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Fig. 6.36 Simulation results obtained from the PV generator according to the variation in irradiance

Figure 6 36 Simulation results obtained from the PV generator according to the variation in irradiance

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The basic element of a photovoltaic system (PV) is solar cells which convert the sunlight energy directly to direct current. A typical solar cell consists of a PN junction formed in a semi-conductor material similar to a diode. Semi-conductor material most widely used in solar cells is silicon. Each material gives different efficiency and has different cost. There are several types of solar material cells:
The basic element of a photovoltaic system (PV) is solar cells which convert the sunlight energy directly to direct current. A typical solar cell consists of a PN junction formed in a semi-conductor material similar to a diode. Semi-conductor material most widely used in solar cells is silicon. Each material gives different efficiency and has different cost. There are several types of solar material cells:
Fig. 1.4 Market share of crystalline silicon 4. Dye-sensitized solar cell (DSC) is formed by a photo-sensitized anode and an electrolyte. Its efficiency is around 11.1%.
Fig. 1.4 Market share of crystalline silicon 4. Dye-sensitized solar cell (DSC) is formed by a photo-sensitized anode and an electrolyte. Its efficiency is around 11.1%.
Fig. 1.2, Monocrystalline silicon cell [2]
Fig. 1.2, Monocrystalline silicon cell [2]
Fig. 1.5 Market share of thin-film
Fig. 1.5 Market share of thin-film
Fig. 1.7 Efficiency of different material cells in laboratory [2]
Fig. 1.7 Efficiency of different material cells in laboratory [2]
The MPP is reached when The left member of Eq. 1.7 is the incremental internal resistance of the PV generator (the minus sign is due to the choice for that device of the generator reference directions). The right member is the apparent resistance of the load. Thus, one can consider Eq. 1.7 as the equation defining the resistance adaptation of the load the internal resistance of the PV generator.
The MPP is reached when The left member of Eq. 1.7 is the incremental internal resistance of the PV generator (the minus sign is due to the choice for that device of the generator reference directions). The right member is the apparent resistance of the load. Thus, one can consider Eq. 1.7 as the equation defining the resistance adaptation of the load the internal resistance of the PV generator.
Fig. 1.10 Current versus voltage Ipv—Vpv characteristic for a solar cell
Fig. 1.10 Current versus voltage Ipv—Vpv characteristic for a solar cell
Fig. 1.12 Temperature effect on electrical characteristic [31] Fig. 1.11 Irradiance effect on electrical characteristic
Fig. 1.12 Temperature effect on electrical characteristic [31] Fig. 1.11 Irradiance effect on electrical characteristic
Fig. 1.14 Stand-alone PV system with battery storage powering DC and AC loads Figure 1.14 shows a diagram of a typical stand-alone PV system powering DC and AC loads [7].
Fig. 1.14 Stand-alone PV system with battery storage powering DC and AC loads Figure 1.14 shows a diagram of a typical stand-alone PV system powering DC and AC loads [7].
Thus, if the conductor is perfect, we have:
Thus, if the conductor is perfect, we have:
1.4.1 Estimating the Size of a Photovoltaic System
1.4.1 Estimating the Size of a Photovoltaic System
1.5 Maintenance of Photovoltaic Systems Fig. 1.19 Flowchart of estimating the size of a PV [11] We have to calculate the sunshine available for the panels on an average day during the worst month of the year. It is called the insolation value.
1.5 Maintenance of Photovoltaic Systems Fig. 1.19 Flowchart of estimating the size of a PV [11] We have to calculate the sunshine available for the panels on an average day during the worst month of the year. It is called the insolation value.
Fig. 1.20 Flowchart of
Fig. 1.20 Flowchart of
LS eS OS eee Ole ee lee eee Figure 2.7 shows the corresponding radiance as a function of the zenith angle. We can see that this second order approximation is not realistic since it leads to 1egative values of the radiance. In fact, the function /,(t’,) thus obtained is a smooth function unable to correctly describe the directional properties of radiance near the ground level, because at that boundary the sky and soil radiances do not 1ave the same form. 2.1.3.8 Enhanced Approximation for Hemispherical Radiance
LS eS OS eee Ole ee lee eee Figure 2.7 shows the corresponding radiance as a function of the zenith angle. We can see that this second order approximation is not realistic since it leads to 1egative values of the radiance. In fact, the function /,(t’,) thus obtained is a smooth function unable to correctly describe the directional properties of radiance near the ground level, because at that boundary the sky and soil radiances do not 1ave the same form. 2.1.3.8 Enhanced Approximation for Hemispherical Radiance
In literature, there are several mathematical models that describe the operation and behavior of the photovoltaic generator. For example, Borowy and Salameh [29] have given a simplified model, with which the maximum power output can be calculated for a module once photovoltaic solar irradiance on the photovoltaic module and the temperature is found, and Jones and Underwood [30] also intro- duced a simplified model of the maximum power output which has a reciprocal relationship with the temperature module and logarithmic relationship with the solar radiation absorbed by the photovoltaic module. In addition, Jones and Underwood have given the thermal model of the temperature module photovoltaic through the evaluation of many factors. These models differ in the calculation procedure, accuracy and the number of parameters involved in the calculation of the current-voltage characteristic.
In literature, there are several mathematical models that describe the operation and behavior of the photovoltaic generator. For example, Borowy and Salameh [29] have given a simplified model, with which the maximum power output can be calculated for a module once photovoltaic solar irradiance on the photovoltaic module and the temperature is found, and Jones and Underwood [30] also intro- duced a simplified model of the maximum power output which has a reciprocal relationship with the temperature module and logarithmic relationship with the solar radiation absorbed by the photovoltaic module. In addition, Jones and Underwood have given the thermal model of the temperature module photovoltaic through the evaluation of many factors. These models differ in the calculation procedure, accuracy and the number of parameters involved in the calculation of the current-voltage characteristic.
We have with [,, (A) is the photocurrent that is equal to short-circuit current, Ig (A) is the reverse saturation current of the diode, q is the electron charge (1.602 x 10-'° ©), K Botzman’s constant (1.381 x 10~*° J/K), A is diode ideality factor, Tj is junction temperature of the panels (°K), /g is the current shunted through the intrinsic diode, V,, is the voltage across the PV cell. The simplified equivalent circuit of a solar cell consists of a diode and a current source connected in parallel (Fig. 2.9). The current source produces the photo- current Ipn, which is directly proportional to solar irradiance G. The two key parameters often used to characterize a PV cell are its short-circuit current and its open-circuit voltage which are provided by the manufacturer’s data sheet. The equation of the current voltage J,,-V,, simplified equivalent circuit is derived from Kirchhoff’s law. MUKTW Le...
