Multi-Criteria Optimal Operation Strategy for Photovoltaic Systems in Large-Scale Logistics Parks Concerning Climate Impact

Abstract

Solar power is widely regarded as one of the most promising renewable resources for generating electricity and reducing building energy consumption. Logistics parks, with their low-rise buildings and extensive rooftop areas, offer significant advantages for solar energy utilization via rooftop photovoltaics (PVs). However, limited research has been conducted on the proper operational principles and optimized control strategies for the PV systems of logistics parks, particularly regarding the mismatch between power generation and the loads of various building types under varying climatic conditions. This study proposes four optimal PV operation strategies for large-scale logistics parks across diverse climatic regions, developed using a multi-criteria optimization approach. The strategies optimize the azimuth and tilt angles of PV panels under four adjustment frequencies: annual, semi-annual, seasonal, and monthly. The investigated strategies are validated in a 5500 m² logistics park, comprising refrigerated storage, warehouses, sorting centers, and other facilities. The results indicate that the proposed strategies outperform conventional fixed-angle approaches, with the monthly adjustment strategy delivering the best performance. Economic costs are reduced by 9.26–17.02%, while self-sufficiency can be improved by 2.00–7.08%. Cold regions with high solar radiation show particularly significant benefits, with self-consumption increasing by 82.44–359.04%. This study provides valuable insights and practical guidelines for optimizing PV system operations in logistics parks, offering enhanced energy efficiency and cost-effectiveness.

1. Introduction

Amid escalating global climate change and energy crises, the building sector is a major contributor to global carbon emissions [1,2,3]. In China, the rapid expansion of logistics parks, fueled by urbanization and the surge in e-commerce, has seen considerable growth. This growth has significantly increased energy consumption and carbon emissions [4]. According to the “China Energy Statistical Yearbook”, carbon emissions from the logistics sector of China increased to 34.61 million tons in 2017, accounting for 18% of the country’s total carbon emissions [5].

Logistics parks are defined as logistics industry clusters, planned by the government and managed by a unified entity. Multiple companies establish distribution centers or regional distribution hubs in logistics parks, providing specialized logistics infrastructure and public services. Typically, logistics parks offer significant advantages for solar energy utilization with their various low-rise buildings and extensive rooftop areas, making them ideal for rooftop PV systems [6]. How to effectively utilize renewable solar energy in logistics parks has become an important issue that needs to be addressed [7,8].

Much research has explored the utilization potential of solar energy in offices and commercial buildings and developed corresponding integrated energy systems and optimal operation strategies by incorporating PV equipment into existing power systems. Ding et al. proposed a distributed cooperative operation strategy for multi-agent energy systems integrated with solar energy [9]. Sheikholeslami et al. proposed a solar thermoelectric system for building units in the presence of helical tapes and the jet impingement of hybrid nanomaterial [10]. Dezfouli et al. analyzed the performance of solar solid desiccant cooling systems for energy efficient buildings in tropical regions [11]. Priya et al. proposed an energy yield enhancement solution for the PV system, focusing on the electrical reconfiguration of the arrays during partial shading [12]. However, there are few relevant studies for the logistics park, especially since the logistics park has a large number of roof resources, which can be used for the large-scale laying of PV panels. Existing studies on the use of solar energy in logistics parks have been conducted mostly from the perspective of transport, with less consideration given to the energy needs of the buildings themselves. For example, Wang et al. proposed a planning approach for integrating charging stations and renewable energy sources in low-carbon logistics delivery [8].

Unlike other types of buildings, logistics parks encompass a diverse range of building types, including refrigerated storage, warehouse, sorting center, apartment, office, commercial, canteen, etc. [13]. Distinct building functions are characterized by significantly different load profiles [14,15,16]. Furthermore, solar energy is highly unstable, and the power generation of PV systems is affected by various factors, including climate, PV angles, and panel materials [17,18,19,20]. The complexity of various building loads and the instability of PV power generation pose significant challenges for implementing PV systems in logistics parks (as shown in Figure 1). Mismatches between PV power generation and building loads can lead to increased transportation loss, unsatisfied energy demand, and reduced grid stability [21]. Therefore, to realize the benefits of PV systems and effectively reduce carbon emissions in logistics parks, PV power generation must be aligned with building loads [22], which requires the appropriate operation strategies of PV systems or management measures of the demand side.

Previous studies have demonstrated that regularly adjusting the angles of PV panels can notably enhance their energy generation [23]. Alqaed et al. assessed fixed tilt plans on an annual, quarterly, and monthly basis. The gains in solar radiation were 3.32%, 8.08%, and 9.56%, respectively, compared to horizontal PV installations [24]. Liu et al. explored the benefits of regularly adjusting tilt angles in China, finding that the seasonal adjustments significantly improved winter power generation [25]. However, previous research on PV adjustment strategies has primarily focused on maximizing energy generation. The current optimization studies of PV systems increasingly emphasize integration with building loads [26]. Kurdi et al. used a multi-criteria optimization approach to determine the optimal PV systems design for a commercial building in Los Angeles, considering self-consumption and self-sufficiency, as well as the payback period [26]. Liu et al. evaluated the effects of altitude angle, orientation, PV capacity ratio, and building height on achieving zero-energy buildings based on the principles of self-sufficiency and self-consumption [27]. These studies have introduced metrics, such as self-sufficiency and self-consumption, to assess the load matching performance of PV systems. Self-consumption refers to the percentage of PV power consumed on-site, and self-sufficiency indicates the proportion of the on-site consumption of PV power to the total energy consumption [28]. The economic cost also serves as a crucial criterion for PV systems [29]. As shown in Figure 2, time-of-use electricity pricing policies vary across different cities and regions. Differences in regional electricity tariffs need to be taken into account in the operational optimization of PV systems. However, existing research on periodic PV adjustment strategies have rarely been conducted for logistics parks. Besides, existing research lacks the comprehensive consideration of the matching between PV power generation and building loads and the corresponding economic benefits.

