# Analysis of Instantaneous Energy Consumption and Recuperation Based on Measurements from SORT Runs
## 3 Results
Specifically, the accelerations at higher speeds are associated with a dramatic increase in energy consumption between the \"1:40\" and \"2:25\" marks. At stops, the graph flattens, suggesting that very little power is being used when the bus is not moving. The graph labelled \"Total Recuperation\" shows how much energy is recovered when braking. Recovery rates drop significantly between 1:25 and 2:40, coinciding with times of slowdown. These instances of braking show how efficient regenerative braking devices are at restoring lost energy. On the other hand, the recuperation is always less than the energy used, showing that regeneration partially makes up for the energy lost during acceleration, even though it helps. The overarching pattern is that \"braking phases aid in energy recovery\" and \"acceleration phases drive energy consumption\". The total energy consumption during the test was 1466.07 Wh, while only 542.941 Wh was recovered. Energy recuperation represents only 37.03%. Improving energy efficiency necessitates balancing these processes, which means that adjusting acceleration and braking patterns is key. Less energy is consumed during periods of \"steady driving and stops\", which highlights the possibility of improving operational efficiency through route planning and driving methods. During an SORT cycle, an electric bus's \"instantaneous energy consumption and regeneration\" are shown in Figure 5. Over the course of the three minutes, the graph shows fluctuations between \"positive energy consumption\" and \"negative energy recovery\". \"As the vehicle gains speed\" the energy usage increases dramatically, suggesting a higher need for power. Around \"00:00:15\", \"00:01:45\", and \"00:02:30\", the vehicle's speed profile shows the most noticeable peaks, which correspond to fast accelerations. Regenerative braking periods, on the other hand, are characterised by negative energy levels, which indicate that the energy has been recovered. These dips coincide with the times that the car slows down, which are about \"00:00:50\", \"00:02:10\", and \"00:02:50\". Although regenerative braking aids in energy recovery, it does not completely compensate for the energy required during acceleration, as the magnitude of recuperation is lower than the energy consumed. There are periods of \"steady energy consumption\" or near-zero numbers between these peaks and troughs, which indicate that the driver is maintaining a constant speed or has stopped. Compared with acceleration periods, these steady intervals highlight decreased power demand. \"As acceleration increases\" energy consumption decreases, and \"braking recovers energy;\" this crucial relationship is illustrated by the graph. Improving the effectiveness of these acceleration and braking transitions can lower operating costs and increase overall energy efficiency for electric buses. The instantaneous consumption and recuperation energy (ICRE) during the bus ride were estimated as follows:  
\[IE_{t}=\triangle E_{t}^{+}+\triangle E_{t}^{-}. \tag{20}\]  
for \(1\leq t\leq n\) and \(IE_{0}=0\), where \(\triangle\) is a differential operator. Energy recovery was analysed for the Braking state, while consumption was analysed for the remaining states. The instantaneous energy consumption and recovery, depending on the states, are presented in the following form:  
\[IE_{t}= \begin{cases}\alpha_{0}^{S},&x_{t}=S,\\ \alpha_{1}^{A}v_{t}+\alpha_{2}^{A}a_{t}+\alpha_{3}^{A}v_{t}a_{t},&x_{t}=A,\\ \alpha_{1}^{B}v_{t}+\alpha_{2}^{B}a_{t}+\alpha_{3}^{B}v_{t}a_{t},&x_{t}=B,\\ \alpha_{1}^{D}v_{t}+\alpha_{2}^{D}a_{t}+\alpha_{3}^{D}v_{t}a_{t},&x_{t}=D.\end{cases}  \tag{21}\]  
where the value \(v_{t}\cdot a_{t}\) means energy intensity, which in turn means that the change in speed is determined by acceleration. Energy intensity defines the dynamic characteristic; it combines speed and acceleration, allowing us to analyse the energy consumption during specific manoeuvres. Model (21) presents the linear dependence of ICRE on speed, acceleration, energy intensity and states.