Power Electronics Converters and their Control for Renewable Energy Applications

Power Electronics Converters and their Control for Renewable Energy Applications provides information that helps to solve common challenges with power electronics converters, including loss by switching, heating of power switches, management of switching time, improvement of the quality of the signals delivered by power converters, and improvement of the quality of energy produced by renewable energy sources.

This book is of interest to academics, researchers, and engineers in renewable energy, power systems, electrical engineering, electronics, and mechanical engineering.

• Includes important visual illustrations and imagery of concise circuit schematics and renewable energy applications
• Features a templated approach for step-by-step implementation of the new MPPT algorithm based on recent and intelligent techniques
• Provides methods for optimal harnessing of energy from renewable energy sources and converter topology synthesis 

• Language: English
• Publisher: Academic Press
• Release date: Jun 21, 2023
• ISBN: 9780323914031

Book preview

Chapter 1

Control of grid-connected photovoltaic system

A. Alazrag¹, Lassaad Sbita¹ and Arezki FEKIK²,³,    ¹Process Laboratory, Energetic, Environment and Electrical System, National Engineering School of Gabés (ENIG), University of Gabés, Tunisia, Gabés,    ²Department of Electrical Engineering, University Akli Mohand Oulhadj-Bouria, Bouira, Algeria,    ³Automated Systems Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia

Abstract

In this chapter, we are interested to study the mathematical model of the PV cell, the PV generator, and their characteristics. Then, the control algorithm of the proposed system is detailed. The use of the newest power control mechanism called the maximum power point tracking (MPPT) algorithms leads to the increase in the efficiency of operation of the solar PV array and is effective in the field of utilization of renewable sources of energy. MPPT algorithm controls the power converters to continuously detect the instantaneous maximum power of the PV array. An intelligent method is here applied in the MPPT controller due to its simplicity and easy implementation. The grid-connected PV systems consist of the bidirectional inverter, PV panels, DC–DC inverter system, and AC–DC inverter. A bidirectional interface is made between the PV system and the utility power output with the application of an inverter. Consequently, the performance of the inverters connected to the grid depends largely on the control strategy applied. This chapter presents a comprehensive overview of power converter topologies and control structures for grid-connected PV systems.

The obtained simulation results upon simulation tests of the global system are developed under MATLAB/Simulink environment and are satisfactory.

Keywords

Photovoltaic systems; boost converter; DC–AC converters; fuzzy; MPPT; PLL; filter; grid side; PV; battery; boost; DC–AC; inverter control

