioned, to couple the fixed speed

micro-hydro turbine to the variable speed

centrifugal pump, an EVT machine is employed.

Figure 4 shows the simplified physical structure of

the EVT. The electrical and electromechanical

power flows are denoted with arrows which

describe their possible directions, depending on the

working conditions of each EVT shaft. A three-

phase stator winding is located on the yoke of the

EVT, that is identical to a standard induction

machine and, in our application, is directly

connected to the grid. It produces a rotating

magnetic field whose speed (known as

“synchronous speed”) is established by the grid

frequency. Internal to the yoke there is a cup-shaped

rotor (hereinafter called interrotor).

Fig. 4:. EVT machine physical diagram and power flow.

There are some constructive variants for the

interrotor of an EVT: both faces with permanent

magnets (PM), both faces with squirrel cage,

wounded interrotor, etc. [13] [23]. In this work, an

EVT with a hybrid interrotor, like the one presented

in [23], is used. In this type of EVT, the outer face

of the interrotor has short-circuited conductive bars,

forming a squirrel cage. This allows direct

connection to the grid in a simple way. If PMs

would be used in the outer face of the interrotor,

some kind of synchronization with the grid

frequency would be required. The outer face

interrotor squirrel cage interacts with the rotating

magnetic field produced by the stator and defines an

“EVT External Induction Machine”. Otherwise,

PMs located at the interrotor inner face produce a

magnetic field that rotates at the interrotor

mechanical speed. Internally to the interrotor, there

is the inner rotor, that has a three-phase winding

(similar way to a DFIM machine) with slip rings fed

from a variable frequency drive (irVFD) to set

currents with the desired amplitude and frequency.

The inner rotor winding interacts with the rotating

magnetic field produced by the PMs, defining an

“EVT Internal Induction Machine”.

It has been decided to use the stator winding of the

EVT External IM directly connected to the grid,

because in this way the use of an expensive

converter is avoided, also obtaining greater

simplicity and reliability. In this manner, simple and

cheap soft starter equipment is required for the

connection to the grid.

As the interrotor is mechanically joined to the

turbine, the rotating speed variation is determined

by:

,Point of maximum

power output

PTmax

PTA

TTA

nTA

nTopt

n= (60/2 )ω π

nTmax

irVFD

inner rotor

stator

Link

(shaft 2) to the

pump shaft

(shaft 1) to the

hydro turbine shaft

PirVFD

Prei

stator

PM inner face

cage outer face

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

 󰇛  󰇜 (8)

In (8), JT is the total moment of inertia considering

all the rotating masses linked to the input shaft, TT is

the torque provided by the hydro turbine, given by

(4), TEM1 is the electromagnetic torque that arises

from the interaction of the magnetic rotating field of

the stator and the magnetic field produced by the

bars of the outer face of the interrotor. TEM2 is the

electromagnetic torque that arises from the

interaction between magnetic field provided by PMs

located at the inner face of the interrotor and the

magnetic field produced by the winding of the inner

rotor (which is mechanically transmitted through the

mechanical structure of the interrotor to the input

shaft).

The magnetic field produced by the EVT External

IM stator, rotates at the synchronous speed ωS given

by:

  (9)

where fe1 is the grid frequency and p1 is the number

of pole pairs of the stator winding. As in any

conventional induction machine, for torque

production it is necessary that the interrotor rotates

at a slightly different speed than ωS. At normal

working conditions the interrotor speed is close to

the synchronous speed. In this situation, called “low

slip operation”, it is possible to calculate TEM1 using

a linear approximation given by [24]:

 󰇛 󰇜 (10)

where KG is the slope of the torque-speed

characteristic. This value depends on the magnetic

flux amplitude in the air gap between the stator and

the interrotor and the resistance of the interrotor

outer face bars.

As the inner rotor is mechanically coupled to the

centrifugal pump, the variation of the EVT output

shaft speed ωP is described by the following

expression:

  󰇛 󰇜 (11)

In (11), JP is the total moment of inertia considering

all rotating masses linked to the EVT output shaft

and TP is the resistant torque presented by the

centrifugal pump. This torque can be calculated as

[25]:

  (12)

where KP is a constant, specific for each pump

model, that depends on its design characteristics

[25].

