Optimal Electric Vehicle Charging Strategy for Energy Management in Microgrids Maura Musio, Mario Porru, Alessandro Serpi, Ignazio Marongiu, Alfonso Damiano Dipartimento di Ingegneria Elettrica ed Elettronica, Universit´a di Cagliari Piazza D’Armi, 09123 Cagliari, Italy Email:
[email protected]
Abstract—In the present paper a novel approach for determining the charging profile of Electric Vehicles (EVs) suitable for their integration into microgrids is presented. The main goal of the proposed control strategy is to define the optimal daily charging profile of each EV in order to increase microgrid autonomy. This goal is achieved by means of the optimal control theory, taking into account all system constraints, such as instantaneous energy productions and consumptions, rated power and capacity of EV batteries as well as their mobility habits and requirements. Thus, the microgrid energy systems considered in this paper are firstly presented and briefly analysed, together with their mathematical modelling. Subsequently, the optimal control problem is formulated, leading to the achievement of optimal charging/discharging strategies for each EV in order to optimize microgrid operations. The effectiveness of the proposed optimal EV control strategy is then verified through a simulation case study, which refers to a cluster of two microgrids, which are connected in unconventional manner by means of an EV, operating in Vehicle-to-Grid (V2G) mode. The comparison with a dumb charging strategy is finally reported in order to highlight the worth of the proposed approach.
I.
I NTRODUCTION
The increasing use of Renewable Energy Sources (RESs), supported by economic subsidies and environmental policies, is changing the structure of the power system, contributing to its transformation from a centralized form to a distributed one. The critical issues related to RES production (such as variability, discontinuity and poor predictability), together with peculiarities of distributed generation, are giving rise to new challenges in terms of reliability, control and power quality of electrical power systems. Therefore, the development of novel paradigms based on distributed and self-standing power systems is needed [1]. One of the solutions proposed to overcome these problems and steer the ongoing transformation towards the smart grid consists of managing the electricity distribution system as a cluster of microgrids (MGs). Particularly, a MG is defined as a group of distributed generators, controllable loads and The authors gratefully acknowledge Sardinia Regional Government for the financial support of this research activity (P.O.R. Sardegna F.E.S.R Operational Programme of the Autonomous Region of Sardinia, European Social Fund 2007-2013 - Measures to support competitiveness and innovation - PIA Pacchetti Integrati di Agevolazione ”Industria, Artigianato e Servizi” annualit`a 2010). M. Porru was supported by the Sardinia Regional Government under a Ph.D. scholarship (P.O.R. Sardegna F.S.E. Operational Programme of the Autonomous Region of Sardinia, European Social Fund 2007-2013 Axis IV Human Resources, Objective 1.3, Line of Activity 1.3.1).
978-1-4799-6075-0/14/$31.00 ©2014 IEEE
Energy Storage Systems (ESSs), which are managed as a single power system and capable of operating autonomously in order to locally improve power quality, efficiency and reliability [2]–[5]. These goals are achieved by adopting a smart and appropriate high-level coordination system, i.e. the Energy Management System (EMS) [5], [6], which receives in real-time the information about the current status of each MG and synthesizes the most suitable set-point signals for each unit controller. Key components of MGs are distributed ESSs, because they permit both the time shifting of electricity generation and the compensation of instantaneous energy unbalances [7]. In particular, electrochemical batteries are currently considered one of the most efficient and suitable ESS technologies for MG applications [8]. However, the high cost of energy storage technologies requires careful evaluation and correct sizing on the basis of specific application needs. A feasible solution may be the integration of MGs with other energy systems such as the mobility system; this could reduce investment costs of ESSs, which currently represent the main obstacle for their diffusion. In this context, the Gridto-Vehicle (G2V) [9] and Vehicle-to-Grid (V2G) technologies [10] could be usefully exploited; in fact, if the charging process of Electric Vehicles (EVs) is appropriately managed, for instance by an aggregator [11], EV batteries can be considered either as controllable loads (over G2V only) or distributed ESSs (when working in V2G). On the basis of this, different control strategies and optimization procedures have been proposed in the literature in order to manage the energy flow between the electric and mobility systems. A review of the recent technical literature also reveals different methods for evaluating maximum levels of EV penetration in specific electric distribution systems [11]. In particular, the ancillary actions at distribution level are well-suited for widescale EV diffusion, from the technical and economic points of view. Among these, the most valuable ones are extra power supply, peak load shaving, load shifting, spinning reserve and frequency regulation. Nevertheless, these studies are generally based on a standard centralized power system vision of the supply chain; such an approach is not suitable for smart grids and MGs, which are characterized by an inherent distributed nature. On the basis of the previous considerations, this paper proposes a novel method to optimally integrate EVs in MGs in accordance with V2G paradigm. An optimal control strategy has been consequently developed in order to define the daily
Fig. 1.
