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Modelling Photovoltaic
Systems using PSpice@
Luis Castafier and Santiago Silvestre
Universidad Politecnica de Cataluiia, Barcelona, Spain
JOHN WILEY & SONS, LTD
Copynght 2002 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,
West Sussex PO19 SSQ, England
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PSpice@ is a registered trademark of Cadence Design System, Inc.
Other Wiley Editorial OfBces
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Library of Congress Cataloging-in-Publication Data
CastaAer, Luis.
Modelling photovoltaic systems using PSpice / Luis Castaiier, Santiago Silvestre.
Includes bibliographical references and index.
ISBN 0-470-84527-9 (alk. paper) - ISBN 0-470-84528-7 (pbk. : alk. paper)
systems-Computer simulation. 3. PSpice. I. Silvestre, Santiago. 11. Title.
p. cm.
1. Photovoltaic power systems-Mathematical models. 2. Photovoltatic power
TK1087 .C37 2002
62 1.3 1 '2446~2 1
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-470-845279 (HB) 0-470-84528-7 (PB)
200202741
Preface
Photovoltaic engineering is a multidisciplinary speciality deeply rooted in
physics for solar cell theory and technology, and heavily relying on electrical and electpolrlli;c
engineering for system design and analysis.
The conception, design and analysis of photovoltaic systems are important tasks oh
requiring the help of computers to perform fast and accurate computations or simuhfim.
Today’s engineers and professionals working in the field and also students of dSa&
technical disciplines know how to use computers and are familiar with r~nning .rpeckaliz&
software. Computer-aided technical work is of great help in photovoltaics became a#
the system components are described by nonlinear equations, and the node circuit quaions
that have to be solved to find the values of the currents and voltages, most often do II& have
analytical solutions. Moreover, the characteristics of solar cells and PV generators sarongly
depend on the intensity of the solar radiation and on the ambient temperature. As k are
variable magnitudes with time, the system design stage will be more accurate if a4.1
estimation of the performance of the system in a long-term scenario with realistic tikm
series of radiation and temperature is carried out.
The main goal of this book is to help understand PV systems operation gathering
concepts, design criteria and conclusions, which are either defined or illustrated us&
computer software, namely PSpice.
The material contained in the book has been taught for more than 10 years as an
undergraduate semester course in the UPC (Universidad Politecnica de catahria) in
Barcelona, Spain and the contents refined by numerous interactions with the studats.
PSpice was introduced as a tool in the course back in 1992 to model a basic solar celI and
since then more elaborated models, not only for solar cells but also for PV gemerators,
battery, converters, inverters, have been developed with the help of MSc and PhD -dents.
The impression we have as instructors is that the students rapidly jump into the tool and am
ready to use and apply the models and procedures described in the book by themselvesInteraction with the students is helped by the universal availability of Pspice or mze
advanced versions, which allow the assignments to be tailored to the development: of
the course and at the same time providing continuous feedback from the students on the
xvi PREFACE
difficulties they find. We think that a key characteristic of the teaching experience is that
quantitative results are readily available and data values of PV modules and batteries from
web pages may be fed into problems and exercises thereby translating a sensation of
proximity to the real world.
PSpice is the most popular standard for analog and mixed-signal simulation. Engineers
rely on PSpice for accurate and robust analysis of their designs. Universities and semiconductor manufacturers work with PSpice and also provide PSpice models for new devices.
PSpice is a powerful and robust simulation tool and also works with Orcad CaptureB,
Concept@ HDL, or PSpice schematics in an integrated environment where engineers create
designs, set up and run simulations, and analyse their simulation results. More details and
information about PSpice can be found at http://www.pspice.com/.
At the same web site a free PSpice, PSpice 9.1 student version, can be downloaded. A
request for a free Orcad Lite Edition CD is also available for PSpice evaluation from http://
www.pspice.com/download/default.asp.
PSpice manuals and other technical documents can also be obtained at the above web site
in PDF format. Although a small introduction about the use of PSpice is included in Chapter
1 of this book, we strongly encourage readers to consult these manuals for more detailed
information. An excellent list of books dedicated to PSpice users can also be found at http://
www.pspice.com/publications/books.asp.
