Optimization of Electric Truck Routes for Performing Maintenance Services on the Electric Power Distribution Network

Oening, Ana Paula; Bello, Tiago Lino; Casarin, Eduardo; Marcilio, Débora Cintia; Santos, Signie Laureano França; Macedo, Pablo Lopes

doi:10.1590/1678-4324-2025240869

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Figure 1 Battery Charge - MAI-01 team.

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Figure 2 Battery charge - MAI-02 team.

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Figure 3 Battery charge - MAI-03 team.

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Figure 4 Battery charge - ATI-01 team.

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Figure 5 Battery charge - ATI-02 team.

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Figure 6 Battery recharge - ATI-02 team days 11/03/2020 (in a) and 11/06/2020 (in b)

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Figure 7 Battery charge - ATI-03 Team.

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N number of nodes (clients to be visited) {0}, N+1 warehouse nodes, both related to the same location, were considered twice to ensure that the routing starts and ends at the warehouse V set of customers, ranging from 1 to N V 0 = V ∪ 0 set of customers and the initial warehouse V N + 1 = V ∪ N + 1 set of customers and the final warehouse F set of charging stations V ′ = V ∪ F set of customers and stations V ' 0 = V ' ∪ 0 set of customers, charging points and initial warehouse V ' N + 1 = V ' ∪ N + 1 set of customers, charging points and final warehouse

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dij traveled distance in kilometers (km) from node i to node j , ∀i∈V0', j∈VN+1', i≠j gi recharge rate of an electric vehicle at node i∀ i∈ V′∪0∪N+1 s i = 1 , i f t h e c u s t o m e r i h a s a c h a r g i n g s t a t i o n 0 , o t h e r w h i s e if the customer i has a charging station, ∀i∈V h electric vehicle energy consumption rate per unit of distance [kWh/km] Q electric vehicle battery capacity [kWh]

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x i j = 1 , i f t h e E V t r a v e l i → j 0 , o t h e r w i s e Path defined between node iand node j, ∀i∈V0', j∈VN+1', i≠j r i = 1 , i f t h e E V i s r e c h a r g e d a t n o d e i 0 , o t h e r w i s e Recharge at node i, ∀i∈V pi Track the service start time at node i, ∀i∈V′∪0∪N+1 yi Battery level upon arrival at node i, ∀i∈V′∪0∪N+1 wi Battery charged at node i, ∀i∈V′∪0∪N+1 wi' Battery charge consumed in the path between the previous node to node i, ∀i∈V′∪0∪N+1

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Table 1 Parameters used for the optimization problem.

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Table 2 Optimization results for MAI-01 team.

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Table 3 Optimization results for MAI-02 team.

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Table 4 Optimization results for MAI-03 team.

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Table 5 Comparison between distances traveled in Mairiporã by the optimized and non-optimized truck route.

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Table 6 Optimization results for ATI-01 team.

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Table 7 Optimization results for ATI-02 team.

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Table 8 Optimization results for ATI-03 team.

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Table 9 Comparison between the distances traveled in Atibaia by the electric truck and the combustion truck.

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N	number of nodes (clients to be visited)
{0}, $\{N + 1\}$	warehouse nodes, both related to the same location, were considered twice to ensure that the routing starts and ends at the warehouse
V	set of customers, ranging from 1 to N
$V_{0} = V \cup \{0\}$	set of customers and the initial warehouse
$V_{N + 1} = V \cup \{N + 1\}$	set of customers and the final warehouse
F	set of charging stations
$V^{'} = V \cup F$	set of customers and stations
$V'_{0} = V' \cup \{0\}$	set of customers, charging points and initial warehouse
$V'_{N + 1} = V' \cup \{N + 1\}$	set of customers, charging points and final warehouse

d_ij	traveled distance in kilometers (km) from node i to node j , $\forall i \in V_{0}^{'}, j \in V_{N + 1}^{'}, i \neq j$
g_i	recharge rate of an electric vehicle at node i $\forall i \in V^{'} \cup \{0\} \cup \{N + 1\}$
$s_{i} = \{\begin{matrix} 1, i f t h e c u s t o m e r i h a s a c h a r g i n g \\ s t a t i o n \\ 0, o t h e r w h i s e \end{matrix}$	if the customer i has a charging station, $\forall i \in V$
h	electric vehicle energy consumption rate per unit of distance [kWh/km]
Q	electric vehicle battery capacity [kWh]