We have with [,, (A) is the photocurrent that is equal to short-circuit current, Ig (A) is the reverse saturation current of the diode, q is the electron charge (1.602 x 10-'° ©), K Botzman’s constant (1.381 x 10~*° J/K), A is diode ideality factor, Tj is junction temperature of the panels (°K), /g is the current shunted through the intrinsic diode, V,, is the voltage across the PV cell. The simplified equivalent circuit of a solar cell consists of a diode and a current source connected in parallel (Fig. 2.9). The current source produces the photo- current Ipn, which is directly proportional to solar irradiance G. The two key parameters often used to characterize a PV cell are its short-circuit current and its open-circuit voltage which are provided by the manufacturer’s data sheet. The equation of the current voltage J,,-V,, simplified equivalent circuit is derived from Kirchhoff’s law. MUKTW Le...
We can determine the reverse saturation current Jp by setting J,,=0 (case when 0 output current).
We can determine the reverse saturation current Jp by setting J,,=0 (case when 0 output current).
Thus we obtain, taking into account the fact that, with this model, the photo- current is equal to the short-circuit current:
Thus we obtain, taking into account the fact that, with this model, the photo- current is equal to the short-circuit current:
Fig. 2.13 Bloc diagram of model with ohmic losses
Fig. 2.13 Bloc diagram of model with ohmic losses
Fig. 2.14 PV subsystem bloc diagram of model with ohmic losses [195] Fig. 2.15 Simplified equivalent circuit of solar cell
Fig. 2.14 PV subsystem bloc diagram of model with ohmic losses [195] Fig. 2.15 Simplified equivalent circuit of solar cell
The first model studied in this section is defined, as one of these Sects. 2.2.1 and 2.2.2, by an equivalent circuit. This one consists of a single diode for the phe- nomena of cell polarization and two resistors (series and shunt) for the losses (Fig. 2.15). It can thus be named “one diode model”. This model is used by manufacturers by giving the technical characteristics of their solar cells (data sheets).
The first model studied in this section is defined, as one of these Sects. 2.2.1 and 2.2.2, by an equivalent circuit. This one consists of a single diode for the phe- nomena of cell polarization and two resistors (series and shunt) for the losses (Fig. 2.15). It can thus be named “one diode model”. This model is used by manufacturers by giving the technical characteristics of their solar cells (data sheets).
We can then find the cell parameters at the operating temperature of cells and solar irradiance from: The other parameters are calculated by the following equations:
We can then find the cell parameters at the operating temperature of cells and solar irradiance from: The other parameters are calculated by the following equations:
Fig. 2.16 Flowchart of resolution with parameters P;
Fig. 2.16 Flowchart of resolution with parameters P;
Fig. 2.20 Characteristics [py = f (Vpy) and Ppy = f (Vpy) in STC conditions
Fig. 2.20 Characteristics [py = f (Vpy) and Ppy = f (Vpy) in STC conditions
Fig. 2.21 Effects of solar irradiance changing
Fig. 2.21 Effects of solar irradiance changing
Fig. 2.22 Effects of temperature changing
Fig. 2.22 Effects of temperature changing
Fig. 2.26 PV subsystem (Model No. 2) [195]
Fig. 2.26 PV subsystem (Model No. 2) [195]
Fig. 2.25 Bloc diagram of Model No. 2 [195] The simple relationship of power for a photovoltaic module is
Fig. 2.25 Bloc diagram of Model No. 2 [195] The simple relationship of power for a photovoltaic module is
Fig. 2.27 Characteristics J,, = f(Vpy) and Pp, = f(Vpy) under the STC conditions (Model No. 2)
Fig. 2.27 Characteristics J,, = f(Vpy) and Pp, = f(Vpy) under the STC conditions (Model No. 2)
Fig. 2.29 Effect of temperature changing (model No. 2)
Fig. 2.29 Effect of temperature changing (model No. 2)
Fig. 2.31 Bloc diagram of Model No. 3 [195]
Fig. 2.31 Bloc diagram of Model No. 3 [195]
Fig. 2.33 Effects of solar irradiance changing (Model No. 3) [195
Fig. 2.33 Effects of solar irradiance changing (Model No. 3) [195
Fig. 2.35 Characteristics [,, = f (Vpy) and Ppy = f (Vpy) (Model No. 3) [195]
Fig. 2.35 Characteristics [,, = f (Vpy) and Ppy = f (Vpy) (Model No. 3) [195]
Fig. 2.34 Effects of temperature changing (Model No. 3) [195]
Fig. 2.34 Effects of temperature changing (Model No. 3) [195]
The expression of Vince, can have the following form:
The expression of Vince, can have the following form:
Fig. 2.37 Block diagram of two diode model [195]
Fig. 2.37 Block diagram of two diode model [195]
Fig. 2.38 Characteristics [,, = f (Vpy) and Ppy = f (Vpy) simulation results (two diode model) [195]
Fig. 2.38 Characteristics [,, = f (Vpy) and Ppy = f (Vpy) simulation results (two diode model) [195]
Fig. 2.40 Variations of power for different days of the year (Model No. 1) [9]
Fig. 2.40 Variations of power for different days of the year (Model No. 1) [9]
2.2.4 General Remarks on PV Arrays Models That additional equation allows determining one more parameter using the nom- inal values of a photovoltaic cell or module.
