Real-World Performance and Economic Evaluation of a Residential PV Battery Energy Storage System Under Variable Tariffs: A Polish Case Study

Abstract

This paper presents an annual, real-world evaluation of the performance and economics of a residential photovoltaic (PV) system coupled with a battery energy storage system (BESS) in southern Poland. The system, monitored with 5 min resolution, operated under time-of-use (TOU) electricity tariffs. Seasonal variation was significant; self-sufficiency exceeded 90% in summer, while winter conditions increased grid dependency. The hybrid system reduced electricity costs by over EUR 1400 annually, with battery operation optimized for high-tariff periods. Comparative analysis of three configurations—grid-only, PV-only, and PV + BESS—demonstrated the economic advantage of the integrated solution, with the shortest payback period (9.0 years) achieved with financial support. However, grid voltage instability during high PV production led to inverter shutdowns, highlighting limitations in the infrastructure. This study emphasizes the importance of tariff strategies, environmental conditions, and voltage control when designing residential PV-BESS systems.

1. Introduction

In response to the escalating climate concerns and a global shift towards decentralized energy production, residential energy infrastructure has evolved significantly. Among the most effective and forward-looking approaches at the household scale is to combine photovoltaic (PV) micro-installations with dedicated battery energy storage systems (BESSs) [1]. These hybrid configurations enable prosumer households (users who simultaneously act as both producers and consumers of electricity) to generate electrical energy locally from solar irradiance while also facilitating temporal load balancing by retaining surplus generation. When properly engineered and intelligently managed, a PV–BESS (installation of photovoltaic and battery energy storage system) markedly diminishes dependency on centralized grid infrastructure [2], enhances self-sufficiency ratios [3], and contributes to local decarbonization by minimizing reliance on fossil fuel-derived electricity during peak demand intervals [4].

Residential PV systems typically range up to 10 kW, making them particularly attractive due to their modularity and accessibility, as well as the growing affordability of solar panels and batteries [5]. However, PV systems are primarily limited by their dependency on weather [6] and daytime irradiance patterns [7]. The resulting temporal mismatch between energy generation and household demand often leads to inefficiencies and underutilization of produced energy. Energy storage systems, especially lithium-ion batteries, are increasingly being used to address this issue by capturing excess energy during peak production periods and discharging it during periods of low solar output or peak electricity pricing [8].

In recent years, Poland has experienced a significant increase in the adoption of residential BESSs, which have become a key factor in the evolution of the national energy landscape. In 2024 alone, 37,000 new residential battery systems were installed, representing a faster growth rate than that of new PV micro-installations. The increase in energy storage capacity in 2024 alone amounted to approximately 550 MWh [9]. This acceleration is closely linked to regulatory shifts—particularly the replacement of net-metering with net-billing—which have enhanced the financial viability of storing surplus solar energy for self-consumption, making it more financially viable than exporting it to the grid. Consequently, PV–BESS have become increasingly prevalent among prosumers, who now play a more active role in local energy balancing. These prosumer-driven configurations are economically advantageous and provide ancillary services to the grid, such as peak shaving and voltage stabilization, especially when aggregated at scale in urban distribution networks [10]. Furthermore, as shown in a techno-economic assessment by [11], optimal sizing and operation of PV-BESS can significantly reduce grid dependency while contributing to decarbonization targets and enhancing grid resilience. Collectively, these trends collectively indicate that the expansion of residential energy storage in Poland is set to play a pivotal role in shaping a more decentralized, flexible, and sustainable power system.

One of the key policy instruments accelerating the deployment of residential renewable energy technologies in Poland is the “Mój Prąd” (“My Electricity”) program, which is currently in its sixth edition (Mój Prąd 6.0). This government-led subsidy initiative, managed by the National Fund for Environmental Protection and Water Management (NFOŚiGW), provides financial support to households investing in micro-scale photovoltaic systems and complementary energy technologies, including home battery storage, energy management systems (EMSs), and solar water heaters. Under the 6.0 edition, launched in 2023, applicants can receive up to PLN 7000 (approx. EUR 1650) for PV installations, and an additional PLN 16,000 (approx. EUR 3800) for installing energy storage systems, depending on system configuration and integration with smart energy controls. This version of the program prioritizes self-consumption optimization over energy export, aligning with the national shift from net-metering to net-billing.

Recent studies highlighted the increasing maturity and effectiveness of these PV-BESS. For example, Rojek et al. [12] analyzed smart home installations incorporating PV-BESS with AI-based management algorithms. The authors reported improved predictive control of loads and a notable increase in self-consumption efficiency. Similarly, Korab et al. [13] developed optimal energy scheduling algorithms for homes equipped with PV, demonstrating that intelligently shifting loads in conjunction with storage can significantly reduce peak grid usage.

In the Polish context, the deployment of such systems has gained strategic importance. Dzikuć et al. [14] provided a thorough overview of the role of photovoltaics in Poland’s low-emission energy transition. They emphasized the importance of financial incentives, public acceptance, and environmental necessity in adopting decentralized solar solutions. Complementing this perspective, Sowa [15] stressed that integrating PV with storage is vital for ensuring system reliability and reducing household-level energy losses, particularly in suburban areas with fluctuating consumption patterns.

The integration of PV systems with BESS in residential environments has become a global trend, driven by the need for greater energy autonomy, grid resilience, and enhanced self-consumption. Numerous studies have analyzed technical configurations, economic performance, and control strategies of such hybrid systems under varying climatic and regulatory conditions.

The article by Lei et al. [16] provides a comprehensive overview of the integration of electric vehicles (EVs) into electricity and carbon markets, offering insights highly relevant to the broader issue of grid stability impacted by distributed energy resources such as PV systems. It highlights that, like distributed PV, EVs introduce variability and complexity to load profiles, affecting voltage regulation and reducing system inertia due to widespread use of power electronic converters. This contributes to challenges including voltage fluctuations, frequency instability, harmonic distortion, and protection coordination difficulties arising from two-way power flows. However, advanced inverter controls, vehicle-to-grid technologies, and intelligent market participation through bidding strategies can mitigate these impacts by providing ancillary services like frequency regulation and voltage support. Moreover, Lusimbakio et al. [17] assesses the impact of distributed PV integration on a fragile power grid in the Democratic Republic of Congo, showing that up to about 30% PV penetration improves grid stability by reducing power losses and supporting voltage profiles with a strong short-circuit ratio. Beyond 30%, the grid weakens as the short-circuit ratio falls below recommended levels, harmonic distortions rise sharply, and system inertia drops, causing voltage and frequency oscillations and increasing the risk of instability and loss of synchronism during disturbances. High PV penetration also leads to reverse power flows and overloads. To maintain stability at higher PV shares, the study recommends advanced grid-support solutions like battery storage, harmonic filters, and adaptive protection schemes.

Zhan [18] conducted a detailed study on feedback optimization mechanisms in distributed energy systems incorporating PV and battery energy storage systems. The study emphasized the role of smart dispatch in improving grid responsiveness and local balancing under real-world conditions in the Netherlands. Chandrashekar et al. [19] examined energy management systems integrating household PV installations, energy storage, and vehicle-to-grid technologies. They found that combining these assets for peak shaving and grid support was particularly beneficial in dense urban areas in India. In Morocco, Achour et al. [20] explored a multi-source hybrid setup involving PV, wind, and electric vehicles acting as mobile storage. This configuration proved particularly effective in off-grid and weak-grid scenarios.

In Italy, Shirvani et al. [21] proposed using a hydrogen-based storage system paired with residential PV installations as an alternative to conventional battery storage. Their case studies demonstrated the viability of hydrogen solutions for long-duration storage and seasonal energy shifting in scenarios with high levels of PV penetration. Similarly, Ibrahin et al. [22] conducted a cost-performance analysis of PV and battery energy storage integration under Malaysia’s net energy metering scheme. They concluded that strategic storage sizing is essential for optimal system performance and grid alignment.