Therefore, this study aims to propose novel optimal operation strategies for PV systems adaptive for large-scale logistics parks across multiple climatic regions. A multi-criteria optimization method is developed to identify the optimized altitude and azimuth angles of PV systems. The remainder of this paper is structured as follows: Section 2 describes the outline of the optimal operation strategies proposed for rooftop PV systems in logistics parks. Section 3 presents the results of the load characteristics of various buildings in the logistics parks of different climatic regions, the optimal angle values of PV panels, and the benefits of the proposed operation strategies compared to the baseline strategy. Section 4 discusses the significance and limitations of this study. The concluding remarks are presented in Section 5.

2. Methodology

2.1. The Outline of Proposed Optimal Operation Strategies for PV Systems of Large-Scale Logistics Parks

Figure 3 shows the outline of the four operation strategies proposed for rooftop PV systems in large-scale logistics parks. There are three steps, including building modeling and simulation, multi-criteria optimization, and the analysis of results.

2.2. Building Modeling and Simulation

2.2.1. Study Area and Data Access

The prototype for the logistics parks is based on an actual case of 5500 m². The vector data are obtained from Open Street Maps and Baidu Maps, as shown in Figure 4 and

Table 1. Geometric information of various buildings in logistics park.

Building Type	Number of Floors	Floor Height/m	Window to Wall Ratio	Floor Area/m2	Building Aspect Ratio	PV Panel Installation Area/m2
Refrigerated storage	1	8.0	0.00	600	2.50	480
Sorting center	1	6.0	0.15	1000	1.60	800
Warehouse	1	6.0	0.15	600	2.50	480
Apartment	2	3.2	0.40	750	4.50	600
Office	2	3.5	0.40	400	4.50	320
Commercial	1	4.0	0.40	500	1.80	0
Canteen	2	4.0	0.40	500	1.80	400

. The thermal parameters of enclosure structures, personnel information, and air conditioning systems are configured according to the Chinese building energy conservation standards and ASHRAE 90.1 2019 [30]. To investigate the impact of climatic factors, this study selects five typical cities from different climatic regions in China as sites. The geographical information and climatic characteristics of the cities are illustrated in Figure 5 and

Table 2. Detailed climatic parameters of the selected five cities.

City	Climatic Region in China	Average Summer Temperature	Average Winter Temperature	Sunshine Duration
Harbin	Severe cold region	23.6 °C	−15.6 °C	2480 h
Lhasa	Cold region	15.7 °C	−2.0 °C	2955 h
Changsha	Hot summer and cold winter region	29.5 °C	4.6 °C	1484 h
Guangzhou	Hot summer and warm winter region	28.4 °C	13.0 °C	1659 h
Kunming	Mild region	20.1 °C	9.7 °C	2200 h

.

Based on the data sourced from Solargis [31], solar energy resources in Lhasa, Kunming, and Harbin are significantly higher than those in Guangzhou and Changsha, with Lhasa reaching the highest value of 2444.8 kWh/m². In terms of climate characteristics, Harbin and Lhasa are both located in cold climate regions, where building energy consumption is primarily driven by heating demands. Conversely, Guangzhou and Changsha are situated in hot climate regions, with cooling demands accounting for a larger proportion of energy consumption. Kunming exhibits relatively low overall building energy loads with its mild climate.

2.2.2. Energy Modeling for Logistics Parks and PV Systems

A simulation of the building loads is conducted on the Honeybee platform, which incorporates EnergyPlus, a comprehensive building energy consumption simulation program supported by the U.S. Department of Energy [32]. An hourly building load calculation is performed for the entire logistics park on an annual basis. The parameters and settings for simulation in EnergyPlus are detailed in

Table 3. Construction settings for building load simulation.

