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Modelling the system dynamics of islanding asynchronous
generators
Håkon Molland EdvardsenOslo, Norway
[email protected]
Dietmar WinklerTelemark University College, Norway
[email protected]
Abstract
Asynchronous generators are often used for smallhydro power
stations with an installed power capa-city of under 1MW . The
reason for this is their ro-bustness and low cost. In order do be
able to pro-duce active electrical power with an
asynchronousgenerator once needs to provide enough excitationby
means of reactive power provided by either theelectrical grid or
additional capacitors.
But in asynchronous generators we can also findthe phenomenon of
self-excitation which allows theasynchronous generator to operate
as a standaloneunit. Investigation of the self-excitation
processshows that significant over-voltages can occur if agenerator
with sufficient capacitors is suddenly dis-connected from the
utility grid. The preconditionfor a successive voltage build-up is
that the gener-ator is left with enough capacitive power and a
lowload after the disconnection.
The Lønnestad radial in Seljord, Norway, is adistribution radial
with both asynchronous and syn-chronous generators connected. In
order to investig-ate the system dynamics in the radial after it is
dis-connected from the rest of the 22kV distribution grid,the
radial was modelled and simulated using Model-ica as modelling
language.
Keywords: modelica, asynchronous generators,self-excitation,
islanding, electric power library
1 Introduction
The main share of the electricity produced in Nor-way is based
on utilisation of the nation’s large po-tential of hydro power.
Today are nearly all thelarge waterfalls profitable for hydro power
produc-tion already utilised, or protected against encroach-ment on
nature. Due to this, there has for the last dec-ades been an
expansion in the number of small hydropower stations below 10MW .
This is often minor
projects where the power station is located near asmall
waterfall owned by a local landowner.
These small hydro power stations are often con-nected to already
existing distribution grids, due tothe geographical location and
installed capacity ofthese stations. This is often grids
constructed forlow capacities with purpose to distribute the
electri-city out to the local consumers. Connection of
powerstations in these types of grids will therefore oftenchange
the situation of power flow in the grid, andlead to challenges
regarding voltage stability and re-quirements for faults
detection.
2 Theory
The system that will be described in this paperconsists of a
electrical distribution radial to whichone synchronous generator
and several asynchronousgenerators are connected. This theory
section willonly cover the most important aspects of the
complexpower systems.
2.1 Asynchronous generators
In the industry the asynchronous machine, or in-duction machine,
is used in a wide variety of applic-ations with purpose of
converting electrical power tomechanical work. The asynchronous
machine is veryeconomical, reliable, and easy to control, which
aresome of the reasons for its popularity. There are twomain types
of asynchronous machines based on therotor construction; squirrel
cage type, and wound ro-tor type. The simplicity and low cost, and
the factthat they can be driven as a generator as well as a mo-tor,
makes these machines very beneficial for windpower generation and
small hydro power stations upto 1MW .
Unlike in wind power applications, the wound gen-erator is
seldom used in small hydro power stations.The reason for this is
that generators used in smallhydro power stations generally is
operated on the
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principle of self-excitation without any rotor excita-tion. For
such applications, generators with the squir-rel cage rotors can
with advantage be used instead ofgenerators with wound rotor, since
the squirrel cagemachine has lower cost.
2.1.1 The phenomena of self-excitation
Unlike the synchronous generator which gets itsmagnetisation
from an internal magnetising source,and can be controlled to
operate at a given fre-quency, the induction generator has no
independentcontrol over the air-gap field. The induction gen-erator
needs lagging reactive power to produce themain air-gap and winding
leakage flux [1]. This phe-nomenon is referred to as
self-excitation since thegenerator achieves its magnetising from a
grid, orcapacitors which are connected to the stator termin-als.
The phenomena permit utilisation of an induc-tion generator as a
standalone unit without a voltagesource connected. Due to this the
induction generatoris often referred to as a SEIG (Self-Excited
InductionGenerator).