Chaparro [23] examined the potential for decarbonizing household heating through solar PV and storage-assisted electrification in Germany and the Netherlands. Using Berlin and Amsterdam as test beds, the study demonstrated that domestic batteries can greatly improve system flexibility and reduce reliance on grid electricity during the heating season.

Furthermore, Santos et al. [24] assessed near-zero-energy buildings equipped with PV-BESS under a peer-to-peer energy trading scheme in Portugal. Their results confirmed that coordinating the operation of these systems can drastically reduce grid imports and facilitate energy democratization at the community level.

Alfaverh et al. [25] proposed an innovative approach using supervised and unsupervised machine learning algorithms to manage energy flows and battery performance in household PV systems. Their study demonstrated that predictive control based on electricity price forecasting and user behavior could significantly reduce grid dependency and improve operational efficiency in smart homes.

On a larger scale, Zhao et al. [26] explored a community-integrated energy system combining PV generation with both thermal and electrical energy storage to supply multiple households with electricity, heating, and cooling. Their model showed that coordinated multi-home energy management can lead to substantial improvements in renewable energy utilization, reduced peak loads, and enhanced economic viability of shared energy infrastructure.

In a region-specific case study, Rus-Casas et al. [27] examined the optimal sizing and control of PV batteries for a residential dwelling in southern Spain. Using time-resolved data on solar radiation and electricity pricing, they identified the most cost-effective battery capacity to maximize energy self-sufficiency and minimize electricity costs. Their findings underscore the importance of temporal resolution in energy simulations for accurately predicting the performance of PV-BESS systems under real-world conditions.

Complementing these international findings, Olczak [28] provided a detailed Polish case study analyzing a residential PV micro-installation equipped with microinverters. Using the HOMER software and high-resolution ERA5 weather data, the author validated theoretical energy productivity estimates against real operational data from a 10-panel rooftop system in the Masovian region. The model demonstrated exceptional predictive accuracy, with a mere 1.8% relative annual deviation between the simulated and measured energy output. The study also highlighted the influence of partial shading on panel-level discrepancies and emphasized the diagnostic advantages of microinverter-based systems in real-world conditions.

In the context of the rapid evolution of renewable energy technologies, the integration of PV-BESS has become increasingly relevant for both residential and commercial applications. Despite significant advancements in modeling and simulation techniques, there remains a critical gap between theoretical performance predictions and real-world operational data. Detailed real-world performance analyses that reflect local conditions, user behavior, and seasonal dynamics are needed. PV installations are subject to numerous external factors such as weather variability, shading, equipment degradation, and user behavior. These factors are often oversimplified or even ignored in purely theoretical models, which can be used to simulate system performance based on long-term average meteorological data. The use of such simulation tools is recognized as a valuable direction for future research, particularly for validating long-term performance trends and supporting broader generalization of results.

Showcasing real-world data, a scientific article can highlight the impact of these variables on system performance, thus offering valuable practical insights that are essential for optimizing future installations.

2. Materials and Methods

This article presents an in-depth analysis of the actual operation of a photovoltaic installation combined with a battery energy storage system. Located in a fully inhabited residential building, the installation ensures that the collected data reflects typical household energy consumption patterns and realistic operating conditions. Unlike controlled laboratory experiments or simulation-based studies, this analysis focuses on the real-world performance of the system, accounting for variations caused by seasonal changes, weather conditions, and daily energy demands.

The study spans a comprehensive period of one year, enabling the observation of long-term trends and seasonal variations in performance to be observed. By evaluating the system’s operational parameters over an extended timeframe, the analysis aims to identify the factors influencing the efficiency and reliability of the PV–BESS setup in a residential context. Furthermore, the collected data will enable an evaluation of energy production and storage utilization, offering valuable insights into how the system adapts to changing environmental conditions and user behavior.

2.1. Research Object

The analyzed object is located in the Tarnów County in the Małopolskie Voivodeship, Poland. The building on which the PV installation and the battery energy storage system are mounted has a hipped roof. The Photovoltaic panels are installed on two roof slopes: the southern and the western slopes. On the southern roof slope, 10 vertically oriented PV panels (one string) were installed, while on the western roof slope, 6 horizontally oriented PV panels (second string) were mounted. Figure 1 shows the photovoltaic installation mounted on the roof with a slope of 25°. All PV panels are identical, model Sharp 445 NU-JD445 [29]. Each PV panel is composed of two strings, each containing 72 half-cut monocrystalline cells. The main parameters of the PV panel are summarized in

Table 1. The main parameters of the PV panel [29].

Parameter	Unit	Value
Nominal Power	Wp	445
Total length	m	2.108
Total width	m	1.048
Voltage in MPP	V	38.52
Current in MPP	A	8.67
Power temperature coefficient	%/°C	−0.347
Panel efficiency	%	20.1

. The total power capacity of the photovoltaic installation is 7.28 kWp.

The installation is equipped with a Huawei inverter, model SUN2000-8KTL-M1 (Huawei, Shenzhen, China) [30], which serves as the core component for converting the generated DC power into AC power suitable for household use. This inverter is integrated with a dedicated energy storage system from Huawei, ensuring efficient energy management and optimal performance. The installation also includes a Huawei LUNA2000 (Huawei, Shenzhen, China) electrochemical energy storage unit with the Battery Management System (BMS) [31], with a total capacity of 10 kWh. Moreover, the installation has been equipped with a dedicated electricity meter, the Chint DTSU666-H (Huawei, Shenzhen, China), to ensure proper communication between the inverter and the BESS. The integration of this meter is crucial for accurate monitoring and management of energy flows within the system. It enables the inverter to accurately measure the amount of energy generated, consumed, stored, and exchanged with the grid. This real-time data acquisition is essential for optimizing energy usage and achieving efficient energy management.

This configuration not only supports energy autonomy and enhances the system’s ability to store excess solar energy for use during periods of low production or peak electricity demand. This increases the overall efficiency and reliability of the photovoltaic installation.

Table 2. The main parameters of the PV inverter and BESS [30,31].

Parameter	Unit	Value
Inverter
Rated output power	W	8000
European weighted efficiency	%	98.0
Number of MPPT trackers	Pcs.	2
Max. input current per MPPT	A	13.5
Rated input voltage	V	600
BESS
Number of battery modules	Pcs.	2 (max. 3)
Battery usable energy	kWh	10 (max. 15)
Max. output power	kW	5
Nominal voltage	V	600
Cell technology	-	LiFePO4
Scalability	-	Yes, max. 2 systems in parallel, each system max. 15 kWh

presents the main parameters of the inverter and battery system. Figure 2 presents the schematic diagram of the system with energy flow direction and communication signal between the smart meter, the inverter, and the BESS.

The system, consisting of the inverter and BESS, is managed by the inverter controller. This controller not only oversees the operation of the entire setup but also provides real-time visualization of the installation’s performance. Additionally, it can the capability to record instantaneous data with a frequency of every 5 min and store this information on the manufacturer’s server. This feature enables users to continuously monitor and analyze the energy flow and system efficiency via an online app.

The AC output of the inverter is connected to the three-phase domestic electrical installation, which is then linked to the distribution network via a cable connection and a bidirectional meter. This configuration enables energy to be imported and exported of energy from and to the grid, meaning the system is classified as on-grid. A photovoltaic installation equipped with the Huawei SUN2000-8KTL-M1 inverter (Huawei, Shenzhen, China) and the Luna2000 battery operates by converting solar energy into electricity, managing energy flows between the PV panels, household consumption, the battery, and the grid. During periods of surplus production, excess energy is stored in the Luna2000 battery, which can later supply the household during low solar output or peak demand. The inverter intelligently controls charging and discharging processes to optimize energy use and ensure a continuous supply.

