Economical Hydrothermal Coordination using Intelligent

Economical Hydrothermal Coordination using

Intelligent Computational Techniques

By

Fayyaz Ahmad

CIIT/FA13-PEE-001/WAH

PhD Thesis

In

Electrical Engineering

COMSATS University Islamabad

Wah Campus - Pakistan

Fall, 2019

ii


Economical Hydrothermal Coordination using

Intelligent Computational Techniques

A Thesis Presented to


In partial fulfillment

of the requirement for the degree of

PhD (Electrical Engineering)

By

Fayyaz Ahmad


Fall, 2019

iii

Economical Hydrothermal Coordination using Intelligent Computational Techniques

A Post Graduate Thesis submitted to the Department of Electrical and

Computer Engineering as partial fulfillment of the requirement for the award of

PhD (Electrical Engineering).

Supervisor

Dr. Muhammad Iqbal Associate Professor, Department of Electrical and Computer Engineering, COMSATS University Islamabad (CUI), Wah Campus

Name Registration Number

Fayyaz Ahmad CIIT/FA13-PEE-001/WAH

viii

DEDICATION

To Almighty ALLAH and Holy Prophet Muhammad

(P.B.U.H)

&

To my parents, beloved wife, my dear daughter and my

brave son whose sacrifices have encouraged me to

complete my research work for the accomplishment of

Ph.D.

ix

ACKNOWLEDGEMENTS

I want to start my acknowledgment with the Higher Education Commission (HEC) for

the award of Indigenous Ph.D. Scholarship. I feel that without technical support

provided by my supervisor Dr. Muhammad Iqbal and supervisory committee

especially Dr. Muhammad Naeem and Dr. Muhammad Ashfaq, I would never have

been able to complete my Ph.D. studies research.

I am also grateful to my friends Dr. Usman Ali (The University of Lahore), Engr.

Fahimullah Khanzada (Ministry of Science and Technology), Engr. Mehroz Iqbal

(The University of Engineering and Technology, Taxila), Dr. Danish Mehmood

(Shaheed Zulfikar Ali Bhutto Institute of Science and Technology), Dr. Nadir Ali

Shah (COMSATS University Islamabad), Zeeshan Anjum (The University of

Engineering and Technology, Taxila), Dr. Kamran Nazir (National University of

Technology), Engr. Rashid Jamil Satti (Swedish College), Engr. Muhammad Saeed

(National Transmission and Dispatch Company), Engr. Ali Tariq (Water and Power

Development Authority) and Dr. Muhammad Zubair (Information Technology

University) for their generous support and insightful guidance.

Fayyaz Ahmad


x

ABSTRACT

Economical Hydrothermal Coordination using Intelligent

Computational Techniques

Hydrothermal Coordination is a complex, non-linear, non-deterministic and dynamic

problem. Hydrothermal Coordination is a blend of two tricky sub-problems: Unit

Commitment (UC) and Economic Dispatch (ED). The search space of Hydrothermal

Coordination is turbulent and non-linear.

Due to complex nature of Hydrothermal Coordination, classical approaches fail to

provide suitable results, trends have shifted toward modern intelligent computational

techniques, especially nature-inspired Evolutionary Algorithms (EA). Modern

Evolutionary Algorithms can, in parallel, explore the infinite search space. EA is a

good fit for Hydrothermal Coordination but can provide nearly optimum results.

Therefore, there is a need of an efficient and robust optimization tool.

In the dissertation, the parameter Levelized Cost Of Electricity (LCOE) is used to

choose the most economical option for planning of power plants. For planning and

development of power plants, global context is considered. In the Long-term

Hydrothermal Coordination (LTHTC) study, Markov Chain method has been used to

forecast and estimate the stochastic nature of water inflow. Locality named Ghazi-

Barotha is considered for testing the implementation of Particle Swarm Optimization

(PSO) that has proved the conflicting nature of emission minimization and cost

minimization. The study supports the notion that adopting indigenous resources and

localized manufacturing can result in wiser power plant planning decisions.

A novel hybrid intelligent computational technique has been developed by using an

evolutionary algorithm and the recursive technique. Comparatively better results are

obtained by the stochastic optimizer based on a hybridized version that combines

Chaotic Differential Evolution (CDE) with Sequential Quadratic Programming (SQP).

In the case of Short-Term Hydrothermal Coordination (STHTC), after applying the

proposed computational technique, significant reductions in cost are observed.

Robustness, versatility, and applicability are few of the features demonstrated by the

novel hybridized technique.

xi

Table of Contents

1 Introduction .................................................................................................... 1

1.1 Chapter Summary ......................................................................... 2

1.2 Introduction ................................................................................... 2

1.3 Problem Statement ........................................................................ 3

1.4 Research Objectives ...................................................................... 4

1.5 Usefulness of the Research ........................................................... 4

1.6 List of Contributions ..................................................................... 5

1.6.1 Published Manuscripts ...................................................... 5

1.6.2 Submitted Manuscripts ...................................................... 5

1.7 Thesis Outline ............................................................................... 6

1.8 Chapter Conclusion ....................................................................... 7

2 Literature Review ........................................................................................... 8

2.1 Chapter Summary ......................................................................... 9

2.2 Background ................................................................................... 9

2.3 Literature Survey ......................................................................... 10

2.3.1 Objectives of Hydrothermal Coordination ...................... 22

2.3.2 Constraints of Hydrothermal Coordination ..................... 23

2.3.3 Optimization Techniques Applied to Hydrothermal

Coordination ................................................................................ 24

2.4 Discussion ................................................................................... 25

2.5 Chapter Conclusion ..................................................................... 27

3 Power Plants Development Trend .............................................................. 28

xi

Table of Contents

1 Introduction .................................................................................................... 1

1.1 Chapter Summary ......................................................................... 2

1.2 Introduction ................................................................................... 2

1.3 Problem Statement ........................................................................ 3

1.4 Research Objectives ...................................................................... 4

1.5 Usefulness of the Research ........................................................... 4

1.6 List of Contributions ..................................................................... 5

1.6.1 Published Manuscripts ...................................................... 5

1.6.2 Submitted Manuscripts ...................................................... 5

1.7 Thesis Outline ............................................................................... 6

1.8 Chapter Conclusion ....................................................................... 7

2 Literature Review ........................................................................................... 8

2.1 Chapter Summary ......................................................................... 9

2.2 Background ................................................................................... 9

2.3 Literature Survey ......................................................................... 10

2.3.1 Objectives of Hydrothermal Coordination ...................... 22

2.3.2 Constraints of Hydrothermal Coordination ..................... 23

2.3.3 Optimization Techniques Applied to Hydrothermal

Coordination ................................................................................ 24

2.4 Discussion ................................................................................... 25


3 Power Plants Development Trend .............................................................. 28

xii

3.1 Chapter Summary ....................................................................... 29

3.2 Background ................................................................................. 29

3.3 Levelized Cost of Electricity (LCOE) ........................................ 31

3.3.1 Non-Renewable Energy Sources ..................................... 33

3.3.2 Renewable Energy Sources ............................................. 36

3.3.3 Nuclear Power Plants ...................................................... 39

3.4 Trend of Global Electricity Generation and the Resulting GHG

Emissions ............................................................................................... 40

3.4.1 Global Generation ........................................................... 40

3.4.2 Global Emission .............................................................. 43

3.5 Discussion ................................................................................... 44

3.5.1 Cost .................................................................................. 44

3.5.2 Emission .......................................................................... 44

3.5.3 Reliability ........................................................................ 45

3.5.4 Global Emission Control Strategy ................................... 45


4 Long-Term Hydrothermal Coordination (LTHTC) ................................. 47

4.1 Chapter Summary ....................................................................... 48

4.2 Background ................................................................................. 48

4.3 Electricity Sector in Pakistan ...................................................... 49

4.4 System Model and Problem Formulation ................................... 49

4.4.1 Hydropower Power Plant and Load Demand .................. 49

4.4.2 Thermal System Modeling .............................................. 58

4.5 Proposed Algorithm and Settings ............................................... 62

4.5.1 Proposed Algorithm ........................................................ 62

xiii

4.5.2 Particle Swarm Optimization (PSO) Attributes .............. 64

4.6 Simulation Results ...................................................................... 64


5 Short-Term Hydrothermal Coordination (STHTC) ................................. 74

5.1 Chapter Summary ....................................................................... 75

5.2 Related Work and Case-studies .................................................. 75

5.3 Problem Formulation .................................................................. 79

5.3.1 System Constraints .......................................................... 79

5.4 Chaotic Differential Evolution (CDE) and Quadratic

Programming (QP) ................................................................................. 80

5.5 Simulation and Results ................................................................ 87

5.5.1 Case Study I: ................................................................... 88

5.5.2 Case Study II ................................................................... 90

5.5.3 Case Study III .................................................................. 91

5.5.4 Case Study IV .................................................................. 92

5.6 Comparative Analysis of the Results .......................................... 94

5.6.1 Improvements Observed in Applicability, Robustness and

Versatility .................................................................................. 100

5.6.2 Efficiency of the Proposed Algorithm ........................... 101

5.7 Multi-objective Case Study ....................................................... 101

5.8 Chapter Conclusion ................................................................... 104

6 Conclusion ................................................................................................... 105

6.1 Conclusion ................................................................................ 106

6.2 Future Work .............................................................................. 108

7 References ................................................................................................... 109

xiv

List of Figures

Figure 2.1: Global Electricity Generation by Source (2017) ....................................... 10

Figure 2.2: Flow chart of Genetic Algorithm (GA) ..................................................... 16

Figure 2.3: Objectives of Hydrothermal Coordination ................................................ 22

Figure 2.4: Constraints of Hydrothermal Coordination ............................................... 24

Figure 2.5: Optimization Techniques Applied to Hydrothermal Coordination ........... 25

Figure 3.1: Types of power generation systems with respect to the energy source ..... 30

Figure 3.2: Factors Affecting the Levelized Cost of Electricity (LCOE) .................... 32

Figure 3.3: Global Levelized Cost of Electricity (LCOE) of Power Generation in 2017

...................................................................................................................................... 33

Figure 3.4: Trend of coal-based electricity generation (2008-2017) ........................... 34

Figure 3.5: Trend of global electricity generation by oil (2008-2017) ....................... 35

Figure 3.6: Trend of global electricity generation by gas (2008-2017) ....................... 36

Figure 3.7: Trend of hydel generation in the world in the last decade ........................ 37

Figure 3.8: Trend of geothermal energy generation in the world for the last decade .. 38

Figure 3.9: Trend of biomass energy generation in the world for the last decade ....... 38

Figure 3.10: International trend of nuclear energy generation in the last decade ........ 39

Figure 3.11: Global electricity generation trend observed in the last decade .............. 41

Figure 3.12: G-20 countries power generation major resource [108, 109] .................. 42

Figure 3.13: Percentage emission in the world by different power sources in 2017 ... 44

xv

Figure 3.14: Emission Control Strategy ....................................................................... 46

Figure 4.1: State diagrams of the period January to December ................................... 54

Figure 4.2: Particle Swarm Optimization (PSO) flow chart ........................................ 63

Figure 4.3: Convergence Behavior of Combined Fuel and Emission Minimization

(CFEM) ........................................................................................................................ 65

Figure 4.4: Expected Water Inflow and Discharge ...................................................... 70

Figure 4.5: Reservoir storage profile throughout the year ........................................... 70

Figure 4.6: Load demand vs generation by power plants ............................................ 71

Figure 4.7: Cost of Fuel with respect to Objectives ..................................................... 71

Figure 4.8: Emission with respect to objectives .......................................................... 72

Figure 4.9: Pareto Function of fuel cost and the resulting emissions .......................... 73

Figure 5.1: Flow Chart of Sequential Quadretic Programming ................................... 76

Figure 5.2: Flow Chart of Differential Evolution ........................................................ 78

Figure 5.3: Flow Chart of Chaotic Differential Evolution ........................................... 82

Figure 5.4: Flow Chart of Chaotic Differential Evolution (CDE) Hybridized with SQP

...................................................................................................................................... 85

Figure 5.5: (a) Behavior of the fitness function evaluation; (b) Absolute error of

thermal generation for 100 intervals ............................................................................ 89

Figure 5.6: Behavior of the fitness function value (a) and absolute error of thermal

generation for 100 intervals in (b) ............................................................................... 90





xvi

Figure 5.9: Comparative analysis of the computational budget for case studies I, II,

III and IV ...................................................................................................................... 96

Figure 5.10: Convergence behavior of the fitness for case studies I to IV using hybrid

approach ....................................................................................................................... 99

Figure 5.11: Pareto Front for Multi-objective Case Study ........................................ 103

xvii

List of Tables

Table 3.1: Global CO2 emissions trend ........................................................................ 40

Table 4.1: Average monthly inflow of Ghazi Barotha site from 2010 to 2017 in

Cumecs ......................................................................................................................... 50

Table 4.2: Monthly Average Load-demand ................................................................. 51

Table 4.3: Discretization of States ............................................................................... 53

Table 4.4: State Table from January to June ................................................................ 55

Table 4.5: State Table from July to December ............................................................ 56

Table 4.6: Fuel cost-coefficients and the limitations ................................................... 59

Table 4.7: Emission cost-coefficients and limits ......................................................... 59

Table 4.8: Results of scheduling power plants against the objectives 1,2,3 ................ 66

Table 4.9: Results of scheduling power plants against the objectives 4,5,6 ................ 67

Table 4.10: Results of scheduling power plants against the objectives 7,8,9 .............. 68

Table 4.11: Results of scheduling power plants against the objectives 10, 11 ............ 69

Table 5.1: Parameter Values/Settings for Chaotic Differential Evolution and

Sequential Quadratic Programming ............................................................................. 87

Table 5.2: Optimal Hydrothermal Generation (MW) for Case Study I ....................... 88

Table 5.3: Optimal Hydrothermal Generation (MW) for Case Study II ...................... 89

Table 5.4: Results of generation hydro and thermal generations ................................. 90

Table 5.5: Optimal Hydrothermal Generation (MW) for Case Study III ................... 92

Table 5.6: Optimal Hydrothermal Generation (MW) for Case Study IV ................... 93

xviii

Table 5.7: Comparative study in DE, SQP, and DE-SQP in terms of fitness achieved

...................................................................................................................................... 95

Table 5.8: Comparison between DE, SQP and DE-SQP in term of Load Error .......... 97

Table 5.9: Comparison between DE, SQP, and DE-SQP in term of computational

complexity .................................................................................................................... 98

Table 5.10: Comparison between DE, SQP and DE-SQP in term of cost (US $) ....... 99

Table 5.11: Attributes Observed in our I-IV case studies .......................................... 100

Table 5.12: Efficiency of the Proposed Algorithm .................................................... 101

Table 5.13: Power and heat values in case of extreme objectives ............................. 102

Table 5.14: Percentage of decrease of Cost and Emission ........................................ 103

xix

LIST OF SYMBOLS

Losses due to power transmission at time ‘t’

Total number of thermal units

Cost coefficient for thermal power generation ‘i'





Generated output power in time t of thermal unit ‘i'

Maximum thermal generation limits for unit ‘i'

Minimum thermal generation limits for unit ‘i'

Power demand at time ‘t’

Total number of hydroelectric units

Down ramp rate limit of thermal unit ‘i'

Up ramp rate limit of thermal unit ‘i'

The water discharge rate of the jth reservoir at the time ‘t’

The water storage volume of the jth reservoir at the time ‘t’

ltP

THN

THix

THiy

THiz

THiu

THie

THitP

maxTHiP

minTHiP

dtP

hN

iDR

iUR

hjtQ

hjtV

xx

Water storage minimum limit of reservoir ‘j’

Water storage maximum limit of reservoir ‘j’

Generated power from the jth hydroelectric unit at time ‘t’

Power generation coefficient of jth hydroelectric unit






The lower limit of the jth hydroelectric unit

The upper limit of the jth hydroelectric unit

The minimum water discharge rate of jth reservoir

The maximum water discharge rate of jth reservoir

Time index

Scheduling period

The randomly generated population of candidate solutions

Population size

Short-term Hydrothermal Coordination (STHTC) problem size

minhjV

maxhjV

hjtP

jC1

jC2

jC3

jC4

jC5

jC6

minhjP

maxhjP

minhjQ

maxhjQ

t

T

Pop

Psize

PSTHTCsize

xxi

Weight factor

Crossover rate

Chaotic variable

Cost of the fitness evaluation function

The capital cost of the power plant

The life cycle of the power plant

Operating cost in the year ‘t’

Time value of money

Corporate tax rate

Salvage value of the assets at the end of the life cycle

Energy production

System degradation in the year ‘t’

Depreciation schedule in the year ‘t’

Mass

Work

Volume

Gravitational acceleration

Discharge

℟ Fictional monetary unit

β

Crate

z

fval

cC

cL

cO

Y

Q

vS

Γ

SDt

ds

m

ΔU

V

g

Q

xxii

Storage minimum limits of reservoir ‘j’

Storage maximum limit of reservoir ‘j’

Emission cost coefficient for thermal power generator ‘i'

Emission cost coefficient for thermal power generation ‘i'




Number of rotors

Power output of a generator at time ‘t’

Penalty factor

Efficiency of hydropower plant

Storage at time ‘t’

Expected inflow

Scale parameter

Discharge at time ‘t’

Spillage at time ‘t’

Non-effective discharge

Basic head of reservoir ‘j’

S jmin

S jmax

xTHei

yTHei

zTHei

uTHei

eTHei

Nr

Pt

Ã

ηh

tS

Et

a

Qt

tS

µ t

hj

xxiii

Head correction factor

Exp Expectation

Sti Discrete value state

j Generator number

Nh Total number of hydro generators

fc

xxiv

LIST OF ABBREVIATIONS

LACE Levelized Avoided Cost of Electricity

DE Differential Evolution

SQP Sequential Quadratic Programming

LCOE Levelized Cost of Electricity

ED Economic Dispatch

K.E Kinetic Energy

P.E Potential energy

HTC Hydrothermal Coordination

LTHTC Long-term Hydrothermal Coordination

PSO Particle Swarm Optimization

CDE Chaotic differential evolution

STHTC short-term hydrothermal coordination

ICT Intelligent Computational Techniques

MILP Mixed-Integer Linear Programming

SCUC Short-term Security-Constrained Unit Commitment

PHES Pumped Hydro Energy Storage

UC Unit Commitment

MOABC Multi-Objective Artificial Bee Colony

DEA Data Environmental Analysis

ARIMA Autoregressive Integrated Moving Average

xxv

QOTLBO Quasi-Oppositional Teaching Learning-Based Optimization

ISAPSO Improved Self-adaptive Particle Swarm Optimization

HUCL Hydro Unit Commitment and Loading

HTS Hydrothermal Scheduling

BDI-BFPSO Bacterial Foraging Oriented by Particle Swarm Optimization

AIS Artificial Immune System

OPF Optimal Power Flow

GS Gradient Search

DP Dynamic Programming

EP Evolutionary Programming

DE-SQP Differential Evolution - Sequential Quadratic Programming

RGM Reduced Gradient Method

NRM Newton Raphson Method

GSM Gauss Seidel Method

NMM Nelder-Mead Method

LR Lagrange Relaxation

BD Benders Decomposition

HBA Honey Bee Algorithm

MGA Minority Game Algorithm

BFA Bacterial forging algorithm

FFA Fruit Fly Algorithm

xxvi

QP Quadratic Programming

SAEEP Simulated Annealing Embedded Evolutionary Programming

LEEMA Low-Emissions Electricity Market Analysis

SGA Simple Genetic Algorithm

NPCC National Power Control Center

MINLP Mixed Integer Non-linear Programming

MILP Mixed Integer Linear Programming

GA Genetic Algorithm

1

Introduction

2

1.1 Chapter Summary

This chapter presents an introduction of Hydrothermal Coordination. After that,

problem statement is discussed and later on research objectives are selected. Then the

potential avenues of usefulness of research are discussed. Author contribution in the

knowledge base has been given in the form of submitted and published articles. At the

end of the chapter, layout of the thesis is presented.

1.2 Introduction

The systematic approach of Hydrothermal Coordination results in an optimum mean

of utilizing the available hydro and thermal generation systems keeping in view the

constraints and limitations. Optimum utilization of energy resources by forecasting,

planning, and scheduling of available generation systems have always been a

prominent area in electrical power engineering. Oil prices have been showing an

increasing trend since the 1970s. As an immediate impact, in 1973, revenue worth

about twenty percent of the United States (US) federal budget went into various fuels

for generating electrical energy. The fuel cost continued on escalating and this in turn

effected the case of electricity. In the early 1980s, according to estimates, the US

spent about over forty percent of its total revenue on the production of electricity. It

motivated electrical power researchers and engineers to develop hydrothermal

coordination.

It is a known reality that thermal fuels are irreplaceable. As a result, academic

endeavors aimed at fuel conservation and reduction of energy costs have experienced

phenomenal growth. Hydrothermal Coordination is a technique used to save fuel costs

and conserve time. Another factor worth consideration is assigning weight to each of

the following two factors, i.e. irrigation and power production. It varies from place to

place. For instance, being an agricultural country, in Pakistan, mostly, the irrigation

facet receives more weight than the electricity element.

Hydroelectric systems are connected in the form of chains, or cascaded manner, and

for interruption-free operation, synchronized coordination is essential among the two

interconnected systems. Such factor must be considered in engineering design.

3

Hydroelectric systems are designed keeping in view the inherent geo-climatic and

weather variables such as water inflow, regional boundaries and storage capacity etc.

This makes them distinctly different and incomparable to each other. Owing to the

aforementioned major factors, operating a hydropower plant is a complicated task and

demands a vigilant multi-pronged approach.

Scheduling hydropower plants is also of surmount importance and can be of two types

i.e. long range and short range. In long-range scheduling, the time period stretches

from few weeks to few years and depends on climate profile and other geo-

topographic features. That is, the capacity of Khanpur Dam will be effected in case of

snowfall and rain on Murree hills, Pakistan. Further, decisions about choosing the

types of power plants are also carried in such scheduling category. Composite

simulation techniques are often used to resolve long-range scheduling problems.

Short-term hydropower scheduling deal with time period ranging from few hours to

few weeks. The best possible option is selected based on trade-off between cost and

endpoint requirements.

Hydrothermal coordination aims to ensure maximum utilization of hydropower plants

with minimum dependency on thermal fuels. It creates a balance among the following

variables: power demand, hydro generators and thermal generators. It also depends on

a number of constraints like water release limit, fuel cost, throttle cost and valve-point

loading.

