Modelling photovoltaic systems using pspice pdf

 

    Share. Email; Facebook; Twitter; Linked In; Reddit; CiteULike. View Table of Contents for Modelling Photovoltaic Systems Using PSpice®. Modelling photovoltaic systems using PSpice / Luis Castan˜er, Santiago Silvestre . p. cm. Includes bibliographical references and index. ISBN Request PDF on ResearchGate | On Mar 8, , luis castañer and others published Modelling Photovoltaic Systems Using PSpice.

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    Modelling Photovoltaic Systems Using Pspice Pdf

    Request PDF on ResearchGate | On Mar 18, , smelarpeppame.mlñer and others published Modelling photovoltaic Systems using Pspice. Modelling Photovoltaic. Systems using PSpice. ®. Luis Castan˜er and Santiago Silvestre. Universidad Politecnica de Catalun˜a, Barcelona, Spain. To read the book, you will have Adobe Reader program. You can download the installer and instructions free from the Adobe Web site if you do not have Adobe.

    Photovoltaics is rapidly becoming a mature industry as the performance of photovoltaic system components and the leverage of large-scale industrial production steadily decrease costs. Measures taken by governments and other agencies to subsidize the costs of installations and regulations in several countries concerning the purchase of electricity produced by grid-connected systems are promoting public awareness and the widespread use of environmentally friendly solar electricity. The rapid growth of the industry over the past few years has expanded the interest and the need for education and training worldwide at all levels of photovoltaics, but especially at the system level where more people are involved. Photovoltaic system engineering and system design is often treated only superficially in existing books on photovoltaics. This book appears to be the first including computer modelling of photovoltaic systems with a detailed and quantitative analysis.

    This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Precise photovoltaic PV behavior models are normally described by nonlinear analytical equations. To solve such equations, it is necessary to use iterative procedures.

    Aiming to make the computation easier, this paper proposes an approximate single-diode PV model that enables high-speed predictions for the electrical characteristics of commercial PV modules. Based on the experimental data, statistical analysis is conducted to validate the approximate model. Simulation results show that the calculated current-voltage I-V characteristics fit the measured data with high accuracy. Introduction Photovoltaic PV power market has grown rapidly in the last decade owing to the deterioration of the environmental quality and the escalation of fossil fuel price.

    Before installing a PV system, a good performance estimation of the adopted PV generators is necessary since the initial cost of the system is pretty high [ 1 , 2 ]. For this reason, a reliable and flexible PV model that enables an accurate estimation of the PV generated electricity towards various operating conditions is of significance in the design phase.

    Among numerous modeling approaches in the literature, the most widely used circuit-based PV model is the single-diode model SDM , which consists of a series resistance R s , a shunt resistance R p , and a linear independent current source in parallel to a diode. The more accurate double-diode model DDM is available in [ 3 ].

    It takes into consideration the recombination loss at the space depletion region of solar cells. Calculate the values of the FF and compare with the results given by equation 3.

    After running PSpice the values of the maximum power point are calculated and given in Table 3. Solid line is calculated from values from equation 3. As can be seen for small values of the series resistance, the results agree quite well, and spread out as the series resistance increases.

    To isolate this effect from the others, the series resistance and the second diode can be eliminated from equation 3. The results are shown in Figure 3. It is clear that unless the parallel resistance takes very small values, the open circuit voltage is only very slightly modified. This is not unusual because from equation 3. Small values of the shunt resistance also heavily degrade the fill factor.

    This can be seen in Figure 3. The result indicates that when the recombination diode dominates, the characteristic is also heavily degraded, both in the open-circuit voltage and in the FF.

    The short-circuit current remains constant. Taking into account that in, terrestrial applications, solar cells can easily warm up to 60—65 C and that in space or satellite applications temperatures can be even higher, it follows that a proper modelling of the temperature coefficients of the main electrical parameters is mandatory. Temperature effects in a solar cell can be included in the PSpice model by using the builtin parameters of the diode model included in the equivalent circuit.

    Namely the saturation density current of a diode has a strong dependence on temperature and it is usually given by: This analysis assumes that the short-circuit current is independent of temperature. The netlist now has to be modified to include temperature analysis.

