Research on Central Air Conditioning Systems and an Intelligent Prediction Model of Building Energy Load

Abstract

The central air conditioning system provides city dwellers with an efficient and comfortable environment. Meanwhile, coinciding with their use, the building electricity load is increased, as central air conditioners consume a lot of electricity. It has become necessary to control central air conditioners for storage and to analyze the energy saving optimization of central air conditioner operation. This study investigates the energy consumption background of central air conditioning systems, and proposes an intelligent load prediction method. With a back propagation (BP) neural network, we use the data collected in the actual project to build the cooling load prediction model for central air conditioning. The network model is also trained using the Levenberg–Marquardt (LM) algorithm, and the established model is trained, tested, and predicted by importing a portion of the sample data, which is filtered by preprocessing. The experimental results show that most of the data errors for training, testing, and prediction are within 10%, indicating that the accuracy achievable by the model can meet the practical requirements, and can be used in real engineering projects.

1. Introduction

With the development of the economy and the improvement in living standards, the use of air conditioning is becoming more and more widespread, followed by the continuous increase in power consumption [1,2]. The electricity consumption of air conditioning in first-tier cities has been reported to account for more than 25% of the peak electricity consumption [3]. Central air conditioning is almost indispensable in public places. The central air conditioning system provides efficient work and comfortable living environments for urban residents. However, then comes the problem of power consumption, which is increasingly prominent in buildings [4]. The energy consumption of buildings consists of about 20–40% of the world’s total energy consumption, and the energy consumption of central air conditioning systems accounts for about 40% of the total energy consumption of buildings [5]. Central air conditioning systems in commercial, industrial, and residential buildings in China’s largest cities consume 35% of the total energy consumed in these buildings. It has become necessary to study the simulation of system energy consumption and the intelligent prediction model of building load of central air conditioning, to control the cooling storage of central air conditioning, and to analyze the energy saving optimization of central air conditioning operation [6,7,8].

The central air conditioning system is complicated and has many components. The energy saving operation strategy is not mature, which leads to the serious waste of energy consumption in the central air conditioning system. Much effort has been devoted to designing new air conditioning systems or developing advanced control strategies to reduce energy consumption while maintaining acceptable thermal comfort and indoor air quality (IAQ) [9].

At present, the design load and operation load of most central air conditioning systems do not match. Let us take the household air conditioning system as an example. The actual operation efficiency of the air conditioning system is very low. Most of the time, the air conditioner is operating at 60% of its designed capacity, which is more than 85% over the course of a year. For some large buildings with central air conditioning systems, with the seasonal climate throughout the year, personnel flow, and indoor heat source constantly fluctuating, air conditioning cooling load is also constantly changing. Therefore, most of the time their load rate is low, resulting in the power consumption of the central air conditioning cold storage system accounting for more than 40% of the total power consumption. Due to the lack of effective management measures in energy saving operations, the low performance of central air conditioning energy storage systems often causes serious power waste, but also difficulty in ensuring indoor comfort level. Therefore, it is of great significance to study how to realize the energy saving optimization of the central air conditioning energy storage system [10,11,12].

Many scholars at home and abroad have been devoted to the energy saving research of air conditioning systems. The evaluation of the impact of cooling load prediction accuracy by Wang Lan et al. showed that the higher the prediction accuracy, the more redundant energy consumption can be reduced [13]. Wang et al. investigated the numerical simulation of air distribution of central air conditioning in a tall atrium using CFD technology to simulate the air distribution in the atrium of the large hotel building. The results verified the effectiveness and reliability of the simulated air distribution in large, spacious buildings [14]. Yan et al. proposed an adaptive indoor overheating estimation model based on artificial neural networks to accurately predict the opening behavior of air conditioning [15]. The experimental results showed that the method can be applied to air conditioning control, indoor thermal environment evaluation, and building-related energy saving. Powell et al. modeled the complexity characteristics of large-scale energy systems, and used recursive neural networks to accurately predict the hourly load capacity of regional energy systems 24 h in advance [16]. Zhao and Shan proposed a load forecast fuzzy (LFF) control strategy [17]. They used the predicted load based of the support vector machine (SVM) method as the input parameter of the fuzzy controller, adjusted the heating, ventilation, and air conditioning (HVAC) system in advance, according to the predicted cooling load demand, and carried out feedforward fuzzy control on the HVAC system. The established simulation platform verifies the superiority of the proposed control strategy. Jiao and Xu proposed a method to optimize the power consumption analysis of central air conditioning operation under air conditioning storage control [4]. They used an improved ant colony algorithm to control the power consumption of the central air conditioning operation under central air conditioning system control. The results of the study showed that the method is effective at saving power, and has certain other advantages. Wang et al. proposed a data-mining-powered event-driven optimal control (EDOC) for improving HVAC operation efficiency [18]. The approach can be used to guide the optimal control of building HVAC systems, and is easy for engineers to understand and operate. Aiming at the problems of extensive management and energy waste in the operation of shopping malls, Jing et al. proposed a diagnostic model of shopping mall energy saving based on an improved particle swarm optimization–support vector machine (PSO-SVM) neural network to provide reference for building energy saving management and operation [19]. Xu et al. used Brown’s quadratic polynomial exponential smoothing forecasting method to build a dynamic forecasting model capable of predicting end device loads in real time [20]. The prediction model has the accuracy and reasonableness of dynamic prediction. Compared with the prediction model and control strategy based on the load on the cold source side of the central air conditioning, this method does not suffer from the defects of load concentration and lag effect, or the randomness and uncertainty of the load variation of the air conditioning system. Barone et al. developed a dynamic simulation tool for the heat load/cooling load of standard and retrofit trains, and performed a dynamic evaluation, considering several energy saving measures. This approach brought significant benefits in terms of energy savings, CO₂ emission avoidance, and comfort [21].

