Available via license: CC BY 4.0
Content may be subject to copyright.
energies
Article
Model Predictive Control for Efficient Management of Energy
Resources in Smart Buildings
Francesco Simmini 1,* , Tommaso Caldognetto 1,2 , Mattia Bruschetta 3, Enrico Mion 3and Ruggero Carli 1,3
Citation: Simmini, F.; Caldognetto,
T.; Bruschetta, M.; Mion, E.; Carli, R.
Model Predictive Control for Efficient
Management of Energy Resources in
Smart Buildings. Energies 2021,14,
5592. https://doi.org/10.3390/
en14185592
Academic Editor: Maria Carmela
Di Piazza
Received: 29 July 2021
Accepted: 1 September 2021
Published: 7 September 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1Interdepartmental Centre Giorgio Levi Cases, University of Padova, Via Francesco Marzolo 9,
35131 Padova, Italy; tommaso.caldognetto@unipd.it (T.C.); carlirug@dei.unipd.it (R.C.)
2
Department of Management and Engineering, University of Padova, Stradella S. Nicola 3, 36100 Vicenza, Italy
3Department of Information Engineering, University of Padova, Via Giovanni Gradenigo 6/B,
35131 Padova, Italy; mattia.bruschetta@dei.unipd.it (M.B.); enrico.mion.1@phd.unipd.it (E.M.)
*Correspondence: francesco.simmini@unipd.it
Abstract:
Efficient management of energy resources is crucial in smart buildings. In this work,
model predictive control (MPC) is used to minimize the economic costs of prosumers equipped
with production units, energy storage systems, and electric vehicles. To this purpose, the predictive
control manages the available energy resources by exploiting future information about energy prices,
absorption and production power profiles, and electric vehicle (EV) usage, such as times of departure
and arrival and predicted energy consumption. The predictive control is compared with a rule-based
technique, herein referred to as a heuristic approach, that acts in an instant-by-instant fashion without
considering any future information. The reported results show that the studied predictive approach
allows one to achieve charging profiles that adapt to variable operating conditions, aiming at optimal
performances in terms of economic cost minimization in time-varying price scenarios, reduction
of rms current stresses, and recharging capability of EV batteries. Specifically, unlike the heuristic
method, the MPC approach is proven to be capable of efficiently managing the available energy
resources to ensure a full recharge of the EV battery during nighttime while always respecting all
system constraints. In addition, the proposed control is shown to be capable of keeping the peak
power absorption from the grid constrained within set limits, which is a valuable feature in scenarios
with widespread adoption of EVs in order to limit the stress on the electrical system.
Keywords:
efficient management; energy resources; heuristic approach; model predictive control;
nanogrid; smart buildings
1. Introduction
The deregulation of the electric power industry has recently become a topic of attention
for investors, regulators, and other participants who aim to achieve decarbonization in
the energy sector and a more efficient use of energy [
1
]. In this context, smartgrids allow
the enhancement of the efficiency of electricity utilization from the points of generation to
the end users, and they enable the participation of prosumers on the demand side. Home
nanogrids usually consist of renewable energy sources (RESs) and energy storage systems
(ESSs) that can be used to store or release power when needed. Electric vehicles (EVs) using
electricity produced by renewable sources appear as a promising solution for a sustainable
transportation sector in the near future [
2
–
6
]. EVs use rechargeable battery packs to store
the energy needed for propulsion. Smart buildings can be equipped with charging points
where EV batteries can be recharged, for example, during nighttime [
7
]. On the other hand,
concerns have been raised that are related to the peak power required to allow a proper
recharge of EV batteries [4].
In this field, demand response (DR) will play an important role in the coordination of
energy production and consumption by prosumers [
8
,
9
]. DR programs can be categorized
as (i) incentive-based, where measures affect prosumers’ behavior by providing incentives,
Energies 2021,14, 5592. https://doi.org/10.3390/en14185592 https://www.mdpi.com/journal/energies
Energies 2021,14, 5592 2 of 18
or (ii) price-based, where electricity price variations are used to induce the prosumers to
correspondingly adapt their electricity usage [
10
–
12
]. Under this latter category, time of
use (TOU) and real-time pricing (RTP) are the most commonly adopted approaches to
retail pricing [
9
,
13
]. With TOU, electricity prices are changed in order to follow the shape
of the demand (e.g., higher prices during peak-load periods), while with RTP, prices are
modified to follow the trends of the electricity market.
In such a scenario, the flexible and efficient management of prosumers’ energy re-
sources is crucial in order to make DR a win–win solution for both the electrical system and
the prosumers. The implementation of an efficient management system can be achieved
through the development of advanced control strategies that aim to increase the demand
flexibility and to minimize the economic expenditures of prosumers [
14
]. In this con-
text, model predictive control (MPC) [
15
,
16
] represents one of the most promising control
methodologies for achieving an efficient management of users’ resources. MPC is an
advanced control strategy whose aim is to minimize an objective function over a prediction
horizon while always satisfying a set of system constraints; due to its versatility, it has
been largely adopted in applications in power systems [
17
–
23
]. For example, in [
24
], an
MPC method was developed for a microgrid equipped with photovoltaic (PV) sources
and ESSs while taking both the economic expenditure given by the power exchange with
the upstream grid and the battery’s wear cost into account in the objective function. In
that work, the results of the MPC were studied with respect to the difference between the
purchase and sale prices, but the electricity price was kept constant. Varying electricity
prices were considered in [
25
], in which an energy management system based on MPC
was developed and experimentally tested. The experimental infrastructure was located at
the FlexElec Laboratory in the University of Nottingham, and it comprised an ESS and PV
panels. The target of the MPC was to minimize the electricity bill. In the study, particular
attention was given to the economic performance of the predictive control as different
parameters were varied, such as the ESS capacity and the PV size. In [
26
], the economic
MPC developed was compared with a simple control method that was implemented in a
rule-based manner. The performances of the developed MPC for different price scenarios
were investigated in the paper, and it was underlined that, when compared with simple
control solutions, the MPC presented advantages with time-varying prices and that such
advantages increased as the energy price variability rose.
