Predictive Control Modeling of Regional Cooling Systems Incorporating Ice Storage Technology

Abstract

Due to the hot climate, energy consumption for refrigeration is significantly higher in the subtropical monsoon climate region. Combined with renewable energy and ice-storage technology, a model predictive control model of the regional cooling system was proposed, which was conducive to improving the flexibility of the regional cooling system and the ability of peak shifting and valley filling. In this model, an artificial bee colony (ABC) optimized back propagation (BP) neural network was used to predict the cooling load of the regional cooling system, and the model parameter identification method was adopted, combining utilizing a river-water-source heat pump and ice-storage technology. The results showed that the load prediction algorithm of the ABC-BP neural network had a high accuracy, and the variance coefficient of load prediction root-mean-square error (RMSE) was 16.67%, which was lower than BP, support vector regression (SVR), and long short-term memory (LSTM). In addition, compared with the three control strategies of chiller priority, ice-storage priority, and fixed proportion, the operation strategy optimized by the comprehensive model can reduce the average daily cost by 19.20%, 4.45%, and 5.10%, respectively, and the maximum daily energy consumption by 30.02%, 18.08%, and 8.90%, respectively.

1. Introduction

Based on statistics from the International Energy Agency (IEA), the building sector is among the top three energy-consuming industries, representing 36% of global energy consumption. In this sector, heating, ventilation, and air conditioning (HVAC) systems account for 65% of the energy utilized in buildings [1]. Additionally, buildings generated approximately 39% of global greenhouse gas emissions, highlighting the importance of optimizing HVAC systems for energy efficiency. In practice, HVAC systems typically exhibited large peak power loads and low energy efficiency, with peak-load periods coinciding with urban power peak-load times. This led to grid undersupply during peak loads and oversupply during valley loads. The IEA identified district cooling as a critical energy sector requiring significant action to achieve net-zero emissions by 2050 [2].

District cooling has become an appealing alternative to traditional cooling systems in areas with high energy density such as urban environments [3]. The implementation and advancement of district cooling systems (DCSs) rely on the use of local renewable energy sources and natural resources [4]. These systems primarily rely on a centralized cooling station to generate cold energy, which is then transmitted to end users through pipelines. Due to the integration of local renewable energy sources, DCS has proved to be more efficient than standalone heating and cooling systems [5]. Most current research on district cooling systems focuses on technical and economic optimization. Chan et al. [6] employed a genetic algorithm to determine the optimal configuration of a DCS pipe network, while Dorotich et al. [7] developed an hour-based optimization model for district cooling and heating systems with CO₂ emissions and operating costs as the objective functions. Their results indicated that, for the same CO₂ emissions, the operating cost of district cooling systems was lower than that of standalone cooling systems. Furthermore, extensive literature has addressed the control of district heating and cooling systems [8]. Jingzhao et al. [9] proposed a predictive-control model for district cooling and heating systems based on load forecasting and time delay, and actual measurements at Tianjin University demonstrated that this model not only improved supply–demand matching but also reduced total energy consumption. Laura et al. [10] developed a model predictive control approach for a district cooling system with compressors and absorption chillers to maximize efficiency. Simulation-based experiments showed that this energy-saving method achieved up to 50% savings. Wen Jie et al. [11] presented a robust optimization method to reduce cooling-water system indeterminacy during the design and operation phases of a district cooling system [8].

To reduce the impact of HVAC system operation on the power grid and ensure the stable operation of the power system [8], it is essential to integrate large-scale regional cooling and heating systems with renewable energy and ice-storage technologies [12,13]. This integration helps reduce the peak load on the power system. Additionally, establishing an integrated predictive control model for district cooling systems that combines renewable energy and ice-storage technology is crucial for ensuring efficient and economic operation [14].

Energy demand forecasting is crucial for promoting resource optimization and controlling DCS; therefore, accurate and rapid district cooling system load forecasting is necessary [15]. Improving the performance of the prediction model was a key step in developing energy-saving control strategies for air-conditioning systems, ensuring their economical and efficient operation. In recent years, researchers worldwide have made significant advancements in predicting building heating and cooling loads, utilizing a variety of load forecasting methods such as physical modeling, empirical methods, regression models, and artificial intelligence techniques.

The traditional method for simulating and estimating building cooling loads was based on the building energy modeling programs (BEMPs). The research and development of thermal-process-based BEMPs dates back to the 1980s and resulted in the creation of widely used software such as DeST [16], EnergyPlus [17], and ESP-r [18]. However, using BEMP for cooling load estimation required detailed input on building thermal performance and operating schedules, often necessitating calibration [19,20]. Due to the substantial workload involved, this method was often unsuitable for existing buildings, and the lack of precise inputs reduced prediction accuracy.

