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Independent Demand Side Management System
Based on Energy Consumption Scheduling by
NSGA-II for Futuristic Smart Grid
Prateek Mundra
Research Scholar
Electrical Engg. Deptt.
MANIT, Bhopal
prateek.mundra36@gmail.com
Shweta Mehroliya
Research Scholar
Electrical Engg. Deptt.
UIT RGPV, Bhopal
shwetamehroliya12@gmail.com
Anoop Arya
Associate Professor
Electrical Engg. Deptt.
MANIT, Bhopal
anooparya.nitb@gmail.com
Suresh Gawre
Assistant Professor
Electrical Engg. Deptt.
MANIT, Bhopal
sgawre28@gmail.com
Abstract—Best way to optimize the utilisation of resources
present in electricity grid is Demand Side Management.
Appropriate pricing strategies adopted by the utilities help to
decide user level consumption. Electricity pricing helps the user
in minimising electricity payment by independently scheduling
its appliances usage time and hours in a day. This paper presents
a smart grid situation with existence of a single utility and
multiple consumers. Here we have considered that the utility
adopts time of day pricing strategy. In smart grid, the Demand
Side Management is considered to be multi objective
optimization problem. For a schedule with efficient energy
consumption, the peak to average ratio of total energy demand,
the total energy costs and the every user’s individual daily
electricity charges should be minimised. This paper used NSGA-
II, an advance form of genetic algorithm for solving the multi-
objective optimization problem in order to obtain an optimum
schedule for user’s energy consumption. Simulation results
confirm that by adopting optimum consumption schedule, peak-
to-average ratio of the total energy demand gets reduced and
electricity usage charge can also be reduced successfully. Results
prove that individual user bill can be reduced upto 15% by
adopting the proposed technique, which is a remarkable amount
in terms of today’s electricity bills.
Keywords—Energy Management; Demand Side Management;
Smart Grid; Energy Consumption Scheduling; Smart
Metering; NSGA-II.
I.
INTRODUCTION
The power system should be efficient, reliable and well
within economic constraints after incorporation of renewable
energy resources in order to keep it stable. Existing grid tends
to become instable after integration of large number of electric
machines [1]. During peak hours, demand curve of any
traditional grid is will exhibit very high peak, caused by use of
heavy loads. Thus, to fulfil the peak demand a new power
plant needs to be installed. Generally, thermal power plants are
installed. Excessive usage of them marks high emissions of
Green House Gases (GHGs) [2], which causes a serious
environmental concern. To reduce peak time power
consumption in smart grid, Demand side management is used.
Basic agenda of smart grid is to provide reliable, efficient,
environmental friendly and economic power system [3, 4].
DSM covers all the programs implemented by utilities to
either directly or indirectly have an impact on consumers’
power consumption behaviour. This is done to decrease the
Peak-to-Average Ratio (PAR) of the total load in the smart
grid [5]. Smart grid is used to automate energy management
system on basis of information collected from energy
providers and consumers. Hence load management and energy
efficiency is improved [6]. DSM provides incentives to all
those consumers who shift their loads from peak to off-peak
hours. This results in noteworthy reduction in PAR. The
design aim of residential DSM programs is to either reduce
consumption or shit consumption or even both in majority of
cases [7]. Consumption reduction can be achieved by users by
encouraging energy aware consumption patterns and by
construction of more energy efficient buildings. In spite of
this, there is need for real world solutions by shifting high-
power household appliances to off-peak hours in order to
reduce peak-to-average ratio (PAR) while considering load
demand [8].
An effective tool with utility company is pricing. It is used
to control and shape electricity consumption of users [9].
Some well-known option for the same are: critical-peak
pricing (CPP), day ahead pricing (DAP), time-of-use pricing
(TOU), and real-time pricing (RTP).
In this paper, NSGA II and DAP strategy is worked on in
order to optimize demand response. It’s done by encouraging
consumers to re-scheduling their demand from peak to off-
peak hours. Particularly, a case with three residential
consumers is considered where every user has numerous shift
able and non-shift able electrical devices. This paper,
considered DSM as a multi-objective optimization problem.
