EE30042 Power Electronics
Assignment
This assignment will introduce you to the PSCAD/EMTDC software package
which is used for modelling power electronics in power systems. It is thus
used to model wind turbines, High Voltage DC Transmission, static
compensators, renewable energy generation, complex load behaviour etc.
The assignment has three parts:
1. An introduction to PSCAD/EMTDC where you are introduced to the
theory and background of the software and do online tutorial
2. A walk-through of the simulation of a rectifier system.
3. A design study on the system in 2.
Assessment is via a pro-forma hand-in sheet which you must use and submit
via Blackboard. Please look at the hand-in sheet and what it requires
BEFORE you do anything else.
You should aim to spend a little under 3 hours on each part, with about
1 hour to fill in the hand-in sheet.
To do this assignment you can use either the School’s computer cluster, or
you can download the PSCAD/EMTDC student version (for free) presently
from:
https://pscad.com/products/pscad/free_downloads/
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Part 1 – Introduction to PSCAD
Software required: PSCAD/EMTDC version 4.0.1 or later – student edition
Overview:
In this worksheet you will be introduced to the principles behind time-
stepping simulation programmes for circuits, and will be shown how the
PSCAD/EMTDC programme works. You will also work through the
initial online help for PSCAD/EMTDC. Be warned, since you are in this
first stages of learning to use a new simulation programme, this
worksheet involves a lot of reading though part of this exercise requires
you to work through an online tutorial.
Learning Outcomes:
After completing this worksheet you should be able to
1 Discuss the general principles used by time-stepping circuit
simulation software packages
2 Discuss the principles used by PSCAD/EMTDC to model circuit
elements.
3 Distinguish between electrical signal, mechanical signal and control
signal wires.
4 Be able to model basic circuits in PSCAD and choose time and print
steps.
1.1 Time stepping simulation
We perform time-stepping simulations to examine signals that are a function
of time. Examples include how the speed of a motor changes with time, or
how the voltage at a point in a circuit changes with time. In real life such
signals are analogue and continuous. In a computer simulation we need to
model such signals. There are different ways of doing this, but one common
way is to approximate our continuous analogue signal with one which is
evaluated only at discrete time steps, fig 1.1. This has the advantage that the
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computer has to only evaluate the signal at these time steps, and allows us to
make use of a number of numerical routines for evaluating the mathematical
functions which are used. The computer results are an approximation to the
actual behaviour, but if the time steps are sufficiently small, the approximation
is usually sufficiently good.
Fig. 1.1 Discrete approximation to continuous time signal
We have a whole set of formulas for numerical analysis for this type of
problem, known as Newton-Cotes rules. Two of the most basic are the
rectangle rule (shown in fig. 1.1 main picture and top right) and the trapezoid
rule (shown in fig. 1.1 bottom right).
The rectangle rule essentially assumes that over a small interval, from t4 to t5
in figure 1.1 say, the value of the signal can be approximated by the analogue
signal value at the mid-point of the interval. The trapezoid rule assumes that a
good approximation is given by a straight line function from the value at the
start of the interval, to the value at the end of the interval. More complex
numerical methods exist such as Simpson’s rule, Simpson’s 3/8 rule and
Boole’s rule. However the trapezoid rule works well for periodic signals with a
number of reasonably space time intervals within the period.
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1.2 PSCAD and EMTDC
All computer programmes which try and model real-world objects as a
function of time have the same problem: how to represent these objects in a
simple format that the computer can process. The general principle used is to
model a real world system using differential equations and then manipulate
these equations into a format that can be solved using numerical methods.
Fig 1.2 – Simple RLC series circuit
Most complex circuit elements can be represented by differential equations. In
electrical systems the simple circuit in figure 1.2 would have the equation:
This relates current and voltage. The current equation is second order, since it
has both integral and differential terms. We could rewrite this in the form:
where y=v, x=i, KI=1/C, KP=R and KD=L.