Most current research employs data-driven machine-learning algorithms for cooling load prediction. In reference [21], a short-period multi-step prediction model, based on support vector machines and discrete wavelet transforms, along with a new method for district heating system (DHS) user heat load prediction, was proposed. In reference [22], a short-period heat load prediction algorithm based on a feature fusion long short-term memory model (FFLSTM) was established for DHS optimization and control. Kwok et al. [23] used an artificial neural network (ANN) model to predict energy use in office buildings in Hong Kong, achieving a best RMSE of 11.41%. These experiments demonstrated that while algorithms have advantages in forecasting accuracy, many load forecasting models still face shortcomings in terms of computing time and accuracy requirements.

Furthermore, previous studies have shown that BP neural networks possess strong nonlinear mapping, self-learning, generalization, and fault tolerance capabilities, enabling them to achieve better load prediction results [24]. However, due to the influence of the gradient descent algorithm, weights and thresholds are generated randomly when using BP neural networks [25]. This randomness can cause the algorithm to easily fall into local optima during operation, reducing the accuracy of the output results and affecting the established prediction model [25]. Huang et al. [26] proposed a universal neural embedding initialization framework to address the initialization problem in neural network models. However, while advanced initialization methods may offer performance improvements, they often require additional computational costs or complex parameter tuning, which increases the time and computational resources needed for model training. Furthermore, the practical effectiveness of these methods may be influenced by specific application scenarios, datasets, and network architectures. Therefore, the demand prediction of large-scale regional cooling systems using the BP algorithm combined with ice-storage technology requires further study.

Additionally, ensuring the smooth operation of the power grid [27], minimizing the impact of end users on the grid, and integrating renewable energy sources often involves systems combining heat pumps and heat storage [28]. In the optimization and control of energy storage systems, major methods such as model predictive control (MPC), supervised control, and machine learning control are commonly adopted [8,29]. For optimizing ice-storage systems, the literature commonly reports factors like constant priority, fixed scheduling, refrigerator priority, cold-storage priority [30,31,32], and rule-based optimal control strategies. These strategies have been widely applied to optimize the coefficient of performance (COP) of heat pumps and heat-storage systems, yielding satisfactory results [33,34]. Sun et al. [35] reviewed various heat-storage control strategies and concluded that optimization strategies are more cost-effective than conventional methods. Luo et al. [36] conducted a modeling study on integrating air-conditioning and ITS systems in a shopping center, demonstrating an 11.3% daily operating cost reduction through effective optimization and regulation. Wei Qinglai et al. [37] employed the data-driven adaptive dynamic programming (ADP) method to optimize the control of a cold-storage air conditioner, achieving significant operational cost reductions. Powell et al. [38] utilized mathematical models to optimize coolers and cold stores, treating coolers as a single optimal unit for dynamic optimization approaches. They integrated neural network load forecasting technology, effectively reducing control costs. Chen et al. [39] proposed a dynamic programming-based control scheme to determine the optimal capacity ratio of refrigeration and ice-storage equipment. However, there remains an urgent need to fully utilize renewable energy sources such as rivers and lakes and to develop a comprehensive predictive control model for regional refrigeration systems that integrate ice-storage technology and renewable energy.

In summary, accurately predicting the load demand of large regional cooling systems and optimizing their control through the integration of renewable energy and ice-storage technology is of paramount importance. Recent studies [40,41] indicated that combining the ABC algorithm with the BP neural network model significantly enhanced performance and convergence speed. The global search capability of the ABC algorithm helped prevent the BP network from getting stuck in local optima, enabling it to find more optimal weights and biases. Additionally, it optimized the initial parameter settings, accelerated network convergence, and improved training stability. Furthermore, the ABC algorithm dynamically adjusted the learning rate based on network conditions to control the training speed and stability, mitigating issues like oscillation or overfitting. By employing diversified weight updating strategies, the ABC algorithm enhanced network diversity, thereby improving model generalization and adaptability.

In this paper, an integrated predictive control model of a regional cooling system combining river source heat pumps and ice-storage devices was proposed. The structure and parameters of the ABC-BP load forecasting algorithm were determined through the comprehensive analysis of test data. An optimization scheme for the combined heat pump and ice storage regional cooling system was developed, focusing on minimizing user-side operation costs and system power consumption during peak electricity prices. The model’s accuracy was validated using experimental data, demonstrating its effectiveness in peak-shifting and valley-filling strategies for the power grid, thus alleviating grid pressure.

2. Model and Methodology

Figure 1 depicts the methodology of this study, consisting of four primary components: data preparation, cooling load forecasting model, model optimization control strategy, and model evaluation. In the data preparation phase, cooling-load data were acquired from the building automation system (BAS), and weather data were sourced from the local weather station. The cooling load forecasting model phase involved developing and refining a machine-learning model through prediction algorithms, selection of input features, and prediction mechanisms. Following the cooling load predictions, the model optimization control strategy phase formulated rule-based control logic. Lastly, the model evaluation phase assessed performance using mathematical metrics such as mean absolute error (MAE) and RMSE. The prediction model with the highest accuracy and the control model with the lowest energy cost was identified as the most effective predictive control model for the regional cooling system.

