SỔ TAY VỀ CHẤT LƯỢNG ĐIỆN (Handbook of Power Quality)

Due to the complexity of power systems combined with other factors such as increasing susceptibility of equipment, power quality (PQ) is apt to waver. With electricity in growing demand, low PQ is on the rise and becoming notoriously difficult to remedy. It is an issue that confronts professionals on a daily basis, but few have the required knowledge to diagnose and solve these problems.Handbook of Power Quality examines of the full panorama of PQ disturbances, with background theory and guidelines on measurement procedures and problem solving. It uses the perspectives of both power suppliers and electricity users, with contributions from experts in all aspects of PQ supplying a vital balance of scientific and practical information on the following:frequency variations;the characteristics of voltage, including dips, fluctuations and flicker;the continuity and reliability of electricity supply, its structure, appliances and equipment;the relationship of PQ with power systems, distributed generation, and the electricity market;the monitoring and cost of poor PQ;rational use of energy.An accompanying website hosts case studies for each chapter, demonstrating PQ practice; how problems are identified, analysed and resolved. The website also includes extensive appendices listing the current standards, mathematical formulas, and principles of electrical circuits that are critical for the optimization of solutions. This comprehensive handbook explains PQ methodology with a handson approach that makes it essential for all practising power systems engineers and researchers. It simultaneously acts as a reference for electrical engineers and technical managers who meet with power quality issues and would like to further their knowledge in this area.

Handbook of Power Quality

Edited by

Angelo Baggini

University of Bergamo, Italy

Handbook of Power Quality

Handbook of Power Quality

Edited by

Angelo Baggini

University of Bergamo, Italy

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Library of Congress Cataloging in Publication Data

Handbook of power quality / Edited by Angelo B Baggini.

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN: 978-0-470-06561-7

Typeset in 10/12pt Times by Integra Software Services Pvt Ltd, Pondicherry, India

Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire

Hermina Albert, Nicolae Golovanov, Aleksander Kot

and Janusz Bro ˙zek

1.3.1 Influence of the Frequency Variation on the Actuation Motors 6

1.4.1 Influence of Frequency Variations on Asynchronous Motors 81.4.2 Influence of Frequency Variations on Parallel-Connected

1.4.3 Influence of Frequency Variations on Series-Connected

1.6.4 Frequency Control in an Islanding System and

Krish Gomatom and Tom Short

2.5.1 Size of the End-User Load and Duration Affect Cost 49

2.5.4 Impact of Reliability Events on End-User Productivity 532.5.5 Mapping Reliability to End-User Facility Operating Hours 54

3.4.3 Voltage Control by Means of Reactive Power Flow Change 723.4.4 Voltage Control by Means of Network Impedance Change 74

3.5.1 Voltage Standards in Grid Normal Operating Conditions 763.5.2 Voltage Standards in Grid Disturbed Operating Conditions 76

4.5.3 Modification of the Supply System Configuration 96

4.7.3 Location and Method of Connection of Measuring Instrument 1174.7.4 Technical Specifications for Measuring Instrumentation 118

4.7.6 Techniques of Reporting the Measurement Results 1194.7.7 Methods for Aggregation of Measurement Results 119

Bibliography 131

Araceli Hernández Bayo

5.1.1 Voltage Changes, Voltage Fluctuations and Flicker 135

5.4.2 Electrical Appliances Supplied from LV Networks 155

Angelo Baggini and Zbigniew Hanzelka

7.1.5 Quantities Describing Voltage and

7.4.6 Harmonic Current Values/Magnitudes

7.7.3 Reduction of the Coupling Between Sensitive

7.7.4 Reduction of Load Sensitivity to

Franco Bua, Francesco Buratti and Alan Ascolari

Johan Rens and Piet Swart

9.1 Frequency Analysis of Non-Sinusoidal Waveforms:

9.2.4 Metrological Features of Measurement System 3029.2.5 Harmonic Power Measurement in

9.3.1 Fortesque Transform Redefined for Non-sinusoidal Circuits 307

9.4 IEEE 1459: Power Definitions for Modern Power Systems 3219.4.1 Voltage and Current Quantities under Non-sinusoidal

9.4.7 Fundamental Frequency Active and Reactive Power 327

9.5 Localization of Sources of Waveform Distortion in a Modern

Franco Bua, Francesco Buratti and Antoni Klajn

10.3.2 Voltage-to-Earth and Surface Potential Distribution 33910.3.3 Properties of Earth Electrodes at Lightning Currents 340

