Charge Schedule Optimization and Infrastructure Planning for Solar-Integrated Electric Bus Transit Systems

TL;DR

The paper tackles planning and operation of solar-integrated electric bus depots under renewables variability and ambient-temperature-driven energy use. It develops a two-stage stochastic LP with first-stage decisions $z_j$, $a_j$, $c_j$, $d_j$ and second-stage scenario decisions $x_{b,j,t}^$, $y_{b,j,t}^$, $h_{j,t}^$, solving with Benders' decomposition to manage many scenarios. A concurrent scheduler-based heuristic supplies scenario-specific bus rotations, and the CSP is solved through the L-shaped method, yielding substantial cost savings ($16.48 ext{ extpercent}$ for Durham and $32.00 ext{ extpercent}$ for Canberra) when RES are incorporated, and demonstrating the importance of temperature-aware energy estimates (underestimation up to $27.77 ext{ extpercent}$ and $14.92 ext{ extpercent}$ if ignored). The approach provides actionable guidance for long-term infrastructure sizing (PV area, BESS, grid capacity) and day-to-day, scenario-adaptive charging schedules, enabling more reliable and cost-effective solar-integrated transit operations.

Abstract

As urban transit systems transition towards electrification, using renewable energy sources (RES), such as solar, is essential to make them efficient and sustainable. However, the intermittent nature of renewables poses a challenge in deciding the solar panel requirements and battery energy storage system (BESS) capacity at charging locations. To address these challenges, we propose a two-stage stochastic programming model that considers seasonality in solar energy generation while incorporating temperature-based variations in bus energy consumption and dynamic time-of-use electricity prices. Specifically, we formulate the problem as a multi-scenario linear program (LP) where the first-stage long-term variables determine the charging station power capacity, BESS capacity, and the solar panel area at each charging location. The second-stage scenario-specific variables prescribe the energy transferred to buses directly from the grid or the BESS during layovers. We demonstrate the effectiveness of this framework using data from Durham Transit Network (Ontario) and Action Buses (Canberra), where bus schedules and charging locations are determined using a concurrent scheduler-based heuristic. Solar energy data is collected from the National Renewable Energy Laboratory (NREL) database. We solved the multi-scenario LP using Benders' decomposition, which performed better than the dual simplex method, especially when the number of scenarios was high. With solar energy production at the depots, our model estimated a cost savings of 16.48% and 32.00% for the Durham and Canberra networks, respectively. Our results also show that the scenario-based schedule adapts better to seasonal variations than a schedule estimated from average input parameters.

Figures (14)

• Figure 1: Weekly variations of GTI across the day for Durham (left) and Canberra (right) (Source: https://pvwatts.nrel.gov/)
• Figure 2: Illustration of a charging depot with solar panels and battery energy storage system (BESS). Green captions denote the long-term decisions, and arrows denote the operational, short-term decisions. Red- and blue-colored labels are associated with the grid and solar systems, respectively. Gray labels denote that the charging can be done using both the grid and solar PV systems.
• Figure 3: Charging operations for a bus showing energy levels during trips (purple), charging through grid (red), solar (dark blue) or both (light blue), and idling (yellow)
• Figure 4: Example to illustrate Algorithm \ref{['alg:feasibility_check']}. The numbers next to nodes indicate the charge levels upon reaching it. Gray nodes represent locations where the bus charges according to the CAG strategy.
• Figure 5: Example network (left panel) and Gantt chart (right panel) illustrating the data for the CSP