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Heuristically Optimized Home Energy Management in Smart gird

By

Hafiz Majid Hussain

UET-15S-MSEE-CASE-10

Supervisor

Dr. Abdul Khaliq

Co-supervisor

Dr. Nadeem Javaid

ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT

CENTER FOR ADVANCED STUDIES IN ENGINEERING

UNIVERSITY OF ENGINEERING AND TECHNOLOGY TAXILA

Spring 2017

TABLE OF CONTENTS

Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Final Approval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2: Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3: System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 HEMS architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 Energy consumption model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4 Load categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4.1 Regularly operated appliances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4.2 Shift-able appliances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4.3 Elastic appliances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5 Energy cost and unit price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4: Problem formulation and Proposed solution . . . . . . . . . . .

2

5

6

15

16

16

16

17

17

18

18

19

22

4.1 PAR . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2 User comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Objective function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4 Optimization techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4.1 GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4.2 WDO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.4.3 HSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .

4.4.4 GHSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .

4.5 Feasible region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .

4.5.1 Feasible region for SH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.2 Feasible region for MHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5: Simulations and Discussions . . . . . . . . . . . . . . . . . . . . . . . .

5.1 Simulation and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1.1 Load profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1.2 Cost per hour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1.3 Cost per day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1.4 PAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.15 User comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 6: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 7: References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

24

24

26

27

28

29

31

33

33

37

41

42

43

47

49

50

53

54

55

56

iii

DECLARATION

.

I certify that research work titled “Heuristically Optimized Home Energy Management in

Smart grid” is my own work. The work has not been presented elsewhere for assessment.

Where material has been used from other sources it has been properly acknowledged/referred.

Signature:

Hafiz Majid Hussain

Sp/2015/MSEE/015

iv

ABSTRACT

The smart grid appears an advanced and upgraded form of the power grid. As an essential

component of the smart grid, demand side management (DSM) enhances the energy efficiency of

electricity infrastructure. In this paper, we propose home energy management controller (HEMC)

based on heuristic algorithms to reduce electricity expense, peak to average ratio (PAR), and

maximize user comfort. We consider proposed HEMC for a single home and multiple homes. In

particular, for multiple homes we classify modes of operation for the appliances according to their

energy consumption with varying operation time slots. This strategy influences the consumers to

reshape energy consumption profile in response to electricity cost. In order to achieve an optimal

scheduling of energy consumption profile of the household appliances, we explore heuristic

algorithms, such as wind-driven optimization (WDO), harmony search algorithm (HSA), and

genetic algorithm (GA). We also propose a hybrid optimization algorithm genetic harmony search

algorithm (GHSA) that can schedule energy consumption profile in an appropriate way. The

existing and proposed optimization algorithms are investigated by considering single home and

multiple homes with real-time electricity pricing (RTEP) and critical peak pricing (CPP) tariffs.

Finally, simulation results are conducted which shows proposed algorithm GHSA performs

efficiently to reduce electricity cost, PAR, and maximize user comfort.

v

DEDICATION

Dedicated to my mother Shahida Nasreen

and my sister Engr. Wajeeha samer without whom none of my success would be

possible.

vi

ACKNOWLEDGEMENT

In the name of Allah, We praise Him, seek His help and ask for His forgiveness.

Whoever Allah guides, none can misguide, and whoever He allows to fall astray, none

can guide them aright. First, it is a great privilege for me in expressing most sincere gratitude to

my supervisor, HoD/Chairperson Prof. Dr. Abdul Khaliq chairman department of electrical

engineering CASE, Islamabad, and my co-supervisor Associate. Prof. Dr. Nadeem Javaid for

their support, guidance, encouragement in fulfilling my ambitions. Their kindness, friendly

accessibility, and considerations have been a great encouragement to me. My sincere thanks to

my supervisor and co-supervisor for their valuable support.

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 has 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.

vii

LIST OF ACRONYMS

HEMS Home energy management system

HSA Harmony search algorithm

PAR Peak to average ratio

RES Renewable energy source

RTEP Real-time electricity pricing

TOU Time of use

CPP Critical peak pricing

EDE Enhanced differential

WDO Wind-driven optimization

GA Genetic algorithm

IBR Inclined block rate

BPSO Binary particle swarm optimization

EMC Energy management controller

ILP Integer linear programming

GHSA Genetic harmony search algorithm

GWDO Genetic wind driven optimization

AMI Advanced metering infrastructure

HMCR Harmony memory consideration rate

viii

MKP Multiple knapsack problem

DSM Demand side management

HEMC Home energy management controller

Pm Probability of mutation

Pc Probability of crossover

Vnew Veloctiy in the current iteration

HSA Harmony search algorithm

ix

LIST OF FIGURES

1.1 Abstract picture of smart grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1 HEMS architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.1a Electricity cost and Consumption of SH using RTEP . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1b Electricity cost and Consumption of SH using CPP . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2a Electricity cost and Consumption of MHs using RTEP . . . . . . . . . . . . . . . . . . . . . . . 36

4.2b Electricity cost and Consumption of MHs using CPP . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3a Electricity cost and Waiting time of SH using RTEP . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3b Electricity cost and Waiting time of SH using CPP . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4a Electricity cost and Waiting time of MHs using RTEP . . . . . . . . . . . . . . . . . . . . . . . 38

4.4b Electricity cost and Waiting time of MHs using CPP . . . . . . . . . . . . . . . . . . . . . . . . 39

5.1a RTEP tariff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1b CPP tariff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2a Load profile for SH using RTEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2b Load profile for SH using CPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2c Load profile for MHs using RTEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2d Load profile for MHs using CPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3a Cost per hour for SH using RTEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3b Cost per hour for SH using CPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3c Cost per hour for MHs using RTEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3d Cost per hour for MHs using CPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.4 Cost per day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.5 PAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.6 Average waiting time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

x

LIST OF TABLES

2.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Heuristic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1 Load description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1 GA parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 WDO parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 HSA parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.4 Computational time of heuristic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.1 Load profile comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2 Total cost comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3 PAR comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

xi

Final Approval

This thesis titled

Heuristically Optimized Home Energy Management in Smart grid

By

Hafiz Majid Hussain

Has been approved for

Center for Advanced Studies in Engineering, Islamabad

Supervisor: ___________________________________________________________

Dr. Abdul Khaliq

Associate Professor, Department of Electrical Engineering

Center for Advanced Studies in Engineering, Islamabad

Co-Supervisor: ________________________________________________________

Dr. Nadeem Javaid

Associate Professor, Department of Computer Science

COMSATS Institute of Information Technology, Islamabad

External Examiner: ____________________________________________________

Muhammad Naeem

Assistant Professor, Department of Electrical Engineering

Capital University of Science and Technology, Islamabad

Chapter 1

Introduction

1

1.1 Introduction

The traditional grid is facing numerous challenges, including old infrastructure, lack

of communication, increasing demand for energy, and security issues. To address

these issues, the concept of smart grid has emerged which comprises of information

and communication technologies that allow bidirectional communication between the

utility and consumer. Broadly speaking, smart grid appears as a next generation grid

and incorporates advanced technologies in communication, distributed generation,

cyber security, and advanced metering infrastructure [1]. These features of the smart

grid ultimately enhance the eﬃciency, reliability, and ﬂexibility of the power grid.

The key objective of the smart grid is the transformation of the traditional grid to a

cost eﬀective and energy eﬃcient power grid.

DSM is an essential component in energy management of the smart grid. Generally,

DSM refers to manage the consumer’s energy usage in such a way to yield desired

changes in load proﬁle and facilitates the consumers by providing them incentives

[2]. For this purpose, various DSM techniques have been proposed in literature,

including peak clipping, valley ﬁlling, load shifting, strategic conservation, strategic

load growth, and ﬂexible load shape [3]. Furthermore, DSM is capable of handling

the communication infrastructure between end user and utility and also enables the

integration of distributed energy resources to optimize energy consumption proﬁle.

Recently, one of the crucial DSM activities is demand response (DR), it is presumed

that DR is the subset of DSM in a broader aspect. DR is deﬁned as the tariﬀs or

programs established to inﬂuence the end users to reshape their energy consumption

proﬁle in response to electricity price [4]. DR program is further categorized into two

types; incentive based program and price-based program. Incentive based program

provides monetary incentive to the end user on the base of load curtailment. Various

incentive programs are discussed in the literature, including direct load control (DLC),

curtailable load, demand bidding and buy back, emergency and demand. On the

other hand, price based program provides the price of electricity during diﬀerent time

intervals. The purpose of the price-based program is to reduce electricity usage when

2

the electricity price is high and thus, reduce demand during peak periods. Price-based

programs are; time of use (ToU), RTEP, inclined block rate, CPP, and day ahead

pricing. DR is considered as a key feature in smart grid to improve the sustainability

and reliability of power grid. However, it is examined in the literature that researchers

considered the DSM and DR are interchangeable [5], [6].