10.5 Earthing Arrangements in Protection Against Electric Shock 35510.5.1 Earthing Arrangements as Protection Elements

10.5.2 Earthing Arrangements as Protection Elements

10.6 Role of Earthing in Electronic and Telecommunication Systems 361

10.7.2 Corrosion Caused by Stray (Direct) Currents 372

10.8.2 Measurement of Resistance to Earth of an Earth Electrode 377

Angelo Baggini, David Chapman and Francesco Buratti

11.2 General Criteria for the Study and Choice of the Schemes 389

11.2.2 Scheme of the Grid as a Link Between

11.2.4 The System Supply Section and End Section 400

12 Reliability of Electricity Supply: Appliances and Equipment 403

Roberto Villafáfila-Robles and Joan Bergas-Jané

Andreas Sumper and Samuel Galceran-Arellano

13.3.1 General Features of Monitoring Instruments 452

13.5.4 Power Quality Data Interchange Format (PQDIF) 461

Mircea Chindris and Antoni Sudrià-Andreu

14.1 Impact of Static Converters on the Supply Network 464

14.1.5 Impact on Loads Supplied by Power Converters 481

14.2.1 Impact of Voltage Disturbances on Static Converters 487

Stefan Fassbinder and Alan Ascolari

15.1.1 Characteristics of Inductances and Capacitances 500

15.3.1 Dedicated Filtering Circuits for Individual Frequencies 514

Vu Van Thong and Johan Driesen

Roman Targosz and Jonathan Manson

of a Cash Flow Stream 58618.11.8 Deterministic Approach to PQ Investment Analysis 586

Pieter Vermeyen and Johan Driesen

19.3.1 Emission of Harmonic Distortion by Fluorescent Lamps 598

20.3 Analysis Process of the Customer with Respect to the

20.4 Multiplicity of Goods: Active Categories in the Territory

Annex 2

Angelo Baggini and Zbigniew Hanzelka

Annex 3 Power Theory with Non-sinusoidal Waveforms

Andrzej Firlit

Annex 4 Series and Parallel Resonance

Zbigniew Hanzelka

Araceli HERNÁNDEZ BAYO

Departamento de Ingenieria Eléctrica

Universidad Politécnica de Madrid

Escuela Técnica Superior de

Universitat Politécnica de Catalunya

Av Diagonal, 647 Planta 2

08028 Barcelona

Spain

Janusz BRO ˙ ZEK

AGH-University of Scienceand Technology

30-059 Kraków

Al Mickiewicza 30Poland

Franco BUA

ECD Engineering Consulting and Designvia Maffi 21

27100 PaviaItaly

Francesco BURATTI

ECD Engineering Consulting and Designvia Maffi 21

27100 PaviaItaly

Maurizio CACIOTTA

Università degli StudiFacoltà INGEGNERIADipartimento Ingegneria Elettronicavia della Vasca Navale, 84

