An Occupant-Oriented Calculation Method of Building Interior Cooling Load Design

: Given continued improvement in the thermal performance of building envelopes, interior disturbances caused by occupant behavior now have the greatest impact on building loads and energy consumption. The accurate calculation of interior load during design stage was emphasized in this paper, and a new method was proposed. Indoor occupants were considered as the core of interior disturbances, and the relationship with other interior disturbances was explored. The interior heat release was arbitrarily combined with the representative cooling load to be utilized in building cooling load calculation. Field surveys were conducted in three typical university buildings: an office building, a teaching building, and a library, located in a university in Tianjin, China. The oversized chillers supplying cooling for the buildings resulted from the over-estimating of the indoor occupant number and the power density of electric appliances. Through quantitative analysis, it was observed that the maximum representative interior loads were 196.43, 329.94, and 402.58 W/person, respectively, for the case buildings, at least 50% less than the empirical design data. Compared to the measured cooling load during the testing period, the accuracy of the modified cooling load was greater than 90%. This research is intended to serve as a reference for calculating and optimizing the design loads of cooling systems.


Introduction
Buildings have been widely recognized as one of the main energy consumption sectors and the key to energy efficiency in the whole society [1]. Increasing demand for comfortable built environments has made the energy efficiency of heating, ventilating, and air-conditioning (HVAC) systems the primary objective in the non-residential sector [2]. In order to achieve energy efficiency in buildings, the design and optimization of HVAC systems are particularly important where the energy performance is affected by operational conditions, as well as heating and cooling needs. With the continuous improvement of building energy efficiency standards [3], the thermal performance of building envelopes has notably enhanced. Based on the demarcation of the building structure, three primary factors affect the energy consumption of the HVAC system: exterior disturbances, interior disturbances, and the operational factors of the energy supply system [4,5]. Exterior disturbances include outdoor air conditions and solar radiation. Interior disturbances include indoor occupants and the usage of electric appliances, such as lamps and equipment. Operational factors of the energy supply system include the energy efficiency of chillers, water pumps, and fans. Given the gradual improvement of the thermal insulation of building envelopes, the impact of exterior disturbances on the building cooling/heating loads has a zone cooling and heating supplied by ground source heat pumps, were selected as cases in the research with which to explore the nature of interior disturbances in various building types through field investigation and measurements during the cooling season (August and September) in 2017. In Section 3, characteristics of interior load disturbances of the case buildings were analyzed and quantified. The regularities of indoor occupant number and the relationships between lighting and equipment with indoor occupants were proposed through data fitting. The final description of the interior load disturbance was illustrated. The accuracy of the interior load calculation method was demonstrated in Section 4. The feasibility was proved through building cooling load simulation.

Concept of Load Disturbances
The concept of disturbances comprises the variables that influence the indoor thermal environment. The nature of the indoor thermal environment is primarily determined by exterior and interior disturbances. Generally, the outdoor meteorological parameters, such as air temperature and solar radiation, are classified as exterior disturbances. Occupants, equipment, and lighting can be classified as interior disturbances. Though the thermal change in the indoor environment was caused by exterior air temperature, the window usage or fresh air volume is determined by occupants. So, the fresh air load cannot be strictly attributed to neither exterior nor interior factors. Therefore, fresh air induced from open windows is considered to be a special type of disturbance. Based on the above concepts, the building cooling load constitutes exterior disturbances, interior disturbances, and fresh air disturbances. So, the building cooling load can be calculated by Based on Equation (1), the building cooling loads are divided into three parts: the exterior cooling load, which is caused by exterior disturbances related to the building envelope and solar radiation; the fresh air load caused by the volume of fresh air, which is further related to the number of occupants, and the temperature differential between the inside and the outside of the building; and the interior cooling load, which is caused by heat gain due to interior disturbances.
The exterior cooling load can be easily calculated based on building load simulation software. The fresh air schedule, which is in direct proportion to occupant number, is the key to calculating fresh air load. The interior load calculation is the study object of this paper. So, the interior load can be calculated by

Definition of "Representative Interior Load"
The interior cooling load is caused by heat release due to interior disturbances. In this paper, only readily discernable indoor factors that influence the building cooling load comprise the interior load, namely, indoor occupants, combined with the used lighting and equipment. The cooling load of interior disturbances can be calculated by Based on Equation (3) [19,20], the time-varying number n i,τ and the heat release q i,τ of each load disturbance should be determined separately. It might be difficult if the usage information is not obtained clearly by the designers, especially the usage of lighting and equipment. Indoor occupant number is relatively easy to quantify if the building is used regularly. However, the usage of lighting and equipment is not independent of the indoor occupants. Because the usage of lighting and equipment is decided by the occupant control behaviors, some relationship must exist between the used lamp and equipment number with indoor occupant number, respectively. Based on the relationship, this paper proposed the occupant-oriented "representative interior load". Then, the calculation of interior load can be simplified as q re,τ = ϕ occ · q occ,τ + λ lig,τ · E lig + ∑ eqpi λ eqpi,τ · E eqpi · C τ (4) So, the interior load can be calculated by CL in,τ = n occ,τ · q re,τ Comparing Equations (3) and (5), the indoor occupant number is the basis of interior load. The interior loads can be calculated by the heat release of occupants, used lamps, and equipment. The installed rated power of lamps and equipment is decided by building design. So, the key factors of calculating interior load based on Equations (4) and (5) are the indoor occupant number and the corresponding used lamps and equipment. The problem has been transferred to the quantifying of indoor occupant number and establishing the relationship of used lamps and equipment number with indoor occupant number. The detailed form and parameters should be determined by the following functions.

