informИнформатикаInformatics1816-03012617-6963UIIP NASB10.37661/1816-0301-2021-18-4-79-95inform-1173Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGПодход к оптимизации зарядной инфраструктуры автономных троллейбусов для городских маршрутовApproach to optimizing charging infrastructure of autonomous trolleybuses for urban routeshttps://orcid.org/0000-0003-0832-0829КовалевМ. Я.KovalyovМ. Ya.

Ковалев Михаил Яковлевич - доктор физико-математических наук, профессор, зам. генерального директора по научной работе.

ул. Сурганова, 6, Минск, 220012.

Mikhail Ya. Kovalyov - Dr. Sci. (Phys.-Math.), Professor, Deputy General Director, The United Institute of Informatics Problems of the National Academy of Sciences of Belarus.

Surganova st., 6, Minsk, 220012.

kovalyov_my@newman.bas-net.byhttps://orcid.org/0000-0003-3814-6569РозинБ. М.RozinB. M.

Розин Борис Матвеевич - кандидат технических наук, заведующий сектором.

ул. Сурганова, 6, Минск, 220012.

Boris M. Rozin - Cand. Sci. (Eng.), Head of the sector, The United Institute of Informatics Problems of the National Academy of Sciences of Belarus.

Surganova st., 6, Minsk, 220012.

rozin@newman.bas-net.byШатерникИ. А.ShaternikI. A.

Шатерник Илья Андрианович - инженер-программист.

ул. Сурганова, 6, Минск, 220012.

Ilya A. Shaternik - Engineer-programmer, The United Institute of Informatics Problems of the National Academy of Sciences of Belarus.

Surganova st., 6, Minsk, 220012.

shatoby.i@gmail.comОбъединенный институт проблем информатики Национальной академии наук БеларусиThe United Institute of Informatics Problems of the National Academy of Sciences of Belarus2021311220211847995Copyright © Ковалев М.Я., Розин Б.М., Шатерник И.А., 20212021Ковалев М.Я., Розин Б.М., Шатерник И.А.Kovalyov М.Y., Rozin B.M., Shaternik I.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://inf.grid.by/jour/article/view/1173Ц е л и

Ц е л и. При проектировании системы городского электротранспорта, заряжающегося во время движения, в том числе автономных троллейбусов с батареями увеличенной емкости, актуальной является оптимизация зарядной инфраструктуры для парка такого транспорта. Зарядная инфраструктура выделенных маршрутов состоит из секций контактной сети вдоль маршрутов и стационарных зарядных станций заданного типа на конечных остановках маршрутов. Она предназначена для обеспечения движения троллейбусов и восстановления заряда их батарей, израсходованного на участках автономного хода.

Цель исследования заключается в создании моделей и методов выработки экономически эффективных решений по зарядной инфраструктуре, обеспечивающих функционирование парка автономных троллейбусов с учетом ряда специфических условий. Условия включают обеспечение заданного диапазона автономного хода троллейбусов при заданной скорости расхода энергии на маршрутах и гарантийного срока эксплуатации их батарей, а также предотвращение разряда батарей ниже критического уровня при различных режимах эксплуатации в течение срока их службы.

М е то д ы

М е то д ы. Используются методы теории множеств, теории графов и линейной аппроксимации.

Р е з у л ь т а т ы

Р е з у л ь т а т ы.  Разработана математическая модель задачи оптимизации зарядной инфраструктуры парка автономных троллейбусов. В качестве целевой функции выбраны суммарные приведенные годовые затраты на зарядную инфраструктуру. Модель сформулирована в виде задачи математического программирования с квадратичной целевой функцией и линейными ограничениями.

З а к л ю ч е н и е

З а к л ю ч е н и е. Для решения сформулированной задачи математического программирования могут использоваться стандартные решатели типа IBM ILOG CPLEX, а также, с учетом ее вычислительной сложности, эвристический метод «роя частиц». Решение задачи заключается в выборе конфигурации расположения секций контактной сети на маршрутах и длительностей зарядки троллейбусов на конечных остановках, определяющих соответствующие количества стационарных зарядных станций на этих остановках.

P u r p o s e s

P u r p o s e s.  When designing a system of urban electric transport that charges while driving, including autonomous trolleybuses with batteries of increased capacity, it is important to optimize the charging infrastructure for a fleet of such vehicles. The charging infrastructure of the dedicated routes consists of overhead wire sections along the routes and stationary charging stations of a given type at the terminal stops of the routes. It is designed to ensure the movement of trolleybuses and restore the charge of their batteries, consumed in the sections of autonomous running.

The aim of the study is to create models and methods for developing cost-effective solutions for charging infrastructure, ensuring the functioning of the autonomous trolleybus fleet, respecting a number of specific conditions. Conditions include ensuring a specified range of autonomous trolleybus running at a given rate of energy consumption on routes, a guaranteed service life of their batteries, as well as preventing the discharge of batteries below a critical level under various operating modes during their service life.

M e t ho d s

M e t ho d s. Methods of set theory, graph theory and linear approximation are used.

Re s u l t s

Re s u l t s. A mathematical model has been developed for the optimization problem of the charging infrastructure of the autonomous trolleybus fleet. The total reduced annual costs for the charging infrastructure are selected as the objective function. The model is formulated as a mathematical programming problem with a quadratic objective function and linear constraints.

Co n c l u s i o n

Co n c l u s i o n. To solve the formulated problem of mathematical programming, standard solvers such as IBM ILOG CPLEX can be used, as well as, taking into account its computational complexity, the heuristic method of "swarm of particles".  The solution to the problem is to select the configuration of the location of the overhead wire sections on the routes and the durations of charging the trolleybuses at the terminal stops, which determine the corresponding number of stationary charging stations at these stops.

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The authors declare that there are no conflicts of interest present.