Simulink Modelling of a VSI

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Matlab Simulink Modelling of a Single-Phase

Voltage Controlled Voltage Source Inverter

ABSTRACT

This paper presents a Matlab Simulink model of a single-phase 2kVA Voltage Controlled Voltage Source Inverter. Load voltage RMS feedback control and open-loop control are used to compare the standard Matlab

Simulink and power system blocksets used for theinverter model design. Simulation and experimentalresults using linear and non-linear loads are used tovalidate the accuracy of the model developed.

1. INTRODUCTION

Voltage controlled voltage source inverters (VCVSIs)are widely used in power supplies, power qualitycontrollers, renewable energy, marine and militaryapplications [1]. They are at the heart of applicationsrequiring an AC supply from a DC source. Therefore itis important that they are designed to be robust and

efficient, especially in remote areas and renewableenergy applications where inverter failure can causeinconvenience and the available energy is limited. Thedesign of inverters can be improved using software packages suitable for this application such as MatlabSimulink [2] and PSIM [3]. This can provide insight intothe inverter performance and allows for the analysis ofthe design before it is implemented in hardware and

software, which can lead to improved performance andreduced development and production costs.

In this paper, Matlab Simulink is used to model a 2kVA

single-phase full-bridge VCVSI [4-6]. This software

package is designed for modelling, simulating andanalysing dynamic systems. It supports linear and non-linear systems modelled in continuous time, sampledtime or a combination of both. Therefore it is well suitedto modelling and simulating inverters and controllers inthe analogue and digital domains. A system model

showing the physical components of the single-phaseVCVSI modeled using Matlab Simulink is shown inFigure 1. This inverter uses a low-voltage DC bus(24VDC), which is stepped up to 240VAC using a step-uptransformer (Tx). The transformer provides galvanicisolation and is a simple solution for the stepping up of alow-voltage DC bus. The DC bus in the model

comprises of the battery (Vbatt), lead wire and batteryresistance (Rbatt), and DC filter capacitor (Cdc). Thefull-bridge uses MOSFET switching devices with the

full-bridge output filtered using a low-pass LC filter (Lf

and Cf ). The inductor filter resistance is represented asR Lf with the LC filter-damping resistor being R Cf . The

load connected to the inverter (ZL) is consideredarbitrary (linear and/or non-linear). The PWM generator provides the switching signals for the full-bridge withthe load voltage RMS value used to regulate the load

voltage. The RMS controller is a simple and standard

controller used for inverters only requiring load voltage

RMS regulation. The prototype single-phase 2kVAinverter developed based on the system model in Figure

1 is shown in Figure 2 (a) with its housing shown in

Figure 2 (b). From Figure 2 (a) the DC input and filtercapacitors, MOSFETS, filter inductor and transformer

modeled in Figure 1 are shown. In Figure 2 (b), the userinterface, comprising of an LCD and buttons, statusLEDs, on/off switches and AC output can be clearlyseen.

This inverter in Figure 2 was designed for harshenvironments [7] and to be reliable, efficient and low-

cost. Modeling this inverter allowed for its design to beverified and advanced controllers simulated before theywere implemented. The power of Matlab Simulink provided a suitable development tool for this application.

M. C. Trigg C. V. Nayar

Department of Electrical Engineering Department of Electrical Engineering

Curtin University of TechnologyGPO Box U1987 Curtin University of TechnologyGPO Box U1987

Perth 6845, Australia Perth 6845, Australia

[email protected] [email protected]

Figure 1. Physical components of single-phaseVCVSI with load voltage RMS control

Low-frequencyTransformer

Power Stage

DC Input

DC FilterCapacitors

MOSFETS

Filter Inductor

AC Output

LEDStatus

UserInterface

AluminiumHousing

DC/ACon/off

(a) (b)

Figure 2. Prototype 2kVA single-phase VCVSI

(a) inverter (b) housing



2. MATLAB SIMULINK SYSTEM MODELLING

Matlab Simulink comprises of a range of blocksets suchas communications, control, power system and fuzzylogic etc. depending on application requirements. Forinverter development, the power system blockset provides the required components such as a full-bridge,

batteries, resistors, inductors, capacitors etc. and many

more. Shown in Figure 3 (a) is the power system full- bridge block which is at the heart of the inverter. Itcomprises of the DC input (+ and -), PWM inputs(pulses) for each of the four switches, and the full-bridgeoutput (A and B).