2.2.4 General Remarks on PV Arrays Models That additional equation allows determining one more parameter using the nom- inal values of a photovoltaic cell or module.
connected to the AC mains). According to the power rating of a converter, the switching frequency may range from several kHz for high to medium power converters to more than 1 MHz for very low power converters. The use of a high switching frequency makes easier the filtering of the current and voltage ripples generated at the switching frequency at the input and output of the converter. Moreover, as the energy which has to be stored inside the passive components is lower when the internal frequency is high, the frequency increase allows reducing the size and the cost of the passive components. Unfortunately, an increase of the switching frequency increases the commu- tation losses, so the choice of this frequency results from a compromise which is mainly ruled by the switching speed of the semiconductors. As the commutation losses are lower when the components can commute faster, the optimal switching frequencies grow more and more as the semiconductor performances are imnronved
connected to the AC mains). According to the power rating of a converter, the switching frequency may range from several kHz for high to medium power converters to more than 1 MHz for very low power converters. The use of a high switching frequency makes easier the filtering of the current and voltage ripples generated at the switching frequency at the input and output of the converter. Moreover, as the energy which has to be stored inside the passive components is lower when the internal frequency is high, the frequency increase allows reducing the size and the cost of the passive components. Unfortunately, an increase of the switching frequency increases the commu- tation losses, so the choice of this frequency results from a compromise which is mainly ruled by the switching speed of the semiconductors. As the commutation losses are lower when the components can commute faster, the optimal switching frequencies grow more and more as the semiconductor performances are imnronved
input and output current and voltage, the sizing is governed by the product of the bigger voltage by the bigger current. A big value of the ratio k leads to oversized converter, and then lower efficiency. For that reason, the output voltage is not too large and one can admit that, occasionally, the optimum PV voltage becomes higher than the output voltage. When that case occurs, the converter reduces to direct connection (Fig. 3.4) but it remains possible to short-circuit the PV if necessary by keeping the transistor “on”. The fact that the inductor is in series with input is interesting because it
input and output current and voltage, the sizing is governed by the product of the bigger voltage by the bigger current. A big value of the ratio k leads to oversized converter, and then lower efficiency. For that reason, the output voltage is not too large and one can admit that, occasionally, the optimum PV voltage becomes higher than the output voltage. When that case occurs, the converter reduces to direct connection (Fig. 3.4) but it remains possible to short-circuit the PV if necessary by keeping the transistor “on”. The fact that the inductor is in series with input is interesting because it
3.2.2.3 Example of Application of DC-DC Converter with Photovoltaic: a Battery Charger It is the simplest system where only one converter exists that loads the battery. Then the battery is directly connected to the load (Fig. 3.10).
3.2.2.3 Example of Application of DC-DC Converter with Photovoltaic: a Battery Charger It is the simplest system where only one converter exists that loads the battery. Then the battery is directly connected to the load (Fig. 3.10).
battery bank. We consider as example the circuit of Fig. 3.6 (buck converter). To model the battery charger, we use the equivalent circuit of Fig. 3.11. As long as the battery is not fully charged, the control circuit act on the switches of DC/DC converter in order to maximize the battery current. However, it can estimate the charge of the battery using measurements of battery voltage, current and often temperature and current integral. It can thus limit the battery current if its value is too large considering the battery state of charge. Often, the control circuit can also acts on a relay in order to disconnect the load when the battery is too discharged. In theory, a model of the battery is needed in order to estimate the battery state of charge. Several control circuits include a fuzzy logic controlle1 which can determinate implicitly such a model after some cycles of charge.
battery bank. We consider as example the circuit of Fig. 3.6 (buck converter). To model the battery charger, we use the equivalent circuit of Fig. 3.11. As long as the battery is not fully charged, the control circuit act on the switches of DC/DC converter in order to maximize the battery current. However, it can estimate the charge of the battery using measurements of battery voltage, current and often temperature and current integral. It can thus limit the battery current if its value is too large considering the battery state of charge. Often, the control circuit can also acts on a relay in order to disconnect the load when the battery is too discharged. In theory, a model of the battery is needed in order to estimate the battery state of charge. Several control circuits include a fuzzy logic controlle1 which can determinate implicitly such a model after some cycles of charge.
commercially “solar inverter” often includes several power electronic converters. As a first example, we can have a dual-stage inverter (Fig. 3.15). This topology consists of a DC—DC converter which is used for the MPPT, and a DC-AC inverter. The control signals applied to the power switches of the final stage can then be 180 or 120° conduction at the grid frequency (50 or 60 Hz). Then, commutation losses of the inverter are very low. This is possible without strong oversize output filter if the output from the DC—DC converter is modulated to follow a rectified sine wave. Another example of double stage inverter is given in Fig. 3.16. In the Fig. 3.16, the DC link between the DC—DC converter which carries out
commercially “solar inverter” often includes several power electronic converters. As a first example, we can have a dual-stage inverter (Fig. 3.15). This topology consists of a DC—DC converter which is used for the MPPT, and a DC-AC inverter. The control signals applied to the power switches of the final stage can then be 180 or 120° conduction at the grid frequency (50 or 60 Hz). Then, commutation losses of the inverter are very low. This is possible without strong oversize output filter if the output from the DC—DC converter is modulated to follow a rectified sine wave. Another example of double stage inverter is given in Fig. 3.16. In the Fig. 3.16, the DC link between the DC—DC converter which carries out
Fig. 3.19 Example of complex “solar inverter” topology
Fig. 3.19 Example of complex “solar inverter” topology
Fig. 3.21 Example of complex “solar inverter” with several independent inputs In that case, we can use several stages of the conversion: only the first stage is own to each subarray and subsequent stages are common. So, we can use at first stage a simple circuit such as a transformerless boost (Fig. 3.5) in order to keep a good efficiency in spite of the reduced power. Figure 3.21 shows a circuit made of several boosts, a common fixed duty factor push—pull converter in order to adapt the voltage level and to provide galvanic insulation, a storage capacitor and finally an inverter.
Fig. 3.21 Example of complex “solar inverter” with several independent inputs In that case, we can use several stages of the conversion: only the first stage is own to each subarray and subsequent stages are common. So, we can use at first stage a simple circuit such as a transformerless boost (Fig. 3.5) in order to keep a good efficiency in spite of the reduced power. Figure 3.21 shows a circuit made of several boosts, a common fixed duty factor push—pull converter in order to adapt the voltage level and to provide galvanic insulation, a storage capacitor and finally an inverter.
nigh power quality in compliance with the standards. At the limit case, it is possible to associate a DC/AC converter with each module, which can then be called AC-modules (Fig. 3.24). This solution has the advantage of being totally modular. It is an interesting solution when the photo- voltaic array is subject to complex shadows, since each module can always be used at its optimal power. However, the DC/AC converters are complex since there is a large difference in the input and output voltage levels, and their nominal power is low since each of them controls only one module. Their efficiency is thus relatively low.
nigh power quality in compliance with the standards. At the limit case, it is possible to associate a DC/AC converter with each module, which can then be called AC-modules (Fig. 3.24). This solution has the advantage of being totally modular. It is an interesting solution when the photo- voltaic array is subject to complex shadows, since each module can always be used at its optimal power. However, the DC/AC converters are complex since there is a large difference in the input and output voltage levels, and their nominal power is low since each of them controls only one module. Their efficiency is thus relatively low.
