Cycloconverter drives for ship propulsion

Pełen tekst

(1)

Cycloconverter drives for ship propulsion

* K S S m i t h , BSc(Eng), PhD, AMiEE, *R Y a c a m i n i , B S C , MSC, cEng, MiEE. FIMarE a n d t A C W i l l i a m s o n , B S C , PhD, CEng. MIEE

*Department of Engineering. University of Aberdeen and fDepanmeni of Electrical Engineering, U M I S T

SYNOPSIS

The Royal Navy are considering, amongst other options using electrical propulsion, employ ing variable frequency cycloconverters on the next generation of anti-submarine warfare frigates. The ongoing work in the Engineering Department of Aberdeen University is addressing some of the challenges advanced by electrical propulsion. This paper concentrates on the electrical characteristics of cycloconverter drive systems.

INTRODUCTION

The subject of electrical motor propulsion of ships is one which is being addressed for future use in both the merchant and defence fleets. This paper examines the types of drive units which are being proposed and then sets out to study the system which at the moment looks to be the strongest candidate for use in the next generation of Royal Navy frigates. The power electronic unit considered in most detail is the cycloconverter driving an induction motor.

The operating principles of the cycloconverter are ex-plained and typical examples of this converter's use to date are indicated. The advantages offered by this propulsion method are discussed, as is a method of modelling the cycloconverter and elecuical machines using a lime domain simulation. Using these computer models it is possible to predict the performance of the complete marine propulsion system by including the synchronous generators, power electronic convener, and the propulsion motor in the simulation. The computer models are general purpose and are not restricted to any particular drive configuration. Different convener connections and motor ar-rangements can be readily incorporated into the simulation. This is demonstrated in this paper by examples.

ELECTRICAL PROPULSION OPTIONS

The possibilities of using electrical propulsion rather tiian gas or steam turbines or diesel sets is not anew idea. During the 1920s and 30s the United States aircraft carriers Lexington and Saratoga had turbo-electric drives and the cruise liners Normandie and Scharnhorst were both electrically driven. However, recent advances in power electronics and elecuical machine design suggest thai the use of electrical propulsion will be a cost-effective alternative to the mechanical systems which are currently most commonly used on vessels. Electrical propulsion has already gained a foothold in the industry as drives for large cruise liners and icebreakers.

In the U K , the best known example to date is the much publicised replacement of the Queen Elizabeth II steam tur-bines with two dc link inverter systems supplying synchronous machines which are directly coupled to the propeller shaft.'--The conveners are of the G E C 'synchdrive' design.'"* shaft.'--The synchdrive is used to provide variable frequency control of the synchronous motors between 0 and 60 Hz. For cruising the

K S Smith received his BSc(Eng) and PhD degrees from the University of Aberdeen in 1988 and 1992 respectively. SinceOctot)er 1991 he hasbeen a Lecturer in Engineering at the Department of Engineering, Aber-deen University, with responsibility for the teaching of heavy electrical power engineering. His main fields of interest are the interaction between electrical machines and power electronic converters on closely coupled a c systems such a s offshore oil and gas installations and ships. He has been responsible for harmonic and power system stability measurements on a number of offshore installations in the U K sector of the North S e a .

R Yacamini is currently a Senior Lecturer in the Department of Engineering at Aberdeen University. His previous experience includes 10 years a s a design engineer with English Electnc and G E C in the rectifier and high voltage dc transmission fields. During this time he made extensive u s e of physical simulations for controller design a n d system studies. This industrial period w a s followed by five years as a lecturer at UMIST where he carried out research, using frequency domain computer programs, into H V D C and reactive compen-sators. He took up his present post at Aberdeen in 1982 and h a s been involved in consultancy work for the oil industry for most of this period. The main thrust in his research has been to developtimedomain C A D analysis packages for power electronic applications. H e has published over 50 papers in this and related fields.

A C Williamson obtained his B S c at the University of Bristol and then s p e n d 13 years in industry working on the design and development of a wide range of electhcal

machines with emphasis, towards the e n d , on large turbine generators. Since joining U M I S T (where he obtained his PhD and is now a Senior Lecturer) he has been involved in the development of various power-electrical machine combinations. Typical applications have been high s p e e d engine testing dynamometer, high s p e e d , high power vahable speed drives and wind-turbine driven alternators.

variable frequency conveners are not used. The convener accelerates the synchronous machines up to the same fre-quency as the 60 Hz ship supply and then synchronises its output with the supply. The synchronous motor is then trans-ferred from the convener to the ac system busbars.

In Northern waters around Canada, Finland, and the CIS, icebreakers are required to keep waterways ice free during the

(2)

K S Smith, R Yacamini & A C Williamson AfI switchboard ifcOV 60Hz Ships supplies Aft switchboard ( winter months. A number of icebreakers have

now been built or fitted with electrical pro-pulsion employing cycloconverters. These drives give good performance a l the high power ratings and low speeds which are re-quired for this application. Twelve pulse cycloconverters have recently been installed on the cruise liners Fantasy (US) and Crystal Harmony (Japan) rated at 2 x 14 M W and 2 x

12 M W respectively. This is approaching the power levels required for the propulsion of the next generation of antisubmarine warfare frigates.

The Royal Navy, in considering the de-sign of futiffe warships, must take into con-sideration the required military role of war-ships in a changing political climate, and note the practices being used by the merchant fleet in the design of ships, as these may be aR)li-cable to warship design. Frigates, which will form üie backbone of the fleet into the 21st century, have two major roles. They are re-quired to police international waters and maintain free access to trade routes for the merchant fleet. This is essentially a cruising exercise requiring low cost propulsion. The second and major war time activity of the frigate is in submarine detection. A n impor-tant design feature is therefore to reduce the vibration caused by frigate propulsion sys-tems, as this is transferred to the hull of the ship and becomes water bcMiie noise which can be delected by submarines at a consid-erable distance. Frigates should ideally cre-ate as little wcre-ater borne noise as possible. This reduces the possibility of detection and makes it easier in turn to detect the noise generated by enemy vessels. One possible method of achieving this, which is currently being considered, is to adopt electrical pro-pulsion. This will also reduce running costs and, itisbeUeved, would significantly reduce the noise signature of vessels.' The reduction

in space required ïot modem electrical machines and advances in power electronic converter technology makes electrical propulsion systems a real possibility. Previous designs of machines and power converters were considered too bulky for naval use.* It is widely accepted that on the QE2, the onboard noise levels were reduced following the installation of the electrical propulsion system. This is on a ship where the original steam turbine drives were considered to be quiet. It should be remembered, however, that the converters used on the QE2 only operate during docking and slow cruising, and that audible noise as experienced by the passengers of a cruise liner is different from the water bcäue noise generated by the ships propellers.

Another majcM" advantage which electrical propulsion offers ship designers is the relative freedom with which the prime movers and power electronic converters can be located within the ship structure. The electrical cables linking the generator switchboard, converter, and propulsion motor are more flex-ible than the mechanical shafting required for gas turbine propulsion systems which require linear alignment.