The phenomenon of self-excitation has beenknown for a long time,
and a great deal of researchhas been done in the field of
describing the phe-nomena and its transient behaviour. Various
typesof models have been proposed, but the main part ofthem is
rather complicated models expressed by thePark’s transform[2].
Initiation of the self-excitation process Self-excitation of a
standalone generator may take place ifa sufficient amount of
capacitors is connected to thegenerator. In order to initiate the
self-excitation pro-cess, the residual flux in the rotor iron has
to be highenough. The residual flux will induce a voltage in
thestator when the generator is accelerated to a certainspeed. By
connecting capacitors to the terminals ofthe generator, the induced
stator voltage will cause aflow of current from the stator [3].
For a given capacitor, an SEIG running at no loadrequires only a
minimum speed for the self-excitationto initiate [4].
Voltage build-up in the generator Once the pro-cess of
self-excitation is initiated, the generatorvoltage builds up. The
voltage build up can more eas-ily be understood by looking at the
phasor diagram inFigure 1.
Figure 1: Phasor diagram before and after the self-excitation is
initiated [3]
In this figure it can be observed that a current,Ic, starts to
flow from the capacitors once the self-excitation is initiated.
This current generates a flux,Ψgen, into the generator, with the
same directionas the residual flux, Ψres. Therefore, the
current,Igen, circulating in the stator reinforces the total
flux,Ψtotal . This reinforced total flux causes an evenhigher
stator voltage leading to successive increasein current and flux
[3].
Figure 2 shows the generator magnetising charac-teristic and
capacitance for three different frequen-cies, where the machine
magnetising characteristicis simplified by linear segments with a
knee point.
For a given capacitance and generator saturationcharacteristic,
the intersection of the capacitance lineand the V-I-curve of the
generator moves as the fre-quency increases. The voltage build-up
comes to haltwhen the non-linear magnetisation curve for the
gen-erator intersects the capacitor voltage curve [1]. Thispoint is
the steady state operating point for an in-duction generator
running at no-load with capacitorsconnected. The no-load steady
state operating pointis determined by the non-linear magnetisation
curveof the generator, the value of the capacitors, and thespeed of
the generator.
Figure 2 shows that by increasing the frequency,the generator
curve is moved upwards, while theslope of the capacitor curve
decreases, which res-ults in an increase of steady state operation
voltage.This states that connection of capacitors supplyinga
no-loaded induction generator with a larger react-ive power than
needed may cause over-voltage at thegenerator terminals [3].
The intersection point between the saturation char-acteristic
and the capacitor line can be defined interms of the electrical
frequency [1]:
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Figure 2: V-I curves for induction generator and ca-pacitor at
different frequencies [11]
V (ω) =ωA
1−ω2LdC(1)
I(ω) =ω2AC
1−ω2LdC(2)
Where Ld is the non-linear magnetisation induct-ance defined as
dΨ/dl on the saturated portion of theno-load Ψ− I curve for the
generator, and A is theinterception of the dynamic inductance line
with theordinate, defined as Ψ(I) = A + LdI.
In order to achieve a steady state operation point atany
frequency, the capacitance must satisfy the fol-lowing
expression:
Laω2Ld
>C >1
ω2LaWhere La is the inductance defined by the air-gap
line of the generator. [1]
2.2 Synchronous generators
Three phase synchronous generators are theprimary source for all
the electric energy produced ina power system. One of the reasons
is that the syn-chronous generator gives the opportunity to
decidewhether it is desirable to produce or consume react-ive
power, which gives us the ability to regulate thevoltage and power
flow in an interconnected grid [5].
The rotor contains a field winding which is sup-plied by a DC
source. This voltage results in a fieldcurrent, Ix , which produce
the rotor field in the air-gap between the rotor and stator.
Controlling the ro-tor current and hence the rotor produced field,
makes
it possible to regulate the induced emf and the react-ive power
of the generator.
