4.1 Introduction

In Chap. 3, we discussed the design and implementation of smart IoT devices through an example problem. This was carried out through the solving of a specific application example concerning the problem of securing a building's main power supply against unauthorized use. However, the smart IoT devices use most of the supply energy; hence, the need to self-power smart homes. In this chapter, we report on the design procedure and implementation of a photovoltaic system for the IoT devices.

The increasing world population growth and improving standards of living in developing nations add to the escalated energy demands. Technological advancements have resulted in increased use of products that require energy, leading to significant efforts made by countries to meet the demand by burning more fossils for energy production . However, fossils are finite and cause more harm to the environment than renewable energy sources. Even with environmental concerns and unreliable fossil costs, industries around the world are still dependent on fossils for better power quality and efficiency. For developing countries, the challenge remains the ability to supply quality power to remote and off-grid areas. Renewable energy sources, especially solar, become a solution of choice. Technological advancements offer capabilities for the generation of renewable energy, storage, and off-grid design for localized usage. Off-grid photovoltaic system is a standalone source and alternative to conventional sources of power supply. Recent surveys show that the off-grid photovoltaic system delivers reduced routine cost options compared to the usual conventional power generator [1,2,3,4,5]. An extension of the work presented in this chapter is published in [10]. However, the photovoltaic system has an initial higher cost of installation, while the conventional power generator has a higher running cost [6,7,8,9]. Even with the initial high costs of installation, off-grid systems offer long term economic benefits and energy access to regions where renewable energy sources are abundant. Off-grid photovoltaic system is a scheme that processes ambient solar irradiance and converts it into functional electrical energy for electrical loads. In designing an energy harvesting system for a load of 2000 W, sequentially technical specifications of the energy transducer, the power conditioner, and energy bank are determined. The photovoltaic transducer is one of the most common energy transducers which harvests its energy from abundant solar irradiance in the ambient. The efficiency of the transducer depends mainly on ambient irradiance and temperature, relying on the time of the day and season of the year as well as its characteristics. The goal of the power conditioner is to maximize the output of the energy transducer by optimally matching the impedances of the transducer and the load. Also, it has the capability to adapt to varying inputs and consequentially variations of current and voltage levels at the load. In order to improve the power conditioning efficiency, Maximum Power Point Tracking (MPPT) is incorporated to achieve maximum power transfer [10,11,12]. The MPPT keeps on adjusting the duty cycle of a power switch of the DC–DC converter, accordingly, as the ambient temperature and solar irradiance fluctuates. Although, in Africa context, particularly in Botswana, it receives more than 2000 KW/m2 of irradiance in an hour [13], which is enough to exploit.

This chapter intends to report on the design of a solar array system to be used as a sole energy driver for a standalone photovoltaic system used in powering smart devices in the smart homes. The design is preceded by determining the number of solar panels required to optimize the available space on the rooftop of a portacabin to be used as a self-sufficient energy house. In general, the design of a solar system is informed by the load intended to be driven. The load (usage) is determined either by performing calculations of the amount of energy required by the local appliances using nameplate specifications provided by the manufacturer, or by consulting the utility energy usage report. In this case, however, a different design process was followed due to certain constraints. Specifically, the load that the system can support is sized, which is the opposite of the traditional approach. This is particularly relevant to consumers with limited/fixed spaces. Therefore, this is a bottom-up strategy (sizing the load as opposed to sizing the solar array system). The significance of this approach is that, generally, the space is readily available in the form of home, factory, or office roofing. The traditional approach (top-down strategy where the solar system is sized based on the target load), however, requires flexibility in space available to meet the target load, a luxury that may not always be afforded to consumers especially in congested cities. As such, the design process proposed herein allows the consumer to make an informed and realistic decision on which loads may be shed off the grid. The design process presented here is inherently scalable dependent on the available roof area, solar panel output, and footprint; therefore, it is suitable for homes, factories, and office spaces.

4.2 Technical Specifications of the Design

The chapter reports on the design of a solar array system to be used as a sole energy driver for the departmental green Internet of Things office devices. The design is preceded by determining the number of solar panels required to optimize the available space on the rooftop of a portacabin to be used as a self-sufficient energy house. Details of the design reports and results are presented in [10]. The load (usage) is determined either by performing calculations of the amount of energy required by the local appliances using nameplate specifications provided by the manufacturer or by consulting the utility energy usage report. In this case, however, a different design process will be followed due to certain constraints. Specifically, the load that the system can support will be sized, which is the opposite of the traditional approach. The limitations of this system design, as mentioned earlier, are as follows:

  • Spatial constraints: the spatial limitation due to the fixed size of the target roof.

  • Solar panel size: the number of panels in an array is determined by the size of individual panels. The choice will be limited by the available panels.

  • Single panel output : different solar panels have different power outputs. The more is the power, the better it will be over a given area of space. In this design, there will be a choice between 150 W (at 12 V), 100 W (at 18 V), and 80 W output panels. Space manipulation will play a role since, in general, the more power, the bigger the size of the panel (for a specific manufacturer design).