In this work, the predictive control is used to efficiently manage a home nanogrid
equipped with a PV source, an ESS, and a connection to the upstream grid, with the specific
task of recharging the battery of an EV while fulfilling all of the operational constraints. A
typical scenario that assumes that the EV battery is recharged overnight to take advantage
of the lower prices commonly applied by retailers is considered. By exploiting predictions
of absorption and generation profiles, energy prices, times of departure and arrival of the
EV, and daily EV battery energy consumption, the predictive control manages the available
energy resources with a twofold aim:
• Minimizing the economic costs of the system;
•
Fully charging the EV battery during nighttime while respecting the maximum ex-
changed power constraints at the point of connection with the grid.
The MPC is compared with a simple control method called the heuristic approach that,
unlike the MPC, manages the system in a rule-based fashion without taking any future
information into account. The two control strategies are compared by considering two
different perspectives. The first one regards the economic performances of the approaches
in two different price scenarios—a flat TOU rate and a steep TOU rate. In this context,
the MPC proves to be a better solution than the heuristic approach because it achieves
lower economic costs with greater economic savings for the steep TOU rate, which is
characterized by a high purchase-price variability. In addition, rms current stresses are
reduced thanks to the MPC approach. The second perspective regards the functionality
of the control methods: the MPC is capable of fully recharging the EV battery during
nighttime in scenarios in which the heuristic method is not. This merit is due to the
Energies 2021,14, 5592 3 of 18
smart management allowed by the MPC approach, which is shown to be capable of fully
exploiting the available resources while still satisfying all system constraints.
The organization of the paper is as follows. In Section 2, the system model of the
nanogrid considered is reported. The heuristic approach is described in Section 3.
Section 4
describes the proposed energy management system based on MPC. In Section 5, the
MPC approach and the heuristic method are compared by considering the economic
costs obtained in a seven-day simulation period, while Section 6proposes a functional
comparison between the two control approaches. The conclusions are reported in
Section 7
.
2. System Model
The smart building under consideration is provided with a nanogrid that connects the
energy sources and loads, as shown in Figure 1. The nanogrid is composed of:
•
Connection with the upstream grid with which the nanogrid exchanges power
Pg
.
The maximum power that can be requested from the grid is denoted by
Pg,max
, which
is assumed to be greater than 0 W.
• Photovoltaic (PV) sources, which generate the output power Ppv.
• Loads, which absorb power Pl.
•
An energy storage system (ESS), which generates power
Pst
and has a capacity
Est,N
,
maximum discharging power
Pst,max
, and maximum charging power
Pst,mi n
. The
capacity range of the ESS is given by the closed interval [Est,min,Est,m ax ].
•
An electric vehicle battery (EVB), which generates power
Pev
and has a capacity
Eev,N
.
In this paper,
Pev
is assumed to be non-positive (
Pev ≤
0), i.e., the EVB can not provide
power to the other system resources. The closed interval
[Eev,min ,Eev,max ]
represents
the capacity range of the EVB.
EVB
ESS
PV
Figure 1. Smart building: power values under consideration.
Both the ESS and the EVB are modeled as a dynamic discrete-time system with
∆T
as
sampling interval:
E+
st =Est −∆T Pst ,E+
ev =Eev −∆T Pev , (1)
where
Est
and
Eev
are the stored energy in the ESS and EVB, respectively, with superscript
+referring to the value of the variable at the following time.
The model of the system with
Pst
and
Pev
as inputs can be summarized in the following
discrete-time equation:
E+
st
E+
ev=1 0
0 1Est
Eev+−∆T0
0−∆TPst
Pev . (2)
According to Figure 1, the power balance equation of the nanogrid is given in
the following:
Pl=Ppv +Pst +Pev +Pg. (3)
Energies 2021,14, 5592 4 of 18
3. Heuristic Approach
In this paper, the proposed MPC strategy is compared with a rule-based technique,
which is called the heuristic approach hereinafter.