2.3 Transmission lines
Small hydro power stations are often connected toa local
distribution grid. This grid is usually ownedby the local utility
company, and is normally oper-ated at a voltage level between 11kV
and 22kV .
A distribution grid is normally composed of a com-bination of
overhead lines and underground cables.The overhead lines are used
for long distances andrural areas, while underground cables are
used inurban areas and for underwater crossings. An under-ground
cable is 10 to 15 times more expensive thanan overhead line, and it
is therefore only used in situ-ations where overhead lines are
unsuitable.
From a mathematical point of view, an under-ground cable can be
modelled in exactly the sameway as an overhead line. Here, the
values of theelectrical parameters are the only difference
betweenthem. In a cable, the shunt capacitance is stronglydependent
on whether the three-phase conductors arescreened or not, and on
whether the three conductorsconstitute separate three-phase cables
or one com-mon cable [6].
The typical per unit length series inductance, L,of a cable is
about half the inductance of a similarrated overhead line. On the
other hand, the per unitlength charging current is about 30 times
more thanfor a similar rated overhead line. For a critically
longcable, the charging current can be equal to the max-imum
current of the cable, there will then be no ca-pacity left for
transmission of power.
3 Over-voltage phenomena inGrunnåi
On the 27th July in 2011, several unwanted eventstook place in
Grunnåi power station. By looking atthe damages it could be seen
that significant over-voltages had occurred in the 22kV busbars of
thepower station.
3.1 Damages from the events
On the end termination of one of the incoming sup-ply cables, a
phase to ground fault had occurred. Twopictures of the end
termination and its damage areshown in Figure 3. From the figure it
can be seen
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that there has been heat generation in the end termin-ation.
Figure 3: Phase to ground fault on end terminationof supply
cable
A breakdown of a surge arrester had also occurredunder the
events. Figure 4 shows the surge arresterswith the broken one to
the left. By looking at thebroken surge arrester and the signs of
heat, it is nat-ural to assume that the amount of energy
dissipatedin the surge arrester was higher than its energy
hand-ling capability.
Figure 4: Broken surge arrester to the far-left
Signs of high temperatures and arcs were also seenother places
in the rack of the 22kV busbar, whichcould be signs of a possible
short-circuit due to a highvoltage.
Damages did also occur in other places of the ra-dial this day,
which indicates that the phenomenondid not only take place locally
in Grunnåi.
3.2 The sequence of events
By looking into the logs of the protection relays inGrunnåi and
Seljord sub-station, it was discoveredthat several functionalities
in each of the protectionrelays had started to account for
triggering. Unfor-tunately the clocks in the protection relays were
notsynchronised, so it is impossible to determine whichprotection
relay triggered first.
It is most likely to think that the whole sequencestarted with a
breakdown in the end termination ofthe incoming cable in Grunnåi.
The breakdown wasmost likely caused by a weakness in the end
termin-ation due an installation failure. This error may havecaused
a bad connection or a weakness in the insula-tion which led to heat
generation and degradation ofthe insulation over longer period of
time.
The presumed sequence of events was:
1. Earth circuit fault in Grunnåi due to a breakdown inthe end
termination of a incoming supply cables.
2. The protection relay in the Seljord sub-station detec-ted the
phase to ground fault and disconnected theLønnestad radial from the
rest of the grid in Seljordmomentarily after the fault was
detected.
3. The disconnection resulted in heavy imbalance ofactive power
and reactive power in the now islandedradial.
4. The frequency in the grid increased rapidly sinceGrunnåi did
not correct for the overproduction in theisland.
5. The generator circuit breaker disconnected Grun-nåi from the
grid, due to triggering of the over-frequency relay (51Hz and 0.1
seconds). This leftthe asynchronous generators in Sagbekken 1
andSagbekken 2 and 3 alone in the island.
6. Sufficient amount of reactive power in the grid toinitiate
self-excitation. The self-excitation led to asuccessive voltage
build-up, which resulted in signi-ficant over-voltages in the
grid.
