Technical Optimization of a DC-Coupled Photovoltaic System with Battery Energy Storage for Poultry Farm Applications: A Two-Loop Methodology Based on Energy Utilization Indices

Abstract

This study presents a novel iterative dual-loop methodology for the technical sizing of DC-coupled PV-BESS systems. The method was implemented for a commercial broiler farm characterized by a highly variable electricity demand profile (annual consumption: 7.6 MWh; coefficient of variation: 53%). The methodology introduces two original energy utilization indicators—the photovoltaic-to-converter matching factor (W_{PV_S}) and the photovoltaic-to-BESS matching factor (W_{PV_B})—enabling purely technical optimization independent of economic conditions. Minimization of the radius of curvature of the WPVB characteristic curve is applied as a rigorous mathematical criterion for determining the optimal BESS capacity. Simulation results indicate that the optimal configuration consists of a 9.7 kWp photovoltaic system, a 7 kW DC converter, and a 15 kWh battery storage system. The integration of an optimally sized energy storage system increased the self-consumption coverage ratio from 38% to 59% and improved the photovoltaic energy utilization factor from 35% to 54%. Additional economic analysis demonstrates that the PV-only subsystem achieves a simple payback period ranging from 8 to 18 years, depending on the selected pricing scenario. Consequently, the technically optimal configuration identified using the proposed methodology represents a practically feasible investment for broiler production facilities operating under Polish net-billing conditions. The proposed methodology provides a reproducible, economically independent framework for the design of DC-coupled PV-BESS systems in agricultural prosumer facilities, addressing a critical gap in the optimization literature and offering practical sizing guidelines applicable to similarly high-variability load profiles.

1. Introduction

The accelerating deployment of distributed photovoltaic (PV) systems across Europe is reshaping both electricity generation profiles and the regulatory frameworks governing prosumer energy management. In Poland, the transition from net metering to net billing—introduced under the Act of 29 October 2021—fundamentally altered the economic rationale for PV installations, shifting the optimization objective toward maximization of on-site self-consumption. This regulatory shift has rendered technically optimized, storage-integrated PV systems particularly critical for energy-intensive enterprises in the agricultural sector. Livestock production facilities collectively account for a significant share of electricity consumption in Polish agriculture [1], and their energy costs are rising in line with both increased production intensity and electricity price volatility.

Global energy consumption has grown approximately eightfold since 1950, driven largely by fossil fuel combustion. In 2024, approximately 37.4 billion tonnes of CO₂ was emitted globally [2], intensifying pressure to reduce carbon intensity without compromising energy security [3,4,5,6]. Photovoltaic systems have emerged as one of the most cost-effective renewable technologies, with LCOE declining from approximately €0.37/kWh in 2010 to below €0.05/kWh in recent years [7,8,9]. Despite this advantage, PV systems present inherent technical challenges due to the stochastic nature of solar irradiance, creating temporal mismatch between generation and demand—particularly pronounced in poultry facilities where ventilation power demand is closely coupled to ambient temperature.

Photovoltaic cells are semiconductor devices that directly convert incoming solar radiation into electrical energy through the photovoltaic effect—the generation of an electromotive force in a material following the absorption of photons [10,11,12]. The fundamental operating unit is the p-n junction. When photons with energy exceeding the semiconductor bandgap are absorbed, electron–hole pairs are generated and separated by the built-in electric field at the junction, producing a direct current (DC) output. The most commercially mature technology is crystalline silicon (mono- and polycrystalline), accounting for over 90% of global production capacity, while emerging thin-film (CdTe, CIGS) and perovskite-based architectures offer alternative efficiency–cost trade-offs. Cell efficiency under standard test conditions (STC: G = 1000 W·m⁻², AM 1.5, T = 25 °C) typically ranges from 15% to 22% for commercial polycrystalline and monocrystalline modules, respectively. Module output is subject to temperature-dependent degradation: efficiency decreases as cell temperature increases above 25 °C, governed by the temperature coefficient.

Poultry production facilities—and broiler houses in particular—represent a specific and underexplored category of agricultural electricity consumer whose load profile is shaped by three interacting biological and technological drivers: (I) the discrete, cyclic structure of broiler production (cycles of approximately 43 days separated by approximately 15 days of preparation), which causes abrupt shifts in energy demand at cycle boundaries; (II) the age-dependent thermoregulatory requirements of broilers, which determine the ventilation control thresholds throughout each cycle; and (III) the dual-section fan architecture (continuous base-load fans and threshold-activated peak fans), which creates a bimodal power demand distribution with extreme statistical non-normality. Their load profiles are dominated by ventilation systems operating in base-load and peak-load modes, with peak ventilation closely correlated with solar irradiance—creating a potentially favorable temporal alignment between on-site generation and demand. The literature contains no study that optimizes a complete DC architecture PV-BESS system for such a facility using exclusively technical criteria derived from one-minute-resolution real operational data. This constitutes the primary motivation for the present study.

Direct current (DC)-coupled PV-BESS configurations eliminate the DC/AC inversion stage inherent in grid-connected AC systems, reducing conversion losses and simplifying the power electronics chain. This approach also mitigates associated technical issues, such as increased higher-order harmonic distortion and unbalanced DC capacitor voltages [13]. Yet, systematic optimization of DC-coupled PV-BESS systems—accounting for load-dependent converter efficiency and current-rate-dependent battery efficiency—remains substantially underrepresented in the engineering literature [14,15,16,17]. Energy transmission efficiency within power conversion systems is also an important consideration. Recent advances in solid-state transformer technology have demonstrated the critical role of port-level stability analysis in multi-port DC architectures [18].

The remainder of this paper is structured as follows: Section 1 reviews the state of the art; Section 2 presents the research methodology; Section 3 describes the research object; Section 4 reports simulation results; Section 5 presents a supplementary economic analysis; Section 6 provides discussion; Section 7 states limitations; and Section 8 presents conclusions.