When the EV is connected to the nanogrid (i.e., during nighttime), the heuristic method
devotes all the available resources to the charging process of the EVB; to this purpose, at
each time step, given the current value of the battery’s state of charge
Eev
, by exploiting
(1)
,
the signal ¯
Pev is computed as:
¯
Pev =Eev −Eev,max
∆T. (4)
When the EV is not connected to the nanogrid (i.e., during daytime), signal
¯
Pev becomes:
¯
Pev =0 W . (5)
The heuristic method manages the ESS to achieve
Pg=
0, if possible; at each time step,
it compares the values of Ppv and Pl−¯
Pev :
•
If
Ppv ≤Pl−¯
Pev
, the shortage of power is satisfied by the ESS; when the ESS does not
have enough power capacity or it is empty, the approach computes the grid power
Pg
to satisfy the excess demand. Then:
–If Pgis lower than or equal to Pg,max, the EV charging power is given by:
Pev =¯
Pev ; (6)
–If Pgexceeds Pg,max , the grid power is set to satisfy the upper bound limit:
Pg=Pg,max , (7)
and the resulting EV charging power is yielded by (3):
Pev =Pl−Ppv −Pst −Pg; (8)
•
If
Ppv >Pl−¯
Pev
, the excess power is stored in the ESS; in case the ESS is full or does
not have sufficient power capacity, the unused power is diverted into the grid. As far
as the EVB is concerned, because, in this case, the following inequality holds:
Pg≤0<Pg,max , (9)
the actual power absorbed by the battery is given by:
Pev =¯
Pev . (10)
It is worth noting that, at each time step, the computed power
¯
Pev
is a fictitious signal;
the actual EVB charging power Pev is equal to ¯
Pev if Pg≤Pg,max.
The steps of the heuristic approach are shown in Figure 2.
Energies 2021,14, 5592 5 of 18
no yes
no
no
yes yesno
noyes yes
no yes
Figure 2. Heuristic approach: flowchart.
4. Model Predictive Control
Model predictive control is an advanced model-based control strategy whose aim
is to optimize the evolution of a system over a future time span. At each sampling time,
the predictive control computes the control signal by minimizing a cost function over a
prediction horizon while taking system constraints into account. Only the first input of
the signal is applied; then, the model state is updated and the optimization operation is
iterated by adopting a receding horizon strategy.
In the proposed energy management system formulation, the MPC exploits future
information about the expected power absorption and generation profiles, energy prices,
times of departure and arrival of the EV, and daily EVB energy consumption with the
aim of:
• Minimizing the overall economic costs of the system;
• Managing the system to achieve a full recharge of the EVB overnight.
In this paper, a particular case is considered in which future information about pro-
duction and absorption profiles, departure and arrival times of the EV, and daily EVB
Energies 2021,14, 5592 6 of 18
energy consumption is assumed to be known, as the target is to highlight the advantages
that can potentially be obtained by exploiting predictive approaches. Studying how pre-
diction errors may degrade the performance of the MPC procedure will be the target of
future work.
4.1. Cost Function
The MPC computes the control inputs that minimize the cost function
J
over a predic-
tion horizon Np:
min
{Pst(k),Pev(k)}J=Je−Jf, (11)
with
Je=∆T
Np
∑
k=1cp(k)max(Pg(k), 0) + cs(k)min(Pg(k), 0) + cESS|Pst (k)|, (12)
and
Jf=cfEst(Np). (13)
Je
is the economic cost over the prediction horizon and is given by the sum of the
following three terms:
•
The first term is the cost of purchasing energy;
cp
is the purchase price, and is measured
in EUR/kWh.
•
The second term is the cost of selling energy (this term is negative, resulting in a
positive revenue); csis the sale price, and is measured in EUR/kWh.
•
The third term weighs the degradation of the ESS with the coefficient
cESS
, which is
measured in EUR/kWh and will be defined in Section 4.3. This term considers the
economic cost due to the wear of the storage unit.
The term
Jf
represents an economic value that is proportional to the final state of
charge of the ESS in the prediction horizon via the positive coefficient
cf
, which is measured
in EUR/kWh. High values of
cf
may lead to a fully charged ESS at the end of the prediction
horizon, whilst low values lead to an empty ESS. The best setting of this coefficient depends
on the price scenario under consideration and aims to mitigate the effect of a limited
prediction horizon on the economic cost.
From (1), the following equation holds:
Est(Np) = Est (0)−∆T
Np
∑
k=1
Pst (k). (14)
Then, the cost function Jcan be written as follows:
J=∆T
Np
∑
k=1cp(k)max(Pg(k), 0) + cs(k)min(Pg(k), 0) + cESS|Pst (k)|+cfPst(k). (15)
4.2. System Constraints
The MPC minimizes the cost function in
(15)
in the prediction horizon under the
following constraints for the ESS:
(Est,min ≤Est ≤Est,max
Pst,mi n ≤Pst ≤Pst,max
. (16)
Considering the EVB constraints, when the EV is connected to the nanogrid (i.e.,
during nighttime), the following constraints hold:
Energies 2021,14, 5592 7 of 18
Eev,min ≤Eev ≤Eev,max
Eev(Td,i) = Eev,max
Pev ≤0
, (17)
where
Td,i
refers to the departure time of the EV at the end of the
i
-th nighttime period;
in this way, the MPC procedure ensures, if possible, a full EVB at the departure time.
Otherwise, when the EV is not connected to the nanogrid (i.e., during daytime), the
following equality constraint holds:
Pev =0 . (18)
As regards the grid power, the MPC optimizes the system under the following in-
equality constraint:
Pg≤Pg,max . (19)
4.3. Estimating the Economic Cost of ESS Wear
In the literature dealing with the economic optimization tasks for ESSs, a term in
the cost function is usually added with the aim of preserving the life expectancy of the
storage. In this paper, a common approach is adopted that consists of including a term
that is proportional to the absolute value of the ESS’s exchanged output power in the cost
function [
18
]. The coefficient
cESS
in
(15)
is defined as the ratio between the ESS price and
the total energy throughput bearable by the ESS in its whole usable life:
cESS =CESS
2NcyEst,N
, (20)
where
CESS
is the cost of the ESS,
Ncy
is its expected cycle lifetime, and
Est,N
is its capacity.