Chapter Outline

Outline

1.1 Introduction 1

1.2 PV array characteristics 2

1.2.1 Basic principle of PV cell 2

1.2.2 Photovoltaic module 2

1.3 Modeling of a photovoltaic generator 4

1.3.1 Ideal PV cell 5

1.3.2 Real PV 5

1.3.3 Short-circuit current 6

1.3.4 Open circuit 6

1.3.5 Optimum power 7

1.3.6 Characteristics of PV cell 7

1.3.7 Influence of illumination and temperature on the PV characteristics 7

1.4 DC–DC converter 10

1.4.1 Boost converter 10

1.4.2 DC bus voltage regulation 13

1.5 DC–DC bidirectional converter 14

1.5.1 Boost-mode operation 16

1.5.2 Buck-mode operation 16

1.6 Three-phase inverter 16

1.6.1 Space vector modulation 16

1.7 Control strategy 18

1.7.1 Grid current and voltage control 18

1.7.2 Quadratic DC bus control 20

1.7.3 Three-phase phase-locked loop in the Park area 21

1.7.4 Filter technology 22

1.8 Simulation results and discussion 23

1.9 Conclusion 28

References 28

1.1 Introduction

The worldwide growth of energy demand and the finite reserves of fossil fuel resources have led to the intensive use of renewable energy sources (RESs). Other major issues that have driven strongly the RES development are the ever-increasing impact of energy technologies on the environment and the fact that RESs have become today a mature technology. The necessity for having available sustainable energy systems for substituting gradually conventional ones requires changing the paradigm of energy supply by utilizing clean and renewable resources of energy. Among renewables, solar energy characterizes as a clean, pollution-free, and inexhaustible energy source, which is also abundantly available anywhere in the world. These factors have contributed to make solar energy the fastest-growing renewable technology in the world (Ehsan & Yang, 2018). At present, photovoltaic (PV) generation is playing a crucial role as a solar-based RES application because of unique benefits such as the absence of fuel cost, high reliability, simplicity of allocation, low maintenance, and lack of noise and wear because of the absence of moving parts. In addition to these factors are the decreasing cost of PV panels, the growing efficiency of solar PV cells, manufacturing technology improvements, and economies of scale (Alik & Jusoh, 2017; Fekik, Hamida, Denoun, et al., 2022; Fekik, Hamida, Houassine, et al., 2022; Hamida et al., 2022; Rojas et al., n.d.). PV power generation can be considered as the most promising, widely available, and essential renewable resource. On the other hand, the variable behavior of solar irradiation and, consequently, PV generation renders energy storage important for overcoming several problems that arise in the grid. The integration of PV systems into the grid is becoming today the most important application of PV systems, gaining interest over traditional stand-alone autonomous systems. This trend is being increased due to the many benefits of using RES in distributed (also known as dispersed, embedded, or decentralized) generation (DG) power systems (Ahmed & Salam, 2015; Yazdani & Dash, 2009). These advantages include the favorable fiscal and regulatory incentives established in many countries that influence straightforwardly the commercial acceptance of grid-connected PV systems. In this sense, the growing number of distributed PV systems brings new challenges to the operation and management of the power grid, especially when this variable and intermittent energy source constitute a significant part of the total system generation capacity (Al-Diab & Sourkounis, 2010). This new scenario imposes the need for an effective design and performance assessment tool for grid-connected PV systems, so as to predict accurately their dynamic performance under different operating conditions in order to make a sound decision on whether or not to incorporate this technology into the electric utility grid. This implies not only to identify the current–voltage (I-V) characteristics of PV modules or arrays but also the dynamic behavior of the power electronics interface with the utility grid, also known as photovoltaic power conditioning system (PCS) or PV PCS, required to convert the energy produced into useful electricity and to provide requirements for connection to the grid. This PV PCS is the key component that enables to provide a more cost-effective harvest of energy from the sun and to meet specific grid code requirements. These requirements include the provision of high levels of security, quality, reliability, availability, and efficiency of electric power. Moreover, modern DG applications are increasingly incorporating new dynamic compensation issues, simultaneously and independently of the conventional active power exchange with the utility grid, including voltage control, power oscillations damping, power factor correction, and harmonics filtering. This tendency is estimated to augment even more in future DG applications (Debnath & Chatterjee, 2015). Additionally, energy storage technologies can allow various applications in a system that may not be possible for a single storage technology. In this paper, a control of a PV system connected to the grid is presented. The main components of the studied system are solar arrays connected through a DC bus to a grid-side inverter. Due to the instantaneous changes in solar irradiance and temperature, maximum power point tracking (MPPT) is integrated into the inverter control. This point is called the point of maximum power (MPP). Thus, to operate the PV generator at its maximum power point, different algorithms can be used (Colin, 2003). Among digital MPPT techniques, perturb and observe (P&O) is used to find the point MPP (Camilo et al., 2019; Guichi et al., 2018). The input of P&O is error; the output is the duty ratio of DC–DC converter or its variation. The battery is connected to the DC bus through bidirectional DC–DC converters (Bharath et al., 2018; Li & Shi, 2019). The energy generated by the grid PV system is sent to the grid. This is accomplished through an efficient DC–AC conversion where the MPPT is integrated into the inverter to control active and reactive power levels injected into the grid. The modeling and simulation of the three-phase grid-connected PV generating system in the MATLAB®/Simulink environment allow design engineers to take advantage of the capabilities for control design and electric power systems modeling already built up in specialized toolboxes and block sets of MATLAB and in dedicated block libraries of Simulink. These features allow assessing the dynamic performance of detailed models of grid-connected PV generation.

