Study of the Optimal Control of the Central Air Conditioning Cooling Water System for a Deep Subway Station in Chongqing

Abstract

Cooling water, a crucial component of the central air conditioning setup, exerts a relatively minor direct impact on the thermal comfort of building indoor environments while it has a great effect on the system’s energy efficiency. Numerous studies exist on the cooling water system, particularly focusing on the process by which the cooling tower system operates, but the linkage between the chiller and the cooling tower is typically overlooked. When the connection is long and the passage environment for the pipeline is not conventional, it cannot be neglected for the optimal control for system efficiency improvement and energy consumption reductions. Throughout this research, a control strategy of the cooling water system for deep subway stations with long pipelines is presented. This cooling system was connected with outdoor cooling towers through a corridor about one hundred meters long. In this process, the cooling water temperature is influenced by the corridor’s thermal environment. For this study, an online control strategy optimizes the cooling water temperature, and a simulation platform of the air conditioning cooling water system of the deep subway station was also developed to evaluate the energy-saving potential of the control strategy of this cooling water system. Atop this platform, a simplified heat transfer model of the pipe corridor was created to determine the cooling capacity provided by the cooling water pipe in the corridor. The outcomes suggest that, as opposed to the conventional control mode, the energy-saving ratio of the optimal control strategy during a typical day may reach 4.1%, and the cooling source system’s Coefficient of Performance (COP) might see an increase of about 4.2%. The energy consumption of the water system throughout the whole cooling season may decrease by 9778 kWh, and the energy-saving rate is 4.1%. The results also demonstrate that the cooling water pipes release heat to the air in the corridor most of the time, and the released heat is larger than the absorbed heat. The maximum heat dissipation to the air in the corridor from the cooling water supply and return pipe can be up to 24.3 kW. The cooling effect of the corridor of subway stations with large depths below the ground surface cannot be ignored when optimal control is considered for the cooling water system.

1. Introduction

As the expansion of the economy and urban development intensifies, and urban regions spread, the number of buildings has increased sharply, especially in China [1]. This results in the large social demand for public transportation. Urban rail transit is an important means of transportation for people to travel due to many advantages such as cleanliness, efficiency, convenience, punctuality, and large volume. To alleviate traffic pressure, major cities have constructed efficient, environmentally friendly, and high capacity unban rail transit systems [2,3]. By the end of 2020, subways were in operation in 193 cities across 56 countries/regions [4]. The study by Su and Li [5] shows that the annual energy consumption of subway stations reached as high as 131–144 kWh/m², utilizing energy statistics from 341 subway stations located in diverse climate zones. For a subway station, energy consumption mainly includes the air conditioning (AC) and ventilation system, lighting and power distribution system, signal and monitoring system, and traction power supply system. Among them, the AC and ventilation system comprises roughly 35–50% of the energy consumption of subway stations [6]. The subway AC and ventilation system includes the AC water system and the ventilation system while the AC water system takes 60% and the ventilation takes 40% [7]. These studies on subway stations indicate that reducing the energy consumption of subway AC and ventilation systems constitutes a pivotal factor in improving the energy efficiency and achieving energy-saving in urban rail stations since the system operation should work with the change and fluctuations of passenger flow and environmental climate parameters.

When it comes to the system categorization of the AC system for energy-saving optimization, it is typically divided into the optimization of the AC system and the optimization of the AC water system [8,9,10]. The optimization control of the AC water system mainly focuses on two aspects: one focuses on optimizing the chilled water system, while the other targets optimizing the cooling water system. Optimizing the chilled water system usually refers to the optimization of the supply chilled water temperature and/or the chilled water flow rate. Optimizing the cooling water system often refers to the optimization of the supply cooling water temperature and/or the water flow rate. However, in terms of energy efficiency for air conditioning systems, the issues considered and optimization strategies differ between the chilled water system and the cooling water system. Zhou et al. [11] introduced a strategy for optimizing operational parameters utilizing unsupervised data mining techniques. The unsupervised data mining procedure includes data partitioning, data preparation, using the Apriori algorithm to extract strong association rules, among other steps. The validity of this approach was confirmed using data from a chiller system in a subtropical building. The findings indicated that, after the application of the optimization technique, the energy consumption of the chiller was reduced by 11.6% during the summer study period and by 13.33% in the winter study period. Zhang et al. [12] proposed cooling towers in a data center as a natural cooling source for the water side cooling system. The findings indicate that the natural cooling duration is 32% of the year and the average annual PUE may reach 1.35. Dong et al. [13] carried out research on energy efficiency using natural cooling and found that when the chilled water temperature is set to 20 °C, the COP may increase by approximately 23.7%, and the energy-saving rate is about 19.2%. Kareem et al. [14] used a direct evaporative cooling method to enhance the efficiency of AC systems, resulting in a 5–7.5% increase in cooling capacity. Fang et al. [15] proposed a method that facilitates the optimal matching of the chilled temperature difference within the AC system by maintaining a steady chilled water temperature difference between the inlet and outlet of the terminal unit. This method effectively addresses the chilled water mismatch problem, enhancing the system stability and operational efficiency. The findings show that energy consumption may be reduced by about 12.5% by using this strategy.