Utilizing time-of-use tariffs (TOU, variable electricity pricing) enables the BESS to be charged directly from the grid when electricity prices are low, and stored energy can then be used during periods of high pricing. This strategy becomes particularly beneficial when the PV system does not generate sufficient energy, for example, on cloudy days or in winter. Consequently, the BESS can supply power to the household when PV output is minimal, effectively reducing the cost of electricity by leveraging cheaper energy from the grid during off-peak hours. This approach not only enhances energy autonomy but also optimizes economic efficiency by minimizing reliance on expensive grid energy during peak demand periods.

The weather data used in this study were obtained from a meteorological station located approximately 5 km from the research site in a straight line [32]. The meteorological station is a Davis Pro2 Plus (Huawei, Shenzhen, China) and is capable of providing a wide range of atmospheric data. For the purposes of this study, the external temperature and the intensity of solar radiation incident on a horizontal surface were utilized. Data were recorded every 5 min.

2.2. Economic Aspects

The data collected from the system spans a full year (from 1 September 2023 to 30 August 2024), aggregated on a monthly basis. Annual totals are also provided. This comprehensive dataset includes a range of key energy metrics such as total household energy consumption, total electricity generation by the PV system, electricity taken from the grid, electricity exported to the grid from the PV installation, and direct PV energy usage within the household (including BESS charging). Additionally, it encompasses the direct utilization of PV energy for household devices, the amount of PV-generated energy used for battery charging, and grid-sourced electricity used for battery charging. This detailed and multifaceted data enables a thorough analysis of the operational performance and economic feasibility of the integrated PV-BESS system, offering crucial insights into energy management, self-consumption, and cost optimization.

One of the primary analyses is the energy balance assessment, which aims to determine the system’s overall energy efficiency and self-sufficiency. The self-sufficiency ratio ($SSR$) can be calculated by comparing the total energy consumption from the PV installation ($E_{PV}$) with the total household energy consumption ($E_{cons}$) using the following equation:

$$SSR={\displaystyle \frac{E_{PV}}{E_{cons}}}$$

(1)

where

• $E_{PV}$—total energy consumption of energy generated from PV installation [kWh];
• $E_{cons}$—total household energy consumption [kWh].

It should be noted that the total energy consumption from the PV installation ($E_{PV}$) is the sum of the energy utilized directly in the building from the PV installation and the energy from the PV installation used to charge the energy storage system. This relationship is expressed in Equation (2).

$$E_{PV}=E_{PV-used}+E_{BESS-used}$$

(2)

where

• $E_{PV-used}$—energy directly utilized in the building from the PV installation [kWh];
• $E_{BESS-used}$—energy from the PV installation used to charge the BESS [kWh].

Additionally, the grid dependency ratio ($GDR$) can be calculated (Equation (3)) to determine the extent to which the household relies on external energy sources:

$$GDR={\displaystyle \frac{E_{grid}}{E_{cons}}}$$

(3)

where

• $E_{grid}$—energy imported from the grid [kWh].

Another crucial analysis involves examining self-consumption efficiency. The self-consumption ratio ($SCR$) is calculated (Equation (4)) by comparing the energy used directly from the PV system and energy stored in the BESS with the total energy generated by the PV installation:

$$SCR={\displaystyle \frac{E_{PV-used}+E_{PV-BESS}}{E_{PV}}}$$

(4)

Analyzing the energy export-import balance ($NB$) is essential for evaluating the system’s ability to minimize external energy imports. The net balance is calculated (Equation (5)) as:

$$NB=E_{export}-E_{grid}$$

(5)

where

• $E_{export}$—export energy to the grid [kWh].

The economic analysis of the system is equally important. To evaluate the financial impact, the cost savings ($CS$) from using the BESS during high tariff periods can be calculated as in Equation (6):

$$CS=\left(E_{BESS\_from\_grid }\times P_{high}\right)-(E_{grid-BESS}\times P_{low})$$

(6)

where

• $P_{high}$—peak electricity price [Euro];
• $P_{low}$—off-peak electricity price [Euro];
• $E_{BEES\_from\_grid }$—energy discharged from the battery during peak hours [kWh];
• $E_{grid-BEES}$—energy charged to the battery during off-peak hours [kWh].

To calculate the financial impact of using the BESS when charging it from the PV installation, it can be used the following formula (Equation (7)):

$$FI=E_{BESS-used}\times P_{grid}$$

(7)

where

• $P_{grid}$—price of electricity from the grid [Euro].

The financial performance of the analyzed PV and PV-BESS systems was assessed by applying the Simple Payback Time ($SPBT$) and the return on investment ($ROI$). The parameters in question were derived from simulated annual savings and investment costs. These indicators offer complementary insights into the investment attractiveness and recovery horizon.

$SPBT$ is defined as the time period required for the cumulative net savings generated by the system to equal the initial investment cost, without considering the time value of money. The $SPBT$ is a widely utilized metric in preliminary economic analyses. It offers a straightforward estimation of the time required for the system to reach a point of net benefit. The calculation is as follows:

$$SPBT={\displaystyle \frac{I}{S}}$$

(8)

where

• $I$—initial investment cost [Euro];
• $S$—annual savings from reduced electricity bills [Euro/year].

Return on investment is a financial metric that quantifies the total discounted financial return generated over the system’s operational life relative to its capital cost. This model incorporates the time value of money and can be expressed as follows:

$$ROI=\left({\displaystyle \frac{{\sum }_{i = 1}^n\frac{S_t}{{\left(1+r\right)}^i}-I}{I}}\right)\times 100\%$$

(9)

where

• $S_t$—projected electricity cost savings in year $i$ [Euro], assuming annual growth in electricity process;
• $r$—discount rate [%];
• $n$—operational lifespan of the installation [years].

Due to the varying legal regulations and electricity subsidies in Poland during the analyzed period, the analysis considered both the base prices of the fixed-rate and the variable-rate tariffs. These prices represent the total amounts, including all applicable taxes and charges. For the energy exported to the grid, the applicable energy selling rate was used, since the analyzed installation operates within the net-billing system. This rate specifically pertains to the active energy component during the given period. An average exchange rate of 4.20 PLN/Euro was assumed for the calculations. The key data related to the analyzed tariffs is presented in

Table 3. Electricity prices for the analyzed period [33].

Type of Tariff	Fixed [EUR/kWh]	Peak Price [EUR/kWh]	Off-Peak Price [EUR/kWh]
Fixed rate	0.3020	-	-
Variable rate	-	0.4921	0.1836

below, while the price for energy exported to the grid is summarized in

Table 4. Price for energy exported in the analyzed period [34].

Month	September 2023	October 2023	November 2023	December 2023	January 2024	February 2024
Price [EUR/MWh]	96.386	78.393	89.781	72.655	104.052	76.945
Month	March 2024	April 2024	May 2024	June 2024	July 2024	August 2024
Price [EUR/MWh]	59.012	59.983	60.521	78.683	67.076	57.604

. As it is difficult to determine in which tariff zones the specific amounts of energy stored in the BESS, originating from the PV installation, and from the PV installation were utilized, an average energy price from both the high- and low-cost tariff zones was assumed, amounting to 0.33785 EUR/kWh.

