*2.1. Case Studies*

In order to carried out a complete technical-economic analysis, four DRS cases have been investigated. The same cases have been studied in [21], but without considering the implications in terms of cost and lifetime of the DRS. The first case under test has been presented in [22]. The authors proposed an optimised switch set (SWS) topology for reconfiguration of PV panels based on a particle swarm optimization (PSO) algorithm. Figure 1 shows the optimised topology structure suggested by the authors, in which there are four lines and ten switches.

**Figure 1.** Optimised topology structure proposed in [22], IET: 2018.

From Figure 1, it is possible to observe that the number of switches *n* for each node *m*, is equal to:

$$m\_{\text{case1}} = m \cdot 10 \tag{1}$$

An interesting low-cost method has been presented in [23]. This method does not require any additional MPPT controllers or sensors and it is based on the use of fuzzy logic (FL) which is used to identify shaded, dirty or faulty panels, to estimate the percentage of shading or dust and to evaluate the minimum and maximum voltage values at which PV panels should be connected/disconnected. The validity of this system has been demonstrated through experimental tests. Figure 2 shows the connection of the system with four panels described in case 2.

**Figure 2.** Topology structures obtained with the method proposed in [23], Elsevier: 2015.

The number of switches required for the case 2 can be evaluated as:

$$m\_{\text{case2}} = m + 6 \tag{2}$$

In [24] a photovoltaic array switching algorithm is presented. This algorithm, in order to find the best configuration of a PV array, is based on the use of only two parameters: the array load voltage and the PV module's temperature. The study has been focused on the evaluation of the performance of four PV modules, as shown in Figure 3.

**Figure 3.** Topology structures obtained with the algorithm proposed in [24], reproduced from the proceedings of the TENCON 2009, IEEE: 2009.

The number of switches necessary in case 3 is equal to:

$$m\_{\text{case3}} = \mathfrak{Z} \times (m - 1) \tag{3}$$

The last case taken into account in this work is presented in [25]. Case 4 is a system configuration approach using an adaptive architecture based on a switching matrix. The adaptive strategy is based on the fact that the switching matrix allows one to rearrange the active PV modules in series into multiple strings to meet the required voltage level. Figure 4 shows the proposed switching matrix of case 4.

Also, in this case, the number of switches of the matrix depends by the number of modules in the PV array. The number of switches can be expressed as:

$$n\_{\text{case4}} = 4 \times (m) + 2 \times (dc) + 2 \times (inv) \tag{4}$$

where the terms 2*dc* and 2*inv* represent the switches to connect the PV array with the inverter and the direct current converter. In the next section, the cost estimation analysis is reported.

**Figure 4.** Switching matrix proposed in [25], reproduced from the proceedings of the IECON 2010, IEEE: 2010.

## *2.2. Costs Estimation of DRS*

The cost of each reconfigurator system has been evaluated on the basis of the direct proportionality between the number of switches composing the system and the cost of the technology needed to produce it.

For each of the four considered reconfiguration cases, a cost estimation of the reconfiguration system has been carried out according to the following procedure: for each case, the required amount of components has been evaluated; after that, for each type of electrical component, a specific item which is available on the market has been chosen, compliant with the technical requirements of the system; finally, for each of the selected components, a price is given, as provided by a major distributor of electronics [26].

Generally, the hardware of a dynamic reconfigurator basically consists of three different parts: the switching matrix, the sensing network and the driving circuit. The switching matrix includes all the switches that are used in the reconfiguration system. Taking into account the solutions available in the market, each switch is generally assembled through two parallel-connected devices: an electromechanical relay and a semiconductor device, e.g., a MOSFET [27,28]. A state-solid relay is a valid alternative as well, but it turns out to be more expensive. Whenever the switch has to be put in the off state, the semiconductor switch is closed as first, so that the electromechanical switch can be switched off at a low voltage. When the switch is on, the electromechanical relay guarantees the conduction losses minimization. In this way, the current breaking capability of the electromechanical switch is fully employed, since it is better to be opened at a quite low voltage. The number of parallel-connected MOSFETs arises from the type of electromechanical switches: one MOSFET has to be connected to one single pole single throw (SPST), whereas two MOSFETs have to be connected to one single pole double throw (SPDT). In Table 1 the chosen electromechanical relays are reported along with their respective prices [26,29,30].



In Table 2 the selected MOSFETs and drivers and respective prices are reported as well [26,31,32].


**Table 2.** MOSFET and driver taken into account.

As far as the sensing network, three types of measurements are generally needed: voltage, current and temperature. In all four cases provided in this paper no irradiance sensor is required. The electronics involved in the voltage sensing circuit are normally very cheap, therefore voltage sensors are not considered in the hardware balance for the sake of simplicity. The selected sensors of temperature and current and their price are reported in Table 3. Note that for the current measurement, the selected sensors are compliant with a 6A rated current [26,33,34].

**Table 3.** Selected sensors for current and temperature.


Table 4 provides the details concerning the number of the different components which should be used in the four considered reconfiguration cases: PV modules (Np), SPST and SPDT switches (NSPST and NSPDT), MOSFETs, drivers and sensors. The total price has been calculated according to the cost tables previously reported.


