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Enhanced Differential Evolution Based Energy Management in Smart Grid

  • South West University Chongqing

Abstract and Figures

In this thesis, Home Energy Management System (HEMS) is presented using heuristic optimization techniques: Binary Particle Swarm Optimization (BPSO), Wind Driven Optimization (WDO), Genetic Algorithm (GA), Differential Evolution (DE), Enhanced DE (EDE), Teaching Learning (TL), and our proposed Enhanced Differential Genetic Evolution (EDGE) algorithm. This thesis mainly focuses to reduce energy expense and avoid peak formation in residential sector. Scheduling of household appliances is integral part of HEMS. The energy consumption behavior of appliances is evaluated by placing each appliance in separate class based on usage pattern: interruptible, non interruptible and hybrid loads. Moreover, mathematical model of some appliances is also proposed. The developed model along with optimization algorithms provide more appropriate solution to achieve given objectives. Real Time Pricing (RTP) scheme is used for electricity bill calculation. Simulation results show that scheduled energy cost and Peak to Average Ratio (PAR) in each class is less than that of unscheduled case.
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Enhanced Differential Evolution Based Energy
Management in Smart Grid
Naveed ur Rehman
MS Thesis
Electrical Engineering
COMSATS Institute of Information Technology
Islamabad Pakistan
Fall, 2016
Enhanced Differential Evolution Based Energy
Management in Smart Grid
A Thesis Presented to
COMSATS Institute of Information Technology, Islamabad
In partial fulfillment
of the requirement for the degree of
MS (Electrical Engineering)
Naveed ur Rehman
Fall, 2016
Enhanced Differential Evolution Based Energy
Management in Smart Grid
A Graduate Thesis submitted to Department of Electrical Engineering as partial
fulfillment of the requirement for the award of Degree of M.S (Electrical Engineering).
Registration Number
Naveed ur Rehman
Dr. Shahid A. Khan,
Department of Electrical Engineering,
COMSATS Institute of Information Technology (CIIT),
Islamabad Campus.
November 2016
Final Approval
This thesis titled
Enhanced Differential Evolution Based Energy
Management in Smart Grid
Naveed ur Rehman
has been approved
For the COMSATS Institute of Information Technology, Islamabad
External Examiner: ___________________________________
Supervisor: ________________________________________________
Dr. Shahid A. Khan
Professor, Department of Electrical Engineering,
CIIT, Islamabad
Co-Supervisor: ________________________________________________
Dr. Nadeem Javaid
Associate Professor, Department of Computer Science,
CIIT, Islamabad
HoD: _________________________________________________________
Dr. M. Junaid Mughal
Professor, Department of Electrical Engineering,
CIIT, Islamabad
I Mr. Naveed ur Rehman, CIIT/FA13-REE-090/ISB, hereby declare that I have
produced the work presented in this thesis, during the scheduled period of study. I
also declare that I have not taken any material from any source except referred to
wherever due that amount of plagiarism is within acceptable range. If a violation
of HEC rules on research has occurred in this thesis, I shall be liable to punishable
action under the plagiarism rules of the HEC.
Date: ____________________________
Signature of the student:
Naveed ur Rehman
It is certified that Naveed ur Rehman CIIT/FA13-REE-090/ISB has carried out all
the work related to this thesis under my supervision at the Department of
Electrical Engineering, COMSATS Institute of Information Technology,
Islamabad and the work fulfills the requirements for the award of the MS degree.
Date: ____________________________
Dr. Shahid A. Khan
Professor, Department of
Electrical Engineering,
Co- Supervisor:
Dr. Nadeem Javaid
Associate Professor,
Department of Computer
Science, Islamabad
Dr. M. Junaid Mughal
Professor, Department of Electrical Engineering.
This thesis is dedicated to my teachers, my family and my
I am heartily grateful to my supervisor, Dr. Shahid A. Khan and co-supervisor Dr. Nadeem
Javaid who not only guided me but also motivated me via insightful criticism from the beginning
to the final level that enabled me to complete this thesis.
I would like to acknowledge my family, my friends, and the cooperative COMSENCE lab
attendants. They all kept me motivated and energetic, and this work have not been possible
without them.
Finally, I offer my regard and blessing to everyone who supported me in any regard during the
completion of my thesis.
Naveed ur Rehman
Enhanced Differential Evolution Based Energy Management in
Smart Grid
In this thesis, Home Energy Management System (HEMS) is presented using heuristic
optimization techniques: Binary Particle Swarm Optimization (BPSO), Wind Driven
Optimization (WDO), Genetic Algorithm (GA), Differential Evolution (DE),
Enhanced DE (EDE), Teaching Learning (TL), and our proposed Enhanced
Differential Genetic Evolution (EDGE) algorithm. This thesis mainly focuses to
reduce energy expense and avoid peak formation in residential sector. Scheduling of
household appliances is integral part of HEMS. The energy consumption behavior of
appliances is evaluated by placing each appliance in separate class based on usage
pattern: interruptible, non interruptible and hybrid loads. Moreover, mathematical
model of some appliances is also proposed. The developed model along with
optimization algorithms provide more appropriate solution to achieve given objectives.
Real Time Pricing (RTP) scheme is used for electricity bill calculation. Simulation
results show that scheduled energy cost and Peak to Average Ratio (PAR) in each
class is less than that of unscheduled case.
1 Introduction 1
1.1 Introduction........................... 2
2 Related Work 5
3 Mathematical Approach and Modeling 12
3.0.1 User Priorities . . . . . . . . . . . . . . . . . . . . . . 13
3.0.2 Activity Level . . . . . . . . . . . . . . . . . . . . . . 13
3.0.3 Electricity Pricing . . . . . . . . . . . . . . . . . . . . 13
3.0.4 External Inputs . . . . . . . . . . . . . . . . . . . . . 14
3.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . 14
3.1.1 Objective Function . . . . . . . . . . . . . . . . . . . 14
3.1.2 Devices Operational Constraints: . . . . . . . . . . . 16
4 Heuristic Algorithms 19
4.0.1 BPSO .......................... 20
4.0.2 WDO .......................... 21
4.0.3 GA............................ 24
4.0.4 DE............................ 28
4.0.5 EDE........................... 32
4.0.6 TL............................ 32
4.0.7 EDGE.......................... 36
5 Simulations and Discussion 39
5.0.1 Scenario 1 . . . . . . . . . . . . . . . . . . . . . . . . 40 Energy Consumption Pattern and Electric-
ity Bill Reduction . . . . . . . . . . . . . . 40 PAR...................... 42
5.0.2 Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . 43 Energy Consumption Pattern and Electric-
ity Bill Reduction . . . . . . . . . . . . . . 44 PAR...................... 46
5.0.3 Schenario 3 . . . . . . . . . . . . . . . . . . . . . . . 47 Energy Consumption Pattern and Electric-
ity Bill Reduction . . . . . . . . . . . . . . 48 PAR...................... 48
5.1 Trade-Os............................ 51
6 Conclusion and Future Work 53
7 References 55
1.1 Abstract view of smart grid model . . . . . . . . . . . . . . . 4
4.1 Flow chart of BPSO . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Flow chart of WDO . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Flow chart of GA . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4 Flow chart of DE . . . . . . . . . . . . . . . . . . . . . . . . 30
4.5 Flow chart of EDE . . . . . . . . . . . . . . . . . . . . . . . 34
4.6 Flow chart of TL . . . . . . . . . . . . . . . . . . . . . . . . 36
4.7 Flow chart of EDGE algorithm . . . . . . . . . . . . . . . . 38
5.1 RTP tariff model . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Energy consumption of appliances . . . . . . . . . . . . . . . 42
5.3 Totalcost ............................ 43
5.4 Peak to average ratio . . . . . . . . . . . . . . . . . . . . . . 44
5.5 Energy consumption of appliances . . . . . . . . . . . . . . . 45
5.6 Totalcost ............................ 46
5.7 Peak to average ratio . . . . . . . . . . . . . . . . . . . . . . 47
5.8 Energy consumption of appliances . . . . . . . . . . . . . . . 49
5.9 Totalcost ............................ 50
5.10 Peak to average ratio . . . . . . . . . . . . . . . . . . . . . . 51
2.1 Related work summary . . . . . . . . . . . . . . . . . . . . . 10
2.1 Continue Table 2.1 . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Nomenclature .......................... 15
4.1 Parameter of BPSO . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 Parameter of WDO . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 Parameter of GA . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4 Parameter of DE . . . . . . . . . . . . . . . . . . . . . . . . 29
4.5 Parameter of TL . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1 Parameter of appliances . . . . . . . . . . . . . . . . . . . . 40
5.2 Comparison of cost . . . . . . . . . . . . . . . . . . . . . . . 42
5.3 Comparison of PAR . . . . . . . . . . . . . . . . . . . . . . . 44
5.4 Comparison of cost . . . . . . . . . . . . . . . . . . . . . . . 46
5.5 Comparison of PAR . . . . . . . . . . . . . . . . . . . . . . . 48
5.6 Comparison of cost . . . . . . . . . . . . . . . . . . . . . . . 49
5.7 Comparison of PAR . . . . . . . . . . . . . . . . . . . . . . . 50
Chapter 1
1.1 Introduction
A system that applies advance Information and Communication Technolo-
gies (ICT) in traditional grid is known as smart grid [1]. With the help
of smart grid, we are able to share information between energy supplier
and consumers. With the extensive use of heavy loads like Air Condi-
tioner (AC), Plug-in Hybrid Electric Vehicle (PHEV), water geezer, etc.
