Demand-side management in smart grids with electric vehicle load shifting

Demand-side management in smart grid operation considering
electric vehicles load shifting and vehicle-to-grid support
M.A. López ⇑
, S. de la Torre, S. Martín, J.A. Aguado
Department of Electrical Engineering, Universidad de Málaga, Spain
a r t i c l e i n f o
Article history:
Received 12 February 2014
Received in revised form 16 July 2014
Accepted 19 July 2014
Available online 23 August 2014
Keywords:
Demand-side management
Electric vehicles
Smart grid
Vehicle-to-grid
a b s t r a c t
Demand fluctuation in electric power systems is undesirable from many points of view; this has sparked
an interest in demand-side strategies that try to establish mechanisms that allow for a flatter demand
curve. Particularly interesting is load shifting, a strategy that considers the shifting of certain amounts
of energy demand from some time periods to other time periods with lower expected demand, typically
in response to price signals.
In this paper, an optimization-based model is proposed to perform load shifting in the context of smart
grids. In our model, we define agents that are responsible for load, generation and storage management;
in particular, some of them are electric vehicle aggregators. An important feature of the proposed
approach is the inclusion of electric vehicles with vehicle-to-grid capabilities; with this possibility,
electric vehicles can provide certain services to the power grid, including load shifting and congestion
management. Results are reported for a test system based on the IEEE 37-bus distribution grid; the
effectiveness of the approach and the effect of the hourly energy prices on flattening the load curve
are shown.
Ó 2014 Elsevier Ltd. All rights reserved.
Introduction
The transition towards the Smart Grid (SG) requires to incorpo-
rate new functionalities and capabilities to the existing electricity
grid. Among some identifiable features, distributed generation is
a common characteristic of the SG and, in addition, the nature of
these generators is varied since they can be non-dispatchable
renewable, such as wind turbines or photovoltaic panels, combined
heat and power, fuel cells, microturbines or diesel-powered plants.
Devices which are able to store energy, like electric fixed batteries,
can help the system to smooth the intermittent behavior of renew-
able sources enabling an easier integration. The next generation of
the electricity grid will also pave the way to electrified transporta-
tion [1]. SGs comprise different entities that can interact with each
other bidirectionally, giving the possibility to establish commercial
relationships to serve and request electric energy or to solve tech-
nical problems that could arise, thus empowering the consumer.
These entities within the SG can respond to changes in the prices
at which the energy is bought and sold to the main grid with the
objective of minimizing the costs of the energy they need or
maximizing the income from the energy they sell. Among the
many features that make a grid smart, the essential aspect is the
integration of power system engineering with information and
communication technologies. In turn, this integration can allow
for advances in reliability, efficiency and operational capability [2].
Among other interesting characteristics of SGs, the concept of
Demand-Side Management (DSM) has attracted the attention of
many researchers and, among DSM strategies, demand response
has been widely considered [3–5]. Demand response can be under-
stood as voluntary changes by end-consumers of their usual con-
sumption patterns in response to price signals [6]. Along with
the savings regarding electricity bills, this kind of schemes can be
used to avoid undesirable peaks in the demand curve that take
place in some time periods along the day, resulting in a more ben-
eficial rearrangement [7–10]. Through the use of DSM, several ben-
efits are expected, like the improvement in the efficiency of the
system, the security of supply, the reduction in the flexibility
requirements for generators or the mitigation of environmental
damage, although some challenges have to be overcome starting
from the lack of the necessary infrastructure [11]. In addition,
the introduction of DSM has to be conceived taking into account
other distributed energy resources technologies that could be pres-
ent in SGs [12,13]. In regard to this, several SG projects worldwide
are underway or have been completed [14,15].
http://dx.doi.org/10.1016/j.ijepes.2014.07.065
0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
⇑ Corresponding author.
E-mail addresses: malopezperez@uma.es (M.A. López), storre@uma.es (S. de la
Torre), smartin@uma.es (S. Martín), jaguado@uma.es (J.A. Aguado).
Electrical Power and Energy Systems 64 (2015) 689–698
Contents lists available at ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes

In order to simplify the implementation of the proposed
approach in real systems, most of the actions in the SG are taken
by the agents. In order to take these actions, the agents act on their
own interest; sometimes, however, they make use of additional
information provided by the SG operator. The individual decisions
of the agents can only be slightly corrected by the SG operator
(centralized correction) in order to correct the violation of techni-
cal constraints in the SG, in case they arise.
To make decisions each agent poses an optimization problem to
maximize its profit over a set of periods, they can perform DSM
strategies and Vehicle-to-Grid (V2G). As energy prices are usually
higher for high demand periods, the optimization problems result
in a flattened load curve. Following the regulatory trends in many
countries, in particular in countries in Europe [16], the renewable
generation in the model is also prioritized over the conventional
generation. The framework considers market and technical
Nomenclature
Indexes and sets
t; T index and set for time periods, t 2 T
e; E index and set for the scenarios used to model the uncer-
tainty, e 2 E
i; R index and set for renewable generators belonging to the
agent, i 2 R
j; G index and set for non-renewable generators belonging
the agent, j 2 G
b; B index and set for batteries belonging to the agent, b 2 B
v; H index and set for electric vehicles belonging to the
agent, v 2 H
n; A index and set for demand nodes of the agent, n 2 A
tm; TM index and set of transitions periods for the electric vehi-
cles belonging to the agent, tm 2 TM
jaj the cardinality of a set a
Parameters
We
probability of scenario e
^
kb
t main grid hourly forecasted buying price in time period
t (cents €/kWh)
^
ks
t main grid hourly forecasted selling price in time period t
(cents €/kWh)
PR;e
i;t
renewable power output for generator i in time period t
for scenario e (kW)
X parameter related to capacity constraints of the agents
Hn;t total demand prior to load shifting for bus n in time per-
iod t (kW)
fe fraction of the total demand that can be shifted
/n;t fixed demand for bus n in time period t (kW)
cn;t maximum shiftable demand for bus n in time period t
(kW)
k maximum number of periods that demand can be
shifted (hours)
k rate between maximum shiftable demand and fixed de-
mand, constant for all periods and nodes
kd upper bound for the change in the value of shiftable de-
mand between two consecutive periods, constant for all
the periods and nodes (kW)
lj variable cost for non-renewable generator j (cents €/
kW)
ij fixed cost for non-renewable generator j (cents €)
fj start-up cost for non-renewable generator j (cents €)
1j shut-down cost for non-renewable generator j (cents €)
Pmin
g;j minimum power output for non-renewable generator j
(kW)
Pmax
g;j maximum power output for non-renewable generator j
(kW)
Pd;max
b
maximum discharging power for battery b (kW)
Pc;max
b
maximum charging power for battery b (kW)
Smax
b maximum state of charge for battery b (kWh)
gC charging efficiency for batteries
gD discharging efficiency for batteries
Pmin
v minimum charging or discharging power allowed for
electric vehicles (kW)
Pmax
v maximum charging or discharging power allowed for
electric vehicles (kW)
Smax
v battery capacity of electric vehicle v (kWh)
jt
v kilometers covered by electric vehicle v in time period t
(km)
# average battery consumption (kWh/km)
Variables
PS;e
t power sold in time period t for scenario e (kW)
PB;e
t power bought in time period t for scenario e (kW)
CG;e
t;j
non-renewable generation cost for generator j in time
period t for scenario e (cents €)
PG;e
j;t
r power output for non-renewable generator j in time
period t for scenario e (kW)
Pd;e
b;t
discharging power for battery b in time period t for sce-
nario e (kW)
Pc;e
b;t
charging power for battery b in time period t for sce-
nario e (kW)
Pd;e
v;t discharging power for electric vehicle v in time period t
for scenario e (kW)
Pc;e
v;t charging power for electric vehicle v in time period t for
scenario e (kW)
Ue
n;t optimal demand for bus n in time period t for scenario e
(kW)
Ce
n;t optimal shiftable demand for bus n in time period t for
scenario e (kW)
Me
n;t;t0 amount of demand that goes from time period t to time
period t0
for bus n and scenario e (kW)
Se
b;t state of charge for battery b in time period t for scenario
e (kWh)
Se
v;t state of charge for electric vehicle v in time period t for
scenario e (kWh)
Binary variables
be
t binary variable that takes the value ‘‘1’’ if the agent is
buying in time period t for scenario e, and ‘‘0’’ otherwise
vG;e
t;j
binary variable that takes the value ‘‘1’’ if generator j is
running in time period t for scenario e, and ‘‘0’’ other-
wise
yG;e
t;j
binary variable that takes the value ‘‘1’’ if generator j
starts up in time period t for scenario e, and ‘‘0’’ other-
wise
sG;e
t;j
binary variable that takes the value ‘‘1’’ if generator j
shuts down in time period t for scenario e, and ‘‘0’’
otherwise
yd;e
v;t binary variable that takes the value ‘‘1’’ if electric vehi-
cle v is discharging in time period t for scenario e, and
‘‘0’’ otherwise
yc;e
v;t binary variable that takes the value ‘‘1’’ if electric vehi-
cle v is charging in time period t for scenario e, and ‘‘0’’
otherwise
690 M.A. López et al. / Electrical Power and Energy Systems 64 (2015) 689–698

operation of the grid, and it is illustrated in a case study modeling a
SG based on IEEE 37-bus distribution grid.
The rest of the paper is organized as follows: in Section 2, the
related work and paper contributions are introduced. Then, Sec-
tion 3 presents a proposal for the SG operation, referred as problem
statement, including the description of the operational algorithm
steps previously mentioned. Section 4 focuses on DSM strategies,
describing the optimization problems in detail and providing mod-
els of the different elements included. The case study and results
are presented in Section 5. Finally, conclusions are drawn in
Section 6.
Related work and contributions
Many works are found in the literature investigating DSM ben-
efits and SG modeling. Some of them cover problems regarding
scheduling appliances based on pricing models; for instance, in
[17], a voluntary household load shedding model is studied in
order to keep the system in secure conditions with respect to
demand peaks. Using two different methodologies, the benefits
of DSM for both the consumers and utilities are shown in
[18,19], stressing the importance of identifying the flexible loads.
In comparison to these works, in this paper, operation of appli-
ances is not considered and, instead, a fraction of the initial
demand is assumed to be shiftable. In addition, agents with gener-
ation or storage assets are included in our formulation, while the
previous works only stress the role of consumers.
Other authors study how the demand can be allocated through
optimization problems based on utility functions and other specific
constraints. In [20], the objective of the proposed model is to max-
imize the utility of a consumer subject to a minimum daily con-
sumption level and restrictions over load levels including price
uncertainty. Authors in [21] consider the problem of maximizing
the social welfare expressed as the sum of utilities of consumers
minus the energy provider costs. In [22], a similar approach is pro-
posed but uncertainty in renewable power generation is addressed
and supply and demand are coordinated in two different time
scales. The extension to several energy providers and the joint con-
sideration of distributed and renewable generation units, storage
devices, active demand and EVs is studied in [23]. One common
aspect in these works is that the demand is calculated depending
on the constraints, while in our work the total demand over the
time horizon is known and it is only arranged differently.
Moreover, the proposed model considers the maximization of the
agents profit, whereas the social welfare or the utility functions
are considered in [21–23]. Finally, only in [23] several elements
present in SGs are modeled in a similar way to our proposal and,
although some aspects are similar the way the demand is allocated
is completely different.
Finally, DSM can also be applied to EVs and, for this reason, they
may be also influenced by price signals changing their location or
their consumption pattern if needed. We propose a optimization-
based model applicable to EVs considering that EV load can be
shifted based on charging prices. V2G can be also performed to
get additional profits. Some related papers are described next.
The impact of EVs on the demand profile is analyzed in [24] and,
in [25], the authors try to integrate EVs with demand response
strategies involving the consumer. In these works, EVs contribu-
tion is included through simple policies with no formal mathemat-
ical modeling of EVs load management and without considering
V2G. In [26], a game theoretic approach is proposed to schedule
EVs charging for peak shaving and valley filling while, in [27],
V2G is also considered for this purpose; developing an optimiza-
tion problem that aims at getting a final load profile close to a
target load curve. In [28], a coordination mechanism is proposed
to allocate EVs charging efficiently, stressing the role of renewable
energy. EVs can also be managed to solve technical problems, like
line congestion, through the change in the initial expected charg-
ing pattern [29]. Other authors consider a specific smart load man-
agement approach that can be applied to EVs but focusing on
technical aspects like losses minimization or voltage limits without
including market issues [30].
According to the ideas presented, the main contributions in this
work are:
The formulation of a particular DSM strategy based on optimi-
zation problems where the profit maximization of all the
involved agents is pursued.
An algorithm to optimize the hourly allocation of demand and
generation, taking into account technical constraints and
enabling the EVs and renewable resources integration.
Problem statement
The problem is posed on a SG that includes distributed genera-
tion (renewable and non-renewable), and EVs that can perform
V2G operations. We study the operation in a typical day on a
hourly basis, under the assumption that a similar operation could
be done for each day. The problem is multi-period and thought
to be applied for planning purposes, that is, not in real time.
The agents in the considered SG can be of two types: (a) EVs,
these agents can move among the nodes in the network, also one
agent could aggregate several EVs and (b) agents that are always
connected to the same node, these agents can be composed of a
combination of: loads, renewable generators, non-renewable gen-
erators, and batteries. The SG architecture and examples of possi-
ble agents in the SG are illustrated in Fig. 1.
The focus is on load shifting made by agents in the SG (resched-
uling their loads) based on their profit maximization (generators)
or cost minimization (pure loads). The number of periods that
loads can be shifted, forward or backward, is referred to as ‘‘k’’,
and it is an exogenous parameter in the proposed model. We study
the results for different values of ‘‘k’’ because of two main reasons:
(I) to evaluate the incentive (difference in profit or cost) that agents
have to perform load shifting, and the resulting system perfor-
mance (integration of renewable generation, losses, line apparent
power flows, etc.) and (II) to evaluate the feasibility of the strategy,
the higher the value of ‘‘k’’ the more difficult the strategy will be to
apply for the agents in the real systems. In practice, it is interesting
to understand what different values of parameter ‘‘k’’ mean for
consumers and know other papers dealing with similar concepts.
For instance, values of ‘‘k’’ below 3 h could be applied to cooling
Fig. 1. Agents considered in the smart grid.
M.A. López et al. / Electrical Power and Energy Systems 64 (2015) 689–698 691