As for the cooling side, there is much research on energy performance improvement. Yang et al. [16] proposed an advanced parallel artificial immune algorithm to determine the optimal functioning parameters for the coordinated operation of cooling equipment. The results indicated that, following optimization, the total system energy consumption decreased by 15.19%. Lu et al. [17] presented an optimization control strategy based on a model by using an improved genetic algorithm to reduce the running costs of the condensate loop. Karami and Wang [18] used an algorithm based on particle swarm optimization to seek the ideal control parameters of the chiller. Ma et al. [19] developed a heat transfer model for cooling towers and established an online optimization digital model for the cooling water system. The outcomes of the simulation demonstrate that the proposed optimization method has the potential to decrease energy consumption by 15.3% in comparison to other strategies. Sun and Reddy [20] proposed a universal strategy for refining the management of the current building’s AC system. A CSB-SQP algorithm was formulated by merging the modular system simulation method with the SQP technique. The robustness and efficiency of this approach were demonstrated through an example of a basic cooling system plant. This method offers directions for engineers to achieve optimal management of the building’s AC system across various management conditions by using the optimal method settings. Ma et al. [21] presented a model-based regulatory management tactic for instantaneous management and functioning of buildings’ central cooling water systems. The method utilizes clarified semi-physical models of cooling tower and chiller to forecast the environment quality, system energy consumption, and the system’s reaction to changes in the control configurations. The yearly energy-saving achieved by implementing the suggested model-based regulatory management tactic amounted to 183,495 kWh as opposed to the fixed schedule control technique. Ma et al. [22] took a clarified model to the next level with further development for heat dissipation of a cooling tower. An evaluation method was proposed to analyze the performance of the existing operational state by integrating the heat dissipation model with the power models of other system components, focusing on the efficiency of heat dissipation in the cooling tower. The experimental findings indicate that the heat dissipation computed by the clarified model aligns with the results derived from the experimental data, and that the actual water flow rate at the optimal point corresponds with the water flow rate at the optimal point as determined by the optimization assessment method. Due to the energy consumption of the AC and ventilation system, it accounts for almost half of the overall energy consumption of subway stations hence many researchers also devoted their efforts for improving the energy efficiency in subway stations. Zhang et al. [23] proposed a novel environmental control system by using advanced platform doors and controllable ventilation openings. The outcomes revealed that energy consumption could be decreased by 20.64–60.43% when compared to traditional platform screen door systems. Yang et al. [2] carried out a study of frequency conversion technology on air handling units and chilled water pumps in subway stations for energy efficiency improvement. The result shows that using variable frequency technology can reduce total system energy consumption, although it may increase chiller energy consumption.

Nevertheless, there is a scarcity of studies focusing on energy-saving interventions for cooling water systems in subway stations, as well as the outcome of the cooling water pipe on energy efficiency. In traditional studies, since the cooling water pipelines from the cooling tower to the chiller are short and exposed to the surrounding environment, the condenser inlet cooling water temperature (T_{cd_in}) is taken as the same as the cooling water temperature at the cooling tower outlet. Therefore, the cooling water temperature at the cooling tower outlet is used as an optimization parameter. In China, there are many subway stations 50 m below the ground surface, and some may be 100 m below the ground surface, especially in the mountain city Chongqing. When the subway station is very deep below the ground surface, a pipeline corridor is necessary from the cooling water pipe to connect the chiller condenser in the chiller plant on either side of the station hall or platform and the cooling tower on the ground surface. The cooling water pipeline passes through a corridor hundreds of meters long. This corridor is located beneath the ground surface where the temperature is lower and more stable than the surface air temperature. The pipeline has a cooling effect, and both the air flow and the corridor walls affect the temperature changes in the water in the pipes, which further influences the performance of the cooling tower and the chiller. Therefore, when studying optimization control strategies for air conditioning cooling water systems in deep underground spaces, it is crucial to consider the heat transfer occurring in the cooling water as it flows through the pipeline corridor.

In this study, the subway station of concern is located at Chongqing and is about 100 m below the ground surface. An optimal approach for managing the cooling water system for the deep subway station was developed by considering the cooling effect of the pipeline corridor. For this study, the simplified heat transfer model of the pipe corridor was developed to obtain the cooling effect of the cooling water pipe in the corridor followed by the simulation platform of the AC cooling water system of the deep subway station. An implementation structure of this developed optimal control is also presented to evaluate the energy-saving potential of the control strategy for this cooling water system based on this simulation platform. Building on the simulation results, the control and thermal performance of the “online” implementation of the strategy is presented, including the heat transfer between the supply/return cooling water and the corridor air, although this online is “virtual” in the simulation process. The results show good energy-saving performance with an energy-saving rate of 4.1%.

2. System Overview

The AC water system of concern is a central chilled water system to cool down the equipment and management rooms of a deep underground subway station. This station is a double-layer island platform station, which was constructed by using a concealed excavation method. The deepest section reaches a burial depth of 94.4 m. This central chilled water system is cooled by using an open cooling water loop with cooling towers on the ground surface. Therefore, the cooling water pipeline passes through a conduit corridor extending over one hundred meters to connect with the outdoor cooling towers, as presented in Figure 1.

The graphical representation of this system is shown in Figure 2. It is designed with two chillers based on the cooling load of the subway station. Both chillers are identical and screw-type. Each chiller has the rated cooling capacity of 387 kW, a rated power of 71 kW, an evaporator rated flow of 66.6 m³/h, and an inlet/outlet temperature of 12/7 °C. The condenser has a rated flow of 79 m³/h with an inlet/outlet temperature of 32/37 °C. The chiller system is equipped with two cooling water pumps (Shanghai Liancheng Group Co., Ltd., Shanghai, China), two chilled water pumps (Shanghai Liancheng Group Co., Ltd., Shanghai, China), and two cooling towers. The parallel chilled water pumps are uniformly rated with a flow rate of 67 m³/h, a power output of 15 kW, and a head of 36 mH₂O. The parallel cooling water pumps are uniformly rated with a flow rate of 90 m³/h, a power output of 15 kW, and a head of 33 mH₂O. Each cooling tower (Guangdong Laxun Technology Exploit Co., Ltd., Guangzhou, Guangdong, China) is designed for a rated cooling water flow rate of 100 m³/h with a fan power of 3.0 kW. The design cooling water inlet/outlet temperature is 37/32 °C. This central chilled water system operates all the hours in the cooling season to cool down the equipment and management rooms.

3. Strategy for Optimal Control of Condenser Inlet Cooling Water Temperature

The optimized control strategy of T_{cd_in} is a crucial means to implement energy-saving measures for the efficient functioning of the AC water system. For conventional study, the final temperature of the cooling water after passing through the cooling tower is used as the parameter for optimization since the distance of the cooling water pipeline connecting the chiller and the cooling tower is not long or exposed to the ambient environment, and the T_{cd_in} is the same as the outlet cooling water temperature from the cooling tower. In this study, the pipeline passes through a long pipeline corridor, which is under the ground surface with lower and almost constant temperature than the ambient air temperature on the ground surface. There is a cooling effect for the pipeline, and T_{cd_in} is different from the cooling water temperature exiting the cooling tower. Therefore, T_{cd_in} is taken as the parameter to be optimized.