Home energy management system (HEMS) is considered as an integral part for the

successful DSM of the smart grid [7]. HEMS provides an opportunity for the residen-

tial sector consumers to communicate with the household appliances and the utility

to improve the energy eﬃciency regarding electricity tariﬀ and consumer’s comfort. A

wide range of research has been made to study scheduling problems in HEMS. A hy-

brid genetic particle swarm optimization (HGPO) is proposed to schedule the energy

consumption of appliances in HEMS with the integration of renewable energy sources

(RESs) [8]. A heuristic optimization algorithm, such as GA is used to schedule appli-

ances for the residential, commercial, and industrial sectors [9]. Similarly, in [10], [11],

binary particle swarm optimization (BPSO) and mixed integer linear programming

(MILP) are used to schedule the appliances and mitigate electricity cost and PAR. In

[12], authors propose a general architecture of HEMS based on GA in the presence of

RTEP and inclined block rate to reduce electricity cost and PAR.

In this paper, we propose a HEMC based on an optimization algorithm GHSA for the

optimal scheduling of energy consumption. There are two contributions in the paper.

First, we propose an optimization algorithm GHSA to minimize electricity cost, PAR,

and average waiting time of the appliances. In order to validate the eﬀectiveness

of the proposed algorithm, it is compared with the existing algorithms, including

WDO, HSA, and GA. Second, the paper gives insight the impact of optimization

algorithms on a single home (SH) and multiple homes (MHs) with RTEP and CPP

tariﬀs. Speciﬁcally, for MHs we consider ﬁfty homes with diﬀerent operational modes

of the appliances regarding energy consumption and time interval. Finally, results

of the proposed and existing algorithms are compared which show that our proposed

algorithm performs signiﬁcantly to achieve better results in terms of electricity cost,

PAR, and average waiting time of the appliances.

3

The rest of the paper is structured as follows. Section II presents related research

work. Section III presents a comprehensive study of the system model. Section IV

describes the simulation results along with the discussion. At the end, we present the

conclusion of the paper in section V.

The rest of the thesis is structured as follows. Chapter 2 presents related research

work. Chapter 3 presents a comprehensive study of the system model. Chapter 4

describes the problem formulation and proposed solution. Chapter 5 deals simulation

results along with the discussion. At the end, we present the conclusion of the thesis

in chapter 6.

Power

flow

Figure 1.1: Abstract picture of smart grid

4

Table 1.1: Nomenclature

Symbols Description Symbols Description

Ec,T L Total energy consumption

in a day

Pcur Pressure of air parcel in a

current location

ςRa,TLEnergy consumption of reg-

ularly operated appliances

xnew Position of air parcel in the

new location

ςSa,TLEnergy consumption of

shift-able operated appli-

ances

xcur Position of air parcel in the

current location

ςEa,TLEnergy consumption of elas-

tic operated appliances

xold Position of air parcel in the

previous location

%TL

RaCost per day of regularly

operated appliances

Xnew Updated value of harmony

%TL

SaCost per day of shift-able

appliances

ταEnding time of Operation

after scheduling

%TL

EaCost per day of elastic ap-

pliances

Tmax Maximum time of the appli-

ance operation

εElectricity pricing signal Tmini Minimum time of the appli-

ance operation

ζON-OFF states of appli-

ances

ΥT L Total electricity cost for

ﬁfty homes

aαStarting time of appliance Ω Rotation of the earth

bβEnding time of appliance ∇Pressure gradient

WWaiting time of appliance ρAir parcel density

OtOperation time interval µvelocity of the wind

Vcur Velocity of air parcel in cur-

rent iteration

δV Inﬁnite mass and volume

Vnew Velocity of air parcel in new

iteration

gEarth’s gravity

ςaiEnergy consumed by appli-

ance i

5

Chapter 2

Related work

6

2.1 Related work

With the emergence of the smart grid, the consumer and the utility can exchange

real-time information based on electricity pricing tariﬀs and energy demand of the

consumer. The two way communication beneﬁts not only the consumers, but also

improve stability of the power grid. With this motivation, various models are designed

to schedule energy consumption usage. Authors in [13], comparatively evaluate the

performance of HEMC which is designed to schedule energy consumption on the

basis of heuristic algorithms: GA, BPSO, and ant colony optimization (ACO). For

energy pricing, combined model of ToU and inclined block tariﬀ (IBR) are employed.

Simulation results show that designed model for energy management acts signiﬁcantly

to reduce the electricity cost, PAR, and satisfy user comfort level. However, the

computational complexity and time are increased. In [14], authors aim to reduce

electricity cost, PAR , and considering user comfort. The appliances are classiﬁed

into ﬁve groups by taking consideration of user comfort constraints in response to

RTEP signal. Multiple knapsack problem (MKP) is used for the problem formulation

and an optimization algorithm GA is employed to schedule the load proﬁle. The

proposed model shows eﬃcient results to reduce the electricity cost and improve user

comforts. However, if the number of users increases the proposed algorithm provides

infeasible solution.

Jon et al. [15], propose HEMS model for energy optimization and categorize house-

hold appliances as thermostatically controlled appliances and interruptible appliances.

The major objective of the proposed model is to tackle the uncertainties with a diﬀer-

ent kind of load and reduce the electricity cost while taking into account of the user

comfort. BPSO is amalgamated with integer linear programming (ILP) to solve the

proposed problem. The proposed algorithms are tested with the scrutiny of required

home appliances and day-ahead pricing scheme. However, the scheme will be more

robust by considering RTEP tariﬀ and predictive model. Authors in [16], present an

improved model for the energy consumption of residential appliances. The desired

objective is to minimize the cost by managing energy consumption of the appliances.

Fractional programming (FP) is used for scheduling energy consumption by consid-

7

ering RTEP tariﬀ and distributed energy resources. Despite the cost minimization,

authors do not address the user comfort.

The work in [17], mitigates the energy consumption behavior and the electricity cost.

The DSM techniques take into account in the presence of distributed generation, time-

diﬀerentiated prices, and preference of loads. The minimization problem is solved

using a constructive algorithm with GA while considering the user comfort and en-

ergy cost. The proposed model is tested using radial residential electrical network

to verify the results. However, authors do not mention any strategy to control PAR.

Authors in [18], provide a detailed study of HSA algorithm, the primary steps, its

adaptation, and its specialty in diﬀerent ﬁelds. Also, authors comparatively discuss

the searching criteria of diﬀerent optimization techniques and HSA. Improved ver-

sions of the HSA are proposed, such as improved harmony search (IHS), global best

harmony search algorithm (GBHSA), and chaotic harmony search algorithm (CHSA)

in order to achieve eﬃcient results. Additionally, the contribution of HSA in the

various disciplines are elaborated, including electrical engineering, civil engineering,

computer science, biomedical, economics, and ecology. At the end, authors inferred

that HSA is a better choice by attaining eﬃcient results in many complex scenarios.

Authors in [19], design day ahead scheduling model for microgrids system with the

integration RESs in order to minimize the start up cost and generation cost of the

RESs. To address the problem, the mathematical formulation is carried out as an

optimization problem. Authors, propose an algorithm which is a hybrid of enhance

diﬀerential evolution (EDE) algorithm and HSA. The improvement in the tuning pa-

rameters of EDE and HSA are also carried out which enhances the search diversity.

Moreover, the results of the proposed algorithm are compared with other scheduling

algorithms and the proposed model veriﬁcation is done using IEEE standard bus sys-

tem. As the number of the buses increases, the proposed algorithm shows eﬀective

results, however, convergence rate is decreased and real-time based constraints are

not considered. The work in [20], demonstrates the day ahead load shifting technique

and problem is formulated as a minimization problem. A heuristic-based evolutionary

algorithm is used for solving minimization problem. Three diﬀerent kinds of the area

are considered: residential, commercial, and industrial areas. The primary objective

8

is to reduce the utility bills for the consumers in the mentioned areas. Simulation

results show the substantial saving in electricity cost while reducing peak load de-

mand. The proposed algorithm achieves major results, however, the complexity of

system increases due to the consideration of a large number of appliances and also

user comfort is ignored. Danish et al. in [21], present HEMS model based on heuristic

algorithm BSPO. The aim of the authors is to minimize the electricity cost while con-

sidering user comfort. In this regard, the total time slots i.e., 24 hours is divided into

4 sub time slots to eﬀectively manage the electricity consumption and cost. Simula-

tion results show that proposed HEMS model act signiﬁcantly to achieve the desired

objective. However, the computational time of the system is increased.