Fig 1.3 – Electric motor and pulley system
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Mechanical systems have similar equations. Consider the torque T applied by
the electric motor in figure 1.3 to lift a mass against gravity g.
This is also a second order equation and can be written in the form:
where y=T-mgr, x=, KI=k, KP=B and KD=J.
We could go one step further and model the behaviour of the mechanical
system by an equivalent electrical system, figure 1.4.
Fig 1.4 – Electrical equivalent of mechanical system
Circuit simulation packages use this powerful method of representing
systems. The user draws the system in a Computer Aided Design (CAD)
package. The CAD package, in this case Power Systems CAD (PSCAD),
translates these drawings into differential equations. These equations are
then passed to a solver package such as EMTDC (Electromagnetic
Transients including DC) which represents and solves the differential
equations as a function of time.
These results are then passed back to the CAD package which usually has a
variety of tools for representing the results in an easy to use format.
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Fig 1.5 – Dommel equivalent circuit elements used in EMTDC
EMTDC does not solve the differential equations directly. Instead it uses the
Dommel method [1] to simplify the equations. Inductor type elements and
capacitor type elements are both replaced by current source and resistor
elements, figure 1.5. The current between nodes k and m in the present time-
step ikm(t) is a function of current in the previous time-step ikm(t-t), a resistor
value R and the voltages at nodes k and m in the previous time step e k(t-t)
and em(t-t). The equation used is:
Where R is the value shown in figure 1.5. A lumped resistive element is
modelled as a resistance only.
The more eagle-eyed among you will have noticed that in effect this method is
a way of using the trapezoidal rule to simplify the differential equations so that
they can be solved by a time-stepping algorithm. The trapezoidal rule
represents the differential equations as an approximation to their actual ‘true’
value. This approximation is only true for small changes. This means it is very
important to choose a sufficiently small step size to enable the approximation
used to remain valid.
1. H. W. Dommel, “Digital Computer Solution of Electromagnetic Transients in Single and
Multiphase Networks”, IEEE Transactions on Power Apparatus and Systems, vol. 88, no. 4,
April 1969, pp. 388-399.
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1.3 Signal ‘Wire’ Types
A typical transient simulation package will have a number of different
elements. Mechanical parts, electrical parts and control signals can all be
modelled. Typically, wires connect different model parts.
Fig 1.6 RC Circuit
Electrical parts, for example the capacitor and resistor in figure 1.6, will be
connected by wires. The top wire is at a potential or voltage v1. The wire
carries a current i out of the resistor and into the capacitor. Likewise the lower
wire is at some other voltage v2 but also carries a current. The electrical
‘wire’ will therefore be carrying two pieces of information: a current and
a voltage. A common requirement of electrical parts of circuits is that one
wire is defined as zero volts. In PSCAD this is achieved by attaching the
‘ground’ symbol to one wire. If two different wires have a ‘ground’ symbol
connected to them, these wires are assumed to both be at zero volts and
connected together.
Electrical wires that are connected together form an ‘electrical node.’
Electrical nodes have an additional important value in PSCAD, in that the
‘student version’ of PSCAD/EMTDC which doesn’t require a licence file, is
limited to 15 electrical nodes. The ‘Educational version’ on the University’s
PCs doesn’t have this electrical node limit but has exactly the same
capabilities otherwise.
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Fig. 1.7 Simple system containing electrical and control wires
Another important part of a simulation system is the control. In the real-world
this may be accomplished by analogue circuits or software in a
microprocessor. In a simulation programme, this is typically accomplished by
control function blocks. In figure 1.7 a simple circuit is shown. The
instantaneous current in the wire is measured, some signal processing is
undertaken to find the rms current, and this current is compared with a
reference value (i*). If the measured rms current is greater than the reference
current, the switch is opened. The output of the comparator sends a digital
signal which controls the switch. A latch holds the switch off, until the set
signal reactivates the switch. There are a few keys points here:
1. Control wires (called ‘data’ wires in PSCAD) have only one value
2. Control values can be analogue (e.g. 1.05) or digital (1 or 0, on or off).
3. Signal types must be kept separate. Control (data) wires cannot be
connected to other types of wires. Analogue data wires shouldn’t be
connected directly to digital data wires. In figure 1.7 conversion
blocks are used. A measurement block (transducer) is used to
interface the electrical wire to the control (data) wire. A comparator
block is used to interface the analogue data wires to the digital data
wire. A switch block (actuator) is used to interface the digital data
signal to the electrical wire.