1.3 Problem Statement

Electricity cycle lies in between production and consumption. Within this cycle, there

are numerous complex processes. One of the serious concerns, here, is the power

generation that is eco-friendly, reliable and economically sustainable. Electricity can

be produced from various sources; however, two of the major contributors are

hydroelectric and thermal power plants as their cumulative share is about 70% of the

world’s generated power.

A choice to select the viable energy generation option depends on its resourcefulness

and trade-offs. Through proper coordination between hydropower plants and thermal

4

power plants, cost minimization, as well as emission reduction, can be achieved.

Classical gradient-based techniques, such as Gauss Seidel and Newton Raphson,

cannot handle Hydrothermal Coordination since it is non-differentiable. Recursive

techniques, e.g. Dynamic Programming, can produce marginal results but require a lot

of computational budgets. One of the latest trends of the last decade is toward the

evolutionary algorithms that can handle the vague data and can produce good results

but they are not able to give optimum results.

HTC is a unique problem so it requires a powerful, robust and efficient optimization

technique that can handle a large search space of many constraints and can produce

optimum results. For such coordination activity to sail smoothly, a trade-off is to be

maintained between power demand and emission.

1.4 Research Objectives

Major objectives of the research work are as follows:

• Use of Mathematical modeling of power plants for economic analysis

• Identification of the constraints and objectives of Hydrothermal Coordination

• Conduct economic analysis of power plants

• Utilization of forecasting technique for stochastic problem

• Cost-minimization of electricity production using intelligent computational

techniques

• Implementation of the Evolutionary Algorithm in local settings

• Hybridization of optimization algorithms to obtain desired results

• Perform a critical comparative analysis of the proposed system and the

existing systems

As an ultimate aim the work will culminate in an intelligent computational technique

that integrates hydroelectric power plants with thermal power plants

1.5 Usefulness of the Research

Energy has a significant share in a country’s developmental budget. Apart from

financial elements, the issue of GHG emission also needs proper consideration. The

5

work aims to resolve the issues of energy-related costs and the associated emissions.

After highlighting the pros and cons of various power generation techniques, the work

results in a valuable power-plants selection mechanism that finds value in the

planning and development of the power sector. Besides, the Markov chain forecasting

method has been used for resource assessment of hydropower energy. The proposed

solution, hybrid algorithm, amalgamates evolutionary algorithm and recursive

technique and shows much better performance than each of its amalgams.

1.6 List of Contributions

1.6.1 Published Manuscripts

Paper 1. Fayyaz et al. (2018) “A novel chaotic differential evolution hybridized with

quadratic programming for short-term hydrothermal coordination.” Neural Computing

and Applications, 30(11), 3533-3544. (IF=4.67)

Paper 2. Fayyaz et al. (2018) “Optimal Allocation of Flexible AC Transmission

System Controllers in Electric Power Networks.” INAE Letters, 3(1), 41-64.

Paper 3. Fayyaz et al., (2015) “A Hybrid Algorithm for Energy Management in

Smart Grid.” Network-Based Information Systems (NBiS), 18th International

Conference on 2015 Sep 2 (pp. 58-63). IEEE.

Paper 4. Fayyaz et al. (2015) “An Energy-Efficient Residential Load Management

System for Multi-Class Appliances in Smart Homes.” Network-Based Information

Systems (NBiS), 18th International Conference on 2015 Sep 2 (pp. 53-57). IEEE.

1.6.2 Submitted Manuscripts

1. Hydrothermal Coordination using Intelligent Computational Techniques (A

Comprehensive Review)

2. Multi-objective Hydrothermal Coordination using Particle Swarm

Optimization (A Case Study)

3. Global Power Generation Development in the Context of Levelized Cost of

Electricity and Emission

6

1.7 Thesis Outline

The write-up comprises of six chapters. First two chapters are dedicated to

introduction and literature review. The third chapter provides a discussion about

developing the power plants trends and strategy. Fourth and fifth chapter present

commentary about Long-term Hydrothermal Coordination (LTHTC) and Short-term

Hydrothermal Coordination (STHTC) respectively. Finally, conclusion, in chapter six,

culminates the research work.

Chapter 2

Literature Review

Chapter 3

Power Plants Development Trend

Chapter 4

Long-Term Hydrothermal Coordination (LTHTC)

Chapter 5

Short-Term Hydrothermal Coordination (STHTC)

Chapter 6

Conclusion

References

7

1.8 Chapter Conclusion

This chapter presented an overview of economical hydrothermal coordination using

intelligent computational techniques by introducing and formalizing the problem

statement. Research objective milestones that were achieved during this study ranging

from model selection to economical utilization of resource are presented. Effective

utilization of research is also highlighted. List of Contributions shows our manuscripts

either published or submitted. In the end, the whole thesis outline is presented from

chapter 1 to 6.

8

2 Literature Review Hydrothermal Coordination using intelligent computational techniques (A Comprehensive Review)

9

2.1 Chapter Summary

This chapter presents background of power generation management generally and

HTC specifically. Literature survey is presented after thorough review of numerous

research articles. After literature survey, objectives as well as constraints of HTC are

identified. Later on Intelligent Computational Techniques implemented on HTC are

categorized. In the end, a discussion is done about the merits and demerits of ICT.

2.2 Background

Energy has a pivotal role in the modern-day lifestyle. Modern lifestyle, rapid

industrialization and technological growth etc. have resulted in increased energy

demands. There are various sources to meet the world’s electricity demand. However,

the share of hydroelectric and thermal energy is far more dominant [1]. About 80% of

the world’s electricity comes from either hydropower or thermal generation projects.

Hydrothermal Coordination promises important social, environmental and financial

objectives. Therefore, it remained an eye catcher for researchers in the last few

decades. Hydrothermal Coordination blends two complicated problems of Economic

Dispatch (ED) and Unit Commitment (UC).

Unit Commitment is the selection of power plants which will be on or off by meeting

all the constraints. In Pakistan UC is done by the National Power Control Center

(NPCC). NPCC forecasts the power demand of the coming periods by analyzing the

history of power requirements in the country. After researching power demand,

NPCC initiates agreements with the power plants for the specific periods. Economic

Dispatch mainly deals with the operation of power plants and how much power is to

be taken from the selected power plants while satisfying the operational constraints.

Hydrothermal Coordination is an amalgamation of both ED and UC. Both ED and UC

are nonlinear and non-convex problems, so HTC is also a complex problem. Many

techniques have been used to solve this non-linear, dynamic, multi-objective and

complex problem. This chapter presents a rigorous bibliographical survey addressing

the pertinent topics such as constraints, objectives, and recent updates [2].

10

Figure 2.1: Global Electricity Generation by Source (2017)

At the same time, the issues of climate change and global warming have to be

resolved intelligently. Thus, a trade-off between energy, or Fuel Cost Minimization

(FCM), and environment, or emission reduction, has to be developed [3]. From

Figure 2.1, it is apparent that thermal energy supply options dominate the global

power generation scenario.

In the following paragraphs, an overview of various intelligent computational

techniques to solve the complexities of Hydrothermal Coordination is presented.

Some of the major intelligent computational techniques commented here include

heuristic algorithms, meta heuristic algorithms and hyper heuristic algorithms.

2.3 Literature Survey

Literature teems with the topic of Hydrothermal Coordination. Most often, the terms

Hydrothermal Coordination and Hydrothermal Scheduling are used interchangeably.

This section explores some of the major research developments in the realm of

Hydrothermal Coordination.

11

Arash et al. modified the Imperialistic Competition Algorithm (ICA) and proposed a

novel solution to the Hydrothermal Coordination problem [4]. Authors have

demonstrated that with the addition of wind farms in the power system, the problem

becomes an NP-hard problem. Their proposed modification in the ICA, because of its

convergence, is good for a complex system.

Nguyen et al. proposed Cuckoo Search Algorithm (CSA) for smooth and non-smooth

cost curves of thermal and fixed head hydropower plants [5]. Authors compared the

results of CSA with existing methodologies and it was found that the results of the

proposed technique are quite better especially for non-smooth cost curves.

Pereira et al. highlighted that energy management is one of the most burning issues of

the current era [6]. Authors proposed a model and applied it to the forecast system.

They have proved that with the increased share of wind energy, CO2 emission is

reduced in addition to significant minimization of thermal fuel cost.

Jiang et al. proposed a model to address the case of load fluctuations [7]. It offers

satisfactory results in the case large load fluctuations but when it comes to smaller or

ordinary load fluctuations, the results are not up to the mark.

Gonzalez et al. provided a review of methodologies and approaches used for energy

and reserve market implementations [8]. Authors also highlight the difficulties faced

by the technocrats in energy forecasting and its practical implementation. In the end,

the authors shed light on the need for more research studies on the dual case energy

dispatch and market scenario.

Zabojnik et al. presented a model of the transmission network and power plants that

are based on Mixed-Integer Linear Programming (MILP) [9]. It consists of thermal,

hydro, pumped storage and renewable resources. The authors have worked for an

efficient and fast computing algorithm, mixed-integer linear programming, for

proposed studies. Real world production hydropower plants and pumped storage are

used for comparison and the proposed algorithm is implemented on the Czech

transmission network. Simulation results, when compared with existing solutions,

proved its effectiveness.

12

Norouzi et al. have presented a study of short-term Security-Constrained Unit

Commitment (SCUC) considering thermal and hydropower plants [10]. They have

proposed a dynamic rate of thermal units instead of a fixed rate. A multi-performance

curve related to hydro units is presented. Further, in order to solve the problem

efficiently, a linear model is used to transform it into MILP. In their work, Fuzzy

logic design is used as a decision maker so as to result in an optimized solution. The

proposed method is tested on a IEEE 118-bus system that consists of eight hydro and

54 thermal units. Simulation results demonstrate the superiority of the proposed

solution.

Ardizzon et al. investigated the topic of Pumped Hydro Energy Storage (PHES) and

small hydropower plants for development [11]. They are of the view that in future

advanced challenges need to be addressed well in time for coming forth with viable

turbine design and plant planning solutions. In their research work, management of

resources, as well as their coordination, is addressed. For illustration purposes, PHES

and its combination with either wind or solar is considered. The new design is based

on the computational analysis of fluid dynamics.

Estahbanati et al. addressed the issue of the scheduling problem in reference to the

inherent uncertainties in power system operation [12]. Harmony searching algorithm

is implemented as it is a fast computing algorithm that can solve non-convex and non-

linear problems. The proposed method is applied in a different system and as

expected, efficiency is maintained. The work, as a whole, paves way for a

comprehensive optimization solution for intelligent scheduling of the generation units.

Bakirtzis et al. proposed a study of modeling the Economic Dispatch (ED). Unit

Commitment (UC) includes a specific tool that has the ability to perform up to 24

hours [13]. The first hour uses a better quality of time resolution and detailed

modeling while the last hour considers coarser time resolution and simplified

modeling. Further, a medium-sized system of Greek power system is implemented to

validate the feasibility of the method.

Zhou et al. proposed a probabilistic methodology for the reserves to estimate a load

demand curve [14]. The demand curve is a measure of the cost of unserved energy,

13

expected a loss of load, the ambiguity of generator, load anticipating error and wind

power error. The proposed method is applied to reserve operating schemes in a two-

settlement electricity market with compact economic dispatch and centralized unit

commitment. To illustrate the efficiency of the proposed method, the reserve market

of the power system is modeled and approached to efficient power forecasting.

Steeger et al., after reviewing different varying parameters regarding problems of

Hydrothermal Coordination, proposed a solution for the development over time [15].

In each of the variant parameters, they identified the best possible approach.

Martins et al. proposed a model for scheduling the medium-term hydro-thermal plants

having transmission constraints [16]. The formulation of a non-linear model of

hydropower generation functions, such as discharge rate and storage capacity, is used

for the representation of the cascaded head variation. Transmission networks are

expressed as a power flow model having load over different levels. Authors used the

sparse matrix structure for a mathematical formulation, which allows fast

computational and searching algorithm. The simulation result of the proposed

approach proved its effectiveness, with slight limitations of deep learning.

Ahmadi et al. investigated the problem of a short-term multi-objective framework of

both heat and power economic dispatch [17]. The objective of this problem is to

minimize the total cost and the pollutant effect in the environment. A lexicographic

optimization technique is used to solve a multi-level objective. A fuzzy decision is

chosen as a preferable solution and comprehensive results are obtained, in the end.

The proposed model is tested and its efficiency is demonstrated.

Deane et al. modeled a Pumped Hydro Energy Storage (PHES) system for the future

power generation system [18]. The study is novel as it utilizes wind data for managing

the hydro energy storage system. A stochastic optimization technique is utilized. To

approach the desired demand, a stochastic optimization technique is utilized for this

management operation. The results show that the proposed approach significantly

reduces costs. However, weakness to dynamic variations, as a limitation, still exists.

Lakshmi et al. presented a generation schedule based on Artificial Immune System

[19]. An adaptive algorithm of the artificial immune system is proposed for

14

scheduling both wind and thermal energy systems. The performance of the proposed

approach is tested through a generation system, which consists of ten thermal and two

wind energy system, and in the light of the obtained result, a near optimum schedule

is achieved.

Zhou et al. presented a study of scheduling short-term hydrothermal systems [20]. A

Multi-Objective Artificial Bee Colony (MOABC) algorithm is proposed. The

numerical simulation results of the proposed algorithm, when compared with other

existing methods, prove its superiority and if cost-effective as well as eco-friendly.

Jiekang et al. proposed a hybrid global optimization algorithm to solve a multi-

objective scheduling problem [21]. Management of water volume for generating

electricity is the intended outcome. By combining the Data Environmental Analysis

(DEA) and Electro-Magnetism Algorithm (EMA), an optimum scheduling

mechanism is obtained.

Bhattacharjee et al. proposed an Oppositional Real Coded Chemical Reaction

(ORCCR) algorithm for solving the scheduling problem [22]. The primary objective

is an optimum hourly scheduling mechanism for a power generation system having

different hydrothermal elements. The proposed method is implemented on different

test systems and the results demonstrated its comparative edge.

Wei et al. used minority game algorithm for minimization of losses in the micro grids.

They have utilized the fluctuation in demand as their benefit for coordination among

the micro grids and minimization of the dispatch cost. But they have not proposed the

solution of the opposite case when demand on all micro grids go to peak values [23].

Tian et al. addressed short-term hydrothermal scheduling problem that includes

economics issues and environmental constraints [24]. They proposed a Non-

dominated Gravitational Searching Algorithm (NSGSA-CM), which is tested on

different systems. The simulation results demonstrated its improved performance.

Swain et al. applied the Clonal Selection Algorithm on STHTC [25]. Clonal Selection

Algorithm handles complex non-linear phenomena such as reservoir storage limit,

water discharge limit, power balance constraints and water transport delay etc. The

15

results are compared with those obtained by improved PSO, Genetic Algorithm (GA),

Improved Fast EP (IFEP), Gradient Search (GS), Non-Linear Programming (NLP),

Simulated Annealing (SA), Differential Evolution (DE), Dynamic Programming (DP)

and Evolutionary Programming (EP). From results, it is clear that the Clonal

Selection Algorithm-based approach conserves the computational budget.

Fang et al. presented a study of a hybrid algorithm for the solution of Hydrothermal

Coordination problems [26]. Authors combined Genetic Algorithm (GA) with Fish

Swarm Algorithm (FSA). They used modified GA for global search and modified

FSA for local search. The simulation results obtained were then compared with other

existing methods. It was observed that the hybrid solution can explore more and offer

significant improvements in addition to cost-effectiveness.

The approach proposed by Blaz et al. involves a Hydrothermal Coordination

optimization model based on the generating units [27]. They employed a multi-

objective Genetic Algorithm (GA) which considers the factors of emission, cost and

resource availability. In results, the generation availability showed stability; however,

emissions and fuel costs experienced a nominal increase.

Sampaio et al. described an approach for short-term hydro operation in a fluctuating

market and it was found that Genetic Algorithm (GA) leads to more profit [28].

Prominent factors that affect scheduling, such as head variance, market fluctuation,

pump storage capacity and head loss etc., are considered. The basic flow chart of GA

is given in Figure 2.2.

16

Figure 2.2: Flow chart of Genetic Algorithm (GA)

17

Simoglou et al. analyzed the Greek electricity market for a future period (2014-2020)

[29]. They considered five different energy technologies such as biomass, Solar

Photovoltaic (SPV), wind and Combined Heat and Power (CHP). Simulation results,

done through integrated software tools, signals the viability of large-scale Renewable

Energy System integration.

Behnam et al. considered resolving the self-scheduling issue of risk-constrained

generation system using a nonprobabilistic information gap model based on the

Information Gap Decision Theory [30]. Authors applied their proposed model on a

54-unit thermal generation system and proved that their model is a bit more profitable.

Pousinho et al. presented an MILP-based Approach for a pool based electricity market

and hydropower producer [31]. Authors prove that by adopting their approach

hydropower producers can have 9% more profit as compared to deterministic

approaches.

Koo et al. conducted the load forecasting using two different models [32]. Authors

use k-NN algorithm for load classification of the system. In the research work, they

conclude that Hot Winters have better performance than ARIMA (Autoregressive

Integrated Moving Average).

Batlle et al. presented the techniques for better power expansion planning and

compared them using LEEMA (Low-Emissions Electricity Market Analysis) [33].

Authors considered the thermal cyclic operation costs and proved that startups cost is

also a major factor in generation expansion planning and that it should not be ignored.

Ricardo et al. used Mixed Integer Non-linear Programming (MINLP) and spatial

Hydro Branch & Bound (SHBB) framework for short-term hydro-scheduling of head

dependent systems. Their results demonstrated improvement in performance and

computational time [34].

Tong et al. presented formulation of hydro generation scheduling on the basis of

Mixed Integer Linear Programming (MILP) [35]. Authors considered the linearization

of nonlinear constraints and discussed their impacts. Linearization of tailrace can

make the resulting schedule unacceptable. MILP makes the solution feasible and

18

efficient. Further, it is concluded that real number of water delays can be handled in a

manner ensuring stability of the water balance system.

Gonzalez et al. presented hourly hydrothermal dispatch by using single-node

centralized energy [36]. Authors classify generation technologies. Doing so

accelerates the performance. And, nonlinear constraints, such as elapsed time of

response, ramps, shut down and startup costs etc., are simplified. The proposed model

was applied on a 2010 scenario of Spanish market price. Comparatively better results

were obtained.

Kenneth et al. proposed a model for both demand-side and generation-side

management [37]. On comparing the proposed model with conventional solutions, it

was found able to manage the intermittency issue of Renewable Energy Sources

(RES). Andre Pina et al. presented the framework by using two specific models of

short-term and long-term planning are combined to model Hydrothermal

Coordination [38]. An iterative process is used to combine the results. Significant

reductions in CO2 emissions are observed. However, the model is only productive for

low storage capacity renewable energy systems.

Provas et al. proposed a Quasi-Oppositional Teaching Learning-Based Optimization

(QOTLBO) [39]. Authors used valve point effect and compared the results with the

latest optimization techniques, such as PSO, DE, Modified Differential Evolution

(MDE), Improved Self-adaptive Particle Swarm Optimization (ISAPSO) and neural

network. Findings revealed that the proposed approach had lower trapping chances to

the local minima.

Erlon et al. proposed a model for Hydro Unit Commitment and Loading (HUCL) and

provided the schedule of the day ahead [40]. Authors used an integrated optimization

technique keeping in view cascaded plants. The proposed model complied with the

generation limits and demonstrated improved performance for the basin.

Huifeng et al. presented a new methodology to address the issue of short-term

Hydrothermal Scheduling (HTS) [41]. They considered a heuristic technique and

employed three multi-objective Evolutionary Algorithms. An elitist archive is used to

19

put the non-dominant participants, and this improves the convergence and efficiency,

comparatively though.

Moein et al. solved the Hydrothermal Coordination problem considering the AC

constraints of bus voltages and transmission flow [42]. The methodology is based on

Benders Decomposition method that is improved by Particle Swarm Optimization and

Bacterial Foraging Algorithm. Authors compared the results of Bacterial Foraging

Oriented by Particle Swarm Optimization (BDI-BFPSO), with other techniques, such

as Benders Decomposition Improved by Particle Swarm Optimization (BDI-PSO),

Conventional Benders Decomposition and Benders Decomposition Improved by

Bacterial Foraging Algorithm (BDI-BFA). Their proposed methodology proved to be

effective, in results, but at the cost of trapping in minima. Rui. Zhang et al. considered

the issue of global warming in their Hydrothermal Coordination model [43]. The

proposed solution optimizes the generation system. However, an attempt to reduce

emissions increases in costs of the the generation system.

Javier et al. compared two models i.e. Mixed Integer Non-Linear Programming

(MILP) and Mixed Integer Linear Programming (MILP). The authors applied a non-

linear quadratic function for head and water discharge. It is shown that MINLP is

characterized by greater efficiency and water savings [44].

Xiaohu et al. made use of optimal Economic Dispatch (ED) to estimate risk [45].

Authors used PSO, considering the value at risk, and integrated risk management for

assessing the risk. An optimal tradeoff is approached between the profit and risk for a

hybrid system. It has been concluded that accurate forecasting of wind reduces the

risk.

Xie et al. discussed the issues faced by generation companies while attempting to

integrate wind power plants [46]. They discussed the fundamental problems i.e.

limited predictability and internal temporal variations. It is proposed that under

hazards, operational hurdles can be countered using intelligent computational

techniques.

Costas et al. proposed a self-scheduling hydro production model [47]. Its major aim is

to maximize profit keeping in view the upcoming market trends. Residual demand

20

curve depicts a comparison between the interaction of competitors and load demand.

The curve can be modified to meet the criterion of optimal pumped-hydro bids. To

remove the uncertainty in load demand, water inflow and competitors’ offers,

stochastic multistage programming, based on MILP, is used.

Kamal et al. proposed a Hydrothermal Coordination model based on improved PSO

[48]. Unlike its predecessors, the new PSO did not converge prematurely to a sub-

optimal solution. When compared to Modified Hybrid Differential Evolution

(MHDE) and GA, the proposed solution showed better results.

Cheng et al. proposed a technique based on Progressive Optimality Algorithm (POA)

[49]. Due to high-head real-time operations, short-term scheduling is difficult for

large scale cascaded hydropower plants. Prior to applying optimization, accumulative

mathematical techniques are used to identify forbidden operations zones. The

proposed technique is tested in China, and the results indicated that it can deal with

the complexities of multi-vibration zones.