    This is highlighted in the netlist that follows: The results of the simulation are shown in Figure 3. Using the cursor on the probe plots, the values of the open-circuit voltage for the various temperatures can be easily obtained.

    They are shown in Table 3. This result is consistent with a theoretical deduction that can be made from the temperature derivative in equation 3. Replacing equation 3. Typically for silicon solar cells a value of 6.

    A modification to the subcircuit of the solar cell to account for this temperature coefficient of the short-circuit current can be made and it is shown in Example 3. A short circuit current of 4. As an example, Table 3. PSpice also allows the simulation of the I V characteristics of a solar cell after a given radiation fluence. The procedure to carry out this exercise consists of several steps: Step nr 1: Calculate the value of J0 in BOL conditions.

    This means the FF that the solar cell with zero series resistance would have. This is given by equation 3.

    Modelling Photovoltaic Systems Using PSpice Solutions Manual

    Calculate the series resistance in BOL conditions. Write the solar cell model taking into account the degradation characteristics given by the constants in Table 3. It is assumed that the series resistance does not change after irradiation. If the BOL data are the following: Consider that the solar cell can be modelled by a single diode and has a shunt resistance of infinite value. Before solving the problem with PSpice, we will illustrate here the steps previously described, in order to calculate some important magnitudes considering the values of the degradation constants in Table 3.

    Step nr 1 From equation 3. Moreover, the series resistance is internally calculated from equation 3. The correspondence between the names in the PSpice code and the names in the equations is the following: Parameter in PSpice code Parameter in equations 3.

    The maximum power delivered by the solar cell can now be computed as This value is approximately equal to the expected value of the maximum power after degradation as can be calculated using the degradation constants for the maximum power given in Table 3.

    This means that the built-in temperature analysis of PSpice is difficult to use because PSpice runs a new analysis for every value of the temperature.

    Usually what is available as a result is a file or a time series of irradiance and temperature values. Moreover, if solar cells are not made of one of the well-known semiconductors such as silicon, GaAs or Ge, the important physical data required to model the temperature effects of a solar cell are not easily available.

    Instead, most frequently the data available come from data sheets or published material by the manufacturers and concern values of electrical magnitudes from photovoltaic measurements, such as the short-circuit current, open-circuit voltage and maximum power under some standard conditions, and the temperature coefficients. If this is the case, the model of a solar cell including a diode is not very practical and is of limited use. For this reason we introduce a behavioural model, based on voltage and current sources, which is able to correctly model the behaviour of an arbitrary solar cell under arbitrary conditions of irradiance and temperature, with electrical data values as the only input.

    The model assumes that the solar cell can be modelled by two current sources and a series resistance. The model is composed of a subcircuit between nodes 10 14 12 13 as shown in Figure 3. The derivative in equation 3. Tr is the reference temperature which is usually considered 25 C in some cases K are considered.

    This g-device is written as: The value of the temperature involved in equation 3. The open-circuit voltage can also be written for the new temperature and irradiance values. In PV systems the information about the evolution of the coordinates of the maximum power point during a given period of time is important because the electronic equipment used to connect the photovoltaic devices to loads are designed to follow this maximum power point. The PSpice code can also provide this information in two accessible nodes of the cell subcircuit.

    All we need are the coordinates of the maximum power point at standard conditions Vmr and Imr. This is available from most of the data sheets provided by the manufacturers. In that case the current of the maximum power point at arbitrary conditions of irradiance and temperature can be considered to scale proportionally with the irradiance and linearly with the temperature with the temperature coefficient of the short-circuit current: These values have been taken from M.

    Green, K. Emery, D. King, S. Igari, W. These values have been estimated for a 1 cm2 cell from www. The result is shown in Figure 3. Although in the next chapters we will be extensively using time series of these variables it is convenient here to address two important points that help understanding of the PSpice simulation of PV systems, and not only solar cells: Apparently, such simulations require long CPU time, are unavailate or cumbersome.

    An easy way to overcome these problems is to consider two different units of time: This means that if we assign 1 microsecond of internal PSpice time to 1 hour of real time, a one-day simulation will be performed in a few seconds on any standard PC computer.

