Modular modeling of an electric system on board a ship for use in engine room simulators

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MODULAR MODELING OF AN ELECTRIC

SYSTEM ON BOARD A SHIP FOR USE IN

ENGINE ROOM SIMULATORS

7:0)p

LI

ING. K. DE LANGE MECHANICAL ENGINEERING MARINE SYSTEMS DESIGN' DELFT UNIVERSITY OF TECHNOLOGY

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SYSTEM ON BOARD A SHIP FOR USE IN

ENGINE ROOM SIMULATORS

A GENERIC MATHEMATIC MODEL FOR THE EXCITING UNITS

AND CONSUMER UNITS

ING. K. DE LANGE MECHANICAL ENGINEERING MARINE SYSTEMS DESIGN DELFT UNIVERSITY OF TECHNOLOGY

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Summary

In this report, the investigation to a mathematical simulation model for a simulator of an

electric system on board of a ship is described.

In the subsequent chapters the following issues are dealt with:

a description of the structure on board of a ship, in order to create an idea what an electric system on board of a ship is and what kind of hardware has to be simulated

a list of demands to determine all requirements, limits and constraints for the simulation

model

The choices of the mathematical models, based on the list of demands; preliminary investigations are discussed:

The choice of the rotary current machine models is discussed and their mathematics are derived; their Simulink models are simultaneously built Matlab-Simulink

the same goes for the exciter model. the static load model.

*the transformer model,

frequency controller with dc-loop, drive system dynamics

- the assembly of all previous discussed models in a complete electric network model

- the necessity of determining the network frequency in a floating network, since no infinite bus is present

- An example of a network model is given and discussed

Simulation results are compared with measurements on a real network with two generator sets; graphs are given and the deviations are quantified for four tests.

Load acceptance test for one generator Load rejection test for one generator

*Active power share test between two generators Reactive power share test between two generators The conclusions that are drawn are:

*A generic simulation model, based almost 100% on first principles and mean value and that can run real time is developed

The resemblance of simulation results and real measurements is very good; within +/- 5%, with very small machines

The accuracy with larger machines (>1 MW) is expected to be even better With the model future sailors can train all aspects from practice

It can be hard to get all data from manufacturers

Several (fundamental) improvements have been made with respect to the work of Boetius Elaborate literature about floating electric networks was not found

Recommendations are:

Testing of at least two other electric networks

*The implementation of conditional algorithms like over-current protection

-* * * * *

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Glossary/List of symbols

Symbols

A Area, Matrix (in combination with dq) _{[m2], [-]}

d-axis Direct axis

DRP Droop [ok]

E,e Voltage

Force [N]

f Frequency

Current, Mass Inertia

'Gain

L Inductance [henry]

M Mutual inductance [henry]

mi Mass [kg]

n Speed, number

Power, Active 'power

Pole pairs _[-I

Reactive power [VAr]

q-axis Quadrature axis _[-I

R Resistance _[Q]

Complex power

Time _[s]

T Temperature, Torque, Time constant [K], [Nm], [s]

X Reactance

Admittance

[al

Z Impedance

_Pi

Greek symbols

Angle [rad]

6 Power angle [rad]

Power factor angle [rad]

Ti Efficiency _ELM]

(I) Angle [rad]

PI-constant: 3.1415927 _[-]

Angle between d-axes and phase a [rad]

Time delay. time constant _[s]

Angular speed, frequency [rads-1]

Flux _[weber],[Vs] S. [V] [Hz] [A],[kgmils] [VA] [Q]

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Suffices

id

Damper windings in d-axis direction

1 q _{Damper windings in q-axis direction}

Stator phase a, b or c

In combination with L, stator phase self inductance

ab (or ac) In combination with M, mutual inductance

sf With M, mutual inductance between stator and field windings

ag Air gap between rotor and stator

asm Asynchronous machine

sid

With MI, mutual inductance between stator and d-axis damper windings

s1q With M. mutual inductance between stator and q-axis damper windings

av Average value

base Base value of variables

bus Network bus or rail

d-axis value of stator variables

d0' (q0') In combination with T. Transient open circuit time constant

dO" (q0") In combination with T, Sub transient open circuit time constant

With T and K, exciter time constant and gain

eff Effective value

el Electric

de Diesel engine

exc Exciter system

Field winding quantity

gen Generator

im Imaginary part of complex number

ldl Damper windings in d-axis direction

Damper windings in q-axis direction

sign

_{Leakage reactance (in combination with L)}

load Load

max Maximum value

min Minimum value

mas Master generator

nom Nominal value

Primary side of transformer

Phase Phase (a, b or c)

q-axis value of stator values

pu Per unit

Rotor

rat Rated value or output

re Real value of complex number

Secondary side of transformer, Stator. Synchronous reactance

stat Static

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1 Introduction

In the present nautical education more and more use is made of simulation technologies. This is done to train future sailors on different situations when they are either behind the wheel or behind the buttons in the engine room. In this way, the exercises can be virtually

done so that no real hardware is used no damage will occur when a mistake happens. This is getting more and more interesting due to the increase in both the shipping traffic and the complexity of ships.

A specific point is the production of electricity in the engine rooms on board of ships. This will be dealt with in this report since the present ship electric system simulators can be improved. This goes especially for the area of on-first-principles-based simulation models and on being generic.

In this report a solution will be found to make a good basis for a generic simulation model for

electric systems on board of ships. Chapter 2 explains the structure of such an electric

system. Chapter 3 gives the requirements for a mathematical model that has to simulate an electric system on board of a ship. Chapter 4 discusses some preliminary investigations to a simulation model In this same chapter the mathematics are derived for various components in the electric system, like synchronous machines, asynchronous machines, transformers,

impedances, drive systems, etc. The mathematic models are chosen on basis of the

requirements in chapter 3. Chapter 5 discusses the problems with determining the electric network frequency in a floating network. In this stage of the project, an appeal has been done on inventiveness. The implementation of all the various models in one network is given in this chapter too. Chapter 6 gives simulation results from the developed mathematic model and measurement results on a real electric system. Both data are compared with each other. The conclusions are given in chapter 7. Literature is given in chapter 8.

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2 Description of the structure of an electric system on board of a ship

This report mainly handles about simulating an electric system on board of al ship. Therefore it is obvious to start with a brief explanation about the ins and outs of such a system. This will

give the reader a little more grip throughout the following theoretic discussion. Note: it is

assumed that the reader is in the possession of fundamental knowledge about both power plant theory and modelling.

