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FACULTY OF ENGINEERING
DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING
DESIGN AND ANALYSIS OF OPTIMAL POWER PLANNING
PROJECT INDEX: PRJ 137
BY
MAINA DUNCAN KANIARU
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SUPERVISOR: PROFESSOR M.K. MANGOLI
PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENT FOR THE AWARD OF THE DEGREE
OF
BACHELOR OF SCIENCE IN ELECTRICAL AND ELECTRONIC ENGINEERING OF
THE UNIVERSITY OF NAIROBI 2014
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DECLARATION OF ORIGINALITY
1) I understand what plagiarism is and I am aware of the university policy in this regard.
2) I declare that this final year project report is my original work and has not been submitted
elsewhere for examination, award of a degree or publication. Where other people’s work or my
own work has been used, this has properly been acknowledged and referenced in accordance with
the University of Nairobi’s requirements.
3) I have not sought or used the services of any professional agencies to produce this work
4) I have not allowed, and shall not allow anyone to copy my work with the intention of passing it
off as his/her own work.
5) I understand that any false claim in respect of this work shall result in disciplinary action, in
accordance with University anti-plagiarism policy.
Signature: ……………………………………………………………………………………
Date: …………………………………………………………………………………………
NAME OF STUDENT: MAINA DUNCAN KANIARU
REGISTRATION NUMBER: F17/28658/2009
COLLEGE: Architecture and Engineering
FACULTY/SCHOOL/INSTITUTE: Engineering
DEPARTMENT: Electrical and Information Engineering
COURSE NAME: Bachelor of Science in Electrical and Electronic Engineering
TITLE OF WORK: DESIGN AND ANALYSIS OF OPTIMAL POWER PLANNING
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CERTIFICATION This report has been submitted to the Department of Electrical and Information Engineering,
University of Nairobi with my approval as supervisor:
………………………………
Professor M.K. Mangoli
Date:………………………
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DEDICATION To my parents, for bringing out the best in me from a tender age
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ACKNOWLEDGEMENTS First and foremost, I wish to thank the Almighty God for his undeserving favor throughout my
academic life. His guidance has propelled me through university challenges.
I wish to extend my profound thanks and gratitude to my supervisor, Professor Maurice Kizito
Mangoli for introducing me to the exciting research of power system planning and allowing me
independence in carrying out this work. I am most grateful for his sound guidance, kindness,
meticulous supervision and persistence.
I would also wish to appreciate my lecturers and non-teaching staff at the University of Nairobi;
Department of Electrical and Information Engineering for their selfless effort that enabled me
achieve my goals during the entire course of my studies.
I would also wish to appreciate my fellow students for their cooperation all through this project
and five years of study.
I would also wish to appreciate my friend, Catherine Nyarangi Ongangi, for continuous
encouragement and helping me through project and coursework challenges.
Last but not least, I appreciate my parents, Mr. and Mrs. Maina, together with my siblings whose
love and encouragement has been instrumental throughout my education.