    This approach has been used in this book when necessary. In order to facilitate the understanding a warning has been placed in all figures with differences between PSpice internal time units and real time units. PSpice is, however, a tool that only handles electrical magnitudes.

    This means that the only internal variable units in PSpice are restricted to electrical units. In PV systems it is obvious that non-electrical magnitudes have to be handled and this then forces the use of electrical equivalents for non-electrical magnitudes.

    For example, if we want to enter temperature data we have to convert the temperature to a voltage source, for example, in such a way that 1 V of the voltage source corresponds to one degree Celsius of temperature. So the internal PSpice unit is an electrical unit volt and the real unit is a thermal unit C therefore making a domain conversion.

    In order to avoid confusions, warnings are issued through the book when necessary. In fact we have used such domain conversion in Chapters 1 and 2 because we have handled spectral irradiance and wavelength, but we want to stress this domain conversion issue again here due to the importance it will take from now on. As an example of the points raised above, let us consider an example assuming we know 10 irradiance and temperature couples of values for one day and we want to know the time evolution of the main PV magnitudes of a solar cell.

    The values of irradiance and temperature are entered in the PSpice code as a piecewise linear voltage source where the internal unit of time is considered as one microsecond corresponding to one hour of real time. The subcircuit is changed modifying the v-sources for the irradiance and temperature as follows: The internal unit of time is the microsecond and the real time unit is the hour. Find the values of the open-circuit voltage and short-circuit current.

    Write the PSpice code of a solar cell working at 27 C with the following parameter values: Plot the I V characteristics for the following irradiance values: List the values for Isc and Voc for all irradiance values. Write the PSpice code of the same solar cell at the same temperature but in darkness. Plot the I V characteristic in a semilog plot log I vs. Notice that the curve is not linear at high currents. List the values of V in this plot for approximately the same Isc values of the previous list.

    The purpose of this problem is to demonstrate this method. Plot the I V characteristic for two irradiance values: Call this value V1. The properties of series and parallel connections of solar cells are first described and the role played by bypass diodes is illustrated. Conversion of a PV module standard characteristics to arbitrary conditions of irradiance and temperature is described and more general or behavioural PSpice models are used for modules and generators extending the solar cell models described in Chapter 3.

    In most photovoltaic applications, voltages greater than some tens of volts are required and, even for conventional electronics, a minimum of around one volt is common nowadays. It is then mandatory to connect solar cells in series in order to scale-up the voltage produced by a PV generator. This series connection has some peculiar properties that will be described in this chapter.

    PV applications range from a few watts in portable applications to megawatts in PV plants, so it is not only required to scale-up the voltage but also the current, because the maximum solar cell area is also limited due to manufacturing and assembly procedures.

    This means that parallel connection of PV cells and modules is the most commonly used approach to tailor the output current of a given PV installation, taking into account all the system components and losses. A number of cases can be distinguished, depending on the irradiance levels or internal parameter values of the different cells. Figure 4. The output of the array is between nodes 43 and 0 and node 45 is the node common to the two cells.

    This is shown in Figure 4. This a common situation due, for example, to the presence of dirt in one of the solar cells. This is achieved by modifying the value of the voltage source representing the value of the irradiance in cell number 2. As can be seen the association of the two solar cells, as could be expected by the series association, generates a short circuit current equal to the short circuit current generated by the less illuminated solar cell namely 0.

    What also happens is that the voltage drop in the two cells is split unevenly for operating points at voltages smaller than the open circuit voltage. This is clearly seen in the bottom graph in Figure 4. As can be seen, for instance, at short circuit, the voltage drop in cell number 1 is mV as measured using the cursor whereas the drop in cell number 2 is — mV ensuring that the total voltage across the association is, of course, zero.

    This has relevant consequences, as can be seen by plotting not only the power delivered by the two solar cell series string, but also the power delivered individually by each solar cell as shown in Figure 4.

