Reviews of Photovoltaic and Energy Storage Systems in Buildings for Sustainable Power Generation and Utilization from Perspectives of System Integration and Optimization

Abstract

This paper focuses on the latest studies and applications of Photovoltaic (PV) systems and Energy Storage Systems (ESS) in buildings from perspectives of system configurations, mathematic models, and optimization of design and operation. Mathematical models, which can accurately calculate PV yield and support integrating green electricity and energy storage into the grid, were reviewed. Using these mathematic models, various configurations and factors affecting PV system performance were explored. Key findings reveal that PV systems, which operate without using fossil fuels and emitting carbon dioxide, can significantly reduce buildings’ dependence on fossil energy and achieve deep decarbonization. Factors, such as temperature and solar radiation, need to be considered in improving PV performance and yield. Except from classifying different PV systems and discussing renewable energy generation performance, operation strategies of power systems with PV generation and storage, were also summarized to enhance green energy utilization and economic performances. This paper offers guidance on designing and operating high-efficiency PV-ESS in buildings.

1. Introduction

Carbon neutralization strategies [1] have led to the development of an investment and dispatch model designed for an urban energy system, supporting the city’s 2030 carbon neutrality goal. Z.M. Liu et al. [2] proposed a two-phase economic decarbonization plan, which was increasing renewable penetration to reduce fossil fuel reliance, followed by a carbon cap for deep decarbonization. Using photovoltaic (PV) power generation and energy storage in buildings is a highly effective strategy to achieve carbon neutralization in building energy systems. The International Energy Agency (IEA) reported that buildings accounted for 40% of global energy use and 33% of greenhouse gas emissions [3]. Integrating PV systems and energy storage helps buildings reduce fossil fuel dependence, cutting carbon emissions significantly. In Germany, buildings with PV and energy storage systems have reduced grid electricity use by up to 90% [4]. By the end of 2023, building-integrated PV systems had a global installed capacity of 1419 GW, reflecting rapid adoption growth [5].

Solar energy is considered an important renewable energy (RE), which can be applied to both photovoltaic (PV) and solar thermal power generation. Since January 2020, California has mandated all new residential buildings to meet near-NZEB targets under Title 24 standards [6]. J. Yi [7] reported that HVAC systems could integrate about 65% of variable renewable energy without compromising reliability. H.X. Sun et al. [8] proposed a decision-making method for high-density urban areas, aiding large-scale (Building Integrated PV) BIPV adoption.

Power grids combining photovoltaics, battery storage, and diesel generators offer higher reliability and lower life cycle costs across diverse market conditions compared to traditional diesel-based systems [9]. For a power system that combines photovoltaics and lithium battery storage with other renewable fuels, renewable fuels are normally used to supplement PV generation. This technology has immense prospects as it explores the value of hybrid systems that comprise how PV and lithium-ion battery storage could evolve over time [10]. Furthermore, it can bring economic benefits to all parties involved, creating mutual benefits for all stakeholders under the existing tariff framework.

The negative impacts of integrating green electricity and energy storage on the power grid, as well as their corresponding solutions, were also studied. According to a study by Liu et al. [11], the integration of RE sources into the power supply system may add strain to the existing utility grid. To address this challenge, a solution implementing a business model that incorporated a grid penalty cost was proposed. This model considered local time-of-use electricity price, and both imported power from the grid and exported power to the grid [12]. Additionally, a new approach estimated renewable energy’s maximum penetration and its effects on the public power grid [13], indicating that grid capacity was saturated when PV and wind power accounted for 25% and 60%, respectively, of total generation [13].

Currently, energy storage has various applications in power systems. For large-scale application, Compressed Air Energy Storage (CAES) and Pumped Hydro Storage (PHS) are suitable for large-scale applications. CAES compresses air using excess power during off-peak periods. Compressed air is decompressed in a compression chamber and fed to turbines during peak periods, boosting energy production. PHS stores energy using two reservoirs, one of which is positioned above the other. Water is pumped from the lower to the upper reservoir during off-peak hours, converting electricity into potential energy. During peak load hours, the water flows from the upper reservoir to the lower reservoir, activating the generator and converting potential energy into electricity.

As for the Energy Storage System (ESS) in buildings, it has been studied and applied worldwide. A. Ramos et al. [14] analyzed the application of ESS in Finland buildings. G.L. Pu et al. [15] studied the lithium battery industry in China. A.M. Ershad et al. [16] studied the techno-economic relationship between solar PV and battery storage in India’s electricity system. A. Dougherty et al. [17] analyzed ESS in the industry sector in the US. D.N. Karamov et al. [18] shared operational real-life experience on ESS in buildings with autonomous PV systems in Siberia and the Russian Far East. Although it is not possible for electricity produced by renewable energy to cover all the electricity consumption during the day and night, it fulfills two primary aims. First, it promotes renewable energy use; second, it enables peak shaving. Peak shaving and valley filling is a strategy to balance the disparity between electricity consumption during daytime and nighttime. During peak hours in the daytime, when electricity usage is high in offices and factories, renewable energy may not fully meet the demand. However, during the night, power demand decreases while renewable energy continues to be generated. Consequently, surplus off-peak electricity is stored and used during peak hours to balance supply and demand.

Customer-sited energy storage can partially replace coal plants, delivering more flexible renewable energy to the power system [19]. S.Y. Chen et al. [19] found that in Sichuan, storing electricity during low loads enabled 9 GW of renewable energy integration while reducing 15 GW of coal capacity. Peak shaving is the most important effect of energy storage. Given the flexibility of an Energy storage system (ESS), the local electricity system (LES) offers peak-shaving services to grid operators based on monthly tariffs [20]. Peak shaving optimizes energy supply and can lower grid charges for industrial users [21]. The smoother the power consumption from the grid, the lower the grid charges that need to be paid.

Beyond purely technical operation, integrating occupant-side behavioral measures can further amplify the benefits of PV-ESS installations. A personalized comfort demand-response controller for HVAC (PICO) improved peak-time energy productivity (comfort gain per unit energy) by up to 18.37% in office scenarios [22]. In Malaysian commercial buildings equipped with PV-BES, rule-based demand response combined with dynamic tariffs cut daily energy use by 19.02–20.9% and peak demand by 33.1–49.82% across four seasonal cases [23]. At the industrial scale, coupling demand response with PV-BES shaved monthly peaks enough to lower electricity bills by 6.9% and CO₂ emissions by 8.6% in a food-manufacturing plant [24]. Typical measures include pre-cooling HVAC, scheduling EV charging and deferrable appliances, and issuing real-time price signals or dashboard prompts to shape user behavior. When coordinated with LES-based peak shaving, these occupant-centered strategies can shorten the pay-back time of small-scale storage projects by roughly one-third.

There are various methods for energy storage in buildings, such as battery storage, thermal storage, and hydrogen storage. Studies have been conducted about load-shifting, peak-shaving, and valley-filling strategies to balance electricity supply and demand with energy storage. Y. Zhang et al. [25] used hydrogen storage for seasonal storage, utilizing hydrogen from warm months for peak shaving in colder periods. S.L. Cao et al. [26] proposed a zero-emission building integrated with hydrogen vehicles. The electricity generated by the on-site RE generation system was primarily used to meet the building’s electricity demands. The surplus part was used to produce H2 at the on-site H₂ generation system. A. Mayyas et al. [27] proposed storing grid excess energy as hydrogen using proton exchange membrane reversible fuel cells. The system mainly has the following two functions. First, low-cost electricity is used to produce hydrogen, which is later converted into electricity when electricity price rises. Second, hydrogen is produced cheaply and used in applications like fuel-cell electric vehicles. As for hydrogen storage, the electrolysis cell can be preferentially utilized to harness high-power peaks [28]. J. Pascual et al. [29] proposed a strategy to reduce power peaks and fluctuations in electro-thermal microgrids.

Various energy storage methods have been explored for buildings, including thermal, electrical, and hydrogen storage systems. For example, Cao et al. [27] proposed a hybrid zero-emission building system that integrates geothermal heat pumps, solar thermal systems, and on-site hydrogen production for storing electricity, hot water, and hydrogen, which can be used for powering hydrogen vehicles. Goyal et al. [30] developed a dual-circuit thermal energy storage (TES) system, integrated with air-conditioning units, where heat collected from PV panels is stored in a hot water tank, enabling load shifting and operational flexibility. A Khordehgah et al. [31] study introduced a photovoltaic-thermal (PV/T) system, combining thermal and electrical storage, which effectively regulates temperature and stores excess thermal energy in a hot water tank. Amabile et al. [32] designed an energy management system that uses photovoltaic energy to heat domestic water, optimizing self-consumption through smart control of the Electric Water Heater (EWH). Additionally, Jarvinen et al. [33] explored passive thermal storage methods integrated into building envelopes, showing that pre-cooled energy can be stored and discharged for thermal regulation. Finally, Zhou et al. [34] demonstrated a direct-driven photovoltaic cold storage system, where solar energy drives refrigeration processes, enhancing cold storage efficiency and reducing reliance on the grid.

While there have been extensive studies on the integration of Photovoltaic (PV) systems and Battery Energy Storage Systems (BESS) in building energy systems, the contribution of this paper lies in its holistic approach to system integration, covering not only the technical design and optimization of individual components but also the operation strategies, which cater to multi-objective optimization of economic and environmental performance. This paper consolidates the most recent advancements in PV and ESS technologies, focusing specifically on multi-disciplinary design considerations, real-time optimization techniques, and the role of smart grid technologies in building energy systems. The novelty of this paper also lies in its comparison of various optimization strategies for both system design and operation, providing a comprehensive overview of how these strategies can be applied to maximize efficiency, minimize costs, and reduce reliance on traditional grid power.

This review follows a progressive logic of “foundational analysis→system integration→ dynamic optimization→summary and outlook” to construct a multi-level research framework: First, at the foundational layer (Section 2 and Section 3), by analyzing the technical potential of photovoltaic (PV) power generation—such as the efficiency of Building-Integrated Photovoltaics (BIPV) and temperature effects—and the complementary characteristics of energy storage systems (ESS) (e.g., battery lifespan and hydrogen-based long-duration energy storage), the boundaries of their standalone performance and the necessity for synergy are clarified. Second, at the integration layer (Section 4), a PV-ESS collaborative configuration method is proposed. A multi-objective optimization model balances economic costs—including the Levelized Cost of Energy (LCOE) and Net Present Value (NPV)—with environmental goals (carbon emission reduction), achieving system-level design. Subsequently, at the optimization layer (Section 5), the framework extends from static design to dynamic operation. Intelligent strategies such as time-of-use electricity price response and Vehicle-to-Grid (V2G) technology are employed to enhance system flexibility. Finally, at the summary and outlook layer (Section 6), the review summarizes key research findings on the integration and optimization of PV systems and ESS in buildings and highlights its contributions to interdisciplinary research directions (e.g., Artificial Intelligence (AI)-driven forecasting and retired battery reuse).

2. Photovoltaic Power Generation

Building Integrated Photovoltaic (BIPV) is a RE generation technology in buildings. In this section, different configurations of BIPV were classified first. Then, mathematic models to calculate PV power generation were summarized. Lastly, optimized results to increase the power generation of BIPV were concluded.

