1. Introduction
The issue of power losses has gained significant attention over recent years. The European Union (EU) has recently proposed the recast COM/2021/558 [
1] of the Energy Efficiency Directive 2012/27/EU [
2], in which Article 25 provides the guidelines for member states’ energy authorities to include the assessment of power losses as a separate section in their annual progress achieved in energy efficiency improvements. The recast highlights the necessity of power loss reduction, since they constitute a significant amount of the annual produced energy at distribution level, as presented by the Council of European Energy Regulators (CEER) [
3]. Specifically, according to the report [
3], the annual distribution power losses of the member states are presented separately, and the conclusions insist on the need for a power loss decrement in order to improve the efficiency of the systems. The issue of power losses from the perspective of the Distribution Network’s (DNs) efficiency is also addressed in a technical report [
4], which indicates that the Distribution System Operators (DSOs) should be encouraged to reduce the distribution losses, since they are the key actors to ensure the efficient operation of the system.
Apart from the efficiency of the distribution systems, the power losses directly affect the energy price. The EU Agency for the Cooperation of Energy Regulators (ACER) published a report referring to the methodologies of distribution tariff methodologies [
5]. According to the report, the cost of the power losses is either transferred directly onto the final consumers as distribution tariffs or is included in the bid price in the energy markets. Either way, the consumers are charged for the systems’ losses.
Despite the effort of the EU to minimize the losses of the systems, the power grids are facing new challenges. The environmental crisis has triggered several changes towards the reduction of greenhouse gas emissions (CO
2). At the end of 2019, the European Commission announced the European Green Deal, which is a set of policies aiming to transform the EU into the first climate neutral continent [
6]. The main aim of the European Green Deal is the 55% reduction of greenhouse gas emissions by 2030 and the 100% reduction by 2050. In order to meet these objectives, in July 2021, the European Commission presented a set of proposals, including the decarbonization of the transport sector. Based on this, the member states should provide appealing incentives and recommendations to the consumers in order to replace their conventional cars with hydrogen Fuel Cell Vehicles (FCVs) [
7] or Electric Vehicles (EVs), i.e., Plugged-in Hybrid EVs (PHEVs) [
8] or Battery EVs (BEVs) [
9]. Apart from FCVs, the uncertainties of EVs, i.e., time of arrival and State-of-Charge (SoC), in combination with their uncontrolled charging can increase the peak demand of energy consumption and consequently can lead to extensive power losses [
10]. Thus, it is essential to employ methods in order to alleviate the negative impacts of EVs’ integration into DNs [
11].
Considering the aforementioned issues, two well-established techniques towards the minimization of power losses are Network Reconfiguration (NR) [
12] and the optimal charging of EVs [
13]. These two techniques refer to different voltage levels and in many studies are mainly employed separately. On the one hand, NR is applied to Medium-Voltage (MV) systems in order to determine the optimal topology of DN in terms of power loss minimization [
14]. Even though in studies [
15,
16,
17,
18] the integration of EVs was also considered, their charging plan was not studied. Instead, the EVs were utilized to examine the hosting capacity of the system [
15] or only to formulate the daily load curve [
16,
17,
18]. Despite previous studies, a different approach was presented in [
19]. Specifically, in [
19], the authors focused on the optimal size and location of EV charging stations under NR, considering the impact of charging stations into the DN [
20]. On the other hand, the smart charging of EVs is used for Low-Voltage (LV) DNs and deals with power losses, voltage violation and transformer overloading issues, due to the high penetration and uncontrolled charging of EVs [
21]. The problem of optimal EV charging has been addressed from different perspectives, such as power loss minimization and improvement of voltage profile [
13], peak demand reduction [
22] and decrement of greenhouse gas emission [
23].