in residential sector, the energy demand during specific hours is consider-
ably increased. Hence, there is an intense need to develop such methods
which are beneficial for reducing peak demand. Demand Side Management
(DSM) greatly reduces green house gas emission by utilizing PHEV and
renewable energy. The main objective of DSM strategies is to efficiently
utilize given energy by taking necessary steps which encourage consumers
to flatten their load curve [2]. About 40% energy of the world is consumed
by the residential sector. Due to mismanagement in the use of available
energy in this sector, million of dollars are wasted. This huge amount of
money can be saved by using appropriate scheduling schemes that modify
the operation of different appliances according to price signal.
Different scheduling techniques are developed for scheduling residential ap-
pliances in such a way that these techniques ensure to flatten load curve.
This is done by shifting few appliances to off peak hours or by turning off
some appliances in these hours. In this way, peak load demand reduces to
sufficient level thereby, reducing Peak to Average Ratio (PAR) and total
energy cost. Our work focusses on different scheduling techniques by using
heuristic and stochastic algorithms for efficient management of energy to
achieve two goals: reducing peaks in peak hours and minimizing electricity
Existing mathematical optimization techniques such as linear Program-
ming (LP) [3], Nonlinear Programming (NP), Mixed Integer Non Linear
Programming (MINLP) and convex programming are not effective to tackle
above mentioned multi objective problems. These techniques are also in-
efficient when taking large number of controlling appliances for scheduling
because their computational time increases with increasing number of ap-
pliances. Modern heuristic techniques like Particle Swarm Optimization
(PSO), Ant Colony Optimization (ACO) and Genetic Algorithm (GA) out-
perform in complex multi-objective problems, however, still lack in terms
of accuracy and computational time. An advanced Differential Evolution
(DE) stochastic based optimization algorithm uses mutation, crossover and
population size was developed [4]. It has many attractive features com-
pared to previous evolutionary algorithms such as easy coding, simplicity,
good convergence speed and fewer control parameters, however, sometimes
its performance has slow convergence rate and less accuracy. To tackle the
problem with DE, Enhanced DE (EDE) is formulated in which several trial
vector generation strategies are improved. This modification increases its
accuracy as well as convergence rate [5].
In this thesis, we evaluate seven heuristic algorithms: GA, Wind Driven
Optimization (WDO), Binary PSO (BPSO), DE, EDE, TL and Enhanced
Differential Genetic Evolution (EDGE) to achieve the desired objectives
and compare their results. The three basic factors: energy consumption
pattern, total cost, and PAR are considered. On the bases of above men-
tioned factors, we compare the performance of each algorithm in three
different scenarios: interruptible, non interruptible and hybrid loads. The
hybrid loads contain both interruptible and non interruptible class of ap-
pliances. Many research works are still based upon the ways to improve
performance of these algorithms in order to make them compatible with
increasing demand. The rest of thesis is organized in seven chapters. The
first chapter discusses the existing work, chapter 2 presents related work,
mathematical approach and modeling is given in chapter 3. Heuristic al-
gorithms is discussed in chapter 4. Simulation results and trade-offs are
briefly discussed in chapter 5. The conclusion and future work is presented
in chapter 6. Finally,references are given in chapter 7.
Figure 1.1: Abstract view of smart grid model
Chapter 2
Related Work
The traditional power system confronted numerous challenges during last
two decades. The obsolete infrastructure, energy resources shortage, high
electricity demand as well as environmental aspect have affected the ef-
ficiency and reliability of traditional grid. The major source of energy
consumption is household appliances. Furthermore, with the invention of
PHEV [6], overall load on traditional grid increases because sufficient en-
ergy is consumed by PHEV. It also disturbs the balance between demand
and supply which causes numerous challenges to generating side i.e. black-
out, overloading and frequency drop. This demand supply gap is filled ei-
ther by searching alternate energy sources or by efficiently managing given
energy. The first solution increases overall electricity cost, however, man-
aging energy is an cost effective solution. In this regard, many researchers
around the world are working to optimally schedule smart appliances to
achieve above objectives. Some of the papers relating to appliance schedul-
ing are discussed as follow. The Direct Load Control (DLC) [7] is old form
of Energy Management System (EMS) in which consumer gives permis-
sion to utility to disconnect certain appliances in order to maintain energy
consumption within the threshold. Consequently, utility give benefits to
consumers by giving incentives and rebates. In past, various smart con-
trollers are used with the aim to minimize electricity cost. Nowadays, new
techniques including Home EMS (HEMS) can communicate with the users
through smart meters.
Authors investigate the problem of residential appliances scheduling in [8]
using Real Time Pricing (RTP) scheme. This paper derives by proposing
an automatic and optimal residential energy consumption technique which
tries to achieve favorable tradeoff between minimizing cost and inconve-
nience of both electrical and thermal appliances. They also considered
seasonal price variation. The results of proposed MINLP model prove to
be effective in terms of energy usage reduction, however, with the limita-
tions of high computational power.
In [9], the authors discuss the problem of peak demand during certain
hours. Authors introduce the concept of clustering and smart charging to
benefit consumers in terms of cost reduction. Aggregator’s duty is to ef-
ficiently utilize energy within cluster by automatically scheduling battery
and appliances. The results show that by appropriately scheduling storage
devices and carefully designing real time pricing, customers can get maxi-
mum saving on their electricity bills.
In [10], the authors present an analytical model based on recursive formula
to reduce peak demand. In this paper, four different scenarios for social
welfare model with the aim to reduce cost and peak demands is presented.
The results of proposed model efficiently calculate peak demand for finite
number of appliances.
The work in [11] provides an overview of BPSO technique, the basic con-
cepts, structure, variants as well as its application in power system opti-
mization problems. The authors in [12] propose an Improved PSO (IPSO)
technique for scheduling of home appliances. They consider Critical Peak
Pricing (CPP), Time of Use (TOU) and demand response signal to mini-
mize energy consumption cost and peak demand. In this paper, they ana-
lyze the effect of energy management on distribution transformer. Results
show that proposed scheduling algorithm reduce the need of large distri-
bution transformer. Moreover, results also prove that proposed algorithm
is an efficient solution to reduce cost and PAR.
