Energy Recovery in Water Distribution Systems by a Pump ...

Energy Recovery in Water Distribution Systems by a Pump

Running as Turbine (PAT) – Grid Isolated Case

Bernardo Tomás Ribeiro de Brito Capelo

Thesis to obtain the Master of Science Degree in

Electrical and Computer Engineering

Supervisors: Prof. Paulo José da Costa Branco

Prof. Helena Margarida Ramos

Examination Committee

Chairperson: Prof. Rui Manuel Gameiro de Castro

Supervisors: Prof. Paulo José da Costa Branco

Members of Committee: Prof. Petra Amparo López Jiménez

May 2017

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Acknowledgements

The accomplishment of this work would not have been possible without the help of a few people. First,

I would like to thank my supervisors, Prof. Paulo José da Costa Branco and Prof. Helena Margarida

Ramos, for their guidance and encouragement. I would like to thank Eng. Modesto Pérez Sánchez, for

his help and guidance through this project. In addition, I would like to thank to my family and girlfriend,

for constant support and motivation. Finally, I want to thank my group of colleagues and friends, for the

companionship and motivation during the difficult times.

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Abstract

The optimization of Water Distribution Systems (WDS) was the objective of many studies over the past

years. The reduction of the excessive water pressure in some nodes of a Water Distribution Network

(WDN), to reduce the water leakages, has been some of the main motivations of the studies of WDS.

Adding the high costs related to water pumping, the study changed from pressure reduction to combine

energy recovery and pressure reduction. Large efforts were made in this topic for the last years, and a

viable solution seems to be the use of Pump as Turbine (PAT), providing both the pressure control and

energy savings.

In this context, this work aims the analysis of the application of Pump as Turbine isolated from the grid.

A hydraulic pump is usually assembled with a squirrel cage induction generator, due to its low cost and

simplicity. Therefore, working as a PAT, the induction machine needs an external source of reactive

power. In this work, the proposed solution is the use of a bank of capacitors across the stator phases.

This induction machine application is named self-excited induction generator (SEIG). Both simulation

and experimental work is performed, in order to analyse the SEIG behaviour. The obtained results show

that this application can be an interesting solution for combining water pressure reduction with energy

generation, although for the specific system SEIG + PAT tested in laboratory, the global efficiencies

obtained were lower than expected, and so, an optimization of the system needs to be performed.

Keywords

Self-Excited Induction Generator (SEIG), Pump as Turbine (PAT), Water Distribution Networks (WDNs)

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Resumo

A otimização de sistemas de distribuição de águas tem sido objetivo de muitos estudos nos últimos

anos. A redução do excesso de pressão em alguns nós de uma rede de distribuição de águas,

permitindo a redução de perdas de água, é uma das principais motivações destes estudos. Adicionando

os elevados custos relacionados com o bombeamento de água, novos estudos têm-se focado na

combinação da redução de pressão e recuperação de energia. Grandes esforços foram feitos neste

tema nos últimos anos, e uma possível solução viável é a utilização da bomba a funcionar como turbina

(PAT), permitindo tanto o controlo de pressão como recuperação de energia.

Neste contexto, este trabalho tem como foco a análise da aplicação da PAT isolada da rede. Uma

bomba hidráulica é normalmente usada com uma máquina de indução com rotor em gaiola, devido à

sua simplicidade e baixo custo. Funcionando como gerador, a máquina de indução requer de uma fonte

externa de reativa. Neste trabalho, a solução proposta consiste em colocar um banco de

condensadores ligado às fases do gerador. Esta aplicação, gerador isolado, tem o nome de gerador de

indução autoexcitado (SEIG). De forma a analisar o comportamento de um SEIG aplicado a um sistema

PAT, foi realizado trabalho de simulação e experimental. Os resultados obtidos demonstram que esta

aplicação é uma solução interessante na combinação da redução dos excessos de pressão e geração

de energia. Ainda assim, para o caso do sistema testado experimentalmente em laboratório, o

rendimento global obtido apresenta valores inferiores ao esperado sendo, por isso, necessário a

realização de uma otimização do sistema.

Palavras-chave

Bomba como Turbina, Gerador de Indução Autoexcitado, Redes de Distribuição de Água

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Table of Contents

Acknowledgements ................................................................................................................................. iii

Abstract … ................................................................................................................................................v

Resumo .. ............................................................................................................................................... vii

Table of Contents .................................................................................................................................... ix

List of Figures .......................................................................................................................................... xi

List of Tables ......................................................................................................................................... xiii

List of Acronyms ..................................................................................................................................... xv

List of Symbols ..................................................................................................................................... xvii

1. Introduction ............................................................................................................................ 1

1.1. Objectives ................................................................................................................................ 2

1.2. Thesis Structure ....................................................................................................................... 3

2. State of Art: Review on Pump as Turbine (PAT) ................................................................. 5

2.1. PAT Regulation Designs .......................................................................................................... 6

2.1.1. Hydraulic Regulation ............................................................................................. 8

2.1.2. Electrical Regulation .............................................................................................. 8

2.1.3. Other Design Combinations .................................................................................. 8

2.2. Variable Operating Strategy (VOS) .......................................................................................... 9

2.2.1. VOS for Hydraulic Regulation .............................................................................. 10

2.2.2. VOS for Electrical Regulation .............................................................................. 13

2.2.3. Comparison of Results ........................................................................................ 16

2.3. System Effectiveness ............................................................................................................. 16

2.4. Economic Analysis ................................................................................................................. 18

2.4.1. VOS Economic Feasibility ................................................................................... 18

2.4.2. Optimal Management of Leakage Reduction and Energy Recovery .................. 20

2.5. Conclusions ............................................................................................................................ 21

3. Self – Excited Induction Generator .................................................................................... 23

3.1. Proposed System ................................................................................................................... 25

3.2. Simulation – Analytical and Computational Models ............................................................... 26

3.2.1. Analytical Model................................................................................................... 26

3.2.2. Computational Model ........................................................................................... 30

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3.3. Experimental Setup ................................................................................................................ 31

3.3.1. Induction Machine – characteristic parameters determination ............................ 33

3.3.2. DC Motor characteristic equations and its electric efficiency .............................. 36

3.4. Model Application: Analytical and Computational Simulation ................................................ 38

3.4.1. Analytical analysis – capacitance determination ................................................. 38

3.4.2. Dynamic analysis - computational model ............................................................ 42

3.4.3. Analysis of Simulations Results ........................................................................... 46

3.5. Experimental Work ................................................................................................................. 47

3.5.1. Tests and Results ................................................................................................ 47

3.6. Analysis and validation of simulation methods ...................................................................... 52

3.6.1. Comparison of required capacitances ................................................................. 52

3.6.2. Comparison of generator performances .............................................................. 55

3.7. Conclusions ............................................................................................................................ 57

4. SEIG application to a hydraulic PAT system .................................................................... 59

4.1. Experimental Setup ................................................................................................................ 59

4.2. Steady state operation: experimental tests and results ......................................................... 60

4.2.1. Analysis of the required capacitances and system behaviour ............................ 61

4.2.2. Global efficiency curves of the system ................................................................ 64

4.2.3. Hydraulic Q-H curve of PAT ................................................................................ 66

4.3. PAT – hydraulic efficiency curves .......................................................................................... 67

4.4. Analysis of transient state operation ...................................................................................... 68

4.5. Conclusions ............................................................................................................................ 75

5. Conclusions and Future Work ............................................................................................ 77

5.1. Conclusions ............................................................................................................................ 77

5.2. Future Work ........................................................................................................................... 78

Bibliography ......................................................................................................................................... 79

Apendix ................................................................................................................................................ A1

A. Equipment used in experimental applications ....................................................................... A1

B. Datasheet of the Induction Machine used in experimental and simulation analysis ............. A3

C. Tables with Experimental results of SEIG application ........................................................... A4

D. Tables with Experimental results of PAT application ............................................................. A8

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List of Figures

Figure 1.1 – Illustrative scheme of the project in which this work is inserted. …………………………… 2

Figure 1.2 – Illustrative scheme of the case study of this work. …………………………………………... 3

Figure 2.1 – Characteristic curves for pump and turbine operating modes [7] …………………….……. 5

Figure 2.2 – Illustrative scheme of hydraulic and electrical regulation modes, adapted from [10] ...….. 7

Figure 2.3 – Scheme of PAT operating conditions for ER (right) and HR (left) [10] ..…………………... 7

Figure 2.4 – Daily Pattern from a PRV station [9] .………………………………………………………….. 9

Figure 2.5 – Working conditions of the PAT [9] ..…………………………………………………..………. 10

Figure 2.6 – Efficiency variation as function of BP, for different machines with HR mode [10] .…….. 12

Figure 2.7 – Regulation region and operating points for ER mode (BP = 22 m and D = 210 mm) [10]….13

Figure 2.8 – Efficiency variability of different machines, with different impeller diameter [10] .......…... 14

Figure 2.9 – Modified solution for the efficiency variability, with ER mode [10] ...…………………….... 15

Figure 3.1 – Illustrative image of both types of induction machines [19] ...……………………………… 22

Figure 3.2 – Equivalent circuit of an induction machine, adapted from [20] ...………………………….. 22

Figure 3.3 – Simplified equivalent of an induction machine, adapted from [20] .……………………..… 23

Figure 3.4 – Illustrative scheme of a IG system, grid connected [21] .…………………………………... 23

Figure 3.5 – Illustrative scheme of the self-excited induction generator system [21] ..……………….... 24

Figure 3.6 – Equivalent circuit of a Self-Excited induction generator, adapted from [27] .……..……… 25

Figure 3.7 – Equivalent circuit of SEIG with changes of (3.1) and (3.2) .………………………………... 26

Figure 3.8 – Simplified equivalent circuit of SEIG .………………………………………………………… 27

Figure 3.9 – Scheme of experimental installation used for the tests .……………………………………. 31

Figure 3.10 – Assemble Workbench for experimental tests .……………………………………………... 32

Figure 3.11 – No-load equivalent circuit of induction machine [30] .……………………………………... 33

Figure 3.12 – Equivalent circuit of an induction machine for blocked rotor case, adapted from [30] … 35

Figure 3.13 – DC Motor’s equivalent circuit, separate excitation case [31] .……………………………. 36

Figure 3.14 – Curve of Rotational Losses of the DC Motor .…………………………………………….... 38

Figure 3.15 – Description of the variation of bank’s capacitances with rotational speed, for specific

resistive loads .………………………………………………………………………………………………… 39

Figure 3.16 – Variation of the Capacitance as function of rotational speed, for different values of load

inductance – for a constant R = 230Ω .………………...………………………………………………..…... 41

Figure 3.17 – Illustrative scheme of the tests sequence of the simulation .……………………………... 42

Figure 3.18 – Simulation results of capacitance variation with rotational speed, for each load .……… 43

Figure 3.19 – Simulation results of SEIG efficiency curves .……………………………………………… 44

Figure 3.20 – Curve of capacitances that maximize efficiency, as function of the resistive load .….… 45

Figure 3.21 – Illustration of the sequence of the tests performed .………………………………………. 47

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Figure 3.22 – Experimental results of capacitance required as function of rotational speed of generator,

for constant values of load .………………………………………………………………...…………………. 48

Figure 3.23 – Graphic of the SEIG Efficiency variation as function of rotational speed, for constant

load values ...……………………………………………………………………………………….………….. 49

Figure 3.24 – SEIG efficiency curve – average of most curves expressed in figure 3.23 …………….. 49

Figure 3.25 – Graphic of minimum capacitance in function of load .………..…………………………… 51

Figure 3.26 – Illustration of the comparison between the simulated and experimental results, for a

specific load of R = 230 Ω .…………………………………………………………...……………………….. 53

Figure 3.27 – Illustration of the minimum loads able to be handled by the generator, both experimental

and simulation cases .……………………………………………………………………………………….… 54

Figure 3.28 – Comparison between experimental and simulation efficiency variations, for

R = 230Ω …..…………………………………………………………………………………………………… 55

Figure 3.29 – Capacitance variation as function of load value – simulation and experimental comparison

– that maximizes the efficiency …………………………………………....…………………………………. 56

Figure 4.1 – Photos of the Installation assembled in Hydraulic Laboratory .…………………………..... 59

Figure 4.2 – Illustrative Scheme of the generating system .………………………………………………. 60

Figure 4.3 – Illustrative scheme of the hydraulic system assembled, adapted from [33] .…………….. 60

Figure 4.4 – Illustration of the sequence of the tests performed .………………………………………… 61

Figure 4.5 – Illustrative variation of the capacitance required as function of the rotational speed, for a steady flow regime …………………..……………………………..………………………………...……….. 62

Figure 4.6 – Global efficiency variations as function of the bank capacitances, for a constant flow

regime .…………………………………………………………………………………………………………. 62

Figure 4.7 – Curve of capacitances associated with the maximum global efficiency, as function of the

load values .……………………………………………………………………………………………………. 64

Figure 4.8 – Illustration of the sequence of tests performed with PAT .…………………………………. 64

Figure 4.9 – Illustration of the global efficiency curves as function of flow .…………………………….. 65

Figure 4.10 – Hydraulic Head/Flow Curves of the PAT .…………………………………………………... 66

Figure 4.11 – Illustration of the resultant PAT efficiency curves, as function of flow .………………….. 68

Figure 4.12 – Illustration of the hydraulic transient behaviour, pressure variation – close and open valve

cases – for N = 1560rpm .……………………………………………………………………………………... 69

Figure 4.13 – Illustration of the electrical transient phenomenon for N = 1560 rpm (R = 230Ω and

C = 15 µF) – close valve case .………………………………………………………………………………. 70


C = 15 µF) – open valve case ….…………………………………………………………………………….. 71


C = 35 µF) – open valve case ………………………………………………………………………………... 73

Figure 4.16 – Simulink simulation results, of the generator excitation phenomenon, for the same load

and prime mover power input, with different capacitance values .………………………………………... 74

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List of Tables

Table 2.1 – Possible combinations of PAT regulation modes, adapted from [12]. …………………...…. 8

Table 2.2 – VOS results for Hydraulic Regulation [10]. .…………………………………………………... 12

Table 2.3 – VOS results for ER mode [10]. ….………………………………………….………………….. 15

Table 2.4 – Comparison between HR and ER – variation of BP influence on efficiency [10]. ……….. 16

Table 2.5 – VOS results for HR mode [11]. ….……………………………………………………………... 17

Table 2.6 – VOS results for ER mode [11]. …….…………………………………………………………... 18

Table 2.7 – Assessment of economic viability for both HR and ER modes, adapted from [10]. ….….. 19

Table 3.1 – Nameplate Information of both machines. ……………………………………………………. 31

Table 3.2 – Tested ranges of the resistive load and capacitances. …………………………………………... 33

Table 3.3 – Induction motor test results for no-load case. ………………………………………………… 34

Table 3.4 – Induction motor blocked rotor test results. ……………………………………………………. 35

Table 3.5 – Characteristic parameters of the induction machine in study. ……………………………… 36

Table 3.6 – Capacitance determination data results of figure 3.16. ……………………………………… 40

Table 3.7 – Limit reactance value associated to each different resistive value. ………………………... 41

Table 3.8 – Best efficiency points of the SEIG simulated results. ………………………………………... 45

Table 3.9 – Maximum efficiency points, for each tested load. ……………………………………………. 50

Table 3.10 – Comparison between obtained capacitance results for a specific load, R = 230 Ω. ….… 52

Table 3.11 – Comparison of results for the lower possible loads. ……………………………………….. 54

Table 4.1 – Synthetization of the Results .…………………………………………………………………... 63

Table 4.2 – Combinations of load and capacitance used to achieve the N values for the tests below

…………………………………………………………………………………………………………………… 65

Table 4.3 – Combinations of load and capacitance used to achieve the N for the tests below, with

correspondent 𝜂𝑒𝑙 .…………………………………………………………………………………………….. 67

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List of Acronyms

AC Alternating Current

BEP Best Efficiency Point

CFD Computational Fluid Dynamics

DC Direct Current

ER Electrical Regulation

HR Hydraulic Regulation

IG Induction Generator

PAT Pump running as Turbine / Pump as Turbine

PRV Pressure Reducing Valve

SEIG Self-Excited Induction Generator

VOS Variable Operating Strategy

WDN Water Distribution Network

WDS Water Distribution System

WTS Water Transmission System

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List of Symbols

A Amp

𝑎 Stator frequency in values per unit

𝑏 Rotational speed in values per unit

𝐶 Capacitance value of the excitation system of the SEIG

𝑓 Induction generator actual stator frequency [Hz]

𝑓𝑠 Grid frequency [Hz]

F Farad

𝑔 Gravitational acceleration [m/s2]

𝐻𝑖 Available head drop [mwc]

Hz Hertz

𝐼0 Phase current for no load condition

𝐼𝑎 DC motor armature current

𝐼𝑐𝑐 Phase current for short-circuit / blocked rotor case

𝐼𝑓 DC motor field current

𝐼𝑚 Magnetizing current

𝐼𝑟′ Rotor current

𝐼𝑠 Stator phase current

𝐿𝐿 Load inductance

𝐿𝑚 Magnetizing inductance

𝐿𝑟 Rotor inductance

𝐿𝑠 Stator inductance

𝑁 Rotational speed of the induction machine [rpm]

𝑁1 Number of stator windings

𝑁2 Number of rotor windings

𝑁𝑠 Synchronous frequency [rpm]

𝑝 Number of pole pairs of the induction machine

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𝑃0 No load active power

𝑃𝑐𝑐 Short-circuit active power

𝑃ℎ𝑦𝑑 Hydraulic power available

𝑃𝐼𝑁 Total power at the entrance of the DC motor

𝑃𝑙𝑜𝑠𝑠 DC motor total losses

𝑃𝑚𝑒𝑐 Mechanical power

𝑃𝑂𝑈𝑇 DC motor mechanical output power

𝑃𝑟𝑜𝑡_𝑙𝑜𝑠𝑠 DC motor rotational losses

𝑃𝑠 Active power of the induction machine

𝑝𝑓 ≡ cos𝜑

Power factor

𝑄0 No load reactive power

𝑄𝑐𝑐 Short-circuit / blocked rotor reactive power

𝑄𝑖 Available flow discharge [l/s]

𝑄𝑠 Induction machine stator reactive power

𝑅𝐶 Induction machine magnetizing resistance, represents the core losses

𝑅𝑒 Resistance value of two stator phase of the induction machine

𝑅𝐿 Load resistance

𝑅𝑟′ Induction machine rotor resistance

𝑅𝑠 Induction machine stator resistance

𝑠 Slip

𝑆0 No load apparent power of the induction machine

𝑆𝑐𝑐 Short-circuit apparent power of the induction machine

𝑈𝑎 DC motor armature voltage

𝑈𝑓 DC motor field voltage

V Volt

𝑉0 Induction machine no load phase voltage

𝑉𝑐𝑐 Induction machine short-circuit phase voltage

𝑉𝑠 ≡ 𝑉𝑡 Induction machine phase voltage

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𝑋𝑐 Capacitor Reactance

𝑋𝐿 Load inductive reactance

𝑋𝑟′ Induction machine rotor reactance

𝑋𝑠 Induction machine stator leakage reactance

𝑌𝐶 Admittance of the bank of capacitors

𝑌𝑖𝑛 Induction machine equivalent admittance

𝑌𝐿 Load admittance

𝑌𝑟 Equivalent admittance of rotor and magnetizing branch

𝑌𝑠 Stator equivalent admittance

𝑌𝑡 Total equivalent admittance of the SEIG

𝜔 Angular frequency of the machine [rad/s]

𝜔𝑟 Rotational speed of the rotor [rad/s]

𝜔𝑠 Synchronous frequency [rad/s]

𝜂𝑒𝑙_𝑠𝑖𝑚 SEIG electrical efficiency – Simulink simulation

𝜂𝑒𝑙 SEIG electrical efficiency

𝜂𝑃𝐴𝑇 PAT efficiency

𝜂𝑔𝑙𝑜𝑏𝑎𝑙 Global efficiency of the system

𝜌 Water Density [kg/m3]

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1

1. Introduction

The awareness of the depletion of natural resources and concern with the global environment has forced

a boost on the development of environmental friendly methods of energy generation. In this context,

investments were made in many renewable energy sources with small environmental impact, including

in hydroelectric power generation. Within the hydroelectric power generation, being one of the most

mature renewable energy sources, there has been an interesting increase in the small-scale and micro-

hydro power sources studies.

In some contexts, such as the case of rural and remote areas, the installation of micro-hydro power

source able to generate and store energy is a good alternative, however in certain cases it revealed

some problems related with costs, due to the need to miniaturize the turbine. With this constraint in

mind, a proposed solution was the use of a pump running in turbine mode (PAT), which represents a

high reduction in the implementation costs. Although it may not be as efficient alternative as a hydro-

turbine, it is considered to be an efficient method of generating energy, having some advantages such

as a simple construction and durability. The use of PAT is also considered a good and economic

approach, in locations where the water supply is relatively constant, such as water transmission systems

(WTS). Pump Manufacturers, in particular KSB, have been active investors in PAT for the past years.

The idea of using Pump running as Turbine is not exactly recent. During the 20st century, researchers

such as Stepanoff [1], Knapp [2], that in 1941 published the complete pump characteristics for a few

pump designs based on experimental investigations, and Kittredge [3], that in 1961 published a study

on centrifugal pumps used as hydraulic turbines (having an advantage, which is the initial cost

reduction), studied the work characteristics of a PAT. However, at that time there was still a lack of

technology to allow a proper use of PAT. Only in recent years, with the advances of technology, the

appearance of converters, sensors and so on, it allowed a completely new kind of control and use of

PAT.