Based on the condition of maintaining the safety and reliability of the equipment, constant regulation of T_{cd_in} can not only enhance the cooling efficiency of the cooling water system, including the condenser and cooling tower, but also can decrease the water system’s energy consumption while simultaneously optimizing both economic and environmental benefits.

3.1. Concept and Flowchart of Strategy

The optimal control strategy for T_{cd_in} is crucial for achieving energy-saving and efficient operation in central AC water systems of deep underground subway stations. The strategy aims to minimize the energy usage of the AC water system as much as possible. The process flow is illustrated in Figure 3.

To accomplish this objective, it is first essential to collect a large amount of the actual operation data of the AC water system for the deep subway station, then calculate the energy consumption (E) of the water system under various operation conditions, and finally find the T_{cd_in} that minimizes energy consumption under the same cooling load and the outdoor weather condition. Based on the optimal cooling water return temperature, the outdoor weather condition, and the indoor cooling load, a least square algorithm was used to establish the optimal control strategy model for the condenser inlet cooling water return temperature. A strategy module was then developed according to this model and integrated into the AC water system platform to enable online control of the AC cooling water system. This platform can monitor “real-time” changes in the operation of the AC water system and predict the optimal cooling water temperature setpoint at the condenser inlet (T_{cd_in,o}) based on the working conditions by using the strategy model. According to this setpoint, the AC water system platform sends the control signal to the cooling tower controller, which may transmit the frequency signal or current signal to the cooling tower fan for variable frequency control. This ensures that the system can quickly respond to weather conditions and cooling load conditions, and then adjust the T_{cd_in} to the optimal setpoint thus achieving the energy-saving and consumption reduction goals.

3.2. Control Strategy Model and Flowchart of Parameter Determination

This strategy of T_{cd_in} proposed in this research uses the optimal control strategy model as shown in Equation (18) to predict T_{cd_in,o} in different working conditions. This model replaces the cooling demand or cooling load with the load rate and provides T_{cd_in,o} based on the load ratio of the chiller and real-time wet bulb temperature.

$$T_{cd\_in,o}=n_0+n_1{T}_{wb}+n_{2}PLR$$

(1)

where T_wb is the outdoor air wet bulb temperature (°C), T_{cd_in,o} is the optimal setpoint of the condenser cooling water temperature (°C), PLR is the cooling load ratio of the chiller expressed as the ratio of the actual cooling load to the rated cooling capacity, and subscripts n₀~n₂ are the parameters of the linear regression model by using the least square method. In practical engineering, the load ratio can be represented by the measured current percentage of the chiller.

Collection of key operation data of the AC water system is essential for developing the optimal control strategy model of T_{cd_in}. To formulate an accurate optimal control strategy, it is necessary to organize and analyze a large amount of operation data from the AC water system and determine the optimal condenser inlet cooling water temperature under various operation conditions. However, in practical engineering, obtaining sufficient and effective operation data may not always be possible, which makes it difficult to analyze the system’s performance and to develop a strategy for T_{cd_in}. This study adopts a simulation-based approach to obtain effective operation data. By adjusting the condenser cooling water return temperature as the control variable on a constructed water system simulation platform, simulations are carried out under various operation conditions. This allows for the collection of extensive and comprehensive operation data of the system. The optimal cooling water return temperature for various conditions during the cooling season is determined with the objective of achieving minimal energy usage. The process of acquiring the operation dataset of the water system is depicted in Figure 4.

With the optimal operation parameter dataset of the AC water system, the T_{cd_in,o} with the minimum energy consumption, the coincident T_wb, and the cooling energy output of the chiller can be extracted by one operation condition. The cooling energy output of the chiller is used for the calculation of the partial load ratio. For all the operation datasets, vector Y and matrix A can be constructed. Utilizing the least square technique, the parameters of the optimal control strategy model can be solved. The flowchart of the linear regression of the control strategy model is illustrated in Figure 5.

4. Simulation Platform of AC Water System

To obtain the yearly operation data of the AC water system with different condenser inlet cooling water temperature setpoints, a simulation platform of this AC water system was constructed. In this platform, the cooling tower models and chiller model are described and validated. It is worth noting that accuracy of the simulation result is very important. In this study, the main models of the platform, i.e., the chiller model and the cooling tower, were validated by using field measurements. This is also the commonly used approach for ensuring the accuracy of the whole simulation [24,25]. There is a cooling effect for the pipeline since it passes through a long underground pipeline corridor so the heat transfer model of pipeline in the corridor was also developed; this model is integrated to evaluate the cooling effect of the long underground pipeline corridor.

4.1. Chiller Model

The chiller model considers the operation characteristics of the screw chiller under partial load and full load conditions in this research. A comprehensive explanation of the model is provided in refs. [26,27]. The outputs of this model include the cooling capacity (Q_ev), the COP, and the actual power consumption of the chiller (W). Under full load, W is related to the theoretical compression power (W_in) of the unit and the power needed to counteract friction losses in the mechanical components (W_lo), as presented in Equation (2). The cooling capacity of the chiller is related to the refrigerant flow rate (M_R), the enthalpy at the evaporator outlet (h₁), and the condenser outlet (h₂), as shown in Equation (3). The heat dissipation of the condenser (Q_cd) is shown in Equation (4). The COP of the chiller can be calculated using the ratio of the cooling capacity to the actual power consumption, as shown in Equation (5). The efficiencies of the evaporator and condenser are shown in Equations (6) and (7), respectively.

$$W=W_{lo}+\alpha W_{in}+W_{in}$$

(2)

$$Q_{ev}=M_R\left(h_1-h_2\right)$$

(3)

$$Q_{cd}=Q_{ev}+W$$

(4)

$$COP={\displaystyle \frac{Q_{ev}}{W}}$$

(5)

$${\epsilon }_{ev}=1-\exp \left(-{\displaystyle \frac{U{A}_{ev}}{c_{p,w}{M}_{wev}}}\right)$$

(6)

$${\epsilon }_{cd}=1-\exp \left(-{\displaystyle \frac{U{A}_{cd}}{c_{p,w}{M}_{wcd}}}\right)$$

(7)

where W is the actual power consumption of the chiller, measured in watts, W; α is the power loss coefficient of the compressor; W_in is the theoretical compression power required to compress the refrigerant, measured in watts, W; W_lo is the power required to overcome friction losses in the mechanical components, measured in watts, W; Q_ev is the cooling capacity of the chiller, calculated based on inlet and outlet chiller water temperature as well as the chilled water flow rate in watts, W; M_R is the mass flow rate of the refrigerant, g/s; h₁ is the enthalpy at the evaporator outlet, J/kg; h₂ is the enthalpy at the condenser outlet, J/kg; c_p,w is the specific heat capacity of water, J/(kg·K); M_wev is the water flow rate in the evaporator, kg/s; M_wcd is the water flow rate in the condenser, kg/s; ε_ev is the efficiency of the evaporator; ε_cd is the efficiency of the condenser; UA_ev is the product of the heat transfer coefficient and the heat transfer area of the evaporator, W/K; and UA_cd is the product of the heat transfer coefficient and the heat transfer area of the condenser, W/K.