  • Array output: it is determined by the size of the array, which is determined by the output of individual units as well as the array configuration.

The rest of the design in terms of battery size, charge controllers, and inverters will depend on the size of the array (output power). The charge controllers at our disposal may not be sufficiently specified for the array application since they are specified for individual solar panels (input voltage 14–30 V at open circuit (12 V nominal voltage) and 6 A/10 A current output). The physical layout of the solar system array atop the house is shown in Fig. 4.1. There is a choice of using the 150 W or 100 W rated solar panels. Moreover, the actual layout may be in a landscape or portrait manner. The 150 W rated solar panels have dimensions 124 × 1.4 × 84 cm, while the 100 W panels are 120 × 3 × 54 cm in dimensions. These physical dimensions are used to determine the possible grid layout scenarios shown in Fig. 4.1. The output characteristics of each grid layout will be assessed in terms of output power, voltage, and current ratings. The ratings will not be determined until the wiring configuration (series, parallel, or hybrid connection) is taken into consideration. Figures 4.2 and 4.3 show the series and parallel configurations for the grid assembly, and a hybrid may also be considered.

Fig. 4.1
figure 1

Solar panel array layout (a) using 150 W panel units in a (4 × 3) grid (b) using 150 W panel units in a (7 × 2) grid (c) using 100 W panel units in a (5 × 4) grid, and (d) using 100 W panel units in a (10 × 2) grid

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Fig. 4.2
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Series array configuration using four (4) solar panels

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Fig. 4.3
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Parallel array configuration using four (4) solar panels

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The configuration chosen for the grid layout determines the charge controller, battery bank, and the inverter size. The behavior of the final grid configuration is governed by basic Kirchhoff’s laws. The capacity of the solar system is determined by the number and rating of individual solar panels. The grid layout of Fig. 4.1c will have a capacity of (100 × (5 × 4)) W = 2000 W, while that of Fig. 4.1b has a capacity of (150 × (7 × 2)) W = 2100 W. Based on the available space and size of a single 100 W panel unit, both the portrait and landscape array layouts (Fig. 4.1c, d) yield the same capacity of 2000 W. Once the configuration is chosen, the voltage and current rating of the solar array will be determined. The system size must match up with the inverter size, which generally comes in numerous sizes.

In the series configuration of Fig. 4.2, we apply Kirchhoff’s voltage law (KVL) in the loop. In such a circuit, the voltage of all the components combines in a summative manner, while the current remains the same. That is, the output current rating of the array will be the same as that rate of a single unit. However, the voltage rating of the array will be the sum of all the voltages rated across each solar panel. Alternatively, the voltage rating of the array is n (the number of solar panels in the array) times the voltage rating of a single solar panel since all the panels are identical. The advantage of this configuration is that the output current of the array is minimized, which enables the design to employ smaller sized wires. In terms of wire sizing, it is common knowledge that the wire size is proportional to the amount of current flowing through the wire. Therefore, each wire is rated for a specific amount of current flowing through it. The smaller is current, and the smaller is the size of the wire.

The alternative solar array configuration is the parallel type, which is shown in Fig. 4.3. In this configuration, Kirchhoff’s current law (KCL) is applied at any of the two nodes. The current output of the solar array is equal to the sum of an individual rated output current of the panels, which is equivalent to n (the number of solar panels in the array) times the current rating of a single solar panel. Since the panels are in parallel, the same voltage that appears across each individual solar panel will similarly appear across the output of the array. That is, the solar array system will have the same voltage rating as the individual panels that constitute it. In comparison with the series configuration, one quickly notices the stark difference in the output current of the respective arrays. The parallel configuration will need much thicker wires out of the panels in order to withstand the output current as compared to the series configuration. Moreover, the requirements of the charge controller will be higher (usually translates into hefty prices) than that of the series configuration. However, the series configuration is prone to the effects of shading. When one of the panels is shaded, the entire array system is driven off. This is typical of series circuits when the loop is opened at any part of the circuit, and the current ceases to flow to the output.

On the contrary, in the parallel configuration, if one of the panels is shaded, only its contribution will be missed. The issues narrated above are not just peculiar to shading; the same will apply if a panel malfunctions or ceases to operate for whatever reason. Using Fig. 4.3 as an example, if one-panel malfunctions, the system will operate at 75% capacity as opposed to not be available. The technical specifications of the design considerations are quantified in Table 4.1. As can be observed from Table 4.1, the amount of amperage that is produced by the parallel configurations is much higher than that of the series configurations. In translation, the charge controller requirements will be more costly for the parallel configuration. The series configuration, however, has a very high voltage rating while producing very little current. It might not be feasible to realize such a high voltage system that is capable of driving light/few loads due to the current limitation. This, therefore, requires that other alternatives be explored in order to obtain a realistic and cost-effective system. A hybrid configuration is proposed as a solution.

Table 4.1 Technical specifications for four (4) possible design configurations
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The proposed system is equally subjected to the same spatial constraints, available solar panels, and individual solar panel output. The expectation is that the final system will benefit from the properties of both the series and parallel configurations, albeit in moderation. The wiring configuration of such a design is shown in Fig. 4.4, which is a hybrid implementation of Fig. 4.1a. The same approach is adopted to implement the designs of Fig. 4.1b–d. The numerical results of these four hybrids wiring configurations are depicted in Table 4.2.