1.1. State of the Art in PV System Optimization

Algorithms for selecting PV system components—particularly for AC systems—have been widely studied [14,15,16,17]. The optimization of ILR (inverter loading ratio) has been extensively investigated [15,16,17,19,20,21,22,23,24,25,26,27,28]; however, reported results show substantial variation.

Table 1. Degree of oversizing PV panel power relative to inverter power in selected studies.

Source	ILR	Battery Storage	Power Grid	Optimization Criterion	Application
[15]	1.0–1.51	No	Yes	Energy yield	Grid-connected AC
[16]	2.4	Yes	Yes	LCOE	Grid-connected AC + BESS
[17]	1.19	Yes	Yes	Techno-economic	Grid-connected AC + BESS
[22]	1.45	No	Yes	Energy efficiency	Grid-connected AC
[23]	1.12–1.25	No	Yes	Net energy yield	Grid-connected AC
[24]	1.1–1.8	No	Yes	Inverter reliability	Grid-connected AC
[25]	1.08	No	Yes	Energy optimization	Grid-connected AC
[26]	<1.1	No	Yes	Energy yield	Grid-connected AC
[27]	1.0	Yes	No	Self-consumption	Off-grid AC + BESS
[28]	1.3–1.7	Yes	Yes	Energy contribution	Grid-connected AC + BESS

summarizes selected studies: the recommended ILR ranges from 1.0 to 2.4, reflecting the complexity of the optimization problem and diversity of methodological approaches applied.

Available optimization methods are often computationally complex [29], or focus on single aspects such as self-consumption [30], LCOE [31], cost [32], or NPV/IRR [33]. Meta-heuristic approaches including particle swarm optimization [34] and C-ADMM [35] impose a computational burden disproportionate to the investment scale typical of agricultural installations. Studies of poultry-farm PV systems [36,37] typically apply fixed oversizing ratios rather than site-specific methodologies. A particularly relevant gap concerns DC-coupled PV-BESS systems, where no systematic methodology accounts for load-dependent converter efficiency and current-rate-dependent battery efficiency under real agricultural operational conditions.

1.2. Research Objectives

Based on the identified research gaps, this study pursues the following specific objectives:

• To develop a reproducible, two-loop iterative methodology for the technical sizing of DC-coupled PV-BESS systems based exclusively on energy-performance indices derived from real operational data.
• The definition and verification of two complementary energy utilization indicators—the photovoltaic system-to-inverter matching coefficient (W_{PV_S}) and the photovoltaic system-to-BESS matching coefficient (W_{PV_B})—enable the optimal sizing of each system component independently.
• To quantify the impact of BESS capacity on self-consumption and PV energy utilization efficiency for a poultry facility with a highly irregular demand profile under Polish climatic conditions.
• To identify the optimal PV-BESS configuration using inflection-point analysis and radius-of-curvature minimization of the W_{PV_B} characteristic curve.
• Supplementary economic assessment of the optimal PV installation with an energy storage system, demonstrating the investment’s profitability under current electricity market conditions in Poland.

1.3. Scientific Novelty

The scientific novelty of this study consists of the following original contributions:

• A novel two-loop iterative optimization algorithm for DC-coupled PV-BESS systems is proposed, integrating load-dependent efficiency profiles of both the DC/DC converter and the battery—an approach not previously reported for agricultural PV applications.
• Two original energy utilization indices (W_{PV_S} and W_{PV_B}) are introduced and formally defined, enabling purely technical, economics-independent optimization of DC PV system components.
• This is the first study to apply radius-of-curvature minimization of the (W_{PV_B}) characteristic as a rigorous mathematical criterion for optimal BESS capacity determination in a DC agricultural PV system.
• One-minute-resolution real operational data are used as the primary optimization input, enabling detailed statistical characterization of the load profile including extreme non-normality (kurtosis exceeding 1100 for peak ventilation in winter).
• The proposed method enables optimization of a DC photovoltaic PV system with energy storage under conditions of relatively high variability in the energy demand profile.

2. Research Methodology

In accordance with the adopted objectives, the proposed methodology is based on two primary datasets: electricity consumption data (recorded at one-minute intervals, IEC 61724-1 Class A [38]) and climatic data (solar irradiance and ambient temperature from IMGW at 60 min intervals, Class C). Due to the differing temporal resolutions, both datasets were standardized by downsampling to 60 min intervals (Class C) prior to optimization calculations.

A novel aspect of the proposed approach is the construction of a DC system and the incorporation of the degree of utilization of rated component power when assessing energy conversion efficiency. The methodology accounts for the dynamic load-dependent efficiency characteristics of both the PV panels and the DC converter, as well as the charging and discharging processes of the battery storage system, with particular attention to the multiplicity of current flows under low-load conditions. The optimization algorithm is shown in Figure 1. It features two iterative loops in a series-parallel structure.

The DC power output from the PV installation is described by Equation (1):

$$P_{\mathrm{M}\mathrm{P}\mathrm{P}\left(\mathrm{D}\mathrm{C}\right)} = n \cdot A \cdot {\eta }_{\mathrm{P}\mathrm{V}\left(\mathrm{T}\right)} \cdot G_{POA}$$

(1)

where n—number of panels; A—panel area (m²); G_POA—plane-of-array irradiance (W·m⁻²); and η_PV(T)—temperature-corrected PV efficiency.

The corrected panel efficiency, incorporating the temperature coefficient, is given by Equation (2):

$${\eta }_{\mathrm{P}\mathrm{V}\left(\mathrm{T}\right)} = {\eta }_{\mathrm{P}\mathrm{V}} \cdot \left(1 + {\beta }_{\mathrm{T}} \cdot \left(T_{\mathrm{P}\mathrm{V}} - 25\right)\right)$$

(2)

where η_PV—module efficiency at 25 (°C); β_T—temperature coefficient (°C⁻¹); and T_PV—module operating temperature (°C).

