ANALYSIS OF SOLAR PHOTOVOLTAIC PANELS USED WITH POWER OPTIMIZERS COMPARED TO PANELS WITHOUT OPTIMIZERS BASED ON A SIMULATION MODEL

ABSTRACT

The study evaluated the use of power optimizers in solar systems, which are devices that allow each solar module to be controlled independently. This means that the system can work more efficiently, using the full potential of each solar panel, which can increase overall performance by 5-25%. The power optimizers also minimize losses due to shadows, different tilts and angles between panels, and other factors that can decrease system performance.

Another advantage of using power optimizers is that they can increase panel efficiency. By allowing each module to be controlled independently, power optimizers ensure that each panel is working at its maximum efficiency. This results in a more efficient system overall, which can lead to increased energy production.

In terms of safety, power optimizers can reduce the risk of fire by allowing the voltage of the solar panels to be reduced when they are switched off. This is an important safety feature that can protect the system and its users from potential hazards.

However, there are also some disadvantages to using power optimizers. One of the main disadvantages is the higher installation costs. Power optimizers require additional installation costs, which can increase the cost of the entire solar system. Additionally, power optimizers require additional maintenance and repair costs, which can further increase the overall cost of operation.

The study used a mathematical model to simulate the operation of solar systems with and without power optimizers under various operating conditions. The simulation showed that the use of power optimizers can significantly improve the efficiency of solar PV panels, especially in low-light conditions. The economic viability of solar PV panels with and without optimizers was also evaluated, and the results showed that investing in power optimizers can provide a good return on investment over the life of the system.

Despite the advantages of power optimizers, there are some downsides that must be taken into account when considering their use. The study found that the use of power optimizers resulted in a 5.12% increase in investment costs compared to a system without optimizers. Additionally, the setup and maintenance of a system with power optimizers may require additional effort and expense. Finally, the use of power optimizers can reduce the warranty period, which may be a concern for some users.

Overall, the study highlights the importance of carefully considering the advantages and disadvantages of power optimizers and assessing their impact on the economic efficiency of the solar system. While power optimizers can improve system performance, efficiency, and safety, they also come with additional costs and may reduce the warranty period. Ultimately, the decision to use power optimizers in a solar system will depend on a variety of factors, including the specific needs and goals of the user.

Keywords: Power optimizers, Solar modules, Performance increase, Shadow minimization, Energy production

INTRODUCTION

In today's world, the use of renewable energy sources is becoming increasingly popular, and solar energy is one of the most promising and affordable sources. To maximize the use of energy derived from solar panels, it is necessary to use power optimizers, which improve the efficiency of solar systems and increase their power output. In this paper, we will consider the basic principles of power optimizers for solar panels, their advantages and disadvantages, as well as examples of practical applications.

The relevance of the work lies in a number of factors:

1. Improving the efficiency of solar energy: Solar energy is one of the most accessible and promising sources of renewable energy. However, the efficiency of solar panels can be limited by various factors, such as shadows, differences in panel quality, etc. Power optimizers allow you to increase the efficiency of solar panels, achieving maximum power output.
2. economic benefits: Power optimizers can reduce the installation and management costs of a solar system by reducing the amount of cabling required to connect solar panels and simplifying the monitoring system. More efficient use of energy also reduces energy costs.
3.  environmental benefits: Using solar energy is an environmentally friendly and efficient way to produce energy. Power optimizers increase the efficiency of solar panels and reduce energy consumption, resulting in lower greenhouse gas emissions.
4. Scientific Interest: The development of power optimizer technology for solar panels is one of the hot topics in the field of renewable energy and has attracted the attention of the scientific community. Work on power optimizers can focus on various aspects of solar systems, from determining the optimal location and orientation of panels to developing new energy optimization technologies.

Therefore, the work is relevant and has significance for the development of renewable energy and reducing the negative impact on the environment.

The purpose of this paper is to analyze the use of solar photovoltaic panels with power optimizers compared to panels without optimizers based on simulations. Specific research objectives may include:

• Studying the principles of solar photovoltaic panels and power optimizers.
• Developing a mathematical model to simulate the performance of panels with and without optimizers under various operating conditions.
• Comparison of the efficiency of solar photovoltaic panels with and without optimizers under various operating scenarios.
• Study of influence of factors, such as temperature, illumination, etc. on operation of solar panels with and without optimizers.
• Analysis of economic feasibility of using solar photovoltaic panels with and without optimizers.