Desired objective is minimization of PAR for utility and
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minimization of energy cost is considered for consumers. An
efficient way to tackle the objective is by using Non
Dominated Sorting Genetic Algorithm II (NSGAII). The
DSM proposed here can be applied conveniently on smart grid
with smart metering components along with communicating
units to control system of utility/power company and
consumers through LAN [10].
Paper organisation: The system model is offered in Section
II. Section III describes the formulation of centralized
problem. Section IV presents the NSGA II approach for
distributed designing. Section V explains the proposed
algorithm. Simulation results are provided in Section VI.
Conclusion is drawn in Section VII.
II.
SMART
GRID
SYSTEM
MODEL
Here a smart grid network with its required facilities to
solve the DSM as a multi-objective optimization problem is
illustrated. The used energy cost model is also given. Based
on these definitions, optimization problems are formulated in
Section III.
Fig. 1. Smart grid system model
A. Model of Power System
Our work is centred on the model that considers a single
utility suppling power to a set of consumers in presumed smart
grid scenario. Same is explained in Fig. 1.
Presented model show a scheme with one utility (i.e., the
power company) and multiple users is taken into account. We
have assumed here that each user is fitted with a smart meter
that contains an Energy Consumption Scheduler (ECS) ability
in order to schedule household energy consumption. The
outgoing power lines from energy source are connected to
smart meters, which are subsequently interconnected through
LAN. The power company and users are all connected to each
other. LAN is used for message exchanges among the smart
meters. Fig. 2 shows users may have the appliances that are
not time shift able. The energy consumption scheduling for
non-shift able appliances is not effected by ECS function.
Fig. 2. Description of Operation of Smart Meter including ECS capability
Consider denotes set of users and number of users be
||=N. For every consumer n , let ݈
denote total load at
hour ‘h’ = {1, 2 ... H} and H=24. To maintain generality,
it is implicit that time granularity is one hour. Daily load for
user ‘n’ is signified by݈
ൌሼ݈
ଵ
ǥ݈
ሽ. Total load connected at
user end at each hour of the day can be calculated as
ܮ
ൌσ݈
ఢQ
(1)
Daily peak and average load levels are computed by
ܮ
ൌ݉ܽݔ
ఢ?
ܮ
ሺʹሻ
ܮ
௩
ൌ
ଵ
ு
σܮ
ఢ?
ሺ͵ሻ
Hence, PAR of load demand is
ܲܣܴ ൌ
ೌೖ
ೌೡ
ൌ
ு௫
ച?
σ
ച?
ሺͶሻ
B. Energy cost model
Cost of generating/distributing electricity by energy
source at each hour h is defined by a cost function
asܥ
ሺܮ
ሻ . Generally, the cost of same load can differ at
different hours of day. Particularly, cost is less at night
contrasted to day time.
Cost function is defined as,
ܥ
ሺܮ
ሻൌܽ
ܮ
ଶ
ܾ
ܮ
ܿ
ሺͷሻ
Where ܽ
Ͳ and ܾ
ǡܿ
Ͳ can be changed at each hour.
III.
PROBLEM
FORMULATION
For every user n , let ‘An’ denotes set of household
appliances like washing machine, fridge, dish-washer, AC,
PHEV etc. For each appliance energy consumption scheduling
vector is defined as
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ܺ
ǡ
ൌሼݔ
ǡ
ଵ
ǥݔ
ǡ
ு
ሽሺሻ
here, scalar ࢞
ǡࢇ
ࢎ
symbolizes single hour energy
consumption planned for appliance ‘a’ by user ‘n’ at hour ‘h’.
The total load of nth user is calculated as
ࢎ
ൌσݔ
ǡ
ǡ݄ א ܪ
א
ሺሻ
In the design illustrated in Fig. 1, for nth user the optimal
energy consumption (vector xn) for each appliance (‘a’ An)
is determined using ECS function in a smart energy meter.