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TABLE OF CONTENTS DECLARATION OF ORIGINALITY .................................................................................................... ii
CERTIFICATION ....................................................................................................................................iii
DEDICATION .......................................................................................................................................... iv
ACKNOWLEDGEMENTS...................................................................................................................... v
LIST OF TABLES .................................................................................................................................... ix
LIST OF FIGURES ...................................................................................................................................x
LIST OF ABBREVIATIONS .................................................................................................................. xi
ABSTRACT ............................................................................................................................................. xii
1.0 CHAPTER 1 ........................................................................................................................................ 1
1.1 INTRODUCTION........................................................................................................................... 1
1.2 IMPORTANCE OF POWER SYSTEM PLANNING ................................................................. 1
1.3 GENERATION PLANNING ......................................................................................................... 2
1.31 Short term generation planning ............................................................................................... 2
1.32 Medium term generation planning .......................................................................................... 4
1.33 Long-term generation planning ............................................................................................... 6
1.4 PROBLEM STATEMENT ............................................................................................................ 8
1.5 LIMITATIONS AND ASSUMPTIONS. ....................................................................................... 8
1.5 CHAPTER BREAKDOWN ........................................................................................................... 9
2.0 CHAPTER 2: HYDROTHERMAL CO-ORDINATION AND OPTIMIZATION METHODS. 10
2.1 HYDRO-ELECTRIC POWER PLANTS ................................................................................... 10
2.2 TYPES OF HYDRO-ELECTRIC POWER PLANTS ............................................................... 10
2.21 Run-of-river plants without pondage .................................................................................... 10
2.22 Run-of-river plants with pondage .......................................................................................... 11
2.23 Storage type plants .................................................................................................................. 11
2.24 Pumped storage plants ............................................................................................................ 11
2.25 Mini and Microhydro plants .................................................................................................. 12
2.26 Hydro plants on different streams ......................................................................................... 12
2.27 Hydro plants on same streams ............................................................................................... 12
2.28 Multi-chain Hydro plants ....................................................................................................... 12
2.3 THERMAL POWER PLANTS ................................................................................................... 14
2.4 HYDROTHERMAL COORDINATION PROBLEM FORMULATION ................................ 17
2.41 Problem objective function ..................................................................................................... 18
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2.42 System constraints................................................................................................................... 18
2.5 REVIEW OF HYDROTHERMAL COORDINATION OPTIMIZATION METHODS ........ 21
2.51 Classical Techniques ............................................................................................................... 22
2.52 Heuristic Techniques .............................................................................................................. 23
2.53 Hybrid Techniques .................................................................................................................. 26
2.6 SURVEY OF WORK PREVIOUSLY DONE ............................................................................ 29
3.0 CHAPTER 3 ...................................................................................................................................... 34
3.1 INTRODUCTION TO TABU SEARCH ..................................................................................... 34
3.2 ELEMENTS OF TABU SEARCH .............................................................................................. 34
3.21 Tabu list and tabu conditions ................................................................................................. 35
3.22 Neighborhood structure .......................................................................................................... 35
3.23 Tabu tenure ............................................................................................................................. 35
3.24 Candidate lists ......................................................................................................................... 35
3.25 Aspiration Criterion................................................................................................................ 35
3.26 Intensification and Diversification ......................................................................................... 36
3.27 Stopping or termination criterion .......................................................................................... 37
3.28 Long term memory ................................................................................................................. 37
3.3 ADVANTAGES OF TABU SEARCH ......................................................................................... 38
3.4 DISADVANTAGES OF TABU SEARCH .................................................................................. 38
3.5 IMPLEMENTATION OF SIMPLE TABU SEARCH IN HTC PROBLEM ........................... 39
3.51 Initial solution.......................................................................................................................... 39
3.52 Search space ............................................................................................................................ 39
