Optimization of the Energy-Comfort Trade-Off of HVAC Systems in Electric City Buses Based on a Steady-State Model

TL;DR

This paper tackles the HVAC energy- comfort trade-off in electric city buses by developing a five-reservoir dynamic thermal model and introducing a steady-state approximation to enable rapid year-round optimization. It formulates a year-round HVAC optimization that minimizes $P_{HVAC}$ under $PMV$-based comfort constraints, using lifting variables, smooth approximations, and an ANN surrogate for $PMV$, solved as four NLPs with CasADi/Ipopt. The authors validate the steady-state approach against full dynamic simulations, demonstrating reasonable fidelity for average performance and enabling two practical case studies: offline year-round design comparisons (highlighting substantial energy savings with HP and air curtains) and causal online control through extracted setpoint profiles. The work shows that steady-state analysis can provide valuable design guidance and online-control setpoints for electric city buses, with clear pathways toward broader validation and extensions to humidity, air quality, and multi-vehicle deployments.

Abstract

The electrification of public transport vehicles offers the potential to relieve city centers of pollutant and noise emissions. Furthermore, electric buses have lower life-cycle greenhouse gas (GHG) emissions than diesel buses, particularly when operated with sustainably produced electricity. However, the heating, ventilation, and air-conditioning (HVAC) system can consume a significant amount of energy, thus limiting the achievable driving range. In this paper, we address the HVAC system in an electric city bus by analyzing the trade-off between the energy consumption and the thermal comfort of the passengers. We do this by developing a dynamic thermal model for the bus, which we simplify by considering it to be in steady state. We introduce a method that is able to quickly optimize the steady-state HVAC system inputs for a large number of samples representative of a year-round operation. A comparison between the results from the steady-state optimization approach and a dynamic simulation reveals small deviations in both the HVAC system power demand and achieved thermal comfort. Thus, the approximation of the system performance with a steady-state model is justified. We present two case studies to demonstrate the practical relevance of the approach. First, we show how the method can be used to compare different HVAC system designs based on a year-round performance evaluation. Second, we show how the method can be used to extract setpoints for online controllers that achieve close-to-optimal performance without any predictive information. In conclusion, this study shows that a steady-state analysis of the HVAC systems of an electric city bus is a valuable approach to evaluate and optimize its performance.

Figures (18)

• Figure 1: Model component overview. Thermal reservoirs are represented as shaded blocks. Red arrows denote heat flows, yellow arrows denote solar heat gain, and blue arrows denote electric power flows. Time dependencies are omitted for clarity.
• Figure 2: Shadow fraction averaged over a specific bus route in Zürich, based on a simulation using GIS software and a three-dimensional model of the city of Zürich Zurich3dswissALTI3D.
• Figure 3: Visualization of the temperature-dependent model components. The solid lines in the right plot correspond to the temperature values representing a thermally neutral environment ($\xspace(t) = 0$). The dashed lines are the corresponding projections onto the ground plane, for clarity.
• Figure 4: Disturbances $\xspace(t)$ on a summer day, recorded on 2019724-1. Thin solid lines represent the time-resolved data, while thick dashed lines represent hourly averages. The shaded segment is the basis for the visualization in \ref{['fig:single-scenario-hot']}. The plots shown on the right are a zoomed version of this segment.
• Figure 5: Visualizations of the model approximations. The left plot shows the approximation \ref{['eq:sqrt-of-abs-approx']}. The right contour plot shows the error of the approximation \ref{['eq:pmv-approx']} for an ambient temperature of $\xspace = \qty{10}{\celsius}$.