**3. LFF Control Strategy**

Control errors caused by system delay effects may cause adjustment effects to not be reflected in time, resulting in greater overshoot and oscillation. This is a detrimental effect on the air conditioning system control. The objective of the optimal control strategy is to solve the problem of time delay in control, which provides the HVAC system with the capability to operate at relatively high efficiency and save energy at various possible conditions in operation. The proposed LFF control strategy has the following characteristics. The predicted load was obtained based on the SVM [27] method and the predicted load was used as the input parameter of the feed-forward controller. The feed-forward controller can control the HVAC system in advance to eliminate the impact of system time delay on the control of the air conditioning system, and this advanced control time is the time delay of the chilled water transmission of the HVAC system. The predicted load and the time of the advance input are used as input parameters for fuzzy control to obtain control signals for the operation of the water pump and the unit. It is worth mentioning that compared with the SWT control strategy, the LFF control strategy controls the unit while controlling the operation mode of the pump. Compared with the feedback control strategy, the LFF control strategy is load-based feedforward control, which ensures the directness and accuracy of the control.

The control logic diagram of the LFF control strategy is shown in Figure 4. As shown in Figure 4, the cooling load was generated by the weather parameters acting on the building model. Based on the SVM method, the cooling load was trained to obtain the predicted cooling load. The predicted cooling load was applied to the fuzzy controller output control signal u to control the operation of the energy system equipment in advance T.

**Figure 4.** The logic diagram of the load forecast fuzzy (LFF) control strategy.

#### **4. The Method of Control Optimizations**

#### *4.1. The Load Forecast Model Based on SVM*

Key to the LFF control technology is the accurate input of the cooling load, which determines the e ffect and quality of control. This paper firstly performs the load simulation calculation on the building model based on TRNSYS, and then the load is predicted by using the support vector machines (SVM) method for the calculated load. SVM is the technique to solve the classification and regression problems [28]. Support vector regression (SVR) is a machine learning method based on statistical learning theory [29].

Support vector machines have strong generalization ability and can e ffectively solve practical problems such as nonlinearity and small samples. It mainly includes ε-SVR and υ-SVR models [30]. The ε-SVR method maps the input space from a low-dimensional feature space to a high-dimensional feature space based on a nonlinear mapping function ϕ*(x)*, and then uses Equation (1) to fit a linear function.

$$f(\mathbf{x}) = \boldsymbol{\omega}^T \times \boldsymbol{\varphi}(\mathbf{x}) + \boldsymbol{b} \tag{1}$$

In the SVM method, the parameters ω and b are determined using the minimum structural risk. The insensitive loss function parameter ε is introduced to obtain optimization Equations (2)–(5) [31].

$$\min \frac{1}{2} \boldsymbol{\omega}^{\mathsf{T}} \boldsymbol{\omega} + \mathsf{C} \sum\_{i=1}^{n} \left( \xi\_{i} + \xi\_{i}^{\mathsf{\*}} \right) . \tag{2}$$

The constraints are as follows:

$$\text{s.t.} \,\text{y}\_i - \boldsymbol{\omega}^T \times \boldsymbol{\upvarphi}(\mathbf{x}\_i) - \mathbf{b} \le \boldsymbol{\varepsilon} \,\text{ } + \,\, \xi\_{i\prime} \tag{3}$$

$$
\omega^{\mathsf{T}} \times \mathfrak{o}(\mathsf{x}\_{\mathsf{i}}) + \mathsf{b} - \mathsf{y}\_{\mathsf{i}} \le \varepsilon + \mathsf{E}^{\ast}\_{\mathsf{i}\,\prime} \tag{4}
$$

$$
\xi\_i \ge 0, \ t\_i^\* \ge 0, \ i = 1, 2, \dots, \ n \tag{5}
$$

The SVM includes two parameters: the penalty parameter "C" as the intrinsic parameter of SVM and the parameter γ in the kernel function. The penalty parameter "C" and the kernel function γ affect the correlation between the complexity, stability, and vector of the model, respectively. A Gaussian kernel function was introduced to represent the complex non-linear relationship between input and output [32]. The Gaussian kernel function is as follows:

$$\mathbf{K}(\mathbf{x}\_{i},\mathbf{x}\_{j}) = \exp(-\gamma \|\mathbf{x}\_{i} - \mathbf{x}\_{j}\|^{2}) \mathbf{y} \, \, \, \, \, \, \, \, \, \tag{6}$$

The load of the building was simulated from 15th June to 15th September which is the actual operation period in summer. The meteorological data used in this paper are those of a typical meteorological year.

The flow chart of the SVM method is shown in Figure 5.

**Figure 5.** The flow chart of the support vector machines (SVM) method.

The specific steps of load prediction based on the SVM method are as follows.


#### *4.2. The Calculation of Time Delay*

The time delay of the system includes the heat transfer delay caused by the terminal equipment of the air conditioning system and the time delay caused by the fluid flow of the air conditioning water system. The air conditioning system, in this case, is a fan coil system, and the heat transfer from the terminal to the air is accomplished by convection, which has a small time delay compared to the water system flow and can be ignored [33]. Therefore, only the time delay caused by the flow of the air conditioning water system is considered here.

The time delay of fluid flow, which is the time required for chilled water to flow from the outlet of the air conditioning system to the most unfavorable terminal, can be calculated from the hydraulics of the pipeline. Equation (7) is the ratio of branch pipe flow to total system flow under the assumption that the flow rates at the respective terminal are the same.

$$\mathbf{x}\_{i} = \frac{m\_{i}}{M} \tag{7}$$

The system is assumed to have a total of *n* branches. The flow rate *Vi* of each section of the main pipe can be calculated by Equation (8).

$$V\_i = \sum\_{j=1}^{i} x\_i \times \left(\frac{D\_n}{D\_i}\right)^2 \times V\_n \tag{8}$$

The time delay of each main pipe is calculated according to the ratio of the length of the main pipe to the flow rate, which can be computed by Equation (9).

$$T\_i = \frac{L\_i}{V\_i} = \frac{L\_i}{\sum\_{j=1}^i x\_i \times \left(\frac{D\_v}{D\_i}\right)^2 \times V\_u} \tag{9}$$

The sum of the time delay of the main sections is the time delay from the outlet of the chilled water to the most unfavorable terminal. The total time delay is calculated as Equation (10). The calculation results are shown in Table 1.

$$T = \sum\_{i=1}^{n} T\_i = \sum\_{i=1}^{n} \frac{L\_i}{\sum\_{j=1}^{i} \mathbf{x}\_i \times \left(\frac{D\_n}{D\_i^\*}\right)^2 \times V\_n} \tag{10}$$


**Table 1.** The theoretical calculation of the time delay caused by the flow.
