The dynamic electric boat charging problem

Vélez, Camilo; Montoya, Alejandro

doi:10.1590/0103-6513.20220114

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Research Article • Prod. 33 • 2023 • https://doi.org/10.1590/0103-6513.20220114 copy

The dynamic electric boat charging problem

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Paper aims

This paper proposes a new optimization problem named the dynamic electric boat charging problem (DEBCP).

Originality

The problem dynamically determines the speed and charging decisions of an electric boat (EB) to be performed in photovoltaic charging stations (PVCSs).

Research method

The objective function is to minimize the charging plus the battery degradation costs. Considering that the energy consumption of the EB and the solar irradiance for the PVCSs are uncertain due to factors external to the operation, the dynamic component of the DEBCP recalculates the solution to the problem as new information related to these variables is known. To solve the problem, we propose a rolling horizon genetic algorithm. This method constantly reevaluates the speed and charging decisions of the operation. Such decisions are made with a genetic algorithm.

Main findings

Our results show that the recalculations help either reducing the cost of the solution when possible or correcting the operation when needed.

Implications for theory and practice

To evaluate our solution method, we built some test instances based on a future fluvial transport operation with an EB that will be implemented in Colombia. We assess the impact of the dynamic recalculations by comparing the results of the DBECP problem to a scenario following a static solution.

Keywords
Electric boat; Speed decisions; Charging decisions; Photovoltaic charging stations; Dynamic recalculations

1: function $C H A R G I N G P O L I C I E S (ϕ, Γ_{0}, Γ_{1}, {\bar{g}}_{j}, f_{s h})$
2: $b e s t C o s t \leftarrow \infty$
3: $ψ \leftarrow 〈〉$
4: $ζ \leftarrow S e t H i g h e s t C h a r g i n g P o w e r s (f_{s h})$
5: while true do
6: $〈c o s t, i s F e a s i b l e, φ, ε, Ω〉 \leftarrow E v a l u a t e S o l u t i o n (ϕ, Γ_{0}, Γ_{1}, {\bar{g}}_{j}, ζ)$
7: if $i s F e a s i b l e = t r u e$ and $c o s t < b e s t C o s t$ then
8: $b e s t C o s t \leftarrow c o s t$
9: $ψ \leftarrow 〈φ, ε, Ω, ζ〉$
10: else if $i s F e a s i b l e = f a l s e$ then
11: break
12: end if
13: $〈κ, ν〉 \leftarrow 〈- 1, \infty〉$
14: ^for $j = 0$ ^to $j = \|S_{p}\|$ ^do
15: if $0 < Ω [j] - ε [j] < ν$ and $LowerChargingPower (j, ζ, f_{s h}) = t r u e$ then
16: $〈κ, ν〉 \leftarrow 〈j, Ω [j] - ε [j]〉$
17: end if
18: end for
19: if $κ = 1$ then
20: break
21: else
22: $ζ \leftarrow D e c r e a s e C h a r g i n g P o w e r (ζ, κ)$
23: end if
24: end while
25: return ⟨ψ, bestCost⟩
26: end function

Instance	$T_{m a x}$ (h)	Departure hour	PVCSs*	Route length (km)	Segments
Pinillos1	4	10:00	5	110	112
Pinillos2	4.5	10:00	5	110	112
Pinillos3	5	10:00	5	110	112
Inn1	6	9:00	9	171.6	174
Inn2	6.75	9:00	9	171.6	174
Inn3	7.5	9:00	9	171.6	174
Achi1	8	7:00	11	208.8	212
Achi3	9	7:00	11	208.8	212
Achi3	10	7:00	11	208.8	212
*Photovoltaic charging stations.

MILP			GA
Instance	Cost (USD)	CPU^* * Central processing unit. time (sec)	Average cost (USD)	Best found cost (USD)	Average CPU time (sec)	Average gap (%)	Best found gap (%)	Speedup
Pinillos1	37.33	6.75	37.49	37.40	2.59	0.43	0.19	2.60
Pinillos2	32.24	25.78	32.51	32.32	2.59	0.84	0.25	9.94
Pinillos3	28.19	83.57	28.28	28.25	2.58	0.33	0.23	32.36
Inn1	83.33	5763.60	83.53	83.51	3.83	0.24	0.21	1503.17
Inn2	70.96	31.98	71.16	71.13	3.94	0.29	0.24	8.12
Inn3	63.85	195.63	64.39	64.19	3.99	0.83	0.53	49.09
Achi1	102.64	339.51	103.54	103.49	4.67	0.87	0.83	72.63
Achi2	90.10	354.59	90.60	90.52	4.80	0.56	0.47	73.93
Achi3	81.44	7200	82.12	81.96	5.23	0.83	0.63	1376.99
Min		6.75			2.58	0.24	0.19	2.60
Max		7200			5.23	0.87	0.83	1503.17
Average		1555.71			3.80	0.58	0.40	347.65

Static scenario				DEBCP
Instance	Cost (USD)	Energy violation (kWh)	Time violation (h)	Cost (USD)	Energy violation (kWh)	Time violation (h)	Gap (%)
Pinillos1	33.48	0	0	32.66	0	0	2.43
Pinillos2	28.91	0	0	28.69	0	0	0.74
Pinillos3	26.53	0	0	26.08	0	0	1.72
Inn1	72.99	0	0	71.00	0	0	2.73
Inn2	62.60	0	0	60.98	0	0	2.58
Inn3	57.07	0	0	55.92	0	0	2.02
Achi1	89.23	0	0	86.06	0	0	3.55
Achi2	80.22	0	0	76.61	0	0	4.50
Achi3	72.87	0	0	70.16	0	0	3.72
Min		0	0		0	0	0.74
Max		0	0		0	0	4.50
Average		0	0		0	0	2.67

Static scenario				DEBCP
Instance	Cost (USD)	Energy violation (kWh)	Time violation (h)	Cost (USD)	Energy violation (kWh)	Time violation (h)	Gap (%)
Pinillos1	38.59	8.69	0.11	39.80	8.38	0.03	-3.14
Pinillos2	33.63	7.98	0.10	34.68	6.14	0.02	-3.14
Pinillos3	30.89	7.85	0.12	31.16	5.30	0.00	-0.88
Inn1	87.47	27.68	0.18	92.11	21.33	0.09	-5.30
Inn2	74.48	22.69	0.15	78.82	18.03	0.06	-5.82
Inn3	67.72	21.52	0.27	71.85	17.20	0.06	-6.10
Achi1	107.95	31.92	0.32	113.51	28.52	0.30	-5.14
Achi2	96.66	29.12	0.40	100.48	23.07	0.12	-3.96
Achi3	88.48	28.07	0.43	92.89	17.23	0.04	-4.99
Min		7.85	0.10		5.30	0.00	-0.88
Max		31.92	0.43		28.52	0.30	-6.10
Average		20.61	0.23		16.13	0.08	-4.28

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[1] * cvelezg10@eafit.edu.co