Remote Temperature Control Strategy of Multi-energy Heat Collection Based on the Internet of Things

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Figure 1. Application architecture of multi-energy heat collection system functions

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Figure 2. Monitoring mode structure of multi-energy heat collection system

Table 1. Information on the adopted sensors

Figure 1 shows the application architecture of six multi-energy heat collection system functions, namely, remote real-time monitoring, sensor monitoring and management, heat collection supply document management, operation and maintenance management module, equipment management, and data statistics and analysis. Three modes, Browser/Server (B/S), Client/Server (C/S) and APP, were used for the hybrid construction of the remote monitoring architecture of the system. Figure 2 shows the detailed implementation process of the monitoring architecture mode.

The mainly detected data of multi-energy heat collection system included four aspects, namely, water temperature, water level, water pressure and flow. Table 1 shows the information on the adopted sensors, that is, the model, purpose and output signal characteristics of the sensors.

For the IoT-based remote temperature control of multi-energy heat collection, an accurate model is usually required to derive an effective controller. However, due to the inaccurate simulation performance, the traditional model is not suitable for the remote temperature control design. Therefore, this paper developed a multi-energy heat collection system model without losing simulation performance using stochastic modeling ideas.

The heat generated by clean energy was stochastic rather than deterministic, leading to indeterministic data measured by sensors. Stochastic model accurately reflected the temperature changes of the system. At the same time, the stochastic disturbance of objective factors, such as climate and location, might help stabilize the system.

This paper focused on the temperature stochastic modeling and parameter estimation of multi-energy heat collection system. Considering the disturbance of heat, produced by clean energy, by objective factors, such as climate and location, based on the assumption of independent and uniformly distributed disturbance, this paper constructed a stochastic differential equation model of the system, and estimated the drift and diffusion terms using the maximum likelihood estimation method.

Let σ_water be the density of tap water, D_e,water be the specific heat capacity of tap water, U be the volume of tap water participating in heat exchange in the system, O_im be the water inlet temperature of the system, W_cov-water be the heat flux between solar energy heat collection input module and internal tap water in the system, W_flr-water be the heat flux between external air and internal tap water, W_ass-water be the heat flux between other clean energy auxiliary heat energy modules and internal tap water, and W_vent be the heat flux loss of tap water caused by objective factors. The following formula gave the duration temperature model expression of the system:

$\begin{aligned} & \frac{\sigma_{\text {water }} D_{e, \text { water }} U d O_{\text {in }}(o)}{d o}= W_{\text {cov_water }}+W_{\text{flr_water}}+W_{\text {ass_water }}+W_{\text {vent }}\end{aligned}$           (1)

Let X_d be the solar panel coverage area of the system, X_h be the heat exchange between solar panel and internal tap water, and O_out be the outlet water temperature of the system. According to the thermodynamic principle, the calculation formula of the heat flux between the solar energy heat collection input module and the internal tap water in the system was:

${{W}_{\operatorname{cov}\_water}}=1.7\frac{{{X}_{d}}}{{{X}_{h}}}{{\left| {{O}_{out}}-{{O}_{in}} \right|}^{0.31}}\left( {{O}_{out}}-{{O}_{in}} \right)$          (2)

Let O_flr be the external air temperature of the system, and l_flr-water be the temperature transfer coefficient from external air to tap water in the system. Similarly, the heat flux calculation formula between external air and internal tap water was constructed as follows:

${{W}_{flr\_water}}={{l}_{flr\_water}}{{X}_{h}}\left( {{O}_{flr}}-{{O}_{in}} \right)$                     (3)

l_flr-water was obtained from the following formula:

${{l}_{flr\_air}}=\left\{ \begin{align}  & 1.7{{\left( {{O}_{in}}-{{O}_{flr}} \right)}^{0.33}},{{O}_{flr}}>{{O}_{in}} \\  & 1.3{{\left( {{O}_{in}}-{{O}_{flr}} \right)}^{0.25}},{{O}_{flr}}<{{O}_{in}} \\ \end{align} \right.$           (4)

Let δ_water be the heat energy absorption coefficient of tap water, and SE_glob be the heat energy supply of other clean energy resources. Then the heat flux between the auxiliary heat energy module of other clean energy resources and the internal tap water was calculated as follows:

${{W}_{ass\_water}}={{\delta }_{water}}\cdot {{X}_{d}}\cdot S{{E}_{glob}}$                 (5)

Let Ψ_vent be the occurrence probability of objective factors, then there was the following formula for calculating the heat flux loss of tap water caused by those factors:

${{W}_{vent}}={{\sigma }_{water}}{{D}_{e,water}}{{\Psi }_{vent}}\left( {{O}_{out}}-{{O}_{in}} \right)$                      (6)