2.1. Data Processing

Load forecasting based on machine learning requires a large amount of data for training and has high requirements for data quality. However, in the real process, due to the large amount of regional energy cooling equipment and the complex systems, sometimes it is inevitable for unexpected situations to appear, such as network connection and sensor failure, result in some “bad values” in the collected historical data, including missing data, noise, outliers, etc. The direct use of model training will reduce the prediction accuracy; therefore, it is necessary to preprocess the relevant data. The preprocessing mainly includes two aspects: missing data filling and load data smoothing.

2.1.1. Complement of Missing Data

The processing of missing data mainly includes two categories. For a period of time, when there is a lot of missing data, we cannot know its change rule and it is difficult to fill, so the method of direct deletion is adopted. For a small amount of missing data, the mean of the adjacent time data is used instead.

2.1.2. Smooth Processing of Load Data

In this study, the researchers employed the time-averaging method for load smoothing preprocessing. By averaging the load data over time, this method effectively smoothed out instantaneous fluctuations in the load values. Specifically, the researchers selected an appropriate time window to apply a moving average to the load data, resulting in a more stable load profile. This provided a robust foundation for subsequent system optimization and control strategies.

2.2. Cooling Load Forecasting Model

The cooling load forecasting model was based on machine learning algorithms utilizing weather data, date information, and historical cooling load as inputs to predict the cooling load for the next 24 h. This time horizon was chosen to meet the daily energy management needs in practical applications, providing a balance between accuracy and usability in real-world scenarios. The model was trained and validated using time-series data from the preceding days to predict the cooling load for the upcoming time window. Subsequently, the prediction window was recursively shifted forward to make sequential predictions. The development of the forecasting model primarily focused on two aspects: the forecasting algorithm and the selection of input features.

2.2.1. Prediction Algorithm

Several machine-learning methods were selected as the core algorithms of the prediction model. These algorithms included BP, LSTM, SVR, and ABC-BP. This study compared the performance of four algorithms, with the model evaluation metrics and their calculated results detailed in Section 2.4. The dataset in this study was randomly split into a training set and a testing set in a 7:3 ratio, with the training set containing 1260 samples and the testing set containing 540 samples. The selection of input parameters used during the training of the predictive model is detailed in Section 2.2.2, with the output being the building’s hourly cooling load. Furthermore, the algorithm with the smallest prediction error was chosen as the final prediction model. The detailed description of the aforementioned algorithms is as follows:

1. Back propagation (BP) trains artificial neural networks by adjusting weights to minimize error, making it effective for nonlinear relationships in feedforward neural networks, but it struggles with time-series data due to its inability to capture long-term dependencies.

In the BP neural network, the hidden layer was set to 15, using the Tanh function as the activation function. The neurons in the output layer received the output from the hidden layer and generated the final predictions through weighted summation and activation functions. The purelin function was used as the activation function in the output layer. Additionally, the newff function was used for network initialization. Subsequently, the training parameters were set, with a maximum of 1000 training iterations, a target error of 10⁻⁶, and a learning rate of 0.01. Finally, the model was trained using the train function.

2. Long short-term memory (LSTM), a type of recurrent neural network, overcomes this by using memory cells and gates to capture long-term dependencies, making it ideal for time-series predictions despite being more complex and computationally intensive.

In the building cooling load prediction model, the architecture included a sequence input layer, an LSTM layer, a fully connected layer, and a regression layer. The LSTM layer was configured with 300 LSTM units to capture long-term dependencies in the sequence data. The maximum number of iterations during training was set to 200. A gradient threshold of 1 was established to prevent gradient explosion. The initial learning rate was set to 0.001, and a piecewise learning rate scheduling strategy was used to gradually decrease the learning rate during training. The learning rate decreased every 50 iterations by a factor of 0.2, reducing the learning rate to 20% of its previous value.

3. Support vector regression (SVR) fits a hyperplane within a margin of tolerance to minimize error, offering robustness in high-dimensional spaces and handling outliers well, but it is less efficient with large datasets and requires extensive hyperparameter tuning.

In the SVR model, the RBF kernel function was chosen for its strong nonlinear mapping abilities. The γ parameter, which controls the kernel’s width, was set to “auto” to let the algorithm determine the optimal value. The penalty parameter C was set to 1 to balance fitting and generalization. The ϵ parameter was set to 0.1, focusing the model on larger errors by ignoring smaller ones.