In order to accurately interpret the economic assessment and operational logic of the BESS, the temporal structure of the applied TOU electricity tariff has been precisely defined. In the analyzed case, the off-peak periods (low tariff) are designated as 1:00–3:00 p.m. and 10:00 p.m.–6:00 a.m. on weekdays and the entire duration of weekends and public holidays. Conversely, peak periods (high tariff) occur between 6:00 a.m. and 13:00 p.m., and 15:00 p.m. and 22:00 p.m. on regular working days. This TOU framework is a critical component of the energy management strategy, guiding the BESS to charge during low-tariff hours and discharge during peak-tariff intervals. This approach maximizes economic benefits by reducing electricity procurement costs. Explicitly including these time boundaries provides the necessary temporal context for interpreting the cost optimization analysis results and supports the rationale for adopting time-sensitive battery control algorithms.

Conducting these comprehensive analyses aims to evaluate the technical performance and economic impact of the PV-BESS. The findings will provide practical insights into energy management strategies for residential installations, particularly in scenarios where time-of-use tariffs are leveraged to reduce operational costs. This in-depth analysis will improve our understanding of how to effectively utilize integrated PV and energy storage systems can be effectively utilized to enhance energy self-sufficiency and reduce grid dependency in residential applications.

2.3. Operational Control Logic of the BESS

The battery energy storage system (BESS) integrated with the photovoltaic installation operates according to a clearly defined, price-guided control algorithm. This control logic aims to maximize economic efficiency by optimizing the timing of energy flows between the photovoltaic (PV) array, the BESS, the residential load, and the electrical grid based on time-of-use (TOU) electricity tariffs.

The state-of-charge ($SOC$) dynamics of the BESS is governed by the following equation:

$$SO{C}_{t+\mathsf{\Delta }t}=SO{C}_t+{\displaystyle \frac{\left(P_{charge}·{\eta }_{charge}-\frac{P_{discharge}}{{\eta }_{discharge}}\right)\mathsf{\Delta }t}{E_{capacity}}}$$

(10)

where

• $SO{C}_t$ and $SO{C}_{t+\mathsf{\Delta }t}$—the battery SOC at time $t$ and $t+\mathsf{\Delta }t$, respectively [%];
• $P_{charge}$—charging power [kW];
• $P_{discharge}$—discharging power [kW];
• ${\eta }_{charge}$ and ${\eta }_{discharge}$—charging and discharging efficiencies of the battery [%];
• $\mathsf{\Delta }t$—time interval [hours];
• $E_{capacity}$—usable energy capacity of the battery [kWh].

The system operates within defined constraints to ensure the longevity and efficiency of the battery:

$$SO{C}_{min}\le SO{C}_t\le SO{C}_{max}$$

(11)

$$0\le P_{charge}\le P_{charge,max}$$

(12)

$$0\le P_{discharge}\le P_{discharge,max}$$

(13)

where $SO{C}_{min}$ and $SO{C}_{max}$ denote the minimum and maximum permissible states-of-charge. In the analyzed system, the battery was always charged up to 100% but discharged only down to 20% to limit battery degradation. $P_{charge}$ and $P_{discharge}$ represent the maximum allowable charging and discharging power, respectively, corresponding to the inverter and battery specifications. In the analyzed system, it is 5 kW.

The operational logic of the system is defined by the following control rules:

• PV to Load: Generated PV power is primarily directed to supply the household load.
• PV to BESS: Excess PV energy not consumed by the load charges the battery until is reached.
• PV to Grid: Surplus PV energy, once the BESS is fully charged, is exported to the grid.
• BESS to Load: During high-tariff periods, the BESS discharges energy to cover household demand, reducing grid energy consumption.
• Grid to BESS: During low-tariff periods, if the battery $SOC$ is below the upper limit, the BESS charges directly from the grid up to $SO{C}_{max}$.

This logic ensures cost-effective operation, leveraging the TOU tariff structure to minimize energy procurement costs and maximize the self-consumption of locally generated PV energy.

3. Results and Discussion

A comprehensive series of analyses was conducted based on the data obtained from a real-world photovoltaic installation combined with an electrochemical energy storage system. These analyses were performed to evaluate the operational performance of such a system. These analyses covered various aspects of energy production, storage, and consumption, providing a detailed understanding of how the installation functions in practice.

3.1. Energy Flow Analysis of the PV-BESS

The results were presented with a breakdown by individual months, enabling seasonal variations and the efficiency of energy utilization throughout the year to be identified. Additionally, to better illustrate the system’s performance, representative graphs were also created depicting typical energy production from the PV installation, the charging and discharging cycles of the energy storage system, and the residential building’s overall energy demand. These visualizations were prepared specifically for winter and summer periods to highlight the differences in production and consumption patterns caused by seasonal changes.

The winter analysis focused on periods of low solar irradiance and increased household energy demand, demonstrating the importance of the BESS in ensuring an uninterrupted energy supply. In contrast, the summer analysis highlighted the system’s ability to maximize self-consumption during peak solar generation. These graphical representations provide valuable insights into the dynamic behavior of the PV-BESS system, demonstrating its ability to adapt to varying environmental and demand conditions.

The results obtained from the analyzed PV-BESS are presented in

Table 5. Monthly energy balance of the PV installation with a battery energy storage system.

	Energy Consumption	Energy Production	Energy Consumption from Grid	Energy from PV to Grid	Energy Consumption from PV	Direct Use of PV Energy	Energy from PV to BESS	Energy from Grid to BESS
	[kWh]
September 2023	367.53	745.16	37.66	415.29	329.87	206.85	123.02	14.35
October 2023	409.66	439.27	89.07	118.68	320.59	173.04	147.55	41.74
November 2023	691.95	131.85	577.52	17.42	114.43	70.11	44.32	233.96
December 2023	859.94	83.19	787.77	11.02	72.17	72.17	0.00	332.72
January 2024	990.61	84.07	913.31	6.77	77.30	77.30	0.00	353.29
February 2024	569.00	212.34	387.28	30.62	181.72	133.48	48.24	172.24
March 2024	621.23	496.13	261.78	136.68	359.45	250.74	108.71	126.39
April 2024	486.41	603.35	106.95	223.89	379.46	242.98	136.48	40.56
May 2024	475.05	936.99	18.17	480.11	456.88	185.79	271.09	11.07
June 2024	488.99	934.57	15.77	461.35	473.22	275.96	197.26	0.00
July 2024	541.41	934.16	30.73	423.48	510.68	367.29	143.39	0.00
August 2024	383.66	873.51	25.51	515.36	358.15	145.77	212.38	0.00
Total	6885.44	6474.59	3251.52	2840.67	3633.92	2201.48	1432.44	1326.32

. The data presented in this table have been derived from a comprehensive year-long analysis, in which a variety of operational parameters and performance metrics of the system have been taken into account.

The presented data encompasses a complete annual period from September 2023 to August 2024, providing a comprehensive monthly analysis of energy production, consumption, and grid interaction. This methodical presentation facilitates a comprehensive examination of the system’s operational efficiency, emphasizing seasonal fluctuations and the aggregate performance of the PV-BESS configuration.

The total energy consumption recorded over the analyzed period amounts to 6885.44 kWh, while the total energy generated by the PV installation is 6474.59 kWh. This finding suggests that the PV system possesses the capacity to generate a substantial proportion of the annual energy consumption of the household, thereby demonstrating a notable degree of potential for energy autonomy. However, significant seasonal discrepancies affect this balance, largely influenced by varying solar irradiance throughout the year.

The analyzed photovoltaic installation that was analyzed yielded a production of only 909.35 kWh/kWp, which is a relatively low value compared to typical PV system yields. However, it should be noted that this low production rate is closely linked to the specific location and configuration of the installation. One of the key factors influencing energy generation is the roof inclination, which in this case is 25°. While this tilt angle is relatively favorable for solar energy capture during the summer months, the orientation of the PV panels has been shown to have a significant impact on the overall energy output.