1.2 PV array characteristics

1.2.1 Basic principle of PV cell

A solar cell (also known as a photovoltaic cell or PV cell) is defined as an electrical device that converts light energy into electrical energy through the PV effect. A solar cell is basically a p-n junction diode. Solar cells are a form of photoelectric cell, defined as a device whose electrical characteristics—such as current, voltage, or resistance—vary when exposed to light as shown in Fig. 1.1 (Jain et al., 2018; Kumar & Singh, 2021; Poonahela et al., 2021).

Figure 1.1 Principle of production of photovoltaic solar energy.

These electrodes do not obstruct light to reach the thin p-type layer. Just below the p-type layer, there is a p-n junction. We also provide a current-collecting electrode at the bottom of the n-type layer. We encapsulate the entire assembly with thin glass to protect the solar cell from any mechanical shock.

When light reaches the p-n junction, the light photons can easily enter the junction, through very thin p-type layer. The light energy, in the form of photons, supplies sufficient energy to the junction to create a number of electron–hole pairs. The incident light breaks the thermal equilibrium condition of the junction. The free electrons in the depletion region can quickly come to the n-type side of the junction (Liu et al., 2021; Teng et al., 2018).

1.2.2 Photovoltaic module

Photovoltaic modules, commonly known as solar panels, are a web that captures solar power to transform it into sustainable energy. A semiconductor material, usually silicon, is the basis of each individual solar cell. It is light-sensitive and generates electricity when struck by the rays of the sun thanks to a physical phenomenon called the PV effect. The module is encapsulated with tempered glass (or some other transparent material) on the front surface and with a protective and waterproof material on the back surface. The edges are sealed for weatherproofing, and there is often an aluminum frame holding everything together in a mountable unit. In the back of the module, there is a junction box, or wire leads, providing electrical connections. In our work, we will use a group of 11 modules in parallel and 21 in series to have a maximum power of 53 kW at 1000 W/m² and 25°C with an optimal current equal to 62.48 A and an optimal voltage equal to 850.5 VA. Photovoltaic generator (GPV) consists mainly of a set of PV cells () arranged in series () and parallel () as shown in Fig. 1.2.

Figure 1.2 Structure of a photovoltaic field.

The PV generator can be characterized by its current–voltage curve, often called "characteristic I=f(V) and P=(V)." Fig. 1.3 ensures the extraction of the optimal power from the PV generator.

Figure 1.3 Characteristic of PV module.

In our work (see Fig. 1.4), we are interested in the PV system connected to the network which consists mainly of a PV generator and a step-up chopper for the extraction of maximum power and a two-level inverter for the injection of PV power to the electrical network.

Figure 1.4 PV system configuration.

1.3 Modeling of a photovoltaic generator

A photovoltaic generator comprises several cells connected in parallel and series combination. Parallel combination of PV cells is responsible for increasing the current, and series connectivity is accountable for increasing the voltage of the PV array.

1.3.1 Ideal PV cell

The use of a single-diode equivalent electric circuit makes it possible to model the characteristics of a PV cell. The mathematical model of a PV cell can be developed using MATLAB/Simulink. The basic equation from the theory of semiconductors that mathematically describes the I-V characteristic of the ideal PV cell is given by Shihab and Rasheed (2019):

(1.1)

(1.2)

(1.3)

Then:

(1.4)

where iph: photocurrent, Icc: short-circuit current of the cell under the standard conditions reference (Eref and Tref), E: sunshine received by the cell (W/m²), Eref: reference sunshine, Kicc: current short-circuit temperature coefficient (A/°C), : thermodynamic potential, Is: inverse current saturation of the diode, q: charge of an electron, KB: constant of Boltzmann, Tj: temperature of the junction (°C), n n: ideal factor of the solar cell.

Fig. 1.5 shows the equivalent circuit of ideal PV cell.

Figure 1.5 Equivalent circuit of ideal PV cell.

The I-V curve is shown in Fig. 1.6.