Parameter		Setting
Climate Data		EPW Files are from EnergyPlus website
Simulation Period		1 July–31 December, Hourly simulation
Construction		Harbin	Lhasa	Changsha	Guangzhou	Kunming
Wall	Refrigerated storage	R = 8.33 m2·K/W	R = 6.67 m2·K/W	R = 10.00 m2·K/W	R = 10.00 m2·K/W	R = 8.33 m2·K/W
	Warehouse /sorting center	R = 2.00 m2·K/W	R = 1.43 m2·K/W	R = 1.25 m2·K/W	R = 0.67 m2·K/W	R = 0.91 m2·K/W
	Apartment	R = 4.00 m2·K/W	R = 2.86 m2·K/W	R = 1.67 m2·K/W	R = 1.43 m2·K/W	R = 1.67 m2·K/W
	Office/commercial/canteen	R = 2.86 m2·K/W	R = 2.00 m2·K/W	R = 1.67 m2·K/W	R = 1.43 m2·K/W	R = 1.25 m2·K/W
Roof	Refrigerated storage	R = 8.33 m2·K/W	R = 6.67 m2·K/W	R = 10 m2·K/W	R = 10 m2·K/W	R = 8.33 m2·K/W
	Warehouse /sorting center	R = 2.50 m2·K/W	R = 1.67 m2·K/W	R = 1.43 m2·K/W	R = 1.12 m2·K/W	R = 1.43 m2·K/W
	Apartment	R = 6.7 m2·K/W	R = 4 m2·K/W	R = 2.5 m2·K/W	R = 2.5 m2·K/W	R = 2.5 m2·K/W
	Office/commercial/canteen	R = 4 m2·K/W	R = 2.5 m2·K/W	R = 2.5 m2·K/W	R = 2.5 m2·K/W	R = 2 m2·K/W
Floor	Refrigerated storage	R = 8.33 m2·K/W	R = 6.67 m2·K/W	R = 10 m2·K/W	R = 10 m2·K/W	R = 8.33 m2·K/W
	Warehouse /sorting center	R = 2.5 m2·K/W	R = 1.67 m2·K/W	R = 1.43 m2·K/W	R = 1.12 m2·K/W	R = 1.43 m2·K/W
	Apartment	R = 2.86 m2·K/W	R = 2 m2·K/W	R = 2.5 m2·K/W	R = 2 m2·K/W	R = 2.5 m2·K/W
	Office/commercial/canteen	R = 2 m2·K/W	R = 1 m2·K/W	R = 2.5 m2·K/W	R = 2.5 m2·K/W	R = 1.5 m2·K/W
Window	Warehouse /sorting center	U = 3.0 W/m2·K SHGC = 0.4	U = 4.0 W/m2·K SHGC = 0.4	U = 4.5 W/m2·K SHGC = 0.4	U = 5.0 W/m2·K SHGC = 0.35	U = 4.5 W/m2·K SHGC = 0.35
	Apartment	U = 2.0 W/m2·K SHGC = 0.4	U = 2.5 W/m2·K SHGC = 0.4	U = 2.5 W/m2·K SHGC = 0.4	U = 2.5 W/m2·K SHGC = 0.35	U = 3.2 W/m2·K SHGC = 0.35
	Office/commercial/canteen	U = 2.5 W/m2·K SHGC = 0.4	U = 2.7 W/m2·K SHGC = 0.4	U = 3.0 W/m2·K SHGC = 0.4	U = 4.0 W/m2·K SHGC = 0.35	U = 3.0 W/m2·K SHGC = 0.35

and

Table 4. Indoor heat disturbance and HVAC settings for building load simulation.

Building Type		Refrigerated Storage	Warehouse	Sorting Center	Apartment	Office	Commercial	Carteen
Indoor load	Density people/m2	0	0	0.05	0.028	0.05	0.086	0
	Active level W/person	0	0	120	95	120	120	0
	Lighting W/m2	3.55	3.55	3.55	9.36	7.97	11.3	6.46
	Infiltration m3/(s·m2)	0.00023	0.00023	0.00023	0.00057	0.00022	0.00023	0.00057
	Equipment W/m2	2.55	2.55	2.55	6.67	9.36	10.98	116.79
HVAC	Heating setpoint	–	0 °C	16 °C	18 °C	20 °C	18 °C	18 °C
	Cooling setpoint	−25 °C	–	28 °C	26 °C	26 °C	26 °C	26 °C

. The workflow of the proposed four optimized strategies for PV systems is shown in Figure 6.

The annual hourly PV power generation is calculated based on Equation (1). The solar radiation received by the PV panel surface is simulated using Ladybug, which is based on the Radiance engine. The total PV power generation for logistics parks is the sum of rooftop PV power generation from individual buildings. The installation areas of PV panels are calculated based on the building rooftop areas and the rooftop PV usable area factor, which is set to 0.8 for the logistics park. Additionally, monocrystalline silicon, known for its high generation efficiency, is chosen as the PV panel material, with a PV conversion coefficient set at 24%. The direct current to alternating current conversion efficiency is set at 85% [33].

$$P_h^G=H_A\times A\times {\eta }_i\times K$$

(1)

where $P_h^G$ is power generation at a given moment. H_A is the solar irradiance on the PV panel, in kW/m². A is installation areas of PV panels in m². η_i is the integrated system efficiency. K is the conversion efficiency.

2.3. Multi-Criteria Optimization

2.3.1. Multi-Criteria Optimization Process

The proposed strategies optimize the azimuth and altitude angles of the PV panels to adjust the power generation of the PV system at different time periods, enabling better alignment with the energy demand of logistics park buildings. Based on the simulated load data of logistics park buildings, the NSGA-II algorithm is employed to optimize the angles of the PV system at different time periods. The optimization objectives are self-sufficiency, self-consumption, power generation, and economic cost. The optimization variables are the azimuth and altitude angles of the PV panels. Based on a comprehensive literature review on similar research studies related to the energy system optimization of buildings, the iteration number is determined as 150, with a population size of 20 per generation [34]. A total of 3000 solutions are generated. The final generation of 20 solutions forms the optimized Pareto front. The settings for mutation probability and crossover rate of the optimization algorithm are 20% and 80%, respectively [1,35], with a random seed of 1 and an optimization variable step size of 1 [34]. The mathematical definitions of four optimization objectives and multi-criteria optimization are described as follows.

$$PG=\sum P_h^G$$

(2)

where $P_h^G$ is the total power generation of each building in the logistics park.

$$SC={\displaystyle \frac{\sum P_h^{GL}}{\sum P_h^G}}$$

(3)

where $P_h^{GL}$ is the amount of power generation consumed on-site. $P_h^G$ is the total power generation of each building in the logistics park.

$$SS={\displaystyle \frac{\sum P_h^{GL}}{\sum P_h^L}}$$

(4)

where $P_h^L$ are the total loads of the park at a specific moment.

$$EC={\displaystyle \frac{{\sum }_{i=1}^{n=D}max\left(0,P_h^l-P_h^G\right)\times C_h}{D}}$$

(5)

where D is day. $C_h$ is the electricity price at a specific moment. Economic cost refers to the cost of electricity for buildings in the logistics park, which is calculated based on the time-of-use electricity pricing policy and the actual electricity consumption of the buildings. Minimizing economic cost specifically refers to minimizing building electricity expenses.

