1. Introduction
The growing availability of electric and plug-in hybrid electric vehicles (both denoted as EVs in this paper) offered by the most significant car manufactures implies a high penetration of EVs in the near future. Worldwide, more than 300,000 EVs were sold in 2014 [
1]. According to [
2], EV sales approximately doubled each year since 2010 in Europe. In 2014, around 65,000 EVs were sold in Europe.
However, the integration of EVs in the distribution network may create new challenges to the distribution system operator (DSO), such as congestion situations in the network and in the HV/MV (high voltage/medium voltage) power transformers [
3,
4]. In addition to electric vehicles, the increasing number of other emerging resources, such as heat pumps, brings more complexity to distribution systems as well. Over the last few years, intelligent EV charge management methods have been proposed in the academic and industrial fields to handle these potential problems, instead of new network investments. In general, a business entity capable of responding to the EV’s and DSO’s requirements is necessary in nearly all of the proposals. Several terms have been proposed and used concerning the entity including “virtual power plants”, “virtual power players”, “aggregators”, or “fleet operators”. These proposed entities have the purpose of coordinating the charge and the discharge processes of the EVs with the goal of optimizing the operation costs and, at the same time, avoiding network problems. In the present paper, the acronym EV-VPP (electric vehicle virtual power plant) is used.
In this study, a two-level coordination approach is proposed to integrate electric vehicles into the power distribution system, with focus on coordination mechanisms used in level II. In level I, to prevent the line congestions and voltage drop problems, the EV-VPP internally respects the line and voltage constraints when making the optimal charging schedules. In level II, to avoid power transformer congestion problems, three different coordination mechanisms of managing the HV/MV power transformer congestion between the DSO and the EV-VPP entities are studied and compared. The three coordination mechanisms include a market-based negotiation mechanism which is previously reported in [
5], a pro-rata mechanism [
6], and a proposed constrained market-based mechanism which is an evolution of the market-based strategy proposed in [
5], taking into account different power transformers limits.
The rest of the paper is organized as follows: the related work is presented in
Section 2;
Section 3 presents the system architecture;
Section 4 shows the proposed methodology for the power transformers’ capacity management;
Section 5 presents the case study considering a 37-bus distribution network; and, finally the conclusions are presented in
Section 6.
4. Capacity Management Coordination Mechanisms between DSO and EV-VPP
At level II, the DSO can adopt different mechanisms to manage the congestion of the HV/MV power transformer. Three different coordination mechanisms are investigated in this study, namely, (1) the market-based negotiation method; (2) the power transformer pro-rata use limit; and (3) the constrained market-based (CMB) control mechanisms using congestion prices and power transformer use limits.
Figure 2 presents a detailed flowchart of the implemented process for the ‘capacity management’ block in
Figure 1. In the first step, each EV-VPP does the scheduling considering the congestion price as zero and the power transformer capacity as their maximum value. Each EV-VPP sends their power demand requirements to the DSO. In this stage, the DSO should evaluate the power transformer’s use and verify the congestion conditions. In the case of a congestion situation, the DSO should determine the congestion price or the power transformer limits for each EV-VPP according the adopted mechanism.
Comparing the three mechanisms, it is possible to say that with the pro-rata mechanism no economical parameter is included. A power limitation is imposed to all EV-VPPs independently of their flexibility to change their initial scheduling (represented by variable ). In the constrained market-based mechanism, the DSO imposes some limits in the power use to each EV-VPP, but also introduces a price-signal, like in the market-based mechanism. The main advantage of this mechanism is that it relies on the imposed power limits that are less strict than the pro-rata mechanism and the price signals are lower than the market-based mechanism. This mechanism can be seen as a middle-term (or compromise) solution between the other two mechanisms. This means that the EV-VPP has more flexibility to change its initial scheduling compared to the pro-rata mechanism and, consequently, will be penalized less due to the smaller price signals introduced by the constrained market-based mechanism.
4.1. Market-Based Mechanism
The market-based mechanism is a paradigm for controlling complex systems with conflicting resources [
29]. It includes the features found in a market, such as decentralized decision-making and interacting agents. Normally, two-way communication is required. For this study, it means that the DSO will interact with the EV-VPP to exchange the power requirements (EV-VPP sends information about the power demand to the DSO) and price information (DSO sends the price to alter the power schedule of the EV-VPPs).