The first of the R N frigates partially to employ electrical propulsion was the Type 23 Anti-Submarine Warfare (ASW) frigate using the combined diesel electrical and gas ( C O D L AG)

600V 50Hz

©

I. » 1 BMW diesel generators Forward switchboard 2 . V65MW Phase controlled thyristor rectifiers ttOVÔOHz 2 .9C5kW motor generator sets G! 2»Rolls Royce Spey gas turbirws

Ships supplies

2 k V5MW, 750V OC propulsion motors 2 « Fixed pitch propellers

Fig 1 : CODLAG propulsion system on the Type 23 ASW frigate

0 ©

© 0

I 4 K 20MW generators _Forward_sw|l chboard I ttOV 60Hz 2 x U 2MW cycloconverters Ships supplies 2 X 1DMW propulsion motors 2x 1MW motor generator sets fctOV 60Hz Ships supplies

Fig 2: General arrangement of an 18 MW electrical propulsion system

Fig 3: Cycloconverter output waveshape composed of segments of the line to line voltage on Input side

Fig 4: General arrangement of two Graetz bridges to form a single phase cycloconverter

(3)

0-5 Ratio of Output frequency to Input frequency

Fig 5: Chart showing the harmonic frequencies present in the output voltage of a single phase cycloconverter

sets have been employed lo isolate the propul-sion and ships service busbars. This is unlike offshore practice where the distortion on the low voltage system is tolerated and only f i l -tered out i f it is found to be absolutely neces-sary.

The dc motors in the C O D L A G system operate under quiet cruise conditions for towed array sonar operation. The output of the con-verter CŒitains harmonics at six, and twelve times the supply frequency, superimposed on the mean dc output level. Additional filtering is connected between the converter and the motor to prevent harmonic fluxes in the motor generating noise on the propeller shaft sys-tem. When fast acceleration is required the gas turbines are used to provide ' sprint' power. The system load at sea varies from about 1.5 M W at low speeds to about 4.5 M W when motors are at foil power. The motors continue to operate at full power when the gas turbines are in use. The harbour load is 0.4 M W .

The Royal Navy is now considering using full electrical iM^opuIsion for the next

genera-Fig 6: Primitive model of a three phase induction motor Fig 7: Primitive model of a three phase, salient pole synchronous machine

system, illustrated in F i g 1.' Generation is at 600V with two 1.65 M W thyristor rectifiers coupled to the generator busbars. These supply 1.5 M W dc motors which are directly coupled to the propeller shaft system. When the rectifiers are in operation severe commutation notching will occur on the generator busbar, producing waveshapes similar to those observed on offshore drilling rigs.* ' If the 440V ship service systems were supplied through step-down transformers from the600W busbar, these commutation disturbances would be reflected through the üansformers and appear throughout the low voltage distri-bution system. This distortion would exceed the levels allowed in naval systems. To overcome this problem rotary converter

tion of frigates.'". A 5000t A S W frigate has to achieve a maximum speed of 30 kn using twin shafts. This requires 18 M W per shaft at 200 rev/min. The design of large dc motors is practically limited to around 8 M W , and tandem designs using three or more dc machines are not considered feasible as the size of the overall propulsion motCH" becomes excessive. It wUl therefore be necessary to use ac machines to reach the required power level in conjunction with variable frequency systems such as cycloconverters. Two alternatives are available for the ac propulsion motors: either induction (asynchronous) or syn-chronous machines. Induction machines are considered to be more rugged and robust, and require less maintenance, as

(4)

K s Smith. R Yacamini & A C Williamson

unlike the synchronous machine there are no electrical termi-nals to the rotor requiring the use of slip rings. The air gap of an induction motor is generally smaller than that of a synchro-nous machine which will make it less able to withstand shock. Induction machines are also generally cheaper than synchro-nous machines. The discussion is therefore ongoing and manufacturers are now looking at the design of induction machines with much larger air gaps, which will give the induction motor the same robusmess as the synchronous machine for this application. The general arrangement of a possible full 18 M W electrical propulsion system is shown in Fig 2.

THE CYCLOCONVERTER

The cycloconverter is a power electronic circuit which converts an ac input to an ac output at a lower frequency. Unlike many of the converters commonly in use today, such as the

'synchdrive' mentioned above, this is achieved without using an intermediate dc link, ie the cycloconverter is a single stage converter. The cycloconverter is not a new power electronic circuit The principles of this converter are described in one of the earliest texts on power electronics." Considerable devel-opment work took place in Germany in the 1930s where cycloconverters were used for unction applications. At this time the principles of grid control, to give a variable output voltage and frequenc were mastered.'^ The cycloconverter generally found an)lication where low

fre-quency, high power ac drives are required. Examples include tube mills,'^ '* and railway traction." More recently the converter has been applied successfully to a mine winder,'* the advances in control techniques giving a performance comparable with that of a dc drive."

The basic building block used in the con-struction of the cycloconverter is the six pulse Graetz bridge. A description of the operation of this converter can be found in standard texts on power electronic circuits.'*" The Graetz bridge is normally used either as a rectifier or as an inverter, converting an ac input to a dc output or a dc input to an ac output. This is controlled by changing the firing instants of the thyristors within the bridge, relative to the three phase supply at the bridge ac terminals. It is possible to pro-duce a low frequency ac output from what would normally be considered as the dc ter-minals of the bridge by continually changing the fuing delay angles of the thyristors. The output ac voltage waveshape is then cran-posed of segments of the input ac line to line voltage as shown in Fig 3. It is possible with the cycloconverter to control independentiy

both the frequency and amplitude of the output voltage. A single six pulse bridge cannot supply both positive and nega-tive half cycles of the output current which necessitates tiie use of a second bridge. This leads to the basic six pulse single phase cycloconverter configuration shown in Fig 4. For this circuit to operate successfully, it is necessary to allow only one bridge to conduct at any time. If üie desired load current is positive, bridge A should be conducting and bridge B switched o f f

Fig 8: General arrangement of a three phase, six pulse, cycloconverter Induction motor drive

(A) 1.3k I.ZJk U - 710-/ il

!

A 1 3UU — aso- 0-r ' hi 1

\ V n '

J\ ' 1 > .33U • Siltl -1' li Kl ' \ 1 1 mi / T 1 Ml 1 1 V " 1 1 A < Mil 1 1 .710

-\ iP ! -\ .

il" / p i / .|k •1.21k I.Ik -.|.7)k , 'i «/ V V W '-Hi; W ' f'

1 0 2ku 4in ai» Hkii IWkii 12(kii 14JIII lOlin IHIIiii 3IUII Ks)

Negative load current should be supplied by bridge B , witii

Fig 9: Simulated currents for the system in Fig 8; solid line Is the motoring condition, dashed is the generating condition

bridge A switched o f f This can be achieved by blocking the üiyristOT gate signals to each bridge at the appropriate time. This is not a trivial problem; determining the correa instant lo transfer load current between bridges has been a m ^ o r problem for cycloconverter designers.