3.53 Neighborhood structure and candidate generations............................................................. 39
3.54 No of iterations and stopping criterion .................................................................................. 40
3.55 Tabu conditions ....................................................................................................................... 40
3.6 ALGORITHM FOR THE HTC PROBLEM USING TS ........................................................... 41
3.7 FLOWCHART .............................................................................................................................. 43
4.0 CHAPTER 4 ...................................................................................................................................... 44
4.1 CASE STUDY ............................................................................................................................... 44
4.2 RESULTS AND ANALYSIS ........................................................................................................ 47
5.0 CONCLUSION AND RECOMMENDATION FOR FURTHER WORK.................................... 56
5.1 CONCLUSION ............................................................................................................................. 56
5.2 RECOMMENDATION FOR FURTHER WORK ..................................................................... 57
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REFERENCES ....................................................................................................................................... 58
APPENDIX A .......................................................................................................................................... 61
APPENDIX B .......................................................................................................................................... 62
APPENDIX C .......................................................................................................................................... 71
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LIST OF TABLES TABLE 4.1: DEMAND TABLE 1 .................................................................................................................................. 45
TABLE 4.2: HYDROGENERATION COEFFECIENTS 1 ................................................................................................... 45
TABLE 4.3: HOURLY RESERVOIR INFLOWS 1 ............................................................................................................. 46
TABLE 4.4: LIMITS OF THE HYDRO NETWORK 1 ........................................................................................................ 46
TABLE 4.5: ERROR DETERMINATION 1.1 (FORWARD-BACKWARD-0.0001) ............................................................... 47
TABLE 4.6: ERROR DETERMINATION 1.2 (FORWARD-BACKWARD-0.00001) ............................................................. 48
TABLE 4.7: ERROR DETERMINATION 1.3 (BACKWARD SENSITIVITY-0.0001) ............................................................. 48
TABLE 4.8: ERROR DETERMINATION 1.4 (BACKWARD SENSITIVITY-0.00001) ........................................................... 49
TABLE 4.9: ERROR DETERMINATION 1.5 (FORWARD SENSITIVITY-0.0001) ............................................................... 49
TABLE 4.10: ERROR DETERMINATION 1.6 (FORWARD SENSITIVITY-0.00001) ........................................................... 50
TABLE 4.11: TABU PARAMETERS 1 ........................................................................................................................... 50
TABLE 4.12: COST COMPARISON 1 .......................................................................................................................... 53
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LIST OF FIGURES FIGURE 2. 1 (LAYOUT OF HYDROELECTRIC PLANT) ................................................................................................... 12 FIGURE 2. 2 (SHEMATIC DIAGRAM OF HYDRO ELECTRIC PLANTS)............................................................................. 13 FIGURE 2. 3 (KENYA HYDRO SYSTEM) ...................................................................................................................... 13 FIGURE 2. 4 (LAYOUT OF THERMAL POWER PLANT) ................................................................................................. 16
FIGURE 3. 1 (FLOWCHART OF SHTC USING TABU SEARCH) ....................................................................................... 43 FIGURE 3. 2 (IEEE BLOCK DIAGRAM OF HYDRO TEST SYSTEM) .................................................................................. 44
FIGURE 4. 1 (MATLAB EXCEL WORKSHEET RESULTS) ................................................................................................ 51 FIGURE 4. 2 (CONVERGENCE CHARACTERISTICS) ..................................................................................................... 51 FIGURE 4. 3 (VOLUME AND DISCHARGE LEVELS) ...................................................................................................... 52 FIGURE 4. 4 (MATLAB EXCEL WORKSHEET-IMPROVED RESULTS) ............................................................................. 54 FIGURE 4. 5 (CONVERGENCE CHARACTERISTICS, VOLUME AND DISCHARGE LEVELS) ............................................... 55
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LIST OF ABBREVIATIONS F total fuel cost of thermal system
Psi, t loading of ith thermal unit at time t
Phi, t generation level of hydro ith unit at time t
Vhi, t storage volume of ith reservoir at time t
Qhi, t water discharge rate of ith reservoir at time t
PD, t load demand at time t
PL, t total transmission line losses at time t
Shi, t spillage of ith reservoir at time t
Ih, it inflow rate of ith reservoir at time t
Hit net head of ith reservoir at time t
α, β, γ thermal generation cost coefficients
Cil,.. ,Ci6 hydro power generation coefficients
Rui set of upstream units directly above ith hydro plant
Rh set of hydro plants in the system
Rs set of thermal units in the system
i, t, T unit index, time index and scheduling period respectively
V, ibegin initial storage volume of ith reservoir
V, iend final storage volume of ith reservoir
TS Tabu Search
GA Genetic Algorithm
PSO Particle Swarm Optimization
ACO Ant Colony Optimization
SA Simulated Annealing
IP Interior Point
HPONN High Performance Feedback Optimization Neural Network
HTC Hydrothermal Coordination
IEEE Institute of Electrical and Electronics Engineering
MW Megawatts
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ABSTRACT Power system planning is making decisions pertaining to the future. The decisions can be on a
daily, weekly, monthly or yearly basis. It is a complex and comprehensive process as the levels of
uncertainties increase as the planning time horizons increase. Focus of this report will be laid on
short term generation planning precisely the hydrothermal coordination problem.