2.1. Configurations of BIPV

PV panels are mainly installed on building envelopes, such as windows, walls, and roofs. There are various forms of BIPV systems, and many studies have been conducted to discuss the performances of different system configurations. Characteristics, advantages, and disadvantages of three types of BIPV systems are summarized in

Table 1. Characteristics, advantages, and disadvantages of three types of BIPV systems.

Application	Characteristics	Advantages	Disadvantages
PV Combined with Windows	Semi-transparent or opaque PV windows Provide natural daylight and views Save cooling energy Influence indoor thermal comfort	Reduce artificial lighting demand Match building aesthetics Generate electricity	Low efficiency of Semi-transparent PV windows High Installation and maintenance costs
PV Combined with Walls	PV panels integrated into building walls or structures	Blends with building design Generates electricity	PV efficiency is low for vertical installation Complex installation and integration may be required
PV Combined with Roofs	PV systems integrated on rooftops optimal panel angles	Generates electricity	high installation and maintenance costs PV efficiency is influenced by roof type and installation angle

.

2.1.1. PV-Roof System

Building roof is a regular place to install PV panels. It has been proved that under certain circumstances, roof-top PV has the potential to cover the building’s energy consumption [35]. Data about roof-top PV applied in European countries is summarized in

Table 2. The number of PV systems and the total capacity per country [31].

Country	Number of PV Systems	Roof-Top PV Capacity	Upper Specific Yield Limit
The Netherlands	978	10.70 MWp	1500 kWh/kWp
Belgium	4308	29.75 MWp	1500 kWh/kWp
Luxembourg	86	1.56 MWp	1500 kWh/kWp
Germany	24,204	325.73 MWp	1500 kWh/kWp
France	474	5.15 MWp	1600 kWh/kWp
Italy	2694	24.23 MWp	1800 kWh/kWp
Total	32,744	397.12 MWp

[31]. These installations contribute significantly to the shift toward renewable energy, as highlighted by a study that evaluated 32,744 roof-top PV systems across European countries from 2012 to 2019. The study found specific yield variations and performance trends that correspond to geographical differences and installation conditions. Specifically, the average specific yield over this period showed a south-north gradient, with countries like Italy achieving the highest yields due to favorable climatic conditions, reaching up to 1246 kWh/kWp in some years. Table 2 illustrates these regional differences, with Italy having an upper specific yield limit of 1800 kWh/kWp compared to 1500 kWh/kWp in northern countries like the Netherlands, Belgium, and Luxembourg. However, it is important to note that in non-temperate regions, PV yields may not follow the same patterns as in temperate regions [36]. For instance, in tropical regions, although the area receives longer sunlight hours, PV systems are theoretically expected to generate higher yields. However, due to the high temperature and high humidity conditions, the efficiency of PV systems is often significantly impacted. High temperatures can cause the PV panels to overheat, thereby reducing their conversion efficiency. Additionally, the higher humidity can lead to water accumulation and mold growth on the panels, increasing the difficulty of cleaning and maintenance, which in turn affects the system’s long-term performance. Moreover, the intense UV radiation and frequent rainfall in tropical regions may accelerate the degradation of PV systems, shortening their lifespan. Therefore, PV systems in tropical regions usually yield less than those in temperate regions. On the other hand, PV systems in desert regions face different challenges. Although desert areas have abundant solar resources, which theoretically should result in higher PV system output, extreme UV radiation and sandstorms can negatively impact system efficiency. The intensity of UV radiation can accelerate the aging of PV materials, reducing the long-term stability and power output of PV cells. Furthermore, the accumulation of sand not only obstructs sunlight from reaching the PV panels, reducing their energy intake but also increases the cleaning and maintenance costs, as regular cleaning is necessary to maintain system efficiency. In desert areas, especially in dry environments, the impact of sand on the PV panels is particularly severe, leading to more frequent cleaning cycles and higher maintenance costs, which present a significant challenge for improving the long-term benefits of PV systems and reducing overall operational costs. Therefore, for PV systems in different climatic zones, the design should not only consider the sunlight hours but also take into account factors such as temperature, humidity, UV radiation, and sand accumulation to ensure the maximum effectiveness of the system in various regions. Additionally, combining roof-top PV systems with battery storage has shown improved performance consistency, as observed in Germany and Belgium [31]. As shown in Figure 1 [33], the blue arrow represents the PV panels, and the red arrow indicates the residential roof. In Figure 1a, the PV panels are independently installed on top of the roof without altering the original building materials. In Figure 1b, the PV panels replace part of the roof and integrate with it, becoming a part of the roofing material. Roof-top PV can be applied to office buildings, residential buildings, and some functional buildings, as shown in Figure 2 [37,38]. The roof-top PV systems were usually combined with battery storage systems in buildings [30,39].

The yields of roof-top PV systems can be influenced by the types of roofs [40]. A. Scherba et al. [41] investigated different roofing technologies, such as a control dark membrane roof, a highly reflective (cool) roof, and a vegetated green roof. And PV panels have been proven to be elevated above various base roofs. Integrating PV panels with various base roofs (black, white, and green) has positive effects on urban heat island mitigation. It was found that PV panels can provide shade when they are placed above roofs, leading to the reduction of solar radiation and lower surface temperature. This effect decreases heat transferred into the urban environment. Specifically, adding PV panels to a black roof can slightly reduce total heat flux, which is the energy transferred from the roof surface to the urban atmosphere above, while the total sensible flux can be reduced by around 50% if a black roof is replaced with a PV-covered white or green roof [38]. G.B. Cavadini et al. [42] estimated the influence of a roof’s configuration on the yield of PV panels. The results showed that, as compared with a conventional roof, vegetated green roofs can raise PV energy yield by 1.8%, and the value is 3.4% for cool roofs. To guarantee an optimized output, a commercial bifacial PV module supporting construction was installed on a white-painted flat roof [43].

Roof-top PV panels can also provide shade for buildings. For a greenhouse covered with roof-top PV panels, radiation can be decreased by 65% and room temperature can be reduced by around 3 to 5 °C [38]. N. Shukla et al. [44] proposed a PV module attached to a shingle roof with adhesive tape. In summer, PV modules reduced peak daytime temperatures on asphalt shingles by 13 °C, as compared to exposed shingles. Roof-top PV reduced daily peak heat flux through a hut’s attic ceiling by 49%, as compared to a reference hut. With the help of Roof-top PV systems, heat transferred from the roof during the daytime can be reduced, and insulation can be provided at night, resulting in a remarkable energy-saving effect. Cooling and heating loads could be reduced by 39.9% and 38.6%, respectively [45].

2.1.2. PV-Wall System

PV panels that are integrated with walls or opaque façades of a building can be referred to in Figure 3 [46,47]. Studies were carried out about system configurations and installations to increase energy yields. Four configurations, namely non-ventilated and ventilated façade combined with mono facial panels, ventilated active façade combined with the bifacial panel, and the bifacial panel added with a reflective surface on the rear side, as shown in Figure 4, were analyzed [48]. Power generation and internal rate of return (IRR) can be increased by up to 19% and 6%, respectively, if the PV panels are installed in south facades [49]. Some novel configurations were proposed to improve the performance. Y.Q. Luo et al. [50] proposed a new compound building envelope system, the walls of which were integrated with PV panels, thermoelectric modules, and battery systems, as shown in Figure 5. The system achieved 72 to 92% energy savings in cold regions, 88 to 100% in mixed zones, and 100% in cooling-dominant zones compared to a reference wall. C. Theokli et al. [47] proposed a ‘corridor type’ double façade PV system with ventilation, the operating methods of which are shown in Figure 6.

2.1.3. PV-Window System

PV panels can be combined with windows in many ways. N. Skandalos et al. [46] investigated the performance of four types of PV windows, namely semi-transparent PV with a-Si/c-Si solar cells, PV overhang, and PV louvers, which can be referred to Figure 7 [46]. The solar cells of semi-transparent PV windows are different, which can be a-Si solar cells or c-Si solar cells [46]. The performance of semi-transparent PV windows depends on window orientation, thermal properties of windows, and PV cell coverage ratio [51,52]. The building’s cooling load can be influenced by the utilization of PV windows. As compared with normal glass windows, a study reported a 9.16% and 63.71% reduction in cooling energy consumption for the application of PV windows in Phoenix, US [53]. The PVSYST software [54] analyzed optimal PV window orientation to reduce cooling load and boost energy production. Using PV windows can reduce annual air conditioning consumption by 27.69% in hot, dry, and humid regions. Besides, indoor thermal comfort is also influenced by PV windows [52,55,56]. PV can also be used as sunshades of windows, in the form of overhangs or louvers, as shown in Figure 7c,d [46]. M.A. Paydar proposed a movable PV-shading system installed over the windows, the optimal conditions of which were determined for each month, as shown in Figure 8 [57].

2.1.4. PV/T System

The photovoltaic-thermal (PV/T) system has the function of generating both power and thermal energy, increasing PV efficiency per unit solar radiation area [58]. PV/T systems can be integrated with roofs [45,58,59,60] and façade [47,52,61,62,63] of a building, which are shown in Figure 9 and Figure 10. In the study of Z.M. Li et al. [60], two PV/T systems were investigated, PV cells which were laminated on an absorbing plate and on the back of a glass cover, respectively. The heat produced by PV/T is collected by flow fluids. The air heated by the PV module was supplied to the interlayer of roofs, as shown in Figure 10 [22,61], where it was heated by an air source heat pump and sent into the occupant’s room for heating. In addition to using the heat directly for heating, the heat can be stored in a storage tank, as shown in Figure 11 [56]. Water [59,61] or other working fluid [18,57] flows in the pipes, which are installed in the PV panels, to collect the generated heat, and release the heat to the storage tank [58], as shown in Figure 9. Hot water can be supplied to occupants [64].

Performances of PV/T system, which combines PV panels and thermal technology to provide cooling and heating without using batteries have been extensively studied. Refrigeration/heating systems that are directly driven by PV/T are viable and efficient choices for off-grid refrigeration and hot water supply, which can significantly improve solar refrigeration efficiency and energy utilization. The findings proved the potential of integrating PV/T modules with direct-driven systems to enhance the performance and sustainability of cooling applications [64]. The average electrical efficiency, thermal efficiency, and overall efficiency of the PV/T system were reported to be 11.23%, 64.25%, and 83.32%, respectively [58]. The average electrical, thermal and overall efficiency of the PV/T system could be 7.2%, 69.3%, and 86.8% during experimental operation [45].

2.2. Yield of PV

In this subsection, the two mathematic models that are regularly used to calculate PV yield were introduced. Then, ways to improve the accuracy of the PV yield calculation models were also summarized. Lastly, the influence of temperature and solar radiation, etc., on PV yields, reported in the literature, were concluded.

2.2.1. Mathematic Models of PV Yield

The power yield of PV panels can be calculated with an equivalent electric circuit, which is known as the I-V equation, as in Equations (1)–(3) [65]:

$$I=I_{SC}\left[1-C_1\left(e^{{\displaystyle \frac{V}{C_2{V}_{OC}}}}-1\right)\right]$$

(1)

$$C_1=\left(1-{\displaystyle \frac{I_m}{I_{SC}}}\right)e^{-{\displaystyle \frac{V_m}{C_2{V}_{OC}}}}$$

(2)

$$C_2={\displaystyle \frac{\frac{V_m}{V_{OC}}-1}{ln\left(1-I_m/I_{SC}\right)}}$$

(3)

where, I and V are current and voltage of the PV panel; I_SC is the short-circuit current and V_OC is the open-circuit voltage; I_m and V_m are the current and voltage at the maximum power output, respectively, under the reference conditions.

