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Enhanced Differential Evolution Based Energy

Management in Smart Grid

By

Naveed ur Rehman

CIIT/FA13-REE-090/ISB

MS Thesis

In

Electrical Engineering

COMSATS Institute of Information Technology

Islamabad – Pakistan

Fall, 2016

ii

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)

By

Naveed ur Rehman

CIIT/FA13-REE-090/ISB

Fall, 2016

iii

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).

Name

Registration Number

Naveed ur Rehman

CIIT/FA13-REE-090/ISB

Supervisor

Dr. Shahid A. Khan,

Professor,

Department of Electrical Engineering,

COMSATS Institute of Information Technology (CIIT),

Islamabad Campus.

November 2016

iv

Final Approval

This thesis titled

Enhanced Differential Evolution Based Energy

Management in Smart Grid

By

Naveed ur Rehman

CIIT/FA13-REE-090/ISB

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

v

Declaration

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

CIIT/FA13-REE-090/ISB

vi

Certificate

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: ____________________________

Supervisor:

____________________________

Dr. Shahid A. Khan

Professor, Department of

Electrical Engineering,

Islamabad

Co- Supervisor:

____________________________

Dr. Nadeem Javaid

Associate Professor,

Department of Computer

Science, Islamabad

Head/Chairperson:

____________________________

Dr. M. Junaid Mughal

Professor, Department of Electrical Engineering.

vii

DEDICATION

This thesis is dedicated to my teachers, my family and my

friends.

viii

ACKNOWLEDGMENT

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

CIIT/FA13-REE-090/ISB

ix

ABSTRACT

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.

TABLE OF CONTENTS

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

5.0.1.1 Energy Consumption Pattern and Electric-

ity Bill Reduction . . . . . . . . . . . . . . 40

5.0.1.2 PAR...................... 42

5.0.2 Scenario 2 . . . . . . . . . . . . . . . . . . . . . . . . 43

5.0.2.1 Energy Consumption Pattern and Electric-

ity Bill Reduction . . . . . . . . . . . . . . 44

5.0.2.2 PAR...................... 46

x

5.0.3 Schenario 3 . . . . . . . . . . . . . . . . . . . . . . . 47

5.0.3.1 Energy Consumption Pattern and Electric-

ity Bill Reduction . . . . . . . . . . . . . . 48

5.0.3.2 PAR...................... 48

5.1 Trade-Oﬀs............................ 51

6 Conclusion and Future Work 53

7 References 55

xi

LIST OF FIGURES

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

xii

LIST OF TABLES

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

xiii

Chapter 1

Introduction

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

bill.

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

2

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.

3

Figure 1.1: Abstract view of smart grid model

4

Chapter 2

Related Work

5

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

6

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

techniques.

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-

7

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

shaving.

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-

ulation.

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.

8

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.

9

Table 2.1: Related work summary

Technique Objective Features Drawbacks

MINLP [8] Cost minimization

Scheduling of

electrical and thermal

appliances have been

proposed

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

System

computational

complexity

increases

Mathematical

recursive

formula [10]

Peak demand

reduction and

social welfare

Mathematical

formulation of four

scenarios to control

power demand

Algorithm

complexity

increases while

considering greater

number of

appliances

IPSO [12]

Minimize

electricity bill and

reduce peak

demand

Mathematical

modeling of three

types of household

appliances

Computational

complexity

increases

GA and MINLP

[13]

Optimize energy

consumption

Case study is

conducted for three

diﬀerent scenarios

Simulations are

not conducted

MILP [16]

Mathematical

modeling of major

household

appliances is

formulated

Minimize energy

consumption, reduce

total cost and avoid

peak formation

Slow convergence

rate

GA [18] Reduce electricity

cost and PAR

Case study under

three diﬀerent kind of

appliances is

conducted

Computational

complexity

increases due to

maximum time

slots

DLC [19]

Reduce peak

demand, improve

network voltage

performance

Customer reward

based demand

response is proposed

Slow convergence

rate

DEPC [20]

Eﬀect of scaling

parameter of DE in

mutation

Scaling factor of

DEPC is variable

instead of ﬁxed in

case of DE

Sometimes

algorithm stuck in

local minima

10

Table 2.1: Continue Table 2.1

Robust

Searching HDE

(RSHDE)[22]

To enhance the

search ability of

DE

Multi direction search

scheme and search

space reduction

scheme is used with

HDE

Huge search area

and uni directional

search ability

degrades its

performance

BDE [23]

Minimize

operational cost of

UCP

Realistic case study User priorities are

compromised

DE [25]

Aﬀect of trial

vector generation

strategies on

performance of DE

Global optimization

problem were

numerically analyzed

through experiment

Not implemented

in HEMS

11

Chapter 3

Mathematical Approach and Modeling

12

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

bill.