Ahmad et al. used honey bee algorithm is selected for optimization of multi objective

problem of ED. Cost and emission reduction is done in a competitive market scenario.

Ramp rate limits and valve point loading constraint is considered. The effectiveness

of the algorithm is checked on IEEE standard bus systems of 6 and 10 units

respectively [50].

Basu et al. presented an Artificial Immune System (AIS) for hydrothermal scheduling

of systems comprising of fixed-head hydro systems and thermal systems [51]. Results

obtained from various experiments are compared with existing algorithms such as

Differential Evolution (DE), Evolutionary Programming (EP) and PSO. Numerical

results demonstrated the comparative superiority of AIS.

Senthil et al. discussed various techniques for hydrothermal scheduling [52]. GA

works fine for problems of hydropower plant while lambda iteration method is

preferred for problems relating to thermal power plants. But on considering the line

flow constraints and line losses, GA-based Optimal Power Flow (OPF) proves to be

better for hydrothermal systems. Results show that the GA-based solution minimizes

21

computation time, gives global optimum solution and reduces computational

complexity.

Balasubbareddy et al. used Fruit fly Algorithm and hybridized with Genetic

Algorithm for the power flow problem. They have used the Pareto front for multi-

objective visualization. Fuzzy logic is selected for best selection of best Pareto values.

But it makes system complex and computational budget requirement increases [53].

Frangioni et al. proposed a hybrid sequential approach [54]. Unit Commitment (UC)

is a fundamental problem in short-term electric power generation scheduling system.

The Lagrangian technique is good for lower bounds; however, it needs a new

mathematical model each time. In the same way, MILP offers better results at times

when lower bound is not good. The scheme proposed by the authors, therefore,

combines these two techniques and as a result, a hybrid version proves to be a far

better solution.

Christopher et al. proposed a Simulated Annealing Embedded Evolutionary

Programming (SAEEP) algorithm to solve short-term scheduling problems in power

generation [55]. The solution was able to find the optimum generation schedule and

the less-expensive alternative.

Kanwardeep et al. proposed a novel congestion management solution for thermal and

hydro systems [56]. A piece-wise linearized performance curve is used and to

evaluate effectiveness of the proposed method, authors used the IEEE 118 and IEEE

57 bus systems.

Sivasubramani et al. proposed a hybrid method, combining Sequential Quadratic

Programming (SQP), a global optimizer, and Differential Evolution (DE), a local

optimizer, for the Hydrothermal Coordination problem [57]. Tests are undertaken in a

multi-chain cascaded reservoir system and the proposed method shows its

efficaciousness.

The comprehensive literature review has explored the topic of Hydrothermal

Coordination from multiple dimensions. Further, the pertinent sub-topics, constraints,

objectives and techniques etc., are being summarized as follows.

22

2.3.1 Objectives of Hydrothermal Coordination

From the literature survey of Hydrothermal Coordination, it is observed that primary

concerns that demand attention are the minimization of fuel cost, emission reduction

and maximization of reliability as shown in Figure 2.3.

Cost minimization mainly depends on the selection of fuels i.e. coal is more

economical than natural gas and crude oil. Selection of power plants is also of

importance because the renewable power plants have minimum operational cost as

compared to all fossil fuel power plants. Grid, transmission and distribution system

are also taken into account in cost minimization because the power plants nearby to

load center have minimum losses.

Figure 2.3: Objectives of Hydrothermal Coordination

Regulations by the government also matter in the cost of power generation e.g. a

domestic user can prioritize his usage of electric iron, water pump and washing

machine etc. if peak time extra charges are implemented (Peak Load Pricing). Peak

load pricing regulation decreases the vertical difference between base load and peak

load. Peak load power plants are often more expensive as compared to base load

23

power plants [58]. Competition policy in pump storage and hydro dominated markets

can also decrease the power generation cost. Often, hydro power plants and pump

storage power plants inject more energy during peak time to get maximum benefit due

to which transmission limits and losses of energy come in discussion [59]. So, in short

some of the policies at the national level do matter in the economic dispatch. Clean

environmental regulation (‘implemented by government’) may eliminate the choice of

using coal for power generation even though coal is cheapest, the regulation max

impact the cost of generation.

Reliability maximization is also an objective of HTC that mainly depends on weather

forecasting, fault recognition at the earliest time possible and maintaining the

infrastructure that is aged. Weather prediction is necessary for stable and reliable

hydro operation [60, 61].

Emission minimization is also a key objective of HTC due to the current global

warming and climate change threats. By good selection of fossil fuels, e.g. by

minimizing usage of coal and crude oil, emissions can be minimized. Fuel

consumption can be saved by using cogeneration plants and combined heat plants.

Fuel saving indirectly minimizes the harmful gas emissions [62].

2.3.2 Constraints of Hydrothermal Coordination

In the literature survey, we have observed that there are various constraints which

need to be tackled in case of Hydrothermal Coordination. Some of the most common

constraints are shown in Figure 2.4. Every case study and scenario has its own

combination of constraints and objectives.

24

Figure 2.4: Constraints of Hydrothermal Coordination

2.3.3 Optimization Techniques Applied to Hydrothermal Coordination

From literature, it is evident that researchers follow different approaches to solve the

problem of Hydrothermal Coordination. In the period 1950-1980, classical techniques

were prominent. In the 1990’s, recursive techniques were common and by the end of

20th century Evolutionary Algorithms (EA) dominated the trend. From the start of the

21st century, the trend shifted toward hybrid schemes. Figure 2.5 shows the most

commonly used optimization techniques categorized into the following three major

groups: classical, deterministic and evolutionary.

25

Figure 2.5: Optimization Techniques Applied to Hydrothermal Coordination

2.4 Discussion

Hydro-thermal Scheduling (HTS), or Hydrothermal Coordination, is a highly

complex, non-linear, non-deterministic, multi-constrained and dynamic optimization

problem. Hydrothermal Coordination addresses two major problems i.e. Economic

Dispatch (ED) and Unit Commitment (UC). The solution solves unit selection and

active power dispatch. Search space of Hydrothermal Coordination is non-linear and

very turbulent. Therefore, there is a need for an efficient and robust optimization tool.

26

There are many techniques to solve the Hydrothermal Coordination problem. It has

been observed that conventional approaches are not successful in leading to

acceptable results for a problem that is non-differentiable, non-convex and complex.

The intrinsic complexities and the failure to resolve the challenges have shifted the

pivot to modern intelligent computational techniques, such as nature-inspired

Evolutionary Algorithms (EA). They offer much better outcomes and are open to

further refinement. Intelligent computational techniques, especially Evolutionary

Algorithms, hybridized with conventional techniques are better than classical

techniques.

Hydrothermal Coordination optimization techniques can be classified into three types:

classical, deterministic and evolutionary. Each of the types is characteristic of its pros

and cons. Classical techniques, such as gradient and NR based algorithms, are more

suitable for smooth fuel-cost curves. However, most of the Hydrothermal

Coordination problems have multiple constraints. In case of the non-smooth and

multi-model curve, there are another two options, i.e., deterministic and evolutionary.

The evolutionary option promises the issue redressal in a versatile and reliable

manner.

Compared to other meta-heuristic algorithms, PSO, DE, BFA, and BA are generally

preferred. However, overall, hybrid techniques offer the best results. Differential

evolution falls under the umbrella of deterministic evolutionary algorithm which has

supremacy over the evolutionary algorithms like GA and Swarm based algorithms.

Moreover, physics of the problem is of the quadratic nature and the differential

quadratic performs better as compared to other recursive techniques dynamic and

linear programming.

27


The chapter presented a rigorous literature survey of economical hydrothermal

coordination using intelligent computational techniques. HTC objectives have been

identified and discussed. The main objective of HTC is the economical operation of

hydro and thermal power plants by effective utilization of the available options. Later

on, HTC constraints are presented that are to be fulfilled. The main constraint of HTC

is that the power generation should be equal to the power demand by considering

transmission losses. In the end, the recent developments in ICT, with their pros and

cons, are discussed keeping in mind the classical, recursive and evolutionary

techniques.

28

3 Power Plants Development Trend

29

3.1 Chapter Summary

The chapter presents a comprehensive study about alternatives in power generation.

Levelized Cost of Electricity (LCOE) is discussed for coming forth with the best

solution. Existing models are compared along with their pros and cons. Finally, a

discussion is made about the suitability of a power plant in different conditions and

scenarios. It has been observed that per annum global electricity generation has

increased from 19.1 to 24.2 Petawatt hour. Similarly, CO2 emission has increased

from 10.5 to 12.9 Gigaton annually.

3.2 Background

In today’s rapidly digitizing global village, electricity demand is increasing owing to

rapid industrialization and modernized living standards. Therefore, electric power

generation and its development receive a significant portion of the national exchequer.

Utilizing a hybrid power generation mechanism and ensuring its optimal operation is

complex and tedious owing to various factors. Some of such factors include nature of

energy resource, availability, emissions, reliability, costs incurred and budget

constraints etc.

Electricity is one of the greatest blessings of science. There are many options for

power generation, each with its advantages and disadvantages. The selection criterion

varies owing to differences in environment, area and situation etc. [63, 64].

Availability of different sources enhances the reliability of the power system,

indirectly though. Source selection depends on the distance between load and

generation site. The density of the consumer population also influences the choice of

source selection [65]. Involving more selection considerations can further increase the

overall cost of the system. Due to high gains, wise selection of energy sources and

judicious component-sizing is mandatory so as to minimize the system costs and other

relevant expenses [66].

Supply Side Management (SSM) is a terminology that deals with clean generation of

electricity with reliability and cost-effective manner [67]. There are two main types of

30

sources: non-renewable and renewable. Most economical energy option is to be

considered, as the basic criterion [68, 69].

There is a significant portion of literature dedicated to demand side management and

distribution management; however, generation management has received little

attention [70]. Therefore, it is important to consider the issue of generation

management. It will significantly reduce costs. Major renewable energy sources

include hydropower, solar energy, wind energy, geothermal energy, tidal and

biomass. Non-renewable sources of energy are coal, oil and natural gas. Figure 3.1

depicts some of the major types of the power generation system.

Figure 3.1: Types of power generation systems with respect to the energy source

A power plant has various associated costs. In addition, there are concerns about

emission and reliability. Normally, parameters such as capital cost and operation cost

are used to choose the appropriate power plant in a given situation [71]. Levelized

Cost Of Electricity (LCOE) is the sum of capital, operation, and maintenance costs

divided by total energy produced in a power plant’s lifetime, keeping in view the

31

capacity factor [72, 73]. Calculating LCOE is an important step in order to select the

most suitable energy option [70]. In the literature, techniques dealing with costs of

power generation consider either economical cost, emission concerns and/or

reliability. There is little research work that considers LCOE.

Green House Gas (GHG) emission is the largest contributor to global warming [74].

According to the International Energy Agency (IEA), by 2040, premature deaths will

increase from 3 million to 4 million and CO2 emission rates will increase by 5% [75].

The situation is deteriorating, and it signals further urgent remedial actions. Present

era scientists, engineers and policymakers need to come forward with practical

solutions. One of the solutions to address the issue of GHG emission is the carbon tax,

a tax levied on the establishments that emit GHG’s. Solid implementation of suchlike

policy can result in the dominance of green technologies [76, 77].

During the last decade, a major chunk of the world’s energy demand came from

China and India. About one-third of the world’s population resides in India and China

[78, 79]. Coal has a major share in their energy generation mix [71]. Recently,

because of climate-friendly international policy endeavors, renewable energy

technologies are receiving attention worldwide [71, 72]. For instance, Germany and

Denmark are at the forefront of considering eco-friendly energy solutions [73].

On the other hand, the United States is investing more on coal and gas-based energy

solutions. US is one of the major suppliers of LNG and fossil fuels after Saudi Arabia,

Iran and Iraq [80].

3.3 Levelized Cost of Electricity (LCOE)

Levelized Cost of Electricity (LCOE) is an approximation of the average price of

a generating station for its lifetime. It is obtained by dividing the life-cycle cost of the

generation source by life-time energy produced, called Levelized Energy Cost (LEC)

[81]. It is also construed as a measure of the overall competitiveness of different

generation sources. The list of inputs required to calculate LCOE includes the

following: fuel cost, capital cost, fixed cost, variable maintenance cost, financing cost,

operational cost and an assumed duty rate for power plant technologies [72]. Fuel cost

32

is nearly negligible in the case of wind and solar power generation technologies.

Operation and maintenance expenses are also relatively less. Therefore, for wind and

solar energy, LCOE, to a large extent, depends on the capital cost of the power plant

[82].

The Levelized Avoided Cost of Electricity (LACE) is cited as another measure of the

overall competitiveness amongst different power generation sources. It measures the

annual economic value of the potential power generating project [83]. Since LACE

depends, to a larger extent, on local geographic variables, it is not that appropriate in

the global context [84]. Keeping in view a power plant’s financial life and utilization

cycle, LCOE predicts the per unit cost of a power plant. Figure 3.2 shows the factors

that can influence LCOE; here economic dispatch is related to variable operational

cost.

Figure 3.2: Factors Affecting the Levelized Cost of Electricity (LCOE)

However, LCOE is significantly influenced by generation technologies that use fuel to

a larger extent. Besides, operation and maintenance costs may also affect LCOE. The

generalized formula for LCOE is given as:

33

(3.1)

In the case of nuclear and non-renewable sources of energy, LCOE has remained

nearly unvaried in the last decade [85, 86]. However, solar energy has experienced a

shift in LCOE by up to 75%.

Among the renewable energy sources, hydropower has the least cost (Figure. 3.3)

followed by wind energy and Solar Photovoltaic (SPV) energy [85, 87, 88]. There are,

however, some issues linked with hydropower, as it involves mass public

displacement, and wind energy, since it is not available during peak load time.

Figure 3.3: Global Levelized Cost of Electricity (LCOE) of Power Generation in 2017

3.3.1 Non-Renewable Energy Sources

About half of world’s electricity demands are met by fossil fuels. Thermal power

plants generate energy from coal, oil, gas and nuclear. Heat is transferred in either of

the three ways i.e. conduction, convection and radiation. Thermal power plants utilize

the steam thrust to move the generation wheel. Two major costs are involved in a

LCOE =Cc − Σt=1

Lc dsΨ t ×Θ + Σt=1LcOcΨ

t × (1−Θ)− SvΨLc

Γ Σt=1LcΨ t × SDt

$-

$0.05

$0.10

$0.15

$0.20

$0.25

Concentra

ting S

olar

Ofshore W

ind

Solar

Photovolta

ic

Geothermal

Biomass

Onshore W

indHyd

ro

Fossi

l Fuels

$0.22

$0.14

$0.10

$0.07 $0.07 $0.06 $0.05

$0.10

Global LCOE of Power Generation-2017 (US$/kWh)

34

thermal power plant: capital cost and operational cost, with both of them depending

on fuel price [89].

3.3.1.1 Electricity Generation by Coal

Coal power plants dominate the energy scenario. In the last decade alone, coal

produced about one-third of electricity on annual basis [90-101]. One of the major

reasons behind preferring coal is its comparatively lower costs. However, the

environmental costs are generally ignored. Normally, electricity is generated by coal

at a smaller scale; however, if used at a larger scale, coal proves to be a useful and

cost-effective option. Coal does come with a drawback i.e. GHG emissions, which are

harmful to health and environment.

Since coal-fired power plants have been used since long, its technology has attained

maturity. To further complement, coal is available widely and is cheap,

comparatively. Coal plants are installed at places where coal is abundant. Adoption of

coal is increasing in Asia Pacific while the case is vice versa in Europe. Figure 3.4

shows the penetration of coal that has increased by 25% in the last decade.

Figure 3.4: Trend of coal-based electricity generation (2008-2017)

3.3.1.2 Electricity Generation by Oil

During the first decade of the 20th century, oil as an energy source received large

attention. Events such as Arab oil embargo of the 1970’s and the concerns behind its

0.00 2.00 4.00 6.00 8.00 10.00 12.00

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Coal)

25%

35

limited supply shifted the attention toward natural gas. Cost of fuel has a pivotal role

to play in ascertaining the power generated from petroleum sources. For instance, as

per Figure 3.5, generation from liquid fuels decreased by about 20% in the last decade

[90-99].

Figure 3.5: Trend of global electricity generation by oil (2008-2017)

3.3.1.3 Electricity Generation by Gas

After coal comes the natural gas fired power plants as they are widely used. Gas can

be easily transported across the borders and is economical. Therefore, it is preferred

over liquid fuels. Such power plants have lower capital costs and can be used as peak

power plants because of lesser startup time. Natural gas power plants grew by about

1/3rd in the last decade (Fig 3.6) [90-99].

0 0.2 0.4 0.6 0.8 1 1.2

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Oil)

-18%

36

Figure 3.6: Trend of global electricity generation by gas (2008-2017)

3.3.2 Renewable Energy Sources

Last decade has witnessed a notable increase in generation and adoption of

Renewable Energy Sources. Such a new arena of renewable energy has opened new

vistas of research as new challenges have emerged. New engineering designs and

types of equipment are being introduced to promote the use of renewable energy

technologies. Owing to their interconnection with environment, the renewable energy

sources demand evaluations from environmental angles as well [102].

Wind energy harnesses the kinetic energy of wind. In contrast to thermal power

plants, which do not depend on site specifications, wind turbines are highly dependent

on geographical features [103]. Wind power is having the advantage of being a clean

energy source. Its major drawback is uncertainty as it is highly dependent on the

natural atmospheric conditions. The average capacity factor of wind power plants is

30%, which is significantly better than that of solar power plants (18%) [104]. Energy

harnessed from Sun is called solar energy. Solar cells are used to obtain electrical

energy from sunlight. The efficiency of a solar cell depends on the material and its

thermal conductivity [105].

One of the most widely used forms of renewable energy, hydroelectricity is produced

when the energy of falling water is transformed into electrical energy with the help of

generators. Unlike coal and oil, hydropower doesn’t emit GHG’s into the atmosphere

0 1 2 3 4 5 6

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Gas)

31%

37

[106]. Hydropower generation has experienced a growth of about 25% in the last

decade (Figure 3.7) [90-99].

Figure 3.7: Trend of hydel generation in the world in the last decade

3.3.2.1 Geothermal Energy

Geothermal energy involves obtaining heat energy from the core of the earth. A

geothermal power plant can be thought of as a modified version of a thermal power

plant. While a thermal plant has a boiler and a burning fuel, the geothermal

counterpart does not demand such elements. In geothermal energy, the heat trapped

underground is made into use by rock catchers and injection wells [107]. Two types

of geothermal plants are being used worldwide: dry-steam plants-and flash-steam

plants. Flash steam power plants are younger as compared to dry steam. The use of

geothermal energy dates back to the 20th century; however, due to lower efficiency it

couldn’t progress then. In the last decade use of geothermal energy has increased by

almost 25% [90-99].

0 1 2 3 4 5

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Hydro)

24%

38

Figure 3.8: Trend of geothermal energy generation in the world for the last decade

3.3.2.2 Biomass

Biomass energy is derived from living things. For instance, bio-fuel, plant or animal

matter and biodegradable wastes can be used to generate electrical energy. Currently,

global power generation from biomass is around 0.5 TWh/annum. Figure 3.9 shows

that biomass generation of electricity has increased about two-fold in the last decade

[90-99]. Biomass reduces the dependence on fossil fuel. Recycling biofuels preserve

landfill space in urban communities.

Figure 3.9: Trend of biomass energy generation in the world for the last decade

0 0.02 0.04 0.06 0.08 0.1

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Geothermal)

27%

0 0.1 0.2 0.3 0.4 0.5 0.6

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Biomass)

93%

39

3.3.3 Nuclear Power Plants

Nuclear energy is derived from fission or fusion of radioactive elements such as

Uranium. It is cleaner alternate to thermal power.

Figure 3.10: International trend of nuclear energy generation in the last decade

In its early days nuclear energy received significant attention. Due to its security

concerns and after the Fukushima Power Plant accident in 2011, progress on nuclear

energy halted. However, new developments in safety solutions and risk management

have subsided some of the concerns. Figure 3.10 shows the trend of electricity

generation from nuclear energy during the last decade. It can be seen that there is a

decreased activity after the closure of plants in 2011. Later, it experienced an upward

trend [90-99]. Normally, nuclear power plants are characterized by high capital costs

and have wastage dumping issues. In contrast, their capacity factor is one of the

highest.

2.2 2.3 2.4 2.5 2.6 2.7

2008200920102011201220132014201520162017

Electricity (PWh)

Year

Net Electricity Generation (Nuclear)

0.1%

40

3.4 Trend of Global Electricity Generation and the Resulting GHG

Emissions

The increased reliance on technological gadgets has resulted in increased energy

demands. An attempt to seek comfort is synonymous with more energy demands.

China and India are the worlds’ largest consumers of energy.

Table 3.1: Global CO2 emissions trend

Power Plant Tonnes CO2/GWh

Generation 2017 (GWh) CO2 (tonnes) Global Emission

Share

Coal 971 9669.2 9388793 72.7%

Oil 733 812.6 595636 4.6%

Natural Gas 499 5360 2674640 20.7%

Solar PV 85 315.5 26818 0.2%

Biomass 45 510.4 22968 0.2%

Nuclear 29 2600.6 75417 0.6%

Hydro 26 3949.3 102682 0.8%

Wind 26 888.4 23098 0.2%

3.4.1 Global Generation

Global power demand is increasing every year steadily. Figure 3.11 shows the global

yearly energy share of each of the nine energy sources: geothermal, biomass/waste,

solar/tidal, wind, hydro, nuclear, gas, oil and coal [90-99].

41

Figure 3.11: Global electricity generation trend observed in the last decade

Furthermore, we reviewed the policies taken by G20 members regarding allocation of

resources for power generation. The reason for taking information of G20 members is

because collectively they account for about 85% of the global economy as well as

housing about 67% of the world’s population and 4/5 of the world trade. Thus they

are considered to be the most successful countries in terms of economic policies and

so their economic policies should be set as examples for other developing or

underdeveloped countries. This is the reason why we chose these countries as

examples for our study into how they chose indigenous resources, indigenous

technology and cheap resources for minimization of costs.

The most prominent example is the Kingdom Of Saudi Arabia. In Saudi Arabia,

Almost 70 percent of energy power plants use Gas while the rest of them use oil as

their primary source of energy. This is because Oil and Gas are the indigenous

resource for Saudi Arabia hence proving that for efficient allocation of resources for

energy production and cost minimization, countries should use resources readily

available to them.