Figure 1.6 Evolution of the current according to ideal photovoltaic cell voltage.

1.3.2 Real PV

The equivalent electrical circuit of a single PV cell is illustrated in Fig. 1.7. A single PV cell can be represented by a diode connected in parallel with a source of current. It also has series and parallel resistances. The shunt resistance Rsh as in (Ehsan & Yang, 2018) is added due to the recombination or leakage of electrons at the junction of the diode, and the series resistance Rs as in (Ehsan & Yang, 2018) is added for the compensation of junction resistance.

Figure 1.7 Equivalent model of a real cell.

The PV cell output in the form of current Ip is given by:

(1.5)

And

(1.6)

From (1.5) and (1.6), we get:

(1.7)

1.3.3 Short-circuit current

This is the current supplied by the PV cell (see Fig. 1.8) when it has a voltage equal to zero terminals Vp=0 V.

Figure 1.8 Real cell in short circuit.

The short-circuit current delivered by the PV cell is described by the following relation:

(1.8)

Where the series resistance of the cell is low, the short-circuit current is deduced from this relation:

(1.9)

1.3.4 Open circuit

This is the voltage delivered by the PV cell when it does not deliver any current. In these conditions, we write:

(1.10)

Voc is given according to this relation:

(1.11)

1.3.5 Optimum power

This is the power supplied by the PV cell when the latter delivers a current optimum Iop under optimum tension Vop:

(1.12)

1.3.6 Characteristics of PV cell

To use the cells in a PV system, it is necessary to associate them in series to increase the voltage. The current is fixed by the surface of each elementary cell but also by the number of cells in parallel. This series–parallel association must be done following precautions because, even if the cells are identical, there are dispersions at the level of their internal parameters. Adding a silicon cell in series corresponds to an increase in total voltage of about 0.6 V (junction voltage). In a series grouping, the cells are crossed by the same current, and the resulting characteristic of the grouping is obtained by the addition of the voltages at a given current (see Fig. 1.9).

Figure 1.9 Characteristics of PV module in series association.

For an association in parallel, we have a dual operation of that of the association in series, and its characteristic is presented in Fig. 1.10.

Figure 1.10 Characteristics of PV module in parallel association.

Finally, the characteristic of a series–parallel association is presented in Table 1.1.

Table 1.1

The curve has three important parameters, namely, open-circuit voltage (Voc), short-circuit current (Isc), and maximum power point (MPP). In this model, single-diode equivalent circuit is considered. The I-V characteristic of the PV device shown in Fig. 1.11 depends on the internal characteristics of the device and external influences such as irradiation level and temperature.

Figure 1.11 I-V characteristics of the PV cell.

1.3.7 Influence of illumination and temperature on the PV characteristics

The electrical characteristic of a PV array varies according to temperature, illumination, internal parameters, and generally the nature of the connected load. We have simulated the behavior of the generator under various constraints. These concepts are indeed necessary to understand the behavior of a PV array. We vary the illumination between 400 and 1000 W/m² and a constant temperature of 25°C. The influence of illumination on I=f (V) and P=f (V) is shown in Fig. 1.12.

Figure 1.12 The influence of illumination on the I=f (V) and P=f (V).

Regarding the variation of the illumination, we note that for a temperature of 25°C, the increase in irradiance leads to an increase in maximum power and a slight increase in open-circuit voltage. The short-circuit current increases dramatically with increasing illumination. This implies that the optimal power generator is almost proportional to the illumination. By varying the temperature between 20°C and 40°C under an irradiance of 1000 W/m², we can see in Fig. 1.13 the influence of temperature on the characteristics I=f (V) and P=f (V).

Figure 1.13 Influence of temperature on the characteristics I=f (V) and P=f (V).

The open-circuit voltage decreases significantly with increasing temperature as the maximum power. By constant, we notice a slight increase in short-circuit current with increasing temperature. For a temperature change, we deduce that the voltage changes significantly while the current remains constant. To get a maximum return, it is essential to work in the area of maximum power of the PV generator. For this, we used a research strategy placed in this area (Ahmed & Salam, 2015). Hence, there is a need to introduce a power converter which will play the role of load source adapter.