devices, through appropriate control signals, due to temperature
restrictions [31]. In addition, air conditioning in commercial and
residential areas has turned out to be the main responsible of
demand peak in some countries and, thus, it is an ideal candidate
for load shifting with higher values of this parameter [32,33]. Val-
ues between 2 h and 8 h have been considered by some authors as
well to study reductions in distribution losses [34].
The agents can sell or buy energy, if it is technically feasible for
them, (from/to) (other agents/the main grid). Each agent makes its
own decisions, and there are not centralized decisions. The main
grid is considered as a slack node with infinite capacity.
The proposed model for the SG operation consists of two
sequential stages, first a market based solution is calculated, and
second the technical feasibility of the previous solution is checked
in a technical operation stage. The SG operation along with these
stages can be integrated in an specific operational algorithm, Fig. 2.
In the first stage each agent makes decisions, for each period,
about the quantities to generate, to buy from the main grid or
the SG, its load shifting, and to sell its generation to the main grid
or to the SG. Agents can choose between trade among them inside
the SG, then the energy prices (selling and purchase) are deter-
mined by an internal auction based on the agents bids, or to trade
with the main grid. The internal auction is ruled by the SG
operator.
Agents have to face two sets of parameters with uncertainty, on
one hand the energy selling/purchase prices to/from the main grid,
and on the other hand the available generation of the renewable
resources. Both sets or parameters are modeled through scenario
trees. They are also data, the initial energy demand for each agent
(for each period) and the rate of that demand they can shift.
To make their decisions, each agent poses an optimization prob-
lem. This problem is a mixed integer linear programming in the
general case and a linear programming in some particular cases.
We give a general description of these optimization problems in
what follows, and they will be described in detail in the next
section.
These optimization problems consists of an objective function
and a set of constraints. Agents make decisions based on their
profit maximization, thus the objective function is the expectation
on the set of scenarios of the agents profit. The agents profit is
defined as the income from selling energy minus the costs from
generation and/or energy purchase. The set of constraints is made
up of the technical constraints for each particular component of
the agent, for instance, the capacity bounds for generators, and
the bounds for the energy flow from/to batteries or EVs.
Finally, in the second stage, a load flow is used to check the
technical feasibility of the previous solution. In this stage, the
active losses in the network lines are calculated (we only consider
the active losses) in the network lines and the technical constraints
are checked, in particular the node voltage bounds and the appar-
ent power in the lines. If some bounds are violated then a correc-
tion to the initial solution is applied, and the new result is again
checked. We apply the correction algorithm described in [35], that
minimizes the changes with respect to the initial solution.
Description of the agent strategy
In this section, the strategy followed by the agents to make their
decisions regarding load shifting is described. In what follows, first
the different SG elements of the agents and the main related
parameters and variables are introduced. Then, the agent optimiza-
tion problem, consisting of an objective function and a set of con-
straints, is presented.
Smart grid elements
The SG elements considered in this work are presented here.
Each agent is considered to be formed of four possible compo-
nents: loads, generators, batteries or EVs.
Loads are characterized by a fraction of the total demand that
can be shifted and they depend on the time period and the node
in the more general case. Thus, the initial predicted demand Hn;t
is defined as the sum of fixed demand /n;t and the shiftable compo-
nent cn;t, expressed as a fraction f e of the total demand, in every
node and time period; this can be written as:
Hn;t ¼ /n;t þ cn;t ¼ /n;t þ fe Hn;t 8t; 8n ð1Þ
Once the agent makes the decision, based on the results from its
optimization problem, the total demand changes to Ue
n;t and the
optimal shiftable demand to Ce
n;t. Fig. 3 illustrates the limits for
demand in the proposed load shifting mechanism.
The maximum number of periods that loads can be shifted for-
ward or backward is an exogenous parameter ‘‘k’’, explained in the
previous section. It is assumed that part of the agent loads can be
Fig. 2. Flow chart of the operational algorithm. Fig. 3. Parameters and variables related to the demand.