Fig. 4.4
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Hybrid wiring configuration of Fig. 4.1a

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Table 4.2 Technical specifications for four (4) possible hybrid wiring configurations
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It can be clearly seen from Table 4.2 that the hybrid wiring configuration moderates both the current and voltage specifications across all design configurations. While this optimization is achieved, the power rating of the system remains unchanged as before, as it can be observed in the third column of Table 4.2. Generally, as it can also be observed from Table 4.2, arranging more solar panels in series than in parallel will bias the system towards a higher voltage and lower current and vice versa. This is only true, provided the solar panels are rated the same (assuming they also have equal spatial footprint). In Table 4.2, Hybrid 3 and Hybrid 4 wiring configurations are derived from solar panels of the same specifications (including size), the same is true for Hybrid 1 and Hybrid 2.

Since the objective of this project is to accommodate energy storage to be used during times when there is no sunshine, the next logical step is to consider a storage system. Batteries are usually used for this purpose. Based on the specifications of this solar system (approx. 2000 W), matching battery size is required. However, the sizing of the battery depends on the operating hours. We will assume an average daily solar reception of 4 h (typical). Therefore, the energy produced by the system will be calculated as 2000 × 4 = 8000 Wh. The battery bank size may now be determined. The most popular batteries used for this purpose currently comes with 12 V, 100/120 Ah capacity with a maximum depth of discharge (DOD) of 70%. This is the maximum capacity of the battery, which could be used before recharging.

When it comes to system voltage capacity, there is generally a rule of thumb [14] that makes recommendations by providing operating ranges, depending on the solar system power (this need not be rigid). Such guidelines are presented in Table 4.3.

Table 4.3 Battery bank system voltage recommendations
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Based on Tables 4.1, and our solar panel system has a capacity of 2000 W; therefore, the battery bank system voltage should be rated at 24 V. We will also consider a 12 V, 120 Ah battery for the battery bank. The charge capacity of the battery bank = Energy required/System voltage = 8000/24 = 1000/3 Ah. With the charge capacity of the battery bank, we are now able to determine the required number of batteries to generate such charge.

$$ \mathrm{Number}\ \mathrm{of}\ \mathrm{batteries}\ \mathrm{required}\ \mathrm{in}\ \mathrm{parallel}=\left(1000/3\right)\div \left(120\ast 0.7\right)=3.97 $$
$$ {\displaystyle \begin{array}{c}\mathrm{Number}\ \mathrm{of}\ \mathrm{batteries}\ \mathrm{required}\ \mathrm{in}\ \mathrm{series}=\mathrm{system}\ \mathrm{voltage}\ \mathrm{considered}/\mathrm{voltage}\ \mathrm{of}\ \mathrm{battery}\\ {}=24\div 12=2\end{array}} $$

Thus, the battery bank should consist of two batteries in series and four batteries in parallel.

Furthermore, we verified the specifications following the method adopted in [14]. We started by looking at the general layout of our design as well as the circuit representation of the system.

The designed off-grid connected photovoltaic system consists of 20 solar panels in a hybrid wiring configuration, eight lead-acid batteries, charge controller, inverter, and the portacabin building. Figure 4.5 shows the schematic diagram of the off-grid PV system, while Fig. 4.6 is the circuit representation of the schematic diagram.

Fig. 4.5
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Schematic diagram of the off-grid PV system

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Fig. 4.6
figure 6

Circuit representation of the off-grid PV system

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In this work, the off-grid system provides enough energy to the secured smart system and the entire building (portacabin). The configuration of our design is as shown in Fig. 4.6, where the PV modules, also termed as generators [14], are connected to the batteries via the charge controller. The batteries then power the entire system via the inverter circuitry.

4.2.1 Equivalent Peak Solar Radiation Hours and Photovoltaic Array Sizing

In our analysis, we introduce the concept of peak solar hours , similar to [14], for the cell temperature of 25 °C, equivalent to the average temperature of the Palapye-Botswana region. If we consider the actual irradiance profile for a particular day as D(t) for which the irradiance of the equivalent day is 1 kW/m2 during a time of peak solar radiation hours (PSRH), we can then write the relationship of the total daily radiation in the actual day, similar to its equivalent day as:

$$ \underset{\mathrm{day}}{\int }D(t) dt=1.\mathrm{PSRH} $$
(4.1)

With the solar cell used in the design with electrical ratings of maximum points of current and voltage of 5.56 A and 18 V, respectively, for which the sun peak hours was found to be 3.25 h, the energy generated per day as simulated using PSIM [15] is given by:

$$ \underset{\mathrm{day}}{\int }{P}_{\mathrm{max}}(t) dt=\underset{\mathrm{day}}{\int }{I}_{mM}(t){V}_{mM}(t) dt=344.2\;\mathrm{Wh}/\mathrm{day} $$
(4.2)
$$ 150\mathrm{W}\times \mathrm{PSRH}=100\mathrm{W}\times 3.25\mathrm{h}=325\;\mathrm{Wh}\_\mathrm{day} $$
(4.3)