Three phase cycloconverters are formed by combining tiiree individual single jAase units. A number of three jAase COTinections are possible which have differing harmonic ef-fects upon both the input and output sides of the converter.

(5)

2Uii Hkii ICiOin lakii aKkn l(s)

FIg 10: Cycloconverter output voltage (motoring condition)

16Un

Fig 11 : Cycloconverter output voltage (generating condition)

Twelve pulse cycloconverter circuits can be formed using four, three phase six pulse bridges.

For the six pulse, single phase cycloconverter, supplied from an infinite busbar, the major harmonics present in the output voltage are given by:^°

f, = 6 p f . ± ( 2 n + l ) f „ (1) For the twelve pulse converter the harmonics are:

f , = 1 2 p f , ± ( 2 n + l ) f „ (2) where f, is the input frequency, f« the output frequency and f^ Üie

harmonic frequencies.

From these equations it is clear that the output voltage of the cycloconverter contains a large number of harmonic terms. The frequencies given by the relationships in equations ( 1 ) and (2) are not in a mathematical sense true harmonics, as the

modulation process present within the cycloconverter gives rise to con^)onents which are neither integer multiples of the input or the output frequencies. The frequency con-tent of tiie output voltage waveshape of a cycloconverter is therefore extremely com-plex, containing a wide range of frequencies. These can be conveniently represented using tiie chart shown in Fig 5.

The amplitudes of these harmonic fre-quencies are a fonction of the output voltage ratio (the depth of modulation control signal to the converter) and the load power factor. Each Une in Fig 5 has associated with it a fixed amplitude, regardless of the frequency ratio. When the output frequency of Üie drive is zero, the harmonics present in the output voltage waveshape correspond to integer multiples of the converter pulse number and tiie supply frequency. For example, a six pulse bridge will contain harmonics of order 6, 12, 18, etc. This corresponds to the left hand part of Fig 5, where the families of harmonics present in tiie cycloconverter originate. When the output frequency of the cycloconverter is increased, the second term in equation (1) becomes non-zero producing frequencies above and below the harmonic parents. This is clearly shown in F i g 5. It should be noted from this chart that at several distinct values of output frequency, the com-ponents given by equations ( 1 ) and (2) will be of very low or even zero frequency, ie dc components of voltage. Alternatively tiiey can produce frequencies very close to, or exacüy equal to the desired output frequency. Under tiiese operating conditions, the dc component could possibly saturate the pro-pulsion motor, or the components close to the wanted output frequency may produce a pro-nounced beating effect of the motor current and voltage waveshapes. It is possible to derive equations which give the frequency content of the current supplied to the cycloconverter from the ac system. A s for the output voltage waveshape this is also found to contain a very wide range of frequencies.

When considering using a cycloconverter for a marine electrical propulsion drive a number of questions must be addressed, including: What effect w i l l the cycloconverter have on the synchronous machines supplying the ac system? How severe will die ac voltage distortion be. and what oscillating torques will be induced on the shaft of the prime mover? Is tiiere a possibility of the oscillating torque exciting a torsional resonance of tiie propulsion motw-propel-ler shaft system? Is one cycloconverter configuration better tiian another for a particular appücation and how is this assessed? How will the system perform under abnormal con-ditions such as semiconductor device failure or unbalanced supply conditions?

Questions such as tiiese can be answered by developing computer models to simulate complete electrical propulsion systems and assess the relative advantages and disadvantages of different converter configurations. For tiiis application C A D software has been used, which allows different cycloconverter topologies to be readily assembled and simulated.

(6)

K S Smith. R Yacamini & A C Williamson

POWER ELECTRONIC

SIMULATION

There is a wide range of computer simula-tion packages available on the software mar-ket which can be ^ p l i e d to the analysis of power electronic and other similar systems. In developing a computer model of a com-plete marine propulsion system it is necessary to describe electrical machines and power electronic converters, to be able to change the arrangement of the components, implement different control strategies, and also smdy the effects of abnormal opo^tion on the p o f orm-ance of the converter.

One such package is the Saba* simulator, which is marketed as a mixed analogue and digital simulation package and has been found particularly useful for this type of applica-tion. The simulation process using this pack-age can be divided into three distinct stpack-ages, involving the input of the system data, per-forming the system analysis, and finally processing and viewing the results of the analysis (post-processing).

The input to the simulator consists of a file describing the system to be analysed. This netUst file can contain references to otiier netlists and components which allows full hierarchical systems to be convenientiy ana-lysed. This feature is particularly useful in developing models of large complex sys-tems, where each subcomponent can be tested individually before being inccMporated into the larger system. When the nethst describing the system is complete, the simulator is in-voked and the netlist information read and checked for errcx's. If no errors are found the simulation can proceed. The numerical inte-gration techniques used by this simulator include first and second csder methods such as Backward-EulerandTr^zoidal methods. The post-processor allows the results of the analysis to be viewed on the computer screen. This takes the form of waveshapes which is convenient as itmaintainsanengineaing 'feel' forthesystem being analysed. Frequency domain spectra can also be di^layed if required.

The unique feature of tiie simulator, which

makes it particularly useful for the simulation of marine cycloconverter prcpulsion systems, is the ability to define the characteristics of new components. This is achieved using the Mast modelling language.'' Mast is very similar to the pro-gramming languages C and Fortran and is used to describe the matiiematical relationships governing the operational charac-teristics of the desired component. The characcharac-teristics of any system can then be programmed, removing the restrictions present in the type of simulators which only represent electrical networks. Mechanical quantities can be directly represented in their own units and not by electrical analogues. The connection points to the templates which describe components can be either electrical (x mechanical nodes. Although the simulator is marketed as an electrical simulate^- this facility allows it to be used as a mechanical simulator, and where electrical machines are used as an electro-mechanical simulator.

I N r . | 6uk ..1 4 Ilk ;uk lOk -- 4 U k -.40k — .•Ok

-Ô 3kii 4I11 (Û11 Util lUkii lÀn l-Âu ItiÙiii ilùii Win

is the generating condition

TUMn Us)

Fig 13: Currents drawn by Individual cycioconvsrters

The programming capabilities of Mast have therefore been used to develop models which describe the operation of induc-tion and synchronous machines, as well as the controller present in the cycloconverter. Electrical machines have been modelled by programming the voltage balance equations of the phase models of the machines in combination with the relation-ships describing the dynamics of the rotor system. In the case of the induction machine, the representation employed in the simulations is shown in Fig 6.^ The machine consists of three stator windings (sa, sb, and sc) and three rotor windings (ra, rb, and rc). The parameters for tiiis model can be calculated from the fundamental equivalent circuit of the machine. The primi-tive model of the synchronous machine implemented is shown in Fig 7. In this representation four windings are shown on the rotor of the synchronous machine, two in the direct and two in the quadrature axis." This allows the effects of synchronous

(7)

lOka llUii aWkii t(s)

Fig 14: Total current drawn from the ac system

Fig 15: Motor current waveshape showing the effect of changing from a four wire to a three wire connection; dashed is four wire, solid Is three

wire

machine saliency to be included in the simulation if necessary. Phase models of electrical machines have been found to be more useful than the more widely used two axis models.^ Using the Saber simulator, it was found that the phase model was more robust and gave shorter run times in many cases. In addition using the phase model it is possible to consider the effects of unbalances within the machine and to show how these would affect the overall performance of the cycloconverter drive.