To formulate such a coordination mechanism, different approaches can be applied to find the equilibrium, such as the uniform price auction mechanism or the shadow price-based penalizing mechanism. In this study, the shadow price-based penalizing mechanism proposed in [
5] is applied to solve the power transformer capacity allocation problem. Firstly, a quadratic cost function, Equation (13), is constructed for the EV-VPP to characterize the cost of deviating from the original power schedules:
where,
and
are the initial and new power supplied by external suppliers to each EV-VPP, respectively.
corresponds to the cost coefficient associated with the power difference between the initial and new power scheduling.
The objective is to minimize the cost Equation (14) of all of the EV-VPPs, as well as respect the constraint from the DSO:
subject to:
where,
corresponds to power transformer capacity.
This is a convex optimization problem, which can be solved by introducing Lagrange multipliers, or shadow prices
. The above optimization problem is transferred into a Lagrange-based problem:
To solve the optimization problem, this study uses a numerically iterative method, which also emulates the market negotiation behavior of the DSO and the EV-VPPs:
- Step 1:
DSO defines a value for , e.g., in the first step. Given the known the problem L is decomposable for each EV-VPP.
- Step 2:
A new optimal charging schedule
of each EV-VPP is calculated by solving the following optimization problem, with the given
:
- Step 3:
After receiving the new schedules from EV-VPPs, DSO updates the shadow price to change the charging schedule of EV-VPPs and the updating method is presented in the following formula:
- Step 4:
Repeating the process in step 2 and step 3, the price is defined as the new congestion price when it converges. The new congestion price will be reused by the EV-VPP in Equations (1)–(12) to reschedule the EVs’ energy plan.
The decision variable of this market-based mechanism is the new power supplied by external suppliers, which is represented by .
4.2. HV/MV Power Transformer Pro-Rata Mechanism
In this mechanism, the DSO imposes limits to the HV/MV power transformers which defines the maximum active power that each EV-VPP can use. A pro-rata approach [
6] (or proportionate allocation) assigns an amount of a fraction, according to its share of the whole. In the initial scheduling, the EV-VPP agents assume that it is possible to use all of the power capacity available in the power transformer. After receiving the initial scheduling from all EV-VPP agents, the DSO agent analyses if a congestion situation occurs in some period. If there is no congestion, the DSO accepts the EV-VPP agent scheduling. In the case of congestion, the DSO should impose HV/MV power transformer use limits for each EV-VPP
considering the initial power requirements for each EV-VPP
:
The new capacity will be reused by the EV-VPP in Equations (1)–(12) to reschedule the EVs’ energy plan.
4.3. Constrained Market-Based Negotiation Mechanism
In this mechanism, the DSO imposes limits on the use of the HV/MV power transformers and imposes congestion prices at the same time. The method can be seen as a combination of the previous described strategies. However, some variations have been introduced to both methods. The main goal is to overcome the drawbacks of the previous methods, meaning that the constrained market-based negotiation mechanism has smaller congestion prices than the market-based mechanism and is more flexible than the pro-rata mechanism because it imposes more relaxed limits on the power transformer use for each EV-VPP in terms of power transformer limits. Each EV-VPP has different price sensitivity according to the demand flexibility, which is related to the number of electric vehicles. With the proposed mechanism, in the first step, a power transformer use limit
is determined for each EV-VPP according to Equation (20):
The main difference with respect to the pro-rata mechanism is the introduction of the
ω parameter. This parameter allows defining different limits in the power transformer use. If
ω = 1, the power transformer use limitations are the same of pro-rata mechanism defined in Equation (19). However, if
ω > 1, less strict power limitations are imposed to the EV-VPPs, representing more flexibility for each EV-VPP. When
ω = ∞, no power limitation is imposed to the EV-VPPs.
Figure 3 presents the impact of
ω in the proposed mechanism.
In fact, the DSO expects, like in the market-based approach, that the EV-VPPs change their scheduling not only because of the power limits, but also because of the increasing congestion prices. In a simple comparison, the market-based mechanism only uses the congestion price to solve the congestion problem, in the pro-rata mechanism, a fixed power limit is imposed to solve the congestion problem, while in the proposed mechanism, an integration of the congestion price and power limit is used.
In the second step, a congestion price
is determined using a similar approach as the one described in
Section 4.1. The main difference is introduced in Equations (15) and (16) with the inclusion of the value determined in Equation (20). In this sense, in the proposed method, Equations (15) and (16) should be replaced by Equations (21) and (22), respectively. Considering that
is higher than the
, the resulted congestion cost will be lower.
Like the market-based mechanism, the decision variable of this proposed mechanism is .