In [13], GA is implemented to schedule appliances in order to manage en-
ergy consumption of residential sector along with the use of Supervisory
Control And Data Acquisition (SCADA). Energy management is done to
maintain balance between demand and supply by keeping energy consump-
tion within maximum power limits. Scheduler checks price signal to op-
timally schedule appliances in particular time slot. Moreover, case study
is carried out by using Intelligent Energy System Laboratory (LASIE). It
consists of three energy generation sources i.e. Photovoltaic (PV), wind
turbine and fuel cell. Finally, the results of proposed technique are also
compared with MINLP.
In [14], a new approach for DSM along with hardware solution is proposed.
The paper mainly focuses to overcome load shedding problem due to its
major drawback i.e. it totally disconnects some feeders. This results to
switch off all the appliances attached with that feeder. To overcome this
problem, load is classified into three categories on the basis of usage pat-
tern. Only low priority appliances are switched off in emergency situation
while high priority appliances are kept in contact.
A comparative study of WDO and PSO is done in [15]. Residential loads
are considered with the objective to reduce cost. Results show that per-
formance of WDO is better than PSO. Moreover, a Knapsack-WDO (K-
WDO) is also studied for the same objective functions. The simulation
results show that the convergence rate of K-WDO is better than existing
Integration of hybrid energy sources in smart home is studied in [16]. In
this work, a structure of small scale hybrid energy sources are considered
for case study which are located in test site at Nazarbayev university. En-
ergy management problem is solved by using GA. Results show that GA
based controller performs an efficient control over a wide range of appli-
ances equipped with renewable energy.
The authors in [17] show the comparison of GA and PSO in terms of compu-
tational cost and computational efforts. Results prove that PSO needs less
computational effort to reach optimal solution compared to GA. The major
drawback of GA is that its computational cost is high. The authors in [18]
has designed EMS to control home appliance power consumption. The en-
hanced GA based EMS is designed for achieving desired objectives: energy
consumption and PAR. In this research paper, RTP scheme is adopted for
electricity bill calculation. The dynamic power threshold is used for peak
Customer reward scheme is introduced in [19] for controlling Demand Re-
sponse (DR) in residential distribution system. In this scheme, peak load
is shaved by reward mechanism which improves voltage regulation in the
feeder. Case study conducted on 11KV/415V, 500KVA transformer has
four feeders. Results show that peak voltages are reduced and protect the
network from overloading and voltage violations.
In [20], authors investigate some known problems in DE algorithm which
affect its performance. The important parameter needs to be addressed
in this paper is selection of appropriate value of scaling parameter. It is
concluded that there is no optimal value of scaling parameter which is good
choice for each problem. It shows that the value of scaling parameter varies
according to problem. Actually, it is found after doing lot of experiments
that a particular value of scaling parameter is good choice for one prob-
lem but can be worst for some other problem. Moreover, they propose a
modified DE algorithm as an alternate to generate trial vectors known as
DE preferential crossover. The generated trial vector lies in feasible region
thereby increasing the convergence rate of the DE algorithm.
The authors in [21] discuss the effect of initial population in overall perfor-
mance of DE algorithm. In past, a lot of research has been done on fine
tuning of certain parameters including: Crossover Rate (CR) and Muta-
tion Factor (F). Yet, there is very few literature available which majoraly
focusses on the role played by initial population in performance of algo-
rithm. In this paper, authors propose new method for generating initial
population known as DE with Nonlinear Simplex (NSDE) method.
A huge combination of solutions in multi dimensional problems affect the
searching ability of Hybrid DE (HDE) algorithm presented in [22]. To over-
come these drawbacks, HDE incorporates two schemes i.e. search space
reduction scheme and multi direction search scheme. These two schemes
help to identify search direction for solutions before generating initial pop-
Binary DE (BDE) is employed for Unit Commitment Problem (UCP) which
aims to schedule each power unit in [23]. The objective is to find minimum
operational cost while satisfying hourly power demand.
The authors in [24] propose a modified DE. The original DE is algorithm
inherently continuous in nature and is considered as powerful optimiza-
tion tool in continuous domain. The angle modulation is used with DE
algorithm for mapping continuous values to discrete. It can tackle most
engineering problems in both continuous and discrete domains.
In [25], authors investigate the effect of new trial vector generation strate-
gies on the performance of DE. In past, only one trial vector which are em-
ployed and tuning is applied on this parameter which limits overall search
ability of algorithm. In this paper, they choose three tuning parameter i.e.
CR, F and population size along with three trial vectors are employed in
each generation which enhance overall search ability and performance of
algorithm. 2.1 presents summary of related work.
Table 2.1: Related work summary
Technique Objective Features Drawbacks
MINLP [8] Cost minimization
Scheduling of
electrical and thermal
appliances have been
Ignore PAR,
reduction in the
number of peak
power plant,
complexity of
system increases
Appliance First
(AF) and First
Come First
Serve (FCFS)
battery charging
policy [9]
Grid stability and
customer saving
Consider smart
charging along with
pricing signal
formula [10]
Peak demand
reduction and
social welfare
formulation of four
scenarios to control
power demand
increases while
considering greater
number of
IPSO [12]
electricity bill and
reduce peak
modeling of three
types of household
Optimize energy
Case study is
conducted for three
different scenarios
Simulations are
not conducted
MILP [16]
modeling of major
appliances is
Minimize energy
consumption, reduce
total cost and avoid
peak formation
Slow convergence
GA [18] Reduce electricity
cost and PAR
Case study under
three different kind of
appliances is
increases due to
maximum time
DLC [19]
Reduce peak
demand, improve
network voltage
Customer reward
based demand
response is proposed
Slow convergence
DEPC [20]
Effect of scaling
parameter of DE in
Scaling factor of
DEPC is variable
instead of fixed in
case of DE
algorithm stuck in
local minima
Table 2.1: Continue Table 2.1
Searching HDE
To enhance the
search ability of
Multi direction search
scheme and search
space reduction
scheme is used with
Huge search area
and uni directional
search ability
degrades its
BDE [23]
operational cost of
Realistic case study User priorities are
DE [25]
Affect of trial
vector generation
strategies on
performance of DE
Global optimization
problem were
numerically analyzed
through experiment
Not implemented
Chapter 3
Mathematical Approach and Modeling
The mathematical model of each appliance shows the overall behavior of
appliance by incorporating all the technical and environmental aspects.
Central Energy Management Controller (EMC) contains the mathemati-
cal model of each appliance and optimization technique. The controller
also uses user priorities, pricing signal and weather forecast information
to properly schedule all the appliances for efficient management of energy.
The nomenclature is given in table 3.1.
3.0.1 User Priorities
The mathematical model of residential appliances must include user pref-
erences such as desired room temperature and required operational hours
for each appliance. The maximum variation in internal room temperature
that a customer can compromise and latest acceptable time to finish a task
is incorporated.
3.0.2 Activity Level
The energy consumption pattern of residential sector is affected by number
of occupants. Furthermore, seasonal variation affects the energy consump-
tion pattern. A term activity level is used here for representing the activity
performed by customer on each appliance. The activity level for each elec-
trical appliance is different for example, the activity level on AC tempera-
ture is not same as it effects on water heater. Thus, the coefficient is used
to represent the effect of activity level on different household appliances.
3.0.3 Electricity Pricing
Different dynamic pricing schemes are used to motivate customer to re-
duce energy consumption during peak price hours. The most popular pric-
ing schemes used in electricity market are TOU, RTP, Fixed Rate Pricing
(FRP) and CPP. RTP signal, due to hourly price variation is used in this
paper. This scheme is popular for more precise measurement of electricity
3.0.4 External Inputs
Environmental conditions have major impact on energy consumption of
temperature dependent appliances. It is difficult to maintain customer
preferred indoor temperature due to the effect of outdoor temperature.