In the contfoller implemented in tiie work described in tiiis paper an open loop strategy has been employed, based upon die well known inverse cosine control method. The logic required to implement this controller, determining tiie thyristor firing instants as weU as die converter group blocking and deblocking signals, has been written into the simulation using the Mast modelling language. Otiier control sfrategies, such as control

of the stator currents to give torque control, can also be implemented.

The basic elements of a ship electrical propulsion system have been modelled; these can be used to study the different systems proposed.

POSSIBLE

CYCLOCONVERTER

PROPULSION SYSTEMS

Full electrical propulsion of a 5000t A S W frigate will require two drives each rated at 18 M W . Present Royal Navy frigate experience of electric drives is limited to the 1.6 M W dc drives used in the C O D L A G system. It is unhkely üiat tiie R N will adopt tiie 18 M W drive in the fu^t instance; instead it is felt tiiat a 4 M W drive, combined wifli existing gas turbine technology in an arrangement similar to the C O D L A G system, is likely to be used as a further step towards tiie 18 M W drive. This smaller drive will itself intixxluce a number of new design problems to frigate electrical engineers. These design questions are related to the topology o f the cycloconverter and changes to the power system itself will be required.

In order to reach the power levels required for electrical propulsion it will be necessary to increase the voltage of the prime mover generators from 440/660V to 3.3 k V , 6.6 k V o r 11 kV. Switchgear rated at tiiese voltage levels is readily available from manufacturers, and has found extensive use on offshore oil and gas recovery platforms. It has also been suggested that it may be advantageous to raise tiie fre-quency of generation frcan 60-90 Hz.

In designing the 4 M W drive a number of different options have to be considered. What should be the pulse number o f the cycloconverter? Should a tiiree or four wire connection to die propulsion motor be used? Should an induction or a synchronous ma-chine be used? Are some transformer con-nections preferable to others? In attempting to answer these questions a large number of different converter configurations must be considered. The computer modelling of the cycloconverter drive allows die relative merits of different converter topologies to be consid-ered and the performance of the complete electrical propulsion system as a single unit to be analysed.

SIMULATION RESULTS

Cycloconverters and motors

In order to illusfrate the characteristics of different con-verter topologies, and also demonstrate tiie usefulness of time domain simulation as a design tool, waveshapes obtained from tiie simulation for a number of different cycloconverters are presented and discussed.

(8)

K s Smith. R Yacamini & A C Williamson

The basic building block used in the design of large cycloconverter drives, as mentioned above, is the six pulse bridge. T w o back to back bridges combined give a cycloconverter with a single phase output and six bridges can be used to give a three phase output. Transformers are required at die input to each phase of die cycloconverter to provide electrical isolation between phases, if the motor phases are not isolated. One of the propulsion options being considered is to use a star connected induction motor. A possible configuration f o r a 4 M W six pulse drive is therefore shown in Fig 8. A switch, S W l , is shown in the neutral wire to the motor. For the first set of simulation results this switch is left closed, giving a four wire motor connection. It will be shown later that if S W l is opened to turn the drive into a three wire connection then changes in the waveshapes associated with the drive will occur. The param-eters of the system analysed have not been chosen to model an existing or planned cycloconverter installation. The purpose of displaying the waveshapes is to emphasise the possibilities for analysis offered by the simulation. In the cases presented for example, the system supply frequency is 50 Hz, rather than the more normal 60 Hz for a ship, or the 90 Hz suggested for future installations. The supply frequency, and indeed all the other parameters of the system including the machine ratings and reactances, can be conveniently changed to allow the study of other systems. More importantly from the designer's point of view, this allows direct comparisons between systems to be made.

The waveshapes obtained from this simulation are shown in Figs 8-14. Two conditions are illustrated corresponding to motoring and generating action in Uie motor with the output frequency of the drive at 15 Hz. For tiie motoring condition üie mechanical power supplied by the motor is 2.4 M W whilst for the generating condition üie power is 4.2 M W . The waveshapes for each of tiiese conditions are shown together on the same graph to allow direct comparisons in the time domain to be made between them.

Figure 9 shows the stator currents for the two cases studied. There is clearly a phase difference present between these waveshapes. This is required to achieve the reversal of power flow, as no phase difference is present in the motor line to neutral voltage as shown in Figs 10 and 11. This is to be expected as the modulating function to the cycloconverter, which determines the reference signal to the inverse cosine controller has not changed. The change in load is achieved by changing tiie polarity of tiie load torque. It should be noted from close inspection of Figs 10 and 11 that with the motor generat-ing, the bridges witiiin the cycloconverter spend considerably more time in inversion than in rectification mode. This is to be expected since power flow is now from the motor shaft back tiirough tiie converter to üie ac power system. The torque waveshape on üie shaft of tiie propulsion motor is shown in Fig 13. The reversal in tiie sign of torque required to produce a reversal in power flow is clear. The currents drawn by the individual cycloconverters are shown in Fig 13. Inspection of tiiese waveshapes shows that there are, in fact, a wide range of frequencies present, including frequencies below the supply frequency. The effect of Üie 120 deg phase displacement between each of tiie single phase cycloconverters is to reduce the number of frequencies present in the current waveshape drawn from the supply system. This waveshape is shown in Fig

14. Although tiie harmonic content is reduced tiiere is still a wide range of frequencies present, including non-integer and sub-harmonic terms.

The results of passing the lime domain data, present in tiie waveshapes presented above, through a Fourier analysis pro-gramme with a resolution of 5 Hz, produced tiie frequencies

Rg 16: Primitive model of an induction motor with a double wound stator

Fig 17: General arrangement of a six pulse cycloconverter supplying a double wound stator

induction motor

shown in Tables I and II. for the motoring and generating conditions respectively. The corresponding harmonic spectra are shown in Appendix 1 for the motoring condition.

Inspection of Tables I and II shows tiiat the harmonics present in the output voltage waveshape of üie cycloconverter agree with those which would be obtained using equations (1 ) and (2), which are based on a frequency domain calculation. The simulations do have the advantage of showing actual waveshapes which the previous analysis does not show. The waveshapes obtained from the simulation also include üie effects of commutation overlap and the iniercoupling that is present between tiie cyclcoconvertcrs. These effects are ig-nored in the frequency domain calculation. The wanted output frequency is 15 Hz, and sideband frequencies appear at odd

(9)

I I I I I I 1 I I 3tn •Uli 6Uii Hkn lUkii I3in Mn Idlkn ItUn 3Xkii ih

Fig 18: General arrangement of a six pulse cycloconverter supplying a double wound stator induction motor

^ i I ! 1 1 1 1 1

Jkn -Uli 6an 8Uii lUkn Okn l*ka IfiOra IWm 2UUn t(s)

Fig 19: Voltage across one stator phase of the double wound motor

multiples of 15 Hz above and below the supply frequency times the converter pulse number, ie 300 Hz. Sidebands also appear cenffed around600 Hz. For example, sidebands cenu-ed around 300 Hz appear at 285 Hz and 315 Hz, and also at 255 Hz and 345 Hz.

