Sizing methodology for photovoltaic systems considering coupling of solar energy potential and the electric load: dynamic simulation and financial assessment

A reliable methodology for the dimensioning of photovoltaic systems is presented in this paper. This method generates technical-financial variables that aid in the choice of the most adequate photovoltaic power system for each project. The techniques that are usually used determine the size of PV power plants considering the monthly average of the solar energy potential of the month with the lowest solar radiation and the electricity to be supplied to satisfy the demand. These conventional techniques generate an uncertainty of at least 40 %, mainly due to the daily dispersion of the solar energy availability and of the electric load. The proposed methodology takes into account a region’s own photovoltaic energy potential and the detailed characteristics of the electric load, matching both with different PV power plants sizes, and analyzing the whole during a time period that guarantees the reliability of the results. The energy coupling is performed integrating the energy parameters (solar energy and electric load) in short time intervals (30 minutes maximum) to determine the supplied energy, the unsupplied energy demand and the unused solar energy. The daily integration of the three factors, using a dynamic simulation and performing a financial evaluation, allows for the identification of the most appropriate PV power plant size for every project. The results indicate that this methodology reduces the uncertainty of the solar power-electric load coupling from 40 % to 2.2 %, which allows a better definition of the financial variables that determine the most appropriate installed solar power for a photovoltaic project.


Introduction
Today, different methodologies to size photovoltaic (PV) systems exist. They allow the calculation of technicalfinancial parameters to improve the possibilities of using this energy source. The available tools are commercial software, spreadsheet templates and mobile applications. The decision of investing in a photovoltaic installation is driven mainly by financial factors, like the payback period, which is calculated based on the technical characteristics of the system and ideal-condition values for factors such as inclination, orientation, solar radiation, electric load, etc. Most of the existing methodologies, suggest using critical low values of solar irradiance and high average values of electric load for the calculation, which results in an oversizing that guarantees the operation of the PV system in any condition [1]; however, this results in a surplus of unused photovoltaic electricity, a higher initial investment cost and finally a longer than expected payback period. The sizing of a PV systems begins with the selection of the most important components: the PV panels, controllers, inverters, and accessories [2][3] that will be used in particular geographical conditions, where solar energy is available and an electric load has to be fed. Moreover, some methodologies include a forecast of the energy demand, the characterization of the photovoltaic potential on the geographical location, and consider different storage technologies [4]. Storage systems significantly increase the costs of PV systems, nevertheless they are an important factor for isolated areas or locations where the network offers low electric power quality. In these places, the sizing of PV systems would depend strongly on the additional cost of batteries and the reliability required from the system during energy outages [5] [6] [7] [8] [9], even in shared storage systems [10].
Lately, genetic algorithms are being used as a tool to optimize the sizing of PV panels and the battery system, with the aim of maximizing the economic benefit obtained from the use of the system in different scenarios [11] [12]. Since PV energy can be an adequate complement for so-called hybrid systems, some techniques have been developed for optimizing the sizing and cost analysis of hybrid PV/wind systems [13] [14], or more complex PV/wind/hydrogen systems plus batteries [15] [16], the sizing being a more complex and less reliable process. Sizing methodologies are applied also for specific loads such as the ones of photovoltaic solar pumping systems: since the load is constant, the sizing of the system is eased, whether or not the system is connected to the network [17] [18]. In some cases, the information of the solar potential available in a specific region is used to estimate the electricity cost reduction (in urban areas) or the energy supply (in rural areas) [13] [19]. All sizing methodologies for PV systems consider technical and financial aspects that allow the use of this renewable technology, however, some aspects are not considered concerning small scale PV applications, like residential use, where the benefits of the investment are not reflected in the daily consumption [20].
One of the keys to reduce the payback period of PV installations is to reduce unused solar energy (surplus), especially when it cannot be injected into the grid because it is generated in an isolated system or due to the lack of a legal framework for its sale in the country. In many cases, the payback period for PV systems is doubled because the production surpluses are not economically exploited, even though some techniques for the generation of heat with PV electricity surpluses exist [21].
In the literature review, much information has been found for a correct sizing of the components of photovoltaic systems, however, none of them propose energy coupling between solar power and the electric load for the sizing of a PV system. Thus, this paper presents a methodology for PV systems sizing considering the coupling of the potential of solar energy and the electrical load through a dynamic simulation and financial evaluation.

Proposed methodology
The most important concepts to perform an energy assessment for a solar photovoltaic project are shown in Figure 1. Available solar power and demand never match perfectly, which does not allow the use of all the solar energy available and the fulfillment of the electricity demand. Nowadays, it is widely believed that to better harness solar energy, energy has to be produced and used immediately [18]. For grid-connected PV systems, all the produced energy is injected to the system, but for isolated PV systems, a percentage of the energy is not used. This unused energy has to be reduced as much as possible while avoiding the perturbation of the electricity supply.
The proposed methodology determines the best match between solar power and electric load, defining the installed solar power that fulfills the maximum demand and reduces the unused solar power. This simulation is performed for different PV power plant sizes until the best option is found (in energy and financial terms). To guarantee the reliability of the results it is necessary to have the electric load characteristics and data and the solar radiation of the months that are considered for the conventional calculation. The rate of acquisition (solar energy and electric load) of the data used must be short (between 15 and 60 minutes). Fig. 1 shows that the methodology is based on direct electricity supply during daylight hours, which means that the solar energy is transformed and consumed immediately. The storage of photovoltaic solar energy for nighttime hours is not considered.

