# Modeling electric vehicle (EV) and charging stations in a parking lot

Hello,

I want to model the occupancy by M electric vehicles (EV) of a set of N EV battery charging stations in a parking lot, for which I have historical data on arrival time, departure time and battery charging per EV per day.

I would like to have a model per EV (as the driving habits and the technical specs of the EV battery are each quite specific).
I was thinking about modeling on one side the presence or not of the EV in the parking for a given day (yes/no) and if present, the arrival time (in the morning usually) and the departure time (in the afternoon usually) or the duration (time spent in the parking, with departure time = arrival time + duration).

I haven’t yet used PyMC beyond the turoial. I see Passenger arrival rate partial pooling model that could be similar in spirit.
So my question, given a specific EV history of data, how can I build a model and train it if I assume:

• presence = Categorical
• arrival time = Normal or Uniform
• departure time = Normal or Uniform
• duration = departure time - arrival time

A first sample of code would greatly help me to start !

My suggestion would be starting with a simple linear model to predict duration. What I would do is:

For the M EV, assuming each with a feature vector with k feature representing the driving habits, technical specs of the EV battery etc, which gives a M*k matrix. This is the input.

The output is the duration and presence. Here I will combine them together so that presence=0 --> duration=0. This is a vector of length M.

Now, say that you record this for 10 days, you will have a repeated measure of 10. The model would look something like:

with pm.Model() as baseline_model:
intercept = pm.Normal(...)
beta = pm.Normal(..., shape=(k, 1))
prediction = intercept + Xinput.dot(beta) # Xinput has shape M*k
sd = pm.HalfNormal(...)
observed = pm.Lognormal(..., mu=tt.exp(prediction), sd=sd, observed=duration) #duration has shape M*10

Notice here duration is modelled using a Lognormal, but a zero-inflated gamma would be more appropriate.

tx @junpenglao for your answer. But I may have not been very clear…

What I have is a sample of my data looks like

car/driver day arrival departure kWh
#1 5/03/2018 08:12 17:30 11,90
#1 7/03/2018 07:41 17:55 6,40
#1 8/03/2018 07:59 19:29 4,50
#1 9/03/2018 08:03 18:39 7,30
#1 12/03/2018 08:07 18:19 13,40
#1 13/03/2018 08:01 19:31 4,90

You can see the car/drive number 1 comes most week days (he did not come on the 6/03/2018). He arrives around 8am and departs betwen 5pm and 7pm and the charging level of the battery (kWh) is between 4 and 7 usually except on mondays where is it more (more use during the week end).

How would I go to fit a model such that:

• some week days, the car/driver is not there (like the 6/03/2018) => guesstimate for p(car is not in parking) ~ 14% (1 day over 8 weekdays observed)
• arrival is normal ==> guesstimate N(08:00, 00:10)
• departure is normal ==> guesstimate N(18:33, 00:49)
• kWh ==> guesstimate N(12.65, 1.06) on Monday, and N(5.78, 1.3) on Tu-Fri
For guesstimates here I just took simple estimate (mean, stdev, …).

I would like to use PyMC to do this estimates and then to enhance the model with more complex relations (like arrival on day D depends on arrival on day D-1, etc).

I guess the simplest thing to try first is model each M car separately, with uniform priors on all the parameters you would like to infer. The model would be more or less what you wrote down above.