Daylighting Performance and Thermal Comfort Performance Analysis of West-Facing External Shading for School Office Buildings in Cold and Severe Cold Regions of China

Abstract

Global energy resources are becoming increasingly scarce, and environmental problems are becoming more serious. The construction industry significantly contributes to energy consumption, and building energy efficiency has become a global concern. A critical aspect of building energy efficiency is exterior shading, which controls sunlight exposure and heat input to the interior. By effectively reducing indoor temperature and light intensity, exterior shading provides a more comfortable learning and working environment. In particular, west-facing exterior shading is essential for building shading and heat protection. This study aims to analyze school office buildings’ light and thermal comfort performance in various climatic zones. These buildings are equipped with west-facing external shading. Numerical analyses were performed using Ladybug Tools 1.6.0 software to evaluate the light and thermal comfort performance of the building. The primary objective of this study is to enhance the light performance and thermal comfort within buildings facing west. The main focus of this research is to examine the effectiveness of four different shading devices in improving light performance and thermal comfort in school office buildings located in severe cold (SC) and cold (C) regions. By studying these specific buildings, valuable insights and recommendations can be provided for selecting suitable shading devices for typical urban buildings in similar regions. The study results demonstrate that in typical cities in SC and C regions, light and thermal comfort are significantly improved with appropriate shading devices by a factor of about 1.5 to 2.5 compared to the no-shading condition (NSC). Beijing shows the most significant improvement among the cities studied, with energy efficiency and comfort improved to 2.6 times that of NSC. At the same time, Urumqi has a relatively lower effect, with an improvement of 1.59 times that of NSC. This study provides an essential reference for selecting suitable west-facing shading devices in typical cities in SC and C regions. It is expected that this will contribute to the construction industry’s efforts to achieve more significant results in energy conservation, emission reduction, and green buildings, ultimately helping to address the energy crisis and environmental pollution problems.

1. Introduction

Buildings account for about a third of global energy consumption and a quarter of carbon emissions [1]. In 2021, the total energy consumption of buildings accounted for about a third of global energy consumption and a quarter of carbon emissions. In 2021, the total energy consumption of China’s building operation commodities was 1.11 billion tce, accounting for about 21% of the total energy consumption; the total carbon dioxide emission related to building operation was 2.2 billion tons, accounting for 22% of the total emission [2]. Of these, educational buildings account for about 15% of the energy consumption of non-residential buildings [3]. Lighting, heating, and cooling are the main components of energy consumption in the building sector [4], with building heating and cooling energy consumption accounting for about 60% of total building energy consumption [5]. As of 2022, there are 3013 colleges and universities in China [6]. A large number of new college buildings have been put into use. However, there is a lack of necessary research on light and thermal comfort in college buildings, resulting in many with high energy consumption and low indoor comfort levels [2]. In particular, architectural shading has failed to receive reasonable attention. Therefore, there is considerable potential to improve indoor lighting and thermal conditions in educational buildings significantly.

Windows are an essential part of the energy-saving design of the building envelope [7]. Solar radiation enters the interior through the windows and provides natural light, while heat energy also affects the building’s energy consumption [8]. Architectural shading reduces solar radiation into the interior, improves indoor thermal comfort in summer, and effectively reduces air conditioning and cooling energy consumption [9,10,11,12]. According to the report “Energy Saving and CO${}_2$ Emission Reduction of Shading Systems in EU 25 Countries”, building shading saves about 25% of building air conditioning energy consumption and 10% of heating energy [13]. However, if the shading devices are not correctly arranged. In that case, they will prevent the building from obtaining proper heat in winter and increase the demand for artificial light, thus increasing energy consumption [14]. Choosing a suitable shading device for a building is an essential task for the architect.

The primary forms of architectural shading are external and internal shading. Domestic and foreign scholars have extensively researched the energy-saving potential of building shading [9,15,16,17,18]. Direct sunlight enters the room through the glass when using an internal sunshade for the shading design. This portion of radiant heat raises the temperature of the inner shade build and transfers heat to the interior. Therefore, most solar heat will enter the room and will not significantly reduce the air conditioning cooling energy consumption [11]. External shading is a more effective way of shading a building than internal shading.

The current research on exterior building shading mainly covers two forms: movable shading and fixed shading [19]. Among the studies on movable shading, vertical [20] and horizontal [21] louver shading have been studied more extensively. These studies focus on analyzing the effects of changes in various parameters of louvered shading devices on the energy efficiency rate and comfort of the building and make recommendations for optimizing the control strategy of the shading devices. Standard parameters studied include the width of the louvers [22], the optimal inclination of the louvers [23], and the reflectance and transmittance of the louver material [24]. In terms of evaluation indexes, the energy consumption index, and energy saving rate; in terms of the thermal comfort index: PMV [25,26], temperature, and cumulative solar radiation [25,27]; and in terms of the light comfort indexes: daylight glare index (DGI) [28,29], daylight glare probability (DGP) [30,31], useful daylight illuminance (UDI) [32,33], and daylight factor (DF) [34,35,36] are often used in the study. In addition, several studies propose optimal control schemes for louver shading in different climate zones, orientations, and periods [31,37,38]. Although the ideal shade is adjusted according to the user’s needs of the movable shade device, the control of the movable shade and the user’s behavior are closely related, and due to the high capital cost and short service life, its application has not yet been widely accepted [37].

Fixed shading has several advantages over movable shading, so its potential for application in building energy efficiency should be considered. First, fixed shading is relatively inexpensive and easy to install and maintain. Secondly, fixed shading has a longer lifespan and can maintain its shading effect over a long period [11]. As a result, most buildings still use fixed shading designs. The exploration and evaluation of fixed external shading is mainly focused on studying horizontal louvered shading (HLS) [14,17,39,40,41]. Currently, the exploration and evaluation of fixed external shading is mainly focused on studying horizontal louvered shading (HLS). Egg crate shading (ES) has been slightly covered [42,43], while relatively little research has been conducted related to baffle shading (BS) and vertical louvered shading (VLS) [39]. The main objective of the research is to investigate the effect of shading devices on daylight and energy to improve performance in terms of indoor illuminance, thermal comfort, and building energy consumption [14,43].