4. The ABC algorithm is an intelligent algorithm that mimics bee foraging. It is a global optimization algorithm that does not need to know all the information about the problem. By comparing the advantages and disadvantages of an object and combining with the local optimization of a single bee colony, the global optimal value is obtained. For the ABC-BP algorithm, the ABC algorithm can optimize the weight initialization of the BP neural networks by performing a global search on the weights through simulating the foraging behavior of bees. This process aims to find better initial weight values, which helps reduce the uncertainty introduced by random initialization. The process of the ABC algorithm optimizing the double-hidden layer BP network is shown in Figure 2.

In the ABC-BP model, the default parameter settings were as follows: the population size was 50, the maximum number of cycles was 500, the number of employed bees and onlooker bees was 25 each, the limit was 100, the learning rate was 0.01, and the maximum training iterations for the BP neural network were 1000. These parameter settings were designed to balance the algorithm’s search capability and computational complexity, ensuring that the model achieved optimal results within a reasonable timeframe.

Furthermore, it is acknowledged that comparing the computational complexity and the number of trainable parameters of different machine-learning models is valuable for understanding each model’s efficiency and feasibility [43,44]. However, the primary focus of this study is on performance accuracy and the effectiveness of the models in real-world applications. Including a detailed comparison of computational complexity might shift the focus from evaluating model performance, which is the main objective of this research. Consequently, this aspect is not addressed in the current study.

2.2.2. Select Input Features

In this study, 13 influencing factors were chosen, such as week and hour factors, dry-bulb temperature, relative humidity, solar radiation intensity, rainfall, pressure, wind speed, temperatures 3 h prior to the forecast day (T-1, T-2, T-3), load 1 h before the prediction time (L-1), and load at the same time on the preceding day (L-24). In order to further reduce the redundant and ineffective information according to the specific situation of the energy station, the Spearman rank correlation coefficient method was used to further screen and reduce the dimension of the input features.

Spearman’s rank correlation coefficient is a correlation coefficient used to measure the strength of the monotone relationship between two variables. Different from Pearson’s correlation coefficient, Spearman’s rank correlation coefficient is a rank statistical parameter with non-parametric properties (independent of distribution) and does not require variables to be normally distributed, which is more widely used. The corresponding calculation expressions are presented as follows:

$${\delta }_s={\displaystyle \frac{{\sum }_{i=1}^N\left(R_i-\overline{R}\right)\left(S_i-\stackrel{=}{S}\right)}{{\left[{\sum }_{i=1}^N{\left(R_i-\overline{R}\right)}^2{\sum }_{i=1}^N{\left(S_i-\stackrel{=}{S}\right)}^2\right]}^{\frac{1}{2}}}}$$

(1)

In these expressions, $R_i$ and $S_i$ represent the ranks of the observed value $i$; $\overline{R}$ and $\overline{S}$ denote the mean ranks of the variables $x$ and $y$, respectively; $N$ is the total number of observations.

The correlation coefficient between each variable and load is calculated as shown in

Table 1. Spearman correlation coefficient between each variable and load.

Input Parameter	Correlation Degree	Input Parameter	Correlation Degree
Hour factor	0.49	T	0.51
Week factor	−0.42	T-1	0.42
Wind speed	0.18	T-2	0.29
Radiation intensity	0.77	T-3	0.19
Pressure	−0.15	L (h-24)	0.88
Precipitation	−0.03	L (h-1)	0.93
Relative humidity	−0.38	/	/

.

According to the correlation analysis results, the correlation degree between different meteorological parameters and the energy cooling load in this region, in order from large to small, is solar radiation intensity > dry-bulb temperature > relative humidity > wind speed > pressure. Moreover, the correlation coefficient of T (h-1) is much higher than that of T (h-2) and T (h-3), so the week factor, hour factor, dry-bulb temperature, relative humidity, solar radiation intensity, and temperature 1 h before the forecast day are selected as the input characteristic parameters of the model.

2.3. Model Control Optimization Strategy

2.3.1. Model Building

To reduce the complexity of the optimization process, the following assumptions are made for the system:

(1)

It is considered that the partial load rate of multiple chillers is the same.

(2)

The maximum cooling capacity of melting ice is solely dependent on the remaining ice in the ice-storage device, disregarding the effects of the refrigerant’s entering and exiting temperatures and other factors.

(3)

In the ice-storage mode, the main engine with dual working conditions always maintains full-load ice storage until the ice-storage termination condition is reached.

(4)

During the operation of the system, the ice-storage device is not considered to charge and discharge cold simultaneously; when there is a cooling demand during the ice-making period at night, the river-source heat pump is turned on for cooling.