ZS The. structure and human interface

The main components of an electric system are:

Synchronous generators (driven by turbines, diesel engines, etc) Excitation systems for the field windings of the synchronous generators Generator breakers

Common rail (interconnects all the electric machinery) Synchronous and asynchronous motors

Transformers

- Resistive and reactive loads (examples are lights, heaters and capacitor banks) The main components of the human interface with this system are:

- Voltmeter for each generator terminal voltage Current meter for each generator terminal current

- Main switch for each generator to connect it with the common rail Frequency meter for each generator

- Start button to start diesel engine

Throttle increase and throttle decrease button for each generator

Terminal voltage setting potentiometer for each generator (in most cases hidden)

One synchronoscope that is connected to the generator that is about to be connected to the live common rail,

The secondary components of the electric system are:

The components that automatically perform the actions that can be done by hand with the human interface components (which is usually the case when the system functions under regular conditions).

cid

c

- Load share regulators

- Reactive load share regulators.)

r---- (7

Pi/

Speed regulators

Voltage regulators that control the terminal voltage of each generator (AVR) C

A human interface of an arbitrary ship's electric system is displayed in figure 1. One can see

the meters and switches and push buttons This interface is the ship's switchboard. This is

the only means of human interaction with and monitoring of the electric machinery, under

normal circumstances.

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To very large extend, the ship's power system can be compared to the power system of the

public grid. Every component of a public grind can be found on board of a ship. One

exception is that the ship's system is in complete island mode. This means that _{no infinite}

bus can be assumed. An infinite bus is a connection in a network, where voltage and

frequency are prescribed, and remain const under any circumstance. If _{one 'diesel engine}

delivers more torque than is required, the whole system will speed up. This means that the ship network frequency is dependant on power balance over the network. When for example a heavy electric motor is abruptly connected to the grid, the frequency will rapidly go down

for a while. The speed regulators of the diesel engines will only be able to compensate this a

few moments later.

One will hardly notice this phenomenon in a public grid. 'Only the currents will' be inadmissible

high. It will become clear,

later on, that this

is

an important issue throughout this

investigation. This goes especially for the modelling.

2.2 Some numbers

For outsiders, a few numbers can be elucidating for emphasizing the importance of an

electric system on board of a ship.

A very good example is a large Carnival cruise ship. this ship is equipped with all imaginable

luxury. One has to think of approximately thousand' cabins that

_{are equipped with air}

conditioning, lights and power connections for private use. Next to that the rooms that are for

public use, like the amusement arcade, recreation rooms, etc. Not to forget the kitchens_and

refrigeration compartments. Last but not least: the ships own electric system to be

operational such as heavy cooling water pumps, bow thrusters,, blowers, etc. Fig. 1:

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This all leads to consumption in extend of 30 MW in electric power! This power will be

generated with several generator sets. The generator voltage will be in order of several kilo Volts.

The frequency on board of a ship is in most cases 60 Hz. Smaller consumers normally

operate on

three-phase 440 V line

voltage. Transformers are placed in several

compartments of the ship,

in order to distribute the power and to account for

single-phase/asymmetric loads.

A smaller example can be found on the Jo Elm from Jo Tankers. This ship is a chemical

tanker. It has four generator sets of each 800 kVA on board. No transformations are made; the generator line voltage is 440V. 60Hz. The power is partially used for heating some of the tanks.

An electric system on board of a ship has to be handled like a public grid system. One can

imagine that this needs skilled operation of professionals, since safety and continuity on

board of ships is very dependent on good electrical management these days. Skilled

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3 List of demands for modelling an electric system on board of a ship

The goal of this project is to create a virtual training environment, in order to train future

sailors to reliably handle the complete electric system. Virtual training has the big advantage

that nobody will be harmed when a mistake happens. No material damage will occur.

Moreover, the virtually displayed electric system can be operated out of the rated limits. This will give the operator more insight into the behaviour of the system.

A touch screen on an LCD screen will replace the switchboard that was shown in figure 1. A mathematical model on the computer will replace the physical machinery. This gives another advantage: the computer modelling can be made parametric. This enables simulating various types of systems, by simply changing the parameters in a separate data list.

The Maritime Simulation Training Centre in Terschelling is interested in such a model. They want to extend their range of practicing possibilities in their electric engine room simulator.

3.1 Discussion of the requirements

Before modelling an electric system on board of a ship, it is of course evident that a clear list

of demands has to be formulated first. It is important that only the desired components,

effects and objectives of a simulation are taken into account in the modelling and that the not wanted effects are indeed left out. This can strongly reduce the complexity of models and the risk of errors during a simulation. Next to that, the necessity for detailed parameters can be reduced.

The demands can be split up in preconditions, such as from external enforced restrictions

and points of departure, such as the demands that the people involved in the MSTC-project dictate to the functioning of the model.

Preconditions:

Pc1

Since the model will be used to run simulations for training future sailors, the

simulations must run real time This means that every change during a simulation must elapse just as quickly as that would be the case in practice. For numerical

control, the simulation time step must be fixed. In this way it is easy to control how

fast the computer calculates every time step.

Pc2 _{The student should have exactly the same interface with the system, as that would be}

in practice the case. One can think of virtual voltmeters, current-meters, frequency

meters, synchronoscopes, buttons to change various regulator settings, etc.

Pc3 _{A selection from the amount of desired features must be made such way, that a}

proper functioning basic simulation model can be obtained in a period of 6 months, starting from the 1st of March 2002.

Points of departure for a 1-phase modelled system:

Pd1 Only the basic behaviour of the electric machines is desired for training future sailors.

However this

should be simulated according

to first principles. High-frequent

phenomena like current and voltage changes on sine-wave level (T < 16.7 msec.) do not have to be determined. Only (the change) of effective value of powers. currents

and voltages (during changes in the network configuration) have to be determined

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Pd2 For making a ship network live, the student must be able to sequentially start one or

more generators and connect them to the network. The model order (number of

equations) must therefore be easily changeable. A virtual interface must be present on which the generators speeds and voltages can be manually adjusted and on which

the actual speeds and voltages are displayed. After checking the right voltage and

speed (= frequency), the subsequent generators must be connected to the network by means of manually switching on the generator breaker.

Pd3 It must be possible to manually connect and disconnect various types of loads on a

live network. Just like with switching more generators to the network, the system order must be easily changeable here too. Parametric models must be made of

synchronous machines, asynchronous machines and the machinery that they drive.

Only the results of the basic behaviour are desired in the simulation. A virtual

interface must be present to connect these machines to the network.

Pd4

The student must be able to manually tune the distribution of active power and

reactive power over the generator sets. A virtual interface must be present to adjust the settings of the voltage controllers and the speed regulators.

Pd5 Protections against over-load, feed back, over and under-speed. over-current and

over-voltage must be implemented in the model. The protections must be activated when the pre-programmed thresholds are reached. A virtual interface must be present

to indicate that a protection has been activated. Next to that, an interface must be

present to reset the activated protection when the conditions are nominal again.

Pd6 It must be possible to simulate blown fuses and short-circuits everywhere in the

electric network. Blown fuses will be of great importance for the order of the model;

just like putting more generators to the network. the model order must be easily

changeable here too

Pd 7 The model must be generic. This means that it should be possible to simulate various

ship electric systems, by only changing the machine parameters and not by changing the way of calculation.