shifted [36]. The agent can access to the necessary information, like
hourly energy prices, generation costs or weather historical data, to
decide how and when it is more favorable to satisfy its demand.
Generators can be of two types: non-renewable and renewable.
Non-renewable generator j is characterized by its operational
cost, that is made up of the variable cost lj, fixed cost ij, start-up
cost fj and shut-down cost 1j. Its operation is mainly conditioned
on the relation between generation costs and energy prices. Tech-
nical bounds for power output, Pmin
g;j and Pmax
g;j , are also considered.
The power supplied by renewable generators, namely photovol-
taic panels and wind turbines, is modeled as a set of scenarios. The
specific values are calculated using real generator models and real
values of wind speed and solar radiation; these values are com-
bined to get an overall number of different scenarios correspond-
ing to representative situations that take place during the year.
We follow the current regulatory trends, proposed in many coun-
tries, in particular in Europe [16], that prioritize the use of low
emission renewable generators over the conventional generators,
even if some subsidy is needed to make the operation feasible. In
this regard in our model the renewable generation is prioritized
over the conventional generators in the optimization problems
assuming a zero generation cost for them (but we do not consider
subsidies explicitly in the model). We consider the renewable gen-
eration as a parameter with values given by an scenario tree, and
that all the available renewable generation is used in the system
(no spillage). In case the renewable generation is greater than
the demand in the SG, the excess of generation is transferred (sold)
to the main grid through the connection node.
Fixed storage devices are represented by bank of electric batter-
ies in this work. Fixed batteries are modeled taking into account
the following aspects: (i) A battery can charge (absorb energy from
the grid) or discharge (inject energy to the grid) considering oper-
ational efficiencies gC and gD respectively, (ii) there is a limit for
the power drawn or supplied by a battery b; Pc;max
b and Pd;max
b , and
(iii) the energy contained in the battery is tracked considering its
State of Charge (SOC) Se
b;t.
Finally, mobile storage devices are represented by electric vehi-
cles. Similar aspects enumerated for fixed batteries are applied for
electric vehicles although some additional considerations are
needed to define appropriately the mobility model.
We consider two models for the EVs, the uncontrolled operation
and the operation controlled by an aggregator [37], because they
model two common situations in real systems, the individual user
and a company fleet.
In the uncontrolled situation we assume that EVs follows a fixed
pattern, that is defined by three kinds of time periods: Transition,
charging periods, and resting periods. During the transition periods
the EVs move on the network and they consume the energy in their
battery. In the charging periods the EVs consume energy from the
network. And during the rest periods the EVs neither consume
their own energy nor charge energy from the network. In this case
the values of the energy flows in each periods are also fixed quan-
tities. Two parameters are needed to determine the energy con-
sumption (kWh) in transitions: (i) Parameter jtm
c is the amount
of kilometers covered in time period tm and (ii) parameter # that
represents the energy consumption in kWh/km.
In the case of operation controlled by an aggregator only the
transition periods and their corresponding energy consumption
are fixed. For the other periods, the aggregator makes the decision
on when to charge and the quantity to consume from the network,
they can perform V2G in these periods.
Optimization problem description
In this section, the mathematical relationships between the
parameters and variables with respect to the elements of each
agent are developed in the form of an optimization problem, for
the general case it is a mixed integer linear programming. First
the objective function is described, and next the set of common
constraints (balancing and DSM), and the set of constraints for each
possible component of the agents (generators, batteries, EVs)
according to the ideas described in Section 4.1 are presented.
The number of equations, continuous variables, binary variables
and execution time for the optimization problem of each agent, as
described in Section 5.1, is given in Table 1. The corresponding val-
ues mainly depend on the SG elements of each agent and they can
be calculated with the following equations:
The number of equations is:
jTjjEj 3 þ 2jGj þ 4jBj þ 3jHj þ 3jAj
ð Þ þ jEj
jBj þ jHj ð1 2jTMjÞ
ð Þ
The number of continuous variables is:
jTjjEj ðjGj þ 3jBj þ 2jHj þ 2Þ þ jAjjEj ð2jTjk k ðk þ 1ÞÞ
The number of binary variables is:
jTjjEj ð3jGj þ jBj þ 2jHj þ 1Þ
The simulations were carried out in a computer Intel Core 2 Duo
@ 3 GHz with 4 GB RAM. The software GAMS (using the CPLEX
optimizer) was used to perform the optimization problems linked
with MATLAB as a support to coordinate the execution of these
problems, store data and make graphical representations.
Regarding the objective function, the agents maximize their
expected profit, that in the more general case is defined by:
maximize
PS;e
t
;PB;e
t
;CG;e
t;j
n o
X
jEj
e¼1
We

X
tf
t¼t0
^
kb
t PS;e
t ^
ks
t PB;e
t
X
jGj
j¼1
CG;e
t;j
!
ð2Þ
where ^
kb
t and ^
ks
t are the hourly forecasted buying and selling market
prices (parameters), PB;e
t and PS;e
t are the hourly power bought and
sold (variables) and CG;e
t;j represents the function of generation costs
for non-renewable generator j, defined in Section 4.2.2, t0 is the ini-
tial time period and tf is the final time period.
For a particular agent, some terms in Eq. (2) are fixed to zero
depending on the agent composition, for instance if it contains only
generators or only loads.
From the historical data in real power systems, for instance in
the Spanish system [38], we observe that average prices are higher
for higher demand. Thus, the consequence of profit maximization
for agents is that they try to shift their load to the periods with
the lowest prices, and the demand curve is flattened.
Common constraints (balancing and DSM)
The constraints common to all the optimization problems
include the energy balancing and DSM constraints.
The balancing constraint relates PB;e
t and PS;e
t with the power
supplied from generators, the bus load and the power drawn or
Table 1
Solving time and number of variables for agents optimization problems.
Agent Equations Continuous Binary Execution time (s)
1 36,960 150,336 3456 1.155
2 19,584 84,096 4608 0.577
3 28,800 125,568 8064 0.796
4 23,040 104,256 4608 0.671
5 19,584 84,096 4608 0.592
6 20,736 103,104 1152 0.827
7 17,280 82,944 1152 0.561
8 3144 2160 2088 0.032