In recent years, the application of intelligent algorithms in decentralized air conditioning systems has gradually become a research hotspot. Li et al. used time delay neural network (TDNN) and Elman neural network (ENN) method prediction methods to provide online modeling for indoor temperature hysteresis characteristics, and the proposed hybrid algorithm has strong application value [22]. Chou et al. proposed a linear auto-regressive integrated motion-averaging model and a nonlinear nature-inspired prediction model based on meta-heuristic optimization. They set this algorithm to predict the 1-day electricity consumption of a distributed air conditioning system. The results of the study showed that the predicted air conditioning electricity consumption and the actual electricity consumption were in good agreement [23]. Yao and Shekhar studied, in detail, and improved the application of model predictive control algorithms in decentralized air conditioning systems. They elucidated the various design parameters that ultimately affect the performance of MPC, and provided a reference for researchers [24].

After careful study of the relevant literature mentioned above, we choose the BP neural network as the modeling algorithm for the load prediction model in this study. In Section 2, we briefly describe the central air conditioning system and determine the instantaneous cooling capacity of the cooling load. The load forecasting model is presented in Section 3. Section 4 details the main contribution of this study. We first show the per-minute data for the actual third-party engineering collection samples. Then, the data are filtered to change the minute-by-minute data into hourly data, and to exclude the abnormal collection data. In the experiments, we perform 24 h ahead and 1 h ahead load prediction modeling, respectively. The accuracy of the two prediction methods is compared through the steps of training, testing, and prediction. Section 5 summarizes the work conducted throughout the study.

2. The Central Air Conditioning System

2.1. The Overview of the Central Air Conditioning System

In a central air conditioning system, the refrigerant transfers the cold air to the chilled water, which is circulated through the cooling water and brought to the air conditioning terminal equipment [25]. The air conditioning terminal equipment transfers the cooling capacity to the indoor environment through heat exchange, and absorbs the heat from the indoor environment and transfers the heat to the chiller through the circulation of chilled water. The chiller, through the evaporator, transfers heat to the refrigerant, which, through circulation, transfers heat to the condenser. The condenser exerts heat and discharges it to the cooling water system. The cooling water transfers the heat to the cooling tower, which exhausts the heat to the atmosphere. A schematic diagram of the working principle of a central air conditioning system is shown in Figure 1.

The central air conditioning refrigeration system can be divided into two main categories. One is the direct refrigeration system, and the other is the indirect refrigeration system. The direct refrigeration system has only one circuit, named the refrigerant circuit, while the indirect refrigeration system contains at least two circuits, named the refrigerant and the refrigerant carrier. In a direct refrigeration system, the evaporator is used directly for cooling the ambient air, while in the indirect refrigeration system, the refrigerant first cools the carrier refrigerant, and then travels through the carrier refrigerant to cool the air. Normally, the refrigerant carrier is the chilled water. The coolant is the cooling water. Large central air conditioning systems are indirect refrigeration systems. For the convenience of the narrative, chilled water is used instead of refrigerant carrier, and cooling water instead of coolant, in the latter.

The central air conditioning system includes the air system, the water system, and the heat and cold source system, of which the water system is the main energy consumption system, consuming more than half of the total energy consumption. Therefore, this study focuses on the water system in central air conditioning systems.

2.2. The Water System

The water system is composed of two parts. One is the chilled water system and the other is the cooling water system. Research on chilled water system energy saving strategies is now relatively mature. By changing the flow rate of the chilled water system and controlling each piece of equipment to operate at the lowest power while meeting the load demand, a reduction in the system’s energy consumption is achieved. Currently, central air conditioning systems are designed for ideal full load operation. However, in actual operation, if various internal and external factors are taken into account, the chances that the actual operating conditions will match the design operating conditions are extremely low. We deduce from this that a large number of devices are not operating at full load most of the time. This therefore results in a waste of power. When it comes to the water system, only 20–30% of central air conditioning water systems operate at full load, while partial load operation accounts for about 70–80% of cases. Therefore, it is very important to realize how to effectively reduce energy consumption and optimize energy saving control under partial load in water systems.