00146 RomaItaly

David CHAPMAN

Copper Development Association

5 Grovelands Business centreBoundary Way

Hemel HempsteadHP2 7TE

UK

Technical University of Cluj-Napoca

Power Systems Dept

15, C Daicoviciu St

400020 Cluj-Napoca

Romania

Johan DRIESEN

Katholieke Universiteit Leuven

Dept Electrical Engineering (ESAT),

Universitat Politècnica de Catalunya

Av Diagonal, 647 Planta 2

TN 37932USA

Zbigniew HANZELKA

AGH-University of Scienceand Technology

30-059 Kraków

Al Mickiewicza 30Poland

Andrzej KANICKI

Technical University of Łod´zInstitute of Electrical PowerEngineering

18/22 Stefanowskigo Str

90-924 Łod´zPoland

Aleksander KOT

AGH-University of Scienceand Technology

30-059 Kraków

Al Mickiewicza 30Poland

Jonathan MANSON

JEL Consulting Limited

6 Staveley RoadChiswickLondonW4 3ESUK

Universitat Politècnica de Catalunya

Av Diagonal, 647 Planta 2

08028 Barcelona

Spain

Andreas SUMPER

CITCEA

Universitat Politècnica de Catalunya

Av Diagonal, 647 Planta 2

Vu Van THONG

Katholieke Universiteit LeuvenDept Electrical Engineering (ESAT),Div ELECTA

Kasteelpark Arenberg 10, bus 2445

3001 HeverleeBelgium

Pieter VERMEYEN

Katholieke Universiteit LeuvenDept Electrical Engineering (ESAT),Div ELECTA

Kasteelpark Arenberg 10, bus 2445

3001 HeverleeBelgium

Roberto VILLAFÁFILA-ROBLES

CITCEAUniversitat Politècnica de Catalunya

Av Diagonal, 647 Planta 2

08028 BarcelonaSpain

Irena WASIAK

Technical University of Łod´zInstitute of Electrical Power Engineering18/22 Stefanowskiego Str

90-924 Łod´zPoland

Power quality (PQ) issues are relatively new: years ago this was a problem concerning onlypower stations and arc furnace engineers It is only recently that the electrical engineeringcommunity has had to deal with the analysis, diagnosis and solution of PQ problems, even

if it has not become a major topic in the industry Professionals are being confronted with

PQ issues on a daily basis, yet only the latest generation of engineers has been trained toface and solve these issues

The main reason is probably due to the fact that PQ is a complex area covering manydifferent topics This is also something that makes a comprehensive book difficult – each

PQ topic can warrant an entire book, but time is more and more a constraint

If PQ issues applied to utility networks are relatively new, the same concepts applied

to customer installations and equipment have attracted the attention of the electrical worldonly in really recent times

The problems related to PQ are often difficult to solve, and may allow differentsolutions, so the choice is not always simple for those engineers and professionals who arenot trained in PQ The optimal solution to a PQ problem is usually a mix of solutions for

a specific situation In such a situation, it is necessary to identify that problem and proposedifferent solutions to allow the technicians to make the optimal choice

Evaluation of solutions is probably the key element in PQ problem solving, chieflyfor economic reasons Actually, some solutions require higher investments, and thus thenecessary management approval, but managers usually lack the knowledge to evaluate theproblems properly

For these reasons, in 2000 a group of academics and industrialists launched a culturalprogramme (www.lpqi.org) co-founded by the European Commission and fully dedicated

to PQ from the perspective of not just power suppliers but electricity users too Seven yearslater this program has more than 100 partners around the world and numerous sub-projectsfocused on specific issues related to PQ It was at one of these, LPQIves (LPQI VocationalEducational System), during the Berlin meeting in April 2005, that the idea for this bookwas born

Basically, the aim of the LPQIves project was to develop a system of vocationaltraining consisting of methodology and content and, in some countries, expert certification.The members of this project came to the conclusion that the book should be on systemcomponents The authors felt that the book should be a manual for participants on educational

students on regular university courses, and as a guidebook for people who seek backgroundinformation on practical solutions to PQ problems.

The unique character of the book is a well-balanced one between a scientific approachand practical knowledge which can be used in everyday situations by people who have only

a fundamental electrical engineering background To reflect this, one of the first decisionstaken by the authors was to illustrate each chapter with a case study of a practical application,its measurements and solution

This multi-use approach makes the book very comprehensive, practice oriented andattractive for a relatively broad audience: namely, scientists looking for links between theirspecific domain and other PQ domains; engineers seeking a methodology and information onthe identification, analysis and solution of a PQ problem; electricity users who need expla-nations of different PQ terms and definitions; managers looking for background information

on the economic consequences of PQ; and students who require a comprehensive manualcovering the whole spectrum of PQ