In this particular installation, a mere 10 out of the 16 PV panels are oriented in a southward direction, a configuration that is optimal for maximizing solar exposure in the northern hemisphere. The remaining six panels are oriented towards the west, a configuration which inherently reduces the energy generation potential, especially during the peak solar hours typically experienced around midday. This configuration results in a non-uniform energy yield throughout the day, with increased generation during the afternoon due to the west-facing panels, but a significant reduction compared to a fully south-facing system.

The combination of a sub-optimal panel orientation and the specific inclination angle is a factor in the relatively low annual specific yield of the installation. Furthermore, localized factors such as partial shading, particularly in the morning for the west-facing modules, have been shown to have a further detrimental effect on efficiency. It is imperative to acknowledge the significance of contemplating both roof inclination and panel orientation in the design of residential PV systems. These variables exert a considerable and direct influence on the system’s energy production capacity.

Notwithstanding the comparatively modest yield, the configuration was chosen based on practical constraints related to the building’s architecture and available roof space. The integration of the system with a BESS helps mitigate the impact of suboptimal orientation by allowing energy storage during peak production periods and usage during low production times. This strategic use of stored energy contributes to enhancing the overall efficiency of the system, notwithstanding the challenges posed by the configuration of the panel layout.

As demonstrated in Table 5, there is a decline in energy production during the colder months (November to February), with a recorded minimum of 83.19 kWh in December. Concurrently, energy consumption peaks in the same period, with the highest value observed also in January (990.61 kWh). This discrepancy can be attributed to a combination of factors, primarily the reduced availability of solar energy and the increased energy demands experienced during the colder months, which are primarily attributed to heating and lighting. Consequently, the household becomes more dependent on the grid to meet its energy demands, as reflected by high grid consumption values (e.g., 913.31 kWh in January).

Conversely, the summer months (May to July) demonstrate a substantially higher energy generation capacity, with May recording 936.99 kWh of production, while consumption remains relatively low (e.g., 475.05 kWh in May). This seasonal disparity leads to an excess of generated electricity, much of which is exported to the grid. It is evident that May exhibits a noteworthy energy export of 480.11 kWh, signifying that the system makes a substantial contribution to the public grid during periods of optimal solar availability.

The interaction between the system and the grid is a pivotal component in determining the efficiency of the installation. The total energy consumption from the grid over the analyzed year was 3251.52 kWh, while the energy fed into the grid from the PV system was 2840.67 kWh. This results in a net grid balance where the installation nearly compensates for the imported energy by exporting excess production, particularly during peak generation months. It is evident that, under optimal management and favorable conditions, the system exhibits the capacity to attain a net-zero energy balance.

A critical component of the installation is the BESS, which plays a pivotal role in managing energy flows. The system has been engineered to capture excess energy during periods of high production output and to discharge this when the PV output is insufficient. The total energy from PV utilized for the purpose of charging the BESS amounts to 1432.44 kWh, whereas the energy drawn from the grid for the purpose of charging the BESS was 1326.32 kWh. The ability to charge the battery from the grid during low-tariff periods, as observed in winter, highlights the strategic utilization of time-of-use tariffs to optimize economic efficiency. For instance, in January, the BESS was charged with 353.29 kWh from the grid, primarily to offset higher energy costs during peak pricing hours.

The assessment of system performance necessitates the consideration of the direct utilization of PV energy within the household, which constitutes a pivotal factor. The total direct use of PV energy is 2201.48 kWh, indicating that a significant proportion of the generated energy is consumed on-site, reducing dependency on external power sources. Furthermore, the direct utilization of PV energy for household consumption, without intermediate storage, amounts to 3633.92 kWh. This emphasizes the system’s capability to meet immediate energy needs efficiently when solar is favorable.

The distribution of energy usage between direct consumption, battery charging, and export to the grid demonstrates the system’s flexibility and its ability to adapt to varying energy demands and production levels. The system’s design, which integrates on-grid functionality with efficient battery management, allows for peak shaving, load shifting, and optimized energy utilization. During periods of minimal solar irradiance, the BESS functions as a storage reservoir, thereby ensuring uninterrupted supply while minimizing the necessity for costly grid energy acquisitions. Conversely, during periods of peak production, the system functions in a manner that is distinct from its role during off-peak periods. In this capacity, it not only addresses the energy requirements of the household but also contributes to the grid by facilitating the distribution of surplus energy.

3.2. Winter Operation of the System

The figures below (Figure 3 and Figure 4) illustrate the dynamic relationship between external temperature and grid load (Figure 3) and energy generation and irradiance (Figure 4) from a PV installation over 31 days (744 h) in January 2024. This analysis focuses on understanding how environmental factors, such as temperature and irradiance, influence PV energy production and grid interaction in a residential setting.

Figure 3 shows hourly grid energy consumption and ambient temperature over the course of January. The winter season is characterized by low solar irradiance and increased energy demand for space heating, which poses a significant challenge to achieving energy self-sufficiency in residential buildings.

Figure 3 shows that energy drawn from the grid was relatively high throughout the month, with multiple sharp peaks, especially during colder periods when temperatures dropped below 0 °C. The largest consumption peaks occurred between hours 190 and 240 and correlated directly with the coldest days of the month. These conditions are clearly indicative of elevated heating requirements, particularly during the nighttime and early morning hours. The increased demand is primarily due to the operation of an air-source heat pump. During extremely low temperatures, the heat pump required additional support from electric resistance heaters to maintain indoor comfort. This auxiliary heating significantly increased the building’s power consumption, as evidenced by the negative power peaks depicted in the graph.

Additionally, the graph shows periods when the BESS was charged directly from the grid. This occurs during periods of reduced energy prices when the time-of-use (TOU) strategy is employed to minimize operational costs. The power drawn from the grid to charge the battery is distinguishable on the graph due to the BESS’s maximum charging power of 5 kW. These charging events are evident as consistent negative peaks, which differ from the more variable household demand.

Figure 4 shows the hourly output power of the PV system alongside solar irradiance levels for January. As expected during winter, PV production depended heavily on solar radiation availability and exhibited substantial daily variability.

The data show that solar irradiance values frequently remained below 100 W/m², with several days of near-zero radiation, especially during hours 120–140 and 360–384, and 576–672. These periods corresponded to dense cloud cover, overcast skies, and snow covering the PV panels. Consequently, the PV system produced limited output during these intervals. On days with clearer skies, such as around hours 480–552 and 672–720, irradiance levels exceeded 300 W/m², resulting in peak PV generation of about 4000 W.

There is a clear correlation between irradiance and PV output; the power curve closely follows the irradiance pattern. However, due to the low sun angle and short daylight hours typical of January, daily generation was restricted to a few hours.

The January analysis reveals a clear seasonal mismatch between energy demand and PV generation. The first chart shows a strong correlation between electricity consumption from the grid and ambient temperature. During colder periods, particularly around hour 200, energy demand increased sharply, likely due to additional heating needs beyond what the heat pump could supply. The second chart shows that PV output was significantly limited by low solar irradiance and short daylight hours. Only a few days had irradiance levels above 400 W/m². Consequently, PV generation was limited in both magnitude and duration. Together, the charts confirm that, when household energy needs peak, renewable production is lowest. This highlights the importance of battery storage systems and intelligent energy management to mitigate winter dependency on the grid.

3.3. Summer Operation of the System

The following figures illustrate the dynamic relationship between external temperature and energy exchange with the electrical grid (Figure 5), energy generation from a PV installation, and irradiance (Figure 6) over a period of 31 days (744 h), corresponding to one month (July 2024).