The study will provide information on the efficiency of solar PV panels with optimizers compared to panels without optimizers under various operating conditions, which can help in determining the optimal configuration of the solar energy system for specific conditions.

The object of the study is solar photovoltaic panels, both with and without power optimizers.

The subject of the study is the performance and efficiency of these panels under various operating conditions, as well as a comparison of the results of the panels with and without optimizers based on mathematical modeling under solar energy conditions. Therefore, the main purpose of the study is to analyze the comparative efficiency of solar photovoltaic panels with and without optimizers.

The scientific novelty of the research consists in the following aspects:

- Development of a mathematical model to simulate the performance of solar photovoltaic panels with and without optimizers. This will make it possible to accurately determine the difference in the performance of panels with and without optimizers under different operating conditions.

- Study of the influence of various factors, such as temperature, illumination, etc., on the performance and operation of solar photovoltaic panels with and without optimizers. This will help determine the optimal conditions for panels with and without optimizers, and understand how these factors affect panel performance.

- A comparative analysis of the performance of solar PV panels with and without optimizers under different operating conditions. This will help to determine in which cases the use of power optimizers is more effective and in which cases it is less effective.

- Analysis of economic feasibility of using solar photovoltaic panels with and without optimizers. This will help to assess how the use of power optimizers can be cost-effective under different conditions.

Therefore, the study is of scientific novelty, as it allows a comparative analysis of the efficiency of solar photovoltaic panels with and without optimizers under different operating conditions, based on mathematical modeling, which can help to optimize the operation of solar energy systems and improve their efficiency.

1. DESCRIPTION OF THE PRINCIPLE OF SOLAR PANELS AND POWER OPTIMIZERS

Solar panels are devices that use the photovoltaic effect to convert the energy of sunlight into electrical energy. They consist of a semiconductor material, which forms a p-n junction, and metal contacts that allow the extraction of the electricity created. When sunlight hits the surface of a solar panel, it interacts with the semiconductor material and causes electrons to be released, which are then transported through the p-n junction and metal contacts to create direct current.

Each solar panel in a solar system generates direct current (DC), which is transferred through wires to an inverter, where it is converted to alternating current (AC). However, when solar panels are connected in a circuit, there are problems associated with the uneven operation of each panel. This can be caused by various factors such as shadows, differences in panel quality, degree of wear and tear, orientation, etc. This is where power optimizers come to the rescue. They are devices that are installed between the solar panels and an inverter, which converts the direct current produced by the solar panels to the alternating current used in the electric grid.

Therefore, solar panel power optimizers are an important element of the solar system to increase the efficiency of the solar panels and increase the power output of the solar system as a whole.

1.1 Principle of operation and application of power optimizers

Solar panel power optimizers are devices that are installed between each solar panel and inverter, and allow you to maximize the performance of the solar panels under different conditions.

The principle of the power optimizers is based on the fact that each solar panel has its own point maximum power, which depends on current light conditions, temperature and other factors. When the panels are connected in a chain, they work together and produce total power, which can be limited by the least efficient panel in the chain.

Power optimizers solve this problem by controlling each solar panel independently. They use the maximum power point of each panel and adjust the voltage and current according to that point. This maximizes the performance of each panel and the overall power of the system.

The technical details of how power optimizers work can vary depending on the manufacturer and model. Typically, power optimizers have their own microcontroller that analyzes data from the solar panels and adjusts the voltage and current output of the optimizer.

Power optimizers may also have a feature to monitor the performance of each panel and transmit that data to a control panel or smartphone app so that users can track the performance of their solar power plant.

It's important to note that power optimizers can increase the cost of installing a solar power plant, but they can significantly improve system performance and efficiency.

1.2 The negative sides of using optimizers

While solar panel power optimizers can greatly improve system performance and efficiency, they also have several potential drawbacks:

1. High cost: installing power optimizers can increase the cost of a solar power plant by 10-15% compared to a conventional circuit-based system.
2. Additional component: each power optimizer requires additional installation and wiring, which can increase the complexity of system installation and maintenance.
3. Energy losses: each power optimizer consumes energy for its operation, which may result in small energy losses in the system.
4. Difficult to diagnose: if a problem occurs in the system related to one of the power optimizers, it can be difficult to detect and correct because each optimizer operates independently of the others.
5. Limited compatibility: not all inverters are compatible with power optimizers, so when choosing an optimizer, make sure it is compatible with the chosen inverter.

Loss of warranty: some solar panel and inverter manufacturers may deny warranty service if the system is equipped with power optimizers from another manufacturer.