Since time-of-use tariffs in China are defined and announced by the local government in each region on a quarterly or annual basis each year, we assume that the tariff structure remains unchanged regardless of whether or not the relevant PV system adjustment strategy is adopted in this study.

$$\mathit{max}{f}_{PG}={\displaystyle \sum _{i=1}^{n=10}}g\left(a{l}_i,a{z}_i\right),s.t.a{l}_i\in \left[\mathrm{0,90}\right],s.t.a{z}_i\in \left[\mathrm{0,360}\right]$$

(6)

$$\mathit{max}{f}_{SS}={\displaystyle \sum _{i=1}^{n=10}}g\left(a{l}_i,a{z}_i\right),s.t.a{l}_i\in \left[\mathrm{0,90}\right],s.t.a{z}_i\in \left[\mathrm{0,360}\right]$$

(7)

$$\mathit{max}{f}_{SC}={\displaystyle \sum _{i=1}^{n=10}}g\left(a{l}_i,a{z}_i\right),s.t.a{l}_i\in \left[\mathrm{0,90}\right],s.t.a{z}_i\in \left[\mathrm{0,360}\right]$$

(8)

$$\mathit{max}{f}_{EC}={\displaystyle \sum _{i=1}^{n=10}}g\left(a{l}_i,a{z}_i\right),s.t.a{l}_i\in \left[\mathrm{0,90}\right],s.t.a{z}_i\in \left[\mathrm{0,360}\right]$$

(9)

$$MaxF={\left[f_{PG},f_{SS},f_{SC},f_{EC}\right]}^T$$

(10)

where max f_PG, max f_SS, max f_SC, and min f_EC are the four optimization goals. The constants 1–10 correspond to the numbers of existing buildings in the logistics park, as shown in Figure 5. al_i is the altitude angles of the PV systems of building i. az_i is the azimuth angles of the PV systems. g(ali, azi) refers to the combination of altitude and azimuth angles of the PV systems. The altitude angles of the PV panels range from 0° to 90°, where 0° indicates that the panel is perpendicular to the roof, and 90° indicates that the panel is laid horizontally. The azimuth angles of the PV panels range from 0° to 360°, with orientations for east, south, west, and north defined as 90°, 180°, 270°, and 0°/360°, respectively.

2.3.2. Optimal Solution Selected from the Pareto Front Set

Since the multi-criteria optimization problem is characterized by the simultaneous optimization of multiple conflicting criteria, there is no absolute optimal solution that can maximize all criteria [26]. Instead, the result is a set of Pareto optimal solutions. Each solution in this set represents a trade-off between different criteria. Therefore, selecting the best solution from the Pareto optimal set requires an approach that balances these trade-offs based on the specific goals and priorities of the decision makers.

To systematically select the optimal solution from the Pareto optimal set, a normalization approach is adopted in this study. This method ensures that all criteria are considered on a comparable scale, allowing for unbiased comparison [36]. The normalization process involves converting the raw data into standardized forms, facilitating the aggregation of different criteria into a single composite score.

The normalization of criteria is performed using the following formulas. Equation (11) is used for criteria that need to be maximized, such as self-consumption, self-sufficiency, and energy generation. Equation (12) is used for criteria that need to be minimized, and it refers to economic cost in this study.

$$x^{\prime }={\displaystyle \frac{x-\mathit{min}\left(x\right)}{\mathit{max}\left(x\right)-\mathit{min}\left(x\right)}}$$

(11)

where x represents the original value. x’ represents the normalized value. min(x) is the minimum value in the solution set, and max(x) is the maximum value in the solution set.

$$y^{\prime }={\displaystyle \frac{\mathit{max}\left(y\right)-y}{\mathit{max}\left(y\right)-\mathit{min}\left(y\right)}}$$

(12)

where y represents the original value. y’ represents the normalized value. min(y) is the minimum value in the solution set, and max(y) is the maximum value in the solution set.

After normalization, different weights are assigned to each metric based on decision priorities. Subsequently, a composite score for each solution is calculated using the weighted sum of the normalized values of all criteria based on Equation (13). The solution with the highest composite score is selected as the optimal solution from the set of 20 optimized solutions.

$$S=w_1\cdot x_1^{\prime }+w_2\cdot x_2^{\prime }+w_3\cdot x_3^{\prime }+w_4\cdot y^{\prime }$$

(13)

where S represents the composite score. $x_1^{\prime }$, $x_2^{\prime }$, and $x_3^{\prime }$ are the normalized values for self-consumption, self-sufficiency, and power generation, respectively. y′ represents the normalized value for daily economic cost. w₁, w₂, w₃, and w₄ are the weight coefficients, which are all assigned a value of 0.25 [37]. The weight coefficients (w₁, w₂, w₃, and w₄) used in the multi-criteria optimization Equation (13) represent the weights given to each of the optimization objectives. In this study, the proposed optimal strategies aim to optimize the angles of the PV panels in logistics parks based on the following four objectives, i.e., self-consumption, self-sufficiency, economic cost, and power generation. According to existing research, when assigning weighting coefficients, we need to consider the priority of optimization to give weight to the indicators [37]. In the research phase, the proposed strategies aim to optimize four objectives simultaneously; each optimization objective is on equal footing, so their weighting factors are all assigned a value of 0.25. In practical engineering applications, the policymaker should assign weight coefficients to each optimization objective according to the optimization priority of the project, increasing the weight coefficients of the prioritized optimization objectives.

3. Results and Analysis

This section presents the load characteristics of various buildings in logistics parks, the optimal angle values of the PV panels across climatic regions, and the optimal benefits of the proposed four strategies compared to the baseline strategy.