A simplified multivariate polynomial model [2] was used to fit the features of RSHP and DOHP owing to its ability to use relatively few independent variables and to be more robust. The chilled-water supply temperature ($T_{eo}$), cooling capacity of the chiller ($Q_{sj}$), and cooling-water return temperature ($T_{ci}$) are the three main independent variables of the model, and eight simplified parameters are used to describe the characteristics of the RSHP and DOHP, as expressed in Equation (2):

$$COP=a_0+a_1·Q_{sj}+a_2·T_{eo}+a_3·T_{ci}+a_4·Q_{sj}^2+a_5·Q_{sj}·T_{eo}+a_6·Q_{zl}·T_{ci}+a_7·T_{eo}·T_{ci}$$

(2)

The chilled water pumps are all variable-frequency pumps. The head flow characteristic curve of their parallel operation can be expressed by Equations (3) and (4):

$$H_0=a_1·q^2+a_2·{\omega }^{-2}·q+a_3$$

(3)

$${\eta }_z=b_1·{\omega }^{-2}·q^2+b_2·{\omega }^{-2}·q+b_3$$

(4)

The input power $P_{pump}$ of the pump is a function of head $H$, flow rate $q$, and efficiency ${\eta }_z$, and its expression is given by Equation (5):

$$P_{pump}=H·q/{\eta }_z\times {10}^{-3}$$

(5)

The optimization objective function is as follows:

$$\min J=r_{D,P}·P_{\max }+{\displaystyle {\sum }_{t=0}^{23}{r}_t·\left[E_{chiller}(t)+E_{pump}(t)\right]}$$

(6)

The value of $r_{D,P}$ and $r_t$ directly refer to the basic electricity price under the two-part system, CNY/kW.

To prevent the unit from freezing and the inverter unit from surging when the outlet temperature is extremely low, the temperature is limited as follows:

$$3 °\mathrm{C}\le T_{s1}(t)\le 9 °\mathrm{C}$$

(7)

2.3.2. Particle Swarm Algorithm Solution

The genetic algorithm (GA), particle swarm optimization (PSO), and simulated annealing algorithm are highly effective for tackling large-scale nonlinear optimization problems. Among these, the PSO algorithm exhibits superior global search capability and optimization efficiency compared with the other two algorithms. Therefore, the PSO algorithm was employed to address the problem. The specific process is illustrated in Figure 3.

To solve the objective function, the maximum number of iterations of the PSO algorithm was set to 3000, the dimension of the search space was 48, the number of particles was 800, the initial population was 500 individuals, the maximum inertia weight was 0.9, the minimum inertia weight was 0.4, and the maximum particle velocity was 2. The inertia weight and learning factors and are dynamically optimized as the number of iterations increases.

2.4. Model Evaluation

Four statistical indicators were used to characterize the prediction accuracy of the above cooling load forecasting models: R², RMSE, CV-RMSE, and MAE. This indicator can be expressed as follows:

$$R^2=1-{\displaystyle \sum _{m=1}^n{(y_m-y_{pre,m})}^2}/{\displaystyle \sum _{m=1}^n{(y_m-\overline{y})}^2}$$

(8)

$$RMSE=\sqrt{{\displaystyle \sum _{m=1}^n{(y_m-y_{pre,m})}^2}/n}$$

(9)

$$CV-RMSE=RMSE/\overline{y}$$

(10)

$$MAE=(\left|\mathsf{\Delta }1\right|+\left|\mathsf{\Delta }2\right|+\cdots +\left|\mathsf{\Delta }n\right|)/n$$

(11)

The performance of the above models is presented in

Table 2. Index value of above models.

Algorithm	${\mathit{R}}^2$	RMSE (kW)	CV-RMSE (%)	MAE (kW)
BP	0.9661	2426.85	18.15%	1617.37
LSTM	0.9129	3726.35	32.48%	2708.47
SVR	0.9247	3565.73	31.03%	2260.29
ABC-BP	0.9788	1774.30	16.67%	1254.85

below:

Table 2 shows that the CV-RMSE for load demand is 16.67%. The ASHRAE Guideline 14 requires that the CV-RMSE should be lower than 30%. Therefore, the ABC-BP model meets the criteria. Furthermore, it can be seen that the R² of the ABC-BP model is not only greater than 0.8 but also is better than other algorithms. Therefore, it can be considered that the model has a high degree of fitting and prediction results.

3. Case Study

3.1. Description of District Cooling System

In order to better illustrate the superiority of the model, this paper takes a regional energy system in Chongqing as a case study. The district cooling system has a central heating and cooling area of 2.44 million m², and the main buildings are office, commercial, and hotel buildings. The total cooling load was 187,517 kW. Under summer cooling conditions, the electric cooling + river-source heat pump + ice-storage cooling mode were enabled, and the river-water-source heat pump alone provided heating in winter. For ice storage, an external ice-melting system upstream of the main engine with a secondary base load was used. Further details are provided in

Table 3. Main equipment performance parameters.

Main Equipment	Number	Cooling Capacity (kW)	Ice Store (kW)	Ice Storage Capacity (GWh)	Water Temperature (°C)
River-source heat pump	10	8403	/	/	4.5/13
Dual-operation heat pump	8	8545	5043	/	3.5/12 −6/−1.9
Ice storage units	320	/	/	33	1.5/3.5
Heat exchanger	6	6615	/	/	/
	8	8544	/	/	/

. Figure 4 shows a schematic of the district cooling system of an energy station.