Pd 8 The modelling must be based on first principles. So implementation of empirically

determined ways of calculation (for example neural networks) must be avoided as much as possible. Only the mean value of changes in time is of interest. It is thus

desired to build up a simulation model according to the FPMV principle:

First Principles and Mean Value.

Pd 9 The model must be implemented in Matlab Simulink®.

Points of departure for a 3-phase system in the future:

Pd10 It should be possible to simulate asymmetric loads, while still clinging on to the FPMV

principle. The needed changes in the model for the synchronous generator have to be investigated.

Pd11 It must be possible to simulate disconnections per phase and short-circuits between

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4 Choice of component models

Looking at the situation now, it is wise to first develop a proper functioning single-phase

network model and to extend this to a three-phase network model. A three-phase model with

asymmetry might need radical changes in the models of synchronous and asynchronous

machines, in order to keep the simulation realistic. Moreover, the added value of simulating asymmetry will be negligible, since a very small percentage of the loads on board of a ship

are 1-phase. Next to that, 1-phase loads are equally divided over the three phases of the

generators as much as possible. In case of short circuits in one or more phases, the

generator breaker will automatically disconnect all three phases at the same time

Emphasize in this investigation lies mainly on the modelling of the synchronous generators in

the floating network. This was the toughest job in the project. Therefore most of the text

handles about these machines. Asynchronous machines will appear to have many analogies with the synchronous machines. All the other components can simply be taken from a book and implemented pretty easily. as will be shown later on.

4.11 Preliminary investigation

With the list of demands in mind, the component models can be set up. Since D. Boetius (my

predecessor) already did a lot of research in

his report OvS 98116 [Boetius, 1998] on modelling an electric network, only the new and innovative aspects will be emphasized.

References will be made to his report in this investigation.

In this paragraph is briefly

explained why the previous investigation in report OvS 00/13 K. de Lange did not provide

sufficient answers.

Looking at <I.o.d. pd2, pd3, pd5, pd6> (being able to synchronize and switching machines to the network), a model is needed that can simulate largersignal stability. This means that the effects during fiercer Changes in the system can be simulated fairly accurate. This is good for

two reasons:

-- The order of magnitude of the involved oscillations have a period >>10 x sine--period time. With larger machines, this effect becomes more and more interesting to display.

- The stability of the simulation will be improved, since in taking the concerned effects into

account. damping is involved.

In other words, the damping characteristics of the generator should be taken into account. The damper winding circuits have to be implemented in the simulation model. The damper windings are intended to damp speed oscillations of the rotor and to damp counter rotating fields during asymmetric load.

Looking at <I.o.d. pd1>, the slower effects definitely should be taken into account. The slower effects are not only mechanical effects, in the electric machines. This means that quite some electric effects should be taken into account.

For a synchronous machine, for example, one has to look at the field winding. This winding is a huge coil with a resistance, in the machine's rotor. It is present to generate the necessary magnetic field for inducing tension in the stator windings. The induction of such a coil can be

a hundreds of mHenrys in the larger machines, the resistance around a few mOhms. The step response of a coil in series with a resistance can simply be described by a first order

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The change of the current in time can be approximated as

1(s) = U/R x 1(T,00 s + 1) (4.1)

Where T = 1-c01iRc311 = in the order of 0.1/0.01= 10 sec. for the larger machines. For the very

small ones (several tens of kWs): 0.6 sec. This means that if a voltage is applied to the coil, it takes 10 seconds before the current has reached 63 percent of its end value (lend = U/Rcoil)!

The field winding plays a big role in controlling the generator terminal voltage and sharing

reactive power (<I.o.d. pd4>). It is therefore obvious that the dynamics of the field circuit have

to be taken into account, especially for the larger machines. In the synchronous machine

paragraph more attention is paid to all these various windings.

The just written paragraph is a new fresh, basic look after the investigation OvS 00/13 by ing.

K. de Lange. In this report an attempt to real time simulate a floating network had already been made. However, the generators were only represented by a

voltage-source-behind-synchronous-reactance.

The magnitude of the voltage-behind-reactance was simply given as a constant. No field

winding dynamics were taken into account. The argument of the voltage was the integral of the rotor speed.

In that way, the whole network could be solved algebraically with complex numbers. The bus bar voltage and frequency could simple be extracted from the algebraic formula.

For more details, refer to [De Lange, 2000].

The concept of the model was working; load share, reactive power share could be done. This was actually an invention on it self, that time. Real time, fixed step could easily be achieved

(clod. Pc1>).

Only,

_{it was correct when one looked in qualitative sense. The actual numbers, so}

quantitatively speaking, could not even be compared with the practice. This was namely the result of the fact that all dynamics of present coils were left out in that model. There was no magnetic interaction between coils considered. Also the damping of the rotor oscillations was

simply done by introducing a damping term in the mechanical equations of motion of the

generator rotor. It is almost impossible to generically determine such a term. since the

damping happens electrically, not mechanically.

Taking all these omissions into account afterwards, and especially looking at the wish to

develop a generic, first principle model (clod. Pd7, Pd8>), it was necessary to model in a

different way. Machine models where magnetic interaction between windings is integrated are necessary to create a reliable simulation result.

It became clear that the work of D. Boetius had to be investigated again and to try to improve the shortcomings of that model. The work in this project is for a small part based on the work of D. Boetius. However, a lot of time had to be invested in logically rebuilding this model in Matlab Simulink® and to get full understanding of the model.

4.2 Synchronous machine

As mentioned earlier, the synchronous machine was the bottleneck in this project. This machine is also the pedestal on which the whole electric network is built. This is both in

practice and in modelling theory. After studying literature it became clear that avery suitable model was the so-called 7th order model.

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The name 7th order is due to the 7 equations of state of the following generator components: Stator winding in the d-axis

Stator winding in the q-axis - Rotor field winding d-axis

Rotor damper winding d-axis Rotor damper winding q-axis

Rotor speed Rotor angle

D-axis and q-axis are mentioned. These two axes are virtually implemented in 2-phase

transformed modelling of a synchronous machine.

This transformation has been invented in the 1920s, To introduce the reader more in this matter, a summary will be given of the mathematical derivation. The theory is taken from

[Boetius, 1998] and slightly altered for the sign conventions and suffices used in this report.

The synchronous machine model will be fairly extensively discussed

in the following

paragraphs. In

these paragraphs the pure machine model

will

be discussed. The

implementation in the floating network will now and then be mentioned in the sideline; this

will be discussed in a separate paragraph.

4.2.1 Synchronous machine schematic

A synchronous machine has two essential elements: the field and the armature. The field

winding is normally on the rotor and the armature is on the stator.

In the armature an

alternating voltage is generated as a result of the relative motion with respect to the magnetic flux field of the field windings. The field winding is excited by direct current. The dc source is called an exciter and is often mounted on the same shaft as the synchronous machine. An

exciter can be a dc machine with brushes or a synchronous machine configuration with or

without slip rings. Its power is a few percent of the rated generator power.