It can be noticed from (11) that TEM2 determines the

operating speed of the pump but also affects the

EVT input shaft speed, as seen in (8). Usually, the

time constants of both the VFD and the inner rotor

winding are much faster than those of the

mechanical and hydraulic parts of the system. For

this reason, it is possible to use the steady state

value of TEM2 to evaluate (11). In steady state and

low slip operation, the value of TEM2 follows an

approximately linear fashion with respect to the

difference in rotational speeds between the

interrotor, and the inner rotor:

 󰇛  󰇜 (13)

In (13), KM is the slope of the torque-speed

characteristic, and its value depends on the flux

amplitude in the air gap between the interrotor and

the inner rotor (produced by the PMs) and the inner

rotor winding resistance. It should be noticed that

ωT acts as the synchronous speed for the inner rotor,

as it is the speed of the rotating PMs. On the other

hand, ωC represents the abscissa displacement

suffered by the torque-speed characteristic, that

depends on the frequency value fe2 provided to the

inner rotor winding by the VFD:

  (14)

In (14), p2 is the pole pairs number of the inner

rotor.

2.3 Water Reservoir

The variation of the water level hr in a reservoir

with vertical walls is described by:

  󰇛 󰇜 (15)

Ar is the reservoir base area, QP is the water flow

rate supplied by the centrifugal pump and QC is the

water flow rate consumed by the irrigation system.

Considering the well-known “affinity laws” [26], it

can be assumed that the water flow rate supplied by

the pump is related to its rotational speed as:

  (16)

In (16), KQ is a constant that depends on the pump

design characteristics and the associated hydraulic

circuit.

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

3 System Power Distribution Analysis

As stated earlier, the grid frequency forces the

turbine to work at almost fixed speed. This situation,

together with the fact that the head does not change,

makes the water flow through the turbine remain

constant as well. Considering the principle of

operation of the turbine, that was explained in

subsection 2.1, it is easy to see that the mechanical

power delivered by the turbine to the input shaft of

the EVT has a near constant value. On the other

hand, the centrifugal pump speed needs to be

regulated to supply the changing flow of water

required for irrigation. This changing speed causes

the mechanical power taken by the pump from the

EVT output shaft to be also variable. It may then

happen that the power required by the pump is less

than that supplied by the turbine or, conversely, that

it is greater than it. This power imbalance means

that the difference must be absorbed or supplied by

the weak grid. To do this, there are two possible

paths: through the EVT stator winding or through

the VFD (it can manage power in a bidirectional

way) and which is also linked to the weak grid. At

this point, the need for a detailed analysis of how

the power is exchanged between all the elements of

the system arises.

First, to carry out the analysis we must establish

certain starting hypotheses and considerations:

1) A turbine with a rated mechanical output power

of PT=50kW for the speed of nT=1000RPM, was

selected.

2) An EVT stator winding with three pole-pairs was

used. According to (9), for p1=3 and considering a

50Hz grid frequency, the resulting synchronous

speed of the External Induction Machine is

nS=1000RPM (as given in (9) multiplied by 60/2π).

3) A three pole-pairs of permanent magnets

arrangement (fixed to the inner face of the

interrotor) is employed. As these constitute the

stator for the internal induction machine, nT acts as

its synchronous speed. The EVT inner rotor also has

a three pole pairs winding.

4) A centrifugal pump that takes from the EVT

output shaft a maximum mechanical power of

PPmax=75kW, at nPmax=1500RPM, was chosen.

The pump power is greater that the turbine power

because is made up of two components: the power

Prei transmitted electromagnetically from the

interrotror to the inner rotor Prei and the power PirVFD

supplied for the irVFD, i.e., PP=Prei+PirVFD, see

Figure 4.

Figure 5 shows the locus of the operating points of

the turbine and the centrifugal pump. Since the

turbine drives the EVT’s interrotor as a weak grid-

tie induction generator, the rotational speed will be

very close to the synchronous speed nS defined by

the grid frequency. On the other hand, as the

selected speed of the turbine has been matched close

to nS, it will always supply maximum power to the

interrotor shaft. Thus, the operating point of the

turbine is closely defined, except for the slip, by (nT,

TT) (point A, Figure 5), shown together with the

hyperbola (in red) that contains all the points of the

T-n plane that has a power value equal to the turbine

one of PT=50kW. Otherwise, the operating points of

the centrifugal pump (nP, TP) define a parabola (in

blue), in accordance with (12). As well as there is a

maximum pump speed at nPmax=1500RPM (point E,

Figure 5), a minimum value is considered at

nPmin=500RPM (point B, Figure 5) below which

pump operation is not expected. This could be the

minimum threshold to overcome the static hydraulic

head of the irrigation facility. Also, there is a

particular pump speed value ne in which the

mechanical power required by the pump is equal to

the power delivered by the turbine (point D, Figure

5). Using the values stated foregoing to compute

(12), a ne=1310 RPM is obtained.