The cooling water system, as an important part of the central air conditioning system, is controlled in a way that has a significant impact on the total energy consumption of the central air conditioning system. Therefore, a reasonable cooling water system control method is important for the energy saving operation of central air conditioning systems. The control schemes for water systems can be divided into two types: constant flow control and variable flow control. When the water system operates at a fixed flow rate, all equipment operates at the conditions set at the beginning, without any optimization control equipment. In practice, the three-way valve is often used to change the amount of water passing through the metered cooler. This method is simple to operate and stable in operation. However, it also has obvious disadvantages. The system water volume is determined based on the maximum load. During the vast majority of the time, the water supply is greater than the required amount of water. Therefore, the pump energy loss is still relatively high. Energy saving optimization of variable flow systems is more in line with the current trend. When a central air conditioning water system transfers heat, chilled water and cooling water are isolated from each other. Chilled water transfers the heat from the user’s end to the chiller, and cooling water transfers this heat from the chiller to the outdoor ambient atmosphere. As shown in the Figure 2 and Figure 3, the transfer of cold air and heat are equal in size and opposite in direction.

The heat transferred by the cooling water is greater than the heat removed by the chilled water from the room, and the difference between the two is the heat generated when the chiller performs its function. Figure 4 shows a line graph based on some of the data collected by a third party, from which the principle can be verified in a clear manner.

3. Load Forecasting Models

3.1. The Overview of Common Forecasting Models

The change in air conditioning load is a typical nonlinear change with stochastic characteristics, such as dynamic, time-varying, multi-disturbance, and uncertainty [26]. Air conditioning loads are also affected by operating hours, system type, weather conditions, and other factors [27]. Therefore, it is very difficult to accurately analyze the process of load variation. To achieve predictive control of a central air conditioning system, we first need an accurate forecast of the cooling load for each hour of the following day. Secondly, the real-time load of the central air conditioning system can be more precisely regulated if the time-by-time cooling load at the next moment can be accurately predicted. It is still expected to achieve more than 90% accuracy through the established model, which can basically eliminate the blindness and hysteresis of chilled water variable flow control.

The widely used modeling and analysis methods include regression analysis, time series analysis, support vector machines, and artificial neural networks. When carrying out load forecasting, the operational characteristics of specific projects and the standards to be achieved are different, and various forecasting methods have their own characteristics; thus, the choice of forecasting methods needs to be focused and traded off.

3.1.1. Regression Analysis

The regression equation between the predicted variable and its various influencing variables is established by analyzing a large amount of data on the various influencing variables related to the predicted variable, i.e., establishing a regression prediction model. It is suitable for medium- and short-term model forecasting [28]. When using regression analysis to build a central air conditioning cooling load prediction model, a large amount of data on the cooling load and its influencing variables monitored by the monitoring system is required to build the prediction model, as follows:

load = f (a₁, a₂, a₃, …, a_n)

(1)

where load is a variable that represents the cooling load. a₁, a₂, a₃, a_n denote the various variables affecting the cooling load, respectively. These variables may be deterministic or stochastic. f represents the mapping relationship between each variable and the cooling load. This analysis method is simple and clear in form and fast in prediction. The disadvantages are high workload, low accuracy, and poor generality, and the robustness is poor when there is a disturbance [29].

3.1.2. Time Series Analysis

The time series analysis algorithm is based on a large amount of historical data, and finds the change pattern of the predicted variable from a large amount of historical data by comparing the similarity of future and past time series. It can be either a smooth time series or a non-smooth time series [30]. This algorithm does not know how the variable of interest affects the variable being predicted until the prediction is made, and predicts the variable being affected at future moments only from the historical data monitored by the system. Time series algorithms can be used when performing cooling load forecasting. The application requires that the cooling load data be arranged in a time series. The advantages of this analysis method are good model portability and simple modeling. The disadvantage is that it cannot make full use of cooling load influencing factors, and it is only applicable to short-term prediction with uniform cooling load variation [31].

3.1.3. Support Vector Machine

The support vector machine algorithm is based on the VC dimensional theory of statistical learning theory and the principle of structural risk minimization to find the best balance between the complexity of the model built and its learning capability using limited sample information [32]. This algorithm differs from the traditional statistical algorithm in that it does not require the use of probability theory and the law of large numbers, and can be applied to other machine learning processes, such as function fitting. Since support vector machine modeling can be performed using a small amount of sample data, and the algorithm possesses strong robustness, support vector machines have significant advantages in solving nonlinear, small-sample, and high-dimensional pattern recognition. X. Xiao et al. presented a novel machine learning framework for quantitatively analyzing the correlated relationship between the process parameters and deposition shape, thus providing an optimal process parameter selection method to control the final deposition geometry; these results practical research implications for the support vector machine [33].

3.1.4. Artificial Neural Networks

Currently, artificial neural network algorithms are the most widely used algorithms when performing load forecasting. Artificial neural networks have some advantages, as follows. First, it has a large number of non-structural and inaccurate laws with self-adaptive capabilities. Second, it can perform information memorization, autonomous learning, knowledge reasoning, and optimal computation. Third, it does not need to build accurate mathematical models. Therefore, compared with other algorithms, this method is simpler in both modeling and computing processes [34]. Of course, it also suffers from difficulties, for example, in determining the network structure, overlearning, dimensional catastrophe, local minima, etc. [35]. Despite these disadvantages, when accurate and convenient load prediction models are needed, neural network methods are often used. Compared with the traditional neural network algorithm, the BP neural network has a stronger self-learning ability, self-adaptation ability, generalization ability, and fault tolerance ability; therefore, after careful consideration, we choose the BP neural network for the prediction of air conditioning cooling load.