The aim of this work is related to an idea for a new application for PAT that has recently emerged and

consists of using it to generate energy in water distribution systems (WDS). The existence of specific

locations in a water distribution network (WDN) where due to high water pressures, there is an increase

in water leakages and can cause serious damages in the pipes, lead to studies with the objective of

reducing the leakages. Currently, a solution for that consists of installing pressure-reducing valves

(PRVs) [4]–[6], reducing the water pressure and leakages, and so preventing investments in

rehabilitation of the pipelines. Therefore, the use of PRVs has been increasing over the last years. By

changing the PRV for hydropower devices, such as PATs, could be an interesting investment, and could

lead to large energy savings. The number of studies in this area has increased over the last few years,

with new ideas for using and controlling PATs in order to achieve the best performances and recover

higher amounts of energy.

Herein, a new approach for PAT application was proposed, more specifically, the application of PAT to

WDSs, with system isolated from the electrical grid.

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1.1. Objectives

This work is part of a project that aims to install a PAT in a PRV station, located in a water distribution

network. Figure 1.1 shows an illustrative scheme of the global project. The project is divided into three

different partial projects. The work performed in this thesis represents the partial project 1.

Figure 1.1 – Illustrative scheme of the project in which this work is inserted.

Usually, a hydraulic pump is assembled with an induction machine. An induction machine, to work,

needs a constant source of reactive power. As a generator connected to the electrical grid, the source

of reactive power is the grid itself. However, when the PAT system is isolated, the induction generator

needs another source of reactive power to be able to work.

A proposed solution consists of installing a bank of capacitors across the phases of the machine, as

shows figure 1.2, in order to provide the reactive power required to the induction generator.

3

The objectives of this thesis can be divided into the following topics:

1. Complete study of the induction generator isolated from the grid;

2. Propose a solution system (figure 1.2);

3. Develop analytical and computational simulation models of the proposed system, and then an

experimental work in laboratory, with induction generator isolated from the grid, to analyse and

verify the work of the system;

4. Experimental work with the proposed solution applied to a hydraulic PAT system. The

experiment consists of assembling a hydraulic circuit and analyse the behaviour of the isolated

PAT + Induction Generator.

Figure 1.2 – Illustrative scheme of the case study of this work.

1.2. Thesis Structure

This thesis is divided into five chapters, described as follows:

- In Chapter 1 is provided an introduction and overview of the work;

- In Chapter 2 is done a brief review of the state of the art related to the use of PAT in WDS,

focusing on the latest works;

- In Chapter 3 is performed a complete study of the Isolated Induction Generator, named the Self-

Excited Induction Generator (SEIG), with both simulation and experimental work;

- In Chapter 4, a pilot hydraulic installation is assembled, in order to perform an experimental

study of a PAT + Induction Generator system, isolated from the grid, for both steady and

transient state operations;

- In Chapter 5, some general conclusions of the performed work are given, and also some

comments on the future work in this theme are made.

4

5

2. State of Art: Review on Pump as Turbine (PAT)

In water supply systems, two types of machine can be used for energy generation, turbines of pumps

working as turbines (PATs). The traditional turbines provide better performances, as they are designed

for that specific application, however they present an expensive investment. Pumps are a more

economic solution, as they can be bought from the market, cheaper than turbines.

Figure 2.1 shows the characteristic curves of an example of centrifugal pump, working in pump operation

and turbine operation.

Figure 2.1 - Characteristic curves for pump and turbine operating modes [7].

The highlighted head and flow points represent the pump best efficiency points, both for pump and

turbine operations, BEP. Besides the head/flow curves, the efficiency (η) and power (P) curves, as

function of flow, are plotted in the figure, for a constant rotational speed.

In water transmission systems, pressure-reducing valves are installed in order to reduce the large

variations and dissipate residual head, therefore the power available is relatively constant, allowing the

use of traditional hydropower devices. In those cases, the use of PAT can be an efficient form of power

generation. In WDSs, the case is completely different, the necessity to fulfil the user demand is the most

important objective. In these systems, there are big variations of demand. Therefore, when designing a

water distribution network, flexibility to provide water for various demands is the main objective. With

this, problems started to emerge. The excessive pressure in some parts of the network can cause pipe

damages, increasing the water leakages. Besides this, another problem is related to the large amount

of energy spent in WDS. Energy consumption is about 80% of the total expenses in water distribution

[8]. The transportation of water to higher levels, done by using pumps, usually represents the

predominant component of the total operating cost of the system. Studies in this topic were done and,

in order to avoid expensive investments in pipes replacement in urban distribution networks, a

suggested solution was by placing PRVs. The valves provided a partial reduction of water losses, by

6

reducing the pressure. This solution has proven to be effective in the reduction of water losses and

pressure control and so, the use of PRVs in water distribution systems has increased significantly.

Over the last years, studies were performed in order to replace the PRVs with small hydropower devices

to generate energy, in order to reduce the energy costs related with the WDSs. Adding this to the existent

problem of water leakages emerged the idea of using PAT. As it was already stated, PAT is considered

a cheap and sustainable solution. However nowadays there is still a lack of information related to PATs

behaviour, which can be a setback.

An important issue when analysing the economical convenience of this application of PAT is the power

available in the specific node of the WDN chosen to install the PAT. In WDSs, unlike the WTSs, the flow

rate and head drop present high variations depending on the user demands, and so the available

hydraulic power changes.

Ramos, Carravetta, Fecarotta and Giudice [9]–[12] described some design strategies for application of

PAT in WDS. Two main regulation designs were proposed, named Hydraulic Regulation [9] and

Electrical Regulation [10], both considered viable solutions. Recent studies also analysed some

combinations of both [12].

Furthermore in this chapter, a brief description of two design procedures proposed is performed, named

Variable Operating Strategy (VOS) [9], [10] and System Effectiveness [11]. The VOS design procedure

is a method to predict the PAT behaviour and find the optimal solution that maximizes the efficiency for

specific working conditions. However, this design does not have into account that the application of a

PAT in WDS means that the system will operate far from the best efficiency points, due to the high

variability in the working conditions (flow and pressure), and so it will cause a decrease in the reliability

of the system. Therefore, to take into account these important factors, System Effectiveness design was

proposed.

2.1. PAT Regulation Designs

An important aspect of this topic is the study of different ways to operate the PAT, in order to achieve

the best efficiencies and generate higher quantities of energy. The efficiency curve of a PAT, as function

of the flow discharge, presents a point of maximum efficiency (QBT, HB

T), named the best efficiency point

(BEP). In a WDN, the working conditions usually achieve values very far from the BEP of the PAT, so

an important objective was to find and study regulation designs that could adapt according with the

operating region, by changing PAT characteristic curves or the working conditions, in order to achieve

better performances. Here, a brief analysis of the different proposed regulation modes is performed,

focusing on the main designs.

An illustrative scheme of a hydropower plant installation is shown in figure 2.2, below. In the scheme

are represented both main regulation designs, electrical and hydraulic. In figure 2.3 are represented the

PAT operating conditions for both regulations.

7

Figure 2.2 – Illustrative scheme of hydraulic and electrical regulation modes, adapted from [10].

Figure 2.3 – Scheme of PAT operating conditions for ER (right) and HR (left) [10].

8

2.1.1. Hydraulic Regulation

As shows figure 2.2, this regulation mode consists of a PAT connected to the grid, with a series/parallel

set of hydraulic valves to help control and adjust the working conditions to a suitable area. The work of

the valves can be described into two different procedures:

1. In case the available head (𝐻𝑖) is higher than the head-drop deliverable by the machine (𝐻𝑖𝑇),

described by the points to the left side of the PAT characteristic curve (figure 2.3 – left), the

valve A will dissipate the excess pressure.

2. In case the flow (𝑄𝑖) is higher, given by the points to the right side of the PAT characteristic

curve, the PAT will produce a head-drop higher than the available head, then the valve B will

open in order to reduce the flow 𝑄𝑖.

2.1.2. Electrical Regulation

This design, instead of valves, consists of installing a regenerative converter between the PAT and the

grid. As shows the characteristic curves of figure 2.3 (right), the idea of this regulation mode, using the

converter, is to change the frequency of the PAT, and so, change its rotational speed to match the load

conditions that are determined by the instant flow discharge and head drop values. Basically, by

changing the rotational speed, the PAT characteristic curve changes, in order to match the required

values of the hydraulic parameters (𝑄𝑖 , 𝐻𝑖).

2.1.3. Other Design Combinations

Besides the two main modes of regulation already described, other possible combinations of both can

be assembled. From the scheme of figure 2.2, table 2.1 presents the other combinations using both the

inverter and one or two valves.

Table 2.1 – Possible combinations of PAT regulation modes, adapted from [12].

Device Case I (HR) Case II (ER) Case III Case IV Case V

Inverter No Yes Yes Yes Yes

Valve A Yes No No Yes Yes

Valve B Yes No Yes No Yes

Analysing all the regulation modes above proposed, cases III – V represent different combinations of

ER and HR.

9

2.2. Variable Operating Strategy (VOS)

This model was proposed with the purpose of analysing the working conditions, the operating region of

a specific case, and help estimate the best PAT solution for that case. The VOS analysis was proposed

for both electrical and hydraulic regulations, comparing the obtained results for both types of PAT

application.

For the study, a daily demand pattern measured from a PRV station located in Pompeii, Italy, was

considered, as shows figure 2.4, containing the variations of flow rate (𝑄) and upstream pressure head

(𝑃𝐻). The value of head drop (𝐻) depends on the minimum pressure required to ensure a correct

pressure distribution through all pipes, named backpressure (𝐵𝑃), and it is given by equation (2.1). In

figure 2.4 is also shown the variation of available hydraulic power (𝑃).

𝐻 = 𝑃𝐻 − 𝐵𝑃 (2.1)

Figure 2.4 - Daily Pattern from a PRV station [9].

For this range of power, the installation of a turbine can be a problem due to its high costs because of

miniaturization of the regulation devices of the turbine. Therefore, the reduction of both manufacturer

and maintenance costs can be achieved by using a PAT instead of traditional turbine. This strategy,

VOS, allows to obtain the optimal PAT solution for each case (𝑄 − 𝐻 and 𝐵𝑃 required), choosing the

best PAT characteristics, impeller diameter and rotational speed.

When designing a hydropower plant in a WDN, there are two main problems: the lack of complete series

of characteristic curves for industrial PAT, and the absence of a strategy for turbine selection and overall

efficiency computation.

Therefore, to determine both characteristic and efficiency curves of a PAT, three different possible ways

were proposed: experimentally [13], by computational fluid dynamics (CFD) [14] and by one-dimensional

10

methods [1]. The most reliable is the experimental analysis, but it requires a huge number of

experimental tests. Therefore, simulation by CFD could be considered a valid alternative. After

determining the characteristic curve of a specific PAT, the results could be extended to any PAT of the

same type (e.g. centrifugal, semi axial,…), similar to the reference PAT (different diameter and rotational

speed), using the Suter parameters [15]. Two different PATs, of the same type, are considered similar

if they have the same specific speed, either turbine (𝑁𝑆𝑇) or pump (𝑁𝑆

𝑃).

𝑁𝑆𝑇 = 𝑁𝐵

𝑇 𝑃𝐵𝑇12

𝐻𝐵𝑇43

𝑁𝑆𝑃 = 𝑁𝐵

𝑃 𝑄𝐵𝑃12

𝐻𝐵𝑃34

(2.2)

The parameters of equation (2.2) are at the best efficiency point (BEP), and are the rotational speed

(𝑁𝐵), flow rate (𝑄𝐵), head drop (𝐻𝐵) and power (𝑃𝐵), for both turbine and pump operating modes.

2.2.1. VOS for Hydraulic Regulation

The working conditions shown in figure 2.4 are expressed below, as function of discharge and head

drop, in figure 2.5.

Figure 2.5 – Working conditions of the PAT [9].

Also, in the figure above is shown the characteristic curve of a PAT example. The area filled by the

working points is named the operating region, as shown.

The proposed model, VOS, was characterized by the following steps:

1. measured pattern of discharge and pressure conditions and the available head is determined

based on the required value of BP;

2. consider a type of PAT (centrifugal, axial…);

3. consider a set of different PAT characteristic curves for the operating region;

11

4. computation of the overall plant efficiency, using the equation below,

𝜂𝑝 =∑ 𝐻𝑖

𝑇𝑄𝑖𝑇𝜂𝑖

𝑇Δ𝑡𝑖𝑛𝑖=1

∑ 𝐻𝑖𝑄𝑖Δ𝑡𝑖𝑛𝑖=1

(2.3)

𝜂𝑝 - Overall plant efficiency; 𝑛 - number of available operating points; 𝐻𝑖𝑇 and 𝑄𝑖

𝑇 - head drop

and discharge delivered by the PAT; 𝜂𝑖𝑇 - PAT efficiency; 𝐻𝑖 and 𝑄𝑖 – available head drop and

discharge; Δ𝑡𝑖 – time interval discretization of the operating points;

5. the PAT that maximizes the overall efficiency is considered the optimal design solution;

6. optimal machine selected from the market, and then the actual efficiency is verified.

However, as already referred before, to perform steps 3 and 4, a wide set of characteristic curves was

needed, with their BEPs characterized. This represented a problem due to the lack of data available to

technicians. Therefore, a proposed solution was using the affinity law [16], equation (2.4), where having

a reference estimated characteristic curve for a PAT (𝐼), allowed to estimate the curves for similar

machines (that verify condition of equation 2.2).

𝑁𝐵𝐼

𝑁𝐵𝐼𝐼 =

𝐷𝐼𝐼

𝐷𝐼(𝐻𝐵𝐼

𝐻𝐵𝐼𝐼)

1/2

= (𝑄𝐵𝐼𝐼

𝑄𝐵𝐼 )

1/2

(𝐻𝐵𝐼

𝐻𝐵𝐼𝐼)

3/4

= (𝑃𝐵𝐼𝐼

𝑃𝐵𝐼 )

1/2

(𝐻𝐵𝐼

𝐻𝐵𝐼𝐼)

5/4

(2.4)

Knowing the diameter, 𝐷𝐼𝐼 and rotational speed 𝑁𝐵𝐼𝐼 of the similar PAT, it was possible to estimate its

BEPs (𝑄𝐵𝐼𝐼, 𝐻𝐵

𝐼𝐼) and produced power (𝑃𝐵𝐼𝐼). This estimation can be used for any machine similar to the

reference machine.

The developed model was applied in two different cases [9], [10]. Here is described an application to a

centrifugal pump, single stage, with a specific speed 𝑁𝑆𝑇 = 44 [rpm, kW], in order to compare with the

Electrical Regulation application [10]. The data used for the application was from the measured pattern

of the PRV station in Pompeii, shown in figure 2.3.

As already said, the available head depended on the backpressure (𝐵𝑃) value. The 𝐵𝑃 is a design

parameter that depends on the downstream network characteristics, and different 𝐵𝑃 values will

produce different scenarios. The considered 𝐵𝑃 values were between 0 and 70 m, in order to include a

wide set of scenarios.

The results are expressed in table 2.2, applied for different impeller diameters 𝐷 [mm] and rotational

speeds 𝑁 [rpm]. Below, in figure 2.6, is shown the variation of efficiency as function of 𝐵𝑃 value of

different machines, for different rotational speeds, as well as for different diameters for the same 𝑁 =

3000 rpm.

For 𝑁 = 3000 rpm, the bold curve, 𝜂𝑝𝐻𝑅|𝑚𝑎𝑥, represented the maximum efficiency curves. For different

diameter machines, the intersection with maximum efficiency curve, i.e., 𝜂𝑝𝐻𝑅|𝑚𝑎𝑥 (𝐵𝑃) = 𝜂𝑝

𝐻𝑅|𝐷 (𝐵𝑃)

represented the points where the correspondent diameter, 𝐷, was the VOS solution.

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Table 2.2 – VOS results for Hydraulic Regulation [10].

BP [m] D [mm] N [rpm] ηpHR |max

10 186 3000 0.59

15 190 3000 0.59

20 191 3000 0.59

25 187 3000 0.56

30 181 3000 0.53

35 176 3000 0.48

40 208 3000 0.47

45 219 1500 0.51

50 232 1500 0.54

55 237 1500 0.55

60 221 1000 0.50

Figure 2.6 – Efficiency variation as function of BP, for different machines with HR mode [10].

13

2.2.2. VOS for Electrical Regulation

For ER mode, as already said, the application of the PAT consists of inserting a regenerative converter

between the machine and the electrical grid. The converter allows changing the frequency of the

machine, and so, the rotational speed will change too. The rotational speed can be determined by the

expression of equation (2.5), as function of the frequency 𝑓 [Hz] and number of pole pairs 𝑝.

𝑁 = 60𝑓

𝑝 (2.5)

For safety reasons, the frequency variation must be limited to a specific range of values. The upper limit

must not be higher than 60 Hz, which the maximum designed frequency. The lower limit should not be

lower than 50 % of the grid frequency, so 25 Hz.

Below, in figure 2.7, are expressed the working conditions for ER mode, for a specific machine with an

optimal diameter 𝐷 = 210 mm and a 𝐵𝑃 = 22 m. In the figure are expressed the characteristic curves

for different frequencies, representing the regulation region, as well as the operating points from the

data shown in figure 2.4. As it is possible to observe, the BEP line crossed all the characteristic curves

in their maximum efficiency points.

Figure 2.7 – Regulation region and operating points for ER mode (𝐵𝑃 = 22 m and 𝐷 = 210 mm) [10].

As shown in the figure above, the highest values of the net head correspond to the highest speeds, and

for higher flow-rates it is required a frequency reduction, in order to reduce the rotational speed.

For ER mode, the VOS was similar to the model developed for HR mode, but with some modifications.

In this model, there was only one design parameter, which was the impeller diameter. Then, for this

regulation mode, the VOS model was described by the following steps:

1. measured pattern of discharge and pressure conditions and the available head is determined

based on the required value of BP;

14

2. consider a type of PAT (centrifugal, axial…);

3. consider a set of different PAT characteristic curves for the operating region;

4. change, for each PAT selected, the rotational speed within the range limit;

5. computation of the overall plant efficiency, using the equation below,

𝜂𝑝𝐸𝑅 =

∑ 𝐻𝑖𝑄𝑖𝜂𝑖𝑇(𝑓)Δ𝑡𝑖

𝑛𝑖=1

∑ 𝐻𝑖𝑄𝑖Δ𝑡𝑖𝑛𝑖=1

(2.6)

𝑛 - number of available operating points; 𝜂𝑖𝑇 - PAT efficiency, dependent on the frequency, 𝑓;

𝐻𝑖 and 𝑄𝑖 – available head drop and discharge; Δ𝑡𝑖 – time interval;

6. the PAT that maximizes the overall efficiency is considered the optimal design solution;

7. near-optimal machine selected from the market, and then the actual efficiency is verified.

Just like already said for HR mode, due to the lack of characteristic and efficiency curves for a set of

PATs, a proposed solution was using the affinity law [16], equation (2.4), where having a reference

estimated characteristic curve for a PAT, allowed to estimate the curves for similar machines.

The application of this design procedure was done to the same centrifugal pump of HR mode (single

stage, 𝑁𝑆𝑇 = 44 [rpm, kW]). In order to compare with the HR results, this application was performed for

the same range of BP values. For each BP value, an optimal diameter was found.

Figure 2.8 shows the ER results, for different machines, as function the BP value. For example, for a

𝐵𝑃 = 22 m, as shown in figure 2.7, the diameter chosen should be 𝐷 = 210 mm, which provided the

higher efficiency of 57 %.

In addition, from figure 2.8, it is possible to observe that for BP values higher than 41 m, the electrical

regulation became impossible for the simulated machines, and so, the ER could not ensure the work for

all the BP values.

Figure 2.8 – Efficiency variability of different machines, with different impeller diameter [10].

15

To increase the elasticity of the ER system, a 𝛥 = 10 % variation of the BP was taken into account, i.e.,

for a specific BP value, for example 22 m, the chosen machine should be able to work between 19.8 m

and 26.4 m. In this specific case, the chosen machine would have an impeller diameter 𝐷 = 215 mm,

instead of the 𝐷 = 210 mm previously chosen. In addition, the new highest 𝐵𝑃 ensured was of 37 m,

and the new best efficiency was of 54.4 %, presenting an average decrease of efficiency of 16.3 %.

Below in figure 2.9 is plotted the same curve of figure 2.8, but considering the 𝛥 = 10 % variation for

every scenario.

Figure 2.9 – Modified solution for the efficiency variability, with ER mode [10].

The VOS results of the ER mode, for the different scenarios considered, are presented in table 2.3,

containing for each 𝐵𝑃 value, the best impeller diameter with the correspondent efficiency.

Table 2.3 – VOS results for ER mode [10].

BP [m] D [mm] ηpER |max

10 238 0.31

15 230 0.40

20 220 0.50

23 216 0.54

25 219 0.54

30 232 0.49

35 251 0.40

37 270 0.28

40 - -

16

2.2.3. Comparison of Results

Looking at both hydraulic and electrical regulation results, in tables 1 and 2, is it possible to observe that

the HR mode presented higher efficiencies for all the 𝐵𝑃 values, although 𝐵𝑃 between 23 m and 37 m

they showed similar efficiencies.

In ER mode, by changing the frequency, the characteristic curve could adjust to the operating point, as

shows figure 2.6. However, the operating point being in the characteristic curve was not enough, and in

some points, the operating point was too far from the BEP, then presenting a low hydraulic efficiency.