Schematic representation of the microgrid structure.
charging/discharging profiles of each EV that operates within MGs. The synthesis of the optimal solution has been carried out referring to an appropriate objective function, which is defined considering the optimal contribution of each EV to the minimisation of the daily energy exchange between the MGs and the main electricity network. In particular, the authors propose an optimal control problem formulation which can be solved by using the control theory of trajectory optimization, originating from the calculus of variation. This choice allows the application of Pontryagin’s Minimum Principle (PMP), which reduces the global problem to a set of instantaneous conditions. This approach permits the achievement of a continuous-time control strategy, taking into account also the constraints related to the state of each EV. Although in recent years the PMP was introduced and extensively implemented in order to control hybrid electric vehicles [12]–[14], up to now there are no applications of the optimal control theory for the energy management of EVs to enhance MG operations. Therefore, a novel formulation based on PMP is proposed in order to synthesize optimal control laws which are calculated considering each EV individually, instead of a group of mobile storage devices. The worth and effectiveness of the proposed approach are subsequently verified through a simulation case study, which refers to two MGs connected in an unconventional manner by means of an EV operating in V2G mode. II.
M ICROGRID STRUCTURE
The optimal EV charging strategy proposed in this paper is developed referring to a cluster of grid-connected MGs, which can be schematically represented by the structure shown in Fig. 1. In this configuration, the main MG (W ) is assumed to be an industrial/commercial area, whereas the satellite MGs constitute a residential zone (H). The main components of W can be listed as follows: •
renewable energy sources;
•
stationary battery electric storage systems (BESSs);
•
electric loads;
•
an EV fleet.
The other MGs (H) are assumed to be much smaller than W , because each of them mainly consists of a single house and an EV. Considering their energy daily demands, W and H could be characterised by complementary load time distribution and power generation, thus offering the opportunity of a cooperative energy integration among MGs. In spite of this, since each MG operates by means of its own connection to the main grid, the power exchange among MGs is not possible. Therefore, in this case, the minimization of the MG energy unbalance can be achieved only by optimally controlling the daily charging/discharging profiles of each EV. In this way, the EV fleet becomes an unconventional and additional power network, connecting each MG to the others. Such a control strategy allows consequently the establishment of the cooperation among MGs, which can effectively improve the efficiency and reliability of each electric power system. In fact, the optimal coordination and control of the power transferred to/from each EV enables the exchange of power among MGs with several benefits, such as the maximization of the self-consumption, the optimization of locally used RES production and the improvement of the global stability of the grid. Clearly, this requires a central management of MG energy consumption and production, dealing also with mobility needs. The EMS used to manage the MGs is assumed to be supported by a real-time monitoring system, able to collect all information about the generated and consumed power of each MG instantaneously. Such an assumption is strengthened by the use of BESSs which enables compensation of forecasting errors [15]. In addition, the EMS can rely on accurate information about the State of Charge (SOC), geo-referenced position and planned daily travel of each EV, assumed to be collected in real-time by means of an appropriate communication system. Finally, EV bi-directional charging infrastructures are considered in both working and residential districts, allowing EV owners to feed their cars and provide V2G services at home as well as at work. III.