delivered from batteries for each agent. According to Eqs. (3)–(5),
variables PS;e
t and PB;e
t cannot be different from zero at the same
time period, that is, whenever one of them is different from zero,
the other one must equal zero. Thus, an agent is not allowed to
buy and sell simultaneously:
PS;e
t PB;e
t ¼
X
jRj
i¼1
PR;e
i;t þ
X
jGj
j¼1
PG;e
j;t þ
X
jBj
b¼1
ðPd;e
b;t Pc;e
b;tÞ
X
jAj
n¼1
Ue
n;t 8t; 8e:
ð3Þ
0 6 PB;e
t 6 be
t X 8t; 8e ð4Þ
0 6 PS;e
t 6 ð1 be
t Þ X; 8t; 8e ð5Þ
where PR;e
i;t ; PG;e
j;t and Pd;e
b;t are the hourly power supplied for renewable
generator i, non-renewable generator j and battery b; Pc;e
b;t is the
hourly power absorbed by battery b and Ue
n;t is the total demand
in node n. Note that terms for batteries are extensible for EVs.
Eqs. (4) and (5), which constitute an application of the Big-M
method [39], assure that an agent cannot buy and sell at the same
time through binary variable be
t . Finally, X is a large enough param-
eter that can be fixed taken into account the capacity constraints for
a particular agent, for instance the capacity of the lines feeding the
agent.
The DSM constraints for each agent, which regulate how the
loads can be shifted between periods, are expressed in the follow-
ing way:
Ue
n;t ¼ /n;t þ Ce
n;t 8t; 8n; 8e ð6Þ
Ue
n;t ¼ Hn;t þ
X
t0
Me
n;t0;t
X
t0
Me
n;t;t0 8t; 8n; 8e ð7Þ
Ce
n;t ¼ cn;t þ
X
t0
Me
n;t0;t
X
t0
Me
n;t;t0 8t; 8n; 8e ð8Þ
X
t0
Me
n;t;t0 6 cn;t 8t; 8n; 8e ð9Þ
Me
n;t;t0 ¼ 0 if
t ¼ t0
; ðaÞ
t þ k t0
or t0
þ k t 8n; 8e ðbÞ
(
ð10Þ
0 6 Ce
n;t 6 k /n;t 8t; 8n; 8e ð11Þ
kd 6 Ce
n;tþ1 Ce
n;t 6 kd 8t; 8n; 8e ð12Þ
In Eq. (6), the optimal demand Ue
n;t (variable) that is really con-
sumed in time period t, is expressed as the sum of fixed demand
/n;t (parameter) and Ce
n;t (variable) which represents the optimal
shiftable for node n in time period t. Total demand for node n
and period t is written in (7) in terms of the amount of energy that
is shifted from other periods t0
to the current period t; Me
n;t0;t, minus
the amount of energy that leaves period t to other period t0
; Me
n;t;t0 ,
for each node n and scenario e. Eq. (8) defines a similar relation
compared to (7) but in terms of the optimal shiftable demand. In
practice, either (7) or (8) should be used. Eq. (9) expresses the limit
for the total amount of energy that can be shifted to other time
periods. The variable Me
n;t;t0 also has to satisfy logical relationships
needed to model load shifting through parameter ‘‘k’’. Condition
(10a) assures that the demand cannot be shifted to the same time
period; condition (10b) sets that demand cannot be shifted more
than k periods forward and backward and it has to stand true 8t
and 8t0
. Finally, to allow for a smooth transition for the final
demand curve, some conditions are applied. These conditions are
represented by a bound in the demand that can be shifted and
bounds for the slope of the curve expressed by Eqs. (11) and (12)
respectively. Parameter k is set depending on the willingness of
the agent to shift the loads conditioned by the activities it develops
in its area. Parameter kd can be chosen taking into account opera-
tional constraints in the grid, like the capability of supporting
sharp demand changes between two consecutive time periods.
Generators modeling
The constraints and equations taken into consideration for
agents with non-renewable generators are given next:
CG;e
t;j ¼ lj PG;e
t;j þ ij vG;e
t;j þ fj yG;e
t;j þ 1j sG;e
t;j 8t; 8j; 8e ð13Þ
vG;e
t;j Pmin
g;j 6 PG;e
t;j 6 vG;e
t;j Pmax
g;j 8t; 8j; 8e ð14Þ
yG;e
t;j sG;e
t;j ¼ vG;e
t;j vG;e
t1;j 8t; 8j; 8e ð15Þ
Eq. (13) defines the generation cost for a non-renewable generator
based on the operational costs defined previously. Binary variables
vG;e
t;j =yG;e
t;j =sG;e
t;j are equal to 1 in case that during the current time per-
iod, the generator: Is already running/starts-up/shuts-down, and 0
in any other case. Eq. (14) establishes the power output technical
bounds, and (15) sets the relation among the binary variables which
represent start-up, shut-down and generator operation.
Renewable generators are modeled following the ideas pre-
sented in Section 4.1.
Fixed batteries modeling
For electric fixed batteries the following constraints are
included in the optimization problem:
0 6 Pd;e
b;t 6 yd;e
b;t Pd;max
b 8t; 8b; 8e ð16Þ
0 6 Pc;e
b;t 6 ð1 yd;e
b;t Þ Pc;max
b 8t; 8b; 8e ð17Þ
0 6 Se
b;t 6 Smax
b 8t; 8b; 8e ð18Þ
Se
b;t Se
b;t1 ¼ gC Pc;e
b;t 1=gD
ð Þ Pd;e
b;t 8t; 8b; 8e ð19Þ
Se
b;t0
¼ Se
b;tf
8b; 8e ð20Þ
Eqs. (16) and (17) models the bounds for the hourly maximum
and minimum power supplied and drawn from battery b; Pd;e
b;t and
Pc;e
b;t , through Pd;max
b and Pc;max
b . Binary variable yd;e
b;t ensures that the
battery is not charging and discharging at the same time. The bat-
tery SOC Se
b;t has to lie between 0 and a maximum value Smax
b
expressed in (18). Eq. (19) represents the energy balance for the
battery through charging and discharging efficiencies. Finally, Eq.
(20) guarantees that the initial and final SOCs, Se
b;t0
and Se
b;tf
respec-
tively, must be identical in order to avoid non-realistic solutions.
Electric vehicles modeling
The constraints that a controlled EV adds to the optimization
problem are similar to the constraints modeled by Eqs. (16)–(20)
described in Section 4.2.3. However, to comply with the standard
IEC 61851, charging and discharging power are modeled as semi-
continuous variables:
yd;e
v;t Pmin
v 6 Pd;e
v;t 6 yd;e
v;t Pmax
v 8t; 8v; 8e ð21Þ
yc;e
v;t Pmin
v 6 Pc;e
v;t 6 yc;e
v;t Pmax
v 8t; 8v; 8e ð22Þ
yc;e
v;t þ yd;e
v;t 6 1 8t; 8v; 8e ð23Þ
where binary variables yc;e
v;t and yd;e
v;t define if EV v is charging or dis-
charging. According to Eqs. (21)–(23) an EV is not allowed to charge
and discharge at the same time period, that is, if the variable repre-
senting charging power Pc;e
v;t is positive and different from zero then
the variable representing discharging power Pd;e
v;t is zero and vice
versa. In addition, charging and discharging power can take values
within the minimum and maximum power bounds, Pmin
v and Pmax
v
respectively.