The operating temperature of a PV module is estimated from Equation (3), based on the NOCT parameter from the panel datasheet:

$$T_{\mathrm{P}\mathrm{V}} = T_{\mathrm{a}} + {\displaystyle \frac{NOCT - 20}{800}} \cdot G_{\mathrm{P}\mathrm{O}\mathrm{A}}$$

(3)

where T_a—ambient temperature (°C); and NOCT—nominal operating cell temperature (defined at G_POA = 800 W·m⁻², AM 1.5, T_a = 20 °C).

The efficiency of the DC converter is described by the piecewise relationship given in Equation (4), derived from the structure proposed by Mielcarek et al. [39], and verified against laboratory measurements. The piecewise model is necessary because the efficiency curve shape changes with loading factor: below 0.1 a quadratic polynomial provides the best fit, while a linear relationship applies above 0.1:

$${\eta }_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} = \left\{\begin{array}{c}-61 \cdot {k_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}}}^2 + 16.7 \cdot k_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} - 0.0637 \mathrm{for} 0 < k_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} < 0.1\\ -0.0096 \cdot k_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} + 0.9918 \mathrm{for} k_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} \ge 0.1\end{array}\right.$$

(4)

where k_DC/DC—loading factor of the DC/DC converter relative to its rated power, defined by Equation (5):

$$k_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} = {\displaystyle \frac{P_{MPP\left(DC\right)}}{P_{nDC}}}$$

(5)

where P_MPP(DC)—power from PV installation (kW); and P_nDC—rated power of the DC converter (kW).

The DC converter efficiency model is derived from the structure proposed by Mielcarek et al. [39], and verified against laboratory measurements. The piecewise model is necessary because the efficiency curve shape changes with loading factor: below 0.1 a quadratic polynomial provides the best fit, while a linear relationship applies above 0.1. The following technical specifications were adopted for the simulation: rated input voltage range 80–160 V DC; rated output voltage 100 V DC; maximum input current 60 A; switching frequency 20 kHz; and standby power consumption < 5 W. These parameters are consistent with commercially available bidirectional DC/DC converters in the 6–19 kW class used for DC-bus PV applications.

The power delivered to the DC bus—theoretically available for production—is described by Equation (6):

$$P_{\mathrm{D}\mathrm{C}} = \left\{\begin{array}{c}{P}_{\mathrm{M}\mathrm{P}\mathrm{P}\left(\mathrm{D}\mathrm{C}\right)} \cdot {\eta }_{\mathrm{D}\mathrm{C}/\mathrm{D}\mathrm{C}} \mathrm{for} P_{\mathrm{M}\mathrm{P}\mathrm{P}\left(\mathrm{D}\mathrm{C}\right)} \cdot 1.02 < P_{\mathrm{n}\mathrm{D}\mathrm{C}}\\ P_{\mathrm{n}\mathrm{D}\mathrm{C}} \mathrm{for} P_{\mathrm{M}\mathrm{P}\mathrm{P}\left(\mathrm{D}\mathrm{C}\right)} \cdot 1.02 \ge P_{\mathrm{n}\mathrm{D}\mathrm{C}}\end{array}\right.$$

(6)

A multiplier of 1.02 accounts for the converter’s input-side power limit under near-rated conditions, whereby the dynamic power supplied on the primary side may exceed rated input power even when the rated value refers to the output.

The surplus and deficit of instantaneous power relative to the facility’s production demand are defined by Equations (7) and (8), respectively:

$$P_{\mathrm{s}\mathrm{u}\mathrm{r}} = P_{\mathrm{D}\mathrm{C}} - P_{\mathrm{Z}} \mathrm{f}\mathrm{o}\mathrm{r} P_{\mathrm{D}\mathrm{C}} > P_{\mathrm{Z}}$$

(7)

$$P_{\mathrm{s}\mathrm{h}\mathrm{o}}=P_{\mathrm{Z}}-P_{\mathrm{D}\mathrm{C}} \mathrm{f}\mathrm{o}\mathrm{r} P_{\mathrm{D}\mathrm{C}} \le P_{\mathrm{Z}}$$

(8)

where P_Z—current electrical power demand for production (kW).

The PV energy utilization index for the system without storage (W_{PV_S}), defining the ratio of energy usefully delivered at the converter output to the total energy available at the PV maximum power point over the calendar year, is given by Equation (9):

$$W_{PV\_S} = {\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}=1}^n}{P}_{DC,i} \cdot \Delta t}{{\displaystyle {\sum }_{\mathrm{i}=1}^n}{P}_{MPP\left(DC\right),i} \cdot \Delta t}}$$

(9)

where Δt—time-averaging interval (h); and i—measurement period index. The optimal PV array and converter size are identified at the maximum of W_{PV_S} (Loop 1).

In the second loop, battery efficiency is described by Equation (10), adapted from Xiaojia Su et al. [40] at a constant temperature of 25 °C:

$${\eta }_{\mathrm{l}\mathrm{a}\mathrm{d}/\mathrm{r}\mathrm{l}\mathrm{a}\mathrm{d}} = {\eta }_{\mathrm{r}\mathrm{e}\mathrm{f}} - k_{\mathrm{r}\mathrm{a}\mathrm{t}} \cdot C_{\mathrm{r}\mathrm{a}\mathrm{t}}$$

(10)

where η_ref = 0.978—reference efficiency; k_rat = 0.0127—current multiplier factor; and C_rat—charge/discharge current ratio.