The rectangles depicted in Figure 5, defined by

pump and turbine speed with their corresponding

torques, reveal the distribution of power flow

through the ports of the EVT machine. From the

above discussion, it is then clear that the EVT

operates with a variable transmission ratio and that a

particular power distribution will be given for each

pump speed.

Fig. 5: Operating points locus of the turbine and the

centrifugal pump.

Figure 6 shows how the magnitudes previously

shown in Figure 5, and the rectangles that represent

the associated powers, take on distinctive relative

proportions in different working situations. For a

better understanding, the representation in the T-n

plane is accompanied by a diagram of the EVT

n[RPM]

nPmin nTnenPmax

T =T

T Pmax

TPe

TPs

TPmin

P =75kW

P =50kW

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

showing the power flow direction in its ports for

each case. The analysis is carried out at some

operating points in the T-n plane that are

representative of typical situations, characterized by

a particular set of power flow directions. What

happens at the points that are at the boundary

between two consecutive situations are also

discussed. The changing physical variable is the

pump speed, which is directly related to the water

flow requirement for irrigation, see (16).

Fig. 6: EVT power flow for different pumps speeds. a)

nPmin<nP<nT, b) nP=nT, c) nT<nP<ne, d) nP=nPmax>nT.

Situation 1 (nPmin<nP<nT) (Figure 6 (a) through (b)).

In this region, the mechanical power consumed by

the pump PP (rectangle defined by points o-I-B-np of

Figure 6 (a) through o-H-C-nT) is lower than the

supplied by the hydro-turbine PT (PP<PT) (o-F-A-

nT). As the torque demanded by the pump TP is

lower than the produced by the turbine TT, the stator

winding will deliver a power PS=PT-Prei=(TT-

TP)(2πnS/60) into ACN, where Prei is the power

transmitted mechanically by the EVT from the

interrotor to the inner rotor. On the other hand, the

pump speed is lower than nT and therefore, the inner

rotor currents should be in negative sequence.

Consequently, the inner rotor is working in

generation mode and its power is collected by the

irVFD and delivered to the ACN. Both the stator

winding power and the irVFD power are injected to

ACN and are available to be consumed by

residential loads (I-F-A-J-nT-nP-B). This power is

PL=PS+PirVFD=PT-PP. As a limiting case of this

region, when nP=nT, the inner rotor winding is fed

with zero frequency (CC) and PirVFD is

approximately zero (Figure 6 (b).

Situation 2 (nT<nP<ne) (Figure 6 (b) through (c)). In

this region, the mechanical power taken for the

pump (o-H-C-nT of Figure 6(b) through o-G-D-ne of

Figure 6(c)) is lower than that delivered by the

turbine (PP<PT). The torque demanded by the pump

keeps being lower than the turbine’s and the stator

winding delivers a power PS=(TT-TP)(2πnS/60) to the

ACN. On the other hand, the pump speed is higher

than nT and therefore, the irVFD feeds the inner

rotor with a positive sequence. Because of this, the

inner rotor is working in motoring mode, and the

irVFD supplies it with a power that in turn is taken

from the ACN. The net remaining electrical power

available for residential loads is PL=PS-PirVFD=PT-

PP>0. A limiting case of this region is when nP = ne,

in which PL=0 since PT=PP and PS=PirVFD. This is

clearly noticed from Figure 6 (c), where the

rectangles G-F-A-M and nT-M-D-ne have equal

areas.

Situation 3 (ne<nP<nPmax) Figure 6 (c) through (d). In

this region, the mechanical power taken for the

pump (o-G-D-ne from Figure 6 (c) through o-F-E-

nPmax of Figure 6 (d)) is greater than that supplied by

the hydro-turbine (PP>PT). The torque demanded by

the pump keeps to be lower than turbine’s and the

stator winding will deliver a power PS=(TT-

TP)(2πnS/60) to the ACN. On the other hand, the

pump speed is still higher than nT and therefore the

irVFD feeds the inner rotor with a positive

sequence. Therefore, the inner rotor is in motoring

mode and the power is taken from the ACN through

the irVFD. The net power taken from the grid being

equal to: PL=PirVFD-PS=PP-PT<0. The limiting case of

this region occurs when nP=nPmax, PS=0 since TT=TP

and Prei=PT. It also occurs that the irVFD provides

the maximum required power PirVFD=PirVFD_MAX=

P =0

P =P

irVFD S

one

(c)

(d)

(a)

P +P =P

irVFD S L

P >0

P =0

irVFD

nPmax

P =P

irVFD L

P <0

irVFD PS

PirVFD

irVFD

PirVFD

irVFD

PirVFD

(b)

Prei

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

PPmax-PT=25kW to meet the pump’s power

requirement.