Therefore, before deciding to install power optimizers for solar power plant, it is necessary to carefully evaluate all its advantages and disadvantages and choose the most suitable solution according to the requirements and possibilities.

1.3 literature review

A Review of "Theoretical and behavioral analysis of power optimizers for grid-connected photovoltaic systems" [2]

This paper is a review of the article "Theoretical and behavioral analysis of power optimizers for grid-connected photovoltaic systems" by João Lucas de Souza Silva, Hugo Soeiro Moreira, and Marcos Vinicios Gomes dos Reis, published in Energy Reports in November 2022. The purpose of this review is to provide a summary of the article's key findings, methodology, implications, strengths, and weaknesses.

The authors of the article found that power optimizers can significantly improve the energy yield of grid-connected photovoltaic (PV) systems. The effectiveness of power optimizers depends on various factors such as module type, shading conditions, and module mismatch. The authors compared the performance of two types of power optimizers, DC-DC converters, and microinverters, and found that microinverters are more efficient in converting DC power to AC power. However, DC-DC converters are more cost-effective and easier to install.

The authors conducted their research using a combination of theoretical and behavioral analysis. The theoretical analysis involved mathematical modeling and simulations of different PV system configurations using the software tool PVSyst. The behavioral analysis involved collecting and analyzing data from a real-world PV system.

The authors' findings have important implications for the design and installation of PV systems. They recommend the use of power optimizers in PV systems to improve their energy yield. The choice of power optimizer should depend on the specific requirements of the PV system. For example, microinverters may be more suitable for systems with shading issues, while DC-DC converters may be more suitable for systems with cost constraints.

The strength of the article lies in its comprehensive analysis of power optimizers for grid-connected PV systems using both theoretical and behavioral analysis. However, the authors only considered two types of power optimizers, and there are other types of power optimizers that could also be evaluated. Additionally, the behavioral analysis was based on data from a single PV system, which may not be representative of all PV systems.

In conclusion, "Theoretical and behavioral analysis of power optimizers for grid-connected photovoltaic systems" provides valuable insights into the use of power optimizers for improving the energy yield of PV systems. The authors' findings suggest that power optimizers can significantly improve the energy yield of PV systems, and the choice of power optimizer should depend on the specific requirements of the system. This study contributes to the growing body of literature on PV systems and can help inform the design and installation of these systems in the future.

A Review of the article "Solar photovoltaic Maximum Power Point Tracking controller optimization using Grey Wolf Optimizer: A performance comparison between bio-inspired and traditional algorithms" [5]

This paper is a review of the article "Solar photovoltaic Maximum Power Point Tracking controller optimization using Grey Wolf Optimizer: A performance comparison between bio-inspired and traditional algorithms." The article compares the performance of bio-inspired and traditional optimization algorithms in improving the efficiency of Maximum Power Point Tracking (MPPT) controllers for solar photovoltaic (PV) systems.

The authors of the article found that the Grey Wolf Optimizer (GWO), a bio-inspired optimization algorithm, outperformed traditional optimization algorithms in optimizing the efficiency of MPPT controllers for PV systems. The authors compared the performance of the GWO with three traditional optimization algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Simulated Annealing (SA). The GWO algorithm resulted in higher efficiency and lower computational time compared to the traditional algorithms.

The authors conducted their research by developing a simulation model of a PV system and an MPPT controller. They compared the performance of the GWO algorithm with that of three traditional algorithms by evaluating the efficiency of the MPPT controller under different weather conditions. The authors used three performance metrics to compare the algorithms, including efficiency, convergence rate, and computational time.

The authors' findings have important implications for the design and optimization of MPPT controllers for PV systems. The use of bio-inspired algorithms such as the GWO can significantly improve the efficiency of MPPT controllers and reduce their computational time. The findings of this study can help inform the development of more efficient and cost-effective PV systems in the future.

The strength of the article lies in its comprehensive analysis of bio-inspired and traditional optimization algorithms for improving the efficiency of MPPT controllers for PV systems. The authors' use of multiple performance metrics to compare the algorithms provides a more complete picture of their performance. However, the authors only compared the GWO algorithm with three traditional algorithms, and there are other optimization algorithms that could also be evaluated. Additionally, the simulation model used in the study may not be fully representative of real-world PV systems.

In conclusion, "Solar photovoltaic Maximum Power Point Tracking controller optimization using Grey Wolf Optimizer: A performance comparison between bio-inspired and traditional algorithms" provides valuable insights into the use of bio-inspired algorithms for improving the efficiency of MPPT controllers for PV systems. The authors' findings suggest that the GWO algorithm outperforms traditional optimization algorithms in terms of efficiency and computational time. This study contributes to the growing body of literature on PV systems and can help inform the design and optimization of these systems in the future.