According to the study by Saez-de-Ibarra et al. [19] and Alipour et al. [41], an increase in operating temperature by 10 °C is associated with a reduction in battery lifetime of nearly 50%, which is consistent with broader evidence that temperature strongly affects electrochemical properties, degradation mechanisms, and performance of lithium-ion cells. Therefore, a constant operating temperature of the batteries was assumed in this study, and its impact will be considered in future work as part of a more detailed economic analysis of such a system.

The charge/discharge current multiplier is determined by Equation (11):

$$k = {\displaystyle \frac{\frac{P_{\mathrm{s}\mathrm{u}\mathrm{r}}}{U_{\mathrm{C}}}}{C}}$$

(11)

where P_sur—surplus power at converter output (W); C—rated battery capacity (Ah); and U_C—battery operating voltage (V).

The battery adopted for simulation is a lithium iron phosphate (LiFePO₄) module with the following nominal specifications: rated capacity 50 Ah at 50 V (2.4 kWh per module); nominal bus voltage 100 V DC; depth of discharge (DoD) 60% (operating range: 20–80% SoC); maximum charge/discharge C-rate: 1C; cycle life: >6000 cycles at 80% DoD; self-discharge rate: <3%/month. These parameters are consistent with commercially available stationary (LiFePO₄) storage systems and were adopted as representative for the simulated capacity range of 0–100 kWh.

The power transferred to and from the battery is given by Equations (12) and (13):

$$P_{\mathrm{l}\mathrm{a}\mathrm{d}} = P_{\mathrm{s}\mathrm{u}\mathrm{r}} \cdot {\eta }_{\mathrm{l}\mathrm{a}\mathrm{d}}$$

(12)

$$P_{rlad}={\displaystyle \frac{P_{sho}}{{\eta }_{rlad}}}$$

(13)

where P_sho—power deficit to meet production demand (kW).

The PV-to-BESS system matching coefficient (W_{PV_B}), characterizing the degree of utilization of total PV-generated electricity including energy recovered from the battery, is given by Equation (14):

$$W_{PV\_B} = {\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}=1}^k}\left(P_{DC,i} - P_{sur,i} + P_{rlad,i}\right) \cdot \Delta t}{{\displaystyle {\sum }_{\mathrm{i}=1}^k}{P}_{MPP\left(DC\right),i} \cdot \Delta t}}$$

(14)

where k—upper limit of summation. The optimal battery capacity is identified at the inflection point of the (W_{PV_B}) characteristic, determined by fitting an exponential function (Equation (14)) and computing the radius of curvature. The self-consumption coverage ratio and PV energy utilization ratio are defined by Equations (15) and (16):

$$W_{men} = {\displaystyle \frac{E_Z - E_{sho}}{E_Z}}$$

(15)

$$W_{eur}={\displaystyle \frac{E_Z-E_{sho}}{E_{DC}}}$$

(16)

where E_Z—annual electricity demand (kWh); E_DC—energy at converter output (kWh); and E_sho—annual energy deficit (kWh).

The exponential fitting function used in nonlinear estimation for the (W_{PV_B}) characteristic is

$${W_{PV\_B}}^{\ast }=a \cdot e^{-{\displaystyle \frac{b}{C}}}+d$$

(17)

where a, b, and d—estimated coefficients; and C—battery capacity (kWh).

The self-consumption coverage ratio (W_{_men}), the fraction of annual electricity demand met by on-site PV generation and battery discharge, and the PV energy utilization ratio (W_{_eur}), the fraction of total DC converter output energy directly consumed for production, are key performance indicators. These metrics quantify the effectiveness of the technical sizing methodology in improving both self-sufficiency and energy utilization efficiency.

3. Characteristics of the Research Object

The measurements presented in this study were conducted in one of six identical livestock buildings used for broiler chicken production, located on a farm in the Mazowieckie Province (Łosice County, central Poland). The total floor area was 2900 m² and internal volume approximately 11,000 m³. Each building was equipped with four chimney fans (rated power: 0.52 kW each) forming the base ventilation section, and three ridge fans (rated power: 1.1 kW each) forming the peak ventilation section.

The electricity demand profile of this facility is intrinsically linked to the biological and technological requirements of broiler production. The base ventilation section (four chimney fans, 0.52 kW each, total 2.08 kW) operates continuously throughout each production cycle to maintain minimum air quality, resulting in a platykurtic, relatively stable base load. The peak ventilation section (three ridge fans, 1.1 kW each, total 3.3 kW) is activated by threshold control: fans switch on abruptly when internal temperature exceeds age-dependent limits (22–35 °C) or when CO₂ concentration surpasses 4600 ppm. This on/off activation mechanism—with no intermediate speed states in the base configuration—produces a strongly bimodal power demand distribution. In winter months (October–March), peak fans are rarely activated (mean peak-section power: 0.00 kW, CV = 2692%), while in summer months (June–July) they operate frequently (mean: 0.42 kW). The resulting CV = 53% at the annual level directly reflects the seasonal cycle of broiler production combined with the threshold-governed fan control logic, not simply weather variability. This is the fundamental reason why the load profile requires a dedicated optimization approach rather than a standard residential or commercial prosumer methodology.

Electrical measurements were performed using a Twelve AS-3plus power quality analyzer at one-minute intervals (IEC 61724-1 Class A [38]). The analyzer was characterized by the following technical parameters: measurement range 0–1000 V (AC/DC), current measurement range 0–1000 A (via CT clamps), power measurement accuracy class 0.5S (EN 62053-22), data logging interval 1 min (configurable), internal memory capacity 512 MB (equivalent to >365 days continuous logging at 1 min resolution), and communication interface RS-485/Modbus RTU.