The regional energy station has established an integrated energy-consumption monitoring and control platform. Through the monitoring module of the platform, the operation status of the on-site machine room equipment can be monitored online for 24 h. The main monitoring parameters of the system monitoring record are shown in

Table 4. Energy control platform monitoring parameter table.

Equipment	Monitored Parameter
Chiller	Start-stop state, operating time, supply and return water temperature, flow, pressure difference, power consumption, automatic control valve opening/switching, current rate
Water pump	Start-stop state, running time, pump frequency, power consumption
Pipe network system	Cooling water supply/return water temperature, chilled water supply/return water temperature, flow rate
Ice-storage device	Ice-storage tank start–stop state, ice-storage tank remaining ice, ice tank inlet and outlet water temperature, flow
River water intake system	River water temperature, flow

below.

In order to ensure the reliability and accuracy of the data obtained from the energy management and control platform, members of our research group conducted a series of investigations and tests on the site of the long-term energy station from June 2020 to September 2021 to understand the normal operating range of each equipment parameter during operation. The field instrument data and the data automatically recorded by the BAS system were analyzed to find the sensors with abnormal data records. During the maintenance phase of the transition season, the operation and maintenance managers of the energy station were assisted to check the important instruments such as sensors, thermometers, and flowmeters of the cold and heat source system and to replace some faulty sensors.

In addition, in order to record the microclimate meteorological data of the area where the energy station is located, the researchers of this project also set up an automatic weather station near the energy station, which can record the meteorological parameters such as outdoor dry-bulb temperature, wet-bulb temperature, relative humidity, wind speed, wind direction, and solar radiation intensity in detail.

3.2. Load Analysis

The end users of regional energy system are diverse, and the change in cooling load is complex. Therefore, it is necessary to study the periodicity and regularity of the load of the system to lay the foundation for the verification of the model.

Figure 5 shows the hourly cooling load data of the energy station in the region for the typical month of summer (July) 2021. The energy station maximum daily load concentrated in 30,000~45,000 kW, only about 25% of the maximum design load. It can be seen from the changes in Figure 5 that the cooling load on Saturday and Sunday is significantly lower than that from Monday to Friday, and the load variation characteristics between working days are also slightly inconsistent. However, due to a certain degree of similarity between user behavior and air-conditioning load patterns, the load characteristics are the same between the same week types, so the load changes also show obvious periodic changes. In this paper, the clustering method is used to analyze the daily load curve of the typical summer months, and the daily load types are determined as shown in

Table 5. The daily load types.

Day Type	1	2	3	4
Week	Monday	Tuesday to Friday	Saturday	Sunday

.

4. Results and Discussion

4.1. Forecasting Results and Performance Analysis of ABC-BP and BP Networks

For visualization, the forecasted and observed values were compared during the summer months from 19–22 August, as shown in Figure 6. It can be observed that the forecasted value of the ABC-BP model was closer to the measured data, with a smaller error compared with the BP model. This improvement was attributed to the enhanced optimization mechanism of the ABC algorithm, which, inspired by the foraging behavior of bees, effectively explored the solution space to identify better initial weights and avoid local minima. Consequently, the ABC-BP model achieved more accurate predictions, demonstrating its ability to better describe the nonlinear relationship between the eight input characteristic values and the load demand. This result highlights the effectiveness of the ABC-BP approach and its potential for widespread use in building performance prediction.

Furthermore, the discrepancy in prediction errors around the value of 75, where the ABC-BP model showed an error of approximately +50% and the BP model showed an error of about −50%, likely occurred due to the differing sensitivities of the models to specific data ranges. The ABC-BP model, which optimized initial weights through the artificial bee colony algorithm, generally performed better but struggled with certain data ranges, leading to overestimation. Conversely, the BP model, reliant on gradient descent, had less consistent performance across different data ranges, resulting in underestimation in this region. This highlights the need for further refinement in both models to handle specific edge cases more effectively.

4.2. Load Distribution Results under Each Control Strategy on a Typical Day

Under the typical daily and hourly loads predicted by the ABC-BP algorithm, the proposed optimization strategy, chiller priority, ice-storage priority, and constant-proportion control strategy were simulated, and the cooling capacity distribution results are shown in Figure 7.

Under the optimization strategy, during the electricity-price flat period (8:00–11:00, 17:00–20:00, and 22:00–24:00), the ice-melting cooling ratio was significantly small, approximately 0.4. Even from 18:00 to 20:00, the RSHP was used for cooling to reserve sufficient ice volume for the peak time of electricity price at night. During the entire cooling process of the clod-storage device, the cooling supply was concentrated during the peak segment of electricity price (11:00–17:00 and 20:00–22:00). During the peak daytime electricity price (11:00–17:00) period, the ice-melting cooling ratio was kept above 0.85, and during this period, only one RSHP was required to be turned on to satisfy the cooling demand. In the peak period at night (20:00–22:00), the use of single melting ice for cooling could effectively avoid the opening of the refrigeration unit during the peak hours.