Harmonic currents flow in the stator winding of die machine at tiie frequencies present in the output voltage w a v e s h ^ . The 15 Hz wanted component produces the mean dc component of tOTque whilst the harmcMiic currents give rise to harmonic components of torque. The largest harmonic torque is at 300 Hz. This harmonic torque is independent of the output fre-quency of the cycloconverter drive. The frefre-quency of this component is determined by tiie frequency of tiie supply system and the converter pulse number, and does, in fact.

appear at the same frequency at which the sidebands present in the cycloconverter out-put voltage are centred, ie at the product of six times tiie supply frequency and tiie ccmverter pulse number. This torque is produced by the action of the pairs of sideband current har-monics centred around this frequency. The wanted component of current at 15 Hz duces a flux wave in the air gap of the pro-pulsion motor which is of positive phase sequence. The first pair of sidebands occur at 285 Hz and 315 Hz. The current at 285 Hz produces a flux wave which rotates in the same direction as the 15 Hz flux wave, ie the 285 Hz flux wave is also of positive phase sequence. The flux associated with the component at 315 Hz will rotate in tiie opposite direction to that at 285 Hz and is therefore of negative phase sequence. The contribution of these components to the mean value of torque is negligible. They do however combine to produce a harmonic pulsating torque at 300 Hz. A similar argument can be applied to tiie otiier sidebands centred around 300 H z . A harmonic torque also s p e a r s at 600 Hz, which is produced by the sideband current harmonics centred around this frequency.

The currents drawn by the individual cycloconverters are very rich in harmonics. Inspection of Tables I and II reveals some large components, eg 20 Hz of 45.46 % and 80 Hz of 25.84 % for the motoring condition. Due to the transformer ccmnections employed and the 120 deg phase shift present at tiie output of each individual cycloccaiverter, many of these harmonics have their ampli-tude significantiy reduced in tiie current drawn from the ac supply system. For example, die COTiponents at 20 Hz and 80 Hz discussed above are reduced to 1.03 % and 0.72 % in die supply current. It should be noted that tiie harmonics generally associated with a six pulse converter, ie 5th, 7tii, U t h , 13tii, etc, are present in both the ac system supply current and the current to the individual cycloconverters. The amplitude of these COTiponents on the ac supply side and on die cycloconverter input are tiie same. N o sig-nificant attenuation of these components occurs.

If the switch S W l in Fig 8 is opened, this has an effect on die current supplied to the propulsion motor. The current waveshapes obtained for the motoring condition studied previously witii the switch closed, and tiiat witii the switch open, are shown togetiier in Fig 15. There is clearly a significant difference between the two w a v e s h ^ s . This effect is due to the output voltage of tiie tiiree phase cycloconverter containing frequencies which are of zero phase sequence. Currents at tiiese frequencies can only flow i f tiiere is a neutral connection to die motor. These components are tiierefore present in tiie earlier waveshapes where the switch S W1 is closed but are absent when it is opened. It should be noted, however, tiiat die presence or absence of zero sequence currents in tiie supply to tiie motor does not affect tiie elecfromagnetic torque produced by tiie machine. This is due to die zero sequence components producing no air gap mmf.

(10)

K S Smith. R Yacamini & A C Williamson

Zero sequence currents can therefore only flow in the stator winding (if a neutral wire is present), and consequentiy the impedance of the induction motor is smallor to components of zero phase sequence as the rotor is not included in the zero sequence equivalent circuit"-^

A n alternative design for the propulsion motor would be to use an induction machine witii a double wound statw winding. The primitive phase model of such a motor is shown in F i g 16, in which the two sets of stator windings are displaced by 30 deg elec-trical, and each phase winding is supplied by a single phase cycloconverter. The 30 deg phase shift present in the stator windings has the effect of cancelling a large number of the harmonic mmfs present in the air g ^ of the machine, and so reduces the ripple present in the induced machine electromagnetic torque. This can be illusu-ated by the results obtained from the computer simulation ior the system shown in F i g 17, which features such a motor. The current supplied to the motor is shown in F i g 18. This waveshape is not signiflcantiy different from that drawn by the three phase, three winding motor shown in F i g 9. The motor line to neutral voltage is shown in Fig 19. This waveshape is seen to contain more high frequency terms due to the increased number of converters supplied from a com-mon busbar. The effects of commutations taking place in other converters are present from the connection at the point of common coupling. Intarcoupling effects between the six stator windings of the machine are also present

The most significant diffCTcnce between the three phase machine and the six phase machine lies in the torque shown in F i g 20. Comparison of this waveshape with Fig 12 clearly shows that the ripple component is reduced. (Note that the dc value between the two cases is different.) The cycloconverter input current shown in F i g 21 is broadly similar to that of Fig 13 as would be expected. The current drawn from the ac system is shown in Fig 22 which displays less harmonic distortion than die earlier case of F i g 14.

These general observations on the time domain waveshapes are confirmed by inspection of tiie results obtained from Fourier analysis shown in Table III.

The frequencies present in tiie motor voltage and the motor current for the double wound machine and the earlier tiiree phase machine are almost identical in both frequency and amplitude. The current drawn from the ac system contains less hamionics tiian tiie earlier case; the side bands previously centred around tiie 50 Hz fundamental are significantiy re-duced. It should be noted that the harmonics characteristic of a six pulse drive, ie the 5th and 7th, are not eliminated as they would be with a twelve pulse converter. They are, however, reduced using the double wound stator.

From the waveshapes and tables of harmcmics presented, it is apparent tiiat the cycloconverter drive with a double wound stator on the propulsion motor offers a number of advantages over a three phase machine. Most significantiy tiie harmonic

3lh 4kii

I i i I i I ! 6Un Kin UKkn 13Jm \43a\ 160m I8O111 ZXkn l(s)

Fig 20: Machine torque for double wound motor

—! 1 1 1 i 1 1 I I 3Jni -till fiUn Bkn Ittkn 12Un 14Cini 160m IHm aXkn t(s) Fig 21: Current drawn by an Individual cycloconverter

content of the torque is reduced, as are the harmonics present in tiie current waveshape from the ac system.

Ships generators

In the earlier sections the effects of the cycloconverter upon the propulsion motor, and especially tiie torque produced by the motor, have been considered in detail. Large cycloconverter drives, if applied to ships, will have a significant effect upon tiie synchronous generators which supply the system. The cycloconverter propulsion system on a frigate would, in fact, be tiie largest single load on tiie frigates electrical system. A n understanding of the possible detrimental effects of the drive on the alternators is therefore required.