3.1 Mathematical Model
Residential electrical loads fall in three categories i.e. interruptible, non
interruptible, and hybrid loads. Water heater, AC, batteries, EV and dish
washer can be place in any category according to user life style. The work-
ing cycle of first class of appliances can be modified. On the other hand,
uninterruptible appliances are those, whose operation cannot be postponed.
The general form of energy optimization model for residential sector is as
minF =objectivef unction (3.1)
pisi(t) = Plimit(t)tτ , i A(3.2)
The above equations ensure that total power consumption of residential
appliances during each time slot does not exceed from specific power limit.
The customers who participate in peak power reduction program given by
utility get huge savings in their electricity bill. The eq. 3.2 is also beneficial
for utility because it avoids peak formation.
3.1.1 Objective Function
Different objective functions are adopted for solving optimization prob-
lems according to end user’s choice. The three major objective functions
in HEMS are total energy cost, energy consumption pattern, and reduce
1) Energy cost: The major objective of consumer is to reduce total en-
ergy cost. This objective is achieved by optimal consumption of energy.
Recently, heuristic based optimization algorithms do this job to reduce
overall energy cost.
2) Energy consumption: The efficient utilization of energy is important
factor in HEMS. The appliances are scheduled by using optimization tech-
niques to consume energy effectively in each hour. The consumer and utility
both get benefit from efficient management of required energy.
3) PAR: The demand of electricity is increased during critical hours. This
Table 3.1: Nomenclature
Symbol Description Symbol Description
i Index of appliances n total number of air parcels
t time interval Pcprobability of crossover
E energy Pmprobability of mutation
C charge r1,2random numbers
k Number of appliances Nitra Number of iterations
max maximum value Popsize population size
min minimum value Xgbest global best value
ch charging Xlbest local best value
dis discharging i Set of appliances = {ac, wh, wm,
dhw, cld}
Xex existing population
Xnew new population
TFTeaching factor
r random number
νnew updated velocity τtotal time period
Vmax maximum velocity τiappliance operating period
Vmin minimum velocity Tfinal(t) Final room temperature at time t
νold current velocity Tini(t) Initial room temperature at time
Pold pressure at current location Tout(t) outside room temperature at time
Fccoriolis force Twh(t) Temperature of water at time t
αconstant for update position Oi(t) Binary variable denoting state of
appliance i at time t
w inertia factor insite Number of bits required for
Fsig sigmoid function ζNumber of occupants
ρdensity of air parcels βNumber of door opening
vini velocity of initial population F Objective function
ωini initial velocity Twh Temperature of water heater
ωfin final velocity Tcold cold water
∆t unit step time Thot Hot water
R universal gas constant φHeating effect on water
c1local pull vwh Activity performed on water
c2global pull Vcold Volume of cold water
Cstor stored charge in battery xjtarget vector
Treq Required temperature vr1mutant vector
OP max
iMaximum continuous operation
hours of appliance i
Fcu Current fitness
f(Uj) fitness values of trial vector Fpr Previous fitness
f(xj) fitness values of target vector Fini initial population fitness
Ujtrial vector Fupd updated population fitness
huge demand increases the probability of peak formation. The ultimate
objective is to reduce peak demand in peak hours. This will enhance grid
4) Multi-objective optimization: The above mentioned objective functions
are used simultaneously in HEMS. The general representation of multi-
objective function is:
where F1,F2and F3are the objective functions representing energy cost,
energy consumption, and PAR respectively. The ϕ1,ϕ2and ϕ3are weight-
ing factors attached with corresponding objective functions. The purpose of
multi-objective function is to solve multi-objective optimization problems,
while considering both user and utility preferences. One of the impor-
tant objective is to choose which weight is suitable for particular objective
function component thus, giving sense of interest and motivation.
3.1.2 Devices Operational Constraints:
Mathematical model of major residential appliances is presented in next
section. Few operational constraints of these models are given below. The
operation time of all appliances is specified by:
Oi(t) = 1if t τi,, i A,
0otherwise (3.4)
Devices such as AC and water heater try to maintain temperature within
specified range according to customer requirement. Therefore, the following
constraints are necessary to model these appliances properly.
Tmin Treq Tmax,tτi, i {ac, wh}(3.5)
Oi(1) = 1, if Ti(0) > Ti(1), i {ac, wh}
0, ifTi(0) < Ti(1), i {ac, wh}(3.6)
Here eq. 3.5 ensures that thermal temperature of appliances lies within
user preferred ranges, and eq. 3.6 guarantees that if the temperature of
device ibefore the model initialization is more than the upper limit, the
appliance is ON in first time interval otherwise it will remain in OFF state.
In addition to above mentioned constraints, each appliance has particular
mathematical equation to model its operation.
1) AC: The model aims to maintain AC temperature within specific range,
while considering all the major aspects that can effect its cooling such as
activity level, difference in indoor and outdoor temperature and number
of occupants. Operational constraints of AC are presented by equation as
Tfinal(t) = Tini(t1) + µ(Tout(t)Tint (t)) (3.7)
+µ(β(t) + ζ) + µOi(t)t=τ, i =ac
The dynamics of indoor temperature of AC are presented by eq. 3.8. The
equation shows that the indoor temperature at a specific interval depends
on initial temperature, activity level of household, difference between in-
door,outdoor temperatures and ON/OFF state of appliance. The cooling
effect of AC due to ON state is represented by β.µeffects on temperature
difference, number of occupants and activity level. The model also consid-
ers temperature threshold i.e. upper and lower level in which variation in
temperature can be acceptable for consumer.
2) Water heater: The magnitude of hourly usage hot water in different
houses varies. It is also observed that usage pattern changes significantly
in normal and weak days. Thus, this issue is taken into account while de-
veloping the model for water heater. The operational constraints of water
heater are shown below:
Twh(t) = Tw h(t1) + υwh(Tcold Thot ) + [φOi(k)Vcoldωwh] (3.8)
The temperature of water heater at specific interval tis a function of water
temperature in previous hour, its usage pattern and effect of ON/OFF state
in its internal temperature.
3) Battery and EV: Nowadays, residential sector is equipped with some
kind of storing devices such as batteries and EVs. They store energy to
reduce peak demand during specific hours when there is shortage of grid
energy. To develop model of each appliance, we assume that energy charge
and discharge in each interval is known. The general model for energy
storing devices is represented by eq. 3.9:
Estor =Estor(t1) + T[Cch(t)Cdis(t)] tτ(3.9)
Emin Estor Emax tτi(3.10)
Eq. 3.10 ensures the charging of energy storage appliances within certain
4) Dishwasher, Washing machine and Cloth dryer: The operational con-
straints of dishwasher, washing machine and cloth dryer are as follows:
Oi(t) = OP max
In addition to the total time slots over which the devices required to operate
according to end user choice during a day are given in eq. 3.11, additional
constraints are considered in modeling such as maximum successive opera-
tion time, coordination of washing machine and cloth dryer in such a way
that both appliances will not start simultaneously and dryer will start its
operation when washing machine completes its operation. The eq. 3.12
given below validates consecutive operation of appliance to handle second
category of appliances known as uninterruptible appliances:
ei(t).ei,t+1.ei,t+2 .et+ (τ1) 1 (3.12)
Sdryer +Swasher 1tτ(3.13)
The Eq. 3.13 avoids cloth dryer and washing machine to operate simulta-
neously. Finally, eq. 3.14 guarantees the start of operation of appliance i2
after the end of total working hours of appliance i1.