Armature windin, Air gap Axis of phase c Field winding d-axis 'Axis of phase a

Fig. 2: Schematic diagram of a three phase synchronous machine

a KA

a/a)1

/vc,0-11

0))

Ntr)

/1AL.52s-There are two types of rotors most commonly used nowadays namely the cylindrical and the

salient pole rotor. The salient pole construction of the rotor can have more poles then the

cylindrical rotor and is often chosen when the prime mover runs at relative low speeds. In the

case the prime mover runs at high speeds (gas and steam turbines) a two-or four-pole

q-axis Axis of phase h

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-cylindrical rotor is used. This will avoid protruding parts on the rotor. which at high speeds will introduce great mechanical stresses.

Fig. 3a: Salient pole rotor construction with two kinds of damping

Fig. 3b: Cylindrical rotor construction

Salient pole rotors often have damper windings in the form of copper or brass rods

embedded in the pole face. These bars are connected to end rings to form short-circuited windings similar to those of a squirrel cage motor. The damper windings are intended to

damp speed oscillation of the rotor.

4.2.2 Basic equations of the synchronous machine

Figure 4 shows the stator and rotor circuits involved in the analysis of the synchronous machine. The stator consists of a three-phase armature winding carrying the alternating

currents. The rotor circuits comprise the field and damper windings. It is assumed that the currents in the damper windings (solid rotor and damper windings) flow in two sets of closed circuits: one along the d-axis (direct-axis; goes through centre of north pole) and one along the q-axis (quadratic-axis; leading the d-axis 90°) as shown in Figure 4.

The electrical angle is the angle by which the d-axis leads the centreline of the phase a

winding in the direction of rotation. Angle e is continuously increasing since the rotor has an

angular velocity

(Orator-Wedge Rotor surface Damper winding Field winding Slot wall e wrotoi P t [rad] (4.2)

(a) Continuous damper _{(b) Non-continuous damper}

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d-axis

a

Fig. 4: Rotor and stator circuit of a synchronous machine

The electric performance equations of a synchronous machine can be determined with the

circuits couplings represented in Figure 4. The rotor field voltage (efd) generates the rotor

field current (is), which induces the flux linkage (wfd) in the field windings. This flux linkage rotates with the rotor and in the stator armature windings (which are stationary) induces the

currents and voltages. The two other windings on the rotor side are short-circuited and represent the damper windings. When the rotor speed accelerates or decelerates these

windings will generate a damper torque to stabilise the system and prevent oscillations of the power angle 8 of the generator. This angle will be discussed later on.

Stator circuit

The instantaneous sinusoidal induced currents and voltages in the three phases of the stator

Currents: Voltages

ia Im cos(wen .t) ea =Ea, -cos(war, -t +0)

2-rr

ib =Im cos(wa,, .t

et, =Em cos(wea t

---3)

27

2-rr

I, =Im .cos(wer,

+T)

ec =Em .cos(wer, t + )

(4.3) With

cl) : power factor angle (angle by which the voltage lags or leads the current lathe

phase)

Em : amplitude of the sinusoidal phase voltage

Im : amplitude of the sinusoidal phase current

The phase voltages and currents are sinusoidal and they are shifted 120° from each other. With these formulas for the currents and voltages the instantaneous and average delivered active and reactive power by the generator can be determined.

armature windings can be written as follow:

Instantaneous delivered active power: S = e +

+ec

ic

[VA)

(4.4)

Average delivered active power.

P=3 Em

.cos) [W]

(4.5)

Average delivered reactive power:

Q= E

_L simp

[VAr]

(4.6)

Normally the phase voltage leads the phase curre t So the power factor q is greater then

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(4) < 0) then generator is said to be consuming reactive power from the network.

With the induction law of Faraday the phase voltage can be expressed in the change of the flux linkage (va) in the phase and the phase current.

e c14.ia R

a dt a a

The flux linking in phase a at any instant is given by:

= Lsm ia Mab *lb Mac .ic + Maid .ifd + Maid i1d Malq

With Lsm Mab Maid Maid Maid

= Stator self inductance

= Mba = Mutual inductance between phases a and b = Mutual inductance between field winding and phase a

= Mutual inductance between d-axis damper circuit and phase a = Mutual inductance between q-axis damper circuit and phase a

Similar expressions apply to voltages and flux linkages of phases b and c. The negative

signs of the stator winding currents are due to the assumed convention (they work against the flux induced by the rotor windings). The stator self and mutual inductances vary with the d-axis angle 04) because the air gap between the rotor poles and the stator varies (especially in the case of salient poles. figure 2). The permeability of the magnetic path is proportional with this gap and the inductance L on its turn is proportional with the permeability (figure 5).

Rotor circuit

In the case of the rotor field windings the permeability and thus the inductances do not vary

because they have a fixed air gap between the rotor and stator (air-gap variations due to

stator slots neglected). The mutual inductances between rotor and stator will vary due to the relative motion between them. The rotor circuit voltage equations are as follow:

dipfd etd dt +Rfd ifd dip_kd _pp

"ld

dt dipk

0 =

dtg +Rid

The instantaneous flux linkages in the rotor circuits are:

(4.9) Llif _Li ' if +Mfld ild tPld =Lid + Mild tPlkq Llq ilq Maid . Maid

ia sine+ib

( la ( ia COSO ib

cos'e

+ib COS ( _2-rr

27

3

'

₂₇

8 +ib

'

+

ib cose

/

A+

21T / ' \

//

A+

2 Tr \ \ (4.10) 3

i

'

+2Tr \ 3 \ 3

+ib -sin

3 \ / 3 (4.7) (4.8) = = = l

(20)

= field winding self inductance

= Mutual inductance between d-axis damper circuit and field winding = Mutual inductance between field winding and phase a (= \I(Laa X Lim) = d-axis damper circuit self inductance

= q-axis damper circuit self inductance

Fig. 5: Varying self-inductance of the armature winding a, plotted against rotor angle

The equations for the stator and rotor circuits describe the electrical performances of the

machine. However these equations contain inductances that vary with angle 0, which varies with time (figure 5). The air-gap between rotor and stator varies with the rotor angle and thus also the leakage inductance. Furthermore the stator voltages and currents sinusoidal varying

with the time, which makes solving the equations much more complex. To obtain simpler

forms of the equations the Park-transformation (or dq-transformation) is done to transform the stator variables into the so-called dq-axes system

4.2.3 Park-transformation

The Park-transformation

(or dq-transformation) transforms the sinusoidal voltage and

currents, in the three phases in the stator, into two components: one in d-axis and one in q-axis direction (figure 4). Because the dq-axes system rotates with the same angular electrical speed as the rotor l()rotors, n) these components have constant values under steady state

condition. The inductances that are varying with the angle also become constant and this

simplifies the equations significantly.