All the models presented in this book, developed for PSpice simulation of solar cells and
PV systems behaviour, have been specially made to run with version 9 of PSpice. PSpice
offers a very good schematics environment, Orcad Capture for circuit designs that allow
PSpice simulation, despite this fact, all PSpice models in this book are presented as text files,
which can be used as input files. We think that this selection offers a more comprehensive
approach to the models, helps to understand how these models are implemented and allows a
quick adaptation of these models to different PV system architectures and design environments by making the necessary file modifications. A second reason for the selection of text
files is that they are transportable to other existing PSpice versions with little effort.
All models presented here for solar cells and the rest of the components of a PV system
can be found at www.esf.upc.es/esf/, where users can download all the files for simulation of
the examples and results presented in this book. A set of files corresponding to stimulus,
libraries etc. necessary to reproduce some of the simulations shown in this book can also be
found and downloaded at the above web site. The login, esf and password, esf, are required
to access this web site.
Contents
Foreword
Preface
Acknowledgements
1 Introduction to Photovoltaic Systems and PSpice
Summary
1.1 The photovoltaic system
1.2 Important definitions: irradiance and solar radiation
1.3 Learning some of PSpice basics
1.4 Using PSpice subcircuits to simplify portability
1.5 PSpice piecewise linear (PWL) sources and controlled voltage sources
1.6 Standard AM1.5G spectrum of the sun
1.7 Standard AM0 spectrum and comparison to black body radiation
1.8 Energy input to the PV system: solar radiation availability
1.9 Problems
1.10 References
xiii
2 Spectral Response and Short-Circuit Current
Summary
2.1 Introduction
2.1.1 Absorption coefficient a(X)
2.1.2 Reflectance R(X)
2.2.1 Short-circuit spectral current density
2.2.2 Spectral photon flux
2.2.3 Total short-circuit spectral current density and units
2.3 PSpice model for the short-circuit spectral current density
2.3.1 Absorption coefficient subcircuit
2.3.2 Short-circuit current subcircuit model
2.2 Analytical solar cell model
2.4 Short-circuit current
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xvii
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viii CONTENTS
3
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
Quantum efficiency (QE)
Spectral response (SR)
Dark current density
Effects of solar cell material
Superposition
DC sweep plots and I(V) solar cell characteristics
Failing to fit to the ideal circuit model: series and shunt resistances
and recombination terms
Problems
References
Electrical Characteristics of the Solar Cell
Summary
3.1 Ideal equivalent circuit
3.2 PSpice model of the ideal solar cell
3.3 Open circuit voltage
3.4 Maximum power point
3.5 Fill factor (FF) and power conversion efficiency (7)
3.6 Generalized model of a solar cell
3.7 Generalized PSpice model of a solar cell
3.8 Effects of the series resistance on the short-circuit current and the
open-circuit voltage
3.9 Effect of the series resistance on the fill factor
3.10 Effects of the shunt resistance
3.1 1 Effects of the recombination diode
3.12 Temperature effects
3.13 Effects of space radiation
3.14 Behavioural solar cell model
3.15 Use of the behavioural model and PWL sources to simulate the response
to a time series of irradiance and temperature
3.15.1 Time units
3.15.2 Variable units
3.16 Problems
3.17 References
4 Solar Cell Arrays, PV Modules and PV Generators
Summary
4.1 Introduction
4.2 Series connection of solar cells
4.2.1 Association of identical solar cells
4.2.2 Association of identical solar cells with different irradiance levels:
hot spot problem
4.2.3 Bypass diode in series strings of solar cells
4.3 Shunt connection of solar cells
4.3.1 Shadow effects
4.4 The terrestrial PV module
4.5 Conversion of the PV module standard characteristics to arbitrary irradiance
and temperature values
4.5.1
4.6 Behavioural PSpice model for a PV module
Transformation based in normalized variables (ISPRA method)
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CONTENTS ix
4.7 Hot spot problem in a PV module and safe operation area (SOA)
4.8 Photovoltaic arrays
4.9 Scaling up photovoltaic generators and PV plants
4.10 Problems
4.1 1 References
5 Interfacing PV Modules to loads and Battery Modelling
Summary
5.1
5.2 Photovoltaic pump systems
DC loads directly connected to PV modules
