# A Cost-Effective and Efficient Electronic Design for Photovoltaic Systems for Solar Hot Water Production

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## Abstract

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## 1. Introduction

_{PR}will depend on the value of the resistance. This operating point can be far from the maxi-mum power point P

_{Pmax}, as shown in Figure 2. Being far from this maximum power point means being in a very low-efficiency situation because only part of the energy available in the photovoltaic field is used.

## 2. Materials and Methods

_{g}. This gate voltage is produced by the control system, and its value depends on the voltage of the photovoltaic modules.

_{ref1}, the gate voltage will be 0 V. At this point the transistor is not conducting electricity, and the photovoltaic modules’ intensity, I

_{S}, will charge the capacitor, which can be seen in Figure 4a. The capacitor’s charge curve is shown in Figure 5, and the equation describing the capacitor charge is shown in (1).

_{ref2}, the gate voltage will be 12 V. Having arrived at this point, the transistor will conduct electricity and the capacitor will deliver a discharge intensity, I

_{C}, over the charge resistance, R

_{L}, which can be seen in Figure 4b. The capacitor discharge curve is shown in Figure 5, and the capacitor charge equation is shown in (2). The photovoltaic modules’ intensity I

_{S}, as shown in Figure 4b, needs to be added to the discharge capacitor current I

_{C}.

_{ref1}and V

_{ref2}, the time elapsed t, and the capacitor’s capacity C. It is worth mentioning how the condenser charge (Equation (1)) depends on R

_{S}, which is the internal resistance of the photovoltaic modules plus the electrical wiring, while the discharge (Equation (2)) depends on the load resistance R

_{L}. This difference causes different charge and discharge condenser times and, thus, also the so-called “on” and “off” periods.

_{L}, R

_{L}being the charge resistance. On the other hand, when the MOSFET is off, the system’s voltage will reach the system’s maximum voltage, that point being the intersection between the curve and the V axis.

_{ref1}and V

_{ref2}. V

_{ref2}is a voltage higher than the reference voltage, determined by the control system through a hardware configured value. V

_{ref1}is a voltage lower than the reference voltage, determined by the control system through a hardware-configured value. The reference voltage, determined by the control system, is equivalent to the maximum power point’s voltage resulting from the grouping of photovoltaic modules.

_{ref1}, resulting in the condenser being charged at that maximum voltage. When the system’s voltage is higher than V

_{ref2}, the control system triggers the MOSFET gate, and the gate voltage V

_{g}reaches a value near 12 V. The current generated by the photovoltaic system runs across the charge resistance. At the same time, the condenser starts discharging and that discharge current runs across the charge resistance, as shown in Figure 7. While the current goes through the MOSFET, the condenser lowers its voltage in the same way the photovoltaic modules do.

_{ref1}, the MOSFET gate is set to “off” because the gate voltage V

_{g}reaches 0 V. The result is that no current moves along the charge. The current generated by the photovoltaic system increases the condenser’s voltage (to a level equal to the voltage at the photovoltaic modules’ terminals). Therefore, while the MOSFET is off, the condenser increases its voltage in the same way the photovoltaic modules do. This voltage surge continues until it reaches V

_{ref2}. At that moment, the MOSFET gate is triggered, and the cycle repeats itself.

_{ref1}and V

_{ref2}. When the voltage moves from V

_{ref2}to V

_{ref1}, the MOSFET is on and transferring power, and the condenser discharge current goes through the charge (this discharge causes the charge current to be higher than the current delivered by the photovoltaic modules, but it is limited by the charge’s resistance value). When the voltage moves from V

_{ref1}to V

_{ref2}, the current produced by the photovoltaic modules charges the condenser because the MOSFET is off and no current passes through the load resistance.

- The system can operate all day if minimum solar exposure is available.
- The system operates in isolation.
- The tank holds sufficient capacity to absorb the energy produced by the solar photovoltaic modules on a high radiation day.
- The system has been developed so that water consumption can be simulated in order to study the system’s heating capacity in different demand scenarios.

_{PR}points, as shown in Figure 12. The voltage corresponding to these P

_{PR}points must be lower than the voltage corresponding to the maximum power or P

_{Pmax}points on each curve.

_{PR}points, as shown in Figure 12. At maximum irradiance, the P

_{Pmax}point voltage of the PV modules is very close to (but higher than) the P

_{PR}point voltage at the intersection of the load line with the IV curve. If these requirements were not met, there would be situations of irradiation in which not all the available energy would be used.

