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TOVPaper-BK7576.lyx
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#LyX 2.2 created this file. For more info see http://www.lyx.org/
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\begin_body
\begin_layout Title
A Reduced Order Model for a TOV Study in a Solar PV Farm
\end_layout
\begin_layout Author
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Ahmad
\begin_inset space ~
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Abdullah
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Electric Power Engineers, Inc
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and the Department of Electrical Power and Machines
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Cairo University, Faculty of Engineering
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e-mail: ahmad.abdullah@ieee.org
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and
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Billy
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Yancey
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Electric Power Engineers, Inc
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e-mail: byancey@epeconsulting.com
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\end_layout
\begin_layout Abstract
With more solar photovoltaic (PV) farms coming online around the world,
special system studies are needed.
One of these studies is Temporary Overvoltage (TOV) study.
The main purpose of a TOV study is evaluating the capability of the surge
arresters (SAs) within the substation selected at the preliminary design
stage of the project.
To assess the capability of the surge arresters accurately, a detailed
electromagnetic transient (EMT) model of the project has to be built.
With the detailed EMT model of a large number of inverters included, the
run time of the model becomes prohibitive even for a single scenario.
In this paper, we propose a method to systematically reduce the order of
the EMT model thus making the model suitable for TOV studies at the substation
level.
The reduced order model response is then benchmarked against the response
of full order model for various TOV scenarios.
Simulation results show near-to identical agreement between the response
of the detailed model and the response of reduced order model.
Additionally, the run time of the proposed reduced model is less than the
run time of the full order model by a factor of ninety six.
\end_layout
\begin_layout Section
Introduction
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LatexCommand label
name "sec:Introduction"
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W
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ith
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the increased penetration of renewable energy into the grid, special system
studies are called upon to assess their impact on various aspects of the
power system.
One of these aspects is evaluating the adequacy the of surge arresters
within the substation.
Surge arrester MCOV and energy handling capability are generally selected
on an ad hoc manner in early design stage.
Assessment of the adequacy of the SAs in the substation ensures that SAs
can ride through the TOV by absorbing an amount of energy that is within
their energy handling capability and that the TOV level is limited to a
value determined by applicable standards.
The IEEE Standard C62.82.1-2010
\begin_inset CommandInset citation
LatexCommand cite
key "IEEEStd1312.1-19961996"
\end_inset
defines TOV as “an oscillatory phase-to-ground or phase-to-phase overvoltage
that is at a given location of relatively long duration (seconds, even
minutes) and that is undamped or only weakly damped; resulting from operation
of a switching device or fault condition
\begin_inset Quotes erd
\end_inset
.
\end_layout
\begin_layout Standard
It can occur when the PV inverter is suddenly disconnected from the grid.
Because inverters act as a constant current source, hence when a circuit
breaker opens the inverter terminal voltage can cause voltage fluctuations.
When this occurs, inverters quickly shut down, but there can be a short
period of time where some inverters can create overvoltage spikes.
This is a concern for PV system owners and utilities since large voltage
spikes can damage other equipment that is still connected in the vicinity.
\end_layout
\begin_layout Standard
Historically, assessment of SAs had been done under specific assumptions
about the nature of TOV.
For example, in conventional gas generation and if the neutral of synchronous
generator is ungrounded, it is known that a single line to ground fault
can cause the phase to ground voltage to increase by a factor of
\begin_inset Formula $\sqrt{3}$
\end_inset
.
This value can be used along with the surge arrester temporary overvoltage
withstand capability curve
\begin_inset CommandInset citation
LatexCommand cite
key "6093926"
\end_inset
to judge the adequacy of the SA.
However due to the nature of the technology used in renewable energy resources,
this might not be true.
Renewable energy resources are generally inverter based generation.
These inverter incorporate a large number of switches and are of various
topologies.
The temporary overvoltage withstand capability is usable for TOVs lasting
at least 10 milliseconds and due to the microprocessor controller used
within these inverters, most TOV events are transient in nature and the
duration of the TOV events in most cases do not exceed milliseconds.