In Figure 3 (b) are the full-bridge block parameters,which allow for the selection of key parameters such asnumber of bridge arms, switch device selection, onresistance etc. This window is common to most blocks to

enable them to be customised for the requiredapplication. At the bottom of most block parameter’s

window is a pull-down menu, which allows key voltages

and currents to be easily measured for the selecteddevice. This data can be displayed and/or sent to theMatlab workspace for further analysis.

Shown in Figure 4 (a) is a scope block with its inputstaken from multimeter blocks. Multimeters allow formeasurement points in a system to be selected based on

a blocks measurements pull-down menu as shown inFigure 3 (b). They also allow for measurements of a

system to be made without having to directly connect

wires to the measurement point; therefore simplifyingthe layout. Also shown is a multiplexer, which allows formultiple signals to be displayed on the same scope axis.The limiter at the first scope input can be used to set themaximum and minimum y-axis limits if only a set

amplitude of a signal needs to be displayed.

In Figure 4 (b) are signal measurements taken with the

scope in Figure 4 (a). The two signals multiplexed ontothe single axis can be seen on the second axis of the

scope. The scope parameters are shown in Figure 4 (c),which allow for the number of axes, time range, formatetc. to be setup as well as an option to save the scope

data to the Matlab workspace, which can be later used incustom plots or analysis. The advantage of sending datato the workspace is that it allows for more flexibility

with plotting compared to the standard scope andenables more readable plots to be created. The

disadvantage is that it requires the setting up of a MatlabM-file, which requires programming using the C programming language.

The inverter system modeled with Matlab Simulink wasachieved using the power system and standard simulink blocksets. The system was analysed by sending therequired signal to scopes and the workspace, whichallowed for analysis and design of the inverter model.

3. MATLAB SIMULINK VCVSI

The Matlab Simulink model of the single-phase VCVSIin Figure 1 is shown in Figure 5. This model, developedusing the Simulink power system blockset, comprises ofcomponents such as power electronic devices (full- bridge and rectifier) and elements such as inductors,capacitors and resistors. The DC model used comprises

of the battery (V batt) and its respective resistance andlead wire resistance (R batt) as well as the filter capacitor(Cdc) and a DC bus current measurement resistor (Idcmeasure), which is of the order of micro-ohms as it isonly used for DC bus current measurement using amultimeter block. The output from the full-bridge block(A and B) comprises of the filter inductor and itsresistance (Lf , R Lf ) and filter capacitor with dampingresistor (Cf , R Cf ). Also included is the step-up

transformer (Tx) and a non-linear load used for analysis.The resistor ‘Rmeasure’ is of the order of micro-ohms

(a) (b)

Figure 3. Matlab Simulink full-bridge

(a) full-bridge block (b) block parameters

Scope

Multimeter

(source selection)

Limiter

Multiplexer

(a)

(b)

(c)

Figure 4. Matlab Simulink signal measurement(a) scope and inputs (b) scope signals (c) scope

parameters



and is only used for load current measurement the sameas ‘Idc measure’. Shown in Table 1 are the specificationsfor the Matlab Simulink inverter model.

The PWM signals for each of the power electronicdevices in the full-bridge come from the PWM generator block. This block allows for the switching frequency and

number of inverter legs to be selected with all PWMsignal multiplexed on a single bus into the full-bridge block (pulses). The input to this block (signal(s)) is thesinusoidal reference for the inverter. The reference for

this model is generated from a sinusoidal referencegenerator in Simulink with load voltage RMS feedback

and open-loop (no feedback) control.

3.1. LOAD VOLTAGE RMS CONTROLLER

The most common controller used in many inverters isload voltage RMS feedback control due to its low-cost

and ease of implementation. For many applications, such

as electronic loads, having a pure sinusoidal waveform isnot critical and therefore load voltage RMS feedbackcontrol provides a cost effective and reliable solution foran inverter design. It is also easily implemented on low-cost 8-bit micro-controllers.

The normalized Matlab Simulink model of the analogueequivalent load voltage RMS feedback controller for theinverter in Figure 2 is shown in Figure 6. It comprises ofa sinusoidal reference (VREF), which provides the maincommand signal (V12h) for the inverter PWM generator.The amplitude of this reference is adjusted based on a

modulation index (ma) and amplified error signal (eRMS),

generated by comparing the ideal load voltage RMSvalue with the actual. The error gain has been selected based on a trial-and-error approach to achieve similarresults to the prototype inverter controller, which uses a

digital RMS controller. The limiter at the output of thecontroller ensures that the command signal is limited (in

this case to ±0.99 = 99%) to prevent DC at the output ofthe inverter.