Authors in [22], present a generic model of DSM in order to optimize energy consump-

tion in the residential sector. In a home environment, energy management controller

(EMC) is used to control energy consumption of the appliances during peak hours.

In this regard, GA based EMC is used for scheduling purpose and RTEP pricing

signal is used for billing mechanism. The performance parameters electricity cost,

PAR and waiting time of the appliances are compared with EMC and without EMC

unit. Simulation results show that GA-based EMC reduces electricity cost, and PAR.

However, GA-based EMC does not provide an eﬀective approach to improve the user

preference. In [23], authors propose a comprehensive model for energy management in

homes with multiple appliances. The proposed model consists of six layered architec-

ture and each layer is connected with other in order to achieve better results in terms

of cost reduction and PAR. The objective of the study is to provide electricity in a

sophisticated manner to the consumer by taking into account theft and fault detec-

tion, greenhouse gases, ToU pricing signal, and single knapsack scheduling algorithm.

Results show that reduction in electricity cost and PAR, however, the architecture of

the proposed model is complicated and sensitive i.e., any inappropriate information

can devastate overall architecture.

The work in [24], provides a comprehensive study of WDO technique, the basic con-

cepts, structure its variants, and its application in electromagnetics. A numerical

study is presented using unimodal and multimodal test functions and results of WDO

and other optimization techniques like; PSO, GA, and diﬀerential algorithm (DE)

9

are compared. Moreover, WDO along with PSO, GA, and DE are applied to three

electromagnetics optimization problems and the results demonstrate the WDO out-

performs PSO, GA, and DE. A recent work in [25], proposes a novel approach of DSM

with the integration of RESs. The energy provider inspects the load proﬁle and the

price of the electricity. Authors aim to reduce the deviation of average load energy

demand by scheduling the energy consumption and storage devices. To solve schedul-

ing problem, authors model the energy consumption and storage as a non-cooperative

game. The simulation results demonstrate the minimization of cost reduction in peak

load of the system.

In [26], authors demonstrate the electricity load scheduling problem for multi-resident

and multi-class appliances using problem ladson generalized bender algorithm while

considering energy consumption constraint. The main objective of proposed algo-

rithm is to protect the private information of the residences and maximize the users

satisfaction. The proposed scheme is eﬃcient by tackling private information of resi-

dence and obtain the optimal load scheduling for each residence in a multi-residential

system. However, due to the slow convergence rate of proposed algorithm overall

computational time is increased. Authors in [27], give insight of scheduling the en-

ergy management in the residential sector and propose two horizon algorithms. The

proposed algorithms are eﬃcient to reduce electricity cost with less computational

time. Moreover, authors also discuss the implementation of proposed algorithms and

challenges related to its implementation. Results ensure the validity of the proposed

model in terms of cost reduction and fast convergence.

Mohsenian et al. in [28], propose an autonomous DSM model in which energy is

provided to multiple homes and each home is equipped with energy management

scheduling (EMS) device. EMS interacts with the utility and consumer to schedule

the energy consumption using distributive algorithms. Authors formulated the prob-

lem as an optimization problem which is solved using game theory approach with

an aim at reducing electricity cost and PAR. Simulation results show that signiﬁ-

cant amount of reduction in electricity cost and PAR. However, user preference is not

addressed. The work in [29], provides an improved HEMS architecture considering

various appliances in the home. Multi- time scale optimization is formulated in order

10

to schedule energy consumption of appliances. A predictive model based-heuristic

solution is proposed and its performance is compared with benchmark algorithms.

Results show the eﬀectiveness of proposed model in terms of electricity cost reduction

and computational complexities. However, PAR is ignored which is a key parame-

ter for load curtailment. In [30], authors present power scheduling based protocol to

keep the electricity cost below a pre-deﬁned budget. Appliances are classiﬁed into two

groups with an aim at reducing peak demand and electricity cost. However, optimiza-

tion of real time appliances is not considered, which exceeds the predeﬁned budget.

Table 2.1 lists the summary of the research work based on heuristic techniques.

11

Table 2.1: Heuristic techniques

Techniques Aims Distinctive attributes Limitations

Hybrid technique

(GA and PSO) [8]

Minimization

of cost and

PAR

HEMS model is considered

with distributed energy

resources and energy

storage system

User comfort is

ignored

EA [9] Cost reduction

Energy optimization in

residential, commercial, and

industrial area

System

complexity is

enhanced

BPSO [10] Cost and PAR

minimization

Working of BPSO in

complex, nonlinear, and

continuous problems

Practical

implementation

is not addressed

MILP [11] Cost

minimization

Scheduling energy

consumption of appliances,

its simplicity

PAR is not

addressed and

user comfort is

ignored

GA [12]

Cost reduction

and user

comfort

Cost reduction by

optimizing energy

consumption and time slots

are divided

System deals

with large

number of

appliances in

multiple sector

which increases

system

complexity

12

GA, BPSO,

ACO [13]

Cost and PAR

reduction by

satisfying user

comfort

HEMC schedules the

appliances by considering

user satisfaction and RESs

integration

System

complexity and

computational

time are

increased

GA [14]

Cost reduction

and user

comfor

Optimizes energy

consumption behavior with

RESs incorporation

Challenges

related to RESs

are not

addressed and

PAR is ignored

Hybrid

technique

(LP and

BPSO) [15]

Cost reduction

and user

comfort

maximization

Thermostatically and

interruptible appliances are

considered with day ahead

pricing model

PAR is not

considered

FP [16] Electricity cost

reduction

Cost eﬃcient model with

distributed energy resources

and practical

implementation of the

model proposed

PAR and user

comfort are not

taken into

account

GA [17] Cost and PAR

reduction

Proposed model is tested

using radial residential

electrical network

System

complexity and

computational

time enhances

HSA [18]

Basic concepts

of HSA, its

structure, and

applications

Improved and hybrid HSA

with application

Real time

implementation

is not considered

13

Hybrid

technique

(EDE and

HSA) [19]

Start up and

generation cost

of RESs

Veriﬁcation is done using

IEEE standard bus system

Computational

time is increased

BPSO [21]

Electricity cost

minimization

considering

user preference

Simplicity and robustness

of BPSO

System

complexities are

increased as

time slot is

divided into sub

time slots

GA [22]

Minimization

of electricity

cost, PAR, and

waiting time

Generic model of DSM with

EMC using RTEP

User comfort is

not addressed

eﬃciently

Single

knapsack [23]

Energy

consumption

optimization

considering six

layer

architecture

Comprehensive model for

energy management

addressing six layer

architecture

Complicated

architecture in

terms of

modeling in

practical

scenario

14

Chapter 3

System model

15

3.1 System model

As mentioned before, for the eﬀective deployment of smart grid, HEMS is crucial.

HEMS can manage, control, and optimize energy consumption in home environment.

As an essential element of HEMS, HEMC is used to schedule energy consumption

based on heuristic techniques to eﬀectively reduce electricity cost and monitor user

preference.

The system model comprises of HEMS architecture, energy consumption model, load

categorization, energy cost and unit price, and problem formulation.

3.2 HEMS architecture

HEMS eﬀectively visualizes the load consumption information in home and con-

tributes towards the energy balancing between the supply and demand side. HEMS

comprises of HEMC, smart meter (SM), advance metering infrastructure (AMI), in-

home display device (IHD), and smart appliances. These advanced tools provide

bidirectional ﬂow of information and power between the utility and consumer to eﬃ-

ciently reduce electricity cost. The pictorial view of HEMS is shown in Figure. 3.1.

Moreover, HEMC consists of embedded system which schedules the energy consump-

tion of the appliances using heuristic optimization algorithms.

3.3 Energy consumption model

We consider a home with a set of appliances A,{a1, a2, a3, . . . , aN}, such that

a1, a2, a3, . . . , aNrepresents each appliance over the time horizon t T,{1,2,3, . . . , T }.

Each time slot represents one hour and the total time interval is 24 hours (T= 24),

in accordance with the single day. The total energy consumption of the appliances in

a day can be mathematically represented as:

Ec,TL=

T

X

t=1 N

X

j=1

E(aj,t)!∀t T, a A (3.1)

16

In smart grid, each home is equipped with HEMC to optimize energy consumption

and reduce electricity cost. Therefore, we categorize the appliances into three groups

which are presented in the following subsection.

