3.1.2. Heating Equipment

(1) Gas boiler model.

GB plays a crucial role as the final guarantee of heating energy. GB will produce heat when the rest of the equipment cannot meet the heat demand of the user. The expression for its heat generation is as follows:

$$H\_{\mathcal{R}^b} = F\_{\mathcal{R}^b} \cdot a \cdot \eta\_{\mathcal{R}^b} \tag{4}$$

where *Hgb* denotes the heat generated by GB, *Fgb* denotes the consumption volume of natural gas, and *ηg<sup>b</sup>* denotes the heat production efficiency of GB.

(2) Heat recovery model.

HR makes full use of the fuel consumption of MT. It recovers the waste heat generated by MT in the process of producing electricity. The mathematical expression of HR is as follows:

$$H\_{lr} = P\_{mt} \cdot COP\_{mt} \tag{5}$$

where *Hhr* denotes the heat recovered by HR from MT and *COPmt* denotes the correlation coefficient of heat production by MT.

(3) Heat exchanger model.

HE connects the heat production of the system with the heat load. The mathematical expression for HE is as follows:

$$H\_{\rm hc} = \frac{H\_{\rm load}}{\eta\_{\rm hc}}\tag{6}$$

where *Hhe* denotes the heat required by HE, *Hload* denotes the heat load demand of the user, and *ηhe* denotes the efficiency of HE.

(4) Thermal storage tank model.

TST is a buffering device for heat. TST is preferentially used to store and release excess heat and lack of heat of the system. The state expression of TST is as follows:

$$H\_{\rm tst}^{t} = H\_{\rm tst}^{t-1} \cdot (1 - \eta\_{\rm tst,loss}) + (H\_{\rm tst,ch}^{t} \cdot \eta\_{\rm tst,ch} - \frac{H\_{\rm tst,disch}^{t}}{\eta\_{\rm tst,disch}}) \tag{7}$$

where *Httst* and *Ht*−<sup>1</sup> *tst* denote the heat of TST at time *t* and *t* − 1, *ηtst*,*loss* denotes the selfrelease rate of TST, *<sup>H</sup>ttst*,*ch* and *<sup>H</sup>ttst*,*disch* denote the heat stored or released at time *t*, and *ηtst*,*ch* and *ηtst*,*disch* denote the efficiency of TST in storing and releasing heat, respectively.