In order to consider PQ from different perspectives and topics, this book has beenorganized to cover five ‘themes’ The first is dedicated to power system issues The second

is fully dedicated to PQ phenomena in terms of physics, parameters, measurements, sourcesand mitigations The last three are dedicated to PQ in practice, PQ problems and economicalaspects of PQ The case studies and other specific content from each chapter are also

available on the companion website, www.wiley.com/go/powerquality

Before you begin what I hope is interesting reading, let me mention that, although

I was still young at the time of the 2005 Berlin meeting, prior to coordinating this group ofcreative authors around the world, I have been indicated as the main author of this book

Angelo Baggini Pavia, Italy

Frequency Variations

Hermina Albert, Nicolae Golovanov, Aleksander Kot

and Janusz Bro˙zek

Frequency is one of the most important parameters in the assessment of a power system’soperational characteristics Being shared by all the points in the power network, it requirescentralized control or at the zone power system levels

The frequency control and maintenance within allowed limits requires the existence

at the system operator level of important power reserves that can be called automatically

to assure at any moment a balance of the set-point frequency value of power tion and generation An ample and reliable information network that provides the systemoperator with necessary data is a prerequisite for control of the system frequency inreal time

consump-Failures in the interconnected power system are events that are felt throughout thesystem, while returning to the stable operation point, and arise from both the auto-mated response of generators in the affected area and through the contributions of neigh-boring areas via interconnection lines To this effect, the system operators of the variouszone systems use special help procedures to achieve recovery of the normal operationalstatus

Effective control of the generation and consumption in each zone of the system bythe system operator, and also good collaboration with system operators in neighboringzone systems, ensures that the frequency can be maintained within the entire system at theset-point value

Handbook of Power Quality Edited by Angelo Baggini

supply voltage frequency, defined as the repetition frequency of the fundamental voltagecurve, measured over a specific time interval.

In each power system, the operational moment of the frequency value depends on theextent to which the demand is met by the power sources

Setting up a nominal power system operational frequency – the frequency valuesupposed to assure this balance – is a matter of optimizing the possibilities of equipmentmanufacture and the requirements of specific producers and customers The selection of a

50 Hz nominal frequency in Europe and 60 Hz in the USA relies on a complex process inwhich the technical aspects, historical matters and companies’ interests all play an impor-tant role

The use of frequency below 30 Hz (the frequency above which the human eye can

no longer distinguish a separate succession of images) was accompanied by disturbingvariations of the luminous flux of incandescent lamps and these frequencies had to beabandoned The frequency of 25 Hz was in use on the Cote d’Azure up to 1955 During theinterwar period, 42 Hz was widely used in Europe, then it switched to 50 Hz, beginning in

1930 The frequency of 42 Hz was used locally up to 1964

The use of transformers is advantageous at high frequency Currently, industry uses on alarge scale transformers operating at 30–50 kHz frequencies (welding transformers, lightingtransformers, etc.) High frequencies which, due to the skin effect, increase linearly withthe frequency of inductive reactance and also increase the dielectric displacement currentsthrough parallel-connected capacitors, are not recommended for power transmission thatprovides economic parameters, at frequencies as low as possible (the use of transmissionlines at direct voltage is an example)

Often, the customer will use direct voltage and in order to obtain it, complex circuitsrectifying the alternative voltage are used

Electric traction, during its first development stage, used alternative voltage phase motors with a collector that required a low frequency For this purpose, 16 2/3 Hz(in Europe) and 20 Hz (in the USA) frequency systems were developed and are still inoperation

single-The increasing development of power electronics nowadays allows the use offrequency converters in industrial processes, which provides optimum frequency for variousprocesses

The requirement of power system interconnection determines the standardization offrequency

Frequency monitoring of the public network and its conservation within required limits

is the duty of the system operator, who is supposed to have at his or her disposal sufficientreserves of active power and adequate power frequency control in order to keep frequencydeviations within allowed limits