However, it was noted that when using the peak solar radiation hours to size and estimate the energy generated per day, one will underestimate the energy delivered by the photovoltaic modules at the days to be estimated, whereas the use of Eq. (4.2) will give better results in terms of energy delivered by the same PV modules for the days been estimated. It is worth to note that we consider the worst-case scenario, whereby the temperature is low to about 15 °C with low irradiance values too. In order to balance the energy generated by the off-grid system, it is necessary to size the PV array system. The energy balancing technique utilized the PSRH concept in writing the energy balance relationship as:

$$ {P}_{\mathrm{G}\hbox{-} \mathrm{Nom}}\mathrm{PSRH}={\mathrm{L}}_E $$
(4.4)

where PG ‐ Nom is the nominal output power of the photovoltaic system for a standard condition [14], LE the consumed energy over the average day by the load in the worst case. We can re-write Eq. (4.4) for two cases (worst-case design and average design) as:

  1. 1.

    Worst-case design of the system:

$$ {P}_{\mathrm{G}\hbox{-} \mathrm{Norm}}{\left(\mathrm{PSRH}\right)}_{\mathrm{min}}={\mathrm{L}}_E $$
(4.5)

where (PSRH)min represents the value of PSRH in the worst month of solar radiation.

  1. 2.

    Average-case design of the system:

$$ {P}_{\mathrm{G}\hbox{-} \mathrm{Norm}}\left(\overline{\mathrm{PSRH}}\right)={\mathrm{L}}_E $$
(4.6)

where \( \overline{\mathrm{PSRH}} \) represents the average value of the 12 monthly PSRH values. However, throughout our design, the average design was utilized. Substituting for current and voltage in the nominal maximum power of the photovoltaic system, Eq. (4.6) becomes

$$ {V}_{\mathrm{GN}}{I}_{\mathrm{GN}}\left(\overline{\mathrm{PSRH}}\right)={\mathrm{L}}_E $$
(4.7)

However, in most applications of a photovoltaic system, a series of parallel connections of PV modules are most common. In this, the photovoltaic system is composed of NS-PV series string of NP-PV identical (parallel) modules and Eq. (4.7) becomes

$$ {N}_{\mathrm{S}\hbox{-} \mathrm{PV}}{V}_{\mathrm{GM}}{N}_{\mathrm{P}\hbox{-} \mathrm{PV}}{I}_{\mathrm{GM}}\left(\overline{\mathrm{P}\mathrm{SRH}}\right)={\mathrm{L}}_E $$
(4.8)

where VGM and IGM represents the voltage and current, respectively, of the maximum power point of the photovoltaic system for the 1Sun AM1.5 standard [14]. This then means that the hybrid connections of the system are determined by the NS ‐ PVNP ‐ PV as:

$$ {N}_{\mathrm{S}\hbox{-} \mathrm{PV}}{N}_{\mathrm{P}\hbox{-} \mathrm{PV}}\frac{{\mathrm{L}}_E}{V_{\mathrm{GM}}{I}_{\mathrm{GM}}\left(\overline{\mathrm{P}\mathrm{SRH}}\right)} $$
(4.9)

However, for an off-grid photovoltaic system, the loads are connected to either a battery or supercapacitor in the form of VCC (DC Voltage). The energy consumed by the loads in the building over a day can now be represented as:

$$ {\mathrm{L}}_E=24\;{\mathrm{V}}_{\mathrm{CC}}\;{I}_{\mathrm{DC}\hbox{-} \mathrm{eq}} $$
(4.10)

where IDC-eq represents the equivalent DC current drawn by the loads over the 24 h of the day. Considering Eqs. (4.8) and (4.10), we have

$$ {N}_{\mathrm{S}\hbox{-} \mathrm{PV}}{V}_{\mathrm{GM}}{N}_{\mathrm{P}\hbox{-} \mathrm{PV}}{I}_{\mathrm{GM}}\left(\overline{\mathrm{P}\mathrm{SRH}}\right)=24{\mathrm{V}}_{\mathrm{cc}}{I}_{\mathrm{DC}\hbox{-} \mathrm{eq}} $$
(4.11)

However, Eqs. (4.8) and (4.10) as equated might not be exactly equal due to the underestimates of peak solar hour concept or overestimates of the photovoltaic energy generation system. Also, other factors might be due to the efficiency of the panels, the charge controller, the MPPT, and the inverting system (DC/AC converter). Hence, it is expected that a factor (safety factor) to augment inequality is added to the system so that Eq. (4.11) becomes

$$ {N}_{\mathrm{S}\hbox{-} \mathrm{PV}}{V}_{\mathrm{GM}}{N}_{\mathrm{P}\hbox{-} \mathrm{PV}}{I}_{\mathrm{GM}}\left(\overline{\mathrm{P}\mathrm{SRH}}\right)=\left({C}_{\mathrm{S}\mathrm{F}}\right)24{\mathrm{V}}_{\mathrm{cc}}{I}_{\mathrm{DC}\hbox{-} \mathrm{eq}} $$
(4.12)

