.ScalableTestSuite.Thermal.DistrictHeating.Models.HeatingSystem

Information

This model represents a district heating system with N heated units, supplied by a heat distribution system. Each heated unit is described as a lumped-parameter energy balance with one temperature Tu, losing heat to the ambient, whose temperature Ta varies sinusoidally with a period of one day. The heat distribution system is also described by a large lumped thermal capacitance with a single temperature Td.

The temperature of each unit is controlled by an on-off controller with hysteresis, which determines the conductance between the heating medium and the unit temperature, mimicking the behaviour of a fan-coil heater. The controller dynamics is nonlinear and subject to bifurcations. If the temperature lies outside of the hysteresis interval, the state x of the controller has one stable state, which is then converted to a 0-1 output by a nonlinear output function sat(). Inside the hysteresis interval, there are two stable states with an unstable state in-between. When the temperature gets higher or smaller than the hysteresis threshold, the current stable state collides with the unstable state and disappears, so that the state x undergoes a fast transition to the other equilibrium.

The unit temperature controller dynamics is extremely stiff, due to the strong nonlinearity of the sat() function and to the wide changes of eigenvalues (including positive values!) during the transition to the new stable state.

The distribution system temperature is instead controlled by a simple proportional controller with a relatively low bandwidth, so that the system can be used as a buffer between the heat supply system and the consumers on the network. Smooth saturations on the control variable are present, to avoid negative heat flows or too high heat flows that would be unrealistic.

The heat capacitances of the units are slightly different from each other, so that the local on-off controller transitions take place asynchronously. Since the large thermal capacitance of the storage system decouples the behaviour of each unit over the time intervals relevant for the simulation of the on-off controllers, this system can be integrated much more efficiently if adaptive multi-rate algorithms are employed, as explained in this paper.

The order of the system is 2*N+1.


Generated at 2024-03-28T19:15:55Z by OpenModelicaOpenModelica 1.22.3 using GenerateDoc.mos