3.2. BP Neural Network

3.2.1. An Overview of the BP Neural Network

The BP neural network, the most used neural network algorithm among artificial neural networks, mainly consists of an input layer, output layer, and several hidden layers. Each layer has several nodes, and each node represents a neuron [36]. A typical BP neural network structure with a single hidden layer is shown in Figure 5.

3.2.2. BP Neural Network Construction

Modeling with BP neural networks starts with determining the number of layers in each of the input, hidden, and output layers of the neural network structure, the number of neurons in each layer, and the excitation function used in each layer. The main steps are as follows.

• Selection of input parameters:

In the actual operating conditions of the central air conditioning system, there are many factors that can have an impact on the cooling load, which can be broadly divided into internal disturbances in the air conditioning area (such as indoor personnel flow, electrical loads, etc.) and external disturbances in the air conditioning area (such as outdoor dry and wet bulb temperature and humidity, solar radiation, etc.). As far as the theoretical level is concerned, any factor affecting the cooling load should be used as an input parameter to the neural network, because the more input parameters, the higher the generalization ability of the neural network, the higher the prediction accuracy, and the smaller the prediction error. However, the computational complexity also increases and the computation time is greatly extended. In practical engineering, many influencing variables are difficult to collect, measure, and record directly; therefore, the number of input parameters to the neural network needs to be traded off. Due to the limited availability of collected data and workload considerations, we select the load of the previous hour of the same day and the load of the same moment of the previous day as input parameters.

2.

Selection of output parameters:

The task of this study is to perform a 24 h advance load forecast and a 1 h advance load forecast. Therefore, the output parameters of this neural network prediction model are chosen to be the hourly load at each moment t.

3.

Neural network structure:

After determining the input and output of the neural network, the next step is to specify how many hidden layers to set and the number of neurons in each layer, which will have a large impact on the network accuracy. Number of hidden layers = 1: any function that “contains a continuous mapping from one finite space to another” can be fitted. Number of hidden layers = 2: with the appropriate activation function, any decision boundary with any precision can be represented, and any smooth map with any precision can be fitted. Number of hidden layers >2: extra hidden layers can learn complex descriptions (some form of automatic feature engineering). In this study, combining precision and speed requirements, we choose a double hidden layer. The number of neurons in each hidden layer is usually determined by first roughly delineating the range according to the empirical Equation (2), and then applying the trial-and-error method to determine the number of each layer.

$$v\approx \sqrt{a+b}$$

(2)

where v represents the number of neurons in the hidden layer, a represents the number of neurons in the input layer, and b represents the number of neurons in the output layer. Considering the neural network error and generalization ability, after several rounds of training and testing, we find that the neural network operates best when the hidden layer nodes are 10 and 20, respectively.

4.

The normalization of data:

Before determining the inputs and outputs and importing the data into MATLAB BP Neural Network toolbox for training, the principle of normalization of the data needs to be known. The actual operational data trained with neural network models have multiple categories, and different categories have different magnitudes. Due to the large variation in the range of the collected data, if the model is trained directly without normalizing the data, it may produce abnormal data with increased disparity from other sample data. This not only prolongs the model learning training time, but may also lead to the failure of the neural network to converge. As a result, in order to obtain the training results quickly, the collected sample data should first be normalized. Since the data used are all positive values, the data normalization process of this study uses a linear transformation method. It processes the data into values between 0 and 1, as shown in Equation (3).

$$x_i=\left|\frac{x_{di}-x_{d\min }}{x_{d\max }-x_{d\min }}\right|$$

(3)

where $x_i$ denotes the input value after normalization, $x_{di}$ denotes the initial input data, $x_{d\min }$ denotes the minimum value in the initial input data, and $x_{d\max }$ denotes the maximum value in the initial input data.

5.

The inverse normalization of data:

When the initial data are normalized, the values are between 0 and 1. However, the output used for neural network model training is also in the range of 0 to 1, and the physical meaning of the expression cannot be seen. Therefore, after completing the training, it is also necessary to inverse normalize the obtained data again to recover the original physical meaning of the data, as shown in Equation (4):

$$y_i=y_{d\min }+o_i\left(y_{d\max }-y_{d\min }\right)$$

(4)

where $y_i$ denotes the predicted output value after inverse normalization, $y_{d\min }$ and $y_{d\max }$ denote the minimum and maximum values of the initial measured output value without normalization, respectively, and $o_i$ denotes the predicted output value after normalization. Finally, when choosing the training algorithm for the improved neural network, the L–M algorithm is selected because of the advantages of fast convergence and low network error. Therefore, the L–M algorithm is chosen as the training algorithm of the improved neural network.

In summary, the number of neurons in the input layer selected for this study is eight, which are the outdoor dry and wet bulb temperature humidity at moment t, moment t − 1, and moment t − 24, and the cooling load of the central air conditioning system at moment t − 1 and moment t − 24. The number of hidden layers is two. The number of output layers is one, which is the cooling load at moment t.