Therefore, to size the PV modules in parallel or series, we can arrive at Eqs. (4.13) and (4.14), respectively, as:

$$ {N}_{\mathrm{S}\hbox{-} \mathrm{PV}}=\left({\mathrm{VC}}_{\mathrm{S}\mathrm{F}}\right)\frac{V_{\mathrm{cc}}}{V_{\mathrm{GM}}} $$
(4.13)
$$ {N}_{\mathrm{P}\hbox{-} \mathrm{PV}}=\left({\mathrm{IC}}_{\mathrm{SF}}\right)\frac{24{I}_{\mathrm{DC}\hbox{-} \mathrm{eq}}}{I_{\mathrm{GM}}\left(\overline{\mathrm{P}\mathrm{SRH}}\right)} $$
(4.14)

where VCSF and ICSF are voltage and current safety factors, respectively.

In our design, we consider the whole building of load consumption of 12,500 Wh per day at 24 V. Each of the solar panels has the following ratings :

$$ {P}_{\mathrm{SP}}=100\mathrm{W};{V}_{\mathrm{OC}}=22.10\mathrm{V},\kern1.6em {I}_{\mathrm{SC}}=6.1\mathrm{A},\kern1.6em {I}_{\mathrm{MP}}={I}_{\mathrm{GM}}=5.56\mathrm{A},\kern1.6em {V}_{\mathrm{MP}}={V}_{\mathrm{GM}}=18\mathrm{V} $$

We then compute the required current drawn by the load over the entire day as:

$$ {I}_{\mathrm{eq}}=\frac{{\mathrm{L}}_E}{24{\mathrm{V}}_{\mathrm{cc}}}=\frac{12,500}{24\ast 24}=21.7\mathrm{A} $$
(4.15)

where \( {\mathrm{L}}_E=\frac{12,500\mathrm{Wh}}{\mathrm{day}} \)

4.2.2 Equivalent Battery Sizing in the Photovoltaic Systems

In [14], a simplified equation governing the sizing of batteries in a standalone system is given by:

$$ {E}_{\mathrm{b}}=\left\{\mathit{\operatorname{MAX}}\left[{\left({E}_{\mathrm{b}\mathrm{al}}\right)}_{\mathrm{max}}+{E}_{\mathrm{b}\mathrm{ackup}},{E}_{\mathrm{cycle}}\left(\frac{1}{x}\right)\right]\right\}\frac{1}{y{\upeta}_{\mathrm{cd}}} $$
(4.16)

and

$$ {E}_{\mathrm{bal}}={\left({E}_{\mathrm{ph}}\right)}_{\mathrm{month}}-{\left({E}_{\mathrm{cons}}\right)}_{\mathrm{month}}={N}_{\mathrm{S}\hbox{-} \mathrm{PV}}\times {N}_{\mathrm{P}\hbox{-} \mathrm{PV}}\times {P}_{\mathrm{maxGr}}\times {\left(\mathrm{PSRH}\right)}_{\mathrm{month}}-{n}_i{\left({E}_{\mathrm{cons}}\right)}_{\mathrm{day}} $$
(4.17)

where Ebackup represents the amount of energy stored to guaranty system operation for a certain number of days, (Ebal)max stands for the maximum seasonal deficit accounting for the operation of a full year, Ecycle the energy deficit due to power mismatch, x the battery daily cycle factor, y the discharge factor maximum depth, and ηcd represents the efficiency of the battery charge and discharge. Also, Eph represents the energy generated by the photovoltaic system, Econs the energy consumed by the load for some time, and nithe number of days in a particular month. Equation (4.16) is measured in Watt-hour (Wh), but it is advisable to measure batteries in Ampere-hour (Ah) as the standard units for batteries, such that Eq. (4.16) becomes

$$ {E}_{\mathrm{b}\_\mathrm{standard}}=\frac{E_{\mathrm{b}}}{V_{\mathrm{cc}}} $$
(4.18)

For our design, we consider a total load of 2000 W, for which we have arrived at 5 × 4 solar panels arrays. We assumed batteries’ daily cycling of less than 15% of maximum discharge depth at 75% with charge-discharge efficiency of 90%. Hence,

$$ {E}_{\mathrm{bal}}=39,004\mathrm{Wh} $$
(4.19)

With backup storage for 7 days,

$$ {\displaystyle \begin{array}{l}{E}_{\mathrm{b}\mathrm{ackup}}=7\times 2000=14,000\mathrm{Wh}{E}_{\mathrm{b}}\\ {}=\left\{\mathit{\operatorname{MAX}}\;\left[39,004+14,000,2000\left(\frac{1}{0.15}\right)\right]\right\}\frac{1}{0.75\ast 0.90}=78,519\mathrm{Wh}\end{array}} $$
(4.20)

and

$$ {\displaystyle \begin{array}{l}{E}_{b\_\mathrm{standard}}=\frac{78,519}{24}=3272\mathrm{Ah}\\ {}{C}_{\mathrm{standard}}=\frac{E_{\mathrm{battery}}}{L_{\mathrm{E}}}=\frac{78,519}{2000}=39.3\;\mathrm{days}\end{array}} $$

From our battery sizing, it is possible to store our harvested energy for use up to 40 days.