Thus, the SA overvoltage withstand capability curve is of no practical
usefulness in case of TOV events due to inverter based technologies.
Hence, it is not always possible to assess the capability of a SA using
the project configuration, grounding scheme and the TOV withstand capability.
\end_layout
\begin_layout Standard
This necessitates a paradigm shift in performing TOV studies.
Building the renewable energy project in an EMT type software becomes a
must to assess the performance of SAs under various scenarios.
Running such models in EMT software requires small solution time step and
thus a long simulation run time.
Moreover, performing many TOV scenarios becomes a daunting task due to
the long simulation run time.
Thus, it is of utmost importance to develop a method to reduce the total
number of switches in the model to reduce the simulation run time.
\end_layout
\begin_layout Standard
Most equivalencing techniques
\begin_inset CommandInset citation
LatexCommand cite
key "Hussein2013"
\end_inset
treat the renewable project as one unit, i.e., the whole project starting
from the main power transformer (MPT) down to the medium voltage collector
system and the low voltage inverters are replaced by a single electrical
component that accurately captures the transient performance of the project
as a whole.
This is done mainly for grid impact studies and specifically for dynamic
simulations.
Popular methods such as the one in
\begin_inset CommandInset citation
LatexCommand cite
key "muljadi2006equivalencing"
\end_inset
is suitable only for power flow and dynamic studies not EMT type simulations.
\end_layout
\begin_layout Standard
In this paper, we provide a way to reduce the order of the solar PV project
at the substation level.
Each feeder of the collector system is reduced on its own to a simple generatio
n resource and an impedance.
Thus the number of the inverters in the EMT is drastically reduced to the
number of the feeders in the system.
It thus possible to study the performance of the SAs in the substation
since they are installed at the beginning of each of these collector feeders.
\end_layout
\begin_layout Standard
The paper is organized as follows.
The full system EMT model is described in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Full-System-Mode"
\end_inset
.
The benchmark response of the inverter as supplied by the manufacturer
is shown in
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Inverter-Benchmark-Tests"
\end_inset
.The methodology is provided in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Methodology"
\end_inset
.
The TOV scenarios used for comparing the full and reduced order model is
provided in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Scenarios"
\end_inset
.
The results of the reduced order model is shown in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Results"
\end_inset
.
Conclusions are offered in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Conclusions"
\end_inset
.
\end_layout
\begin_layout Section
Full System Model
\begin_inset CommandInset label
LatexCommand label
name "sec:Full-System-Mode"
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\begin_layout Standard
The system under study is an 80 MW solar PV project and is shown in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Full-Order-EMT-Model"
\end_inset
.
The project is divided into four collector feeders and two capacitor banks
each rated at 4.5 MVAr.
Each feeder has different number of inverters connected to it.
The configuration of each feeder has been removed from the paper for confidenti
ality reasons.
\end_layout
\begin_layout Standard
The number of inverters on each feeder is shown in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Full-Order-EMT-Model"
\end_inset
.
The project has a total of 45 inverters and each one is capable of producing
1.8 MVA.
Each inverter block in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Full-Order-EMT-Model"
\end_inset
has an DC to AC stage, an LC filter and an inverter step up transformer
(ISU) transformer.
Each ISU transformer is rated at 1.85 MVA and connected in delta-star with
the star connected to the low voltage side of the inverter and ungrounded.
The low voltage is 0.42 kV while the medium voltage is 34.5 kV.
A schematic of the inverter is shown in
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reference "fig:Schematic-of-the"
\end_inset
.
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scale 45
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Full Order EMT model
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name "fig:Full-Order-EMT-Model"
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filename graphics/Inverer.tif
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\begin_layout Plain Layout
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\begin_layout Plain Layout
Schematic of the inverter in the project
\begin_inset CommandInset label
LatexCommand label
name "fig:Schematic-of-the"
\end_inset
\end_layout
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\begin_layout Standard
Surge Arresters exist at the beginning of each feeder inside the substation
as shown in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Full-Order-EMT-Model"
\end_inset
.
