# PoissonScenarioGenerator

> For generating scenarios with random independent arrivals

---

## Description
A `PoissonScenarioGenerator` object randomly generates scenarios according to the following probability distributions:

- The number of EV arrivals at time slot `t` follows a Poisson distribution with parameter `arrival_rates(t)`
- The numbers of EV arrivals at time slots `1`, $\dots$ , `T` are mutually independent.
- No EV is accepted if all the chargers are ocuupied.
- The stay duration of each EV follows a geometric distribution with parameter `Delta/mean_stay_duration`; that is, EVs stay for `mean_stay_duration` minutes on average.
- The stay durations of different EVs are mutually independent.
- `E_min`, `E_cap`, `E_ini`, `E_ref`, `U_min`, and `U_max` are drawn from uniform distributions over the ranges `E_min_range`, `E_cap_range`, `E_ini_range`, `E_ref_range`, `U_min_range`, and `U_max_range`, respectively.
- (Load flattening) `Sigma` is drawn from a uniform distribution over the range `Sigma_range`
- (User friendly) The triple (`W_cs`, `W_pc`, `W_bs`) is sampled among the rows of `Uf_weights` with equal probability.
- The characteristics of EVs are mutually independent.



## Creation

### Syntax
```matlab
gen = PoissonScenarioGenerator()
gen = PoissonScenarioGenerator(Name=Value)
```

### Name-Value Arguments
| Name | Type | Description |
|------|------|--------------|
| `Problem_type` | *"Lf" (default) \| positive integer, scalar* | Type of problem, either "Lf" for load flattening or "Uf" for user-friendly |
| `N_c` | *50 (default) \| positive integer* | Number of chargers |
| `T` | *48 (default) \| positive integer* | Number of time slots comprising a generated scenario |
| `Delta` | *60 (default) \| positive scalar* | Length of time slot [minutes] |
| `P_max` | *200 (default) \| nonnegative scalar* | Maximum aggregate charging power [kW] |
| `P_min` | *-200 (default) \| nonpositive scalar* | Minimum aggregate EV load (i.e., -(maximum aggregate discharging power)) [kW] |
| `D` | *scaled, interpolated KEPCO base load (default) \| T×1 column vector* | Base load profile [kW] (required for load flattening problem) |
| `C` | *interpolated default tariff (default) \| T×1 column vector* | Electricity price profile [KRW] (required for user-friendly problem) |
| `EVs` | *[] (default) \| 1×N_ev EV array* | Array of EV objects |
| `L` | *[] (default) \| (N_c+1)×(N_c+1) symmetric Metzler matrix with zero row sum* | Graph Laplacian describing topology of the aggregator and chargers (for load flattening problem, undirected, index N_c+1 corresponds to the aggregatgor) |
| `W` | *[] (default) \| N_c×N_c nonnegative symmetric stochastic matrix* | Doubly stochastic matrix describing topology of the chargers (for user-friendly problem, undirected) |
| `Uf_weights` | *[1,0,0;0,1,0;...;1/3,1/3,1/3] (default) \| N_g×3 nonnegative matrix with positive row sum* | Weights set for groups in the user-friendly problem |
| `arrival_rates` | *5*ones(T,1) (default) \| T×1 column vector* | Mean number of EVs that arrive at each time slot |
| `mean_stay_duration` | *180 (default) \| scalar >= Delta* | Mean stay duration of EVs [minutes] |
| `Sigma_range` | *[0, 10] (default) \| 1×2 double* | Range of Sigma of EVs (load flattening problem) |
| `E_cap_range` | *[40, 100] (default) \| 1×2 double* | Range of battery capacity of EVs [kWh] |
| `SOC_ini_range` | *[15, 35] (default) \| 1×2 double* | Range of initial SOC of EVs [%] |
| `SOC_ref_range` | *[35, 50] (default) \| 1×2 double* | Range of reference SOC of EVs desired at departure [%] |
| `U_max_range` | *[10, 15] (default) \| 1×2 double* | Range of maximum charging powers of EVs [kW] |
| `U_min_range` | *[-15, -10] (default) \| 1×2 double* | Range of minimum charging powers of EVs [kW] |


### Output Arguments
| Name | Type | Description |
|------|------|--------------|
| `gen` | *PoissonScenarioGenerator object \| AbstractScenarioGenerator object* | A scenario generator that can generates scenarios from a specific distribution |


## Properties
| Name | Type | Description |
|------|------|--------------|
| `params` | *struct* | A struct consisting of the parameters required for generating a scenario |


## Object Functions
| Name | Description |
|------|--------------|
| `generate` | Randomly generate a scenario |