3.1. Load Characteristics of Various Buildings in Logistics Parks

Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12 show the load curves of seven functional buildings and total power generation of PV systems in logistics parks across climatic regions. The total building loads in logistics parks show significant differences across climatic regions, as illustrated in Figure 7. In the winter seasons, the total loads of logistics parks in severe cold climates are the highest, fluctuating between 200 and 500 kW. This can be primarily attributed to the high heating demand under severe winter conditions. In the summer seasons, the total building loads of hot summer and cold winter climates are the highest, with peak loads reaching nearly 700 kW. This is mainly due to the large demand for air conditioning and cooling in hot and humid outdoor environments. In contrast, the cooling demand of severe cold climates is minimal, with total loads fluctuating around 200 to 300 kW. Regarding the mild climatic region, the moderate climate results in almost no significant cooling or heating demand throughout the year, with load fluctuations ranging from 100 to 300 kW.

When referring to the complex building load characteristics of seven functional buildings in logistics parks, refrigerated storages account for the highest load share among all functional types, as illustrated in Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12, especially in the summer seasons. The hourly loads of refrigerated storages in summer can range from 50 to 120 kW due to hot outdoor environment across different climatic regions. Compared to refrigerated storages, the loads of other buildings are significantly lower. This is caused by the higher cooling demand of refrigerated storages than other types of buildings. For instance, in cold climatic regions, the loads of sorting centers and warehouses only can fluctuate between 20 and 60 kW in the summer seasons. This implies that the load characteristics of refrigerated storages will play a crucial role in the operation optimization of PV systems in the logistics park.

When referring to the mismatch between building loads and PV power generation in logistics parks, the baseline strategy of PV systems, which focuses on maximizing power generation, fails to achieve optimal matching in logistics parks. Especially in the winter seasons, the peak generation period of PV systems is concentrated at midday, as shown in Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12. However, the loads of logistics parks are mostly concentrated on nighttime heating demand in the winter seasons. This results in a mismatch between building loads and PV generation during the winter seasons. In the summer seasons, the peak loads of the logistics park occur between noon and evening. Although the power generation peak of PV systems aligns with building loads at midday, it fails to match the load demand of buildings in the evening. Additionally, refrigerated storages and canteens are the primary contributors to building loads in logistics parks, significantly contributing to this mismatch. The results above highlight the necessity of optimizing the operating strategy of PV systems.

Above all, the load characteristics of buildings in logistics parks exhibit significant differences in terms of time schedule, seasonality, and climate. The baseline PV operation strategy fails to effectively match building load demand with power generation, especially in the winter seasons. Among seven types of buildings in the logistics park, refrigerated storages account for the highest load in most instances and exacerbate the mismatch between the supply side and demand side. It is necessary to propose effective PV operation adjustment strategies tailored to building load characteristics and climatic conditions.

3.2. Optimal Angle Values of PV Systems Across Climatic Regions

This section presents the Pareto-optimized solutions and the optimized angles of PV systems in the proposed four optimal operation strategies across climatic regions.

3.2.1. Optimization Process and Selection of Solutions

A Pareto-optimized solution refers to a set of solutions in a given multi-criteria optimization that cannot be further improved in any objective dimensions. In this study, the Pareto optimal set represents the solutions that perform optimally under four objectives for the proposed four strategies. Figure 13 illustrates the optimized angle solutions of PV systems for July under a monthly adjustment strategy across different climatic regions. The points represent optimal solutions for determining the azimuth and altitude angles of PV panels on each building in logistics parks. As shown in Figure 13, the Pareto optimal solutions are distributed at the forefront of the overall feasible solutions, forming the Pareto boundary, which can be clearly identified. This indicates that the optimization algorithm successfully drives the solutions towards the Pareto front, achieving a favorable balance and yielding positive optimization outcomes. Finally, to systematically select the optimal solutions from the Pareto set, a normalization approach is adopted in this study, as elaborated in Section 2.3.2.

Table 5. Optimal solutions for PV panel angles for July under monthly adjustment strategy across climatic regions.

Climatic Region	Angle	Refrigerated Storage		Warehouse				Sorting Center	Office	Apartment	Canteen
Severe cold region	Azimuth angle/°	295	349	2	253	308	267	249	258	280	323
	Altitude angle/°	7	22	7	22	13	5	71	87	2	27
Cold region	Azimuth angle, °	28	84	270	66	279	269	60	286	353	296
	Altitude angle, °	14	39	28	12	43	15	20	9	25	23
Hot summer and cold winter region	Azimuth angle, °	4	72	277	303	308	61	56	341	354	12
	Altitude angle, °	71	85	89	78	79	87	90	85	83	80
Hot summer and warm winter region	Azimuth angle, °	36	33	299	122	137	354	30	277	47	19
	Altitude angle, °	87	87	90	90	90	88	87	90	85	88
Mild region	Azimuth angle, °	95	302	317	315	9	241	188	358	62	87
	Altitude angle, °	1	4	3	36	4	1	4	17	33	5

shows the optimal solutions for PV panel angles under a monthly adjustment strategy for July across climatic regions.

3.2.2. Optimal Angle Values of PV Panels for the Proposed Adjustment Strategies

Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 present the optimized values of the altitude and azimuth angles for the PV panels in logistics parks across climatic regions under five adjustment strategies. The baseline strategy is the traditional strategy only considering maximum power generation. As shown in Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18, the outer ring values represent the PV panel azimuth angles, i.e., 0°/360° for due north, 90° for due east, 180° for due south, and 270° for due west. The distances from the center represent the altitude angles of the PV panels, with 0° indicating a vertical installation to the ground and 90° indicating a horizontal installation facing the sky. Each figure contains ten data points, representing the altitude and azimuth angle values of the rooftop PV panels for ten buildings in logistics parks.