Modeling and Uncertainty Estimation of Building Cooling Load
Based on the above analysis, the procedure of establishing the building cooling load model with the proposed representative interior load applied was shown as Figure 1.
Comparing Equations (3) and (5), the indoor occupant number is the basis of interior load. The interior loads can be calculated by the heat release of occupants, used lamps, and equipment. The installed rated power of lamps and equipment is decided by building design. So, the key factors of calculating interior load based on Equations (4) and (5)

Modeling and Uncertainty Estimation of Building Cooling Load
Based on the above analysis, the procedure of establishing the building cooling load model with the proposed representative interior load applied was shown as Figure 1.  Figure 1. Occupant-oriented, representative interior load establishment and application procedure.  There are three parts in the method proposed in this paper.
(a) First one and the core is the interior cooling load calculation. Three relationships described in Equations (6)- (8) are the emphases. The relationships are formulated in the following sections based on the case study of three typical university buildings. (b) The second part is the basic building cooling load simulation model based on the basic building information, such as building shape, envelope, etc., and indoor and outdoor meteorological parameters. In this paper, the building cooling load simulation models are established with DesignBuilder tool. DesignBuilder is dynamic simulation software that has a comprehensive builder graphical interface and uses EnergyPlus as core calculator [25,26]. The procedure of establishing a building load simulation model based on DesignBuilder is shown in Figure 2. There are three parts in the method proposed in this paper.
(a) First one and the core is the interior cooling load calculation. Three relationships described in Equations (6)- (8) are the emphases. The relationships are formulated in the following sections based on the case study of three typical university buildings. (b) The second part is the basic building cooling load simulation model based on the basic building information, such as building shape, envelope, etc., and indoor and outdoor meteorological parameters. In this paper, the building cooling load simulation models are established with DesignBuilder tool. DesignBuilder is dynamic simulation software that has a comprehensive builder graphical interface and uses EnergyPlus as core calculator [25,26]. The procedure of establishing a building load simulation model based on DesignBuilder is shown in Figure 2.  (c) The third part is the checking and verifying procedure. To verify the accuracy of simulated building cooling loads based on the representative interior load, the Bland-Altman plot method is applied to compare simulated building cooling loads with the measured actual loads. The verification parameter is [27] In general, if the number of points within the bounds of the range of consistency ( accounts for more than 95% of the total points, it can be concluded that the two groups of values have good consistency. (c) The third part is the checking and verifying procedure. To verify the accuracy of simulated building cooling loads based on the representative interior load, the Bland-Altman plot method is applied to compare simulated building cooling loads with the measured actual loads. The verification parameter is [27] In general, if the number of points within the bounds of the range of consistency (d ± 1.96S d ) accounts for more than 95% of the total points, it can be concluded that the two groups of values have good consistency. Three typical university buildings located in a university in Tianjin, China were selected as special cases with which to study the interior load characteristics of various building types. The buildings, together with other four similar teaching buildings, are cooling supplied by a zone energy station. The total covered building area of the energy station was 127,665 m 2 . The main chillers of the energy station are 6 water source heat pumps (WSGP) with a cooling capacity of 19,200 kW. The design cooling load is 142.02 W/m 2 . The basic information of case buildings is shown in Table 1. Three typical university buildings located in a university in Tianjin, China were selected as special cases with which to study the interior load characteristics of various building types. The buildings, together with other four similar teaching buildings, are cooling supplied by a zone energy station. The total covered building area of the energy station was 127,665 m 2 . The main chillers of the energy station are 6 water source heat pumps (WSGP) with a cooling capacity of 19,200 kW. The design cooling load is 142.02 W/m 2 . The basic information of case buildings is shown in Table 1. The design of building envelope and the thermal performance of case buildings were listed in Table 2. Three typical university buildings located in a university in Tianjin, China were selected as special cases with which to study the interior load characteristics of various building types. The buildings, together with other four similar teaching buildings, are cooling supplied by a zone energy station. The total covered building area of the energy station was 127,665 m 2 . The main chillers of the energy station are 6 water source heat pumps (WSGP) with a cooling capacity of 19,200 kW. The design cooling load is 142.02 W/m 2 . The basic information of case buildings is shown in Table 1. The design of building envelope and the thermal performance of case buildings were listed in Table 2. Three typical university buildings located in a university in Tianjin, China were selected as special cases with which to study the interior load characteristics of various building types. The buildings, together with other four similar teaching buildings, are cooling supplied by a zone energy station. The total covered building area of the energy station was 127,665 m 2 . The main chillers of the energy station are 6 water source heat pumps (WSGP) with a cooling capacity of 19,200 kW. The design cooling load is 142.02 W/m 2 . The basic information of case buildings is shown in Table 1. The design of building envelope and the thermal performance of case buildings were listed in Table 2. The construction drawings and load design documents for buildings were examined. The design conditions of interior load disturbances of case buildings are listed in Tables 3-5, respectively.

Library
The design of building envelope and the thermal performance of case buildings were listed in Table 2. The construction drawings and load design documents for buildings were examined. The design conditions of interior load disturbances of case buildings are listed in Tables 3-5, respectively.   Tables 1 and 3-5. The values are extremely different with the generally used recommended data in Ref. [20] listed in Tables 8 and 9 for the teaching building and the office building. The proportion of occupants, lighting, and equipment is different because of various building types. In the two buildings, the occupant and equipment heat releases take more than 90% of the total heat release. In the teaching building, the ratio of occupant, lighting, and equipment is about 42:3:55. The ratio of the office building is 12:8:80. However, in the library, the heat release of occupants is the main part, taking the proportion of 96.65%. It indicates that the over design value of occupants and equipment will result in the over estimating of cooling loads.

Building Usage Data Collection
Various methods, including static [28] and dynamic [29] methods, were adopted in research to obtain building usage data, especially occupant-related information. After Ekwevugbe et al. [30] measured the occupancy in non-domestic buildings and added the information to the building management system. CO 2 sensors and passive infra-red (PIR) detectors were explored. Cameras were also used in automatic monitoring [31]. However, it is really difficult to transform the video information to digital data. So, field survey and infra-red counters were adopted in this paper to obtain the indoor occupancy data. The picture of infra-red counter was shown in Figure 3. The maximum interior heat release of electric appliances under design conditions are 157.39, 177.76, and 72.43 W/m 2 in the teaching building, the office building, and the library, respectively, based on Tables 1, 3, 4, and 5. The values are extremely different with the generally used recommended data in Ref. [20] listed in Tables 8 and 9 for the teaching building and the office building. The proportion of occupants, lighting, and equipment is different because of various building types. In the two buildings, the occupant and equipment heat releases take more than 90% of the total heat release. In the teaching building, the ratio of occupant, lighting, and equipment is about 42:3:55. The ratio of the office building is 12:8:80. However, in the library, the heat release of occupants is the main part, taking the proportion of 96.65%. It indicates that the over design value of occupants and equipment will result in the over estimating of cooling loads.