The dq-transformation matrix (Adcl) is given by [Kundur, 1994]:

With the transformation-matrix Adp the stator voltages and currents are transformed into the dq-components: Adq =2

cos°

cos

-sine

-

sinie

2-rr

0-

cos(19

- sin

(4.11) 2Tr

+-3 +-3

(8

+ 2Tr 3 3 90° 180° 270° 360° With L1 Mfld Mat Lid 1-1q

(21)

Ws WI

ed =En, -cos(ws -t+cpe)

eq =En, sin(ws .t +

e

= network frequency [rad]

=p Wrotor [rad]

When the formulas for the stator voltages and currents (4.3) are substituted in the equations (4.12) and (4.13), the following dq-components of voltage and current are

derived-CJIAj6

c)6/1

fr(4.14)

id =In, cos(ws -t

A) iq =In,

sin(ws .t

0)

(4.16)

At time = 0 it is assumed that the current in phase a is maximal (/m) so the angle Ho is not only

the angle between the d-axis and phase a, but also between the d-axis and the rotating

current vector. This vector is made up of the id and q components. In figure 5 the phasor

diagram is sketched with the dq-axes voltage and current components. It can be seen that the current phasor Im leads the d-axis by angle (40 and lags the voltage phasor Em by the power factor angle (I). The angle 8 is the so-called power angle and represents the angle by which the q-axis leads the voltage phasor. The angular velocity co, is the electrical angular

velocity of the rotating magnetic field in the stator and in steady state is equal to cor

cos 0

2iT'

cos e+

ea

3

ie

2Trj)

3

+ 2Tr

sine sin

sin

eb

[V]

(4.12) RA, case cos 3 (

_{2i r'}

cos 3

27 \

e + la 'k 2.7 3 ( +-2Tr

sine sin

sin

ib _ic

[A]

3 3 With wr + ec [rad] (4.15) - -ed 2

=

q 3_ Id 2 3 = cose

(22)

Imag T

q -axis

Fig. 6: Representation of dq-components of armature currents and voltages as phasors

Velocity ('Jr is equal to the network frequency (wen or (As) in the case there are only two field poles on the rotor For the purpose of analysis only one pole pair is considered because the conditions associated with other poles are identical to those for the pair under consideration.

It is only important to remember that the torque load of the generator works on the shaft that rotates with speed cor and not at the network frequency wen.

From Fig the dq-components of the voltage and current can be determined by:

ed = Er, sin(i)

eq =Em cos(o)

IA/ 17)

id =11 sin(ip+ 6 )

iq = cos4 + 6 )

These voltages and currents are constant values under steady state conditions _{(o),. = cos and}

6, 4), Irr, and Em are constant) and are determined by Em, Im and S. In this model of the

generator the stator terminal voltage Em and 6 are inputs and /, (or rather the stator terminal active and reactive power P and Q) are outputs The relations between the dq-components

of the voltages and currents of the stator armature are derived from the voltage equations _in

the previous paragraph (4.7). By applying the dq-transformation (4.12) and (4.13) to these equations, the following expressions are found:

e d = dipd de dt

cli+ Rs

ckpq _de eq = +Lp0 + Rs dt dt (4.18)

(23)

de de

These equations have the same form as for a static coil except for the Jq and yid

dt

parts which result from the transformation to a rotating reference frame. These components de

are referred to as speed voltages

due to flux change in space) and parts as

dt

transformer voltages (dtp . due to flux change in time). The transformer voltages can be

dt

neglected because they represent effects in the stator circuit , which normally have a much

smaller period time. then the period time that needs to be investigated. These effects decay very rapidly and there is no reason to model them. Especially when one looks at the needed small time step to simulate those fast phenomena. The stator voltage equations are in that case pure algebraic equations.

This was eventually tested on an infinite bus. A model with 5 electrical equations of state was compared with a model with only 3 electrical equations of state in only the 3 rotor windings.

The differences in the change of several quantities in time appeared negligible for these

studies. The voltage equations for the rotor circuits stay the same because they were already

in dq-axes. The relations between the flux linkages and the different currents in stator and

rotor can also be transformed and be written in the following matrix form:

With

Ld ₌ _{Laa,min + 1.5 Laa,max} _Mab,av

Lq= 2.5 Laa.min

1.5 - L55_max _Mab,av

Laamin = minimum value of the stator winding self inductance = maximum value of the stator winding self inductance Laa,max

Mabav = average value of the stator winding mutual inductance

Instead of variation of inductances with the angle 0 now constant values are used, just like

the stator voltages and currents. When all the inductances are known, the inverse

transformation of the matrix form flux linkage equation can be determined. In that case the rotor and stator currents (in dq-axes) can be determined when the flux linkages are known. The power angle 6 is determined with the rotor frequency wr and the network frequency

The rotor frequency is determined in the mechanical motion model of the diesel generator shaft. The network frequency is determined in a special way, since there is no infinite bus

present. This will be dealt with later on.

6 (t) = i3 (to ) + (p * wrolor ws )dt (4.20)

0

With the bus voltage Em and the power angle as inputs the generated currents id and iq in 'rig-axes can be determined. As can be seen from figure 6, these currents have to be projected

14Jd L.Pq 1Pf (P1d 1P1q 0 MY 0 0 Lq 0 0 Mslq Ms1 0 Lf Mild 0 Msld 0 Mild Lid 0 0 -Ms1q 0 0 Id iq If id (4.19) = Ld

(24)

on the real and imaginary axes. The real and imaginary axes represent the complex

dimensions in which the network variables are represented. The bus voltage and the injected currents need to be represented with the same axes, since current and voltage are directly

related to each other through the network. The injected (or removed) current /, by the

generator (or motor) into (from) a network bus is given by:

real + j

With

imseal = id cos(0.57 (8 +Op + iq sin(0.5-rr (6 + 00 -4- (I)) (4.20)

imfeal = sin(0.57 (8 +led + (1))+ iq cos(0.57 (6 +e0 +(p)

The angle 00-f.(1) will be determined by the voltages ed and eq. When the currents and voltages

of the stator armature are determined the delivered active and reactive power of the

generator can be calculated with the dq-components.

Pgen (ed eq 1\N

Qgen = (eq id ed

ig)

[VAr]

(4.21)

These formulas can be validated by inserting the relation for the dq-components in the

formulas for Qg, and Pg. The electric torque of the synchronous machine can be calculated with the following equation from [Hoeijmakers, 1996, page 78].

Igen = d id )* p [Nm] (4.22)

Li;imag

cp)+

(25)

4.2.4 Synchronous machine parameters and per unit representation

In this paragraph the method to determine the machine parameters used in the many

equations from the machine datasheet is discussed. In the datasheet Orai'synchronous

generator the following important machine parameters are given in tti/e per unit 'stem:

Table 1: Parameters normally per unit specified on the generator datasheet

Usually the manufacturers specify reactances (X) instead of inductances (L). But since the reactance is equal to the inductance multiplied by the frequency, these quantities are equal

in per units. The frequency expressed in per units is one (e.g. Xd_{= Ld).}

As can be seen from table 1, there are three types of parameters, namely the sub-transient

parameters. the transient parameters and the synchronous parameters. The sub-transient parameters are the parameters influencing the rapidly changing components (currents,

voltages, etc.) in the machine The transient parameters are those who influence the slowly

changing components and the parameters influencing sustained steady state conditions are

the synchronous parameters.