When talking about a WDN, the values measured should not be considered true. The parameter values

depend on the demand at each moment. Therefore, in table 2.4 are expressed the efficiency impact of

a 𝐵𝑃 variation, for the ER and HR results previously expressed. As it is possible to see, the HR usually

presented higher efficiency and higher flexibility than ER.

Table 2.4 – Comparison between HR and ER – variation of 𝐵𝑃 influence on efficiency [10].

% variation of ηpHR % variation of ηp

ER

BP [m] ηpHR - 10% BP + 10% BP ηp

ER - 10% BP + 10% BP

10 0.586 -0.485 0.387 0.305 -2.349 2.244

20 0.585 1.045 -1.492 0.502 -2.418 2.246

30 0.531 3.356 -5.285 0.488 -4.497 4.126

35 0.484 6.405 -12.791 0.403 -8.473 7.450

2.3. System Effectiveness

The Variable Operating Strategy (VOS), proposed by Carravetta et al [9], [10] and described above,

analysed the overall efficiency and flexibility of different PATs for different scenarios, choosing the

optimal solution for each one. However, this application is for a WDN, where there is a high variation of

the working conditions, forcing the PAT to work far from its BEP, decreasing its reliability.

Therefore, based on the VOS, another design strategy was proposed by Carravetta et al [11],

considering three different factors:

- Capability of the PAT performance;

- Flexibility of the PAT under small variation of the working conditions;

- Reliability of the PAT based on the lifecycle of its components.

The effectiveness of PAT is described by equation (2.7). The factors that compose the equation are the

17

system’s capability (𝜂𝑝), flexibility (𝜙p) and reliability (𝜇𝑃).

𝐸 = 𝜂𝑃𝜙𝑃𝜇𝑃 (2.7)

The effectiveness factors represent, respectively, if the performance of the PAT is according with

expectations, how is the performance for a 𝐵𝑃 variation around the design value and if it operates for a

given time without failing.

The three effectiveness indicators were analysed by Carravetta et al [11]. The effectiveness strategy

was applied for the same centrifugal pump used for the VOS model (single stage, 𝑁𝑆𝑇 = 44 [rpm, kW]),

both for HR and ER mode. Previously, the VOS model focused on the overall efficiency of the PAT, with

the objective of finding the optimal machine for specific work conditions (VOSη). Here, an application of

the system effectiveness was proposed (VOSE).

In tables 2.5 and 2.6 are shown the obtained results for both HR and ER modes.

Table 2.5 – VOS results for HR mode [11].

VOS BP [m] 10 20 30 35

VOSη

D [mm] 186 191 181 176

ηp 0.590 0.595 0.532 0.483

φp 0.997 0.984 0.952 0.893

µp 0.878 0.666 0.868 0.603

E 0.517 0.390 0.440 0.260

VOSE

D [mm] 179 178 171 163

ηp 0.567 0.549 0.499 0.439

φp 0.999 0.990 0.956 0.923

µp 0.933 0.976 0.985 0.971

E 0.529 0.531 0.471 0.394

Looking at table 2.6, it is possible to observe that, for VOSη, the ER mode was not flexible at all, problem

that was already discussed in the previous section 2.2.

Comparing the VOSη and VOSE, it is possible to see that the decrease of capability when applying the

effectiveness was very small. However, the results of the new procedure showed an 𝐸 in HR mode

better than ER mode for all considered 𝐵𝑃 values. The reason of this difference rely on the fact that both

capability and reliability presented lower values when compared to HR mode. On the other side, the

18

flexibility of both modes presented close values.

Table 2.6 – VOS results for ER mode [11].

VOS BP [m] 10 20 30 35

VOSη

D [mm] 237 216 222 234

ηp 0.313 0.527 0.549 0.513

φp 0.000 0.000 0.000 0.000

µp 0.704 0.914 0.917 0.899

E 0.000 0.000 0.000 0.000

VOSE

D [mm] 239 221 231 250

ηp 0.298 0.495 0.495 0.410

φp 0.977 0.976 0.957 0.924

µp 0.686 0.894 0.891 0.809

E 0.199 0.432 0.422 0.306

2.4. Economic Analysis

The study of the installation of PAT in WDN instead of PRVs, allowed the development of application

designs that maximize the overall efficiencies and produced energy for different scenarios.

Besides this, an effort was made to develop economic assessments for each regulation designs

proposed. Carravetta et al [10] performed an economic analysis of VOS for both HR and ER modes.

In addition, Tricarico et al [17], developed a novel methodology for WDS pressure management, to

accomplish both leakage reduction and minimization of the difference between annual pumping costs

and PAT income.

2.4.1. VOS Economic Feasibility

After the strategies and simulations above analysed, Carravetta et al [10] also performed an economic

assessment of both regulation modes (for VOS results of tables 2.2 and 2.3), for the different scenarios

presented in table 2.4.

19

The results are shown in table 2.7. The parameters included in the table are described below.

- PB – power of the machine at the BEP;

- Pmax – maximum output power of the generator;

- CPAT – PAT cost, considered to be 230 €/kW;

- Cgen – generator cost was evaluated on the Pmax on each scenario, considered to be 115 €/kW;

- Cvalve – cost of the hydraulic valves used in HR mode, considered to be 2500€ each;

- Cinve – cost of the inverter used in ER mode, dependent on the generator power, with a cost of

200 €/kW;

- ADEP – average daily energy production;

- PPeme – represents the payback period.

The value considered for the cost of produced energy was of 0.20 €/kWh. The costs of civil works and

maintenance of the equipment were not taken into account because they were more or less similar for

both cases.

Table 2.7 – Assessment of economic viability for both HR and ER modes, adapted from [10].

BP [m] 10 20 30 35

Mode HR ER HR ER HR ER HR ER

D [mm] 186 238 191 220 181 232 176 251

ηp 0.59 0.31 0.59 0.50 0.53 0.49 0.48 0.40

PB [kW] 8.49 29.12 9.69 19.65 7.41 25.63 6.44 37.99

Pmax [kW] 12.79 12.29 10.86 11.92 7.97 9.78 6.71 8.51

CPAT [€] 1953 6698 2230 4520 1704 5895 1481 8738

Cgen [€] 1471 1414 1248 1372 916 1125 772 978

Cinv [€] - 2459 - 2385 - 1957 - 1701

Cvalve [€] 5000 - 5000 - 5000 - 5000 -

Ctot [€] 8423 10570 8478 8277 7620 8977 7253 11418

ADEP [kW/h/day] 226.30 139.92 146.13 123.84 159.67 147.62 84.59 70.49

Daily Income [€/day] 53.26 27.98 29.23 24.77 31.93 29.52 16.92 14.10

PPeme [days] 158 378 290 334 238 304 428 810

20

The obtained results showed that the payback period was shorter for HR mode than for ER mode, for

all the considered scenarios. In the case of the HR mode, the payback period for all the BP considered

was around one year. For ER mode, the case was the same except for the 𝐵𝑃 = 35 m, where the

payback period was higher than two years.

However, as already said, this payback period did not consider the maintenance and civil works.

Therefore, the payback period of the whole hydropower system could be much longer.

2.4.2. Optimal Management of Leakage Reduction and Energy Recovery

As already said, the costs of pumping represent a predominant component of the total operating costs

of the system. With that in mind, Tricarico et al [17] developed an optimization approach, by using the

PAT [9]–[12] application to generate energy and reduce the pumping energy costs.

This study was performed, to the case of the trunk mains model of Sorrento Peninsula, Italy. It supplies

eight urban areas, with around 90,000 user daily, and 70,000 additional user, during the summer. The

proposed simulation method consisted of replacing PRV in pumping stations with PAT. The number of

PATs to place were 10 or 15.

In the results analysis, they concluded that replacing PRVs with PATs presented a good solution and,

for that particular case, if the actual PRVs presented in the system were replaced by PATs, the income

generated could cover almost all of the operation costs related with pumping.

21

2.5. Conclusions

Over the past years, a large effort has been made to find alternatives to PRV, that allow not only the

pressure control and leakage reduction, but also to generate energy. In addition, in WDS, the costs of

pumping represent a predominant component of the total operating costs of the system. Joining both

problems, a proposed solution consisted of the replacement of the PRVs with PATs, allowing large

energy savings.

Carravetta et al [9]–[12], proposed a few regulation modes, with two main designs, Electrical and

Hydraulic regulations. In addition to the regulation modes, two strategies were proposed, that have the

purpose of determining the optimal machine for each specific scenario. According to the obtained

results, both were considered viable solutions, with interesting estimated payback periods. However,

the constant dependence that the working conditions have on the users demand still represents an

issue, due to its difficulty of prediction.

The lack of available characteristic and performance curves represent another constraint. Simulation

methods, like computational fluid dynamics, and the use of affinity law, are considered options to bypass

the problem. However, they can lead to error, which can be an issue if the chosen PAT does not match

the expected characteristic operating conditions, endangering the viability of the project. To contradict

these issues, as already said, some pump manufacturers have been active investors in PAT over the

past years.

Besides this, Tricarico et al [17] developed a method to analyse the influence of the replacement of

PRVs with PATs in the overall costs of operations related to pumping. Again, the results showed that

the used of PAT in WDN can be an interesting application, and can provide large quantity of energy

savings.

Concluding, according to all researches considered here, the replacement of PRVs with PATs it shows

to be a very promising solution for both leakage reduction and energy savings.

Further, in this work, a different approach of PAT application design was proposed, with the system

isolated from the grid.

22

23

3. Self – Excited Induction Generator

An Induction Machine is an alternating current machine. It operates by supplying the stator directly with

alternating current, which will supply the rotor by induction from the stator. It has the same physical

stator as a synchronous machine with a different rotor construction, no needing of DC field current. Due

to its work mode, induction in the rotor by the stator, its rotational speed is always lower than the

synchronous speed (as a motor), and this variation is named slip. There are two types of three-phase

induction machines, wound and squirrel-cage rotor. A wound rotor is composed by a three-phase

winding, and can be accessed by a set of carbon brushes. A squirrel-cage rotor is composed by

conducting bars embedded in slots in the rotor, short-circuited at each end by conducting end rings [18].

Due to its simplicity, the squirrel-cage design presents high advantages, and so it is the most commonly

used. For motor type operation, induction machines are by far the most common type used in industrial

and commercial applications.

Figure 3.1 - Illustrative image of both types of induction machines [19].

The equivalent circuit of an induction machine is expressed in figure 3.2. The circuit represents one

phase of the machine.

Figure 3.2 – Equivalent circuit of an induction machine, adapted from [20].

24

The equivalent circuit can be divided into three different parts, stator, magnetization and rotor. The

resistance 𝑅𝑠 represents the resistance of the stator winding and 𝑋𝑠 represents the stator leakage

reactance. The resistance 𝑅𝐶 represents the core losses and 𝑋𝑚 represents the magnetization

reactance. For the air gap, 𝑁1 and 𝑁2 represent an ideal transformer between stator and rotor windings.

Finally, for the rotor side, 𝑋𝑟 and 𝑅𝑟

𝑠 represent the rotor’s reactance and resistance, respectively.

Below, in figure 3.3, is expressed a simplified model, in which the air gap (ideal transformer) area is

neglected, and so the rotor values are now referred to the primary (stator).

Figure 3.3 – Simplified equivalent of an induction machine, adapted from [20].

Working in generator regime, the induction machine offers advantages in terms of cost and simplicity

for both hydro and wind applications. However, an induction generator needs to have a constant reactive

power source to work. When connected to the grid, as shows figure 3.4, the reactive power is supplied

by the grid. If the purpose is to isolate the system (e.g. for remote areas), an external reactive power

source must be implemented.

Figure 3.4 – Illustrative scheme of a IG system, grid connected [21].

Herein, an analysis of the Induction Generator isolated from the grid is performed. This type of IG

application is named the Self-Excited Induction Generator (SEIG) [22].

http://myelectrical.com/Portals/0/SunBlogNuke/2/WindowsLiveWriter/InductionMotorEquivalentCircuit_D7EF/Induction%20Motor%20Equivalent%20Circuit%20-%20Simplified_2.png

http://myelectrical.com/Portals/0/SunBlogNuke/2/WindowsLiveWriter/InductionMotorEquivalentCircuit_D7EF/Induction%20Motor%20Equivalent%20Circuit%20-%20Simplified_2.png

25

This analysis is divided in two main parts, Simulation and Experimental. In the simulation, two different

models are developed for the SEIG analysis. Then, an experimental work is executed, in order to obtain

both capacitance and performance curves of a specific induction machine. In addition, a comparison

between the simulation and experimental results is performed.

3.1. Proposed System

In this work, the Pump running in turbine mode (PAT) is going to be analysed isolated from the grid. Like

most hydraulic pumps, being assemble with a squirrel-cage induction machine, it cannot operate

isolated from the grid by itself, and so needs an external excitation source.

As expressed below, in figure 3.5, the proposed system is composed by connecting a capacitor bank

across the stator terminals to supply the required reactive power to the induction machine.

When the machine starts rotating, driven by a mechanical prime mover, a small voltage is induced in

the stator with a frequency proportional to the rotational speed of the rotor, due to residual magnetism

present in the rotor from previous utilizations. With this small voltage available, the capacitors produce

current, providing reactive power, 𝑄, increasing the voltage, and stablishing a magnetizing flux in the

machine. So, the induction machine is excited.

Figure 3.5 – Illustrative scheme of the self-excited induction generator system [21].

After the machine is excited, depending on the available power provided by the prime mover, the

generator will produce active power, 𝑃, that will be delivered to the load, and will consume reactive

power, 𝑄, as shown in the scheme of figure 3.5. However, the reactive power produced by the capacitors

needs to be sufficient for both the load and the machine excitation. The main drawback of this SEIG

system is its poor voltage and frequency regulations under variable loads. A change in the load

impedance directly influences the excitation capacitance of the system, because the reactive power

produced by the capacitors is shared by both the machine and load. It also influences the generator

frequency (and consequently, rotational speed) and stator voltage.

26

The prime mover can be any mechanical rotating device. In this work, two different prime movers were

used. For the SEIG analysis, the prime mover chosen was a DC Motor. For the PAT analysis, the prime

mover was the Pump itself.

In figure 3.5, the presented bank of capacitors is connected in a delta design, but it is not the only

connection design. In this project, the wye connection was chosen for the experimental and simulation

procedures. As for the load, there are many options depending on the purpose of the work. Here, the

general type of load considered was RL (resistive-inductive) even though, for experimental procedures,

the considered load was purely resistive.

3.2. Simulation – Analytical and Computational Models

In this section, two different models for the analysis of a self-excited induction generator are developed.

The two models play different roles in the analysis of the system, both of them important. The first

consists of an analytical model that allows determining the capacitance required for different cases. The

second model is a simulation model developed in the MATLAB tool, Simulink.

3.2.1. Analytical Model

The minimum capacitance needed to keep the generator excited for the no load case can be easily

determined by analysing the magnetizing curve of the induction machine that can be obtained

experimentally, for no load [23]. However, when a load is applied, the capacitance value changes,

depending not only on the parameters of the machine, but also on the load applied to the system and

the rotational speed of the generator. Therefore, before starting experiment with the machine or even

assemble the system, it would come in handy to have a model that depending on the machine and load

in question, allows making a first estimation of the range of capacitances needed for that specific

application.

So, with that in mind, in this section was developed a general analytical model that allows determining

the range of capacitances required, for any case. Over the last years, many studies were done in the

SEIG [24]–[26], both simulation and experimentally. The most seen analytical model is the Loop Analysis

model, which works with the equivalent circuit impedances [23]–[29], however it is an iterative model,

turning the analysis more complex. Herein, a different model was developed, focusing on the

admittances of the circuit, based on [27], [28].

The equivalent circuit of a SEIG, based on the equivalent circuit of figure 3.3, is expressed in figure 3.6.

In each phase of the machine, a load and capacitor were added. Considering a load type RL, in this

section the objective is to obtain an expression for the minimum capacitance depending on the rotational

speed, parameters of the machine, the generator’s frequency and the load RL applied to the system.

27

Figure 3.6 – Equivalent circuit of a self-excited induction generator, adapted from [27].

For the SEIG, the stator frequency 𝑓 [Hz] can be different from the grid frequency, 𝑓𝑠 = 50 Hz, therefore

in this analysis is convenient to change the frequency to values per unit, in order to facilitate its

determination. For the rotational speed 𝑁𝑟 [rpm], the same changes were done, converting it in values

per unit as function of the nominal frequency from the stator connected to the grid, 𝑁𝑠 [rpm]. These

changes are expressed in equation (3.1), and they were also applied to the slip equation (3.2).

𝑎 =

𝜔

𝜔𝑠=

2𝜋𝑓

𝑝2𝜋𝑓𝑠𝑝

=𝑓

𝑓𝑠

𝑏 =𝜔𝑟

𝜔𝑠=

𝑁𝑟

𝑁𝑠=

𝑁𝑟

60𝑓𝑠𝑝

(3.1)

𝑠 =𝜔−𝜔𝑟

𝜔=

𝜔

𝜔𝑠−𝜔𝑟𝜔𝑠

𝜔

𝜔𝑠

=𝑎−𝑏

𝑎 (3.2)

So, 𝑎 [pu] and 𝑏 [pu] represent the stator frequency and rotational speed, respectively, in values per

unit. Then, from equations (3.1) and (3.2), the first unknown variable of this model is defined, the

frequency 𝑎 [pu], which only with its determination for each specific case, allows computing the

capacitance values required. Applying the changes of equations (3.1) and (3.2) in the equivalent circuit

of figure 3.6, resulted in figure 3.7, below.

Figure 3.7 – Equivalent circuit of SEIG with changes of (3.1) and (3.2).

28

Then, dividing all parameters by frequency 𝑎, the figure 3.8 is obtained, being this equivalent circuit the

base for the further simplifications and computations.

Figure 3.8 – Simplified equivalent circuit of SEIG.

Applying the nodal analysis to the terminal voltage, 𝑉𝑡, equation (3.3) is obtained. The total

admittance, 𝑌𝑡, is given by equation (3.4),

𝑉𝑡

𝑎∙ 𝑌𝑡 = 0 (3.3)

𝑌𝑡 = 𝑌𝑖𝑛 + 𝑌𝐿 + 𝑌𝐶 (3.4)

where 𝑌𝐶 represents the capacitors admittance, given by equation (3.5) and 𝑌𝐿 represents the load

admittance, described by equation (3.6). The admittance 𝑌𝑖𝑛 represents the induction machine’s

equivalent admittance, as can be detailed expressed in equations (3.7 – 3.9).

𝑌𝐶 = −𝑎2

𝑗𝑋𝐶 (3.5)

𝑌𝐿 =1

𝑅𝐿𝑎+𝑗𝑋𝐿

(3.6)

𝑌𝑖𝑛 =𝑌𝑠𝑌𝑟

𝑌𝑠+𝑌𝑟 (3.7)

𝑌𝑠 =1

𝑅𝑠𝑎+𝑗𝑋𝑠

(3.8)

𝑌𝑟 =1

𝑅𝑟′

𝑎−𝑏+𝑗𝑋𝑟

′+

1

𝑗𝑋𝑚 (3.9)

As shown in the admittance equations above, another unknown variable is the capacitors reactance,

𝑋𝐶 [Ω]. Knowing that the terminal voltage is always different from zero, the condition of equation (3.10)

is obtained.

𝑌𝑡 = 0 ⇔ 𝑅𝑒𝑌𝑡 = 0

𝐼𝑚𝑌𝑡 = 0 (3.10)

29

There are two unknown variables, so to solve the condition shown above, in equation (3.10), the

objective is to simplify both real and imaginary expressions, in order to have the real equation only as

function of frequency 𝑎. Then, it cannot depend on 𝑋𝐶. Solving, in equation (3.11) is expressed the

resultant equation for the real part.

𝐶4𝑎4 + 𝐶3𝑎

3 + 𝐶2𝑎2 + 𝐶1𝑎

1 + 𝐶0 = 0 (3.11)

The coefficients 𝐶𝑛, n = 0,1,2,3 and 4, are described in equations below,

𝐶4 = 𝑅𝐿(𝐿32) + 𝑅𝑟𝑋𝐿

2𝑋𝑚2 + 𝑅𝑠𝑋𝐿

2(𝐿12) (3.12)

𝐶3 = − [2𝑅𝐿𝑏(𝐿32) + 𝑅𝑟𝑋𝐿

2𝑏𝑋𝑚2 + 2𝑅𝑠𝑋𝑙

2𝑏(𝐿12)] (3.13)

𝐶2 = 𝑅𝐿2𝑅𝑟

′𝑋𝑚2 + 𝑅𝐿

2𝑅𝑠(𝐿12) + 𝑅𝐿𝑅𝑟

′ 2(𝐿22) + 2𝑅𝐿𝑅𝑟

′𝑅𝑠𝑋𝑚2 + 𝑅𝐿𝑅𝑠

2(𝐿12) +

𝑅𝐿𝑏2(𝐿3

2) + 𝑅𝑠𝑋𝐿2𝑅𝑟

2′ + 𝑅𝑠𝑋𝐿2𝑏2(𝐿1

2) (3.14)

𝐶1 = −[𝑅𝐿2𝑅𝑟

′𝑋𝑚2 𝑏 + 2𝑅𝐿

2𝑅𝑠𝑏(𝐿12) + 2𝑅𝑟

′𝑅𝐿𝑅𝑠𝑏(𝑋𝑚2 ) + 2𝑅𝐿𝑅𝑠

2𝑏(𝐿12) (3.15)

𝐶0 = 𝑅𝐿2𝑅𝑟

′ 2𝑅𝑠 + 𝑅𝐿2𝑅𝑠𝑏

2(𝐿12) + 𝑅𝐿𝑅𝑟

′ 2𝑅𝑠2 + 𝑅𝐿𝑅𝑠

2𝑏2(𝐿12) (3.16)

and the coefficients 𝐿𝑛 , n = 1… 3, are described in equations below.