Chapter 4
Heuristic Algorithms
The scheduling of appliances is not efficiently handled by past optimiza-
tion mathematical techniques. Their efficiency degrades as number of ap-
pliances increase. Therefore, we apply heuristic algorithms (EDGE, TL,
DE, EDE, WDO, BPSO and GA) to achieve the desired objectives. These
algorithms are population based search methods. They move toward popu-
lation of better fitness variables using deterministic and probabilistic rules.
We discuss most recent search algorithms: DE, EDE, BPSO, GA, WDO,
TL, and EDGE in the following subsections for finding optimal solution.
4.0.1 BPSO
A modified version of PSO, is a nature inspired social behavior optimization
algorithm. The birds and bees start search for food in random direction
and reach a food source by sharing of information.
The HEMS based on BPSO initializes certain parameters at the beginning
of algorithm. These parametric values are necessary for its operation and
are given in table 4.1. Moreover, initial population is generated randomly
Table 4.1: Parameter of BPSO
Parameter values Parameter values
Nitra 500 wi2
Popsize 40 wf0.4
n 7 Vmax 1
c12Vmin -1
in the form of position matrix. This population is modified to discrete
domain. Each bit in the matrix represents the state of appliance, also
initial velocity is generated by using given formula:
vini =vmax 2(rand(swarm, n)0.5); (4.1)
The position of bits in initial population is taken as local best (pbest).
The fitness function of pbest is evaluated and the value having minimum
fitness is selected. The binary values against that fitness value is named as
global best (gbest). Both gbest and pbest are used for updating already
generated velocity and position. This is accomplished by using velocity
update formula which is formulated as [26].
vupd =wvini +c1rand(1) (pbest xini ) (4.2)
+c2rand(1) (gbest xini);
In above equation, w is a weighted factor and is calculated by using formula.
w=wini +wfin wini k
nitra ; (4.3)
The velocity of the particles is mapped between 0 and 1 by using sigmoid
function as follows;
sig(i, j) = 1
1 + exp(vupd)(4.4)
The random values assigned to each particle in a population is compared
with sigmoid function to update old position matrix.
xfin =1 sig(i,j)<rand(1),
0 otherwise.(4.5)
The fitness of this position matrix is calculated and then compared with
old fitness. The minimum fitness in either of two will decide final position
matrix for next generation. This process repeats until stoping criteria is
achieved. Finally, gbest is selected from final position matrix which sat-
isfies each fitness function i.e. cost and PAR . These resulting values are
then converted to binary so that appliances are scheduled according to this
pattern in each hour. Similarly, this whole procedure repeats for remaining
hours. The above discussion is explained through flow chart given in fig.
4.0.2 WDO
WDO is a nature inspired global optimization algorithm. In this, wind
blows with the objective to balance atmospheric pressure. As it can be seen
that wind having infinitely small air parcels experience different forces when
moving in N dimensional space. The combined effect of these forces update
velocity and pressure. In WDO based HEMS, parameters are defined at
start of algorithm which are given in table 4.2. In next step, we generate
random initial population in the form of position matrix. Velocity of air
parcels is also initialized through following formula.
vini =vmax 2(rand(popsizew, npr)0.5); (4.6)
The fitness values of initially generated position matrix are evaluated.
Based on these fitness values position and velocity of the air parcels are
updated in each iteration. The formula for updating velocity is represented
by eq. 4.7 as given in [27].
νnew = ((1 α)νold gxold + [|Pmax
|RT (xmax xold)] old
Algorithm 1 BPSO: Velocity and position update
1: procedure Updating velocity
2: for k= 1 : N itra do
3: Step 1 :
4: Calculate momentum (w) using eq. 4.3
5: Step 2 :
6: for i= 1 : swarm do
7: for j= 1 : ndo
8: vupd =w×vini +c1×rand(1) ×(pbest xini ) + c2×
rand(1) ×(gbest xini)
9: if vupd < V max && vupd > V min then
10: vupd =vupd
11: else
12: if V max > 1then
13: vupd = 1
14: else
15: if V min < 1then
16: vupd =1
17: end if
18: end if
19: end if
20: Step 3 :
21: updating position
22: Sig(i, j) = 1
23: if rand(1) <=Sig(i, j)then
24: x(i, j) = 0
25: else
26: if rand(1) >=Sig(i, j)then
27: x(i, j) = 1
28: end if
29: end if
30: end for
31: end for
32: end for
33: end procedure
Initialization of
Generate initial
Assign pbest from initial
Evaluate fitness function
Minimum value = gbest
Generation < maximum
Update initial velocity
and postion
Calculate fitness of
updated old position
Fcu < Fpr
Keep previous pbest
as final position
Updated position
Population generated on
the basis of updated
position matrix
Fitness function
Maximum fitness =gbest
Figure 4.1: Flow chart of BPSO
Table 4.2: Parameter of WDO
Parameter values Parameter values
Nitra 400 Rt 3
Popsize 30 g 0.2
n 7 alp 0.4
Vmax 1 c 0.4
Vmin -1
The term pressure used in WDO is just like term fitness used in BPSO.
Finally, we update the position of air parcel by updating its velocity. The
position update equation [27] is given below.
xnew =xold + (νnew ×t) (4.8)
New population is generated on the bases of initial and current population.
Now, fitness functions of new population are evaluated and best values
are achieved. This whole process continues untill stoping criteria is met.
Finally, gbest value of the solution is found on the bases of each fitness
criteria as mentioned in above scheme. Bits of generated population show
state of appliances, to simplify the states, we convert given real gbest values
into binary. Above formulation of scheme is explained by flowchart in fig.
4.0.3 GA
GA is bio inspired optimization algorithm in which new genes are formed
which carry characteristics of their parents. In GA, random population
of chromosomes is generated in which each chromosome represents the so-
lution of problem. In our GA based HEMS, appliances are scheduled to
minimize cost and peak to average ratio by facilitating both user and util-
ity. Initial parameters of GA based HEMS are defined in table 4.3. The
Table 4.3: Parameter of GA
Parameter values Parameter values
Nitra 300 Pc0.9
Popsize 10 Pm0.1
n 7 insite 2
algorithm starts with initializing a random population of chromosomes.
The length of chromosome depends on number of appliances used. Each
chromosome represents solution in the form of bits. Each bit in the popu-
lation shows the state of appliance. As the population is generated, fitness
values of objective function are evaluated and also record them as current
best values. Now, it randomly selects two variables for crossover in the
range of appliances being used. These variables decide the certain portion
in both strings to interchange. The selected portion in each chromosome
is swapped with each other to form a new offspring of better fitness. New
offspring values replace current best values. To create further randomness,
Algorithm 2 WDO: Velocity and position update
1: procedure Updating velocity
2: for k= 1 : N itra do
3: Step 1 :
4: Initialize velocity
5: Step 2 :
6: for m= 1 : popsizew do
7: for j= 1 : npr do
8: νnew = ((1α)νold gxold +[|Pmax
Pold |RT (xmax xold)] old
9: if νnew < V max && νnew > V min then
10: νnew =νnew
11: else
12: if νnew < V min then
13: νnew =V min
14: else
15: if νnew > V max then
16: νnew =V max
17: end if
18: end if
19: end if
20: Step 3 :
21: updating position
22: posnew(m, j) = 1
23: if rand(1) <=posnew(m, j)then
24: x(m, j) = 0
25: else
26: if rand(1) >=posnew(m, j)then
27: x(m, j) = 1
28: end if
29: end if
30: end for
31: end for
32: end for
33: end procedure
Generate initial
and assign pbest
Initialization of parameter
Evaluate fitness
function position
Update position matrix
through velocity update
Replace new
position matrix by
Evaluate fitness
function of updated
Fini < Fupd
Keep initial position
matrix array
New population
Assign gbest
Evaluate fitness
Generation < maximum
Figure 4.2: Flow chart of WDO
mutation is applied. Finally, new population based on crossover and muta-
tion is generated which is again evaluated by fitness function. This whole
procedure is repeated until gbest values are achieved. The last and final
step is to translate values into binary to represent the switching state of
appliances. The implementation of GA is described by owchart given in
fig. 4.3.