5.2.1 DC series motor PSpice circuit
5.2.2 Centrifugal pump PSpice model
5.2.3 Parameter extraction
5.2.4 PSpice simulation of a PV array-series DC motor-centrifugal
pump system
5.3 PV modules connected to a battery and load
5.3.1 Lead-acid battery characteristics
5.3.2 Lead-Acid battery PSpice model
5.3.3 Adjusting the PSpice model to commercial batteries
5.3.4 Battery model behaviour under realistic PV system conditions
5.3.5 Simplified PSpice battery model
5.4 Problems
5.5 References
6 Power Conditioning and Inverter Modelling
Summary
6.1 Introduction
6.2 Blocking diodes
6.3 Charge regulation
6.3.1 Parallel regulation
6.3.2 Series regulation
6.4 Maximum power point trackers (MPPTs)
6.4.1 MPPT based on a DC-DC buck converter
6.4.2 MPPT based on a DC-DC boost converter
6.4.3 Behavioural MPPT PSpice model
6.5.1 Inverter topological PSpice model
6.5.2 Behavioural PSpice inverter model for direct PV
generator-inverter connection
6.5.3 Behavioural PSpice inverter model for battery-inverter connection
6.6 Problems
6.7 References
6.5 Inverters
7 Standalone PV Systems
Summary
7.1 Standalone photovoltaic systems
7.2 The concept of the equivalent peak solar hours (PSH)
7.3 Energy balance in a PV system: simplified PV array sizing procedure
7.4 Daily energy balance in a PV system
7.4.1 Instantaneous power mismatch
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x CONTENTS
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.4.2 Night-time load
7.4.3 Day-time load
Seasonal energy balance in a PV system
Simplified sizing procedure for the battery in a Standalone PV system
Stochastic radiation time series
Loss of load probability (LLP)
Comparison of PSpice simulation and monitoring results
Long-term PSpice simulation of standalone PV systems: a case study
Long-term PSpice simulation of a water pumping PV system
Problems
References
8 Grid-connected PV Systems
summary
8.1 Introduction
8.2 General system description
8.3 Technical considerations
8.3.1 Islanding protection
8.3.2 Voltage disturbances
8.3.3 Frequency disturbances
8.3.4 Disconnection
8.3.5 Reconnection after grid failure
8.3.6 DC injection into the grid
8.3.7 Grounding
8.3.8 EM1
8.3.9 Power factor
8.4 PSpice modelling of inverters for grid-connected PV systems
8.5 AC modules PSpice model
8.6 Sizing and energy balance of grid-connected PV systems
8.7 Problems
8.8 References
9 Small Photovoltaics
Summary
9.1 Introduction
9.2 Small photovoltaic system constraints
9.3 Radiometric and photometric quantities
9.4 Luminous flux and illuminance
9.4.1 Distance square law
9.4.2 Relationship between luminance flux and illuminance
Solar cell short circuit current density produced by an artificial light
9.5.1 Effect of the illuminance
9.5.2 Effect of the quantum efficiency
9.6 I(V) Characteristics under artificial light
9.7 Illuminance equivalent of AM1.5G spectrum
9.8 Random Monte Carlo analysis
9.9 Case study: solar pocket calculator
9.5
9.10 Lighting using LEDs
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9.1 1 Case study: Light alarm
9.1 1 .I
9.11.2
Case study: a street lighting system
PSpice generated random time series of radiation
Long-term simulation of a flash light system
9.12
9.13 Problems
9.14 References
Annex 1 PSpice Files Used in Chapter 1
Annex 2 PSpice Files Used in Chapter 2
Annex 3 PSpice Files Used in Chapter 3
Annex 4 PSpice Files Used in Chapter 4
Annex 5 PSpice Files Used in Chapter 5
Annex 6 PSpice Files Used in Chapter 6
Annex 7 PSpice Files Used in Chapter 7
Annex 8 PSpice Files Used in Chapter 8
Annex 9 PSpice Files Used in Chapter 9
Annex 10 Summary of Solar Cell Basic Theory
Annex 11 Estimation of the Radiation in an
Arbitrarily Oriented Surface
Index
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2.70
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353
Introduction to Photovoltaic
Systems and PSpice
Summary
This chapter reviews some of the basic magnitudes of solar radiation and some of the basics of PSpice.
A brief description of a photovoltaic system is followed by definitions of spectral irradiance, irradiance
and solar radiation. Basic commands and syntax of the sentences most commonly used in this book
are shortly summarized and used to write PSpice files for the AM1 SG and AM0 sun spectra, which are
used to plot the values of the spectral irradiance as a function of the wavelength and compare them with
a black body radiation. Solar radiation availability at the earth’s surface is next addressed, and plots are
shown for the monthly and yearly radiation received in inclined surfaces. Important rules, useful for
system design, are described.