Internet

Utility

Company

Smart Meter

HEMC

Elastic Appliances

Regularly operated Appliances

Shift-able Appliances

Power flow

Information flow

Figure 3.1: HEMS architecture

3.4 Load categorization

We have categorized each appliance on the bases of energy consumption, operating

time, and user preference. Suppose An={RaSSaSEa}represents a set of ap-

pliances, where Rais regularly operated appliances, Sashiftable appliances, and Ea

elastic appliances. Table 3.1 shows power ratings and time of operation of the appli-

ances.

1) Regularly operated appliances

These are also called ﬁxed appliances because their energy consumption proﬁle can not

be modiﬁed by HEMC. They are vacuum pump, water pump, dishwasher, and oven.

Regularly operated appliances are represented as (Ra) and their energy consumptions

are represented by ςRa. While power rating of Rais expressed as ξRaand the total

17

energy consumption in a day is given as:

ςRa,TL=

T

X

t=1 X

RaAn

ξt

Ra×ζ(t)!(3.2)

Similarly, the total cost per day of the Rais given as:

%TL

Ra=

T

X

t=1 X

RaAn

ξt

Ra×ε(t)×ζ(t)!(3.3)

Where ζ(t)[0,1] is the operation state of appliances in time interval t Tand ε

represents the pricing signal.

2) Shift-able appliances

These are controllable appliances and their operation time can be shifted to any time

slot without performance degradation, however, once they turn ON their length of

operation must be completed. They are also named as burst load for example, washing

machine and cloth dryer. Shift-able appliances are denoted by (Sa) and power rating

of Sais νSa. The total energy is computed as:

ςSa,TL=

T

X

t=1 X

SaAn

νt

Sa×ζ(t)!(3.4)

The total cost calculated of Sain a day is calculated as:

%TL

Sa=

T

X

t=1 X

SaAn

νt

Sa×ε(t)×ζ(t)!(3.5)

3) Elastic appliances

These are considered as a ﬂexible appliances i.e., their time period and energy con-

sumption proﬁle are ﬂexibly adjusted. They are also named thermostatically-controlled

appliances, such as water heater, air condition, water dispenser, and refrigerator. Let

us consider µEais the power rating of elastic appliances (Ea) and the total energy of

Eais computed as:

ςEa,TL=

T

X

t=1 X

EaAn

µt

Sa×ζ(t)!(3.6)

18

The total cost per day of Eais given as:

%TL

Ea=

T

X

t=1 X

EaAn

µt

Ea×ε(t)×ζ(t)!(3.7)

Let us assume that the total energy consumed (ςT) by appliances in total time interval

24 hours is given:

ςTL=ςRa,TL+ςSa,TL+ςEa,TL(3.8)

Similarly, total cost per day of Ra,Sa, and Eaappliances is calculated:

%TL=%TL

Ra+%TL

Sa+%TL

Ea(3.9)

The energy consumption of each appliance in given time period can be mathematically

shown in matrix form as:

Ec=

ςt1

Ra. . . ς t1

Sa. . . ς t1

Ea

ςt2

Ra. . . ς t2

Sa. . . ς t2

Ea

.

.

..

.

..

.

.

ςT

Ra. . . ς T

Sa. . . ς T

Ea

(3.10)

3.5 Energy cost and unit price

Various electricity tariﬀs are proposed to deﬁne electricity cost for a day or for a short

time period. In our model, we consider RTEP and CPP tariﬀs.

The RTEP tariﬀ is typically updated for each hour during a day and is capable of

contributing better approximation of real time power generation cost. RTEP imple-

mentation requires two way of communication in order to interact with the consumer

in a real time. Therefore, the aim of RTEP is to reduce demand of consumer during

peak demand times. RTEP is also referred as dynamic pricing.

The CPP tariﬀ has resemblance with ToU pricing regarding ﬁx prices in diﬀerent

time intervals. The implementation of CPP during critical event imparts proﬁtable

response to the utility [5]. However, due to stress on the power grid, the prices are

19

replaced by the predeﬁned higher rate in order to reduce energy demand. Thus, the

aim of the CPP tariﬀ is to assure the reliability and sustainability of the power grid.

In our research work, we consider RTEP and CPP tariﬀs because in normal operation

of power grid, the RTEP behaves more ﬂexibly as compared to other pricing signals.

During critical conditions (high electricity demand and low generation) of the power

grid consumers have to pay high electricity prices in the respective days or hours.

Thus, both pricing signals are considered and electricity cost is reduced by scheduling

energy consumption in oﬀ-peak hours.

20

Table 3.1: Load description

Appliances

group

Appliances Power ratings

(kW)

Time of oper-

ation (hours)

Vacuum

pump

0.6 6

Regularly op-

erated appli-

ances

Water pump 1.18 8

Dish washer 0.78 10

Oven 1.44 18

Shift-able ap-

pliances

Washing ma-

chine

[3.60 0.5 0.38 ] [5 4 3]

Cloth dryer [4.4 2 0.8] [4 3 2]

Refrigerator [1 0.75 0.5] [18 16 15]

Elastic appli-

ances

AC [1.5 1.44 1] [15 13 14]

Water heater [4.45 1.2 1] [7 5 4]

Water Dis-

penser

[1.5 1 0.5] [11 10 9]

21

Chapter 4

Problem formulation and Proposed solution

22

In this research work, we considered SH and MHs with household appliances and our

desired objectives are: to reduce electricity cost by scheduling energy consumption

in low price hours (oﬀ-peak hours), to maintain grid stability by minimizing PAR,

and to maximize user comfort level. We formulate our objective function using MKP

approach which is based on the following assumptions:

•Assuming Anas number of items (N).

•Each of the items comprises of two attributes i.e., weight and the value. The

weight of the items expresses the energy usage of the appliances in time interval

(t). And the value of the items denotes the energy cost of the appliances.

However, the weight of the appliances is independent of the time interval.

•We consider Nnumber of knapsacks in order to limit power consumption of

each category of the appliances and also to limit the total power capacity (Cg).

By considering aforementioned assumptions, the utility and consumers can actively

cooperate in energy demand management in order to reduce electricity cost and PAR.

To achieve the grid sustainability, total energy consumption of the appliances in each

time interval t Tshould not exceed Cg. For this reason, we limit the total energy

consumption as:

0≤ςTL≤Cg(4.1)

If the constraint in Eq. 4.1 is satisﬁed the inadequacy of power and stresses on the

grid can be eliminated.

4.1 PAR

PAR is the ratio of the maximum aggregated load consumed in a certain time frame

and the average of the aggregated load. PAR informs about the energy consumption

behavior of the consumers and the operation of the power grid. The high PAR

jeopardizes the grid stability and increases the electricity cost. While reduction in

PAR simultaneously enhances the stability and reliability of the power grids and

23

reduces the electricity bill of the consumers. Mathematically, it is expressed as:

Lpeak =max

tTςT(t) (4.2)

Lavg =PT

t=1 ςT(t)

T(4.3)

Lpeak and Lavg show the maximum aggregated load and average load in a time frame

(t). ς(t) represents the total energy consumption of the appliances in an hour.

P AR =Lpeak

Lavg

=

T max

tTςT(t)

PT

t=1 ςT(t)(4.4)

4.2 User comfort

In energy optimization, the load is shifted from peak hours to oﬀ-peak hours in order

to reduce electricity cost. In this context, Raconsumption patterns are not changed

and they must run with ﬁrst preference, whereas Saand Eaoperation time interval

(Ot) are ﬂexibly shifted. Saand Eacan be delayed to operate during peak hours to

reduce electricity cost, however, it incurs discomfort to the consumer. To evaluate

waiting time of appliances, we assume starting and ending time instant of appliances

aαTand bβT, such that (aα< bβ) and ταis the time period of appliances to ﬁnish

their operation and Wis expressed as waiting time of the appliances.

W=|τα−aα|

|bβ−Ot−aα|(4.5)

Wavg =PAn

a|τα−aα|

PAn

a|bβ−Ot−aα|(4.6)

Where, Eq. 4.6 shows the average waiting time of the appliances.