5. Simulation Results
This section presents a case study considering the distribution network presented in [
30] and shown in
Figure 4. The distribution network is composed by 37 buses, connected to the high-voltage network through two 10 MVA power transformers. The distribution network supplies energy to 1908 consumers: 1850 domestic consumers (DM), two industries (Ind), 50 commerce-oriented stores (Co), and six service buildings (SB) [
31]. Regarding EVs, a penetration of around 50% of the total number of vehicles is assumed, i.e., 1053 EVs.
Table 1 shows the number of EVs and the number of each type of consumer for every EV-VPP. The EVs’ characteristics were determined based on the characteristics of some real models and driving patterns presented in [
32]. The study assumes that all of the reactive power is supplied by the capacitor banks that are connected to the secondary side of the power transformers. It is also assumed that four EV-VPPs manage the EVs in different parts of the distribution network, and the total power transfer capacity is 19 MW in all periods.
The spot market price was taken from the Nordpool Spot market, of which the lower price period of one day may result in peaks that increase the probability of congestion violations. In the initial scheduling, the information concerning the power transformer use or congestion price is provided by the DSO, each EV-VPP uses the forecast load demand, and the network characteristics determined by the DSO for making schedules for next day.
The optimization problem at level I has been solved using the general algebraic modeling system (GAMS) software [
33]. GAMS has different solvers to solve this mixed-integer non-linear programming (MINLP) optimization problem and the DICOPT solver was selected [
34]. This solver separates the mixed-integer programming (MIP) and non-linear programming (NLP) parts of the optimization problem. The CPLEX and CONOPT solvers are used to solve MIP and NLP, respectively. The DICOPT solver uses the “outer approximation”, “equality relaxation”, or “augmented penalty” to coordinate the solutions obtain in each part of the optimization problems (MIP and NLP). This is done by creating relaxed problems for the CPLEX and CONOPT to solve, and then the relaxed problems are decreased until the stopping criteria are reached. Therefore, DICOPT is an iterative process that only stops when the MIP and NLP solvers obtain solutions with a difference less than a pre-defined error (by default this is 0.01%). DICOPT does not guarantee a global optimum solution, because MINLP problems have non-convexities (e.g., non-convex constraints) resulting in local optima. At level II, the optimization problem is solved using CVX, a package for specifying and solving convex programs [
35].
Figure 5a shows the aggregated power schedule of EV-VPPs and
Figure 5b shows the EVs charge scheduling after the first scheduling process. The graphics show the scheduling for one day (96 periods of 15 min). In
Figure 5a, it is also possible to see the market prices (line blue) and the power transformer capacity (line green).
As seen in
Figure 5, the EV-VPPs attempt to schedule the greatest part of the EV charges to periods with a lower energy price. In some cases, like in EV-VPP2, it is necessary to schedule the EVs charge during the day due to the intensive EV use. The initial scheduling causes the congestion of the HV/MV power transformer between periods 73 and 80 (periods of 15 min). This situation is, partly, caused by the intensive charging level of EVs, which reaches more than 3 MW due to the lower prices in those periods.
The three mechanisms presented in
Section 4 to avoid the congestion situations are tested and the results are presented in
Figure 6 (market-based mechanism),
Figure 7 (pro-rata mechanism), and
Figure 8 (constrained market-based mechanism). The results indicate that, in the present case study, the congestion can be effectively solved after three information exchanges (or iterations) between the DSO and the EV-VPPs in all of the mechanisms.
Analyzing
Figure 6,
Figure 7 and
Figure 8, all negotiation mechanisms can be adopted for solving the congestion problem in all time periods, since it is shown in
Figure 6a,
Figure 7a and
Figure 8a that the sum of the four EV-VPPs’ schedules is lower than the power transformer capacity indicated by the green line. However, the strategies have very different impacts on the final scheduling of each EV-VPP. In the market-based approach (
Figure 6), the congestion price is very high (around 0.25 €/kWh) leading to a re-scheduling of the EVs charge to other periods, but also the discharge in the periods initially with congestion. The discharge is intensively used in the congestion periods, because the discharge price is lower than the defined congestion price. In the DSO perspective, the power transformer congestion was solved but the excessive response of the EV-VPPs caused large fluctuations in power demand and a new unexpected ‘off-peak’ period in the initially congested periods, which is because of the excessive discharge of EVs in the congested periods.
Concerning the use of pro-rata strategy (
Figure 7), the power transformers are used at their maximum capacity during the initially congested periods. This situation has a particular impact in EV-VPPs 3 and 4 because of their lower demand flexibility in the congested periods. To guarantee the new power supply limits imposed by DSO when using the pro-rata mechanism, EV-VPPs should use the EVs’ discharge to supply all consumers’ demands, increasing their operation costs. From the DSO perspective, this mechanism allows a constant demand profile during the initially congested periods.