In addition, two constraints are included representing the
mobility model adopted:
Se
v;te
¼ Smax
v 8v; 8e ð24Þ
Se
v;tmþ1 ¼ Se
v;tm
jtm
c # tm 2 TM; 8v; 8e ð25Þ
Eq. (24) states that EV SOC Se
v;t has to be maximum in period te. The
EV SOC is reduced according to (25) when it is moving during time
period tm, that is, in transition between two connections to the grid
[37,40].
Case study and results
To illustrate how the proposed method works, it is applied to a
case study for the SG depicted in Fig. 5. Different operating condi-
tions characterized by the number of periods that loads can be
shifted, parameter ‘‘k’’, are studied. The SG consist of 8 agents, with
2 renewable generators, 5 non-renewable generators, 2 batteries
and 14 EVs on a network based on the IEEE-37 bus distribution grid
[41].
In what follows, first the data for the case study are described
and second the main results regarding the questions posed in Sec-
tion 3 are presented and discussed.
Case study data
The data for the case study are: (i) the initial demand curve of
the agents, (ii) the scenario tree for energy prices and renewable
generation, and (iii) the parameters for the DSM constraints and
the models for the technical operation of the agents.
A typical demand curve from a real distribution grid is assumed
and selling/purchase prices are set to represent three different sce-
narios; hourly average historical values for prices [38] are defined
along with a high prices scenario, defined by the extreme value of
the blue bar, and a low prices scenario, defined by the extreme
value of the orange bar, and corresponding to the 110% and 90%
of the average prices respectively, Fig. 4. The sum of the hourly
demand along the 24 h of the day is constant although DSM oper-
ations can change the hourly values, that is, the demand is
rearranged.
Load buses, generators, batteries and EVs considered in the case
study are represented in Fig. 5, where grid areas belonging to the
seven defined SG agents are labeled with circled numbers. Another
agent, an EV aggregator, is responsible for providing the energy
needed by EV owners to perform their daily trips.
In relation to renewable generators, Fig. 6 shows the hourly
power output for the wind and the photovoltaic plants considered.
Note that 4 scenarios are used for each renewable source. Combining
them, 16 scenarios are obtained, representing typical situations.
The values of fe ¼ 0:15 and k ¼ 2:5 are relatively small and
have been considered in order to limit the load shifted without
implying non-realistic activities re-scheduling of the agents. Also,
we consider a maximum value of k = 12, because a larger value
implies in practical terms a great re-scheduling effort for agents,
and the solutions would have to be defined over intervals of more
than 24 periods (several days). The parameter kd is fixed to a value
of 0.75 kW considering the average amount of energy trade in the
system and the power capacity installed.
A total number of 14 EVs is considered here. For the EVs uncon-
trolled charging pattern, EVs charge at a rate of 3.7 kW [42,43] dur-
ing four time periods at the end of the day, as soon as they arrive
from the last journey of the day; then the EVs idle for the remain-
ing time periods. It is also considered that each EV performs two
journeys, called transitions, and each one is attached to a particular
time period. The assumption of two journeys per day and the
charging timing preference is a reasonable assumption as shown
for example in surveys like [44]. During transitions, EVs consume
a certain amount of energy equal to half the total EV individual
charging and they commute between the initial node represented
Fig. 4. Demand curve and price scenarios.
Fig. 5. IEEE 37-bus distribution case study.
Fig. 6. Renewable generators scenarios.

in Fig. 5 and the closest node, assumed for the purpose of this
work. Specifically, the battery consumption during journeys is
taken as 6.66 kWh for uncontrolled and controlled charging while
3.33 kWh is chosen for controlled charging with V2G allowed, as
described in next section. For an average energy consumption of
0.18 kWh/km, these values provide common daily travelled dis-
tances in European countries [37,40]. Maximum battery energy
level is 16.5 kWh [45] for each EV and charging and discharging
efficiencies are assumed to be 0.90 and 0.95 respectively. Table 2
shows the time periods for which either a transition or a charging
operation takes place as explained in Section 4.2.4. Uncontrolled
charging represents a probable charging pattern that EVs could fol-
low in absence of control or price signals and it constitutes a refer-
ence to compare with other operation strategies. Similar
approaches are found in [44,46].
In addition, a controlled operation where EVs respond to prices
is considered. The performed journeys, and battery energy con-
sumption, are the same as stated in Table 2 for uncontrolled charg-
ing, although the hourly charging power, and consequently the
SOC, will be different because they are variables in the correspond-
ing optimization procedure.
Case study results and discussion
In order to illustrate the performance of the proposed model,
some results referred to the final electricity load curve and EVs
charging with DSM strategies are presented. According to the ideas
presented in Section 3, the influence of parameter ‘‘k’’ on the
agents profits and costs is studied and the system performance is
analyzed in terms of active power losses and line apparent power
flows.
Firstly, the effect of the number of periods ‘‘k’’ that loads can be
shifted on flattening the demand curve is shown in Fig. 7. For four
different values of ‘‘k’’, the final electricity load curve is repre-
sented; obtained once the corresponding optimization problems
are performed for each agent according to the ideas presented in
Section 3. Results reveal that higher values of this parameter allo-
cate the demand more efficiently, in other words, the total grid
load is more uniformly distributed along time periods. Note that
the load is shifted from time periods when higher prices are
expected, for instance the end of the day, to time periods with
lower expected prices, e.g. night and some afternoon time periods.
To compare the final demand curve for different values of param-
eter ‘‘k’’, the standard deviation rk and demand range Dr
k, defined as
the difference between the hourly maximum and minimum values
of the demand, are given in Table 3. It is demonstrated that as the
value of ‘‘k’’ is increased the standard deviation and demand range
are reduced and, on that account, the load curve is flatter.
The combined impact of EVs and DSM strategies on the load
curve is analyzed next. For EVs operating under uncontrolled
charging, considering the charging pattern given in Table 2, the
demand peak is increased with respect to the initial load curve
when DSM is not applied, Fig. 8. When EVs are charged responding
to hourly prices, and DSM is performed at the same time, the load
shifting makes it possible to reduce the demand peak and flatten
the final load curve; shifting the charging to the night hours where
prices are more favorable.
If V2G is allowed, i.e. EVs discharge is permitted in the optimi-
zation problem, for a battery energy consumption in transitions
according to Table 2, no V2G is finally carried out. This result can
be justified taking into account that the particular EV constraints
are satisfied if the SOC of the EVs is high enough to perform the
arranged journeys and V2G. In other words, if consumption in tran-
sitions and the maximum SOC for EVs are of similar magnitude,
there is no flexibility for allowing V2G in a economical way. If con-
sumption in transitions is reduced to one half of the initial consid-
ered amount, V2G takes place in the most favorable time periods,
Fig. 9. Similar results could have been obtained increasing the
capacity of the battery of the EVs and keeping the previous battery
energy consumption in journeys.
Regarding EVs behavior, the SOC for EV1 vehicle, when different
strategies are applied, is depicted in Fig. 10. For uncontrolled
charging, the EV charges at the end of the day until maximum bat-
tery energy level. In case controlled charging is considered, the EV
charges during night hours taking advantage of better buying
prices. Additionally, if V2G is available, the EVs discharges at time
periods t20 and t21 when higher selling prices are expected provid-
ing additional profits.
Finally, some economical and technical aspects of the proposed
approach, profits/costs of the agents and system performance, are
presented. For different values of the parameter ‘‘k’’, total income,
Table 2
Electric vehicle connection pattern for uncontrolled charging.
EVs Transitions Charging periods
EV1–EV4 t7; t19 t20; t21; t22; t23
EV5–EV6 t8; t19 t20; t21; t22; t23
EV7 t8; t18 t19; t20; t21; t22
EV8–EV9 t8; t15 t16; t17; t18; t19
EV10–EV11 t9; t20 t21; t22; t23; t24
EV12 t9; t19 t20; t21; t22; t23
EV13–EV14 t9; t18 t19; t20; t21; t22
Fig. 7. Daily electricity load curves for several values of k.
Table 3
Standard deviation and demand range for different values of k.
k 0 3 6 9 12
rk (kW) 264.99 203.40 144.93 94.74 74.81
Dr
k (kW) 769.69 556.58 414.40 324.40 241.56
Fig. 8. Daily electricity load curves with EVs charging.

