PoissonScenarioGenerator

For generating scenarios with random independent arrivals

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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

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	5ones(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