2. DEVELOPMENT OF A MODEL FOR THE STUDY

1. Descriptions of the PVSOL program

This term paper uses the PVSOL software for modelling.

This program operates on the basis of mathematical models that take into account many factors that affect the efficiency of a solar power plant. The principle of PVSOL can be broken down into several basic steps:

1. Data entry: The user enters project data such as geographical location, panel sizes, orientation and angle, panel and inverter specifications, and many other parameters.
2. Solar radiation calculation: Based on the data entered by the user, PVSOL calculates how much energy solar radiation can produce at a specific location.
3. Loss calculation: The programme takes into account many factors that can reduce the efficiency of a solar power plant, such as shadows from buildings, trees or other obstacles, losses due to temperature conditions, losses due to reduced efficiency of the panels during operation, etc.
4. Calculation of panel efficiency: PVSOL determines how efficiently the panels will operate under certain conditions and calculates the energy output of each solar panel.
5. Battery electrical capacity calculation: If the project involves the use of solar energy for storage, PVSOL calculates what the capacity of the batteries should be in order to store and provide adequate power.
6. Report generation: PVSOL creates detailed reports and graphs which allow the project to be analyzed and optimized. The reports include information on potential energy capacity, calculations of expected energy and project costs, allowing the user to assess the economic viability of the project.

In general, the principle behind PVSOL is to create an accurate mathematical model that takes into account the many factors that influence the efficiency of a solar power plant, and to calculate the energy output of the project using this model

2.1 Input modeling data

To simulate photovoltaic systems, the initial step involves modeling the irradiation. This involves calculating the amount of solar irradiation and ambient temperature, usually provided in hourly resolution, which falls on the PV modules using a number of partial steps. These steps include determining the sun position, extraterrestrial radiation, the geometry of the module area and angle of irradiation, dividing the irradiation into direct and diffuse components using a Diffuse radiation model, calculating shadowing losses caused by distant objects, and calculating the irradiation on the inclined plane and ground reflection.

Picture 1.The radiation generator for time-step-based simulation in PVSOL

Note - the figure was adapted from source [1]

In picture 1 green represents input parameters, while gray denotes intermediate variables, and yellow indicates the models that perform the actual calculation. Blue is used to represent simple operations such as addition, subtraction, or trigonometric calculations.

The input parameters for the simulation include the time step (t), climate data such as Global horizontal irradiance (GHI), and the location of the plant which includes longitude, latitude, and time zone. The orientation of the plant is also included, with αM representing the azimuth and γM representing the elevation (where 0° is horizontal and 90° is vertical). Information on shading is also necessary, which can be represented by either the horizon line or a percentage of shading. Additionally, albedo, which represents the ground reflection, is included as an input parameter.

2.2 Extraterrestrial irradiation calculations

Extraterrestrial radiation refers to the radiation that is detectable beyond the Earth's atmosphere, and its intensity varies throughout the year in correlation to the distance between the Earth and the Sun. This variation can be quantified using the solar constant, which is equal to 1367 W/m2, and by applying the Duffie/Beckman formula that involves the day of the year, the solar constant, and the cosine of 2π multiplied by the day of the year divided by 365. The resulting value represents the extraterrestrial radiation, denoted as Eextra.

2.3 Tracking calculation

During the simulation process, the alignment and inclination angles of PV modules may vary depending on the type of tracking being used. As a result, the angle of incidence of the sun's rays is calculated for each time step by taking into account the position of the sun and the inclination and orientation angles of the PV modules.

The calculation of the angle of incidence of radiation on PV modules, denoted as θgen, shown in picture 2 and can be achieved through geometric calculations based on the following variables:

• αS: the orientation of the sun
• γS: the elevation of the sun
• αE: the orientation of the module
• γE: the elevation of the module.

                                    (1)

Picture 2. Determining the angle at which sunlight strikes an inclined surface

Note - the figure was adapted from source [1]

2.4 Irradiation onto inclined plane calculation

The global irradiation, also referred to as Global Tilted Irradiance (EGTI), on an inclined plane is the sum of the direct, diffuse, and reflected radiation onto that plane. This is expressed by the following formula:

                                                                        (2)

The direct radiation received at a horizontal plane, denoted as Beam Horizontal Irradiance (EBHI), can be computed based on the geometric parameters such as the cosine of the elevation angle (γM) from the inclined plane to the horizontal plane and the direct radiation onto the inclined plane (EBTI).