0

5000

10000

15000

20000

25000

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Cost2010

Tera

Wh

Year

Net Global Generation Geothermal

Biomass/Waste

Solar/Tidal

Wind

Hydro

Nuclear

Gas

Oil

Coal

26%

42

Figure 3.12: G-20 countries power generation major resource [108, 109]

Another example of exemplary resource allocation is by India and China. Although

Coal is not indigenous to India or to China but due to the cheap nature of it, India and

China both have started using it excessively in power generation. This shows how

cheap resources attract G20 members even if the resource is not indigenous to their

countries. Hence, the cost of the resource also plays an important role while deciding

which primary resource to use for power generation [110].

Another example of excellent resource allocation can be seen in the USA. Here,

researchers have developed technologies which have led to the creation of a new type

of Gas called Shale Gas. This was possible due to technological advancement as well

as presence of Gas as the indigenous resource of the USA. United States has not only

0 20 40 60 80

ArgentinaAustralia

BrazilCanada ChinaFrance

GermanyIndia

IndonesiaItaly

JapanRepublic of Korea

MexicoRussia

Saudi ArabiaSouth Africa

TurkeyUnited Kingdom

United StatesThe European Union

Percentage of total generation of the country

Coal

Oil

Gas

Nuclear

Hydro

43

started using Gas as the primary source of power generation, accounting for 42% of

total power generation in the country, but has also made it as one of their exports.

This further proves how a G20 member makes use of indigenous technology

combined with indigenous resources to reap benefits in the form of cost minimization

and in the form of exports [111].

Brazil is another member of the G20 which has been successful in using their

indigenous resource as the primary source of power generation. Brazil has always

been blessed with water. In 2007, per capita water availability for Brazil reached

43,027 m3 per year, above the world average of 8,209 m3 per capita in the same year.

Brazil has made full use of this blessing and has setup various hydro power plants

which constitute of about 67% of power generation in Brazil. Thus, Brazil is a perfect

example of how using indigenous resources for power generation can help an

economy prosper into a G20 member [112].

Another country which used indigenous technologies to gain recognition on a global

scale is Germany. Using their technologies, Germany has successfully integrated

Renewable Resources such as Wind and Solar into their power generation and now

they account for a major portion (Wind constitutes around 25% of power generation

while Solar constitutes around 23%) of resource allocation. This is a perfect example

of a country which used its technologies to gain efficiency in power generation and is

rightfully included in the G20 [113].

3.4.2 Global Emission

About 98% of global GHG emissions emanate from fossil fuel based power plants

(Fig 3.13) [90-99]. Ironically, coal power plants alone are responsible for about 80%

of GHG emissions. Emissions that are being seen in the figure 3.13 by renewable

energy sources are the life cycle GHG. Major chunk of the emissions by renewables

considered here is because of manufacturing power plant require fossil fuel power.

Here, it can be said that there is no power source with zero emission [114, 115].

44

Figure 3.13: Percentage emission in the world by different power sources in 2017

Owing to severity of the issue (Figure 3.13), an emission control strategy is proposed.

3.5 Discussion

Global power generation is increasing. In the last decade alone, the annual growth met

557 Terawatt hours (TWh). With the same trend, it would double by 2045. One of the

major key findings of the study is that the trend of international power generation

growth is related to Levelized Cost Of Electricity (LCOE) and emission reduction.

LCOE of renewable energy sources, especially Solar Photovoltaic (SPV) and

Offshore Wind Energy is decreasing rapidly.

3.5.1 Cost

Power plants running on indigenous resources of energy are a far better option,

comparatively, as they are economical and are easily maintained. Transmission costs

constitute a significant portion of overall expenses in the case of centralized grids.

Solar power plants, on the other hand, save such transmission costs to a larger extent.

3.5.2 Emission

Renewable energy power plants should be preferred to conventional fossil-fuel energy

sources. Ignoring the renewable energy options will entail extra costs for emission

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

Coal Oil NaturalGas

Solar PV Biomass Nuclear Hydro Wind

72.7%

4.6%

20.7%

0.2% 0.2% 0.6% 0.8% 0.2%

Global CO2 Emission of Power Plants (2017)

45

reductions. Besides, carbon pricing, which also promises transition to renewable

energy options, will also enable the governments to accumulate huge revenue.

3.5.3 Reliability

On a general note, non-renewable energy options are considered more reliable than

renewable energy options. However, they come with additional drawbacks such as

GHG emissions and social costs. A diversified energy mix should be preferred

instead. Adding power storage mechanisms such as pump storage and compressed air

to renewable energy plants can make it more reliable.

3.5.4 Global Emission Control Strategy

Carbon emissions can be controlled if the stakeholders adopt a three-pronged

approach:

• Climate Finance

There are, currently, many governmental programs which dedicate subsidies

for fossil fuel power plants. Suchlike subsidies should be withdrawn

immediately. Instead, initiatives providing subsidies to renewable energy

plants should be encouraged. In doing so, phase-out compensation for fossil

fuel power plants should be paid by the respective governments.

• Carbon Pricing

Imposing a carbon tax can encourage the adoption of renewable energy

sources. It also decreases GHG emissions. For a consumer, the carbon tax will

serve either of the two purposes: enable a transition to renewable energy or

encourage the innovation of emission-free alternates.

• Domestic Policies

In addition to national and global levels, policies for encouraging eco-friendly

initiative should be adopted on domestic scale as well. City governments and

municipal establishments should play an integral part. This will enhance skill

development and entrepreneurship in the area of energy.

46

Figure 3.14: Emission Control Strategy


The chapter presented an overview of the global electricity generation and the LCOE

trend. Guidelines for effective resource utilization are also outlined. The rising GHG

emission levels are an alarming concern. Policymakers should, therefore, come forth

with initiatives that promise pragmatic outcomes. Some countries are spearheading

the adopting of renewable energy options. Still, the share of RES in the national

energy mix is minute, as compared to fossil fuels. Among RES, hydroelectric power

has a significant share in the global electricity mix. Drastic steps are needed to

counter the challenge of GHG emissions.

.

47

4 Long-Term Hydrothermal Coordination (LTHTC)

48

4.1 Chapter Summary

The chapter addresses Long-term Hydrothermal Coordination (LTHTC), which deals

with durations lasting from 1 week to 1 year. Forecasting the resource and addressing

the complexity are two of the main focuses of this chapter. Primary objectives are cost

minimization and emission reduction. A case study about a local power project is

considered for investigation purposes. For forecasting, Markov Chain, a stochastic

prediction model, is used. Intelligent computation for the optimal trade-off is carried

out by Particle Swarm Optimization (PSO).

4.2 Background

Worldwide, a major portion of electricity demand is met by hydroelectric and thermal

power projects. One of the emerging challenges is to devise a coordination

mechanism between these two sources. Such coordination leads to maximum

efficiency. Secondly, fossil fuel is a finite resource. Introducing Economic Dispatch

(ED) can reduce fuel consumption. Rising emission levels is another issue. GHG’s

emitted from thermal power plants, such as CO2, NO2 and SO2 etc, have caused

environmental problems such as ozone depletion, acid rain and rising temperature.

Emissions can be reduced by adopting eco-friendly energy options. Hydropower

plants can provide energy on larger scales in an eco-friendly manner. Hydropower

plants are, therefore, one of the best alternates.

Predicting the potential of water is not deterministic or understood in advance. Rather,

it is stochastic and remains variable. Finite nature of fossil-fuel and the associated

environmental hazards have encouraged the adoption of clean energy. Solar and wind

energy is gaining acceptance from the public. Here, Markov Chain method is used to

ensure maximum utilization from the stochastic nature of hydropower. This method is

important as it can truly predict the stochastic nature of hydropower for intended

outcomes. Moreover, Particle Swarm Optimization (PSO) technique has been used.

The primary objective of the chapter is to aim for a solution that is economical and

possess minimal environmental costs. One of the proposed solutions uses a

combination of the hydropower plant, for providing base load, and other energy

options, such as thermal plant and renewable energy, for the rest of the load. The

49

results were finalized using the following strategies: Economic Load Dispatch,

Economic Emission Dispatch and Combined Load and Emission Dispatch.

4.3 Electricity Sector in Pakistan

Pakistan is a South Asian country and so has a developing economy. This developing

economy has given rise to industries around the country which has further led to the

creation of demand for electricity. Being a developing country, Pakistan is not a

stranger to high birth rates which is a major reason for the increasing population of

the country. This increase in population has further led to increase in domestic

demand for electricity which is another problem for the country. Due to the huge

influx of new industries and the increasing population of a developing country,

Pakistan has still not been able to meet the demand for electricity in the country and

the supply demand gap for electricity has touched 7 GW in the past years.

Pakistan is blessed with 5 Rivers including River Indus which has more volume of

water than River Nile. Due to these resources, Pakistan makes around 99 percent of its

electricity by Hydro and Thermal Power Plants (Pakistan Energy Year Book 2017).

Pakistan has 4 major Hydro Power Plants i.e. Tarbela, Ghazi-Barotha, Mangla and

Neelum Jhelum. From these 4, we have selected Ghazi-Barotha as our case study for

this chapter.

4.4 System Model and Problem Formulation

Hydropower generation depends on water inflow, which is susceptible to seasonal

variations. Therefore, simultaneously scheduling thermal generating units and

ensuring control of GHG emissions is one of the major challenges. Using Particle

Swarm Optimization on a monthly basis can help solve the problem.

4.4.1 Hydropower Power Plant and Load Demand

Hydropower plants occupy a major share in modern power systems. They offer

affordable and clean energy with minimum operational costs. For analysis purposes, a

local site of Ghazi Barotha, Pakistan has been taken into consideration. Historical data

about water inflow and average energy demand of Khyber Pakhtoonkhwa (KP)

50

province is obtained from repositories of Water and Power Development Authority

(WAPDA) (Table 4.1) [116]. Table 4.2 shows the monthly average load demand of

Khyber Pakhtunkhwa (KP).

Table 4.1: Average monthly inflow of Ghazi Barotha site from 2010 to 2017 in Cumecs

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

2010 856 950 1100 1600 1600 1600 1600 1560 1510 1550 1220 600

2011 1200 1066 870 1580 1600 1700 1600 1600 1327 1300 1150 605

2012 1400 688 831 1300 1600 1600 1620 1580 1580 1520 922 580

2013 1300 800 1100 1200 1600 1620 1650 1700 1500 1300 1000 700

2014 1235 1000 750 1250 1600 1600 1675 1600 1493 1500 1000 720

2015 1000 700 600 1470 1675 1700 1700 1600 1140 950 860 800

2016 434 1061 831 1065 1622 1606 1649 1607 1571 1380 1516 980

2017 245 871 720 957 1600 1615 1661 1683 1701 1348 1240 707

The dominant challenge lies in predicting the water inflow, because of its randomly

probabilistic behavior. Therefore, previous year inflow data was essential to predict

the next year’s inflow.

51

Table 4.2: Monthly Average Load-demand

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Avg. Demand (MWh)

1814 1519 1636 1841 2255 2567 2459 2239 1737 1522 1318 1213

4.4.1.1 Hydropower System Modeling

There are many forecasting methodologies, e.g. average method, weighted

average method and extrapolation etc. Markov Chains is used in the research work as

it is robust and advanced [117-119]. The energy available in flowing water is in the

form of potential or kinetic energy.

The potential energy can be derived as follows:

(4.1)

(4.2)

(4.3)

(4.4)

where, P is power in watts

(4.5)

P.E = mgh

Qρ = mV

∴m = ρV

P.E = ρVgh

P = P.Et

= ρVght

= ρghVt

P = ρghVt=ηρghQ

52

And, in case of flowing/running water, the energy of water is kinetic

energy (KE), which can be expressed mathematically as:

(4.6)

(4.7)

where, the variables ρ, A, v, and V denote water density (kg/m3), area (m2), the

velocity of water flow (m/sec) and volume of flowing water (m3) respectively.

(4.8)

(4.9)

where, water density is in kg/m3 (1000 kg/m3), water discharge in m3/sec and

acceleration due to gravity in m/sec2.

From Equation 4.9, it can be inferred that power is directly proportional to flow rate,

cross-sectional area, density of water and efficiency.

4.4.1.2 Stream-inflow and Markov Chain

Markov chain is one of the most popular and accurate methods for forecasting the

water inflow. It is a stochastic procedure which makes use of possible scenarios and

recurrent patterns in order to forecast the current event.

Markov chain can be mathematically expressed as,

K .E = 12mv2

K .E = 12ρAxv2

P = K .Et

= 12ρAxv2

t= 1

2ρA xtv2 = 1

2ρAvv2

P = 12ηρAv3

53

(4.10)

From Equation 4.10, it can be seen that the probability of a particular state, for

example 𝑋"#$, depends on all of the previous states, i.e. 𝑋" = 𝑦, 𝑋"($ = 𝑦"($.

4.4.1.3 State Formation and Discretization

In Markov chain rule, fragments of large data are transformed into discrete states.

Forming discrete states with each representing the mean data value resolves the issue

arising from the complexity of large data volume. Actual data and the relevant

discretized values are tabulated as Table 4.3.

Table 4.3: Discretization of States

State Actual data (𝑪𝑴𝑺) Discretized value (𝑪𝒖𝒎𝒆𝒄𝒔)

1 1600 and above 1700

2 1400 to 1599 1500

3 1200 to 1399 1300

4 1000 to 1199 1100

5 800 to 999 900

6 600 and below to 799 700

4.4.1.4 Transition Matrix (T-Mat) Formation

Transition matrix, or T-Mat, which comprises of states distinguished as separate

entities, lies at the heart of Markov chain methodology. In a single-step Markov chain

model, two consecutive periods are selected and then converted into states using

Transition matrix. The process is illustrated in Figure 4.1

P( y, z) = P(Xa+1 = z Xa = y,Xa−1 = ya−1,...)

54

January

February

March

April

May

June

July

August

September

October

November

December

Figure 4.1: State diagrams of the period January to December

55

Table 4.4: State Table from January to June

12-1 1 2 3 4 5 6

→ J A N

12-1 1 2 3 4 5 6 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 1 0 1 5 0 0 0 0.5 0 0.5 6 0 1 3 0 1 1 6 0 0.17 0.5 0 0.17 0.17

1-2 1 2 3 4 5 6

→

F E B

1-2 1 2 3 4 5 6 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 1 3 0 0 0 2 1 0 3 0 0 0 0.67 0.33 0 4 0 0 0 0 0 1 4 0 0 0 0 0 1 5 0 0 0 0 1 0 5 0 0 0 0 1 0 6 0 0 0 1 1 0 6 0 0 0 0.5 0.5 0

2-3 1 2 3 4 5 6

→

M A R

2-3 1 2 3 4 5 6 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 2 1 4 0 0 0 0 0.67 0.33 5 0 0 0 2 0 1 5 0 0 0 0.67 0 0.33 6 0 0 0 0 1 1 6 0 0 0 0 0.5 0.5

3-4 1 2 3 4 5 6

→

A P R

3-4 1 2 3 4 5 6 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 1 0 1 0 0 0 4 0.5 0 0.5 0 0 0 5 0 1 1 1 0 0 5 0 0.33 0.33 0.33 0 0 6 0 1 1 0 1 0 6 0 0.33 0.33 0 0.33 0

4-5 1 2 3 4 5 6

→

M A Y

4-5 1 2 3 4 5 6 1 1 0 0 0 0 0 1 1 0 0 0 0 0 2 2 0 0 0 0 0 2 1 0 0 0 0 0 3 3 0 0 0 0 0 3 1 0 0 0 0 0 4 1 0 0 0 0 0 4 1 0 0 0 0 0 5 1 0 0 0 0 0 5 1 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

5-6 1 2 3 4 5 6 → J U N

5-6 1 2 3 4 5 6 1 8 0 0 0 0 0 1 1 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

56

Table 4.5: State Table from July to December

6-7 1 2 3 4 5 6

→ J U L

6-7 1 2 3 4 5 6 1 8 0 0 0 0 0 1 1 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

7-8 1 2 3 4 5 6

→

A U G

7-8 1 2 3 4 5 6 1 6 2 0 0 0 0 1 0.75 0.25 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

8-9 1 2 3 4 5 6

→

S E P

8-9 1 2 3 4 5 6 1 1 3 1 1 0 0 1 0.17 0.5 0.17 0.17 0 0 2 0 2 0 0 0 0 2 0 1 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

9-10 1 2 3 4 5 6

→

O C T

9-10 1 2 3 4 5 6 1 0 0 1 0 0 0 1 0 0 1 0 0 0 2 0 3 2 0 0 0 2 0 0.6 0.4 0 0 0 3 0 0 1 0 0 0 3 0 0 1 0 0 0 4 0 0 0 0 1 0 4 0 0 0 0 1 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

10-11 1 2 3 4 5 6

→

N O V

10-11 1 2 3 4 5 6 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 1 1 1 0 2 0 0 0.33 0.33 0.33 0 3 0 1 1 2 0 0 3 0 0.25 0.25 0.5 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 0 0 1 0 5 0 0 0 0 1 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0

11-12 1 2 3 4 5 6

→

D E C

11-12 1 2 3 4 5 6 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 1 0 2 0 0 0 0 1 0 3 0 0 0 0 0 2 3 0 0 0 0 0 1 4 0 0 0 0 0 3 4 0 0 0 0 0 1 5 0 0 0 0 1 1 5 0 0 0 0 0.5 0.5 6 0 0 0 0 0 0 6 0 0 0 0 0 0

57

4.4.1.5 Expectations of the Stream Inflow

A value obtained from a random process predicts the forthcoming states. Thus, stream

flow is found as a result of such a process. The process starts by selecting a row,

calculating its result and picking the random state. As a next step, the very row is

selected, its expectations are considered and another state is picked. The process

continues. Mathematically, it can be expressed as follows:

(4.11)

For instance, if row 5 is picked from T-Mat and its expectation is obtained, the values

of the state can be recalled from state tables i.e. Tables 4.3-4.5. The expectation, Exp,

can be calculated as follows: 0.66(1100) + 0.34(900) + 0(700). Therefore, in this

case, the expectation from the above equation will be Exp = 1032. The states along

with their respective conversions and probabilities can be expressed with the help of a

state diagram as shown in Figure 4.1.

Maximum possible hydropower is calculated and distributed among the hydropower

units. On-site, there are five turbines installed with each having the capacity of 290

MW totaling to about 1450 MW. Other particulars of the site are as follows: head

height is 70 meters; monthly discharge capacity is 1600 cubic meter per second

(cumecs); minimum reservoir storage capacity is 800 cumecs and maximum reservoir

storage capacity is 1200 cumecs. The reservoir storage capacity at the end of

December is 1000 cumecs.

4.4.1.6 Reservoir Operation

The operation of reservoir plays a significant role when making a decision about the

discharge of water. Water discharge in hydroelectric depends on the availability of

water and the predicted inflow. In order to ensure continuous availability of water, the

reservoir operation needs to be improved.

)(,....)()( 2211 nn StPStPStPExp +++=

58

4.4.1.7 Reservoir Storage Continuity

• Water storage limitations

Water storage limit describes the maximum and a minimum capacity of a water

storage reservoir. Storage attains the maximum efficiency when the reservoir attains

full capacity. However, it is not possible all the times. Therefore, when the reservoir

operates on half capacity, it is considered acceptable.

(4.12)

• Reservoir constraints

The reservoir continuity equation is given as follows:

(4.13)

• Water discharge and generation limits

Water discharge limits indicate the minimum and maximum water discharge from a

reservoir, and can be expressed as,

(4.14)

In the same manner, there are maximum and minimum power generation figures of a

hydroelectric generating station.

(4.15)

4.4.2 Thermal System Modeling

Hydrothermal Coordination is characterized by cost minimization of thermal power

units. The cost of fuel and emission minimization depends on various factors and is,

therefore, does not remain same all the times. Both such costs are addressed.

Vhjmin <Vhj <Vhj

max

Vhj(t+1) =Vhjt + Et+1 −Qt − S t

Qhjmin <Qhj <Qhj

max

hj

min

P ≤hjtP ≤

hj

max

P , jεhN , t ε T

59

Coefficients and limitations of fuel-cost and emission cost are tabulated in Tables 4.6

and 4.7 respectively.

Table 4.6: Fuel cost-coefficients and the limitations

Unit A B C K I Pmin Pmax

1 ($/MWh) 100 2.45 0.0012 160 0.038 50 180

2 ($/MWh) 120 2.32 0.0010 180 0.037 40 300

3 ($/MWh) 150 2.10 0.0015 200 0.035 50 400

4 ($/MWh) 100 2.34 0.0012 160 0.038 50 420

Table 4.7: Emission cost-coefficients and limits

Unit X Y Z D G PMin PMax

1 (lb/h) 60 -1.355 0.0105 0.4968 0.01925 50 180

2 (lb/h) 45 -0.600 0.0080 0.4860 0.01694 40 300

3 (lb/h) 30 -0.555 0.0120 0.5035 0.01478 50 400

4 (lb/h) 60 -1.355 0.0105 0.4968 0.01925 50 420

4.4.2.1 Fuel Cost Minimization (FCM)

Hydrothermal Coordination involves proper scheduling schemes and therefore, saves

significant thermal energy units. Mathematically, fuel cost can be expressed as

follows:

60

(4.16)

The equation (4.16) is only valid for a single steam turbine. In the case of a multi-

steam turbine, the equation changes as follows:

(4.17)

Similar to hydropower plants, thermal generating stations also have a range of limits

for maximum and minimum power generation.

(4.18)

4.4.2.2 Emission Cost Minimization (ECM)

The other vital objective of Hydrothermal Coordination is the minimization of

emission costs. Emissions produced from the burning of fossil fuels negatively impact

the environment. From equation 4.19, it can be inferred that it is essential to minimize

the usage of thermal power in order to reduce GHG emission.

(4.19)

where, total system emission cost and can be equated as:

(4.20)

This equation is valid for a single steam turbine; however, for multiple turbines, the

equation transforms as follows:

minF(PTH ) = xTHi + yTHiPTHit + zTHiPTHit2⎡⎣ ⎤⎦

i=1

NTH

∑t=1

T

∑

F(PTH ) = xTHi + yTHiPTHit + zTHiPTHit2 + uTHi × sin eTHi × PTHi

min − PTHit( ){ }⎡⎣⎢

⎤⎦⎥i=1

NTH

∑t=1

T

∑

THi

min

P ≤THitP ≤

THi

max

P

E(PTHit ) = et PTHit( )i=1

NTH

∑t=1

T

∑

et (PTHit ) = xTHEi + yTHEiPTHit + zTHEiPTHit2

61

(4.21)

4.4.2.3 Combined Fuel and Emission Minimization (CFEM)

So far, the issues relating to fuel and emission have been dealt with gently.