Algorithm 3 GA: Crossover and mutation process
1: procedure Crossover and mutation
2: if Pc>0.9then
3: Step 1 :
4: Randomly select two parent chromosomes
5: Step 2 :
6: Select crossover point
7: Step 3 :
8: Produce offspring
9: of f spring1 = [parent1(bit1 :
crossoverpoint)P arent2(crossoverpoint + 1 : endpoint)]
10: off spring2 = [parent2(bit1 :
crossoverpoint)P arent1(crossoverpoint + 1 : endpoint)]
11: Step 4 :
12: Update offspring in population
13: end if
14: if Pm>0.1then
15: Randomly select a chromosome for mutation
16: Step 5 :
17: Randomly select one or more bits
18: Step 6 :
19: Invert selected bit
20: end if
21: end procedure
meter initia
Generate initial
Generation < maximum
Assign pbest
Evaluate fitness
Assign gbest
Select two individuals
From current
Fitness function
Assign gbest
Figure 4.3: Flow chart of GA
4.0.4 DE
DE is a stochastic population based search algorithm. The algorithm works
by having a population of agents. These agents move in a search space by
updating their original position using algebraic formula. If a new position is
better than previous one, it will replace existing position of agent otherwise
discarded. This process is repeated for several iterations until satisfactory
results are obtained. After defining certain parameters of the algorithm
Table 4.4: Parameter of DE
Parameter values Parameter values
Nitra 100 xl50
Popsize 30 xu100
n 7
given in table 4.4, the population containing vectors is chosen randomly
within certain bounds. Following formula is used for generating initial
population xini .
xini =xl+rand(1)(xuxl) (4.9)
where rand(1) is a random number between 0 and 1, xland xuare lower
and upper bounds respectively. The generated vectors in initial population
are normalized between 0 and 1 because these normalized values can easily
be translated into binary at the end of algorithm. In our HEMS, we need
binary values to show switching states of home appliances. The first step
after population generation is to select target vector. Mostly, first vector
from a population is considered as target vector. In the next step, we
randomly select three vectors xr1,xr2and xr3from existing population.
The difference of two vectors is added in third vector to form mutant vector
as shown by eq. 4.10 [28].
vr1=xr1+F(xr2xr3) (4.10)
The F is taken in given range [0 2]. Crossover is used to obtain trial
vector by sharing some information between target and mutant vector. CR
decides how much information is taken from both vectors i.e mutant and
target vectors. This can be done by generating random number, if it is
less than CR, mutant vector is taken as trial vector otherwise target vector
becomes trial vector. The equation used to express this whole process is
given below.
Uj=vj, if(randb(j)CR,
xj, if(randb(j)> CR (4.11)
At last, fitness function values of trial vectors formed after mutation and
crossover are compared with the corresponding target vector fitness. Vector
having minimum fitness value will survive for next generation.
xj=Uj, iff (Uj)f(xj),
xj, otherwise (4.12)
These above mentioned steps continue until some stopping criteria is achieved.
The final vector obtained after fitness function evaluation is taken as gbest
and converted to binary. Appliances are scheduled according to final com-
bination of bits in resultant vector. This whole procedure is explained in
fig. 4.4.
Generate initial population
n of parameter
Norm ulation
Select target value from a
initially population
rial vector genera
Generation < maximum
Fitness function of trial
vector is calculated
Fitness values of trial and
target vector are
um fitness values in
ill update initial
Fitness function
alues obeying fitness
ert real values of
gbest into binary
Figure 4.4: Flow chart of DE
Algorithm 4 DE: Mutation, Crossover and Selection process
1: procedure mutation
2: Step 1 :
3: Randomly select three vectors
4: Step 2 :
5: Take difference of last two vectors
6: Step 3 :
7: best vector is assigned as xj
8: Step 4 :
9: Add this difference into xjto form a Vj
10: Step 5 :
11: Randomly select crossover rate to calculate trial vector
12: if rand(1) > CR then
13: Uj=Vj
14: else
15: if rand(1) < CR then
16: Uj=xj
17: end if
18: end if
19: Step 6 :
20: Evaluate fitness of xjand Uj
21: if f(Uj)< f(xj)then
22: xj=Uj
23: else
24: if f(U1)< f(x1)then
25: Uj=xj
26: end if
27: end if
28: end procedure
4.0.5 EDE
EDE is considered as most powerful and robust optimization tool in recent
years. DE is although famous yet, it lacks in terms of its performance
due to slow convergence rate and less accuracy. The appropriate tuning
of control parameters can improve its accuracy and convergence speed.
The parameters required for tuning include CR, F and NP. All the steps
and parameters of EDE are similar to DE, however, the modification in
this algorithm is done at a stage of generating trial vectors. We use 100
iterations to obtain feasible solution. In every iteration, five groups of
trial vectors are generated. The first three trial vector are obtained by
taking three distinct CR values i.e. 0.3, 0.6 and 0.9. Moreover, fourth trial
vector aims to speed up the convergence rate while the last one increases
the diversity of population. Equations for generating five groups of trial
vectors are given in [5]:
Uj=vj, if(rand(1) 0.3,
xj, if(rand(1) >0.3(4.13)
Uj=vj, if(rand(1) 0.6,
xj, if(rand(1) >0.6(4.14)
Uj=vj, if(rand(1) 0.9,
xj, if(rand(1) >0.9(4.15)
Uj=rand(1).vj+ (1 rand(1)).xj(4.17)
All these trial vectors are evaluated by using fitness function. Finally, the
trial vector having minimum fitness function value will be considered as
final trial vector. The last step after generating trial vector is same as
discussed in above algorithm. This particular modification in DE proves to
be an efficient alternate for improving the overall performance of algorithm
which is given in fig. 4.5.
4.0.6 TL
This algorithm is based on the teaching learning process of the class. The
learner improves his skills by gaining knowledge from teacher and colleagues
as well. We initialize the parameters of this algorithm shown in table 4.5
and then generate a matrix of random population in which each row rep-
resents a number of learner and columns show number of subjects studied.
Algorithm 5 EDE: Trial vector generation strategies
1: procedure Crossover
2: Step 1 :
3: Select three crossover rates to generate three Uj
4: if rand(1) > CR1then
5: Uj=Vj
6: else
7: if rand(1) < CR1then
8: Uj=xj
9: end if
10: end if
11: if rand(1) > CR2then
12: Uj=Vj
13: else
14: if rand(1) < CR2then
15: Uj=xj
16: end if
17: end if
18: if rand(1) > CR3then
19: Uj=Vj
20: else
21: if rand(1) < CR3then
22: Uj=xj
23: end if
24: end if
25: Step 2 :
26: Multiply randomly selected number by xjfor fourth Uj
27: Step 3 :
28: Multiply xjby 1-rand(1)
29: Step 4 :
30: Take product of vjand random number
31: Step 5 :
32: Add both resultant vectors taken in step 4 and 5 to obtain fifth Uj
33: end procedure
population of vectors
wi bounds
Norm value
Select target vector
Generate mutant vector
Generate five group of trial
vector er
Evaluate fitness function
Final trial vector is
ing minimum
pare trial vector and
target vector to update
initial population
Generation < maximum
Evaluate fitness
ert real gbest
values into binary
Figure 4.5: Flow chart of EDE
Moreover, the mean of whole population is taken column wise then fitness
value of each row is calculated using fitness function. The row having max-
imum fitness is considered as a teacher. The new population is generated
by using eq. 4.18 as given in [29].