E LECTRIC V EHICLES
In this paper, it is assumed that each EV user lives within H and works at W , each EV belonging to either W or H in accordance with its user daily routine. Consequently, if EVs are plugged-in at work they can feed W facilities or
absorb RES extra production, while they can feed household loads when they are plugged-in at home. The sequence of charge/discharge management actions aims at the reduction of the energy unbalance between MGs and the main grid. The balance service due to V2G operations can be delivered by EVs only within the limits imposed by driver mobility needs and in accordance with EV battery and power infrastructure constraints. A. Mathematical modelling of EV storage systems The time evolution of the energy stored in the battery of the j-th EV can be described by the following continuous state equation: pdj (t) e˙j (t) = − + ηc · pcj (t) (1) ηd ej (t0 ) = e0j where: •
IV.
O PTIMAL V2G CONTROL STRATEGY
A. Mathematical modelling of V2G integration in MGs In order to find out at any time-instant the optimal controls s∗j and the corresponding responses e∗j that minimize the chosen performance criterion function J, the SOC, the position and the travel time-table of each EV are assumed known. Referring to the proposed MG structure and with the aim of modelling all the possible configurations of this energy system, a classification of EV locations is firstly introduced. It takes into account individual mobility daily states in terms of possible EV interaction with each MG. In particular, at the generic time t, each EV can be in one of these conditions: 1) 2) 3)
at home (H); at work (W ); moving (M ).
Therefore, the instantaneous electric power balance at H and W , can be respectively introduced as: gjH (t) + rjH (t) + sH j (t) = 0
ej (t) is the battery energy storage state at instant t for the j-th EV;
•
ηc and ηd represent the overall charging and discharging efficiency, respectively;
•
e0j is the battery energy storage state at the initial time t0 for the j-th EV;
•
pdj (t) denotes the power effectively delivered to the grid by the j-th EV;
•
pcj (t) is the power effectively drawn from the grid by the j-th EV.
It is worth noting that pcj and pdj are alternatively equal to zero, since each EV cannot supply and absorb energy from the grid simultaneously. As a consequence, the general term sj , denoting the power effectively exchanged with the grid by the j-th EV, can be obtained by (2) sj (t) = pcj (t) + pdj (t)
(2)
In particular, the power sj takes positive values when discharging and negative when charging. Moreover, sj is constrained by the EV power exchange boundaries (3), defined by the maximum battery charge/discharge current and by the maximum power flow permitted by the grid interconnection line. sminj ≤ sj (t) ≤ smaxj
(3)
In addition, the stored energy ej must be constrained in order to preserve both the battery rated performance and lifetime, as well as always guarantee an appropriate energy reserve, necessary for the daily mobility needs. On the basis of these considerations, the constraints imposed on ej lead to: eminj ≤ ej (t) ≤ emaxj
(4)
where eminj and emaxj are the lower and upper bounds of ej for the j-th vehicle, respectively.
W
W
j ∈ {1, ..., N }
W
g (t) + r (t) + s (t) = 0
(5) (6)
Considering (5), it is referred to the j-th individual dwelling. In particular sH j denotes the power exchanged by the j-th EV associated to the corresponding j-th house, gjH is the power supplied by the main grid to the j-th house, whereas rjH indicates the corresponding electric demand. In (6), g W is the total power delivered (drawn) to (from) the main grid by W , sW being the power exchanged by all the EVs plugged at work, obtained as sW (t) =
N X
sW j (t)
(7)
j=1
where N represents the total number of EVs managed in the involved group of MGs considering that just an EV is associated to each dwelling of the residential district H. Finally, rW indicates the residual load of W , defined as follows: W rW (t) = PRES (t) + LW (t) (8) W being the power generated by RES and LW denotes the PRES electric demand of the whole industrial/commercial area.