4. Case Study: The Training, Testing, and Prediction of the Model

4.1. Data Acquisition and Preprocessing

The sample data were collected from 1 August 2020 0:00 to 31 August 2020 23:59, with 45 parameters. These are calorimeter—instantaneous cooling capacity of chilling side (kW), total power consumption of system (kW), total power of chiller (kW), current integrated energy efficiency ratio (EER) of system, instantaneous cop of chiller, total power consumption of system (kWh), calorimeter—total cooling capacity of chilling side (kWh), calorimeter—instantaneous cooling capacity of cooling side (kW), calorimeter—total cooling capacity of cooling side (kWh), total cooling pipe supply water temperature (°C), cooling main return water temperature (°C), heat meter—cooling main instantaneous flow rate (m³/h), cooling main water supply temperature (°C), cooling main return water temperature (°C), heat meter—cooling main instantaneous flow rate (m³/h), total load/mainframe current percentage (%) of unit 1, total load/mainframe current percentage (%) of unit 2, power consumption of No. 1 cooling water pump (kW), power consumption of No. 3 cooling water pump (kW), total power consumption of No. 1 cooling water pump (kWh), total power consumption of No. 2 cooling water pump (kWh), total power consumption of No. 3 cooling water pump (kWh), power consumption of No. 1 cooling tower fan (kWh), power consumption of No. 2 cooling tower fan (kWh), power consumption of No. 1 cooling tower fan (kW), power consumption of No. 2 cooling tower fan. The units for these parameters are power consumption (kW), outdoor temperature (°C), outdoor humidity (%). Some of the data for these parameters are shown in Figure 6.

We collected data every minute. Each parameter has more than 44,000 pieces of data. Taking the instantaneous cooling capacity on 1 August 2020 as an example, as shown in Figure 7, it can be seen that the central air conditioning system in the Military Games Village starts at 6:00 a.m. and shuts down at 21:00 p.m.

After repeated verification, the central air conditioner was started at 6:00 and turned off at 21:00 for the remaining 30 days. Due to the length of the article, we only show one example, on 1 August 2020, as shown in Figure 8.

Since we aim to achieve hourly load forecasting, we perform an initial screening of the collected sample data. Considering that outside the time period of 6:00 to 21:00, the central air conditioners are off, we only perform the initial screening within this time period. It should be noted that since the neurons at the input have outdoor dry and wet bulb temperature, humidity, and cooling load eigenvalues corresponding to the t − 24 moment, we filter out the data from 2 August 2020 to ensure that these eigenvalues could be collected.

While preprocessing the data, we found the following abnormal data.

• The instantaneous cooling capacity at 19:00 on 3 August 2020 was 0, while the instantaneous cooling capacity at 18:59 was 551.5 kw; thus, the data collected at 18:59 were used as the collection data at 19:00.
• The instantaneous cooling capacity at 20:00 on 3 August 2020 was 0, while at 20:01 it was 540.7 kw; thus, the data collected at 20:01 were used as the collection data at 20:00.
• The instantaneous cooling capacity at 17:00 on 9 August 2020 was 0, while the instantaneous cooling capacity at 17:01 was 550.7 kw; thus, the data collected at 17:01 were used as the collection data at 17:00.
• The instantaneous cooling capacity at 18:00 on 9 August 2020 was 0, while at 18:01 it was 557.1 kw; thus, the data collected at 18:01 were used as the collection data at 18:00.
• The instantaneous cooling capacity at 21:00 on 9 August 2020 was 0, while at 21:01 it was 35.3 kw; thus, the data collected at 21:01 were used as the collection data at 21:00.
• The instantaneous cooling data collected on 12 August 2020 were all 0 from 09:00 to 21:00. We speculate that there was a problem with the collection process, resulting in no data being collected.

Therefore, the data from 12 August 2020 could not be incorporated into the algorithm for training and prediction, and thus, we could not satisfy the initial intention to include all data from 2 August 2020 to 31 August 2020 in the algorithm. As a result, we divided the dataset into two groups. The data collected from 2 August 2020 to 11 August 2020 were divided into one group, and the data collected from 13 August 2020 to 31 August 2020 were divided into another group. Since the latter data were collected for a longer period of time and the data sample was larger, we chose this dataset as the learning target. Additionally, considering that the BP neural network algorithm used in this study has multiple neuron inputs for the data corresponding to the moment t − 24, we modified the start time to 14 August 2020. Figure 9 shows the data collected on 14 August 2020 after preprocessing. Figure 10 and Figure 11 show a graph of the hourly cooling load before and after pretreatment, respectively, for the above sample.

In the experiments, two load predictions were performed, which were predicting the next day’s cooling load 24 h in advance and predicting the next hour’s cooling load 1 h in advance. We compared the results of these two predictions.

4.2. Forecast 24 Hours in Advance

Since the load is predicted 24 h in advance, any data related to the t − 1 moment during the preprocessing process are discarded. Therefore, the number of neurons in the input layer of this BP neural network is five, and the number of neurons in the output layer is one. The cooling load at the moment t is shown in Figure 12.

The dataset to be used for the 24 h advance forecast is in the form of an Excel spreadsheet, and includes 16 × 6 × 18 = 1728 pieces of data. The input layer includes 16 × 5 × 18 = 1440 pieces of data, and the output layer contains 16 × 1 × 18 = 288 pieces of data.