    It can be seen that the power delivered by solar cell number 2, which is the less illuminated, may be negative if the total association works at an operating point below some 0. This indicates that some of the power produced by solar cell number 1 is dissipated by solar cell number 2 thereby reducing the available output power and increasing the temperature locally at cell number 2. The analysis of this problem is extended to a PV module later in this chapter. The extension of this behaviour for a situation in which one of the solar cells is completely in the dark, or has a catastrophic failure, converts this solar cell to an open circuit, and hence all the series string will be in open circuit.

    This can be avoided by the use of bypass diodes which can be placed across every solar cell or across part of the series string. This is illustrated in the following example. Example 4. Assume that cell number six is completely shadowed. To avoid the complete loss of power generation by this string, a diode is connected across the faulty device in reverse direction as shown in Figure 4.

    The bypass diode is connected between the nodes 53 and 55 of the string.

    Modelling Photovoltaic Systems Using PSpice

    The results are shown in Figure 4. It can be seen that the total maximum voltage is 5. These two curves allow a proper sizing of the diode. It may be concluded that a bypass diode will save the operation of the array when a cell is in darkness, at the price of a reduced voltage. Scaling of current can be achieved by scaling-up the solar cell area, or by parallel association of solar cells of a given area or, more generally, by parallel association of series strings of solar cells.

    Such is the case in large arrays of solar cells for outer-space applications or for terrestrial PV modules and plants. The netlist for the parallel association of two identical solar cells is shown below where nodes 43 and 0 are the common nodes to the two cells and the respective irradiance values are set at nodes 42 and As can be seen the short circuit current is the addition of the two short circuit currents.

    This is due to the power losses by series and shunt resistances. The following example illustrates this case. The solution uses the netlist above and replaces the irradiance by the values of cases A and B in sequence.

    The result is shown in Figure 4. In terrestrial applications the PV standard modules are composed of a number of solar cells connected in series. The number is usually 33 to 36 but different associations are also available.

    The connections between cells are made using metal stripes. In PSpice it would be easy to scale-up a model of series string devices extending what has been illustrated in Example 4. There are, however, two main reasons why a more compact formulation of a PV module is required. The first reason is that as the number of solar cells in series increases, so do the number of nodes of the circuit.

    Generally, educational and evaluation versions of PSpice do not allow the simulation of a circuit with more than a certain number of nodes. The second reason is that as the scaling rules of current and voltage are known and hold in general, it is simpler and more useful to develop a more compact model, based on these rules, which could be used, as a model for a single PV module, and then scaled-up to build the model of a PV plant.

    In fact the PSpice code can be written in such a way that the value of I0 is internally computed from the data of the open circuit voltage and short circuit current as shown below. Substituting equation 4. On the other hand, the value of the PV module series resistance is not normally given in the commercial technical sheets.

    However, the maximum power is either directly given or can be easily calculated from the conversion efficiency value.

    Most often the value of Pmax is available at standard conditions. From this information the value of the module series resistance can be calculated using the same approach used in Section 3.

    To do this, the value of the fill factor of the PV module when the series resistance is zero is required. We will assume that the fill factor of a PV module of a string of identical solar cells equals that of a single solar cell.

    This comes from the scaling rules shown in equations 4. The above netlist includes practical values of a commercial PV module: The model described in this section is able to reproduce the whole standard AM1. We face, however, a similar problem to that in Chapter 3 concerning individual solar cells, that is translating the standard characterisitcs to arbitrary conditions of irradiance and temperature.

    The next sections will describe some models to solve this problem. The standard conditions are for terrestrial applications, AM1. Therefore, what the user knows, are the nominal values of the electrical parameters of the PV module, which are different from the values of these same parameters when the operating conditions change. The conversion of the characteristics from one set of conditions to another is a problem faced by designers and users, who want to know the output of a PV installation in average real conditions rather than in standard conditions and those only attainable at specialized laboratories.

    Most of the conversion methods are based on the principles described in Chapter 3; a few important rules are summarized below: Moreover, there is a significant difference between the ambient temperature and the cell operating temperature, due to packaging, heat convection and irradiance.

    Blaesser [4. Thus any transformation is now possible as shown in the following example. A voltage coordinate transformation section has been added to the section calculating the characteristics under standard temperature and the new irradiance conditions and then the voltage shift transformation of equation 4.