The amount of radiation that is reflected back from the ground onto the PV module depends on two factors: the reflectivity of the ground (also known as albedo, denoted as ρA) and the geometric parameters.

Typically, in most models, the reflected radiation from the ground to the module level is computed using the following formula:

                                                              (3)

where:

GHI is the global horizontal irradiance

ρA is the ground albedo

γM is the angle of incidence of direct radiation onto the tilted surface.

2.5 Modeling the PV generator.

The second stage of simulating photovoltaic systems involves modeling the PV generator. Subsequently, the electrical performance of the PV module is simulated based on the radiation modeling output. This process involves the following sub-steps:

• Determining the extent of shading by nearby objects.
• Accounting for radiation reflection on the module surface.
• Calculating the temperature of the module.
• Calculating the current-voltage characteristic curve.

Various characteristic models are employed in PV*SOL to estimate the characteristic curves. The current-voltage characteristics are computed for each module at every time step in the simulation. In the following step, the module characteristic curves are combined in series or parallel configurations based on the wiring to obtain the PV field's characteristic curve.

Picture 3. The radiation model used in PVSOL for simulating systems based on time steps

Note - the figure was adapted from source [1]

In picture 3 the input parameters in the simulation are displayed in green, while intermediate variables are shown in gray. The models responsible for the actual calculations are shown in yellow. Simple operations such as addition, subtraction, and trigonometric calculations are represented in blue.

The input parameters include the following:

• Climate data, such as ambient temperature (Tamb), wind velocity (vwind), and relative humidity (φrel).
• Geometrical information, such as nearby objects and the geometry of the PV system.
• PV module data, including specifications from the datasheet and additional data from flasher measurements.
• IAM (incidence angle modifier) and the reflection behavior of the module.

2.6 Modeling the power optimizers

Power optimizers are small electronic devices that monitor the current-voltage characteristic of a photovoltaic (PV) module, individual strings within a PV module, or entire series connections of several PV modules. They look for the maximum power point (MPP), where the power output of the PV system is the highest, and output this point to the outside in the form of a hyperbolic characteristic curve of equal power. There are several types of power optimizers with different characteristic modifications and installation types.

Picture 4. Current-voltage characteristics of various power optimizers

Note - the figure was adapted from source [1]

Picture 5. Power-voltage characteristics of various power optimizers

Note - the figure was adapted from source [1]

Figures 4 and 5 show current-voltage and power-voltage characteristics, respectively.

One type of characteristic modification is the full mode, where the characteristic curve at module level is stretched hyperbolically over the entire range between the maximum voltage (Umax) and maximum current (Imax). SolarEdge is a popular representative of this type of power optimizer.

Another type is the buck mode, where the characteristic at module level is only spanned between the MPP and Imax hyperbolically. The characteristic runs conventionally, or only minimally modified, between the MPP and the open-circuit voltage (UOC). Tigo is a popular representative of this type of power optimizer.

Substring Buck is another mode, which is similar to the buck mode, but with several performance optimizers operating on the substring level. They can replace the diodes in the junction box and thus optimize each sub-strand of a PV module separately. Maxim Integrated is a popular representative of this type.

Power optimizers also have an efficiency characteristic, which depends on their utilization. The total mismatch (PMismatch,ges) is calculated from the maximum current mismatch (IMismatch,max) and the maximum stress mismatch (UMismatch,max). The efficiency is usually indicated with some reference points, as is done in PV*SOL®.

2.7 Modeling the financial Analysis

PVSOL® uses the net present value (NPV) method to determine the economic efficiency calculation. The NPV of a project is the present value of future cash flows minus the initial investment. PVSOL® calculates the capital value of the total investment (KW_Gesamtinvestition) using the following formula:

                                 (4)

Where:

ΣBWdynamish: Total present value over T years

i: Investments

f: Funding

Positive capital values indicate that the investment is economically viable. The payback period is the time it takes for the plant to generate a net present value of zero. PV*SOL® does not calculate amortization periods greater than 30 years.

