loads exceeds the generation, the extra active power is supplied by decreasing the generator’s rotation speed, which results in a downward drift in frequency [@regulation]. On the other hand, the balance of the reactive power can influence the voltage stability. The excess of reactive power will lead to voltage increase, while the insufficiency of reactive power will lead to voltage decrease [@reactivepower]. Therefore, the demand and supply of both active power and reactive power should always be balanced.

Generally, the system operator schedules the power plants by estimating the load. If the load fluctuates significantly around the predefined value, the power plants are incentivized to ramp up and ramp down. However, this results in low efficiency and high cost from committing spinning reserves [@spinningreserve]. Therefore, the fluctuation of the active power and reactive power at the generators with and without EV charging can be used as a metric to evaluate the stress that the charging stations impose on the grid. In particular, we use the 2-norm deviation of generating power (real power and reactive power) of all generators in the power system to calculate the impacts of EV charging.

$$B={\left\lVert\mathbf{P}_{\textrm{g}}^{\textrm{base}}-\mathbf{P}_{\textrm{g}}^{\textrm{EV}}\right\rVert}^2_2+
{\left\lVert\mathbf{Q}_{\textrm{g}}^{\textrm{base}}-\mathbf{Q}_{\textrm{g}}^{\textrm{EV}}\right\rVert}^2_2,$$

where $\mathbf{P}_{\textrm{g}}^{\textrm{base}}=[P_1^{\textrm{base}},P_2^{\textrm{base}},\cdots,P_M^{\textrm{base}}]$ is a vector representing the active power 