1. Introduction
Urban areas have been dealing with various challenges. These challenges include sustainable development, enhancing services provided to citizens, reducing carbon generation, decreasing emissions of pollutants, and improving the utilization of resources. These challenges have drawn attention to more efficient energy management (EM) within urban areas. A smart city (SC) is a concept developed to achieve a more energy-efficient urban area [
1]. A comprehensive scheme of an SC considers the entire energy systems presented in the model. This includes transportation systems such as plug-in electric vehicles (PEVs) and subway systems (SWSs), and distributed energy systems such as Photovoltaics (PVs), Heat Pumps (HPs), and batteries. Considering the interconnection and cooperative operation of various energy systems within the SC model causes the model to become more energy-efficient and flexible in supplying the total demands of the system.
Creating sustainable and better-functioning transportation systems is among the main goals of smart cities [
2]. High air pollution and traffic congestion are the main challenges facing urban transportation systems [
3]. Hence, a more efficient, secure, and eco-friendly transport system is highly valued for the design of present and future cities. Transportation systems are among the major consumers of energy, and smart management of them is of great importance in lowering the energy consumption of the SC model. The interconnections between all different parts, including the transportation systems and distributed energy systems, must be modeled to obtain a more comprehensive and efficient SC model.
PEVs and subways (SWs) are among the most utilized parts of the transportation systems in cities. PEVs constitute 5% of the loads in an electric grid [
3,
4]. Therefore, they need to be managed efficiently in order to obtain a sustainable SC model. PEVs can also be used as a distributed resource for the grid when they are parked in a parking lot and are being discharged. A handful of researchers have focused on the optimal management of PEVs and the challenges they add to the model. In [
5], an optimized bidirectional vehicle-to-grid (V2G) system operation is presented that carries out the day-ahead scheduling of PEVs’ charging/discharging. An adaptive control method to manage PEV charging/discharging for load leveling and peak shaving is presented in [
6]. Ref [
7] presents a novel EM scheme for optimal integration of PEVs into a distribution system that involves two layers for active and reactive power management. The SWS is the other major component of the transportation system. Consequently, many researchers have studied SWSs and assessed their impact on different parts of the entire system, and different studies are considered as approaches to improve the efficiency of urban SWSs. Regenerative braking energy (RBE) is considered to be a solution for the efficient EM of SWSs. In [
8], a timetable optimization method was proposed to utilize the braking energy (BE). This method is based on adjusting the departure and arrival time of trains to use the BE of the arriving train directly from the train that is leaving. Another method utilizes energy storage systems (ESSs) to reserve the BE for later consumption. A novel method combining timetable optimization and onboard ESS utilization was proposed in [
9]. Wayside placement of an ESS is an alternative way of implementing an ESS in urban SWSs. In [
10], a wayside ESS and its different ways of connecting to the system, including connection via the bidirectional converters and direct connection, are studied. Another method employs reversible substations to feed the RBE back to the upstream AC grid [
11].
Different types of distributed energy resources (DERs) are incorporated into the SC model to benefit from their advantages toward a more efficient SC. Stationary batteries can be utilized for EM by storing electricity at off-peak hours and decreasing purchased power from the grid. Air pollutants and greenhouse gasses are among the most noticeable challenges of modern society. PVs are extensively utilized in residential, commercial, and industrial sectors to convert light energy into electricity and reduce air pollutants [
12]. Finally, electrification of heating by utilizing HPs along with renewable power generation is recognized as an important factor in reducing carbon dioxide in the process of supplying heat [
13]. Considering these factors leads to the motivation of incorporating DERs into the SC model.
As stated above, the interconnection between PEVs, metro systems, and DERs in the SC must be considered to attain a more realistic and efficient EM in the SC model. The following papers are some examples of the research conducted in this regard. A programming model is used to investigate the synergy between DERs and transportation systems in the context of an SC [
14]. However, the proposed model is a simple linear model and the investigated scenarios are limited. In addition, the destruction cost of the batteries is not investigated in the total cost of the scheme. Similarly, in [
15], a linear layout for co-optimization operation and planning of PEVs, SWSs, and different types of DERs was presented based on V2G and vehicle-to-SW (V2S) concepts, considering the uncertainties of DERs and PEVs. The authors of [
16] proposed an optimization problem to minimize the entire cost of the energy and apply RBE to achieve optimum operation in SCs. The proposed model is linear and the uncertain behavior of transportation systems and loads is depicted. A management framework utilizing V2G and V2S is proposed in [
17] to attain the maximum performance of the transportation systems. Additionally, blockchain technology has been employed to enhance the security of exchanged information in the SC.
In [
18], the authors propose the multi-swarm differential evolutionary particle swarm optimization algorithm to optimize a mixed-integer nonlinear programming problem for energy management in an SC. However, the interconnection between different parts of the SC model is not covered thoroughly.