The temperature of the PV panel (T_c) is obtained with Equation (4) [65]:

$$T_c=T_a+t_c·R$$

(4)

where R is the total solar radiation on the inclined PV panel, W/m²; T_a is the ambient temperature, °C; t_c is the temperature coefficient of PV panel, °C·W⁻¹·m².

Considering the change of solar radiation and ambient temperature, I can also be expressed as Equation (5) [65]:

$$I=I_{SC}\left[1-C_1\left(e^{{\displaystyle \frac{V-DV}{C_2{V}_{OC}}}}-1\right)\right]+DI$$

(5)

$$DI=\alpha ·{\displaystyle \frac{R}{R_{ref}}}·DT+\left({\displaystyle \frac{R}{R_{ref}}}-1\right)·I_{SC}$$

(6)

$$DV=-\beta ·DT-R_S·DI$$

(7)

$$DT=T_C-T_{ref}$$

(8)

where R_ref and T_ref are the reference values of the solar radiation and the PV temperature, which were usually taken as 1 kW/m² and 25 °C, respectively; α is the temperature coefficient of current variation under the reference solar radiation, A/°C; β is the temperature coefficient of voltage variation under the reference solar radiation, V/°C; R_S is the resistance of PV panels, Ω.

The power P of the photovoltaic array under any solar radiation intensity and ambient temperature can be represented by Equation (9) [65]:

$$P=IV=\left(I_{SC}\left(1-C_1\left(e^{{\displaystyle \frac{V-DV}{C_2{V}_{OC}}}}-1\right)\right)+DI\right)V$$

(9)

The above PV yield simulation model can be used when the types and parameters of the PV panels are determined [42]. The power output (P_out) is obtained as Equation (10):

$$P_{out}=I_t·A_m·{\eta }_{OC}$$

(10)

where, I_t is solar radiation, W/m²; A_m is the area of PV panel, m²; η_OC is the panel conversion efficiency at operating conditions, which depends on panel cell temperature, calculated by Equation (11):

$${\eta }_{OC}={\eta }_{ref}·\left[1-\beta ·\left(T_{cell}-T_{ref}\right)\right]$$

(11)

where, η_ref is the panel conversion efficiency at reference conditions (usually with an irradiance of 1000 W/m² and an ambient temperature of 25 °C); β is the temperature coefficient of the cell, 1/°C, T_cell is the cell temperature, °C; T_ref the ambient temperature at reference conditions, °C.

2.2.2. Forecasting Models of PV Yield

The mathematical model is based on physical equations, while the forecasting model is based on physical principles and data. The accuracy of the mathematical model cannot be guaranteed if boundary conditions are changed, or physical parameters are different from the setting values in the model. As compared with mathematic models, the forecasting model can be more adaptive to the change in operating conditions and has higher self-study and self-adaptive abilities, and better transportability. The forecast models of PV systems can predict PV yield, performance degradation, and energy loss, providing references for PV panel operation [53,66]. The forecasting models used extreme learning machine algorithms, including the Gated Recurrent Unit forecasting model, the Scaled Persistence Model, the Artificial Neural Network, and the Multivariate Polynomial Model [34,67,68]. These forecasting models, which take into consideration the PV yield models and weather predictions models [60], are capable of forecasting PV yield one day ahead or even one hour ahead, based on historical data of PV power generation.

Solar radiation and the PV panel’s temperature are two key operating parameters influencing the accuracy of the PV yield forecasting models. Studies were carried out to propose an accurate solar radiation estimation model. Deep learning was regularly adopted, which combines the CNN, LSTM, and Orgill models, to forecast the hourly global horizontal irradiance [69,70,71], taking the building surfaces into consideration [8,63,70]. As compared with PV temperature, using ambient temperature to calculate the PV panel’s power output makes results inaccurate. Therefore, models and algorithms [42,72,73,74] were used to predict PV temperature.

Caravanning et al. [42] predicted PV panel temperatures by integrating a rooftop energy balance model with the System Advisor Model (SAM), using detailed simulation of roof surface characteristics to accurately estimate the thermal conditions that influence PV efficiency. Orazio et al. [72] predicted the temperature of PV panels under environmental conditions using the Nominal Operating Cell Temperature (NOCT) and the Sandia National Laboratory (SNL) models, finding that prediction accuracy could be improved by adjusting empirical coefficients in the SNL model. Kaplanis et al. [73] predicted PV temperature using physics-based semi-empirical models and Artificial Neural Networks (ANN), incorporating environmental conditions, operational states, and aging effects of PV modules. Ananda et al. [74] predicted the temperature of roof-mounted solar PV power stations by employing a novel inverse heat transfer technique based on the Salp Swarm Algorithm (SSA), which efficiently and accurately estimated key properties and location-specific process parameters using limited on-site data.

It was found that variability and unpredictability factors, such as environmental conditions, system performance fluctuations, measurement and modeling errors, and operational factors in the PV yield forecast model, may influence the accuracy of the results. Studies have been carried out to propose methodologies to generate vast sets of stochastic scenarios to forecast PV yield, taking into consideration weather and other PV parameters [67,75]. Then, a scenario reduction technique was proposed to reduce the vast scenarios to several typical scenes [51,76,77]. Lastly, a probabilistic forecast is proposed [78,79] to study the yield characteristic under probabilistic power flow [80]. Probabilistic Power Flow Models and Photovoltaic (PV) Power Generation Forecast models were developed using data-driven forecasts based on various algorithms [81,82]. Scenario generation-reduction technique and probabilistic forecast are used for uncertainty quantification. Then the uncertainty will serve as an input to the power generation forecast model to improve the calculation accuracy [51,67,75].

2.2.3. Methods to Increase PV Yield

With the above models, parametric and optimization studies can be carried out to find ways to improve PV yield. Solar radiation and PV temperature are key factors affecting PV yield. M. Chen et al. [51] compared the power generation of PV windows under annual solar radiation in different places in the world. Shading caused by other obstacles around buildings results in the reduction of PV yield [70,83]. The PV panel’s orientation also influences power generation [51,84]. The tilt angle and orientation of solar panels significantly affect the amount of solar radiation received, thereby influencing the PV yield. Optimal angles vary with location and season [84]. Adjusting the tilt angle can enhance annual energy production by up to 8% [85]. For example, Sharma et al. [85] conducted a real-time data acquisition study on a 5 kWp PV system in Chandigarh, India, with panels installed at various angles (10°, 20°, 25°, 30°, and 40°). By adjusting the tilt angle monthly, they observed an increase in annual energy yield, equating to an additional 336 to 400 kWh compared to fixed angles at 30° or 40°. This demonstrates the benefits of seasonal angle adjustments to optimize energy output throughout the year. By calculating hourly power output of different orientations, the optimal orientations which have the highest yield in the whole year or in each month can be found. The PV panels can be installed with the orientation being fixed at the optimum value, or with the orientation changing each month [43,57,63].

The temperature of PV panels needs to be known to calculate PV yield [48,86]. With a 1 °C increase in the PV panel’s temperature, 0.14 kWh/m² would be reduced per year [42]. Therefore, a PV/T system, which can take away heat generated during power yield and keep PV temperature low, shows better performance than regular PV panels [56,60]. Reducing solar panel temperature by 25% led to a 12~15% increase in electrical output [59,87]. In addition to PV/T, backside ventilation is another way to reduce the temperature of PV panels, as shown in Figure 5, Figure 6, Figure 7 and Figure 11. Performances of PV panels with different backside ventilation designs, such as and type of panels, are compared [48,72]. The studies showed that a well-designed air gap can significantly improve the thermal performance of PV panels by facilitating better air circulation and heat dissipation, leading to lower panel temperatures and higher efficiency. The type of panel also plays a crucial role. The bifacial panels allowed for additional energy generation from reflected light, which can be further influenced by the presence of a reflective surface or the size of the air gap behind the panel. The results indicated that different designs were suitable for different scenarios with different thermal performances, highlighting the importance of considering both air gap size and panel type in the design of PV systems to optimize their performance across various conditions. With this method, thermal performance could be improved by 16% and the peak PV temperature could be reduced by 3.5 °C [52], resulting in a 4.5% enhancement in power yield [88].

Furthermore, to translate these thermal-control strategies into real building-energy savings, PV/T-storage modeling outcomes should inform policy incentives and design guidelines. Building authorities, guided by the Energy Performance of Buildings Directive (EPBD), can offer tax credits, green-rating points, and dynamic feed-in tariffs that favor battery-coupled BIPV façades, thereby reducing capital costs and pay-back times [48]. For architects and MEP consultants, a practical BIPV-storage integration guide is recommended:(1) keep a ≥0.04 m ventilated cavity instrumented with PT100 temperature [72] and HD29.371 air-velocity sensors [33] to track cooling performance, (2) size thermal/electrical storage through TRNSYS or SAM load-matching—as illustrated by the 15 kWh battery paired with a 6.4 m² PV/T array in Khordehgah et al. [87], (3) adopt the 4.5–5.5% annual yield (and bill) increase validated for ventilated or bifacial façades over monofacial BIPV [88]. Besides, the aging rate of the ventilated PV panels is much smaller than the non-ventilated PV panels [33].

In addition to the aforementioned methods, applying optical coatings and light-enhancing materials to photovoltaic (PV) panels can significantly improve light absorption and conversion efficiency. For example, optical films and light waveguide materials can optimize the propagation path of light, increase the angle of incidence, and improve reflectivity, maximizing the PV panel’s absorption of sunlight. These optical materials not only increase the light capture efficiency of PV cells but also reduce reflection losses, thereby improving the overall energy conversion efficiency of the PV system [89]. Furthermore, integrating PV systems with green roofs is a novel environmentally friendly optimization solution. By installing PV panels on rooftops and combining them with plant greenery, not only can the building’s appearance and urban greenery be improved, but the operating temperature of the PV panels can also be effectively reduced. Plants help cool the PV panels through evaporation, preventing efficiency degradation due to high temperatures. This integration not only enhances the aesthetic value of the building but also improves the efficiency of the PV system through temperature control [89]. Additionally, thermal homogenization design and the application of nanomaterials are effective ways to improve PV system performance. Thermal homogenization design can optimize the thermal management of PV modules, reduce localized overheating caused by temperature differences, and ensure uniform temperature across the PV panels, thereby improving system stability and efficiency. Nanomaterials, such as quantum dots or nanocoatings, can effectively enhance light absorption and charge separation efficiency within PV systems. Through the innovative application of these materials, the conversion efficiency and durability of PV systems are significantly improved, thus extending the system’s lifespan and increasing long-term energy output [90].