Hydrothermal coordination is the scheduling of hydro and thermal power plants in order to meet
the demand (residential, industrial and commercial). Focus on the hydrothermal coordination
problem is mainly the scheduling the hydro plants and assuming a composite thermal power plant.
The location and special operating characteristics of hydro plants are important considerations in
hydro-thermal coordination. The problem is quite different if the hydro stations are located on the
same stream or on different ones. In the former case, the water transport delay may be of great
importance. An upstream station will highly influence the operation of the next downstream
station. The latter will also influence the upstream plant as well. Close hydraulic coupling of
stations adds an interesting dimension to the problem.
Tabu search optimization technique is a metaheuristic technique used to find the global optimum
(from the local optimum) by generating a neighborhood solution and searching through the
neighborhood for a better solution. The objective of this project is to use tabu search optimization
technique in reducing the cost of thermal generating costs by optimizing the use of reservoir water
for hydropower generations. Different types of generations will be explored, illustrated and
accuracies to the hydrothermal coordination problem determined.
The developed algorithm was tested on the IEEE hydrothermal system consisting of 4 hydro units
and a composite thermal generator. The results obtained were compared with results obtained from
HPONN and GA.
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1.0 CHAPTER 1
1.1 INTRODUCTION [1]A power system is mainly composed of three elements; generation, transmission and load.
Power system planning is a process in which the aim is to decide on new as well as optimizing and
upgrading existing system elements, to adequately satisfy the loads for a foreseen future. Planning
can either be:
a) Short term planning
b) Medium term planning
c) Long term planning
Short term power planning involves planning on a time scale of between 1-day to 1-week to few
months. This is usually referred to as operational planning and is focused on optimizing the already
available electrical infrastructure. Medium term power planning involves planning on a time scale
of few months to 2-3 years. This involves optimizing and upgrading the already existing
infrastructure. Long term power planning involves planning on a time scale of 3yrs and above.
The main aim of this planning is building new electrical infrastructure whilst minimizing the
investment costs. The three power system elements can be planned in the above mentioned time
horizons each integrated with each other for example medium term planning results are to be used
for short term planning.
1.2 IMPORTANCE OF POWER SYSTEM PLANNING 1. Reduces operation and future investment costs.
2. Enables good use of renewable and non-renewable resources.
3. Improves voltage stability and the support network.
4. Different scenarios can be modelled and analyzed.
5. Faults in the network can be easily detected and diagnosed.
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1.3 GENERATION PLANNING Generation planning can either be:
• Short term generation planning
• Medium term generation planning
• Long term generation planning
1.31 Short term generation planning The short term generation planning functions are focused on planning horizons as long as a year
in length and as short as the next calendar day. The purpose of short term generation planning is
to meet the functional requirements for the power plant coordination, unit commitment and
economic dispatch problem, wholesale transactions and fuel supply functions.
[2]Seasonal planning activities occur on as needed basis to enhance reliability and improve
economics. Reliability provides a continuous supply of power to customers in spite of unforeseen
circumstances that can disrupt production and delivery of power. Economics involves providing
power to customers at the lowest reasonable cost while observing constraints and being ready to
deal with unforeseen circumstances.
The primary responsibilities of short term generation planning are:
i. Power plant coordination
ii. Unit Commitment
iii. Economic Dispatch
iv. Wholesale Power Transactions
v. Natural gas and fuel oil supply
vi. Responding to unforeseen equipment outages, weather events etc.