The chiller model requires the identification of two characteristic parameters: W_lo and α. Using the performance data provided in the chiller manual, both parameters are identified as W_lo = 26,500 W and α = −0.426. Chiller power consumption under different operations can be calculated after inputting the identified characteristic parameters into the model and configuring the operation parameters based on the operation conditions specified in the product manual. The calculated power consumption of this chiller (i.e., model prediction) can be compared to the power data from the product manual at different operation conditions. The results are depicted in Figure 6. As depicted in this figure, there is some deviation between the model-predicted power consumption and the actual power consumption from the chiller manual under various operating conditions. However, the relative error falls within the range of −5% to +5%, indicating that the chiller model is capable of forecasting the W with believable accuracy.

4.2. A Heat Transfer Model of the Pipeline in the Corridor

The cooling water supply and return pipes of the station’s AC system need to pass through a long conduit corridor to connect to the outdoor cooling towers. The airflow in the corridor and the corridor walls affects the temperature of the water in the pipes. To obtain a more profound understanding of the heat exchange characteristics of the cooling water in the corridor, a streamlined heat network (RC) model of the conduit corridor is constructed to analyze the temperature variations in the water while it travels through the corridor. The heat exchange processes include air-to-rock heat exchange within the corridor, air-to-pipe wall heat exchange, and pipe wall-to-cooling water heat exchange. Based on these heat transfer processes, a streamlined heat transfer model of the conduit corridor is developed, as presented in Figure 7, which includes the cooling water supply and return pipe RC model, the corridor air RC model, and the corridor wall RC model. The surface temperature of the corridor wall (T_p) is related to the corridor air (T_a) by thermal resistance (1/hA), and the effect of heat accumulation in the ground during the year is represented by the thermal capacitance nodes C₃, C₄, C₅, etc. The temperatures of these nodes of the ground soil are initiated by the ground temperature. In fact, this ground temperature is taken as the average of yearly outdoor air temperature.

The 2R1Cmodel is used to represent the heat transfer process of the cooling water supply and return pipes with the convective heat transfer between the pipe walls and the corridor air represented by convective heat transfer resistance [10]. On the basis of the energy-saving of the water, the energy-saving equations for the average temperatures T_w1 and T_w2 in the cooling water supply and return pipes can be expressed by Equations (8) and (9).

$$C_{w1}{\displaystyle \frac{d{T}_{w1}}{dt}}={\displaystyle \frac{T_{w1\_in}-T_{w1}}{R_{w1}}}+{\displaystyle \frac{T_a-T_{w1}}{R_{w2}+1/\left(h_{ap1}{A}_1\right)}}$$

(8)

$$C_{w2}{\displaystyle \frac{d{T}_{w2}}{dt}}={\displaystyle \frac{T_{w2\_in}-T_{w2}}{R_{w3}}}+{\displaystyle \frac{T_a-T_{w2}}{R_{w4}+1/\left(h_{ap2}{A}_2\right)}}$$

(9)

where C_w1 and C_w2 are the thermal capacitances of the water in the cooling water supply and return pipeline, respectively, J/K; T_w1 and T_w2 are the average temperatures of the water in the cooling water supply and return pipelines, respectively, °C; T_{w1_in} and T_{w2_in} are the outlet water temperature of the cooling water supplying from the condenser and the outlet water temperature of the cooling water returning from the cooling tower, respectively, °C; T_a is the average air temperature in the corridor, °C; h_ap1 and h_ap2 are the convective heat transfer coefficients between the corridor air and the supply and return pipe walls, taken as 13.96 W/(m²·K); A₁ and A₂ are the surface areas of the cooling water supply and return pipelines, respectively, m²; R_w1 and R_w2 are the thermal transfer resistances related to the water flow rate and the water side convective heat transfer coefficient in the supply water pipeline, W/(m²·K).; R_w3 and R_w4 are the thermal transfer resistances related to the water flow rate and the water side convective heat transfer coefficient in the return water pipeline, W/(m²·K).

In the RC model for the corridor air, there are heat transfer processes between the walls and the air of the cooling water return and supply pipes, as well as between the air and the internal wall of the pipeline corridor. In the corridor cavity, the air temperature is also affected by the mass air flow rate and related to the inlet air temperature. Therefore, it is essential to add three convective heat transfer resistances at the air node to represent the heat transfer between the corridor air and the cooling water pipes, as well as to represent the heat transfer between the corridor air and the internal wall of the pipeline corridor. By considering the air in the corridor as a whole and using its average temperature to represent the system, the energy-saving equation for T_a can be expressed by Equation (10). The thermal resistance $R_{a1}$ can be calculated as Equation (11), which is related to the mass flow rate of the corridor air.

$$C_a{\displaystyle \frac{d{T}_a}{dt}}={\displaystyle \frac{T_{a\_in}-T_a}{R_{a1}}}+{\displaystyle \frac{T_p-T_a}{1/\left(hA\right)}}+{\displaystyle \frac{T_{p1}-T_a}{1/\left(h_{ap1}{A}_1\right)}}+{\displaystyle \frac{T_{p2}-T_a}{1/\left(h_{ap2}{A}_2\right)}}$$

(10)

$$R_{a1}={\displaystyle \frac{1}{2M_a{c}_{p,a}}}$$

(11)

where C_a is the thermal capacity of the corridor air, J/K; T_a is the average temperature of the corridor air, °C; T_{a_in} is the inlet temperature of the corridor air, °C; T_p is the internal wall surface temperature of the corridor, °C; T_p1 and T_p2 are the wall temperatures of the cooling water supply and return pipelines, respectively, °C; h is the convective heat transfer coefficient between the corridor air and the surrounding wall, 13.96 W/(m²·K); A is the surface area of the internal wall of the corridor, m²; M_a is the mass flow rate of the corridor air, kg/s; and c_p,a is the air-specific heat of the corridor air, J/(kg·K).