Although scholars have conducted many studies at home and abroad on exterior building shading systems, there are some problems in most of the previous simulation studies.

• Previous research on architectural shading devices has mainly focused on a particular type of device. In contrast, China’s SC and C regions are characterized by significant differences in geography and climatic conditions, so it is necessary to select appropriate shading devices according to different geographic and climatic conditions.
• Previous studies have focused on the south façade of the building, while the west façade is also the focus of building shading and heat protection.
• Most previous studies have focused on the active external shading of buildings, and relatively few studies have been conducted on fixed shading of buildings.

Research objectives:

• Multi-objective optimization design to improve the light and thermal comfort performance of the interior of a west-facing building.
• Evaluating the parameters of exterior building shading devices under different goal orientations, analyzing the factors affecting the external shading effect of different urban buildings, and providing a basis for the design of each parameter of shading devices. This study helps architects choose the proper exterior shading devices.
• Analyzing optimal solutions with different goal orientations to evaluate the light and thermal comfort performance of four shading devices in different cities.

2. Literature Review

Fixed shading means that the shading device is fixed to the building façade and cannot be moved or adjusted. This type of shading is widely used in the field of building energy efficiency. This review describes several common types of exterior fixed shading in building energy efficiency, including horizontal louvers, vertical louvers, egg crate shading, and baffles.

2.1. Horizontal Louver Shading

Horizontal louver shading is a common type of fixed shading. Studies have shown that parameters such as solar altitude angle, slat angle of horizontal louvers, shape, width, number, color, and depth all impact shading effectiveness and energy consumption [14,39,40]. By studying south-facing residential buildings, Gon Kim and Hong Soo Lim et al. found that energy consumption is minimized at a solar altitude angle of 76°, at a slat angle of 0°, and at a slat angle of 60°, energy consumption is maximized [17]. In addition, the results of Nariman Rafati and Morteza Hazbei et al. showed that changes in louver depth had the most significant impact on daylight absorption and energy consumption [41]. When heat is needed to enter the room, the top surface of the shutters should be light colored, thus bringing some of the sun’s energy into the room [14]. Therefore, these parameters must be considered comprehensively to achieve the best shading effect and energy consumption control when designing horizontal louver shading.

2.2. Vertical Louver Shading

Vertical louver shading is another common type of fixed shading. Adjusting the angle of the slats of vertical louvers can block sunlight at different angles, and the most effective shading directions are southeast and southwest [39]. Research has shown that the application of vertical shading devices can significantly reduce the energy demand of buildings in Tallinn, Estonia. Energy consumption was reduced by 25% by adjusting the slat angle [9].

2.3. Egg Crate Shading

Egg crate shading is a shading device that combines vertical and horizontal shading methods. Studies have shown that egg crate shading is more effective in reducing indoor air temperatures and discomfort time [43]. In the summer months, egg crate shading can reduce solar radiation entering the house by 45–50%. In hot and humid climates like Malaysia, the use of egg crate shading devices can save more cooling energy compared to vertical and horizontal shading [42]. However, egg crate shading provides an enormous amount of daylight, but the quality of the daylight is not as good as that of vertical shading [44]. Therefore, when choosing an egg crate shading device, one needs to consider the trade-off between the amount of daylight and the required quality of daylight.

2.4. Baffle Shading

Baffle shading is a popular choice for fixed shading devices in modern buildings, as it helps improve daylight uniformity and lighting quality [45]. Research has shown that the use of baffle shading devices can increase the illumination at the back of a room during hot and dry summer months, such as in Madrid [46]. Lightweight baffle shading effectively blocks sunlight, reducing lighting energy consumption by around 5% [47]. Berardi and Anaraki’s study highlighted that factors like window shape and façade orientation also affect the effectiveness of baffle shading [48]. Therefore, when designing and selecting baffle shading devices, these factors should be considered to achieve the best shading effect and lighting quality.

In conclusion, fixed shading methods are crucial for improving building energy efficiency. Each method has its strengths and weaknesses, and it is essential to consider local geographical and climatic conditions when selecting and designing shading devices to optimize building design and enhance comfort. Additionally, conducting in-depth studies on the parameters of different shading methods and their impact on shading effectiveness and energy consumption can provide more precise guidance for energy-saving building designs.

3. Methodology

3.1. Research Methodology and Workflow

The accuracy of the LBT energy consumption simulation study was first verified using measured data from field tests. Based on this, an analytical model of the baseline building was developed. Typical cities representing the SC and C climate zones were selected. Shading devices were parameterized using Grasshopper (GH) 1.0.0007 software, with eleven design parameters chosen as input variables to create four different types of shading devices: horizontal louvered shading (HLS), vertical louvered shading (VLS), egg crate shading (ES), and baffle shading (BS). Three optimization objectives were selected as outputs. Subsequently, multi-objective NSGA-II optimization was performed using Wallacei X software 2.70 to obtain the optimal solution set and design parameters for exterior building shading devices under different goal orientations. The factors influencing the effectiveness of external shading in different cities were analyzed, providing a basis for the design of each parameter of the shading device (refer to Figure 1).

3.2. Ladybug Tools Simulation Verification

In this study, LBT energy simulation software was used to analyze the energy-saving daylighting characteristics of building external shading. LBT is an energy simulation plug-in for GH that works in concert with GH [49] and a variety of operators to customize various parts of a building highly. The LBT Honeybee [45] module includes the EnergyPlus engine for energy simulation and the Radiance and Daysim engines for daylight simulation. PMV, solar irradiance, daylighting, and glare of the simulated building can be analyzed simultaneously. EnergyPlus, Radiance, and Daysim are building energy simulation tools that are already widely used. Numerous scholars at home and abroad have verified the accuracy of the software [50,51].