It is worth noting that since the aim of the MPC is to fully charge the EVB during night-
time with the constraint
Pev ≤
0, no EVB degradation cost is included in the cost function
(15)
; the inclusion of a battery degradation cost would not modify the
optimization results.
5. Economic Comparison
In this section, the economic performances of the MPC and the heuristic method are
compared by considering different price scenarios. The first price scenario considers a
TOU tariff with low purchase-price variations, and it is based on rates that are currently
available in Italy. The second tariff considers typical Australian TOU rates with a high
purchase-price variation between nighttime and daytime.
The nanogrid under consideration is provided with an ESS with a nominal capacity
of 13.5 kWh and maximum output power of 4 kW, which corresponds to a commercial
size for the considered application [
27
]; it is assumed that the ESS can be used in the range
[Est,min ,Est,max ]
, where
Est,min
and
Est,max
are equal to 2 and 13.5 kWh, respectively. The
ESS is assumed to have an expected lifetime of 5000 cycles and a cost of 7030 EUR, which
means that cESS =0.0521 EUR/kWh.
The EV is provided with a battery with a nominal capacity of 42 kWh, which is an
average and representative value considering the current storage capacities of EVs of
small/medium
size [28]
. The EVB can be used in the range
[Eev,min ,Eev,max ]
, where
Eev,min
and
Eev,max
are equal to
6
and 42 kWh, respectively. A typical scenario is considered in
which the driver leaves home in the morning and returns home in the afternoon or in
the evening. The times of departure and arrival of the EV and the corresponding battery
energy consumption during the week are reported in Table 1. An average consumption of
28.49 kWh per 100 statute miles is assumed, which is typical for the size of the considered
EV, considering a driver traveling, on average, about 33.40 statute miles per day [29]. It is
assumed that the EV connects to the nanogrid at the time of arrival.
Energies 2021,14, 5592 8 of 18
Table 1. The departure and arrival times and EVB energy consumption considered.
Day of the Week Departures Arrivals Energy Consumption
Wednesday 6 a.m. 18 p.m. 10.80 kWh
Thursday 6 a.m. 18 p.m. 7.20 kWh
Friday 6 a.m. 18 p.m. 10.80 kWh
Saturday 7 a.m. 21 p.m. 3.60 kWh
Sunday 7 a.m. 21 p.m. 19.80 kWh
Monday 6 a.m. 18 p.m. 10.80 kWh
Tuesday 6 a.m. 18 p.m. 3.60 kWh
In the simulations, the model sample time is 60 s, while the control sample time is
set to one hour for both the MPC and the heuristic method. The prediction horizon is set
to 24 h in the predictive controller; this choice represents a proper trade-off between the
reliability of predictions and energy cost minimization; shorter prediction horizons would
bring an increase in the economic costs.
The two control procedures are compared in a seven-day simulation period, where
the load and PV data refer to an installation of a rated load power of 3 kW and a rated
PV generation unit of 4 kW; the average daily energy absorbed by the loads is about
16.15 kWh/day, while the average daily PV energy generated is about 13.26 kWh/day.
5.1. Scenario 1: MPC—Flat Time-of-Use Rate
A TOU retail tariff typically applied in the Italian market is adopted in this
scenario [30];
it is characterized by a slightly varying purchase price based on three time intervals:
(i) high
consumption (midday hours), (ii) low consumption (nighttime), and (iii) weekends. Prices
in the second and third intervals usually coincide in the Italian market.
As regards the selling price, in Italy, a state-run net metering scheme for power
injections of small generators is employed; excess PV energy is sold at market price, and
then, at the end of the year, the prosumer receives a payment based on the injected and
absorbed energy [31].
In this price scenario, the coefficient
cf
is set to 0.17 EUR/kWh. It was verified that
both lower and higher values can bring an increase in the economic cost; with lower
values, the controller cannot exploit all of the available PV power to charge the ESS, while
with higher values, the discharge of the ESS when demand exceeds production cannot be
guaranteed, even in the case of the availability of energy in the ESS.
Figure 3shows the energy prices and the predictive control simulation results. The
cost of energy (Figure 3a) is 0.2642 EUR/kWh from 8 a.m. to 8 p.m. and 0.2424 EUR/kWh
from 8 p.m. to 8 a.m. on working days, while on the weekend, it is a constant signal that is
equal to 0.2424 EUR/kWh. The sale price changes on a daily basis, with small variations.
In the simulations, it was assumed that the sale price for the upcoming day is known at
4 p.m.; in case of an unknown sale price at a specific time in the prediction horizon, the
controller is fed with an average value based on the three previous days.
Energies 2021,14, 5592 9 of 18
(a) Purchase and sale prices
(b) Power
(c) State of charge of the ESS
(d) State of charge of the EVB
Figure 3. MPC results with the flat TOU rate in a simulation of one week.