4.3 Objective function

Generally, objective function in optimization problem is deﬁned as follows [17]:

minimize

F(c) = f1(c), f2(c), f3(c),...fn(c)

24

subject to:

gj(c)≤0, j = 1,2,3,...m

hk(c) = 0, k = 1,2,3,...n

cl

p≤cp≤cu

p, p = 1,2,3,...q

Where F(c) represents objective functions, gj(c) is inequality constraint, while hk(c)

shows equality constraint and cl

p,cU

pshows lower and upper bound of decision vari-

ables. In this context, we introduce objective function given as:

minT

X

t=1

ε(t)

An

X

ai

ςai(t)×ζ(t),

T

X

t=1

Wavg (t)(4.7)

subjected to:

ςTL≤Cg(4.8a)

P AR =

T max

tTςT(t)

PT

t=1 ςT(t)≤Tmax (4.8b)

Tmin ≤t≤ T max (4.8c)

bβ

X

t=aα

νt

Sa=ςSa,TL, νt

Sa= 0,∀t T \ Ta(4.8d)

bβ

X

t=aα

µt

Ea≤ςEa,TL, µt

Ea= 0,∀t T \ Ta(4.8e)

0≤νt

Sa≤ςt

Ea,TL,∀t T(4.8f)

ςmini

Ea,TL≤µt

Ea≤ςmax

Ea,TL,∀t T(4.8g)

Wavg ≤5 (4.8h)

T

X

t=1

ςTL(t)unsche =

T

X

t=1

ςTL(t)sche,∀t T(4.8i)

Eq. 4.7 depicts objective function i.e., minimization of cost per day and waiting time

of the appliances. Eq. 4.8a-Eq. 4.8i are constraints of the objective function. Eq.

4.8a shows the total power consumption of appliances should not overreach the power

25

grid capacity. Eq. 4.8b limits the PAR less than Tmax the ideal value of Tmax is

equal to 1 which shows perfect ﬂat load proﬁle and can not obtain by any scheduling

algorithms. Eq. 4.8c guaranteed that time scheduled by appliances should not violet

the restriction. Eq. 4.8d and Eq. 4.8e are constraints represent the energy load

balance equation of Saand Eain any time slot (t). While Eq. 4.8f and Eq. 4.8g

indicate the maximum and minimum energy consumption of Saand Eaappliances in

each hour of the operation. Eq. 4.8h shows the maximum time that user postpone

the operation of Saand Ea. At last, Eq. 4.8i clearly demonstrates the total energy

consumption of the appliances in scheduled case and unscheduled case are always

equal i.e., the HEMC schedules the appliances by taking into account that appliances

must complete their length of operation.

4.4 Optimization techniques

Generally, mathematical techniques provide an accurate solutions to the problem

which is either feasible or infeasible. However, they are incapable of addressing the

complex problems due to the curse of dimensionality, slow convergence rate, and

complex calculations. While heuristic optimization algorithms are not guaranteed

the exact solution and provide approximate solutions, however, they are capable of

handling complex calculations. In spite of approximate solutions, optimization algo-

rithms are fair enough to converge faster, reach the desired solution, and applicable

in all ﬁelds of engineering and computer science [31]. For this purpose, we computed

our problem as an optimization problem and four heuristic optimization techniques:

WDO, HSA, GA, and GHSA are employed. The technique and algorithm are inter-

changeable used for optimization purpose in this paper. Each heuristic optimization

technique is explained as follows:

26

4.4.1 GA

GA is an adaptive algorithm based on the biological process [9]. Initially, a set of

random solutions is generated called chromosomes and the set of the chromosome is

considered as a population. Each chromosome comprises of genes and the value of

gene is either binary or numerical value. We consider the value of gene as 1 or 0 which

actually shows ON and OFF states of the appliances. The ﬁtness of each chromosome

is evaluated using Eq. 17 and the stochastic operators, crossover and mutation are

used to generate new populations. Two point crossover with crossover rate Pc= 0.9

is used and the obtained chromosome is further mutated through mutation process

which diversiﬁes the search space of the algorithm the mutation rate is considered

Pm= 0.1. The process of crossover and mutation enables to reach at global optimal

results. At the end, binary array [0 0 1 0 0 0 0 0 1 1] is obtained which shows the

appliance is ON at 3, 9 and 10 location of the array. We then ﬁnd out electricity

cost and energy consumption to achieve our desired objective. The optimal results

are obtained by considering the parameters in the table 4.1.

Table 4.1: GA parameters

Parameters Values

Maximum itera-

tion

200

Population size 30

Pc0.9

Pm0.1

The process is continued until the best optimal vector is achieved. Additionally, in

comparison to other existing optimization techniques, GA is more robust and solves

the complex non-linear problem with high convergence rate. GA also exhibits the

property of independence of problem domain and imparts divergent solution in a

single iteration.

27

4.4.2 WDO

WDO is the meta-heuristic algorithm which is inspired by the atmospheric motion of

wind. In WDO, inﬁnitely small air parcels move in a search space and wind blows

to equalize pressure on air parcels using four diﬀerent forces. These forces are cariols

forces, pressure gradient forces, gravitational forces, and the frictional forces. Coriolis

force tends to move the wind horizontally i.e., rotate the wind around the earth, while

pressure gradient force is deﬁned as; a change in wind pressure over distance covered

by the wind. When both coriolis force and pressure gradient force are equal they

balance the wind pressure horizontally. Furthermore, the gravitational force pulls

the wind towards its center and it is in the vertical direction, while the friction force

lowers the speed of the wind which in turn slow down the speed of coriolis force. All

of these forces are expressed mathematically as [21]:

CF=−2Ω ×µ, (4.9)

PGF =−∇P δV , (4.10)

Fg=ρδV g, (4.11)

Ff=ραµ, (4.12)

At ﬁrst, the random solution (vi) is generated using Eq. 4.13.

vi=Vmax ×2×(rand(populationsize, n)−0.5).(4.13)

Each of the random solution is evaluated using ﬁtness function and relatively good

solutions are reproduced, while bad solutions are neglected. In each step, position and

the velocity of the air parcel is evaluated and the new value of velocity is assigned to

each air parcel. The Eq. 4.14 shows the updated velocity (Vnew ) of air parcels

Vnew = (1 −α)Vcur −Vcur ×g(R×T|1

j−1|

(xnew −xold)) + cVcur

Pcur

,

(4.14)

Vnew =Vmax if Vnew > Vmax (4.15)

Vnew =Vmin if Vnew < Vmax (4.16)

28

After updating the velocity of the particle. New generation is obtained using Eq. 4.17

and the process will continue until stopping criteria is reached i.e., optimal scheduling

of energy consumption and minimization of electricity cost.

xnew =xcur + ( Vnew × 4t),(4.17)

The optimal results are obtained by considering the parameters in the table 4.2.

Table 4.2: WDO parameters

Parameters Values

Maximum itera-

tion

200

Population size 30

Vmin 0.9

Vmax 0.1

RT 3

α0.4

DimMax 5

DimMin -5

g 0.2

4.4.3 HSA

HSA is the music inspired technique proposed by Zong Woo [18]. In HSA each musi-

cian plays note repeatedly to improve its harmony and generates new random variable

according to Eq. 4.18. Tuning parameters are also adjusted to achieve best harmony.

The initial population is generated randomly as:

Xij =Li+rand(Ui−Li) (4.18)

29

Where Ui, Lishows upper and lower bound. Eq. 4.18 shows randomly generated

variables in matrix form:

HM =

X1

1X2

1X3

1. . . Xm

n

X1

2X2

2X3

2. . . Xm

n

.

.

..

.

..

.

..

.

.

Xn

1Xn

2Xn

3. . . X m

n

(4.19)

The initial population generated (HM) by Eq. 28 is compared with the harmony

memory consideration rate (HMCR). HMCR speciﬁes the probability of employing

the value of randomly generated matrix. However, suitable HMCR rate is considered

as 70% to 90% of the value from the entire pool of harmony memory (HM). The

condition for HMCR is:

Xnew =

X{x1i, x2i, x3i. . . xHM }, W ith P (H M CR)

X{x1, x2, x3. . . xN}, W ith P (1 −HM C R).

(4.20)

The values are selected from HM and their pitch are adjusted using pitch adjust-

ment ratio (Par). Par diversify the search space and increases the optimality of the

algorithm. Par can be adjusted as:

Xnew =

Y ES, W ith P (P ar)

N O, W ith P (1 −P ar ).

(4.21)

After achieving new harmony vector ﬁtness function is evaluated using Eq. 4.7. If

new harmony vector is better than worst harmony replace the worst harmony in the

HM. The new harmony is binary coded string and shows the appliances ON/OFF

states. The optimal results are obtained by considering the parameters in the table

4.3.