The characteristics of non-linear loads, such as diode and thyristor bridges, on die performance of synchronous ma-chines has been studied previously These works show that for wound rotor machines which do not display the effect of

(11)

akii lakii IHkii 3irkii l(s) Fig 22: Total current drawn from the ac system

(N .,1 12.3k .

akii 2U(kn l(s)

Fig 23: Torque on the shaft of an aKemator supplying a three phase, six pulse 4 MW cycloconverter drive

ent system components, are included auto-matically in tiie time domain simulation.

Figure 23 shows tiie torque on tiie shaft of tiie alternator when the cycloconverter is run-ning. This waveshape is seen to be rich in harmonics, which are tabulated m Table IV and also shown graphically in Appendix I. The most significant of these is at 300 Hz (30 %), produced by tiie action of the 5ti3 and 7ti3 harmonic currents, drawn by the cycloconverter, which flow in the alternator stator. It should also be noted tiiat tiiere are a number of lower frequencies present in this waveshape some of which have relatively large amplitudes, forexamplea 15 Hzcompo-nent of 3.8 % and 30 Hz of 6.8 %. There is clearly a possibiüty of these or other such low frequencies exciting a resonance of the prime mover-altemator rotor system, careful con-sideration of which will be required. The current flowing in die stator windings is shown in Fig 24. It should be noted that the amph-tudes of the frequencies present in this waveshape are not significantiy different from those obtained using tiie earher simpler repre-sentation of the supply system by an emf behind a fixed inductance. If Üüie simulation had been perfOTmed with a synchronous ma-chine displaying more significant sahency this would not have been the case.

The simulation results given in this section have shown tiiat tiie Saber time domain simu-lation package has been developed to model a range of cycloconverters and electrical ma-chines, and used to perform system calcula-tions for the complete electrical propulsion system as one unit, not as separate parts. The interaction between the constituent parts of the system is therefore maintained in tiie simulation.

CONCLUSIONS

sahency, tiie machine can be represented by an emf behind a fixed reactance. For a machine which does display saliency, tiie ccHnmutating reactance is no longer constant and a more ccMnplex machine model is required. The foil phase model discussed in the section on power electmoic simulation is therefore used in the ship propulsion simulations to represent the alternator supplying the cycloconverter drive.

T o demonstrate the complete simulation o f the cycloconverter propulsion system, \he synchronous machine model was combined with tiie earher six pulse cycloconverter supplying a three (^ase three winding induction motor. The signals which this simulation provides, in addition, to those obtained eariier, are the electromagnetic torque on tiie shaft of the alternator, the currents flowing in the damper windings and also the terminal voltage of the machine. With tiiis simulation the effects of tiie time varying commutating reactance of tiie alternator and all the intercoupling present between the

differ-In tiiis paper, tiie operating principles of the cycloconverter have been discussed. This converter s p e a r s at tiie moment to be tiie most hkely candidate for use in the next generation of Royal Navy frigates, should tiie Navy adopt ac elecuical propulsion. It has been demonstrated that it is now possible to analyse the complete electrical propulsion system, including die synchronous generators, cycloconverters and tiie propulsion motors which may be found on future marine installations. As a design tool this computer simulation is extremely useful. The way in which the parameters of one system building block affect tiie performance of another can be readily calculated. The computer simulation is not restricted to any one particular converter configuration and can tiierefore be used to assess die advantages and disadvantages of different electrical propulsion system arrangement.

The computer models have been achieved using tiie Saber simulator, tiius taking advantage of a modem computer aided engineering software package. Of particular importance is tiie Mast modelling language, which can be used to describe die operating characteristics of new components which may not be

(12)

K S Smith. R Yacamini tSc A C Williamson

available in the system library. This has been used particularly in tiiis work to define die characteristics of electrical machines which supply and fed from the power electronic converters. The hierarchical nature of tiie simulation package allows the different com-ponents of the system to be developed sepa-rately and tiien added into the complete sys-tem simulation. This also allows the syssys-tem topology to be readily changed. The ability to simulate mixed electro-mechanical systems has been emphasised. This ability is being extended at Aberdeen University into the analysis of motor noise generation and the behaviour of shaft systems and propellers.

The results obtained from a number of different system studies have been used to illustrate the usefulness of this metiiod for analysing the performance characteristics of different cycloconverter systems.

Fig 24: Current flowing in the motor windings of an alternator connected to a 4 MW cycloconverter drive

ACKNOWLEDGEMENTS

The authors would like to acknowledge the Science and Engineering Research Council for providing funding and M r D Bain. Reprographics Section, Department of Engineering. Aberdeen University, for preparing illustrations.

REFERENCES

1. J B Borman. T h e electrical propulsion system of tiie QE2: some aspects of the design and development'. G E C Publication No 3493-353.

2. P Bloom, 'QE2 goes diesel electric'. Modern Power Systems (USA). Vol 6, No 9, pp 19-23 (1986).

3. D Finney, 'The synchdrive - a synchronous motor variable speed drive system', GEC Journal for Industry. Vol 5, No 3, pp 108-114 (October 1981).

4. D Finney. 'Synchdrive converters for high voltage motors', GEC Journal for Industry, V o l 7, No 1, pp 25-30 (February 1983).

5. W J Levedhal, "Integrated ship machinery systems re-\/isiied\NavalEngitu;ersJournal,pp93-0\ (May 1989) 6. J V JoUiff and D LGreene, 'Advanced integrated electric propulsion: a reality of tiie eighties'. Naval Engineers Journal, pp 232 - 254 (April 1982).

7. E J Greer, 'Electrical power engineering in modem surface warships'. GEC Review, Vol 2, No 3, pp

151-157(1986).

8. K S Smitii and R Yacamini, 'Commutation voltage spikes on isolated offshore power systems', Proc 24th Universities Power Engineering Conference, Belfast, pp 417-420 (September 1989).

9. R Yacamini, L Hu and R Fallaize, 'Calculation of commutation spikes and harmonics on offshore plat-fomis'. lEE Proc, Vol 137, Pt B , No 1 (January 1990). 10. P TNonon and M Murphy, 'Realising the potential - f u l l

electric propulsion of surface warships'. RINA Inter-national Symposium on the Future of Surface Warships, London (June 1990). 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

H Rissik, The Fundamental Theory of Arc Converters, Chapman and Hall Ltd (1939).

R Feinberg, 'Frequency changing using mercury arc mutators', y / f f , pp 531-543 (1939).

E Blauenstein. 'The first gearless tube m i l l ' , Brown-Boveri Review, Vol 3, pp 96-105 (1970).

J Langer. 'Static frequency changer supply system for synchronous motors driving tube mills'. Brown-Boveri Review, Vol 3, pp 112-119 (1970).

W Faust, 'Static frequency changers for 16 2/3 c/s railway networks' Brown-Boveri Review, pp 519-525 (August 1964).