In the proposed constrained market-based mechanism (
Figure 8), the congestion price is substantially lower than in the market-based mechanism, leading to a more balanced (or compromised) variation of the EVs’ charge scheduling. The power transformer constraints were solved after three negotiation iterations. EVs’ discharge are not used in EV-VPP 1 due to the imposed supply limits that are, in fact, higher than the power transformer capacity, allowing a relaxation of the constraints. On the other hand, EV-VPP2, EV-VPP3, and EV-VPP4 are more sensitive to the price due to the higher energy requirements of their EVs. For the DSO, this mechanism leads to a relaxation of the power transformers near their limit, improving the global operation efficiency.
Table 2 shows the EVs’ operation costs (Op.cost.) by each EV-VPP and the variation in percentage concerning the initial scheduling.
In
Table 2, it is possible to see that the market-based mechanism significantly increases the EVs’ operation costs for all VPPs because of the increase of the charging costs, but also because of the payments with the discharged energy. The pro-rata mechanism presents less variation in terms of operation cost for each VPP. The constrained market-based mechanism imposes less EV-discharge showing the higher flexibility of this method. However, the EV-VPPs have more costs since the congestion price is applied to all of the power consumption. Note, the choice of the parameter
ω influences the operation cost of EV VPPs, and the following table (
Table 3) shows the difference when
ω varies.
In addition to these main findings, note that the pro-rata mechanism requires less communication between the DSO and the EV-VPPs compared to the other two mechanisms, since the market-based mechanism and constrained market-based mechanism need to negotiate several times to reach the congestion price. However, the (constrained) market-based mechanisms allow the power transformer capacity allocations via an economic method, which may truly reflect the needs of the EV users. This leads us to the future work on defining a proper EV VPP cost function to characterize the cost of deviating from the original power schedules. Note that, furthermore, even the constrained market-based mechanism increases the operation cost of EV VPP, however, it solves the grid congestion problem which otherwise needs to be solved by upgrading the grid. The grid upgrading implies a cost that will also be distributed to the EV VPPs. In this study, we do not compare the cost differences since that requires a long-term perspective study. Summarizing the advantages for each player, it is possible to mention that, for the DSO, all of the mechanisms could avoid the network investments. For the EV-VPPs, the introduction of price signals will increase their costs. However, when the pro-rata mechanism is used, the EV-VPP can be forced to shed some loads or not deliver energy to charge EVs, with consequences to the EVs’ owners. From the EVs’ owner’s perspectives, the pro-rata mechanism can be the worst mechanism due to the possibility of not delivering the required energy during trips. This situation it is also possible in the constrained market-based mechanism but with less probability due to the relaxed limits imposed by this mechanism.
6. Conclusions and Discussion
The growing use of EVs introduces new constraints to power system operation and management. One of the most important impacts are the congestion situations created by high EV charge demands during specific periods of the day. In a competitive environment, the system operators should assure equal opportunities for all network users supplying energy in every period for all resources. However, this is impossible without high investments to reinforce the network capacity, or without a coordination of the network use.
This paper proposes and compares three different coordination mechanisms for negotiation between the DSO and the aggregators’ EV-VPPs (electric vehicles virtual power plant), considering the possibility of EV charge and discharge. The three different mechanisms include: (1) the market-based approach; (2) the pro-rata mechanism; and (3) the constrained market-based approach. The constrained market-based mechanism uses the market-based principles, but considers different power transformer capacities. The main advantage of this mechanism is the fairness, since it is fairer than the market-based strategy, which leads to lower congestion prices. In addition, compared to the pro-rata mechanism, the constrained market-based mechanism imposes more relaxed power consumption limits. This aspect is important to the EV-VPPs with smaller flexibility to change their initial scheduling. Additionally, the pro-rata mechanism the power transformer will be used under their nominal capacity during the original congestion periods while, in the constrained market-based mechanism, the power transformer capacity is used at an average of 95% of their capacity, allowing some capacity to respond to uncertainties. Taking into account the obtained results, it is possible to conclude that the proposed constrained market-based mechanism has advantages to the DSO and to the aggregators, resulting in a balanced solution concerned with solving the congestion problem.
In future work, the authors intend to develop the methodology to include other distributed energy resources, especially considering photovoltaic (PV) generation. To include PV generation in the study, it is suggested that two types of setup could be used, considering the PV connection scheme in reality: (1) PV would benefit more if the produced electricity is sold out to system; (2) there is no price difference between selling electricity to the system or use it locally. These two different setups will influence the schedule of PV and EVs in the study.