All equipment (installations) in the European power network are projected to operate at

a rated frequency of 50 Hz Actually, due to the fact that under normal operating conditionsthe frequency in the power system varies in terms of power variation and according tothe response speed of its control systems, while under fault and post-fault conditions itsvariation depends on the efficiency of the measures adopted to clear the fault, the electricpower quality normally requires limits that allow for the frequency variations

1.1 FREQUENCY QUALITY INDICES

In order to characterize the power system frequency, under normal operating conditions, thefollowing indices are used:

• f, the frequency deviation allowing evaluation of slow frequency variations:

where fris the rated frequency (50 Hz or 60 Hz) and f is the real frequency (Hz);

• relative frequency deviation, f (%):

According to standard EN 50160/2006 [1], the rated frequency of the supply voltage is

50 Hz Under normal operating conditions, the mean value of the fundamental frequencymeasured over 10 s stays within the following range:

• for systems with synchronous connection to an interconnected system:

50 Hz± 1 % i.e 49.5–50.5 Hz for 995 % of the year

50 Hz+ 4 %/ − 6 % i.e 47–52 Hz for 100 % of the time

• for systems with no synchronous connection to an interconnected system (e.g supplysystems on certain islands):

50 Hz± 2 % i.e 49–51 Hz for 95 % of the week

50 Hz± 15 % i.e 42.5–57.5 Hz for 100 % of the time

Figure 1.1 shows the curve of frequency variation under normal operating conditions, thevalues indicated being contained within allowable standard limits

Regarding transient regimes, it is required that the extensive variations of frequencymust be rapidly decreased in order to fall within the frame of the trumpet curve (Figure 1.2)set in compliance with system safety conditions [2] That is,

Figure 1.1 Frequency variations within 500 s

Figure 1.2 Frequency variation during a fault in a power network

where A is the experimental value; f0 is set frequency value; and T is a time constantresulting from the relation

T= 900

lnAd for T≤ 900 s and d = 20 mHz (1.5)Relation (1.5) considers that the post-transient regime begins within 900 s Consequently,the frequency must be in the range f0± 20 mHz

1.2 FREQUENCY MEASURING

The frequency reading is obtained every 10 s As power frequency may not be exactly

50 Hz within the 10 s time interval, the number of cycles may not be an integer number.The fundamental frequency output is the ratio of the number of integral cycles counted

Figure 1.3 Assessment of frequency quality in a power system

during the 10 s time interval, divided by the cumulative duration of the integer cycles Inorder to avoid determination errors, it is required to ensure mitigation of harmonics andinterharmonics, thus limiting the possibility of unwanted voltage passage through zero The

10 s measuring intervals should not overlap

The frequency measurement is performed by class A equipment, with r error, thatdoes not exceed 50 mHz and is not affected by a variation of the total harmonic distortion(THD) of the voltage up to 20 %

The evaluation of system frequency quality relies on the following procedure:

• monitoring the duration tm (Figure 1.3) over one week, based on the data obtained on

• determination of N2(the number of 10 s intervals) in which the frequency is below 47 Hz

or over 52 Hz while the voltage is within±15 % of the contracted voltage;

• checking conditions N/N ≤ 005 and N = 0

The power system interconnection and the steps taken to maintain the frequency withinrequired limits render deviations from the normalized values very rare phenomena In thisway, an analysis of the influence of frequency variations on the final customers is onlyperformed for a reduced interval about± 3 Hz of the rated value and for rather short periods.Within this reduced variation field, a considerable number of static customers (about

40 % of total consumption) are not affected by the frequency variations (rectifier installations,resistance ovens, electric arc ovens, etc.)