Shown in Figure 7 are waveform measurements (A to E)taken for the load voltage RMS controller in Figure 6

with a 2kW linear load. It shows the sinusoidal reference

(VREF), modulation index (ma), normalized load voltageRMS value (VLoad RMS), load voltage (VLoad) and theinverter command signal (V12h). It can be seen from the

load voltage RMS value (plot ‘C’) and modulation index(plot ‘B’) that as the RMS value decreases themodulation index increases to compensate.

The model in Figure 6 and waveforms measured inFigure 7 show the ease by which a standard invertercontroller can be developed with Matlab Simulink andsignal measurements taken. As the number of scopes in asystem increases, multimeter blocks (Figure 4 (a)) can beused to eliminate the connecting wires from the system

to the scope making the model easier to manage and

Table 1. Specifications of the 2kVA inverter

Parameter Label Value Unit

Rated Power − 2 kVA

Rated output frequency f Load 50 Hz

Rated output voltage VLoad 240 V

Battery voltage Vbatt 24 VBattery and lead wire resistance Rbatt 30 mΩ

DC filter capacitance Cdc 88000 μF

Inverter switching frequency f sw 10 kHz

Inverter output frequency 2x f sw 20 kHz

Filter inductor Lf 10 μH

Filter inductor resistance RLf 1 mΩ

Transformer turns ratio N 18 -

AC filter capacitor Cf 4 μF

LC filter damping resistance RCf 10 Ω

SinusoidalReference

Generator andController

Rcf

Cf

Non-Linear Load

40Ω1000μF

4mH

Vbatt

Figure 5. Matlab Simulink model of 2kVA Voltage Controlled Voltage Source Inverter with non-linear load

ModulationIndex Reference(ma-ref)

Error Gain

VLoad RMS

VREF

ModulationIndex (ma)

erms k-erms

A

B

C D

Scope

E

Figure 6. Matlab Simulink model of a VCVSI

analogue load voltage RMS feedback controller

A

B

C

D

E

(VREF)

Figure 7. Load voltage RMS feedback controllersignal measurements for 2kW linear load



follow. Figure 6 also showed the use of a multiplexer,which allows for multiple signal to be displayed on thesame axis as shown in Figure 7 for signals ‘B’ and ‘C’.

4. SIMULATION AND EXPERIMENTAL R ESULTS

Simulation results for the Matlab Simulink invertermodel developed in Figure 5 were compared with

experimental results for the 2kVA inverter in Figure 2. Two types of control methods were used to compare theSimulink model and prototype inverter: open-loop andload voltage RMS feedback control. Open-loop controlallowed for the inverter model accuracy to beinvestigated without any effects caused by closed loop

control. The load voltage RMS feedback control allowedfor the accuracy of the compete system (power systemand standard Simulink blocksets) to be investigated. Foreach of these two control methods, linear and non-linearloads were connected to the inverter to provide two casesto compare the model accuracy.

The non-linear load (considered a worst-case scenario) isshown connected to the inverter model in Figure 5 andcomprised of a full-bridge rectifier, choke (Lchoke), filtercapacitor (CL) and load resistor (R L). The choke, or

power factor correction (PFC) inductor was included asthis is commonly used in power supplies to reduce the

rate of change in load current (diload/dt), improvinginverter performance. The DC ripple of the load wasaround 14%. The linear load comprised of only the loadresistor (R L) without the full-bridge rectifier, choke orcapacitor. Signals measured were load voltage (VLoad), battery current (i batt), filter inductor voltage (VLf ) andcurrent (iLf ). The load current can be found from the

filter inductor current as iLoad=(iLf /N)-iCf . As iCf isgenerally much smaller than iLf , iLoad≈(iLf /N). For theexperimental results only the DC bus voltage (Vdc) and

battery current (i batt) could be measured, and not the DC bus current (idc) as it was not accessible.

4.1. LOAD VOLTAGE OPEN-LOOP CONTROL

Open-loop control was used to compare the simulationand experimental results for the 2kVA inverter withoutthe effect of the load voltage RMS feedback controller.

For the Matlab Simulink model and 2kVA inverter, themodulation index was set to obtain 240V at no-load. The

linear and non-linear loads were then connected to theinverter for comparison.