4.2.1. Division of Training Set and Test Set

The training set accounts for about 70% of the total samples for the data imported using the BP neural network. We select the hourly data from 14 August 2020 to 27 August 2020 as the training set, and save this part of the data in a separate table as “training set.xlsx”. We select the hourly data from 28 August 2020 to 30 August 2020 as the test set, and save this part of the data in a separate table as “test set.xlsx”. We save the hourly data for the last day, 31 August 2020, as the forecast input in the table, entitled “input sample.xlsx”.

We input the training set and test set into MATLAB. After training and testing, we obtain the best-fit results. Then, inputting the hourly data of 31 August 2020, we naturally output the hourly cooling load forecast data for this day. Subsequently, the predicted hourly cooling load data are compared with the actual tested hourly cooling load data. The structure diagram of BP neural network algorithm is shown in Figure 13. The data-fitted images of the training results are shown in Figure 14, Figure 15 and Figure 16.

As shown in Figure 14, the blue line indicates the actual measured value of the test sample, and the red line indicates the predicted value of the test sample. From the figure, it can be seen that after several training sessions, the test data have a good fit of 91%.

As shown in Figure 15, the blue line indicates the mean square error of the training dataset with the number of training generations, and the green line indicates the mean square error of the validation dataset with the number of training generations. We can see that the mean square error is already smoothly below 10⁻², and reaches 0.002 when the training reaches the fifth generation.

The gradient parameter curve indicates the gradient change in the error surface, and the parameter mu indicates the adjustment range of the weight error. As can be seen in Figure 16, the error gradient decreases as the number of training generations increases, reaching 0.00096 at the eleventh generation. However, the weight error reaches 10⁻⁵, and training is stopped after the error reaches the initially set adjustment range.

Figure 17 depicts the tracking of the output of the load prediction network model relative to the target output. The blue line shows the tracking of the training set, the green line indicates the trace of the validation set, and the red line indicates the trace of the test set and the black line shows the overall tracking. It can be clearly seen that for the overall data, the linear correlation between the prediction model output and the actual measurements is 0.94, which indicates a high degree of linear correlation.

Therefore, by combining the visualization results of the above data, it can be tentatively determined that the output of our established BP neural network model can track the target well. The next step is to save and export the results, write, and run the program to visualize the training, test, and prediction results separately, and analyze the training set, test set, and hourly load prediction data for the whole day of 31 August 2020, one by one.

4.2.2. The Analysis of the Training Set

By writing the code for the training set predicted 1 h in advance, the MATLAB program was ran to generate a graph of the fitting results for the training set, and analysis of the absolute and relative errors of the training set fitting was performed.

In Figure 18, the blue line indicates the actual measurements of the training set and the red line indicates the predicted values of the training set. As can be seen from the figure, the tracking fit between the predicted output and the actual measurements achieves a good result.

Figure 19 represents the absolute error of the predicted values of the training set 1 h ahead. From the figure, it can be seen that the absolute errors of the vast majority of the 224 training samples are kept within 60 kW, and only very few data have absolute errors exceeding 100 kW.

As shown in Figure 20, the relative errors of most of the data are guaranteed to be within 10%, and only very few data points have relative errors of more than 50%. Combining Figure 19 with Figure 20, it can be seen that the BP neural network is well trained and has a good fit.

4.2.3. The Analysis of the Test Set

By writing the code to predict the test set 1 h in advance, the MATLAB program was ran to generate the fitting results of the test set, and analyzed the absolute and relative errors of the test set fitting was performed.

In Figure 21, the blue line indicates the actual measured values of the test set and the red line indicates the predicted values of the test set 1 h in advance. As can be seen from the figure, the tracking fit between the predicted output of the test set and the actual measured values is good.

As can be seen in Figure 22, the absolute error of the vast majority of the 48 test samples remained within 50 kw, with only very few data points exceeding 100 kW in absolute error.

In Figure 23, it can be seen that most of the relative errors in the test set are within 10%, and only very few data points exceed 50%.

4.2.4. The Analysis of the Prediction Set

By writing the code to predict the prediction set 1 h in advance, the MATLAB program was ran to generate the fitting results of the prediction set, and analysis of the absolute and relative errors in the fitting of the prediction set was performed.

In Figure 24, the blue line indicates the hour-by-hour load forecast for day 31 predicted 1 h in advance, and the red line indicates the actual measured load value. It can be seen that the fit is not that perfect, but it is within the acceptable range.

As shown in Figure 25, among the 16 samples, there are 11 samples with absolute errors below 50 kW, 4 samples with 50–100, and only 1 sample with more than 100, and the absolute errors are within the acceptable range.

As can be seen in Figure 26, there are 10 relative errors that are all below 10%, occupying more than half. There are four that are between 10% and 20%, while the two data points at both ends have large errors, both with relative errors over 50%. This is due to the large fluctuations in instantaneous load before and after the start-up and shutdown of the central air conditioning system chiller, which makes it difficult to obtain accurate predictions. In contrast, when the air conditioner is in normal operation, the transient load fluctuations are not as large and good prediction accuracy can be obtained.