7. The high voltage led to a large voltage drop acrossthe surge
arresters in Grunnåi. The amount of en-ergy dissipated in the surge
arrester was higher thanits energy handling capability. This caused
one ofthe surge arresters to breakdown.
8. The high voltage exceeded the dielectric strength ofair
inside the rack of the busbars. The air becameionised and arcing
occurred inside the rack. Thisarcing led to low impedance in the
grid, and the pro-cess of self-excitation came to halt.
This is the presumed sequence of events, basedon the damages and
grid configuration. Followingchapter presents simulations from the
Lønnestad ra-dial where different scenarios are carried out.
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Figure 5: Overview of the Lønnestad radial
4 Description of the grid
For investigation of the over-voltage phenomena inGrunnåi power
station, only the Lønnestad radial isof interest. This is the 22kV
radial where the Grun-nåi power station and Sagbekken power
stations areconnected. The radial is mainly built up with
cables,where the total length of 22kV cables is 17.9km. Anoverview
of the Lønnestad radial is shown in Fig-ure 5. The total power
consumption in the radial willvary throughout the day, but is
assumed to be 250kWwith a power factor equal to 0.96 during the
workinghours.
4.1 Grunnåi power station
Grunnåi hydro power station is the largest powerstation in the
Lønnestad radial with a synchronousgenerator of 15.06MW . The
turbine is governed withan infinite droop control, which means that
the powerstation runs at a constant power set-point independ-ently
of the electrical frequency in the grid. Figure 6shows a picture of
the synchronous generator insidethe power station.
4.2 Sagbekken power stations
Sagbekken 1 and Sagbekken 2 and 3 are two mi-cro power stations
that utilise the water from thesame river. Both of the power
stations are equipped
Figure 6: Grunnåi power station with its generator
with asynchronous generators with squirrel cage ro-tor, where
Sagbekken 1 has three units with a totalinstalled capacity of 400kW
, and Sagbekken 2 and 3has four units with a total installed
capacity of475kW .
Each of the powers stations is equipped with pro-tection relays
that operate a common generator cir-cuit breaker in each station.
Figure 7 shows the fourgenerator units in Sagbekken 2 and 3.
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Figure 7: The four generator units in Sagbekken 2and 3
5 Power system simulations
The power system of the Lønnestad radial wasmodelled and
simulated using Modelica [7] as mod-elling language and Dymola[8]
as simulation tool.Several models of the power system were created
tosimulate different scenarios. A small project librarywas build
for the power system, containing the dif-ferent power system
models, main components, andsubsystems developed for the
models.
The power systems model developed for the Løn-nestad radial are
based on the Electric PowerLibrary[9] which is a commercial library
developedby the Swedish company Modelon[10]. The librarygives the
opportunity to model, simulate, and analyseelectric power systems,
including AC three phasesystems, AC one phase systems, and DC
systems.The models can be used for both steady state andtransient
mode for simulation and initialisation.
Some components like the protection relays andRMS voltage
sensors were not available in theElectric Power Library and were
therefore cre-ated using the Modelica Standard Library [11].
The following sections will give you a brief intro-duction to
the models used and the investigated ef-fects. A more complete and
thorough documentationis also available in [12].
5.1 Simulation models
Each of the power-station models consist of modelfor the
generator-turbine unit and a protection relayunit. Figure 8 shows
an example how the differentpower stations are build up in
principle.
Figure 8: Sub-model Sagbekken 1
5.2 Investigation of the self-excitation pro-cess
To be able to investigate the process of self-excitation with
different grid configurations, themodel in Figure 9 was
created.
Figure 9: Model used for investigation of the self-excitation
process
The model consists of a 100kW asynchronous pro-duction unit and
an equivalent distribution line whichis connected to an infinite
grid. The investigationwas carried out as sensitivity analysis
where differentloads and capacitors where compared in order to
de-termine their impact on the system. At t = 1secondthe circuit
breaker was opened, which brought thepower plant into islanded grid
operation with a givencapacitive power and resistive load
connected.