2.3. Long-Term Field Performance and Market Evolution of Building PV

Over the past two decades, field monitoring of 120 PV systems shows that crystalline-silicon modules experience median performance losses of about 0.6–0.7% yr⁻¹ (inter-quartile range 0.4–0.9% yr⁻¹), whereas thin-film modules degrade more rapidly, typically 0.8–1.1% yr⁻¹. These values are derived from the STL and YoY analyses shown in Figure 12 of the performance-loss-rate benchmarking study [91]. Ignoring this degradation would lead to an 8–12% underestimation of the 25-year LCOE. Over the same period, global cumulative PV capacity soared from about 1 GW in 2000 to 1 419 GW in 2023, corresponding to a compound annual growth rate of roughly 36% [5]. Figure 13 charts the 2000–2024 uptake of building-integrated and distributed PV; its post-2008 S-curve hints at a further 25% cost-learning reduction potential in the coming decade. Daily-resolution yield records from 32,744 ≤ 30 kWp rooftop PV systems in six European countries (2012–2019) reveal a pronounced south-north specific-yield gradient (800–1500 kWh·kWp⁻¹·yr⁻¹) and show no statistically significant decline in median performance ratio (0.72–0.76) during the first eight years of monitored operation [31].

3. Energy Storage System Using Storage Battery

For buildings, there exists a mismatch between the electricity consumption of end users and the electricity yield from PV panels, leading to a waste of green energy. To alleviate this mismatch problem, a battery energy storage system (BESS) is usually utilized, which can bring considerable economic benefits. Through charging and discharging, BESS shifts electricity from peak to off-peak periods of PV generation [92,93]. As compared with the scenarios without BESS, the grid energy bills could be reduced by 5 to 10%, and the lifetime net present value of the energy supply system could be increased by 23.4 to 96.4% [12]. It was reported that the BESS reduces electricity costs by 57% and total costs by 32% [94,95].

3.1. Working Principles of Storage Battery

3.1.1. Mathematic Model

The charging status of the battery is usually expressed with SOC (state of charging) [47], which could be calculated with Equation (12):

$${SOC}_{i+1}={SOC}_i+{\displaystyle \frac{I_{c,i}∆t}{Q_{batt,I}}}-{\displaystyle \frac{I_{d,i}∆t}{Q_{batt,I}}}$$

(12)

where i and i + 1 mean the present time node and the next time node, respectively; I_c and I_d mean charging and discharging current to the battery (A); Δt is time step (h); Q_batt,I is battery capacity (Ah).

Assuming the working voltage is V, power is calculated as $P=IV$. Equation (12) can be re-written as Equation (13):

$${SOC}_{i+1}={SOC}_i+{\displaystyle \frac{P_{c,i}∆t}{Q_{batt,P}}}-{\displaystyle \frac{P_{d,i}∆t}{Q_{batt,P}}}$$

(13)

where P_c and P_d are the charging and discharging power (W); Q_batt,P is battery capacity (Wh).

To ensure battery safety, SOC should be maintained between 0.2~0.95. The cycle life of a battery refers to the number of charge and discharge cycles a battery can undergo before its performance declines to a certain predetermined level. This predetermined level is often defined as the point at which the battery’s capacity falls to 80% of its initial capacity [96]. The criterion of the battery’s end-of-service is that the maximum capacity is 80% of the original capacity under standard conditions [97]. Equations to calculate cycle life (CL) in literature are summarized. The empirical relationship between CL and battery’s surface temperature is represented in Equation (14):

$$CL\left(T\right)={a·T}^3-{b·T}^2+c·T+d$$

(14)

where CL is the cycle life of the battery; T is the operating temperature (°C).

The empirical relationship between CL and the depth of the discharge (DoD) is represented in Equation (15):

$$CL\left(DoD\right)=e·exp(f·DoD)+g·exp(h·DoD)$$

(15)

The empirical relationship between CL and the constant I_d till 100% DoD, is represented in Equation (16):

$$CL\left(I_d\right)=i·exp(j·I_d)+k·exp(l·I_d)$$

(16)

where I_d is the discharge current (A).

The empirical relationship between CL and the constant $I_c$ is shown in Equation (17):

$$CL\left(I_c\right)=m·exp(n·I_c)+o·exp(p·I_c)$$

(17)

The coefficients in Equations (14)–(17) are listed in

Table 3. The coefficients in Equations (14)–(17) [97].

a	b	c	d	e	f	g	h
0.0039	1.95	67.51	2070	$6.009\times {10}^9$	−0.011879	$6.009\times {10}^9$	−0.011879
i	j	k	l	m	n	o	p
4464	−0.1382	−1519	−0.4305	5963	−0.6531	321.4	0.03168

.

3.1.2. Performance Influence Factors

Performances, such as efficiency, reliability, etc., of BESS would decrease with time, which is called an aging problem. Aging of BESS results from the decrease of capacity and voltage with charge and discharge cycles [98]. Therefore, many experiment studies were carried out to investigate the aging problem of batteries. It has been proved that the aging of the battery is influenced mainly by the operating temperature, depth of discharge, discharge current rates, and charge current rates [85].

Mathematic models were proposed to study performance degradation, such as lifetime cost during the lifecycle [99,100,101,102,103] of BESS. The Enhanced Single Particle Model (ESPM) is a mathematical model for battery aging that simulates both calendar aging and cycle aging effects through a set of coupled partial differential and algebraic differential equations. This model predicts the degradation trajectory of battery capacity under specific power schedules taking the current applied to NMC batteries as input. ESPM effectively simulates the real operational aging process of batteries, offering a powerful tool for understanding and mitigating battery aging [100].

Based on the performance degradation models of storage batteries, methods were proposed to control the battery operation from perspectives of temperature [104,105], battery cycles [18,106], economy [107] and SOC [108,109], and scheduling [110]. M. Song et al. [104] and A. Solntsev et al. [105] proposed a specific method to control temperature, which was realized by employing a dual-circuit temperature control system using antifreeze in the external circuit and transformer oil in the internal circuit. This method was proved to be able to effectively dissipate heat directly from the battery electrode contacts, thereby enhancing the efficiency of battery temperature control [104,105]. Karamov et al. [18] and Q.Q. Yang et al. [106] proposed an advanced Model Predictive Control (IMPC) strategy, which aimed to optimize the charging and discharging behaviors of electric vehicles and local batteries, effectively extending battery life while maintaining grid service quality, and achieving economic and sustainable battery operation. Sergio et al. [107] introduced the method of extending the battery degradation limit and implementing Time-of-Use (TOU) rates to enhance the economic efficiency of battery storage combined with photovoltaic systems in commercial buildings, achieving significant energy cost savings. S. Vonsien et al. [108] and D.W. Su et al. [109] proposed a method to control battery operation, which resulted in an optimized design of the battery energy storage system’s capacity that accounts for charge/discharge rate characteristics. This optimization enhances the regulatory capabilities and performance of the power system by ensuring the BESS configuration is precisely tailored to improve responsiveness and efficiency. J.O. Lee et al. [110] proposed an innovative approach for battery operation control, utilizing a new battery degradation cost formulation and an auxiliary State of Charge (SOC) tracking method. By integrating piecewise linear approximation with optimization scheduling problems, the method can significantly reduce battery degradation costs and enhance battery lifespan, achieving economical and efficient operation of BESS.

To extend the battery’s lifetime, forecast-based strategies were proposed, aiming to reduce the average SOC of the battery by limiting the stored energy based on predicted energy demand during nighttime [111]. To reduce the cost, the battery’s degradation limit is regulated to reduce the frequency of replacing the battery and the cost [98]. As for the degradation cost, the min/max thresholds of SOC were optimized through the surrogate Lagrange relaxation method [112]. SOC can be predicted by a Markov Decision Process (MDP) model [113] and can be controlled in real-time operation [110,114,115].

3.1.3. Passive Techniques in PV-BESS Design

Passive techniques play an important role in designing and sizing PV-BESS systems, which can improve energy efficiency without the need for active controls. For instance, incorporating natural ventilation in battery housing can help dissipate heat, maintaining optimal operating temperatures and prolonging battery life [116]. Utilizing thermal mass within building structures can enhance energy flexibility by reducing temperature fluctuations, which decreases the energy required for climate control and helps shift peak loads, thereby alleviating the overall demand on the PV-BESS system [117]. By carefully designing building orientation, insulation, and material selection, passive solar gains can be maximized, potentially reducing the size requirements for both PV and battery storage components [118].

3.2. Applications

3.2.1. Centralized BESS

Many studies were carried out to investigate performances of such hybrid energy generation and storage system applied in a city or a community. BESS can engage in electricity grid regulation by supplying energy during periods of relatively low demand and providing additional support to the grid during peak demand periods, which can effectively realize peak shaving and optimize energy distribution [119,120,121]. Salameh simulated an energy system, which included a standalone PV, diesel generator, and BESS applied in Khorfakkan City, Sharjah [122,123,124,125]. Nieta carried out a simulation study on a local energy system, including BESS and rooftop PV panels, in a stadium in Norway [20]. A school in Cardiff was equipped with PV and BESS [126], enabling it to generate its own renewable energy and store excess electricity for later use. This setup led to a reduction of the school’s grid dependency and helped cut greenhouse gas emissions through optimizing the utilization of renewable energy.

3.2.2. Customer-Sited Distributed BESS

Batteries in buildings can be charged with renewable energy and discharged to meet electricity requirements [127,128]. In the study of the multi-objective planning optimization model under different power supply states in microgrid lithium iron phosphate BESS [99], a park’s microgrid system, that included PV, the grid, and BESS, was optimized to enhance economic and stable operation. Electrical loads were met using renewable energy and batteries, thereby reducing operating costs and increasing energy supply reliability [99]. In a residential home with PV and BESS, the batteries are primarily charged using renewable energy, which will be discharged to meet the home’s electrical demand [129]. A smart energy system with PV and BESS was equipped in a campus office to store surplus PV electricity and meet energy demands, improving efficiency and sustainability [130]. A building equipped with PV and BESS utilized solar energy to charge batteries, which were then used to supply electricity to the building, resulting in optimized energy usage and reduced dependence on traditional power sources [110]. U.G.K. Mulleriyawage et al. [131] investigated the adoption of Mixed-Integer Linear Programming (MILP) for operational optimization of households equipped with PV and BESS in Australia. BESS is charged from the grid during a low-price period or with surplus solar energy, and discharged during a high-price period, which can maximize solar usage, reduce costs, and enhance self-sufficiency through calculating Return on Investment (ROI) to reduce reliance on the grid [131].

In summary, PV and BESS can be applied to various scenarios. Studies were carried out mainly to optimize energy utilization through charging with renewable sources and discharging based on electrical demands, aiming to improve efficiency, sustainability, and economic performance, thereby enhancing self-sufficiency and reducing grid reliance.

3.2.3. Electrical Vehicle

Electric vehicles (EVs) are a part of the modern transportation system. Storage batteries in EVs can charge electricity from renewable energy sources and provide electricity to the building [132]. When applied in a residential building, EVs can store excess electricity during the peak period of RE generation and provide electricity if RE cannot cover residential electricity consumption [129,133]. Considering the operation of EVs and RE generation, with appropriate control strategies, EVs can be an effective way to store energy [130,134,135].

In addition, the RE storage potential of EVs can be further exploited by optimizing the locations and sizes of charging lots [134,135,136,137,138,139]. Equipping the charging lot with on-site storage batteries and managing multiple BESSs using linear optimization and time series modeling can reduce peak power demand at the point of common coupling by up to 44.9% [119,128,140,141]. To enable electric vehicles (EVs) to transfer electricity with the grid in a dynamic and mutually beneficial manner, the Vehicle-to-Grid (V2G) technology is proposed [130,139,142,143]. This technology enables electric vehicles to not only draw energy from the grid but also to feed electricity back into the grid, thereby offering a solution to balance demand and supply and enhance grid stability. Furthermore, it leverages the battery storage capacity of EVs, transforming them into mobile energy storage units that can contribute to peak load management and the integration of renewable energy sources.