It was difficult to calculate Ψ_vent accurately considering the influence of objective factors, such as season, climate and location. Let α_TC and ω_TC be the undetermined constants, and the disturbance of objective factors was regarded as the derivative of Brownian motion Y(o), that is, Y(o)=dY(o)/do, then there was:

${{W}_{vent}}={{\sigma }_{water}}{{D}_{e,water}}\alpha _{TC}^{{}}\left( {{O}_{out}}-{{O}_{in}} \right)+{{\omega }_{TC}}Y\left( o \right)$                  (7)

The above formula was transformed into the form of nonlinear stochastic differential equation:

$d{{O}_{in}}\left( o \right)=g\left( {{O}_{out}},{{O}_{in}},{{O}_{flr}} \right)do+{{\omega }_{TC}}dY\left( o \right)$                   (8)

where,

$\begin{aligned} & g\left(O_{\text {out }}, O_{\text {in }}, O_{f l r}\right)= \frac{1.7 X_d}{\sigma_{\text {air }} D_{e, \text { water }} U X_h}\left|O_{\text {out }}-O_{\text {in }}\right|^{0.31}\left(O_{\text {out }}-O_{\text {in }}\right)  +\frac{l_{f l_{\text {water }}} X_g}{\sigma_{\text {water }} D_{e, \text { water }} U}\left(O_{f t t}-O_{\text {in }}\right)  +\frac{\delta_{\text {water }} \cdot X_d \cdot S E_{\text {glob }}}{\sigma_{\text {air }} D_{e, \text { water }} U X_h}+\frac{\alpha_{T C}}{U}\left(O_{\text {out }}-O_{\text {in }}\right)\end{aligned}$                    (9)

At the same time, when the continuous time path of parameters in the system was observed at equidistant time points, let Δo be the discretization step and ρ_i be the independent parameter sequence M(0,1), then, there was the following based on formula 8:

$\begin{align}  & O_{in}^{i}=O_{in}^{i-k}+g\left( O_{out}^{i-k},O_{in}^{i-k},O_{flr}^{i-k} \right)\Delta o +{{\omega }_{TC}}\sqrt{\Delta o{{\rho }_{i}}},i=1,2,... \\ \end{align}$             (10)

Let O₀, O₁, O₂...O_m be the parameter observation sequence based on the above formula, and G_i-1=ε(O_j,j≤i-1), then the conditional probability density function expression of G_i-1,O_i was given by the following formula:

$\begin{aligned} & g\left(O_i / G_{i-1}\right)=\frac{1}{\sqrt{2 \pi \Delta o} \omega_{T C}}  \exp \left\{\frac{1}{-2 \omega_{T C \Delta o}^2}\left[O_{\text {in }}^i-O_{\text {out }}^{i-l}-g\left(O_{\text {out }}^{i-l}, O_{i n}^{i-l}, O_{f r i}^{i-1}\right) \Delta o\right]^2\right\}\end{aligned}$             (11)

For the given G₀, the following formula gave the joint conditional probability density function expression of (O₁, O₂...O_m):

$\begin{aligned} & \left(O_1, O_2, \ldots, O_m \mid G_0\right)=\left(\frac{1}{\sqrt{2 \pi \Delta o} \omega_{T C}}\right)^n \\ & \coprod_{i=1}^n \exp \left\{\frac{1}{-2 \theta_{T C \Delta o}^2}\left[\begin{array}{l}O_{\text {in }}^i-O_{\text {out }}^{i-l}- \\ g\left(O_{\text {out }}^{i-k}, O_{\text {in }}^{i-1}, O_{f l r}^i\right) \Delta o\end{array}\right]^2\right\}\end{aligned}$               (12)

The log-likelihood function was given by the following formula:

$\begin{aligned} & K_m\left(\alpha_{T C}, \omega_{T C}\right)=-\frac{m}{2} \log 2 \pi \Delta o-m \log \omega_{T C} -\frac{1}{-2 \omega_{T C}^2 \Delta o} \sum_{i=1}^m\left[\begin{array}{l}O_{\text {in }}^i-O_{o u t}^{i-1}- \\ g\left(O_{\text {out }}^{i-1}, O_{\text {in }}^{i-1}, O_{f l r}^i\right) \Delta o\end{array}\right]^2\end{aligned}$               (13)

$\left\{\begin{array}{l}\frac{\partial K_m\left(\alpha_{T C}, \omega_{T C}\right)}{\partial \phi_{T C}}=0 \\ \frac{\partial K_m\left(\alpha_{T C}, \omega_{T C}\right)}{\partial \omega_{T C}}=0\end{array}\right.$          (14)