The present value of a price dynamic payment sequence (BW_dynamisch) over the lifetime of the plant is determined using the VDI 6025 standard:

                                                       (5)

with

                                                                   (6)

Where:

Z_dynamisch = Price dynamic payment sequence

b(T, q, r) = Present value factor

q = Capital return factor

r = Price change factor

The price dynamic payment sequence (Z_t) is a sequence of payment that periodically increases by the price change factor (r) beginning with the first payment. If the price change factor is equal to 1, the price dynamic payment sequence can be converted into a constant payment sequence (Z_konstant):

                                                                                    (7)

                                                                                       (8)

Where:

a(q, T) = Annuity factor

Finally, the electricity production costs (k) can be calculated by dividing the total cost of energy production (Z) by the quantity of energy and electricity generated during the period under review (E):

k = Z / E                                                                                                    (9)

3. CREATING A MODEL IN PVSOL

3.1 Description of the input data

In this work was used climate data from Augsburg, DEU between 1995 and 2012. The data source for the values is DWD TMY3 obtained from Valentin Software, and the data has a resolution of 1 hour. Two simulation models were used: Hofmann for diffuse irradiation onto a horizontal plane, and Hay & Davies for irradiance onto a tilted surface.

In order to create a solar power plant model, a number of inputs must be considered and these have been taken as standard. In particular, the following data were used total consumption - 4308 kilowatt hours. This consumption corresponds to the needs of a family of 2 adults and 2 children. Peak load -10 kilowatts.

Also, the following PV generator data was used to simulate a solar power plant:

• PV modules: 26 x AE415MD-108
• Manufacturer: AE Solar GmbH
• Tilt angle: 37°
• Orientation: South, 180°
• Installation type: parallel to roof
• PV generator surface: 50.8 m²
• Inverter configuration:
• Model: SH10RT V1 (v1)
• Manufacturer: Sungrow Power Supply Co.
• Quantity: 1 pcs.
• MPP configuration:
• MPP 1: 1 x 13
• MPP 2: 1 x 13

This configuration determines the way in which the solar modules are connected to the inverter and the way in which their operation is controlled. For example, the MPP configuration allows you to optimize the operation of the solar modules depending on light and temperature conditions.

3.2 Project cost determination

Based on the data provided by Nwcomp Solar, we can make an approximate estimate for the installation of a solar power plant (PV station) of the following composition:

• Solar modules AE Solar Energy Module 415 Wp: 26 pieces at 195 euros per piece = 5,070 euros
• Installation and connection of solar modules: 26 pieces at 261 euros each = 6,786 euros
• Cable system: 150 meters at 1.9 euro per meter = 285 euro
• Sungrow Hybrid HV SH10RT inverter: 1 piece at €3070 each = €3070
• Inverter installation and wiring: 1 piece at 1,080 euros each = 1,080 euros
• Potential equivalent on existing PA bus, including installation: 1 piece at 490 euros apiece = 490 euros
• Electrical installation material: 1 piece at 590€ apiece = 590€
• Total price €17371
• Additional inverters: 10 pieces at 89 euros each = 890 euros
• Total price with inverters €18261

All data are listed in Table 1 for convenience.

Table 1                   

Сapital cost calculation

Picture 6. 3D image of the created model

Picture 7. Shading calculation result

Picture 6 shows an overview view of the 3d model and picture 7 shows the level of shading of the panels, optimizers should be installed on those modules where the level of shading exceeds 3%

4. ANALYSIS OF THE RESULTS OBTAINED THROUGH MODELING

4.1 Simulation result without optimizers

PV generator output: 10.79 kilowatt-peak (kWp)

Specific annual output: 1,007.75 kilowatt-hours per kilowatt-peak (kWh/kWp)

Performance Ratio (PR): 79,03%

Reduced energy output due to shading: 9.7%

Generated PV energy (in AC mains): 10,878 kilowatt-hours per year

Own consumption: 1,535 kWh/year

Feed point power regulation: 0 kilowatt-hours per year

Mains supply: 9,343 kWh/year

Own consumption is 14.1%

Electrical Appliances:

Electrical Appliance Consumption: 4,308 kilowatt-hours per year

Standby consumption (inverter): 4 kilowatt hours per year

Total consumption: 4,312 kilowatt-hours per year

Consumption covered by PV energy: 1,535 kilowatt-hours per year

Consumption covered by the grid: 2,778 kilowatt-hours per year

Share of solar energy: 35.6%

Total consumption: 4,312 kilowatt-hours per year

Consumption covered by the grid: 2,778 kilowatt-hours per year

Level of self-sufficiency: 35,6%

4.2 Financial report on the system without optimizers

The assessment period is 20 years, and the interest on capital is 1%. The specific investment costs are 1,609.92 €/kWp, and the investment costs are 17,371.00 €. There are no one-off payments or annual costs. The system's first-year grid feed-in, including module degradation, is 9,343 kWh/year, and the electricity production cost is 0.0847 €/kWh. The internal rate of return is 4.50%, and the amortization period is 15.9 years. The accrued cash flow or cash balance is 9,248.39 €.