Since an EV cannot be in more than one location at the W same time, EV control powers sH j and sj are alternative equal to zero and their corresponding relationship can be defined by (9): H M sj (t) = sW (9) j (t) + sj (t) − rj (t) where rjM is the power required by the j-th EV over M . B. Optimal control problem formulation Since the goal of the optimal control is the minimization of daily energy exchanged by overall W and H with the main electric grid, the optimization problem can be formulated as follows: J(s∗j (t)) = min J(sj ) ∀j ∈ {1, ..., N } Z T N X (10) J(sj (t)) = g W (sj (t))2 + gjH (sj (t))2 dt 0
j=1
subject to e˙j (t) = −(α · sj (t) + β · |sj (t)|)
(11)
ej (t0 ) = e0j
(12)
In particular, (11) is obtained by the combination of (1) and (2), α and β being defined respectively as: 1 1 + η α = c 2 ηd (13) 1 1 β = − ηc 2 ηd Finally, as reported in Sections III and IV, the control and state variables are bounded by (3) and (4) for all t ∈ [0, T ]. The solution of such an optimal control problem is derived by applying the Euler-Lagrange approach and, in particular, its generic formulation in terms of Pontryagin’s minimum principle, which will be described in the following section.
Since the Hamiltonian function does not depend explicitly on the state variables ej , (18) leads to: λ˙ ∗j = 0 =⇒ λ∗j ≡ cost ∀j ∈ {1, ..., N }
This result is quite significant because, besides reducing the computation effort, it assures also a global optimal control [13]. Furthermore, according to PMP, (10) is minimized when the control variables satisfy the minimum condition (20). H(s∗j (t), e∗j (t), λ∗j , t) ≤ H(sj (t), e∗j (t), λ∗j , t)
C. PMP for EV management in a cluster of MGs
ej (T ) = eTj
(14)
and such that the performance criterion (10) is minimized, (3) and (4) being always satisfied. Then, the PMP requires the definition of the Hamiltonian function which can be formulated as H = J(sj (t)) +
N X
λj (t)e˙ j (t)
(15)
j=1
λj being the adjoint variables and assuming λ0 = 1 (regular case). By introducing (5), (6), (10) and (11) in (15), the Hamiltonian becomes: N 2 X 2 H = rW (t) + sW (t) + rjH (t) + sH j (t) + j=1 (16) −λj (t) α · sj (t) + β · |sj (t)| On the basis of the Euler-Lagrange equations, the necessary optimality conditions assume the form reported in (17) and (18) for the state and adjoint variables respectively. e˙ ∗j =
∂H ∂λj
∂H λ˙ ∗j = − ∂ej
(17) (18)
(20)
As many physical and engineering problems, the proposed control system is characterized by bounded control variables, which means that the optimal controls s∗j must satisfy the following optimality condition derived from (20). ∗ sj (t) = s˜j (t) (21) sminj ≤ s˜j (t) ≤ smaxj where s˜j is obtained by
The above defined optimal problem can be analytically solved by applying the PMP, finding the optimal control law which minimizes the cost functional (10). Starting from these considerations, the problem statement can be formulated as follows: Find a vector of optimal controls s∗j and the corresponding vector of optimal responses e∗j such that the dynamic system described by (11) is transferred from the initial state (12) to a final given state
∀t ∈ [0, T ] (19)
2 rW (t) +
∂H = 0, resulting in : ∂sj
N X H s˜W ˜H j (t) + 2 rj (t) + s j (t) + j=1
− λj (α + σβ) = 0
(22)
σ = sign(˜ sj (t))
Moreover, it’s worth noting that the state inequality constraints are handled by introducing an augmented Hamiltonian, called Lagrangian function, formed by adjoing the constraints (4) to the Hamiltonian (15) using a multiplier function µj [16]. Finally, for the sake of the optimality it is assumed that the final state condition (14) is equal to the initial state (12). In fact, this is usually imposed in energy storage optimization problems [13], [14] in order to preserve a defined reference state at the end of the control horizon. V.