3.3 Empirical Modeling of the Converters
3.3 Empirical Modeling of the Converters
Unfortunately, manufacturer data are usually insufficient in order to determine all the coefficients of (Eq. 3.14). When manufacturer gives values of efficiency for several input voltages, it is generally for different configurations of the converter obtained by changing the turn numbers of transformer windings, so obtaining several and different values of the nominal input voltage. Then, there are as many different expressions of losses as different configurations, but often the data for each configuration describe the losses only for the nominal input voltage of that conficuration.
Unfortunately, manufacturer data are usually insufficient in order to determine all the coefficients of (Eq. 3.14). When manufacturer gives values of efficiency for several input voltages, it is generally for different configurations of the converter obtained by changing the turn numbers of transformer windings, so obtaining several and different values of the nominal input voltage. Then, there are as many different expressions of losses as different configurations, but often the data for each configuration describe the losses only for the nominal input voltage of that conficuration.
3.6.4 Control Systems for Inverters Most distributed energy resources are not suitable for direct power transfer to the electrical grid due to the characteristics of the energy produced. Therefore, power electronic interfaces (inverter or converter) and their control systems are required for interfacing the distributed energy resources with the electric grid. The importance of the inverter is increased because its role has two important aspects. First, it extracts and manages the maximum power from the source. Second, it conditions the input power in order to deliver clean and compliant power to the grid.
3.6.4 Control Systems for Inverters Most distributed energy resources are not suitable for direct power transfer to the electrical grid due to the characteristics of the energy produced. Therefore, power electronic interfaces (inverter or converter) and their control systems are required for interfacing the distributed energy resources with the electric grid. The importance of the inverter is increased because its role has two important aspects. First, it extracts and manages the maximum power from the source. Second, it conditions the input power in order to deliver clean and compliant power to the grid.
nominal efficiency could be observed [73]. PV arrays must be installed so that they maximize the amount of direct exposure to the sun. That usually means placement in an area clear of shading, in a southward direction and at an angle equal to the latitude of the location. The power provided by the PV array varies with solar irradiance and temperature, since these parameters influence the I-V characteris- tics of solar cells. In order to optimize the energy transfer from the PV array to the load, it is necessary to force the working point to be at the maximum power point (MPP) [31, 63].
nominal efficiency could be observed [73]. PV arrays must be installed so that they maximize the amount of direct exposure to the sun. That usually means placement in an area clear of shading, in a southward direction and at an angle equal to the latitude of the location. The power provided by the PV array varies with solar irradiance and temperature, since these parameters influence the I-V characteris- tics of solar cells. In order to optimize the energy transfer from the PV array to the load, it is necessary to force the working point to be at the maximum power point (MPP) [31, 63].
Table 4.1 Control action for different operating points of the power—voltage characteristic of a photovoltaic generator
Table 4.1 Control action for different operating points of the power—voltage characteristic of a photovoltaic generator
Fig. 4.3. MPPT control scheme and voltage regulation of Vpy
Fig. 4.3. MPPT control scheme and voltage regulation of Vpy
This control places the system at maximum operating point (Vopt, Lop). The first system with MPPT was introduced in 1968 for a space system [65]. Over the years, several MPPT algorithms have been developed and widely adapted to determine the maximum power point [31, 66, 67]. The control technique the most used consist to act on the duty cycle automatically to place the generator at its optimal value whatever the variations of the metrological conditions or sudden changes in loads which can occur at any time. The main components of the MPPT circuit are its power stage and the controller. The two configurations of MPPT scheme are represented in Figs. 4.5 and 4.6. In Fio 485 the nower ctace innit voaltace Vand ecirrent 7 are need hv the parameter « is continuously turned until the PV array is loaded at its MPP. Many methods have been developed to determine the maximum power point (MPP). In Ref. [68], to track MPP, a look-up table on a microcomputer is employed. It is based on the use of a database that includes parameters and data such as typical curves of the PV generator for different irradiances and tempera- tures. In Ref. [69], curve-fitting method is used, where the nonlinear characteristic of PV generator is modeled using mathematical equations or numerical approxi- mations. These two algorithms have as disadvantage that they may require a large
This control places the system at maximum operating point (Vopt, Lop). The first system with MPPT was introduced in 1968 for a space system [65]. Over the years, several MPPT algorithms have been developed and widely adapted to determine the maximum power point [31, 66, 67]. The control technique the most used consist to act on the duty cycle automatically to place the generator at its optimal value whatever the variations of the metrological conditions or sudden changes in loads which can occur at any time. The main components of the MPPT circuit are its power stage and the controller. The two configurations of MPPT scheme are represented in Figs. 4.5 and 4.6. In Fio 485 the nower ctace innit voaltace Vand ecirrent 7 are need hv the parameter « is continuously turned until the PV array is loaded at its MPP. Many methods have been developed to determine the maximum power point (MPP). In Ref. [68], to track MPP, a look-up table on a microcomputer is employed. It is based on the use of a database that includes parameters and data such as typical curves of the PV generator for different irradiances and tempera- tures. In Ref. [69], curve-fitting method is used, where the nonlinear characteristic of PV generator is modeled using mathematical equations or numerical approxi- mations. These two algorithms have as disadvantage that they may require a large
Fig. 4.4 [,,(Vpy) and Ppy(Vpy) characteristics [9]
Fig. 4.4 [,,(Vpy) and Ppy(Vpy) characteristics [9]
memory capacity, for calculation of the mathematical formulations and for storage of the data. Open-circuit voltage photovoltaic generator method is employed in Ref. [70], it approximates linearly the voltage of PV generator at the MPP to its open-circuit voltage and a linear dependency between the current at the MPP and the short-circuit current for the short-circuit photovoltaic generator method pre- sented in Ref. [71]. These methods are apparently simple and economical, but they are not able to adapt to changeable environmental conditions. Santos et al. present perturb and observe (P&O) method which is based on iterative algorithms to track continuously the MPP through the current and voltage measurement of the PV module. Most control schemes use the P&O technique because it is easy to implement [73-76] but the oscillation problem is unavoidable. Conductance incremental method presented in Ref. [76] requires complex control circuit. The two last strategies have some disadvantages such as high cost, difficulty, com- plexity and instability. Intelligent based control schemes MPPT have been introduced (fuzzy logic,