Building Usage Data Collection
Various methods, including static [28] and dynamic [29] methods, were adopted in research to obtain building usage data, especially occupant-related information. After Ekwevugbe et al. [30] measured the occupancy in non-domestic buildings and added the information to the building management system. CO2 sensors and passive infra-red (PIR) detectors were explored. Cameras were also used in automatic monitoring [31]. However, it is really difficult to transform the video information to digital data. So, field survey and infra-red counters were adopted in this paper to obtain the indoor occupancy data. The picture of infra-red counter was shown in Figure 3. The usage information of lamps and equipment can also be obtained by field survey. However, for office buildings with relatively private office rooms, the cameras were installed for field monitoring of key office rooms. Two multiple-occupant offices, an administration office and a scientific research office, were selected as examples to represent the usage information of the two types of office rooms. In addition, rooms occupied or not were recorded one by one through on-site survey in the office building.
The time interval of data record was 1 h. The investigation was conducted for two time periods, August 1st to 15th 2017 and September 1st to 15th 2017, respectively. The cooling period of Tianjin is from June 15th to September 15th. The first survey period is generally the hottest days during the year; however, it is during summer holiday. The second investigation period is the relatively cool days and was one week after fall opening in 2017. So, the two time periods of August 1st to 15th 2017 and September 1st to 15th 2017 were recognized as holidays and general used period, respectively. The usage information of lamps and equipment can also be obtained by field survey. However, for office buildings with relatively private office rooms, the cameras were installed for field monitoring of key office rooms. Two multiple-occupant offices, an administration office and a scientific research office, were selected as examples to represent the usage information of the two types of office rooms. In addition, rooms occupied or not were recorded one by one through on-site survey in the office building.
The time interval of data record was 1 h. The investigation was conducted for two time periods, August 1st to 15th 2017 and September 1st to 15th 2017, respectively. The cooling period of Tianjin is from June 15th to September 15th. The first survey period is generally the hottest days during the year; however, it is during summer holiday. The second investigation period is the relatively cool days and was one week after fall opening in 2017. So, the two time periods of August 1st to 15th 2017 and September 1st to 15th 2017 were recognized as holidays and general used period, respectively.
In order to validate the proposed interior cooling load calculation method, the actual cooling load should also be measured. To calculate the actual cooling load, the outdoor meteorological parameters, indoor air temperature, and cooling capacity were tested at the same time. The outdoor meteorological parameters, including temperature, solar radiation, air speed, indoor temperature, and cooling energy consumption, were measured. Test instruments installed in the three buildings included HOBO U10-003 thermographs (temperature accuracy range ±0.4 • C), relative humidity accuracy range ±5%), UT-230A dynamometer (accuracy range ±0.01 W), infrared thermometer (accuracy range ±1.5%), anemometer (accuracy range ±0.01 m/s), and AZ-8778 black bulb thermometer (accuracy range ±0.8 • C). The test interval was set to 10 min to avoid missing data. U10-003 thermographs and flow meters were installed on the inlet and outlet pipes of buildings to measure the cooling capacity.
Data during August 1st to 7th and September 1st to 7th was adopted to analyze the characteristics of interior cooling load and quantify the representative interior cooling load in Sections 3 and 4.1, Sections 4.2 and 4.3. The other part of data was used to validate the proposed method and results in Section 4.4.

Indoor Occupants Analysis
The variation of cooling load originated from the energy demand change of occupants. Indoor occupant number is the premise of the perspective interior load. Several approaches were adopted in building occupant modeling. Widen et al. [32] combined the Markov chain and bottom-up approach to model the indoor occupancy rate and the lighting demand. Andersen et al. [33] applied an inhomogeneous Markov chain to described the indoor occupancy rate of an office building located in San Fransisco. Two states, namely, high and low occupancy rate, were defined and described separately. The aggregated performance was verified for occupants on the building level. Some research only focused on the presence/absence state of occupants. Based on the hypothesis of a certain value of indoor occupant number, the arrival and departure times were selected as key times interrupting the presence state of occupants. J. Page et al. [34] proposed stochastic models for private offices and multiple-occupant offices, respectively. All this research considered the indoor occupant number as a stochastic parameter. However, the results of stochastic analysis proved that a steady probability, namely, the average condition, existed in the indoor occupant number or indoor occupancy rate for a long time for regularly used buildings. So, the average time-varying indoor occupant number was taken as the object in this paper to generate the schedule of indoor occupants, and data fitting approach was adopted.
If the indoor occupant number can be obtained directly and conveniently, the measured data will be the most accurate original data. Because the form of schedule is the easiest way to combine occupant behavior and building load simulation software [35], the measured data based on building on-site survey and infrared counters was adopted to be analyzed. The key to accurate modeling is the time interval of measured data. If the time interval is too small, the data amount will increase, and quantifying will be more difficult. However, if the time interval is too large, the validation will be doubted. The time intervals of relative research vary from 5 min to hours [36,37]. In order to explore the proper time interval of indoor occupant data, data fitting with different time intervals was explored in a multiple-occupant (full-check occupant number ≥ 8 [38]) scientific research office. The description of proper time interval should satisfy the acceptable goodness of fit (R 2 ), which, in general, is no less than 0.9 [39]. The measured indoor occupant data with time interval of 10 min was shown in   Table 6. Based on the results in Table 6, 1 h can be considered as the proper time interval for the quadratic polynomial based on the following reasons. R 2 is higher than 0.9 in the morning period, namely, 8:30-12:30, under all time intervals. However, R 2 is lower than 0.9 under 30 min time interval, though it is higher than 0.9 under the time interval of 1 h during 12:30-18:30. It means some fluctuations are hidden in 1 h. In order to find the fluctuations' present time, data during 13:30-18:30 and 12:30-17:30 were refitted. It turns out that the goodness of fit of quadratic polynomials under 4 time intervals are raised, especially in 13:30-18:30. So, the occupant number during lunch time is more stochastic than at other times. However, because the indoor occupant number is relatively low, the design cooling load will not be affected. So, the proper time interval for obtaining indoor occupant number was deemed as 1 h.
The measured, time-varying occupant number of the case buildings is in accordance with a trimodal distribution. The so called "trimodal distribution" means there are three maximums in different time periods of the hourly indoor occupant values. The key difference between occupant number of university buildings and that of the general office buildings is the usage during evening period. Many occupants use buildings in the evening. Particularly, the indoor occupant number of library in the evening is similar to or even more than that during the afternoon period.
Based on the above analysis, the quadratic polynomials with 1 h time interval as the input parameter are the proper relationship with which to describe the trimodal distribution of indoor occupant number. The function form is  Table 6. Based on the results in Table 6, 1 h can be considered as the proper time interval for the quadratic polynomial based on the following reasons. R 2 is higher than 0.9 in the morning period, namely, 8:30-12:30, under all time intervals. However, R 2 is lower than 0.9 under 30 min time interval, though it is higher than 0.9 under the time interval of 1 h during 12:30-18:30. It means some fluctuations are hidden in 1 h. In order to find the fluctuations' present time, data during 13:30-18:30 and 12:30-17:30 were refitted. It turns out that the goodness of fit of quadratic polynomials under 4 time intervals are raised, especially in 13:30-18:30. So, the occupant number during lunch time is more stochastic than at other times. However, because the indoor occupant number is relatively low, the design cooling load will not be affected. So, the proper time interval for obtaining indoor occupant number was deemed as 1 h.
The measured, time-varying occupant number of the case buildings is in accordance with a trimodal distribution. The so called "trimodal distribution" means there are three maximums in different time periods of the hourly indoor occupant values. The key difference between occupant number of university buildings and that of the general office buildings is the usage during evening period. Many occupants use buildings in the evening. Particularly, the indoor occupant number of library in the evening is similar to or even more than that during the afternoon period.
Based on the above analysis, the quadratic polynomials with 1 h time interval as the input parameter are the proper relationship with which to describe the trimodal distribution of indoor occupant number. The function form is