4.3. Energy Consumption Analysis of Each Strategy on a Typical Day

Figure 8 shows the hourly operating power under the four operating strategies on a typical day. As observed in Figure 8, during the peak segment of the electricity price, the consumption of power with the optimized control strategy is always maintained at the lowest level, and its power consumption is 2309.8 kW. Compared with the chiller priority, ice-storage priority, and constant proportion, the power consumption of the optimization strategy was reduced by 75.59%, 27.96%, and 22.94%, respectively. It can be observed that the optimization strategy can reduce the superposition of the grid peak load better. In the low-electricity-price stage, the optimization strategy, ice-storage priority, and constant proportion need to be iced. However, a sudden change occurred at 7 o’clock because the terminal load was large at 7 o’clock. Furthermore, it was in the ice-storage stage at this time, and the melting ice cannot be used for cooling; therefore, the RSHP was required to be turned on for cooling. Therefore, at this time, the immediate power consumption of the optimization strategy, constant proportion, and ice-storage priority control strategy reached their maximum values.

Table 6. Power consumption analysis of different control strategies.

	Optimization Strategy	Chiller Priority	Ice-Storage Priority	Constant Proportional
Total electricity consumption	132,897.6	111,528	133,086.7	142,060
Peak power consumption	11,294.89	59,797.43	27,452.89	28,924.35
Flat-section electricity consumption	29,710.6	43,463.67	13,741.74	21,243.61
Valley-section electricity consumption	91,892.08	8266.86	91,892.08	91,892.08
Peak shift rate	4.29	0	1.18	1.07

summarizes the daily total power consumption and power consumption at each stage of each operation strategy. From the perspective of gross power consumption, under this load condition, the chiller priority control strategy was equivalent to the traditional control strategy without an ice-storage device. This eliminated the energy loss of ice storage; thus, the gross consumption of energy was the smallest. Because the optimization strategy optimized the chilled-water outlet temperature of the RSHP and kept the unit running at a better partial-load rate, it reduced the consumption of energy by 0.14% and 6.89%, respectively, when compared with the ice-storage priority and the constant proportional control strategy.

In addition, to better represent the ability of each operating strategy to shift the power consumption of the peak section, we introduced the peak shift rate $X_{Yd}$, which is expressed as follows:

$$X_{Yd}=(A_{Wf}-A_{Yf})/A_{Wf}$$

(12)

where $A_{Yf}$ and $A_{Wf}$ represent the power consumption of the peak power segment with and without the cold-storage system, respectively.

Considering the chiller priority control strategy as the benchmark, the peak-shift rates of the optimization strategy, ice-storage priority, and constant proportion were 4.29, 1.18, and 1.07, respectively. It can be seen that the optimization strategy has the strongest peak-shaving ability and can significantly reduce power consumption during the peak period such that the maximum power required is reduced.

4.4. Operating Costs of Various Strategies on a Typical Day

Table 7. Daily operating costs under different control strategies.

Strategy	Electricity Bill in Operation (CNY)	Cost-Saving Percentage (%)
Optimization strategy	65,905.85	/
Chiller priority	110,394.11	40.30%
Ice-storage priority	73,674.61	10.54%
Constant proportional	81,361.84	19.00%

compares and analyzes the daily operating costs under the different control strategies. Evidently, compared with the three control schemes of the chiller priority, ice-storage priority, and constant proportion, the cost reduction of the optimization strategy was 40.30%, 10.54%, and 19.00%, respectively. During the peak segment of the electricity price, the total melting-ice volume of the optimized control strategy accounted for 79.0% of the total daily ice-melting and cooling capacity; therefore, it could transfer the peak load to the electricity price valley to the greatest extent.

4.5. Operating Analysis of Optimization Strategy under Other Typical Design Conditions

Table 8. Operation comparison of different control strategies under different working conditions.