memory capacity, for calculation of the mathematical formulations and for storage of the data. Open-circuit voltage photovoltaic generator method is employed in Ref. [70], it approximates linearly the voltage of PV generator at the MPP to its open-circuit voltage and a linear dependency between the current at the MPP and the short-circuit current for the short-circuit photovoltaic generator method pre- sented in Ref. [71]. These methods are apparently simple and economical, but they are not able to adapt to changeable environmental conditions. Santos et al. present perturb and observe (P&O) method which is based on iterative algorithms to track continuously the MPP through the current and voltage measurement of the PV module. Most control schemes use the P&O technique because it is easy to implement [73-76] but the oscillation problem is unavoidable. Conductance incremental method presented in Ref. [76] requires complex control circuit. The two last strategies have some disadvantages such as high cost, difficulty, com- plexity and instability. Intelligent based control schemes MPPT have been introduced (fuzzy logic,
Fig. 4.7 Block diagram of Perturb and Observe method
Fig. 4.7 Block diagram of Perturb and Observe method
Fig. 4.8 Flowchart of Perturb and Observe method
Fig. 4.8 Flowchart of Perturb and Observe method
4.2.3 Incremental Conductance Technique
4.2.3 Incremental Conductance Technique
In turn, Eqs. 4.6 and 4.7 are used to determine the direction in which a perturbation must occur to shift the operating point toward the MPP, and the perturbation is repeated until Eq. 4.5 is satisfied. Once the MPP is reached, the MPPT continues to operate at this point until a change in current is measured which will correlate to a change in irradiance on the array Fig. 4.13. The relationship between voltage and current, for the one-exponential model, is siven by the following equation: Equation 4.4 explains that the operating voltage is below the voltage at the maximum power point if the conductance is larger than the incremental conduc- tance, and vice versa. Thus, the task of this algorithm is to track the voltage operating point at which conductance is equal to incremental conductance. Hence,
In turn, Eqs. 4.6 and 4.7 are used to determine the direction in which a perturbation must occur to shift the operating point toward the MPP, and the perturbation is repeated until Eq. 4.5 is satisfied. Once the MPP is reached, the MPPT continues to operate at this point until a change in current is measured which will correlate to a change in irradiance on the array Fig. 4.13. The relationship between voltage and current, for the one-exponential model, is siven by the following equation: Equation 4.4 explains that the operating voltage is below the voltage at the maximum power point if the conductance is larger than the incremental conduc- tance, and vice versa. Thus, the task of this algorithm is to track the voltage operating point at which conductance is equal to incremental conductance. Hence,
Fig. 4.15 Flowchart of the incremental conductance method
Fig. 4.15 Flowchart of the incremental conductance method
The block diagram of Incremental Conductance method is the same as that of Perturb & Observe method Fig. 4.14. Ficure 4.15 shows the flowchart of this method.
The block diagram of Incremental Conductance method is the same as that of Perturb & Observe method Fig. 4.14. Ficure 4.15 shows the flowchart of this method.
Incremental Conductance (INC) method is simple and easy to implement and its tracking efficiency is very high. It is able to tell whether the current working point is at the MPP or not, in case of ideal conditions. But in the measurements, the operating point could oscillate around the MPP. In the modified INC method, we added the part which monitors the maximum and minimum values of the power oscillations on the PV side. These values can be used to find out how close the current operating point is to the MPP, thereby slowing down the increment of the reference, in order not to cross the MPP [113].
Incremental Conductance (INC) method is simple and easy to implement and its tracking efficiency is very high. It is able to tell whether the current working point is at the MPP or not, in case of ideal conditions. But in the measurements, the operating point could oscillate around the MPP. In the modified INC method, we added the part which monitors the maximum and minimum values of the power oscillations on the PV side. These values can be used to find out how close the current operating point is to the MPP, thereby slowing down the increment of the reference, in order not to cross the MPP [113].
4.2.6 MPPT Controls Based on Relations of Proportionality These methods are based on proportional relationships between parameters of optimal maximum power point (op, Vopt) and the characteristic parameters of the panel (/,., Voc). 4.2.6.1 Constant Reference Voltage Algorithm
4.2.6 MPPT Controls Based on Relations of Proportionality These methods are based on proportional relationships between parameters of optimal maximum power point (op, Vopt) and the characteristic parameters of the panel (/,., Voc). 4.2.6.1 Constant Reference Voltage Algorithm
Fig. 4.18 Power—voltage characteristic P,(Vpy) of PV generator a-Variable irradiance, constant temperature b-Variable temperature, constant irradiance Fig. 4.19 Block diagram of open circuit voltage method [9]
Fig. 4.18 Power—voltage characteristic P,(Vpy) of PV generator a-Variable irradiance, constant temperature b-Variable temperature, constant irradiance Fig. 4.19 Block diagram of open circuit voltage method [9]
Fig. 4.21 Block diagram of Short circuit current method [9]
Fig. 4.21 Block diagram of Short circuit current method [9]
where the control saturate if xg + k,o is out of range, where k, is a positive scaling constant Fig. 4.24.
where the control saturate if xg + k,o is out of range, where k, is a positive scaling constant Fig. 4.24.
Table 4.3 Fuzzy rule table [63]
Table 4.3 Fuzzy rule table [63]
The power variation (APpy,) is either in the positive direction or in the negative me. The value of AP,, can also be small or on the contrary large. This control ullows the research of the optimum point while being based on the expert observations. From these judgments, the reference photovoltaic voltage Vpy ser 1S ncreased or decreased in a small or large way in the direction which makes it dossible to increase the power Ppy. TOL. ....,%*...... # ge dQ QT a, ee ey en ee Se ee
The power variation (APpy,) is either in the positive direction or in the negative me. The value of AP,, can also be small or on the contrary large. This control ullows the research of the optimum point while being based on the expert observations. From these judgments, the reference photovoltaic voltage Vpy ser 1S ncreased or decreased in a small or large way in the direction which makes it dossible to increase the power Ppy. TOL. ....,%*...... # ge dQ QT a, ee ey en ee Se ee
Fig. 4.26 Structure of MPPT fuzzy controller
Fig. 4.26 Structure of MPPT fuzzy controller
Fig. 4.27 Membership functions of AP,,, AVpy and of AVpy, re pv?