Xnew =Xex +r(XT eacher (TF)M ean) (4.18)
Fitness values of newly generated population are compared with old pop-
Table 4.5: Parameter of TL
Parameter values Parameter values
Nitra 200 xl-10
Popsize 20 xu12
n 7 TF2
ulation. The row with minimum fitness in either of two will decide whether
population is updated on the basis of existing or new population. Now the
learner phase: we compare the fitness values within same population. The
value with minimum fitness will survive for next generation. This whole
process continues until termination criteria is achieved. Finally, global best
solution is found and than converted to binary. The appliances are sched-
uled according to global best values in each hour. The above discussion is
explained through flow chart given in fig. 4.6.
Algorithm 6 TL: Teacher and learner phase
1: Teacher phase :
2: Initialize all parameter
3: Generate initial population and calculate mean
4: Assign best solution as teacher
5: Update population by using eq. 4.18
6: Compare fitness of existing and new population
7: Learner phase :
8: Randomly select two rows within population
9: Again compare fitness of selected rows in a population
10: Maximum fittest row will survive for next generation
11: Final population is compared with existing population to update pop-
12: Select global best solution by evaluating fitness function
n of
Generate initial
population of
te mean
column wise
Assign best solution
as teacher
Generate new
population on the
basis of mean and
best solution
Fex < Fnew
Keep previous
Record new
Select two rows within
Row having better
fitness update new
Again compare
updated and initial
criteria achieved
pare fitness of both
Global solution
achieved from final
Figure 4.6: Flow chart of TL
4.0.7 EDGE
EDGE is our proposed algorithm which is hybrid of EDE and GA. The
performance of EDE is improved by incorporating crossover and mutation
process of GA. This modification in EDE algorithm gives more optimal so-
lutions because now results are achieved by tuning the parameter of both
algorithms. Simulation results show that proposed algorithm is effective
in achieving better cost reduction relative to remaining algorithms. The
working of proposed algorithm is explained in two phases. In first phase,
we follow similar steps of EDE algorithm as discussed above. Crossover and
mutation is applied in next phase. The population which is obtained before
and after crossover and mutation steps are compared. New population is
generated on the basis of best solution achieved in either of two popula-
tions. Finally, the value with minimum fitness in resultant population is
considered as global best solution. The flow chart of proposed algorithm is
shown in fig. 4.7.
E parameter
n p
andom population
of vectors within certain
Normalize each value
n en
! "
Select target vector
Randomly select three
Generate mutant vector i
Generate five group of trial
Evaluate fitness function of
each trial vectors
Final trial vector is selected
having minimum fitness
pare trial vector with
target vector and update initial
Generation < maximum
Fitness function evaluation
Assing gbest
Select two individuals from
current population
! p
Figure 4.7: Flow chart of EDGE algorithm
Chapter 5
Simulations and Discussion
For simulations, we consider a home which is equipped with 7 smart ap-
pliances. These appliances are categorized into interruptible, non inter-
ruptible and hybrid loads. The performance of above mentioned heuristic
population based optimization algorithms is evaluated to achieve the fol-
lowing objectives: 1) optimal energy consumption pattern, 2) minimum
electricity cost, and 3) avoid peak formation. The parametric values of
appliances necessary for scheduling are taken in advance which is given in
table 5.1. Subject to fair comparison, we use RTP scheme for bill calcu-
Table 5.1: Parameter of appliances
Appliances Power rating (KWh) Appliances Power rating (KWh)
AC 1.5 Iron 1
Dishwasher 1.5 Washing ma-
EV 5.5 Cloth dryer 4
Battery 1.6
lation are given in fig. 5.1. The reason of using dynamic pricing model
instead of fixed is to facilitate consumer to make informed decisions that
can equally benefice in achieving above objectives. In this model, electric-
ity price varies on hourly basis with user demand. The utility generates
price signal in accordance to load requirement by users. Therefore, price
of electricity increases where demand is high and vice versa.
5.0.1 Scenario 1
This section deals with the performance of different optimization algorithms
on the bases of performance metrics i.e. energy consumption pattern, total
cost, and PAR by taking each appliance as interruptible nature. Energy Consumption Pattern and Electricity Bill Reduction
The average energy consumption of various appliances using optimization
algorithms is shown in fig. 5.2. The maximum energy consumption before
scheduling is 12 KWh, which is reduced to 11.1 KWh, 10.1 KWh, 8.6 KWh,
7.8 KWh and 7.1 KWh in case of EDGE, BPSO, WDO, TL, GA, EDE and
DE algorithms. The result in fig. 5.2 verifies that each algorithm sched-
ules appliances optimally to maintain energy consumption within maxi-
mum threshold limit. During first low peak hours 1:00 7:00, the average
Time (hours)
Cost (cent/KWh)
RTP signal
Figure 5.1: RTP tariff model
energy consumption of DE, WDO and BPSO is almost 25% more than
remaining algorithms. Moreover, it is noticed that there is a significant
change in energy consumption behavior of EDGE algorithm during peak
hours starting from 7:00 15:00. In these time slots, EDGE algorithm
consumes minimum amount of energy as compared to other algorithms. In
remaining time slots, 15:00 24:00, each algorithm schedules maximum
of its appliances to complete their working hours. From the above discus-
sion, it is concluded that EDGE algorithm is more cost effective than other
algorithms because it contains tuning parameters of both GA and EDE
algorithms. These parameters enable EDGE algorithm to reach most opti-
mal solution, thereby, consuming maximum energy in low peak hours and
minimum in high peak hours. It can be seen in fig. 5.3 that total cost of
energy consumption in each algorithm is less than unscheduled case. Also,
the values of energy consumption cost are given in table 5.2, which reveal
that maximum reduction in electricity bill is achieved by EDGE algorithm
and its price is equivalent to 967 cents.
1 2 3 4 5 6 7 8 9 10 111213 14 15 161718 19 20 212223 24
Time (hours)
Energy consumption (KWh)
Figure 5.2: Energy consumption of appliances
Table 5.2: Comparison of cost
Scheduling algorithms Cost
Decrement in cost (%)
Unscheduled 1235 - -
BPSO 1149 86 6.96
WDO 1225 10 0.8
DE 1106 129 10.4
TL 1165 70 5.66
GA 1126 109 8.82
EDE 1130 105 8.50
EDGE 927 308 24.9 PAR
Fig. 5.4 illustrates the performance of given scheduling algorithms with
respect to PAR reduction. It is clear from the fig. 5.4 that PAR is signif-
icantly reduced in GA, TL, EDE and DE while BPSO, EDGE and WDO
Total Cost (Cent)
Figure 5.3: Total cost
have almost an equal amount of PAR reduction. These algorithms are de-
signed to avoid peak formation in any hour during a day. Peak formation
is major issue in traditional grid which directly affects consumer to pay
high electricity bill as well as utility suffers high demand. It is obvious
from results mentioned in table 5.3 that maximum reduction in PAR is
achieved in case of EDE algorithm due to its optimal scheduling pattern in
all time slots. The increased demand of consumer causes peak formation
which leads to load shedding and blackout of generating systems.
5.0.2 Scenario 2
In this section, appliances are scheduled by considering each appliance in
uninterruptible scenario using optimization algorithms to compare their
performance. The performance is measured on the basis of same perfor-
mance metrics as discussed in above section.
