UAM System Optimization
Problem Formulation
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$n_{i}^{k}(t)$ = # of idle aircrafts at vertiport i of SOC k at time t -
$u_{ij}^{k}(t)$ = # of flights departing for vertiport j from vertiport i at time t -
$C_{i}^{xy}(t)$ = # of aircrafts at vertiport i that begin to charge at t with an initial SOC of x and a target SOC of y -
$\gamma_{k}$ is the charging time needed to transition from$SOC_{k-1}$ to$SOC_{k}$ -
$K$ is the # of SOCs.$K = 32$ -
$\tau_{ij}$ is the flight time from vertiport i to j -
$\kappa_{ij}$ is the # of SOCs dropped in flight from vertiport i to j
The dynamic equation is then:
Therefore, an aircraft can be in one of the three states at any given point in time: (1) idle (2) charging (3) flight
Stationarity Condition
T = number of timesteps + 1 + max flight time