Some authors have also developed methodologies in order to combine both NR and optimal EV charging scheduling. Several studies have been conducted considering two optimization stages, meaning that NR and optimal EV charging are subjected to different objective functions. For instance, the authors in [
24] deployed NR in order to minimize power loss, voltage deviation and load balancing indexes, while the smart charging scheduling was applied to improve peak-valley filling. A similar approach was also presented in [
25], in which instead of load balancing, the voltage stability index was included. A two-stage optimization methodology was also presented in [
26], where the objective to be minimized in MV DN was the cost of power, losses and switching, while in LV DN it was the charging cost. The combination of NR alongside with EV’s coordinated charging under the same objective function has also been examined. Despite the aforementioned studies, the combination of NR alongside with EV’s coordinated charging under the same objective function has also been examined. The researchers in [
27] proposed a methodology considering the minimization of power losses and the power cost. A similar approach was presented in [
28], in which the authors developed a methodology in order to minimize the total power cost of the system.
In the aforementioned studies, the smart charging of EVs is assumed to be implemented in charging stations. A different perspective was presented in [
29], where the proposed methodology was implemented considering residential chargers. The main objective of the charging plan was cost minimization along with the peak-valley filling. The authors in [
30] also considered that EVs will be charged in residential infrastructure. Still, the minimization of power losses referred only to MV DN. In both studies, the authors did not take into account the topology of LV DN.
A brief description of the implemented methodologies so far is presented in
Table 1. From the literature, it has been identified that the majority of the proposed methodologies examine the impact of EV charging scheduling at the MV level. Yet, the existing studies are based on the assumption that EVs will be plugged in charging stations or charging lots. The residential charging infrastructure is omitted, even if in some countries the installation of charging slots in blocks of flats is obligatory [
31]. Although in studies [
29,
30] the authors included residential chargers, the charging scheduling is implemented by assuming that EVs are connected to charging stations or charging lots. Consequently, the topology of LV DNs is not of concern, since all EVs are plugged in at a single charging point. Considering the aforementioned, the novelty of the present paper lies in the fact that it considers the topology of LV DN and examines the impacts of smart charging scheduling at the LV level.
Based on this and taking into account the efforts of the EU towards power loss minimization, in this study a two-stage optimization scheme is proposed, including NR and EV smart scheduling. In the first stage, a day-ahead smart charging plan is proposed at LV DN, considering the technical constraints of DNs [
2] as well as the key role of aggregators in DNs’ operation [
32]. More specifically, the aggregator, which is responsible for the LV DN, applies the smart EV charging schedule to a real LV DN of 109 nodes in order to minimize the power losses of the network. The proposed methodology is a distributed one. Considering that at each node of the MV DN a LV DN is connected, the EV charging scheduling is applied at each LV DN individually. A similar approach, in terms of distributed control algorithms, is presented in papers [
33,
34,
35], where the authors employed distributed algorithms in order to minimize the total energy cost of the EVs’ fleet. In the second stage, the DSO applies the NR to determine the next day’s optimal topology of the MV DN, considering the load curve formulated after the deployment of the charging plan at the LV DNs. This can lead to further reduction of power losses at the MV DN. In both stages, the Unified Particle Swarm Optimization (UPSO) metaheuristic algorithm is employed, considering the complexity of the problem.
Therefore, the main contributions of the present study can be summarized as follows:
Real-time hourly EV smart charging scheduling update in LV DNs that deals with uncertainties in EVs’ time of arrival due to forecasting errors.
Consideration of residential EV charging by taking into account the layout of a real LV DN and using real data about the loading of the network and its electrical characteristics, i.e., lines’ length and impedance.
Power loss minimization in LV DNs due to the proper time allocation of EVs’ charging that in turn results in smoother loading for the nodes of the MV DN and in lower power losses at the MV network.
Further power loss reduction by planning the NR application on the MV DN for the next day. The optimal reconfigured topology for the MV DN is constant for the whole day in order to avoid frequent switching operations, e.g., hourly NR, that could result in frequent disturbances and could impose the need for the frequent replacement of the switches.
Simple and straightforward cooperation between the DSO and potential aggregators in order to minimize the power losses and improve the power quality and the efficiency in both MV DN and LV DNs.
The rest of the paper is organized as follows.
Section 2 presents the mathematical formulation of the objective function as well as the description of the proposed smart charging algorithm and the NR. In
Section 3, the analysis of UPSO for both charging scheduling algorithm and NR is presented.