$x_{i j} = \{\begin{matrix} 1, i f t h e E V t r a v e l i \to j \\ 0, o t h e r w i s e \end{matrix}$	Path defined between node iand node j, $\forall i \in V_{0}^{'}, j \in V_{N + 1}^{'}, i \neq j$
$r_{i} = \{\begin{matrix} 1, i f t h e E V i s r e c h a r g e d a t n o d e i \\ 0, o t h e r w i s e \end{matrix}$	Recharge at node $i, \forall i \in V$
p_i	Track the service start time at node i, $\forall i \in V^{'} \cup \{0\} \cup \{N + 1\}$
y_i	Battery level upon arrival at node $i, \forall i \in V^{'} \cup \{0\} \cup \{N + 1\}$
w_i	Battery charged at node $i, \forall i \in V^{'} \cup \{0\} \cup \{N + 1\}$
w_i^'	Battery charge consumed in the path between the previous node to node $i, \forall i \in V^{'} \cup \{0\} \cup \{N + 1\}$

Parameter	Operational Base
Distances (d_ij)	Obtained through Google API Distance Matrix Data
Maximum charger capacity ( capacity_charger)	Warehouse node - 40 kWh Other nodes - 20 kWh
Existence of charging stations (s)	All nodes have charging stations in this work, because the EV can charge in the electrical systems.
Electric vehicle energy consumption rate (h)	0.8 kWh
Electric vehicle battery capacity (Q)	160 kWh
Penalties in the objective function	Pen₁ = 2, Pen₂ = 0.05
Value M	9999
Maximum solver run time for each problem	500 sec (≈ 8 min)

Day	Travel distance (km)	Travel time (min.)	Recharged?	Time to get the solution (sec)	Visited points number
11/03/2020	67.63	142.13	No	1.54	15
11/04/2020	76.68	151.52	No	54.19	15
11/05/2020	72.07	165.50	No	41.96	17
11/06/2020	59.12	123.25	No	17.59	15

Day	Travel distance (km)	Travel time (min.)	Recharged?	Time to get the solution (sec)	Visited points number
11/03/2020	60.77	137.93	No	97.23	15
11/04/2020	74.99	180.46	No	7.31	15
11/05/2020	45.48	114.40	No	192.07	16
11/06/2020	77.20	157.41	No	5.94	14

Day	Travel distance (km)	Travel time (min.)	Recharged?	Time to get the solution (sec)	Visited points number
11/03/2020	72.35	112.18	No	72.89	16
11/04/2020	168.00	240.00	No	500.00	16
11/05/2020	51.92	123.50	No	1.74	15
11/06/2020	78.76	159.53	No	387.22	15

Distances (Km) - Optimized route
Team	11/03/2020	11/04/2020	11/05/2020		11/06/2020	Total
MAI-01	67.63	76.68	72.07		59.12	275.50
MAI-02	60.77	74.99	45.58		77.20	258.54
MAI-03	72.35	168.00	51.92		78.76	371.03
Total	200.75	319.67	169.57		215.08	905.07
Distances (Km) - Non-optimized route
Team	11/03/2020	11/04/2020	11/05/2020	11/06/2020		Total
MAI-01	103.70	91.44	169.08	140.75		504.97
MAI-02	100.10	172.70	49.60	128.30		450.70
MAI-03	152.60	126.30	134.90	105.70		519.50
Total	356.4	390.44	353.58	374.75		1,475.17

Day	Travel distance (km)	Travel time (min.)	Recharged?	Time to get the solution (sec)	Visited points number
11/03/2020	78.03	118.20	No	500	18
11/04/2020	74.41	118.13	No	500	17
11/05/2020	73.15	110.30	No	500	14
11/06/2020	72.50	104.50	No	500	14

Day	Travel distance (km)	Travel time (min.)	Recharged?	Time to get the solution (sec)	Visited points number
11/03/2020	402.39	500.35	Yes	500	17
11/04/2020	124.18	182.71	No	500	23
11/05/2020	111.47	189.51	No	500	15
11/06/2020	349.39	328.38	Yes	500	16

Day	Travel distance (km)	Travel time (min.)	Recharged?	Time to get the solution (sec)	Visited points number
11/03/2020	123.58	186.45	No	77	15
11/04/2020	162.50	217.56	No	500	20
11/05/2020	131.28	160.86	No	500	16
11/06/2020	122.97	168.01	No	84	15

Distances (Km) - Optimized route
Team	11/03/2020	11/04/2020	11/05/2020	11/06/2020	Total
ATI-01	78.03	74.41	73.15	72.50	298.09
ATI -02	402.39	124.18	111.47	349.39	987.43
ATI -03	123.58	162.50	131.28	122.97	540.33
Total	604.00	361.09	315.90	544.86	1,825.85
Distances (Km) - Non-optimized route
Team	11/03/2020	11/04/2020	11/05/2020	11/06/2020	Total
ATI -01	104.35	92.60	100.10	108.85	405.90
ATI -02	567.17	14.,04	125.10	396.00	1,235.31
ATI -03	237.00	258.93	231.90	234.23	962.06
Total	908.52	498.57	457.10	739.08	2,603.27