**Table 4.** Components considered for each case.

Note: Each driver is supposed to drive one MOSFET.

## *2.3. Lifetime Estimation of DRS*

The lifetime of each reconfiguration solution has a significant contribution to the overall economical impact, even though in the scientific literature this aspect is generally neglected [35] Regarding this, the most important issue to be addressed is the lifetime of the relays, due to their mechanical characteristics. Both the electrical and the mechanical endurance are reported in the technical datasheets. Indeed, both the electrical and the mechanical behaviour of the relay are affected by the switching operations. More in detail, the electrical endurance, given by the maximum number of cycles recommended to not affect the electrical behaviour of the relay, is usually much shorter than the maximum number of cycles recommended not to affect the mechanical behaviour. Therefore, being first in the time course, only the electrical endurance has been considered in the overall lifetime estimation.

As reported in the technical datasheets, the maximum number of cycles for the selected SPST switches is 105, whereas for the selected SPDT switches this value is 60 <sup>×</sup> 103 [29,30]. In order to evaluate the actual number of switching operations for each reconfiguration case, the specific algorithm as well as the irradiance conditions should be exactly known. Nevertheless, being these data due to the designer in the first case and unpredictable in the second, a simple approach has been here adopted. Considering NSPST and NSPDT the number of SPST and of SPDT respectively, the probability of a switching operation for each of them has been considered to be 1/NSPST and 1/NSPDT. These are meant to be the probability values whenever the algorithm and the irradiance condition lead to a reconfiguration operation. As far as the hours of sunlight and the frequency of reconfiguration are concerned, two "worst case" values have been considered: 16 h of sunlight and 1 reconfiguration every minute. Even though these values are generally peak values across the whole day, these are meant to be the average values, so that a "worst case" situation is taken into account. In Table 5, the number of considered sunlight hours, the number of considered reconfiguration operations per minute and the electrical endurance of SPST and SPDT are given, referenced as ESPST and ESPDT, respectively.


**Table 5.** Main characteristics of the proposed study case of reconfiguration.

According to the 16 light hours and one reconfiguration per minute, 350,400 operations are calculated per year, so that the corresponding number of reconfiguration per switch is calculated, according to (5):

ESPDT <sup>60</sup> <sup>×</sup> 103

$$R\_{y\text{ren},\text{SPST}} = R\_{\text{gv}} \cdot (1/\text{N}\_{\text{SPST}})\\R\_{y\text{ren},\text{SPDT}} = R\_{\text{gv}} \cdot (1/\text{N}\_{\text{SPDT}})\\\mathbf{N}\_{y\text{,SPST}} = E\_{\text{SPST}} / R\_{y\text{ren},\text{SPST}}\\\mathbf{N}\_{y\text{,SPDT}} = E\_{\text{SPDT}} / R\_{y\text{ren},\text{SPDT}} \tag{5}$$

where: *Ryr* is the number of reconfigurations per year; *Ryrsw,SPST* and *Ryrsw,SPDT* are the number of reconfigurations per year per switch for SPST and SPDT respectively; *Nyr,SPST* and *Nyr,SPDT* express, in terms of number of years, the endurance of SPTS and SPDT switches respectively.

Table 6 reports the data referring to both types of switches and to the four considered cases of reconfiguration, obtained from (5). Note that the number of total reconfigurations *Ryr* has been considered the same for all the cases.


**Table 6.** Estimated number of reconfigurations per year and endurability of the switches in the four cases, for the "worst case" condition.

According to that, the total cost evaluation, including the overall system, is considered and reported in Table 7 for different cases of years to come before the switches are changed.


**Table 7.** Cost evaluation according to the estimated endurability, as reported in Table 6 in the four cases, for the "worst case" condition.

The economical contributions concerning the switches and the overall system, as reported in Table 7, arise from the data reported in Tables 1 and 2, respectively. Note that the configurations with the lowest number of switches are less convenient if only the price of the switches is considered, supposing that in the same number of years they require to be changed a higher number of times. On the contrary, if the total cost of the reconfigurator is considered, the cases with the lowest number of switches are the most convenient. Indeed, the initial price in terms of sensors, drivers and MOSFETs is generally higher if the number of mechanical switches is higher, due to the higher hardware complexity. Note as well as that if a low number of switches is associated to a more complex algorithm, so that the reconfiguration frequency is higher, the frequency of maintenance increases. As an example, Table 8 refers to two reconfigurations per minute in case 2, whereas the number of reconfigurations per minute in the other cases is kept at 1.

**Table 8.** Cost evaluation if in case 2 (case of minimum number of switches) the number of reconfigurations per minute is 2 instead of 1.


One can see that in this case the most convenient solution, after 30 years, is the one corresponding to the case 3. Although the obtained economical results of this comparison among different reconfiguration cases shall not be critically considered, what is significant in this paragraph is the proposed approach for an economical estimation of the system lifetime.