Electrical measurements were performed using a Twelve AS-3plus power quality analyzer at one-minute intervals (IEC 61724-1 Class A [38]). Microclimate parameters were monitored using a VIRGO microclimate controller with TEMP-201 temperature sensor and RHT-CO₂-10K combined sensor. The fan control algorithm implemented two thresholds: internal temperature limit in the range 22–35 °C (depending on bird age) and CO₂ concentration limit of 4600 ppm.

The measurement campaign covered 1 February 2019 to 17 March 2020. Eight complete production cycles were recorded (average 43 days each), followed by approximately 15 days of preparation. Stocking density: 56,000 ROSS 308 broiler chickens per cycle. Annual electricity consumption: 7.6 MWh; monthly mean: 630 kWh; and coefficient of variation: 53%. Monthly consumption ranged from 290 kWh (October) to 1487 kWh (June), driven by the cycle-based schedule (Figure 2).

In the autumn–winter period (October–March), monthly consumption stabilized at approximately 800 kWh due to predominant base-section fan operation. During the remainder of the year, consumption increased to 1000–1600 kWh, driven by peak-section fans activated to maintain thermal comfort at elevated outdoor temperatures (Figure 3).

Hourly power demand profiles were derived for five sub-periods (Figure 4a–e). A statistical summary is presented in

Table 2. Statistical indicators for the load profile by season and ventilation section.

Season/Section	Mean (kW)	SD (kW)	CV (%)	Range (kW)	Skewness	Kurtosis	Section
October–March	0.77	0.45	58	2.03	0.51	−1.04	Base
October–March	0.00	0.06	2692	2.32	32.39	1100.96	Peak
April/May/August/September	0.94	0.57	61	2.08	0.49	−0.95	Base
April/May/August/September	0.06	0.34	581	3.30	6.98	52.20	Peak
June–July	1.12	0.76	68	1.90	0.14	−1.70	Base
June–July	0.42	0.91	215	3.30	2.10	3.11	Peak

.

The statistical characterization reveals extreme non-normality in the peak ventilation section’s power demand distribution: in winter months (October–March), the coefficient of variation reaches 2692%, skewness exceeds 32, and kurtosis surpasses 1100—indicating a highly leptokurtic distribution dominated by rare, high-magnitude events (full-load peak fan operation). This extreme non-normality is a direct consequence of the threshold-activated fan control algorithm: when internal temperature exceeds age-dependent limits 22–35 °C or when CO₂ concentration surpasses 4600 ppm. When the controller’s temperature or CO₂ threshold is not met—as is typically the case for 85–90% of winter hours—peak power demand is zero, producing the observed spike in kurtosis. This mechanism is characteristic of all modern broiler production facilities using fixed-speed fans with discrete microclimate control, and its implications for PV-BESS sizing are analyzed in detail in Section 4.2. In the base section, kurtosis ranges from −0.95 to −1.70 (platykurtic distribution). A south-facing PV installation with 30° tilt was assessed. The resulting irradiance profile is illustrated in Figure 5.

4. Simulation Results

Simulations were performed using polycrystalline PV panels with rated power 405 Wp (STC), active area 1.8 m², temperature coefficient β_T = 6.5 × 10⁻³ °C⁻¹, NOCT = 48 °C. The PV modules used in the simulation are representative of current-generation polycrystalline silicon technology with the following complete set of parameters at STC (G = 1000 W·m⁻², AM 1.5, T_cell = 25 °C): open-circuit voltage V_OC = 47.5 V; short-circuit current I_SC = 10.9 A; voltage at maximum power point V_MPP = 39.2 V; current at maximum power point I_MPP = 10.3 A; module efficiency η = 22.5%; number of cells: 144 (half-cell configuration); and power tolerance: 0/+5 Wp; NOCT: 48 °C. The PV manufacturer is not disclosed to avoid promotional bias. The installation is south-facing with 30° tilt. For the DC converter, a simulation step of 1 kW was applied over the range 6–19 kW.

4.1. PV System Without Energy Storage

Figure 6 presents the family of (W_{PV_S}) curves as a function of PV peak power for different DC converter ratings. An envelope of maximum (W_{PV_S} = 0.974) is visible, representing maximum annual DC generation efficiency. As converter rated power increases, the characteristic curves become progressively asymmetric: the rate of index increase prior to the optimum is lower than the rate of decrease beyond it—implying that PV oversizing above the optimal point is more detrimental than a comparable degree of undersizing. The simulation grid for Figure 6 was constructed with a PV peak power resolution of 0.5 kWp across the range 2–25 kWp, yielding 47 calculation points per converter rating curve, and 14 converter rating curves from 6 to 19 kW (1 kW step). This resolution is sufficient to characterize the maximum of W_{PV_S} with an uncertainty of less than 0.3 kWp. Additional calculation points were introduced in the vicinity of the optimal configuration (8–12 kWp range) with a finer resolution of 0.1 kWp to improve the precision of optimum identification.

Figure 7 presents annual PV energy overproduction and energy deficit as functions of DC converter power. A threefold increase in installed PV capacity—from 6 kW to 18 kW—results in more than a fourfold increase in overproduction, while reducing the annual energy deficit by only approximately 20%. This confirms that unlimited PV capacity expansion is technically inefficient under Polish net-billing conditions.

Figure 8 presents the results of the first optimization loop: the optimal PV oversizing factor relative to DC converter rated power. The rated power of the PV array should exceed the DC converter rated power by approximately 40% (ILR ≈ 1.40). Figure 9 presents the self-consumption coverage ratio (W_men) and PV energy utilization ratio (W_eur) as functions of DC converter rated power. The two indicators intersect in the 6–7 kW range. Even the largest PV installation analyzed cannot cover more than approximately 50% of the annual demand, with a PV energy utilization ratio of only 17%.