In order to assess the accuracy of the LBT energy simulation software for the simulation study of energy consumption in teaching office buildings, a set of on-site comparative real-world measurements was conducted from 7 July to 8 July 2023, in the teaching office of a university in Urumqi.

An experimental validation was conducted to verify the parameters related to the light and thermal environments in the simulation results. The thermal environment, which is influenced by solar radiation and indoor temperature, was verified using the indoor dry bulb temperature. For the light environment, multiple parameters, such as glare value and illuminance, play a role. However, since the glare value cannot be directly measured through experiments, the illuminance level was used as a measure to assess the light environment. To collect data for validation, time-by-time measurements of indoor and outdoor temperatures, as well as illuminance levels, were taken at specific moments in time. These measurements were collected at two test-building work surface measurement points. By comparing the simulated values with the measured data, the accuracy of the parameters related to the light and thermal environments in the simulation results could be evaluated and validated. This validation process helps ensure the reliability of the simulation and the effectiveness of the selected shading device parameters.

3.2.1. Introduction to Field Experiments

The experimental subjects are two neighboring offices in a university building in Urumqi, and the building is oriented east–west. One is a reference room without louvers, and the other is a study room with louvers for shading as shown in Figure 2. The building was completed in 2021 and consists of five floors, with four above ground and one below. The study room and the reference room are located on the third floor of the building. The two experimental rooms are 4.9 m long, with a balcony peeking out 1.8 m, 3.8 m wide, and 4.2 m high as shown in Figure 3. The room has a window on the east façade, with a window-to-wall area ratio of 0.48, a solar heat gain coefficient (SHGC) of the window of 0.5, and a heat transfer coefficient of the envelope K-value of 0.5, which is in line with China’s “General Specification on Energy Saving and Renewable Energy Utilization for Buildings”. The existing shading form is vertical shading. The field experiment consisted of installing exterior louvered shading devices on the exterior windows of the study room for comparison with the reference room. The exact specifications of the test building and blinds are shown in

Table 1. Thermal parameters of envelope structure.

Parameters	Description
Heat transfer coefficient of envelope K	exterior wall = 0.35 W/(m${}^2$·K)
	interior wall = 2.93 W/(m${}^2$·K)
	roof = 0.25 W/(m${}^2$·K)
	ground = 2.93 W/(m${}^2$·K)
west window–wall ratio (WWR)	0.48
glass	Solar heat gain coefficient (SHGC) = 0.5
	K = 2.35 W/(m${}^2$·K)

and

Table 2. Louver specification.

External Louver Shading Device	Description
	Louver width = 0.025 m
	Louver count = 150
	Louver Angle = 45°
	Louver thickness = 0.002 m

.

3.2.2. Comparative Field Tests

During the test, data were measured and recorded by one experimenter in each room. During the test, data were measured and recorded by one experimenter in each room. The specifications of the experimental equipment are shown in

Table 3. Experimental equipment specifications.

Experimental Apparatus	Type Specification	Measurement Range	Error Range	Picture
Illuminometer ST-80C	Illuminometer ST-81C	0.1 to 199,900 lx	4%
temperature and humidity sensor	COS-03	temperature 20 to 60	temperature 0.2
		humidity 0 to 95	humidity 2 RH
small trolley	/	/	/
tape measure	/	0 to 50 m	0.5 mm

. The measurement of air temperature and outdoor ambient temperature in shaded and unshaded rooms was taken using a self-calculating digital thermometer (Kenda Renke Temperature and Humidity Sensor COS-03), with data collected every 10 min (the minimum self-calculating interval for COS-03 is 10 min). The time of the illuminance experiment was 8 July 2023, at 11:00 a.m. The measurement points are shown in Figure 4. During the illumination experiment, in order to avoid the interference of the experimenter with the ambient illumination, the light-sensitive element of the illuminometer (Illuminometer ST-80C, Beijing, China) was placed on a 0.75 m trolley, and the experimenter stood on the side far away from the window to measure and record the experimental data. The accuracy of the LBT software was verified by comparing the changes in room temperature under both simulated and measured conditions and the illuminance values at the same points at the same time of the experiment.

Outdoor meteorological parameters replace the typical meteorological annual temperature and humidity data during the test period with the measured outdoor temperature and humidity data to form new meteorological data as the meteorological data input parameters during the simulation period for the test building.

3.2.3. Comparison of Measured and Simulated Data

By comparing and analyzing the measured data with the simulated data, the measured data and the LBT simulated data coincide, and the changing trend is similar in the case of the same outdoor meteorological data as shown in Figure 5 and Figure 6. Comparing the correlation (RMSE${}_{rel}$) and root mean square error (RMSE) of the measured and simulated data, the RMSE${}_{rel}$ of the temperature of the study room and the reference room are 0.974 and 0.970, respectively, and the RMSE${}_{rel}$ of the illuminance of the study room is 0.999. The closer the RMSE${}_{rel}$-value is to 1, the higher the correlation between the predicted and actual values. The RMSE for the temperature of the study room and the reference room were 0.075 and 0.102, respectively, and the RMSE for the illuminance of the study room was 15.48. The closer the RMSE is to 0, the closer the predicted value is to the actual value. From the RMSE${}_{rel}$-value and RMSE results, the high correlation between the simulated and measured data verifies the accuracy of the LBT energy simulation software. In addition, if there is an error between the actual temperature measured in the field and the simulation results, it may be because people are entering and leaving the experimental room during the test period, which has a specific impact on the ambient air temperature; the error in the illuminance may be because the simulation data ignore the impact of the window frames on the illuminance as well as that related to the cleanliness of the glass:

$$RMSE=\sqrt{\frac{1}{N}\sum _{i=1}^n{(Y_i-f\left(x_i\right))}^2}$$

(1)

Range [0, +∞) equals 0 when the predicted value matches the actual value exactly, i.e., a perfect model. The more significant the error, the larger the value:

$$RMS{E}_{rel}=\frac{RMSE}{\overline{L_m}}$$

(2)

The range [0,1] equals 1 when the predicted value matches the actual value exactly, i.e., the perfect model. The more significant the error, the closer the value is to 0:

3.3. Baseline Model

The benchmark model is established based on the measured model’s boundary conditions. The advantage is that the accuracy of the model’s boundary conditions is verified above, and the thermal parameters of the enclosure are shown in

Table 4. Typical city.