𝐿1 = 𝑋𝑚 + 𝑋𝑟 (3.17)

𝐿2 = 𝑋𝑚 + 𝑋𝑠 (3.18)

𝐿3 = 𝑋𝑚𝑋𝑟′ + 𝑋𝑠(𝑋𝑚 + 𝑋𝑟

′) (3.19)

After obtaining the roots of equation (3.11), the real and positive root corresponds to the frequency. If

there are not any real and positive roots, it means that the generator cannot be excited. By replacing

the frequency in the imaginary part that, after simplification, can be described by equation (3.20), it is

possible to obtain the capacitors reactance.

𝑋𝐶 = −𝐴4𝑎

4+𝐴3𝑎3+𝐴2𝑎

2+𝐴1𝑎1

𝐵2𝑎2+𝐵1𝑎

1+𝐵0 (3.20)

The coefficients from equation (3.20) are given below.

𝐴4 = − 𝑋𝐿𝐿3 (3.21)

𝐴3 = 𝑋𝐿𝑏𝐿3 (3.22)

𝐴2 = 𝑅𝐿𝑅𝑟′𝐿2 + 𝑅𝐿𝑅𝑠𝐿1 + 𝑅𝑠𝑅𝑟

′𝑋𝐿 (3.23)

𝐴1 = −𝑅𝐿𝑅𝑠𝑏𝐿1 (3.24)

30

𝐵2 = 𝑋𝐿𝐿1 + 𝐿3 (3.25)

𝐵1 = −(𝑋𝐿𝑏𝐿1 + 𝑏𝐿3) (3.26)

𝐵0 = −𝑅𝑟′(𝑅𝐿 + 𝑅𝑠) (3.27)

Finally, knowing both the value of frequency, 𝑎, and capacitors reactance, 𝑋𝐶, it is possible to determine

the minimum capacitance required to keep the generator excited for a specific load and intended

rotational speed, shown in equation (3.28).

𝐶𝑚𝑖𝑛(𝑁𝑟 , 𝑅𝐿 , 𝐿𝐿 , 𝑅𝑠, 𝐿𝑠, 𝐿𝑚, 𝑅𝑟 , 𝐿𝑟) =1

2𝜋∙𝑎∙50∙𝑋𝐶 (3.28)

3.2.2. Computational Model

The analytical model developed in 3.2.1 provides the tools to compute and analyse the range of

capacitances required for a specific induction machine. Here, with the purpose of performing a dynamic

analysis of the SEIG system, in terms of efficiencies, voltage, current and power of the induction

generator, a computational model is developed. By simulating the intended system, the results obtained,

being close or not to reality, represent a first idea and view of what to expect from the application of a

specific SEIG.

To develop the simulation model, the software chosen was a MATLAB tool, Simulink that provides a big

library, with a wide variability of useful tools in Electrical Systems - Power Systems area. The simplified

scheme of the simulations model is the circuit of figures 3.5 and 1.2.

In the simulation model, unlike the proposed system figure 3.5, there is a three-phase power source. As

already stated, in a real induction machine working as a SEIG, when achieves a considerate rotational

speed, a small voltage appears in the stators terminals due to residual magnetization from previous

works, which allows the capacitors to produce reactive power, exciting the machine. However, when

simulating a SEIG work, that small voltage does not exist, it behaves like ideal work conditions.

Therefore, in order to be able to work isolated from the grid, in the beginning of each simulation test, the

machine needs to be connected to the grid, an only after a very short period it is switched to the load

and capacitors bank, isolating the system.

31

3.3. Experimental Setup

In order to analyse the behaviour of a SEIG, an experimental system was assembled in Electrical

Machines Laboratory. The objective of these experimental tests was to analyse the performance of a

SEIG, efficiency curve of the generator and required capacitors bank, as well as the bank influence on

the system.

The scheme of the experimental system is represented in figure 3.9. In the assembled system, the prime

mover chosen was a DC motor, connected to the SEIG currently in study.

Figure 3.9 – Scheme of experimental installation used for the tests.

An important step is to check the parameters of both machines, to understand the limit values for both

of them. Therefore, in table 3.1 are expressed the machines’ nameplate information. In addition, the

datasheet of the Induction Machine can be visualized in appendix B.

Table 3.1 – Nameplate Information of both machines.

3 phase Induction Machine Siemens DC Machine Siemens

Grid Frequency 50 Hz Armature Voltage 230 V

Nominal Power 550 W Armature Current 4.4 A

Nominal Phase Current 1.6/2.8 A (Υ/Δ) Nominal Speed 1500 rpm

Nominal Phase Voltage 230/400 V (Υ/Δ) Nominal Power 1 kW

Power Factor 0.74 Field Voltage 220 V

Nominal Speed 910 rpm Field Current 0.55 A

32

The assembled workbench is shown in the figure 3.10, below. In the legend of the figure are described

all the materials used in the experimental tests. The detailed information about some equipment can be

seen in Appendix A.

Figure 3.10 – Assemble Workbench for experimental tests: a) 1 - resistive load, 2 – digital multimeter

and 3 – DC power source; b) 4 – Induction generator and 5 – DC motor; c) 6 – auto-transformer; d) 7

– digital multimeter FLUKE, 8 – digital tachometer, 9 – bank of capacitors, 10 – digital multimeter, 11 –

digital amperimeter and 12 – Full-bridge diode rectifier.

The load chosen for the experiments was purely resistive. In table 3.2 are expressed both load and

capacitance ranges used.

12

33

Table 3.2 – Tested ranges of the resistive load and capacitances.

In this experimental work, two different machines were used, as shown in table 3.1 and in figure 3.11 –

b) 4 and 5. Before starting the experimental tests, an important step was the characterization of both

machines.

3.3.1. Induction Machine – characteristic parameters determination

As shown in the equivalent circuit, in figure 3.3, an induction machine is characterized by a set of

parameters that allow simulating its operation.

Therefore, in order to simulate the proposed system, an estimation of the parameters needs to be done.

One way to make the estimation is by experimental tests with the machine, by testing the machine in

two different conditions, no load and blocked rotor test [18].

Before starting the tests, with recourse to a digital multimeter, connecting it between two phases of the

machine, it was possible to estimate the stator resistance value.

𝑅𝑒 = 2𝑅𝑠 = 34.9 Ω ; 𝑅𝑠 = 17.45 Ω

For the tests executed in this section, a small set of materials was required: an autotransformer, a digital

multimeter FLUKE and digital tachometer.

No load Tests

The equivalent circuit for the no load case is expressed in figure 3.11. With these tests, an information

about the exciting current and no load losses was given.

Figure 3.11 – No load equivalent circuit of induction machine [30].

Minimum Maximum

Load – RL (Ω) 40 600

Bank – C (µF) 5 175

34

As shows figure 3.11, the no load equivalent circuit considers only the stator and magnetizing

parameters. Performing the tests with the induction motor applying different voltages, measuring the

phase current (𝐼0), the active power (𝑃0), the apparent power (𝑆0), power factor and rotational speed (𝑁),

the obtained results are below, in table 3.3.

Table 3.3 – Induction motor test results for no load case.

Using the equations below, with the set of results #1 of table 3.3, a set of calculations can be done, in

order to determine the magnetizing resistance (𝑅𝐶) and reactance (𝑋𝑚) parameters.

𝑄0 = 𝑆0 sin 𝜑 (3.29)

𝐺𝑚 =

𝑃0

𝑉02 =

1

𝑅𝐶

𝐵𝑚 =𝑄0

𝑉02 =

1

𝑋𝑚

(3.30)

Test Phase V0 [V] I0 [A] P0 [W] S0 [VA] cos(ϕ) N [rpm]

#1 L1

L2

L3

Total

228

225

230

-

1.46

1.44

1.47

-

72

68

65

199

333

324

338

995

0.220

0.185

0.193

0.199

996

#2 L1

L2

L3

Total

200

198

202

-

1.13

1.12

1.14

-

49

40

43

133

228

222

230

692

0.216

0.181

0.189

0.194

991

#3 L1

L2

L3

Total

161.3

158.8

163.1

-

0.83

0.82

0.85

-

31

22

27

74

134

130

139

403

0.226

0.178

0.198

0.197

984

#4 L1

L2

L3

Total

119.3

118.5

120.6

-

0.58

0.58

0.58

-

15

14

16

45

69

69

70

208

0.231

0.200

0.217

0.218

976

#5 L1

L2

L3

Total

80.7

80.2

82.1

-

0.38

0.39

0.39

-

8

7

9

25

30

31

32

93

0.273

0.239

0.283

0.263

950

35

Blocked Rotor Tests

Inhibiting the rotor from rotating, the objective was to increase the phase voltage until the current

achieves the nominal value, 𝐼𝑐𝑐 = 1.6 A. When that point was achieved, the measures taken were the

same as for no load. The induction machine’s equivalent circuit for this case can be simplified as shows

figure 3.12, where the magnetization branch of the circuit is neglected and also the slip is considered

𝑠 = 1, due to the speed being 𝑁 = 0 rpm.

Figure 3.12 – Equivalent circuit of an induction machine for blocked rotor case, adapted from [30].

Table 3.4 contains the results of the experimental tests with the blocked rotor.

Table 3.4 – Induction motor blocked rotor test results.

Phase Vcc [V] Icc [A] Pcc [W] Scc [VA] cos(ϕ)

L1

L2

L3

72

71.4

73.7

1.52

1.54

1.58

82

79

86

109

109

116

0.753

0.727

0.745

Total - - 247 334 0.743

Using the equations (3.31 – 3.32) below, with the results of table 3.4, a set of calculations can be done,

in order to determine the stator and rotor reactances (𝑋𝑠 and 𝑋𝑟′), as well as the rotor resistance (𝑅𝑟

′).

𝑄𝑐𝑐 = 𝑆𝑐𝑐 sin𝜑 (3.31)

𝑅 = 𝑅𝑠 + 𝑅𝑟

′ =𝑃𝑐𝑐

𝐼𝑐𝑐2

𝑋 = 𝑋𝑟′ + 𝑋𝑠 =

𝑄𝑐𝑐

𝐼𝑐𝑐2 𝑎𝑛𝑑 𝑋𝑟

′ ≅ 𝑋𝑠 (3.32)

36

Finally, after performing the experimental tests, in tables 3.3 and 3.4, and using those results in

equations above (3.29 to 3.32), the parameters of the induction machine were estimated.

Table 3.5 – Characteristic parameters of the induction machine in study.

For simplification reasons, the resistance 𝑅𝑐 was neglected further in this work, both for analytical and

computational simulations of the induction machine. Therefore, the magnetization branch was simply

given by the magnetizing reactance, 𝑋𝑚.

3.3.2. DC Motor characteristic equations and its electric efficiency

For the DC machine, its equivalent circuit for steady state condition is simpler to estimate. As shows

figure 3.13, both armature and field circuits, in steady state operation, can be described by resistances.

The values of these resistances can be determined, using a digital multimeter – function ohmmeter – in

the terminals of both circuits. Below, are the obtained values for both resistances.

Armature: 𝑅𝑎 = 6 Ω; Field: 𝑅𝑓 = 318,7 Ω

Figure 3.13 – DC Motor’s equivalent circuit, separate excitation case [31].

In this work, the purpose of the DC machine was to work as a prime mover, in order to help analyse the

behaviour of the induction generator in study. Therefore, an analysis of the DC machine was important.

First, get the nameplate information that was already expressed in table 3.1. Then, the important was

to analyse the DC motor [31], its efficiency, and so, its losses. This allowed, further in the analysis of the

Parameter 𝑹𝒔(Ω) 𝑳𝒔 =𝑿𝒔

𝟐𝝅𝒇 [mH] 𝑹𝒄(Ω) 𝑳𝒎 =

𝑿𝒎

𝟐𝝅𝒇 [H] 𝑹𝒓

′(Ω) 𝑳𝒓 =𝑿𝒓

′

𝟐𝝅𝒇 [mH]

Value 17.45 49.40 783.68 0.51 16.96 49.40

37

experimental results, to separate DC motor efficiency and induction generator efficiency.

Considering the case of separate excitation, shown in figure 3.13, the DC Motor steady state conditions

can be expressed by the set of equations (3.33) and (3.34).

𝐼𝑓 = 𝑈𝑓

𝑅𝑓

𝑈𝑎 = 𝑅𝑎 ∙ 𝐼𝑎 + 𝑘∅∅𝑢(𝐼𝑓) ∙ 𝜔𝑟

𝑘∅∅𝑢(𝐼𝑓) ∙ 𝐼𝑎 = 𝑇𝑐

(3.33)

𝑇 = −(𝑘∅∅𝑢)

2

𝑅𝑎∙ 𝜔𝑟 +

𝑈𝑎

𝑅𝑎∙ 𝑘∅∅𝑢 (3.34)

The power flow in the DC Motor, in a more simplified form, can be expressed by equations (3.35), (3.36)

and (3.37).

𝑃𝐼𝑁 = 𝑈𝑎 ∙ 𝐼𝑎 + 𝑈𝑓 ∙ 𝐼𝑓 (3.35)

𝑃𝑙𝑜𝑠𝑠 = 𝑅𝑎 ∙ 𝐼𝑎2 + 𝑅𝑓 ∙ 𝐼𝑓

2 + 𝑃𝑟𝑜𝑡_𝑙𝑜𝑠𝑠 (3.36)

𝑃𝑂𝑈𝑇 = 𝑃𝐼𝑁 − 𝑃𝑙𝑜𝑠𝑠 (3.37)

In equation (3.36), the losses by Joule effect in 𝑅𝑎 and 𝑅𝑓 can easily be determined because they only

depend on the values of armature and field currents, measured during the tests. On the other way, the

rotational losses 𝑃𝑟𝑜𝑡_𝑙𝑜𝑠𝑠 are not that easy to determine. For this experiment, an approximate estimation

was made by testing the DC Motor for no load conditions. In no load conditions, all of the power

measured in armature and field are losses. Therefore, by separating the Joule losses from the rotational

losses (mechanical and magnetic), an estimation of the last ones can be achieved.

Therefore, for no load condition the resultant equation (3.38) comes from joining equations (3.35) and

(3.36).

𝑃𝑟𝑜𝑡_𝑙𝑜𝑠𝑠 = 𝑃𝐼𝑁 − (𝑅𝑎 ∙ 𝐼𝑎2 + 𝑅𝑓 ∙ 𝐼𝑓

2) (3.38)

Figure 3.14 shows the experimental results obtained. For further tests, the rotational losses curve was

approximated to a quadratic function, also in figure 3.14. This estimation, made for no load conditions,

is going to be considered constant, for different values of load.

38

Figure 3.14 – Curve of Rotational Losses of the DC Motor.

3.4. Model Application: Analytical and Computational Simulation

In this section, an application of the simulation models is performed. The induction machine

characteristic parameters, already estimated, are expressed in table 3.5.

3.4.1. Analytical analysis – capacitance determination

The analytical model, developed in 3.2.1, can be used for any induction machine and for any resistive-

inductive (RL) load. Using the simplified equations (3.11), (3.20) and (3.28), an estimation of the required

capacitances can be achieved. From equation (3.11), an estimation of the generator frequency is

obtained, then to be applied in equation (3.20), to obtain the reactance of the bank. Finally, with equation

(3.28), using the estimated values of capacitor reactance and generator frequency, the capacitance

value is determined. In this case, the model was applied to the induction machine in study, characterized

in tables 3.1 and 3.5.

To facilitate the analysis of the model, the calculations were performed with recourse to MATLAB. The

tests were carried out by stablishing a load value and then analyse the variation of the capacitance

needed to keep the generator excited as function of the rotational speed. Two types of load were used,

resistive (R) and resistive-inductive (RL) loads.

Prot_loss = 6E-06N2 + 0,0099N + 8,5082R² = 0,9996

0

5

10

15

20

25

30

35

40

0 200 400 600 800 1000 1200 1400 1600 1800

Pro

t_lo

ss

(W)

N (rpm)

39

Load – R

Stablishing the load resistance, in figure 3.15 is described the variation of capacitance with rotational

speed of the machine. The speed values chosen were between 500 rpm and 1500 rpm. The range of

loads was between 40 Ω and 600 Ω.

Figure 3.15 – Description of the variation of bank’s capacitances with rotational speed, for specific

resistive loads.

Analysing figure 3.15, for a specific load, the capacitance value applied influenced highly the rotational

speed of the system. The capacitance required to keep the generator excited increased as the speed

decreased, so lower the speed higher the capacitance needed. The same occurred for the load variation,

where lower the resistance, higher the capacitance required, for the same rotational speed. For high

values of load, as shown above, for 300 Ω ≤ 𝑅𝐿 ≤ 600 Ω, the capacitance variation curve was very

similar, and so, the variation of capacitance with speed presented more or less the same results for the

different loads applied.

Another important aspect is that when the load resistance was lower, as shown in 𝑅𝐿 = 100 Ω and

𝑅𝐿 = 85 Ω, the range values of rotational speed in which the generator could operate decreased more

and more. For 𝑅𝐿 = 100 Ω, the range of rotational speeds available was 𝑁 = [600 1300] rpm, and for

𝑅𝐿 = 85 Ω was 𝑁 = [700 950] rpm. For 𝑅𝐿 < 85 Ω, according to the analytical results, it should not be

possible to excite the generator.

In table 3.6 is expressed a more detailed description of the results obtained in the graphic of figure 3.15.

For each load are expressed the capacitance required and the resultant stator frequency, for a specific

rotational speed.

500 600 700 800 900 1000 1100 1200 1300 1400 15000

50

100

150

200

250

300

350

400

N (rpm)

C (

µF

)

R = 600

R = 300

R = 150

R = 100

R = 85

40

Table 3.6 – Capacitance determination data results of figure 3.15.

RL=600 Ω RL=300 Ω RL=150 Ω RL=100 Ω RL=85 Ω

N (rpm) C (µF) f (Hz) C (µF) f (Hz) C (µF) f (Hz) C (µF) f (Hz) C (µF) f (Hz)

1500 6.7 72.1 8.8 69.7 16.7 64.7 - - -

1400 8.3 67.3 10.6 65.1 19.4 60.5 - - -

1300 10.4 62.4 13.1 60.4 23.2 56.2 55.1 50.0 -

1200 13.2 57.5 16.6 55.6 28.3 51.9 58.6 47.0 -

1100 17.2 52.6 21.4 50.9 35.5 47.5 67.8 43.5 -

1000 23.0 47.7 28.5 46.2 45.9 43.1 82.9 39.7 -

950 27.0 45.3 33.3 43.8 53.0 40.9 93.6 37.7 161.2 34.7

900 31.9 42.8 39.2 41.4 61.9 38.7 107.3 35.7 172.1 33.2

800 46.2 37.9 56.5 36.6 87.8 34.2 148.3 31.6 227.7 29.6

700 70.9 32.9 86.5 31.8 133.2 26.4 224.1 27.3 379.1 25.1

600 117.8 27.9 144.2 26.9 223.7 25.0 398.5 22.7 -

500 222.3 22.8 275.9 21.9 453.2 20.0 - - -

Load - RL

Here, a brief analysis of load RL is performed and compared to the previous numerical results for loads

R. Stablishing both resistance and inductance values, an analysis of the variation of the required

capacitance with rotational speed is performed. In figure 3.16, for a constant resistive load 𝑅𝐿 = 230 Ω,

are expressed the variation curves of capacitance as function of rotational speed, for different values of

load inductance (𝐿𝐿 [H]).

As shows figure 3.16, the increase of the load inductance, represented a both an increase of the

capacitance required and a huge decrease on the range of rotational speeds in the operating region.

For this specific resistive load, the maximum possible inductive reactance was 𝐿𝐿 = 0.14 H. The

frequency value obtained for this limit was 21 Hz.

By changing the resistive load, other simulations were performed, and the same variation behaviour

was obtained. As smaller the resistance value, shorter was the working range of inductances. Therefore,

the added inductive load had a considerable influence on the capacitances required and the range of

rotational speeds in the operating region of the generator.

This behaviour was already expected, as when this type of load is applied, the capacitance required

would need to be sufficient for both the machine and load. Therefore, when compared to the resistive

41

load, it presents more limitations.

Figure 3.16 – Variation of the Capacitance as function of rotational speed, for different values of

inductive load – for a constant 𝑅𝐿 = 230 Ω.

For the different values of resistive load, there was a maximum limit reactance associated. Below, in

table 3.7, are expressed the simulated resistance values and its maximum possible inductance. Also, in

the table are registered the frequency values and rotational speeds for each case.

Table 3.7 – Limit reactance value associated to each different resistive value.

RL (Ω) 85 100 120 150 170 200 230 300 450 600

LL (H) 0.009 0.045 0.080 0.092 0.105 0.124 0.140 0.172 0.223 0.271

f (Hz) 27.3 25 25 23.1 23.2 21.5 21.4 19.9 20 19.5

N (rpm) 750 700 700 650 650 600 600 550 550 550

As already said, the limit reactance decreased with the decrease of the resistance value. For the

minimum resistance value possible (as shown in the numerical analysis for load - R), 85 Ω, the maximum

possible inductance was 𝐿𝐿 = 9 mH.