Lamps Usage Analysis
The lamps in the teaching building and the office building are available to be controlled by the occupants. The used lamp number was obtained by on-site survey.
As shown in the Figure 5, the regulation of the number of lamps that change with time is similar, though the number of lamps in use is different each day. In the teaching building, the number of lamps in use is escalated over time, while the number decreased slightly at lunch time and sharply at night in the office building. The usage habit varies for occupants in different buildings. So, the time-varying number cannot describe the control rule of lamps for all buildings. The relationship of lamps usage with indoor occupants should be explored.

Lamps Usage Analysis
The lamps in the teaching building and the office building are available to be controlled by the occupants. The used lamp number was obtained by on-site survey.
As shown in the Figure 5, the regulation of the number of lamps that change with time is similar, though the number of lamps in use is different each day. In the teaching building, the number of lamps in use is escalated over time, while the number decreased slightly at lunch time and sharply at night in the office building. The usage habit varies for occupants in different buildings. So, the timevarying number cannot describe the control rule of lamps for all buildings. The relationship of lamps usage with indoor occupants should be explored. Among the three case buildings, lamps installed in the library are unified switched on or off by an automatic controller. The lighting control strategy, namely, the usage rate of the installed lamps for all the operational days, is shown in Figure 6. Among the three case buildings, lamps installed in the library are unified switched on or off by an automatic controller. The lighting control strategy, namely, the usage rate of the installed lamps for all the operational days, is shown in Figure 6. The installed lighting density of the library is 7.67 W/m 2 . As shown in Figure 6 75% of the lamps will be switch on at 8:00, and this will increase to 100% at 18:00. 12% lamps remain in use for security reason at night.
Above all, for buildings in which the lamps are controlled by occupants, the in-use number is generally varying with indoor occupant number. For buildings, such as the library, in which the lamps are controlled by automatic center, the in-use number is decided by the control strategy.

Equipment Usage Analysis
The installed equipment in the teaching building and the library were listed in Tables 4 and 5, respectively. Only one computer with one projector and screen are used in an in-class room. Occupants can use laptops when self-studying. The equipment heat release when self-studying is determined by the simultaneously used laptops in the teaching building and the library.
Though the computers and laptops are the main equipment, other equipment will be used: (1) Electrical boilers are installed in hot water rooms in the teaching building. Because the machine rooms are not air-conditioned, the heat release will not be accounted into interior loads. Based on the above analysis, the trimodal distribution pattern of the occupant number is consistent with the rules of building energy consumption [37]. So, the usage pattern of electric appliances, generally lamps and equipment, is considered to have certain relationships with indoor occupants. In Section 4, the relationship of indoor occupants with other interior load disturbances is discussed after modeling the indoor occupant number in Section 4. The quantification of representative interior load can be calculated.  The installed lighting density of the library is 7.67 W/m 2 . As shown in Figure 6 75% of the lamps will be switch on at 8:00, and this will increase to 100% at 18:00. 12% lamps remain in use for security reason at night.

Indoor Occupant Number
Above all, for buildings in which the lamps are controlled by occupants, the in-use number is generally varying with indoor occupant number. For buildings, such as the library, in which the lamps are controlled by automatic center, the in-use number is decided by the control strategy.

Equipment Usage Analysis
The installed equipment in the teaching building and the library were listed in Tables 4 and 5, respectively. Only one computer with one projector and screen are used in an in-class room. Occupants can use laptops when self-studying. The equipment heat release when self-studying is determined by the simultaneously used laptops in the teaching building and the library.
Though the computers and laptops are the main equipment, other equipment will be used: (1) Electrical boilers are installed in hot water rooms in the teaching building. Because the machine rooms are not air-conditioned, the heat release will not be accounted into interior loads. Based on the above analysis, the trimodal distribution pattern of the occupant number is consistent with the rules of building energy consumption [37]. So, the usage pattern of electric appliances, generally lamps and equipment, is considered to have certain relationships with indoor occupants. In Section 4, the relationship of indoor occupants with other interior load disturbances is discussed after modeling the indoor occupant number in Section 4. The quantification of representative interior load can be calculated.