Climate District	Representative City	Longitude	Latitude	Extreme Maximum Temperature (°C)
IC	Urumchi	87.65	43.80	42.1
IIA	Lanzhou	103.88	36.05	39.8
IIB	Turpan	89.20	42.93	47.7
IIB	Beijing	116.28	39.93	41.9

. Unlike the actual building, which has east-facing open windows, this study is designed to investigate the thermal comfort and daylighting performance of west-facing external shading, so the actual building is rotated by 180° to remove the existing constructed shading. In order to reduce the computational time during the subsequent multi-objective optimization, the model is simplified to a single room. Since the study room’s interior walls, floor, and roof have adjacent rooms, the interior walls, floor, and roof are set as adiabatic boundaries, and the final simplified model is shown in Figure 7.

The meteorological data (.epw) used in this study are the China Standard Weather Data (CSWD) downloaded from the LBT Meteorological Data website, which contain hourly dry bulb temperature, air humidity, and total solar radiation data.

Simulation of Working Conditions

The simulated working conditions of the baseline model will affect the thermal comfort situation inside the room. The indoor personnel density is set to 0.04 persons/m${}^2$, the personnel activity is the office, the metabolic rate is set to 1 met, and the thermal resistance of the personnel’s clothing is set to 0.7 clo. The equipment power is set to 8 W/m${}^2$, and the corresponding condition is a single-person office with one LCD monitor and one laptop computer. The lighting power is set to 8 W/m${}^2$, which is in line with the provisions of our "General Specification for Energy Saving and Renewable Energy Utilization in Buildings" for the limited value of lighting power density in ordinary offices. The infiltration rate is 0.0003 (m${}^3$/s per m${}^2$ facade). The nature of the office building use was set to have an occupancy rate of 1 for weekday mornings from 10:00 a.m. to 18:00 a.m. and 0 for the rest of the day. The period of 15 July–15 August was set to be the summer vacation time, and 15 January–15 February was the winter vacation time, with the occupancy rate for the summer and winter vacations being 0. This study aimed to investigate the thermal comfort and daylighting performance of the baseline model in non-air-conditioned conditions, and therefore, no HVAC was set up.

3.4. Selection of Typical Cities

GB50176-2016: Thermal Design Code for Civil Buildings divides China into 5 first-class climate zones and 11 climate sub-zones and puts forward different design requirements for building design in each climate zone [52]. The severe cold and cold area includes five climate subzones, which are severe cold A zone (IA), severe cold B zone (IB), severe cold C zone (IC), cold A zone (IIA), and cold B zone (IIB). Since the thermal design principle of IA and IB mentions that summer heat protection does not need to be considered, it is not considered the study area of this paper. This paper takes IC, IIA, and IIB as the scope of the study. The design requirements of the code for IIB mention that the thermal insulation requirements in winter must be met, and the heat protection in summer must be taken into account, with particular reference to the heat protection of the Turpan Basin. Therefore, based on choosing a city in each of the three sub-climatic zones, IIB additionally chooses Turpan. Four different cities in the IC, IIA, and IIB regions were finally determined to represent the thermal subzones to which they belong, Urumqi, Lanzhou, Turpan, and Beijing, as shown in Table 4.

3.5. Evaluation Indicators

3.5.1. UDI

UDI refers to the annual working plane of natural light in the useful daylight illuminance range of the proportion of time, the percentage of useful natural lighting illuminance hours. This indicator is intended to judge the natural light level for the location of the user’s vision as “useful”, neither too dim (less than 100 lx) nor too bright (more than 2000 lx). UDI can be evaluated in three ranges: values between 100 and 2000 lx indicate that natural light is adequate at the location, values less than 100lx indicate a deficient level of natural light, and values over 2000 lx can cause glare [24]. It has been shown that unsuitable shading designs can substantially reduce the UDI [19]. Therefore, the UDI is used in this study to evaluate indoor daylighting performance. The benchmark building model is an office, according to the provisions of the General Specification for Energy Efficiency and Renewable Energy in Buildings for the standard value of illuminance in an ordinary office, the plane at the height of 0.75 m from the ground is set as the working surface, and nine measurement points are arranged indoors as shown in Figure 8. The UDI of all the measurement points on the working surface of the benchmark model is obtained by using the HB-R software 1.6.0 to calculate the UDI. Then the point with the worst daylighting effect is taken as the reference point, i.e., the minimum value of the UDI of all measurement points is taken as the reference value to evaluate the daylighting performance of different shading methods.

3.5.2. PMV${}_{NCC}$

Thermal comfort is a subjective satisfaction rating of a person’s thermal surroundings. Fanger’s thermal comfort equation is the most influential and widely accepted thermal comfort research result. Fanger’s Thermal Comfort Equation describes the relationship between various environmental factors, activity levels, and the amount of clothing worn that affect a person’s thermal comfort. There are six parameters affecting indoor human thermal comfort, namely two subjective factors, i.e., human activity and clothing thermal resistance, and four objective factors, i.e., air temperature, air humidity, mean radiant temperature, and airflow rate [53], for which the PMV is calculated as follows. The indoor thermal comfort calculation module categorizes comfort conditions into three classes: unacceptably cold conditions (−1), neutral (comfortable) conditions (0), and unacceptably hot conditions (1). In order to quantitatively compare the indoor thermal comfort for different shading device conditions, the number of hours with PMV${}_{NCC}$ equal to 0 out of 8760 h in a year was accumulated in this study to derive the PMV${}_{NCC}$ for the whole year. The thermal comfort of the study interior with different shading devices can be derived by comparing it with the no-shading condition as follows, and the measurement points are shown in Figure 9:

$$\begin{array}{cc}\hfill PMV& =(0.303e^{-0.033M}+0.028)\{(M-W)-3.05\times {10}^{-3}\times [5.733-6.99(M-W)-P_a]\hfill \\ \hfill & -0.42\times [(M-W)-58.15]-1.7\times {10}^{-5}M(5.867-P_a)-0.0014M(34-t_a)\hfill \\ \hfill & -3.96\times {10}^{-8}{f}_{cl}\times [{(t_{cl}+273)}^4-{(t_r+273)}^4]-f_{cl}{h}_c(t_{cl}-t_a)\}\hfill \end{array}$$