1.1 The Photovoltaic System
A photovoltaic (PV) system generates electricity by the direct conversion of the sun’s energy
into electricity. This simple principle involves sophisticated technology that is used to build
efficient devices, namely solar cells, which are the key components of a PV system
and require semiconductor processing techniques in order to be manufactured at low cost
and high efficiency. The understanding of how solar cells produce electricity from detailed
device equations is beyond the scope of this book, but the proper understanding of the
electrical output characteristics of solar cells is a basic foundation on which this book is
built.
A photovoltaic system is a modular system because it is built out of several pieces or
elements, which have to be scaled up to build larger systems or scaled down to build smaller
systems. Photovoltaic systems are found in the Megawatt range and in the milliwatt range
producing electricity for very different uses and applications: from a wristwatch to a
communication satellite or a PV terrestrial plant, grid connected. The operational principles
though remain the same, and only the conversion problems have specific constraints. Much
is gained if the reader takes early notice of this fact.
2 lNTRODUCTlON TO PHOTOVOfTAlC SYSTEMS AND PSPlCE
The elements and components of a PV system are the photovoltaic devices themselves, or
solar cells, packaged and connected in a suitable form and the electronic equipment required
to interface the system to the other system components, namely:
0 a storage element in standalone systems;
0 the grid in grid-connected systems;
0 AC or DC loads, by suitable DCDC or DC/AC converters.
Specific constraints must be taken into account for the design and sizing of these systems
and specific models have to be developed to simulate the electrical behaviour.
1.2 Important Definitions: lrradiance and Solar Radiation
The radiation of the sun reaching the earth, distributed over a range of wavelengths from
300 nm to 4 micron approximately, is partly reflected by the atmosphere and partly
transmitted to the earth’s surface. Photovoltaic applications used for space, such as satellites
or spacecrafts, have a sun radiation availability different from that of PV applications at the
earth’s surface. The radiation outside the atmosphere is distributed along the different
wavelengths in a similar fashion to the radiation of a ‘black body’ following Planck’s
law, whereas at the surface of the earth the atmosphere selectively absorbs the radiation at
certain wavelengths. It is common practice to distinguish two different sun ‘spectral
distributions’ :
(a) AM0 spectrum outside of the atmosphere.
(b) AM 1.5 G spectrum at sea level at certain standard conditions defined below.
Several important magnitudes can be defined: spectral irradiance, irradiance and radiation
as follows:
(a) Spectral irradiance ZA - the power received by a unit surface area in a wavelength
differential dX, the units are W/m2pm.
(b) Irradiance - the integral of the spectral irradiance extended to all wavelengths of
interest. The units are W/m2.
(c) Radiation - the time integral of the irradiance extended over a given period of time,
therefore radiation units are units of energy. It is common to find radiation data in J/m2-
day, if a day integration period of time is used, or most often the energy is given in kWh/
m2-day, kWh/m2-month or kWh/m2-year depending on the time slot used for the
integration of the irradiance.
Figure 1.1 shows the relationship between these three important magnitudes.
Example 1.1
Imagine that we receive a light in a surface of 0.25 m2 having an spectral irradiance which
can be simplified to the rectangular shape shown in Figure 1.2, having a constant value of
IMPORTANT DEFINITIONS: IRRADIANCE AND SOLAR RADIATION 3
r
Spectral Irradiance Radiation
inadiance )- Wlm’ + kWh/m2-day
Wim’pni
i
Spectral irradiance
Wavelength
Figure 1.2 Spectrum for Example 1.1
1000 W/m2pm from 0.6 pm to 0.65 pm and zero in all other wavelengths. Calculate the
value of the irradiance received at the surface and of the radiation received by the same
surface after 1 day.
Solution
The irradiance is calculated by integration of the spectral irradiance over the wavelength
range (0.6 to 0.65 Fm)
W W lOOOdX = 0.05 x 1000- = 50- m2 m2 Irradiance =
As the irradiance is defined by unit of area, the result is independent of the amount of area
considered. The radiation received at the 0.25 m2 area, comes now after integration of the
irradiance over the period of time of the exercise, that is one day:
W
m* Irradiance . dt = 0.25 m2 24 h x 50- = 300 Wh-day
As can be seen from Example 1.1, the calculation of the time integral involved in the
calculation of the irradiance is very straightforward when the spectral irradiance is constant,
and also the calculation of the radiation received at the surface reduces to a simple product
when the irradiance is constant during the period of time considered.