C ASE OF STUDY
In order to evaluate the effectiveness of the proposed optimal control approach, a case study is analysed, showing a possible application of the optimal problem formulation presented in the previous sections. The case study is based on a MG that has the same characteristics described in Section II. In particular, the energy system is supposed to be basically constituted of two MGs: a family-run company W and a house H, where one of the employers lives. In addition, the latter is assumed to drive an EV to commute. In this case, the mathematical formulation can assume the form reported in the following. In particular, (10) can be expressed as: J(s∗ (t)) = min J(s(t)) Z T W 2 H 2 J(s(t)) = g (s(t)) + g (s(t)) dt
(23)
0
As a consequence, the Hamiltonian defined by (16) becomes: 2 2 H = rW (t) + sW (t) + rH (t) + sH (t) + (24) − λ α · s(t) + β · |s(t)|
Finally, it is possible to synthesize the optimal controls s∗ by combining (9) and (22), taking into account the position of the EV. In particular, if the EV is in W , the following occurs: sH (t) = 0 (25) sW (t) = λ (α + σβ) − rW (t) 2 whereas (26) applies when the EV is plugged at home sH (t) = λ (α + σβ) − rH (t) (26) 2 W s (t) = 0 The proposed optimal control strategy for this case study is implemented in Matlab environment over a period T of 24 h, with a 1 minute time-resolution. For this purpose, the main characteristics of the electric vehicle and its mobility habits, W load and generator as well as H load have to be defined. First of all, an EV daily travel program is considered and reported in Table I. The EV energy consumption is set equal to 0.2 kW h/km. Such a value is quite high compared to nominal consumptions reported in data-sheets of many commercial EVs. Nevertheless, real world test cases found consumption values for compact cars very close to that assumed in this study [17]. Moreover, a battery capacity of 30 kW h is considered. However, since the SOC range of the battery is limited to increase its lifetime, in the simulations the SOC is bounded
TABLE I.
EV DAILY PLANS FOR 30 KM COMMUTING DISTANCE
0:007:00 Home Work
8:0117:00
17:0118:00
X
18:0124:00 X
X
Moving
X TABLE II.
Home Work
7:018:00
X
L OAD AND RES P OWERS
Unit
Load Power
kW kW
6 15
RES Power PV Wind 10 3
to a range of 20% − 80%. As a consequence, the usable battery capacity is limited to 18 kW h. In addition, 3 kW bi-directional power grid connections are considered in both W and H, whereas the overall charging and discharging efficiencies are set to 90% and 85% respectively. Regarding MGs, whose main parameter are summed up in Table II, the electric load and generation of W and H are referred to two different scenarios. These are chosen considering the power balance condition between the W MG and the main grid. In particular, Case A is characterized
W Fig. 2. The forecasted daily evolution of PRES in pu with respect to the EV maximum bi-directional power in Case A (cyan) and Case B (orange).