(3)

• M: is the metabolic rate, in watts per square meter, W/m${}^2$;
• W: is the effective mechanical power, in watts per square metre, W/m${}^2$;
• $P_a$: is the water vapor partial pressure, in pascals, Pa;
• $t_a$: is the water vapor partial pressure, in pascals, °C;
• $t_r$: is the mean radiant temperature, in degrees Celsius, °C;
• $f_{cl}$: is the clothing surface area factor;
• $t_{cl}$: is the clothing surface temperature, in degrees Celsius, °C;
• $h_c$: is the convective heat transfer coefficient, in watts per square metre kelvin, W/(m${}^2$·K).

3.5.3. Cumulative Solar Radiation

For buildings in the SC and C areas, solar radiation in summer increases cooling energy consumption, which is an unfavorable factor for energy conservation; solar radiation in winter reduces heating energy consumption, which is a favorable factor for energy conservation [54,55]. Due to the difference in solar altitude angle between winter and summer, suitable shading devices can significantly reduce summer solar radiation and have a relatively small impact on winter solar radiation. It has been shown that there is a strong correlation between solar radiation and building energy consumption. Since the simulated conditions used in this study are non-air-conditioned, in order to quantitatively compare the effects of different shading devices on the overall building energy consumption of the study rooms, this study introduces the cumulative solar radiation shading coefficient (SF) and the cumulative solar radiation impact factor (IF), which are referenced to the previous studies and are improved based on which they apply to the present study [56], with the formulas as follows:

For cooling periods:

$$S{F}_C=\frac{Q_C}{Q_{CS}}$$

(4)

Q${}_C\in$ (0,+ ∞ ); Q${}_{CS}$∈(0,+ ∞ ).

For heating periods:

$$S{F}_H=\frac{Q_H}{Q_{HS}}$$

(5)

Q${}_H$∈(0,+ ∞ ); Q${}_{HS}$∈ (0,+∞ ).

$$IF=\frac{S{F}_C}{S{F}_H}$$

(6)

IF > 1: The shading effect is negative;

IF < 1: The shading effect is positive.

QC: Accumulated solar radiation in the study room without shading during the cooling period;

QCS: Accumulated solar radiation in the study room with shading during the cooling period;

QH: Accumulated solar radiation in the study room without shading device during the heating period;

QHS: Accumulated solar radiation in the study room with the shading device during the heating period.

In the simulation, the cooling period was set as June to August, and the heating period was set as December to February. Nine measurement points were uniformly arranged in the study room to calculate the cumulative solar radiation at each measurement point in the room in winter and summer under the conditions of different shading devices, respectively, and accumulated to obtain the total solar radiation in the study room in summer and winter, respectively. The influence coefficient of solar radiation was obtained by using the formula.

3.6. Description of the Simulation Variables

The types of shading devices used to study the thermal comfort and daylighting performance of exterior building shading include horizontal louvers (HLS), vertical louvers (VLS), egg crate shading (ES), and baffle shading (BS), as shown in Figure 9.

Each shading device was parameterized through the GH software. The design variables for the horizontal shading device include the number of horizontal louvers (NHS), the width of horizontal louvers (HSW), the rotation angle of horizontal louvers (HSA), and the distance between the louver slats and the window (DSW); the variables for the vertical louvers include the number of vertical branching louvers (NVS), the width of vertical louvers (VSW), the rotation angle of vertical louvers (VSA), and the louver slat to window distance (DSW); the variables of the egg crate shading device include the number of horizontal louvers (NHS), the width of the horizontal louvers (HSW), the rotation angle of the horizontal louvers (HSA), the number of vertical louvers (NVS), the width of the vertical louvers (VSW), the rotation angle of the vertical louvers (VSA), and the distance between the louver slats and the window (DSW); and the variables of the baffle shading device include the length of the horizontal baffle (HBW), the rotation angle of the horizontal baffle (HBA), the length of the vertical baffle (VBW), and the rotation angle of the vertical baffle (VBA). The rotation angle of the louvers is shown in Figure 10, and the specific parameters of the variables of the louvers are shown in

Table 5. Variables of the shadings.

Shade	Design Variables	Units	Abbreviate	[Start,Stop,Step]
HLS	Number of Horizontal Slats	quantity	NHS	[1,35,1]
	Horizontal Slats Width	m	HSW	[0.05,0.3,0.05]
	Horizontal Slats Angle	degree	HSA	[0,180,15]
	Distance between shade and windows	m	DSW	[0,0.4,0.1]
VLS	Number of Vertical Slats	quantity	NVS	[1,15,1]
	Vertical Slats Width	m	VSW	[0.05,0.3,0.05]
	Vertical Slats Angle	degree	VSA	[0,180,15]
	Distance between shade and windows	m	DSW	[0,0.4,0.1]
ES	Number of Vertical Slats	quantity	NVS	[1,15,1]
	Vertical Slats Width	m	VSW	[0.05,0.3,0.05]
	Vertical Slats Angle	degree	VSA	[0,180,15]
	Distance between shade and windows	m	DSW	[0,0.4,0.1]
	Number of Horizontal Slats	quantity	NHS	[1,35,1]
	Horizontal Slats Width	m	HSW	[0.05,0.3,0.05]
	Horizontal Slats Angle	degree	HSA	[0,180,15]
BS	Vertical Baffle Width	m	VBW	[0.2,1.6,0.2]
	Vertical Baffle Angle	degree	VBA	[0,90,15]
	Horizontal Baffle Width	m	HBW	[0.2,1.6,0.2]
	Horizontal Baffle Angle	degree	HBA	[0,90,15]

.