4 Simulation Results

To verify the validity of the theoretical and

graphical analysis previously presented in Section 3,

a series of simulations were carried out. To perform

them, a computer model of the irrigation system has

been built, based on the equations presented in

Section 2 and implemented using existing blocks in

the MATLAB-Simulink package library. This

dynamic model allows not only the study of the

power distribution in steady state (predicted by the

analysis done in Section 3) but is also capable of

representing the temporal evolution from one state

to another. The numerical values of the most salient

parameters of the system model, are given below:

Turbine:

Semi-Kaplan type, rated power PTA=50kW at

nTA=1000RPM (see Figure 3), rated efficiency

nT=87%, optimal speed nTopt=900RPM, runaway

speed nTmax=1800RPM, total head (static and

dynamic) H=6.5m, rated flow Q=0.922m3/s.

EVT:

External IM: rated power PS=50kW (input shaft

mechanical power), stator: 3-phase 3 pole- pair

winding directly connected to the AC grid, rotor:

squirrel cage type, rated slip s=5%.

Internal IM: rated power Pir=75kW (output shaft

mechanical power), stator: 3-pole PM array, internal

rotor: 3-phase 3 pole-pair winding fed by and ideal

irVFD, rated slip s=5%.

Centrifugal pump: maximum mechanical power

PPmax=75kW at nPmax=1500RPM. The pump speed is

adjusted by a PI control loop (with a nested internal

torque loop) in the irVFD.

Weak grid:

380VAC/50Hz

To facilitate the comparison between the values

obtained by simulation and the ones predicted by

theoretical analysis, an ascending pump speed nP

profile with a stepped waveform has been

considered. The values of each step are: 500, 1000,

1310 and 1500RPM, which are in correspondence to

the points B, C, D and E of Figure 6. The transitions

of the speed profile were made smooth, with the

intention of representing a typical control action to

change the flow for maintaining a desired water

level in the irrigation reservoir.

Figure 7 shows how the torque of the different

system components evolve over time as the speed of

the pump varies, Figure 7 (a). Figure 7 (b) shows the

electromagnetic torque of the internal rotor

necessary to drive the pump at the desired speed,

opposing the antagonistic torque exerted by the

pump on its shaft, Figure 7 (c). An excess of

electromagnetic torque (with respect to the

stationary value) is appreciated, which is associated

with overcoming the internal rotor and pump

assembly inertia. The torque with which the

hydraulic turbine drives the interrotor of the EVT is

shown in Figure 7 (d), can be seen that (after the

initial start-up transient) it is almost constant, since

the speed of the turbine, Figure 7 (f), is always close

to its rated value of 1000RPM. This is so because

the EVT input shaft speed is practically fixed by the

EVT External IM, whose stator presents a resistant

electromagnetic torque (Figure 7 (e)), which varies

abruptly with small speed changes, due to the high

slope of its torque-speed characteristic (denoted as

KG in (10)). Regarding TEM1, it can be seen how it

decreases as the torque transmitted to the pump

shaft by electromagnetic means, TEM2, increases.

Fig. 5: System torques evolution during pump speed

changes.

The rounded value of the system torques and turbine

speed for each pump speed are shown in Table 1.

Table 1. System torque values in [Nm] and turbine speed,

for each pump speed, in [RPM].

TEM2=TP

TEM1

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

451

1043

500

454

400

1038

1000

212

463

251

1024

1310

362

471

109

1010

1500

475

1000

Fig. 8: System powers evolution during pump speed

changes.

Table 2. System power values, in [kW], for each pump

speed, in [RPM].

Prei

PirVFD

49.3

47.3

500

49.4

41.9

5.9

2.9

-2.9

1000

49.6

26.3

22.7

0.2

1310

49.8

11.5

38.3

49.5

13.3

-2

1500

49.9

74.2

28.2

-27

Figure 8 shows the evolution of the powers in the

different components of the system, associated with

torques and speeds shown in Figure 7. Firstly,

Figure 8 (a) shows the mechanical power supplied

to the EVT input shaft from the turbine, which

remains practically at its rated value of 50 kW, as it

was previously explained. The electrical power

generated by the stator of the EVT External IM is

shown in Figure 8 (b). This power is obtained by

subtracting from the turbine power, the mechanical

power transmitted via electromagnetic coupling to

the internal rotor, shown in Figure 8 (c). Figure 8 (d)

shows how the mechanical power demanded by the

pump increases as its speed increases. This power is

supplied in part by the transmitted power, and partly

by the irVFD, shown in Figure 8 (e). Finally, Figure

8 (f) shows the power flowing through the link that

connects the irrigation station to the weak grid and

the residential loads, which is formed by the power

supplied by stator of the EVT External IM minus

the power absorbed by the irVFD. The rounded

values of different system powers for each pump

speed value are listed in Table 2.

