## 2 Innovative System Configuration, Dynamics Equations, and the Simulator
### System Dynamics Equations
#### 2.2.2 Derivation of System Dynamics Equations  
According to Figure 1 and Equations (1) and (2), the IHTMS was decomposed into eight control volumes of coolant pipes and two heat source bodies, as illustrated in Figure 3.  
1. [label=(0)]
2. Pipe 1: the pipe 1 was defined as a pipe interconnected to the output of the fuel cell coolant channel and the input of pipe 3. The input energy was from the heated coolant from the fuel cell, while the output energy was delivered to pipe 3. Another heat convection was released to the ambient atmosphere. The dynamics equation was formulated as: \[\dot{T}_{p1}=\frac{\dot{m}_{fc}C_{v,w}\big{(}T_{w,fc}-T_{p1}\big{)}-\dot{m}_{fc }C_{v,w}\big{(}T_{p1}-T_{p3}\big{)}-h_{p1}A_{p1}\big{(}T_{p1}-T_{amb}\big{)}}{ \rho_{w}V_{w,p1}C_{v,w}}\] (3) where subscripts _fc, w, p1, p3_ represent fuel cell, water, pipe 1 and pipe 3, respectively. 3. Pipe 2: similar to pipe 1, pipe 2 was a pipe interconnected to the output of the battery coolant channel and the input of pipe 3. The input energy was from the battery coolant while the output energy was sent to pipe 3. The heat convection was released to the ambient atmosphere as well. The dynamics equation was formulated as: \[\dot{T}_{p2}=\frac{\dot{m}_{bat}C_{v,w}\big{(}T_{w,bat}-T_{p2}\big{)}-\dot{m}_ {bat}C_{v,w}\big{(}T_{p2}-T_{p3}\big{)}-h_{p2}A_{p2}\big{(}T_{p2}-T_{amb}\big{)} }{\rho_{w}V_{w,p2}C_{v,w}}\] (4) where subscripts bat, \(p2\) represent battery and pipe 2, respectively. 4. Pipe3: the input of pipe 3 was linked to the outputs of pipe 1 and pipe 2, while the pipe 3 output was at the front of electromagnetic valves of the heat exchanger and pipe 5. The input energy was the summation of output energy of pipe 1 and pipe 2, where the output mass flow rate was the summation of those of pipe 1 and pipe 2 (\(\dot{m}_{p3}=\dot{m}_{p1}+\dot{m}_{p2}\)). The output energy was sent to the heat exchanger or pipe 5 depending on the status of valve 1 and valve 2. The heat convection to the atmosphere was another energy loss. The dynamics equation was formulated as: \[\dot{T}_{p3}=\frac{\big{[}\dot{m}_{fc}C_{v,w}\big{(}T_{p1}-T_{p3}\big{)}+\dot{ m}_{bat}C_{v,w}\big{(}T_{p2}-T_{p3}\big{)}\big{]}-k_{1}\dot{m}_{p3}C_{v,w} \big{(}T_{p3}-T_{w}\big{)}-k_{2}\dot{m}_{p3}C_{v,w}\big{(}T_{p3}-T_{amb}\big{)} -h_{p3}A_{p3}\big{(}T_{p3}-T_{amb}\big{)}}\] (5) where \(k_{1}\) and \(k_{2}\) were \"loop-switch\" parameters. If the system was in inner-loop mode, \(k_{1}=0\) and \(k_{2}=1\); whereas in outer-loop mode, \(k_{1}=1\) and \(k_{2}=0\). Subscripts _he, p5_ stand for heat exchanger and pipe 5, respectively. 5. Pipe 4: the input of pipe 4 was at the output of the proportional valve, while the outputs were linked to the entrances of the coolant channels of the emulated battery and the fuel cell. The input energy was the output energy from the heat exchanger (outer loop) or from pipe 5 (inner loop), where the output energy (and coolant mass  
Figure 2: Heat and temperature variation of a control volume: (**a**) coolant pipe, (**b**) body. flow) was separated into two paths: to the battery or to the fuel cell. Still, the heat convection to the atmosphere was another energy loss. The dynamics equation was formulated as: \[\dot{T}_{p4}=\frac{k_{1}\dot{m}_{p5}C_{v,w}\big{(}T_{br-}T_{pd}\big{)}-k_{2}\dot{m }_{p5}C_{v,w}\big{(}T_{p5-}T_{pd}\big{)}-\big{[}\dot{m}_{f_{c}C_{v,w}}\big{(}T_{ pd-}T_{m,fc}\big{)}+\dot{m}_{br4}C_{v,w}\big{(}T_{pd-}T_{m,br}\big{)}\big{]}-h_{pd}A_{ pd}\big{(}T_{pd-}T_{amb}\big{)}}{\rho_{w}V_{w,pd}C_{v,w}}.\] (6) where subscript \(p4\) means pipe 4. 5. Pipe 5: the inputs of pipe 5 were the outputs of valve 1, while the output was the entrance of the proportional valve. The input energy was the output energy from valve 1, where the output energy was delivered to pipe 4. The heat convection to the atmosphere was another energy loss.