3.7. Optimization Objectives

This study performs multi-objective optimization using GH built-in plug-in Wallacei X. Wallacei X is applied NSGA-II as the main evolutionary algorithm. The NSGA-II algorithm is chosen to generate a Pareto optimal solution set, which is traded off between different search objectives to obtain a combination with better overall performance. The main parameters of the iterative optimization are shown in

Table 6. The main parameters of the iterative optimization.

Boundary Conditions	Description
Generation Size	30
Generation Count	30
Crossover Probability	0.9
Crossover Distribution Index	20
Mutation Distribution Index	20
Random Seed	1

.

The UDI at the most unfavorable point of the study room, the PMV${}_{NCC}$ of the study room for the whole year, and the IF coefficient were used as the optimization objectives as shown in

Table 7. Optimization objectives.

Optimization Objectives	Description
F1	Maximization f (PMV${}_{NCC}$)
F2	Maximization f (UDI)
F3	Maximization IF

. To facilitate the comparison of the data at a later stage, the UDI and the PMV${}_{NCC}$ were divided by the value of the no-shading condition as shown in the following equations:

$$f\left(UDI\right)=\frac{UDI}{UD{I}_{NSC}}$$

(7)

• UDI: UDI for shading conditions.
• UDI${}_{NSC}$: UDI for no shading conditions.

$$f\left(PM{V}_{NCC}\right)=\frac{PM{V}_{NCC}}{PM{V}_{NCC-NSC}}$$

(8)

• PMV${}_{NCC}$: PMV${}_{NCC}$ for shading conditions.
• PMV${}_{NCC-NSC}$: PMV${}_{NCC}$ for no shading conditions.

However, since Wallacei X performs calculations based on the minimum value of the objective function, it is necessary to multiply all three optimization objectives by −1 to obtain the solution sets of the three objective functions in Wallacei X. When analyzing the solution sets of the Pareto front, the values are again multiplied by −1 to obtain the optimal solution sets of the three objectives.

4. Results

After 30 generations of iterative calculations, the 30th generation of the Pareto front solution set for the four shading devices in four typical cities yielded the PMV${}_{NCC}$, UDI, and IF values. Additionally, the corresponding control parameters of the shading devices were obtained alongside these values. For subsequent data analysis, the annual comfort hours, annual UDI percentage, summer cumulative solar radiation, and winter cumulative solar radiation were divided by the NSC values. When these values are more significant than 1, it means that the performance of these three objectives is optimized. Considering minor errors caused by different computer configurations, the metrics of PMV${}_{NCC}$, UDI, and IF were deemed optimized when their values exceeded 1.2. The purpose of this is to ensure that if one metric is optimized, the other two metrics are also not lower than the unshaded condition. By comparing the Pareto optimal solutions of four shading devices, the differences in the photo-thermal performance of the four shading forms in the west orientation of the building are analyzed. Based on the optimization results, the maximum values and the overall best design parameters under different objective orientations are derived.

According to the results, the most significant IF improvement was observed with the use of shading devices relative to PMV${}_{NCC}$ and UDI. Specifically, in Urumqi, Lanzhou, and Turpan, the impact of using horizontal louvered shading devices on buildings was most significant in the westward direction, resulting in enhancements ranging from 2.1 to 2.7 times that of the NSC, As shown in Figure 11. In Beijing, the use of egg crate shading devices led to an IF value that was 4.13 times higher than the NSC. The results indicate that the cumulative solar radiation entering the room is significantly reduced during the summer months. However, the reduction in cumulative solar radiation is relatively small during the winter months, which is beneficial for reducing the overall energy consumption of the building throughout the year. For specific shading parameters, please refer to Appendix A.

According to the results of the PMV${}_{NCC}$, the use of appropriate shading devices significantly improved the year-round thermal comfort hours in the four cities under non-air-conditioned conditions. The impact of shading devices varied across the cities, with different types of shading devices showing the most significant improvements in each city. In Urumqi and Turpan, the use of horizontal louvered shading devices had the most significant impact on buildings, resulting in enhancements ranging from 1.6 to 2.1 times the NSC. In Beijing, baffle shading devices led to the most significant improvement, with a lift of 2.45 times the NSC. In Lanzhou, the most significant improvement was achieved with egg crate shading, reaching 2.8 times the NSC, As shown in Figure 12. For specific shading parameters, please refer to Appendix A.

From the UDI results, Urumqi and Turpan still have the highest UDI values after using horizontal shading. Beijing and Lanzhou have the most advantageous use of egg crate shading devices, As shown in Figure 13. In terms of overall UDI values, Urumqi has the lowest UDI, and Beijing has the highest. Refer to Appendix A for specific shading parameters.

To compare the overall performance of the four shading devices, the PMV${}_{NCC}$, UDI, and IF values were averaged for the 30th generation Pareto frontier solution set. The average size of the optimal solution sets for each shading device was then compared. If there were minor differences in the values, an analysis of variance (ANOVA) was conducted. This approach allowed for a comparison of the combined optimal performance of the four shading devices. The combined analyses reveal that the use of suitable shading devices in all four cities leads to a significant improvement in performance. Particularly in Beijing, the average integrated performance value can reach 2.3–3.3 times the NSC, resulting in substantial enhancements in daylight and thermal comfort. On the other hand, the performance enhancement in Urumqi is relatively lower:

$${\sigma }^2=\frac{\sum {(X-\mu )}^2}{N}$$

(9)

• ${\sigma }^2$: Sample variance;
• X: The variable;
• $\mu$: Sample mean;
• N: The number of sample cases.

5. Discussion

In this study, a two-step process was employed to synthesize and compare shading devices. Firstly, the feasibility of utilizing fixed shading for the west orientation of buildings was verified by analyzing the optimization results of four shading devices in each city. Secondly, the optimal configuration parameters were explored by studying the relationship between different objectives and parameters. This approach allows the configuration of the shutters to be adapted to the daylight and energy objectives of the studied city in order to achieve optimal performance.