Figure 5 shows the hourly energy exchange profile with the electrical grid (labeled “Grid”) and the ambient temperature (“Temperature”) recorded in July, a summer month. The temperature pattern follows a regular daily cycle, with nighttime lows around 15 °C and daytime highs that often exceed 30–35 °C. These elevated temperatures are characteristic of the summer season and are associated with increased cooling demand within the household, particularly in the afternoons. This is reflected in the power exchanged with the grid. During the nighttime and early morning hours, electricity is drawn from the grid (negative values). During the daytime, when solar generation exceeds instantaneous demand and battery capacity is saturated, surplus electricity is exported to the grid (positive values). Grid export intensity typically coincides with periods of peak ambient temperature and irradiance. Around midday, notably, the exported power reaches its highest values, indicating significant PV generation and system self-sufficiency. Negative peaks during the day mainly correspond to periods when the air-source heat pump operates to heat domestic hot water (DHW). When the ambient temperature exceeds 24 °C, the heat pump’s compressor protection system activates, and electric resistance heaters are triggered to maintain the hot water supply. These instances manifest as discrete negative peaks, indicating a surge in electricity demand from the grid to power the heaters (with a total power output of 9 kW).

Figure 6 supplements this analysis by displaying the relationship between PV system output power (PV) and solar irradiance (Irradiance). As expected, the two variables are strongly correlated, and they have nearly symmetric daily generation profiles under clear sky conditions. Maximum irradiance values often exceed 900–1000 W/m², resulting in PV power outputs of over 7 kW and occasionally approaching the system’s rated capacity. These high levels of generation occur consistently throughout the month except on cloudy days, which cause irregularities and sudden dips in irradiance and PV power. The shape and distribution of the PV output curve demonstrate the system’s high performance during the summer when long days and intense sunlight create ideal conditions for energy production. The elevated, stable PV output during this period reduces dependency on grid electricity and increases the export of surplus energy. Notably, the PV system’s efficiency remains high despite elevated ambient temperatures, which can sometimes reduce voltage and overall module performance.

Together, these two figures provide a comprehensive picture of how the system behaves during the summer, clearly showing the advantages of PV generation under high irradiance and temperature conditions. The correlation between solar availability, power output, temperature, and grid exchange underscores the importance of seasonal analyses and validates the installation’s effectiveness during peak production periods.

3.4. Power Balance of the System

In order to provide a clearer representation of the energy flow within the system, including PV energy production as well as the import and export of energy to the grid, figures have been presented below. As illustrated in Figure 7 and Figure 8, the operation of the installation was observed on a specific day during the summer period (22 July 2024). The designated timeframe for the analysis aligns with the period during which the PV installation was engaged in active energy generation, specifically between 6:00 and 20:00. This focused visualization allows for a comprehensive understanding of the system’s performance during peak solar hours, thereby illustrating how the installation manages energy production and interacts with the grid throughout the day.

Figure 7 shows the power balance of the PV installation, representing various power flows within the system throughout the selected day. The x-axis indicates the time in hours from 6:00 to 20:00, corresponding to the active generation period of the PV system. The y-axis shows the power values in watts (W). The following variables are depicted:

• PV (orange line): Power generated by the PV installation.
• Charge/Discharge (green line): The power utilized to charge the energy storage system (positive values) or power discharged from the battery (negative values).
• Pcons (blue dashed line): Power consumed by household devices, excluding the power needed for battery charging.
• PVgrid (purple line): Power exported to the grid, representing surplus energy not utilized within the building.

The graph illustrates the conventional summer power generation profile, exhibiting a pronounced peak around midday, with an approximate output of 6000 W. The PV system’s power production undergoes a steady increase from approximately 6:00, reaching its maximum between 12:00 and 14:00, a timeframe that aligns with elevated levels of solar irradiance. During this peak generation period, the household’s energy demand is relatively low compared to production, leading to surplus energy being exported to the grid. The positive peaks of the PVgrid line are indicative of the system’s effective management of electricity generation, with excess electricity being efficiently fed into the distribution network.

The charge/discharge line is indicative of the dynamics of the BESS. As the day progresses, the PV production system experiences an increase in output, resulting in a surplus of energy. Initially, the excess energy is allocated to the process of charging the battery. Positive values indicate active charging when the generated power exceeds the immediate consumption within the house. During the early hours, the BESS efficiently stores the excess energy produced by the PV installation. Around 11:00, the battery reaches 100% charge capacity, as indicated by the leveling off of the charge/discharge line. At this point, any further surplus energy generated by the PV system, which can no longer be stored, is directly exported to the grid. This transition is evident in the graph, where the PVgrid line exhibits a sharp increase concomitant with the stabilization of the charge/discharge line.

Conversely, when power demand temporarily exceeds PV generation, the battery discharges, as evidenced by the negative peaks. The system’s intelligent design aims to optimize energy flow, thereby maximizing self-consumption and minimizing reliance on external grids. Ensuring that the battery is fully charged prior to energy export optimizes energy retention within the household, thereby enhancing energy autonomy.

A critical component of the power management strategy is the effective utilization of PV energy. During the peak production hours, direct household consumption (Pcons) remains relatively stable, indicating that the majority of generated power is either stored in the battery or exported to the grid.

Figure 8 focuses on the voltage stability in the grid during the same period, presenting the PV power generation (orange line) and the voltage levels across the three phases of the electrical network: Phase A (blue line), Phase B (purple line), and Phase C (green line). The graph also includes a red line representing the voltage limit of 253 V, which is the maximum allowable voltage for proper inverter operation.

One of the critical challenges depicted in the graph is the issue of excessive grid voltage, which can exert a substantial influence on the PV system’s operational stability. During periods of maximum solar generation, particularly between 11:00 and 15:00, voltage levels on all three phases frequently exceed the threshold of 253 V. This voltage rise coincides with the peak PV output, indicating that high local generation, combined with limited local consumption and grid capacity, leads to voltage instability.

In instances where the voltage in the grid exceeds the critical value of 253 V for a brief period or 256 V abruptly, the inverter automatically shuts down to protect the system and adhere to grid regulations. This phenomenon is visible on the graph as sudden drops in the PV power line, where generation temporarily ceases. Concurrently, the atmospheric conditions were optimal, with a complete absence of cloud cover in the sky. This ensured the stability of the installation. It has been demonstrated that each time the voltage decreases to an acceptable level, the inverter restarts. However, it should be noted that frequent shutdowns have been shown to reduce the overall energy yield and efficiency of the system.

This issue is particularly problematic during sunny and warm days when PV generation is at its peak, but local grid consumption is relatively low. In such scenarios, the inability to export energy effectively results in frequent inverter shutdowns, causing a loss of potential solar energy production. Moreover, this challenge highlights the necessity for grid reinforcement or adaptive control strategies, such as dynamic reactive power compensation or energy storage integration, to stabilize voltage levels and maintain continuous PV operation.

3.5. Economic Analysis of a PV Installation with BESS

As illustrated in

Table 6. Annual operational and economic performance of the PV installation with BESS.