4. Control (data) wires have a ‘from’ and a ‘to’. Data flows from the rms
block to the comparator input in figure 1.7 for example.
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Mechanical parts, are treated by different simulation programmes in different
ways. PSCAD/EMTDC treats mechanical blocks as control blocks. Speed is
one control signal, torque is another. So a motor would be connected to a
load by two wires: a torque wire sending a signal from the motor to the load
and a speed wire sending a signal from the load to the motor. Other
programmes (e.g. SABER) treat mechanical systems like electrical systems,
i.e. a motor would be connected to the load by one wire which has both speed
and torque properties.
1.4 Starting with PSCAD/EMTDC
When you first start PSCAD, a window similar to figure 1.8 will appear.
Fig. 1.8 PSCAD main window
Click on ‘Help’ on the ‘main menu’ at the top of the screen. Select the menu
item ‘Table of contents’. You now have access to the online programme help.
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Main Menu
In future ‘Help Table of contents’ will be used to mean “the sub-menu item
‘Table of contents’ within the ‘Help’ menu”. If it is not already selected, select
the ‘Contents ‘ tab on the left hand side. Select the PSCAD menu item by
clicking on the square box to the left of ‘PSCAD’ so that the plus in the box
becomes a minus. Your screen should now look like figure 1.9
Figure 1.9 PSCAD Help window
Tasks
1. Open the sub-menu ‘The PSCAD Environment’. Read through all the
items of the sub-menu. Work through the ‘Tutorial: my first simulation.’
Note if you click on any underlined blue text, you will get more information
on that subject. At this stage you may want to skip some of the detail - not
all of the sections are immediately helpful to the first time user. However
as you progress it is worth going back and looking over these sections
again for this detailed information.
2. Read through ‘PSCAD Features and Operations’ in the help menu.
Again, at this stage you may want to skip some of the detail but it is worth
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reading through the detail later. However please pay attention to the
‘Projects Viewing Errors and Warnings’ section. Work through the tutorial
‘Creating a new Project’ and save your project. Note: in the electrical
palette on the right hand side of the PSCAD window, electrical nodes
are the solid dots, data nodes are circles.
3. Load your saved voltage divider from the previous step. Run the project
and look at the results. Bring up the ‘project settings’ window (look in the
PSCAD contents ‘Basic Features and Operations Projects Editing
Project Settings’ if you need help). At the moment you are plotting the
results on to the output graph every 1000s. Change the plot step to
10000s. The output traces should now look different. Why? (Answer at
end of worksheet)
Change the plot step back to 3000s and change the time step to 3000s.
Again do you notice a difference? (Answer at end of worksheet)
4. Read through ‘PSCAD Online Plotting and Control.’ Again, at this stage
you may want to skip some of the detail but it is worth reading through the
detail later.
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Quiz:
Select the appropriate answer(s) from this self-test quiz.
1. PSCAD/EMTDC models electrical circuits using differential equations
simplified using the trapezoidal rule (TRUE/FALSE).
2. If the time-step used is large in PSCAD/EMTDC
a. The programme runs more quickly
b. Results will be inaccurate
c. The PC memory storage used will be decreased
3. Mechanical connection ‘wires’
a. Do not exist in PSCAD/EMTDC it is an electrical package only
b. Should not be connected to electrical ‘wires’
c. Carry inertia and speed information
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Answers:
Task 3
The ‘plot step’ sets how often results from the simulation are displayed on
the output graph. If the plot step is too large, the data output becomes
distorted. If the plot step is very small, you save a lot of data, use a lot of
hard-disk space on your computer, and slow the simulation down.
