Steady state with or without initial energy storage

How do you find the mean store energy in a steady-state regime?

In the steady-state regime, the mean store energy converges towards the sum of the expectation values for each car (9) E S = ∑ j x j ɛ m (j) = ∑ j a j ′ (r j) a ′ (r j) + b ′ (r j) ɛ m (j), where r j is the relative daily range for the j th car.

How can a steady-state energy storage model be used in EVs?

The model, together with a vast longitudinal series of travel records from Denmark, is then used to determine the steady-state distribution of SoC levels, which in turn can be used to estimate a corresponding steady-state energy storage potential in a fleet of EVs. 2.1. Charge decision

What is the convergence of SOC towards steady-state mean level?

Convergence of SoC towards steady-state mean level for 5 randomly selected vehicles. Solid lines show the absolute deviation of mean SoC level μ k at the k th day with respect to μ k = N. Coloured shaded regions represent σ / 2 (half s.d.) windows for the respective SoC level.

How does a steady-state distribution of SOC affect a fleet?

In this subsection, we show that knowledge of the steady-state distribution of SoC values f d (a ′, b ′; x) in a fleet offers not only a means to assess the decision to charge, but also the ability to estimate the average energy stored and charge demand across the entire fleet of EVs daily.

When should solar energy be stored?

Even if the storage technology is available, as it is the case in the model, storage must only begin after fossil has been abandoned at day because the installed solar capacity has become high enough and solar energy accounts for a significant fraction of electricity generation.

Should electricity be stored at night or day?

It is never optimal to store electricity when coal is used night and day. It would be different absent storage possibilities: then fossil fuel use at day might tend to zero asymptotically and this steady state would be reached.