Figure 5.4: Peak to average ratio
Table 5.3: Comparison of PAR
Scheduling algorithms PAR Difference Decrement in PAR
Unscheduled 2.79 - -
BPSO 2.58 0.21 7.52
WDO 2.58 0.21 7.52
DE 1.81 0.98 35.1
TL 2 0.79 28.31
GA 2 0.79 28.31
EDE 1.65 1.14 40.86
EDGE 2.58 0.21 7.52 Energy Consumption Pattern and Electricity Bill Reduction
In fig. 5.5, the energy consumption patterns of uninterruptible appliances
are shown. These appliances would not be interrupted, once they are set in
ON state. The energy consumption cost of these appliances is slightly dif-
ferent from appliances used in scenario 1 due to their consecutive operation
while energy consumption behavior is almost same as in simulation section
of scenario 1. Majority of appliances are still scheduled in low peak hours
and few in peak hours. The simulation results of fig. 5.6 show that EDGE
algorithm behaves efficiently in reducing electricity bill. During low peak
hours 1:00 9:00, EDGE algorithm consumes minimum energy compared
to other algorithms. This value is slightly increased in peak hours, how-
ever, major portion of energy is consumed in low peak 17:0024:00 hours
to reduce electricity bill. In fig. 5.6, each algorithm shows significant reduc-
1 2 3 4 5 6 7 8 9 10 111213 14 15 161718 19 20 212223 24
Time (hours)
Energy consumption (KWh)
Figure 5.5: Energy consumption of appliances
tion in electricity bill. The electricity bill without scheduling appliances is
about 1235 cents. This value is further reduced by using given algorithms
and finally, maximum cost saving is achieved in case of EDGE algorithm
because it contains tuning characteristics of both GA and EDE algorithms.
However, its energy consumption cost is slightly more than interruptible
appliances as discussed above in scenario 1. The cost comparison of each
technique is shown in table 5.4.
Table 5.4: Comparison of cost
Scheduling algorithms Cost (cent) Difference
Decrement in cost (%)
Unscheduled 1235 - -
BPSO 1132 103 8.34
WDO 1176 59 4.77
DE 1218 17 1.37
TL 1064 171 13.84
GA 1220 15 1.21
EDE 1166 69 5.58
EDGE 1046 189 15.30
Total cost (Cost)
Figure 5.6: Total cost PAR
Fig. 5.7 shows the effectiveness of all considered scheduling algorithms
with respect to PAR reduction. These algorithms are beneficial for peak
reduction in any hour. Mostly, user is interested in minimum electricity
bill. However, utility wants balanced energy supply. The results in table
5.5 show that each algorithm proves to be helpful in PAR reduction by
considering maximum grid capacity. It is clear from fig. 5.7 that EDE
reduces peak up to 1.65% by optimally scheduling appliances in each time
slots while, EDGE reduces up to 2.58%. The performance of all these algo-
rithms is improved by maximum energy capacity constraint, which benefits
both in terms of reduced electricity bill by avoiding peaks and balanced en-
ergy supply by utility. Finally, EDE is preferred choice for uninterruptible
appliances due to its maximum PAR reduction ability.
Figure 5.7: Peak to average ratio
5.0.3 Schenario 3
The last section deals with hybrid class of appliances in which AC, batteries,
dishwasher, EV and iron are taken in interruptible class while washing
machine and cloth dryer are considered in uninterruptible class. Cloth
dryer will be scheduled for few time slots immediately after the washing
machine completes its working hours. Their performance is measured on
Table 5.5: Comparison of PAR
Scheduling algorithms PAR Difference Decrement in PAR
Unscheduled 2.79 - -
BPSO 2 0.79 28.31
WDO 2 0.79 28.31
DE 2.16 0.63 22.58
TL 2.23 0.56 20.07
GA 2.23 0.56 20.07
EDE 1.65 1.14 40.86
EDGE 2.58 0.21 7.52
the bases of same objective functions as used above using optimization
algorithms. Energy Consumption Pattern and Electricity Bill Reduction
In fig. 5.8, the energy consumption of hybrid appliances are shown. More-
over, it is obvious from the simulation results that each algorithm efficiently
utilizes available energy to reduce electricity bill and avoids peak forma-
tion. However, TL and EDGE have slightly different energy consumption
patterns because TL consumes more energy in few time slots with respect
to other algorithms during peak 11:00 15:00 hours however, EDGE con-
sumes maximum energy in least price 17:0024:00 hours. It is concluded
from above discussion that EDGE acts better in reducing electricity bill.
The electricity bill comparison using five different optimization algorithms
is shown in fig. 5.9. The electricity bill charged by scheduling appliances
using above algorithms is less than unscheduled case. These results of table.
5.6 prove that each algorithm is effective in bill reduction. The simulation
results show that electricity bill reduction for each algorithm which is found
to be minimum in case of EDGE algorithm due to its precise results which
are obtained after tuning parameters of GA and EDE algorithms. PAR
In this section, impact of five different optimization algorithms on peak
reduction is evaluated. The percentage decrement of PAR is shown in
table 5.7 and is most essential parameter in smart grid. The appropri-
1 2 3 4 5 6 7 8 9 10 111213 14 15 161718 19 20 212223 24
Time (hours)
Energy consumption (KWh)
Figure 5.8: Energy consumption of appliances
Table 5.6: Comparison of cost
Scheduling algorithms Cost (cent) Difference
Decrement in cost (%)
Unscheduled 1235 - -
BPSO 1107 128 10.36
WDO 1140 95 7.69
DE 1127 108 8.74
TL 1158 77 6.23
GA 1075 160 12.9
EDE 1185 50 4.04
EDGE 1018 217 17.5
ate knowledge of grid capacity is helpful in reducing peak demand. Fig.
5.10 shows PAR reduction values in scheduled and unscheduled cases. It
is maximum in case of BPSO because of its local and global exploration
ability. In traditional grid, there is no method to control peak formation
which results in charging high electricity bill to the users and utility suffers
Total Cost (Cent)
Figure 5.9: Total cost
huge demand. The increased demand in particular hours makes generating
system unstable or there is a probability that whole system will collapse.
Smart grid provides flexibility to efficiently handle this parameter using
optimization algorithms to avoid from any sudden mishap and maintains
balance between demand and supply.
Table 5.7: Comparison of PAR
Scheduling algorithms PAR Difference Decrement in PAR
Unscheduled 2.79 - -
BPSO 2.7 0.09 3.22
WDO 2 0.79 28.31
DE 2.37 0.42 15.05
TL 2 0.79 28.31
GA 2.23 0.56 20.07
EDE 1.65 1.14 40.86
EDE 2.58 0.21 7.52
Figure 5.10: Peak to average ratio
5.1 Trade-Offs
The discussion of simulation results in above section shows that there ex-
ists a trade-off between different objectives: total cost and PAR in each
scenario. Although, each algorithm is capable to achieve desired objec-
tive but their performance varies in some aspects. BPSO, WDO, TL, GA,
DE, EDE, EDGE are compared in terms of above mentioned objectives; as
shown in tables VII-XIII. The analysis in these tables proves that EDGE
based HEMS provides significant reduction in electricity bill in each sce-
nario. However, this algorithm has certain limitations in achieving second
objective i.e. high PAR. On the other hand, BPSO based HEMS charges
high electricity bill to consumers. Meanwhile, this algorithm shows vari-
ation in PAR in each scenario, which is effectively reduced in scenario 2
and increased in scenario 1. The HEMS architecture based on WDO and
TL, on average performs better than rest of the algorithms because both
algorithms show minimum trade-off between each objective discussed in
previous section. Moreover, the comparative study given in each table val-
idates that GA reduces electricity bill slightly more than BPSO and WDO
based HEMS in first and last scenario. Finally, EDE algorithm outperforms
to reduce PAR.
Chapter 6
Conclusion and Future Work
In this thesis, we investigate different optimization algorithms to schedule
household appliances for efficient management of energy. The performance
of given algorithms is evaluated by taking each appliance in three different
scenarios and compare their results. Moreover, mathematical modeling of
major house hold appliances: AC, batteries, dishwasher, EV, iron, washing
machine and cloth dryer is proposed. These models are beneficial because
they provide more control over appliances resulting in better performance
regarding to given objectives: PAR, total cost, and energy consumption
pattern. The simulation results show that the EDGE algorithm is relatively
more effective in terms of electricity bill reduction. In future, we will extend
our work in dynamic scheduling for solving multi- objective optimization
Chapter 7
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