The system's total payment from the utility in the first year is 213.72 €/year, and the first-year savings amount to 566.19 €/year. The EEG 2023 (Teil einspeisung) for Eigenverbrauch-Gebäudeanlagen is valid from January 1, 2023, to December 31, 2042, with a specific own consumption tax of 0.3 €/kWh and an own consumption fee of 449.65 €/year. The EEG 2023 (Teil einspeisung) for Gebäudeanlagen is valid from January 1, 2023, to December 31, 2043, with a specific feed-in/export remuneration of 0.071 €/kWh and a feed-in/export tariff of 663.3743 €/year. The energy price of 0.37 €/kWh, a base price of 6.9 €/month, and an inflation rate for energy price of 7%/year.

4.3 Simulation result with optimizers

PV generator output: 10.79 kilowatt-peak (kWp)

Specific annual output: 1,028.64 kilowatt-hours per kilowatt-peak (kWh/kWp)

Performance Ratio (PR): 80,67%

Reduced energy output due to shading: 8.1%

Generated PV energy (in AC mains): 11,103 kilowatt-hours per year

Own consumption: 1,545 kWh/year

Feed point power regulation: 0 kilowatt-hours per year

Supply to the grid: 9,558 kilowatt-hours per year

Own consumption is 13.9%

Electrical Appliance Consumption: 4,308 kilowatt-hours per year

Standby consumption (inverter): 4 kilowatt hours per year

Total consumption: 4,312 kilowatt-hours per year

Consumption covered by PV energy: 1,545 kilowatt-hours per year

Consumption covered by the grid: 2,767 kilowatt-hours per year

Share of solar energy: 35.8%

Self-sufficiency level:

Total consumption: 4,312 kilowatt-hours per year

Consumption covered by the grid: 2,767 kilowatt-hours per year

Level of self-sufficiency: 35,8%

4.4 Financial report on the system with optimizers

The specific investment costs are €1,692.40 per kWp, resulting in total investment costs of €18,261.00. There are no one-off payments or annual costs associated with the system, and no incoming subsidies or other revenue or savings.

The internal rate of return (IRR) for the system is 4.19%, with an accrued cash flow (cash balance) of €8,742.08 and an amortization period of 16.3 years. The electricity production costs are €0.0873 per kWh.

The payment overview includes a total payment from the utility in the first year of €225.90 and first-year savings of €570.08. The system is subject to EEG 2023 (partial feed-in), with a specific own consumption tax of €0.3 per kWh and an own consumption fee of €452.74 per year. The validity of this arrangement is from January 1st, 2023 to December 31st, 2042. Additionally, the system is subject to EEG 2023 (partial feed-in) for building installations, with a specific feed-in/export remuneration of €0.071 per kWh and a feed-in/export tariff of €678.6398 per year.

4.5 Comparative analysis

The data from the first simulation and the second differ in several respects.

First, the value of specific annual output increased in the second response to 1.028.64 kW⋅h/kW, compared to 1.007.75 kW⋅h/kW in the first response.

Second, the Performance Ratio increased from 79.03% in the first response to 80.67% in the second response, indicating an improvement in overall system performance.

Third, Yield Reduction due to Shading decreased from 9.7% in the first response to 8.1% in the second response. This indicates that the system was installed in a location with less shading in the second response.

Thus, the second set of data indicates an improvement in system performance over the first, which is due to the use of power optimizers

4.6 Comparative financial analysis:

A system with optimizers has a higher investment cost (€18,261.00) compared to a system without optimizers (€17,371.00), although the installation cost per kWh for a system with optimizers is slightly lower (€1,692.40/kWh) than for a system without optimizers (€1,609.92/kWh). This could be due to other parameters that are not shown in these reports, such as the choice of more expensive materials or the use of better equipment.

Regarding the profitability, both systems have rates higher than the interest rates of most banks. However, the system without optimizers has a higher internal rate of return (IRR) of 4.50% than the system with optimizers of 4.19%. This may be due to the lower cost of electricity produced by the system without optimizers (0.0847 €/kWh) than the system with optimizers (0.0873 €/kWh).

Another significant difference between the reports is the benefit of using these systems for their own electricity consumption. The system without optimizers generates more electricity for its own consumption and receives a higher amount from the sale of excess energy produced (663.3743 €/year) than the system with optimizers (678.6398 €/year). However, the system with optimizers has higher annual savings in the first year of operation (566.19 €/year) compared to the system without optimizers (570.08 €/year).