More value can be added by handling the very issues together. This can be

done by adding a ‘penalty factor’.

(4.22)

In Equation 4.22, TOC is the sum of costs. Further, the penalty factor can

be obtained through the following equation:

(4.23)

4.4.2.4 The Objective Function

Objective function with weights and penalty can be written as follows:

(4.24)

here, w1 is the weighted fuel objective and w2 is the weighted emission objective.

The variables P and E have already been derived in equations 4.19 and 4.20

respectively.

The Weighted Objectives Method is a technique used to convert multi objective

function to a simple objective function. This is done by assigning values known as

weights to the variables according to the importance of the variable. The Object

Weight technique assigns weight no greater than 1 and no less than 0 although the

sum of the weights should always be equal to 0. This technique can also be used to

convert more than 10 objectives into a single function and so is used quiet frequently

et = xTHEi + yTHEiPTHit + zTHEiPTHit2 + uTHEi exp(eTHEiPTHit )

minTOC = F(PTHit )+℘E(PTHit )

℘=F(PTHi

max ) / PTHimax

E(PTHimax ) / PTHi

max

minTOC = w1F(PTHit )+ w2λuE(PTHeit )

62

to make simple objective functions. In our problem, we have two conflicting variables

i.e cost minimization and mission rates. To make this multi objective function into a

single function, we have used objective weight technique and thus have been able to

solve a problem simply.

There are some constraints, however, associated with power demand as stated in the

following equation:

(4.25)

The above equation signifies that sum of powers can never exceed or be less than the

demand.

4.5 Proposed Algorithm and Settings

4.5.1 Proposed Algorithm

The main algorithm used in the research work is Particle Swarm Operation (PSO)

technique. It provides accurate results for stochastic values using population

optimization as its primary process. The solution utilizes bio mimicry and learns from

the behavior of birds and fish when they struggle for food in groups. PSO is more

efficient than Genetic Algorithm (GA) in obtaining results, particularly in the case of

random values, which is frequent in power systems. Figure 4.2 depicts the flow-

diagram of PSO algorithm:

Σt=1T PTHi

t + Σt=1T Phj

t + Σt=1T Pwk

t + Σt=1T Psl

t − Pdemandt = 0

63

Figure 4.2: Particle Swarm Optimization (PSO) flow chart

64

The hydro unit receives the base load and therefore non-thermal load is solved first.

The excess load is then given to the thermal unit. Being stochastic, hydro units are

dealt using the Markov Chains rules. Monte Carlo Iterations are used to balance the

randomness caused by the stochastic nature hydro units.

4.5.2 Particle Swarm Optimization (PSO) Attributes

Dynamic swarm inertia, rather than the static one, was used for the velocity update

process. The Swarm Inertias C1 and C2 were 0.5 and 2.0 respectively in a consecutive

manner. This resulted in enhancement of convergence acceleration and facilitated

more accuracy. By doing so, it is inferred that in order to achieve the best possible

performance, C1 and C2 should be altogether set to the value of 2.50, with assigning

weight to the variables pbest, or local best, and gbest, or global best, in the evolution

process. Using the Particle Swarm Optimization (PSO), a 2-dimensional array of

thermal power and time is formed for each of the power populations. The platform of

MATLAB v 7.12.0 was used for simulation purposes on an Intel (R) Core (TM) i3

workstation having a 4 GB RAM with 1.70 GHz processor.

4.6 Simulation Results

Two hundred (200) PSO generations with 200 iterations of Monte Carlo were

considered. The time period considered is January to December of the following year.

Simulations were run for 11 weights, with each representing a trade-off between Fuel

Cost Minimization (FCM) and Emission Minimization (EM). The eleven weights had

two variables as an array with values stretching from [1,0] to [0,1] and an interval of

0.1 was considered. Each of the individual weights added up 1. The algorithm tries to

minimize the emission as well as fuel cost.

PSO was also consulted to find the convergence of Combined Fuel and Emission

Minimization (CFEM), a parameter which depicts fuel cost and emission as a

combined variable. Figure 4.3 shows the convergence behavior of CFEM.

65

Figure 4.3: Convergence Behavior of Combined Fuel and Emission Minimization

(CFEM)

The algorithm seeks to approach the desired level of minimum cost and reduced

emissions. It must do so while staying within the limit. Initially hydro power is

considered, and then thermal power plants are considered in the next stage. While in

hydropower a water reservoir acts as a power bank. The reservoir can be used all the

year around. Detailed scheduling of all the power plants is shown in Tables 4.8-4.11.

66

Table 4.8: Results of scheduling power plants against the objectives 1,2,3

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 120 231 258 222 290 290 290 280 35

Feb 1681 180 300 209 293 290 290 76 0 0

Mar 1769 180 296 322 231 290 290 123 0 0

Apr 2053 180 179 233 130 290 290 290 290 130

May 2435 180 300 290 198 290 290 290 290 234

Jun 2695 180 300 323 420 290 290 290 290 274

Jul 2549 180 300 314 250 290 290 290 290 290

Aug 2319 143 213 220 269 290 290 290 290 290

Sep 2017 90 209 156 103 290 290 290 290 286

Oct 1958 175 214 173 50 290 290 290 263 168

Nov 1517 128 181 201 50 290 290 288 75 0

Dec 1362 155 197 242 114 290 290 35 0 0 Objective Weights [F,E] = [0,1] Fuel Cost (M$)=15.295 Emission(Mtons)=25.688

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 180 202 226 223 290 290 290 280 35

Feb 1681 174 288 324 196 290 290 76 0 0

Mar 1769 180 297 133 419 290 290 123 0 0

Apr 2053 180 145 169 228 290 290 290 290 130

May 2435 146 286 327 210 290 290 290 290 234

Jun 2695 180 300 400 343 290 290 290 290 274

Jul 2549 173 299 268 304 290 290 290 290 290

Aug 2319 180 300 157 208 290 290 290 290 290

Sep 2017 156 117 163 136 290 290 290 290 286

Oct 1958 180 300 145 222 290 290 290 263 168

Nov 1517 150 237 225 50 290 290 288 75 0

Dec 1362 145 249 173 151 290 290 35 0 0

Objective Weights [F,E] = [0.1,0.9] Fuel Cost(M$) =15.253 Emission(Mtons)=25.990

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 120 231 258 222 290 290 290 280 35

Feb 1681 180 300 209 293 290 290 76 0 0

Mar 1769 180 296 322 231 290 290 123 0 0

Apr 2053 180 179 233 130 290 290 290 290 130

May 2435 180 300 290 198 290 290 290 290 234

Jun 2695 180 300 323 420 290 290 290 290 274

Jul 2549 180 300 314 250 290 290 290 290 290

Aug 2319 143 213 220 269 290 290 290 290 290

Sep 2017 90 209 156 103 290 290 290 290 286

Oct 1958 175 214 173 50 290 290 290 263 168

Nov 1517 128 181 201 50 290 290 288 75 0

Dec 1362 155 197 242 114 290 290 35 0 0 Objective Weights [F,E] = [0.2,0.8] Fuel Cost (M$)=15.124 Emission(Mtons)=25.999

67


Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 180 300 144 207 290 290 290 280 35

Feb 1681 180 300 275 227 290 290 76 0 0

Mar 1769 180 300 343 207 290 290 123 0 0

Apr 2053 179 217 201 125 290 290 290 290 130

May 2435 172 295 217 282 290 290 290 290 234

Jun 2695 180 294 328 420 290 290 290 290 274

Jul 2549 180 300 312 253 290 290 290 290 290

Aug 2319 167 258 218 202 290 290 290 290 290

Sep 2017 137 174 202 58 290 290 290 290 286

Oct 1958 180 276 240 145 290 290 290 263 168

Nov 1517 120 247 148 56 290 290 288 75 0

Dec 1362 165 199 215 50 290 290 35 0 0

Objective Weights [F,E]=[0.3,0.7] Fuel Cost(M$)=15.093 Emission(Mtons)=26.032

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 180 300 212 139 290 290 290 280 35

Feb 1681 180 300 275 226 290 290 76 0 0

Mar 1769 158 274 324 273 290 290 123 0 0

Apr 2053 159 270 152 142 290 290 290 290 130

May 2435 137 270 337 224 290 290 290 290 234

Jun 2695 180 300 323 419 290 290 290 290 274

Jul 2549 180 300 332 233 290 290 290 290 290

Aug 2319 180 229 204 232 290 290 290 290 290

Sep 2017 130 210 182 50 290 290 290 290 286

Oct 1958 180 249 139 278 290 290 290 263 168

Nov 1517 138 108 296 120 290 290 288 75 0

Dec 1362 138 195 230 153 290 290 35 0 0


Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 180 300 229 122 290 290 290 280 35

Feb 1681 180 300 233 269 290 290 76 0 0

Mar 1769 180 300 328 221 290 290 123 0 0

Apr 2053 180 200 126 216 290 290 290 290 130

May 2435 125 286 325 230 290 290 290 290 234

Jun 2695 180 300 322 420 290 290 290 290 274

Jul 2549 180 300 275 290 290 290 290 290 290

Aug 2319 180 214 316 135 290 290 290 290 290

Sep 2017 89 246 187 50 290 290 290 290 286

Oct 1958 180 300 400 223 290 290 290 263 168

Nov 1517 180 108 130 162 290 290 288 75 0

Dec 1362 125 245 301 50 290 290 35 0 0


68


Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 173 213 232 213 290 290 290 280 35

Feb 1681 180 300 254 248 290 290 76 0 0

Mar 1769 180 300 233 317 290 290 123 0 0

Apr 2053 151 147 145 280 290 290 290 290 130

May 2435 121 295 329 224 290 290 290 290 234

Jun 2695 180 300 324 419 290 290 290 290 274

Jul 2549 180 300 217 347 290 290 290 290 290

Aug 2319 180 300 212 153 290 290 290 290 290

Sep 2017 141 144 237 50 290 290 290 290 286

Oct 1958 180 300 208 159 290 290 290 263 168

Nov 1517 157 207 248 50 290 290 288 75 0

Dec 1362 140 222 191 163 290 290 35 0 0

Objective Weights [F, E] = [0.6,0.4] Fuel Cost(M$) =14.972 Emission (Mtons) =26.323

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 170 208 176 276 290 290 290 280 35

Feb 1681 139 293 328 221 290 290 76 0 0

Mar 1769 180 300 316 234 290 290 123 0 0

Apr 2053 154 134 221 213 290 290 290 290 130

May 2435 180 219 266 301 290 290 290 290 234

Jun 2695 180 300 326 416 290 290 290 290 274

Jul 2549 180 300 305 259 290 290 290 290 290

Aug 2319 123 289 221 211 290 290 290 290 290

Sep 2017 143 250 128 50 290 290 290 290 286

Oct 1958 174 265 379 284 290 290 290 263 168

Nov 1517 110 256 232 63 290 290 288 75 0

Dec 1362 170 211 204 131 290 290 35 0 0

Objective Weights [F, E] = [0.7,0.3] Fuel Cost(M$) = 14.896 Emission (Mtons) = 26.388

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 169 209 218 180 290 290 290 280 35

Feb 1681 146 259 149 157 290 290 76 0 0

Mar 1769 180 300 313 223 290 290 123 0 0

Apr 2053 111 239 226 121 290 290 290 290 130

May 2435 180 300 239 221 290 290 290 290 234

Jun 2695 180 300 301 418 290 290 290 290 274

Jul 2549 180 298 341 226 290 290 290 290 290

Aug 2319 179 299 235 132 290 290 290 290 290

Sep 2017 99 213 64 182 290 290 290 290 286

Oct 1958 55 235 50 251 290 290 290 263 168

Nov 1517 145 116 157 50 290 290 288 75 0

Dec 1362 145 190 233 128 290 290 35 0 0 Objective Weights [F, E] = [0.8,0.2] Fuel Cost (M$) = 14.732 Emission (Mtons) = 26.394

69

Table 4.11: Results of scheduling power plants against the objectives 10, 11

In the case of hydropower plants, the primary focus is to control the constraints,

reduce the limitations and ensure smooth functioning of the power plant. The

expected inflow resulting from the Markov Chain is shown in Figure 4.4.

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 158 203 192 184 290 290 290 280 35

Feb 1681 159 290 131 224 290 290 76 0 0

Mar 1769 180 300 329 214 290 290 123 0 0

Apr 2053 145 282 153 130 290 290 290 290 130

May 2435 177 299 225 253 290 290 290 290 234

Jun 2695 180 268 345 416 290 290 290 290 274

Jul 2549 180 300 336 228 290 290 290 290 290

Aug 2319 180 242 237 186 290 290 290 290 290

Sep 2017 118 166 142 132 290 290 290 290 286

Oct 1958 180 300 137 299 290 290 290 263 168

Nov 1517 76 266 119 192 290 290 288 75 0

Dec 1362 179 237 145 149 290 290 35 0 0

Objective Weights [F, E] = [0.9,0.1] Fuel Cost (M$) = 14.692 Emission (Mtons) = 26.449

Month Demand (MW)

PTH1 (MW)

PTH2 (MW)

PTH3 (MW)

PTH4 (MW)

PH1 (MW)

PH2 (MW)

PH3 (MW)

PH4 (MW)

PH5 (MW)

Jan 2035 122 137 349 129 290 290 290 280 35

Feb 1681 53 228 216 216 290 290 76 0 0

Mar 1769 180 300 239 297 290 290 123 0 0

Apr 2053 127 223 140 208 290 290 290 290 130

May 2435 180 300 235 225 290 290 290 290 234

Jun 2695 180 300 400 319 290 290 290 290 274

Jul 2549 180 300 282 282 290 290 290 290 290

Aug 2319 180 197 305 163 290 290 290 290 290

Sep 2017 159 127 222 50 290 290 290 290 286

Oct 1958 131 134 187 140 290 290 290 263 168

Nov 1517 156 138 131 127 290 290 288 75 0

Dec 1362 180 209 140 181 290 290 35 0 0 Objective Weights [F, E] = [1,0] Fuel Cost(M$) = 15.237 Emission (Mtons) = 26.501

70

Figure 4.4: Expected Water Inflow and Discharge

The annual monthly reservoir water inflow is shown in Figure 4.5. water inflow is

more in summer season due to the ice melting on the mountain of north.

Figure 4.5: Reservoir storage profile throughout the year

71

Figure 4.6 depicts the monthly electrical power generated from Thermal and Hydro,

power plant. Load demand is more during the summer season as compared to winter,

due to the air-conditioning requirement in Pakistan.

Figure 4.6: Load demand vs generation by power plants

Figure 4.7: Cost of Fuel with respect to Objectives

13.6

13.8

14

14.2

14.4

14.6

14.8

15

15.2

15.4

[0,1] [0.1,0.9] [0.2,0.8] [0.3,0.7] [0.4,0.6] [0.5,0.5] [0.6,0.4] [0.7,0.3] [0.8,0.2] [0.9,0.1] [1,0]

Cos

t in

M$

Objective Weightage [F,E]

Cost

72

Figure 4.7 represents the cost of fuel with respect to its objective weightage. It can be

observed from the graph that as the variable F, or weight of fuel cost, increases, the

fuel cost decreases. The case is vice versa for coordinate E, or objective weightage of

the GHG emissions.

Figure 4.8: Emission with respect to objectives

Figure 4.8 shows emissions with respect to the objective function. It can be observed

from the graph that as the variable F, or objective weightage of fuel-cost, increases,

emissions increase. And, as objective weightage of emissions, or E, decreases, the

proportion of emissions increase.

Pareto distribution of emission versus the cost of fuel is shown in Figure 4.9. It is

observed that the cost of fuel and emission are conflicting objectives. Here, the

algorithm tries to minimize both the cost of fuel and the GHG emissions. However, it

does so to a certain limit. As the cost decreases, the emission increases. Therefore,

practically, most of the cheaper thermal power plants are often characterized by

increased levels of air pollution.

25.2

25.4

25.6

25.8

26

26.2

26.4

26.6

[0,1] [0.1,0.9] [0.2,0.8] [0.3,0.7] [0.4,0.6] [0.5,0.5] [0.6,0.4] [0.7,0.3] [0.8,0.2] [0.9,0.1] [1,0]

Em

issi

on in

Mlb

s

Objective Weightage [F,E]

Emission

73

Figure 4.9: Pareto Function of fuel cost and the resulting emissions


The major objective of hydrothermal power systems is to meet energy requirements as

well as to protect the environment. In this chapter, Markov Chain is used to predict

the water inflow of Ghazi Barotha Hydropower Plant. Particle Swarm Optimization

(PSO) is implemented to handle the disparate problems by assigning unique

weightage to each of the objectives. This has, in turn, led us to come forth with

results, which depict the conflicting nature of emission and fuel.

14.0

14.2

14.4

14.6

14.8

15.0

15.2

15.4

25.6 25.7 25.8 25.9 26.0 26.1 26.2 26.3 26.4 26.5 26.6

Cost

in M

illio

n Do

llars

(M$)

Emssion in Million Pounds (Mlbs)

74

5 Short-Term Hydrothermal Coordination (STHTC)

75

5.1 Chapter Summary

The chapter addresses Short-term Hydrothermal Coordination (STHTC), which deals

with durations lasting from 1 hour to 1 week. A viable global optimizer, based on

Chaotic Differential Evolution (CDE), is combined with Sequential Quadratic

Programming (SQP), an efficient local search technique. This results in an efficient

Short-term Hydrothermal Coordination (STHTC) scheme. A multi-objective

optimization framework is established for minimizing the total cost of thermal

generators with valve-point loading effects. The proposed model is implemented on

various systems comprising of hydro generating and thermal units. Monte Carlo

simulations are used to analyze and validate the reliability, stability and effectiveness

of the proposed framework.

5.2 Related Work and Case-studies

In the power sector, optimum coordination of demand and generation substantially

impacts the budget. Most of the research endeavors are focused on minimization of

cost and power losses [120, 121]. To a larger extent, electrical power systems of the

day comprise of thermal and hydropower plants connected via transmission networks

[122]. One of the foremost objectives in power systems is to meet power demand

economically by utilizing the optimal mix of generation technologies. Huge savings in

fuel cost are achieved if the available hydro-electric resources are utilized in a manner

ensuring minimal wastage of water [123]. One of the major objectives of

Hydrothermal Coordination is cost minimization of the power generation systems.

This is achieved by adopting a multi-pronged approach keeping in view multiple

factors such as transmission losses, available resources, fuel cost, load variations and

valve point loading etc.

Derivative-free methods have the ability to converge and are less likely to get stuck in

local minima when attempting to seek a global solution. Besides, their computational

complexity is also not an issue, most of the times [124-126].

76

Figure 5.1: Flow Chart of Sequential Quadretic Programming

Since the last decade of the twentieth century, many intelligent computational

techniques have merged together. evolutionary computational methods have been a

prominent choice for power system optimizers [127, 128].

Some of the commonly used techniques are Genetic Algorithm (GA), Differential

Evolution (DE), Particle Swarm Optimization (PSO) and Ant Colony Optimization, to

name a few. Inability to handle multiple constraints and sticking to local optima are

77

few of the constraints particular to conventional techniques. The latest technique, on

the other hand, resolved such constraints [129-131].

In the research work, nature-inspired evolutionary technique combined with an

efficient local search optimizer, Sequential Quadratic Programming (SQP), is

developed in order to enable an Economic Dispatch (ED) of a dynamic and non-linear

STHTC problem.

A multi-objective optimization framework is established for minimizing the total cost

of thermal generators in order to satisfy the power balance constraint as well as

generator operating and hydro discharge limits.

A multi-objective optimization framework is established for minimizing the total cost

of thermal generators along with valve-point loading effects. This has been done to

meet the power balance constraints and ensure the limits of generator operation and

hydro discharge.

Three computational techniques, i.e. SQP, DE and its hybrid version, are applied on

four different cases of Hydrothermal Coordination. The comparison is made on the

basis of fitness evaluation, mean square error and the behavior of computational

complexity. Hydrothermal Coordination problem has been receiving the attention of

the researchers for the last 100 years. [132-134].

However, during the last decade, the latest developments in optimization techniques

and the introduction of new hardware gadgets made it a hot research topic [135-137].

Some conventional techniques have been employed to solve this nonlinear, non-

deterministic and an NP-hard problem. Such techniques include lambda gamma

iteration method [138], gradient method [139], Dynamic Programming (DP) [140]

and Newton-Raphson method [141] etc., with each characterized by its pros and cons

[142, 143].

78

Figure 5.2: Flow Chart of Differential Evolution

79

Although conventional techniques can offer a reasonable and timely solution, they are

unable to handle more constraints and are prone to stick in the issue of local minima.

The schemes, like priority list method, a class of weighted procedures, and forward

Dynamic Programming (DP) approach, received attention from researchers as such

schemes handled the problem of Unit Commitment (UC) in an elegant manner. [144,

145] Despite, the probability of getting stuck in the local minimum persists. Almost

similar problems have been observed in the Lagrange relaxation method and the class

method based on Karush Kuhn Tucker equations [143, 146].

In this chapter, case studies consulted are taken from [120, 147-150]; section 4

contains the discussion; and conclusion is presented in the end.

5.3 Problem Formulation

One of the chief aims of Hydrothermal Coordination is to minimize the fuel cost and

address the power demand constraints. The objective function for Hydrothermal

Coordination is given in Equation 4.17.

5.3.1 System Constraints

In each interval of the scheduled time, the output power produced by hydroelectric

and thermal power plants must balance the expected power demand and transmission

line losses.

(5.1)

Hydroelectric power production depends on water discharge and water head; both of

them are directly related to the storage volume of the reservoir.

(5.2)

Power losses due to transmission are given as in Equation 5.3.

PTHit + Phjtj=1

Nh

∑ = Pdt + Plt , t ∈Ti=1

NTH

∑

Phjt = C1 jVhjt2 +C2 jQhjt

2 +C3 jVhjtQhjt +C4 jVhjt +C5 jVhjt +C6 j

80

(5.3)

The above-mentioned equation indicates that each thermal generation unit has certain

upper and lower generation limits. The output power extracted from a unit should be

in the given generation range. Thermal power plants also have lower and upper limits

of generation given in Equations 4.18. Similarly, there are limits to hydroelectric

power as shown in Equation 4.15.

The power produced from a thermal unit ‘i’ during a particular interval should not

exceed the power generated in the previous interval by a certain defined amount. In

the same way, the power produced should not be less than the power generated in the

previous interval by a certain limit.