(i) 

The optimal angle values when adopting different adjustment strategies

As shown in Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18, the altitude and azimuth angles of the PV systems under the baseline strategy across climatic regions are relatively similar. In all regions, the results of the baseline strategy suggest high altitude angles between 70° and 90° and azimuth angles close to 180°. This can be attributed to the south-facing PV panels and higher altitude angles receiving more direct sunlight, providing higher generation potential compared to other angles [38]. The proposed annual adjustment strategy, although similar to the baseline strategy in being a fixed annual approach, considers multiple objectives. The results show that the optimized angles of PV panels under annual adjustment strategy vary significantly compared to the baseline strategy across climatic regions, as shown in Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18. The altitude angles under the annual strategy across climatic regions are significantly reduced compared to the baseline strategy. The azimuth angles shift from being concentrated in the south to being more distributed in the east and the west. These are likely due to the fact that the optimization preferentially selected azimuth angles closer to the east–west direction and lower altitude angles to reduce the PV power generation, while the energy demand of the buildings is met. Regarding the semi-annual adjustment strategy, the optimal angles of PV panels show minimal differences compared to the annual adjustment strategy. This arises from the finite variation in solar radiation between the annual and semi-annual periods, especially in areas like Changsha and Guangzhou, where solar radiation intensity is relatively low throughout the year.

As for the proposed seasonal adjustment strategy, it adjusts the angles of the PV panels according to seasonal variations and climatic conditions. The altitude angles in spring and summer are significantly higher than in autumn and winter across five climatic regions. For instance, in Changsha, altitude angles range between 80° and 90° during spring and summer, while in autumn and winter, they vary between 20° and 70°. This owes to the PV panels with higher altitude angles receiving more direct sunlight throughout the day compared to those installed vertically, better matching the high cooling load demands in the spring and summer seasons. Regarding azimuth angles, the values under the seasonal strategy across climatic regions are generally oriented towards the northeast and northwest in spring and summer and towards the southeast and southwest in autumn and winter. For instance, in Harbin, azimuth angles are concentrated around 270° and 90° during spring and summer, shifting towards 180° in autumn and winter. One of the reasons is the higher solar radiation intensity in spring and summer, compared to autumn and winter.

As for the proposed monthly adjustment strategy, it optimizes the angles of PV panels based on the monthly building load characteristics of the logistics park and climate features. Compared to other adjustment strategies, monthly adjustment is a further refinement of seasonal adjustment. The results show that the optimized PV panel angles for each corresponding month of the seasons in the monthly adjustment are similar to those in the seasonal adjustment. This may be attributed to the restricted climatic variation between months within the same season. In light of the above, it indicates that the monthly strategy results in the confined variations of PV panel angles compared to seasonal strategy but requires higher adjustment frequency and bigger operational costs.

Above all, the optimal angle values of the proposed four adjustment strategies are affected by the adjustment frequency. These findings offer a straightforward operation recommendation for PV systems in large-scale logistics parks. Explicitly, the proposed four strategies in this study enable the more precise adjustment of PV panel angles compared to the baseline strategy based on the climatic characteristics and building loads, particularly with monthly adjustments. However, in different regions, the difference in the optimal angle values of PV panels between the monthly strategy and seasonal strategy is not particularly significant. This indicates that, in practical engineering projects, while pursuing the high-precision adjustments of PV systems may have theoretical value, increasing the frequency of adjustments may not necessarily yield the expected substantial returns. Therefore, policymakers need to weigh the investment costs against the actual benefits to choose more reasonable optimization strategies.

(ii) 

The optimal angle values across different climatic regions

The angle optimization results vary significantly across climatic regions due to differences in climatic characteristics. As for severe cold regions, cold regions, and mild regions, the range of altitude angles is generally lower than those of hot summer regions, with more azimuth angles directed towards the east and west, as shown in Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18. For instance, in these regions, the altitude angle values for PV panels are generally smaller during spring and summer, mostly ranging from 20° to 60°. This may be due to the average temperature of these regions in the spring and summer seasons being lower than hot summer regions, resulting in a mild climate. Building cooling demand in these regions is lower, and the PV generation of lower altitude angles is sufficient to meet its self-sufficiency.

As for hot summer regions, the altitude angles are generally higher, and the azimuth angles are more inclined towards the south compared to other regions, as shown in Figure 16 and Figure 17. This can be attributed to the cooling load of the refrigerated storage being higher in hot climatic conditions, leading the PV systems prioritizing a south orientation and higher altitude angles to enhance power generation. Besides, the solar radiation intensity in hot summer regions is significantly lower compared to cold regions and mild regions, resulting in more excessive power generation. This is also one of the reasons why south azimuth angles and higher altitude angles are prioritized in hot summer regions. Specifically, in Changsha and Guangzhou, the altitude angles range from 70° to 90° during the spring and summer, while the altitude angle values range from 0° to 40° in Lhasa.

Above all, the optimal angle values of the proposed four adjustment strategies are highly affected by the climatic characteristics. In cold regions with abundant solar resources, the optimal altitude angle values of the proposed four strategies in large-scale logistics parks are lower than those in hot summer regions. The optimal azimuth angle values in cold regions are more in favor of the east or west directions, while hot regions are more inclined to the south directions. Therefore, in practical engineering applications, policymakers should determine the angles of PV systems in large-scale logistics parks based on local climatic conditions and solar radiation intensity. The research data and results presented in this study provide essential data support and valuable references for engineering projects.

3.3. Optimal Benefits of the Proposed Four Strategies Compared to the Baseline Strategy

Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23 visualize the objective values of each operation strategy to directly quantify the benefits of the multi-criteria optimization strategies compared with the baseline strategy. The left vertical axis represents the specific values of each objective, and the right vertical axis represents the increase/decrease ratios of objective values of the four proposed operation strategies relative to the baseline strategy. Overall, four adjustment strategies across five climatic regions demonstrate significant improvements in reducing the economic cost and enhance the matching between building loads and PV power generation.