EV batteries retain 70~80% of their capacity at retirement, which can be used in the BESS of buildings [144]. Y.L. Ni et al. [145] developed a data-driven model to estimate retired LiFePO4 battery capacity, achieving 2.18% RMSE (Root Mean Square Error) using the first 10% of data, which demonstrated superior accuracy and efficiency in estimating battery capacity for second-use applications. R. Jing et al. [128] proposed a distributed energy system (DES) that reused retired EV batteries, where the framework was designed to enhance profitability across the entire supply chain while ensuring equitable distribution of profits among all stakeholders involved. K. Gur et al. [146] analyzed the economic potential of reusing EV batteries as stationary storage batteries, considering electricity prices and government policies that guarantee fixed payments for renewable energy supplied to the grid. Investments in residential solar panels and batteries, battery-only, commercial/industrial level solar panels and batteries, and used electric vehicle battery energy storage systems, were also considered for grid frequency control [144]. M.A. Cusenza et al. [144] studied an environmental impact assessment system that combined load match analysis and life cycle assessment. This system was powered by PV and the grid, using retired Li-ion EV batteries as the BESS, aiming to find the optimal BESS capacity to improve load matching and reduce environmental impacts, demonstrating the synergistic effect between the construction and automotive industries. Y. Gao et al. [147] designed a grid-connected PV storage microgrid, in which 17 retired LiFePO4 batteries were used. The annual average energy efficiency of the retired battery bank was 96.16% [147]. On a monthly basis, the combined supply of energy from PV panels and BESS met an average of 40% of the total demand for electricity. This indicates that the integration of PV with retired lithium iron phosphate (LiFePO4) batteries within the microgrid can effectively contribute to the electricity requirements, underscoring the significant role of renewable energy sources and storage solutions in addressing energy consumption needs [147]. An electric/thermal hybrid energy storage system for an integrated energy system designed for business parks or industrial areas, utilizing second-life batteries, was proposed [102]. The proposed hybrid energy storage systems, which leverage second-life batteries, can significantly enhance the sustainability and economic efficiency of park-level integrated energy systems through cost reduction and service life extension.

3.3. Comparison Among Different Energy Storage Methods

C. Luerssen et al. [148] analyzed the optimized life cycle cost (LCC) of a PV-powered cooling system. Seven configurations with battery and thermal energy (chilled water and ice) storage were compared. For the scenarios with both batteries and thermal energy storage, optimized fuel cost savings reached 51~77% as compared to the diesel-powered baseline. For the scenarios with just batteries, the highest fuel cost-saving ratio after optimization was only 39~48%, as compared with the baseline. However, investment was 27~50% higher for systems with both thermal energy and battery storage compared to those with only batteries. Y. Zhang et al. [25] compared hydrogen and battery storage. Under the pessimistic cost scenario, hydrogen storage showed a lower Self Sufficiency Ratio (SSR) and Net Present Value (NPV). While under the optimistic cost scenario, hydrogen storage achieved higher NPV. Considering grid fluctuations, hydrogen storage outperformed in NPV, SSR, and Grid Indicator.

4. Optimization of PV-BESS System’s Design Parameters

4.1. Economic Performance Indexes

Note: For consistency, all monetary values presented in this paper have been converted to U.S. dollars (USD). When converting from Euro (€), the average exchange rate of 1 € = 1.1 USD for the year 2025 has been applied.

In recent years, renewable energy technologies have generated attention for reducing carbon emissions, providing sustainable energy sources, and offering financial benefits. Through appropriate operation strategies, annual operation costs can be reduced using the PV-storage battery power system [10]. The analysis of economic performances typically concentrated on evaluating the placement and capacity of storage batteries, along with managing excess power generation, either through fixed capacity limits or by dynamically adapting to the fluctuating demands of the grid. The study also considered the implications of these management strategies on key stakeholders such as electricity consumers and grid operators [92].

Self-consumption ratio is the proportion of electricity consumed by users to total PV-generated electricity. It can be used to assess profitable combinations of PV panels and batteries. Self-sufficiency rates (the capability to meet their own electricity needs through self-generated power) of 75% and 65% were achieved in Germany and Ireland, respectively [149].

A critical aspect of assessing their viability and long-term sustainability lies in calculating the Levelized Cost of Energy (LCOE). LCOE considers factors such as initial investment, operational costs, and revenues to evaluate the economic feasibility of various energy systems.

LCOE [99] is calculated with Equation (18):

$$LCOE={\displaystyle \frac{{IC}_0+{\sum }_{t=1}^{\tau }\left({IC}_t+C_{omt}\right){\left(1+d\right)}^{1-t}}{{\sum }_{t=1}^{\tau }{W}_t{\left(1+d\right)}^{1-t}}}$$

(18)

where IC₀, IC_t are initial capital construction costs and the investment in the year of operation, respectively; C_omt is the main equipment maintenance and repair cost; W_t is the electricity transmission in the year t [kWh]; d is a discount rate; and τ is the calculation period.

In the study of photovoltaic system design and optimization, values of the above economic and technical parameters in Equations (4)–(18) of PV panels were suggested, as listed in

Table 4. Economic and technical parameters of PV panels [99].

Parameters	Numerical Value
Cost of investment: IC0	232 $/kW
Operation and maintenance: Comt	0.005 $/kW
cost
Rated power: Pout	260 W
Conversion efficiency: ηOC	0.97
Rated temperature: Ta	25 °C
Temperature coefficient: β	0.47
Life cycle: CL	20 years

.

Net Present Value (NPV) and Internal Rate of Return (IRR) can be adopted to evaluate the financial feasibility of projects. IRR represents the interest rate at which the project’s NPV becomes zero, indicating the breakeven point.

NPV is calculated with Equation (19) [149]:

$$NPV=R_{ev}-C=R_{{feed}_{in}}+R_{purchase}-C_{inv}-C_{operation}-C_{rep}+R_{liquid}$$

(19)

where R_ev and C are the revenues and the costs of a PV-storage system.

The financial revenues $R_{{feed}_{in}}$ [USD] from the grid feed-in are based on the energy feed-in $E_{{feed}_{in}}$ [kWh/a], the feed-in tariff e_PV [USD/kWh], and a yearly performance degradation, b, in Equation (19), of 1% for the PV system, which is calculated with Equation (20):

$$R_{{feed}_{in}}=\sum _{y=1}^{T_{inv}}{E}_{{feed}_{in}}·e_{PV}·{\left(1-b\right)}^y·{\left(1+IRR\right)}^{-y}$$

(20)

Households without PV-storage rely entirely on the grid, while those with it use self-generated electricity to cut costs. The amount of saving, $R_{purchase}$ [USD]), is calculated with Equation (21):

$$R_{purchase}=\sum _{y=1}^{T_{inv}}{E}_{EV}·P_{elect,y=0}·{\left(1+{\displaystyle \frac{{∆P}_{elect,y}}{P_{elect,y=0}}}\right)}^y·{\left(1-b\right)}^y·{\left(1+IRR\right)}^{-y}$$

(21)

The investment, $C_{inv}$ [USD], includes acquiring and installing the PV and battery storage systems. The investment for the PV system is calculated from the specific PV investment cost $p_{PV,y=0}$ [USD/kWh] and the peak power of the PV system $P_{{PV}_{max}}$ [kW_p]. The investment for the lithium-based battery storage system is calculated from the specific battery investment costs, $p_{Batt,y=0}$ [USD/kWh], and the storage capacity $W_{{Batt}_{max}}$ [kWh]. The installation costs for the PV-storage system, $P_{Inst}$ [USD], which can also be considered. Thus, the initial investment is calculated with Equation (22):

$$C_{inv}=\left(P_{{PV}_{max}}·p_{PV,y=0}+W_{{Batt}_{max}}·p_{Batt,y=0}+P_{Inst}\right)·\left(1+VAT\right)$$

(22)

Along with the initial investment, the operator of the PV-storage system must also pay the annual maintenance costs, $a_{{PV}_{main}}$ [USD/(a·kW)], the annual hire of the meters, $A_{meter}$ [USD/a], and the annual PV insurance premium, $A_{{PV}_{ins}}$ [USD/a].Thus, the annual operating cost is calculated with Equation (23):

$$C_{operation}=\sum _{y=1}^{T_{inv}}\left(P_{{PV}_{max}}·a_{{PV}_{main}}+A_{meter}+A_{{PV}_{ins}}\right)·{\left(1+i_{Inf}\right)}^y·{\left(1+IRR\right)}^{-y}$$

(23)

PV systems are assumed to last 20 years, while battery life depends on cycle stability or calendar lifetime. Lithium-ion batteries have a cycle stability of Z_max = 5000 cycles, and a 20-year calendar lifetime. If the battery must be replaced within 20 years, the replacement investment for the battery storage system, $C_{rep}$ [USD], needs to be considered, which is calculated with Equation (24):

$$C_{rep}=\sum _{y=1}^{T_{inv}}{W}_{{Batt}_{max}}·p_{Batt,y}·f_y·\left(1+VAT\right)·{\left(1+IRR\right)}^{-y}$$

(24)

Batteries replaced within the planning horizon have a significant liquidation value. For a fair comparison between systems involving a storage replacement investment and systems without any replacements, it is important to include the liquidation value, $R_{liquid}$ [USD], in all calculations, which is calculated with Equation (25):

$$R_{liquid}=W_{Batt}·p_{Batt,T}·{\displaystyle \frac{{\sum }_{y=1}^{T_{inv}}{Z}_y}{Z_{max}}}·{\left(1+IRR\right)}^{-T_{inv}}$$

(25)

Through analyzing the interplay between costs and revenues, the decision of whether to invest in renewable energy can be reached.

Life cycle cost (LCC) [136] can be calculated with Equation (26):

$$LCC=CAPEX+\sum _{t=1}^n{\displaystyle \frac{{OPEX}_t}{{\left(1+i\right)}^t}}+C_{replacement}^{total}-V_{residual}$$

(26)

where the CAPEX is the capital expenditure (USD/kW), OPEX is the operational expenditure, $C_{replacement}^{total}$ are the component replacement costs, and $V_{residual}$ is the residual value at the end of the project. The OPEX are discounted with i = 0.111 over the project lifetime n = 20. While $V_{residual}$ is set to zero. The other three components are explained as follows.

The CAPEX consists of the CAPEX for PV and battery and the chiller investments. Therefore, the system component sizes are multiplied by the specific costs:

$$CAPEX=c_{CAPEX}^{PV}·P^{PV}+c_{CAPEX}^{Batt,energy}·E^{Batt}+c_{CAPEX}^{Batt,power}·P^{Batt}+c_{CAPEX}^{chiller}·{\dot{Q}}^{chiller}$$

(27)

where $c_{CAPEX}^{PV}$ and $c_{CAPEX}^{chiller}$ are the specific investment costs for the PV system and the chiller plant, (USD/kW). The specific costs for the battery investment consist of $c_{CAPEX}^{Batt,energy}$ (the investment for the DC battery packs) and $c_{CAPEX}^{Batt,power}$ (the investment for the battery inverter and adjacent equipment on the AC side).