Mathematically, it can be represented in terms of Up Ramp (UR) and Down Ramp

(DR) as shown in Equations 5.4 and 5.5 respectively.

(5.4)

(5.5)

There are several challenges which hamper the smooth operation of a hydropower

plant. These include maintaining a balanced quantity of water, lowering the power

plant limitations and ensuring multipurpose storage etc. Stated earlier, the equations

4.12 and 4.14 are used to express the storage volume and discharge rate of reservoir

respectively.

5.4 Chaotic Differential Evolution (CDE) and Quadratic

Programming (QP)

Differential Evolution (DE) algorithm is a robust meta-heuristic method for function

minimization/maximization. It was proposed by Ken and Storm in 1997 [151]. DE is

Plt = PitBijPjtj=1

NTH +Nh

∑i=1

NTH +Nh

∑ + Boii=1

NTH +Nh

∑ Pit + Boo

PTHit − PTHi(t−1) ≤URi

PTHi(t−1) − PTHit ≤ DRi

81

a population-based stochastic algorithm with few parameters; but, because it is not a

gradient-based method, it offers an excellent solution to the non-smooth, multimodal

and non-convex problems [152] [153]. As compared to other Evolutionary algorithms,

DE is less stochastic but more greedy and uses simple arithmetic operators [154].

DE differs from the Genetic Algorithm (GA) in that it uses perturbing vectors. The

perturbing vectors cause diversity in each of the sample space. Besides, the

amplification factor in DE searches for the candidate solution thoroughly on the

solution surface [155].

DE finds its use in various research areas such as electrical power simulations, optical

systems optimization, radio network designs and water pumping systems optimization

[156]. DE has some drawbacks. To overcome some of the common drawbacks of DE,

chaotic theory is made into use.

DE should be made chaotic enough to assure diversification. This enabled the handle

to move through the whole search space. As a result, the probability of being caught

in local optima is reduced significantly and the parameter control strategy is further

enhanced Flow chart of the chaotic DE is shown in Fig. 5.3.

More precisely, to create diversity in the search space, the behavior of a chaotic

system is encapsulated in the differential evolutionary algorithm using Gaussian

randomness. As a result, the algorithm will perform the search operation thoroughly.

The vector representation and factor of DE algorithm is also coupled with the chaotic

variable. This guarantees the parallelism in n-dimensions and improves the

computational searching of the proposed scheme.

SQP is an iterative method that falls under the class of barrier methods and it can be

used efficiently for nonlinear optimization of complex systems having linear and/or

non-linear constraints. Flow chart of SQP is shown in Fig. 5.1.

82

Figure 5.3: Flow Chart of Chaotic Differential Evolution

83

The capability of transforming a complex problem into the subproblems has been

exploited keeping in view the STHTC constraints such as load demand, generating

limits and valve-point loading effect. SQP requires the objective function and its

constraints as a Lagrangian function so as to minimize the energy cost, which is

subject to the defined constraints. Such local search scheme finds its applications in

combinatorial problems, image classification and power system stability analysis etc.

The SQP’s built-in subroutine is used as a local optimizer.

Major steps involved in the optimization of hybrid approach DE-SQP are explained as

follows:

Step 1: Parameter Setup

An initial weight vector is generated in a random manner. The real bounded values

are equal to the number of design parameters involved in STHTC. Variables such as

user-defined population size, length of one vector, the boundary constraints of the

optimization, the mutation factor, stopping criteria and other essential parameters,

along with the respective values, are shown in Table 5.1.

Step 2: Initialization of an Individual Population

Set generation N=0 with a population of i=1, …., M individuals.

The individuals have random values generated as a uniform probability distribution in

an n-dimensional problem space.

Step 3: Fitness Evaluation

Evaluate the energy function as defined for each objective function up to an

acceptable range of the fitness value ε.

Step 4: Differential Operation

The value of mutation operation, that adds a vector differential to a population vector

of individuals, is taken from the range [0.1,1]. Search stagnation is avoided by making

use of a mutation factor that controls the amplification of the difference between two

individuals.

84

Step 5: Recombination Operation

Recombination is employed to generate a trial vector. It is done by replacing certain

parameters of the target vector with the corresponding parameters of a randomly

generated donor vector. The recombination rate is taken in a logarithmic manner in

order to obtain mature exploitation of the search space.

Step 6: Selection Operator

The procedure of producing better off-springs is obtained in this step. Here, the

criterion of comparing the fitness of the current individual acts as stability to enter the

next generation. Similarly, the fitness cost of each trial vector is compared with that of

its parent target vector.

If the cost of the target vector is lower than that of the trial vector, the target is

allowed to advance into the next generation. Else, the target vector is replaced by the

trial vector in the next generation.

Step 7: Stopping Criteria for Chaotic Differential Evolution (CDE)

Set the generation number for N=N+1 and proceed to step 3 until a stopping criterion

is fulfilled. The criterion is problem dependent based on the following conditions:

i) A maximum number of generations is achieved. ii) Fitness value ε less than 10-12 is achieved. iii) Function tolerance is lower than a certain pre-defined criteria.

Step 8: Hybrid with SQP

One of the best elements obtained from Chaotic DE is passed as a starting point to the

SQP algorithm. This fine-tunes the unknown adaptive parameters of the STHTC

problem. The flow chart DE-SQP is shown in Fig. 5.4.

85

Figure 5.4: Flow Chart of Chaotic Differential Evolution (CDE) Hybridized with SQP

86

The detailed pseudo-code of the proposed scheme is given as follows:

Input: Psize, STHTCsize, β, Crate, ζ

Output: Rbest= [PTHit Phj]

Population ←initilize population(Psize, STHTCsize)

Evaluatepopulation(Pop)

Rbest ← getbestcandiadte(Pop)

While(stopingcriteria() not met)

newpop←Ø

for popiϵ Pop

Ri←newsample(popi,population, STHTCsize, β,Crate,ζ)

If (fval (Ri)≤ fval (popi))

newpapulation← Ri

Else

newpapulation← popi

End

End

Pop ←newpopulation

Evaluatepopulation(Pop)

Rbest←getbestcandidate(Pop)

End

Return(Rbest)

87

5.5 Simulation and Results

Four scenario-based hydrothermal test systems have been investigated and the

simulation results are presented. The simulation results are based on various

performance criteria such as dollar cost, energy fitness function, the absolute error of

load and generation, and the temporal computational complexity. The level and

percentage of the convergence for chaotic DE, SQP and hybrid approach are also

computed for a large number of iterations. The algorithms are implemented by using

MATLAB version 7.12.0 (R 2011a) on the Intel(R) Core (TM) i3-4010U CPU @

1.70 GHz machine with 4GB RAM.

Table 5.1: Parameter Values/Settings for Chaotic Differential Evolution and

Sequential Quadratic Programming

Chaotic Differential Evolution Sequential Quadratic Programming

Parameters Values/ Settings Parameters Values/ Settings

Generations 500 Start point The random or best

result of CDE

Population size 360 No of variables Generation Unit

Dependent

Population Range [-1 1] Iterations 1000

Function Tolerance 10-30 Max. Function

Evaluations 50000

Stall Generation Limit

200 Function Tolerance 0

Nonlinear Constraints tolerance

10-30 Nonlinear

Constraints tolerance

0

Fitness Limit 10-35 Derivative approach

Finite forward difference

X-Tolerance 10-18 X-Tolerance 10-18

Bounds As given in

thermal units Bounds

As given in thermal units

Others Default Others Default

88

5.5.1 Case Study I:

The test system considers a cascade of four hydro and three steam power plants in

order to meet the overall load of 1050 MW. A period of one week is considered for

the scheduling period which is further divided into 100 intervals. The system has been

simulated using the optimization solvers based on chaotic DE, SQP, and DE-SQP.

Table 5.1 lists the values and setting of the parameters of the solvers used.

Electric power of about 200MW is obtained from hydropower plants; while the

remaining power is obtained by the system using three available steam power plants.

The operation is carried out in an economical fashion. Table 5.2 shows the optimal

values of hydrothermal and steam generation. The behavior of steam power plant, as a

fitness evaluation of the energy function, is shown in Figure 5.5 (a). The absolute

difference between the remaining power load and thermal generation is depicted in

Figure 5.5(b). It is quite evident from the figure that the value of the fitness achieved

lies within the range 10-11 to 10-13 while the difference of thermal generation stretches

from 10-05 to 10-06. It is worth mentioning that the cost of DE-SQP is much lower than

that of DE and SQP when taken separately.

Table 5.2: Optimal Hydrothermal Generation (MW) for Case Study I

Solver Power

Plant DE SQP DE-SQP

Optimal Hydro Generation Ph (MW) 200 200 200

Optimal Thermal

Generation

Ps1(MW) 368.0882 415.7895 389.2278

Ps2 (MW) 239.6326 289.4737 260.7722

Ps3 (MW) 242.2792 144.7368 200

89

(a)

(b)

Figure 5.5: (a) Behavior of the fitness function evaluation; (b) Absolute error of thermal generation for 100 intervals

Table 5.3: Optimal Hydrothermal Generation (MW) for Case Study II

t(h) ph1

(MW)

ph2

(MW)

ph3

(MW)

ph4

(MW)

Pgt

(MW)

Cost

(103 $) 1 21.60 17.47 43.98 44.20 62.77 3597.68 2 28.08 16.24 41.06 43.72 40.90 2245.36 3 31.02 16.18 39.88 47.46 35.46 1983.18 4 21.01 20.41 38.83 42.13 67.63 3962.82 5 37.03 15.93 38.41 53.76 44.87 2455.54 6 34.18 19.38 32.50 49.44 74.51 4521.18 7 33.24 22.92 35.78 44.62 93.43 6298.71 8 48.17 22.43 30.89 52.03 96.50 6620.86 9 60.70 22.85 35.02 58.83 92.60 6213.33

10 56.53 31.32 31.49 53.28 137.36 11807.85 11 65.33 32.21 35.42 63.37 153.67 14343.23 12 55.45 29.30 34.85 59.14 131.26 10927.52 13 50.80 34.22 39.34 60.99 164.65 16201.02 14 62.13 29.34 41.75 71.71 145.07 12973.61 15 59.60 25.41 44.59 72.71 107.69 7875.86 16 46.61 26.77 42.18 66.97 107.47 7849.89 17 44.97 24.27 43.11 68.84 88.84 5834.52 18 41.09 22.26 43.60 69.43 73.62 4446.19 19 34.13 20.96 43.50 68.37 63.03 3616.75 20 38.38 15.51 46.19 75.20 34.71 1949.64 21 38.54 17.39 44.08 74.63 35.36 1978.84 22 26.41 23.67 42.22 64.35 53.35 2956.72 23 39.58 9.71 42.27 72.97 25.48 1579.30 24 28.02 13.00 40.61 64.28 44.09 2413.00

Total Cost = 144652.61

90

5.5.2 Case Study II

This test system comprises of four hydropower plants and equivalent thermal

generation plant to meet the load requirement. The entire scheduling period is one day

which is further divided into 24 equal intervals. The optimal values of the

hydrothermal generation and steam generation are presented in Table 5.3. The

behavior of the power plant is shown in Figure 5.6 (a) as a fitness evaluation of the

energy function. Figure 5.6(b) shows the absolute difference between the required and

generated power.

(a)

(b)

Figure 5.6: Behavior of the fitness function value (a) and absolute error of thermal generation for 100 intervals in (b)

It is very clear from the figure that the value of the fitness achieved lie in the range

from 10-12 to 10-15 while the difference of thermal generation ranges from 10-06 to 10-

07. It can be observed that the cost for DE-SQP is much lesser when compared to each

of the DE and SQP.

Table 5.4: Results of generation hydro and thermal generations Min Max mean Std. CB DE 153.59 161.43 156.112 0.689 46.7 SQP 170.129 181.62 175.9 1.643 87.5 DE-SQP 144.652 162.89 155.654 0.697 97.38

91

It is evident from the results of case study in Table 5.4 that DE-SQP has lower costs

and slightly more computational budget as compared to DE and SQP.

5.5.3 Case Study III

In this test system, the system comprises of thirteen steam power plants and

equivalent hydropower generation. In the total power demand, 400MW is provided by

hydropower plants free of cost and the remaining power is met by thermal power

plants. The system has been simulated using the optimization solvers based on chaotic

DE, SQP and DE-SQP. Table 5.1 shows the values and setting of the parameters of

the solvers.

(a)

(b)


The optimal solution of the hydrothermal values is presented in Table 5.5. Figure 5.7

(a) and Figures 5.7 (b) depict fitness evaluation of the energy function and absolute

difference between demanded and generated power respectively. It can be seen that

the value of the fitness achieved lies in the range 10-12 to 10-16 while the difference of

thermal generation ranges from 10-06 to 10-08. Here, also, the cost of DE-SQP is lower

than that of DE and SQP.

92

Table 5.5: Optimal Hydrothermal Generation (MW) for Case Study III

Solver DE SQP DE-SQP


Optimal Thermal

Generation

Ps1(MW) 26.9588 352.8772 98.7181922

Ps2(MW) 41.85882 186.676 99.2111282

Ps3(MW) 42.8607 186.9355 100.032396

Ps4(MW) 199.4378 122.1997 179.999958

Ps5(MW) 200.0579 122.1997 179.999958

Ps6(MW) 211.0128 122.1997 179.999958

Ps7(MW) 152.4702 122.1997 157.433046

Ps8(MW) 137.5302 122.1997 145.186288

Ps9(MW) 203.039 122.1997 179.999958

Ps10(MW) 119.2916 81.46589 119.419249

Ps11(MW) 174.2788 81.46589 119.999956

Ps12(MW) 143.426 88.69074 119.999956

Ps13(MW) 147.7774 88.69074 119.999956

Cost ($) 3020.8913 4394.600398 1648.481294

5.5.4 Case Study IV

Here, forty steam power plants and equivalent hydropower generation is considered.

The total power demand is 12000 MW of which hydropower plants generate

1500MW and the steam power plants supplies the remaining power. The optimal

solution found by the algorithms is tabulated in Table 5.6. The behavior of steam

power plants is shown in Figure 5.8(a) as a fitness evaluation of the energy function.

Figure 5.8 (b) shows the absolute difference between the demanded and generated

power. The results of the figure are drawn at a semi-log scale to identify the

difference in each independent run. It is quite evident from the table that the hybrid

scheme shows supremacy in term of cost per MW than that of chaotic DE and SQP.

There is a slight computational complexity of hybrid scheme; however, such intricacy

is negligible owing to superior outcomes of cost minimization.

93

Table 5.6: Optimal Hydrothermal Generation (MW) for Case Study IV Solver Power Plant DE SQP DE-SQP


Optimal Thermal Generation

Ps1(MW) 132.2539582 92.06804958 114

Ps2(MW) 139.2677773 92.06804958 114

Ps3(MW) 163.4171438 103.1292689 120

Ps4(MW) 177.1651195 159.0703263 183.7098418

Ps5(MW) 140.9268812 82.94105742 97

Ps6(MW) 167.7413554 119.7551227 140

Ps7(MW) 176.1009267 246.5760182 239.2873291

Ps8(MW) 237.2224228 253.6054895 269.2385135

Ps9(MW) 185.7263532 253.6054895 244.0047197

Ps10(MW) 232.3491264 252.1995952 266.850625

Ps11(MW) 173.6844415 295.9887427 276.3542302

Ps12(MW) 194.0661898 296.7075639 286.8509457

Ps13(MW) 196.0262765 394.5579307 351.0504

Ps14(MW) 186.0605753 394.5579307 346.1671317

Ps15(MW) 229.7251196 394.5579307 367.5632823

Ps16(MW) 268.7190231 394.5579307 386.6704321

Ps17(MW) 285.1172317 421.2699216 394.7055833

Ps18(MW) 327.2881577 421.2699216 415.3695108

Ps19(MW) 339.1840995 463.3969137 446.6986891

Ps20(MW) 340.9184334 463.3969137 447.5487986

Ps21(MW) 400.4456321 466.77106 476.7176762

Ps22(MW) 331.1034731 466.77106 442.7395591

Ps23(MW) 315.5877954 466.77106 435.1361993

Ps24(MW) 306.4064802 466.77106 430.6376298

Ps25(MW) 362.7246052 466.77106 458.2338338

Ps26(MW) 331.7683512 466.77106 443.0647432

Ps27(MW) 119.3841058 110.6349608 134.9967919

Ps28(MW) 107.1727912 110.6349608 129.013211

Ps29(MW) 53.50256196 110.6349608 102.7158613

Ps30(MW) 135.8759898 82.94105742 97

Ps31(MW) 157.4549128 153.4467493 174.0534244

Ps32(MW) 155.1604129 153.4467493 172.928325

Ps33(MW) 153.1323907 153.4467493 171.934534

Ps34(MW) 221.233994 169.0703263 200

Ps35(MW) 174.2553217 169.0703263 187.384766

Ps36(MW) 215.1853029 169.0703263 200

Ps37(MW) 60.20898716 86.09979762 85.60153412

Ps38(MW) 131.7594186 86.09979762 110

Ps39(MW) 117.3141014 86.09979762 110

Ps40(MW) 306.6807263 463.3969137 430.7718759

Cost ($) 3176931.4 3661678.233 2777718.62

94

(a)

(b)


For the hybrid approach, it is evident from Figure 5.8 that the value of the fitness

achieved lies within the range 10-20 to 10-25 and the difference of thermal generation

ranges from 10-10 to 10-12.

5.6 Comparative Analysis of the Results

The comparative study for Case I to IV is also thoroughly investigated based on the

behavior of their computational time complexity, fitness analysis, load error and

statistical analysis. For each of the case studies, i.e. case I to case IV, the behavior of

time analysis for 100 independent runs is shown in Figure 5.9 (a) to Figure 5.9 (d), for

each of DE, SQP and DE-SQP approaches. It is evident from the respective figures

that the computational budget of local search is very small. However, the probability

to remain trapped is high in local minima and time for DE and DE-SQP is same

approximately. Also, the fitness values achieved in hybrid approach is better than DE.

95

Table 5.7: Comparative study in DE, SQP, and DE-SQP in terms of fitness achieved

Case

Study Solver Min Max Mean STD Var Mode

1

DE 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

SQP 1.2374E-12 1.2374E-12 1.2374E-12 6.0890E-28 3.7076E-55 1.2374E-12

DE-

SQP 0.0000E+00 1.1058E-11 1.2374E-12 2.4940E-12 6.2200E-24 0.0000E+00

2

DE 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

SQP 8.8948E-16 8.8948E-16 8.8948E-16 0.0000E+00 0.0000E+00 8.8948E-16

DE-

SQP 0.0000E+00 2.4514E-13 8.8948E-16 9.2651E-14 8.5842E-27 0.0000E+00

3

DE 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

SQP 8.7560E-14 2.2660E-12 2.1721E-12 3.0447E-13 9.2704E-26 2.2656E-12

DE-

SQP 7.7525E-17 7.6447E-13 4.3402E-13 1.8722E-13 3.5052E-26 7.7525E-17

4

DE 3.3162E+06 6.0206E+06 4.4814E+06 5.3298E+05 2.8407E+11 3.3162E+06

SQP 3.3087E-24 3.3087E-24 3.3087E-24 0.0000E+00 0.0000E+00 3.3087E-24

DE-

SQP 1.6466E-15 8.3930E-12 3.3087E-24 2.6583E-12 7.0667E-24 1.6466E-15

96

(a)

(b)

(c)

(d)

Figure 5.9: Comparative analysis of the computational budget for case studies I, II,

III and IV

The statistical parameters such as mean, mode, minimum, maximum, variance and

standard deviation explain the effectiveness of an algorithm in a realistic manner. A

number of independent runs have been used to seek the convergence of the optimizer.

The respective results are tabulated in Table 5.8.

97

Table 5.8: Comparison between DE, SQP and DE-SQP in term of Load Error

Case Study Solver Min Max Mean STD Var Mode

1

DE 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

SQP 1.1124E-06 1.1124E-06 1.1124E-06 0.0000E+00 0.0000E+00 1.1124E-06

DE-SQP 0.0000E+00 3.3253E-06 2.1843E-06 7.8786E-07 6.2072E-13 0.0000E+00

2

DE 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

SQP 2.9824E-08 2.9824E-08 2.9824E-08 0.0000E+00 0.0000E+00 2.9824E-08

DE-SQP 0.0000E+00 4.9512E-07 3.0860E-07 1.8998E-07 3.6094E-14 0.0000E+00

3

DE 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

SQP 2.9591E-07 1.5053E-06 1.4660E-06 1.5232E-07 2.3201E-14 1.5052E-06

DE-SQP 8.8048E-09 8.7434E-07 6.2598E-07 2.0640E-07 4.2599E-14 8.8048E-09

4

DE 1.8210E+03 2.4537E+03 2.1133E+03 1.2490E+02 1.5601E+04 1.8210E+03

SQP 1.8190E-12 1.8190E-12 1.8190E-12 0.0000E+00 0.0000E+00 1.8190E-12

DE-SQP 4.0578E-08 2.8971E-06 2.1071E-06 8.2651E-07 6.8311E-13 4.0578E-08

From the table, it is clear that the mean value of the fitness achieved for the hybrid

approach is consistently better than that of DE and SQP. Almost similar behavior has

been observed in the case of standard deviation as well. Comparative analysis of the

load error is also determined for 100 independent runs of the DE, SQP and DE-SQP

algorithms.

The mean fitness value achieved using 100 independent runs is computed using the

relation given in Equation 5.6.

98

(5.6)

Similarly, the comparative study for DE, SQP, and DE-SQP in term of computational

complexity for case study 1 to 4 is provided in Table 5.9 using the relation given in

equation 5.7.

