Mathematical models of vapor-compression systems for multivariable control of the refrigerant dynamics and indoor air conditions

Abstract

Detailed steady and transient state models of vapor compression (VC) systems have been suggested in this work so that the governing parameters of the refrigerant dynamics such as pressure, enthalpy and temperature could be predicted at different operating conditions. The steady and transient state models were validated with experimental data collected during startup and steady state operations. The experimental setup was equipped with a thermostatic expansion valve, a reciprocal compressor and plate heat exchangers for the condenser and evaporator. Recirculated water was adopted as secondary fluid for heat transfer with R-134a refrigerant. The steady state model was developed from first principles with the refrigerant conditions being determined at each junction between the components of the VC system. A steady state matrix was built to determine the model outputs and it could be adopted for similar problems such as steady state modelling of single-condenser-and-multi-evaporators systems. The refrigerant pressures through the evaporator and condenser were in agreement with experiments. Other refrigerant conditions such as enthalpy and temperature through the components were also validated with experiments. The evaporator and condenser modelling in transient state required special attention and Navier-Stokes equations were adopted for this purpose along with a finite volume scheme for discretization of the condenser and evaporator into 3 and n-control volumes. A transient state matrix was also built for outputs’ prediction in transient operating conditions such as startup and shutdown. The refrigerant conditions namely pressure and enthalpy through the evaporator and condenser were validated with experiments. The transient state model was then improved and converted into a control-oriented model with 12 state variables. The control-oriented model considered phase change in the condenser and evaporator namely, superheat, two-phase and subcooling. Model predictive control (MPC) was implemented on the control-oriented model after a model linearization around a steady state point carefully selected from the steady state experiments performed for validation of the steady state modelling. MPC implementation enabled to control superheat and evaporating pressure simultaneously with consideration of the coupling effect between superheat and capacity regulation. MPC was integrated in Simulink with satisfactory performances regarding disturbance rejection and reference tracking. Building up on satisfactory MPC performance for multivariable control of the refrigerant dynamics, a proportional integral derivative (PID)-MPC controller was implemented on a Chiller-Fan coil unit (FCU) to control simultaneously, indoor temperature, humidity and CO2 level with the coupling effect between humidity and temperature taken into consideration. PID was implemented on a sub layer control loop located at the first heat exchanger and fresh air temperature was maintained within settings to level-out with room temperature to prevent from imbalanced loads. Disturbance rejection and set point tracking were satisfactory without necessarily increasing the supply fan and compressor speeds. MPC was implemented on an upper layer control loop located at a secondary heat exchanger to regulate simultaneously indoor humidity, temperature and CO2 level. The coupling effect between humidity and temperature was well taken care of by the MPC loop and CO2 level regulation was performed without additional load as fresh air intake was carefully pre-cooled using the primary heat exchanger controlled with a PID loop. The performance of the sub layer PID was satisfactory with regards to stability, maximum overshoot and settling time whilst reference tracking and disturbance rejection were satisfactory with the upper layer MPC.