Classification of Indoor Occupants
Different occupants may cause different interior load. Based on this criteria, the indoor occupants should be categorized in case buildings: (1) For the teaching building, students taking class only use lamps and teaching projection equipment, such as computers and projectors. About 50% of lamps and a computer and projector are generally used in an in-class room, while for self-studying students, the teaching projection equipment is not allowed to be turned on. Laptops can be used. Students that come to the library to borrow and return books are the second type. The third type of occupants is the self-studying students. Personal mobile computers, namely, laptops, can be used.
Based on this classification, the occupant number was investigated for each type of occupant of the case buildings. For the teaching building, the hourly indoor occupant number of each room was investigated. For the office building, the total indoor occupant number was tested hourly, and the usage information was recorded based on building patrolling. For the library, the total indoor occupant number was investigated hourly both based on infrared counters and building patrolling. Thus, the different types of indoor occupants can be counted hourly. The average occupant numbers were analyzed in Section 4.1.2. Based on the time series of types of indoor occupants, the used appliances were analyzed in Section 4.2.

Time-Varying Indoor Occupant Number
(1) Teaching building For the teaching building, because the rooms that are in class are different during the week, the occupant number of the teaching building varies during general used period. However, the used light and equipment number is not related to the indoor occupant number if a room is in-class, so the in-class room number and the occupant number of self-studying were recorded during field investigation (shown in Figures 7 and 8 respectively). The average indoor occupant number per room during holidays is shown in Figure 9.
For the teaching building, because the rooms that are in class are different during the week, the occupant number of the teaching building varies during general used period. However, the used light and equipment number is not related to the indoor occupant number if a room is in-class, so the in-class room number and the occupant number of self-studying were recorded during field investigation (shown in Figures 7 and 8 respectively). The average indoor occupant number per room during holidays is shown in Figure 9.   As illustrated in Figures 8 and 9, the indoor occupant number can be divided into three time periods. So, the relationship of indoor occupant number with time of the case teaching building can be illustrated as   As illustrated in Figures 8 and 9, the indoor occupant number can be divided into three time periods. So, the relationship of indoor occupant number with time of the case teaching building can be illustrated as , .  As illustrated in Figures 8 and 9, the indoor occupant number can be divided into three time periods. So, the relationship of indoor occupant number with time of the case teaching building can be illustrated as n occ,cls.τ = n se,cls.τ + ∑ n inc,cls.τ = a occ τ 2 + b occ τ + c occ se,cls. × (n cls − n inc,cls ) + n inc,cls.τ × n inc,cls t ∈ 0 : 00 − 6 : 30 a m τ 2 + b m τ + c m se,cls. + 50 × n inc,cls t ∈ 7 : 30 − 12 : 30 a a τ 2 + b a τ + c a se,cls. + 50 × n inc,cls t ∈ 13 : 30 − 17 : 30 a n τ 2 + b n τ + c n se,cls. + 50 × n inc,cls t ∈ 18 : 30 − 22 : 30 (11) (2) Office building Based on the analysis of indoor occupants in the teaching building, the emphasis should be put on the time-varying indoor occupants of different types that were divided. For the office building, rooms can be classified as administration rooms, scientific research rooms, and meeting rooms. As shown in Figure 2 Only one meeting room is installed for one floor in the case building and is seldom used.
Based on the above division methods, the indoor occupant number analyzing results of the office building is shown in Figure 10. Only one meeting room is installed for one floor in the case building and is seldom used. Based on the above division methods, the indoor occupant number analyzing results of the office building is shown in Figure 10.  As shown in Figure 10, only scientific research workers use the offices during weekends and holidays. However, the occupant number in weekends is less than that of holidays, because some of the postgraduate doctoral and master students are still working during summer holidays. In addition, scientific research workers tend to work in the office building on holidays because of quiet work environment. The scientific research workers are more than the administration workers during weekdays. The time-varying schedule of administration workers is fixed during weekdays. Guests are a relatively small amount of occupants in the office building, less than 5% of the total indoor As shown in Figure 10, only scientific research workers use the offices during weekends and holidays. However, the occupant number in weekends is less than that of holidays, because some of the postgraduate doctoral and master students are still working during summer holidays. In addition, scientific research workers tend to work in the office building on holidays because of quiet work environment. The scientific research workers are more than the administration workers during weekdays. The time-varying schedule of administration workers is fixed during weekdays. Guests are a relatively small amount of occupants in the office building, less than 5% of the total indoor occupant number. So, the emphasis of indoor occupant in the office building should be put on the scientific research occupants.
Based on the above analysis, the indoor occupant number of the office building can be described as The time periods are same with the divisions of the teaching building.
(3) Library The indoor self-studying occupant number of the library is similar to that of the teaching building. The difference of total indoor occupant number counted by the infrared counters and the self-studying occupant number investigated by building patrolling is the borrowing and returning occupant number. The six book managers are not counted anymore. The time-varying occupant number during holidays and in the general used period of the library are shown in Figure 11.
The time periods are same with the divisions of the teaching building.
(3) Library The indoor self-studying occupant number of the library is similar to that of the teaching building. The difference of total indoor occupant number counted by the infrared counters and the self-studying occupant number investigated by building patrolling is the borrowing and returning occupant number. The six book managers are not counted anymore. The time-varying occupant number during holidays and in the general used period of the library are shown in Figure 11. The indoor occupant number of general used period of the library is much more than that of holidays, both the self-studying and the borrowing and returning books occupant number. The borrowing and returning books occupant number is generally fixed at about 140 during holidays and 330 during the general used period, respectively. The self-studying occupant number varies with The indoor occupant number of general used period of the library is much more than that of holidays, both the self-studying and the borrowing and returning books occupant number. The borrowing and returning books occupant number is generally fixed at about 140 during holidays and 330 during the general used period, respectively. The self-studying occupant number varies with time. The distribution pattern is consistent with the quadratic polynomials, shown in Figure 5.
Based on the above analysis, the indoor occupant number of the office building can be described as n occ,lib.τ = n se.,lib.τ + n br.,lib.τ + n ma.,lib.τ = a occ τ 2 + b occ τ + c occ se.,lib. + 140 + 6 holidays a occ τ 2 + b occ τ + c occ se.,lib. + 300 + 6 general used (13) Based on the analysis of indoor occupant number of the three case buildings, the quadratic polynomials divided by time periods are suitable to describe the number of all the types of occupants. The independent variable is time, with a time-step of 1 h. The goodness of fit R 2 is generally above 0.9, which satisfies the accuracy requirement. Constant value can be recognized as a special form of quadratic polynomial. Based on the characteristics of indoor occupant number, the occupant-oriented representative interior load can be calculated based on the relationship of lamps and equipment in use with indoor occupants.