(5.7)

Table 5.9: Comparison between DE, SQP, and DE-SQP in term of computational

complexity Case


1

DE 25.7830 57.6757 33.5441 4.4063 19.4158 25.7830

SQP 0.0337 2.1092 0.0672 0.2065 0.0426 0.0337

DE-SQP 25.7974 57.8232 33.5714 4.4207 19.416 25.7974

2

DE 5.0349 9.1769 6.8964 0.8990 0.8082 5.0349

SQP 0.0409 0.1612 0.0514 0.0137 0.0002 0.0409

DE-SQP 5.0569 9.2737 6.9402 0.912 0.8084 5.0772

3

DE 32.4815 51.7848 40.5578 3.6145 13.0643 32.4815

SQP 0.0610 0.2841 0.0938 0.0343 0.0012 0.0610

DE-SQP 32.54 52.0225 40.6578 3.6476 13.0654 32.54

4

DE 472.1110 604.7093 507.3392 39.0906 1528.0744 472.1110

SQP 0.4338 0.7292 0.4999 0.0569 0.0032 0.4338

DE-SQP 472.6688 606.6227 508.2392 39.3652 1528.15 472.6688

It is quite clear from Table 5.9 that the computational budget in term of time

complexity increases with the increase in a number of generators. An important

parameter is a cost, in US$, for the production of power in MW. In this regard, a

comparative study is also carried out for DE, SQP and DE-SQP algorithms. The

results are given in Table 5.10. The dominance of DE-SQP is observed in the Table

5.10 as the mean value of the cost for DE-SQP is lower than that of global search

scheme and local search algorithm individually.

MF = 1ℜ

1N

fval − f̂valk

k=1

N

∑2⎛

⎝⎜

⎞

⎠⎟j

j=1

ℜ

∑

MET = 1ℜ

ET j

j=1

ℜ

∑

99

Table 5.10: Comparison between DE, SQP and DE-SQP in term of cost (US $) Case


1

DE 8.6784E+03 8.9003E+03 8.7525E+03 1.2192E+02 1.4865E+04 8.4411E+03

SQP 8.5966E+03 8.7655E+03 8.6966E+03 5.4845E+12 3.0079E+23 8.6266E+03

DE-SQP 8.4210E+03 8.7175E+03 8.5354E+03 8.5599E+01 7.3272E+03 8.5110E+03

2

DE 153.59E+03 198.59E+03 176.11E+03 2.2439E+03 1.5472E+07 198.59E+03

SQP 157.70E+03 191.77E+03 168.78E+03 3.0023E+03 9.0140E+09 191.77E+03

DE-SQP 144.65E+03 189.54E+03 157.79E+03 1.9676E+03 3.8714E+08 189.54E+03

3

DE 3.0208E+03 1.5460E+07 1.2160E+07 1.1092E+06 1.2303E+12 1.0103E+07

SQP 4.3946E+03 1.0748E+05 4.7934E+04 1.0724E+04 1.1500E+08 3.7678E+04

DE-SQP 1.6484E+03 8.1544E+04 4.5256E+04 8.7267E+03 7.6155E+07 3.4304E+04

4

DE 3176.93E+03 1.3276E+09 1.0549E+09 8.9049E+07 7.9297E+15 9.0242E+08

SQP 3661.68E+03 2.7777E+06 3.2418E+06 9.6010E+05 4.3193E+10 1.6980E+06

DE-SQP 2777.72E+03 6.7488E+06 1.9396E+06 2.0783E+05 9.2179E+11 2.0505E+06

The convergence behavior is observed for 100 independent runs to validate the

stability of the DE-SQP. The results are drawn in Figure 5.10 on the semi-log scale in

order to make clarity among the various case studies. It is quite evident from the

figure that overall convergence lies from 10-11 to 10-16. Moreover, approximately 88%

of the independent runs are found to be stable for case 1, case 3 and case 4 in the

range from 10-11 to 10-13 while it is 70% for case study 2 with a precision that lies in

10-13.

Figure 5.10: Convergence behavior of the fitness for case studies I to IV using hybrid

approach

100

5.6.1 Improvements Observed in Applicability, Robustness and Versatility

In the application of DE, SQP and DE-SQP on hydrothermal coordination, it is

observed that in applicability that DE fitness is lower as compared to DE-SQP, and

SQP stuck in local minima. From the figures 5.5-5.8, it is observed that the fitness

variance of DE-SQP is 10-11 to10-23 much more as compared to DE and SQP as shown

in Table 5.11. DE fitness even goes to 105 in a case that is a divergence. So, our

proposed technique is more robust. DE-SQP is able to handle any type of case study

with a greater number of constraints and objective because of its hybrid nature that is

its versatility.

Table 5.11: Attributes Observed in our I-IV case studies

Optimizer Applicability Robustness Versatility

DE Lower fitness

comparatively 105 to10-8

Case study one is

relatively easier and

manageable using the

local, global and

hybrid approach,

However Case study 4

is a complex system of

plants that is still

manageable using the

proposed scheme that

reflect the versatility in

the method using the

same parameters

values and setting

SQP

Sometimes get

Stuck in local

minima

10-11 to10-15

DE-SQP

More fitness and no

local minima is

observed

10-11 to10-23

101

5.6.2 Efficiency of the Proposed Algorithm

DE-SQP is more efficient with respect to DE and SQP that can be observed from the

Table 5.12. In four cases two times DE struck in local optima as it is clear in the mean

value efficiency column.

Table 5.12: Efficiency of the Proposed Algorithm

Case Study

% of Efficiency % of Efficiency (Min Cost in $) (Mean Cost in $)

DE-SQP vs DE DE-SQP vs SQP DE-SQP vs DE DE-SQP vs SQP

1 3% 2% 2% 2% 2 6% 8% 10% 7% 3 45% 62% 9% 6% 4 13% 24% 13% 40%

5.7 Multi-objective Case Study

Here, four steam power plants, two combined heat and one is only heat plant. This

case study is taken from [17, 157]. The total power and heat demands are 600MW

and 150MWth respectively. Objectives of the study are minimization of fuel cost and

emission reduction. We have used Pareto Function to find the results of conflicting

objectives. Objective 1 is taken as cost minimization and objective 2 is taken as

emission minimization. Pareto front is shown in Fig 5.11. Values of Power and heat

taken from the plants are given in Table 5.13.

102

Table 5.13: Power and heat values in case of extreme objectives

Plants

DE-SQP F1,F2=[1,0]

Power in MW and heat in MWth

DE-SQP F1,F2=[0,1]

Power in MW and heat in MWth

P1 71.18196206 42.63799491

P2 98.53981394 48.51623351

P3 174.9971518 59.59845054

P4 124.9079094 83.56406851

P5 93.37306534 247

P6 44.00009743 125.6832525

H5 32.51221228 6.21E-23

H6 75.80518747 26.97321355

H7 41.68260025 123.0267864

Cost ($) 10352 17996

Emission (kg) 28.43 6.6

103

Figure 5.11: Pareto Front for Multi-objective Case Study

Hereby, the results of our proposed technique are compared with [17] and [147], for

better understanding of percentage of decrease in cost and emission with the related

work. DE-SQP saves 20% and 42% cost respectively as compard to [17] and [147],

as is evident in Table 5.14.

Table 5.14: Percentage of decrease of Cost and Emission

Methods Demand (MW)

Cost ($) (Cost)

Emission (Kg)

% Decrease Cost Emission

Proposed 1600 10352.36 6.6064 - - Lexicography

[17] 1600 12,908.90 14.572 19.69599

54.66374

SGA-II [147] 1600 17749.31 16.9208 41.67531

60.95693

104


Based on the simulation results, major findings are as follow:

• The stochastic optimizer based on Chaotic Differential Evolution - Sequential

Quadratic Programming (DE-SQP) and the hybrid scheme provide an alternate

platform to optimize Hydrothermal Coordination.

• The fitness value obtained by the DE-SQP outperforms that of DE and SQP

schemes. Similarly, the cost per MW of DE-SQP is lower when compared to

other optimizers.

• The fitness value for case-studies 1, 2, 3 and 4 lie in the following ranges:10-11

to 10-13; 10-12 to 10-15; 10-12 to 10-16; and 10-20 to 10-25.

• The convergence of the proposed scheme is validated through Monte Carlo

simulations. It has been observed from the graphs that the convergence

percentage for DE-SQP, SQP and DE is 100, 90 and 95 respectively.

• The computational complexity of DE-SQP is slightly higher than that of DE

and SQP. However, this effect can be overshadowed by the cost of supremacy

in DE-SQP absolute error.

• Another advantage of the proposed scheme is its simplicity, ease of

implementation, good convergence and accuracy.

105

6 Conclusion

106

6.1 Conclusion

The research endeavor deals with the topic of power plant planning from the

perspectives of planning as well as operations. It includes theoretical background,

mathematical problem formulation, and framework design, etc. Both short-term, as

well as long-term facets of power system planning, are presented. The work considers

non-linearity and realistic attributes to devise solutions. The thesis is a novel

contribution to the area of hybrid intelligent computational techniques and aims to

counter the complexities of Hydrothermal Coordination. The efficient Hydrothermal

Coordination scheme has various applications owing to its versatility and robustness.

This chapter summarizes the major findings of the research work, which are as

follows:

• Energy is an indispensable commodity and its importance can never be

ignored. Our work presents a comprehensive study of alternatives in power

generation. As a parameter, Levelized Cost of Electricity (LCOE) is consulted

to come forth with a viable solution. Various existing models are compared. It

has also been found that in order to reap maximum benefits, the strategy must

encourage the utilization of indigenous resources and localization of

technology.

• A multi-pronged approach needs to be adopted to assure emission

minimization and energy prosperity simultaneously: fossil-fueled power plants

subsidies should be withdrawn immediately in favor of subsidies to renewable

energy plants; a carbon tax regime should be implemented; in addition to

global and national, eco-friendly initiatives should be adopted on the domestic

scale as well.

• There are several constraints associated with Hydro-thermal Scheduling

(HTS), or Hydrothermal Coordination. For instance, it requires the power

generation to be equal to the power demand. Major factors that need to be

addressed, therefore, include reliability maximization, weather variations, and

resource control, etc. HTC is a highly complex, non-linear, non-deterministic,

107

multi-constrained, and dynamic optimization problem. It blends Economic

Dispatch (ED) and Unit Commitment (UC). Also, the search space of

Hydrothermal Coordination is non-linear and turbulent.

• Forecasting the resource and addressing the complexity are two of the main

focuses of Long-term Hydrothermal Coordination (LTHTC). A case study

about a local power project is considered for investigation purposes.

Intelligent computation for the optimal trade-off is carried out using Particle

Swarm Optimization (PSO). Markov Chain, a stochastic prediction model,

is used to predict the water inflow of Ghazi Barotha Hydropower Plant.

Moreover, we implemented Particle Swarm Optimization (PSO) algorithm to

handle the disparate problems and to assign unique weightage to each of the

objectives. This has, in turn, led us to come forth with the optimum utilization

of resources in the conflicting nature of objectives.

• While dealing with Short-term Hydrothermal Coordination (STHTC), the

evolutionary algorithms option promises the issue redressal in a versatile and

reliable manner. A viable global optimizer, based on Chaotic Differential

Evolution (CDE), is combined with Sequential Quadratic Programming

(SQP), an efficient local search technique. A multi-objective optimization

framework is established for minimizing the total cost of thermal generators

with valve-point loading effects. This results in an efficient Short-term

Hydrothermal Coordination (STHTC) scheme.

• Our scheme demonstrates to be superior when compared to extant

counterparts. In the application of DE, SQP and DE-SQP on hydrothermal

coordination, it is observed that DE fitness is lower as compared to DE-SQP,

and SQP is stuck in local minima. Further, it has been found that the fitness

variance of DE-SQP is 10-11 to 10-23 much better as compared to DE and

SQP. From the case studies, we found that the hybrid improved technique is

more robust as compared to individual techniques and avoids the divergence.

DE-SQP is able to handle any type of case study with a greater number of

constraints and objectives because of its hybrid nature that is its versatility. In

108

comparison to Differential Evolution, our proposed technique demonstrates to

be efficient within the range of 3% to 45%. And, when compared to

Sequential Quadratic Programming, our proposed technique showed efficiency

within the range of 2% to 62%.

• Our proposed scheme is far more efficient when compared to Lexicography

and SGA-II. The fuel consumption can be minimized by using cogeneration

plants and combined heat plants. In the scenario of a multi-objective case

study, a cogeneration case study is selected. The objectives of the study are

minimization of fuel cost as well as emission by meeting the heat requirement

as well as power demand. The results of our proposed technique are compared

with recent techniques of Lexicography and SGA-II, for better understanding

of the percentage of decrease in cost and emission with the related work. DE-

SQP saves 20% and 42% cost as compared to Lexicography and SGA-II

respectively. In terms of emission minimization, our proposed technique offers

savings of up to 55% and 61% when compared to Lexicography and SGA-II

respectively. We have considered only one objective at a time either cost

minimization or emission reduction. Pareto Function is also used to verify the

convergence of the technique.

6.2 Future Work

Undoubtedly, innovation in research and development is a never-ceasing process. Hydrothermal Coordination is no exception. In the future, as a follow-up of our research work, novel nature-inspired methods can be used to come forth with intelligent solutions aimed at more accuracy, less cost, and emission. The constraints relating to manpower, the uncertainty of the power plant (forecasting, generation, operation, financial) and other real-time parameters may be added in the mathematical modeling of STHTC and LTHTC systems along with viable linear and nonlinear metrics. The penetration of emerging technologies in daily lives is rapidly increasing. Energy modeling studies can be carried out to come forth with decreased complexity and assured outcomes. Moreover, future Hydrothermal Coordination solutions are reckoned to adopt a transdisciplinary approach by incorporating data science, artificial intelligence, and blockchain, etc.

109

7 References [1] M. T. Van Vliet, J. R. Yearsley, F. Ludwig, S. Vögele, D. P. Lettenmaier, and

P. Kabat, "Vulnerability of US and European electricity supply to climate change," Nature Climate Change, vol. 2, pp. 676-681, 2012.

[2] M. Afzal and M. K. Madhav, "Economic Load Dispatch and Unit Commitment Solution Using Advanced Optimization approach-A Review."

[3] A. S. Manne and R. G. Richels, "CO2 emission limits: an economic cost analysis for the USA," The Energy Journal, pp. 51-74, 1990.

[4] A. Mahari and K. Zare, "A solution to the generation scheduling problem in power systems with large-scale wind farms using MICA," International Journal of Electrical Power & Energy Systems, vol. 54, pp. 1-9, 2014.

[5] T. T. Nguyen, D. N. Vo, and A. V. Truong, "Cuckoo search algorithm for short-term hydrothermal scheduling," Applied Energy, vol. 132, pp. 276-287, 2014.

[6] S. Pereira, P. Ferreira, and A. Vaz, "Short-term electricity planning with increase wind capacity," Energy, vol. 69, pp. 12-22, 2014.

[7] R. Jiang, M. Zhang, G. Li, and Y. Guan, "Two-stage network constrained robust unit commitment problem," European Journal of Operational Research, vol. 234, pp. 751-762, 2014.

[8] P. González, J. Villar, C. A. Díaz, and F. A. Campos, "Joint energy and reserve markets: Current implementations and modeling trends," Electric Power Systems Research, vol. 109, pp. 101-111, 2014.

[9] J. Zábojník and M. Dvořák, "Power grid simulation model for long term operation planning," Applied Thermal Engineering, vol. 70, pp. 1294-1305, 2014.

[10] M. R. Norouzi, A. Ahmadi, A. E. Nezhad, and A. Ghaedi, "Mixed integer programming of multi-objective security-constrained hydro/thermal unit commitment," Renewable and Sustainable Energy Reviews, vol. 29, pp. 911-923, 2014.

[11] G. Ardizzon, G. Cavazzini, and G. Pavesi, "A new generation of small hydro and pumped-hydro power plants: advances and future challenges," Renewable and Sustainable Energy Reviews, vol. 31, pp. 746-761, 2014.

[12] M. Estahbanati, "Hybrid probabilistic-harmony search algorithm methodology in generation scheduling problem," Journal of Experimental & Theoretical Artificial Intelligence, vol. 26, pp. 283-296, 2014.

[13] E. Bakirtzis, P. N. Biskas, D. P. Labridis, and A. G. Bakirtzis, "Multiple time resolution unit commitment for short-term operations scheduling under high renewable penetration," Power Systems, IEEE Transactions on, vol. 29, pp. 149-159, 2014.

[14] Z. Zhou and A. Botterud, "Dynamic scheduling of operating reserves in co-optimized electricity markets with wind power," Power Systems, IEEE Transactions on, vol. 29, pp. 160-171, 2014.

[15] G. Steeger, L. A. Barroso, and S. Rebennack, "Optimal bidding strategies for hydro-electric producers: A literature survey," Power Systems, IEEE Transactions on, vol. 29, pp. 1758-1766, 2014.

[16] L. Martins, A. Azevedo, and S. Soares, "Nonlinear Medium-Term Hydro-Thermal Scheduling With Transmission Constraints," Power Systems, IEEE

110

Transactions on, vol. 29, pp. 1623-1633, 2014. [17] A. Ahmadi, M. R. Ahmadi, and A. E. Nezhad, "A lexicographic optimization

and augmented ϵ-constraint technique for short-term environmental/economic combined heat and power scheduling," Electric Power Components and Systems, vol. 42, pp. 945-958, 2014.

[18] J. Deane, E. McKeogh, and B. Gallachóir, "Derivation of intertemporal targets for large pumped hydro energy storage with stochastic optimization," Power Systems, IEEE Transactions on, vol. 28, pp. 2147-2155, 2013.

[19] K. Lakshmi and S. Vasantharathna, "Gencos wind–thermal scheduling problem using artificial immune system algorithm," International Journal of Electrical Power & Energy Systems, vol. 54, pp. 112-122, 2014.

[20] J. Zhou, X. Liao, S. Ouyang, R. Zhang, and Y. Zhang, "Multi-objective artificial bee colony algorithm for short-term scheduling of hydrothermal system," International Journal of Electrical Power & Energy Systems, vol. 55, pp. 542-553, 2014.

[21] W. Jiekang, G. Zhuangzhi, and W. Fan, "Short-term multi-objective optimization scheduling for cascaded hydroelectric plants with dynamic generation flow limit based on EMA and DEA," International Journal of Electrical Power & Energy Systems, vol. 57, pp. 189-197, 2014.

[22] K. Bhattacharjee, A. Bhattacharya, and S. H. nee Dey, "Oppositional real coded chemical reaction based optimization to solve short-term hydrothermal scheduling problems," International Journal of Electrical Power & Energy Systems, vol. 63, pp. 145-157, 2014.

[23] C. Wei, Z. M. Fadlullah, N. Kato, and A. Takeuchi, "GT-CFS: A game theoretic coalition formulation strategy for reducing power loss in micro grids," IEEE Transactions on Parallel and Distributed Systems, vol. 25, pp. 2307-2317, 2013.

[24] H. Tian, X. Yuan, B. Ji, and Z. Chen, "Multi-objective optimization of short-term hydrothermal scheduling using non-dominated sorting gravitational search algorithm with chaotic mutation," Energy Conversion and Management, vol. 81, pp. 504-519, 2014.

[25] R. Swain, A. Barisal, P. Hota, and R. Chakrabarti, "Short-term hydrothermal scheduling using clonal selection algorithm," International Journal of Electrical Power & Energy Systems, vol. 33, pp. 647-656, 2011.

[26] N. Fang, J. Zhou, R. Zhang, Y. Liu, and Y. Zhang, "A hybrid of real coded genetic algorithm and artificial fish swarm algorithm for short-term optimal hydrothermal scheduling," International Journal of Electrical Power & Energy Systems, vol. 62, pp. 617-629, 2014.

[27] B. Gjorgiev, D. Kančev, and M. Čepin, "A new model for optimal generation scheduling of power system considering generation units availability," International Journal of Electrical Power & Energy Systems, vol. 47, pp. 129-139, 2013.

[28] G. Sampaio, J. Saraiva, J. Sousa, and V. Mendes, "Optimization of the operation of hydro stations in market environment using Genetic Algorithms," in European Energy Market (EEM), 2013 10th International Conference on the, 2013, pp. 1-8.

[29] C. K. Simoglou, P. N. Biskas, S. I. Vagropoulos, and A. G. Bakirtzis, "Electricity market models and RES integration: The Greek case," Energy

111

Policy, vol. 67, pp. 531-542, 2014. [30] B. Mohammadi-Ivatloo, H. Zareipour, N. Amjady, and M. Ehsan,

"Application of information-gap decision theory to risk-constrained self-scheduling of GenCos," Power Systems, IEEE Transactions on, vol. 28, pp. 1093-1102, 2013.

[31] H. M. Pousinho, J. Contreras, A. G. Bakirtzis, and J. P. Catalao, "Risk-constrained scheduling and offering strategies of a price-maker hydro producer under uncertainty," Power Systems, IEEE Transactions on, vol. 28, pp. 1879-1887, 2013.

[32] B.-G. Koo, M.-S. Kim, K.-H. Kim, H.-T. Lee, J.-H. Park, and C.-H. Kim, "Short-term electric load forecasting using data mining technique," in Intelligent Systems and Control (ISCO), 2013 7th International Conference on, 2013, pp. 153-157.

[33] C. Batlle and P. Rodilla, "An enhanced screening curves method for considering thermal cycling operation costs in generation expansion planning," Power Systems, IEEE Transactions on, vol. 28, pp. 3683-3691, 2013.

[34] R. M. Lima, M. G. Marcovecchio, A. Queiroz Novais, and I. E. Grossmann, "On the computational studies of deterministic global optimization of head dependent short-term hydro scheduling," Power Systems, IEEE Transactions on, vol. 28, pp. 4336-4347, 2013.

[35] B. Tong, Q. Zhai, and X. Guan, "An MILP based formulation for short-term hydro generation scheduling with analysis of the linearization effects on solution feasibility," Power Systems, IEEE Transactions on, vol. 28, pp. 3588-3599, 2013.

[36] P. González, J. Villar, C. Diaz, and F. A. Campos, "Hourly energy and reserve joint dispatch with a hydro-thermal technological based representation," in European Energy Market (EEM), 2013 10th International Conference on the, 2013, pp. 1-8.

[37] K. Bruninx, D. Patteeuw, E. Delarue, L. Helsen, and W. D'haeseleer, "Short-term demand response of flexible electric heating systems: the need for integrated simulations," in European Energy Market (EEM), 2013 10th International Conference on the, 2013, pp. 1-10.

[38] A. Pina, C. A. Silva, and P. Ferrão, "High-resolution modeling framework for planning electricity systems with high penetration of renewables," Applied Energy, vol. 112, pp. 215-223, 2013.

[39] P. K. Roy, A. Sur, and D. K. Pradhan, "Optimal short-term hydro-thermal scheduling using quasi-oppositional teaching learning based optimization," Engineering Applications of Artificial Intelligence, vol. 26, pp. 2516-2524, 2013.

[40] E. C. Finardi and M. R. Scuzziato, "Hydro unit commitment and loading problem for day-ahead operation planning problem," International Journal of Electrical Power & Energy Systems, vol. 44, pp. 7-16, 2013.