Energies 2021,14, 5592 10 of 18
Power profiles are given in Figure 3b, while the states of charge of the ESS and the
EVB are reported in Figure 3c,d, respectively (in Figure 3d, the time interval in which the
EV is not connected to the nanogrid is shaded). It can be observed that that the ESS charges
if the production exceeds the load during the daytime, while during the nighttime, power
is driven from the ESS to the EVB, if possible (e.g., during the night between Saturday
and Sunday); if the ESS cannot provide enough energy to charge the EVB, the predictive
control purchases the required energy from the grid during the low-price periods. Notably,
the MPC proves to be able to fully charge the EVB by smartly managing available energy
resources with minimal economic expenditures.
5.2. Scenario 2: MPC—Steep Time-of-Use Rate
A tariff currently applied in the Australian electricity market is considered in this
scenario [
32
]. It is characterized by a high variability in purchase price based on the
following time intervals: (i) peak (midday hours), (ii) shoulders (morning, late evening,
and weekend), and (iii) off-peak (nighttime). Furthermore, Australian retailers apply
a daily charge between 0.90 and 1.20 AUD/day; in this case, a daily supply charge of
1.10 AUD/day is considered. As regards the selling price, in Australia, a flat rate that varies
between 0.09 and 0.12 AUD/kWh is adopted; here, a sale price
cs
equal to 0.12 AUD/kWh
is applied. In the tests performed, an exchange rate of 0.6 EUR/AUD is considered.
In this price scenario, the coefficient
cf
is set to 0.15 EUR/kWh. As described above,
both lower and higher values can lead to an increase in the economic cost.
Figure 4reports the simulation results for the MPC approach. On working days,
the purchase price is 0.2376 EUR/kWh from 3 p.m. to 9 p.m. (peak), 0.1295 EUR/kWh
from
7 a.m.
to 3 p.m. and from 9 p.m. to 10 p.m. (shoulder), and 0.1086 EUR/kWh from
10 p.m.
to 7 a.m. (off-peak). On the weekends, it is 0.1295 EUR/kWh from 7 a.m. to
10 p.m.
(shoulder) and 0.1086 EUR/kWh from 10 p.m. to 7 a.m. (off-peak). The sale price is a
constant signal that is equal to 0.072 EUR/kWh.
Differently from the previous price scenario, on Wednesday, the ESS charges during
the off-peak time, thus exploiting the grid with the aim of satisfying the daytime demand
during the peak price period, since the ESS is empty at the beginning of the considered
period and the controller predicts a lack of generation in the prediction horizon; this is due
to the daily purchase price difference, which is higher than 2
cESS
[
26
]. It is worth noting
that the ESS is used only to satisfy the demand during the peak period of the working days,
while on the shoulders and off-peak times, the grid is exploited to satisfy the load and to
charge the EVB. Unlike in the previous scenario, there is no power transfer from the ESS to
the EVB. This happens because, at the shoulder and off-peak times, the difference between
the purchase and selling prices is lower than 2
cESS
; the use of the ESS would increase the
economic costs with respect to the solution of exploiting the grid to charge the EVB due to
the cost of wear of the storage. Similarly to scenario 1, the MPC buys energy to charge the
EVB during the lowest price period (from 10 p.m. to 7 a.m.).
Energies 2021,14, 5592 11 of 18
(a) Purchase and sale prices
(b) Power
(c) State of charge of the ESS
(d) State of charge of the EVB
Figure 4. MPC results with the steep TOU rate in a simulation of one week.
Energies 2021,14, 5592 12 of 18
5.3. Simulation with the Heuristic Approach
Figure 5reports the simulation results for the heuristic method. The same results are
achieved for the two price scenarios considered, since the implementation of the algorithm
of the heuristic approach does not depend on energy prices. During the daytime, when
production exceeds absorption, excess PV power is diverted into the ESS or, if the storage is
full, into the grid. Instead, when the PV power is lower than the load, the deficit is satisfied
by the ESS or, if empty, by the grid. At the arrival time, the heuristic approach uses all of
the available resources to charge the EVB, and then exploits the power provided by the ESS
with an upper bound of 4 kW and that of the grid with an upper bound of 3 kW. As seen
with the MPC, during the nighttime, the heuristic method is capable of fully recharging the
EVB before the next departure time.
(a) Power
(b) State of charge of the ESS
(c) State of charge of the EVB
Figure 5. Results of the heuristic approach in a simulation of one week.
Energies 2021,14, 5592 13 of 18
5.4. Economic Costs
In this subsection, the performances of the predictive control and the heuristic method
are evaluated by comparing the economic costs achieved in the simulations reported above.
The economic costs for the MPC and the heuristic approach in the considered price
scenarios are reported in Table 2; the overall economic cost consists of the three terms
defined in Section 4.1:
1. Energy purchase: cost of energy purchase,
2. Energy sale: cost of energy sale (this term is negative),
3. ESS wear: economic cost due to the wear of the ESS,
as well as the charge, which comes from a fixed daily value of 0.66 EUR/day in Scenario 2,
while in Scenario 1, there is no charge.
Table 2. Economic costs in the considered interval of one week.