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Resources must be scheduled to serve the load plus operating reserves in each hour. Operating
reserves is comprised of regulating reserves and contingency reserves. Regulating reserves come
from generators that follow moment to moment changes in load to keep generation and load
balanced. Contingency reserves come from generators that can ramp up quickly to replace energy
from a generator that has a sudden mechanical breakdown. This is important because of the
following uncertainty:
i. Actual load will be different than forecasted load.
ii. Power plants and other resources may not operate as planned.
iii. Transmission system may not operate as planned.
Power plants typically have constraints or limitations associated with their operation that must be
observed to ensure a feasible plan. Typical power plant constraints are:
i. Minimum load and maximum load
ii. Ramp rates
iii. Time to start up and shut down
iv. Minimum time to run after being started
v. Minimum time to be off after shutdown
Purchased power typically has constraints:
i. Size of purchased power
ii. Shape of purchased power (number of hours)
iii. Reliability (firm vs. non-firm)
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1.32 Medium term generation planning This involves a planning horizon of 1-3 years and it involves multiobjective formulations. They
include:
i. Maintenance scheduling
ii. Fuel supply contract issues
iii. Hydro energy generation reserves schedules
iv. Emission allocation
v. Energy demand management
Medium term maintenance scheduling used to be undertaken in a [3] centralized manner in pre-
deregulation area, but needs a re-look in the new environment. In the current deregulated
environment, each generating company seeks to maximize its profit and in order to do so, can often
compromise the system security and reliability aspects by not developing appropriate maintenance
schedules. In restructured power systems, ill planned maintenance schedules can lead to
unexpected rise in prices and may also impinge on the market operation, while introducing market
inefficiencies. Maintenance costs include constant and variable costs. [4]Constant costs are
independent on whether a unit is working or under maintenance conditions. Variable costs are
proportional to the generation unit working and its exhausting conditions in its long-term
operation.
Emission allocation; besides minimizing the cost, environmental issues are an important issue.
Fossil-fired plants produce atmospheric emissions with various fuels at various cost bases, such as
coal, gas and oil. One emission material CO2 (carbon dioxide ) is the major cause to endanger the
ozonosphere, causing global warming with another theory that gases, especially carbon dioxide,
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are being trapped in atmosphere to cause greenhouse effect. The power industry is certainly a
major contributor (about one-third) to global CO2 emissions. In recent years, rigid environmental
regulations and CO2 emission force utility planners to consider emission as a cost and an important
constraint in generation expansion planning. A form of tax is introduced to discourage release of
harmful gases to the environment.
Hydro energy generation reserves schedules; Hydro power plants can use the energy stored in their
reservoirs avoiding fuel expenses with thermal unit. The availability of hydro energy is limited by
reservoir storage capacities. The major decision point in hydro scheduling is to release water in
such way that the immediate financial gain equals the expected future value of water. The expected
future value of water is presented as a function of reservoir level, present inflow and time.
Energy demand management, also known as demand side management (DSM), is the modification
of consumer demand for energy through various methods such as financial incentives and
education. Usually, the goal of demand side management is to encourage the consumer to use less
energy during peak hours, or to move the time of energy use to off-peak times such as nighttime
and weekends. Peak demand management does not necessarily decrease total energy consumption,
but could be expected to reduce the need for investments in networks and/or power plants for
meeting peak demands. An example is the use of energy storage units to store energy during off-
peak hours and discharge them during peak hours. Energy demand management activities should
bring the demand and supply closer to a perceived optimum.
Fuel supply contract issues. An energy source is defined as secure on this site if electricity
generators can be sure of obtaining enough of the relevant fuel to maintain an adequate electricity
supply. Countries that rely on fuel that must be constantly imported to power their electricity
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supply expose themselves to potential energy security issues, including fluctuating international
market prices and disruptions to fuel supplies caused by geopolitical disturbances.