Final Component Specification

  1. 1.

    Solar inverter: rated at 2000 W

  2. 2.

    Charge controller (MPPT): 24 V delivering 30–40 A

  3. 3.

    Batteries for battery bank: 8 × 120 Ah rated batteries

  4. 4.

    Solar panels: 20

4.3 Design of Photovoltaic System and MPPTs

A solar panel is a transducer that houses several photovoltaic (PV) cells connected in parallel or series depending on the application intended. To design and simulate the PV system, it is necessary to model the PV cell and study the characteristics of I–V and P–V plots because they define the PV behaviors . Figure 4.7 illustrates an equivalent circuit of a PV cell consisting of a current source connected in parallel with a forward-biased PN junction diode and a shunt resistance RSH all in series with resistance RS. While the current and voltage relationship is expressed in Eq. (4.22). Figures 4.8 and 4.9 illustrate a PV cell showing current and voltage relationships under the irradiance variations at 25 °C provided by a model at Eq. (4.22). The fixed temperature and varying irradiance influence the performance of a PV cell [16], as illustrated in Figs. 4.8 and 4.9.

Fig. 4.7
figure 7

Equivalent photovoltaic cell circuit, where IPV = Current generated from irradiance incident on the solar cell , ID = Diode Current, RS = Parasitic Series Resistance, RSH = Parallel Shunt Resistance, VOC = Open-Circuit Voltage

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Fig. 4.8
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An I–V plot of irradiance variations at 25 °C for solar panel

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Fig. 4.9
figure 9

A P–V plot of irradiance variations at 25 °C for solar panel

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Concerning the current source IPV feeding the diode and a voltage across the resistances in Fig. 4.7, the Kirchoff’s Current Law expresses the current, IL as [17]:

$$ {I}_{\mathrm{L}}={I}_{\mathrm{PV}}-{I}_{\mathrm{D}}-{I}_{\mathrm{SH}} $$
(4.21)

The current and voltage relationship in the PV cell is expressed as [17]:

$$ {I}_L={I}_{\mathrm{PV}}-{I}_{\mathrm{s}}\left\{\exp \left[\frac{q\left(V+{\mathrm{IR}}_{\mathrm{S}}\right)}{{\mathrm{KT}}_{\mathrm{C}}A}\right]-1\right\}-\frac{V+{\mathrm{IR}}_{\mathrm{S}}}{R_{\mathrm{S}\mathrm{H}}} $$
(4.22)

The current flowing through the diode is defined as

$$ {I}_{\mathrm{D}}={I}_{\mathrm{s}}\left\{\exp \left[\frac{V+{\mathrm{IR}}_{\mathrm{S}}}{{\mathrm{KT}}_{\mathrm{C}}A}\right]-1\right\} $$
(4.23)

The shunt current is defined as

$$ {I}_P=\frac{V+{\mathrm{IR}}_{\mathrm{S}}}{R_{\mathrm{S}\mathrm{H}}} $$
(4.24)

The power generated, P = IV, where I = IL, V = VOC,

$$ P=V\left\{{I}_{\mathrm{PV}}-{I}_{\mathrm{S}}\left[\exp \left(\frac{q\left(V+{\mathrm{IR}}_{\mathrm{S}}\right)}{{\mathrm{KT}}_{\mathrm{C}}A}\right)-1\right]-\frac{V+{\mathrm{IR}}_{\mathrm{S}}}{R_{\mathrm{S}\mathrm{H}}}\right\} $$
(4.25)

where IPV = Generated Current, IL = Load Current, IS = Reserved saturated Current of the Diode Parallel resistance, IP = Current flowing through, V = Voltage across the PV Cell, TC = Operating Temperature, q = Charge of an electron (1.6 × 10−19C), K = Boltzmann’s constant (1.38 × 10−23J/K).

A typical voltage across PV cell terminals is between 0.4 V and 0.5 V dependent on the operating ambient solar irradiance and temperature [18]. In an optimal design, when a load is connected to the cell, the voltage could be 0.25 V or 0.35 V [18]. The influence of ambient irradiance variations on the relationships among voltage, current, and power is demonstrated in Figs. 4.8 and 4.9.

4.3.1 Influence of Ambient Solar Irradiance on PV Cell

The simulated plots in Figs. 4.8 and 4.9 demonstrated that the performance of the solar panel strongly depended on ambient solar irradiance. The plots showed that the maximum power varies to change in ambient solar irradiance. In the simulated 100 W, 8.95(ISC) and 22.8(VOC) solar panel, the highest power and current generated were 109.552 W and 8.8539 A, respectively, from 1000 Wm−2 irradiance, while the lowest power and current were 17.0082 W and 1.7708 A, respectively. The output voltage of a PV depends on the ambient irradiance slightly and in a logarithmic trend [19,20,21].