From the above output graphs of the comparison results between the training, testing, and prediction of the load prediction model 24 h in advance and its corresponding actual measured values, it can be seen that the predicted output follows the actual measured values very well. The prediction output also follows the actual load well when the environmental variables, such as temperature and humidity change, are present, resulting in a change in the actual measured cooling load, and the nonlinear relationship between the input and output of the training data is well simulated. Therefore, this model of 24 h advance load forecasting can be used in practical engineering applications.

4.3. Forecast One Hour in Advance

4.3.1. Division of Training Set and Test Set

Since the load is predicted 1 h in advance, the preprocessed data related to the moment t − 24 can be retained. Therefore, the number of neurons in the input layer of this BP neural network is eight, and the number of neurons in the output layer remains as one, i.e., the cooling load at time t. The number of hidden layers was taken as three.

A total of 16 × 9 × 18 = 2592 data points in the Excel sheet are used for the 1 h advanced forecast, of which 16 × 8 × 18 = 2304 data in the input layer and 16 × 1 × 18 = 288 data in the output layer.

As with the 24 h advance prediction, we still choose the hourly data from 14 August 2020 to 27 August 2020 as the training set, and save this part of the data in a separate table as “training set.xlsx”. We use the hourly data from 28 August 2020 to 30 August 2020 as the test set, and save this part of the data in a separate table as “Test set.xlsx”. We save the hourly data of the last day, 31 August 2020, as the forecast input in the table, entitled “Input samples.xlsx”. The above three tables were saved in the folder “t − 1”.

Subsequently, we input the training set and test set into MATLAB. After training and testing, the hour-by-hour cooling load prediction data for 31 August 2020 is output by inputting the hour-by-hour data for 31 August 2020 after the best-fit results were obtained. The predicted hour-by-hour cooling load data are compared with the actual detected hour-by-hour cooling load data.

As shown in Figure 27, the blue line indicates the actual measured value of the test sample, and the red line indicates the predicted value of the test sample. From the figure, it can be seen that after several training sessions, the test data have a good fit of 93.4%.

As shown in Figure 28, the blue line indicates the mean square error of the training dataset with the number of training generations, and the green line indicates the mean square error of the validation dataset with the number of training generations. From the figure, it can be seen that the mean square error is already smoothly below 10⁻², and reaches 0.004 when the training reaches the fourth generation.

The gradient parameter curve indicates the gradient change in the error surface, and the parameter mu indicates the adjustment range of the weight error. As can be seen in Figure 29, the error gradient decreases continuously with the increase in training generations. It reaches 0.00389 at the tenth generation, while the weight error reaches 10⁻⁵. The training is stopped after the error has reached the initially set adjustment range.

Figure 30 depicts the tracking of the output of the load prediction network model with respect to the target output. The blue line shows the tracking of the training set, and the black line shows the overall tracking. It can be clearly seen that the linear correlation between the prediction model output and the actual measurements is 0.95, which indicates a high linear correlation.

Therefore, by combining the visualization results of the above data, it can be tentatively determined that the output of the established BP neural network model can track the target well. The next step is to save and export the results, write, and run the program to visualize the training, testing, and prediction results separately, and analyze the training set, testing set, and hourly load prediction data for the whole day of 31 August 2020, one by one.

4.3.2. The Analysis of the Training Set

By writing the code to predict the training set 24 h in advance, we ran the MATLAB program to generate the fitting results of the training set and analyze the absolute and relative errors of the training set fitting.

In Figure 31, the blue line indicates the actual measured values of the training set and the red line indicates the predicted values of the training set 24 h in advance. As can be seen from the figure, the tracking fit between the predicted output and the actual measurements achieves good results, and all the predicted values are positive.

Figure 32 represents the absolute error of the predicted values of the training set 24 h in advance. As can be seen from the figure, the absolute error of the vast majority of the 224 training samples remained within 60 kW, and only very few data points had an absolute error of more than 100 kW, and none of the errors exceeded 300 kW.

As shown in Figure 33, the relative errors of the majority of the data are controlled within 10%. There are only very few data points with relative errors over 50%, and the relative errors of all data do not exceed 300%.

As far as the training set is concerned, this BP neural network is well trained and the goodness of fit is very good.

4.3.3. The Analysis of the Test Set

By writing the code to predict the test set 24 h in advance, we ran the MATLAB program to generate the fitting results of the test set and analyze the absolute and relative errors of the test set fitting.

In Figure 34, the blue line indicates the actual measured values of the test set and the red line indicates the predicted values of the test set 24 h in advance. As can be seen from the figure, the tracking fit between the predicted output of the test set and the actual measured values is good.

Figure 35 represents the absolute error of the predicted values of the test set. As can be seen from the figure, the absolute error of the vast majority of the 48 test samples remained within 40 kW, and only very few data points had an absolute error of more than 60 kW.

As shown in Figure 36, the relative errors of the 1 h ahead forecasts are mostly within 10%, with only very few data points exceeding 50%.

4.3.4. The Analysis of the Prediction Set

By writing the code to predict the prediction set 24 h in advance, we ran the MATLAB program to generate the fitting results of the prediction set and analyze the absolute and relative errors of the prediction set fitting.