4.2. PV System with Energy Storage

Figure 10 presents the W_{PV_B} coefficient—the ratio of total energy utilized for production (including battery discharge) to total PV energy at maximum power point (Equation (12))—as a function of battery capacity for selected PV installation sizes (listed in

Table 3. Summary of selected performance parameters of the analyzed PV installation configurations.

PnDC kW	Pp kWp	EDC kWh	Wmen C = 0%	Weur C = 0%	Ebat kWh	Wmen C = 15%	Weur C = 15%	ILR	ΔWmen %
6	8.5	7013	36	38	1422	54	56	1.42	+18
7	9.7	8013	38	35	1613	59	54	1.39	+21
8	10.5	8680	40	31	1748	60	51	1.31	+20
9	13.4	11,020	43	29	1860	66	46	1.49	+23
10	14.6	12,020	44	27	1934	68	43	1.46	+24
11	15.8	13,025	45	26	1991	70	41	1.44	+25
12	17.0	14,025	46	24	2040	72	39	1.42	+26
13	18.2	15,026	47	23	2018	74	37	1.40	+27
14	20.7	17,030	48	21	2150	76	33	1.48	+28

Note: E_bat—energy consumed from battery for production (kWh); ILR = P_p/P_nDC; ΔW_men—absolute increase in self-consumption coverage ratio with 15 kWh storage. Bold row: identified optimal configuration (P_nDC = 7 kW, P_p = 9.7 kWp, C = 15 kWh).

). Battery operation was limited to the 20–80% state-of-charge range and operating voltage was set at 100 V. Unlike W_{PV_S}, the W_{PV_B} curve is monotonically increasing. Optimization relies on identification of characteristic inflection points rather than a maximum. The battery capacity simulation range was extended to 0–200 Ah (0–20 kWh at 100 V bus) with a resolution of 10 Ah (1 kWh), yielding 20 calculation points per PV installation size curve. An additional set of simulation points was computed in the 100–180 Ah range at 5 Ah resolution (1.6 kWh steps) to improve the precision of the inflection-point identification. In total, Figure 10 presents results for seven PV installation sizes (6, 7, 8, 9, 10, 12, and 14 kW DC converter ratings) and at least 20 battery capacity points per curve.

The tangent intersection method identifies an optimal battery capacity of approximately 150 Ah (15 kWh at 100 V bus). The W_{PV_B} characteristics were fitted using nonlinear exponential estimation (Equation (14)). The coefficient of determination R² was not lower than 0.9996 across all fitted curves. Figure 11 presents the radius of curvature of the fitted curves.

The minimum radius of curvature—corresponding to maximum curvature change—occurs at a battery capacity of 15 kWh across all analyzed installation sizes, confirming the engineering tangent intersection result. Figure 12 shows that a 100% increase in battery capacity—from 15 kWh to 30 kWh—improves the energy utilization ratio by only four percentage points, demonstrating strongly diminishing marginal returns.

Figure 13 compares performance with and without the 15 kWh optimal storage. For a DC converter power of 7–8 kW, storage increases the self-consumption coverage ratio from approximately 0.40 to 0.60. Figure 14 presents monthly electricity demand with and without the optimized PV-BESS system. From March to October, the system reduces grid energy requirements by approximately 40%, while during November–February, its contribution is minimal.

5. Supplementary Economic Analysis

The primary contribution of this study is the technically optimal PV-BESS configuration identified through the two-loop methodology described in Section 2. By design, the proposed optimization is independent of electricity prices, subsidy levels, and discount rates—a deliberate methodological choice that ensures the results remain valid across different regulatory regimes and remain reproducible without economic parameter assumptions. This approach is novel in the PV-BESS optimization literature, where economic criteria typically dominate the objective function [31,32,33]. Nevertheless, to assist practitioners in assessing investment viability and to respond to the practical needs of poultry farm operators, this section presents a supplementary techno-economic analysis of the identified optimal configuration (P_nDC = 7 kW, P_p = 9.7 kWp, C = 15 kWh BESS).

It is explicitly noted that the economic analysis does not alter the technically optimal configuration—it demonstrates the economic implications of implementing that configuration under current Polish market conditions.

5.1. Capital Cost Structure

The capital expenditure (CAPEX) structure for the optimal PV–BESS configuration was estimated under three scenarios: (I) budget, (II) premium, and (III) average. The detailed cost breakdown of individual components is presented in

Table 4. Capital expenditure structure for the optimal PV-BESS configuration (P_nDC = 7 kW, P_p = 9.7 kWp, C = 15 kWh BESS).

Component	Quantity	Cost of a Budget Installation PLN/EUR	Cost of the Premium Version PLN/EUR	Average Installation Cost PLN/EUR
PV array (polycrystalline, 405 Wp)	9.7 kWp	5280/1239	8640/2028	6960/1634
DC/DC converter	7 kW	2500/587	4700/1103	3600/845
LiFePO4 BESS (15 kWh, BMS incl.)	15 kWh	10,950/2570	25,800/6056	18,375/4313
Equipment subtotal	-	6200/1455	7800/1831	7000/1643
Installation & commissioning (18%)	-	6200/1455	12,500/2934	9350/2195
TOTAL CAPEX	-	31,130/7308	59,440/13,953	45,285/10,630

Note: EUR conversion at exchange rate 4.3 PLN/EUR (2025 average).

.

The analysis assumes photovoltaic modules (polycrystalline, 405 Wp), a 7 kW-rated DC/DC converter, and a LiFePO₄ battery system with a total capacity of 15 kWh. Installation, wiring, protection equipment, and system commissioning costs were estimated at 18% of equipment costs, in accordance with Polish benchmarks for PV installations in the agricultural sector [42,43].