    This is schematically shown in the circuit in Figure 4. This parameter helps in relating the ambient temperature to the real operating temperature of the cell. A simple empirical formula is used [4. Of course the determination of the value of NOCT depends on the module type and sealing material. After a series of tests in a number of PV modules, an average fit to the formula in equation 4.

    This simple equation 4. For an arbitrary value of the irradiance and temperature, the short-circuit current is given by: As in Chapter 3, the available data provided by the PV manufacturers for the modules, is normally restricted to the short-circuit current, open-circuit voltage and maximum power point coordinates at standard reference conditions AM1.

    Module temperature coefficients for short-circuit currents and open-circuit voltages are also given. The behavioural PSpice modelling of a single solar cell described in Chapter 3 can be extended to a PV module, and it follows that the maximum power point coordinates are given by: The subcircuit, shown in Figure 4. Also two nodes generate values for the coordinates of the maximum power point to be used by MPP trackers.

    These data have been taken from www. As an example of the importance of the effect of the cell temperature, the above model has been run for two PV modules, one made of crystalline silicon [4. The results of the values of the coordinates of the maximum power point are plotted in Figure 4.

    As can be seen, the voltage at the maximum power point has a maximum at moderate irradiance values, thereby indicating that the irradiance coefficient of the maximum power point voltage, which will increase the value as irradiance increases, is compensated by the temperature coefficient, which produces a reduction of the voltage at higher irradiances due to the higher cell temperature involved.

    Of course, this dissipation can be of much greater importance if only one of the cells of a PV module is completely shadowed.

    Dissipation of power by a single solar cell raises its operating temperature and it is common to calculate the extreme conditions under which some damage to the solar cell or to the sealing material can be introduced permanently.

    One way to quantify a certain safe operation area SOA is to calculate the power dissipated in a single solar cell number n by means of: The result for the commercial module simulated in Section 4. The safe operation area is the area between the two curves. The first case is generally the case of outer-space applications where the arrays are designed especially for a given space satellite or station.

    In terrestrial applications arrays are formed by connecting PV modules each composed of a certain number of series-connected solar cells and eventually bypass diodes.

    We will concentrate in this section on the outer-space applications to illustrate the effects of shadow and discuss terrestrial applications in Chapter 5. Generally the space arrays are composed of a series combination of parallel strings of solar cells, as shown in Figure 4.

    The bypass diodes have the same purpose as described earlier, this is to allow the array current to flow in the right direction even if one of the strings is completely shadowed. In order to show the benefits of such structure, we will simplify the problem to an array with 18 solar cells and demonstrate the effect in Example 4.

    There are four-strings in series each string composed of three solar cells in parallel. Each cell has the same characteristics: Plot the voltage drops across the bypass diodes and the power dissipation. Solution We will assume that the irradiance of the shadowed cells is zero. The corresponding netlist is an extension of the netlist in Example 4.

    Taking into account that if no bypass diodes were used the total output power would be zero due to the complete shadow of one of the series strings cells 1 to 3 , there is some benefit in using bypass diodes. The same netlist allows us to plot the individual diode voltage as shown in Figure 4. As can be seen diodes D4 and D5 remain in reverse bias along the array operating voltage range 0 to 3.

    These diodes dissipate significant power when they are direct biased. Such is the case of satellite solar cell arrays or special size modules to be integrated in buildings.

    Scaling rules are required to relate the characteristics of the PV plant or generator to individual PV module characteristics.

    The steps described in Section 4. Applying these rules to the generator it is straightforward to show that: The figure is not shown because it is identical to the one of a single PV module with the voltage and currents scaled up according the scaling rules. Which designs satisfy the specifications? Depending on the complexity and characteristics of the final loads connected to the photovoltaic system, different elements can be found as a part of the photovoltaic system itself.

    These different elements may be: Depending on the nature of the loads, their interface to the photovoltaic system implies different complexity grades.

    The study of the different connection options of the photovoltaic modules to the rest of the photovoltaic system components is the objective of this chapter.