13

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

follows:

minF =objectivef unction (3.1)

X

i∈A

pisi(t) = Plimit(t)∀t∈τ , 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

PAR.

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

14

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

t

Pold pressure at current location Tout(t) outside room temperature at time

t

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

crossover

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

15

huge demand increases the probability of peak formation. The ultimate

objective is to reduce peak demand in peak hours. This will enhance grid

stability.

4) Multi-objective optimization: The above mentioned objective functions

are used simultaneously in HEMS. The general representation of multi-

objective function is:

F=F1ϕ1+F2ϕ2+F3ϕ3(3.3)

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,∀t∈τi, 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

16

activity level, diﬀerence in indoor and outdoor temperature and number

of occupants. Operational constraints of AC are presented by equation as

follows:

Tfinal(t) = Tini(t−1) + 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(t−1) + 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(t−1) + T[Cch(t)−Cdis(t)] ∀t∈τ(3.9)

Emin ≤Estor ≤Emax ∀t∈τi(3.10)

Eq. 3.10 ensures the charging of energy storage appliances within certain

thresholds.

4) Dishwasher, Washing machine and Cloth dryer: The operational con-

straints of dishwasher, washing machine and cloth dryer are as follows:

X

t=τi

Oi(t) = OP max

i,∀t∈τi(3.11)

17

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:

X

xa

ei(t).ei,t+1.ei,t+2 .et+ (τ−1) ≥1 (3.12)

Sdryer +Swasher ≤1∀t∈τ(3.13)

Fi1≥Fi2+τi(3.14)

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.

18

Chapter 4

Heuristic Algorithms

19

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

c22

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 =w∗vini +c1∗rand(1) ∗(pbest −xini ) (4.2)

+c2∗rand(1) ∗(gbest −xini);

20

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.

4.1.

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

Pold

|RT (xmax −xold)] −cνold

Pold

(4.7)

21

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

1+exp(−vupd)

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

22

Start

Initialization of

parameter

Generate initial

population

Assign pbest from initial

populationt

Evaluate fitness function

Minimum value = gbest

Generation < maximum

generation

Update initial velocity

and postion

Calculate fitness of

updated old position

matrix

Fcu < Fpr

Keep previous pbest

as final position

matrix

Updated position

matrix

Population generated on

the basis of updated

position matrix

Fitness function

evaluation

Maximum fitness =gbest

End

No

Yes

Yes

No

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

23

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.

4.2.

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,

24

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 = ((1−α)νold −gxold +[|Pmax

Pold |RT (xmax −xold)] −cνold

Pold

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

1+exp(−νnew)

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

25

Start

Generate initial

population

and assign pbest

Initialization of parameter

Evaluate fitness

function position

matrix

Update position matrix

through velocity update

formula

Replace new

position matrix by

pbest

Evaluate fitness

function of updated

population

Fini < Fupd

Keep initial position

matrix array

New population

matrix

Assign gbest

Evaluate fitness

function

End

Generation < maximum

generation

No

Yes

No

Yes

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 ﬂowchart given in

ﬁg. 4.3.

26

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

27

Start

meter initia

Generate initial

population

Generation < maximum

generation

Assign pbest

Evaluate fitness

function

Assign gbest

Select two individuals

From current

population

er

ulation

End

Fitness function

evaluation

Assign gbest

No

Yes

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

28

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)(xu−xl) (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(xr2−xr3) (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)

29

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.

Start

Generate initial population

n of parameter

Norm ulation

betw

Select target value from a

initially population

Random

vectors

rial vector genera

crossover

Generation < maximum

generation

Fitness function of trial

vector is calculated

Fitness values of trial and

target vector are

compared

um fitness values in

ill update initial

population

Fitness function

evaluation

End

alues obeying fitness

criteri

ert real values of

gbest into binary

Yes

No

Figure 4.4: Flow chart of DE

30

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

31

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).xj.(4.16)

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.

