Artificial Intelligence-based Approach For Electric Vehicle Travel Behavior Modeling

Abstract

Nowadays, environmental pollution and the limitation of fossil fuels are taken into consideration by many countries. Worries over the pollution from fossil fuels in the transportation sector have prompted the inclination to use electric vehicles (EVs) instead of the conventional internal combustion engines. It is predicted that at least 10% of the US transportation fleet will be changed to EVs by 2020, and they could have 50% of vehicle market share by 2050. Furthermore, by increasing the penetration of the renewable energy resources in the power system, we can use these clean energies to charge EVs; in this way, we can solve air pollution and fossil fuels problems. Implementing this procedure needs many infrastructures to handle the charging demand of the EVs properly. It should be mentioned that by increasing the penetration of the EVs in the power system, we are confronted with large load demand by sharp stochastic behavior which can have significant effects on the power system parameters such as voltage variations and power loss. To handle this problem, we need to charge EVs in smart mode by considering the power system constraints. In this way, some internal units between EV owners and power system operator, which are named as aggregators, are considered. These units buy electricity energy from the power system operator and sell it to the customers (EV owners). The main goal of these units is to find the optimal charging procedure of EVs by considering power system limitations and minimizing the EV owners charging cost. Here, the main challenge for aggregators to find the optimal charging solution is to model the EVs travel behavior and estimate the value and time of their charging demand in a precise manner. If they can estimate these parameters accurately, it is highly profitable for them and has a significant effect on their income. In this regard, we need to find the precise approach to forecast the EVs travel behavior with high accuracy which has a potential to handle large dimension data; because in the near future by increasing the penetration of the EVs in the transportation fleet, we will face big data problem. To handle the large dimension data sets, machine learning tasks, which are developed based on artificial intelligence concept, can be regarded as the best solution, and these approaches have acceptable performance on other data engineering tasks such as time series forecasting, image and voice processing, and pattern recognition. In this chapter, we introduce an artificial intelligence-based approach for modeling the EVs travel behavior and describe it in full details.

Graphical Abstract

Appendix A

The Nomenclature is presented as follows

2.1.1 Indices

i	Input data index
g	Output sample index
j	Hidden layer index
k	Iteration number index
l	Electric vehicle index
p	Node of power network index
q	Node of power network index
S	Layer index
t	Time sample index
u	Equipment index

2.1.2 Parameters

B(p, q)	Susceptance value between bus p and bus q
C inf	Cost of charging infrastructure
C eff	EV’s efficiency factor
Cap bat, l	l-th EV’s battery capacity
G(p, q)	Conductance value between bus p and bus q
M	Number of input data variables for LM
n 0	Input data dimension
n	Number of power system nodes
N T	Number of training neurons for LM
N w	Weight dimension for LM
${N}_{w_L}$	Weight dimension of lower bound neurons for LM
${N}_{w_U}$	Weight dimension of upper bound neurons for LM
n pev	Overall number of EVs
n eq	Overall number of equipment
nd	Dimension of sample data
${P}_{max}^u$	Maximum value of active power for each equipment
${Q}_{max}^u$	Maximum value of reactive power for each equipment
SOC dep	Minimum SOC value of every EV at departure time
V max	Maximum value of node’s voltage
V min	Minimum value of node’s voltage
ρ chr	Coefficient of the charging efficiency
η w	Training factor for weights
η ψ	Training factor for activation function in flexible mode

2.1.3 Variables

Ca(t)	Active power cost at time t
Cr(t)	Reactive power cost at time t
d(k)	Target value in k-th iteration
${e}_j^s(k)$	Internal error of neuron j in k-th iteration for layer S
ejM(k)	Internal error of neuron j f in k-th iteration for input data M in LM
${e}_{jM_L}(k)$	Internal error of lower bound neuron j in k-th iteration for input data M in LM
${e}_{jM_u}(k)$	Internal error of upper bound neuron j in k-th iteration for input data M in LM
eL − M(k)	Overall error vector in LM method for k-th iteration
E	Overall value of sum square error
E(k)	Overall value of sum square error in k-th iteration
${f}_j^s(k)$	Actuation function of neuron j for layer S k-th iteration
H(k)	Hessian matrix for k-th iteration
I(k)	Identity matrix for k-th iteration
J(k)	Jacobian matrix for k-th iteration
La(t)	Active load at time t
Lr(t)	Reactive load at time t
net(k)	Activation function input in iteration k
${net}_j^s(k)$	Activation function input for neuron j in layer S in iteration k
${net}_{Lj}^s(k)$	Lower bound of activation function input for neuron j in layer S in iteration k
${net}_{Uj}^s(k)$	Upper bound of activation function input for neuron j in layer S in iteration k
Os(k)	Output of layer S in iteration k
${O}_j^s(k)$	Output of neuron j in layer S in iteration k
${O}_U^s(k)$	Output of upper bound neuron for layer S in iteration k
${O}_L^s(k)$	Output of lower bound neuron for layer S in iteration k
${O}_{Uj}^s(k)$	Output of upper bound neuron j for layer S in iteration k
${O}_{Lj}^s(k)$	Output of lower bound neuron j for layer S in iteration k
Pu(t)	Active power value for u-th equipment at time t
${P}_l^{chr}(t)$	Charging rate value for l-th EV at time t
PEVa(t)	Active power of EV at time t
PEVr(t)	Reactive power of EV at time t
Plossa(t)	Active power loss value at time t
Plossr(t)	Reactive power loss value at time t
Qu(t)	Reactive power value of u-th equipment at time t
Ra(t)	Purchased active power value at time t
Rr(t)	Purchased reactive power value at time t
SOCinit, l(t)	Initial value of SOC for l-th EV at time t
SOCdep, l(t)	Departure value of SOC for l-th EV at time t
SOCl(t)	Value of SOC for l-th EV at time t
Tl l	Trip length value for l-th EV
${w}_j^s(k)$	Vector of weights for j-th neuron in layer S for k-th iteration
${W}_{U_j}^S(k)$	Vector of weights for j-th upper bound neuron for k-th iteration in layer S
${W}_{L_j}^S(k)$	Vector of weights for j-th lower bound neuron for k-th iteration in layer S
${W}_{ij}^S(k)$	Vector of weights between i-th input sample and j-th neuron in hidden layer S in k-th iteration
V(p, q, t)	Voltage of line between node p and q at time t
Vp(t)	Voltage of p-th node time t
X	Vector of input data
X i	Vector of i-th input data sample
Y g	Vector of g-th output data sample
X C
$\hat{Y_g}$	Vector of g-th target data sample
${\lambda}_j^s$	Upper bound factor for neuron j in layer S
${\gamma}_j^s$	Lower bound factor for neuron j in layer S
μ(k)	Decision value of iteration k in LM
θ p, t	Angel of voltage for p-th node at time t
θ q, t	Angel of voltage for q-th node at time t
ψ(k)	Variable of actuation function at iteration k