Correction: Zhang et al. Design of Coordinated EV Traffic Control Strategies for Expressway System with Wireless Charging Lanes. World Electr. Veh. J. 2025, 16, 496

Yingying Zhang; Yifeng Hong; Zhen Tan

doi:10.3390/wevj16100588

,

and

¹

School of Innovation and Entrepreneurship, Zhejiang Fashion Institute of Technology, Ningbo 315211, China

²

Nottingham University Business School China, University of Nottingham Ningbo China, Ningbo 315100, China

³

Nottingham Ningbo China Beacons of Excellence Research and Innovation Institute, University of Nottingham Ningbo China, Ningbo 315100, China

^*

Author to whom correspondence should be addressed.

World Electr. Veh. J.2025, 16(10), 588;https://doi.org/10.3390/wevj16100588

Version Notes

Order Reprints

Error in Tables

In the original publication [1], there was a mistake in Tables 1 and 3 as published. Some notations in the tables are inconsistent with those used in the model; thus, their definitions or numerical values need to be replaced by those consistent with the model. The corrected Table 1 and Table 3 appear below.

Table 1. Notations of the model.

Table 3. Electrical energy received and consumed on expressway segments in kWh.

Error in Equations

In the original publication [1], there was a mistake in Equations (6)–(8), (10)–(12), (16)–(21), and (23), as published. Some expressions are incorrect due to mis-indexing of the variables, introduction of unnecessary variables, or duplication of the same equations. The corrected Equations appear below.

N_{p} = N_{p - 1} + \sum_{o = 1}^{S} Q_{o p} - \sum_{d = 1}^{S} N_{d p}^{o u t} = N_{0} + \sum_{p^{'} = 1}^{p} (\sum_{o = 1}^{S} Q_{o p^{'}} - \sum_{d = 1}^{S} N_{d p^{'}}^{o u t}) .

(6)

T \cdot \sum_{p = 1}^{P} (N_{0} + \sum_{p^{'} = 1}^{p} (\sum_{o = 1}^{S} Q_{o p^{'}} - \sum_{d = 1}^{S} N_{d p^{'}}^{o u t})),

(7)

T \cdot \sum_{p = 1}^{P} \sum_{p^{'} = 1}^{p} \sum_{d = 1}^{S} N_{d p^{'}}^{o u t} = T \cdot \sum_{p = 1}^{P} [(P - p + 1) \cdot \sum_{d = 1}^{S} N_{d p}^{o u t}],

(8)

E_{o d}^{r e c} = p^{t x} \sum_{o \leq s \leq d} t_{s}^{t x},

(10)

t_{s}^{t x} = \frac{N_{s}^{t a} \cdot N^{t c} \cdot L^{t c}}{V_{s}},

(11)

N_{s}^{t a} = \frac{L_{s}}{L^{t a}} .

(12)

T \cdot \sum_{p = 1}^{P} (\sum_{o = 1}^{S - 1} (\sum_{s = o}^{S - 1} (N_{o s p} - N_{o (s + 1) p}) E_{o s}^{i n c}) + N_{S S p} E_{S S}^{i n c}) \cdot

(16)

N_{o s p} = \sum_{i = 1}^{I} N_{i o s p} \forall o \in \{1, \dots, S\}, s \in \{o, \dots, S\} p \in \{1, \dots, P\} \cdot

(17)

maximize α \sum_{p = 1}^{P} ((P - p + 1) \cdot \sum_{d = 1}^{S} N_{d p^{'}}^{o u t}) + β \sum_{p = 1}^{P} (\sum_{o = 1}^{S - 1} (\sum_{s = o}^{S - 1} (N_{o s p} - N_{o (s + 1) p}) E_{o s}^{i n c}) + N_{S S p} E_{S S}^{i n c}),

(18)

N_{o s p} \leq R_{o s p} \cdot N_{o o p} \forall s \in \{1, \dots, S\}, p \in \{1, \dots, P\}, o \in {1, \dots, s},

(19)

\sum_{p^{'} = 1}^{p} N_{i o o p^{'}} \leq \sum_{p^{'} = 1}^{p} Q_{i o p^{'}} \forall i \in \{1, \dots, I\}, o \in \{1, \dots, S\}, p \in {1, \dots, P},

(20)

N_{s p x} \leq C_{s} \forall s \in \{1, \dots, S\}, p \in \{1, \dots, P\}, x \in {1, \dots, s + 1},

(21)

\{\begin{matrix} \frac{N_{i o s p}}{R_{o s p}} = \frac{N_{i o (s + 1) p}}{R_{o (s + 1) p}} o \leq s < s_{i o}^{m i n} \\ \frac{N_{i o s p}}{R_{o s p}} \geq \frac{N_{i o (s + 1) p}}{R_{o (s + 1) p}} s_{i o}^{m i n} \leq s < S \end{matrix} \forall i \in \{1, \dots, I\}, o \in \{1, \dots, S - 1\}, p \in {1, \dots, P},

(23)

Text Correction

There was an error in the original publication [1]. To avoid confusion, the omission of the scalar

T

in forming (18) by combining (8) and (16) should be stated. A correction has been made to 3.3.3. The WCL Traffic Control Model, Paragraph 3:

In the objective function (18),

α

and

β

are two positive weights chosen by the traffic operator, which will be referred to as ‘trade-offs’ in the rest of the paper. Note that the scalar

T

is omitted in (18) as it is involved in both (8) and (16). The allocation of trade-offs

α

and

β

will determine the priority among the two components in the objective. When the two components have comparable magnitude (as in the case of our numerical example), one can simply set

α + β = 1

.