Strategy	Cost-Saving Percentage	Cost-Saving Percentage (%)	Total Energy Consumption (kWh)	Energy-Saving Ratio (%)	${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (kW)	${\mathsf{\Delta }\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (%)
25% of design load
Optimization strategy	76,332.9	/	142,500.3	/	4284.3	/
Chiller priority	122,640.8	37.8%	124,608.5	−14.4%	10,769.6	60.2%
Ice-storage priority	83,078.3	8.1%	144,514.0	1.4%	6843.7	37.4%
Constant proportional	86,980.5	12.2%	148,190.2	3.8%	5021.6	14.7%
50% of design load
Optimization strategy	194,836.7	/	263,003.8	/	14,356.1	/
Chiller priority	246,745.4	21.0%	248,557.1	−5.8%	21,868.1	34.4%
Ice-storage priority	205,591.3	5.2%	265,016.3	0.8%	17,381.8	17.4%
Constant proportional	205,712.6	5.3%	267,511.4	1.7%	15,910.4	9.8%
75% of design load
Optimization strategy	321,119.0	/	384,491.6	/	25,817.4	/
Chiller priority	376,435.6	14.7%	375,839.7	−2.3%	33,567.8	23.1%
Ice-storage priority	331,632.3	3.2%	388,446.9	1.0%	28,519.5	9.5%
Constant proportional	329,319.0	2.5%	389,617.5	1.3%	26,979.5	4.3%
100% of design load
Optimization strategy	457,815.5	/	518,284.7	/	36,288.9	/
Chiller priority	473,335.8	3.3%	510,199.5	−1.6%	37,180.9	2.4%
Ice-storage priority	463,766.4	1.3%	522,764.6	0.9%	39,438.8	8.0%
Constant proportional	459,792.4	0.4%	519,773.6	0.3%	38,929.1	6.8%

summarizes the operating costs, energy consumption, and maximum power during the peak periods for different strategies at 25–100% of the design load. The use of both kWh and kW in Table 8 serves specific purposes: kWh represents the total energy consumption over time, which is crucial for evaluating overall efficiency and cost-effectiveness; kW indicates the maximum power demand during peak periods, which is essential for managing peak loads and optimizing operating costs. Including both measures provides a comprehensive understanding of the system’s performance under different strategies.

Except for the host priority strategy, in terms of the average total energy consumption under the design load, compared with the ice-melting priority control strategy and the constant-proportion control strategy, the average energy-saving percentages of the optimization strategy were 1.025% and 1.775%, respectively. Simultaneously, in terms of the average cost savings under the design load, compared with the chiller priority, ice-storage priority, and constant-proportion control strategies, the average cost-saving percentages of the optimization strategy were 19.2%, 4.4%, and 5.1%, respectively. In terms of the maximum daily power consumption, compared with the chiller priority, ice-storage priority, and constant-proportion control strategies, the average power-saving percentages of the optimization strategy were 30.0%, 18.1%, and 8.9%, respectively. In addition, as the load rate decreased, the optimized operation strategy could achieve a better goal of reducing the maximum power demand in the peak power price segment. It can be observed that under various load conditions, the operating electricity cost of the optimization strategy and the maximum power in the peak electricity price segment were the lowest. Therefore, the optimization strategy could achieve better control effects.

5. Conclusions

This study developed an integrated predictive control model for regional cooling systems, incorporating renewable energy sources and ice thermal storage to enhance cooling load management. The research yielded the following key findings and identified several areas for future investigation:

• The study demonstrated that integrating the ABC algorithm with the BP neural network markedly improved load forecasting accuracy. The ABC-BP model achieved a correlation coefficient R² of 0.97 and a coefficient of variation in the CV-RMSE of 16.67%, surpassing the performance of traditional BP, SVR, and LSTM models. This advancement highlights the efficacy of metaheuristic optimization in refining neural network predictions. Future research could explore the potential of hybrid models that integrate ABC-BP with cutting-edge machine learning techniques, such as deep learning and ensemble methods, to further enhance forecasting precision and adapt to complex and dynamic operational environments.
• The proposed optimization strategy, which integrates river-source heat pumps with ice storage, demonstrated superior performance compared with conventional control strategies such as chiller priority, ice-storage priority, and constant proportion. The model reduced average daily operational costs by up to 19.20% and peak power consumption by up to 30.02%. These results underscore the potential of optimization strategies to deliver significant cost savings and operational efficiencies. Future work could investigate the model’s scalability across diverse climatic regions and varying cooling demands and evaluate its adaptability to different operational scenarios to validate its robustness and versatility.
• The integrated control model effectively minimized energy consumption and peak power demand, leading to substantial cost savings and enhanced operational efficiency. The model’s capability to manage peak loads and optimize energy use illustrates its potential for broad implementation in energy management systems. Further research could examine the integration of this model with real-time dynamic pricing and advanced energy management systems to better address market fluctuations and enhance economic performance. Additionally, exploring the synergy between this model and emerging smart-grid technologies could provide new insights into optimizing regional cooling systems.
• Despite its contributions, the study faced several limitations. The model’s performance was evaluated under specific climatic and operational conditions, which may not fully represent other environments. Additionally, reliance on historical data for load forecasting may not account for future climatic anomalies or sudden shifts in energy prices. The computational complexity of the optimization algorithm may also restrict its application in smaller-scale systems. Future research could focus on addressing these limitations by testing the model in a range of environmental conditions, incorporating adaptive forecasting techniques to account for future uncertainties, and developing more computationally efficient algorithms to enhance practical applicability.