Those specific costs are multiplied by the system sizes, i.e., the chiller cooling capacity ${\dot{Q}}^{chiller}$, the PV system size $P^{PV}$, the battery capacity $E^{Batt}$, and the battery inverter power $P^{Batt}$.

The annual OPEX (${OPEX}_t$) equals the annual expenses for Operation and Maintenance (O&M) and the annual fuel costs ($C_{fuelt}$):

$${OPEX}_t=C_{O\&M}^{total}+C_{fuelt}$$

(28)

The annual $C_{O\&M}^{total}$ is determined by calculating the O&M for each component using the specific O&M costs and summing them:

$$C_{O\&M}^{total}=c_{O\&M}^{chiller}·{\dot{Q}}^{chiller}+c_{O\&M}^{PV}·P^{PV}+c_{O\&M}^{Batt,}·E^{Batt}$$

(29)

where $c_{O\&M}^{chiller}$, $c_{O\&M}^{PV}$, $c_{O\&M}^{Batt,}$ are the specific O&M costs for the chiller plant, the PV system and the battery system, (USD/kW·year).

The economic and energy benefits of hybrid renewable energy systems with storage can be evaluated by the above performance indexes. Their meanings and functions were categorized as listed in

Table 5. Economic and Investment Parameters for Energy System Analysis.

Indicator	Parameter	Description and Analysis
Economic Indicators	$LCOE$ (Levelized Cost of Energy)	- Indicates unit cost of electricity generation over the system’s lifespan, including capital, operating costs, and discounting.
	$NPV$ (Net Present Value)	- Assesses system profitability by comparing revenues and costs’ present value. Positive NPV indicates a profitable project.
	IRR (Internal Rate of Return)	- The discount rate making NPV zero indicates return on investment; higher IRR implies better feasibility.
Energy Optimization	$R_{{feed}_{in}}$	- Revenue from grid feed-in, considering energy feed-in, feed-in tariff, and performance degradation over time.
	$R_{purchase}$	- Cost savings from using self-generated electricity, considering electric vehicle usage, price changes, and performance degradation.
Investment Analysis	$C_{inv}$ (Investment)	- Initial investment in PV and battery systems, including installation costs.
	$C_{operation}$ (Operating Costs)	- Yearly costs for PV system maintenance, meters, and insurance, considering inflation and discounting.
	$C_{rep}$ (Replacement Costs)	- Replacement investment for battery storage systems if needed within the project’s timeframe.
	$R_{liquid}$	- Liquidation value for replaced batteries.
Comprehensive Evaluation	$LCC$ (Life Cycle Cost)	- Total cost over the system’s lifetime, including capital expenditure (CAPEX), operational expenditure (OPEX), replacement costs, and residual value.

.

Beyond traditional cost analysis, national policy incentives and carbon pricing mechanisms play a crucial role in the promotion of PV-ESS systems. For example, policies like Germany’s EEG Act and the U.S. ITC tax credit significantly reduce the initial investment cost of PV-ESS systems through subsidies and tax incentives, thereby accelerating their market adoption [150,151]. For instance, the ITC policy provides investors with up to a 30% tax credit, meaning a $100,000 investment in a PV-ESS system could save $30,000 in tax expenses. With such policy support, investors can achieve higher Net Present Value (NPV) and shorter Investment Payback Period (IRR), promoting the commercialization of PV-ESS technologies. Additionally, sensitivity analysis of carbon pricing mechanisms (such as carbon taxes and trading) reveals their impact on the economic viability of PV-ESS systems. As carbon emission policies become stricter, the introduction of carbon pricing will further enhance the competitiveness of PV-ESS systems. For example, assuming a carbon tax of \$50 per ton, the Levelized Cost of Electricity (LCOE) of the PV-ESS system could decrease by approximately 10%. This change is based on estimates from similar scenarios in existing literature, and the exact value may vary depending on different market and policy contexts. Further sensitivity analysis can help validate this trend. Considering both policy incentives and carbon pricing, the investment payback period of PV-ESS systems may shorten from 8 years to 5 years, with NPV increasing by approximately 20–30%. Therefore, carbon pricing not only promotes the use of low-carbon energy but also accelerates the market penetration of PV-ESS systems, providing investors with a more attractive economic analysis.

4.2. Optimized Design Parameters of the System’s Components

There are lots of components in the PV-BESS system, such as the PV panels, storage batteries, and different types of end-users of electricity. Considering initial investment, operation cost, and maintenance cost [80,131,152], size optimal design sizes of the components in the system need to be conducted from perspectives of technical, economic, and environmental performances [11,77,149].

With the appropriate design of PV and BESS’s sizes and capacities, a better matching can be achieved between supply and demand. Parameters such as the ambient environment [63], PV system configuration [8,56], energy system location [46,83], and system power consumption were found to significantly influence PV-BESS design parameters [46,153]. Optimizing design parameters involves reducing the grid charge [21], RE generation curtailment [17,131], system investment [102,154,155] and operation cost, improving supply-demand matching [144], and the stability of the power grid [109,156,157]. In addition to the design parameters, the optimal location of a central BESS system is also necessary [156]. Novel optimal design methodologies of PV-BESS systems were also proposed [21,62,102,154,155], such as employing second-life battery energy storage systems (SL-BESS) and thermal energy storage systems (TESS) for enhanced performance optimization and control, considering the aging of the PV and BESS [109,157].

For a PV-BESS system, optimization objectives of system design are multiple [64,99,158]. The optimization of a residential PV-BESS system targets to minimize the total annual cost considering both energy and battery degradation-based costs [131], while maximizing the investor’s profits [152]. This is achieved by employing commonly used financial evaluation methods such as the net present value (NPV), internal rate of return (IRR), and simple payback period (SPB), while considering the diverse characteristics of households, including size, employment status, and energy efficiency [152]. The multi-objective function of a local energy system targets to minimize investment costs and CO₂ emissions simultaneously.

The solution methods, such as the genetic algorithm (GA) [25,153], NSGA-II [11,120,159], random walk-latin hypercube sampling (RWLHS) [80], game theory-based modeling framework [2], the global Pareto Search algorithm [160], Newton Weighted Sum Frisch method (NWSFA) [99], and stochastic programming [77], are applied to address the multi-objective optimization problem [161]. In real-world engineering applications, the selection of optimization algorithms requires a comprehensive consideration of factors such as convergence speed, computational cost, accuracy requirements, and the complexity of the problem. Different algorithms are suitable for different optimization problems. For example, the genetic algorithm is well-suited for large-scale, multi-objective, and complex problems but has slower convergence speed and higher computational costs; NSGA-II excels in handling multi-objective optimization but may face higher computational overhead in high-dimensional problems; Random Walk-Latin Hypercube Sampling is suitable for nonlinear optimization problems with unknown models, but it has slow convergence and high computational costs; game theory-based modeling frameworks can handle multi-party game problems but require complex models and substantial computational resources. The Global Pareto Search Algorithm can effectively find optimal solutions for multi-objective problems but typically requires more computational resources. The Newton Weighted Sum Frisch Method is efficient for nonlinear problems but is sensitive to initial conditions. Stochastic programming is very effective for optimization problems involving uncertainty but has high computational costs. Therefore, in practical applications, it is often necessary to combine multiple optimization strategies (such as hybrid algorithms, heuristic methods, and parallel computing) to balance these trade-offs and ensure the best solution is obtained within the constraints of limited computational resources and time.

Table 6. Comparison of different algorithms.

Algorithm	Applicable Scenarios	Advantages	Limitations	Convergence Speed	Computational Cost
Genetic Algorithm (GA)	Suitable for complex, multi-objective, and constrained optimization problems, especially when the solution space is large	Strong adaptability, global search ability, can avoid local optima	May require large computational resources, prone to local optima	Moderate	High
NSGA-II	Suitable for multi-objective optimization problems, especially when there are conflicts between objectives	Efficient non-dominated sorting and crowding distance calculation, can effectively balance multiple objectives	Convergence may not be optimal, high computational cost in high-dimensional problems	Slow	Moderate
Random Walk-Latin Hypercube Sampling (RWLHS)	Used for high-dimensional complex problems, especially when the objective function is unknown or hard to represent	Can effectively generate random samples, suitable for optimization with unknown or nonlinear problems	Not suitable for highly complex optimization problems, high computational cost, slow convergence	Slow	High
Game Theory-Based Modeling Framework	Suitable for optimization problems involving multiple decision-makers and competitive or cooperative relationships	Can handle conflicts and collaboration between multiple participants	Model complexity, requires a deep understanding of participants’ strategies and goals, high computational cost	Moderate	High
Global Pareto Search Algorithm	Suitable for multi-objective optimization problems, especially when there are conflicts between objectives	Can effectively find the optimal solution between multiple objectives, suitable for multi-objective and multi-constrained scenarios	Requires large computational resources, slow convergence in complex problems	Slow	High
Newton Weighted Sum Frisch Method (NWSFA)	Suitable for nonlinear multi-objective optimization problems, especially with complex constraints	Good for handling nonlinear problems and offers high computational efficiency	Requires strong mathematical background, limited application scope, sensitive to initial conditions	Fast	Moderate
Stochastic Programming	Suitable for optimization problems involving uncertainty, especially decision problems with random variables	Can handle uncertainty, suitable for optimization under uncertain environments	Slow convergence, high computational cost in large-scale problems	Slow	High

analyzes the application scenarios, limitations, and comparisons of convergence speed and computational cost for different algorithms.

The optimization approaches for different participant objectives in the electricity system, such as energy suppliers, grid operators, and consumers, yield varied results [92,126]. For example, in a case study of a school in Cardiff with a 50 kW PV system and a 20 kWh battery storage system, when it was operated under a centralized optimization approach, operating costs can be reduced for the National Power System (NPS) by integrating battery storage, while the local energy system (LES), represented by the school, faced increased costs [126]. This discrepancy underscores the variation in optimization goals among the system’s participants. The NPS aims for overall system efficiency and cost reduction, while individual LES units, such as the school, target their own cost savings and energy usage optimization.

5. Operation Optimization of the PV-BESS System in Buildings

5.1. Measures to Improve Economic Performance

The Primary aim of using PV-BESS is to bring economic benefits. To enhance the economic efficiency of the system, G. Aniello et al. [152] proposed methods, such as energy storage systems, load control, smart energy management systems, and the integration of electric vehicles and heat pumps. These methods and technologies can work synergistically to optimize the economic performance of residential PV systems, reducing energy costs and enhancing self-sufficiency. T. Salameh et al. [125] conducted performance analyses of an integrated standalone hybrid solar PV, fuel cell, and diesel generator power system with a battery energy storage system or supercapacitor energy storage system. The simulation results showed that for the hybrid energy system with a supercapacitor energy storage system, the fraction of renewable energy was 68.1%, the levelized cost of energy was 0.346 USD/kWh, and greenhouse gas reduction was 83.2%, which was equivalent to saving 814,428 gallons of diesel. Various forms of energy can be combined, such as hydro [77], wind [28,94,95,120,127,162,163], fossil fuel [125], and hydrogen energy storage, including hydrogen storage tanks [25,28,77,94,125,133] and HV [127], hydropower pump storage [120,126], and supercapacitors [164]. For such an energy system with multiple energy sources, as shown in Figure 14 [120], with proper energy management and energy storage strategies [120,127], electricity cost can be reduced by 22.2%, resulting in minimal energy demand from the grid, the annual demand of which was only 5%.