Therefore, from the perspective of capacitance and rotational speed ranges of the working region of the

induction generator, as it is observed above, in figure 3.16, when applying a load of RL type, the

inductance value presented a high influence on the working ranges. Therefore, if this type of load is

applied to a SEIG system, it should be done a thorough analysis of the system, in order to fully

500 600 700 800 900 1000 1100 1200 1300 1400 15000

100

200

300

400

500

600

700

N(rpm)

C(µ

F)

L = 3 mH

L = 65 mH

L = 80 mH

L = 95 mH

L = 110 mH

L = 125 mH

L = 140 mH

42

understand its limits as function of the load.

Further, in this work, the RL load was not used, being both computational and experimental analysis

performed for a purely resistive load.

3.4.2. Dynamic analysis - computational model

The Simulink model developed in section 3.2.2 was applied here for the induction machine characterized

in tables 3.1 and 3.5. The results of the analytical model application were used as a base for the

simulation ranges of capacitances.

This simulation had two main objectives. First, the analysis of the required capacitances, as already

performed in the analytical model. Second, the analysis of the induction generator’s efficiency variations

with load, capacitance and rotational speeds proposed.

In the analytical model, the simulation was performed for both resistive and resistive-inductive loads.

Here however, the main purpose was to execute analysis of capacitance ranges and efficiency, in order

to compare with analytical results and have an estimation of what to expect from the experimental

analysis of the SEIG system. Therefore, the load chosen was purely resistive, with the same load range

chosen for both analytical simulation and experimental work, between 40 Ω and 600 Ω.

The flowchart of figure 3.17 shows the sequence in which the tests were performed, for each load value.

Figure 3.17 – Illustrative scheme of the tests sequence of the simulation.

43

As shows the flowchart, first, the load value was stablished, and then the prime mover power, 𝑃𝑝𝑚, was

applied. The simulations were performed by determining the minimum capacitance required, and then

increasing its value and running it again, registering all the measured values. The measured values

corresponded to the stator voltages (𝑉𝑠) and currents (𝐼𝑠), the active power (𝑃𝑠), apparent power (𝑆𝑠),

power factor, rotational speed (𝑁) and mechanical power (𝑃𝑚𝑒𝑐).

Required Capacitance Determination

First, just like the results of the analytical model, figure 3.18 shows the variation of the capacitor values

with the intended rotational speed, for each specific load.

According to the results, for rotational speeds 𝑁 = [500 1500] rpm, the range of capacitances required

to make sure that the machine can reach any position in that speed interval, for any load value, it should

be between [7.5 180] µF.

Figure 3.18 – Simulation results of capacitance variation with rotational speed, for constant load.

Efficiency Analysis

As already said, when connected to the grid, the induction generator efficiency is as function of the slip.

In turn, the slip is as function of the synchronism speed, which is related to the grid frequency (𝑓𝑠 =

50 Hz). As an isolated generator, the case is completely different. The stator frequency is not the grid

frequency anymore, and is constantly changing, as function of the rotational speed of the rotor.

Therefore, the efficiency curves will also change significantly.

From the same simulation results of figure 3.18, an analysis of the efficiency curves of the induction

generator can be performed. In each simulated point, both mechanical and electrical power output

400 600 800 1000 1200 1400 1600 18000

20

40

60

80

100

120

140

160

180

N (rpm)

C (

µF

)

R = 600

R = 200

R = 150

R = 120

R = 100

R = 85

44

values were registered, so its efficiency can be calculated, simply by using the equation below (3.39).

𝜂𝑒𝑙_𝑠𝑖𝑚 =𝑃𝑠

𝑃𝑚𝑒𝑐 (3.39)

Figure 3.19 shows the results of the efficiency as function of rotational speed. For different loads, the

efficiency curve changes. For most loads, the maximum efficiency variation was small, at most 8% of

efficiency. However, as the load decreased, the operating ranges of rotational speed decreased as well.

This occurrence was more visible for 𝑅𝐿 ≤ 120 Ω, where there was also a big decrease in the

efficiencies. According to the simulation results, with the exception of the particular cases of 𝑅𝐿 ≤ 120 Ω,

the best efficiencies of the generator were registered for the range of rotational speed, 𝑁 =

[1000 1350] rpm, where the efficiencies were usually above 60 %.

Figure 3.19 – Simulation results of SEIG efficiency curves.

Analysing both figures above, for each load, the efficiency curve presented a maximum efficiency point,

and that point as a capacitance and rotational speed associated with it. In the table 3.8, below are

expressed those points for each simulated resistive load.

400 600 800 1000 1200 1400 1600 180010

20

30

40

50

60

70

N (rpm)

Eff

icie

ncy (

%)

R = 600

R = 200

R = 150

R = 120

R = 100

R = 85

45

Table 3.8 – Best efficiency points of the SEIG simulated results.

Sim. Test RL (Ω) C (µF) N (rpm) η (%)

#1 600 17,5 1119 68.9

#2 365 17,5 1188 69.9

#3 300 17,5 1151 71.1

#4 265 20 1185 69.2

#5 230 25 1094 69.0

#6 200 25 1145 67.9

#7 170 30 1105 65.3

#8 150 30 1184 63.8

#9 100 60 1083 44.6

#10 90 85 993 33.8

#11 85 115 898 25.6

Figure 3.20 illustrates the content of table 3.8. The required capacitance presented very small variations

for 𝑅𝐿 = [200 600] Ω. However, for 𝑅𝐿 < 200 Ω the capacitances showed a variation almost exponential.

For loads lower than 85 Ω, the excitation of the generator became impossible.

Figure 3.20 – Curve of capacitances that maximize efficiency, as function of the resistive load.

0

15

30

45

60

75

90

105

120

135

0 50 100 150 200 250 300 350 400 450 500 550 600 650

C (

µF

)

RL(Ω)

𝐶 = 495𝑒−0.02𝑅𝐿

, 𝑓𝑜𝑟 𝑅𝐿 ≤ 150 Ω

𝐶 = −6 ∙ 10−7𝑅𝐿3 + 0.0008𝑅𝐿

2 − 0.37𝑅𝐿 + 71.97 , 𝑓𝑜𝑟 𝑅𝐿>150 Ω

46

3.4.3. Analysis of Simulations Results

The purpose of the simulation work performed in this section was to estimate the behaviour of a specific

induction machine working as a SEIG. Both models developed in section 3.2 were applied here.

Although the results of the analytical model were also simulated in Simulink, the usefulness of the

analytical model is in the automatic computation of the required capacitance ranges, something that

with the Simulink model it needed to be done by trial and error. Therefore, by using analytical simulation

it allowed to estimate the capacitances, then used in the Simulink simulation.

According with the obtained results, as already said, the capacitance required influences highly the

speed of the generator, and depends on the load applied. For higher values of load resistance, the

capacitance required presented small variations, however, as the resistance decreased the needed

capacitance increased more and more. In addition, there is an expected limit for the resistive load of

𝑅𝐿 = 85 Ω, in which for lower values the generator cannot be kept excited. Both simulations obtained

this load limit. However, when analysing the capacitance ranges, for each resistive load, they presented

considerable differences. In the analytical case, as the rotational speed decreased, at some point, the

capacitance started to increase rapidly, achieving much greater values than for the Simulink case.

In the analytical results of table 3.6, the frequency values for each case were included, to enhance and

verify the constant variation of its value, proportional to the rotational speed, and also dependent on the

capacitance and load values applied to the SEIG. This high dependence proved the difficulty in

frequency control, already stated in the beginning of this chapter.

As for the resistive-inductive load, only a brief analytical analysis was performed, in order to see the

influences of the load inductance in the system. As it was expected, it presented a high influence the

capacitance needed. When inductive load was added to the system, the bank started to provide reactive

power to the load as well, and so, it needed to be sufficient to satisfy both load and machine. Therefore,

in case this load is applied to the system, a careful analysis must be performed, in order to fully

characterize the bank and the system’s limitations.

The simulation efficiency results (figure 3.20), as already stated, for most of the load values used, the

best efficiencies of the generator were registered for the range of rotational speed, 𝑁 =

[1000 1350] rpm, with values usually above 60 %. Different loads applied presented different maximum

efficiency values. For most loads, the efficiency curve presented small variations, however, for 𝑅𝐿 ≤

120 Ω, the performance got worse. In addition, for lower values of load, the ranges of rotational speed

in the working region decreased significantly.

Concluding, this two developed simulation methods presented some differences of results, in some

cases considerable differences, but the general behaviour of the SEIG was equal on both simulations,

and so, even before the experimental application, the simulation performed here shows that the work of

a SEIG presents considerable limitations, and is highly influenced by the bank capacitance and load

values.

47

3.5. Experimental Work

The experimental setup assembled, as shown before in figures 3.9 and 3.10, consisted in a system

composed by a DC motor connected to a SEIG. Herein, an experimental analysis of the required range

for the bank of capacitors was performed, as well as an estimation of the efficiency curve of the generator

for different loads, as function of the rotational speed.

3.5.1. Tests and Results

The flowchart of figure 3.21 shows the followed sequence of the tests performed. For each load value,

first, using a DC power source, a constant current 𝐼𝑓 and voltage 𝑈𝑓 is applied in the DC motor field

circuit. Then, with recourse to a three-phase auto-transformer and a diode rectifier, apply current to the

armature of the DC motor to a value around its nominal value, register the armature voltage 𝑈𝑎 and

measure the resultant rotational speed 𝜔𝑚. Determine the minimum value of capacitance able to keep

the generator excited. Register all the measured values of induction generator (stator voltage - 𝑉𝑠, stator

current - 𝐼𝑠, active power - 𝑃𝑠, reactive power - 𝑄𝑠 and power factor - cos 𝜑). Then, increasing the

capacitance, repeat and register.

In the beginning of the experimental work, an important occurrence observed was the inability of the

system to be excited with a load applied. Every time the generator started working, during the excitation

phenomenon, the generator had to be at no load condition, an only after the generator was excited, the

switch changed position, applying load to the system. This was the reason of the presence of a switch

in the scheme of the experimental installation, in figure 3.9.

Figure 3.21 – Illustration of the sequence of the tests performed.

48

The tests were done for the range of loads and capacitances expressed in table 3.2. The estimation of

the efficiency is described by equations (3.40) and (3.41). In equation (3.41), 𝑃𝑠 is the active power of

the generator, and 𝑃𝑚𝑒𝑐 is the mechanical power, and it is given by the total power in the dc motor minus

all the losses associated with it, as it was described in equations (3.35-3.38), in section 3.3.2.

𝜂𝑒𝑙 = 𝑃𝑠

𝑃𝑚𝑒𝑐 (3.40)

𝑃𝑠 = 3 ∙ 𝑉𝑠 ∙ 𝐼𝑠 ∙ cos𝜑

𝑃𝑚𝑒𝑐 = 𝑃𝐼𝑁 − 𝑃𝑙𝑜𝑠𝑠

(3.41)

Analysis of Required Capacitance values

Below, in figure 3.22 is represented the capacitance variation with rotational speed. The experimental

results for the capacitances behaviour with rotational speed were in accordance with the simulation

results. The increase in capacitors resulted in a decrease of rotational speed. The first difference that

stand out was the minimum possible load in which the generator could work with. Here, the minimum

load obtained was around 𝑅𝐿 = 120 Ω.

Figure 3.22 – Experimental results of capacitance required as function of rotational speed of

generator, for constant values of load.

Generator Efficiency Curves

From the same set of tests results of figure 3.22, the efficiency curves of the generator were estimated,

using equations 3.40 and 3.41, described above. Figure 3.23 illustrates the obtained results.

0

20

40

60

80

100

120

140

160

180

200

400 650 900 1150 1400 1650

C (

µF

)

N (rpm)

R = 600 Ω

R = 365 Ω

R = 300 Ω

R = 265 Ω

R = 230 Ω

R = 200 Ω

R = 170 Ω

R = 150 Ω

R = 120 Ω

49

Figure 3.23 – Graphic of the SEIG efficiency variation as function of rotational speed, for constant

load values.

As the results show, with different loads, for the same rotational speed, the efficiencies were not always

the same. For most of the loads applied (200 Ω ≤ 𝑅𝐿 ≤ 365 Ω), the efficiencies obtained were very

similar, as it is possible to verify, having very small variations (for the exact same rotational speed),

usually less than 5 % of efficiency.

However, for low or high loads (𝑅𝐿 = 600 Ω and 𝑅𝐿 < 200 Ω), the variation of the efficiency presented

considerable differences. For both of them, the efficiencies were lower than for the other loads tested.

Figure 3.24 – SEIG efficiency curve – average of most of the curves expressed in figure 3.23.

10

20

30

40

50

60

70

300 500 700 900 1100 1300 1500 1700

Eff

icie

ncy (

%)

N (rpm)

R = 600 Ω

R = 365 Ω

R = 300 Ω

R = 265 Ω

R = 230 Ω

R = 200 Ω

R = 170 Ω

R = 150 Ω

R = 120 Ω

ηel = -5E-05N2 + 0,1445N - 36,185

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400 1600 1800

Eff

icie

ncy (

%)

N(rpm)

50

Besides these differences, depending on the load, the interest of this application was to find the

capacitance that allowed achieving the best efficiency of the system. So, with that in mind, one efficiency

curve of generator was estimated, shown in figure 3.24. This curve was estimated by considering an

average efficiency of the curves of figure 3.23. Although, due to presenting high discrepancies, for this

estimation the curves for 𝑅𝐿 = 600 Ω, 𝑅𝐿 = 170 Ω, 𝑅𝐿 = 150 Ω and 𝑅𝐿 = 120 Ω were not taken into

account. This curve was useful for efficiency calculations, further in this work.

The data of all the result analysis performed here can be accessed in appendix C, with tables for each

different applied load value.

Minimum and Ideal Capacitances

Analysing the efficiency curves of the generator, for each load there was a point of maximum efficiency.

In this case, for all the tested loads, the point of maximum efficiency was the minimum capacitance

needed to keep the generator excited. In table 3.9 are described those specific points for each load.

Figure 3.26 illustrates table 3.9.

Table 3.9 – Maximum efficiency points, for each tested load.

For higher values of resistive load, the capacitance needed did not change much as shows figure 3.25.

However, as the load decreased (in this case, when 𝑅𝐿 ≤ 200 Ω), its value started to increase

exponentially, and with it, the maximum speed the generator can achieve decreased the same way. As

can be observed in table 3.9, this caused a limitation of efficiency for those cases, because the maximum

efficiencies of the generator were achieved for speeds of 𝑁 = [1200 1500] rpm, where 𝜂𝑒𝑙 ≥ 60 %, and

so, if the maximum speed decreased, at some point, it was not able to reach the best efficiency zone.

Test Load –RL (Ω) C (µF) Global Efficiency (%) N (rpm)

#1 600 12.5 62.8 1515

#2 365 15.5 63.8 1380

#3 300 15.5 63.0 1438

#4 265 15.5 64.5 1472

#5 230 15.5 61.8 1553

#6 200 19.5 61.2 1440

#7 170 31.4 53.1 1190

#8 150 40.0 52.9 1134

#9 120 62.0 45.0 965

51

Figure 3.25 – Graphic of minimum capacitance as function of load.

Therefore, the SEIG application presents some limitations that need to carefully analysed, because

depending on the load applied and rotational speed intended, this induction machine may or may not

be a good fit for that specific application.

0

10

20

30

40

50

60

70

0 100 200 300 400 500 600 700

C (

µF

)

RL(Ω)

𝐶𝑚𝑖𝑛 = 281.59𝑒−0.013𝑅𝐿 , 𝑓𝑜𝑟 𝑅𝐿 ≤ 230

𝑎𝑠𝑑𝑠𝑠𝑠𝐶𝑚𝑖𝑛 = −0.0086𝑅𝐿 + 17.916 , 𝑓𝑜𝑟 𝑅𝐿 > 230

52

3.6. Analysis and validation of simulation methods

In this chapter, simulation and experimental work was performed to analyse a Self-Excited Induction

Generator. For simulation, two models were used, an analytical and a Simulink model, representing two

different ways to simulate the SEIG system. Then, an experimental setup was assembled to analyse

the real performance of the SEIG.

Herein, a comparison between experimental and simulation results was performed, analysing both the

results of the required capacitances and of the performance curves of the SEIG.

3.6.1. Comparison of required capacitances

For a chosen load value, 𝑅𝐿 = 230 Ω, an analysis of the required capacitor values obtained, both by

simulation and experimentally, was performed. The results are expressed in table 3.10, below.

In addition, in table 3.10 are expressed the variation in percentage between the simulation and

experimental results.

Table 3.10 – Comparison between obtained capacitance results for a specific load, 𝑅𝐿 = 230 Ω.

Capacitance Values Required – C (µF) Variation (%) : (Csim – Cexp)*100/Cexp

N (rpm) Experimental Simulink Analytical Simulink Analytical

1550 15.60 13.50 9.60 -13.46 -38.46

1315 19.65 18.00 15.10 -8.40 -23.16

1045 31.41 27.25 28.70 -13.24 -8.63

1000 34.90 29.60 32.70 -15.19 -6.30

920 39.30 34.85 41.90 -11.32 6.62

799 59.50 46.30 64.50 -22.18 8.40

635 88.00 76.00 135.30 -13.64 53.75

560 121.20 102.00 208.50 -15.84 72.03

Figure 3.26 illustrates, for the same load value 𝑅𝐿 = 230 Ω, the variation of the required capacitance

with the rotational speed, for both simulation and experimental results.

53

Figure 3.26 – Illustration of the comparison between the simulated and experimental results, for a

specific load of 𝑅𝐿 = 230 Ω.

Analysing both figure 3.26 and table 3.10, some conclusions are important to enhance. First, comparing

the Simulink with experimental results, the capacitance values simulated were very similar, although

they were always lower than the experimental, with an error more or less constant, around 13%. Second,

looking at the experimental and analytical results, for 𝑁 ≥ 800 rpm, they presented more or less similar

values, with exception for 𝑁 = 1550 rpm, in which the error variation is about 38%. However, for speeds

𝑁 < 800 rpm, the behaviour got a lot different. Lowering the speed caused an increase of the

capacitance, much faster than in the other two cases, achieving for 𝑁 = 560 rpm, an error of 72 %, as

presented in table 3.10. These differences are probably related to some factors that were not taken into

account in the analytical equations, and that for lower rotational speeds have high influences on the

capacitance values.

For most of the analysed loads, the behaviour was the same as for 𝑅𝐿 = 230 Ω. Although, there was

another difference between simulations and experimental results that is important to enhance. As the

load resistance value decreased, for both computational and analytical simulations, the limit resistance

value in which the generator could be excited is 𝑅𝐿 = 85 Ω. However, the experimental results showed

otherwise, having the limit resistance around the 𝑅𝐿 = 120 Ω. Below, in table 3.11 and figure 3.27, are

expressed both the experimental and simulation results, for the limit load cases.

As show the results of table 3.11, there were different limit load values for experimental and simulation

cases. The areas filled with white, represent the experimental and simulation operating points, while the

areas filled with grey, represent the non-operating points for experimental and simulation results.

400 600 800 1000 1200 1400 1600 18000

50

100

150

200

250

300

N (rpm)

C (

µF

)

Experimental

Analytical

Simulation

54

Table 3.11 – Comparison of results for the lower possible loads.

RL = 150 Ω RL = 120 Ω RL = 85 Ω

N

(rpm)

Cexp

(µF)

Csimulink

(µF)

Canalytical

(µF)

Cexp

(µF)

Csimulink

(µF)

Canalytical

(µF)

Cexp

(µF)

Csimulink

(µF)

Canalytical

(µF)

1500 - 21.5 16.7 - - 25.7 - - -

1490 - - 31.7 - - -

1250 - 27.5 25.5 - 36.9 35.5 - - -

1135 40 32 32.6 - 41.7 44.1 - - -

1035 49.9 37.5 41.8 - 47.5 55.2 - - -

965 50.8 42.3 50.7 62 53 66.2 - - 163.3

930 - 112.5

850 53.5 73.2 66 93.9 - 122.5 194.2

750 78.2 68 107.1 104.8 84 136.3 - 154 279.1

700 79 133.2 96.5 169.5 - 190 379.1

650 104.8 92.5 169.9 175.1 114.5 216.8 - - -

555 175.1 135 297.2 - 170 391 - - -

Figure 3.27 – Illustration of the minimum loads able to be handled by the generator, both experimental

and simulation cases.

500 600 700 800 900 1000 1100 1200 1300 1400 15000

50

100

150

200

250

300

350

400

N (rpm)

C (

µF

)

Exp - R = 150

Num - R = 150

Sim - R = 150

Exp - R = 120

Num - R = 120

Sim - R = 120

Num - R = 85

Sim - R = 85

55

3.6.2. Comparison of generator performances

In the previous sections, 3.4.2 and 3.5.1, an analysis of the generator efficiencies was performed by

simulation and experimentally. Herein, for a chosen load, 𝑅𝐿 = 230 Ω, a comparison between the

experimental and simulated results was made.

Figure 3.28 shows the variation of the efficiency with rotational speed. The obtained results presented

considerable differences. The simulated efficiency presented a maximum around the 1200 rpm, as the

experimental efficiency presented a maximum around the 1450 rpm. However, thinking more in general,

both curves presented more or less the same area where the efficiencies were above 50 %.

These results were more or less the same for other resistance values, with exception of the lower

resistances mentioned before.

Figure 3.28 – Comparison between experimental and simulation efficiency variations, for 𝑅𝐿 = 230 Ω.

As shows the figure above, besides the rotational speeds associated with the best efficiencies, another

difference between the curves was the maximum efficiency achieved. In simulation, the generator

achieved efficiencies of around 70 %, while in experimental results the maximum efficiency was around

65 %. However, for the load value of figure 3.28, the maximum efficiency obtained experimentally was

around 61 %.