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Correction Statement

This article has been republished with a minor correction to the correspondence contact information. This change does not affect the scientific content of the article.

Reference

Zhang, Y.; Hong, Y.; Tan, Z. Design of Coordinated EV Traffic Control Strategies for Expressway System with Wireless Charging Lanes. World Electr. Veh. J. 2025, 16, 496. [Google Scholar] [CrossRef]

Table 1. Notations of the model.

Indices
$s \in {1, \dots, S}$	Index used for the expressway segments
$o \in {1, \dots, S}$	Index used for the origin on-ramps
$d \in {1, \dots, S}$	Index used for the destination off-ramps
$p \in {1, \dots, P}$	Index used for the time periods
$i \in {1, \dots, I}$	Index used for the initial SOC types of EVs
Traffic model variables and parameters
$N_{p}$	Total number of vehicles on the expressway during period $p$ , [veh per hour, veh/h]
$N_{o s p}$	Number of vehicles allowed to enter the expressway from on-ramp $o$ during period $p$ and will pass the end of segment $s$ , [veh/h]
$N_{d p}^{o u t}$	Total number of vehicles leaving the expressway via off-ramp $d$ during period $p$ , [veh/h]
$N_{s p}$	Total number of vehicles passing the end of the expressway segment $s$ during period $p$ , [veh/h]
$Q_{o p}$	Total vehicle demand in period $p$ for entering the expressway from on-ramp $o$ , [veh/h]
$R_{o s p}$	Ratio of vehicles entering the expressway from on-ramp $o$ during period $p$ and will pass through the beginning of expressway segment $s$ , with $o \leq s$
$C_{s}$	Vehicle carrying capacity of expressway segment $s$ , [veh/h]
$L_{s}$	Length of the expressway segment $s$ , [kilometer, km]
$t_{s}$	Average travel time through the expressway segment $s$ , [hour]
$V_{s}$	Average speed of an EV traveling on the expressway segment $s$ , [kilometer per hour, km/h]
$T_{o s}$	Average travel time from on-ramp $o$ to the end of expressway segment $s$ , with $o \leq s$ , [hour]
EV charging model variables and parameters
$N_{i o s p}$	Number of EVs with initial SOC type $i$ allowed to enter the expressway from on-ramp $o$ during period $p$ and will pass the end of segment $s$ , [veh/h]
$N_{i o p}^{m i n}$	The minimum number of EVs with initial SOC type $i$ required to enter the expressway from on-ramp $o$ during period $p$ , [veh/h]
$Q_{i o p}$	Demand of EVs with initial SOC type $i$ in period $p$ for entering the expressway from on-ramp $o$ , [veh/h]
$s_{i o}^{m i n}$	The index of the segment that any EV with initial SOC type $i$ entering the expressway from on-ramp $o$ must at least pass through if no further than its destination off-ramp, which is generally bigger for a lower SOC level.
$E_{o d}^{i n c}$	Electrical energy increased by an EV which enters and leaves the WCL system from on-ramp $o$ and off-ramp $d$ , [kilowatt-hours, kWh]
$E_{o d}^{r e c}$	Electrical energy received by an EV which enters and leaves the WCL system from on-ramp $o$ and off-ramp $d$ , [kWh]
$E_{o d}^{c o n}$	Electrical energy consumed by an EV which enters and leaves the WCL system from on-ramp $o$ and off-ramp $d$ , [kWh]
$E_{s, 0}^{c o n}$	Electrical energy consumption of an EV by traveling throughout segment $s$ with stable speed, [kWh]
$E_{o, i n}^{c o n}$	Electrical energy additional to $E_{s, 0}^{c o n}$ consumed by an EV due to speed variation in merging traffic entering the system via on-ramp $o$ , [kWh]
$E_{d, o u t}^{c o n}$	Electrical energy additional to $E_{s, 0}^{c o n}$ consumed by an EV due to speed variation in merging traffic leaving the system via off-ramp $d$ , [kWh]
$N_{s}^{t a}$	Total number of segmented transmitter arrays on expressway segment $s$
$t_{s}^{t x}$	Time for the EV to receive electrical energy from the DWPT system on expressway segment $s$ , [hour]

Table 3. Electrical energy received and consumed on expressway segments in kWh.

Energy received	$p^{t x} t_{1}^{t x}$	$p^{t x} t_{2}^{t x}$	$p^{t x} t_{3}^{t x}$	$p^{t x} t_{4}^{t x}$	$p^{t x} t_{5}^{t x}$	$p^{t x} t_{6}^{t x}$	$p^{t x} t_{7}^{t x}$
Energy received	1.54	3.08	3.08	3.08	1.54	2.46	3.69
Energy consumed	$E_{1,0}^{c o n}$	$E_{2,0}^{c o n}$	$E_{3,0}^{c o n}$	$E_{4,0}^{c o n}$	$E_{5,0}^{c o n}$	$E_{6,0}^{c o n}$	$E_{7,0}^{c o n}$
Energy consumed	0.65	1.30	1.30	1.30	0.65	1.04	1.56

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Correction: Zhang et al. Design of Coordinated EV Traffic Control Strategies for Expressway System with Wireless Charging Lanes. World Electr. Veh. J. 2025, 16, 496

Error in Tables

Error in Equations

Text Correction

Correction Statement

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