Fig. 4. The forecasted daily evolution of rW in pu with respect to the EV maximum bi-directional power in Case A (cyan) and Case B (orange)
Fig. 3. The forecasted daily evolution of LW in pu with respect to the EV maximum bi-directional power in Case A (cyan) and Case B (orange)
Fig. 5. The forecasted daily evolution of rH in pu with respect to the EV maximum bi-directional power in Case A (cyan) and Case B (orange)
by an inversion in the power flow, whereas in the Case B the balance is always negative. The profiles are chosen to be coherent with a real operating condition and for this reason they are extracted from the real data of Sardinian RESs power plants and residential and commercial districts [18]. In greater details, the evolution of RES production in Case A is typical of a sunny and poor windy day, as can be seen in Fig. 2. W In contrast, in Case B PRES assumes a more fluctuating daily evolution and a much lower peak value than in Case A. Similar considerations can be made for the W district load depicted in Fig. 3, in which the peak demand of Case B doubles the one in Case A. As a result of the profiles described above, the evolutions of the power flow exchanged between the W MG and the power system are shown in Fig. 4. It can be noticed that in Case A a RES overproduction occurs during the central hours of the day, whereas in Case B the W MG is always seen by the grid as a load, because LW is always higher W than PRES . The evolutions of household load are shown in Fig. 5. Finally, accurate forecasting of MGs power production and consumptions is assumed to be available in order to achieve a global optimization one-day ahead. In order to test the proposed optimal control strategy, both cases are compared with a scenario in which the EV is not introduced and the one in which the EV is recharged by a dumb strategy. The latter provides a complete recharge of the EV battery as soon as it is plugged into the socket, in order to reach the 80% of the SOC. In the proposed optimal control strategy, the initial and final SOC is assumed equal to 50%, in order to avoid high average SOCs which negatively affect the battery lifetime and to be initially ready to exchange energy with the power grid [19]. A. Case A This scenario is characterised by a H load that features two consumption peaks in the morning and in the late evening, and by a W high renewable production, particularly concentrated during the working hours. Referring to this energy configuration, the entire MG system is simulated implementing both the optimal control strategy and the dumb charging one. In Fig. 6 the daily trends of the optimal control s∗ and the corresponding evolution of e∗ are reported. Both quantities are compared with those obtained in the dumb charging. These results can be better analysed also considering the daily trends of the power exchanged between the MGs and the main grid, reported in Fig. 7. In the following the results of the optimal control strategy are used in order to support a qualitative energy balance description of the control actions into the MGs. The lower sub-plot of Fig. 7 shows the energy performance of the proposed optimal control. The coloured areas highlight the effects of V2G to the minimization of energy flow between MGs and the main grid. The comparison with the dumb charging, reported in the upper sub-plot, highlight the obtained improvement. This result can be described in details in the following. In the first part of the day, the EV is discharged to cover the morning house loads only two hours before to leave: this in fact ensures to cover the highest load peak and have enough energy to commute at the same time. Then, at work, the EV starts charging about 20 minutes after his arrival in order to be able to absorb the most of surplus energy around midday. Here, the power drawn by the EV is limited by the
Fig. 6. The daily evolutions of s∗ and e∗ in Case A: dumb charging (red) and optimal control strategy (green).
Fig. 7. The daily evolutions of the power exchanged between the MGs and the main grid in Case A: without EV (black), dumb charging (on the top, in red) and optimal control strategy (on the bottom, in green). The orange areas represent the energy absorbed by the EV, whereas the cyan ones represent the energy delivered by the EV storage system.
Fig. 8. The daily evolutions of objective function in Case A: without EV (black), dumb charging (red) and optimal control strategy (green).
boundaries on the control variable s, as highlighted in Fig. 6. As soon as the EV is plugged at home in the evening, the V2G process is enabled and the vehicle discharges in order to cover partially the house electrical demand during the evening peak hours. Finally, at the end of the day when the lowest demand is expected, the EV is gradually recharged up to the desired final SOC (50%). The time evolutions of the objective function J depicted
in Fig. 8 and its final values reported in Tab. III corroborate the effectiveness of the proposed optimal control. In fact, as expected, the implemented EV smart management substantially reduces (by 34%) the performance criterion respect to the dumb charging result. Furthermore, it is interesting to point out that J is also optimized respect to the MGs system without EVs, indicating the worth of the presented optimal EVs management for the reduction of the MGs dependence from the main grid and for the increase of their energy autonomy. Clearly, these outcomes strictly depend on the production and consumption profiles, which in this case are mainly characterized by a great excess of RES energy generation. Since the proposed optimal strategy aims at effectively working regardless of the PV and wind productions, a worse scenario is analysed in the following.