D G Taylor, 'Squirrel cage induction motor cyclo-converter drive at Wearmouth Colliery ' A ' pit friction winder. Part 1. Development of drive system for winder application', Afm/>2^ Technology,pp 4-9 Oanuary 1988). D M Cross, 'Squirrel cage induction motor cyclo-con-vertcr drive at Wearmouth Colliery ' A ' pit friction winder. Part 2, Drive control and regulating system'. Mining Technology, pp 11-15 (January 1988). C W Lander. Power Electronics, McGraw-Hill (1987). J G Kassakain, M F Schlecht and G C Verghese, Prin-ciples of Power Electronics, Addison-Wesley (1991). B R Pelly. Thyristor Phase Controlled Converters and Cycloconverters, Wiley, New York (1971 ).

MAST reference manual (Ver 3.01), Analogy Ltd. Beaverton, Oregon, U S A (1990).

A K De Sarkar and G J Berg, 'Digital simulation of tiiree phase induction rc\oiors\IEEEPAS, Vol P A S 89, No 6, pp 1031-1037 (July 1970).

P C Krause, Analysis of Electric Machinery, McGraw-H i l l , New York (1986).

B Adkins and R G Harley, The General Theory of Al-ternating Current Machines, Chapman and Hall (1975). A C Williamson, 'The effects of system harmonics upon machines'. International Conference on Harmonics in Power Systems, U M I S T , Manchester, England (1981). G C Jain, 'The effect of voltage waveshape on tiie performance of a three phase induction motor', IEEE

(13)

Trans Power Apparatus arui Systems, V o l PAS-84, pp 561-566.

27. W J Bon wiek and V H Jones, 'Performance of a syn-chronous generatOT witia a bridge rectifier', Proc lEE, V o l

133, Pt C, N o 6, pp 1338-1342 (September 1972). 28. W J Bon wiek and V H Jones, 'Rectifier loaded

synchro-nous generatOTS with damper windings', Proc lEE, V o l 120, N o 6, pp 659-666 (June 1973).

29. W J Bonwick 'Voltage waveform distortion in syn-chronous generators witii rectifier loading', Proc lEE, V o l

127, N o 1, pp 13-19 (January 1980).

30. S Moriyasu and C Uenosono, ' A n analysis of tiie char-actOTstics of a synchronous machine connected to a dc link', Archiv für Electrotechnic, V o l 69, pp 111-120 (1986).

APPENDIX 1

FREQUENCY DOMAIN SPECTRA

The following section contains tiie frequency domain spec-tra (Figs 25-32) for some of the waveshapes presented in the section cm simulation results. The spectra have been presented to supplement die tables of harmonics (Tables I - I V ) refer-enced in the text

APPENDIX 2

SIMULATION VERIFICATION

At the time of writing this paper tiie information available in tiie public domain regarding tiie types of cycloconverter systems and the parameters for the drives proposed for warship propulsion is extremely limited. As no cycloconverter propul-sion for frigates currentiy exists, verification of the computer model against a real system is not possible.

As the simulator has a modular approach to developing submodels of the various components which comprise the cycloconverter drive, it has been possible to test each of these individually and compare the performance of tiie submodel with the results of tests published previously for these items. This approach has been used to verify the accuracy of the induction and synchronous machine submodels with both sinusoidal and distorted busbar waveshapes. Assistance of a technical nature on the modelling of modem cycloconverters was received from M r Derek Taylor of C E G E L E C , Rugby. Comparisons in botii tiie time and frequency domains, between site measured and simulated waveshapes for the cycloconverter output voltage and currents, gave confidence in the ability of the simulation to model correctiy a cycloconverter. The assistance of M r Taylor in this exercise is gratefully acknowl-edged.

(14)

K s Smith. R Yacamini & A C Williamson

Table I: Fourier analysis for motoring condition

T a b l e N o 1 255 0 .00 .00 10.73 20.40 .00 260 0 2.84 3.20 .00 .00 .00

M o t o r i n g C o n d i t i o n 265 0 .00 .00 .00 .00 .00 270 0 .00 .00 .00 .00 .00 Freq Syscem Cyclo Motor Motor Motor 275 0 .00 .00 .00 ,88 .00 Current Current Current Voltage Torque 280 0 .62 8.86 .00 .00 .00 285 0 .00 .00 6.76 29.66 .00 0.0 .56 .86 .00 .00 100.00 290 0 .00 2.53 .00 .00 .00 5.0 .00 .00 1.09 .00 2.28 295 0 .00 .00 .00 .51 .00 10.0 1.45 6.58 .00 .00 3.34 300 0 .00 .00 .00 .00 8.29 15.0 .00 .00 100.00 100.00 2.91 305 0 .00 .00 .00 .00 .00 20.0 1.03 45.46 .73 .00 3.28 310 0 .00 4 .48 .00 .00 .00 25.0 .88 .00 1.25 .00 2.09 315 0 .00 .00 4.37 20.73 .00 30.0 2.13 1.21 .64 .00 1.92 320 0 .73 4.61 .00 .00 .00 35.0 1.54 .00 1.17 .91 .82 325 0 .00 .00 .00 .00 .00 40.0 1.99 3.49 .55 .00 1.33 330 0 .00 .00 .00 .00 .00 45.0 1.31 .00 8.14 3.25 .00 335 0 .00 .00 .00 .00 .00 50.0 100.00 100.00 .53 .00 .60 340 0 1.21 1.39 .00 .00 .00 55.0 1.08 .52 .89 .54 .00 345 0 .00 .00 2.07 5.50 .00 60.0 1.12 .95 .00 .00 .00 350 0 5.10 5.22 .00 .00 .00 65.0 1.37 .00 .74 .00 .00 355 0 .00 .00 .00 .00 .00 70.0 2.69 2.93 .00 .00 .00 360 0 .00 .00 .00 .00 .00 75.0 1.14 .00 2.80 3.19 .00 365 0 .00 .00 .00 .00 .00 80.0 .72 25.86 .00 .00 .00 370 0 .00 .79 .00 .00 .00 85.0 .93 .55 .00 .67 .00 375 0 .00 .00 .00 .00 .00 90.0 .53 .66 .00 .00 .99 380 0 .00 3.67 .00 .00 .00 95.0 .69 .55 .00 .00 .00 385 0 .00 .00 .00 1.05 .00 100.0 .72 .90 .00 .00 .00 390 0 .00 .00 .00 .00 .00 105.0 .00 .52 2.15 3.10 .00 395 0 .00 .00 .00 .00 .00 110.0 .72 8.68 .00 .00 .00 400 0 .00 .67 .00 .00 .00 115.0 .00 .00 .00 .64 .00 405 0 .00 .00 .00 1.B2 .00 120.0 .00 .00 .00 .00 .00 410 0 .00 .90 .00 .00 .00 125.0 .56 .00 .00 .79 .00 415 0 .00 .00 .00 .50 .00 130.0 .68 1.90 .00 .00 .00 420 0 .00 .00 .00 .00 .00 135.0 .57 .00 2.58 2.76 .00 425 0 .00 .00 .00 .52 .00 140.0 2.76 3.27 .00 .00 .00 430 0 .00 1.70 .00 .00 .00 145.0 .00 .00 .00 .64 .00 435 0 .00 .00 .00 2.14 .00 150.0 .00 .00 .00 .00 .00 440 0 .72 .86 .00 .00 .00 155.0 .00 .00 .00 .55 .00 445 0 .00 .00 .00 .00 .00 160.0 1.83 2.31 .00 .00 .00 450 0 .00 .00 .00 .00 .00 165.0 .00 .00 1.41 2.73 .00 455 0 .00 .00 .00 .00 .00 170.0 .78 2.04 .00 .00 .00 460 0 3.22 3.24 .00 .00 .00 175.0 .00 .00 .00 .00 .00 465 0 .00 .00 1.04 3.77 .00 180.0 .00 .00 .00 .00 .00 470 0 .00 .70 .00 .00 .00 185.0 .00 .00 .00 .00 .00 475 0 .00 .00 .00 .76 .00 190.0 .52 11.31 .00 .00 .00 480 0 .00 .00 .00 .00 .00 195.0 .00 .00 1.70 4 .44 .00 485 0 .00 .00 .00 .68 .00 200.0 .00 1.91 .00 .00 .00 490 0 .00 4.83 .00 .00 .00 205.0 .00 .00 .00 .00 .00 495 0 .00 .00 .88 6.71 .00 210.0 .00 .00 .00 .00 2.53 SOD 0 .00 .80 .00 .00 .00 215.0 .00 .00 .00 .60 .00 505 0 .00 .00 .00 .00 .00 220.0 .00 23.71 .00 .00 .00 510 0 .00 .00 .00 .00 1.56 225.0 .00 .00 3.69 12.33 .00 515 0 .00 .00 .00 .60 .00 230.0 .56 1 .54 .00 .00 .00 520 0 .00 4.46 .00 .00 .00 235.0 .00 .00 .00 .00 .00 525 0 .00 .00 1.64 13.45 .00 240.0 .64 .00 .00 .00 .00 530 0 .00 1.12 .00 .00 .00 245.0 .00 .00 .00 .00 .00 535 0 .00 .00 .00 .00 .00 250.0 14.30 14.80 .00 .00 .00 540 0 .00 .00 .00 .00 .00