Relationship of Lamps in Use with Indoor Occupants
The relationship between lamps usage and indoor occupants was analyzed based on occupant types: (1) Teaching building In in-class rooms, generally 50% of lamps are used because of the usage of projector and screen. In self-studying rooms, the corresponding average of used lamps and indoor occupant number is shown in Figure 12.
Based on the analysis of indoor occupant number of the three case buildings, the quadratic polynomials divided by time periods are suitable to describe the number of all the types of occupants. The independent variable is time, with a time-step of 1 h. The goodness of fit R 2 is generally above 0.9, which satisfies the accuracy requirement. Constant value can be recognized as a special form of quadratic polynomial. Based on the characteristics of indoor occupant number, the occupant-oriented representative interior load can be calculated based on the relationship of lamps and equipment in use with indoor occupants.

Relationship of Lamps in Use with Indoor Occupants
The relationship between lamps usage and indoor occupants was analyzed based on occupant types: (1) Teaching building In in-class rooms, generally 50% of lamps are used because of the usage of projector and screen. In self-studying rooms, the corresponding average of used lamps and indoor occupant number is shown in Figure 12. An increasing tendency to reach the maximum is illustrated in Figure 12. In the morning period, the number of used lamps increases before 9:30 and then stays at a certain value until 11:30. The number of used lamps is not decreased with indoor occupants during lunch time, indicating that the lamps are not turned off by leaving occupants. The number of used lamps increases again when occupants go back to the classroom in the afternoon and is kept as another certain value. The value is higher than the value in the morning period, which is generally the maximum value. The increasing step reveals the lamps control habit of indoor occupants turning on actively and tuning off passively.
(2) Office building Similar regularities can be seen from the investigation data of offices. Guests coming to the office building would not change the usage state of lamps. The key to lighting control is the workers in offices. The detailed number of lamps in use can be counted in an on-site survey. In order to quantify  An increasing tendency to reach the maximum is illustrated in Figure 12. In the morning period, the number of used lamps increases before 9:30 and then stays at a certain value until 11:30. The number of used lamps is not decreased with indoor occupants during lunch time, indicating that the lamps are not turned off by leaving occupants. The number of used lamps increases again when occupants go back to the classroom in the afternoon and is kept as another certain value. The value is higher than the value in the morning period, which is generally the maximum value. The increasing step reveals the lamps control habit of indoor occupants turning on actively and tuning off passively.
(2) Office building Similar regularities can be seen from the investigation data of offices. Guests coming to the office building would not change the usage state of lamps. The key to lighting control is the workers in offices. The detailed number of lamps in use can be counted in an on-site survey. In order to quantify the relationship between the used lamps and indoor occupants, all the measured data of hourly used lamp and indoor occupant number are correspondingly shown in Figure 13. Phase steps are clearly shown in Figures 12 and 13. The division of phases was the indoor occupant number. So, the control pattern of lighting can be described as "0-p-1" model. The detailed relationships of the teaching building and the office building are Equations (13) and (14), respectively. ,.
Because the lamps installed in the library are unified switched on or off by an automatic controller, no relationship was shown with indoor occupants.

Relationship of Equipment in Use with Indoor Occupants
The time-varying laptop number corresponding with self-studying occupants are shown in Figure 14. Phase steps are clearly shown in Figures 12 and 13. The division of phases was the indoor occupant number. So, the control pattern of lighting can be described as "0-p-1" model. The detailed relationships of the teaching building and the office building are Equations (13) and (14), respectively. n lig.,cls. =      0 n se,cls.τ = 0 g lig. · n se,cls.τ h lig. + 16 × n cls 0 < n se,cls.τ < n lim.,lig.,cls. 700 × (1 ± 10%) n se,cls.τ ≥ n lim.,lig.,cls.

Relationship of Equipment in Use with Indoor Occupants
The time-varying laptop number corresponding with self-studying occupants are shown in Figure 14. About 15% and 30% of occupants use laptops in the teaching building and the library, respectively, as illustrated in Figure 14. The number of laptops in use is generally synchronous changing with indoor occupant number. So, the relationship between indoor occupants and laptops in self-studying classrooms is linear.
As for other equipment installed in buildings, the research results in Ref. [40] were adopted, and the heat release of other equipment was considered as 10% additional to the computers and laptops. Based on the above analysis, the relationship between the number of pieces of equipment in use and indoor occupants is listed in Table 7. Table 7. Description of the relationship between equipment and indoor occupants of case buildings.

Building Equipment Type Description
Teaching building  Table 7, the equipment installed in buildings is divided into three types, namely, computers, laptops, and other. The in-use number can be linearly described by the indoor occupant number. About 15% and 30% of occupants use laptops in the teaching building and the library, respectively, as illustrated in Figure 14. The number of laptops in use is generally synchronous changing with indoor occupant number. So, the relationship between indoor occupants and laptops in self-studying classrooms is linear.
As for other equipment installed in buildings, the research results in Ref. [40] were adopted, and the heat release of other equipment was considered as 10% additional to the computers and laptops. Based on the above analysis, the relationship between the number of pieces of equipment in use and indoor occupants is listed in Table 7. Table 7. Description of the relationship between equipment and indoor occupants of case buildings.
As listed in Table 7, the equipment installed in buildings is divided into three types, namely, computers, laptops, and other. The in-use number can be linearly described by the indoor occupant number.