In both simulation and experimental analysis, a curve of ideal capacitance as function of the applied

load was presented, in order to observe the load influence on the bank. Below, in figure 3.29, are plotted

both variation curves. As already concluded and verified above, there are some differences in the

obtained results.

400 600 800 1000 1200 1400 16000

10

20

30

40

50

60

70

N (rpm)

Eff

icie

ncy (

%)

effe

effs

56

Figure 3.29 – Capacitance variation as function of load value – simulation and experimental

comparison – that maximizes the efficiency.

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600 700

C (

µF

)

RL (Ω)

Experimental

Simulation

57

3.7. Conclusions

The work performed in this chapter had the purpose of analysing the operation and performance of a

SEIG, further to be applied in a PAT system. To estimate and understand the range of the needed bank

of capacitors, two models were developed. First, a theoretical analytical model, allowing the computation

of the range of capacitances, for a given load. Then, for the estimated values, a simulation model was

developed, to analyse the behaviour of the SEIG operation. These two models allowed a complete

estimation of its performance. In order to verify and understand the real behaviour of a SEIG, an

experimental workbench was assembled, for a specific induction machine.

When working connected to the grid, the induction machine presents an efficiency variation as function

of the slip, which is referred to the grid frequency. However, in this case, as showed the results of

sections 3.4 and 3.5, for an isolated system, the efficiency presented different results. The frequency of

the system was not fixed, being constantly changing, as function of rotational speed, capacitance and

load values. Then, in this case, the efficiency variation was analysed as function of rotational speed.

As shown in section 3.6, comparison of experimental and simulation results, the estimated performances

differed considerably from the real ones, in some cases. In capacitance determination, the Simulink

model presented similar results for most applied loads. The analytical model is simpler and easier to

use, when compared to the Simulink model, but showed more variations, then being less reliable.

Therefore, the simulation in Simulink is the more reliable for estimating the range of capacitances.

However, analysing the simulated and experimental performances, there were considerable differences.

Therefore, the use of the developed theoretical and computational simulation models can be a useful

tool for the estimation of the range of capacitances required, and to have a first idea of the expected

performance of the generator. However, an experimental analysis of the SEIG is always advised, to

verify the real values of capacitances required and performance of the generator.

The SEIG, as shown in the experimental work results, presents considerable limitations. Therefore,

before choosing the generator, it is important to perform a full characterisation of the intended

application, the intended load for the system, in order to avoid problems related to the SEIG limitations

observed here.

For the particular application to a hydraulic PAT system, there is an interest in regulating the rotational

speed depending on the hydraulic parameters, head and flow, available at each moment, to increase

the system performances. With this proposed SEIG system, that interest can be accomplished by the

bank of capacitors.

58

59

4. SEIG application to a hydraulic PAT system

In chapter 3, it was done an exhaustive study about the self-excited induction generator, where analytical

and computational models were developed in order to help to predict its behaviour. In addition,

experimental tests were performed to compare and verify the numerical results. All of the SEIG study

was with the purpose of its application to a PAT system.

Here, a pilot installation was assembled in the Hydraulic Laboratory, in order to perform experimental

work to analyse the behaviour of the system, constituted by a SEIG connected to a hydraulic PAT. First,

a set of experimental tests was executed in order to analyse the capacitance - rotational speed - load

relationship, for a steady flow regime. Then, an analysis of the system’s behaviour was performed, for

different working conditions. Finally, an analysis of the transient state imposed to system was executed.

4.1. Experimental Setup

The assembled workbench is presented in Figure 4.1. In the legend are described all the equipment

and materials used in the experimental work. The detailed information of some equipment can be

accessed in appendix A. The used pump was a KSB Etanorm 32-125, and can be accessed at [32].

Figure 4.1 – Photos of the installation assembled in Hydraulic Laboratory: a) 1 – PAT, 2 – induction

generator, 3 – compressed air reservoir, 4 – pressure sensors; b) 5 – digital multimeter FLUKE, 6 –

three-phase wye resistive load; c) 7 – bank of capacitors, 8 – switch, 9 – digital multimeter.

60

In figures 4.2 and 4.3 are represented two schemes of the assembled experimental system. In figure

4.2 is expressed the electrical part, with the induction generator, capacitors, switches and load. Figure

4.3 shows the general hydraulic circuit assembled in hydraulic laboratory for the experimental tests. The

system was composed by a compressed air reservoir, a v notch weir, a pump, a set of valves allowing

to change the flow, a flow meter, pressure sensors and the PAT.

Figure 4.2 – Illustrative Scheme of the generating system.

Figure 4.3 – Illustrative scheme of the hydraulic system assembled, adapted from [33].

4.2. Steady state operation: experimental tests and results

Herein, an analysis of the PAT system for a steady state operation was performed. The experimental

procedures were divided into two different types. First, the analysis of the capacitances required to keep

the generator excited by changing the load and the intended rotational speed. Second, with the results

of the first set of tests, specific operation points were chosen (load, capacitance and rotational speed),

stablishing a rotational speed and then the system was tested for different hydraulic conditions, in order

to estimate the global efficiency curves of the system.

61

4.2.1. Analysis of the required capacitances and system behaviour

The experimental setup, shown in figures 4.1, 4.2 and 4.3, consisted in a system composed by a closed

hydraulic circuit and a pump running as turbine (PAT) with an induction generator. The objectives of

these first experimental tests, as already stated, were to analyse the system efficiency dependence on

the capacitance value used for the induction generator’s excitation system, and to analyse the relation

between capacitance value, rotational speed and load.

These tests were made using the sequence shown in the flowchart of figure 4.4. For a chosen load, first,

a constant flow regime is applied in the system’s pipeline (usually around 𝑄𝑖 = 4.6 l/s). Then, determine

the minimum value of capacitance able to keep the induction generator excited for the applied load.

Register all the measured values (Hydraulic –𝑄𝑖,𝐻𝑖; Mechanical - 𝑁; Electrical - 𝑉𝑠,𝐼𝑠,𝑆𝑠,𝑃𝑠 and 𝑝𝑓).

Increasing the capacitance value, repeat the sequence. The capacitance was increased until the

rotational speed reached a low value, around 600 rpm.

Figure 4.4 – Illustration of the sequence of the tests performed.

The range of capacitances used is expressed in table 3.2, and the range of resistive loads 𝑅𝐿 ≤ 265 Ω.

The global efficiency of the system was estimated using the measured values, and is expressed by the

equations below (4.1 and 4.2), where 𝑃𝑠 represents the active power of the generator, and 𝑃ℎ𝑦𝑑

represents the available hydraulic power.

𝜂𝑔𝑙𝑜𝑏𝑎𝑙 = 𝑃𝑠

𝑃ℎ𝑦𝑑 (4.1)

𝑃𝑠 = 3 ∙ 𝑉𝑠 ∙ 𝐼𝑠 ∙ cos 𝜑

𝑃ℎ𝑦𝑑 = 𝜌 ∙ 𝑔 ∙ 𝑄𝑖 ∙ 𝐻𝑖

(4.2)

62

Below, in figure 4.5, are expressed the obtained results for the capacitance variation with rotational

speed, for each applied load.

Figure 4.5 – Illustrative variation of the capacitance required as function of the rotational speed, for a

steady flow regime.

In this case, different from the SEIG results, the lowest possible resistive load observe was 𝑅𝐿 = 113 Ω.

In figure 4.6, are plotted the same results of figure 4.5, but for the efficiency variation with the

capacitance value.

Figure 4.6 – Global efficiency variations as function of the bank capacitances, for a constant flow

regime.

0

20

40

60

80

100

120

140

160

500 700 900 1100 1300 1500

C (

µF

)

N (rpm)

R = 265 Ω

R = 230 Ω

R = 200 Ω

R = 170 Ω

R = 150 Ω

R = 125 Ω

R = 113 Ω

5

10

15

20

25

30

0 15 30 45 60 75 90 105 120 135 150

Eff

icie

ncy (

%)

C (µF)

R = 265 Ω

R = 230 Ω

R = 200 Ω

R = 170 Ω

R = 150 Ω

R = 125 Ω

R = 113 Ω

63

As already stated in the previous experimental work with the SEIG, it is possible to observe that for the

same resistive load, the increase of the capacitance caused a decrease in the rotational speed. As the

load decreased, at some point, the range of rotational speeds in the operating region of the system also

decreased. For instance, for loads 𝑅𝐿 = 125 Ω and 𝑅𝐿 = 113 Ω, the maximum speeds were around 𝑁 =

850 rpm, as observed in figure 4.5.

As for the efficiency, the results showed that the higher efficiency values were related to the lower

capacitances (higher rotational speeds). However, these values described the generator efficiencies

with the big influence of the PAT efficiency related to the specific flow point. Therefore, an important

procedure is to test the system for different hydraulic work conditions, to estimate the global performance

of the system, and later, the PAT efficiency curves.

In table 4.1 and figure 4.7, are expressed and represented the synthetized results of the tests, showing

the best efficiency operating points for each load and respective capacitance. Once again, proving the

results of previous tests, the results regarding the capacitances needed to keep the generator excited

depending on the load showed the same as the results shown in figure 3.26. So, the behaviour of the

system as the load resistance value decreased started to become exponential, making it impossible at

some point, for the available capacitances, and probably for any capacitance, to keep the generator

excited.

Table 4.1 – Synthetization of the Results.

However, there is one difference from the results of the previous work with the SEIG. For the SEIG case,

the minimum capacitances needed were also the best efficiency points for each load. In this case as

observed in figure 4.6, for the higher loads, the minimum and ideal capacitances were different values.

This occurred due to being different systems. In this case, Generator + PAT, the maximum efficiency

points differed, as it can be observed in table 4.1, where they were obtained for rotational speeds around

𝑁 = 1200 rpm, different from results of table 3.9 (only generator).

Test Load –RL (Ω) C (µF) Global Efficiency (%) N (rpm)

#1 265 19.5 24.6 1233

#2 230 19.5 25.1 1276

#3 200 24.8 24.6 1213

#4 170 31.4 23.1 1140

#5 150 40.0 21.1 1136

#6 125 68.4 17.4 854

#7 113 78.2 15.9 857

64

Figure 4.7 – Curve of capacitances associated with the maximum global efficiency, as function of the

load values.

4.2.2. Global efficiency curves of the system

After the analysis of the required capacitors and its influence on the system, the next step was to retrieve

the global efficiency curves of the system. Being a hydraulic system, the efficiency values depend highly

on the flow and head values. As already stated and verified before, other efficiency dependences of the

system are the rotational speed of the generator and its load value.

Therefore, as illustrates the flowchart of figure 4.8, for this experimental procedure, the first step was to

choose the load and capacitance values (so, setting the rotational speed of the system). Then, apply a

constant flow (𝑄𝑖 [𝑙/𝑠]) to the circuit. Register all the measured parameter values (Hydraulic –𝑄𝑖,𝐻𝑖;

Mechanical - 𝑁𝑟; Electrical - 𝑉𝑠,𝐼𝑠,𝑆𝑠,𝑃𝑠 and 𝑝𝑓). Then, change the working conditions, and repeat the

same tests, until reaches the limit of the operating region.

Figure 4.8 – Illustration of the sequence of tests performed for performance analysis.

0

10

20

30

40

50

60

70

80

90

50 100 150 200 250 300

C (

µF

)

Load - RL (Ω)

𝐶 = −3 ∙ 10−5𝑅𝐿3 + 0.0198𝑅𝐿

2 − 4.7788𝑅𝐿 + 406.69

65

The tests were done for different values of load and capacitance, in order to be able to stablish different

values of rotational speeds, and with this analysing the hydraulic behaviour of the system. In table 4.2

are expressed the different pairs of load/capacitance chosen for this experimental procedures. In figure

4.9 are expressed the obtained efficiency curves.

Table 4.2 – Load and capacitance combinations used to stablish the speed values for the tests below.

As shown in figure 4.9, the best efficiency points of each curve were usually registered for flow values

between 4,5 l/s and 5,0 l/s. The highest efficiencies were achieved for the curve 𝑁 = 1200 rpm, with

values around 27 %. For rotational speeds higher or lower, the efficiency values decreased gradually.

Figure 4.9 – Illustration of the global efficiency curves as function of flow.

N (rpm) RL (Ω) C (µF)

1525 230 15.5

1370 230 18.5

1200 265 19.5

1130 230 24.8

1050 230 31.4

931 230 34.9

813 230 49.9

700 150 78.2

5

10

15

20

25

30

2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0

Eff

icie

ncy (

%)

Qi (l/s)

N = 1525

N = 1370

N = 1200

N = 1130

N = 1050

N = 931

N = 813

N = 700

66

In addition, for flows lower than 3.5 l/s, the system efficiency was never higher than 20 %, and if the flow

went below 2.5 l/s, the system stopped generating energy, a situation to avoid. Therefore, when applying

this system to a WDN, where the flow and pressure have high variations, the overall efficiency may

decrease even more.

Another aspect to enhance is that, as lower as the speed was, more flat was the efficiency curve, and

for higher speeds the shape of the curve was the opposite, increasing the slope. So, lower the speed,

higher was the range of flows of the operating region, like for the curve of 𝑁 = 700 rpm.

All the detailed information about the data results of figure 4.9 is available in appendix D, with tables

correspondent to each different curve observed.

4.2.3. Hydraulic Q-H curve of PAT

From the same data of the previous results of 4.2.2, in figure 4.10 are expressed the hydraulic curves

of head and flow for each rotational speed and for the runaway working condition.

Figure 4.10 – Hydraulic head/flow curves of the PAT.

An important observation of the results of figure 4.10 was the existence of an inferior limit of flow in

which for lower values, the generator stopped being excited and so it stopped generating energy. This

value depended on the rotational speed, which was a reflexion of the capacitance value applied to the

generator. As shows figure 4.10, higher the rotational speed, lower the range of flow in the operating

region. The lowest value observed was about 2.5 l/s, only for 𝑁 = 700 rpm case.

0

2

4

6

8

10

12

14

16

1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

Head (

mw

c)

Qi (l/s)

N = 1525 N = 1370

N = 1200 N = 1130

N = 1050 N = 930

N = 813 N = 700

Runaway

67

4.3. PAT – hydraulic efficiency curves

In sections 3.5 and 4.2 the experiment was focused on two parts. In section 3.5 was performed the study

of the generator itself, and the results provided an estimated efficiency depending on the rotational

speed. Section 4.2 was centred on the overall system, allowing to retrieve the global efficiencies of the

whole system.

Therefore, using the results of the previous sections, here the focus was turned to the PAT efficiencies.

𝜂𝑔𝑙𝑜𝑏𝑎𝑙(𝑁) = 𝜂𝑒𝑙(𝑁) ∙ 𝜂𝑃𝐴𝑇(𝑁) (4.3)

The system efficiencies are related as it shows equation (4.3), with 𝜂𝑔𝑙𝑜𝑏𝑎𝑙 represented in figure 4.9,

and 𝜂𝑒𝑙 shown in figures 3.23 and 3.24. The variations of these two efficiencies shown in their respective

figures were expressed as function of different variables. The electrical efficiency was expressed as a

function of rotational speed, whereas the global efficiency was expressed as function of flow rate, for a

constant rotational speed. For the PAT efficiency, the variation expected is as function of flow rate, being

the factor that influences the most the turbine performance. For the same rotational speed, the electrical

efficiency is the same no matter what is the hydraulic power available.

Therefore, using the 𝜂𝑒𝑙 results of figures 3.23 and 3.24, expressed below in equation (4.4), and the

rotational speed values expressed in table 4.2, it was possible to achieve the 𝜂𝑒𝑙 shown in table 4.3.

𝜂𝑒𝑙(𝑁) = −5 ∙ 10−5 ∙ 𝑁2 + 0,1445 ∙ 𝑁 − 36,185 (4.4)

Table 4.3 – Combinations of load and capacitance used to achieve the speeds for the tests below,

with correspondent 𝜂𝑒𝑙.

N (rpm) RL (Ω) C (µF) ηel (%)

1525 230 15.5 61.03

1370 230 18.5 61.78

1200 265 19.5 59.81

1130 230 24.8 58.17

1050 230 31.4 55.69

931 230 34.9 50.81

813 230 49.9 44.58

68

Then, using equation (4.3), the PAT efficiency curves were determined, as shows figure 4.11.

Figure 4.11 – Illustration of the resultant PAT efficiency curves, as function of flow.

The PAT efficiency, just like in global efficiency results, showed its maximum values for flows between

4,5 l/s and 5,0 l/s. However, the maximum efficiencies of the turbine were obtained for rotational speeds

of 𝑁 = 810 rpm and 𝑁 = 930 rpm. For 𝑁 = [1050 1200] rpm the efficiency values were close to the best

efficiencies for the flow ranges mentioned above. Although, for speeds 𝑁 > 1200 rpm, the efficiency

decreased considerably. Therefore, the maximum efficiency areas of the PAT and generator are not the

same, and so, the system is not optimized.

4.4. Analysis of transient state operation

The steady state analysis of the SEIG applied to a PAT system, study material until now, is of great

importance. However, it only considers constant working conditions, without any variations, that are

situations that occur a lot in a real application, in a WDN. Therefore, an experimental procedure was

performed, considering big variations of the working conditions. Different flow variations were analysed,

closing totally or partially the system valve. Herein, an analysis of the transient behaviour was

performed, for a total close of the valve, for the electrical side of the system. In addition, an illustrative

example of the hydraulic transient phenomenon was given.

15

20

25

30

35

40

45

50

2,5 3,0 3,5 4,0 4,5 5,0 5,5

Eff

icie

ncy (

%)

Qi (l/s)

N = 1525

N = 1374

N = 1200

N = 1128

N = 1050

N = 930

N = 813

69

This experimental procedure was divided in two parts:

- Open valve: the excitation of the SEIG, beginning with the machine standstill, opening the circuit

valves, for a specific hydraulic parameters, and then analysing the excitation phenomenon, first

for no load, and then switching to the load applied.

- Close valve: the system was working in steady state condition for a specific hydraulic working

conditions. The circuit valve was closed, stopping the flow of water through the PAT, and then

the behaviour of the SEIG was registered.

The study was performed for the different rotational speeds presented in table 4.2. Both hydraulic and

electrical transient phenomenon were registered. The electrical transient was registered with recourse

to an oscilloscope. Herein, an analysis of the transient was performed for a specific case, for rotational

speed 𝑁 = 1560 rpm.

Case – rotational speed 𝑵 = 𝟏𝟓𝟔𝟎 𝐫𝐩𝐦

Figure 4.12 illustrates the pressure variations, correspondent to the hydraulic transient. Two variations

are visible in the figure, which describe both closing and opening the valves.

The experiment started with the valve open (Figure 4.1a, blue valve in the left bottom of the picture), the

system was excited and the water was flowing through the PAT, with a constant flow and constant

values of upstream and downstream pressure (so, constant head drop). Then, the valve was closed

manually (highlighted block A), and as it is possible to observe, there was a big variation of pressure,

that can cause high amount of water leakages, as occurred many times during these experimental tests.

The maximum peak of pressure achieved was about 7.44 bar (77.33 m w.c.). In addition, as it was

suppose, the pressure drop (upstream and downstream) disappeared.

Figure 4.12 – Illustration of the hydraulic transient behaviour, pressure variation – close and open

valve cases – for 𝑁 = 1560 rpm.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80

Pre

ssure

(m

wc)

Time (s)

Pressure UpstreamMeasured (mwc)Pressure DownstreamMeasured (mwc)

A

B

70

After stabilise the pressure, at 𝑡𝑖𝑚𝑒 = 60 s, the valve was opened (highlighted block B), stablishing

again the pressure drop. Here, the transient was more soft, did not present big variations, when

compared to the situation of closing the valve.

For the electrical transient, both voltage and current variations were observed and registered, when

opening or closing the valve. Figures 4.13 and 4.14, below, show their evolution in both situations. In

the figures, the voltage signal read by the oscilloscope corresponded to the phase voltage subjected to

an amplitude reduction, using a transformer with a 400 V – 20 V transformation, so 1/20 ratio.

Figure 4.13 – Illustration of the electrical transient phenomenon for 𝑁 = 1560 rpm (𝑅𝐿 = 230 Ω and

𝐶 = 15 µF) – close valve case: a) Full registered form; b) zoomed plot of highlighted block C.

When the valve was closed (Figure 4.12 – A), the water stopped flowing through the PAT, and so the

generator stopped generating energy, as shows highlighted block C of figure 4.13.

As the valve as opened (figure 4.14), two different phenomenon occurred. As the generator started

rotating, before connecting to the resistive load, the excitation needed to be done for no load, only

-5

-3

-1

1

3

5

0 1 2 3 4 5 6 7 8 9 10

Voltage (

V)

| C

urr

ent

(A)

Time (s)

Voltage

Current

-3

-2

-1

0

1

2

3

4,8 5 5,2 5,4

Voltage (

V)

| C

urr

ent

(A)

Time (s)

Voltage

Current

C

a)

b)

71

connected to the capacitors. Only when the machine was excited, the system switched to connect the

resistances in parallel with the machine and capacitors.

Therefore, when the valve was opened and the machine started rotating and was magnetized by the

bank (highlighted block D), both voltage and current increased significantly. These initial peaks of

voltage and current are important, because if they achieve values higher than accepted and remain for

a considerable period of time, can cause damages to the machine.

