The Component Temperature Constraints Parallel Connections
The component Temperature Constraints Parallel Connections allows for the consideration of different temperature levels in heat generators connected in parallel.
Component Template
The component template Temperature_Constraints_Parallel_Connections.e-ctpl is located in the Component template library folder Operational Side Conditions.
Integration Into a Scheme
The following figure shows as an example how to integrate the component into a scheme.
How the Component Works
The system is optimized according to the Temperature Constraints Parallel Connections. Tutorial 65 demonstrates how the component works.
To set a lower limit on the flow temperature of a parallel connection, the power outputs (\( \dot{Q}\)) of the parallel components are set in relation (\( \beta\)) to one another. The total mass flow rate is the sum of the individual mass flow rates of the parallel branches. Given the flow temperatures \( T\) of the individual heat generators, the ratio of the mass flows can be calculated to achieve a specific mixing temperature \( T_{mix}\). This mass flow ratio and the selection of a reference generator in the parallel connection are used to establish the power constraint that guarantees the mixing temperature.
All other generators (low temperature, \(LT\)) are controlled by a ratio to the reference generator (high temperature, \(HT\)) as follows.
\( \begin{equation} \begin{aligned} \beta &= \dfrac{\dot{Q}_{HT}}{\dot{Q}_{LT}} \\[.3cm]
&= \dfrac{(T_{HT} -T_{in})\cdot (T_{mix} -T_{LT})}{(T_{LT}-T_{in})\cdot (T_{HT}-T_{mix})} \\[.3cm]
&= \dfrac{T_{HT} -T_{in}}{T_{LT,n}-T_{in}} \\[.3cm] \end{aligned}\end{equation}\\\)
\( \begin{equation} \begin{aligned} \dot{Q}_{HT}\geq\dot{Q}_{LT}\cdot \beta\\\end{aligned}\end{equation}\\\)
By formulating the equation as an inequality, sufficient degrees of freedom are preserved, and the HT component is allowed to perform more work if the LT component has reached its maximum load or if operating the HT component is more cost-effective.
Please watch also the background information in the articles Special Features of Operating Constraints, Series and Parallel Connection of Heat Components and Compliance With Temperature Specifications for Parallel Connections.
Input Data
Select a unit that can consistently provide an outlet temperature above the minimum required supply temperature at all times for use as the reference heat supplier.
If you have activated the Material property Heat/Cooling Temperature dependent, check the box next to the Temperature-dependent material property. In this case, the supply temperatures (outlet temperatures) are specified directly in the heating and cooling components. In models with multiple demand components, the same outlet temperature must be set in all components, and one of the demand components can be selected under Reference to unit.
Output Data