Based on the above analysis, the following was obtained:

$\left\{\begin{array}{l}\sum_{i=1}^m\left[O_{\text {in }}^i-O_{\text {out }}^{i-1}-g\left(O_{\text {out }}^{i-1}, O_{\text {in }}^{i-1}, O_{f l r}^{i-1}\right) \Delta o\right]=0 \\ -\frac{m}{\omega_{T C}}+\frac{1}{3 \omega_{T C}^3 \Delta o} \sum_{i=1}^m\left[\begin{array}{l}O_{\text {in }}^i-O_{\text {out }}^{i-1}- \\ g\left(O_{\text {out }}^{i-1}, O_{i n}^{i-1}, O_{f l r}^{i-1}\right) \Delta o\end{array}\right]^2=0\end{array}\right.$              (15)

Further, the following was obtained:

$\left\{\begin{array}{l}\hat{\alpha}_{T C}=\frac{\sum_{i=1}^m\left[O_{i n}^i-O_{i n}^{i-1}-Y_{i-1}\right]}{\sum_{i=1}^m\left(O_{\text {out }}^i-O_{i n}^{i-1}\right) \Delta o} \\ \hat{\omega}_{T C}=\sqrt{\frac{\sum_{i=1}^m\left[O_{i n}^i-O_{\text {out }}^{i-1}-g\left(O_{\text {in }}^i, O_{\text {out }}^{i-1}-g\left(O_{o u t}^{i-1}, O_{\text {in }}^{i-1}, O_{\text {flr }}^i\right) \Delta o\right)\right]^2}{3 m \Delta o}}\end{array}\right.$             (16)

where,

$\begin{aligned} & Y_{i-1}=\frac{1.7 X_d}{\sigma_{\text {water }} D_{e, \text { water }} U X_h}\left|O_{o u t}^{i-1}-O_{i m}^{i-1}\right|^{0.31}  \left(O_{\text {out }}^{i-1}-O_{i n}^{i-1}\right)+\frac{l_{f l r_{a i r}} X_h}{\sigma_{\text {water }} D_{e, \text { water }} U}\left(O_{f l r}^{i-1}-O_{i n}^{i-1}\right)  +\frac{\delta_{\text {water }} \cdot X_d \cdot S E_{\text {glob }}}{\sigma_{\text {water }} D_{e, \text { water }} U X_h}\end{aligned}$                (17)

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Figure 5. Water tank outlet temperature curve in all working conditions

According to the remote temperature control mode of multi-energy heat collection proposed in this paper, Figure 5 shows the outlet temperature change curve of water tank in all working conditions of the system. According to the experiment, with the influence of objective factors (season, climate and location, etc.) and unknown uncertain factors (model error, time-varying, etc.), the system control kept the outlet temperature of water tank constant in each working condition, and the temperature fluctuation was controlled within the preset range.

According to the disturbance degree of objective and uncertain factors and without considering the interactions of those factors, this paper selected the calculation orthogonal table of control increment at the new time to determine the experimental scheme. Table 2 shows the proportional, integral and derivative (PID) parameters of the thyristor controlling the system heat flow and the mean square error of inlet temperature of the heat collection tank in all schemes.

Table 2. Experimental results of remote temperature control strategy of multi-energy heat collection

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1) Test node temperature

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2) Temperature error

Figure 6. Model test results

Table 3. Variance analysis of multi-energy heat collection remote temperature control experiment

Figure 6 shows the model test results, that is, the error values of measured and predicted temperature and theoretical temperature at different test nodes. The actual measured and predicted temperature of the test node was closely related to the solar radiation value, because the solar energy collection module in the multi-energy heat collection system was the core heating module, and other clean energy modules were the auxiliary thermal energy modules. The figure shows that the temperature of the system in this experiment changes with time, which verified the effectiveness of the model in this paper in the remote temperature control results of the system.

The data of 18 groups of experimental results were further analyzed. Table 3 shows the variance analysis results of the remote temperature control experiment.

According to the table, when the thermal flow of the system was controlled by the thyristor, the analog input was the main factor of remote temperature control of multi-energy heat collection, and the PID control parameters were the secondary factor of temperature control. Based on the variance analysis results, the optimal multi-energy heat collection cooperation strategy was obtained. That is, the analog input maximum voltage of thyristor was 2.6 V, and the PID control parameters were 51, 4, and 2.

According to the analysis results, when the heat produced by clean energy was disturbed by objective factors, such as climate and location, the controlled multi-energy heat collection system had rapid temperature response, short adjustment time, and relatively ideal control effect and robust performance.