[41] H. Zhang, J. Zhou, Y. Zhang, N. Fang, and R. Zhang, "Short term hydrothermal scheduling using multi-objective differential evolution with three chaotic sequences," International Journal of Electrical Power & Energy Systems, vol. 47, pp. 85-99, 2013.

[42] M. Parastegari, R.-A. Hooshmand, A. Khodabakhshian, and M. Vatanpour,

112

"AC constrained hydro-thermal generation scheduling problem: Application of Benders decomposition method improved by BFPSO," International Journal of Electrical Power & Energy Systems, vol. 49, pp. 199-212, 2013.

[43] R. Zhang, J. Zhou, and Y. Wang, "Multi-objective optimization of hydrothermal energy system considering economic and environmental aspects," International Journal of Electrical Power & Energy Systems, vol. 42, pp. 384-395, 2012.

[44] F. J. Díaz, J. Contreras, J. I. Muñoz, and D. Pozo, "Optimal scheduling of a price-taker cascaded reservoir system in a pool-based electricity market," Power Systems, IEEE Transactions on, vol. 26, pp. 604-615, 2011.

[45] X. Li and C. Jiang, "Short-term operation model and risk management for wind power penetrated system in electricity market," Power Systems, IEEE Transactions on, vol. 26, pp. 932-939, 2011.

[46] L. Xie, P. Carvalho, L. A. Ferreira, J. Liu, B. H. Krogh, N. Popli, et al., "Wind integration in power systems: Operational challenges and possible solutions," Proceedings of the IEEE, vol. 99, pp. 214-232, 2011.

[47] C. G. Baslis and A. G. Bakirtzis, "Mid-term stochastic scheduling of a price-maker hydro producer with pumped storage," Power Systems, IEEE Transactions on, vol. 26, pp. 1856-1865, 2011.

[48] K. K. Mandal and N. Chakraborty, "Optimal scheduling of cascaded hydrothermal systems using a new improved particle swarm optimization technique," Smart Grid and Renewable Energy, vol. 2, p. 282, 2011.

[49] C. Cheng, J. Shen, and X. Wu, "Short-term scheduling for large-scale cascaded hydropower systems with multivibration zones of high head," Journal of Water Resources Planning and Management, 2011.

[50] H. Vennila, T. R. D. Prakash, and T. Ruban, "A Solution for Environmental Constrained Economic Dispatch Problems using Honey Bee Algorithm," International Journal of Computer Applications, vol. 975, p. 8887, 2012.

[51] M. Basu, "Artificial immune system for fixed head hydrothermal power system," Energy, vol. 36, pp. 606-612, 2011.

[52] V. S. Kumar and M. Mohan, "A genetic algorithm solution to the optimal short-term hydrothermal scheduling," International Journal of Electrical Power & Energy Systems, vol. 33, pp. 827-835, 2011.

[53] M. Balasubbareddy, "Multi-objective optimization in the presence of ramp-rate limits using non-dominated sorting hybrid fruit fly algorithm," Ain Shams Engineering Journal, vol. 7, pp. 895-905, 2016.

[54] A. Frangioni, C. Gentile, and F. Lacalandra, "Sequential Lagrangian-MILP approaches for unit commitment problems," International Journal of Electrical Power & Energy Systems, vol. 33, pp. 585-593, 2011.

[55] C. C. A. Rajan, "Hydro-thermal unit commitment problem using simulated annealing embedded evolutionary programming approach," International Journal of Electrical Power & Energy Systems, vol. 33, pp. 939-946, 2011.

[56] K. Singh, N. Padhy, and J. Sharma, "Congestion management considering hydro–thermal combined operation in a pool based electricity market," International Journal of Electrical Power & Energy Systems, vol. 33, pp. 1513-1519, 2011.

[57] S. Sivasubramani and K. S. Swarup, "Hybrid DE–SQP algorithm for non-convex short term hydrothermal scheduling problem," Energy Conversion and

113

Management, vol. 52, pp. 757-761, 2011. [58] M. A. Crew, C. S. Fernando, and P. R. Kleindorfer, "The theory of peak-load

pricing: A survey," Journal of regulatory economics, vol. 8, pp. 215-248, 1995.

[59] L. F. Rangel, "Competition policy and regulation in hydro-dominated electricity markets," Energy Policy, vol. 36, pp. 1292-1302, 2008.

[60] H. Ge and S. Asgarpoor, "Reliability and maintainability improvement of substations with aging infrastructure," IEEE Transactions on Power Delivery, vol. 27, pp. 1868-1876, 2012.

[61] S. Shamugavel, "Reliability driven resource Scheduling algorithms for grid Computing," 2014.

[62] S. Zharkov, "Assessment and Enhancement of the Energy Supply System Efficiency with Emphasis on the Cogeneration and Renewable as Main Directions for Fuel Saving," International Journal of Energy Optimization and Engineering (IJEOE), vol. 3, pp. 1-20, 2014.

[63] D. Pudjianto, C. Ramsay, and G. Strbac, "Virtual power plant and system integration of distributed energy resources," IET Renewable Power Generation, vol. 1, pp. 10-16, 2007.

[64] A. Hussain, M. Amin, R. Khan, and F. A. Chaudhry, "Optimal Allocation of Flexible AC Transmission System Controllers in Electric Power Networks," INAE Letters, pp. 1-24, 2018.

[65] H. L. Willis, "Analytical methods and rules of thumb for modeling DG-distribution interaction," in Power Engineering Society Summer Meeting, 2000. IEEE, 2000, pp. 1643-1644.

[66] S. Doty and W. C. Turner, Energy management handbook: Crc Press, 2004. [67] M. Ashari, W. Keerthipala, and C. V. Nayar, "A single phase parallely

connected uninterruptible power supply/demand side management system," IEEE Transactions on Energy Conversion, vol. 15, pp. 97-102, 2000.

[68] F. Emir, "Selecting Renewable Energy Sources for Small Island Using Analytical Hierarchy Process (AHP)," Eastern Mediterranean University (EMU)-Doğu Akdeniz Üniversitesi (DAÜ), 2014.

[69] F. Chaudhry, M. Amin, M. Iqbal, R. Khan, and J. Khan, "A novel chaotic differential evolution hybridized with quadratic programming for short-term hydrothermal coordination," Neural Computing and Applications, pp. 1-12, 2017.

[70] F. Ueckerdt, L. Hirth, G. Luderer, and O. Edenhofer, "System LCOE: What are the costs of variable renewables?," Energy, vol. 63, pp. 61-75, 2013.

[71] E. S. Rubin, C. Chen, and A. B. Rao, "Cost and performance of fossil fuel power plants with CO2 capture and storage," Energy policy, vol. 35, pp. 4444-4454, 2007.

[72] P. L. Joskow, "Comparing the costs of intermittent and dispatchable electricity generating technologies," American Economic Review, vol. 101, pp. 238-41, 2011.

[73] X. Ouyang and B. Lin, "Levelized cost of electricity (LCOE) of renewable energies and required subsidies in China," Energy Policy, vol. 70, pp. 64-73, 2014.

[74] H. Akbari, "Shade trees reduce building energy use and CO2 emissions from power plants," Environmental pollution, vol. 116, pp. S119-S126, 2002.

114

[75] S. J. Davis, K. Caldeira, and H. D. Matthews, "Future CO2 emissions and climate change from existing energy infrastructure," Science, vol. 329, pp. 1330-1333, 2010.

[76] R. S. Haszeldine, "Carbon capture and storage: how green can black be?," Science, vol. 325, pp. 1647-1652, 2009.

[77] D. Pearce, "The role of carbon taxes in adjusting to global warming," The economic journal, vol. 101, pp. 938-948, 1991.

[78] M. Asif and T. Muneer, "Energy supply, its demand and security issues for developed and emerging economies," Renewable and Sustainable Energy Reviews, vol. 11, pp. 1388-1413, 2007.

[79] J. J. L. Rodriguez, A. M. Prina, D. Acosta, M. Guerra, Y. Huang, K. Jacob, et al., "The Prevalence and Correlates of Frailty in Urban and Rural Populations in Latin America, China, and India: A 10/66 Population-Based Survey," Journal of the American Medical Directors Association, 2018.

[80] Q. Wang, X. Chen, A. N. Jha, and H. Rogers, "Natural gas from shale formation–the evolution, evidences and challenges of shale gas revolution in United States," Renewable and Sustainable Energy Reviews, vol. 30, pp. 1-28, 2014.

[81] K. Branker, M. Pathak, and J. M. Pearce, "A review of solar photovoltaic levelized cost of electricity," Renewable and sustainable energy reviews, vol. 15, pp. 4470-4482, 2011.

[82] L. Hirth, F. Ueckerdt, and O. Edenhofer, "Integration costs revisited–An economic framework for wind and solar variability," Renewable Energy, vol. 74, pp. 925-939, 2015.

[83] M. Cai, Y. Wu, H. Chen, X. Yang, Y. Qiang, and L. Han, "Cost‐Performance Analysis of Perovskite Solar Modules," Advanced Science, vol. 4, 2017.

[84] C. Clauser and M. Ewert, "The renewables cost challenge: Levelized cost of geothermal electric energy compared to other sources of primary energy–Review and case study," Renewable and Sustainable Energy Reviews, 2017.

[85] M. Taylor, K. Daniel, A. Ilas, and E. Y. So, "Renewable power generation costs in 2014," International Renewable Energy Agency: Masdar City, Abu Dhabi, UAE, 2015.

[86] A. Hazlehurst, "Economic analysis of solar power: Achieving grid parity," ed: Stanford, CA: Stanford graduate school of business, 2009.

[87] "IRENA.Renewable Power Generation Costs in 2017. Available online: http://www.irena.org/publications/2018/Jan/Renewable-power-generation-costs-in-2017."

[88] "Lazard. In Lazard’s Latest Annual Levelized Cost of Energy Analysis (LCOE 11.0). 2017. Available online: https://www.lazard.com/perspective/levelized-cost-of-energy-2017."

[89] S. Chu and A. Majumdar, "Opportunities and challenges for a sustainable energy future," nature, vol. 488, p. 294, 2012.

[90] A. Chambers and N. Nakicenovic, "World Energy Outlook 2008," ed: IEA/OECD, 2008.

[91] I. I. E. Association, "World energy outlook 2009," ed: IEA, Paris, 2006. [92] F. Birol, "World energy outlook 2010," International Energy Agency, vol. 1,

2010. [93] M. v. Hoeven, "World energy outlook 2011," International Energy agency,

115

2011. [94] M. Van der Hoeven, "World energy outlook 2012," International Energy

Agency, Tech. Rep. ISBN, vol. 1033656550, 2012. [95] P. Olejarnik, "World energy outlook 2013," International Energy Agency:

France, 2013. [96] N. Scenario, M. East, and P. Cedex, "World energy outlook 2014 factsheet,"

Paris: International Energy Agency, 2015. [97] B. Fatih, "World energy outlook 2015," International Energy Agency, p. 1,

2015. [98] B. Obama, "The irreversible momentum of clean energy," Science, vol. 355,

pp. 126-129, 2017. [99] IEA., World Energy Outlook 2017: Organisation for Economic Co-operation

and Development, OECD, 2017. [100] "World Bank World Development Indicators. Available at

http://data.worldbank. org/data-catalog/world-development-indicators.," Accessed 20 June (2018).

[101] "Lizzard Company. (2015, Nov.). Lizard’s levelized cost of energy analysis-version 9.0. [Online]. Available: https://www.lazard.com/media/2390/lazards-levelized-cost-of-energy-analysis-90.pdf."

[102] S. Jacobsson and A. Bergek, "Transforming the energy sector: the evolution of technological systems in renewable energy technology," Industrial and corporate change, vol. 13, pp. 815-849, 2004.

[103] S. Emeis, Wind energy meteorology: atmospheric physics for wind power generation: Springer, 2018.

[104] G. Mokryani, Y. F. Hu, P. Papadopoulos, T. Niknam, and J. Aghaei, "Deterministic approach for active distribution networks planning with high penetration of wind and solar power," Renewable Energy, vol. 113, pp. 942-951, 2017.

[105] M. A. Green, "Solar cells: operating principles, technology, and system applications," 1982.

[106] C. Bermann, "Impasses and controversies of hydroelectricity," Estudos avançados, vol. 21, pp. 139-153, 2007.

[107] W. E. Glassley, "Geothermal Energy, Geology and Hydrology of," Encyclopedia of Sustainability Science and Technology, pp. 1-13, 2017.

[108] M. Ram, M. Child, A. Aghahosseini, D. Bogdanov, A. Lohrmann, and C. Breyer, "A comparative analysis of electricity generation costs from renewable, fossil fuel and nuclear sources in G20 countries for the period 2015-2030," Journal of cleaner production, vol. 199, pp. 687-704, 2018.

[109] I. R. E. Agency, "Renewable Capacity Statistics," ed: International Renewable Energy Agency Abu Dhabi, 2017.

[110] C. Shearer, R. Fofrich, and S. J. Davis, "Future CO2 emissions and electricity generation from proposed coal‐fired power plants in India," Earth's Future, vol. 5, pp. 408-416, 2017.

[111] R. Lueken, K. Klima, W. M. Griffin, and J. Apt, "The climate and health effects of a USA switch from coal to gas electricity generation," Energy, vol. 109, pp. 1160-1166, 2016.

[112] W. C. d. S. Júnior, "Water and Energy Nexus under Climate Change Scenarios: Lessons from Brazil," New Water Policy & Practice, vol. 4, pp. 7-

116

18, 2018. [113] F. Benhmad and J. Percebois, "Photovoltaic and wind power feed-in impact on

electricity prices: The case of Germany," Energy policy, vol. 119, pp. 317-326, 2018.

[114] G. G. Emissions, "Comparison of Lifecycle Greenhouse Gas Emissions of Various Electricity Generation Sources."

[115] A. Mollah, S. Sattar, M. Hossain, A. Salahuddin, and H. Ar-Rashid, "Prospects of nuclear energy for sustainable energy development in Bangladesh," International Journal of Nuclear Energy Science and Engineering, vol. 5, p. 28, 2015.

[116] http://www.wapda.gov.pk/. [117] R. N. Hoffman and E. Kalnay, "Lagged average forecasting, an alternative to

Monte Carlo forecasting," Tellus A: Dynamic Meteorology and Oceanography, vol. 35, pp. 100-118, 1983.

[118] M.-S. Lee, B. Elango, and S. P. Schnaars, "The accuracy of the Conference Board's buying plans index: A comparison of judgmental vs. extrapolation forecasting methods," International Journal of Forecasting, vol. 13, pp. 127-135, 1997.

[119] F. Gagliardi, S. Alvisi, Z. Kapelan, and M. Franchini, "A probabilistic short-term water demand forecasting model based on the Markov Chain," Water, vol. 9, p. 507, 2017.

[120] A. J. Wood and B. F. Wollenberg, Power generation, operation, and control: John Wiley & Sons, 2012.

[121] N. J. Redondo and A. Conejo, "Short-term hydro-thermal coordination by Lagrangian relaxation: solution of the dual problem," IEEE Transactions on Power Systems, vol. 14, pp. 89-95, 1999.

[122] B. Gorenstin, N. Campodonico, J. Costa, and M. Pereira, "Stochastic optimization of a hydro-thermal system including network constraints," in Power Industry Computer Application Conference, 1991. Conference Proceedings, 1991, pp. 127-133.

[123] P.-H. Chen and H.-C. Chang, "Genetic aided scheduling of hydraulically coupled plants in hydro-thermal coordination," IEEE Transactions on Power Systems, vol. 11, pp. 975-981, 1996.

[124] I. Farhat and M. El-Hawary, "Optimization methods applied for solving the short-term hydrothermal coordination problem," Electric Power Systems Research, vol. 79, pp. 1308-1320, 2009.

[125] I. Farhat and M. El-Hawary, "Short-term hydro-thermal scheduling using an improved bacterial foraging algorithm," in Electrical Power & Energy Conference (EPEC), 2009 IEEE, 2009, pp. 1-5.

[126] J. Castro and J. A. González, "A nonlinear optimization package for long-term hydrothermal coordination," European Journal of Operational Research, vol. 154, pp. 641-658, 2004.

[127] P.-H. Chen, "Pumped-storage scheduling using evolutionary particle swarm optimization," IEEE Transactions on Energy Conversion, vol. 23, pp. 294-301, 2008.

[128] V. Hinojosa and C. Leyton, "Short-term hydrothermal generation scheduling solved with a mixed-binary evolutionary particle swarm optimizer," Electric Power Systems Research, vol. 92, pp. 162-170, 2012.

117

[129] X. Yuan, B. Cao, B. Yang, and Y. Yuan, "Hydrothermal scheduling using chaotic hybrid differential evolution," Energy Conversion and Management, vol. 49, pp. 3627-3633, 2008.

[130] D. N. Simopoulos, S. D. Kavatza, and C. D. Vournas, "An enhanced peak shaving method for short term hydrothermal scheduling," Energy conversion and management, vol. 48, pp. 3018-3024, 2007.

[131] S. Kumar and R. Naresh, "Efficient real coded genetic algorithm to solve the non-convex hydrothermal scheduling problem," International Journal of Electrical Power & Energy Systems, vol. 29, pp. 738-747, 2007.

[132] M. E. El-hawary and G. S. Christensen, "Functional optimization of common-flow hydro-thermal systems," IEEE Transactions on Power Apparatus and Systems, pp. 1833-1839, 1972.

[133] R. P. Thompson, "Weather sensitive electric demand and energy analysis on a large geographically diverse power system ߞApplication to short term hourly electric demand forecasting," IEEE Transactions on Power Apparatus and Systems, vol. 95, pp. 385-393, 1976.

[134] H. Happ, "Optimal power dispatchߞA comprehensive survey," IEEE Transactions on Power Apparatus and Systems, vol. 96, pp. 841-854, 1977.

[135] W. Uturbey and A. S. Costa, "Dynamic optimal power flow approach to account for consumer response in short term hydrothermal coordination studies," IET Generation, Transmission & Distribution, vol. 1, pp. 414-421, 2007.

[136] L. Lakshminarasimman and S. Subramanian, "Hydrothermal coordination using modified mixed integer hybrid differential evolution," International Journal of Energy Technology and Policy, vol. 5, pp. 422-439, 2007.

[137] H. Dashti, A. J. Conejo, R. Jiang, and J. Wang, "Weekly Two-Stage Robust Generation Scheduling for Hydrothermal Power Systems," 2016.

[138] L. Ferreira, T. Andersson, C. Imparato, T. Miller, C. Pang, A. Svoboda, et al., "Short-term resource scheduling in multi-area hydrothermal power systems," International Journal of Electrical Power & Energy Systems, vol. 11, pp. 200-212, 1989.

[139] H. Brannlund, J. Bubenko, D. Sjelvgren, and N. Andersson, "Optimal short term operation planning of a large hydrothermal power system based on a nonlinear network flow concept," IEEE Transactions on Power Systems, vol. 1, pp. 75-81, 1986.

[140] J. Tang and P. B. Luh, "Hydrothermal scheduling via extended differential dynamic programming and mixed coordination," IEEE Transactions on Power Systems, vol. 10, pp. 2021-2028, 1995.

[141] G.-X. Luo, H. Habibollahzadeh, and A. Semlyen, "Short-term hydro-thermal dispatch detailed model and solutions," IEEE Transactions on Power Systems, vol. 4, pp. 1452-1462, 1989.

[142] R. Bansal, "Optimization methods for electric power systems: An overview," International Journal of Emerging Electric Power Systems, vol. 2, 2005.

[143] H. Y. Yamin, "Review on methods of generation scheduling in electric power systems," Electric Power Systems Research, vol. 69, pp. 227-248, 2004.

[144] P. K. Singhal and R. N. Sharma, "Dynamic programming approach for solving power generating unit commitment problem," in Computer and Communication Technology (ICCCT), 2011 2nd International Conference on,

118

2011, pp. 298-303. [145] C. E. Zoumas, A. G. Bakirtzis, J. B. Theocharis, and V. Petridis, "A genetic

algorithm solution approach to the hydrothermal coordination problem," IEEE transactions on power systems, vol. 19, pp. 1356-1364, 2004.

[146] M. Ventosa, M. Rivier, A. Ramos, and A. García-Alcalde, "An MCP approach for hydrothermal coordination in deregulated power markets," in Power Engineering Society Summer Meeting, 2000. IEEE, 2000, pp. 2272-2277.

[147] M. Basu, "Improved differential evolution for short-term hydrothermal scheduling," International Journal of Electrical Power & Energy Systems, vol. 58, pp. 91-100, 2014.

[148] R. Gnanadass, P. Venkatesh, and N. P. Padhy, "Evolutionary programming based optimal power flow for units with non-smooth fuel cost functions," Electric power components and systems, vol. 33, pp. 349-361, 2004.

[149] C.-C. Kuo, "A novel coding scheme for practical economic dispatch by modified particle swarm approach," IEEE Transactions on Power Systems, vol. 23, pp. 1825-1835, 2008.

[150] M. P. Camargo, J. L. Rueda, I. Erlich, and O. Añó, "Comparison of emerging metaheuristic algorithms for optimal hydrothermal system operation," Swarm and Evolutionary Computation, vol. 18, pp. 83-96, 2014.

[151] R. Storn and K. Price, "Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces," Journal of global optimization, vol. 11, pp. 341-359, 1997.

[152] R. E. Perez-Guerrero and J. R. Cedeno-Maldonado, "Economic power dispatch with non-smooth cost functions using differential evolution," in Proceedings of the 37th Annual North American Power Symposium, 2005., 2005, pp. 183-190.

[153] J. Ilonen, J.-K. Kamarainen, and J. Lampinen, "Differential evolution training algorithm for feed-forward neural networks," Neural Processing Letters, vol. 17, pp. 93-105, 2003.

[154] T. Krink, B. Filipic, and G. B. Fogel, "Noisy optimization problems-a particular challenge for differential evolution?," in Evolutionary Computation, 2004. CEC2004. Congress on, 2004, pp. 332-339.

[155] A. Kumar, "Power Economic Dispatch with Valve-Point Loading Effects and Multiple Fuels Using Chaotic Based Differential Evolution," THAPAR UNIVERSITY, PATIALA, 2011.

[156] J. Yadav, N. Patidar, J. Singhai, S. Panda, and C. Ardil, "A combined conventional and differential evolution method for model order reduction," Measurement, vol. 183, p. 15885, 2009.

[157] M. Basu, "Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II," International Journal of Electrical Power & Energy Systems, vol. 53, pp. 135-141, 2013.

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