Fig. 4.27 Membership functions of AP,,, AVpy and of AVpy, re pv?
Fig. 4.28 Membership function plots in Matlab [9]
Fig. 4.28 Membership function plots in Matlab [9]
<Fig. 4.30 Simulation results of fuzzy logic controller versus theoretical PV array characteristic, temperature 7; is changed from 10 to 50°C at constant irradiance (1000 Wim’). (a): Pov(Vpy), (b):Ppy Upy), (€):Ipv (Vpy) a. Power-voltage characteristic of a PV module for different temperatures. b. Power-current characteristic of a PV module for different temperatures. c. Current-voltage characteristic of a PV module for different temperatures [31] Fig. 4.33 Architecture of the PBA algorithm
<Fig. 4.30 Simulation results of fuzzy logic controller versus theoretical PV array characteristic, temperature 7; is changed from 10 to 50°C at constant irradiance (1000 Wim’). (a): Pov(Vpy), (b):Ppy Upy), (€):Ipv (Vpy) a. Power-voltage characteristic of a PV module for different temperatures. b. Power-current characteristic of a PV module for different temperatures. c. Current-voltage characteristic of a PV module for different temperatures [31] Fig. 4.33 Architecture of the PBA algorithm
Fig. 4.36 Photovoltaic system with MPPT control by neuro-fuzzy networks
Fig. 4.36 Photovoltaic system with MPPT control by neuro-fuzzy networks
Fig. 4.37 Block diagram of a PV system based on Genetic algorithm [110]
Fig. 4.37 Block diagram of a PV system based on Genetic algorithm [110]
Fig. 4.38 Efficiency comparison of different MPPT methods
Fig. 4.38 Efficiency comparison of different MPPT methods
5.1.1.2 Nickel-Hydrogen Batteries
5.1.1.2 Nickel-Hydrogen Batteries
Table 5.1 Zebra battery properties [122] 5.1.1.7 Sodium-Metal Chloride Batteries Sodium-Metal Chloride Battery is also known as ZEBRA (zero emission battery research activity) battery and it is a system operating at around 270-350°C [119, 120]. The chemical reaction in the battery converts sodium chloride and nickel to nickel chloride and sodium during the charging phase. During discharge, the reaction is reversed. Each cell is enclosed in a robust steel case. A ZEBRA battery is designed for a 2 h discharge with peak power capability as required [119-122]. The normal operation can be written as:
Table 5.1 Zebra battery properties [122] 5.1.1.7 Sodium-Metal Chloride Batteries Sodium-Metal Chloride Battery is also known as ZEBRA (zero emission battery research activity) battery and it is a system operating at around 270-350°C [119, 120]. The chemical reaction in the battery converts sodium chloride and nickel to nickel chloride and sodium during the charging phase. During discharge, the reaction is reversed. Each cell is enclosed in a robust steel case. A ZEBRA battery is designed for a 2 h discharge with peak power capability as required [119-122]. The normal operation can be written as:
Table 5.2 Comparison of different Li-ion batteries [114]
Table 5.2 Comparison of different Li-ion batteries [114]
Table 5.3 Comparison of different batteries [118]
Table 5.3 Comparison of different batteries [118]
Table 5.4 Peukert constant e Rate of charge/discharge e Environmental temperature e Age/Shelf life 5.1.2.1 Electrochemical Battery Models 5.1.2.2 Peukert Equation
Table 5.4 Peukert constant e Rate of charge/discharge e Environmental temperature e Age/Shelf life 5.1.2.1 Electrochemical Battery Models 5.1.2.2 Peukert Equation
Fig. 5.8 Modified Thevenin model 5.1.3.5 Thevenin Battery Model
Fig. 5.8 Modified Thevenin model 5.1.3.5 Thevenin Battery Model
out in order to vary the parameters, such as state of charge, current density and temperature.
out in order to vary the parameters, such as state of charge, current density and temperature.
Fig. 5.12 Modified Thevenin equivalent battery model
Fig. 5.12 Modified Thevenin equivalent battery model
Fig. 5.13. Model from a series experimental test [137]
Fig. 5.13. Model from a series experimental test [137]
5.1.5.7 Practical Identification of Battery Impedance In practice, the determination of batteries impedances is often made on stationary batteries. The basic principle is to impose on the battery an excitation in voltage or current [31]. Measurement at weak frequency gives more information on elec- trochemical operation because the internal kinetics of the battery has thus the time
5.1.5.7 Practical Identification of Battery Impedance In practice, the determination of batteries impedances is often made on stationary batteries. The basic principle is to impose on the battery an excitation in voltage or current [31]. Measurement at weak frequency gives more information on elec- trochemical operation because the internal kinetics of the battery has thus the time
Fig. 5.31 Circuit measurement of battery impedances
Fig. 5.31 Circuit measurement of battery impedances
Fig. 5.32 Measured signals S; current and S, voltage
Fig. 5.32 Measured signals S; current and S, voltage
Fig. 6.1 General configuration of a photovoltaic pumping system [62]
Fig. 6.1 General configuration of a photovoltaic pumping system [62]
DC motor and a centrifugal pump. There are two configurations of PV pumping systems based on DC motor. In the first system (Fig. 6.2), the motor could be connected directly to the PV generator. For allowing operation of the pumping system at maximum power, the motor controller has to be able to perform the tracking of the MPP. eee — =e eae “ s a
DC motor and a centrifugal pump. There are two configurations of PV pumping systems based on DC motor. In the first system (Fig. 6.2), the motor could be connected directly to the PV generator. For allowing operation of the pumping system at maximum power, the motor controller has to be able to perform the tracking of the MPP. eee — =e eae “ s a
Fig. 6.3 Photovoltaic system loaded by DC motor via DC—DC buck-boost converter Fig. 6.4 Equivalent circuit of DC Shunt motor
Fig. 6.3 Photovoltaic system loaded by DC motor via DC—DC buck-boost converter Fig. 6.4 Equivalent circuit of DC Shunt motor
The dynamical model of DC shunt motor can be written as
The dynamical model of DC shunt motor can be written as
The nonlinear dynamical mathematical model is given by:
The nonlinear dynamical mathematical model is given by:
6.2 PV Pumping Systems Based on AC Motor
6.2 PV Pumping Systems Based on AC Motor
Fig. 6.10 RMSE and MBE results for the centrifugal pumps C, [62]
Fig. 6.10 RMSE and MBE results for the centrifugal pumps C, [62]
Fig. 6.11 RMSE and MBE results for the centrifugal pumps C, [62]
Fig. 6.11 RMSE and MBE results for the centrifugal pumps C, [62]
We obtain the following mathematical model:
We obtain the following mathematical model:
with L,, as the magnetizing inductance of the motor and L, and L, are the stator and rotor inductances and
with L,, as the magnetizing inductance of the motor and L, and L, are the stator and rotor inductances and
Fig. 6.16 RMSE and MBE results for the centrifugal pumps D, [62]
Fig. 6.16 RMSE and MBE results for the centrifugal pumps D, [62]
Fig. 6.18 Subsystem of an IM fed by an MLI inverter
Fig. 6.18 Subsystem of an IM fed by an MLI inverter
The undesirable harmonics of a square wave can be eliminated and the funda- mental voltage component can be controlled as well by what is known as the harmonic elimination method. In this method, notches are created in the square wave at predetermined angles (Fig. 6.19). It can be shown that the notch angles can be controlled to eliminate certain harmonic components and control the fun- damental voltage [158].