(i) 

The optimal benefits of the four adjustment strategies

The monthly adjustment strategy of the PV systems most significantly reduces economic cost and improves the matching between supply and demand in logistics parks, followed by seasonal, semi-annual, and annual adjustment strategies. For instance, compared to the baseline strategy, the monthly adjustment strategy achieves economic cost reductions of 9.69% to 17.02%, while annual strategies can reduce economic cost by 5.8% to 10.5%, semi-annual strategies from 6.9% to 11.8%, and seasonal strategies from 7.6% to 15.99%. This indicates that the interval of PV panel adjustments is closely related to the effectiveness of the PV system. According to the results of this study, shorter adjustment intervals allow for better adaptation to climatic and weather variations, yielding greater benefits. However, the differences in performance between monthly adjustments and seasonal adjustments are limited, which indicates that high adjustment frequencies do not necessarily yield substantial benefits for PV systems.

(ii) 

The optimal benefits across different climatic regions

The proposed four adjustment strategies yield better benefits in Harbin, Lhasa, and Kunming, while the improvement in Guangzhou and Changsha is not significant. The average annual solar intensity in Harbin, Lhasa, and Kunming is higher than that in other regions, providing a foundation for better PV power regulation. PV power generation is proportional to the solar radiation potential [39]. The PV adjustment strategies proposed in this paper aim to adjust the power generation of the PV system according to the building loads. When solar resources are abundant, the optimization strategies have greater room for adjustment to better match the building load demand, allowing for more optimization scope to respond to the criteria. Specifically, the monthly adjustment strategy enhances self-consumption by 82.44% to 359.04% in Lhasa compared to the baseline strategy, while the monthly strategy achieves the enhancement of self-consumption from 8.72% to 101.78% in Changsha. The seasonal strategy can reduce economic costs by 3.35% to 9.26% in Lhasa compared to the baseline strategy, while the seasonal strategy achieves a reduction in economic cost of about 2%. The above data indicate that the benefits of the proposed adjustment strategies show significant differences across different climatic regions. This may be related to the distinctions between the solar energy potential, time-of-use electricity pricing policies, and building load characteristics of each region. The average annual solar intensity in Harbin, Lhasa, and Kunming is higher than that in other regions, providing a foundation for better PV power regulation.

(iii) 

The optimal benefits on the four optimization objectives

The proposed four adjustment strategies show the greatest improvement in self-consumption, followed by economic cost, self-sufficiency, and power generation. The monthly adjustment strategy can enhance self-consumption over 80% compared to the baseline strategy in regions such as Lhasa and Kunming. However, the proposed optimized strategies can improve self-sufficiency by only 2% to 7%. The proposed four strategies even lead to a reduction in power generation compared to the baseline strategy; although, it is only reduced by 2% to 5%. This may be due to the baseline strategy solely focusing on maximizing power generation, but the proposed four strategies need to balance multiple objectives, including power generation, economic cost, self-consumption, and self-sufficiency. The optimization algorithm aims to increase the self-consumption rate of PV systems in the logistics park to promote the on-site utilization of generated power, which involves optimizing the PV panel angles to minimize excess power generation after matching the building load requirements. Furthermore, there are differences in the benefits of various objectives across different months. The proposed strategies show the most significant improvement in economic cost and self-sufficiency between May and September, primarily due to abundant solar resources during the summer. However, the enhancement in self-consumption during the summer seasons is lower. This can be attributed to the fact that adjusting power generation to meet energy demand may simultaneously increase excess power generation, reducing self-consumption.

Above all, among the proposed four strategies, the monthly adjustment strategy performs the best, while the improvement is not significantly different from the seasonal strategy. These findings align with the results of the optimal angle values discussed in Section 3.2.2. In practical projects, policymakers should balance the costs and benefits associated with adjustment frequency. Regarding the optimization objectives, the proposed strategies demonstrate superior performance in reducing economic costs and improving self-consumption, particularly in cold regions with high solar radiation.

4. Discussions

This study conducts a multi-criteria optimization of PV systems in logistics parks and proposes four optimal operation strategies correspondingly. The multi-criteria, including power generation, self-consumption, self-sufficiency, and economic cost, are simultaneously considered and optimized to determine the optimal altitude and azimuth angles. Compared to the baseline strategy that focuses solely on maximizing power generation, the proposed optimal strategies emphasize a more balanced improvement of energy and economic efficiency.

To test the energy/economic performance and demonstrate the climate adaptability of the proposed strategies, a representative logistics park of 5500 m² located in China is adopted to validate the strategies. It encompasses a diverse range of building types, including refrigerated storage, warehouse, sorting center, apartment, office, commercial, canteen, etc. By adopting the proposed PV system adjustment strategy, it is possible to effectively achieve the increase in self-consumption and the reduction in the cost of electricity consumption. Besides, the results obtained in this study can provide practical guidance for determining the optimal angles of PV panels by year, season, or month for real-world logistics parks. For example, in severe cold regions with abundant solar energy, like Harbin, we recommend adjusting the PV panels to the east and west in the spring and summer and to the south in the autumn and winter, while preferring an altitude angle of 0° to 40°. However, in hot regions with barren solar energy, like Guangzhou, we prefer to use high altitude angles of 70° to 90°. In practical applications, policymakers can combine the relevant data in this study to make decisions.

