# Analysis of Instantaneous Energy Consumption and Recuperation Based on Measurements from SORT Runs
## 3 Results  
Based on the available data from the SORT and the mathematical tools described above, energy consumption was studied depending on the vehicle speed. On this basis, the energy consumption of the vehicle was determined. During the passage of the electric bus, the collected and recovered energy was recorded, where the readings were presented in the form of time series \(\left\{E_{t_{j}}^{+}\right\}_{0\leq j\leq n}\) and \(\left\{E_{t_{j}}^{-}\right\}_{0\leq j\leq n}\) respectively. The impact of the bus passage on the collected and recovered energy, or, more precisely, the speed and acceleration of the vehicle, was analysed. The vehicle's journey is described by staying in the states \(A\)--acceleration, \(B\)--braking, \(D\)--driving, and \(S\)--stop. The sequence of states creates cycles. To identify the states, we analyse the bus speed (km/h). The speed reading is presented as a time series \(\left\{v_{t_{j}}\right\}_{0\leq j\leq n}\) where \(v_{0}=0\). To classify the states, we determine \(v_{min}\) (the minimum vehicle speed below which we assume that the car is in the stopped state) and \(\alpha_{min}\) (the absolute value of acceleration below the level \(\alpha_{min}\), which indicates constant driving or stopping). Based on the sequence of readings of vehicle speed \(\left\{v_{t_{j}}\right\}_{0\leq j\leq n}\) and vehicle acceleration \(\left\{a_{t_{j}}\right\}_{0\leq j\leq n}\) where \(a_{0}=0\) and \(a_{t_{j}}=\frac{v_{t_{j}}-v_{t_{j}-1}}{t_{j}-t_{j}-1}\) for \(j\geq 1\), we define the states as follows:  
\[x_{t}= \begin{cases}S,&v_{t_{j}}<v_{min}\quad\text{or}\quad v_{t_{j}}=0,\\ A,&v_{t_{j}}\geq v_{min}\quad\text{and}\quad a_{t_{j}}>\alpha_{min},\\ B,&v_{t_{j}}\geq v_{min}\quad\text{and}\quad a_{t_{j}}<-\alpha_{min},\\ D,&\text{other}.\end{cases} . \tag{19}\]  
Below, the measurements for each second were analysed, so \(t_{j}=j\) for \(0\leq j\leq n\), i.e., \(v_{t_{j}}=v_{j}\), \(a_{t_{j}}=v_{j}\). The speed and states of the vehicle are shown in Figure 3, while Figure 4 shows the energy consumption and recuperation during the test. In an SORT, an electric bus's speed is shown in Figure 3, with the \"Stop\" phase represented by orange, \"Acceleration\" by red, \"Driving\" by blue, and \"Braking\" by green. To mimic real-life urban and suburban operations, the bus accelerates, maintains consistent speeds, brakes, and stops in a cyclical rhythm. Different driving scenarios that are typical of SORT 1, SORT 2, and SORT 3 conditions are reflected in the acceleration phases, with the first reaching around 20 km/h and the subsequent phases peaking at about 40 km/h and 50 km/h, respectively. As the vehicle develops momentum, its energy consumption rises, as seen in the \"Acceleration\" stages, which include constant speed increases. During the \"Braking\" stages, the vehicle smoothly decelerates, allowing the engine to recover lost energy. \"Stop\" phases are essential for evaluating idle energy use as they depict times of the vehicle's speed. Figure 4: Total energy consumption and recovery. Figure 3: Vehicle speed and states. inactivity, whereas \"Driving\" segments show regular speeds where energy consumption stabilises. When looking at energy efficiency, these transitions are crucial, as seen in the graph. Even if braking regenerates part of the energy lost during acceleration, the former still requires a substantial amount. This test is ideal for gauging battery life, power consumption, and recovery effectiveness as it mimics normal bus operations with its repeated stop-and-go pattern. By gaining a better grasp of these interdependencies, electric bus route optimisation, energy management, and overall operational efficiency can be achieved. In Figure 4, we can see how the electric bus's total energy consumption and total energy recuperation relate to each other throughout the SORT cycle. During acceleration stages, the energy usage rises steadily, as seen in the \"Total Consumption\" graph.