The undesirable harmonics of a square wave can be eliminated and the funda- mental voltage component can be controlled as well by what is known as the harmonic elimination method. In this method, notches are created in the square wave at predetermined angles (Fig. 6.19). It can be shown that the notch angles can be controlled to eliminate certain harmonic components and control the fun- damental voltage [158].
Fig. 6.20 Angles notches for different harmonic ranks
Fig. 6.20 Angles notches for different harmonic ranks
Then, the following system of transcendental equations is obtained: In a quarter-cycle symmetrical waveform, only the sine odd harmonics exist. Therefore, the coefficients are given by:
Then, the following system of transcendental equations is obtained: In a quarter-cycle symmetrical waveform, only the sine odd harmonics exist. Therefore, the coefficients are given by:
minimization PWM technique. In this method, the total harmonic voltage distor- tion factor (THD) is minimized. The minimization of this quantity and the control of the fundamental are achieved by an appropriate positioning of the switching angles. Considering that higher harmonics are easier to filter, we take into account harmonics until nth with a weigh decreasing with frequency. The THD perfor- mance factor is then defined as:
minimization PWM technique. In this method, the total harmonic voltage distor- tion factor (THD) is minimized. The minimization of this quantity and the control of the fundamental are achieved by an appropriate positioning of the switching angles. Considering that higher harmonics are easier to filter, we take into account harmonics until nth with a weigh decreasing with frequency. The THD perfor- mance factor is then defined as:
X» = , L, the magnetizing reactance (Q), w, the angular frequency of the supply (rd/s), @-ac the motor speed (rd/s) and ea eee es lr eee Assuming thatR,, is infinite, the stator current 7, and the rotor current J, in the elements X, and R,/g are related by the phasorial expression
X» = , L, the magnetizing reactance (Q), w, the angular frequency of the supply (rd/s), @-ac the motor speed (rd/s) and ea eee es lr eee Assuming thatR,, is infinite, the stator current 7, and the rotor current J, in the elements X, and R,/g are related by the phasorial expression
Fig. 6.22 Induction motor equivalent circuit
Fig. 6.22 Induction motor equivalent circuit
Fig. 6.26 Vector control of the PV pumping system based on induction machine
Fig. 6.26 Vector control of the PV pumping system based on induction machine
Power converted in mechanical power, stator current and stator power will be:
Power converted in mechanical power, stator current and stator power will be:
6.2.4 Vector Control of the PV System Based on Induction Machine
6.2.4 Vector Control of the PV System Based on Induction Machine
Fig. 6.27 Block diagram of the conventional direct torque control of induction motor drives Table 6.2 Switching table for the conventional DTC A configuration of the DTC scheme is represented in Fig. 6.27. In this system the instantaneous values of flux and torque can be calculated from stator variables and mechanical speed or using only stator variables. Stator flux and torque can be controlled directly and independently by properly selecting the inverter switching configurations. With a three-phase voltage source inverter, six non-zero voltage vectors and two zero-voltage vectors can be applied to the machine terminals. The stator flux can be estimated using measured current and voltage vectors
Fig. 6.27 Block diagram of the conventional direct torque control of induction motor drives Table 6.2 Switching table for the conventional DTC A configuration of the DTC scheme is represented in Fig. 6.27. In this system the instantaneous values of flux and torque can be calculated from stator variables and mechanical speed or using only stator variables. Stator flux and torque can be controlled directly and independently by properly selecting the inverter switching configurations. With a three-phase voltage source inverter, six non-zero voltage vectors and two zero-voltage vectors can be applied to the machine terminals. The stator flux can be estimated using measured current and voltage vectors
Fig. 6.30 Simulation diagram of stator flux control
Fig. 6.30 Simulation diagram of stator flux control
Fig. 6.31 Simulation diagram of the electromagnetic torque control
Fig. 6.31 Simulation diagram of the electromagnetic torque control
Fig. 6.33 Evolution of the torque, speed, stator current and stator flux with a speed reference 6.2.5.4 DTC of IM Fed by a PV Generator
Fig. 6.33 Evolution of the torque, speed, stator current and stator flux with a speed reference 6.2.5.4 DTC of IM Fed by a PV Generator
Fig. 6.34 Simulation of direct torque control of the induction generator fed by PV generator
Fig. 6.34 Simulation of direct torque control of the induction generator fed by PV generator
Fig. 6.37 Maximum power point tracking with DC motor
Fig. 6.37 Maximum power point tracking with DC motor
Fig. 6.38 Maximum Power Point Tracking with AC motor
Fig. 6.38 Maximum Power Point Tracking with AC motor
Fig. 6.39 Working parameters of three-pumps with a total head of 20 m [62]
Fig. 6.39 Working parameters of three-pumps with a total head of 20 m [62]
Fig. 6.45 Water produced by 1000 pumps of type C. with an average working time of 5 h, an input power of 950 W at different heads
Fig. 6.45 Water produced by 1000 pumps of type C. with an average working time of 5 h, an input power of 950 W at different heads
Fig. 7.3. Configuration of the hybrid system with DC and AC buses