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5.2.1 Self-excited induction generator withoutcapacitors
Figure 10 shows how the SEIG behaves when it issuddenly brought
into islanded operation without ca-pacitors connected to the
generator terminals. Beforedisconnection it can be observed that
the generatoroperates in steady state where it produces 98.4kWwith
active power, and consumes 67.1kvar with re-active power. As the
induction machine no longer isable to produce the main air-gap and
winding leakageflux after the disconnection, it can be seen how
thevoltage reaches zero when the machine de-excites.Due to the
constant mechanical torque, Tm, on therotor, it can be seen in
Figure 10 how the angular ve-locity, ωr, increases when the
electrical torque, Te,disappears:
dωrdt
=Tm−Te
J
Figure 10: SEIG with no capacitor, disconnection att = 1s
5.2.2 Self-excited induction generator with ca-pacitors
The unloaded SEIG’s behaviour with different ca-pacitors after a
disconnection is shown in Figure 11.From the figure it can be seen
that the SEIG needsat least 10kvar of capacitive power in shunt
withthe generator to initiate a successful voltage build-up after a
disconnection. The figure also shows that
a further increase of the capacitive power results inshorter
time from the disconnection to the voltagebuild-up and a lower peak
voltage. This is becauselarger capacitors provide the minimum
amount of re-active power required for self-excitation at a
lowerangular velocity than smaller ones.
Figure 11: SEIG voltage with different capacitors,disconnection
at t = 1s
5.2.3 Self-excited induction generator with ca-pacitors and
load
To simulate a resistive load’s impact on the SEIG, asensitivity
analysis was performed with different res-istive loads. For all the
different loading scenarios, a30kvar capacitor bank was connected
in shunt withthe generator terminals.
By comparing the 10kW simulation in Figure 12with the similar
no-load simulation in Figure 11, itcan be observed that the load
has a considerable in-fluence on the new operating point. The 10kW
loadreduces the maximum over-voltage of the 100kWgenerator from
10kV to 1.4kV .
For the simulation with the 90kW load, it can beobserved that
the load is too large to initiate thevoltage build-up immediately
after the disconnec-tion. As the rotor accelerates, it can be seen
that theself-excitation is initiated after t = 2.5seconds when
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the angular velocity is large enough for the capacit-ors.
Figure 12: SEIG with 30kvar capacitors and differ-ent loads,
disconnection at t = 1s
5.3 Simulation with phase to ground fault atGrunnåi
In order to investigate the over-voltage that oc-curred at the
22kV busbar in Grunnåi on the 27th July2011, the simulation model
in Figure 13 was cre-ated. At t = 1second a phase to ground fault
occursat phase A. Simultaneously as the phase to groundfault
occurs, the circuit breaker in Seljord substationdisconnects the
Lønnestad radial from the rest of thegrid due to momentary
triggering settings in the pro-tection relay.
Figure 14 shows how the voltages changes whenthe phase to ground
fault occurs at phase A, caus-ing the system to go from a balanced
system to anunbalanced system. By looking at the figure it canbe
clearly seen that the radial has enough capacitivepower and low
enough load to initiate self-excitationprocess in the Sagbekken
power stations once theGrunnåi power station is disconnected.
Figure 15 shows that it took 1.5 seconds from thephase to ground
fault occurring at the Grunnåi powerstation before all the
generators in the radial were dis-
Figure 14: Voltage at Grunnåi busbar, phase toground fault at T
= 1s
Figure 15: Disconnection times, phase to groundfault at T =
1s
connected. During this time the over-voltage reachedits maximum
value of 53.36kV and was continuouslyover 30kV for 0.7seconds at
phase C.