The standard machine parameters from table 1 can be used to determine the parameters

used in the voltage and flux linkage equations from the previous paragraph. In this project, there is purposely chosen to calculate with real values, instead of the given dimensionless

values. In this way, real voltages, currents, powers, ohms and speeds are calculated and

directly available in the simulation model. There is no need to convert dimensionless values. The model has an educational goal. not an explicit network analysis function.

Since manufacturers represent the generator parameters in

the per unit system, the

dimensionless data have to be converted to real values. The conversion is taken from [Kundur, 1994]. pages 91-93 and 150-159. The explanation will be restricted to only the

formulas. Calculating the real values from the data in the datasheet is a puzzle. This puzzle

is embedded in an initialisation file that supports the Simulink model. Only the datasheet

Parameters

Rated complex power kVA base (kVA]

Ugh [V]

Rated phase voltage

Rated frequency if [Hz]

Pole pair number _ID _IA

J [kgm2] Moment of inertia Synchronous reactance X Xq Xd Transient reactance Xq' Sub-transient reactance Xd" Xq"

Transient open circuit time constant Tdo' [S]

Tq0 [s]

Transient time constant Td' [s]

Sub-transient time constant Td" [s]

Sub-transient open circuit time

constant

-idols] Tqc,"[s]

Armature time constant

Stator leakage reactance Xssiqm

Stator resistance Rs

Rotor resistance Rr

(26)

parameters have to be filled in, and the file automatically converts them to parameters that

are necessary for the simulation. The formulas are orderly given in appendix 2. Short

explanation: suffix '_syn means related to synchronous machine. Suffix '_syn_pu' means per unit value related to synchronous machine.

4.2.5 Synchronous machine steady state calculation

Next to determination of the parameters. the pre-calculation of the state

in which a

synchronous machine has to start is

important. This means that before running the

simulation initial values for the integrators in the model have to be given. The generator will only be steadily started if the right initial values are calculated. The start values are based on

the prescribed start power (P syn), reactive power (Q syn), rotor speed (cu rot) and phase

voltage (U ph)

When these values are given, the whole synchronous machine model can be calculated by hand for one time step. This is performed in the same synchronous machine initialisation file Formulas are given in appendix 2. They are taken from literature [Kundur, 1994].

The order of calculation is as follows: - P. Q, U, fare given

Rotor start speed follows from f(1 integrator that integrates torque/J) The power factor is calculated

- The load angle is calculated (1 integrator that integrates rotor speed) The dq-components of stator current and voltage are calculated The start value for the field current is calculated

In stead state the damper winding currents are zero

- All start currents are known, so the initial fluxes can be calculated (5 integrators if stator transformer voltages are taken into account)

The start value for the driving torque follows from the start fluxes and currents The start value for the terminal impedance follows from start P, Q and U

(27)

-4.2.6 Simulink synchronous machine model

A step-by-step explanation of the implemented formulas in the Simulink synchronous

machine model will now be given. The structure of the model is in subsystems This means that every separate calculation is indeed placed in a separate virtual box. Figure 7 gives the outer shell of the model. One can easily see the inputs (red. left hand side) and the outputs (blue, right hand side).

Fig. 7: Simulink 7th order synchronous machine model Inputs:

E t/w et

: terminal voltage from network model or from infinite bus [V, r/s]

- U fd

: field voltage [V]

w gen : rotor speed from drive system dynamics model [r/s]

- Gen brk : input for generator breaker [ON

Outputs:.

-It

: complex current that model injects into network [A]

- Leff gen

: magnitude of complex generator current [A]

P gen active electric machine power [kW]

Q_gen : reactive electric machine power [kVar]

S gen : complex electric machine power _[kVA]

Synchr : synchronoscope output; angle between dq-frame and network

frame _[rad]

T gen : Electric torque [Nm]

Inside the model the several calculations (sub-systems) can be found. The _{sequence of}

discussion will go from top left to bottom right. P gen u_gen Sync r_gen 7th Order Generator Model -e n en

(28)

Dern. ermine voltage & Frequency

LOOK Angle

Fig. 8: Inside synchronous machine model Voltage equations

The voltage equations block is based on the discussion and derivation of the equations in the

previous paragraph. However, the equations of state of the stator circuit are converted to

pure algebraic equations In other words: the integrators are left out and the so created

algebraic loop had to be solved in Simulink. This appeared to be a fundamental part of this investigation; so a little attention will be paid to this first.

Problem algebraic loop stator circuit

More than a month had to be invested in solving this algebraic loop, according to first

principles. In the report of Boetius the loop was broken by means of putting a first order system with small time constant and unity gain in the loop. This was a solution that only

functioned under specially tuned circumstances. Actually, the tuning of the time constant of

that first order system was based on trial and error. Moreover, this solution forced the

simulation solver to work with variable step. A fixed time step is wanted in order to force a simulation to run real time (if the computer is always fast enough to run the simulation at

least real time).

Last, but not least, the stator equations of state are left out to skip effects with small time

constants. So introducing first order systems with small time constants does not really solve this problem.

After having experimented with memory blocks in Simulink, it became clear that those memory blocks did not function the way it was expected: the new input value for the next

calculation step is the output value from the previous calculation step. When a memory was implemented in the algebraic loop, the calculation crashed rapidly or in some cases became very unstable This nasty problem occurred in several attempts for the modelling.

It became clear that erasing the rapid effects in the stator circuit already introduced a lot of trouble to solve the complete network. The integrators were left out, so the loop in the stator-.

network circuit turned from a loop with differential equation into an algebraic loop. The

models that were tested in this stage of the project were:

voltage Vecto

INSIDE GENERATOR MODEL

K Voltage Equation, Dernuy

itU

do-currents In Complex Components Electric argue omen' Vector

ermtnal voltage Electric Pont, n dq-components

gen S_Ren

(Lill

(29)

- The model from Boetius

- A model from [Kundur, 1994] pages 848-855. In this model, the stator circuit is algebraically solved and the speed terms in the voltage equations are left out.

The model from Boetius did not allow any other solution than the first order system in the

stator equations. The fixed time step could in any case not be implemented. This had also to

do with the determination of the load angles for the several generators. The way of

determining those angles was based on zero point tracking. Especially during fierce changes in the calculation, a very small time step would be necessary to keep the simulation stable and running. It appeared not to be possible to invent a new solution on the basis of the model from Boetius. The model however has been fully implemented in Simulink.

The second model was from Kundur. The book is not very clear for an outsider concerning

models for floating networks. Looking at the fact that this model was specially rewritten to leave out the stator equations of state, it was interesting to implement this in a network.

Unfortunately, it appeared that the omission of the speed terms in the voltage equations

made the model more suitable for connection to an infinite bus than to a floating network.

Next to that, still the algebraic loop in the stator circuit existed.