30

Table 4.3: HSA parameters

Parameters Values

Maximum itera-

tion

100

Population size 30

HMCR 0.9

P Amin 0.4

P Amax 0.9

Bwmin 0.0001

Bwmax 0.1

4.4.4 GHSA

We propose heuristic optimization algorithm by combining the attributes of GA and

HSA in order to achieve better results as compared to existing algorithms. It is noticed

in [18], that HSA has quality to perform searching with high speed i.e., converges at

faster rate, while GA has capability to search for global optimal solution. For this

reason, we combine the attributes of GA and HSA to achieve global optimal solutions

with faster convergence rate. Moreover, we have seen that GA reduces electricity

cost, however, incapable of handling the user comfort. On the other hand, HSA

eﬃciently addresses user comfort of the end user. Thus, we incorporate complete

steps of HSA then we adopt crossover and mutation steps of GA. Hence, results show

that hybrid algorithm performs better in terms of cost minimization and user comfort

maximization compared with other existing optimization techniques. Table 4.4 shows

the computational time (sec) for existing and proposed algorithms.

31

Algorithm 1: GHSA

Initialization of parameters;

Randomly generate population using Eq. 4.18;

for i=1:HMS do

for j=1:Ncdo

Randomly generated Xi

jin HM ;

end for

end for

End of initialization step;

while Maximum number of iteration reached do

Construction and assessment of new candidate;

if (rand(0,1) ≤HMCR) then

Choose randomly from existing harmony

if (rand(0,1) ≤par) then

Adjust the tone randomly using par

end if

else

Select pair x, y randomly from existing harmony

if rand(0,1) ≤Pcthen

crossover (x,y)

end if

if rand ≤Pmthen

mutate (x,y)

end if

end if

Evaluate ﬁtness function a: F(a) using Eq. 4.7 ;

End of the construction and assessment step;

Construction and assessment of new candidate: a ;

if F(a) has best value than the worst member of HM then

Replace the worst HM member with new candidate: a

else

Discard a

end if

End of HM update;

Until a preset criterion is met

end while

32

Table 4.4: Computational time of heuristic techniques

Schemes Techniques Computational

time (sec)

WDO 2.61

HSA 2.01

SH GA 1.5

GHSA 1.43

WDO 100.21

HSA 96.1

MHs GA 70.46

GHSA 60.33

4.5 Feasible region

Feasible region is deﬁned as the set of optimal points which satisﬁes all the constraints

given in a scenario, including inequalities, equalities, and integer constraints. We

consider feasible region of electricity cost versus energy consumption and electricity

cost versus average waiting time for a SH and MHs using RTEP and CPP tariﬀs.

4.5.1 Feasible region for SH

In this segment, we ﬁgure out the feasible region for electricity cost and energy con-

sumption of SH by considering RTEP and CPP tariﬀs. Firstly, we consider a SH with

RTEP tariﬀ and the electricity cost per hour is given:

ξT L(t) = An

X

ai

ς(ai,t)×ε(t)×ζ(t)!. t T(4.22)

33

Similarly, the total electricity cost is calculated as:

ξT L =

T

X

t=1 An

X

ai

ς(ai,t)×ε(t)×ζ(t)!. t T(4.23)

To minimize the Eq. 4.23 we introduce constraints regarding RTEP tariﬀ and energy

consumption of the appliances are:

R1: 1.215 ≤ξT L(t)≤3.7

R2:ξT L ≤21.6

R3: 1.5≤ς(t)≤13.84

In Figure. 4.1a points P1, P2, P3, P5, and P6show the feasible region of electricity

cost and energy consumption. The electricity cost is calculated using RTEP tariﬀ and

the unscheduled cost per hour is 3.71 cents. The total cost per day is 21.6 cents and

based on the parameters electricity cost and energy consumption the constraints are

deﬁned. The constraint R1shows that the electricity cost in hour should not exceed

3.71 cents including peak hours and oﬀ-peak hours. Constraints R2shows total cost

per day should not increase than the 21.5 cents as total cost shown here is in the

unscheduled case, therefore, the scheduling algorithms must schedule the cost in such

way that it does not violate the limit as in R2. While the constraint R3shows the

total energy consumption of the appliances must be with in limits i.e., between 1.5

and 13.84 kWh to reduce electricity cost. Similarly, Figure. 4.1b shows feasible region

for SH considering CPP tariﬀ and the constraints are given as:

C1: 1.215 ≤ξT L(t)≤6.37

C2:ξT L ≤37.5

C3: 1.5≤ς(t)≤13.84

Constraints associated with CPP show that the electricity cost of an hour should not

exceed 6.37 cents. Constraint C2shows the cost for a single day should be less than

37.5 cents. While the constraint C3shows for the optimal scheduling of the energy

34

Energy consumption (kWh)

0 2 4 6 8 10 12 14

Cost (cents)

0

5

10

15

20

25

30

35

40

P1(1.5,4.09)

P2(1.5,1.21)

P4(13.84,37.78)

P6(7.9,21.5)

P3(13.84,11.08)

P5(13.84, 21.5)

Figure 4.1a: Feasible region of energy consumption for SH using

RTEP

Energy consumption (kWh)

0 2 4 6 8 10 12 14

Cost (cents)

0

10

20

30

40

50

60

70

80

P1(1.5,8.20)

P2(1.5,1.21)

P5(13.84,38.2)

P4(13.84,75.7)

P3(13.84,11.22)

P6(7,38.2)

Figure 4.1b: Feasible region of energy consumption for SH using

CPP

consumption, energy consumed in an hour should be with in limits of 1.5 kWh and

13.84 kWh.

We also computed feasible region for waiting time of the appliances in order to de-

termine the user comfort. User comfort is inversely related with the waiting time of

35

Average waiting time (hours)

012345

Cost (cents)

5

10

15

20

25

P2(5,18.6)

P3(5,10)

P4(1.36,18.6)

P1(0,21..5)

Figure 4.2a: Feasible region of average waiting time for SH using

RTEP

Average waiting time (hours)

012345

Cost (cents)

10

15

20

25

30

35

40

P3(5,15)

P2(5,32.4)

P1(0,37.7)

P4(1.48,37.7)

Figure 4.2b: Feasible region of average waiting time for SH using

CPP

the appliances and electricity cost. We consider maximum 5 hours average waiting

time for the appliances i.e., allowable delay in day for the SH scheme. In Figure. 4.2a

points P1, P2, and P3show the feasible region for electricity cost and average waiting

time using RTEP tariﬀ. The point P1shows that the average waiting time of the Sa

and Eaare restricted to zero then the electricity cost is reached to a maximum value

36

i.e., 21.5 cents whereas, point P2shows the average waiting time of Sais 5 hours

then the cost is reduced to 18.6 cents. While point P3shows that the average waiting

time of all the appliances, including Saand Rais 5 hours then the cost is reduced to

10 cents, however, in this case consumers have to pay less cost, but compromise its

comfort level. Similarly, in Figure. 4.2b point P1shows that the consumers have to

pay maximum cost 37.7 cents when the average waiting time is zero. Whereas, point

P2shows that the cost is reduced to 18.6 cents when the average waiting time of the

Sais 5 hours. While point P3presents that the cost is decreased to 15 cents as the

average waiting time of the appliances is increased to 5 hours. The feasible region

of Figure. 4.2a and Figure. 4.2b depicts the trade-oﬀ between the electricity cost

and average waiting of the appliances. In order to minimizes the trade-oﬀ optimal

scheduling of the energy consumption proﬁle is essential in peak hours and oﬀ-peak

hours.