    The simplest load is a resistor R. Figure 5. In the example shown in Figure 5. This is the voltage common to the PV module output and the resistor load. This result means that a resistor load sets the operating point of a PV module, and by extension of a PV system, generally, at a different point than the maximum power point. As a result it can be concluded that the power transfer from the PV generator to the load is not optimized in the general case in this direct connection, unless interface circuits are inserted between the PV system and the load.

    This will directly affect the transfer of electrical power to the load. In the simple case of a resistor as a load, analysed here, the result of a direct connection will be that the power efficiency will change as long as irradiance and temperature change.

    An important effect of a direct connection to a resistor is that no power can be delivered to the load by night, which in many applications is a key specification.

    Modelling Photovoltaic Systems Using PSpice - PDF Free Download

    Suitable models for DC motors and centrifugal pumps can be derived for PSpice simulation. Moreover a back electromotive force emf is induced in the armature winding and is related to the magnetic flux and to the angular frequency!

    The differential equations governing the dynamic operation of the DC motor are: There are more complicated PSpice models that take into account these effects, however, these are beyond the scope of this book, and the reader is referred to reference [5. As a result of this load torque an equilibrium is reached for a value of the angular speed. Moreover, the centrifugal pump has a characteristic curve relating the pumping head, H, the angular frequency and the resulting flow Q.

    These types of curves are widely available in commercial technical notes or web pages, and are generally given for a constant value of the angular speed. It is assumed that these curves can be approximated by a second-degree polynomial as follows: A schematic circuit showing how the different parameters relate in a DC motor-pump connection is shown in Figure 5. It should be noted that the input power is a function of the output angular speed due to the generator Ecm in the armature winding equivalent circuit.

    This means that the first two blocks in Figure 5. First for the pump, the data of the characteristic curve are taken and summarized in Table 5. Step 1 Obtain the values of the main operational parameters under nominal conditions. That is the values of Pin and S. Step 2 Assume a value for the input voltage if not known, and a value for the armature and field winding resistances.

    Step 3 Calculate Km.

    However, some reasonable assumptions can be made if the dynamic response is considered. In order to calculate the small-signal dynamic performance of the motor-pump combination, the variational method to linearize equations can be used and then Laplace transforms taken. We can deduce from equation 5. This means assuming! Example 5. Simulate the electrical and mechanical response of the motor-pump system when a small step of 1 V amplitude is applied to the input voltage while at nominal operation conditions.

    Taking into account equation 5. This subcircuit is used to simulate the transient response of the motor and pump, as follows: It is seen that the flow remains at zero until approximately 7. The electrical power required reaches the predicted W in Table 5.

    The model described in this section is used in Chapter 7 to simulate long-term pumping system behaviour. Of course, a battery is necessary to extend the load supply when there is no power generated by the PV modules in absence of irradiance, or when the power generated is smaller than required. The battery will also store energy when the load demand is smaller than the power generated by the PV modules.

    A battery is an energy storage element and can be interpreted as a capacitive load connected to the PV generator output. As can be seen in Figure 5. The batteries have acceptable performance characteristics and lifecycle costs in PV systems. In some cases, as in PV low-power applications, nickel—cadmium batteries can be a good alternative to lead—acid batteries despite their higher cost.

    Lead—acid batteries are formed by two plates, positive and negative, immersed in a dilute sulphuric acid solution. The positive plate, or anode, is made of lead dioxide PbO2 and the negative plate, or cathode, is made of lead Pb. The chemical reactions at the battery, in the charge and discharge processes are described below: On the contrary, while in discharge mode, the current flows out of the positive terminal, the battery voltage, Vbat , decreases and the charge stored decreases supplying charge to the load.

    In addition to the two main operation modes, the complex battery behaviour is better modelled if two additional operating modes are considered: When the battery charge is close to the recommended minimum value and the circuit conditions force the battery to further discharge, the undercharge state is reached, characterized by a strong decrease of the electrolyte internal density, causing sedimentation at the bottom of the battery elements.

    This process strongly reduces the total battery capacity and, if the battery remains in this mode for a long time, irreversible damage can be caused. The last mode of operation, or overcharge mode, is reached when the battery charge exceeds the maximum recommended value. At this point two different effects appear: In this mode the battery shows an effective reduction of the available battery capacity.