Every energy source has strengths and weaknesses, such as its inherent limitations on security of
supply, which could contribute to the likelihood of an energy gap, when supply falls short of
demand, and might cause interruptions to the electricity supply. Reducing dependence on constant
imports of fuel to generate electricity can help to mitigate security of supply issues. This could
include using renewable sources such as wind and marine, which don't depend on imported fuels,
alongside fuels that come from a range of suppliers and can be stored. The Kenya Government
favors a diverse mix of generating technologies where the strengths of one energy source
compensate for another's weaknesses.
1.33 Long-term generation planning Long-term planning models deal with a time horizon of 3 years and above. [1]Long-term
generation planning problem consists of determining the ideal technology, expansion size, siting
and timing of construction of a new power plant capacity in an economic fashion. This is to ensure
that installed capacity adequately meets the projected demand growth. The main target of national
power system planning is to find an optimal power capacity mix in the system which gives
minimum investment costs. Long term generation planning is involved with the following costs:
i. Investment costs
ii. Salvation value of investment costs
iii. Fuel costs and fuel inventory costs
v. Non-fuel operation and maintenance costs
vi. Cost of energy not served (ENS)
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Investment costs: This term represents the cost of a power plant, in terms of Sh/kW. The total
investment cost is the product of this value with the power plant capacity.
Salvation value of investment costs: Salvation value is the real value of an asset/equipment,
remaining, at a specific time and after considering the depreciation rate.
Fuel inventory costs: What does it cost to manage your fuel inventory? How timely do you receive
inventory levels? Have you ever experienced downtime in your operations because of a fuel run-
out resulting from a breakdown in your inventory management procedures?
Fuel costs: The fuel cost of a plant is, in fact, dependent on its production level (i.e. f (Psi, t)). In
other words, the cost varies with the production level. For simplicity, however, the cost (sh/MWh)
is considered to be fixed here. Total cost is calculated from the product of this value and the energy
production of the unit.
Non-fuel operation and maintenance costs: Operation and Maintenance (O & M) is the process
required for the proper operation of power plants, defined in terms of the number of days per year.
These costs are independent of energy production (in terms of sh/kW month); the total value is
calculated from the product of this value times the plant capacity times 12 (12 months).
Cost of unserved energy: This means energy that cannot be delivered depending on capacity
deficiency. The COUE is the value (in shillings per kWh) that is placed on a unit of energy not
supplied due to an unplanned outage of short duration. Optimal planning decisions would result
from the power system planner balancing the total COUE against the incremental cost to supply
the energy not served.
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1.4 PROBLEM STATEMENT The main purpose of the project is to understand optimal system operation by studying in detail
the theory behind hydrothermal coordination, formulation of the hydrothermal coordination
problem and its solution using Tabu Search algorithm. Tabu Search technique is to be understood
in detail and be used to write a software program in Matlab programming software package to
solve the hydrothermal coordination problem. The effectiveness of TS is verified on an IEEE
hydrothermal system consisting of 4 hydro plants and 1 composite thermal generator.
The objectives can thus be stated as:
To optimize the use of water as a resource for maximum hydro power output to reduce the
use of thermal power.
To understand tabu search and use it to find the optimal solution.
1.5 LIMITATIONS AND ASSUMPTIONS. Data acquisition from Kengen proved to be a difficult endeavor as data required was not
understandable to the organization. Also, data provided was not interpretable and not all of it was
availed. There has been limited research on the use of tabu search in the hydrothermal coordination
problem.
Hydro test system provided by IEEE does not provide water spillage data and data from the
previous scheduling period which are important for the present day scheduling. Also, it is assumed
that the system is lossless.
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1.5 CHAPTER BREAKDOWN The project report has been organized into five chapters as follows:
Chapter 1; Introduction to the power system planning.
Chapter 2; Literature review of the hydrothermal coordination problem and survey of work
previously done.
Chapter 3; Methodology and design focusing on TS optimization method.
Chapter 4; Data analysis of the simulation results obtained from chapter 3
Chapter 5; Conclusion is presented and recommendations for further work stated.