32

Algorithm 5 EDE: Trial vector generation strategies

!h

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

33

Start

E

parameter

andom

population of vectors

wi bounds

Norm value

betw

Select target vector

Random

vectors

Generate mutant vector

uation

Generate five group of trial

vector er

Evaluate fitness function

ectors

Final trial vector is

ing minimum

fitness

pare trial vector and

target vector to update

initial population

Generation < maximum

generation

Evaluate fitness

function

ert real gbest

values into binary

End

No

Yes

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

34

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

!h

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-

ulation

12: Select global best solution by evaluating ﬁtness function

35

Start

I

n of

parameter

Generate initial

population of

students

C

te mean

column wise

Assign best solution

as teacher

Generate new

population on the

basis of mean and

best solution

Fex < Fnew

Keep previous

solution

Record new

solutions

U

population

Select two rows within

population

Row having better

fitness update new

population

Again compare

updated and initial

population

T

ermination

criteria achieved

No

C

pare fitness of both

rows

Global solution

achieved from final

population

Yes

Yes

No

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

36

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.

37

Start

S

E parameter

n p

l

u

n

andom population

of vectors within certain

bounds

Normalize each value

betw

n en

! "

Select target vector

Randomly select three

vectors

Generate mutant vector i

#

mutation

Generate five group of trial

vectors

Evaluate fitness function of

each trial vectors

Final trial vector is selected

having minimum fitness

$p%

pare trial vector with

target vector and update initial

population

Generation < maximum

generation

Fitness function evaluation

Assing gbest

End

No

Yes

Select two individuals from

current population

$p&&p

er

M'pn

(

! p

ulation

Figure 4.7: Flow chart of EDGE algorithm

38

Chapter 5

Simulations and Discussion

39

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-

chine

0.7

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.

5.0.1.1 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

40

Time (hours)

8

10

12

14

16

18

20

22

24

26

28

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.

41

1 2 3 4 5 6 7 8 9 10 111213 14 15 161718 19 20 212223 24

Time (hours)

0

2

4

6

8

10

12

Energy consumption (KWh)

Unsch

BPSO

WDO

DE

TL

GA

EDE

EDGE

Figure 5.2: Energy consumption of appliances

Table 5.2: Comparison of cost

Scheduling algorithms Cost

(cents)

Diﬀerence

(cents)

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

5.0.1.2 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

42

Unsch BPSO WDO DE TL GA EDE EDGE

0

200

400

600

800

1000

1200

1400

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.

43

Unsch BPSO WDO DE TL GA EDE EDGE

0

0.5

1

1.5

2

2.5

3

PAR

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

5.0.2.1 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-

44

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 17:00→24:00 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)

0

2

4

6

8

10

12

Energy consumption (KWh)

Unsch

BPSO

WDO

DE

TL

GA

EDE

EDGE

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.

45

Table 5.4: Comparison of cost

Scheduling algorithms Cost (cent) Diﬀerence

(cent)

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

Unsch BPSO WDO DE TL GA EDE EDGE

0

200

400

600

800

1000

1200

1400

Total cost (Cost)

Figure 5.6: Total cost

5.0.2.2 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

46

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.

Unsch BPSO WDO DE TL GA EDE EDGE

0

0.5

1

1.5

2

2.5

3

PAR

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

47

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.

5.0.3.1 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 17:00→24:00 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.

5.0.3.2 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-

48

1 2 3 4 5 6 7 8 9 10 111213 14 15 161718 19 20 212223 24

Time (hours)

0

2

4

6

8

10

12

14

Energy consumption (KWh)

Unsch

BPSO

WDO

DE

TL

GA

EDE

EDGE

Figure 5.8: Energy consumption of appliances

Table 5.6: Comparison of cost

Scheduling algorithms Cost (cent) Diﬀerence

(cent)

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

49

Unsch BPSO WDO DE TL GA EDE EDGE

0

200

400

600

800

1000

1200

1400

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

50

Unsch BPSO WDO DE TL GA EDE EDGE

0

0.5

1

1.5

2

2.5

3

PAR

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

51

based HEMS in ﬁrst and last scenario. Finally, EDE algorithm outperforms

to reduce PAR.

52

Chapter 6

Conclusion and Future Work

53

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

problems.

54

Chapter 7

References

55

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