4 INTRODUCTION TO PHOTOVOLTAIC SYSTEMS AND PSPICE
It is obvious that this is not the case in photovoltaics. This is because the spectral
irradiance is greater in the shorter wavelengths than in the longer, and of course,
the irradiance received at a given surface depends on the time of the day, day of the year,
the site location at the earth's surface (longitude and latitude) and on the weather conditions.
If the calculation is performed for an application outside the atmosphere, the irradiance
depends on the mission, the orientation of the area towards the sun and other geometric,
geographic and astronomical parameters.
It becomes clear that the calculation of accurate and reliable irradiance and irradiation
data has been the subject of much research and there are many detailed computation
methods. The photovoltaic system engineer requires access to this information in order to
know the availability of sun radiation to properly size the PV system. In order to make things
easier, standard spectra of the sun are available for space and terrestrial applications. They
are named AM0 and AM1.5 G respectively and consist of the spectral irradiance at a given
set of values of the wavelength as shown in Annex 1.
1.3 Learning Some PSpice Basics
The best way to learn about PSpice is to practise performing a PSpice simulation of a simple
circuit. We have selected a circuit containing a resistor, a capacitor and a diode in order to
show how to:
0 describe the components.
0 connect them.
0 write PSpice sentences.
0 perform a circuit analysis.
First, nodes have to be assigned from the schematics. If we want to simulate the electrical
response of the circuit shown in Figure 1.3 following an excitation by a pulse voltage source
we have to follow the steps:
I. Node assignation
According to Figure 1.3 we assign
-L
- node(0)
Figure 1.3 Circuit used in file 1earning.cir
LEARNING SOME PSPlCE BASICS 5
(0) GROUND
(1) INPUT
(2) OUTPUT
In Spice NODE (0) is always the reference node.
2. Circuit components syntax
Resistor syntox
rxx node-a node-b value
Capacitor syntax
cxx node-a node-b value
According to the syntax and the nodes assignation we must write:
rl 1 2 1 K; resistor between node (1) and node (2) value 1 KOhm
cl 2 0 1 n; capacitor between node (2) and node (0) value InF
Comments can be added to the netlist either by starting a new line with a * or by adding
comments after a semicolon (;).
Sources syntax
A voltage source is needed and the syntax for a pulsed voltage source js as follows.
Pulse volhge source
vxx node+ node- pulse ( initial-value pulse-value delay risetime falltime pulse-length
period)
where node+ and node- are the positive and negative legs of the source, and all other
parameters are self-explanatory. In the case of the circuit in Figure 1.3, it follows:
vin 1 0 pulse (0 5 0 lu lu 1Ou 20u)
meaning that a voltage source is connected between nodes (1) and (0) having an initial value
of 0 V, a pulse value of 5 V, a rise and fall time of 1 ps, a pulse length of 10 p and a period of
20 ps.
6 INTRODUCTION TO PHOTOVOLTAIC SYSTEMS AND PSPICE
3. Analysis
Several analysis types are available in PSpice and we begin with the transient analysis,
which is specified by a so-called ‘dot command’ because each line has to start with a dot.
Transient analysis syntax (dot command)
.tran tstep tstop tstart tmax
where:
first character in the line must be a dot
tstep: printing increment
tstop: final simulation time
tstart: (optional) start of printing time
tmax: (optional) maximum step size of the internal time step
In the circuit in Figure 1.3 this is written as:
.tran 0.1~ 40u
setting a printing increment of 0.1 ps and a final simulation time of 40 ps.
4. Output (more dot commands)
Once the circuit has been specified the utility named ‘probe’ is a post processor, which
makes available the data values resulting from the simulation for plotting and printing. This
is run by a dot command:
.probe
Usually the user wants to see the results in graphic form and then wants some of the node
voltages or device currents to be plotted. This can be perfomed directly at the probe window
using the built-in menus or specifying a dot command as follows:
.plot tran variable-1 variable-2
In the case of the example shown in Figure 1.3, we are interested in comparing the input
and output waveforms and then:
.plot tran v(1) v(2)
The file has to be terminated by a final dot command:
.end