In previous studies, the nonlinear effects of the network model, the consideration of depth of discharge (DoD) for a more realistic battery model, as well as the effects of the subway, electric vehicle (EV), and DER have not been investigated simultaneously, and issues such as the effect of EVs entering the network have only been investigated separately. Therefore, in this paper, for the first time, to show the network model more realistically, nonlinear effects have been considered in the system model, and also to be closer to the real battery model, the DOD of the battery has been considered. In addition, in the proposed SC model, EVs and subways, as well as different types of DER, have been discussed simultaneously. Also, in this article, real models of PV, HP, and EV have been used to obtain a real model of an SC.
Two main methods exist for solving optimization problems similar to the problem in this research. The first one is using exact algorithms that can provide an exact global optimum. However, the execution time of the exact algorithms is raised exponentially in proportion to the number of variables [
19]. In contrast, approximate optimization algorithms can find optimal/near-optimal solutions in a reasonable amount of time [
20]. The grey wolf optimization algorithm (GWOA) is a nature-inspired optimization algorithm. GWOA has been widely used due to its simplicity, fewer control variables, and easy implementation [
20]. However, GWOA has some deficiencies that researchers have attempted to overcome in the i-GWOA provided in [
20]. Further explanations are provided in
Section 3 of this paper.
The objective of this paper is the optimal planning and operation of the SC model considering synergies between SWSs and PEVs in the presence of different DER technologies. Multiple scenarios are considered to assess the proposed layout. Additionally, the destruction cost of the batteries is calculated and added to the total cost. This adds some nonlinear terms to the problem, and, as a result, an intelligent algorithm must be utilized to solve the problem. To solve this optimization problem, the i-GWOA was utilized and was observed to be fully capable of solving the optimization problem in this study.
The main contributions of this study are presented as follows:
A comprehensive SC layout considering PEVs, metro system, DER technologies, and the interconnection between them is presented.
The total cost of the SC model is improved by utilizing the i-GWOA that is illustrated through different case studies and scenarios.
Various DER technologies, such as PV, HP, and batteries are incorporated into the model and their impact is analyzed.
The destruction cost of batteries is considered along with losses regarding PVs and HPs to achieve a more realistic and comprehensive model.
Different kinds of algorithms such as GA, PSO, DE, BBO-DE, and GWOA are compared to find the best and fastest way to solve the SC problem.
The remainder of the paper is organized as follows.
Section 2 describes the mathematical formulation of the problem.
Section 3 presents the solution of the i-GWOA. The proposed SC model and case study descriptions are provided in
Section 4. The simulation outcomes and discussion are presented in
Section 5. Finally, the conclusions and future horizons of the work are presented in
Section 6.
6. Conclusions
The idea developed in this study was to demonstrate the impact of coordinated planning and operation of different segments in an SC and to model them to calculate the extent to which they affect the entire cost of the system. An iGW optimization algorithm was utilized to solve the optimization problem owing to the nonlinearities in the problem formulation.
In addition, the destruction cost of the batteries was added to the OF, and the energy losses relevant to the PV and HP systems were considered. Four different case studies in two PEV scenarios were conducted, and the results are discussed. The optimization algorithm showed good convenience by enhancing both the simulation runtime and numerical results compared with similar studies in the literature.
Four different case studies are considered in this paper to thoroughly demonstrate the impact of interconnections between PEVs and SWSs, along with the impacts of implementing various DERs in this model. In the first case, there is no interconnection between the PEVs and the SWS, and DERs are not considered. The second case study assesses the interconnection between PEVs and the SWS without considering DERs. In the third case study, DERs were considered, but the PEVs and SWS were optimized separately. Finally, in the fourth case study, both DER technologies and the connection between PEVs and SWSs were considered. In the first scenario, the entire cost is 37.2 Million Euro when 25 PEVs are considered. The entire cost gradually rises when the number of PEVs increases. This growth was caused by increasing the PEV loads, as the other costs remained the same. In addition, the SWS remains the same because no interconnection is considered. In the second case study, the entire cost was lower than the first case. This is caused by a decrease in SWS costs because of the interconnection, and thus, the SWS is able to take advantage of the higher storage capacity provided by PEVs. For the third case study, although the SW costs are the same as in the base case, and the investment costs are higher, it can be noted that the entire cost is lower than in the previous cases. This occurred as a consequence of the electrical and thermal generation of PV and HP, respectively, resulting in less energy being bought from the grid, in addition to load shifting being considered. Finally, in the fourth case study, where both the interconnection and presence of DER technologies are considered, the total cost shows a significant decrease.
The obtained results validate the benefits of interconnections between PEVs and SWSs and utilizing DER technologies in an SC model. However, many areas of this work can be developed in the future. One of these areas is considering further DER technologies, such as wind turbines, to completely model an SC. Another area that can be developed is the modeling of the uncertainties that can arise in the model, such as the behavior of PEVs, DER power output, and residential loads. To complete the discussion of the SC, the SC model can be completed by considering water desalination, as well as discussions related to cyber security and artificial intelligence to predict energy prices and network and subway loads. Also, the proposed system can be solved in a multi-objective problem that considers cost and emission together to reduce costs and emissions. Furthermore, the cyber security issue and secure transmitted data in an SC is one of the interesting topics that can be considered.