4.1.1. LINEAR LOAD – OPEN-LOOP CONTROL

Shown in Figure 8 (a) and (b) are experimental andsimulation results respectively of the VCVSI with open-

loop control and the 2kW linear load (R L=28.8Ω). For

both results it can be seen that the load voltage hasreduced from 240V to around 199V (83%), resulting in a

reduced load power of around 1375W (PLoad =VLoad

2/R L=199

2/28.8). This can also be confirmed by

equation (1) as given at the top left corner of Figure 8 (a)

and (b).

⎟ ⎠

⎞⎜⎝

⎛ ≅=

N

i.V.iVP Lf

LoadLoadLoadLoad (1)

From the experimental results in Figure 8 (a) it can beseen that there is some distortion in the load voltagewaveform at the zero crossing point. This is due to

hardware dead-time used to provide a small time delay between the turning off of one switch and turning on ofthe other switch in the same full-bridge leg.

This prevents the DC bus being shorted resulting incurrent shoot-through. This dead-time was not

implemented in the Matlab Simulink inverter model andtherefore is not present in the simulation waveforms. Itcan be seen in Figure 8 that all voltage and currentwaveforms have a similar shape and RMS values.

4.1.2. NON-LINEAR LOAD – OPEN-LOOP CONTROL

Shown in Figure 9 (a) and (b) are experimental and

simulation results respectively for the VCVSI with thenon-linear load. From Figure 9 it can be seen that theload voltages from the experimental and simulationresults have reduced from 240V to 200V (83%) and thatthe load voltage waveform is distorted. The distortion inthe filter inductor voltage (VLf ) can also be clearly seen

in both experimental and simulation results. From thesimulation results, the load voltage THD has increased

from 2.69% to 8.89% while the load current THD hasincreased significantly from 2.69% to 60.4% due to the

non-linear load. The results in Figure 8 and Figure 9show the accuracy of the Matlab Simulink invertermodel developed with the power system blockset for both linear and non-linear analysis. They also confirmthe accuracy of the inverter model developed.

VLoad = 199VRMS

(49.82Hz)

iLf = 127ARMS

ibatt = 65.5ARMS

VLf

Dead-timeDistortion

PLoad = 1404W

(a)

Load = 201VRMS

iLf = 125ARMSibatt = 69ARMS

iLoad = 6.95ARMS VLoad THD = 2.69% iLoad THD = 2.69%

PLoad = 1397W

(b)

Figure 8. Single-phase VCVSI withopen-loop control and 2kW linear load

(a) experimental (b) simulation



4.2. LOAD VOLTAGE RMS FEEDBACK CONTROL

As load voltage RMS feedback control is a standardcontrol method used for inverters, simulation andexperimental results were compared using this type of

controller with the linear and non-linear loads. Theseresults can then be compared with those obtained using

open-loop control to show the effect of the load voltageRMS feedback control on inverter performance. Whilethe Matlab Simulink RMS controller in Figure 6 is ananalogue version of the digital RMS controllerimplemented in the prototype 2kVA inverter in Figure 2,it is shown to be an accurate model for both linear and

non-linear loads.

4.2.1. LINEAR LOAD – RMS CONTROL

Shown in Figure 10 (a) and (b) are experimental andsimulation results respectively for the VCVSI with loadvoltage RMS feedback control and a 2kW linear load

(R L=28.8Ω). For both results it can be seen that the loadvoltage RMS value has reduced from 240V to around235V (98%) resulting in a reduced load power of around1917W (PLoad =VLoad

2/R L=2352/28.8).

Comparing the results in Figure 8 and Figure 10 with thelinear load for open-loop and RMS control respectively,

it can be seen that the shape of the waveforms are almostidentical. The main differences are in the magnitudes of

the waveforms (due to open-loop and RMS control) andthe slight load voltage distortion caused by the RMS

controller. This distortion can also be seen in Figure 7,

which is due to the slow response of RMS control.

4.2.2. NON-LINEAR LOAD – RMS CONTROL

Shown in Figure 11 (a) and (b) are experimental andsimulation results respectively for the VCVSI with RMS

feedback control and the non-linear load. For bothresults it can be seen that the load voltage RMS valuehas increased from 240V to around 245V (102%). Thisis due to the distortion in the load voltage waveformcausing the rectified DC value for the RMS feedbackcontrol to reduce and therefore for the modulation indexto increase. The set-point used to set the load voltage is

generally performed using a linear load and therefore theregulation for a non-linear load can be expected to beworse as is the case in Figure 11.