costs of non-renewable generation and costs of the energy bought,
considering all the involved agents, are represented in Fig. 11.
Although non-renewable generation cost increase as ‘‘k’’ grows,
the income and costs of the energy bought increase and decrease
respectively at a higher peace. Hence, the overall agents profit is
improved through DSM utilization.
From the technical point of view, total active losses slightly
decrease as parameter ‘‘k’’ gets higher while average maximum
line apparent power is reduced up to a certain limit, Fig. 12. The
effect of DSM in losses is important at first but the variation is
not very clear based on the value of ‘‘k’’ so that the power flow
in lines is of similar magnitude in the different cases. However,
the grid is less stressed during the last hours of the day when
DSM is applied but high values of ‘‘k’’ can provoke the opposite
behavior.
In regard to EVs, in Fig. 13, total EVs charging costs and EVs dis-
charging income are represented for the different cases considered.
When EVs charge under the uncontrolled approach the average
costs for an EV full charge can be estimated in 22.30 € while in con-
trolled charging with and without V2G are roughly 9.90 € and
9.25 € respectively. Thus, DSM offers clear benefits to owners of
EVs although the V2G use deserves a deeper consideration due to
the small difference in charging prices.
Conclusion
A SG model relying on DSM strategies has been proposed. In this
model, agents are modeled through optimization problems, with
the possibility of flattening of the daily electricity load curve, shift-
ing the demand from one time period to other time periods in
response to hourly prices. It has been shown that it can be applied
to common grid loads and EVs charging, helping to allocate the
demand more efficiently.
The particular characteristics of the load curve, the require-
ments for EVs mobility, as well as the hourly prices configuration,
have been taken into account. Some input data of the model have
to be chosen to allow for a suitable management of load shifting
and EVs charging from each agent’s point of view, achieving a bet-
ter use of the existing infrastructure through a reduction in losses
and line power flows. For instance, small values of parameter ‘‘k’’,
around 3 or 4 time periods, allow to maximize the expected profits
or to minimize the costs of the agents and to improve the shape of
the load curve. Results have shown that the deviations with
respect to the mean for the final load curve can be decreased more
than 70% with a significant reduction between the hourly maxi-
mum and minimum values of the demand.
V2G capabilities have been also considered, thus including the
possibility of obtaining additional profits for EVs owners and
reducing the demand in time periods with high demand. The effect
Fig. 9. Daily electricity load curves with V2G allowed.
Fig. 10. State of charge for different strategies EV 1.
Fig. 11. Total income and costs.
Fig. 12. Total losses and maximum power.
Fig. 13. Income and costs.