5.1. Evaluate Four Urban Performance Enhancements

Based on the optimized comparison of four shading devices in four cities, the following conclusions are drawn. Regardless of the city, the application of fixed shading devices can effectively improve the thermal comfort and daylighting performance of west-facing rooms of a building to 1.5 to 3 times the NSC, As shown in Figure 14. Several studies have also demonstrated the positive impact of fixed shading devices on building energy efficiency, daylighting performance, and thermal comfort. A study by Francesco De Luca revealed a substantial 40–60% reduction in cooling energy consumption in east–west oriented buildings [10]. Similarly, Jianjian Zhang Lin Ji significantly improved indoor thermal comfort performance through the study of Sanya, China [26]. Kontadakis’ study showed a 150% increase in UDI compared to NSC when using static shading devices [57]. The conclusions of this study are consistent with the optimized performance studies of fixed shading devices. However, the final enhancement values are slightly different due to differences in geographic location and climate. In conclusion, it is demonstrated that west-facing fixed external shading holds great potential for enhancing daylighting performance, thermal comfort, and energy consumption in buildings.

In Beijing, the implementation of shading devices showed a more pronounced effect, with a significantly lower performance enhancement effect in Urumqi compared to the other three cities. Upon analyzing the reasons behind this disparity, it can be observed that Urumqi falls within the severe cold region, experiencing prolonged periods of low temperatures during winter and relatively brief periods of hot weather in summer. In contrast, Beijing is situated in a cold region with more frequent hot weather during summer compared to Urumqi. The findings of the study conclusively demonstrate the significant influence of climate on the effectiveness of shading devices, a correlation that numerous scholars in the field have affirmed [44,58,59]. For instance, Huimin Huo and Wei Xu also analyzed the light and thermal comfort performance of external shading for buildings in regions with severe cold and cold climates in China, and their conclusions were similar to those of this paper [60]. This study reinforces the existing findings and further demonstrates the energy-saving potential of exterior building shading in regions with severe cold and cold climates.

Different goal-oriented assessments from shading effectiveness:

When IF is goal-oriented, HLS is appropriate for Urumqi, Lanzhou, and Turpan, and ES for Beijing. The reasons behind the suitability of these shading devices for specific locations are closely related to geographical location and climate. The solar altitude angle and angle of direct sunlight in Urumqi, Lanzhou, and Turpan differ due to their geographical locations. This difference can be attributed to the effect of latitude. Kun Lai and Wen Wang conducted a study that supports the argument that the solar altitude angle significantly affects the shading effectiveness. Their study demonstrated that shading devices become more effective as latitude decreases, with the most significant effects observed at latitudes between 30.0° and 40.0° [61]. Therefore, their findings strongly support the potential for implementing westward fixed shading at high latitudes. Overall, it is crucial to consider geographical location, climate, and specific goals when assessing the effectiveness of shading devices.

Based on the goal-oriented study of UDI, it is recommended that HLS be used in the design of Urumqi and Turpan, and ES be used in Lanzhou and Beijing to ensure the uniformity of indoor illuminance. Previous studies have shown that BS shading reduces the entry of natural light [19], in contrast to HLS and ES shading devices, which are better able to achieve daylighting uniformity to meet the UDI requirements [39].

Based on the PMV${}_{NCC}$ as a goal-oriented study, it is recommended that HLS be used in Urumqi and Turpan, ES in Lanzhou, and BS in Beijing. There are significant differences in the PMV${}_{NCC}$ results for different cities, with Urumqi, Turpan, and Lanzhou all having less effective BS than HLS and ES. In contrast, Beijing has the best results using BS. These differences can be attributed to the warm, temperate, semi-humid continental climate of Beijing and the arid or semi-arid climates of Urumqi, Turpan, and Lanzhou. It is worth noting that ambient humidity plays a role in the effectiveness of shading devices. Allen Khin Kiet Lau’s research on shading devices in hot and humid climates in Malaysia found that the application of egg crate shading devices resulted in improved indoor comfort during summer compared to vertical and horizontal shading. Therefore, the influence of climatic conditions needs to be taken into account when selecting shading devices when PMV${}_{NCC}$ is goal-oriented.

This study provides compelling evidence for the effectiveness of utilizing shading devices for buildings with a west orientation. Furthermore, the selection of appropriate shading devices in the design process should be guided by specific goal-oriented criteria, ensuring that the energy efficiency and comfort requirements are met. Whether the focus is on PMV${}_{NCC}$, IF, or UDI, shading devices have proven to significantly enhance both thermal comfort and daylight performance within buildings. However, it is crucial to consider the influence of geographic location and climatic conditions when choosing the most suitable shading devices for different cities. This consideration is of the utmost importance in the design of buildings across various urban contexts.

5.2. Assessment of Shading Device Parameters in Four Cities

According to the findings of the study, as mentioned earlier, and the examination of various cities, the design and optimization of shading devices should take into account the quantity and angle of the shading slats. Other research has also confirmed the correlation between the number of louvers, their angle, and the UDI [23,32,33], which aligns with the outcomes of the present study.

When choosing the number of sunshade slats, Urumqi, Lanzhou, and Beijing are suitable for wide and widely spaced sunshade slats. At the same time, Turpan is suitable for narrow and less widely spaced horizontal sunshade slats. Due to its geographic location, Turpan has an average of more than 3000 h of sunshine throughout the year and a hot, dry summer with 12–13 h of sunshine, so the number of sunshade slats is much higher than in the other three cities. The number of sunshade slats is negatively correlated with the width when oriented to IF. Increasing the width or number of shading slats can affect the entry of direct sunlight into the room. Therefore, in the specific program design, the number and width of the sunshade can be changed according to the styling requirements to obtain a suitable design for the sunshade device.