On setting the frequency control steps, and lacking further information, it is generallyconsidered that load self-control is 1 % per Hz; that is, the load decreases by 1 % if thefrequency goes down by 1 Hz

The static safety limit is the 20 mHz difference, identical to the one for primary controlaction

1.3.1 Influence of the Frequency Variation on the Actuation Motors

The asynchronous and synchronous driving motors, connected directly to the supply network,

and used extensively in industrial actuation, have a power–frequency characteristic P= T · dependent on the mechanical characteristic of the load involved, T

the variation curves of the power according to frequency for various types of customers.Curve 1 corresponds to receivers that in the analyzed frequency field have a consumptionindependent of frequency Curve 2 corresponds to types of hoisting installations, minelifts, beet conveyers, etc., that with a uniform load have practically a speed-independentcoupling and therefore the power consumption is proportional to the frequency Curve 3 ischaracteristic of viscous loads (calenders for paper fabrication, plastic mass hot processingmachines, textile industry machines, etc.) Curve 4 corresponds to a large number of receiverswith a parabolic mechanical characteristic (ventilation pumps) and thus a cubic characteristicpower–frequency [5]

The speed of asynchronous or synchronous motors connected directly to the electricpower supply network varies in proportion to the applied voltage frequency The frequencyvariation leads to the corresponding modification of the process productivity throughout thesupply with a reduced frequency

Figure 1.4 Power consumption of various types of receivers versus frequency variation

1.3.2 Capacitor Bank and Harmonic Filters

The reactive power Q generated by the capacitor bank is directly proportional to the supplyvoltage frequency

where C is the capacitor bank capacity and U is the voltage at its terminals

From the relation (1.6) one can notice the fact that variation of the supply voltagefrequency modifies the reactive power determined by the capacitor battery and thus itcan influence the value of the power factor at the supply busbars In most cases, for theallowed range of frequency variation, the influence on the power factor is not important.The frequency variation effects are particularly felt when the capacitor batteries are parts ofthe harmonic filters Under normal operating conditions (for a frequency equal to the ratedone) the parameters Lh and Ch of the resonant circuit are tuned on harmonic h so that thecircuit impedance for this frequency is actually zero, i.e

With decreasing supply voltage frequency, the input impedance of resonant circuitsbecomes capacitive and can determine overloading of a rank h circuit due to inferior rankharmonics which are not completely filtered

1.3.3 Transformers and Coils in the Power Network

The maximum value of the magnetic flux  determined by the application of voltage U

to the terminals of a magnetic circuit winding is obtained through the relation



√

2· U

where U is the actual value of the voltage applied to the winding terminals; f is frequency;

and w is the number of coils of the winding.

Analysis of the relation (1.8) reveals that for a certain configuration of the magneticcircuit, the frequency cut leads to an increase in magnetic flux and therefore of magneticinduction accompanied by possible operation in the non-linear zone of the magnetic char-acteristic In this way, the transformer’s no-load losses increase It can also result in adistortion of the electric current in the circuit So, the magnetic circuit operating at reducedfrequency becomes a non-linear element of the network The cut of the voltage frequency tothe transformer’s terminals also results in cutting of its leakage reactance, X= 2· ·f ·L,

as well as magnetizing reactance, X = 2 · · f · L (Figure 1.5), so that it results in an

Figure 1.5 Transformer simplified electric circuit

increase in the voltage to the transformers’ output and an increase in the no-load operatingcurrent At the same time, the coils’ reactance decreases, affecting the characteristic of thenetwork in which the coil is connected

1.4 INFLUENCE OF FREQUENCY ON USERS’ EQUIPMENT

The supply voltage frequency in the public electrical network, under current conditions inEurope, has very low variations in regular operation Under emergency conditions, however,transient conditions emerge in which the frequency variations range within the limits of theso-called trumpet curve

Practical calculations can consider the electrical network supply voltage frequency to

be constant and equal to 50 Hz

An industrial electrical network mostly uses driving systems with asynchronous motorssupplied via frequency converters which allow control of the asynchronous motor’s rotationalspeed within large limits in practical cases from zero to double the rotational speed obtainedwith 50 Hz supply (Figure 1.6)

1.4.1 Influence of Frequency Variations on Asynchronous Motors

An analysis of the behavior of an asynchronous motor on variation in frequency can beperformed based on a simplified equivalent diagram (Figure 1.7) This simplified diagramuses the following notation:

Figure 1.6 Asynchronous motor variable frequency supply

Figure 1.7 Simplified equivalent electric circuit for an asynchronous motor

• U1is the supply voltage per phase;