Maximum Interior Load Density
The design interior load should be the maximum data considering all interior load disturbances. Based on the definition of representative interior load, the basic of the interior load is the indoor occupant density. In this section, the modified design occupant density is discussed, and the representative interior load for per occupant is proposed for the case buildings.
(1) Indoor occupant density Based on the analysis in Section 4.1, the indoor occupant numbers of case buildings during holidays and general used days are different and should be considered separately.
For the teaching building, the measured maximum indoor occupant number was 600 during the general used period. The present time was 10:30-12:00 in the morning, namely, the 3rd and 4th class. The maximum data of the holidays was about 380 presented at 15:30 in the afternoon. So, the design indoor occupant densities during general used period and holidays are 0.1 and 0.06 person/m 2 correspondingly. The original design occupant density is 0.5 person/m 2 . The occupant density of in-class rooms is about 0.52 person/m 2 , which is 5 times higher than the average occupant density of the whole building. This is because of the function design of the teaching building. Teaching buildings should satisfy the demand for taking classes and self-studying at the same time. The probability of in-class for a class room was set at 50% as the maximum in the case teaching building. In addition, the actual occupant number of in-class rooms is lower than the design value. So, the actual occupied rate is much lower than the original design data.
The maximum indoor occupant numbers of the office building were 91 and 108 during the holidays and the general used period, respectively. The present time is also different. During holidays, the indoor occupant number at 15:30 in the afternoon is much more than that in the morning and evening. However, in general used days, the guests in some days might be more than other days and often occur in the morning. Hence, the maximum indoor occupant number might exist in the morning. For workers in the office building, the maximum occupant number presented is in the afternoon, around the on-duty time of 14:30-15:30. In the library, the maximum indoor occupant number of 2196 showed at 16:30 and 20:30 during the general used period. The maximum data during holidays, which is 24.81% smaller than the above data, occurred at around 10:30 and 16:30 during holidays.
Based on the above analysis, the maximum occupant number of the case buildings generally occurred in the afternoon of general used period. The measured maximum indoor occupant density of the case building was summarized and compared with original design data in Table 8. As listed in Table 8, the modified design index of indoor occupant density was 80-90% smaller than the original design data. In addition, the design data should be different for holidays and general used period. Correction factors of holidays among 0.6-0.85 should be considered during the design of university buildings.
(2) Representative interior cooling load Based on the relationships between other interior load disturbances and indoor occupant number analyzed in Section 4.2, the maximum used lamp number and computer/laptop number can be calculated for case buildings.
The heat release of appliances is transformed from electric power. For lamps, the rated power can be considered as the amount of heat release. However, for computers and laptops, the actual input power is much lower than the rated power. The distribution of input power various with the usage intensity. The Markov-Monte Carlo method of calculating the input power of computers in Ref. [40] was adopted. The time-varying input power was measured for computers and laptops used in case buildings. The calculated steady input power of computers is listed in Table 9. The main activity of occupants in the case buildings is sit and walk slightly. The heat release was considered as 70 W/person [20].
Based on the above analysis, the heat release per occupant can be calculated. So, the representative interior loads per occupant are 196.43, 329.94, and 402.58 W/person, respectively, in the teaching building, the office building, and the library.

Time-Varying Occupant Oriented Representative Interior Load
The time-varying indoor occupant number of the case buildings is described as Equations (10)- (12). The results of the undetermined coefficients through data fitting are listed in Table 10. Based on the average time-varying data of indoor occupant number and the representative interior load per occupant, the time-varying interior cooling load can be calculated. The results are shown in Figure 15.

Modified Cooling Load Results Validation and Discussion
This section illustrated the validation and assurance rate of the modified design interior cooling load. Based on the building information in Section 2.4.1, the simulation models of the case buildings based on DesignBuilder tool are shown in Figures 16-18, respectively.

Modified Cooling Load Results Validation and Discussion
This section illustrated the validation and assurance rate of the modified design interior cooling load. Based on the building information in Section 2.4.1, the simulation models of the case buildings based on DesignBuilder tool are shown in Figures 16-18 Based on the average time-varying data of indoor occupant number and the representative interior load per occupant, the time-varying interior cooling load can be calculated. The results are shown in Figure 15.

Modified Cooling Load Results Validation and Discussion
This section illustrated the validation and assurance rate of the modified design interior cooling load. Based on the building information in Section 2.4.1, the simulation models of the case buildings based on DesignBuilder tool are shown in Figures 16-18, respectively.