In this research, the AC water system operates in the summer. The air in the corridor is mainly from the subway tunnel, and its initial temperature is consistent with the tunnel air temperature, which is also being cooled by the tunnel surface. In fact, it is also affected by the piston effect, as T_a is not consistent with the outdoor air temperature. The tunnel air temperature can be determined according to the heat transfer model of the subway tunnel together with the outdoor air temperature. When analyzing the process of the heat transfer of the cooling water pipeline in the pipeline corridor, only T_{a_in} for 4 months from June to September was selected as the outdoor air temperature, and T_{a_in} as well as the boundary condition are presented in Figure 8. The highest outdoor air temperature is 36.5 °C. The mass flow rate of the corridor air can be determined by using the sectional area and the measured sectional air velocity as 3.2 m/s.

The RC model for the surrounding rock structure of the corridor is divided into three sections, i.e., the upper structural layer, the core layer, and the lower structural layer by using the top and bottom of the corridor as boundaries. Taking node T₁ as an example in the simplified RC model of the corridor surrounding rock structure, its heat balance equation is given by Equation (12).

$$C_1{\displaystyle \frac{d{T}_1}{dt}}={\displaystyle \frac{T_{top}-T_1}{R_1}}+{\displaystyle \frac{T_2-T_1}{R_2}}$$

(12)

In the equation, T_top is the ground temperature, °C; R₁~R₂ are the thermal resistances of the soil at different locations in the model, K/W; and C₁ is the thermal capacities of the corresponding soil layers, J/K.

4.3. Cooling Tower Model

The cooling tower models include heat and mass balance-based models, ε-NTU models, data-driven models, and numerical simulation models. The heat transfer unit method is used to model the cooling tower since it is a widely used model due to the simplicity in calculation, broad applicability, and good accuracy. The equivalent specific heat of the air side, c_pe, can be calculated as Equation (13). Given the product of the heat transfer coefficient and area UA between the air and water, the NTU and the ε of the cooling tower can be obtained as Equations (14) and (16). The heat transfer rate between the cooling water and the outdoor wet air can be determined using Equation (17). After calculating the heat exchange between the air and water, T_{wb_out} and the cooling water temperature at the cooling tower outlet can be calculated using Equation (18) and Equation (19), respectively.

$$c_{pe}=\left(h_{a\_out}-h_{a\_in}\right)/\left(T_{wb\_out}-T_{wb\_in}\right)$$

(13)

$$NTU={\displaystyle \frac{UA·c_{pe}/c_p}{C_{min}}}$$

(14)

$$\omega ={\displaystyle \frac{C_{min}}{C_{max}}}$$

(15)

$$\epsilon ={\displaystyle \frac{1-exp\left[-NTU\left(1-\omega \right)\right]}{1-\omega ·exp\left[-NTU\left(1-\omega \right)\right]}}$$

(16)

$$Q=\epsilon C_{min}\left(T_{w\_in}-T_{wb\_in}\right)$$

(17)

$$T_{wb\_out}=T_{wb\_in}+Q/\left(c_{pe}·m_a\right)$$

(18)

$$T_{w\_out}=T_{w\_in}-Q/\left(c_{pw}·m_w\right)$$

(19)

where c_pe is the equivalent specific heat of the air, J/(kg·K); h_{a_in} is the enthalpy of the air at the cooling tower inlet, J/kg; h_{a_out} is the enthalpy of the air at the cooling tower outlet, J/kg; T_{wb_in} is the wet bulb temperature of the air at the cooling tower inlet, °C; T_{wb_out} is the wet bulb temperature of the air at the cooling tower outlet, °C; T_{w_in} is the temperature of the cooling water at the cooling tower inlet, °C; C_min is the smaller value between the heat capacity of the cooling water and the heat capacity of the ideal saturated moist air; C_max is the larger value between the heat capacity of the cooling water and the heat capacity of the ideal saturated moist air; ω is the heat capacity ratio; Q is the heat exchange rate of the cooling tower, W; T_{w_out} is the temperature of the cooling water at the cooling tower outlet, °C; m_a is the air flow rate of the cooling tower, kg/s; and m_w is the cooling water flow rate, kg/s.

The cooling tower is powered by the fan. The flow rate and power of the fan are related to the fan input frequency, and they can be simplified as the relationships shown in Equations (20) and (21).

$$m_a=m_{a\_de}{\displaystyle \frac{f_a}{f_{a\_de}}}$$

(20)

$$P_{ct}=P_{ct\_de}\left[a_3{\left({\displaystyle \frac{f_a}{f_{a\_de}}}\right)}^3+a_2{\left({\displaystyle \frac{f_a}{f_{a\_de}}}\right)}^2+a_1{\displaystyle \frac{f_a}{f_{a\_de}}}+a_0\right]$$

(21)

where m_a is the actual air flow rate of the cooling tower fan, kg/s; m_{a_de} is the rated air flow rate, kg/s; f_a is the actual frequency for the cooling tower fan, Hz; f_{a_de} is the rated frequency of the cooling tower fan, usually 50 Hz; P_ct is the actual power consumption of the cooling tower fan, W; P_{ct_de} is the rated power consumption of the cooling tower fan, W; and a₀, a₁, a₂, and a₃ are the fitting coefficients used in the relationships.

In the cooling tower model, the value of UA can be identified based on data from the product technical manual as UA = 32,700 W/(m²·K). By varying the frequency of the cooling tower fan from 30 Hz to 50 Hz with one Hz increments, the real-time power consumption of the fan is recorded at each frequency. Based on the collected data, the fitting coefficients for the cooling tower can be determined.