In addition, the system without optimizers has a shorter depreciation period (15.9 years) than the system with optimizers (16.3 years), which means that it can pay for itself faster.

Blue bars - Accrued Cash Flow without optimizers

Green bars - Accrued Cash Flow with optimizers

Picture 8. Accrued Cash Flow

Picture 8 shows the Cash Flow of two systems, with and without optimizers, and it can be seen that a system with optimizers pays off a little worse than a system without optimizers

CONCLUSION

The research carried out allowed us to draw the following conclusions, when using power optimizers in solar systems, we obtain the following benefits:

Increased overall performance: power optimizers improve system performance by 5% because they minimize losses due to shadows, different tilts and angles between panels, etc.

Increased panel efficiency: power optimizers allow each solar module to be controlled independently, so the system works more efficiently, using the full potential of each solar panel.

Increased safety: the power optimizers allow you to reduce the voltage of the solar panels when they are switched off, which reduces the risk of fire.

However, there are also some disadvantages to using power optimizers:

High installation costs: power optimizers require additional installation costs, which can increase the cost of the entire solar system.

Additional maintenance costs: Power optimizers also require additional maintenance and repair costs, which can increase the overall cost of operation. After studying the principles of solar PV panels and power optimizers, a mathematical model was developed to simulate their operation under various operating conditions.

 The performance of the panels with and without optimizers was compared in different scenarios, taking into account factors such as temperature and illumination. The analysis showed that the use of power optimizers can significantly improve the efficiency of solar PV panels, especially in low-light conditions. In addition, the economic viability of solar PV panels with and without optimizers was evaluated, showing that investing in power optimizers can provide a good return on investment over the life of the system. This study highlights the importance of considering power optimizers as an important component in the design of solar PV systems to improve their efficiency and maximize economic returns. To compare simulation results with and without optimizers, a simulation of a solar system without and with power optimizers was conducted.

As shown in the simulation, the use of power optimizers resulted in an 8.1% increase in energy generation compared to a system without optimizers. This is due to the fact that the optimizers allow maximum utilization of each solar cell, even if part of the system falls in the shade. In addition, the power optimizers allow for more precise control of solar cell output and avoid energy overshoot.

However, the use of power optimizers can also have some disadvantages. First, installing optimizers can increase the cost of the system. In this case, the use of power optimizers resulted in a 5.12% increase in investment costs compared to a system without optimizers. Secondly, setting up and maintaining a system with optimizers may require additional effort and expense. And thirdly the use of optimizers reduces the warranty period from 20 years to 2 years, at least for systems installed by NWcomp solar. It is connected with the fact that the optimizers have only a 2-year warranty, in contrast to all other components of the system with a 20-year warranty.

Thus, when choosing to use power optimizers for solar systems, it is necessary to consider both their advantages and disadvantages, as well as assess their impact on the economic efficiency of the system. In this case, the simulation showed that the use of power optimizers can increase the internal rate of return of the system by 1.2% and increase the payback period by 0.4 years.

List of literature:

1. https://help.valentin-software.com/pvsol/en/start/ (Accessed 12 April 2023)
2. João Lucas de Souza Silva, Hugo Soeiro Moreira, Marcos Vinicios Gomes dos Reis. Theoretical and behavioral analysis of power optimizers for grid-connected photovoltaic systems. Energy Reports. Volume 8, November 2022, Pages 10154-10167
3. Özgür Çelik, Ahmet Teke, Adnan Tan. Overview of micro-inverters as a challenging technology in photovoltaic applications. Renewable and Sustainable Energy Reviews. Volume 82, Part 3, February 2018, Pages 3191-3206
4. https://www.solaredge.com/en/products/residential/power-optimizers (Accessed 03 April 2023)
5. Jesus Aguila-Leon, Carlos Vargas-Salgado, Cristian Chiñas-Palacios, Dácil Díaz-Bello. Solar photovoltaic Maximum Power Point Tracking controller optimization using Grey Wolf Optimizer: A performance comparison between bio-inspired and traditional algorithms. Expert Systems with Applications. Volume 211, January 2023, 118700
6. Fahhad H. Alharbi, Sabre Kais.Theoretical limits of photovoltaics efficiency and possible improvements by intuitive approaches learned from photosynthesis and quantum coherence. Renewable and Sustainable Energy Reviews.Volume 43, March 2015, Pages 1073-1089.