The total current output by PVG is described by the relation (1.13):

(1.13)

If one takes into account that the series resistance is infinitely small while the shunt resistance is relatively important, we then write:

(1.14)

The optimum power of a PV generator is followed by this expression:

(1.15)

It is then necessary to look for the coordinates of the point which verifies the following condition:

(1.16)

Then deducing, the optimum point has coordinates:

(1.17)

1.4 DC–DC converter

A DC–DC converter is an electronic circuit which converts a source of direct current (DC) from one voltage level to another (Chen et al., 2021; Rao et al., 2018). The DC–DC converters are widely used in regulated switch-mode DC power supplies and in DC motor drive applications. Switch-mode DC–DC converters are used to convert the unregulated DC input into a controlled DC output at a desired voltage level. The heart of MPPT hardware is a switch-mode DC–DC converter. MPPT uses the converter for a different purpose: regulating the input voltage at the PV MPP and facilitating load matching for maximum power transfer. A switching converter consists of capacitors, inductors, and switches. All these devices ideally do not consume any power, resulting in high efficiencies of switching converters.

If the device is in the ON state, the voltage drop across it will be close to zero, and hence, the dissipated power will be very small. During the operation of the converter, the switch will be switched at a constant.

1.4.1 Boost converter

Boost converter is also called as step-up converter circle in blue color in Fig. 1.14. It converts low input voltage to high output voltage. It functions like a reversed buck converter (Colin et al., 2010; Rekioua & Matagne, 2012). Boost converter circuit consists of inductor, diode, switch, and capacitor. By making the switch ON and OFF periodically, the boost converter works. When the switch is ON, the inductor stores the energy, and when the switch is OFF, the sum of inductor energy and supply appears at the output.

Figure 1.14 Boost converter.

The key principle that drives the boost converter is the tendency of an inductor to resist changes in current by either increasing or decreasing the energy stored in the inductor magnetic field. In a boost converter, the output voltage is always higher than the input voltage. A schematic of a boost power stage is shown in Fig. 1.14.

1. [0 to DT] When the switch is closed, current flows through the inductor in the clockwise direction, and the inductor stores some energy by generating a magnetic field. Polarity of the left side of the inductor is positive.

(1.18)

2. [DT to T] When the switch is opened, the current will be reduced as the impedance is higher. The magnetic field previously created will be reduced in energy to maintain the current toward the load. Thus the polarity will be reversed (meaning the left side of the inductor will become negative). As a result, two sources will be in series causing a higher voltage to charge the capacitor through the diode.

(1.19)

1.4.1.1 Inductance sizing

The boost output voltage is given by the formula:

(1.20)

where D is the duty cycle.

The inductance value depends on the ripple of the input current. To calculate the minimum value of the inductance, the ripple is considered equal to 5% of the minimum current in this work:

(1.21)

(1.22)

Then:

(1.23)

where T and F are, respectively, the period and frequency of the switching.

1.4.1.2 Boost control

The efficiency of solar cell is very low. In order to increase the efficiency, methods should be undertaken to match source and load properly. One such method is the MPPT. The working is based on the maximum power transfer theorem. The main usage of the MPPT algorithm lies in maximizing the efficiency of energy conversion. The MPPT algorithm tracks the voltage where the power is maximum. The maximum power is traced after a few seconds of time delay. The I-V and P-V curves that define the solar PV panel characteristics pose a nonlinear relationship with temperature and irradiance. The MPPT techniques are incorporated in PV systems so as to ensure maximum power harvest from the solar panels. Yet, on the characteristic curve of the solar panel, a unique point is present where the whole system works with maximum efficiency. This point is referred to as MPP as shown in Fig. 1.3. This point needs to be calculated, traced, and applied with control techniques in order to ensure that the PV system is sustained at this unique point so that maximum power for various applications can be harvested. MPPT is used for sustaining the system at maximum power, obtaining this power from the solar PV module, and then coupling that power to the load (Al-Diab & Sourkounis, 2010; Debnath & Chatterjee, 2015). A DC–DC converter acts as an interface between the load and the module. It is used to fulfill the need of transferring maximum power from the PV module to the load.