## 3. Results

## 4. Discussion

- -
- Estimated DHW demand.
- -
- DHW tank volume for it to work as a system buffer.
- -
- Configuration and layout of the photovoltaic modules so that the required level voltage is obtained for the heating resistance operation.
- -
- Type and value of the electric thermal resistance.
- -
- Strategy for MMP tracker monitoring.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

AC | Alternating Current |

ADS | Analog to Digital Converter |

DHW | Domestic Hot Water |

DAC | Digital to Analog Converter |

DC | Direct Current |

EU | European Union |

MOSFET | Metal Oxide Semiconductor Field-Effect Transistor |

MPPT | Maximum Power Point Tracking |

PV | Photovoltaic |

PV/T | Photovoltaic/Thermal |

SAHP | Solar-Assisted Heat Pump |

ST | Solar Thermal |

SWH | Solar water heating |

## Symbology

C | Capacitance of parallel capacitor (C) |

I | Photovoltaic module current (A) |

Ic | Charging/discharging capacitor current (C) |

IPmax | Maximum power point current (A) |

PPmax | Maximum power point of photovoltaic modules (W) |

PPR | Load resistance operating point (W) |

RL | Load resistance (Ω) |

RS | Series resistance of photovoltaic modules (Ω) |

V | Photovoltaic module voltage (V) |

Vg | MOSFET gate voltage (V) |

VPmax | Maximum power point voltage(V) |

Vref1 | Initial capacitor charging voltage (V) |

Vref2 | Initial capacitor discharging voltage (V) |

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**Figure 1.**Average price for PV rooftop systems in Germany (10–100 kWp). Author’s chart, source Fraunhoffer ISE.

**Figure 2.**(

**a**) Equivalent circuit of a PV module that powers a resistor (RL) with an operating point (PPR). (

**b**) Type curve.

**Figure 9.**Pictures showing the experimental facility: (

**a**) photovoltaic modules; (

**b**) electronic system; (

**c**) hot water tank.

**Figure 14.**V-I curves of the photovoltaic system (Data from Supplementary Materials).

**Figure 15.**V-P curves of the photovoltaic system (Data from Supplementary Materials).

**Figure 16.**Heating curve on 9 January 2020 (Data from Supplementary Materials).

**Figure 17.**System power curve on 9 January 2021 (Data from Supplementary Materials).

**Figure 18.**PV system voltage and load voltage vs. time (Data from Supplementary Materials).

**Figure 19.**PV system current and load current vs. time (Data from Supplementary Materials).

**Figure 20.**PV system power and load power vs. time (Data from Supplementary Materials).

**Figure 21.**Cost of solar thermal (ST) vs. solar photovoltaic (PV) DHW generation, depending on demand.

Mod | Simb | Unit | Nom |
---|---|---|---|

Peak Power | P_{PPV} | W | 330 |

Panel surface area | A_{PV} | m^{2} | 1.94 |

Efficiency | E_{ff} | % | 17.01 |

Operating temperature | T | °C | −40 to 85 |

Short circuit current | I_{SC} | A | 9.14 |

Open circuit voltage | V_{OC} | V | 46.9 |

Nominal current | I_{N} | A | 8.74 |

Nominal voltage | V_{N} | V | 37.8 |

Mod | Simb | Unit | Nom |
---|---|---|---|

Nominal Power | P_{NWH} | W | 3000 |

Tank Volume | V | L | 300 |

Heating electrical resistance | V_{N} | V | 37.8 |

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**MDPI and ACS Style**

Cámara-Díaz, L.; Ramírez-Faz, J.; López-Luque, R.; Casares, F.J. A Cost-Effective and Efficient Electronic Design for Photovoltaic Systems for Solar Hot Water Production. *Sustainability* **2021**, *13*, 10270.
https://doi.org/10.3390/su131810270

**AMA Style**

Cámara-Díaz L, Ramírez-Faz J, López-Luque R, Casares FJ. A Cost-Effective and Efficient Electronic Design for Photovoltaic Systems for Solar Hot Water Production. *Sustainability*. 2021; 13(18):10270.
https://doi.org/10.3390/su131810270

**Chicago/Turabian Style**

Cámara-Díaz, Luis, José Ramírez-Faz, Rafael López-Luque, and Francisco José Casares. 2021. "A Cost-Effective and Efficient Electronic Design for Photovoltaic Systems for Solar Hot Water Production" *Sustainability* 13, no. 18: 10270.
https://doi.org/10.3390/su131810270