• R1 is the stator winding electric resistance;

• L1is the stator winding leakage inductivity as compared to the rotor winding;

• I1is the stator winding electric current value;

• Uh is the air gap equivalent voltage;

• Lh is the inductivity corresponding to the machine magnetization flux;

Assuming that a magnetization current I1+ I

2 is actually negligible, torque Meldeveloped

by the machine can be written as

The machine’s mechanical feature is Tel

indicated in Figure 1.8 for various supply voltage frequencies

Analysis of the curves in Figure 1.8 outlines the reduction of supply frequencycompared to increased rated frequency frf1< fr, breakdown torque Tkand starting torque

Figure 1.8 Asynchronous machine mechanical features for various supply voltage frequencies

machines For a frequency above the rated frequency, the working machines’ driving speedincreases.

Actually, the curves in Figure 1.8 cannot be used because, for reduced frequencies, themachine magnetization current leads to magnetic circuit saturation

To keep the induction constant within the machine magnetic circuit, the followingcondition has to be met:

U1

For frequencies above the rated frequency, the condition (1.10) would allow operation with

a voltage above the rated one, but this is not allowed due to the inadmissible electricalrequirement of the machine’s electric insulation Thus, the relation between machine supplyvoltage and frequency is as shown in Figure 1.9

Relation (1.9) indicates that, to meet condition (1.10), the breakdown torque is actuallyconstant, which determines the mechanical characteristics used to obtain the form shown inFigure 1.10

Analysis of the curves in Figure 1.10 underlines the fact that the use of asynchronousmotors fed with variable frequency voltage ensures control within a large range of the speed

of rotation without causing further losses throughout the control process

Figure 1.9 Voltage–frequency characteristic of asynchronous motor supply with variable frequency

Figure 1.10 Mechanical characteristics of an asynchronous motor fed with variable frequency thatmeets the constant magnetic induction condition for frequencies under the rated frequency

Obviously, the use of an asynchronous motor fed with variable frequency voltage hasimportant technological advantages which triggered the widespread use of this rotational speedcontrol system in modern industry Still, it is necessary to consider that, at low speeds, furthermachine cooling is required (the fan on the machine shaft determines a low air flow due tothe low driving speed) and also that lacking appropriate measures to limit the electromag-netic disturbances, the system can lead to the occurrence of harmonics and interharmonicswhich could affect the quality of the electric power supplied to other consumers in the area

1.4.2 Influence of Frequency Variations on Parallel-Connected

Condensers and Coils

Until now, the use of the control diagram in Figure 1.6 was only possible for motors fedfrom a low-voltage network due to the lack of technical and economic solutions acceptablefor the medium-voltage zone

Currently, these solutions exist, and therefore the medium-voltage motors too can befed directly with variable frequency voltage

Existing installations for medium-voltage motors supplied with variable frequency use

an intermediate reduced voltage circuit and an increased frequency converter outlet voltage(Figure 1.11)

Transformer T2 operation at variable frequency requires the magnetic induction to bekept at a value that should not exceed the saturation limit As in the case of the asynchronousmachine, to keep the induction equal to the rated induction, for frequencies under the ratedfrequency it is necessary to meet the condition (1.10) between the terminal voltage andsupply voltage frequency In the specific case shown in Figure 1.11, the condition (1.10) ismet, being required by the asynchronous motor operation

Obviously, the condition (1.10) has to be met by the transformers of another type thatcan operate at frequencies other than the rated frequency

One case often met is that where pieces of equipment are designed for 60 Hz operatingsystems Their utilization in 50 Hz frequency systems requires the supply voltage to bereduced some 20 % against their rated voltage

Figure 1.11 Medium-voltage asynchronous motor supply with variable frequency

and 60 Hz have larger losses with the 50 Hz supply For low-power equipment the lossesare irrelevant For equipment of larger power it is required to consider operation atreduced frequency.