4.4. Simulation Platform

Based on the components and models, such as the heat transfer model of the pipeline together with the corridor, the models of the cooling tower, and the chiller together with the fan, the simulation platform for the AC water system of the deep subway station is shown in Figure 9. This system mainly includes six components, including the cooling tower module (Type 295), water collector module (Type 292), water distributor module (Type 292), heat transfer calculation module of the pipeline corridor (Type 298), water pump module (Type 294), chiller module (Type 296), and parameter output module (Type 25c). The chiller module, the heat transfer calculation module of the pipeline corridor, and the cooling tower module are coded based on the formulas mentioned earlier. The other modules are the Trnsys-embodied modules. The bold blue lines in the figure represent the connections between various devices in the cooling water system, facilitating the exchange of key parameters. The bold red lines represent the connections between devices in the chilled water system for transmitting information. The platform imports outdoor air temperature and the hourly cooling load for the cooling season through a data reading module. This platform uses some Trnsys-embodied modules such as distribution and collection manifolds to transmit the related parameters, completes the cooling water circulation process and the chilled water circulation process, and outputs the relevant operation parameters of the AC water system.

5. Parameters of Optimal Control Strategy

To formulate the optimal control strategy of the condenser inlet cooling water temperature (T_{cd_in}), the operation data of the AC water system need to be collected for the parameter determination of the optimal control strategy model. The simulation platform was developed and simulated to represent the “real-time” operation of the AC water system in this research.

To ensure the validity of the simulation, the setpoint of T_{cd_in} should not be lower than the lowest value of T_wb in the cooling season. The range of T_wb in the cooling season is 17.7 °C~30.9 °C, and the scope of the cooling water backwater temperature setting can be expanded to 17.7 °C~31.9 °C. To gain the optimal solution of T_{cd_in} more accurately, the interval of 0.1 °C is taken. In total, 142 setpoints are used in the AC water system platform for each operation condition including the outdoor air condition and the load condition. Then, 142 sets of operation data of the cooling season are obtained, which include the cooling capacity of chiller, T_{cd_in}, the pump energy consumption (E), and the fan energy consumption, as well as the weather condition, etc.

After that, E of the water system is calculated to find T_{cd_in,o}, which has the minimum E of the AC water system under the same condition. Then, the operation data at this condition is retrieved as a dataset of the optimal operation parameters of the AC water system. These operation datasets are used to fit the strategy model using Equation (1) to determine T_{cd_in,o}.

The optimal operation data of the cooling load conditions of 190 kW and 270 kW are presented for analysis, as shown in

Table 1. Optimal operation data at cooling load conditions of 190 kW and 270 kW.

Cooling load 190 kW
Outdoor air wet bulb temperature (°C)	19.6	21.7	22.9	23.2	24.5	25.6	26.7
Minimum E of the water system (kWh)	68.3	70.4	71.7	72.2	73.5	74.7	76.0
Optimal condenser inlet cooling water temperature (°C)	21.8	23.6	24.8	25.1	26.2	27.1	28.2
Cooling load 270 kW
Outdoor air wet bulb temperature (°C)	19.6	21.7	22.9	23.5	24.4	25.6	26.7
Minimum energy consumption of the water system (kWh)	78.7	80.9	82.6	83.5	84.5	86.4	87.6
Optimal condenser inlet cooling water temperature (°C)	22.1	23.9	24.9	25.5	26.2	27.4	28.2

. It can be seen that the minimum E of the water system rises when T_wb is higher even if the cooling load is the same. It can also be observed that a higher cooling load results in a higher minimum E of the water system even when T_wb is the same. The corresponding T_{cd_in,o} also becomes slightly higher.

To gain a deeper insight into the correlation between T_{cd_in} and the energy consumption of the AC water system at a specified operation condition, the operation data with a cooling load of 190 kW and T_wb of 25.6 °C are presented in

Table 2. Operation data with different setpoints of T_{cd_in}.

Setpoint (°C)	Condenser Inlet Cooling Water Temperature (°C)	Frequency (Hz)	Fan Energy Consumption (kWh)	Chiller Energy Consumption (kWh)	Total Energy Consumption of the Air Conditioning System (kWh)	Water System COP
25.6	26.28	50.00	6.49	42.06	78.55	2.41
25.7	26.29	50.00	6.49	42.06	78.55	2.41
25.8	26.29	50.00	6.49	42.06	78.55	2.41
25.9	26.31	50.00	6.49	42.09	78.58	2.41
26.0	26.37	46.54	5.38	42.16	77.54	2.45
26.1	26.43	43.37	4.50	42.24	76.74	2.47
26.2	26.49	40.58	3.83	42.32	76.15	2.49
26.3	26.56	38.12	3.30	42.41	75.71	2.51
26.4	26.64	35.93	2.88	0.04	75.38	2.52
26.5	26.71	33.98	2.55	42.59	75.14	2.52
26.6	26.79	32.24	2.27	42.69	74.96	2.53
26.7	26.87	30.67	2.05	42.80	74.84	2.53
26.8	26.96	29.25	1.86	42.90	74.76	2.54
26.9	27.04	27.96	1.70	43.01	74.71	2.54
27.0	27.13	26.79	1.56	43.12	74.68	2.54
27.1	27.22	25.72	1.44	43.23	74.67	2.54
27.2	27.31	24.74	1.34	43.35	74.69	2.54
27.3	27.40	23.84	1.25	43.46	74.71	2.54
27.4	27.49	23.01	1.17	43.58	74.75	2.54
27.5	27.59	22.23	1.10	43.70	74.80	2.54
27.6	27.68	21.48	1.03	43.83	74.86	2.53
27.7	27.78	20.73	0.97	43.95	74.91	2.53
27.8	27.83	20.12	0.92	44.01	74.93	2.53
27.9	27.83	20.00	0.91	44.01	74.92	2.53
28.0	27.83	20.00	0.91	44.01	74.92	2.53

. It can be used to assess the change in E of the water system at different setpoints of T_{cd_in}. Since T_{cd_in} cannot be lower than the T_wb and the lower limit of the fan frequency makes the cooling water temperature reach the maximum, the operation data under this load condition with T_{cd_in} ranging from 25.6 °C to 28.0 °C are used for analysis, and the operation data of the water system under the selected working conditions are shown in Table 2. It is noted that the cooling water pump and the chilled water pump are constant, and the total power consumption in one hour is 30 kWh.