After a lot of trial and error in Simulink, it became clear that Simulink surprisingly has a

memory effect of its own in algebraic loops. This was a pity to ascertain after so much time. Let this be a hint for other future Simulink projects with algebraic loops. Manuals of Simulink should be thoroughly investigated to get this phenomenon clear to the bottom. Unfortunately time ran out during this project to do this.

The model that was chosen in this project is a part of the model that Boetius had used

[Kundur, 1994] and [Hoeijmakers, 1996]. The changes made were leaving out the first order

systems in both the stator voltage equations and the current output of the model, since it

appeared here to be possible now. The first model was born that could run in steady state in a network. De model injects a current into the network and receives a voltage directly from the network. The load angle delta was held only a constant for that steady state. This had to be done for verification of the proper functioning of the algebraic loop in the stator/network

circuit. The simulation could not be made dynamic yet, since there was still no means to

determine the network frequency. The intention was to find a solution that was much more based on first principles, than the solution by Boetius. The new solution should be calculated with a fixed time step too.

Inside 'Voltage equations block

Voltage Equations

Fig. 9: Inside 'voltage equations' block

L_tnv

110(.. 1111 PSI

(30)

The mathematics for this block are:

Inside 'Voltage eduations1 block

One can clearly see in figure 10 that the two upper flux calculations (psi d and psi_ q) are

without integrators.

It can also be seen that an inner algebraic loop is created with the

previous block.

Rewriting the voltage equations for the stator circuit (e is replaced by u)

dtpd de ciLlid ud = lp

_+R

id where = 0 dt q dt s dt dyd

d8clq-ig

u=

± ((id + R - i where = 0 q dt dt s q dt gives: Rs id - ud (-1-)q = Wrotor - p

Rs iq +uq

Pd Rotor circuit: dtpf D i dip, Uf +1xf . if Rt -if dt dt

dy

. did0

= dt6

+ Rid Hid -->

= Rid iId

(0, because damper is short circuited) (4.25)

dt

ip,q

0 = cl +Rig -lig dipiq

= Rig - lig

(0, because damper is short circuited)

dt dt Wrotor p (4.23) (4.24) id Ld 0 M51 Moo iq 0 Lq 0 0 _Msig if Msf 0 Lt _Mfld 0 inverse tiff id 0 0 Mfld Lid 0 1P-Id 0 Mst (1 0 0 Lig _{1111q_} = 0 q

(31)

Fig. 10: inside 'voltage equations1' block

The 'Mux'

block multiplexes several signals to one vectorized signal: signall=u[1], signal2=u[2], etc.

Inside 'Electric torque block

'New

Fig. 11: Inside 'electric torque' block

The 'Demux' block splits a vectorized signal into separate signals.

Tgen = (4)(1 Ig

gid .iy .)* P_sYn "

tNm,

Where p_syn is the number of pole pairs.

u (4.26) u_1 110-pm_f IIII, 1_1 I to u[11-R_I .syn1421 11,a V00101 pto_ d d Mu, Id

1_11

sill j-R 1 d_syn't,[21 pto_ 11 II 1 q M ul1I-R_ I q_syn'u[2) . q u[1)-R_s_syn'u[211/(3_sYn't,i311 w_ d

M 000-up 1+R_ s_ synu 121)/(p_ syn'o[3])

psi_d

(32)

Inside 'Load angle block

Fig. 12: Inside 'Load angle' block

ö(t) = 8 (to ) +

(p_syn * wrotor w )dt

0

Inside 'Terminal voltage in do-components' block

MuA

delta

-up rsin(u[2])

url rcos(u[2])

Fig. 13: Inside 'Terminal voltage in dq-components' block

ec, = E_t I *sine,

e =

IE tl *oos8

.11)-u_d U_C; (4.27) (4.28)

The factor ,r3 is chosen to make the calculation power invariant. This means thaton basis

of a single phase voltage the total power is calculated So the power calculated in the

dq-system is equal to the power calculated in the network dq-system.

The signs in front of the sin- and cos-functions are chosen so that the dq-frame on the rotor lies on the network frame that the machine power is positive when the machine is in motoring mode and negative when it is in generating mode. This is off course the sign convention in the generator model too (opposite to the convention in [Boetius, 1998]).

Et is the complex voltage that comes from the network. The network model

does not

necessarily need to be more than an impedance in the form of

Uimpedance is equal to the network voltage E t. So when a generator model (or more) injects a (sum of) current value(s) into the simple equation of the impedance, than the impedance will immediately return a value for the voltage, that on its turn is fed back to the generator model.

lul sq r1(3)

(33)

Inside 'Terminal voltage in dq-components block

Fig.14: Inside 'dq_currents in complex plane' block

The whole calculation in this block is based on the representation in figure 6:

= it,real Itimag

With

itfeal = id

cos(0,57 +6 < E_t)-4-

sin(0.57 +6 < E

) Itreal =

sin(0.57 +8

- <

E_t)+ iq cos(0.57 +6

<E_t)

The dq-components in the dq-frame of the currents are transformed back to the network frame components. The angle of the network frequency (<_E t) will be more or less kept

fixed. This will be dealt with in the paragraph of the determination of the network.

The outer algebraic loop (current output-network-voltage input) can easily be recognized.

Also in this loop are no first order systems and no memories integrated. This will prove to be one of the first improvements to the work of Boetius.

Inside 'Electric powers' block

M (urt ru(31+u[2]u14])11 000

u[2]u[3]-u ru [4])/1000

Fig. 15: Inside 'Electric powers' block Refer to formula (4.21)

<I-a s

ux

llcos(of 1 Dr u121+(sin(il ri Dru[3])/sq 0(3)

(-(Sin (0(1 Dr.12)-(CU s(.111))%111De syn (3

t5prtiol2(2.0(31.2))/(sqn(3)) 'CZ) pen P_g en ;)_gen sgrt(u[1]^2+u[2]^2) S_g er (4.30) NA x--10. pt/2+1111,q1[2]

(34)

Remaining calculations

The load angle 6. is displayed in a periodic way. This is used when a synchronous machine model is disconnected from the network and has to be synchronized with it. In this case, the load angle is a measure of the position of the dq-machine frame to the network frame. When a machine has to be synchronized in practice, the voltage, phase order and frequency have

to be equal to that of the network. Phase order and frequency difference are checked by

looking at delta: it should be 0 or very close to 0. The instrument in practice is called a

synchronoscope. In the model it is simply done by a display. More will be discussed in later paragraphs.

4.2.7 Skipped effects in the synchronous machine model

Although a lot of effects are taken into account in the model, there are still some effects that are not simulated.

Three-phase asymmetric loads. If asymmetric loads have to be simulated, the model must be converted to a model that produces at least two sine waves (Clarke transformation over

the Park transformation [Rondel, 1997]). This is necessary since asymmetric loads do not

produce a circular rotary field in the generator anymore; the field will be elliptic. This can only

be described by sine wavy changes over the asymmetric load. The dq-components of the

generator voltages and currents will not be constant values in steady state anymore; they will also be sine wavy. The amplitude depends on the magnitude of asymmetry. It is obvious that

sine wavy quantities are not desired in the drawn up list of demands. Especially when one

looks at the solving of the algebraic loops and the requirement of real time simulation.