of the EVs on the load curve for the case study presented is small
and bigger fleets of EVs have to be considered to improve the flat-
tening of the load curve.
Acknowledgment
The authors would like to acknowledge the financial support
from the Ministerio de Economía y Competitividad through Project
ENE-2011-27495 and from the Junta de Andalucía through
Proyecto de Excelencia with Ref. 2011-TIC7070.
References
[1] Farhangi H. The path of the smart grid. IEEE Pow Energy Mag 2010;8:18–28.
[2] Blumsack S, Fernández A. Ready or not, here comes the smart grid! Energy
2012;37:61–8.
[3] Gellings C. The smart grid: enabling energy efficiency and demand
response. Fairmont Press; 2009.
[4] Huang D, Billinton R. Effects of load sector demand side management
applications in generating capacity adequacy assessment. IEEE Trans Pow
Syst 2012;27:335–43.
[5] Kostková K, Omelina L, Kycina P, Jamrich P. An introduction to load
management. Electr Pow Syst Res 2013;95:184–91.
[6] Albadi M, El-Saadany E. Demand response in electricity markets: an overview.
In: IEEE power engineering society general meeting, June 2007. p. 1–5.
[7] Rahimi F, Ipakchi A. Demand response as a market resource under the smart
grid paradigm. IEEE Trans Smart Grid 2010;1:82–8.
[8] Palensky P, Dietrich D. Demand side management: demand response,
intelligent energy systems, and smart loads. IEEE Trans Ind Inf 2011;7:381–8.
[9] EU Commission Staff Working Document: incorporing demand side flexibility,
in particular demand response, in electricity markets; 2013. http://
ec.europa.eu/.
[10] Logenthiran T, Srinivasan D, Shun TZ. Demand side management in smart grid
using heuristic optimization. IEEE Trans Smart Grid 2012;3:1244–52.
[11] Strbac G. Demand side management: benefits and challenges. Energy Policy
2008;36:4419–26.
[12] International Energy Agency – Annual Report, 2012. http://www.ieadsm.org/
.
[13] Siano P. Demand response and smart grids: a survey. Renew Sustain Energy
Rev 2014;30:461–78.
[14] Smart Grid Global Impact Report, 2013. http://www.smartgridimpact.com/.
[15] Smart Grids Proyects Portal, 2013. https://portal.smartgridsprojects.eu/.
[16] European Commission. A policy framework for climate and energy in the
period from 2020 to 2030; 2014. http://ec.europa.eu/.
[17] Gyamfi S, Krumdieck S. Price, environment and security: exploring multi-
modal motivation in voluntary residential peak demand response. Energy
Policy 2011;39:2993–3004.
[18] Kinhekar N, Padhy NP, Gupta HO. Multiobjective demand side management
solutions for utilities with peak demand deficit. Int J Electr Pow Energy Syst
2014;55:612–9.
[19] Gudi N, Wang L, Devabhaktuni V. A demand side management based
simulation platform incorporating heuristic optimization for management of
household appliances. Int J Electr Pow Energy Syst 2012;43:185–93.
[20] Conejo A, Morales J, Baringo L. Real-time demand response model. IEEE Trans
Smart Grid 2010;1:236–42.
[21] Samadi P, Mohsenian-Rad A-H, Schober, R, Wong, V, Jatskevich J. Optimal real-
time pricing algorithm based on utility maximization for smart grid. In: First
IEEE international conference on smart grid communications
(SmartGridComm); October 2010. p. 415–20.
[22] Jiang L, Low S. Multi-period optimal energy procurement and demand
response in smart grid with uncertain supply. In: 50th IEEE conference on
decision and control and european control conference (CDC-ECC); December
2011. p. 4348–53.
[23] Mercurio A, Di Giorgio A, Quaresima A. Distributed control approach for
community energy management systems in presence of storage. In: 20th
Mediterranean conference on control automation (MED); July 2012. p. 1303–8.
[24] Darabi Z, Ferdowsi M. Aggregated impact of plug-in hybrid electric vehicles on
electricity demand profile. IEEE Trans Sustain Energy 2011;2:501–8.
[25] Shao S, Pipattanasomporn M, Rahman S. Grid integration of electric vehicles
and demand response with customer choice. IEEE Trans Smart Grid
2012;3:543–50.
[26] Sheikhi A, Bahrami S, Ranjbar A, Oraee H. Strategic charging method for
plugged in hybrid electric vehicles in smart grids; a game theoretic approach.
Int J Electr Pow Energy Syst 2013;53:499–506.
[27] Wang Z, Wang S. Grid power peak shaving and valley filling using vehicle-to-
grid systems. IEEE Trans Pow Deliv 2013;28:1822–9.
[28] Oviedo RM, Fan Z, Gormus S, Kulkarni P. A residential {PHEV} load
coordination mechanism with renewable sources in smart grids. Int J Electr
Pow Energy Syst 2014;55:511–21.
[29] López M, Martín S, Aguado J, de la Torre S. V2G strategies for congestion
management in microgrids with high penetration of electric vehicles. Electr
Pow Syst Res 2013;104:28–34.
[30] Masoum A, Deilami S, Moses P, Masoum M, Abu-Siada A. Smart load
management of plug-in electric vehicles in distribution and residential
networks with charging stations for peak shaving and loss minimisation
considering voltage regulation. IET Gener Transm Distrib 2011;5:877–88.
[31] Stadler M, Krause W, Sonnenschein M, Vogel U. Modelling and evaluation of
control schemes for enhancing load shift of electricity demand for cooling
devices. Environ Modell Softw 2009;24:285–95.
[32] Brown RE, Koomey JG. Electricity use in california: past trends and present
usage patterns. Energy Policy 2003;31:849–64.
[33] Tso GK, Yau KK. A study of domestic energy usage patterns in Hong Kong.
Energy 2003;28:1671–82.
[34] Shaw R, Attree M, Jackson T, Kay M. The value of reducing distribution losses
by domestic load-shifting: a network perspective. Energy Policy
2009;37:3159–67.
[35] López M, Martín S, Aguado J, de laTorre S. Optimal microgrid operation with
electric vehicles. In: Innovative smart grid technologies (ISGT). Europe
(UK): Manchester; 2011. p. 1–8.
[36] López M, Martín S, Aguado J, de la Torre S. Market-oriented operation in
microgrids using multi-agent systems, in: Power engineering, energy and
electrical drives (POWERENG), Torremolinos (Spain); May 2011. p. 1–6.
[37] García Valle R, Peças Lopes JA, et al. Electric vehicle integration into modern
power networks. Springer; 2013.
[38] REE, information system of the system operator in the spanish electricity
market (E-SIOS).. http://www.esios.ree.es; [Last access September 2013].
[39] Fortuny-Amat J, McCarl B. A representation and economic interpretation of a
two-level programming problem. J Oper Res Soc 1981;32:783–92.
[40] Soares F, Lopes JP, Rocha P. A stochastic model to simulate electric vehicles
motion and quantify the energy required from the grid. In: 2011 Power system
computation conference (PSCC), Stockholm (Sweden), 2011.
[41] IEEE 37-bus Distribution Feeder. http://ewh.ieee.org/soc/pes/dsacom/
testfeeders; [Last update August 2013].
[42] Yilmaz M, Krein P. Review of charging power levels and infrastructure for
plug-in electric and hybrid vehicles. In: 2012 IEEE international electric
vehicle conference (IEVC); 2012. p. 1–8.
[43] Lopes JP, Soares F, Almeida P. Integration of electric vehicles in the electric
power system. Proc IEEE 2011;99:168–83.
[44] Mobile energy resources in grids of electricity (MERGE) deliverable D1.1, 2010.
http://www.ev-merge.eu/.
[45] Mitsubishi motors UK. http://www.mitsubishi-cars.co.uk/; 2014 [Last
access April 2014].
[46] Clement-Nyns K, Haesen E, Driesen J. The impact of charging plug-in hybrid
electric vehicles on a residential distribution grid. IEEE Trans Power Syst
2010;25:371–80.

Demand-side management in smart grids with electric vehicle load shifting

Recommended

Recommended

More Related Content

Similar to Demand-side management in smart grids with electric vehicle load shifting

Similar to Demand-side management in smart grids with electric vehicle load shifting (20)

Recently uploaded

Recently uploaded (20)

Demand-side management in smart grids with electric vehicle load shifting