	SSR	GDR	SCR (with BESS)	SCR (Without BESS)	NB	CS	FI	DPV
	[%]				[kWh]	[EUR]
September 2023	89.75	10.25	44.27	27.76	377.63	4.43	41.56	69.88
October 2023	78.26	21.74	72.98	39.39	29.61	12.88	49.85	58.46
November 2023	16.54	83.46	86.79	53.17	−560.10	72.18	14.97	23.69
December 2023	8.39	91.61	86.75	86.75	−776.75	102.64	0.00	24.38
January 2024	7.80	92.20	91.95	91.95	−906.54	108.99	0.00	26.12
February 2024	31.94	68.06	85.58	62.86	−356.66	53.14	16.30	45.10
March 2024	57.86	42.14	72.45	50.54	−125.10	38.99	36.73	84.71
April 2024	78.01	21.99	62.89	40.27	116.94	12.51	46.11	82.09
May 2024	96.18	3.82	48.76	19.83	461.94	3.42	91.59	62.77
June 2024	96.77	3.23	50.64	29.53	445.58	0.00	66.64	93.23
July 2024	94.32	5.68	54.67	39.32	392.75	0.00	48.44	124.09
August 2024	93.35	6.65	41.00	16.69	489.85	0.00	71.75	49.25
Annually	52.78	47.22	56.13	34.00	−410.85	409.17	483.95	743.77

, a thorough evaluation of the operational and economic performance of the examined PV installation integrated with a battery energy storage system (BESS) over the course of a year is presented, with the data categorized by month. The data set encompasses key performance indicators, including the self-sufficiency ratio ($SSR$), grid dependency ratio ($GDR$), self-consumption ratio ($SCR$) both with and without BESS, net balance ($NB$) of energy export and import, cost savings ($SC$s) from utilizing BESS during high tariff periods, financial impact ($FI$) of using BESS when charging from PV, and direct PV ($DPV$) financial impact, which reflects the economic benefit of directly using PV-generated energy within the household.

The $SSR$ is indicative of the extent to which the household’s energy requirements are met by the PV and BESS systems, independent of the external grid. The annual average SSR is 52.78%, indicating that slightly more than half of the household’s energy consumption is covered by PV installation and stored energy. The highest SSR values occur during the summer months (July and August), reaching 94.32% and 93.35%, respectively. This high level can be attributed to the optimal solar conditions and effective utilization of the BESS. In contrast, winter months (January and February) show significantly lower $SSR$ values of 7.80% and 31.94%, respectively, signifying a decline in solar generation and an escalation in heating demand.

The $GDR$ is a metric that indicates the proportion of a household’s energy consumption that is derived from the grid. The annual average $GDR$ is 47.22%, indicating a balanced reliance on both self-generated and grid-supplied electricity. During the winter period, the $GDR$ peaks at 92.20% in January, indicating a high degree of grid dependency due to limited PV generation and high energy demands, especially for heating. Conversely, in May and June, the $GDR$ drops to 3.82% and 3.23%, respectively, showing minimal grid interaction during peak solar months. As expected, the sum of the self-sufficiency ratio ($SSR$) and the grid dependency ratio ($GDR$) equals 100% for each month, reflecting their complementary nature in the context of total household energy consumption.

The $SCR$ quantifies the proportion of the generated PV energy that is directly utilized within the household, as opposed to being exported to the grid. The average annual $SCR$ with BESS is 56.13%, which is significantly higher than the 34.00% obtained without BESS. This increase indicates the positive impact of the battery system on maximizing the local utilization of generated energy. Notably, in November, December, and January, the $SCR$ peaks at 86.79%, 86.75%, and 91.95%, respectively, indicating that during lower generation months, most of the produced energy is consumed directly or stored rather than exported. Conversely, August and September exhibited lower $SCR$ values (41.00% and 44.27%, respectively) attributable to augmented production and constrained storage capacity.

The $NB$ is indicative of the discrepancy between the energy exported to the grid and the energy imported from it. The presence of negative values signifies a scenario in which the quantity of energy imported exceeds that exported. This phenomenon is particularly evident during the winter months, as evidenced by the notable example of −906.54 kWh in January. This observation reflects a high level of grid consumption, which is attributable to the comparatively low PV output. Positive balances are observed during summer months (e.g., 489.85 kWh in August), when surplus energy is generated and exported. The annual net balance of −410.85 kWh indicates a marginal energy deficit over the course of the year, primarily attributable to winter consumption.

The $CS$ is indicative of economic benefit driven from the utilization of BESS during high tariff periods. The annual $CS$ amounts to EUR 409.17, indicating that strategic charging and discharging of the battery system can significantly reduce electricity costs. The highest recorded monthly savings were observed in January (EUR 108.99) and December (EUR 102.64), which correspond to periods of elevated energy costs and optimal BESS utilization.

The $FI$ for utilizing the BESS when charging from PV sources is EUR 483.95 per year. This calculation underscores the economic benefits of using self-generated energy for charging purposes, as opposed to drawing from the grid. The maximum value is observed in May (EUR 91.59), at which point the battery effectively supports energy demands, thereby reducing the necessity to purchase expensive grid power.

The $DPV$ financial impact, which measures the savings from directly utilized PV-generated energy within the household, reaches EUR 743.77 annually. This value underscores the significant cost reduction achieved by prioritizing direct consumption over exporting surplus energy to the grid. The maximum monthly $DPV$ values are observed in July (EUR 124.09) and June (EUR 93.23), which reflects the optimal utilization of solar energy during the summer months.

Furthermore, it is imperative to consider the revenue derived from the exportation of energy to the grid during each month under analysis. This revenue is a significant factor in the overall economic assessment of the PV installation combined with the BESS. The utilization of the data presented in Table 4 facilitates the calculation of the total annual revenue derived from the sale of surplus energy to the grid. The analysis indicates that the total annual revenue from energy export is EUR 199.70. This value represents an important financial benefit, as it mitigates a portion of the energy expenditures incurred during periods when grid power is necessary, particularly during months with diminished PV production. The inclusion of this revenue in the economic analysis provides a more comprehensive understanding of the system’s financial performance. Furthermore, it highlights the economic viability of integrating a PV installation with grid interaction.

3.6. Financial Performance of PV-Based Systems

The subsequent section presents a thorough comprehensive comparative analysis of various installation configurations to assess their economic and operational performance. This encompasses a range of scenarios, meticulously designed to accurately reflect the potential benefits and limitations inherent in each configuration. The baseline scenario represents a traditional setup without a PV installation and BESS, using a fixed electricity price throughout the year (Case 1). This scenario serves as a point of reference for the evaluation of the financial impact of the integration of renewable energy systems.

The second scenario (Case 2) involves a PV installation without a BESS, also using a fixed electricity price. This configuration highlights the merits of solar energy generation while acknowledging the constraints imposed by its inability to store energy, particularly with regard to self-consumption and reliance on the grid.

The third scenario (Case 3) combines a PV installation with BESS while operating under a variable electricity pricing model. This configuration exemplifies a sophisticated energy management strategy, whereby the system capitalizes on the versatility of battery storage to enhance energy utilization, particularly during periods of high and low tariff rates. This configuration enables strategic charging during low-cost periods and discharging during peak pricing, aiming to maximize cost savings and energy self-sufficiency.

As illustrated in

Table 7. Comparative analysis of annual electricity costs and financial benefits for different PV and BESS configurations.

	Electricity Cost	FI	DPV	Egrid	Net Annual Cost
	[EUR]
Case 1	2079.40	-	-	-	2079.40
Case 2		-	664.85	299.20	1115.35
Case 3		483.95	743.77	199.70	651.98

, a comparative analysis of the annual electricity costs and financial benefits associated with different configurations of a residential PV installation, with and without BESS, is provided. The table delineates three discrete cases to illustrate the economic impact of integrating PV and BESS under varying operational scenarios.

Case 1 represents the baseline scenario without PV and BESS, where the entire electricity demand is met from the grid at a fixed electricity cost. In this case, the total annual electricity cost amounts to EUR 2079.40, as the household relies entirely on grid power. Given the absence of PV generation or energy storage, the net annual cost remains commensurate with the total electricity cost.

Case 2 illustrates a configuration in which the household is equipped with a PV installation, yet lacks a BESS. This configuration operates under a fixed electricity tariff. In this scenario, the net annual cost is reduced considerably to EUR 1115.35. This decline is predominantly attributable to the direct PV savings, which amount to EUR 664.85, achieved by utilizing the generated solar energy directly within the household. Moreover, the system generates EUR 299.20 from the exportation of surplus energy to the grid. Given the configuration’s absence of a BESS, the financial impact of energy storage is not applicable. The decline in the net annual cost, as compared to Case 1, underscores the financial benefit of utilizing solar energy directly for household consumption and exporting surplus production to the grid.

