Assignment

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/

Mike Barnes Page 1 09/04/2023

https://pscad.com/products/pscad/free_downloads/

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


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.


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


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.


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.


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.


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.


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.


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


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.


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


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


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.


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.


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


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


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.


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.


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.


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.


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.


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


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.


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


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


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.


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.


Assignment

Documents

continuous time signal

function of time

discrete time steps

trapezoid rule

computer simulation

mechanical signal

electrical signal

simpsons rule