4.3.2 Influence of Ambient Temperature on PV Cell

Solar panel changes with variations of ambient temperature based on Figs. 4.10 and 4.11. The variations of a temperature inversely affect the voltage, while the current increases slightly with an increase in temperature [22, 23]. Figure 4.11 demonstrates that the PV output power increased with decreased ambient temperature .

Fig. 4.10
figure 10

I–V plot of temperature variations at fixed irradiance for 150 W solar panel

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Fig. 4.11
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A P–V plot of temperature variations at fixed irradiance for 150 W solar panel

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4.3.3 Maximum Power Point Tracking

The installation of a solar panel is costly compared to conventional utilities on an interim basis, but in the long term, it is cheap and eco-friendly if the constraints of PV cells are optimized. Thus optimization will reduce the output cost and optimize the inputs to maximize power output despite irregular ambient irradiance and temperature levels. However, the relationship between current, voltage, and power plotted in Figs. 4.12 and 4.13 demonstrated that they have non-linear behaviors, and the tracking of the maximum power will be tricky .

Fig. 4.12
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I–V relationship of PV cell

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Fig. 4.13
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P–V relationship of PV cell

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The curves illustrating PV generated current running from 0 A to the short-circuit current, ISC varying in respect to PV terminal voltages running from 0 V to open-circuit voltage, VOC. Also, the curves revealed the tracking point of generated current IMPP and voltage VMPP, which matches the maximum power PMPP. Optimized operations of PV cells need to be performed to achieve maximum power transfer. However, to maintain maximum power transfer, an MPPT consisting of an electronic circuit and algorithm is integrated, as shown in Fig. 4.14. It is an intelligent sub-system of the photovoltaic system which controls the non-linear behavior of the solar panel under irregular ambient irradiance and temperature levels.

Fig. 4.14
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P–V relationship of PV cell

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Several MPPT algorithms exist in literature such as perturb and observe (P&O), incremental conductance, fuzzy logic, neural network, which aimed at differentiating results depending on sensed quantities and experimental conditions [24]. In this work, we chose the P&O method as it is accepted to be the most efficient technique in most cases. A simplified flowchart of the algorithm is given in Fig. 4.15.

Fig. 4.15
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Basic Perturb and Observe algorithm

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The algorithm is implemented in PSIM when the solar panel follows the average irradiance measured in the location of the project. The MPPT uses a buck converter designed to fulfill the relationships between the input and output quantities, as shown in Fig. 4.16. In this case, the solar arrays have an output voltage of 90 V, and the output battery needs 24V. A smoothing inductor is connected to the battery to limit its current ripple to 0.2 A. The 24 V battery bank should supply both DC and AC loads in the house, and for this purpose, a single-phase inverter combined to a 24 V–230 V transformer is used to provide AC loads. The complete system given in Fig. 4.17 is terminated by a fourth-order Chebyshev low pass filter, which cancels the high-frequency harmonics from the square signal given by the inverter. The ideal transformer has a transformation ratio of 325/24 to guarantee suitable voltage for most AC appliances in the house.

Fig. 4.16
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Implementation of Perturb and Observe algorithm by simulation

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Fig. 4.17
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24 VDC and 230 VAC outputs from the solar system

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4.4 Photovoltaic Modules Connected to a Load via Battery

4.4.1 Lead Acid Battery

Currently, charging and discharging of electrical energy in energy bank are the straight forward achievement with batteries and lead-acid battery dominates among its kind [25]. For a standalone PV system, the battery is commonly used as an energy bank and typically has a lifecycle of 2–3 years. Conventionally, the off-grid system powered by solar panels lead-acid battery is the main energy bank to regulate, store the excess electrical energy from the panel, and deliver when needed. The lead-acid battery consists of about six cells of about 2 VDC, each connected in series to make about 12 VDC. The batteries encounter numerous operational constraints such as self-discharge, variation in ambient temperature levels, lifecycles, the mode of regulations of a DC–DC converter. Optimizing these constraints determine the performance of the battery and its lifespan. Therefore, it is important to note that energy bank in PV system requires to be well designed to avoid shorter lifecycles and frequent failures. It uses voltage based processes for charging, and it takes 12–16 h to charge fully, and higher charge currents reduce the charging time [26]. Additionally, the open-circuit voltage VOC of the battery is directly proportional to the electric charge Q stored in a period t. The fully charged battery with its highest aggregate of charges QH, and state of charge (SoC) at time t is expressed as [27]:

$$ \mathrm{SoC}(t)=\frac{Q(t)}{Q_{\mathrm{H}}(t)} $$
(4.26)

4.4.2 Battery Charge and Discharge System

Currently, the essence of the battery charge and discharge in the off-grid system is to replenish the depleted electrical energy and regulate the supply. Its optimal target is to reduce the electrical energy drawn from the battery to extend the lifetime of the energy bank.