𝐼𝑠𝑝𝑒𝑎𝑘

= 5 A ; 𝑉𝑠𝑝𝑒𝑎𝑘

= 205 V

In this case, the peak voltage values were within the limit, but the peaks of current were very high,

compared to the nominal current of the generator, 𝐼𝑠𝑛𝑜𝑚𝑖𝑛𝑎𝑙 = 1.6 A. In this registered variation, the

excitation procedure only lasted three seconds, so there was no problem. However, if in a real

application this situation of high peaks of current occurs frequently, and for longer periods, there is the

danger of overheating. To prevent these situations of current peaks, and also of voltage peaks, an option

is to excite the machine with a different capacitance value, to reduce their peak amplitude, and only

when the system is switched to the load, the capacitance is stablished in the intended value.


𝐶 = 15 µF) – open valve case: a) Full registered form; b) zoomed plot of highlighted block D; c)

zoomed plot of highlighted block E.

-12

-8

-4

0

4

8

12

0 1 2 3 4 5 6 7 8 9 10

Voltage (

V)

| C

urr

ent

(A)

Time (s)

Voltage

CurrentD

E

-15

-10

-5

0

5

10

15

3,1 3,2 3,3 3,4 3,5 3,6

Voltage (

V)

| C

urr

ent

(A)

Time (s)

VoltageCurrent

-8

-6

-4

-2

0

2

4

6

8

6 6,5 7 7,5 8

Voltage (

V)

| C

urr

ent

(A)

Time (s)

VoltageCurrent

a)

b) c)

72

Finally, when the machine was excited, the load was added to the system by a switch (highlighted block

E). The voltage and current slowly stablished into their final and steady values. However, this case was

one of the cases in which the stablishing takes more than usual. As can be observed, when switching,

the current and voltage values first decreased a lot, the effected of the load presence, and constantly

increased and decreased, evolving gradually to the steady final value.

Proposed solution for the high peaks of phase current during excitation

When applying an isolated PAT system in a WDN, there is a constant change in the flow and head drop,

and so in the hydraulic available power. The idea studied in this work was to stablish the capacitance of

the bank, depending on the working conditions at each instant, in order to adjust to the rotational speed

that allowed achieving the best efficiencies.

As already shown in the steady state study of the system, there is a minimum limit flow, and if the water

flow goes below that value, the system cannot generate energy. Therefore, every time the flow reaches

that kind of values, the generator will stop generating, and when the flow increases, has to restart the

excitation procedure again.

Related to that, the presence of high peaks of current associated with the excitation of the machine can

become a problem, if at some point, due to the high variability of the flow, the system as to constantly

restart itself, being every time submitted to high currents. If this situation extends for long periods, hours,

the overheating is a problem, and is important to avoid.

A proposed solution, instead of stablishing the ideal capacitor for the PAT work, for specific working

conditions, was changing the capacitor value in excitation moment, in order to reduce the peaks of

current, and only after the generator was excited and connected to the load, the capacitance was

restored to its intended value.

As an example, below is shown the electrical transient experimental results during the opening of the

system valve, for the same conditions as before, for a rotational speed 𝑁 = 920 rpm.

In this case, the initial peak current was lower, 𝐼𝑠𝑝𝑒𝑎𝑘

= 3 A, and even before connecting to the load, the

current peak values decreased instantly to 𝐼𝑠𝑝𝑒𝑎𝑘

= 1.5 A. Also, the transition when the system was

connected to the load presented a more soft evolution (highlighted block G), compared to the previous

case (highlighted block E), stablishing faster to its final value. The capacitance and load values

associated to both cases are expressed in table 4.2. Therefore, for the same load 𝑅𝐿 = 230 Ω, changing

the capacitor value from 15 µF to 35 µF, allowed a significant reduction of current peaks during excitation

of the generator.

73


𝐶 = 35 µF) – open valve case: a) Full registered form; b) zoomed plot of highlighted block F; c)

zoomed plot of highlighted block G.

The same analysis was done using the Simulink model developed in chapter 3. For the same input

mechanical power, increasing the capacitance allowed to control the peak values of the phase current

during the excitation of the generator.

Below, in figure 4.16, are expressed the simulation results for the excitation of the machine for different

capacitor values. In both cases, a) and b), the two different areas were highlighted, showing two switch

variations, at the third and seventh seconds of the simulation. As already said in the introduction of the

Simulink model, in chapter 3, in the beginning of each simulation, the machine was connected to the

grid, and only after three seconds, the system switched and became isolated. So, for 𝑡𝑖𝑚𝑒 = [3 7] s, the

excitation phenomenon was registered, and then, at 𝑡𝑖𝑚𝑒 = 7 s, the load was applied to the system.

As showed the results of the figure 4.16, an increase in the capacitance, besides decreasing the

rotational speed of the generator, also reduces the current values in the excitation period, before

switching the system to the load. For the phase voltage, the same evolution was observed.

-4

-3

-2

-1

0

1

2

3

4

4 5 6 7 8 9 10

Curr

ent

(A)

Time (s)

𝐼𝑠𝑝𝑒𝑎𝑘 = 3 𝐴

G

F

-4

-3

-2

-1

0

1

2

3

4

4,2 4,4 4,6 4,8 5 5,2

Curr

ent

(A)

Time (s)-2

-1,5

-1

-0,5

0

0,5

1

1,5

2

6 6,2 6,4 6,6 6,8 7

Curr

ent

(A)

Time (s)

a)

c) b)

74

Figure 4.16 – Simulink simulation results, of the generator excitation phenomenon, for the same load

and prime mover power input, with different capacitance values.

Therefore, this proposed solution can be a viable way to reduce the peaks of current and voltage during

excitation. In future work, a more detailed study of this should be done, in order to analyse if this solution

it is worth for different cases.

3 4 5 6 7 8 9 10-4

-3

-2

-1

0

1

2

3

4

Time (s)

Cu

rre

nt

(A)

3 4 5 6 7 8 9 10-4

-3

-2

-1

0

1

2

3

4

Time (s)

Cu

rre

nt

(A)

a)

𝐶𝑒𝑥𝑐 = 15 µF

𝑁 = 1460 rpm

𝑅𝐿 = 230 Ω


= 3.2 A

b)

𝐶𝑒𝑥𝑐 = 40 µF

𝑁 = 960 rpm

𝑅𝐿 = 230 Ω


= 2.1 A

75

4.5. Conclusions

In this chapter, an experimental work was performed to analyse the Self-Excited Induction Generator

applied to a PAT system in a hydraulic closed circuit. The main focus was a steady state analysis of the

system, but a brief analysis of the transient state was also performed.

The steady state experimental work, shown in figures 4.9 and 4.10, was important in order to find the

operating conditions that allows achieving the best efficiency, depending on the available working

conditions, flow and head. By using a bank of capacitors as external excitation system of the generator,

when changing its capacitance, the rotational speed changes as well and so, it is possible to adjust the

system to better working conditions, according to the available flow at each moment. The highest value

of efficiency obtained was around 𝜂𝑔𝑙𝑜𝑏𝑎𝑙 = 27 %, a low value, compared to the maximum SEIG electrical

efficiency obtained in the previous section, of about 𝜂𝑒𝑙 ≈ 65 %. This occurred due to the presence of

the PAT, which had a maximum efficiency for rotational speeds around 𝑁 = 1000 rpm, of 𝜂𝑃𝐴𝑇 = 45 %,

different from the generator’s ideal working speeds, and so affecting the performance of the global

system.

The work performed allowed to retrieve and verify the capacitance variation with rotational speed, for

different loads applied to the system. In addition, the characteristic curves of the PAT were determined,

providing the lower limit values of flow, important data information for further application in real case.

For the transient behaviour, the electrical transient in the excitation of the generator presented in some

cases high peaks of current and voltages. In WDS, there is a high variation of the working conditions,

achieving many times flow values lower than the limit of the generating system (Figure 4.10). Therefore,

in the worst scenario, the generator will need to be excited constantly, for long periods, and so it can

become an issue, because of the high peaks obtained during excitation. The solution proposed here,

consisting of increasing the capacitance value during the excitation phenomenon, reducing the

amplitude of the peak values, represents an interesting alternative. After the system is excited and the

load is included, the capacitance can be changed to the value that better fits the working conditions,

and so, it does not affect the performance of the system.

76

77

5. Conclusions and Future Work

5.1. Conclusions

The study of the application of PAT in WDS has increased over the last years. Different methods for

PAT control and regulation have been proposed and analysed. According to recent works, Electrical

and Hydraulic regulation modes are the two designs more studied, both of them applications with the

system connected to the electrical grid.

In this work, a new approach was proposed, by isolating the system from the grid. As main objective,

an analysis of the performance of a SEIG applied to a hydraulic PAT system was performed. Inserted

in project that aims the PAT application in a specific WDN, this work intended to analyse a specific PAT

+ IG system, further to be applied in the real case. The work was divided into two parts: SEIG analysis

and PAT analysis.

Concerning the SEIG study, the chosen form of excitation was by connecting a bank of capacitor across

the generator stator phases, to provide the needed reactive power. The SEIG performance presents

very different results from the grid connected IG application. There is a big difficulty on controlling the

frequency, which is constantly changing, as function of the rotational speed. Therefore, the analysis of

the generator efficiency was performed as function of rotational speed, capacitance and load applied. A

high dependence on the capacitance value was observed. When working with this type of system, in

order to obtain the best performances, a thorough study of the intended load as well as the system

dependence with the bank’s capacitance, and the ranges required for the bank, is of great importance.

In addition, the rotational speed is highly dependent of the capacitor value, and its variation needs to be

well analysed and described.

The application of the SEIG in a hydraulic PAT system, allowed estimating the both global and PAT

efficiency curves, as well as the characteristic curves of the PAT as function of flow. From the global

efficiency obtained, a conclusion to retrieve is that the system is not optimized. The best performance

areas of the SEIG and the PAT are obtained for very different values of speed, so an optimization of the

system is required. In addition, in experimental work, a set of limitations of the system were verified, of

both load and flow conditions. Under variable load conditions, the load value highly influences the

needed capacitance and rotational speed. Therefore, the intended application needs to be well defined

an analysed, in order to correctly choose the generating system, and avoid the occurrence of this

problems.

From a general perspective, the application of this isolated IG + PAT system can be an interesting

solution for combining the pressure reduction in WDS with energy generation. Although it does not

present very promising efficiency ranges, the presence of the bank of capacitors allows, by changing its

value, to change the rotational speed, and adapt it to the working conditions at each moment, in order

to achieve better performances.

78

5.2. Future Work

From the work performed here, some problems and limitations were observed. To improve the system

performance and prepare it for the real case application, in the future some important work should be

done. The development of a controlling system that, depending on the working conditions, applies

different capacitance value, in order to achieve higher efficiencies, is an important part of this system

application in a real case. In addition, an optimization of the system, finding a more suitable pair of

SEIG+PAT for the system, allows achieving higher efficiencies, and so, generation of more energy.

So, the future work related to this project can be summarized by the following topics:

Assemble a new hydraulic pilot circuit, to perform more experimental tests with the isolated

PAT;

Develop a controlling electronic system to maximize the global efficiency, according to the

working conditions;

Optimization of the system for a real case study, according to its working specifications, by

selecting a more suitable hydraulic pump and induction generator;

79

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82

A1

Apendix

A. Equipment used in experimental applications

Power Logger Fluke 1735

Tektronix TDS 2001/2012C Oscilloscope

Model: Fluke 1735 three-phase power logger

Memory: 4MB flash memory – 3.5MB for

measuring data

Sample Rate: 10.24 kHz

V-RMS wye resolution: 0.1V

Operating Error: ±0.5% of measured value +10

digit

A-RMS resolution: 0.01A

Operating Error: ±1% of measured value +10

digit

Brand: Tektronix

Model: TDS 2001/2012C

Analog Bandwidth: 100 MHz

Sample Rate: 2 GS/s

Record Length: 2.5k Point

Analog Channels: 2

A2

Capacitor banks Esselte Studium

Three-phase bank of resistances Oficel

Brand: ESSELTE STUDIUM

Power: 3.2 kVAr

Frequency: 50 Hz

Maximum capacitance: 3·60 µF

Connections:

Δ - 3·220 V ; 1.2 - 8.4 A

Y - 3·380 V ; 0.7 – 4.9 A

/// - 220V ; 2.1 – 14.5 A

Brand: Oficel

Range: 40 – 600 Ω

Brand: ESSELTE STUDIUM Connections:

Power: 5.1 kVAr Δ - 3·220 V ; 1.9 - 13.4 A

Frequency: 50 Hz Y - 3·380 V ; 1.1 – 7.7 A

Maximum capacitance: 3·115 µF /// - 220V ; 3.3 – 23.1 A

A3

B. Datasheet of the Induction Machine used in experimental

and simulation analysis

A4

C. Tables with Experimental results of SEIG application

Load resistance – R = 600 Ω

DC MOTOR INDUCTION GENERATOR

Ua (V) Ia (A) Uf (V) If (A) Pin

(W)

Pmec

(W)

N

(rpm)

Us (V) Is (A) Ps (W) Ss

(VA)

fp C (µF) Eff

(%)

200.0 2.24 141.8 0.34 496.2 392.0 1515 232 1.05 246 721 0.346 12.4 62.8

183.8 4.32 139.0 0.33 839.9 659.7 1378 287 1.65 367 1433 0.258 15.6 55.6

173.1 4.20 139.0 0.33 772.9 601.3 1281 266 1.65 308 1311 0.235 18.7 51.2

166.8 4.26 141.6 0.33 757.6 584.2 1215 253 1.69 292 1292 0.226 19.7 50.0

154.7 4.30 141.6 0.33 711.5 538.9 1110 231 1.72 240 1191 0.201 24.8 44.5

139.9 4.20 141.6 0.33 634.4 469.6 985 202 1.69 189 1026 0.184 31.4 40.2

134.3 4.10 141.9 0.33 597.6 438.6 945 190 1.66 169 952 0.177 34.9 38.5

128.0 4.32 141.3 0.33 599.0 431.2 885 180 1.72 147 930 0.156 39.3 34.1

123.0 4.20 149.0 0.37 571.0 401.7 837 166 1.69 127 839 0.155 49.9 31.6

119.7 4.23 149.0 0.37 560.7 390.5 807 160 1.69 114 814 0.15 50.8 29.2

114.5 4.23 149.0 0.37 539.5 368.9 763 146 1.65 104 725 0.146 59.5 28.2

112.0 4.26 149.3 0.37 532.4 360.7 740 143 1.66 95 710 0.134 60.6 26.3

102.0 4.27 149.5 0.37 490.9 320.3 650 125 1.69 57 632 0.09 78.2 17.8



Ua

(V)

Ia (A) Uf (V) If (A) Pin (W) Pmec

(W)

N

(rpm)

Us

(V)

Is

(A)

Ps (W) Ss

(VA)

fp C (µF) Eff (%)

181.3 4.15 140.6 0.38 806.2 622.6 1380 228 1.40 397 948 0.42 15.6 63.8

168.5 4.13 140.4 0.38 749.0 570.1 1278 215 1.40 347 889 0.392 18.67 60.9

160.9 4.18 140.6 0.38 725.6 546.3 1204 205 1.41 324 858 0.377 19.65 59.3

148.3 4.18 140.4 0.38 672.7 496.3 1093 188 1.41 274 802 0.341 24.82 55.2

134.8 4.24 140.5 0.38 624.2 447.6 977 171 1.44 231 744 0.309 31.41 51.6

131.7 4.23 141.7 0.38 610.7 434.7 939 165 1.45 214 725 0.295 34.9 49.2

124.1 4.27 141.5 0.38 583.3 406.9 871 155 1.48 187 689 0.267 39.3 46.0

118.9 4.14 141.6 0.38 545.6 376.7 830 144 1.48 163 631 0.260 49.9 43.3

115.3 4.16 141.7 0.38 532.9 363.8 796 139 1.48 149 610 0.243 50.8 41.0

111 4.24 141.2 0.38 523.7 351.3 758 131 1.49 138 580 0.239 59.5 39.3

108.4 4.24 141.6 0.38 512.7 341.0 733 127 1.49 127 566 0.225 60.6 37.2

97.2 4.10 141.6 0.38 451.6 288.6 640 113 1.50 85 499 0.172 78.2 29.4

94.7 4.24 141.7 0.38 454.7 285.2 611 104 1.50 78 470 0.166 88.0 27.4

89.9 4.23 141.8 0.37 433.2 265.4 568 94 1.51 64 423 0.151 104.8 24.1

79.5 4.13 141.5 0.37 381.1 219.7 485 73 1.43 40 306 0.130 157.8 18.2

77.9 4.18 141.8 0.37 378.5 214.9 466 67 1.42 34 285 0.120 175.1 15.8

A5



Ua

(V)

Ia

(A)

Uf (V) If (A) Pin

(W)

Pmec

(W)

N

(rpm)

Us

(V)

Is (A) Ps (W) Ss

(VA)

fp C

(µF)

Eff (%)

200.0 4.20 141.5 0.39 895.8 705.3 1438 221 1.44 462 962 0.483 15.6 63.1

188.1 4.29 149.0 0.39 865.4 673.6 1332 212 1.46 423 936 0.452 18.7 62.8

174.4 4.24 149.6 0.39 798.4 610.9 1245 198 1.45 377 862 0.436 19.7 61.7

158.7 4.31 149.3 0.38 741.0 555.7 1129 184 1.46 322 802 0.399 24.8 57.9

144.0 4.29 149.6 0.37 673.7 494.2 1003 166 1.47 263 725 0.363 31.4 53.2

138.5 4.25 149.5 0.37 644.5 468.0 961 159 1.49 240 690 0.348 34.9 51.3

130.1 4.29 149.5 0.37 613.6 437.2 890 148 1.47 208 652 0.319 39.3 47.6

126.2 4.40 149.5 0.37 610.6 429.4 856 144 1.50 197 646 0.307 49.9 45.9

121.9 4.37 149.5 0.37 588.0 409.1 820 138 1.51 179 618 0.289 50.8 43.7

117.0 4.35 149.5 0.37 564.3 387.2 780 127 1.50 160 571 0.282 59.5 41.3

114.0 4.35 149.5 0.37 551.2 374.7 754 124 1.49 150 556 0.267 60.6 40.0

103.0 4.27 149.3 0.37 495.1 324.3 662 109 1.50 102 489 0.210 78.2 31.4



Ua

(V)

Ia

(A)

Uf (V) If (A) Pin (W) Pmec (W) N

(rpm)

Us (V) Is

(A)

Ps

(W)

Ss

(VA)

fp C (µF) Eff (%)

199.5 4.22 140.5 0.41 899.8 702.7 1472 210 1.45 468 888 0.523 15.6 64.5

184.5 4.29 141.2 0.39 845.7 653.6 1371 196 1.42 421 835 0.504 18.7 64.4

173.8 4.12 141.3 0.39 771.2 589.8 1283 183 1.38 368 756 0.486 19.7 62.4

159.3 4.25 141.3 0.39 731.8 547.5 1155 172 1.4 323 722 0.448 24.8 59.0

144.0 4.27 140.9 0.39 669.3 487.4 1024 156 1.42 273 668 0.41 31.4 56.0

137.8 4.16 141.2 0.39 627.6 452.6 977 149 1.42 246 623 0.395 34.9 54.3

129.9 4.23 141.4 0.39 603.9 427.0 903 141 1.43 219 600 0.364 39.3 51.3

125.0 4.27 141.2 0.38 587.8 410.1 865 135 1.43 199 572 0.351 49.9 48.5

119.1 4.02 141.4 0.38 532.9 368.5 822 127 1.38 175 524 0.334 50.8 47.5

114.3 4.04 141.3 0.38 515.7 351.4 780 118 1.4 159 493 0.325 59.5 45.2

112.3 4.18 141.5 0.38 523.3 352.8 758 117 1.42 155 499 0.308 60.6 43.9

100.2 4.06 141.6 0.38 460.6 298.1 658 104 1.43 110 441 0.249 78.2 36.9

97.3 4.23 141.3 0.38 464.8 295.1 630 98 1.44 100 421 0.236 88.0 33.9

92.6 4.21 141.5 0.38 443.5 275.0 585 89 1.44 84 386 0.217 104.8 30.5

83.6 4.25 141.5 0.38 408.6 239.9 505 71 1.44 55 303 0.18 157.8 22.9

81.0 4.25 141.7 0.38 398.0 229.1 482 65 1.43 46 280 0.16 175.1 20.1

A6



Ua

(V)


(W)

N

(rpm)

Us (V) Is

(A)

Ps

(W)

Ss

(VA)

fp C (µF) Eff

(%)

210 4.20 141.1 0.40 938.7 743.0 1553 193 1.44 459 826 0.562 15.6 61.8

195 4.30 141.5 0.37 890.9 701.8 1415 186 1.45 432 810 0.535 18.7 61.6

186 4.29 141.5 0.37 849.4 663.7 1315 179 1.43 405 780 0.52 19.7 61.0

166.3 4.21 141.5 0.37 752.5 573.6 1194 157 1.41 325 661 0.495 24.8 56.7

148.6 4.32 141.5 0.37 693.6 512.8 1045 145 1.4 278 612 0.455 31.4 54.2

142.8 4.29 141.5 0.37 665.1 486.5 1004 140 1.39 257 584 0.442 34.9 52.8

132.4 4.19 141.5 0.37 607.1 435.4 920 130 1.36 219 534 0.41 39.3 50.3

128.1 4.21 141.5 0.37 591.7 419.8 880 126 1.37 203 519 0.394 49.9 48.4

123.5 4.22 141.5 0.37 573.5 401.9 842 121 1.37 187 494 0.376 50.8 46.5

118.6 4.25 141.5 0.37 556.4 384.2 799 114 1.38 174 476 0.366 59.5 45.3

114.8 4.22 141.5 0.37 536.8 366.6 770 110 1.37 158 450 0.349 60.6 43.1

101.1 4.06 141.7 0.37 462.9 302.6 665 97 1.35 113 392 0.288 78.2 37.3

98 4.14 141.8 0.37 458.2 294.5 634 92 1.36 102 377 0.273 88.0 34.6

93.4 4.14 141.8 0.37 439.1 276.2 592 84 1.39 87 350 0.249 104.8 31.5

89.8 4.18 141.6 0.37 427.8 263.4 559 78 1.39 75 326 0.232 121.2 28.5

84.2 4.18 141.3 0.37 404.2 240.6 513 67 1.39 58 276 0.206 157.8 24.1

81.6 4.15 141.7 0.37 391.1 229.3 491 62 1.37 49 254 0.192 175.1 21.4



Ua (V) Ia

(A)