In Figure 37, the blue line indicates the hourly load forecast for August 31 predicted 24 h in advance, and the red line indicates the actual measured load value. It can be seen that the fit is very good.

As shown in Figure 38, among the 16 samples, there are 14 samples with absolute errors below 60 kW, 1 sample from 60 kW to 100 kW, and only 1 sample above 100 kW, indicating that the absolute errors are within the acceptable range.

From Figure 39, it can be seen that the relative error is below 10% with 14, occupying more than 85%, the only relative error more than 10% is still associated with the data points at both ends; with a large error, the relative error are more than 50%. Due to the large fluctuation of instantaneous load before and after the start-up and shutdown of the central air conditioning system chiller, it is difficult to obtain accurate prediction, while after the air conditioner is in normal operation, the instantaneous load fluctuation is not so large, and the good prediction accuracy can be obtained.

From the above output graphs of the comparison results between the training, testing, and prediction of the load prediction model 1 h in advance and its corresponding actual measured values, it can be seen that the predicted output follows the actual measured values very well. The predicted output also follows the actual load well when the temperature and humidity changes are considered, which in turn causes the actual measured cooling load to change. Moreover, the nonlinear relationship between the input and output of the training data is very well simulated. Therefore, this model for predicting load 1 h in advance can be used in practical engineering applications.

4.4. Discussion

By writing the code, we combined the fitted values and the absolute and relative errors of the 1 h ahead prediction with the 24 h ahead prediction. Then, we ran the MATLAB program to generate an image of the two combined, and compared them.

As shown in Figure 40, the blue line is the actual value, the red line is the predicted value 1 h in advance, and the green line is the predicted value 24 h in advance. It is difficult to compare the two predicted values because of the large number of samples in the training set and the close alignment of the two predicted values. However, it can be tentatively determined that the training set with 1 h ahead prediction is a better fit, while the individual BP prediction values in the 24 h ahead prediction data are negative and no longer physically meaningful.

As shown in Figure 41, in the comparison of the absolute error graphs of the fitting effect, the blue line is the absolute error of prediction 1 h in advance, and the green line is the absolute error of prediction 24 h in advance. It is very obvious that the blue line is within the green line, which means the absolute error is smaller. The absolute error of the 1 h ahead prediction does not exceed 300 kW, while the absolute error of the individual BP prediction value of the 24 h ahead prediction exceeds 400 kW.

It is also clear, from the comparative analysis graph of relative errors in Figure 42, that most of the relative errors for the 1 h ahead prediction are smaller than those for the 24 h ahead prediction. All the relative errors for the 1 h ahead prediction do not exceed 300%, while the relative error plot of the training set for the 24 h ahead prediction has a relative error of over 400% for individual BP prediction values.

The test set section, as shown in Figure 43, is a comparative analysis graph of the absolute errors for the test set. As can be seen from the figure, the blue line is within the green line overall, and all absolute errors predicted 1 h in advance do not exceed 150 kW, while individual absolute errors predicted 24 h in advance exceed 150 kW. It can be concluded that the errors predicted 1 h in advance are smaller as far as the test set is concerned.

As can be seen from Figure 44, the numerical curve predicted 1 h earlier is closer to the actual value and the fit is better.

As can be seen from Figure 45, most of the absolute errors of the 1 h ahead prediction are within the green line; therefore, the absolute errors of the 1 h ahead prediction are also smaller.

From the relative error shown in Figure 46, it can be seen that most of the relative errors of 1 h ahead prediction are below the green line, i.e., the relative errors are smaller. Combining the above comparative analysis graphs of the training set, test set, and prediction set, we can conclude that the 1 h ahead prediction accuracy is higher.

5. Conclusions

This study begins with an overview of central air conditioning systems. The working principle and process of central air conditioning systems is investigated. The water system part is analyzed with emphasis on the freezing side instantaneous cooling capacity as the key research object. We present several common prediction models and analyze the advantages and disadvantages of each. In this study, a central air conditioning cooling load prediction model is established using data collected from the actual operation of a real project and selecting a BP neural network. We import the data into MATLAB after preprocessing the data and processing the anomalous data; apply the BP neural network for training, testing, and prediction; and generated the fitted effect and error plots. Furthermore, we compare the 24 h ahead forecast with the 1 h ahead forecast. The research results show that most of the data errors of both predictions reach within 10%, and the accuracy meets the practical requirements; thus, these data can be applied to actual engineering projects. Among them, the data predicted 1 h in advance are more accurate. By predicting the cooling load in advance, the air conditioning system can be adjusted and controlled in advance, thus solving the problem that the parameters do not follow the change in cooling load due to the time lag in the control process. In addition, the higher the accuracy of cooling load prediction, the more redundant energy consumption can be reduced. The established central air conditioning cold load prediction model can accurately predict the cold load of a building’s central air conditioning system (e.g., central air conditioning systems in airport terminals, subway stations, etc.). On the premise of meeting the cold load demand with the lowest energy consumption of system operation as the goal, the air conditioning system can be adjusted and controlled in advance to achieve energy saving operation of the central air conditioning system, thus achieving the goal of improving efficiency, saving energy, and reducing emissions. In further study, we will focus on incorporating other intelligent algorithms to improve the accuracy of neural network algorithms.