User’s daily load profile is shaped due to (7). Subsequently,
feasible choices of energy consumption scheduling vectors is
identified based on user’s energy needs.
En,a denotes pre-calculated total daily energy
consumption for every user n and every appliance a An.
Same has been exemplified in [11]. To reduce energy cost or
PAR we don’t intend to alter the amount of energy
consumption, rather energy consumption is systematically
managed and shifted in this paper.
In our case, flexible selection of time interval for
scheduling the appliances is provided, i.e. beginning ߙ
ǡ
א
ܪ and the end ߚ
ǡ
אܪof a time intervalሺߙ
ǡ
൏ߚ
ǡ
).
Example, in order to have it’s PHEV ready before going to
work, ߙ
ǡ
ൌͳͳPM and ߚ
ǡ
ൌͺAM can be selected by user.
Thus, certain constraints are imposed on vector xn,a.
Predetermined daily consumption is equal to hours for which
appliance can be scheduled, given by
σݔ
ǡ
ൌܧ
ǡ
ఉ
ǡೌ
ୀఈ
ǡೌ
ሺͺሻ
And
ݔ
ǡ
ൌ Ͳǡ݄ א ܪ̳ܪ
ǡ
ሺͻሻ
here,ܪ
ǡ
ൌሼߙ
ǡ
ǥߚ
ǡ
ሽ. User should provide a time
interval which is either greater than or equal to time interval
required to complete operation. Example, consider a PHEV
with normal charging time 3 hours [11]; thus,ߙ
ǡ
െߚ
ǡ
͵. (8) and (9) clearly portrays that, cumulative sum of daily
energy consumption of connected appliances/loads is equal to
total energy consumed by all appliances/loads in the system
for 24 hours. Thus, following energy balance relationship
always holds true,
σܮ
אு
ൌσσ ܧ
ǡא
ఢQ
ሺͳͲሻ
A. PAR Minimization
Substituting (1), (7), (8), and (9) in (4), PAR in terms of
energy consumption scheduling vectors x1...xN can be re-
written as
ு ௫
אಹ
ሺσσ ௫
ǡೌ
ೌചಲאQ
ሻ
σσ ா
ǡೌೌചಲאQ
ሺͳͳሻ
Generally, a low PAR is favoured. With ample knowledge
about users’ requirements, consumption pattern and smart
grid, an efficient energy consumption scheduling can be
written off as,
݉݅݊
௫
אǡאQ
ு௫
אಹ
ሺσσ ௫
ǡೌ
ೌചಲאQ
ሻ
σσ ா
ǡೌೌചಲאQ
ሺͳʹሻ
Considering optimisation variables x1...xN, H and
σσ ܧ
ǡఢ
אQ
are fixed. Thus can be omitted from
objective function and equation (12) is re-written as,
݉݅݊
௫
אǡאQ
݉ܽݔ
אு
ሺσσ ݔ
ǡ
ఢ
אQ
ሻ
ሺͳ͵ሻ
B. Energy cost minimization
Proposed energy cost model can be used as an efficient
energy consumption scheduling for minimizing energy costs
of every user. This is stated by,
݉݅݊
௫
אǡאQ
σܥ
ு
ୀଵ
ሺσσ ݔ
ǡ
ఢ
אQ
ሻ
ሺͳͶሻ
Because the proposed energy cost model is a convex
combination of energy cost of each user; therefore, the total
cost becomes minimum when the cost of each user becomes
minimum. By considering the objective functions Eq. 13 and
Eq. 14, a multi-objective optimization problem is defined that
considers the benefit of utility and users also. An intelligent
optimization approach like as NSGAII can solve this
problem easily.
IV.
THE
NSGA-II
A set of optimal solutions (fundamentally known as
Pareto-optimal solutions) are obtained in place of a single
optimal solution because of a multi-objective problem.