The obtained simulation results show a good

correlation with the theoretical analysis carried out

in Section 3, thus demonstrating its validity.

5 Conclusions

In this work, an irrigation system for rural areas has

been proposed. It is suitable for the case where, in

addition to disposing of the essential water resource,

there is a weak distribution grid with a power

capacity enough to supply existing residential loads,

but it is incapable to deliver the power required for

irrigation purposes. As it was conceived, the system

presents some novel aspects and very interesting

advantages:

- The centrifugal pump, responsible for feeding

water to the elevated reservoir, is coupled to a Semi-

Kaplan microturbine through an EVT Induction

Machine (IM). This provides higher efficiency than

the traditional system, based on two electrical

machines interconnected by variable frequency

drives that must handle the system full power.

- The proposed EVT is based exclusively on

induction machines, both for the External and

Internal Machines. This makes the coupling very

simple, reliable, and robust.

- The EVT External IM stator winding is directly

connected to the AC grid, avoiding the use of an

expensive and complex electronic converter. Any

synchronization mechanism with the grid is not

needed. Simple soft-start equipment is only

required.

- The EVT Internal IM rotor winding is powered by

a VFD for adequate control and variation of the

centrifugal pump speed. This means that the VFD

only must handle a fraction of the total pumping

power.

- The micro-hydro turbine operates at almost fixed

speed, delivering its rated power all the time. Thus,

the best use of its capacity is achieved.

- An adequate component sizing makes it possible to

achieve a limited power exchange with the weak

grid. When the pump power exceeds the power

delivered by the turbine (50kW), some assistance

from the weak grid is required. The power taken

from the grid reached the moderate amount of

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

25kW, in the worst case (maximum pumping

power).

Regarding the operation of the proposed system, an

analytical and graphic study has been carried out to

evaluate the distribution of mechanical and

electrical powers among its components, including

the exchange with the weak grid, for typical

working situations defined by different pump

speeds. The results obtained through computer

simulations have shown very good agreement with

the analytical results and there were no anomalies in

the transition between stationary operating points.

As a future work, it is planned to explore the

possibility of including a high-capacity storage

system for maximum usage of the hydraulic

resource and minimum power exchange with the

weak grid. The flow battery is a very attractive

device for this application. To reach the proposed

objectives, a relatively complex supervisory control

system must be developed, to manage and

coordinate the energy interchange between the

system components. Both topics will be the subject

of future research.

Acknowledgement:

The authors express their gratitude to UNLP,

CONICET, CIC, and ANPCyT, since without the

support of these institutions, this work would not

have been possible.

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Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

Marcelo G. Cendoya has conducted the research on

the semi-Kaplan turbine, focusing on its design

parameters and sizing for the studied application. He

has developed the system model and has carried out

the computer simulation. He has participated in the

conception of the system topology. He has

collaborated with the writing and revision of the

manuscript.

Santiago Verne has conducted the research on

irrigation systems and on EVT devices. He has

participated in the conception of the system

topology. He has collaborated in the system

analysis. He did the writing of the manuscript and

its editing. He has made the figures.

Pedro E. Battaiotto has collaborated in the

conception of the system topology and the analysis

of the EVT operation inside the system. He has

carried out the revision and correction of the

manuscript.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

UNLP Proyecto 11/I255 “Electrónica de Potencia y

Sistemas de Control Avanzado Aplicados a Fuentes

de Energía Alternativas”. 1/2020 - 12/2023.

CONICET PIP 112-2020-0102801CO “Control

Avanzado y Electrónica de Potencia Aplicados a la

Optimización de Sistemas Basados en Energías No

Convencionales”. 12/2021 – 12/2024.

ANPCyT PICT N°2018-03747 “Control,

Electrónica e Instrumentación: Aplicaciones en

Energías Alternativas e Ingeniería Biomédica”.

11/2019 – 11/2022.

Conflict of Interest

The authors have no conflicts of interest to declare

that are relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

_US.

International Journal of Electrical Engineering and Computer Science

DOI: 10.37394/232027.2023.5.4

Marcelo G. Cendoya,

Santiago A. Verne, Pedro E. Battaiotto

E-ISSN: 2769-2507

Volume 5, 2023