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2.0 CHAPTER 2: HYDROTHERMAL CO-ORDINATION AND
OPTIMIZATION METHODS
2.1 HYDRO-ELECTRIC POWER PLANTS [5]In hydro-electric plants energy of water is utilized to move the turbines which in turn run the
electric generators. The energy of water utilized for power generation may be kinetic or potential.
The kinetic energy of water is its energy in motion and is a function of mass and velocity, while
the potential difference is a function of the difference in level/head of water between two points.
In either case continuous availability of water is a basic necessity; to ensure is, water collected in
natural lakes and reservoirs at high altitudes may be utilized or water may be artificially stored by
constructing dams across flowing streams. The ideal site is one in which a good system of natural
lakes with substantial catchment area, exists at high altitude.
2.2 TYPES OF HYDRO-ELECTRIC POWER PLANTS
2.21 Run-of-river plants without pondage As the name indicates, it a run-of-river plant without pondage does not store water and uses the
water as it comes. There is no control on flow of water so that during high floods or low loads
water is wasted while during low run-off the plant capacity is considerably reduced. Due to non-
uniformity of supply and lack of assistance from a firm capacity the utility of these plants is much
less than those of other types. The head on which these plants work varies considerably. Such a
plant can be made a great deal more useful by providing sufficient storage at the plant to take care
of the hourly fluctuations in load. This lends some firm capacity to the plant. During good flow
conditions these plants may cater to base load of the system, when flow reduces they may supply
the peak demands. Head water elevation for plant fluctuates with the flow conditions. These plants
without storage may sometimes be made to supply the base load, but the firm capacity depends on
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the minimum flow of river. The run-of-river plant may be made for load service with pondage,
though storage is usually seasonal.
2.22 Run-of-river plants with pondage Pondage usually refers to the collection of water behind a dam at the plant and increases the stream
capacity for a short period, say a week. Storage means collection of water in upstream reservoirs
and this increases the capacity of the stream over an extended period of several months. Storage
plants may work satisfactorily as base load and peak load plants. This type of plant, as compared
to that without pondage, is more reliable and its generating capacity is less dependent on the flow
rates of water available.
2.23 Storage type plants A storage type plant is one with a reservoir sufficiently large size to permit carry over storage from
the wet season to the dry season. Water is stored behind the dam and is available to the plant with
control as required. Majority of hydro-electric plants are of this type.
2.24 Pumped storage plants Pumped storage plants are employed at the places where the quantity of water available for power
generation is inadequate. Here the water passing through the turbines is stored in tail race pond.
During low loads period this water is pumped back to the head reservoir using the extra energy
available. This water can be again used for generating power during peak load periods. Pumping
of water may be done seasonally or daily depending upon the conditions of the site and the nature
of the load on the plant. Such plants are usually interconnected with steam or diesel engine plants
so that off peak capacity of interconnecting stations is used in pumping water and the same is used
during peak load periods. Of course, the energy available from quantity of water pumped by the
plant is less than the energy input during pumped operation. Again while pumped water the power
available is reduced on account of losses occurring in prime movers.
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2.25 Mini and Microhydro plants In order to meet with the present energy crisis partly, a solution is to develop mini (5m to 20m
head) and micro(less than 5m head) hydro potential in our country. By proper planning and
implementation, it is possible to commission a small hydro-generating set up of 5MW within a
period of one and half year against the period of a decade or two for large capacity power plants.
Micro-hydro power plants make use of standardized bulb sets with unit output ranging from 100
to 1000KW working under heads between 1.5m to 10m.
2.26 Hydro plants on different streams The plants are located on different streams and are independent of each other.
2.27 Hydro plants on same streams When hydro plants are located on the same stream, the downstream plant depends on the
immediate upstream plant.