5.2. Annual Savings and Simple Payback Period

Annual economic savings are calculated as the monetary value of grid electricity displaced by on-site PV-BESS generation. The electricity purchase price for Polish agricultural small and medium enterprises was 0.90 PLN/kWh in 2025, inclusive of distribution tariff components. Under the net-billing regime, surplus PV energy fed to the grid is credited at the day-ahead market price, which is significantly lower than the purchase price. This asymmetry further justifies the self-consumption orientation of the technical optimization.

With the optimal configuration W_men = 59%, 4484 kWh/year of electricity demand is covered by on-site generation, yielding annual gross savings of 4036 PLN/year. Annual operation and maintenance costs are estimated at 1% of CAPEX. Because the equipment market exhibits high price volatility based on brand tier and component origin, the system economics were evaluated across three CAPEX scenarios: budget class (31,130 PLN), average market (45,285 PLN), and mid-range class (59,440 PLN).

Depending on the chosen hardware tier, the net annual savings range from 3442 PLN to 3725 PLN/year. The simple payback period (SPB) for the full system spans a remarkably wide interval:

• 8.4 years in the budget-class scenario.
• 12.6 years under average market conditions.
• 17.3 years in the mid-range class scenario.

For comparison, the PV-only subsystem (without BESS) achieves an SPB of 8.4, 11.5, and 14.9 years across the three respective scenarios. Consequently, the incremental investment in the 15 kWh battery yields an incremental payback of 8.3 years for budget components, extending to nearly 22 years for mid-range components. This critical finding demonstrates that while the technical optimum is fixed (15 kWh), the economic viability of the battery component currently depends almost entirely on the investor’s hardware selection and risk appetite regarding budget-tier brands.

5.3. Economic Sensitivity Analysis

The economic analysis was limited to the simulation of selected indicators over an electricity price range of 0.7–1.2 PLN/kWh, taking into account three installation cost scenarios. The results of the sensitivity analysis of the simple payback period (SPB) with respect to electricity price for the three hardware scenarios of the complete PV-BESS system are presented in

Table 5. Sensitivity of simple payback period (SPB) to electricity purchase price—full PV-BESS system.

Electricity Price (PLN/kWh)	SPB–Budget (Years)	SPB–Average (Years)	SPB–Mid-Range (Years)
0.70	11.0	16.9	23.4
0.80	9.5	14.4	19.9
0.90	8.4	12.6	17.3
1.00	7.5	11.2	15.3
1.10	6.7	10.1	13.7
1.20	6.1	9.2	12.4

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The results of the presented analysis indicate that the investment costs incurred for the technically optimal PV installation will be recovered within a period not exceeding approximately 8 years for the budget-class configuration and 17 years for the premium configuration, assuming the current electricity price level. Considering the global upward trend in electricity prices, this period may be reduced to approximately 6 years and 12 years, respectively, if the electricity price reaches 1.2 PLN/kWh.

6. Discussion

6.1. DC Architecture Efficiency and Optimal ILR

The optimal PV array oversizing relative to the DC converter rated power of approximately 40% (ILR ≈ 1.39–1.42) is consistent with the upper portion of the range reported for AC-connected PV systems (1.0–2.4, Table 1). The physical mechanism is the same in both AC and DC architectures: the trade-off between clipping losses under high irradiance and converter underutilization losses under low irradiance. Similar findings were reported by [42,43], who identified that oversizing PV modules by 30–50% relative to converter power allows better utilization of available solar radiation under variable operating conditions. A key distinction of the present methodology is that the W_{PV_S} index explicitly incorporates the load-dependent efficiency profile of the DC/DC converter (Equation (4)), which exhibits pronounced non-linearity at loading factors below 0.1—a condition occurring frequently under low irradiance.

6.2. Self-Consumption and Energy Utilization Without Storage

For the PV system without storage, even at maximum investigated converter power (19 kW), self-consumption coverage does not exceed approximately 50%, with a PV energy utilization ratio of only 17%. These values are consistent with findings of [44], who demonstrated that in commercial prosumer systems without storage, self-consumed PV energy rarely exceeds 50–60% for profiles with significant intraday and seasonal variability. The rapid divergence between overproduction and deficit curves (Figure 7)—where threefold PV capacity increase causes fourfold increase in overproduction but only 20% deficit reduction—directly reflects the poor temporal alignment between PV generation and facility demand in autumn–winter months.

6.3. BESS Integration: Optimal Sizing and Diminishing Returns

The presented methodology for the technical optimization of the PV system design is complementary to the results of the simplified economic analysis. At the same time, it provides a foundation for more advanced economic evaluation methods, including forecasting approaches. However, the economic optimality of this capacity is strongly dependent on both the equipment price level and electricity prices. In the budget-class cost scenario, the technical optimization aligns perfectly with the financial rationale, delivering an additional battery system payback period of only 8.3 years—well within the expected cycle life of LiFePO₄ batteries. In contrast, for mid-range equipment, the incremental storage payback exceeds 21 years, shifting the purely economic optimum toward a PV-only configuration, unless subsidies are applied. This gap between the technical optimum and the financial boundary quantitatively captures the trade-off that farm operators must navigate, balancing system reliability and the longevity of premium hardware against investment profitability.

6.4. Implications of Non-Normal Load Distributions for Optimization Robustness

The extreme departure from normality observed in the peak ventilation section’s power demand distribution (kurtosis > 1100, skewness > 32 in winter months) poses a specific challenge for energy system optimization. The arithmetic mean of hourly power demand systematically underestimates both the frequency and magnitude of short-duration peak demand events. In the context of BESS sizing, this implies that a battery capacity optimized exclusively on the basis of mean hourly profiles may fail to capture the full energetic benefit of storage during periods of high peak-fan activation. This non-normality is not a statistical artifact but a direct consequence of the broiler ventilation control architecture: the microclimate controller activates peak fans in a discrete on/off manner based on age-dependent temperature thresholds. In winter, the threshold is rarely exceeded, resulting in a near-zero mean for the peak section but a non-zero probability of full-load activation during unusually warm winter days or when CO₂ accumulates rapidly in younger flocks. The present methodology partially mitigates this by using one-minute-resolution data before downsampling. However, the sensitivity of the optimal battery capacity to data temporal resolution remains a subject for future investigation.