(15)

Table I: Fourier analysis for motoring condition (cont) 545.0 .00 .00 .00 .88 .00 835.0 .00 .00 .00 .72 .00 550.0 4.20 4 .27 .00 .00 .00 840.0 . 0 0 .00 .00 .00 .00 555.0 .00 .00 1.38 6.18 .00 845.0 .00 .00 .00 .00 .00 560.0 1.76 1.86 .00 .00 .00 850.0 1.61 1.67 .00 .00 .00 565.0 .00 .00 .00 .67 .00 855.0 .00 .00 .57 3.61 .00 570.0 .00 .00 .00 .00 .00 860.0 1.69 1.69 .00 .00 .00 575.0 .00 .00 .00 .55 .00 865.0 .00 .00 .00 .00 .00 580.0 .00 2.92 .00 .00 .00 870.0 .00 .00 .00 .00 .00 585.0 .00 .00 .54 5.21 .00 875.0 .00 .00 .00 .92 .00 590.0 .00 2.07 .00 .00 .00 880.0 .00 1 .80 .00 .00 .00 595.0 .00 .00 .00 .00 .00 885.0 .00 .00 .00 .95 .00 600.0 .00 .00 .00 .00 1.15 890.0 .00 .92 .00 .00 .00 605.0 .00 .00 .00 .62 .00 895.0 .00 .00 .00 .00 .00 610.0 .00 2.11 .00 .00 .00 900.0 .00 .00 .00 .00 .00 615.0 .00 .00 .55 5.10 .00 905.0 .00 .00 .00 .81 .00 620.0 .00 2.56 .00 .00 .00 910.0 .00 1.24 .00 .00 .00 625.0 .00 .00 .00 .00 .00 915.0 .00 .00 .00 4.03 .00 630.0 .00 .00 .00 .00 .00 920.0 .00 1.36 .00 .00 .00 635.0 .00 .00 .00 .52 .00 925.0 .00 .00 .00 .96 .00 640.0 .96 .85 .00 .00 .00 930.0 .00 .00 .00 .00 .00 645.0 .00 .00 .85 4.60 .00 935.0 .00 .00 .00 .00 .00 650.0 2.34 2.48 .00 .00 .00 940.0 .85 1.63 .00 .00 .00 655.0 .00 .00 .00 .65 .00 945.0 .00 .00 .00 4.04 .00 660.0 .00 .00 .00 .00 .00 950.0 1.03 1.08 .00 .00 .00 665.0 .00 .00 .00 .58 .00 955.0 .00 .00 .00 .87 .00 670.0 .77 1 .00 .00 .00 .00 960.0 .00 .00 .00 .00 .00 675.0 .00 .00 .51 4.65 .00 965.0 .00 .00 .00 .00 .00 680.0 .00 1.34 .00 .00 .00 970.0 1.03 .61 .00 .00 .00 685.0 .00 .00 .00 1.12 .00 975.0 .00 .00 .00 2.10 .00 690.0 .00 .00 .00 .00 .00 980.0 .00 1.37 .00 .00 .00 695.0 .00 .00 .00 .00 .00 985.0 .00 .00 .00 .00 .00 700.0 .00 1.86 .00 .00 .00 990.0 .00 .00 .00 .00 .00 705.0 .00 .00 .00 4 .47 .00 995.0 .00 .00 .00 .00 .00 710.0 .00 1 .34 .00 .00 .00 1000.0 .00 1.72 .00 .00 .00 715.0 .00 .00 .00 .00 .00 720.0 .00 .00 .00 .00 .00 725.0 .00 .00 .00 .00 .00

Table prepared using a Fourier analysis with a 730 .0 .00 2.07 .00 .00 .00 resolution o f 5 H z . 735.0 .00 .00 .54 5.94 .00 740.0 .74 .91 .00 .00 .00 745.0 .DO .00 .00 .00 .00 750.0 .00 .00 .00 .00 .00 755.0 .00 .00 .00 1 .56 .00 760.0 2.15 2.17 .00 .00 .00 765.0 .00 .00 .78 4.33 .00 770.0 .00 .00 .00 .00 .00 775.0 .00 .00 .00 1.11 .00 780.0 .00 .00 .00 .00 .00 785.0 .00 .00 .00 .84 .00 790.0 .00 1 .80 .00 .00 .00 795.0 .00 .00 .00 3.96 .00 800.0 .00 .95 .00 .00 .00 805.0 .00 .00 .00 .00 .00 810.0 .00 .00 .00 .00 .51 815.0 .00 .00 .00 .00 .00 820.0 .00 2.04 .00 .00 .00 825.0 .00 .00 .00 2.27 .00 830.0 .00 1.13 .00 .00 .00

Obraz

Updating...

Cytaty

Updating...

Powiązane tematy :