The ‘time step’ sets the size of time step the simulation takes. If it is too
large (i.e. 3000s in this case) you distort your results. If the time step is
too small, your simulation takes a long time to run, since the programme
has to solve the circuit values for every time step. As a rule of thumb
your time step should be at least 10 times smaller (and ideally 100
times smaller) than the period of the fastest event in your simulation
or the shortest time constant in your control. In our simulation the
fastest thing is the 60Hz ac source with a period of 16.7ms, our time step
should be an absolute maximum of 1.6ms (1600s).
Quiz
1. True
2. a and c ( b is wrong because ‘results may be inaccurate’)
3. a
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Part 2 – Three-Phase Rectifier
Overview:
In this part you will build a 3-phase rectifier in PSCAD/EMTDC and
perform a set of harmonic analyses on it. You will investigate the
impact of component sizing on harmonics.
2.1 Construction of Rectifier Circuit
Fig. 2.1 Basic Three-Phase Rectifier Circuit in PSCAD/EMTDC
Construct the circuit shown in figure 2.1. The 3-phase voltage source can be
found in the ‘Master Library’ under ‘Sources.’ Double click on the voltage
source to bring up the block’s properties and setup the configuration menu as
shown in figure 2.2. You can also right-click on the block and select
‘Properties’ instead of double-clicking.
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Fig. 2.2 Voltage source ‘configuration’ sub-menu
You should choose an ‘inductance only’ source impedance for the voltage
source. You can give this inductance a per-phase value if you select the
‘Positive Sequence RRL’ screen in the voltage source window, figure 2.3.
Give the inductance a 1mH value as shown below.
Fig. 2.3 Voltage source impedance sub- menu
The ‘configuration’ window for the voltage-source (figure 2.2) only sets up the
values of the base voltage magnitude and frequency. The actual values of V
and f are set in another window, figure 2.4. Select 400V and 50Hz as the
output values for your voltage source.
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Fig. 2.4 Voltage source ‘source values’ sub- menu
Fig. 2.5 Workspace electric palette
Connection lines can be found on the right hand side of the workspace in the
electric palette (figure 2.5). The voltage meters, current meters, resistors and
capacitors can be found in ‘Master Library Passive Elements’ or on the
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passive components
wire (connection) tool
data connection
ground (0V)
electrical node
output channel connector
meters
graph frame
electric palette. Setup these components so that they have the values shown
in figure 2.1.
Add the electrical nodes shown in figure 2.1. The pairs of electrical nodes A, B
and C electrically connect the rectifier input to the 3-phase voltage source
lines.
The diodes can either be found in the main ‘Master Library’ page, in the
‘HVDC & FACTS’ sub-menu. Double click the diode to select its configuration
menu and make sure that the diode snubber is turned off, as in figure 2.6.
Figure 2.6 Diode Configuration menu
The power meter can be found in ‘Master Library Meters.’ The three-phase
view can be found on the lower-left hand side of the page. More information
on the use of this and all other components can be found by clicking the help
button on the lower right hand side of the component configuration menu.
All meter outputs are data signals. Add ‘data labels’ (or data connections i.e.
round blue circles) as shown in figure 2.1. Data labels can be found on the
electric palette (figure 2.5). To change phase voltage (Va and Vb) to line
voltage (Vab) you will need a subtraction block which you can find in the
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Master Library sub-menu CSMF. To display data signals, ‘output channel’
symbols (the arrow into a graph symbol) have to be added to a data wire or
connector. This stores the data signal to a file for later display.
The default output unit for voltage is kV, for current kA and for power MVA. If
you double click on an output channel symbol you can change these values.
Select voltage output channel Va and scale the output by 1000, so that the
output is V instead of kV. Add a title and a unit for output display. Then set the
voltage limits to 600V to -600V, figure 2.7.