Comparing the results in Figure 9 with those in Figure 11 with the non-linear load, it can be seen that the shape of

all waveforms are almost identical with the only maindifference being their RMS values. These results showthat the RMS controller is only capable improving theregulation of the load voltage but is incapable ofimproving the shape of the waveform, especially when anon-linear load is present

Comparing the experimental and simulation results for

open-loop and load voltage RMS feedback control withthe linear and non-linear loads, it can be seen that theMatlab Simulink inverter model developed in Figure 5 is

an accurate model of the 2kVA prototype inverter

VLoad = 199VRMS

(49.98Hz)

iLf = 168ARMS

ibatt = 68.4ARMS

VLf

PLoad = 1.35kWQLoad = 1.19VarSLoad = 1.80kVA

PF = 0.75

(a)

VLoad = 204VRMS


iLoad = 8.30ARMS

VLoad THD = 8.89% iLoad THD = 60.4%

(b)

Figure 9. Single-phase VCVSI withopen-loop control and non-linear load


VLoad = 235VRMS

(50.15Hz)

iLf = 149ARMS

ibatt = 93.8ARMS

PLoad = 2.00kWQLoad = 0VAr

SLoad = 2kVA

VLf

PF = 1

(a)

Load = 234VRMS


iLoad = 8.05ARMS VLoad THD = 6.34% iLoad THD = 6.34%

PLoad = 1884W

(b)

Figure 10. Single-phase VCVSI withRMS feedback control and 2kW linear load




presented in Figure 2. The development of this model

enables the prototype 2kVA inverter to be analysed andoptimized as well as providing a solid platform for thedevelopment of more advanced controllers.

5. CONCLUSIONS

This paper presented a Matlab Simulink model of a

single-phase 2kVA Voltage Controlled Voltage SourceInverter with load voltage RMS feedback control. The

inverter model was developed with the Matlab powersystems blockset while the load voltage RMS feedbackcontroller was developed with the standard Simulink blockset.

Open-loop control was used to show the accuracy of themodel developed without the closed loop RMSfeedback. The RMS feedback was then used to show theaccuracy of the complete inverter system (inverter andcontroller). Linear and non-linear loads were used for theopen-loop and RMS controllers to compare the accuracy

of the model for two distinct load conditions.

The inverter and RMS controller models developed with

Matlab Simulink was shown to provide accurate resultsand provided valuable insight into inverter performance.

Matlab Simulink was shown to be a powerful tool for thedevelopment of a single-phase VCVSI and load voltageRMS feedback controller.

R EFERENCES

[1] N. Mohan, T. M. Undeland, and W. P. Robbins,

Power Electronics - Converters, Applications,and Design, 2nd ed: John Wiley & Sons, Inc.,

1995.[2] "Matlab 6, Release 12.1." Natick,

Massachusetts: The MathWorks

(www.mathworks.com), 2006.[3] "PSIM Version 7.0." Woburn, MA: Powersim

Inc. (www.powersimtech.com), 2006.[4] M. Trigg, "Digital Sinusoidal PWM Generation

using a Low-cost Micro-controller BasedSingle-Phase Inverter," presented at ETFA2005, Catania, Italy, 2005.

[5] M. C. Trigg, H. Dehbonei, and C. V. Nayar,"Digital Sinusoidal PWMs for a Micro-controller based Single-Phase Inverter. Part 1:

Principles of digital sinusoidal PWMgeneration," IJE Power electronics and

instrumentation hardware, 2005.

[6] M. C. Trigg, H. Dehbonei, and C. V. Nayar,"Digital Sinusoidal PWMs for a Micro-controller based Single-Phase Inverter. Part 2:Performance assessment - experimental," IJE Power electronics and instrumentation

hardware, 2005.[7] H. Dehbonei, M. Trigg, and C. Nayar, "A

Novel Sinewave Inverter for HarshEnvironment," presented at AUPEC 2005,Hobart, Tasmania, Australia, 2005.

Load = 246VRMS

(49.97Hz)

iLf = 210ARMS

ibatt = 125ARMS

PF = 0.75Q = 1.96kVArP = 2.25kWS = 3kVA

VLf

(a)

VLoad = 245VRMS


(b)

Figure 11. Single-phase VCVSI withRMS feedback control and non-linear load


Simulink Modelling of a VSI

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