## 4 Regulation Method and Characteristics Analysis
### Pump Bypass Model and Control Characteristics Subsection
As shown in Figure 11b, a bypass valve is used to optimize and modify the flow pressure curve of TCB in order to construct the ideal output characteristic; the bypass valve is used to compensate for the downstream flow resistance of the thermal bus; the inlet and outlet of the bypass valve are in the same position with the TCB. The main resistance element of the drive unit is connected in series with the drive pump and connected in parallel with the bypass valve. The actual flow characteristics of the bypass valve are as below:  
\[Q_{mv}=f_{v}(\Delta P_{o},K_{v}) \tag{6}\]  
where \(K_{v}\) is valve opening, \(\Delta P_{o}\) is pressure difference in TCB (pressure difference in bypass valve) and \(Q_{mv}\) is flow rate through the bypass valve. The flow rate of the bypass valve  
Figure 11: The basic structure and characteristics of the circuit based on pump bypass: (a) pump bypass model; (b) adjusting characteristic curves. shall be at least within the constant pressure regulating range of the TCB. Therefore, the limit flow rate of bypass valve in the TCB under extreme conditions is  
\[ \begin{cases}Q_{mv,max}=Q_{mp}^{*}-Q_{m0,min}=f_{v}(\Delta P_{o}^{*},K_{v,max}) \\ Q_{mv,min}=Q_{mp}^{*}-Q_{m0,max}=f_{v}(\Delta P_{o}^{*},K_{v,min})\end{cases}  \tag{7}\]  
The ideal flow rate characteristics of bypass valve should be  
\[Q_{mv}=\frac{Q_{mv,max}-Q_{mv,min}}{K_{v,max}-K_{v,min}}(K_{v}-K_{v,min})+Q_{ mv,min},(\Delta P_{o}=\Delta P_{o}^{*}) \tag{8}\]  
where \(K_{v,max}\) is maximum design opening of valve, \(K_{v,min}\) is minimum design opening of valve; the flow rate at 100% valve opening is as follows:  
\[Q_{M}=\frac{1-K_{v,min}}{K_{v,max}-K_{v,min}}Q_{mv,max}-\frac{1-K_{v,max}}{K_{v,max}-K_{v,min}}Q_{mv,min} \tag{9}\]  
where \(Q_{M}\) is flow rate when the valve opening is 100% and the pressure difference between the inlet and outlet is \(\Delta P_{o}\). Combining Formula (8), the max flow rate is as follows:  
\[Q_{M}=\frac{1-K_{v,min}}{K_{v,max}-K_{v,min}}({f_{o,n}}^{-1}(\Delta P_{o})-Q_{ m0,min})-\frac{1-K_{v,max}}{K_{v,max}-K_{v,min}}({f_{o,n}}^{-1}(\Delta P_{o})-Q_{ m0,max}) \tag{10}\]  
As shown in Figure 11b and Formula (10), if \(Q_{m0}>Q_{m0,max}\), the actual opening of the bypass valve is less than the minimum opening of the constant pressure zone; with the further reduction in the system flow resistance, the output flow rate of the drive pump \(Q_{mp}\) increases obviously; the pressure difference between the drive pump \(\Delta P_{p}\) and the thermal bus \(\Delta P_{o}\) decreases; the flow rate of bypass valve reduces and the output flow rate of the drive unit \(Q_{m0}\) increases. Load resistance characteristic curve continues to move to the right; the output pressure difference regarding TCB \(\Delta P_{o}\) is close to zero and the output flow rate \(Q_{m0}\) is close to maximum. When \(Q_{m0}<Q_{m0,min}\), the bypass valve will reach its maximum opening, with the outlet flow resistance increasing; it will cause the flow of the pump \(Q_{mp}\) to decrease; at the same time, the pressure difference between the drive pump \(\Delta P_{p}\) and TCB \(\Delta P_{o}\) will increase. This will cause the flow rate of bypass valve to increase and the output flow rate of the drive unit \(Q_{m0}\) to reduce. When the outlet flow resistance increases to complete shutdown, the output flow rate of the drive pump \(Q_{m0}\) is close to zero, and the output pressure difference in the drive pump \(\Delta P_{o}\) reaches the maximum value. Figure 12 shows the output characteristic curve of the drive pump and drive unit. The drive pump selected in this paper is a kind of centrifugal shield pump. At a fixed speed, the output flow rate decreases as the flow resistance increases; the pressure head provided by the pump decreases as the output flow increases. In combination with Figure 12 and Formula (10), the relationship between bypass valve characteristics and the control range of the TCB can be obtained according to the actual requirements of the thermal control system.