Energy parameters Solar power
The available solar power for electricity production depends on solar irradiance and the photovoltaic array size.
Demand during daylight hours Electric power that has to be supplied by the PV system immediately after production during daylight hours. Electric power that has to be supplied out of daylight hours. Since energy storage is not considered, this electricity demand cannot be fulfilled by the PV system. The analyzed uncertainties are shown in Table 1. The measurement instruments and equipment used for this study were conventional and widely used in the industry.

Dynamic simulation and financial assessment
In order to validate the technology, historical data from a typical residential building was used. The building had, besides of residential apartments, business offices, a sports field and a gym. The monthly cost of peak and out of peak periods was obtained from the electricity bills ( Table 2). The detailed energy consumption was not available in the documentation, so it was measured. The energy demand for June 2018 is shown in Fig. 2, as an example. The demand varies from 5 kW to 65 kW, which indicates a high dispersion in electricity consumption. Fig. 3 represents the hourly energy demand. It shows that the highest consumption occurs between 8 h and 23 h, mainly due to the kind of activities performed in the building. The consumption during this period of the day is between 30 kW and 60 kW. This information is relevant for the definition of the kind of photovoltaic system that will be installed. The Figure shows that the consumption during sunlight hours does not exceed 40 kW. This value is different than the average that could be calculated with the conventional method. In this case, the maximum consumption occurs during nighttime.  The same dispersion is observed in the analysis of the solar energy potential. Solar radiation values for June are shown in Fig. 4. The granularity of this information does allow for the estimation of the energy potential and the electricity generation [13], nevertheless, reducing this data to one only value (yearly-monthly average) is not appropriate for PV systems dimensioning. When obtaining monthly-hour averages (in solar power and electricity demand) and considering, for example, a peak installed power of 30 kW and a photovoltaic array efficiency of 0.10, the uncertainty reaches higher relative values of approximately 40 % (Fig.  5). When calculating the energy supply (also Fig. 5), the error margin is considerable and not adapted to dimensioning. In financial terms, this error does not to guarantee a correct utilization and harnessing of the solar technology. Using equations from (4) to (9), the important variables for analysis are determined (power and energy). Then, the energy coupling is performed. A sample of this process is shown in Fig. 6. Demand, solar power, supplied energy and unsupplied energy are shown. The energy values are integrated in the time interval established during a defined period. This methodology is applied in a Microsoft Excel® sheet. In this study case, the energy integration (solar power and electricity demand) was performed in 15 minutes intervals during the whole year of 2018. The simulation is performed for different PV power plant sizes to identify the scenario that better satisfies the demand and diminishes the unused solar power. The results of the simulation are shown in Fig. 7, Fig.  8 and Fig. 9 uncertainties table). To determine the optimal PV power plant size to be installed, it is necessary to perform an energy balance for all the period. Integrating power over time, the energy values are obtained (the supplied energy, the unsupplied energy and the unused energy) for every plant size. Fig. 7, Fig. 8 and Fig. 9 show three graphics each. The upper shows the variation of solar power and demand, the one in the middle shows demand, supplied energy and unsupplied energy. The lower shows the solar power, the supplied energy and the unused energy.
It can be seen that when the installed solar power is increased, the supplied energy (red area) increases as well, the unsupplied energy (blue area) diminishes and the unused solar energy (yellow area) increases.
In order to define the most appropriate solar power for an installation, it is necessary to reduce the unsupplied and the unused energy.  The energy (and financial) balance is shown in Fig. 10. The percentages of supplied and unused energy are shown for every PV power plant size. Fig. 10 also shows the percentage of the costs of supplied and unsupplied energy. Fig. 10 constitutes a tool that can be used by the solar PV system designer as an aid for dimensioning. In this study case, it is observed that the most appropriate solar plant size is between 30 and 60 kW. For plant sizes from 50 to 60 kW, the supplied energy percentage is almost constant and the unused energy percentage increases, which can be a determining factor to discard the 60 kW PV plant.
It is also observed that the main and the secondary vertical axis are equivalent, but are in different units (cost and energy, respectively). Thus, this graphic provides important information that can aid for a right decision. Concerning the financial assessment, Fig. 11 shows the payback period for the investment for the different PV power plant sizes. Two scenarios are considered: sale of the unused energy and the loss of the unused energy. This information is important, not only to analyze if the investment is feasible, but also to decide of the location of the solar power plant, since it would have to be close to sites where the connection to the electric grid for energy sale is allowed or there is a project for it. It can be observed that for the studied PV power plant sizes, the payback period is almost constant when energy sale is considered, but otherwise, it increases.

Conclusions
A reliable methodology for photovoltaic systems dimensioning has been presented in this article. Technical-financial variables that provide an aid for the dimensioning of photovoltaic projects have been presented.
The proposed methodology considers the typical energy potential of a region and the detailed characteristics of the electric load. Both parameters are matched to different solar plant sizes and analyzed during a period that guarantees the reliability of the results.
The energy coupling is performed integrating the power (PV system and electric load) in short time intervals to determine the supplied energy, the unsupplied energy and the unused energy.
The daily integration of these three factors (through a dynamic simulation and financial assessment), determines the most appropriate PV plant size for every undertaking.
The results show that this methodology reduces the uncertainty of the fulfillment of the demand, hence increasing the reliability of financial estimations that allow the choice of the most appropriate PV plant size.