All surge arresters at the medium voltage level are MOV type and have the
same MCOV and energy handling capability.
The V-I characteristics of the surge arresters are obtained from
\begin_inset CommandInset citation
LatexCommand cite
key "jonathanwoodworth2014"
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and is shown in
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reference "fig:Voltage-Current-(V-I)-Characteri"
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.
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filename graphics/SA 24 kv.png
scale 50
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Voltage-Current (V-I) Characteristics of the medium voltage arrester
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LatexCommand label
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\end_inset
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\end_layout
\end_inset
The project connects to the POI at 138 kV thorough a main power transformer
which has a rating of 89 MVA.
The feeder circuit breakers are EMA type breakers
\begin_inset CommandInset citation
LatexCommand cite
key "EMAbreakers"
\end_inset
.
These circuit breakers are equipped with a mechanically interlocked switch
on the load side that grounds the load side within 1 cycle of opening the
circuit breaker's main contacts.
\end_layout
\begin_layout Section
Inverter Benchmark Tests
\begin_inset CommandInset label
LatexCommand label
name "sec:Inverter-Benchmark-Tests"
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As has been stated in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Introduction"
\end_inset
, the inverter response in fundamentally different from conversational synchrono
us machines.
To be able to successfully reduce the order of the model and design the
benchmark scenarios in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Scenarios"
\end_inset
, the response of the inverter under specific scenarios has to be known.
The manufacturer supplied two benchmark cases.
The first one is a load rejection test in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Load-reject-test"
\end_inset
and the second one is a line to line fault in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Phase-A-to"
\end_inset
.
The fault is performed at the inverter terminals with the ISU transformer
terminals connected to a stiff grid.
It can be seen from both
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Load-reject-test"
\end_inset
and
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Phase-A-to"
\end_inset
that the load rejection test produces the worst TOV as opposed to conventional
power systems where generally the single line to ground fault causes the
highest TOV.
\begin_inset Float figure
wide false
sideways false
status collapsed
\begin_layout Plain Layout
\align center
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filename graphics/load rejection.PNG
scale 40
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\begin_layout Plain Layout
Load rejection test
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LatexCommand label
name "fig:Load-reject-test"
\end_inset
\end_layout
\end_inset
\end_layout
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\end_layout
\end_inset
\begin_inset Float figure
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filename graphics/Ab-B fsault.PNG
scale 45
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\begin_layout Plain Layout
Phase A to Phase B fault on the inverter terminal
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name "fig:Phase-A-to"
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\begin_layout Section
Methodology
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name "sec:Methodology"
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\begin_layout Standard
Just as any electrical source can be represent by its Thevenin's or Norton's
equivalent
\begin_inset CommandInset citation
LatexCommand cite
key "watson2003power,bobrow1997elementary"
\end_inset
, the inverters within the solar PV project can be modeled as such depending
on the technology used within the inverter.
However, most manufacturers of solar PV inverters use a technology that
make the inverters act as a current source or a voltage controlled current
source.
Due to that, Norton's equivalent model would be most suitable.
A Norton's equivalent consists of two parts: the Norton's current source
and the impedance in parallel with it.
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\begin_layout Standard
The Basic idea behind the method in this paper is to represent each feeder
by a pseudo-Norton's equivalent.
The pseudo-Norton's equivalent will consist of two parts: a pseudo-Norton
source and an impedance in parallel.
The pseudo-Norton's source will be responsible for equivalencing the low
frequency response of the feeder, while the impedance in parallel will
be equivalencing the high frequency response of the feeder.
This effectively means that the step response of the pseudo-Norton's source
should correspond to the low frequency response portion of the overall
feeder response.
This also means that the step response of the impedance in parallel should
correspond to the high frequency response portion of the overall feeder
response.