5.2. Operation Optimization Process

To improve the efficiency of the PV-BESS system, studies were carried out to propose a comprehensive energy management process for the optimization operation of the system, as illustrated in Figure 15.

For an energy system with batter planning, it is necessary to investigate the power load demand curves of electricity consumers, which may have different patterns in different seasons [77,120,123,125,129] for different users [137]. An empirical model was proposed to accurately estimate the electricity demand of residential buildings in Switzerland, in which four energy consumption categories were summarized [165]. The PV generation curves can be obtained from the Government Bureau of Statistics, or the simulation results of models [166]. Subsequently, novel optimization frameworks of energy management can be developed to match power supply and demand. An energy system with several components was usually described with mixed-integer linear problem (MILP) model [20,28,130,167]. While MILP models are widely used in energy management optimization, they are computationally intensive and become increasingly challenging as the system size grows. Recent advancements in optimization frameworks have introduced more efficient solutions. In particular, Liang et al. [168] proposed a least squares approximation method that addresses the dynamic conversion efficiency of bidirectional converters (BDCs) in hybrid AC/DC microgrids. This method simplifies the complex trigonometric relationships that characterize BDC behavior, transforming the original non-convex optimization problem into a computationally efficient convex form. By applying this method, significant computational savings are achieved, reducing the solution time by more than two orders of magnitude compared to traditional MILP models. The proposed approach demonstrates its high efficiency and applicability, particularly in optimizing hybrid microgrids that involve multiple energy interfaces, such as photovoltaic and energy storage systems in buildings. This addition enhances the completeness of the discussion, providing a more efficient alternative to MILP models for real-world applications. Based on the energy system model, energy management included battery operation and power trade with the grid. Appliance usage was optimized with decision-making strategies [100,119,128,169,170] for different objectives, which was discussed in detail in Section 5.3.

With power demand and supply being known or estimated, control methods need to be implemented to guarantee optimal operation, with the aim of managing PV penetration, minimizing energy losses, and maintaining the stability of the system [20,137,138]. Control methods, such as model predictive control [171], fuzzy logic control [138], hill climbing search control algorithm [163], artificial neural network (ANN) control [61], etc. are normally implemented in the energy system. Control targets of the energy system include the time and capacity of charging and discharging of the battery [99,110], SOC of the battery [29,172], supply-demand matching between power demand and PV generation [29], etc.

5.3. Operation Strategies

There are various operation strategies proposed for the PV-BESS system, aiming to optimize the following four aspects.

(1)

Energy transfer optimization

In the study of X. Luo et al. (2021), the power-flow calculation was adopted to analyze the energy interaction among power generation, grid, and power demand of a district solar-based integrated energy system [173]. A sharing economy model allows residential communities to share solar generation and storage capacity [95,123]. The results showed that optimized energy-sharing strategies could not only significantly enhance the system’s self-consumption rate and reduce reliance on the grid, but also offer economic benefits to participating residents by providing cost-saving opportunities. This underscores the value of system optimization and energy management for renewable use and better economics.

(2)

Smoothing the power profiles and reducing the peaks in generation

Flexible Power Point Tracking (FPPT) algorithm [166] and Maximum Power Point Tracking (MPPT) algorithm [32,163,164] for a PV and battery energy storage system were employed to store excess power or supply lacking power. As compared to MPPT, FPPT demonstrates significant advantages in reducing the required capacity for the BESS, lowering costs, and enhancing the system’s capability to smooth power fluctuations.

(3)

Increasing power usage from PV and reducing power usage from the grid

A dynamic filtration-based power management algorithm was developed for buildings, which prioritized the utilization of power generated by PV and battery-supercapacitor instead of using power from the grid [164]. This algorithm significantly increased the proportion of energy consumed by the building, reducing reliance on the grid, and thereby optimizing both energy conservation and economic benefits.

(4)

Improving the humanization

The energy management decision-making strategies were developed considering different priority stakeholders, such as end-users, grid operators, and investors [92,95,126,127,174]. Two main principles of the decision-making strategies in the electric network are decentral, in which households control their storages, and central [126], in which the flexibilities are fully leveraged to maximize the community benefit [122]. The end-users have their own PV panels and can share the remaining electricity from PV with neighbors. They also have their own storage batteries and can share remaining stored electricity and storage capacity with neighbors. Besides, they can sell or buy electricity from gird [100,123].

Generally, the conventional rule-based operation strategy of the energy system prioritizes using storage batteries to supply insufficient electricity before turning to the grid. In addition to that, some novel strategies have been developed for different targets, such as minimizing cost [95,126,131], maximizing profit [113,128], bringing the best peak shaving effects [19,31], minimizing utilization of storage [166], maximizing renewable energy consumption [64,150], minimizing degradation cost [110], etc. Similar to the optimization design, the optimization objectives can be multiple [119,130]. For example, a multi-objective techno-economic optimization framework focuses on reducing operation costs and energy losses simultaneously [167]. The energy distribution frameworks in the literature were based on the game model [170,174], supply chain profit-allocation model [116], and Monte-Carlo tree search algorithm [124] for different optimization objectives. To solve the multi-objective problem, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) [127], Genetic algorithm (GA) [25,26,137,145], Newton Weighted Sum Frisch method (NWSFA) solution model [99], and ε-constraint method combined with fuzzy criteria [167] have been regularly adopted.

In exploring the optimization operation of PV-BESS systems, emphasis has been placed on multi-objective approaches that cater to various stakeholders’ needs, from end-users to grid operators. These strategies aim to balance economic efficiency, energy consumption, and the integration of renewable resources, ensuring that the energy system operates optimally under varying conditions. Among those strategies, three main approaches stand out, namely time-of-use pricing, demand response, and accurate forecasting techniques. To effectively compare these operation strategies,

Table 7. Comparison of Different Operation Strategies.

Operation Strategy	Advantages	Disadvantages	Suitable Scenarios	Impact on Economic and Energy Efficiency
Time-of-Use Pricing (TOU)	Reduces energy costs by shifting usage to off-peak times	Requires accurate forecasting and user participation	Residential and commercial buildings with flexible loads	Improves economic efficiency, reduces peak demand
Demand Response (DR)	Enhances grid stability, reduces energy costs	Relies on user participation and technology integration	Buildings with smart devices and control systems	Optimizes energy usage, lowers operational costs
Accurate Forecasting Techniques	Improves energy management decisions	Requires advanced data analytics capabilities	Systems with variable load and generation patterns	Increases system reliability, optimizes battery usage
Flexible Power Point Tracking (FPPT)	Reduces battery capacity requirements, lowers costs	May capture less energy compared to MPPT	PV systems with limited storage capacity	Balances energy capture with storage limitations
Maximum Power Point Tracking (MPPT)	Maximizes energy capture from PV panels	Requires larger battery capacity, higher costs	Systems prioritizing maximum energy output	Enhances energy efficiency, higher initial investment

summarizes their advantages, disadvantages, suitable scenarios, and impacts on economic and energy efficiency.

The following sections provide detailed discussions of these strategies.

(1)

Time-of-use: considering peak, valley, and flat power prices

Time-of-use (TOU) rate has better economic benefits than the flat rates [107,175,176], because the system can selectively reduce electricity purchases during peak price periods, and store grid electricity at lower prices for peak demand. Techno-economic analysis over a 25-year period revealed that systems with TOU rates yielded a 10% lower Net Present Cost (NPC) compared to flat rate systems, particularly for configurations with a 6-h battery capacity [107]. Compared with the maximum self-consumption (MSC) strategy, the TOU strategy has advantages in battery aging, gird burden, economic performance, and PV generation consumption [131,177]. Specifically, the TOU strategy leads to a state of health (SOH) of 0.967 for the battery, outperforming the MSC strategy economically when battery costs are below 1600 CNY/kWh, and effectively reduces the grid burden by optimizing energy import and export based on electricity price periods [177].

The TOU cost model, assessing grid imports and exports during peak and off-peak periods, was designed to enhance flexibility and economic performance between the PV-BESS system and the grid [12]. In practice, this model has led to significant economic benefits, resulting in a reduction of grid penalty costs by up to 164.41% and an increase in the lifetime net present value (NPV) by 96.17%, while also facilitating a decrease in carbon emissions by up to 91.36% in zero-energy scenarios compared to baseline scenarios [12]. The economic analysis can be utilized to guide policy development to reduce overall system costs [19,167,178]. For instance, in a 33-bus distribution system, the inclusion of reactive power services led to a reduction in operation costs and energy losses by 11.95% and 36.40%, respectively. This demonstrates the economic benefits of integrating reactive power support from BESS in the operation of the smart distribution system (SDS) [167].

The scheduling of the RE, grid, and BESS can be based on the economic tradeoff, which is made between online price (the sum of renewable energy generation costs, grid electricity prices, and BESS operation and degradation costs) and the benefits of increased reliability and efficiency in energy supply. This approach optimizes the mix of renewable energy usage, grid dependency, and BESS dispatch to minimize costs while ensuring that energy demand is met, and system reliability is maintained. Case studies indicated that considering battery degradation in BESS models led to a 6.0% profit increase in one month and tripled the battery lifespan, thus enhancing both the economic and operational efficiency of the system [143].

(2)

The demand response [130]

Demand Response (DR) is an electricity system management strategy that facilitates consumers to adjust their electricity usage during specific periods to align with changes in power supply. DR enhances solar energy utilization and lowers system costs [173], by managing excess feed-in and reducing renewable energy curtailment [179]. The flexible loads provided by the DR allowed the current electricity generation, distribution, and consumption infrastructure to be more fully utilized [180]. According to case studies in Germany, the implementation of DR strategies, especially load shifting, could not only prevent the curtailment of RE but also could achieve up to a 35% efficiency improvement in the energy system, demonstrating the significant potential of demand side response in optimizing energy utilization and reducing system costs [179].

A typical scenario of using DR strategy is the power-to-heat technologies, applied in residential, commercial, and industrial buildings. The generated electricity can be used to power heating or cooling appliances at the appropriate moment for load shifting [76,179]. The appliances include freezers, water heaters, space heating/cooling, etc. in the residential buildings [29,172]. Some of the household appliances can be directly connected to the PV power generator [32,75]. The heating or cooling load demands are estimated and the appliances could be controlled by several methods, such as model predictive control, and rule-based control [171]. The controllable devices in the building, such as space heaters, air conditioners, water heaters, electric vehicles, and batteries, can lower neighborhood peak demand by up to 73% during critical periods without affecting occupant comfort [129]. The impact of briefly switching off the HVAC system according to the PV output variation was also analyzed. The simulation results showed that indoor temperature would rise by 2 °C within the first 50 min while maintaining an acceptable thermal comfort range and reducing HVAC energy demand from the grid by 60% during the cooling season [181].

The energy demand for the residential household appliances can be regulated by adjusting the electric price [165]. This is achieved through a pricing policy that increases the price of electricity during peak demand times, encouraging households to shift their usage to off-peak periods. By closely monitoring and adjusting electricity prices, utility companies can influence household consumption patterns, thereby optimizing the energy supply and reducing peak load pressures [165].

