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TOVPaper.lyx~
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#LyX 2.2 created this file. For more info see http://www.lyx.org/
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\begin_document
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\begin_body
\begin_layout Title
A Reduced Order Model for a TOV Study in a Solar PV Project
\end_layout
\begin_layout Author
\begin_inset Flex Author Name
status open
\begin_layout Plain Layout
Ahmad
\begin_inset space ~
\end_inset
Abdullah
\begin_inset Flex Author Mark
status open
\begin_layout Plain Layout
1
\end_layout
\end_inset
and Billy
\begin_inset space ~
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Yancey
\begin_inset Flex Author Mark
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2
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\begin_inset Flex Author Affiliation
status collapsed
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\begin_inset Flex Author Mark
status open
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1
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Electric Power Engineers, Inc and the Department of Electrical Power and
Machines
\begin_inset Newline newline
\end_inset
Cairo University, Faculty of Engineering
\begin_inset Newline newline
\end_inset
Cairo, Egypt 12613
\begin_inset Newline newline
\end_inset
E-mail: ahmad.abdullah@ieee.org
\end_layout
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status collapsed
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2
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Electric Power Engineers, Inc
\begin_inset Newline newline
\end_inset
Austin, TX, USA 78738
\begin_inset Newline newline
\end_inset
Email: byancey@epeconsulting.com
\end_layout
\end_inset
\end_layout
\begin_layout Abstract
Special system studies are needed to assess the different preliminary designs
of solar photovoltaic (PV) projects.
One of these is a Temporary Overvoltage (TOV) study.
The main purpose of a TOV study is to evaluate the capability of the surge
arresters (SAs) within the substation.
To assess the capability of the SAs accurately, a detailed electromagnetic
transient (EMT) model of the project has to be built.
With the detailed EMT model, which has a large number of inverters, 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 at the substation level thus making the model suitable for
TOV studies.
The response of the reduced order model is then benchmarked against the
response of the full order model of an 80 MW solar PV project for various
TOV scenarios.
Simulation results show satisfactory agreement between the response of
the detailed model and the response of the reduced order model.
Additionally, the run time of the proposed reduced order model is less
than the run time of the full order model by a factor of ninety six.
\end_layout
\begin_layout Keywords
Solar power generation, Photovoltaic systems, Electromagnetic transients,
Surge arresters, Transient overvoltage, Surge protection, Temporary Overvoltage
\end_layout
\begin_layout Section
Introduction
\begin_inset CommandInset label
LatexCommand label
name "sec:Introduction"
\end_inset
\end_layout
\begin_layout Standard
With 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 the 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
This 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 TOV 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 inverters 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.
The model must include all inverters as well as all SAs characteristics
in order to accurately represent the project.
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 (inverters) 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 model is drastically reduced
to the number of the feeders in the collector system.
It thus possible to study the performance of the SAs in the substation
since they, generally, are installed at the beginning of each of these
collector feeders.
\end_layout
\begin_layout Standard
The paper is organized as follows.
The detailed 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 detailed 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 summarized in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Conclusions"
\end_inset
.
\end_layout
\begin_layout Section
Detailed System Model
\begin_inset CommandInset label
LatexCommand label
name "sec:Full-System-Mode"
\end_inset
\end_layout
\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 a 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
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Schematic-of-the"
\end_inset
.
\begin_inset Float figure
wide false
sideways false
status collapsed
\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename graphics/Project.tif
scale 45
\end_inset
\begin_inset Caption Standard
\begin_layout Plain Layout
Full Order EMT model
\begin_inset CommandInset label
LatexCommand label
name "fig:Full-Order-EMT-Model"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\begin_inset Float figure
wide false
sideways false
status collapsed
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\align center
\begin_inset Graphics
filename graphics/Inverer.tif
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\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
\end_inset
\end_layout
\end_inset
\end_layout
\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, have the
same MCOV of 24.4 kV and have the same energy handling capability of 219
kJ.
The V-I characteristics of the SAs are obtained from
\begin_inset CommandInset citation
LatexCommand cite
key "jonathanwoodworth2014"
\end_inset
and is shown in
\begin_inset CommandInset ref
LatexCommand formatted
reference "fig:Voltage-Current-(V-I)-Characteri"
\end_inset
.
\begin_inset Float figure
wide false
sideways false
status collapsed
\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename graphics/SA 24 kv.png
scale 50
\end_inset
\begin_inset Caption Standard
\begin_layout Plain Layout
Voltage-Current (V-I) Characteristics of the MV surge arrester
\begin_inset CommandInset label
LatexCommand label
name "fig:Voltage-Current-(V-I)-Characteri"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
The project connects to the Point of Interconnection (POI) at 138 kV thorough
the MPT 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"
\end_inset
\end_layout
\begin_layout Standard
As has been stated in
\begin_inset CommandInset ref
LatexCommand formatted
reference "sec:Introduction"
\end_inset
, the inverter response in fundamentally different from conventional synchronous
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 tests has to be known.
The inverter manufacturer supplied two benchmark tests.
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 infinite bus.
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
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\begin_inset Graphics
filename graphics/load rejection.PNG
scale 40
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\begin_inset Caption Standard
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Load rejection test (upper curve is voltage - lower curve is current)
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name "fig:Load-reject-test"
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\end_inset
\end_layout
\end_inset
\begin_inset Float figure
wide false
sideways false
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\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename graphics/Ab-B fsault.PNG
scale 45
\end_inset
\begin_inset Caption Standard
\begin_layout Plain Layout
Phase A to Phase B fault on the inverter terminal
\begin_inset CommandInset label
LatexCommand label
name "fig:Phase-A-to"
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\end_inset
\end_layout
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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
makes 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 frequency 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
frequency response.
The construction of the pseudo-Norton's source is provided in
\begin_inset CommandInset ref
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reference "subsec:The-pseudo-Norton-source"
\end_inset
while the construction of the impedance in parallel is provided in
\begin_inset CommandInset ref
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reference "sec:The-impedance-in-paralel"
\end_inset
.
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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
LatexCommand cite
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 ISU 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 have to be modeled by a suitable
frequency dependent model.
The user has two choices:
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\begin_layout Enumerate
Perform a frequency scan on the feeder with all inverters removed from the
project (ISU transformers have 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.
The first choice 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 choice 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 from this equivalenc
ing 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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wide false
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\begin_layout Plain Layout
\align center
\begin_inset Graphics
filename graphics/Project_eqlent.tif
scale 50
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\begin_inset Caption Standard
\begin_layout Plain Layout
Reduced Order Model
\begin_inset CommandInset label
LatexCommand label
name "fig:Reduced-Order-Model"
\end_inset
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Section
TOV Scenarios