Fig. 9. The daily evolutions of s∗ and e∗ in Case B: dumb charging (red) and optimal control strategy (green).
B. Case B The same simulation results developed in Case A are reported for Case B in Figs. 9-11. The Case B reflects a situation that can frequently happen during the fall or winter months. In fact, the electricity generation from RES is very poor and at each hour of the day W and H have to resort to the main grid in order to cover their electric loads. As a consequence, the introduction of an EV worsens in any case the MGs energy unbalance since it needs to be recharged during the day, increasing the total load to be supplied by the main grid, as highlighted by the orange areas in Fig. 10. Nevertheless, referring to the results shown in Figs. 9-11 and Table III, the optimal control of the EV allows the achievement of better results respect to the case of an uncontrolled charging, reducing by 13% the value of the objective function. In particular, the proposed optimal control enables the EV recharge only during the hours when the electricity demand is the lowest, such as in the early morning, evening and at night, concentrating the discharge periods at work where the highest peak loads are expected. This action is highlighted by the cyan areas in Fig. 10. Moreover, it’s worth observing, by the analysis of Fig. 9, that, initially, the battery charges up to its maximum SOC in order to be able to commute and to provide energy at work at the same time, reducing consequently the local power unbalance. From these considerations, it is evident that the proposed EV control strategy can optimally manage the charge/discharge processes even in the conditions of both low RES production and high peak load, as highlighted by the results reported for this case.
Fig. 10. The daily evolutions of the power exchanged between the MGs and the main grid in Case B: without EV (black), dumb charging (on the top, in red) and optimal control strategy (on the bottom, in green). The orange areas represent the energy absorbed by the EV, whereas the cyan ones represent the energy delivered by the EV storage system.
C. State of Charge Analysis An important aspect to be considered when dealing with EVs charging algorithms is the influence of the management strategy on the battery lifetime. The technical literature [19], [20] suggests that one of the parameters most affecting the battery ageing is the average SOC. In fact, especially high SOCs are demonstrated to be a strong acceleration factor for the reduction of the battery calendar life. In particular, such states-of-charge correspond to high electrode potentials, causing electrolyte decomposition and finally the reduction of the battery capacity [19]. Moreover, studies [19], [20] highlight that the cycling effect, which is more emphasized in V2G applications, contributes to the overall battery ageing less than long rest periods at high SOCs, hence the latter being the main cause of battery ageing.
Fig. 11. The daily evolutions of objective function in Case B: without EV (black), dumb charging (red) and optimal control strategy (green).
Starting from these considerations, the average SOC has been calculated for the cases A and B and compared with the dumb charging. The results are reported in Tab. IV and allows to give some interesting remarks, especially when analysed together with the SOC profiles shown in Figs. 6 and 9. Particularly, it is evident that the proposed optimal EV management strategy decreases standstill time at high SOCs. As a consequence, in both cases, the average SOCs
TABLE III.
S CENARIOS O BJECTIVE F UNCTION RESULTS
MGs without EVs
Dumb Charging
Optimal Control
Case A
3056.8
3780.6
2490.9
Case B
6922.8
8286.1
7342.4
TABLE IV.
[11]
[12]
[13]
AVERAGE SOC RESULTS [14]
Dumb Charging
Optimal Control
Case A
0.76
0.49
Case B
0.76
0.54
[15]
[16]
are drastically lower than that recorded for the dumb charging approach. VI.
C ONCLUSION
An optimal control approach oriented to define the charging profile of electric vehicles suitable for supporting their integration into microgrids is presented. The proposed control algorithm is reported and its effectiveness is tested on a case study. The simulation of a cluster of two microgrids, which are connected in unconventional manner by means of an electric vehicle operating in Vehicle-to-Grid mode, is carried out. The results of the proposed optimal control strategy is compared with those obtained with the implementation of a dumb charging approach highlighting for the analysed case study an improvement by the energy point of view. R EFERENCES [1]
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