6 Discussion
The investigation of the self-excitation processshows how the
dynamics of the generator changeswhen different capacitors and
loads are connectedto the generator terminals. For a generator
runningat no load with capacitors connected to the termin-als,
there exists a minimum speed for self-excitationto occur. If the
capacitors do not provide sufficientexcitation to initiate the
self-excitation at the givenspeed, the loss of the utility grid
causes a sudden in-
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Figure 13: Model of Lønnestad radial with phase to ground
fault
crease in the slope of the equivalent capacitor lineseen by the
generator [1]. This change may cause acomplete or partial loss of
the generator excitation.Due to this, the generator fails to
produce an electro-magnetic torque large enough to overcome the
mech-anical torque, which results in acceleration of the
ro-tor.
Unless the residual flux is lost, the self-excitationcan be
initiated when the angular velocity has in-creased such that the
reactive power from the capacit-ors is sufficient. Once the process
of self-excitationis initiated, the terminal voltage starts to
build up.The generator reaches its new stable operating pointwhen
the dynamic magnetisation line of the gener-ator intersects the
linear capacitor line.
For asynchronous generators connected to a utilitygrid with much
reactive power in form of capacitorsor cables, it is crucial with
quick detection and lowtrigger time for over-frequencies to avoid
unwantedover-voltages.
The simulations shows that the reactive power inthe grid is
great enough initiate self-excitation thatresults in harmful
over-voltages, independently ofwhether the load is connected or
not. It is seen thatthe voltage build-up happens quickly. It takes
below0.4 seconds from the radial is brought into islandedoperation
to the voltage reaches its peak value.
Significant over-voltages can also occur when a
phase to ground fault arise at Grunnåi busbar. Re-gardless of
whether Grunnåi power station is con-nected or a phase to ground
fault arise, the self-excitation of the Sagbekken stations will
result inharmful over-voltages. For all the simulations,
themagnitude and length of the over-voltages are greaterthan the
thermal stability limit of the surge arrestersin Grunnåi power
station.
Correct parameters for the protection relays are es-sential for
providing sufficient protection of the grid.This is also the
easiest way to protect the Lønnestadradial against harmful
over-voltages. Simulationsshow that the peak value of the angular
velocity canvary dependent on the load scenario. Correct
para-meters for detection of over-voltages are thereforemost
important for the protection relays.
7 Conclusion
This paper investigates the system dynamics in theLønnestad
radial when it is brought into islanded op-eration. Modelling and
simulation of the transientbehaviour of an asynchronous generator
is a fairlycomplex task that requires good knowledge of elec-tric
machinery and dynamic systems. Due to this,there is often a lack of
knowledge in small utilitycompanies when it comes to the
asynchronous gen-
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erator.The asynchronous generator has the opportunity to
operate as a standalone unit if the amount of reactivepower in
the cables or capacitors is sufficient. For theLønnestad radial, it
was proven that the amount ofreactive power in the grid is large
enough to initiateself-excitation of all the seven asynchronous
gener-ators in the radial.
The self-excitation leads to fast voltage build-upsthat results
in a harmful over-voltage in the distribu-tion grid. For the
simulations with load connected,it was observed that the
over-voltage in the distribu-tion grid reached its maximum voltage
of circa 50kV ,only 0.4 seconds after the radial was brought into
is-landed operation.
This is a type of over-voltage that requires a greatdeal of
knowledge regarding self-excitation to en-sure good protection of
the grid. Normal protectionmethods as surge arresters will not be
adequate, sincethese are designed to protect against surge
voltages,and not transient over-voltages with several
secondsduration. Simulations performed in this paper showthat it is
crucial with correct protection parametersin the Sagbekken stations
to protect equipment inthe Lønnestad radial against over-voltages
caused bythe generators. To avoid unwanted voltage build-ups,
correct parameters for over-voltage detection isthe most important
protection. It is recommendedto have momentarily disconnection when
the voltageexceeds a given value.
8 Acknowledgements
The work was carried out as part of the Masterthesis of Håkon
Molland Edvardsen [12] in cooper-ation with Skagerak Energi,
Porsgrunn, Norway andunder supervision of Dietmar Winkler.
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DOI10.3384/ECP14096969