Energy consumption (kWh)

0 50 100 150 200 250 300 350

Cost (cents)

0

100

200

300

400

500

600

700

800

900

1000

P4(351,947.7)

P3(351,284.3)

P6(240,648.4)

P5(351,648.4)

P2(75,60.8)

P1(75,202.5)

Figure 4.3a: Feasible region of energy consumption for MHs

using RTEP

4.5.2 Feasible region for MHs

The feasible region of electricity cost and energy consumption for MHs is determined

using RTEP and CPP tariﬀs. Similar to previous subsection, we consider MHs using

37

Energy consumption (kWh)

0 50 100 150 200 250 300 350

Cost (cents)

0

200

400

600

800

1000

1200

1400

1600

1800

P3(351,284.3)

P4(351,947.7)

P5(351,1087)

P1(75,284.3) P2(75,60.7)

P6(243,1087)

Figure 4.3b: Feasible region of energy consumption for MHs

using CPP

Average waiting time (hours)

0 50 100 150 200 250

Cost (cents)

100

200

300

400

500

600

700

P4(38.24,580)

P1(0,648.8) P2(250,580)

P3(250,150)

Figure 4.4a: Feasible region of average waiting time for MHs

using RTEP

RTEP and CPP tariﬀs and the total cost is calculated as:

ΥT L =

50

X

N=1

T

X

t=1 An

X

ai

ς(ai,t)×ε(t)×ζ(t)!. t T(4.24)

38

Average waiting time (hours)

0 50 100 150 200 250

Cost (cents)

100

200

300

400

500

600

700

800

900

1000

1100

1200

P2(250,600)

P1(0,1087)

P4(75,600)

P3(250,150)

Figure 4.4b: Feasible region of average waiting time for MHs

using CPP

Constraints associated with electricity cost and energy consumption for MHs using

RTEP are given as:

S1: 50.6≤ξT L(t)≤94.4

S2: ΥT L ≤648.43

S3: 75 ≤ς(t)≤351

In Figure. 4.3a the shaded region shows the feasible region of electricity cost and

energy consumption of MHs using RTEP tariﬀ. Constraint S1indicates the cost per

hour must be restricted with in limits of 50.6 and 94.4 cents per hour. While the cost

per day is restricted to 648.43 cents by the constraint S2. Constraint S3presents that

the energy consumption should not exceed upper and lower bound which is 75 and

351 kWh. Figure. 4.3b shows the feasible region of the electricity cost and energy

consumption for MHs using CPP tariﬀ. The constraints related to electricity cost and

energy consumption for MHs using CPP are:

39

W1: 58.7≤ξT L(t)≤156.8

W2: ΥT L ≤1087

W3: 75 ≤ς(t)≤351

Similar to prior Constraints, constraint W1indicates that electricity cost in an hour

should be restricted by upper and lower bound i.e., 58.7 and 156.8 cents. Constraint

W2shows that heuristic algorithm should schedule the cost such that it should not

increase 1087 cents. While constraint W3simply means that for minimization of

electricity cost, energy consumption of the appliance should not exceed the given

values as in W3.

In Figure. 4.4a points P1, P2, and P3illustrate the feasible region of electricity

cost and average waiting time of MHs using RTEP tariﬀ. In the case of MHs, we

consider maximum 250 hours average waiting time for the appliances in day. The

point P1shows that the electricity cost is maximum when the average waiting time is

zero, while point P3represents that total cost is reduced to 150 cents as the average

waiting time of the appliances reaches up to 250 hours for MHs. However, at this

stage user comfort is decreased. P2shows the cost is reduced to 580 cents when the

operation time of Sais delayed to 250 hours in MHs. Similarly, Figure. 4.4b shows the

feasible region bounded by the points P1, P2, and P3with CPP tariﬀ. The maximum

cost in case of CPP is raised to 1087 cents at zero average waiting time. Whereas,

P2shows the cost when operation time of Sais delayed. While P3shows that the

average waiting time is maximum for all the appliances the cost is minimum i.e., 150

cents. Moreover, to address the trad-oﬀ in a better way, optimal scheduling of the

appliances and user preference should monitor equally and appropriately.

40

Chapter 5

Simulations and Discussion

41

5.1 Simulations and Discussion

In this section, we inspect the numerical simulation of four heuristic algorithms and

their performances are evaluated in terms of electricity cost, PAR, and user comfort.

A hybrid algorithm is proposed and simulation results are compared with existing

algorithms using MATLAB 2014b with Intel(R) Core(TM) i5-2450M CPU @ 2.50

GHz and 6 GB of RAM on Windows operation system .

We assume SH and MHs with household appliances which are categorized into three

groups: Ra,Sa, and Ea. While arbitrary operational time and power ratings are

assigned to Saand Raappliances in the case of MHs. Our objectives are to minimize

electricity cost, PAR, and waiting time of the appliances. In this regard, heuristic

algorithms are incorporated like; WDO, HSA, GA, and proposed algorithm GHSA.

Comparative analysis is made among heuristic algorithms and unscheduled case by

adopting RTEP and CPP tariﬀs (shown in Figure. 5.1a and Figure. 5.1b) and results

are demonstrated the proposed algorithm eﬃciently addressed the objectives. The

performance parameters comprise of load proﬁle, cost per hour, electricity cost per

day, PAR, and user comfort. The detail of each parameter is provided as follows:

Time (hours)

1 2 3 4 5 6 7 8 9 1011 12 1314 15 16 17 1819 20 21 22 23 24

Price (cents/kWh)

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

RTEP signal

Figure 5.1a: RTEP tariﬀ

42

Time (hours)

1 2 3 4 5 6 7 8 9 1011 12 1314 15 16 17 1819 20 21 22 23 24

Price (cents/kWh)

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

CPP signal

Figure 5.1b: CPP tariﬀ

Time (hours)

1 2 3 4 5 6 7 8 9 1011 12 1314 15 16 17 1819 20 21 22 23 24

Load (kWh)

0

2

4

6

8

10

12

14 Unscheduled

WDO

HSA

GA

GHSA

Figure 5.2a: Load proﬁle of SH with RTEP

5.1.1 Load proﬁle

The energy consumption of appliances for SH and MHs using RTEP and CPP tariﬀs

is shown in Figure. 5.2a-Figure. 5.2d. It can be seen that during peak hours i.e., 7 to

15 hours each heuristic algorithm performs better than unscheduled case. In Figure.

5.2a maximum unscheduled load during peak hours is 13.84 kWh, and among other

heuristic algorithms GA schedules the peak load competently to 5.01 kWh. While

43

Time (hours)

1 2 3 4 5 6 7 8 9 1011 12 1314 15 16 17 1819 20 21 22 23 24

Load (kWh)

0

2

4

6

8

10

12

14 Unscheduled

WDO

HSA

GA

GHSA

Figure 5.2b: Load proﬁle of SH with CPP

Time (hours)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Load (kWh)

0

50

100

150

200

250

300

350

400

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.2c: Load proﬁle of MHs with RTEP

in Figure. 5.2b GHSA schedules the peak load to 3.73 kWh which is comparatively

less than existing heuristic algorithms and unscheduled load (13.84 kWh). Similarly,

Figure. 5.2c and 5.2d illustrate the load proﬁle for MHs using RTEP and CPP tariﬀs

and the energy consumed by unscheduled load during peak hours is 351 kWh, however,

compared with the existing algorithms GHSA is scheduled the load to 60.29 kWh and

136.09 kWh for MHs using RTEP and CPP tariﬀs, respectively. The overall results

show that proposed algorithm performs better to schedule the load proﬁle for SH and

44

Time (hours)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Load (kWh)

50

100

150

200

250

300

350

400

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.2d: Load proﬁle of MHs with CPP

Time (hours)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Cost per hour (cents/hour)

0

0.5

1

1.5

2

2.5

3

3.5

4

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.3a: Cost per hour of SH with RTEP

MHs compared to existing algorithms and unscheduled case. Table 5.1 presents load

proﬁle in peak hours of the appliances in unscheduled case, scheduled case, percentage

decrement, and improvement of heuristic algorithms.

45

Table 5.1: Load proﬁle comparison

Schemes Techniques

Unscheduled WDO HSA GA GHSA

SH with RTEP

Load proﬁle

(kWh)

13.84 8.66 6.01 5.01 5.80

Percentage

decrement

— 37.42% 56% 63.80% 63.29%

Improvement — 5.18 7.83 8.83 8.76

SH with CPP

Load proﬁle

(kWh)

13.84 5.12 6.37 5.10 4.95

Percentage

decrement

— 63.21% 53.97% 63.15% 65.12%

Improvement — 9.27 7.47 8.74 10.12

MHs with RTEP

Load proﬁle

(kWh)

351 128.88 125.28 241.46 124.29

Percentage

decrement

— 63.28% 65.92% 31.20% 65.72%

Improvement — 222.12 290.72 109.54 290.71

MHs with CPP

Load proﬁle

(kWh)

351 114.49 140.38 134.68 136.01

Percentage

decrement

— 67.38% 60% 61.6% 61.25%

Improvement — 236.51 210.62 216.32 214.99

46

Time (hours)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Cost per hour (cents/hour)

0

1

2

3

4

5

6

7

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.3b: Cost per hour of SH with CPP

Time (hours)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Cost per hour (cents/hour)

0

10

20

30

40

50

60

70

80

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.3c: Cost per hour of MHs with RTEP

5.1.2 Cost per hour

The electricity cost per hour is calculated using Eq. 4.22. The results in Figure.