Uf (V) If

(A)

Pin (W) Pmec (W) N

(rpm)

Us

(V)

Is (A) Ps

(W)

Ss

(VA)

fp C

(µF)

Eff (%)

191.2 4.30 149.3 0.37 877.4 687.6 1440 170 1.49 421 762 0.550 19.7 61.2

174.2 4.38 149.3 0.37 818.2 629.0 1298 157 1.51 369 695 0.531 24.8 58.8

154 4.27 149.3 0.37 712.8 532.6 1121 140 1.42 295 599 0.493 31.4 55.4

148.7 4.35 149.3 0.37 702.1 518.9 1071 137 1.44 281 588 0.479 34.9 54.2

137.9 4.3 149.3 0.37 648.2 469.7 977 127 1.42 243 539 0.448 39.3 51.7

133.8 4.33 149.3 0.37 634.6 455.5 932 125 1.43 226 528 0.432 49.9 49.6

128.5 4.31 149.3 0.37 609.1 432.0 888 119 1.45 209 506 0.415 50.8 48.4

124.2 4.38 149.3 0.37 599.2 419.3 846 112 1.44 194 486 0.402 59.5 46.3

121 4.37 149.3 0.37 584.0 405.3 813 110 1.44 184 474 0.385 60.6 45.4

107.8 4.37 149.3 0.37 526.3 349.7 703 99 1.45 136 422 0.322 78.2 38.9

104.3 4.35 149.3 0.37 508.9 333.9 670 92 1.44 120 393 0.305 88.0 35.9

99.6 4.40 149.3 0.37 493.5 316.6 626 85 1.45 102 369 0.279 104.8 32.2

90 4.35 149.3 0.37 446.7 273.9 544 67 1.44 66 288 0.228 157.8 24.1

A7



Ua

(V)

Ia

(A)

Uf (V) If (A) Pin (W) Pmec (W) N

(rpm)

Us (V) Is

(A)

Ps

(W)

Ss

(VA)

fp C (µF) Eff (%)

158.8 4.23 141.5 0.37 724.1 544.3 1190 129 1.44 289 554 0.52 31.4 53.1

151.8 4.19 141.5 0.37 688.4 512.2 1125 124 1.43 266 524 0.51 34.9 51.9

139.2 4.22 141.5 0.37 639.5 464.4 1015 117 1.39 233 482 0.482 39.3 50.2

134.2 4.24 141.5 0.37 621.4 446.2 965 112 1.39 218 467 0.469 49.9 48.9

128.3 4.25 141.6 0.37 597.7 423.1 913 108 1.37 200 444 0.45 50.8 47.3

123.3 4.28 141.6 0.37 580.1 404.7 878 101 1.36 188 404 0.446 59.5 46.4

120.4 4.29 141.6 0.37 568.9 393.8 842 100 1.37 177 410 0.428 60.6 45.0

105.8 4.27 141.5 0.37 504.1 332.4 718 90 1.36 133 362 0.367 78.2 40.0

102.4 4.19 141.8 0.37 481.2 314.7 682 85 1.38 122 352 0.346 88.0 38.8

97.1 4.22 141.8 0.37 461.7 294.9 634 78 1.38 103 325 0.319 104.8 34.9

87.7 4.25 141.8 0.37 424.6 257.8 549 63 1.38 69 263 0.263 157.8 26.8

85.7 4.23 141.8 0.37 414.4 248.9 530 59 1.39 59 245 0.243 175.1 23.7



Ua

(V)

Ia (A) Uf (V) If (A) Pin (W) Pmec (W) N

(rpm)

Us (V) Is

(A)

Ps

(W)

Ss

(VA)

fp C (µF) Eff (%)

157.0 4.28 144.7 0.38 726.9 543.6 1134 123 1.53 288 564 0.513 40.0 53.0

144.7 4.29 144.7 0.38 675.7 494.2 1033 113 1.50 249 508 0.493 49.9 50.4

137.7 4.35 144.7 0.38 654.0 470.6 971 109 1.49 231 483 0.479 50.8 49.1

131.7 4.33 144.7 0.38 625.2 444.0 920 103 1.46 210 456 0.463 59.5 47.3

127.1 4.40 144.7 0.37 613.2 431.0 871 101 1.47 199 444 0.448 60.6 46.2

111.0 4.37 144.7 0.37 539.0 361.0 741 90 1.44 152 389 0.390 78.2 42.1

106.5 4.29 144.7 0.37 510.9 337.6 705 84 1.42 132 357 0.370 88.0 39.1

101.1 4.35 144.7 0.37 493.8 318.4 649 78 1.43 114 335 0.340 104.8 35.8

91.6 4.30 144.7 0.37 446.7 277.2 567 62 1.42 76 264 0.288 157.8 27.4

90.0 4.36 144.7 0.37 445.2 272.8 555 59 1.42 66 250 0.264 175.1 24.2



Ua

(V)


(W)

N

(rpm)

Us (V) Is

(A)

Ps

(W)

Ss

(VA)

fp C (µF) Eff

(%)

137.9 4.22 141.3 0.37 634.8 459.7 965 94 1.55 207 434 0.475 62.0 45.0

122.9 4.26 141.3 0.37 576.4 402.0 834 85 1.53 170 389 0.434 78.2 42.3

122.0 4.31 141.3 0.37 578.7 401.9 822 80 1.55 157 376 0.417 88.0 39.1

113.8 4.31 141.3 0.37 543.3 367.7 756 74 1.52 132 338 0.389 104.8 35.9

111.0 4.28 141.3 0.37 528.4 354.6 735 68 1.53 113 310 0.364 121.2 31.9

107.5 4.21 141.3 0.37 505.4 336.0 705 59 1.55 85 272 0.315 157.8 25.3

99.4 3.91 141.7 0.37 441.6 287.8 655 53 1.46 66 228 0.300 175.1 22.9

A8

D. Tables with Experimental results of PAT application

Rotational Speed – N = 1525 rpm


HYDRAULIC PARAMETER ELECTRICAL PARAMETER

Q (l/s) pressure_up (bar)

pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

5.010 2.153 1.168 10.047 1525

112 0.57 230 15.5 493.791 22.682

4.761 2.127 1.163 9.833 1525

107 0.57 230 15.5 459.245 23.299

4.620 2.135 1.164 9.904 1525

107 0.57 230 15.5 448.880 23.837

4.510 2.108 1.158 9.690 1525 91.4 0.65 176 101 0.57 230 15.5 428.716 23.559

4.461 2.092 1.154 9.568 1525 88.00 0.63 165 95 0.57 230 15.5 418.701 22.689

4.421 2.082 1.151 9.496 1526 86.50 0.61 157 90 0.57 230 15.5 411.850 21.853

4.272 2.052 1.145 9.251 1530 79.60 0.57 135 77 0.57 230 15.5 387.711 19.860

4.176 2.033 1.141 9.098 1532 76.40 0.54 123 70 0.57 230 15.5 372.730 18.780

4.060 2.017 1.137 8.976 1536 72.00 0.81 110 63 0.57 230 15.5 357.502 17.622

3.878 1.996 1.13 8.833 1544 65.50 0.47 93 52 0.57 230 15.5 336.043 15.474

3.845 1.987 1.131 8.731 1546 63.00 0.45 85 48 0.57 230 15.5 329.336 14.575

3.752 1.97 1.124 8.629 1551 59.50 0.43 75 42 0.57 230 15.5 317.616 13.224

3.599 1.956 1.122 8.507 1561 55 0.39 63 35 0.57 230 15.5 300.343 11.653



pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

4.820 2.057 1.168 9.068 1374 54.7 0.4 60 107 0.55 230 18.5 428.764 24.955

4.750 2.047 1.164 9.007 1374 56.0 0.40 65 104 0.55 230 18.5 419.685 24.780

4.620 2.029 1.159 8.874 1374 91.9 0.72 182 101 0.55 230 18.5 402.189 25.113

4.495 1.993 1.154 8.558 1374 88.7 0.69 171 94 0.55 230 18.5 377.364 24.910

4.421 1.978 1.151 8.435 1374 85.8 0.67 160 88 0.55 230 18.5 365.843 24.054

4.271 1.948 1.145 8.191 1373 81.3 0.64 142 79 0.55 230 18.5 343.174 23.020

4.181 1.935 1.143 8.078 1373 78.7 0.62 135 74 0.55 230 18.5 331.341 22.334

4.100 1.918 1.138 7.956 1377 75.4 0.59 125 68 0.55 230 18.5 319.998 21.250

3.956 1.893 1.133 7.752 1379 70.3 0.52 109 59 0.55 230 18.5 300.842 19.612

3.850 1.875 1.13 7.599 1381 66.5 0.49 100 52 0.55 230 18.5 287.003 18.118

3.745 1.851 1.124 7.415 1381 60.0 0.44 80 44 0.55 230 18.5 272.430 16.151

3.620 1.842 1.12 7.364 1380 58.5 0.41 70 39 0.55 230 18.5 261.526 14.912

3.450 1.825 1.12 7.191 1381 52.5 0.4 56 30 0.55 230 18.5 243.376 12.327

A9





pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

4.931 2.007 1.18 8.435 1203 -- -- 210 105 0.50 265 19.5 408.047 25.732

4.721 1.974 1.174 8.160 1203 -- -- 198 99 0.50 265 19.5 377.914 26.196

4.66 1.957 1.169 8.038 1203 95.50 0.69 196 98 0.50 265 19.5 367.436 26.671

4.593 1.95 1.169 7.966 1207 93.0 0.67 189 93 0.50 265 19.5 358.936 25.910

4.531 1.938 1.169 7.844 1205 93.0 0.67 184 91 0.50 265 19.5 348.650 26.101

4.506 1.927 1.166 7.762 1204 91.0 0.65 178 89 0.50 265 19.5 343.119 25.939

4.425 1.903 1.161 7.568 1204 88.50 0.64 167 84 0.50 265 19.5 328.539 25.568

4.321 1.878 1.157 7.354 1203 85.50 0.63 156 78 0.50 265 19.5 311.737 25.021

4.239 1.856 1.154 7.160 1203 82.50 0.61 147 73 0.50 265 19.5 297.762 24.516

4.191 1.845 1.151 7.079 1203 81.00 0.60 142 70 0.50 265 19.5 291.036 24.052

4.099 1.828 1.145 6.967 1203 77.50 0.56 130 65 0.50 265 19.5 280.135 23.203

3.991 1.796 1.141 6.681 1203 74.00 0.54 117 58 0.50 265 19.5 261.573 22.174

3.92 1.813 1.145 6.814 1204 73.00 0.53 111 55 0.50 265 19.5 262.018 20.991

3.801 1.77 1.135 6.477 1203 69.00 0.50 100 49 0.50 265 19.5 241.513 20.289

3.723 1.775 1.132 6.559 1205 66.50 0.48 94 46 0.50 265 19.5 239.537 19.204

3.701 1.738 1.126 6.242 1205 63.50 0.46 85 43 0.50 265 19.5 226.642 18.973

3.538 1.712 1.12 6.038 1209 57.50 0.42 71 35 0.50 265 19.5 209.579 16.700

3.491 1.703 1.118 5.967 1210 54.50 0.39 65 32 0.50 265 19.5 204.350 15.659

3.257 1.68 1.12 5.712 1215 48.50 0.35 54 26 0.50 265 19.5 182.505 14.246



pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

5.060 2.08 1.171 9.272

109 0.51 230 24.8 460.239 23.683

4.870 1.99 1.168 8.384

100 0.51 230 24.8 400.562 24.965

4.680 1.928 1.158 7.854 1128 85.2 0.71 178 91 0.51 230 24.8 360.583 25.237

4.561 1.899 1.154 7.599 1130 82.6 0.17 169 85 0.51 230 24.8 340.005 25.000

4.476 1.869 1.15 7.334 1128 80.1 0.66 158 80 0.51 230 24.8 322.024 24.843

4.355 1.842 1.147 7.089 1128 77.3 0.64 148 74 0.51 230 24.8 302.860 24.434

4.257 1.817 1.142 6.885 1128 74.4 0.61 136 69 0.51 230 24.8 287.526 23.998

4.170 1.803 1.141 6.752 1130 73.3 0.61 131 66 0.51 230 24.8 276.225 23.894

4.112 1.787 1.138 6.620 1130 71.0 0.59 124 63 0.51 230 24.8 267.034 23.592

3.932 1.744 1.131 6.253 1131 65.5 0.54 106 53 0.51 230 24.8 241.181 21.975

3.752 1.713 1.123 6.018 1132 61.5 0.51 91 46 0.50 230 24.8 221.505 20.767

3.580 1.671 1.118 5.641 1137 54.8 0.46 75 38 0.50 230 24.8 198.097 19.183

3.515 1.667 1.115 5.630 1138 53.1 0.44 72 35 0.50 230 24.8 194.148 18.027

3.382 1.647 1.109 5.488 1139 49.1 0.41 60 29 0.50 230 24.8 182.064 15.928

3.277 1.638 1.108 5.406 1153 46 0.39 52 26 0.50 230 24.8 173.789 14.961

3.112 1.616 1.106 5.202 1153 39.8 0.33 40 20 0.50 230 24.8 158.810 12.594

A10





pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A) Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

5.1 1.98 1.18 8.160 1050

96 0.51 230 31.75 408.253 23.515

4.94 1.966 1.177 8.048 1050

93 0.51 230 31.75 390.008 23.846

4.78 1.922 1.17 7.670 1050

86 0.51 230 31.75 359.679 23.910

4.705 1.918 1.169 7.640 1050 75.0 0.74 166 85 0.51 230 31.75 352.623 24.105

4.7 1.926 1.171 7.701 1050

87 0.51 230 31.75 355.070 24.502

4.615 1.906 1.167 7.538 1050 74.0 0.74 162 82 0.51 230 31.75 341.260 24.029

4.561 1.893 1.166 7.415 1050 73.0 0.73 157 79 0.51 230 31.75 331.790 23.810

4.49 1.87 1.162 7.222 1050 71.5 0.71 149 76 0.51 230 31.75 318.089 23.893

4.275 1.813 1.154 6.722 1050 66.5 0.66 129 66 0.51 230 31.75 281.897 23.413

4.078 1.757 1.144 6.253 1052 61.5 0.62 110 56 0.51 230 31.75 250.136 22.388

3.8 1.687 1.131 5.671 1050 54 0.53 84 44 0.51 230 31.75 211.411 20.813

3.65 1.656 1.125 5.416 1058 49.5 0.48 72 37 0.51 230 31.75 193.935 19.079

3.41 1.62 1.118 5.120 1060

29 0.51 230 31.75 171.288 16.931

3.25 1.59 1.109 4.906 1058

23 0.51 230 31.75 156.422 14.704

2.91 1.558 1.104 4.631 1060

15 0.51 230 31.75 132.196 11.347



pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

4.94 1.928 1.169 7.742

931

84.0 0.45 230 35.6 375.178 22.389

4.71 1.88 1.156 7.385

931 78.00 0.73 169 77.0 0.45 230 35.6 341.215 22.566

4.635 1.864 1.155 7.232

931 77.50 0.73 167 75.0 0.45 230 35.6 328.825 22.808

4.561 1.839 1.152 7.007

930 76.00 0.71 159 71.0 0.45 230 35.6 313.535 22.645

4.47 1.82 1.152 6.814

930 74.00 0.69 153 69.0 0.45 230 35.6 298.781 23.094

4.354 1.785 1.146 6.518

930 71.50 0.67 142 63.0 0.45 230 35.6 278.393 22.630

4.211 1.741 1.14 6.130

930 68.00 0.63 129 57.0 0.45 230 35.6 253.238 22.508

4.054 1.703 1.136 5.783

930 65 0.6 114 51 0.45 230 35.6 230.004 22.173

3.86 1.662 1.131 5.416

928 60.50 0.56 100 44.0 0.45 230 35.6 205.093 21.454

3.74 1.631 1.126 5.151

929 57.00 0.53 89 40.0 0.45 230 35.6 188.987 21.165

3.375 1.57 1.116 4.631

930 49.00 0.45 65 29.0 0.45 230 35.6 153.320 18.915

3.285 1.531 1.109 4.304

931 45.00 0.42 55 26.0 0.45 230 35.6 138.713 18.744

2.981 1.494 1.104 3.978

940 35.00 0.32 39 17.0 0.45 230 35.6 116.331 14.613

A11





pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

5.070 1.943 1.18 7.783 703

58 0.42 150 96.6 387.081 14.984

5.010 1.926 1.175 7.660 703

57 0.42 150 96.6 376.484 15.140

4.870 1.905 1.173 7.466 703

56 0.42 150 96.6 356.705 15.699

4.771 1.854 1.164 7.038 703 51.50 0.79 121 51 0.42 150 96.6 329.403 15.483

4.651 1.826 1.161 6.783 699 50 0.77 117 49 0.42 150 96.6 309.483 15.833

4.571 1.803 1.159 6.569 701 49.2 0.76 111 47 0.42 150 96.6 294.555 15.956

4.560 1.79 1.155 6.477 699 48.9 0.75 110 45 0.42 150 96.6 289.740 15.531

4.510 1.78 1.154 6.385 699 48.3 0.74 107 44 0.42 150 96.6 282.501 15.575

4.388 1.745 1.148 6.089 699 46.5 0.71 100 41 0.42 150 96.6 262.126 15.641

4.201 1.684 1.139 5.559 699 43.9 0.67 89 38 0.42 150 96.6 229.096 16.587

4.080 1.661 1.134 5.375 698 42.2 0.65 82 35 0.42 150 96.6 215.149 16.268

3.870 1.631 1.131 5.100 697 40.7 0.62 76 31 0.42 150 96.6 193.620 16.011

3.760 1.583 1.123 4.692 698 38.3 0.55 66 27 0.42 150 96.6 173.067 15.601

3.570 1.532 1.117 4.233 699 35.2 0.54 56 24 0.42 150 96.6 148.247 16.189

3.510 1.516 1.113 4.111 697 33.3 0.51 54 22 0.42 150 96.6 141.541 15.543

3.400 1.486 1.109 3.845 699 32.0 0.48 46 20 0.42 150 96.6 128.259 15.593

3.230 1.463 1.106 3.641 701 30.0 0.46 41 17 0.42 150 96.6 115.382 14.734

3.020 1.428 1.101 3.335 701 25.8 0.39 32 12 0.42 150 96.6 98.815 12.144

2.920 1.386 1.094 2.978 715 22.5 0.33 23 9 0.42 150 96.6 85.317 10.549

2.527 1.352 1.089 2.683 725 17.4 0.27 16 6 0.42 150 96.6 66.501 9.022



pressure_down (bar)

H (mwc)

N (rpm)

Us (V)

Is (A)

Ss (VA)

Ps (W)

PF R (Ω)

C (uF)

P_Hyd (W)

global eff (%)

5.11 1.945 1.175 7.854 813

77 0.41 230 57.7 393.714 19.557

5.06 1.932 1.178 7.691 813

76 0.41 230 57.7 381.761 19.908

5.01 1.911 1.171 7.548 813

74 0.41 230 57.7 370.970 19.948

4.89 1.885 1.17 7.293 813

71 0.41 230 57.7 349.852 20.294

4.764 1.873 1.166 7.211 813 73.50 0.75 167 68 0.41 230 57.7 337.024 20.177

4.731 1.866 1.165 7.150 813 73.00 0.75 164 67 0.41 230 57.7 331.849 20.190

4.63 1.839 1.16 6.926 813 71.50 0.73 157 63 0.41 230 57.7 314.572 20.027

4.554 1.809 1.159 6.630 812 69.50 0.71 149 60 0.41 230 57.7 296.194 20.257

4.331 1.749 1.146 6.151 812 65.00 0.67 131 52 0.41 230 57.7 261.321 19.899

4.26 1.719 1.14 5.906 811 62.50 0.65 122 49 0.41 230 57.7 246.807 19.854

4.15 1.697 1.139 5.692 810 61.50 0.63 116 46 0.41 230 57.7 231.714 19.852

3.991 1.659 1.133 5.365 812 58.50 0.59 103 41 0.41 230 57.7 210.057 19.519

3.79 1.616 1.125 5.008 807 55 0.56 91 36 0.41 230 57.7 186.204 19.334

3.6 1.557 1.118 4.478 807 49 0.50 73 30 0.41 230 57.7 158.138 18.971

3.452 1.536 1.114 4.304 807 47 0.47 67 27 0.41 230 57.7 145.765 18.523

3.342 1.516 1.111 4.131 808 45 0.45 62 24 0.41 230 57.7 135.435 17.721

3.14 1.475 1.106 3.764 808 40 0.41 48 19 0.41 230 57.7 115.938 16.388

2.901 1.435 1.099 3.427 807 35 0.35 35 15 0.41 230 57.7 97.534 15.379

A12

Energy Recovery in Water Distribution Systems by a Pump ...

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