The construction of the pseudo-Norton's source is provided in
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reference "subsec:The-pseudo-Norton-source"
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while the construction of the impedance in parallel is provided in
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reference "sec:The-impedance-in-paralel"
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.
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\begin_layout Subsection
The Pseudo-Norton's Source
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name "subsec:The-pseudo-Norton-source"
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\begin_layout Standard
The pseudo-Norton's source will consist of an inverter stage with its associated
controls, a filter as well a transformer.
Generally speaking, any inverter must contain a filter to shape the output
waveforms by rejecting the high frequency switching harmonics.
Inverter manufacturers can use transformerless
\begin_inset CommandInset citation
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key "inzunza20056"
\end_inset
technology but this is outside the scope of this paper.
The validity of the current methodology is yet to be investigated under
transformerless technology.
\end_layout
\begin_layout Standard
To construct the pseudo-Norton's source, the inverter MVA rating must be
scaled up by a factor equal to the total number of inverters on the feeder.
Many vendors supply proprietary EMT models of their inverters that has
the number of inverters or the MVA variable.
If the user is using a custom EMT model, then the model must have the MVA
rating or the number of inverters variable.
The controls of the inverter are to kept the same without any change.
The values of the inductance and the capacitance of LC filter are also
to be scaled up by the number of inverters.
Lastly, the ISU transformer MVA rating is also to be scaled up by a factor
equal to the number of inverters without changing the per unit impedance
of the ISA transformer.
\end_layout
\begin_layout Standard
In this paper, we used a confidential model supplied by the manufacturer.
The model has proprietary control algorithms, proprietary switching topology,
LC filer and an ISU transformer.
We only scaled the model as described in this section.
\end_layout
\begin_layout Subsection
The Impedance in Parallel
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name "sec:The-impedance-in-paralel"
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\begin_layout Standard
It is necessary that the parallel impedance represents the high frequency
response of the collector system.
Since it is typical in power flow studies to represent the cable sections
in the collector system using pi-models, the reader is to be warned against
such representation in EMT type analysis as this representation is only
valid at the power frequency.
The parallel impedance is nothing other than a frequency dependent impedance
that captures the high frequency response of the cable sections in collector
feeder.
Thus the cable sections along the feeder has to be modeled by a suitable
frequency dependent model.
The user then has two choices:
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\begin_layout Enumerate
Either do a frequency scan on the feeder with all inverters removed from
the project (transformer has to be open circuited as well as the feeder
breaker).
Using that frequency scan, the user can use vector fitting
\begin_inset CommandInset citation
LatexCommand cite
key "gustavsen1999rational,morched1983transmission"
\end_inset
to construct a frequency dependent model.
Passivity has to be enforced upon the resulting fitting by insuring that
negative resistance is not a result of the fitting.
Negative resistance causes instability in the EMT simulations.
\end_layout
\begin_layout Enumerate
Keep the feeder intact without performing a vector fitting.
This means that the cable sections are to be kept in the model but without
the inverters, LC filters or the ISU transformers.
\end_layout
\begin_layout Standard
Theoretically, both methods should represent the same impedance, i.e., .
Method 1 above can be done very quickly in PSCAD/EMTDC.
However, PSCAD/EMTDC does not enforce passivity on the resulting frequency
dependent model.
Due to that, the authors used the second method and they will treat the
first method in a separate publication.
\end_layout
\begin_layout Standard
The authors also noted that for the equivalencing to produce satisfactory
results, some cable sections in feeder have to be left out in this equivalencin
g process.
It turned out that the first cable section has to be removed from this
frequency dependent impedance.
The overall reduced order model is shown in
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reference "fig:Reduced-Order-Model"
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.
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filename graphics/Project_eqlent.tif
scale 50
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\begin_inset Caption Standard
\begin_layout Plain Layout
Reduced Order Model
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name "fig:Reduced-Order-Model"
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\end_inset