Control Methodology Scenario 1: Flat TOU Rate Scenario 2: Steep TOU Rate
Purchase Sale ESS Charge Overall Purchase Sale ESS Charge Overall
MPC (EUR) 22.13 −0.09 4.24 0 26.28 12.53 −1.65 2.74 4.62 18.24
Heuristic approach (EUR) 22.69 −0.09 4.23 0 26.83 15.68 −0.08 4.23 4.62 24.45
As far as the overall economic costs are concerned, the economic savings of the MPC
compared to the heuristic strategy are 2.05% in Scenario 1 and 25.40% in Scenario 2, rising
up to 31.32% if the charge is not considered. The performance of the MPC increases with
the increase in the daily price variability. In Scenario 1, which is characterized by a low
daily variability of the purchase price, low savings are achieved, while in Scenario 2, much
greater savings are achieved due to the high variation in the purchase price.
The MPC proves to be a better solution than the heuristic technique because it obtains
lower economic costs by smartly managing available energy resources. Notably, such smart
control actions are not possible with techniques that act in an instant manner, such as the
heuristic approach considered here. It is worth remarking that the economic advantages
obtained increase as the daily price variability rises [26].
Statistical results from the different cases are shown in Figure 6; the MPC substantially
exhibits the advantage of providing lower
I2
g
(which is related to network losses) and
lower
I2
st
and
I2
ev
(which are associated with battery degradation and converter losses) with
respect to the heuristic method.
Figure 6.
Statistical results in the considered interval of one week:
Ig=Pg/Vg,N
,
Ist =Pst/Vst,N
,
Iev =Pev/Vev,N
,
Vg,N
= 230 V,
Vst,N
= 50 V,
Vev,N
= 400 V.
Vg,N
,
Vst,N
, and
Vev,N
refer to the nominal
voltage of the grid, the ESS, and the EVB, respectively.
Energies 2021,14, 5592 14 of 18
6. Functional Comparison
In this section, the MPC approach and the heuristic method are compared from a
functional perspective. As in the example in the previous section, a seven-day simulation
period is considered. The ESS and the EVB have the same characteristics as those introduced
in Section 5. The planned schedule of departures and arrivals of the EV is provided in
Table 3
. Unlike in the example in the previous section, a much greater discharge of the EV
battery in three days of the week (i.e., Friday, Saturday and Sunday) is considered. During
the daytime, the EV is assumed to exploit all available energy stored in the battery (36 kWh).
Table 3.
Functional comparison: planned departure and arrival times and EVB energy consumption.
Day of the Week Departures Arrivals Energy Consumption
Wednesday 6 a.m. 18 p.m. 10.80 kWh
Thursday 6 a.m. 18 p.m. 7.2 kWh
Friday 6 a.m. 21 p.m. 36 kWh
Saturday 7 a.m. 22 p.m. 36 kWh
Sunday 7 a.m. 20 p.m. 36 kWh
Monday 6 a.m. 18 p.m. 10.80 kWh
Tuesday 6 a.m. 18 p.m. 3.60 kWh
In the tests performed here, the control sample time is set to one hour for both control
approaches; the MPC is implemented with a one-day prediction horizon. As far as the grid
power is concerned, Pg,max is set to 3 kW.
In the simulations, the average daily energy absorbed by the loads is about
16.15 kWh/day
,
while the average daily energy generated by the PV panels is about 16.76 kWh/day.
Figure 7shows the simulation results for the MPC approach in the flat TOU rate
scenario. It is worth noting that, on Friday, Saturday, and Sunday, MPC successfully
manages the energy resources (i) to fully charge the EVB during the nighttime and (ii) to
respect the upper bound of 3 kW for the maximum power absorbed from the grid. On
the one hand, during the daytime on Friday and Sunday, since there is lack of production,
the predictive controller uses the grid to charge the ESS until reaching the state of charge
that ensures a full EVB at the departure time of the following day. On the other hand, on
Saturday, the MPC smartly manages available resources by exploiting the grid to satisfy
the demand in the afternoon with the aim of leaving enough energy for nighttime charging
in the ESS.
Figure 8shows the simulation results for the heuristic approach. It is worth noting
that, unlike the MPC, the heuristic approach is not able to ensure a full EVB before the
departure times on Saturday, Sunday, and Monday. In detail, at the arrival time on Friday
and Sunday, the ESS is empty, so it cannot provide energy to the EVB during the next
night. On Saturday, the heuristic approach badly manages the ESS, since it exploits the
stored energy in the afternoon before the arrival time of the EV; the remaining energy at the
arrival time is not enough to guarantee a full EVB on Sunday morning. As a consequence
of poor resource management, there is a decrease in the mileage with respect to what is
planned (Table 3) on Saturday and Sunday because the driver has to satisfy the lower
bound constraint of the EVB (6 kWh). Indeed, differently from the MPC case, the actual
EVB energy consumption obtained with the heuristic method decreases by about 26% on
Saturday and 9% on Sunday. It is worth remarking that, in this scenario, an economic
comparison between the MPC and the heuristic method would be meaningless, as the
mileage of the EV is different in the two cases.
In the above example, the heuristic approach shows the functional disadvantage of not
being able to fully charge the EVB during the nighttime; on the other hand, this is possible
through the use of predictive control techniques that manage the available resources by
exploiting future information. The previous example highlights the potential for MPC in
future contexts, since, by smartly managing available energy resources, it can guarantee
Energies 2021,14, 5592 15 of 18
the desired functionalities, which cannot be always ensured by simple heuristic techniques.