Absence of any additional information, can’t result in one of
the Pareto optimal solutions better over other. Thus, a user
must obtain as many Pareto optimal solutions as feasible. By
putting emphasis on a particular Pareto-optimal solution at a
time, classical optimization methods (including the multi-
criterion decision-making methods) gets converted to single-
objective optimization problem [13-14]. When above method
is to be used for obtaining multiple solutions, it needs to be
applied numerous times with a hope of finding a different
solution for each simulation run.
It’s imprecise to obtain an optimum solution for a multi-
objective optimization problem, but a set of solutions can be
obtained in regard to several objective functions [15],[16]. To
solve this problem several methods have been generated till
date. Of them, some convert multi-objective optimization
problem to a single objective optimization problem. NSGA-II
has been proved applicable and robust in handling mixed
integer programs. Pareto optimal sets are a set of non-
dominated solutions of multi-objective optimization problem.
These solutions don’t dominate on each other in regard to
different objective functions.
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V.
PROPOSED
ALGORITHM
Initialise the population. After initialisation, sort the
population based on non-domination into each front.
Example, in current population first front is an entirely non-
dominant set and second front is dominated by individuals in
first front only and fronts are further created similarly. Every
individual in very front is allotted a rank (fitness) value which
is based on front to which they belong. Fitness value of 1 is
allotted to individuals in first front and fitness value of 2 is
assigned to individuals in second front and so on. Along with
fitness value, crowding distance (measure of how close an
individual is to its neighbours) is computed for every
individual. For better diversity in population, large average
crowding distance is desired.
Based on rank and crowding distance of binary tournament
selection, parents are selected from population. For an
individual to be selected, it’s rank should be lesser compared
to other or it’s crowding distance be greater compared to other.
Through crossover and mutation, selected population
generates off springs.
The existing population and existing off springs are sorted
again based on non-domination. Of them, only best N
individuals are nominated (‘N’ is population size).
Individual’s selection is dependent on rank and on-crowding
distance of last front.
VI.
SIMULATION
RESULTS
In the studied benchmark smart grid system we have
considered N=3 consumer/users. It is presumed that each user
has appliances with strict energy consumption scheduling i.e.,
non-shift able operations. Considered appliances may be
refrigerator (daily usage Average: 1.35 kWh, 1.4 kWh and 1.2
kWh for user 1, 2 and 3, respectively). Moreover, 2 shift able
appliances are selected for each user. Smart meter with ECS
capability can schedule appliances with soft energy
consumption scheduling only. Considered appliances can be
washing machine with daily usage Average: 1.1 kWh, 0.8
kWh and 1 kWh for user 1, 2 and 3, respectively, Water Heater
for at least 1-hour use in day with daily usage Average: 1kWh
for all 3 user. In our simulation model, the user consumptions
are summarised in Table I.
T
ABLE
I. U
SER CONSUMPTIONS
’
MODEL
Appliance
consumption (kWh)
Appliance
No.
User No.
1 2 3
Refrigerator 1 1.35 1.4 1.2
Washing M/c 2 1.1 0.8 1
Water Heater 3 1 1 1
Fig. 3. Scheduled energy consumption and analogous cost with unused
ECS units. Here PAR is 1.53 and total daily cost is Rs. 31.98.
Fig. 4. Scheduled energy consumption and analogous cost when ECS units
are deployed. Here, PAR is 1.24 and total daily cost is Rs. 24.42.
For simulation model, assumptions include that load
demand is higher during evening hours and lower during night
hours. Therefore, each user has an arbitrarily chosen grouping
of the selected shift able and non-shift able loads to be run at
different times of day. Quadratic energy cost function is
assumed as in Eq. (5). To avoid complexities, assume
that ܾ
ൌܿ
ൌͲ
؞
݄ א ܪ . Also ܽ
ൌܴݏǤͲǤͲ͵Ȁܹ݄݇
ଶ
during day i.e., from 8:00 to 24:00 and ܽ
ൌܴݏǤͲǤͲʹȀܹ݄݇
ଶ
during night i.e., from 24:00 at night to 8:00.