Figure 2.7 Output channel selector configuration menu
Change the other voltage output channel symbols in the same way (note: you
may find it easier to copy each output channel and just change the title).
Change the current channel scales to A (with limits of +/-60A) and the power
scales to kW and kVAr respectively (with limits of 0/+100KVA).
2.2 Output Graph and Simulation Set-up
Add an output graph frame (see figure 2.5). Right click on the graph-frame
title-bar and select ‘add analogue graph’, in the menu that pops up, three
times. You may need to resize the graph to see all three graphs.
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To add an output signal to a graph, right-click on the ‘output channel’ symbol
and select ‘Graphs/Meters/Controls > Add as Curve’. Right-click on the graph
you want to add a signal to, and select ‘Paste Curve.’ Add Edc to the top
graph, Idc and Ia to the middle graph and Va, Vb and Vab to the bottom
graph.
Before you can run your simulation you need to set the runtime length and the
plot-step and time-step settings. Right-click on your project name in the left-
hand project window (‘Main branch page’) and select ‘Project Settings’. Set
the runtime duration to 1 second, the time-step to 50s and the plot-step to
100s. Give your project a name and save it to file. You can now run your
project (select the green arrow on the main toolbar, or ‘Build Run’ on the
main menu).
If you have any errors in your project, you will get an error report in the
‘Output Window’ at the bottom of the workspace, figure 2.8 for example.
Figure 2.8 Error Report
If you double-click on the error (“Signal ‘Van’ at connection ‘A’ does not have
a source” in this case), PSCAD will bring up an arrow in the workspace
window to help show you where the problem is, figure 2.9.
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To help you, PSCAD help has a list of common error messages. Select Help
on the main menu bar in PSCAD and the ‘Index’ tab on the left hand side.
Search for ‘error messages’, double-click on this in the help window and
select ‘Common Output Window Messages.’
Figure 2.9 Error Help Arrow
Note: a weakness of PSCAD in Windows is that occasionally other
programmes can interfere with it and it will not simulate. In this case
make sure you’ve saved you programme and restart your PC.
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Figure 2.10 Initial Results
Once you have fully debugged you simulation, compare your results with
figure 2.10. If you right-click on a graph and select ‘Zoom Reset all Extents’
you can change the way the results are displayed. As you can see there are
other ‘Zoom’ options too, and ‘short-cut’ keys are shown for each case next to
the items in the sub-menu. At this point you may want to reread some of the
sections in the online help ‘PSCAD Online Plotting and Control’ section,
especially the section on ‘Dynamic Aperture Adjustment’.
2.3 Plotting Powers
Add the control systems function blocks (CSMF library) in figure 2.11 to
convert P and Q to apparent power.
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Figure 2.11 Calculating apparent power and results
Add a further graph with P, Q and S. Rescale the outputs so that the units of
all powers are kW, KVAr and KVA respectively (instead of MVA). You should
see a result similar to Figure 2.11.
2.4 Harmonic Analysis
In this section you will add circuits to analyse the harmonic output current of
the circuit. Set up circuit shown in figure 2.12. The FFT block can be found in
the ‘meters’ sub-library, though since it is configured for a general 3-phase
operation, it may look slightly different. Setup the FFT block configuration
menu as shown in figure 2.13.
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Figure 2.12 Harmonic analysis circuit
Figure 2.13 FFT configuration menu
The output signal Vm from the FFT block is a data bus signal, effectively a
matrix of different data signals. In this case there are seven signals, one for
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each harmonic. To extract them, use the extraction links provided by PSCAD.
You can find them next to the FFT block in the ‘Meters’ library (data taps can
also be found on the ‘electric palette’ in the main workspace). To extract the
nth harmonic you need to change the properties of a data tap so that ‘array
index number’ equals n, i.e. to get the 3rd harmonic, the index number must be
3.
Run the simulation and resize the window to ‘all extents’. You should see a
result like figure 2.14.