Moreover, while satisfying the additional requirements of EV charging, the MPC is shown
to be capable of keeping the peak power absorption from the grid constrained within
nominal limits, which is an aspect of relevant concern considering the expected widespread
use of electric vehicles.
(a) Purchase and sale prices
(b) Power
(c) State of charge of the ESS
(d) State of charge of the EVB
Figure 7.
Functional comparison: results of the MPC with the flat TOU rate in a simulation of
one week.
Energies 2021,14, 5592 16 of 18
(a) Power
(b) State of charge of the ESS
(c) State of charge of the EVB
Figure 8. Functional comparison: results of the heuristic approach in a simulation of one week.
7. Conclusions
This paper shows the application of model predictive control for the efficient manage-
ment of prosumers’ energy resources in the presence of local energy storage capabilities
and an electric vehicle (EV). The aim of the predictive control developed here is the mini-
mization of the economic cost with the constraint of ensuring a full EV battery at departure
times. The proposed predictive approach is compared with a heuristic method that man-
ages the available resources in an instantaneous rule-based manner. The simulation results
show that, on the one hand, the MPC provides lower costs in scenarios in which both
strategies are able to fully charge the EV battery during the night. On the other hand, it
can guarantee a full recharge in scenarios in which the heuristic method is not capable
of doing so. In summary, the simple scenario considered here allowed us to highlight
the remarkable advantages of using predictive approaches in such an application, even
while considering different energy pricing schemes. It is shown that the MPC algorithm,
through optimal management of the available resources, allows one to (i) to meet functional
Energies 2021,14, 5592 17 of 18
objectives, such as the full recharge of the EV battery, (ii) allow the economic management
of local resources, (iii) reduce rms current values at the interface with the mains and the
local energy storage system, and (iv) keep the power exchanged with the mains within
nominal ranges.
Future developments of the presented research may include the study of the effect of
prediction errors on the performance of the MPC procedure and a sensitivity analysis of
the MPC’s performance as different parameters vary (e.g., length of the prediction horizon,
energy storage capacities, PV system size).
Author Contributions:
Conceptualization, F.S., T.C., M.B., E.M. and R.C.; methodology, F.S. and T.C.;
software, F.S.; validation, F.S.; investigation, F.S. and T.C.; writing—original draft preparation, F.S.;
writing—review and editing, F.S., T.C., M.B. and E.M.; supervision, R.C. All authors have read and
agreed to the published version of the manuscript.
Funding:
This research was funded by the Interdepartmental Centre Giorgio Levi Cases, University
of Padova, NEBULE project.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Erdinc, O.; Paterakis, N.G.; Mendes, T.D.P.; Bakirtzis, A.G.; Catalão, J.P.S. Smart Household Operation Considering Bi-Directional
EV and ESS Utilization by Real-Time Pricing-Based DR. IEEE Trans. Smart Grid 2015,6, 1281–1291. [CrossRef]
2.
Tushar, W.; Yuen, C.; Huang, S.; Smith, D.B.; Poor, H.V. Cost Minimization of Charging Stations With Photovoltaics: An Approach
With EV Classification. IEEE Trans. Intell. Transp. Syst. 2016,17, 156–169. [CrossRef]
3.
Shi, Y.; Tuan, H.D.; Savkin, A.V.; Duong, T.Q.; Poor, H.V. Model Predictive Control for Smart Grids With Multiple Electric-Vehicle
Charging Stations. IEEE Trans. Smart Grid 2019,10, 2127–2136. [CrossRef]
4.
Wang, L.; Qin, Z.; Slangen, T.; Bauer, P.; van Wijk, T. Grid Impact of Electric Vehicle Fast Charging Stations: Trends, Standards,
Issues and Mitigation Measures—An Overview. IEEE Open J. Power Electron. 2021,2, 56–74. [CrossRef]
5.
Pavi´c, I.; Pandži´c, H.; Capuder, T. Electric vehicle based smart e-mobility system—Definition and comparison to the existing
concept. Appl. Energy 2020,272, 115153. [CrossRef]
6.
Bellocchi, S.; Klöckner, K.; Manno, M.; Noussan, M.; Vellini, M. On the role of electric vehicles towards low-carbon energy
systems: Italy and Germany in comparison. Appl. Energy 2019,255, 113848. [CrossRef]
7.
Jian, L.; Xue, H.; Xu, G.; Zhu, X.; Zhao, D.; Shao, Z.Y. Regulated Charging of Plug-in Hybrid Electric Vehicles for Minimizing
Load Variance in Household Smart Microgrid. IEEE Trans. Ind. Electron. 2013,60, 3218–3226. [CrossRef]
8.
IRGC. Demand-Side Flexibility for Energy Transitions: Ensuring the Competitive Development of Demand Response Options; Technical
Report; International Risk Governance Council (IRGC): Lausanne, Switzerland, 2015.
9.
Palensky, P.; Dietrich, D. Demand Side Management: Demand Response, Intelligent Energy Systems, and Smart Loads. IEEE
Trans. Ind. Inform. 2011,7, 381–388. [CrossRef]
10.
Haider, H.T.; See, O.H.; Elmenreich, W. A review of residential demand response of smart grid. Renew. Sustain. Energy Rev.
2016
,
59, 166–178. [CrossRef]
11.
