# MPPT Control Systems for PV Power Plants

Shailendra Rajput and Moshe Averbukh

Ariel University, Ariel, Israel

## Introduction

### Economic Aspects of PV Power Sources

Solar energy production has increased substantially during the past decade (Figure 1.1). This significant growth is because this is one of the cheapest sources of electricity. Graphical representations of price declination for 1 MWh of power from PV models, compared with other energy sources, can explain this situation. In 2014-2015, PV electricity cost achieved grid-parity; nowadays, they are 1.2-2.5 times cheaper than electricity from other types of energy plants. Owing to this tendency of reduced PV prices, the solar electricity market is a fast-growing trading sector in the global economy and is, today, estimated at more than $10 billion/year, with the increasing potential of further increase. Most economic prognoses predict further continuation in price reduction that makes PV solar electricity the most outstanding and the most promising of power sources in the near future (Figure 1.2).

FIGURE 1.1 Relative growth of solar electricity production during the past decade [1].

FIGURE 1.2 The cost reduction of PV modules per watt of power [2].

### Major Requirements for PV Facilities Control

The most common request for facilities control can be expressed by the economic reason assuming a minimum of Levelized Cost of Electricity (LCOE) [3]:

The numerator of the expression (1.1) represents some constant and negligibly variable parameters. The denominator represents, the total lifetime of PV modules, which is accounted for today as ~25 years of service life. The service life of PV modules depends not only on the semiconductor manufacturing technology, but environmental

FIGURE 1.3 Typical I-V and P-I curves of the PV module.

conditions also affect the service life of PV modules. Consequently, total life costs (including the initial cost, transportation, installation, and maintenance) may be assumed as a constant value. Therefore, the LCOE is mainly influenced by the total lifetime energy, which should be maximized to achieve minimum LCOE.

Output characteristics of both the PV module and the load are necessary to determine the real electricity production. It is well known that PV cells generate DC current. Hence, a special DC-AC inverter should be applied to use the AC load in modern networks. Taken together, all of this leads to the need to estimate the PV plant’s functionality connected to variable loads. An analytical description of the output characteristics of PV modules is required.

### PV Characteristics

Typical output characteristics of the PV module are presented in Figure 1.4. It can be seen that the output power depends on solar irradiation and temperature. PV systems follow the law of energy conservation. Power is a derivative of the solar energy that is converted to electrical energy using the principles of semiconductors.

The variable *I-V* curve points out that power generation from the PV modules does not remain constant. PV power depends not only on the solar intensity and temperature but also on the characteristics of load. The operating point representing the voltage-current combination is at the intersection of the panel, and load characteristics determine output, and the power should be maximized. The operating or working point can be found graphically or analytically to solve the equation of output characteristics (/ = *f(V))* for the PV module and for a given load. The analytical solution requires strict description of a function *I = f(V)* for a module. The equivalent PV circuit can utilized for this purpose. There are different representations of the equivalent circuit [5]. Two types of equivalent circuits are mostly used: single-diode and double-diode models (Figure 1.5a and b).

FIGURE 1.4 Typical output characteristics of the PV module (a) for different temperatures, (b) for different solar irradiations.

FIGURE 1.5 (a) Single-diode equivalent circuit, and (b) double-diode equivalent circuit

*(Ip.* photocurrent proportion to solar intensity and temperature, *l _{D}:* diode current,

*K*

_{s}, K_{sh}:serial and shunt equivalent resistances).

The equivalent circuit is analyzed using the Kirchhoff circuit law. For a singlediode circuit,

where /, is the load current, *l _{Dl}* is the diode current, and

*IsH*is the current of the shunt resistance. The diode current is expressed using the Shockley equation:

where *I _{S}p, V_{h} a_{t}, k_{B}, T* and

*q*are the reverse saturation current, cell output voltage, diode constant, Boltzmann constant (1.3806503 x 10

^{23}J/K), junction temperature (K), and the electron charge (1.60217646 x 10~

^{I9}C), respectively. The current in shunt resistance is given by:

After combining equations (1.2)—(1.4), we get:

The expression (1.5) represents the output characteristic of the PV module. For double-diode circuit, Equations (1.2) can be written as:

Further,

where /_{л/>|} and I_{S}d_{2} represent the diffusion and saturation current, respectively. *I _{Dl}* and Id, represent the first and double diode current.

*I,*and

*V,*characterize the module output as variable parameters. Other parameters must be determined and assessed before the application of Equations (1.5) and (1.7). There are plenty of literature resources dedicated to this purpose [6-8]. The operating point depends on the parameters of the load and the current characteristic of the PV module and can be positioned in each place on the

*I-V*curve. There is a special point

*{V*at which the output power becomes maximum (

_{mpp},I_{mpp})*P*

_{mpp}). The optimal parameters

*(v*,„

_{mpp}, I_{pp}) constantly change depending on the intensity of the solar irradiation, the temperature changes through the day, and the variation in intensity in different seasons in a year. The PV facilities should be connected with an electronic control circuit to generate maximum energy. For example, the DC-DC converter matches the load to the PV module and ensures maximum power generation from PV modules. In other words, the operating point changes corresponding to the variability of the MPP location. These electronic devices ensure maximum power in each moment and is hence called the maximum power point tracker (MPPT). All these electronic devices are designed using the DC-DC converters. However, they are based on different functional algorithms and different circuit topologies.

### Presence of Single and Multiple Maximum Points

The typical PV module has a restricted outcome with a maximum voltage of ~40V and a current of ~8—10 A. Several modules are connected serially in an array to provide significantly more power. Further, such arrays may be oriented or arranged in parallel strings connected to an MPPT. The array characteristics of an «-serially connected PV module array may differ significantly from those of the individual module. If the PV array comprises evenly irradiated individual modules, the output characteristic has one maximum only (Figure 1.4). However, a large array with tens of PV modules may be irradiated unevenly. Such events take place during cloudy weather when some of the modules can be shadowed. Those modules that received lower dose of irradiation prevent nominal current flow leading to diminished photocurrent (Figure 1.5). Therefore, the simple design of the «-serially connected PV module array is not applicable because the output power drops drastically for uneven irradiations. To prevent such shortcomings, each module is equipped with a bypass diode to avoid any disadvantages arising due to partial shading (Figure 1.6). If some modules are illuminated weakly, then the photocurrent *(l _{ph})* decreases significantly.

FIGURE 1.6 «-Serially connected PV modules represented by the equivalent circuit and equipped with bypass diodes (*D*_{hp}).

FIGURE 1.7 The presence of local maxima in the characteristic of the unevenly irradiated solar array.

However, the array continues to supply nominal current to bypass the weak module through the bypass diode. This solution allows for the continuation of the electrical power from normally irradiated modules. As a result, the output voltage and characteristics of the array are changed so that instead of a single maximum, several maxima (two, three, or more) can appear in the output characteristic (Figure 1.7). A detailed explanation for the presence of multiple maxima is obtained by considering the simplified equivalent circuits of PV modules [9]. It should be emphasized that single or plural maxima for the MPPT algorithms is important. The control system must find the global maximum (GM) and then keep operating on it.