Unlike other approaches that rely on complex or expensive technologies, these methods are designed to be low-cost and user-friendly, making them highly feasible for broader adoption. By validating these strategies across five distinct climatic regions in China, this research not only accounts for the impact of climatic conditions but also underscores the adaptability of these optimal strategies to diverse environmental conditions. The findings highlight that, in regions with abundant solar resources, such as Lhasa and Harbin, the proposed strategies significantly reduce economic costs and enhance matches between PV generation and building loads.

Among the four adjustment strategies, the monthly adjustment strategy demonstrates outstanding optimization benefits. However, the marginal differences between the monthly and seasonal strategies suggest that increasing the adjustment frequency does not always lead to substantial returns for PV systems in large-scale logistics parks. For example, in Harbin, the monthly adjustment strategy can increase power generation, self-consumption, and self-sufficiency by up to 17.0%, 7.08%, and 76%, respectively, while reducing electricity costs by up to 17% compared to the baseline strategy. In contrast, with the seasonal adjustment strategy, self-consumption, self-sufficiency, and power generation can be improved by up to 15.9%, 6.63%, and 50%, respectively, while electricity costs reduced by up to 16.7%. For the semi-annual adjustments strategy and annual fixed strategy, their optimal performance declined significantly relative to the seasonal and monthly strategies, e.g., self-consumption can only be improved by up to 34% and 15%. According to the data, the performance difference between the monthly adjustment strategy and the seasonal adjustment strategy across various indicators is relatively small, often within 2%. This may be due to the fact that the climatic characteristics as well as the intensity of solar energy vary less from month to month within the same season. Based on the above analysis, the inter-seasonal adjustments are more advantageous. However, the seasonal adjustment strategy requires only a quarter of the adjustment frequency of the monthly strategy, significantly reducing the operational and maintenance costs of the potential labor cost and programming cost. This finding has significant implications for policymakers in practical projects, emphasizing the need to weigh adjustment costs against potential benefits. By bridging the gap between theoretical optimization and practical implementation, this study offers a pragmatic solution for enhancing PV system performance across different climatic conditions.

The implementation of the proposed PV system optimization strategies in real-world logistics parks faces several challenges, particularly regarding the technical feasibility of different adjustment frequencies for PV panels in practice. Regarding the specific adjustment of PV panels, manual adjustment is a flexible and low-cost approach [40]. However, the associated operational costs of manual adjustment would include labor expenses, which can vary significantly depending on local economic conditions and the wage rates in different logistics parks. In practical engineering applications, the decision to adopt manual adjustments must be made considering the specific labor costs and economic environment. In terms of automation possibilities, the automated control methods based on building management systems (BMSs) are widely used currently [41]. The control program can record the monthly PV panel angles determined by the optimization algorithm and control the angle of the PV system at regular intervals. If the BMS of the logistics park includes a compatible program interface, this method can be considered. While it does not incur labor costs, automated adjustments come with their own set of challenges, including potential concerns over the security and privacy of the data of the company.

The limitations of this study are also summarized as follows, which are to be addressed in the subsequent research of the authors. (i) The adjustment frequency concerned is by month, season, and year, without extending to daily, hourly, or real-time online adjustments, which will be further investigated for logistics parks. (ii) Energy storage systems and other renewable sources, like wind or geothermal energy, are not considered in this study. Future research could focus on exploring the integration of multiple renewable resources with storage systems to better support carbon neutrality for large-scale logistics parks. (iii) The optimization strategies of PV systems proposed in this paper are to be applied in real projects and enhanced through practical application. Future research could focus on the online real-time performance evaluation and improvement of the proposed strategies in actual large-scale logistics parks.

5. Conclusions

The instability of PV power generation and the complexity of various building loads in large-scale logistics parks create great challenges for matching the supply and demand side. This study, therefore, presents multi-criteria optimal operation strategies for PV systems in large-scale logistics parks by optimizing the altitude and azimuth angles of PV panels. Compared with the conventional strategy only considering power generation, the performance of the proposed four strategies is validated under different climatic conditions. Based on the test results, the main conclusions can be drawn as follows.

• The proposed four strategies can achieve better performance than the baseline strategy that fixes the PV panel angles on a yearly basis. The monthly adjustment strategy has the best performance, followed by the seasonal strategy, semi-annual strategy, and annual strategy. The performance improvements between the monthly adjustments and seasonal adjustments are finite. In practical applications, seasonal adjustments can be prioritized to minimize the operational and maintenance costs. The decision makers need to weigh the investment costs against the actual benefits to choose more reasonable optimization strategies.
• The proposed four adjustment strategies show the greatest improvement in self-consumption, followed by economic cost, self-sufficiency, and power generation. Applying the proposed four optimized strategies of PV systems in logistics parks, the increase in self-consumption reaches 82.44% to 359.04%, and the reduction in economic costs can run up to 17.02%, compared to the baseline strategy. However, the increase in self-sufficiency and power generation from the proposed optimized strategies is not significant, with growth rates of only 2% to 7%.
• Climatic factors significantly affect the benefits of adjustment strategies. Cold regions with higher solar potential experience greater optimization benefits. In hot regions with lower solar radiation intensity, such as Changsha and Guangzhou, the benefit gaps among the proposed four strategies are relatively small. This means that operators of logistics parks in regions like these can choose the annual strategy or semi-annual strategy to reduce the frequency of adjustment adaptively, in order to balance the costs of regulation and control.
• Climatic factors significantly affect the optimized angle values of PV panels. In hot regions with lower solar radiation intensity, the optimized azimuth angles of PV panels tend to south orientations and the altitude angles tend to higher angles. Specifically, in regions like Guangzhou and Changsha, the optimized PV panels generally face south with an altitude angle between 70° and 90°, while the panels are often oriented east or west with an altitude angle between 20° and 60° in Lhasa.