Wang, Z.; Gu, C.; Li, F.; Bale, P.; Sun, H. Active Demand Response Using Shared Energy Storage for Household Energy
Management. IEEE Trans. Smart Grid 2013,4, 1888–1897. [CrossRef]
12.
Asadinejad, A.; Tomsovic, K. Optimal use of incentive and price based demand response to reduce costs and price volatility.
Electr. Power Syst. Res. 2017,144, 215–223. [CrossRef]
13.
Eid, C.; Koliou, E.; Valles, M.; Reneses, J.; Hakvoort, R. Time-based pricing and electricity demand response: Existing barriers
and next steps. Util. Policy 2016,40, 15–25. [CrossRef]
14.
Kong, W.; Luo, F.; Jia, Y.; Dong, Z.Y.; Liu, J. Benefits of Home Energy Storage Utilization: An Australian Case Study of Demand
Charge Practices in Residential Sector. IEEE Trans. Smart Grid 2021,12, 3086–3096. [CrossRef]
15. Wang, L. Model Predictive Control System Design and Implementation Using MATLAB; Springer: London, UK, 2009.
16. Maciejowski, J.M. Predictive Control with Constraints; Prentice Hall: Harlow, UK, 2002.
17.
Raimondi Cominesi, S.; Farina, M.; Giulioni, L.; Picasso, B.; Scattolini, R. A Two-Layer Stochastic Model Predictive Control
Scheme for Microgrids. IEEE Trans. Control. Syst. Technol. 2018,26, 1–13. [CrossRef]
18.
Parisio, A.; Rikos, E.; Glielmo, L. A Model Predictive Control Approach to Microgrid Operation Optimization. IEEE Trans.
Control. Syst. Technol. 2014,22, 1813–1827. [CrossRef]
Energies 2021,14, 5592 18 of 18
19.
Qi, W.; Liu, J.; Christofides, P.D. Supervisory Predictive Control for Long-Term Scheduling of an Integrated Wind/Solar Energy
Generation and Water Desalination System. IEEE Trans. Control. Syst. Technol. 2012,20, 504–512. [CrossRef]
20.
Hu, J.; Xu, Y.; Cheng, K.W.; Guerrero, J.M. A model predictive control strategy of PV-Battery microgrid under variable power
generations and load conditions. Appl. Energy 2018,221, 195–203. [CrossRef]
21.
Lei, M.; Yang, Z.; Wang, Y.; Xu, H.; Meng, L.; Vasquez, J.C.; Guerrero, J.M. An MPC-Based ESS Control Method for PV Power
Smoothing Applications. IEEE Trans. Power Electron. 2018,33, 2136–2144. [CrossRef]
22.
Shan, Y.; Hu, J.; Li, Z.; Guerrero, J.M. A Model Predictive Control for Renewable Energy Based AC Microgrids Without Any PID
Regulators. IEEE Trans. Power Electron. 2018,33, 9122–9126. [CrossRef]
23.
Patrinos, P.; Trimboli, S.; Bemporad, A. Stochastic MPC for real-time market-based optimal power dispatch. In Proceedings of the
2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA,
12–15 December 2011
;
pp. 7111–7116.
24.
Guo, Y.; Sheng, S.; Anglani, N.; Lehman, B. Optimal Power Management for Grid-Connected Microgrid Considering Modelling
of Different Electricity Cost and Battery Degradation Cost. In Proceedings of the 2019 20th Workshop on Control and Modeling
for Power Electronics (COMPEL), Toronto, ON, Canada, 16–19 June 2019; pp. 1–7.
25.
Elkazaz, M.; Sumner, M.; Pholboon, S.; Davies, R.; Thomas, D. Performance Assessment of an Energy Management System for a
Home Microgrid with PV Generation. Energies 2020,13, 3436. [CrossRef]
26.
Simmini, F.; Agostini, M.; Coppo, M.; Caldognetto, T.; Cervi, A.; Lain, F.; Carli, R.; Turri, R.; Tenti, P. Leveraging Demand
Flexibility by Exploiting Prosumer Response to Price Signals in Microgrids. Energies 2020,13, 3078. [CrossRef]
27. Tesla Powerwall. 2021. Available online: https://www.tesla.com/powerwall (accessed on 18 February 2021).
28.
Rivera, S.; Kouro, S.; Vazquez, S.; Goetz, S.M.; Lizana, R.; Romero-Cadaval, E. Electric Vehicle Charging Infrastructure: From
Grid to Battery. IEEE Ind. Electron. Mag. 2021,15, 37–51. [CrossRef]
29.
Plötz, P.; Jakobsson, N.; Sprei, F. On the distribution of individual daily driving distances. Transp. Res. Part Methodol.
2017
,
101, 213–227. [CrossRef]
30.
Torriti, J. Price-based demand side management: Assessing the impacts of time-of-use tariffs on residential electricity demand
and peak shifting in Northern Italy. Energy 2012,44, 576–583. [CrossRef]
31.
ARERA. DCO 322/2012/R/eel: Review of the Integrated text on “Scambio sul Posto” Measure [Revisione del Testo Integrato per lo Scambio
sul Posto]; ARERA: Milano, Italy, 2012.
32.
Australian Government. Energymadeeasy. 2021. Available online: https://www.energymadeeasy.gov.au/ (accessed on
24 February 2021).