Clearly, the energy consumption (E) of the AC water system initially declines and then increases as the setpoint of T_{cd_in} is incremental. The minimum E is 74.67 kWh with a setpoint of 27.1 °C, a fan frequency of 25.72 Hz, and an energy-saving rate of 5.0% when compared to E at a fan frequency of 50 Hz. It can also be observed that E of the chiller increases 0.1 kW and E of the fan decreases more for the increase in T_{cd_in} by 0.1 °C due to the fact that the fan frequency decreases gradually.

All the optimal operation datasets can be constructed following the flowchart in Figure 4. The coefficients of the optimal control strategy model as shown in Equation (1) can be determined by applying the least square method following the flowchart of the control strategy model in Figure 5. The resultant coefficients are n₀ = 1.8096, n₁ = 0.9076, and n₂ = 3.2657.

The principle of the least square method is to find a set of parameters n (n₀, n₁, n₂) that minimize the sum of the square residuals between the prediction and the actual “measurement”. To analyze the accuracy of the optimal control strategy model, a contrastive study is conducted between the predicted T_{cd_in,o} by using the model and the actually “measured” T_{cd_in,o}. T_{cd_in,o} can be predicted by using the model when the regressed parameters are substituted into the optimal control strategy model, and the partial load ratio as well as T_wb. The comparison between the prediction and the actual “measured” temperature is shown in Figure 10. The results indicate that the predicted T_{cd_in,o} when using the optimal control strategy model agrees well with the actual “measured” condenser inlet cooling water temperature with R² = 0.9951.

6. Implementation of Optimal Control Strategy and Result Analysis

6.1. Implementation Architecture of Optimal Control Strategy

When implementing the optimal control strategy model of the condenser inlet cooling water, a module of the optimal control strategy model was formulated in TRNSYS 18. This module was then integrated with the AC water system platform to enable “online” optimal control of T_{cd_in} for this system. This integrated platform is shown as Figure 11. This platform may implement the online “real-time” optimal control strategy of T_{cd_in} that uses the variables of T_wb and the chiller partial load ratio. The optimization control strategy module continuously collects T_wb and the chiller partial load ratio, and then calculates the optimal condenser inlet cooling water temperature (T_{cd_in,o}) setpoint that minimizes E of the AC water system. Based on this setpoint and the feedback “sensor-measured” T_{cd_in}, the cooling tower controller calculates the control signal by using a PI control algorithm. Then, the control signal is sent to the variable frequency drive of the cooling tower fan for enabling “real-time” variable frequency control of the fan. This ensures that T_{cd_in} approaches the optimal setpoint and the AC water system operates in a most energy-efficient state.

The hourly cooling load of the AC system for the equipment and management rooms in the cooling season is calculated in accordance with the measured chilled water flow rate and inlet and outlet chilled water temperature. The hourly outdoor T_db and T_wb profiles are presented in Figure 12. Compared with other months, August has generally high outdoor air temperatures with the temperature ranging from 19.4 °C to 38.9 °C, and wet bulb temperatures ranging from 17.7 °C to 30.9 °C. In the cooling season, the hourly cooling load is between 120 kW and 340 kW, and only a chiller is needed to meet the cooling demand.

6.2. The Control and Thermal Results of Online Implementation of the Strategy

This central chilled water system operates 24 h in the cooling season. The outdoor air conditioning and cooling load profiles of the cooling season from 1 June to 30 September are compiled as input for the platform of the AC water system. The operation data of this system by using the optimal control strategy of T_{cd_in} are obtained through simulation. Partial results are presented to analyze the control performance, as shown in Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18.

During the cooling season, T_wb, cooling demand, and other working conditions are constantly changing. These conditions directly affect the operation efficiency of the cooling water system mainly involving the chiller and the cooling tower fan. To maintain the efficient operation of the AC water system and minimize E, the optimal control strategy module in this platform continuously adjusts the frequency of the two cooling tower fans according to the setpoint T_{cd_in,o}. The frequencies of these two fans are the same. The frequency of the fan output after the optimal control is shown in Figure 13. The fan frequency in June is a little high, fluctuating around 35 Hz, while the frequency of the fan in other months is mostly between 30 Hz and 35 Hz. It is worth noting that the lowest E of the cooling water system may not always comply with the lower frequency of the fan after optimal control.

The power of these two cooling towers is presented in Figure 14. The change trend of the total power of the cooling tower is consistent with the trend of the fan frequency, and the value is basically between 1.5 kW and 3.0 kW. Compared to the designed power of the fan using 50 Hz, the total power of both cooling towers is reduced by about 4.5 kW~3.0 kW. In addition to the power of the cooling tower changing with the frequency of the fan, the power of the chiller changes, as shown in Figure 15. It can be noted that only one operating chiller is required in the cooling season. Compared to that in June, the power of the chiller in July, August, and September is larger, which is consistent with the changing trend of the cooling load, as presented in Figure 12. The minimum power of the chiller is 27.6 kW and the maximum is 72.4 kW. The average value is about 45.6 kW.

This research aims at developing an optimal control strategy for T_{cd_in}. Only the cooling water side is of much concern for optimal control while the flow rate of the chilled water and the supply and return temperatures of the chilled water do not change significantly before or after optimization. After implementing the optimal control strategy, the changes in T_{cd_in} and the supply cooling water temperature from the chiller condenser are presented in Figure 16. In the process of optimizing and controlling the cooling water system, the supply cooling water temperature from the condenser shows a certain fluctuation with a range of 21.3 °C~34.7 °C while T_{cd_in} fluctuates between 19.5 °C and 32.0 °C. The difference between the supply and return water temperature is about 2.3 °C.

The actual heat transfer in the pipeline corridor after the optimal control of the water system is analyzed. The heat exchange between the supply cooling water and the corridor air is shown in Figure 17 while the heat exchange between the return cooling water and the corridor air is shown in Figure 18. In Figure 17, the cooling water supply pipe mainly releases heat to the air in the corridor. The amount of heat is significant and can be up to 12.5 kJ. In Figure 18, the cooling water return pipe absorbs heat from the air in the corridor while the absorbed heat is still less than the released heat. In general, the corridor still plays a cooling role for the cooling water pipe. The maximum heat release of the cooling water supply and return pipe in the corridor is 24.3 kJ.