Modified Cooling Load Results Validation and Discussion
This section illustrated the validation and assurance rate of the modified design interior cooling load. Based on the building information in Section 2.4.1, the simulation models of the case buildings based on DesignBuilder tool are shown in Figures 16-18, respectively.  The time-varying interior loads for the three buildings were input in the form of schedule. The above-calculated time series of occupant-oriented representative interior cooling load was set for main functional building, for example, classrooms for the teaching building and offices for the office building. The occupancy rate and appliance density were set as 0 for other spaces, such as washing room, corridor, etc. The fresh air was controlled by minimum requirement, namely, 8 L/(s·person) for the teaching building and library and 10 L/(s·person) for the office building [20]. The comparison of the simulated results and measured cooling loadis shown in Figures 19-21, respectively.  The time-varying interior loads for the three buildings were input in the form of schedule. The above-calculated time series of occupant-oriented representative interior cooling load was set for main functional building, for example, classrooms for the teaching building and offices for the office building. The occupancy rate and appliance density were set as 0 for other spaces, such as washing room, corridor, etc. The fresh air was controlled by minimum requirement, namely, 8 L/(s·person) for the teaching building and library and 10 L/(s·person) for the office building [20]. The comparison of the simulated results and measured cooling loadis shown in Figures 19-21, respectively. The time-varying interior loads for the three buildings were input in the form of schedule. The above-calculated time series of occupant-oriented representative interior cooling load was set for main functional building, for example, classrooms for the teaching building and offices for the office building. The occupancy rate and appliance density were set as 0 for other spaces, such as washing room, corridor, etc. The fresh air was controlled by minimum requirement, namely, 8 L/(s·person) for the teaching building and library and 10 L/(s·person) for the office building [20]. The comparison of the simulated results and measured cooling loadis shown in Figures 19-21, respectively.  As shown in Figures 19a, 20a, and 21a, the simulated cooling data has a good consistency with measured data. The average error rates are 7.37%, 1.70%, and 9.54%, respectively, for the teaching building, the office building, and the library. This means the accuracy satisfies the requirement of more than 90%. The errors lie in the following aspects. Firstly, the indoor air temperature changes with time at practice. However, the design indoor air temperature should be a certain value. Secondly, the sun-shading is not considered during simulating, which may cause relatively high error in buildings with large windows. So, the error rate of the library is higher than other buildings. Comparing the error rates of case buildings, it can be inferred that the proposed method is more accurate for buildings with relatively fixed usage habits. In the office building, the workers are permanent over a long time period, at least one or two years. So, the variations in occupant behaviors and requirements are small. However, the occupants change every day, even every hour. Occupant behavior might be extremely different when using lamps and equipment. Though the cluster effect can be summarized, errors are inevitable. Validation is necessary to estimate the inevitability. Figures  19b, 20b, and 21b show the consistency check results. Only 5,4 and 7 out of 220 sets of data are out of range for the teaching building, the office building, and the library, respectively. This indicates that the simulated cooling loads are very close, at least 92.73%, to the actual cooling load when taking the indoor occupants and the occupant-oriented representative cooling load into account.
The design cooling load should be the maximum hourly cooling load under design conditions. Based on the commonly used design cooling load calculation method of cooling load coefficient method in Ref. [19,20], the modified cooling loads are listed in Table 11. In order to compare the modified cooling load indexes with the recommended values in relative standards [20], the cooling load intensity (CLI, W/m 2 ) was calculated by Based on the percentage of interior load in total design cooling load, the recommended interior cooling load can be calculated and is listed in Table 11. The over-estimating rates of interior cooling load on the basis of recommended data are at least more than 50%. In the teaching building, the overestimating rate is even 5-7 times greater. In addition, the cooling capacity of installed WSHPs in the zone energy station is about 1.61 times higher than modified cooling load, indicating the design problems of oversizing chillers. As shown in Figures 19-21a, the simulated cooling data has a good consistency with measured data. The average error rates are 7.37%, 1.70%, and 9.54%, respectively, for the teaching building, the office building, and the library. This means the accuracy satisfies the requirement of more than 90%. The errors lie in the following aspects. Firstly, the indoor air temperature changes with time at practice. However, the design indoor air temperature should be a certain value. Secondly, the sun-shading is not considered during simulating, which may cause relatively high error in buildings with large windows. So, the error rate of the library is higher than other buildings. Comparing the error rates of case buildings, it can be inferred that the proposed method is more accurate for buildings with relatively fixed usage habits. In the office building, the workers are permanent over a long time period, at least one or two years. So, the variations in occupant behaviors and requirements are small. However, the occupants change every day, even every hour. Occupant behavior might be extremely different when using lamps and equipment. Though the cluster effect can be summarized, errors are inevitable. Validation is necessary to estimate the inevitability. Figures 19-21b, show the consistency check results. Only 5,4 and 7 out of 220 sets of data are out of range for the teaching building, the office building, and the library, respectively. This indicates that the simulated cooling loads are very close, at least 92.73%, to the actual cooling load when taking the indoor occupants and the occupant-oriented representative cooling load into account.
The design cooling load should be the maximum hourly cooling load under design conditions. Based on the commonly used design cooling load calculation method of cooling load coefficient method in Ref. [19,20], the modified cooling loads are listed in Table 11. In order to compare the modified cooling load indexes with the recommended values in relative standards [20], the cooling load intensity (CLI, W/m 2 ) was calculated by Based on the percentage of interior load in total design cooling load, the recommended interior cooling load can be calculated and is listed in Table 11. The over-estimating rates of interior cooling load on the basis of recommended data are at least more than 50%. In the teaching building, the over-estimating rate is even 5-7 times greater. In addition, the cooling capacity of installed WSHPs in the zone energy station is about 1.61 times higher than modified cooling load, indicating the design problems of oversizing chillers. In this research, the teaching building, office building, and library were taken as examples to show the application of the proposed method. Actually, the proposed occupant-oriented representative interior load calculation method is suitable for all buildings in which occupants are able to control the energy consumption appliances. The method provides a solution to the significant problem of building usage conditions that should be considered not only in building load design but also in energy system management. For the buildings with fixed control patterns of appliances, such as canteens, the occupant-oriented concept of this paper is meaningful to optimize the management strategies of energy systems.

Conclusions
An occupant-oriented interior cooling load calculation method was proposed in this paper to improve the accuracy of the building interior cooling load design. The nature of the interior cooling load disturbances was explored. The definition of representative interior load was proposed, quantified, and verified by the application of the building cooling load calculation. Typical university buildings were taken as special cases to obtain building usage data, including the time-varying number of indoor occupants, lamps, and equipment in use. The survey covered both generally used days and holidays, weekdays, and weekends, which is sufficient to support the usage analysis of university buildings. The following conclusions can be drawn.
(1) The proposed occupant-oriented representative interior load is a combination of all interior disturbances. Occupants are the core of interior cooling loads. Occupants should be categorized based on their equipment usage. Through quantitative analysis, it was observed that the maximum representative interior loads were 196.43, 329.94, and 402.58 W/person, respectively, for the case buildings, indicating the different natures of occupants in various building types. (2) The time-varying indoor occupant number followed a trimodal distribution of university buildings, which could be described by quadratic polynomials with the time interval of 1 h. The used lamps and equipment were in exponential and linear relationships with the indoor occupants, respectively. Considering the maximum indoor occupant number, the design interior cooling load of the case buildings was modified as 17. 36, 9.96, and 18.12 W/m 2 , respectively, counting for 50.80%, 17.12%, and 30.14% of the total cooling loads. The over-estimating rate of the interior cooling loads resulted in the oversized chillers, which were proved to be more than 50%.
(3) The proposed representative interior load calculation method can easily be applied in the building load simulation by inputting the time-varying schedules. A consistency rate of more than 90% has been achieved in the case buildings. The feasibility and accuracy can be proved to be meaningful with regard to the proposed occupant-oriented interior cooling load design method.

Patents
A prediction method of office energy consumption (CN2014105880898).
Author Contributions: Z.W. designed the experiments, analyzed the data, and wrote the paper, Y.D. conceived and improved the paper; H.D. and F.Y. performed the experiments; N.Z. conducted the investigation.