From Fig. 4.18, the generated current can be expressed in Eq. (4.27). The figure has three main units: the energy harvesting source, battery, and the load. An example of battery is the lead-acid battery, and a 12 VDC lead-acid battery of 2.45 V per cell contains six cells, which produces 14.7 V across its terminal. At full charge, the battery voltage will get to 14.7 V, as shown in the charging curve of Fig. 4.19. At an initial voltage of 12.96 V, the battery gradually increased to the highest value of 14.7 V and remains nearly constant, depending on the age or self-discharging nature of the battery. In the discharging curve in Fig. 4.20, from the 14.7 V, it reduced gently equally depending on the age, self-discharge, and operating temperature of the battery.

$$ {I}_{\mathrm{pv}}={I}_{\mathrm{batt}}+{I}_{\mathrm{load}} $$
(4.27)
Fig. 4.18
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A diagram of the off-grid system powered by solar panel

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Fig. 4.19
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Charging behavior of 200 Ah–12 V Lead-Acid Battery

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Fig. 4.20
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Discharging behavior of 200 Ah–12 V Lead-Acid Battery

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The lead-acid battery in operation is made up of positive electrode, lead dioxide (PbO2), and the negative electrode, lead (Pb) in an electrolyte (H2SO4) [28]. The forward direction in Eq. (4.28) represents chemical reactions that occur during discharge, where electrical energy is delivered to the load. Charging occurs in the backward direction in Eq. (4.28), where electrical energy is taken from the energy source.

$$ \mathrm{Pb}+{\mathrm{SO}}_4^{2-}{\displaystyle \begin{array}{c}\overset{\mathrm{discharge}}{\to}\\ {}\underset{\mathrm{charge}}{\leftarrow}\end{array}}{\mathrm{PbSO}}_4+2{\mathrm{e}}^{-} $$
(4.28)
$$ {\mathrm{PbO}}_2+{\mathrm{SO}}_4^{2-}+4{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}{\displaystyle \begin{array}{c}\overset{\mathrm{discharge}}{\to}\\ {}\underset{\mathrm{charge}}{\leftarrow}\end{array}}\;{\mathrm{PbSO}}_4+2{\mathrm{H}}_2\mathrm{O} $$
(4.29)
$$ {\mathrm{PbO}}_2+\mathrm{Pb}+2{\mathrm{H}}_2{\mathrm{SO}}_4{\displaystyle \begin{array}{c}\overset{\mathrm{discharge}}{\to}\\ {}\underset{\mathrm{charge}}{\leftarrow}\end{array}}\kern0.62em 2{\mathrm{PbSO}}_4+2{\mathrm{H}}_2\mathrm{O} $$
(4.30)

4.5 Simulation Results

From a typical daily solar irradiance in Botswana, the system is simulated with only the battery to see if the MPPT algorithm stuck well to the theoretical maximum power. The solar panel and the battery voltages and currents are shown in addition to the power to see the overall performances. The switches are all supposed ideal to make the study easy and to focus on the main components of the circuit. Simulation in Fig. 4.21a showed that the MPPT performs well as its output power is in the same range of the theoretical output power with a maximum deviation of 60 W at midday. The battery voltage always remains at equal value during the day.

Fig. 4.21
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MPPT performance on (a) a typical day of 24 h in Botswana and (b) a random irradiance

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The general performance of the MPPT algorithm is also tested in Fig. 4.21b on a random irradiance to confirm its efficiency in terms of detecting the maximum power in any situation. The PV curve showed that the maximum power point is reached at Vsp = 85.19V in Fig. 4.22 with a power of 1933.17W corresponding to a current of 22.69 A.

Fig. 4.22
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The PV curve of the solar arrays showing the maximum power point

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The outputs of the system from simulation, for both DC and AC loads, led to satisfactory results with a constant 24 VDC and 230 VAC outputs without distortion in Fig. 4.23. The panel average output voltage is about 90 V. These results obtained from simplified models showed the feasibility of the green-house based on the same specifications as in the simulation. The losses caused by components will need to be included for the practical model, but the whole concept will be the same as in the simulations.

Fig. 4.23
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The panel and the battery voltages and the output sinusoidal signal

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4.6 Summary

In this chapter, we report on the design and simulation of a standalone photovoltaic system to support the Internet of Things Sensor Devices, following modeling and sizing procedures. In most cases, the lack of or little knowledge of the sizing of the system's parameter causes a hazard to most of the houses that utilize renewable energy sources. Also, the efficiency of these panels that are used for the energy harvesting purpose depends on the sunlight, for which the amount of harvested energy is also influenced by ambient temperature and solar irradiation, and the entire system depends solely on Maximum Power Point Tracker (MPPT) system. Changes in solar irradiance and temperature conditions, in addition to variations in load demands, cause power imbalances. The design and consideration of MPPT help in compensation for the changes. This paper further reports on the procedures for determining the number of solar panels required to optimize the available space on the rooftop. This is generally a feasible and practical way of erecting solar systems as opposed to seeking alternative spaces to assemble the solar arrays. In general, the design of our standalone system was informed by the amount of energy the solar array system can produce under spatial constraints (available roof area), solar panel output, and footprint. As such, a PV standalone system with battery storage is designed and simulated, and the mathematical calculation for the intended 2000 W energy source is done, along with a proper layout of the design configurations. The simulation results also confirmed the mathematical models of the design.