Figure 2.14 FFT configuration menu
Note that the outputs take about 0.25s to reach steady state. If you look at the
properties of the voltage source block you will notice that the ‘input time
constant’ is set to 0.05s. This setting controls how fast the AC input voltages
ramp up from zero at the start. The voltage source will reach steady state
after about 5 time-constants. PSCAD ramps voltage sources up from 0V at
the start to allow a controlled start-up of the system and to avoid large
oscillations by applying large voltages to initially discharged components.
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2.5 Investigation of the Effect of Line Impedance
First reconfigure the source impedance so that the series impedance between
the 3-phase source and the rectifier has a fault level of 10pu on a 1MVA base
and an X/R ratio of 2 (try this yourself and then see the end of this section
for the working).
Run the programme and take a copy of Va, Vb, Vab, Edc, Idc and Ia. It should
look similar to Figure 2.15
Figure 2.15 Output voltages
Enter the values of per-phase voltage harmonics in the table in the hand-in
sheet (Task A). Hint: first you will need to wait until the simulation finishes.
Hold the cursor over the graph of harmonics, at some point on the time axis
where the simulation has reached steady-state and read off the values of
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voltage harmonics. Enter these into the first column of the ‘table of harmonics’
at the end of this worksheet along with the real and reactive power
transferred.
Now enter the values of per-phase current harmonics (Hint: you can either
produce another setup like figure 2.12 for current Ia or replace the data label
Va in figure 2.12 with the label Ia and rerun the simulation). Also enter the
peak and minimum dc link voltage values.
What happens if you halve the short-circuit level (i.e increasing the source
impedance, in this case doubling the series resistance and inductance)?
Record your values for P, Q and voltage and current harmonics in the table
with twice the series line impedance. You may have to make a ‘best guess’ if
these oscillate a bit.
Now return your source impedance values back to what they were for
Z=0.1pu. Increase the dc link capacitance value to 3300F and repeat your
harmonic, power and dc voltage measurements, entering values into the
table.
Add a dc inductor of value 1mH to your rectifier with Cdc=3300uF, Figure 2.16
and repeat your harmonic, power and dc voltage measurements, entering
values into the table.
Fig. 2.16 DC Inductor
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Impedance Calculation
The ‘fault level of 10pu’ means that that if a fault to ground were applied at the
rectifier side of the line impedance, 10pu fault current would flow from the AC
source i.e. the line impedance is given by:
The power base given is 1MVA, and the voltage base is 400V line-to-line or
230V phase (the ac circuit voltage). The line impedance is:
This is both the impedance of the three-phase single-line equivalent circuit,
and the series impedance per phase.
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Part 3 – Design Study
You are asked to design a three-phase rectifier for an industrial system fed
from 400V line-line rms. at 50Hz. The 60kW load can be represented by a DC
resistance at 500V nominal. Your diode conduction losses can be modelled
by a 1V on-state voltage-drop in series with a 10m resistance. Your AC line
has an X/R ratio of 3 and a 0.06pu impedance on a 60kW base.
The specification requires that the peak-to-peak ripple in the DC output is no
more than 10V, and that the input voltage distortion of no individual line-to-line
voltage harmonic may be greater than 6.5% of the 400V rms (nominal) input
voltage at the point of connection of the inverter to the network.
Design your remaining components for minimum cost and best AC voltage
utilisation (i.e. maximum DC output voltage). Justify your answer (see hand-in
sheet).
Notes:
1. As with all design problems there will be trade-offs. Improving one thing
will make something else worse. There is often no single ‘best answer’.
You must justify your final choice.
2. Given point 1 above, it is likely that people will end up with different
design choices.
3. If you are using extra AC inductance, the ‘point of connection’ to the
grid will be on the AC source side of the inductors NOT on the inverter-
side of the inductors.
4. You may use any value of component, even zero. Some values may be
more sensible than others (e.g. manufacturer ‘preferred values’, see
component catalogues).
5. If you run out of electrical nodes on the student version ,you can use
the educational version on the A-floor SSB cluster.
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