# Dynamic Energy Consumption Modeling for HVAC Systems in Electric Vehicles
## 1 Introduction  
The development of electric mobility we are witnessing in the present years requires a parallel improvement in sustainable technologies integrated into vehicles, with the aim of energy savings. The heating, ventilation and air conditioning system (HVAC) is one of the most energy-consuming appliances in a vehicle. The design and the energy consumption assessment of HVAC systems for automotive systems are usually based on steady-state approaches, where the subsystems (such as the evaporator, the condenser and the compressor) are described by proper correlations. However, HVAC works always under unsteady conditions, as in a vehicle, the thermal loads are continuously changing during driving. Therefore, it is crucial to obtain a model capable of describing the behavior of an HVAC system under unsteady conditions to perform a full assessment of the energy exchanged between the subsystems (such as the evaporator, the condenser and the compressor) during the working cycle and the interaction between the vehicle cabin and the external environment. This model can give different results with respect to the usual steady-statemodeling approaches, which assume that the variables of interest do not change over time. Some works are available in the literature on dynamical modeling of HVAC systems. [PERSON] et al. [1] present a lumped parameter dynamic model of a vapor compression cycle used for electronic cooling. In this model, the dynamics of heat exchangers is coupled with static empirical models of the compressor and expansion valve. The model is validated by comparison with experiments under different operating conditions. Performance optimization is achieved by obtaining the minimum compressor power consumption together with the maximum critical heat flux. [PERSON] et al. [2] introduce a simplified dimensionless model to describe the transient behavior of a vapor compression refrigeration system. The purpose of the study is to optimize the heat transfer area of the heat exchangers, minimizing the system pull-down time. [PERSON] et al. [3] propose a 1D transient model for refrigeration systems where the subcomponents are independently validated. The method is applied to a domestic freezer and tested under varying ambient temperatures and thermostat settings. [PERSON] et al. [4] present an optimization strategy for the vapor compression refrigeration cycle, which by analyzing the characteristics and interactions of each component within the cycle minimizes the total operating cost of the energy-consuming devices subject to the constraints of mechanical limitations, component interactions, environment conditions and cooling load demands. Recent works deal with model predictive control strategies to optimize the operation of the thermal management system by intelligently managing the energy allocation between different components [5]. [PERSON] et al. [6] review the literature on integrated thermal management systems for electric vehicles. They first introduce the research status of each subsystem then focus on the analysis of the advances to obtain the performance evaluation of the integrated systems shown. The discussed solutions, however, are characterized by experimental studies, showing the need of validated dynamic simulations to support the prototyping phase. [PERSON] and [PERSON] [7] provide a comprehensive discussion on electric vehicle energy management systems, focusing on equivalent circuit models and discussing associated simulation resources and software packages. They also present an illustrative case study on the thermal modeling and simulation of lithium ion batteries using the equivalent circuit model. The dynamic simulation of HVAC systems for automotive applications has only recently appeared in the literature. [PERSON] et al. [8] present a review related to the modeling of the cabin thermal environment.