Section 4 includes the description of the examined LV DN and MV DN. Additionally, in
Section 4, the results of the study are presented and discussed. Finally,
Section 5 concludes the paper.
3. Proposed Algorithm
The problem of power loss minimization that is faced in this work is a non-linear non-convex optimization problem. A summary of the variables and the constraints are presented in
Table 2. More precisely, the problem’s objective to be minimized is non-linear and is subjected to equality and inequality constraints. Additionally, both NR and EV smart scheduling methodologies include continue and integer variables. Thus, in the present study, the UPSO, which is a metaheuristic algorithm, is utilized for both EVs’ charging planning and NR. The UPSO comprises two widely used PSO variants, i.e., Local PSO (LPSO) and Global PSO (GPSO). On the one hand, LPSO enables the better exploitation of the problem’s domain. However, its main disadvantage is the longer convergence. On the other hand, the GPSO can lead to fast convergence and therefore better exploration of the problem’s solution space. Yet, the algorithm’s exploration feature is prone to local minima. Thus, the UPSO combines the merits of the two variants, i.e., the exploration and exploitation capabilities of GPSO and LPSO. Although UPSO cannot ensure the optimal solution, it has the ability to efficiently deal with non-linear non-convex problems and provide a near optimal solution under a simple and straightforward formulation.
The selection of UPSO is based on the results presented in research [
37]. Specifically, the authors compared the efficiency of several metaheuristic algorithms including LPSO, GPSO and UPSO. Even if they addressed the problem of optimal siting and sizing of distributed generation, the main points of the addressed problem are similar to the problem of the present study. More precisely, the objective function of both studies is the minimization of the system’s power losses. Additionally, both problems are subjected to the same equality and inequality constraints. Moreover, both studies deal with mixed integer problems. The results of study [
37] indicate that the computational burden of UPSO is comparable to LPSO and UPSO.
The UPSO is a population-based algorithm that is executed iteratively. The population of the algorithm, i.e., swarm, is defined as:
where
N indicates the number of swarm particles (
). Each particle is a vector of a candidate solution and denotes a position at the solution space. The particles’ dimensions depend on the number of problem’s variables. After each iteration (
i), the velocity vector (
) of each particle
n is calculated [
38] and the positions are updated as:
3.1. UPSO Formulation for EV Smart Charging
The UPSOs’ particle formulation for the EV charging scheduling is based on the examined time period and the number of EVs that are plugged in and are not fully charged. Specifically, the particles are a
matrix expressed as follows:
where
is the
nth particle for the EV charging planning;
is a binary variable equal to 1 in case EV
k charges at time
h. Otherwise, it is equal to zero. The dimensions of the particles alternate dynamically at each execution, since the algorithm is executed each time new arrivals are predicted. Therefore, at each execution the algorithm deals with different number of EVs and different number of remaining hours.
3.2. UPSO Formulation for NR
The formulation of UPSO’s particles for the NR application depends on the number of loops. In order to define the particles’ dimensions and the domain of the particles’ elements, we have to define first the number of loops and the branches included in each loop. This is achieved by iteratively closing one tie switch at a time and getting the lines that formulate the loop. The iterative process is presented in
Table 3.
The NR’s particles are one-dimensional arrays and are expressed as follows:
where
is the
ith particle for the NR;
is an integer variable denoting the index of the sectionalizer or tie switch that will open at loop
j. Each loop of the system consists of different number of sectionalizers, thus the domain of each element is defined as:
where
indicates the total number of sectionalizers and tie switch included in loop
j. In case the element
is equal to zero, no changes are applied to loop
j.
The elements of the particles denote the index of sectionalizer or tie switch that will open at loop j. Therefore, in order to ensure the radial topology of the system, before we open the tie switch or sectionalizer, we close the tie switch of the loop. In this case, it is possible to open again the tie switch. Additionally, there might be sectionalizers belonging to several loops. If there is more than one element of a particle that indicates to open the same sectionalizer, the sectionalizer of the first loop opens and the rest of the loops remain unchanged.