Modelling Photovoltaic Systems Using PSpice - 45271 01

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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.

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.

(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

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

USING PSPICE SUBCIRCUITS TO SIMPLIFY PORTABILIlY 7

0s 1 ops 20ps 30ps 40ps Time 0 V(1) 0 V(2)

Figure 1.4 Input and output waveforms of simulation of circuit learningxir

The file considered as a start-up example runs a simulation of the circuit shown in

Figure 1.3, which is finally written as follows, using the direct application of the rules and syntax described above.

*learning. cir r1121K; resistorbetweennode (1) andnode (2) value1KOhm c1201n; capacitor betweennode (2) andnode (0) value1nF vin 1 Opulse (0 5 0 lu 1 u 1Ou 20u) ; voltage source between node (1) andnode (0) .tranO40u .probe .plottranv(l) v(2) .end

The result is shown in Figure 1.4 where both input and output signals have been plotted as a function of time. The transient analysis generates, as a result of the simulation graphs, where the variables are plotted against time.

1.4 Using PSpiee Subcircuits to Simplify Portability

The above example tells us about the importance of node assignation and, of course, care must be taken to avoid duplicities in complex circuits unless we want an electrical connection. In order to facilitate the portability of small circuits from one circuit to another, or to replicate the same portion of a circuit in several different parts of a larger circuit without having to renumber all the nodes every time the circuit is added to or changed, it is

8 INTRODUCTION TO PHOTOVOLTAIC SYSTEMS AND PSPICE possible to define ‘subcircuits’ in PSpice. These subcircuits encapsulate the components and electrical connections by considering the node numbers for internal use only.

Imagine we want to define a subcircuit composed of the RC circuit in Figure 1.3 in order to replicate it in a more complex circuit. Then we define a subcircuit as:

Subcircuit syntax

.subckt name external-node- 1 external-node-2 params: parameter-l = value- 1 parameter-2 = value-2 where a number of external nodes have to be specified and also a list of parameter values. The file containing the subcircuit does not require analysis sentences or sources, which will be added later on to the circuit using the subcircuit. This file can be assigned an extension .lib indicating that it is a subcircuit of a library for later use.

For the RC circuit we need two external nodes: input and output, and two parameters: the resistor value and the capacitor value to be able to change the values at the final circuit stage.

Warning: inside a subcircuit the node (0) is forbidden. We will name the nodes for external connection - (1 1) for the input, (12) for the output and (10) for the reference.

* rc. lib .subckt rc 12 1 loparams: r=l c=l rl 1 12 {r} cl12 10 {C} .ends rc

Now, every time an RC circuit is to be included in a larger circuit, such as the one depicted in Figure 1.5 where two RC circuits of different component values are used, the RC circuit described in the subcircuit is used twice by means of a sentence, where a new component with first letter ‘x’ - a description given by the subcircuit name - is introduced as folIows:

Syntax for a part of a circuit described by a subcircuit file x-name node-1 node-2 node-i subcircuit-name params: param-1 = value-1

Figure 1.5 Circuit using the same RC subcircuit twice

PSPICE PIECEWISE LINEAR (PWL) SOURCES AND CONTROLLED VOLTAGE SOURCES 9

Applying this syntax to the circuit in Figure 1.5 for the RC number 1 and number 2 it follows:

xrcl 2 1 0 rc params: r= 1 k c= 1 n xrc232Orcparams:r=lOkc=lOn indicating that the subcircuits named xrcl and xrc2, with the contents of the file rc.lib and the parameter values shown, are called and placed between the nodes 2, I and 0 for xrcl and between 3 2 0 for xrc2. Finally the netlist has to include the file describing the model for the subcircuit and this is done by another dot command:

.include rc.lib

So the total file will now be:

* learning-subckt.cir xrcl2 10 rc params: r = lk c= In xrc2 3 2 0 rc params: r = 10k c =10n .include rc.lib vin10pulse (050 lululOu2Ou); voltagesourcebetweennode (1) andnode (0)

.tranO.lu40u

.probe .plot tranv(1) v(2) v(3) .end

1.5 PSpice Piecewise linear (PWL) Sources and Controlled Voltage Sources

In photovoltaic applications the inputs to the system are generally the values of the irradiance and temperature, which cannot be described by a pulse kind of source as the one used above. However, an easy description of arbitrarily shaped sources is available in PSpice under the denomination of piecewise linear (PWL) source.

 Vxx node+ node- pwl time-1 value-1 time-2 value-2

Syntax for piecewise linear voltage source

This is very convenient for the description of many variables in photovoltaics and the first example is shown in the next section.

A PSpice device which is very useful for any application and for photovoltaics in particular is the E-device, which is a voltage-controlled voltage source having a syntax as follows.

Syntax for €-device e-name node+ node- control-node+ control-node- gain

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