When choosing the angle of the sun visor slats, the optimum angle of rotation of the horizontal sun visor slats is usually about 45°. As direct sunlight enters the interior from the westward direction of the building, the sun’s altitude angle is lower, and the angle of incidence of westward sunlight is smaller. In this case, the angle of turn of the horizontal sunshade slats needs to be minor, typically less than 45°. Ensure that sunlight is blocked as it slants in from above, reducing the amount of direct sunlight entering the room. It has been demonstrated that the best shading effect is achieved when the angle of the louver slats is around 45°.

When choosing the angle of the shading slats, the optimal angle of rotation of the horizontal shading slats is usually about 45°. This angle is particularly effective in blocking direct sunlight from entering the interior of a building. By positioning the slats in this manner, the sunlight is intercepted as it slants in from above, effectively reducing the amount of direct sunlight entering the room. Numerous studies have shown that the optimal shading effect is achieved when the angle of the louver slats is approximately 45° [62].

The angle of the vertical louvers is related to the solar azimuth and the intensity of solar radiation. When direct sunlight enters a west-facing room, the intensity of solar radiation decreases as the sun moves from southwest to west. In order to ensure comfort in the room and to avoid excessive sunlight, it is necessary to choose the appropriate angle for the vertical louvers. Based on existing research and theoretical experience, the angle of turn of the vertical shading slats is typically 56° [63]. The recommended VLS turning angles for this study range from 135° to 150°; the reason for the large gap with previous studies is the different initial rotation direction of the design. This range makes full use of solar radiation while effectively controlling indoor daylight and reducing indoor heat accumulation.

The optimal angle of rotation for horizontal slats of the ES is centered around 60° to 90°, and the optimal angle of rotation for vertical slats is centered around 120° to 150°. In both cases, the slats are more perpendicular to the window. As a result of the increased number of slats, the entry of direct sunlight was reduced. To increase direct winter sunlight while blocking out direct summer sunlight, by adjusting the angle of the slats, it is possible to strike a balance between reducing solar gain and allowing natural light to enter the room.

The optimal turning angles for BS shades are 60° and 75°, while the optimal turning angles for vertical panels range from 0° to 30°. Unlike louvered shading, BS shading devices do not let light into the room through gaps in the slats. In order to ensure that the natural lighting in the room is not affected, the width of the horizontal panels should not be too small; otherwise, the vertical panels will be too close to the windows, affecting the indoor illumination.

In summary, the design and optimization of shading devices require careful consideration of various parameters based on the specific goal orientation. If the goal is to achieve a comfortable indoor environment based on the UDI, a smaller number of shading slats may be selected to ensure indoor illuminance. When targeting IF and PMV, select the appropriate number and angle of shading slats for specific needs to meet indoor comfort and daylight requirements, As shown in Figure 15. In addition, factors such as the sun’s altitude angle, geographic location, and climate have a significant impact on shading effectiveness. Designers need to consider different target orientations, climate characteristics, and geographic locations to select appropriate parameters for shading devices. The number and angle of shading slats are rationally adjusted to improve the energy efficiency, indoor illumination, and comfort of the building.

The novelty and contribution of the present research are twofold. First, this study verifies the potential of using fixed shading for the west orientation of the building. For the applicability of westward fixed external shading devices in school office buildings, four sunshade programs applicable to the westward direction were selected for comparison to obtain the most suitable sunshade devices for cold and cold regions. Secondly, this study considered a variety of parametric variables affecting shading, including the width, number, corner, and spacing of louvers from the window, as well as the length and rotation angle of the baffle; it also considered the relationship between different goal orientations (UDI, IF, and PMV) and the design of the shading device, which provides a reference for users with different needs.

In this study, the climatic characteristics of different cities are considered, and based on this, an optimized comparison of shading devices is carried out, which helps in designing and improving the external shading devices for buildings in different regions. Additionally, the study employs diverse goal-oriented approaches to evaluate the performance of shading devices comprehensively. The findings of this research provide specific types and parameters of shading devices, enabling designers to make informed decisions regarding energy-efficient building design. Furthermore, these results can be extrapolated to guide the energy-efficient design of buildings in other cities with similar climatic and geographical conditions.

6. Conclusions and Further Research

This study primarily examines the daylight and thermal comfort performance of four types of shading devices in school office buildings located in cold and frigid areas. The focus is on the west direction of the building. The aim is to offer guidance for choosing suitable shading devices for the west side of buildings in such regions. The conclusions of the study can be summarized as follows:

(1)

After conducting an optimized comparison of the four types of shading devices in four different cities, it was concluded that regardless of the city, the use of fixed shading devices significantly enhanced the thermal comfort and daylighting performance of rooms on the west side of the building. The improvement was observed to be 1.5 to 2.5 times the NSC.

(2)

Designers must take into account various factors, such as target orientations, climatic characteristics, and geographical locations when selecting the parameters of shading devices. This includes considering the appropriate number and angle of shading slats, which should be adjusted rationally.

There are still areas that can be further improved. First, the study did not use energy consumption indicators for a comprehensive assessment, focusing only on the light environment, thermal comfort, and cumulative indoor solar radiation of the building. Although the impact of shading devices on energy consumption during heating and cooling periods can be understood through cumulative solar radiation, the lack of energy consumption metrics can limit the visual assessment of overall effectiveness. Therefore, the introduction of energy consumption indicators could be further considered in subsequent studies. A more detailed design of the schedules for individual cities was carried out to obtain more accurate results.

In addition, a discussion of the prospects for practical application of the building’s west-facing exterior shading devices selected in this study is also an essential direction for improvement. Although the optimal design of shading devices was derived from simulation and data analysis in this study, there are some limitations and challenges that may be faced in practical applications. Therefore, further research could explore the prospects for the practical application of shading devices and evaluate them for different building types and scenarios.

In conclusion, this study provides some guidance for the selection of west-facing external shading devices for schools and office buildings in severe cold regions of China. However, there is still some room for improvement. This includes the introduction of energy consumption indicators for a comprehensive assessment, consideration of the whole life cycle costs of shading devices, and a discussion of the prospects for practical applications. These improvements will further refine the results of this study and provide more focused guidance for policy making and practice in related fields.