5.3a-Figure. 5.3d depict electricity cost per hour with the comparison of heuristic

algorithms. It is observed that each algorithm tends to schedule the cost in low

pricing hours i.e., oﬀ-peak hours. In Fig. 5.3a results show that the cost is reduced

to 2.61, 1.72, 1.12, and 1.34 cents/hour by WDO, HSA, GA, and GHSA, respectively.

47

Time (hours)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Cost per hour (cents/hour)

0

20

40

60

80

100

120

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.3d: Cost per hour of MHs with CPP

SH with RTEP SH with CPP MHs with RTEP MHs with CPP

Total cost (cents)

0

200

400

600

800

1000

1200

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.4: Electricity cost per day

Similarly, Figure. 5.3b shows maximum unscheduled cost is 6.83 cents/hour and

it is reduced to 2.25, 2.04, 2.02, and 1.60 cents/hour using WDO, HSA, GA, and

GHSA, respectively. Figure. 5.3c and 5.3d represent results for MHs using RTEP

and CPP tariﬀs. All heuristic algorithms are compared with each other and also with

unscheduled case. The unscheduled cost per hour during peak hours for MHs using

RTEP and CPP is 94.38 and 156.78 cents/hour while proposed algorithm is reduced

it to 20.28 and 58.46 cent/hour, respectively, which represents maximum reduction

48

SH with RTEP SH with CPP MHs with RTEP MHs with CPP

PAR

0

5

10

15

20

25

Unscheduled

WDO

HSA

GA

GHSA

Figure 5.5: PAR of SH and MHs with RTEP and CPP

SH with RTEP SH with CPP MHs with RTEP MHs with CPP

Average waiting time (hours)

0

50

100

150

200

250

Allowed delay

WDO

HSA

GA

GHSA

Figure 5.6: Average waiting time of SH and MHs using RTEP and CPP

compared to other existing algorithms.

5.1.3 Electricity cost per day

The primary objective of our work is the minimization of electricity cost. The elec-

tricity cost is reduced using heuristic algorithms to schedule the energy consumption

proﬁle and also with the constraints mention in section 3. Figure. 5.4 illustrates the

49

electricity cost per day (total cost) for SH and MHs using RTEP and CPP tariﬀs.

In detail, total cost for SH using RTEP tariﬀ in unscheduled case is 21.53 cents and

using heuristic algorithms: WDO, HSA, GA, and GHSA the total cost is reduced to

18.65, 17.04, 16.01, and 15.10 cents, respectively. Likewise, SH with CPP tariﬀ the

total cost for unscheduled case is 38.23 cents and the heuristic algorithms: WDO,

HSA, GA, and GHSA are reduced the total cost to 25.68, 23.98, 22.63, and 20.21

cents, respectively. In the case of MHs, using RTEP tariﬀ the total cost is reduced

from unscheduled case i.e., 648.83 cents to 320.74, 480.36, 445.36, and 284.39 cents

by WDO, HSA, GA, and GHSA, respectively as shown in Fig. 9. Accordingly, for

MHs the total cost associated with CPP tariﬀ is 631.02, 643.18, 608.18, 500.01 cents

using WDO, HSA, GA, and GHSA, respectively. The overall eﬀects of the total cost

associated with RTEP and CPP rates in the case of SH and MHs are analyzed which

show that the proposed algorithm GHSA outperforms the other existing algorithms.

Table 5.2 shows the total cost, percentage decrement, and improvement of heuristic

algorithms.

5.1.4 PAR

PAR describes the behaviour of the consumer’s load proﬁle and directly aﬀects the

operation of the power grids. Figure. 5.5 illustrates PAR of scheduled and unsched-

uled case for SH and MHs with RTEP and CPP tariﬀs and results show that each

heuristic algorithm is competent to reduce PAR compared to unscheduled case. PAR

comparison of unscheduled and scheduled case for MHs using RTEP and CPP tar-

iﬀs shows that the proposed algorithm GHSA is reduced the PAR, even the number

of the homes is increased. Table 5.3 represents PAR, percentage reduction of PAR,

and improvement of heuristic algorithms. It is evident from Figure. 5.5 that GHSA

exhibits maximum reduction in PAR comparative to the existing algorithms. More-

over, In order to reduce PAR, load proﬁle of the consumer should schedule eﬀectively

which ensures the reliability and stability of the power grids. In our work, we employ

heuristic algorithms to reduce the PAR by scheduling the load in oﬀ-peak hours.

50

Table 5.2: Total cost comparison

Schemes Techniques

Unscheduled WDO HSA GA GHSA

SH with RTEP

Total cost

(cents)

21.53 18.65 17.04 16.01 15.01

Percentage

decrement

— 13.37% 20.58% 25.63% 29.86%

Improvement — 2.88 4.49 5.52 6.43

SH with CPP

Total cost

(cents)

37.5 25.68 23.98 22.63 20.21

Percentage

decrement

— 31.52% 36.05% 39.65% 46.19%

Improvement — 11.82 13.52 14.87 17.21

MHs with RTEP

Total cost

(cents)

648.43 320.74 480.36 445.36 284.39

Percentage

decrement

— 50.54% 25.91% 31.31% 56.06%

Improvement — 327.69 168.07 303.7 364.04

MHs with CPP

Total cost

(cents)

1087 631.02 643.18 608.18 500.21

Percentage

decrement

— 41.94% 40.82% 44.04% 54.04%

Improvement — 445.98 443.82 478.82 587

51

Table 5.3: PAR comparison

Schemes Techniques

Unscheduled WDO HSA GA GHSA

SH with RTEP

PAR 5.01 4.31 3.24 3.73 3.09

Percentage

decrement

— 13.97% 35.32% 25.54% 38.32%

Improvement — 0.7 1.77 1.28 1.92

SH with CPP

PAR 5.01 4.68 3.48 3.64 3.13

Percentage

decrement

— 6.58% 30.53% 27.34% 37.52%

Improvement — 0.33 1.53 1.37 1.88

MHs with RTEP

PAR 22.46 12.78 14.70 12.70 11.73

Percentage

decrement

— 43.09% 34.55% 43.45% 47.77%

Improvement — 11.78 9.84 11.48 12.78

MHs with CPP

PAR 24.54 13.92 12.98 14.01 12.01

Percentage

decrement

— 43.27% 47.01% 42.66% 50.08%

Improvement — 10.62 11.56 10.53 12.53

52

5.1.5 User comfort

The average waiting time of the appliances is calculated which refers to user comfort.

User comfort disturbs when the user faces minimum amount of delay in order to oper-

ate the appliance. However, if the waiting time of the appliances increases eventually

cost of electricity reduces. In this vein, there is sort of trade-oﬀ between waiting time

of appliances and electricity cost. Figure. 5.6 shows average waiting time for SH and

MHs using RTEP and CPP tariﬀs with heuristic algorithms: WDO, HSA, GA, and

GHSA. The maximum allowable delay i.e., average waiting time of the appliance in

case of SH using RTEP and CPP tariﬀs is 5 hours, however, the proposed algorithm

GHSA is achieved minimum average waiting time of appliances compared with the

existing algorithms i.e., 4.3 hours and 2.4 hours, respectively. Similarly, for MHs max-

imum allowed delay is 250 hours using both pricing tariﬀs and the proposed algorithm

GHSA is achieved minimum delay compared with other heuristic algorithms i.e., 170.9

hours and 175 hours, respectively. Among other existing techniques GHSA is capable

of minimizing the average waiting which in turn increases user comfort. Although,

it is stated that there is trade-oﬀ between electricity cost and waiting time, however,

proposed algorithm GHSA performs eﬃciently to minimize the trade-oﬀ compared to

other existing optimization algorithms.

53

Chapter 6

Conclusion

54

6.1 Conclusion

HEMS can eﬀectively and intelligently control home appliances by providing real-time

load management. In this paper, we proposed HEMC based on heuristic algorithm

GHSA for SH and MHs. Simulation results are conducted on the basis of SH and

MHs with household appliances by adopting RTEP and CPP tariﬀs. In addition, for

MHs arbitrary power ratings and time of operations are assigned to the appliances.

HEMC performance is evaluated on the bases of existing optimization algorithms:

WDO, HSA, GA, and proposed algorithm GHSA. Feasible regions are computed which

ensures the validity of the proposed algorithm GHSA in the case of SH and MHs.

Moreover, Comparative analysis of heuristic algorithms is performed which shows

the better performance of GHSA in terms of cost reduction, PAR reduction, and

user comfort maximization. Finally, it is assured that the proposed HEMC based on

GHSA is the reliable and eﬃcient solution for the future smart grid.

55

Chapter 7

References

56

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