A. Performance comparison
Figure 3 and Figure 4 depict simulation results on total
scheduled energy consumptions of ECS function in smart
grid, without and with smart meters, respectively.
On comparison of results in Figs. 3 and 4, it can be
observed that when ECS function is not implemented, value
0 5 10 15 20 25
0
2
4
6
8
10
Time (Hours)
Load (kWh)
0 5 10 15 20 25
0
0.5
1
1.5
2
2.5
3
Time (Hours)
Cost (Rs.)
0 5 10 15 20 25
0
1
2
3
4
5
6
7
8
Tim e (Ho urs)
Load(kWh)
0 5 10 15 20 25
0
0.5
1
1.5
2
Time (Hours)
Cost (Rs.)
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of PAR is 1.53 and value of energy cost is Rs. 31.98. But at
same time, when ECS function is implemented, value of PAR
reduces to 1.24 (i.e., 18% less) and value of energy cost
reduces to Rs. 24.42 (i.e., 23% less). In reality, for later case,
load is more evenly distributed across different hours of day.
Conversely, Fig. 5 shows pareto optimal front variation
between the resulting PAR with total energy cost when the
algorithm proceeds. A solution is said to belong to Pareto set
iff there is no other solution which can enhance at least one of
the objectives without worsening any other objective function.
Set of all Pareto optimal solutions are called Pareto optimal
set.
Fig. 5. Pareto optimal set of solutions
B. User payment
Proposed distributed DSM strategy is beneficial for every
end user because it leads to less total energy cost and lower
PAR in aggregate load demand. To observe this, daily
payment for all users are depicted in Fig. 6. It is clear that all
users will be paying considerably less to utility provided, ECS
is enabled in smart meter. Only in such a case users will
willing participate in proposed automatic DSM system.
Fig. 6. Cost Comparison for each user without and with optimization
In Fig. 8, PAR in every user’s load has been plotted, then
compared to the PAR in aggregate load across all the users.
For every user n , individual PAR is estimated by,
ܲܣܴ
ൌ
ு௫
ച?
σ
ച?
(15)
It can be seen in Fig.8 that the PAR in every user’s
individual load is significantly more than the PAR in
aggregate load. This confirms our discussion, it is not
necessary for the utilities to get the loads balanced
individually. It is opposite to design objective in real-time
pricing tariffs that expects every individual end user to shift
its consumption from peak to off-peak hours.
Fig. 7. PAR in every user’s individual every day load and its comparison
to PAR with aggregate load for all users.
VII.
CONCLUSIONS
This paper explains application of demand side
management (DSM) in a smart grid by formulating multi
objective optimization problem by means of NSGA-II. Major
objectives focused here are, reduction in both, peak to average
ratio of total energy demand and total energy cost. As the
objective function of the energy cost is a complex combination
of summation of individually demanded energy by users; the
optimal solution of DSM, which is derived using NSGA-II,
decreases the peak to average ratio of total energy demand and
charge from every user. Thus, utility companies and users are
willing to participate in proposed DSM.
A
CKNOWLEDGMENT
This Publication is an outcome of the R & D work undertaken
in the project under the Young Faculty Research Fellowship,
Visvesvaraya PhD Scheme of Ministry of Electronics &
Information Technology, Government of India, being
implemented by Digital India Corporation (formerly Media
Lab asia).
We would also like to show our gratitude to Maulana Azad
National Institute of Technology, Bhopal for providing us the
required facilities during the course of this research.
26.5 27 27.5 28 28.5 29 29.5 30 30.5 31 31.5
1.2
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
Cost (Rs.)
PAR
22.522.0 23.5 24.023.0 24.5 25. 0 25.5 26.0 26.5
21.5
1 2 3
0
2
4
6
8
10
12
User Number
Cost (Rs.)
cost before optimization
cost after optimization
11.5 22.5 3
1.25
1.3
1.35
1.4
1.45
User No .
PAR
PAR in aggregate load=1.24
individual PA R with ECS deploym ent
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