In the study of energy management systems (EMS) that integrate renewable energy sources (RES), electric vehicles (EVs), and energy storage systems (ESS) in microgrids [130], energy management of an office building was under DR strategies. The operation involved optimizing a mixed-integer linear programming model that integrated PV generation curves, EV charging and discharging schedules, and BESS management. Specifically, it adjusted the energy flow between the PV-BESS system and the grid in response to dynamic electricity prices, aiming to minimize energy costs while considering the uncertainty of PV production and stochastic arrival and departure times of EVs [130]. The operation schedule, charging point, and drivers’ time and charging needs of EVs are controlled by an incentive-based demand response model that considers price elasticity [112,133,182]. EVs can mitigate fluctuations in power demand [112], by managing their SOC [176]. Specifically, this involves dynamically adjusting the charging and discharging processes of EV batteries based on real-time energy supply and demand conditions [112]. Through intelligent SOC management strategies, EVs can store excess energy during low-demand periods and supply it back to the grid or locally during peaks, improving grid stability and efficiency [112,176].

(3)

Power demand forecasts

Power demand forecasts have been studied extensively, because accurate short-term power load and power demand predictions are crucial for scheduling load generation, bridging the generation-demand gap, and reducing electricity losses [99,183].

PV generation can be estimated with weather conditions, such as solar radiation and ambient temperature [176], being forecasted [169,184]. For example, a study showed that integrating weather forecasting with PV output models can significantly improve prediction accuracy, cutting mean absolute percentage error (MAPE) by up to 30% as compared to models without weather data [184]. With models, such as the agent-based electricity market model [185], electricity prices can also be forecasted. For instance, the Agent-based market model for the investigation of renewable and integrated energy systems (AMIRIS) was applied to evaluate the impact of renewable energy integration on the German electricity market, forecasting a significant decrease in day-ahead market prices by 2030 due to increased renewable energy supply. With PV generation and electricity price being predicted, the energy consumption profiles of an energy system, such as the expected values of critical electricity demand, heat demand, and water demand, can be predicted by models, such as the stochastic model predictive control (MPC) [186], the theory-guided deep-learning load forecasting (TgDLF) [183], and the Long Short-Term Memory (LSTM)-Autoencoder model [184]. For instance, the application of the LSTM-Autoencoder model in a large-scale energy system revealed that critical electricity demand peaks could be accurately forecasted, showing a 5% to 10% improvement in prediction accuracy over traditional methods [184]. Similarly, the TgDLF model was able to predict heat demand with a precision rate exceeding 90%, effectively capturing seasonal variations and peak demand periods [183]. Lastly, the stochastic MPC approach demonstrated its capability to forecast water demand with high reliability, adjusting predictions based on real-time data and historical patterns, thus ensuring optimal resource allocation and system stability [186].

When RE is insufficient, the power demand forecast becomes crucial for BESS operation and management [187]. Forecasting energy demand during the night can reduce the average SOC of BESS and the levelized cost of electricity, and finally relieve grid stability pressures of the grid [111]. To achieve optimal economic benefits, a two-stage optimization approach for battery operation can be employed, considering both the day-ahead and intraday market adjustments [114]. In the first stage, Approximate Dynamic Programming (ADP) is used to estimate long-term operating costs by forecasting electricity prices and demand patterns, creating an optimal daily battery schedule. In the second stage, a rolling horizon procedure is applied to refine this schedule intraday, leveraging short-term updates on electricity prices and load demands to dynamically adjust battery operations. For example, implementing this two-stage model in a customer-premise Battery Energy Storage System (BESS) with a capacity of 1.2 MWh and a rated power of 0.5 MW demonstrated a 1.62% reduction in daily operating costs and an improvement in PFR reliability by reducing failure rates from 5% to 2.06%. This research delves into the development and application of a novel optimization framework to enhance the economic and operational efficiency of battery storage systems in the electricity market, by integrating day-ahead planning with real-time operational adjustments. The findings underscore the significant potential of this approach in optimizing energy storage operations, thereby facilitating a more stable and efficient integration of RE sources into the power grid. R. Tu et.al. [187] studied the performance and optimal configuration of a Grid-Connected PV power supply system in a data center’s centralized water-cooling system. It was found that with storage batteries, the mismatch problem between electricity generated from photovoltaic panels and electricity consumed by the water-cooling system was significantly reduced, boosting PV electricity utilization by 27.64% on typical days.

Also, the optimal operating status or parameters of equipment in an energy system can be predicted and controlled [99]. In the study of integrating electric thermal storage batteries into residential renewable energy systems, a control strategy forecasting the energetic state of electric and thermal subsystems in a household was proposed [29]. The research further delved into the development and implementation of a hybrid energy system combining PV panels, wind turbines, and electric thermal storage units, aiming at enhancing energy efficiency and self-sufficiency in residential microgrids [29]. The findings underscored the potential for significant improvements in the utilization of RE sources and the reduction of reliance on external power supplies, thereby contributing to the broader goal of sustainable energy development [29]. The status of BESS, such as the degradation and capacity of EVs, can be predicted based on an improved MPC for battery management [106]. By developing an improved MPC strategy, the research offers a new method for EV battery management to predict and mitigate the aging and capacity decline of the BESS [106]. The study proved that this strategy could effectively extend battery life, offering significant support for the sustainable development of EVs [106]. Besides, a flexible direct current distribution system of buildings, which integrated photovoltaics and energy storage [188], was extensively studied, with many novel technologies and applications being introduced.

5.4. Integration of PV-BESS with CCHP Systems

An emerging approach in building energy management is the integration of integrated energy systems (IES) that simultaneously handle cooling, heating, and electrical loads—often referred to as trigeneration or combined cooling, heating, and power (CCHP) systems [189]. Recent advancements have demonstrated that integrating PV and BESS with CCHP systems can significantly enhance overall energy efficiency. For instance, Ref. [189] designed an IES that incorporated PV, BESS, and absorption chillers for a commercial building, achieving a notable reduction in primary energy consumption compared to conventional systems. Specifically, during a typical summer day, the multi-CCHP system managed by the Mixed Integer Nonlinear Programming (MINLP) approach reduced total operating costs to 167,656.1 RMB—a 4.6% reduction compared to the single-CCHP setup’s 175,745.5 RMB. Additionally, the multi-CCHP system lowered GHG emissions to 163,293.4 kg, a 4.3% decrease from the single-CCHP’s 170,718.8 kg. This multi-generation approach leverages waste heat recovery and load balancing across different energy demands, optimizing resource utilization.

While the integration of PV and BESS with CCHP systems offers notable efficiency improvements, the performance of IES is sensitive to the variability in load profiles and the inherent uncertainty of solar generation. Accurate modeling of these factors is essential for optimizing system operation. Ref. [190] explored the impact of load profile variations on a PV-BESS microgrid system, applying stochastic energy management techniques to account for uncertainties in renewable generation. Their results demonstrate that optimized scheduling strategies can effectively mitigate these uncertainties, improving system reliability and operational cost efficiency. Additionally, predictive algorithms leveraging machine learning have been developed to forecast load demand and solar generation more accurately, thereby improving the operational decisions of IES [191,192].

6. Conclusions

This paper focuses on the latest studies and applications of Photovoltaic (PV) systems and Energy Storage Systems (ESS) in buildings from perspectives of system configurations, mathematic models, and design and operation optimizations. The following conclusions can be summarized:

(1)

Photovoltaic power generation systems in buildings were introduced. The power yield of PV systems was influenced by factors such as temperature, solar radiation, roof type, and panel orientation. Models to calculate or forecast PV yield were summarized, and strategies to enhance energy generation were concluded.

(2)

Energy Storage Systems (ESS) in buildings play a crucial role in balancing electricity generation and consumption. Mathematic models of ESS were introduced, showing that the aging of batteries was mainly related to operating temperature, depth of discharge, discharge current, and charge current. Performance degradation models and operation strategies were proposed to extend batteries’ lifespan. Applications of typical ESS, such as centralized and customer-sited distributed systems, as well as in electric vehicles, were summarized, and related operation strategies were concluded.

(3)

Optimizations of the PV-BESS system during design processes were summarized, from perspectives of technical, economic, and environmental performances, which is a multi-objective optimization problem. With appropriate optimization algorithms, optimal design parameters of PV-BESS can be determined, leading to a better matching between supply and demand. The ambient environment, PV system configuration, energy system location, and power consumption were found to significantly influence the values of the design parameters of the PV-BESS system.

(4)

Optimization methods and technologies were summarized for the operation of PV-BESS systems in buildings. Energy management strategies and optimization processes for the PV-BESS system were concluded. It is also a multi-objective optimization problem, aiming to minimize cost, maximize profit, bring the best peak shaving effects, minimize utilization of storage, maximize renewable energy consumption, minimize degradation cost, and so on. Three mainstream operation strategies as well as corresponding applications were then summarized.

Over the past few years, research in PV and energy storage systems within buildings has evolved from focusing on individual component efficiencies to a more holistic view encompassing system integration, optimization, and smart control. There’s a noticeable shift towards the development of IES that integrates multiple energy forms and services. The convergence of PV-BESS with advanced control strategies, passive design techniques, and energy management systems reflects the growing emphasis on maximizing energy efficiency and resilience. Future research could focus on developing lifetime prediction models for repurposed electric vehicle batteries to accurately forecast the aging effects and assess their performance and reliability in secondary applications. For example, models based on parameters such as ambient temperature, charge/discharge rates, and depth of discharge can help extend the battery’s lifespan in energy storage systems, further improving the economic feasibility and reliability of PV energy storage systems. Additionally, the application of game-theoretic mechanisms in the distributed PV market is another important direction for future research. By designing appropriate incentive mechanisms, the collaboration of distributed energy resources (DERs) can be promoted, optimizing resource allocation in the electricity market. Interdisciplinary collaboration, especially the integration of architecture, energy, and information technologies, will further promote the optimized integration of PV systems with buildings, improving building energy efficiency. For example, collaboration between architects and energy experts, combined with smart home systems, can enhance building energy management efficiency and drive the construction of green buildings. These research directions will provide critical support for the technological advancement and market application of PV energy storage systems, aiding the realization of the energy transition. In addition, in the future, developing an integrated simulation tool based on the PV (Photovoltaic) and ESS (Energy Storage System) models discussed in this paper would be highly valuable for building designers and energy managers. This tool would integrate the I-V equations and SOC models, allowing for the simulation and optimization of the configuration of PV systems and energy storage systems, helping users make more informed decisions to optimize energy use and storage. For example, Tu’s research [187] proposed an optimization method combining PV and energy storage systems, which significantly enhances the performance of PV systems in data center applications. Based on this, a simulation tool could be developed that integrates real-time meteorological data, building electricity demand, and the dynamic adjustments of PV and ESS to optimize building energy efficiency. With this simulation tool, users could predict energy output, storage performance, and economic benefits of different configurations during the design phase, and optimize the system in real-time during the operational phase, ultimately improving the overall efficiency of the PV-ESS system.

Overall, this paper highlights the importance of integrating renewable energy, energy storage, and optimization strategies in building energy systems, with a specific focus on advancements in photovoltaic (PV) and energy storage systems (ESS) configurations, optimization techniques, and emerging trends. Key contributions include insights into artificial intelligence-driven predictive controls and the use of second-life batteries, which enhance system performance and sustainability. Additionally, the development of a flexible direct current distribution system that integrates photovoltaics and storage presents a transformative approach to building power systems, supporting the shift toward sustainable energy independence.