Fig. 7.3. Configuration of the hybrid system with DC and AC buses
Table 7.1 Classification of hybrid systems by power range [194]
Table 7.1 Classification of hybrid systems by power range [194]
Fig. 7.4 Block diagram of the hybrid photovoltaic/diesel generator system
Fig. 7.4 Block diagram of the hybrid photovoltaic/diesel generator system
fig. 7.5 Centralized AC bus architecture
fig. 7.5 Centralized AC bus architecture
Fig. 7.8 Wind turbine [185]
Fig. 7.8 Wind turbine [185]
Fig. 7.7 Centralized DC bus architecture The mechanical speed evolution is determined from the total torque Tyec applied to the electrical generator rotor
Fig. 7.7 Centralized DC bus architecture The mechanical speed evolution is determined from the total torque Tyec applied to the electrical generator rotor
Induction machines are largely used in the field of wind energy conversion. Fo! standalone operations, the squirrel induction machine is preferred because it is robust, needs little maintenance and does not need an auxiliary supply for mag. netizing it. The simplest way to use it as an autonomous generator consists ir connecting its stator windings to a capacitor bank in parallel to the load. The remaining magnetic flux, added to the magnetizing current through the capacito: bank yields the built up of the electromotive force and its increase to a usefu value. This approach is very cheap and is well adapted to convert the wind energy into an electrical one for isolated areas or areas faraway from the distribution gric
Induction machines are largely used in the field of wind energy conversion. Fo! standalone operations, the squirrel induction machine is preferred because it is robust, needs little maintenance and does not need an auxiliary supply for mag. netizing it. The simplest way to use it as an autonomous generator consists ir connecting its stator windings to a capacitor bank in parallel to the load. The remaining magnetic flux, added to the magnetizing current through the capacito: bank yields the built up of the electromotive force and its increase to a usefu value. This approach is very cheap and is well adapted to convert the wind energy into an electrical one for isolated areas or areas faraway from the distribution gric
Table 7.2 The different combinations
Table 7.2 The different combinations
Fig. 7.11 Supervisor of hybrid wind/photovoltaic/ diesel generator system
Fig. 7.11 Supervisor of hybrid wind/photovoltaic/ diesel generator system
Fig. 7.14 Hybrid wind/photovoltaic system
Fig. 7.14 Hybrid wind/photovoltaic system
Fig. 7.15 Daily consumption profile of a rural house [9]
Fig. 7.15 Daily consumption profile of a rural house [9]
Fig. 7.17 Areas of photovoltaic panels and wind turbines
Fig. 7.17 Areas of photovoltaic panels and wind turbines
Fig. 7.18 Number of photovoltaic panels and wind turbines as a function of the fraction of the load
Fig. 7.18 Number of photovoltaic panels and wind turbines as a function of the fraction of the load
Fig. 7.19 Characteristic Ipy(Vpy) panel with photovoltaic power Reference P,.¢ , produced [9]
Fig. 7.19 Characteristic Ipy(Vpy) panel with photovoltaic power Reference P,.¢ , produced [9]
Fig. 7.21 Characteristic Pw(@) with photovoltaic power Reference Pref py produced (Case 3)
Fig. 7.21 Characteristic Pw(@) with photovoltaic power Reference Pref py produced (Case 3)
7.3.3.4 Application of the Control of Hybrid Photovoltaic/Wind System
7.3.3.4 Application of the Control of Hybrid Photovoltaic/Wind System
7.3.4 Hybrid Photovoltaic/Wind//Hydro/Diesel System
7.3.4 Hybrid Photovoltaic/Wind//Hydro/Diesel System
Fig. 7.24 Profile of wind speed (V,,) for a day. a Summer day. b Winter day
Fig. 7.24 Profile of wind speed (V,,) for a day. a Summer day. b Winter day
Fig. 7.25 Photovoltaic power output, maximum (Ppy max) and reference power (Prefs). a Summer day. b Winter day
Fig. 7.25 Photovoltaic power output, maximum (Ppy max) and reference power (Prefs). a Summer day. b Winter day
Fig. 7.26 Wind power output, maximum (Py max) and its reference (Prep w). a Summer day. b Winter day
Fig. 7.26 Wind power output, maximum (Py max) and its reference (Prep w). a Summer day. b Winter day
Fig. 7.29 Total power required, power output (Pw + Ps) and power supplied by batteries. a Summer day. b Winter day Fig. 7.28 Power supplied by batteries. a Summer day. b Winter day
Fig. 7.29 Total power required, power output (Pw + Ps) and power supplied by batteries. a Summer day. b Winter day Fig. 7.28 Power supplied by batteries. a Summer day. b Winter day
Fig. 7.30 Description of hybrid photovoltaic/wind//hydro/diesel system
Fig. 7.30 Description of hybrid photovoltaic/wind//hydro/diesel system
Fig. 7.32 Description of a hybrid photovoltaic-Electrolyzer-fuel cell System [193]
Fig. 7.32 Description of a hybrid photovoltaic-Electrolyzer-fuel cell System [193]
Fig. 7.34 Description of a hybrid photovoltaic-Electrolyzer-fuel cell system with DC indirect coupling Fig. 7.33 Description of a hybrid photovoltaic-Electrolyzer-fuel cell system with DC direct coupling
Fig. 7.34 Description of a hybrid photovoltaic-Electrolyzer-fuel cell system with DC indirect coupling Fig. 7.33 Description of a hybrid photovoltaic-Electrolyzer-fuel cell system with DC direct coupling
Fig. 7.35 Description of a hybrid photovoltaic-Electrolyzer-fuel cell system with AC coupled 1193]
Fig. 7.35 Description of a hybrid photovoltaic-Electrolyzer-fuel cell system with AC coupled 1193]
with Py = Patm as the initial condition. Fig. 7.38 Cathode model
with Py = Patm as the initial condition. Fig. 7.38 Cathode model
Fig. 7.48 Solar-wind-hydrogen energy cycle
Fig. 7.48 Solar-wind-hydrogen energy cycle
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