6.3. Energy Efficiency Evaluation

To evaluate the overall effectiveness and energy-saving effectiveness of the optimal control strategy of T_{cd_in}, a detailed analysis of the water system operation statistics before and after the optimal control strategy was conducted for a typical day. On this typical day, the outdoor air temperature and the cooling demand of the AC water system are presented in Figure 19. The outdoor T_db ranges between 27.3 °C and 30.8 °C, and T_wb ranges from 24.1 °C to 26.8 °C. The cooling demand of the AC water system remains within the range of 200 kW to 250 kW.

The system operation mode before the implementation of the optimal control strategy of T_{cd_in} is referred to as the existing mode. The system operation mode after implementing the optimal control strategy is referred to as the optimal mode. In the existing mode, one chilled water pump, one chiller, and one cooling water pump are operating while two cooling towers are in operation. The supply chilled water temperature is set to 7 °C, and the frequencies of the pumps and cooling tower fans are set to 50 Hz. In the optimal mode, the frequency of the cooling tower fans is adjusted according to the optimal control strategy while other the operating conditions remain unchanged. Figure 20 shows the profiles of T_{cd_in} with the existing mode and the optimal mode. The controlled T_{cd_in,o} closely followed the setpoint values, indicating the effectiveness of the optimal control strategy of T_{cd_in}. Compared to that of the existing mode, T_{cd_in} with the optimal mode fluctuates between 25.7 °C and 28.0 °C with an increase of approximately 0.5 °C to 0.8 °C.

The total power consumption of the water system and the change in the cooling source COP of the water system after implementing the optimal control strategy (i.e., optimal mode) was analyzed in order to further explore the influence of the optimal control strategy on the performance of the water system. The energy efficiency improvement by the optimal control strategy (i.e., with the optimal mode) was also evaluated. As demonstrated in Figure 21, the total power of the water system equipment with the optimal mode is reduced by about 3.5 kW when compared to the existing mode. On this daily cycle, the energy-saving rate of the water system reaches 4.1% after implementing the optimal control strategy of T_{cd_in}. As presented in Figure 22, the cooling source COP of the AC water system is improved to some extent, which is about 4.2% higher than that with the existing mode.

Table 3. Monthly energy consumption of air conditioning water system.

Energy Consumption (kWh)	June	July	August	September
Existing mode	53,887	61,630	64,303	58,071
Optimal mode	51,527	59,112	61,770	55,702
Energy-saving	2360	2518	2533	2369
Energy-saving rate	4.4%	4.1%	3.9%	4.1%

shows the monthly energy consumption of the chiller, cooling tower, and the entire water system in the entire cooling season under both the existing mode and the optimal mode. It is mentioned that the total energy consumption of the air conditioning water system (i.e., the AC water system) refers to the sum of the power consumption of the chiller, the chilled water pump, the cooling water pump, and the cooling tower fan. By comparing the total energy consumption of the AC water system under both modes, it is evident that the energy-saving rates in June, July, August, and September are 4.4%, 4.1%, 3.9%, and 4.1%, respectively, indicating that the optimal control strategy of T_{cd_in} can result in certain energy-saving effects, and the energy-saving rate mainly fluctuates around 4%.

Under the existing mode, the total energy consumption of the AC water system is 237,890 kWh, as presented in

Table 4. Total energy consumption of air conditioning water system in entire cooling season.

Energy Consumption (kWh)	Chiller	Cooling Tower Fan	Entire Water System
Existing Mode	131,000	19,020	237,890
Optimized Mode	133,408	6834	228,112
Saving amount	−2408	12,186	9778

. After implementing the optimal control strategy of T_{cd_in}, the energy consumption is reduced to 228,112 kWh, achieving an energy-saving rate of 4.1%. During the optimal control process, the energy consumption of the chiller increased by 2408 kWh while the energy consumption of the cooling tower decreased significantly by approximately 12,186 kWh.

Considering the changes in the two parameters of power consumption and cooling source COP, it can be understood that the optimal control strategy of T_{cd_in} effectively improves the overall energy efficiency of the AC water system. This increase means that the AC water system with the optimal control strategy consumes less energy at the same cooling amount thus further improving the energy efficiency of the system. This improvement is not only reflected in the direct reduction in energy consumption, but is also reflected in the increase in the cooling efficiency of the system, which is of great significance to reduce operation costs, improve energy efficiency, and meet the increasingly stringent energy efficiency standards.

7. Conclusions

This study presents an optimal control strategy for the AC cooling water system of a subway station about 100 m below the ground surface by addressing the cooling effect of the corridor. For the performance quantitative assessment of the optimal control strategy, the simulation platform of this AC cooling water system was also presented, where the simplified heat transfer model of the pipe corridor was used to present the cooling effect of the cooling water pipe in the corridor. Based on the AC cooling water system platform, the least square method was used to determine the optimal setpoint of T_{cd_in}. The validation results show that the predicted T_{cd_in,o} using the optimal control strategy model agrees well with the actual “measured” condenser inlet cooling water temperature with R² = 0.9951.

This optimal control strategy model of T_{cd_in} was coded as a module in TRNSYS 18 and integrated with the AC water system platform to enable the “online” optimal control of T_{cd_in} for this system. With the optimal control strategy module, the optimal setpoint of T_{cd_in} can be predicted and used to control the cooling tower fans. The outcomes show that the controlled T_{cd_in} may follow the predicted optimal value well in the whole cooling season and indicate that the lowest energy consumption of the cooling water system may not always comply with the lower frequency of the fan after optimal control. The analysis of the cooling effect of the corridor also demonstrates that the cooling water pipes in the corridor may release and absorb heat from the air in the corridor at different times while the released heat is more significant than the absorbed heat. The maximum heat dissipation of the cooling water supply and return pipe to the air in the corridor can be up to 24.3 kW. A detailed analysis of the cooling water system’s operation data before and after implementing the optimization control strategy was conducted to evaluate its effectiveness and energy-saving characteristics. The outcomes show that the energy-saving rate of the optimal control strategy of T_{cd_in} (i.e., the optimal mode) for a typical day reached 4.1%, and the cooling source COP improved by approximately 4.2% when compared to the conventional control (i.e., the existing mode). Over the entire cooling season, the energy consumption of the AC cooling water system was reduced by 9778 kWh, achieving an energy-saving rate of 4.1%.