Case 3 represents the most advanced configuration, combining a PV installation with a BESS and utilizing a variable electricity tariff. The integration of BESS in this particular scenario has been shown to enhance economic efficiency, yielding a net annual cost of EUR 651.98, which is the lowest among the three cases. This significant cost reduction is a result of several factors: $FI$ of EUR 483.95 derived from charging the BESS with PV energy and discharging it during high-tariff periods, $DPV$ of EUR 743.77 from using solar energy directly in the household, and additional revenue from energy exported to the grid amounting to EUR 199.70. The variable electricity tariff in this configuration enables strategic management of energy flows, wherein the BESS is charged during low-cost periods and discharged when grid prices are higher, thereby optimizing the overall cost savings.

The comparison clearly demonstrates that integrating a BESS with a PV system under a variable tariff scenario (Case 3) yields the most significant cost reduction. The utilization of direct PV savings, strategic battery management, and revenue from surplus energy export collectively result in a significant reduction in the annual electricity expenditures.

In order to ensure a comprehensive evaluation of the analyzed PV and BESS installations, it is essential to consider both variants with and without external funding, taking into account the associated investment costs. In the absence of financial support (Variant 1), the cost of the standalone PV installation is estimated at EUR 9400. Conversely, the integrated system, which encompasses the PV installation and the battery energy storage system (BESS), is projected to incur a total cost of EUR 16,900. These values reflect the full investment required for setting up the systems independently of any subsidy programs.

On the other hand, in the second variant (Variant 2), which includes financial support, the costs are significantly reduced. The price of the PV installation alone is reduced to EUR 7970, while the cost of the combined PV and BESS installation is EUR 12,910. This reduction is indicative of the impact of the subsidy, thereby rendering the installation of the integrated system more economically viable.

As illustrated in

Table 8. Annual financial performance and payback time of PV and PV + BESS installations.

	Net Annual Cost	Savings	SPBT
			Variant 1	Variant 2
	[EUR]		Years
PV	1115.35	964.05	9.8	8.3
PV + BESS	651.98	1427.42	11.8	9.0

, a comparative analysis is provided of the net annual cost, annual savings, and Simple Payback Time ($SPBT$) for two configurations of a residential energy system: a standalone PV installation and a PV-BESS system. The analysis encompasses two distinct financial scenarios.

The annual savings indicate the reduction in electricity expenses compared to a baseline scenario (Case 1) without any renewable energy system. The PV installation alone achieves EUR 964.05 in annual savings, while the integration of the BESS increases the savings to EUR 1427.42. The observed increase can be attributed to the BESS’s capacity to store excess PV energy and subsequently discharge it during periods of elevated grid prices. This capability contributes to the enhancement of cost efficiency.

The $SPBT$ is a financial metric that reflects the number of years required to recover the initial investment through accumulated savings. For the PV-only configuration, the $SPBT$ is 9.8 years (Variant 1) and 8.3 years (Variant 2), indicating a faster return on investment when financial support is included. In contrast, the PV-BESS has a longer SPBT of 11.8 years (Variant 1) and 9.0 years (Variant 2). The discrepancy between these variants underscores the considerable impact of financial support on enhancing the economic viability of integrating a combined PV and BESS.

Furthermore, the long-term financial performance of the proposed PV and PV-BESS was assessed by calculating the $ROI$ indicator. $ROI$ is a metric that calculates the ratio of net financial gain to the initial investment, taking into account the time value of money over the system’s lifetime. The financial evaluation was conducted for a 12-year operational period. The study’s findings indicated that a 5% annual growth in electricity prices would lead to increased savings due to reduced grid electricity purchases. The cost of capital was reflected in the $ROI$ calculations using a 5% discount rate. The calculated $ROI$ values for each configuration are summarized in

Table 9. Comparison of ROI values for different system configurations and investment variants.

	ROI
	Variant 1	Variant 2
	[%]
PV	17.21	38.24
PV + BESS	−3.47	26.36

.

The results of the study indicate that the PV-only configuration with financial support offers the most favorable financial performance, yielding a return of 38.24%. The addition of a battery increases annual savings but also significantly raises the initial investment, resulting in a lower $ROI$ of 26.36% in the subsidized scenario.

In the absence of subsidies, the PV-only installation generates a moderate positive $ROI$ of 17.21%, while the PV-BESS configuration yields a negative $ROI$ of –3.47%. This suggests that, under the stipulated conditions, the investment does not recoup its costs within the 12-year timeframe, considering the cost of capital.

The results clearly demonstrate that while the PV-only system offers a reduced payback period, integrating a BESS enhances both financial savings and energy independence. Nonetheless, the extended payback period for the PV-BESS setup underscores the need to balance the higher initial investment with the long-term financial benefits, especially considering variable electricity tariffs. The inclusion of funding significantly improves the economic attractiveness of both configurations, reducing the payback time and optimizing financial sustainability.

4. Conclusions

The empirical investigation of the operational functionality of a photovoltaic micro-installation, integrated with a battery energy storage system, installed on a residential building, yielded substantial insights into the real-world performance and economic viability of such systems. The study, which was conducted over the course of an annual cycle, enabled the assessment of the system’s energy production, storage, consumption, and economic impact under varying seasonal and environmental conditions.

The results demonstrate that integrating a BESS with a PV installation leads to a substantial augmentation in energy self-sufficiency, particularly during the summer months when solar irradiance levels are at their peak. The $SSR$ for the combined PV-BESS system reached values exceeding 90% in the summer, indicating a high level of energy autonomy. However, during the winter months, the $SSR$ decreased significantly, indicating the challenges posed by reduced solar generation and increased energy consumption. This seasonal variation underscores the pivotal function of BESS in preserving energy balance during periods of diminished PV output.

From an economic perspective, the inclusion of BESS has been demonstrated to be advantageous, particularly in contexts where electricity tariffs are subject to variation. The financial analysis revealed that charging the BESS during low-tariff periods and discharging during high-tariff periods significantly reduced the net annual electricity cost compared to a system without energy storage. The calculated cost savings from using BESS during high tariff periods amounted to approximately EUR 409 annually. Moreover, the direct utilization of PV-generated energy within the household resulted in additional savings amounting to EUR 743.

Notwithstanding the financial advantages, the analysis also identified certain challenges, particularly related to grid voltage stability. The occurrence of excessive grid voltage during periods of peak solar production results in the temporary shutdown of inverters, thereby reducing the overall energy yield. This issue underscores the necessity for enhanced grid infrastructure and adaptive voltage regulation strategies to address the expanding number of prosumer installations.

A comparative analysis of three scenarios—no PV and BESS, PV-only, and PV with BESS—was conducted to highlight the economic advantage of integrating energy storage, particularly when combined with time-of-use tariffs. While the standalone PV system offered a quicker return on investment, the PV-BESS configuration provided greater long-term savings and enhanced energy independence. Furthermore, the inclusion of financial support significantly improved the economic viability of the system, reducing SPBT to 9.0 years for the integrated configuration.

In conclusion, the present study demonstrates that residential PV systems combined with BESS offer substantial benefits in terms of energy autonomy, cost savings, and grid support. However, the effectiveness of such systems is highly dependent on local environmental conditions, tariff structures, and grid infrastructure. Therefore, careful consideration of these factors is essential when planning and optimizing residential renewable energy installations. Future research should focus on developing adaptive control strategies to mitigate grid voltage issues and enhance the resilience of PV-BESS in residential applications.