The duty cycle D of the boost is controlled through an MPPT algorithm, via an appropriate electrical signal, to extract the maximum power that the PV generator can provide. The MPPT control can be more or less complicated to search for the PPM. In general, it is based on the variation of the boost duty cycle as a function of the evolution of the latter's input parameters (I and V and consequently of the power of the generator) until it is placed on the PPM.

There are many operating principles of more or less efficient MPPT algorithms based on the properties of the PV generator. We are interested to study the P&O algorithm.

1.4.1.3 Principle of perturb and observe commands

The P&O control principle consists in causing a disturbance of low value on the voltage VPV, which generates a variation of the power. Fig. 1.15 shows that if an increase in voltage causes an increase in power, the operating point is to the left of the PPM, and if, on the contrary, the power decreases, it is to the right. In the same way, we can make a reason for a decrease in tension. Then, for a voltage disturbance, if the power increases, the direction of the disturbance is maintained. If not, it is reversed so that the operating point converges to the PPM.

Figure 1.15 P&O algorithm.

Fig. 1.16 illustrates the organigram of P&O control (Fekik, Hamida, Denoun, et al., 2022; Fekik, Hamida, Houassine, et al., 2022). To determine the power at each instant, two sensors are needed to measure the values of voltage and current.

Figure 1.16 Organigram of P&O control.

The size of the DC bus is an essential step in order to implement a control strategy. In fact, to ensure correct operation of the inverter, the DC bus voltage must be greater than the effective value of the composed voltage U at the connection point.

(1.24)

In general, Vdcref is equal to:

(1.25)

It is assumed that the voltage ripples do not exceed 5% of their medium values.

(1.26)

The load provided by the capacitor is given by:

(1.27)

Then:

(1.28)

where

1.4.2 DC bus voltage regulation

PI controller is used for adjusting the voltage of the DC bus. To synthesize this regulator, we will start with the expression of the capacitor current.

(1.29)

By applying the Laplace transform to the previous equation, we get:

(1.30)

The diagram illustrating the regulation of the DC bus voltage is given in Fig. 1.17.

Figure 1.17 DC bus voltage regulation.

The PI controller transfer function is given by the following equation:

(1.31)

The open-loop transfer function of the control system is given by the equation:

(1.32)

The feedback transfer function is:

(1.33)

Then:

(1.34)

Similar form of this equation is:

(1.35)

where ξ represents the amortization coefficient, and ωn represents the proper pulsation of the system.

So by identification, we will have:

(1.36)

1.5 DC–DC bidirectional converter

By analyzing the figure above, we can see in Fig. 1.18 the presence of three specific points on the characteristic (Q-V): these three points are the full load voltage (E0), the voltage corresponding to the end of the exponential zone (Eexp), and the corresponding voltage at the end of the nominal zone (En).

Figure 1.18 Battery discharge curve (Q–V).

The charge and discharge equations are given as follows (Debnath & Chatterjee, 2015):

• Discharge:

(1.37)

• Charge:

(1.38)

where

Fig. 1.19 shows the discharge characteristic of the storage system used and the evolution of its voltage for different discharge currents.

Figure 1.19 Characteristic VB=f(t) for different discharge currents.

The bidirectional DC–DC converter shown in Fig. 1.20 is a combination of boost and buck converters. Such a converter is used to charge and discharge the battery.

Figure 1.20 Circuit of the DC–DC bidirectional converter.

1.5.1 Boost-mode operation

The boost mode is applied for the discharging procedure of the battery storage. The figure shows the circuit of the boost-mode operation of the converter, where the direction of the inductor current is from the lower voltage side to the higher voltage side. The averaged large signal inductor current, iL, and the DC bus output voltage, Vdc, in a continuous conduction mode (CCM) of operation can be found using the equations