Identically, the utilization of parallel-connected coils, at a frequency other than therated frequency, requires analysis of the conditions when saturation limits are exceeded andlosses increase

Induction keeping to the rated value requires control of the voltage to terminals as percondition (1.10)

1.4.3 Influence of Frequency Variations on Series-Connected

Condensers and Coils

It is customary in variable frequency circuits of asynchronous motors to use filters consisting

of parallel-connected condensers and series-connected coils

Reactive power Q generated by a parallel-connected condenser of capacity C and fedwith variable frequency voltage U is given by

Q= C ·  · U2= C · 3·U2

The asynchronous motor supply by meeting condition (1.10) determines that, at frequency operation, the reactive contribution of the condenser connected to the motorterminals must be greatly reduced

low-Coils connected in series with the motor fed with variable frequency have an inductivereactance proportional to the actual frequency going through the coil, which is to beconsidered on sizing the filtering circuit connected in series with an asynchronous motor

1.5 GOVERNING OF TURBINE SPEED

The frequency variations are determined by variations of the active power in the system, duemainly to variations in the final users’ consumption Frequency stabilization at the set-pointvalue requires a permanent adjustment of the electric power required at the generators’ termi-nals with the mechanical moment at their shafts (performed by the actuation equipment).The frequency control (generator rotational speed) is performed by means of theautomated speed regulator (ASR) The main function of an ASR is to provide a constantspeed to the electric generator rotation using the valves of the turbine for control, according

0set-point value, determined bythe active power modification

Figure 1.12 Speed regulator in the power plant

Figure 1.13 Centrifugal regulator operation system

The speed regulator should determine the steam (water) flow increase to the turbine

The first speed regulators were of mechanical–hydraulic type and changed the signalfor turbine shaft rotational speed into a linear displacement with a negative slope via acentrifugal system (Figure 1.13), which imposed a linear speed of rotation characteristicwith a slightly negative slope (Figure 1.14, curve Pd2) on the variation of the torque forthe actuation turbine shaft The speed regulator actuates on admitting steam (water) into theturbine by a value z proportional to the variation f of the frequency (speed of rotation

of the generator shaft) that controls the coupling with the turbine shaft and therefore its

Figure 1.14 Frequency modification on load increase within power system

the coupling with the turbine shaft would correspond to the curve Pd1.

Consider set-point frequency f0, while the power required at the generator terminalshas a characteristic Pc1 Characteristics Pd1and Pd2are controlled so that operation point Acorresponds to the set-point frequency value and to the power required PA

If the power requested increases corresponding to characteristic Pc2, for the case ofdefault of the automated speed regulator, the new operation point is established at point B1for a rotational speed (frequency) that is generally unacceptable (beyond allowed variationlimits) The use of ASR ensures a new operation point B2 corresponding to a frequencylower than the frequency set-point value but close enough to it The power transmitted

by the generator increases the value PB, thus complying with the power demand in thesystem

The main disadvantage of mechanical–hydraulic regulators is the low sensitivity (no

in accuracy due to wear

Currently, mechanical–hydraulic regulators have been replaced by electric–hydraulicregulators having the same operating principle yet with higher accuracy through replacingthe speed measuring system and mechanical systems with high-performance electronicsystems that are very reliable and accurate These systems also allow control by means ofadditional signals for effective control of the electric power generation system

Figure 1.15 presents the diagram of such a speed regulator

Y that will command the fluid turbine admission system The integrated-type regulatorgenerates a new balance condition between the active power released by the generator and

0.The astatic regulators are specific to the isolated systems considering that, within aninterconnected system, the recommended specification of the same set speed for the differentunit regulators leads to an unstable operation of the frequency control process within thesystem

Figure 1.15 Schematic diagram of an astatic speed regulator

and w is the number of coils of the winding.

Analysis of the relation (1.8) reveals that for a certain configuration of the magneticcircuit, the frequency cut...

Analysis of the curves in Figure 1.10 underlines the fact that the use of asynchronousmotors fed with variable frequency voltage ensures control within a large range of the speed

of rotation... to the occurrence of harmonics and interharmonicswhich could affect the quality of the electric power supplied to other consumers in the area

1.4.2 Influence of Frequency Variations