6.5. Seasonal Performance and Practical Implications

The seasonal analysis (Figure 14) reveals that from March to October, the optimized system reduces monthly grid energy demand by approximately 40%, while in November–February, the system’s contribution is minimal. This seasonal asymmetry is consistent with Polish PV performance data reported in [45,46,47]. For farm operators and PV system designers, the results provide three actionable guidelines: (i) a PV array oversizing of 40% relative to DC converter rated power (ILR ≈ 1.39–1.42) represents the technically optimal starting configuration; (ii) 15 kWh of battery storage doubles the practical value of the PV installation; (iii) the PV-BESS system should be considered a seasonal supply supplement rather than a primary energy source—winter requirements will continue to be met predominantly from the grid.

7. Limitations

While the proposed methodology demonstrates strong potential, several limitations should be acknowledged:

• Single-case validation. The methodology was validated for one broiler production building in Mazowieckie Province. It is explicitly noted that all data presented in this article—including electricity consumption, load statistics, and optimization results—pertain to a single building of 2900 m² floor area and do not represent aggregated farm-level data. Generalizability to other poultry species (layers, turkeys, ducks), alternative housing systems, multi-building configurations, or other climatic regions of Poland and Europe requires further investigation. Future studies should validate the proposed methodology across at least two to three additional buildings with contrasting load profiles and climatic exposures.
• The battery efficiency model proposed by Su et al. [40] was parameterized at a reference temperature of 25 °C. In agricultural environments, energy storage systems may be exposed to seasonal ambient temperatures ranging from approximately −15 °C to +40 °C, which can significantly affect round-trip efficiency by approximately ±5% relative change per 10 °C deviation from the reference temperature for LiFePO₄ chemistry. Furthermore, considering the findings of Saez-de-Ibarra et et al. [19] and Alipour et al. [41], who demonstrated that an increase in temperature of 10 °C above 25 °C may reduce battery lifetime by up to 50%, the present study assumes that, given the relatively small battery capacity, it is preferable to maintain appropriate operating conditions rather than allow for a significant reduction in service life. It should also be noted that battery costs constitute a significant share of the total investment cost of a PV–BESS installation.
• Temporal data resolution mismatch. Downsampling Class A (1 min) consumption data to Class C (60 min) may mask sub-hourly peak demand events that influence optimal BESS sizing, particularly for the highly leptokurtic peak-section distribution.
• Absence of grid interaction modeling. The study assumes that surplus PV energy cannot be economically sold to the grid (post-net-billing Polish context). Under net-metering regulations or feed-in tariff regimes, the optimal configuration may differ.
• The supplementary economic analysis presented in Section 5 was based on Polish market prices applicable in 2025 and assumed a fixed annual electricity price escalation rate. The analysis showed that the technically optimal configuration is consistent with the economic viability assessment under realistic scenarios. However, it does not constitute a full lifecycle cost analysis or an investment appraisal based on forecasts not only of electricity prices, but also of energy yield from the PV plant and the process energy demand. For site-specific investment decisions, it is recommended to conduct a comprehensive economic optimization incorporating time-of-use tariffs, battery degradation curves, and tax considerations.
• The technical optimization did not account for the degradation of photovoltaic panels, as this is a method for selecting solar system components. The study did not forecast changes in energy consumption or production over time, as this was not the objective of the research. Therefore, only simple indicators of the investment’s profitability at the time of its implementation were determined.

8. Conclusions

This study presented and validated a novel two-loop iterative methodology for the purely technical optimization of DC-coupled photovoltaic systems with integrated battery energy storage, applied to a commercial broiler production facility (annual demand: 7.6 MWh, CV: 53%). The following conclusions are drawn:

• The proposed two-loop optimization algorithm—based on iterative maximization of W_{PV_S} (Loop 1) and radius-of-curvature minimization of the W_{PV_B} characteristic (Loop 2)—provides a computationally efficient, technically rigorous method for sizing DC PV-BESS systems without recourse to economic parameters or meta-heuristic algorithms.
• For the analyzed broiler production facility, the optimal DC PV-BESS configuration consists of a 9.7 kWp PV array, a 7 kW DC/DC converter, and a 15 kWh BESS—corresponding to ILR ≈ 1.39 (40% oversizing), derived through a DC-specific methodology based on real operational data.
• The integration of the optimally sized 15 kWh BESS increased W_men from 38% to 59% and W_eur from 35% to 54%—a relative improvement of approximately 55% in both indicators—confirming the effectiveness of the proposed sizing methodology under Polish net-billing conditions.
• Beyond 30 kWh BESS capacity, the incremental improvement in PV energy utilization decreases to less than 4% per doubling of storage capacity, providing a technically grounded upper boundary for BESS sizing that is independent of electricity prices.
• The extreme non-normality of the peak ventilation load profile (kurtosis > 1100 in winter) raises important methodological questions regarding mean-based energy balance calculations for BESS sizing. Future work should investigate temporal resolution sensitivity, temperature-dependent battery efficiency, PV degradation effects, and full techno-economic analysis.
• The supplementary economic analysis showed that the PV system selected solely on the basis of technical criteria, with parameters of P_p = 9.7 kWp, P_nDC = 7 kW, and storage capacity C = 15 kWh, achieves a simple payback period ranging from 8 to 18 years, depending on the selected pricing variant. Considering that the expected operational lifetime of the installation is 25 years, even the replacement of batteries after 6000 cycles provides satisfactory results and the prospect of generating a financial surplus for the renewal of such an installation.