    If the overcharge remains the battery enters into saturation and no more charge will be stored. As can be seen, after a slow increase of the voltage, overcharge and saturation regions produce a stagnation of the element voltage. As soon as the discharge is started, the battery voltage drops quite sharply and then tends to smaller values until the underdischarge zone is reached when a drop to zero volts occurs. This parameter is given for certain measurement conditions by the manufacturers, usually by measuring the charge delivered by the battery in a given period of time at a given discharge rate and temperature.

    Depending on the length of time considered for the discharge, different nominal capacities can be defined. Most standard time lengths provided by the manufacturers are 5 h, 10 h and h.

    According to these time lengths, nominal capacities, C5 , C10 and C are defined and given in units of Ah, where the subscript index indicates the discharge time length. In the case of a discharge the discharge rate is the time length needed for the battery to discharge at a constant current.

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    The discharge rate coincides with the capacity subscript index considered in the previous section. The battery capacity is a function of the charge and discharge rates. The battery capacity increases for longer discharge rates, this effect appearing as a consequence of the deeper electrolyte penetration into the battery plate material. The SOC value is the ratio of the available charge at a given time divided by the maximum capacity and is written as follows: As can be seen in equation 5.

    This dependence has to be taken into account for correct modelling of the battery behaviour. We will be using within the battery model the following parameters for the SOC: A lead—acid battery PSpice model, implementing a dynamic estimation of the SOC Wh , is described in this section allowing an accurate simulation of the battery behaviour. The model is based on the equations described by Lasnier and Tang in reference [5.

    The model has the following input parameters: SOCm Wh , maximum battery capacity. The electrical battery model is composed of a voltage source V1 in series with a resistor R1 , as shown in Figure 5.

    The values of V1 and R1 depend on the battery operation mode at a given time. Although all modes of operation can be taken into account in the model we restrict ourselves here to the two main modes of operation: The implementation of the model consists basically of assigning different expressions to the values of V1 and R1 in each different mode as follows: The battery model is represented by the PSpice equivalent circuit shown in Figure 5.

    As can be seen, these switches connect the battery output nodes to the corresponding internal voltage sources and resistors depending on the operation mode, which is identified by the sign of the current Ibat: The estimation is performed as described by the following equation: Equation 5.

    As time has units of seconds, some terms have to be divided by so that SOC is in Wh. As can be seen, to simplify the numerical resolution of equation 5.

    This is done as follows: The battery model subcircuit implemented by this netlist has three access nodes, shown at Figure 5. This is why the effects of temperature have not been considered here for the battery although they can be easily included, see [5. The following Example 5. Solution The circuit is depicted in Figure 5.

    The PSpice netlist is the following: The two different battery modes of operation, charge and discharge, can be clearly identified by the sharp voltage changes at the current zerocrossings. The SOCn has a periodical evolution according to the battery current forced by this simulation. This is illustrated in Example 5. Warning the y-axis is the value of the normalized SOC adimensional Example 5.

    Compute the values of the internal source V1 and R1 from the equations 5. Solution After calculation the resulting parameter values are included in the modified file as follows: In a real PV system, the irradiance and temperature values evolve during the observation time according to meteorological conditions and site location.

    Pspice offers a very good schematics environment, Orcad Capture for desing entry, in order to enter circuit designs that allow pspice simulation, despite this fact, all pspice models presented in this book are presented as text files, and the corresponding net list can also be used also for design entry into Pspice and simulation.

    We think that this selection offers a more comprehensive approach to the presented models, makes easy to understand how these models are implemented and allows quickly adaptation of these models to different PV system architectures and design environments just easily including the necessary file modifications in each case, attending to the user necessities.

    A second reason for the above mentioned selection of design entry into Pspice is that text files are transportable to other Spice existent versions without relevant effort, this is not possible if the selected design entry is by schematic option.

    By other hand the translation of the presented models as net list files, to the equivalent schematic format is direct in most cases. All models presented in the book for solar cells and the rest of components of a PV system can be fount in this site, where users can download the corresponding net lists for pspice simulation of all the examples and simulation results presented in the book. Introduction to Photovoltaic Systems and PSpice.