The effects of asymmetry are studied a little and the conclusion could be quickly drawn that it

is possible to implement asymmetry, but real time would not be possible yet due to the

required small time step.

Damping terms that are dependent on acceleration, instead of speed. Only the effects of

the damper windings take care of the damping during oscillations. The damping torque is

equal to the rotor speed variation times a constant. But when one closely looks, there are

also damping terms present that are equal to the rotor acceleration times a constant. This will influence a little the rotor speed change during transient behaviour. In other words, the model will simulate a little more rotor speed overshoot than in practice would be the case.

-Saturation is not taken into account. This means that field intensity keeps being proportional to the current through a coil. In practice, over a certain current limit, the field intensity will rise

muchness than proportional to the current.

It _{is assumed that the stator windings are sinusoidally distributed. In practice this is} _not

exactly the case. This will cause harmonics in the voltage produced. These harmonics will introduce counter-rotating fields in the machine. The effects of these fields are thus left out - Starting with a slow rotor speed introduces small time constants in the voltage equations

(refer to formula (4.24)). since the rotor speed is implemented in the denominator ofthe

speed terms in these equations. Starting with a zero rotor speed gives troubles anyway. So

for training starting up of generator sets a temporarily modification should be made in _the

voltage equation. However, the same training goal can already be achieved when the rotor start speed is for example reduced to half. This will not directly need a smaller time step.

For steady state calculation a cylindrical rotor is assumed: X d=X q

(35)

4.3 Asynchronous machine

As was mentioned before. the asynchronous machine, or induction machine, has a lot of

analogies with the synchronous machine. In fact, the asynchronous machine is a

synchronous machine without the field winding. The damper windings are now the full driving force for the machine, instead of the reluctance force due to the rotor field.

4.3.1 Asynchronous machine T-diagram

There are two ways of modelling an asynchronous machine; quasi-static and analogous with the synchronous machine model. The first is done on basis of the T-diagram or 6-diagram of the machine. A short explanation is given below for comparison purpose.

Pag

Rs

Xs

Xr

Fig. 16: Equivalent circuit of an asynchronous machine

The power transferred across the air gap from stator to rotor (Pad of a 3-phase AC motor is determined as follows:

3 R

P = (4.31)

ag

2s

r2

The power transferred to the shaft is equal to the air gap power minus the rotor resistance

losses (Po). Psh Flag

=3

(R

r 3 1- s = 2 Ir 2

The delivered torque can be determined with the shaft power:

12 2

(4.32) =

(36)

Psh P

T = shsh

2

ws

s)-with (4.33)

w, = The angular velocity of the rotor in rad/s

To determine the currents Is and Ir the effective impedance of the motor Zeff must be

calculated from the equivalent circuit in Fig.. The following equation is valid for Zeff.

(R

Xm j , X, j

Zen = R -E Xs j +

R (4.34)

r + (Xm + X, ). j

The stator current is determined from E, and Z.

I, =

Es _(4.35)

Z

From these equations a model with current output and voltage input can be made, just like

the synchronous machine model. But one can see that a lot of dynamics, for example the

rotor dynamics. are left out. This is not consistent with the choice of the synchronous

machine model. Here it was proven that it was useful to take the rotor dynamics into account. So in this project it is seen as an improvement to model the asynchronous machine the same

as the synchronous machine, at least for the larger machines in the network In [Boetius,

1998] only the quasi-static model was worked out.

Just like with the synchronous machine the stator dynamics will be left out in the dq-model.

(37)

4.3.2 Asynchronous machine model

Since the asynchronous machine model is a derivative of the synchronous machine model only the differences will be discussed and displayed.

.as

GM Order ASM Modell

Fig. 17: Asynchronous machine model Inputs:

- E t/w el

: terminal voltage from network model or from infinite bus [V,r/s]

- w asm : rotor speed from drive system dynamics model [r/s]

Outputs:

- it

: complex current that model injects into network [All

- l_phaseeff : magnitude of complex machine current [All

- P asm : active electric machine power [kW]

- Q_asm : reactive electric machine power [kVAr]

- S_asm : complex electric machine power [kVA]

- T asm : Electric torque [Nm]

P_asm

(38)

ecias I a

Fig. 18: Inside asynchronous machine model Field winding omission

The field winding circuit is left out, so the matrices and voltage and current vectors reduce

from a length of 5 to a length of 4. Every parameter that has to deal with the field circuit can be forgotten. This can be seen in the multiplexers and demultiplexers in the model.

The function of delta

Although the rotor speed is asynchronous with the speed of the rotating stator field still an

angle delta is determined. This angle is not really the load angle anymore, but a continuously increasing (or decreasing) angle, when the machine is loaded. This will induce low frequent sine wavy values for the dq-voltage components. Due to the wavy dq-voltages, currents will

continuously be induced in the rotor windings. This can be compared with an oscillating

synchronous machine. Currents will only be induced in its damper windings in this case So the loaded asynchronous machine in steady state differs in this from the loaded synchronous

machine in steady state. The dq-voltages are constant in a synchronous machine in steady state.

4.3.3 Asynchronous machine parameters

In this paragraph the method to determine the machine parameters used in the

many equations from the machine datasheet is discussed. The determination of the parameters will

go in a different way than the synchronous machine. It is possible to do it in a similar way,

but this way is easier to get the data by oneself, by means of a few simple measurements.

In appendix 5 a datasheet of a tested and implemented asynchronous motor is given Two tests are necessary: the no-load test and the locked rotor test have to be performed. This

was actually done during the test period on the Maritime Institute Willem Barentz on

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Modular modeling of an electric system on board a ship for use in engine room simulators

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MODULAR MODELING OF AN ELECTRIC

SYSTEM ON BOARD A SHIP FOR USE IN

ENGINE ROOM SIMULATORS

SYSTEM ON BOARD A SHIP FOR USE IN

ENGINE ROOM SIMULATORS

A GENERIC MATHEMATIC MODEL FOR THE EXCITING UNITS

AND CONSUMER UNITS

Contents

Summary

Glossary/List of symbols

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1 Introduction

impedances, drive systems, etc. The mathematic models are chosen on basis of the

2 Description of the structure of an electric system on board of a ship

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public grid. Every component of a public grind can be found on board of a ship. One

bus can be assumed. An infinite bus is a connection in a network, where voltage and

later on, that this

an important issue throughout this

2.2 Some numbers

are equipped with air

refrigeration compartments. Last but not least: the ships own electric system to be

three-phase 440 V line

in order to distribute the power and to account for

board of ships is very dependent on good electrical management these days. Skilled

3 List of demands for modelling an electric system on board of a ship

that nobody will be harmed when a mistake happens. No material damage will occur.

Since the model will be used to run simulations for training future sailors, the

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