2.28 Multi-chain Hydro plants These hydro plants are located on different streams as well as same stream.
FIGURE 2. 1 (LAYOUT OF HYDROELECTRIC PLANT)
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FIGURE 2. 2 (SHEMATIC DIAGRAM OF HYDRO ELECTRIC PLANTS)
FIGURE 2. 3 (KENYA HYDRO SYSTEM)
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2.3 THERMAL POWER PLANTS [6]A thermal power station is a power plant in which the prime mover is steam driven. Water is
heated, turns into steam and spins a steam turbine which drives an electrical generator. After it
passes through the turbine, the steam is condensed in a condenser and recycled to where it was
heated; this is known as a Rankine cycle. The greatest variation in the design of thermal power
stations is due to the different fossil fuel resources generally used to heat the water. Some prefer
to use the term energy center because such facilities convert forms of heat energy into electrical
energy. Certain thermal power plants also are designed to produce heat energy for industrial
purposes of district heating, or desalination of water, in addition to generating electrical power.
Globally, fossil fueled thermal power plants produce a large part of man-made CO2 emissions to
the atmosphere, and efforts to reduce these are varied and widespread.
Almost all coal, nuclear, geothermal, solar thermal electric, and waste incineration plants, as well
as many natural gas power plants are thermal. Natural gas is frequently combusted in gas turbines
as well as boilers. The waste heat from a gas turbine can be used to raise steam, in a combined
cycle plant that improves overall efficiency. Power plants burning coal, fuel oil, or natural gas are
often called fossil-fuel power plants. Some biomass-fueled thermal power plants have appeared
also. Non-nuclear thermal power plants, particularly fossil-fueled plants, which do not use co-
generation are sometimes referred to as conventional power plants.
The energy efficiency of a conventional thermal power station, considered salable energy produced
as a percent of the heating value of the fuel consumed, is typically 33% to 48%. As with all heat
engines, their efficiency is limited, and governed by the laws of thermodynamics. By comparison,
most hydropower stations in the United States are about 90 percent efficient in converting the
energy of falling water into electricity. [4]
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The energy of a thermal not utilized in power production must leave the plant in the form of heat
to the environment. This waste heat can go through a condenser and be disposed of with cooling
water or in cooling towers. If the waste heat is instead utilized for district heating, it is called co-
generation. An important class of thermal power station are associated with desalination facilities;
these are typically found in desert countries with large supplies of natural gas and in these plants,
freshwater production and electricity are equally important co-products.
[5]The Carnot efficiency dictates that higher efficiencies can be attained by increasing the
temperature of the steam. Sub-critical fossil fuel power plants can achieve 36–40% efficiency.
Super critical designs have efficiencies in the low to mid 40% range, with new "ultra critical"
designs using pressures of 4400 psi (30.3 MPa) and multiple stage reheat reaching about 48%
efficiency. Above the critical point for water of 705 °F (374 °C) and 3212 psi (22.06 MPa), there
is no phase transition from water to steam, but only a gradual decrease in density.
Currently most of the nuclear power plants must operate below the temperatures and pressures that
coal-fired plants do, since the pressurized vessel is very large and contains the entire bundle of
nuclear fuel rods. The size of the reactor limits the pressure that can be reached. This, in turn, limits
their thermodynamic efficiency to 30–32%. Some advanced reactor designs being studied, such as
the very high temperature reactor, advanced gas-cooled reactor and supercritical water reactor,
would operate at temperatures and pressures similar to current coal plants, producing comparable
thermodynamic efficiency.
The direct cost of electric energy produced by a thermal power station is the result of cost of fuel,
capital cost for the plant, operator labor, maintenance, and such factors as ash handling and
disposal. Indirect, social or environmental costs such as the economic value of environmental
impacts, or environmental and health effects of the complete fuel cycle and plant
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decommissioning, are not usually assigned to generation costs for thermal stations in utility
practice, but may form part of an environmental impact assessment.
FIGURE 2. 4 (LAYOUT OF THERMAL POWER PLANT)
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2.4 HYDROTHERMAL COORDINATION PROBLEM FORMULATION [7]The optimal scheduling of generation in a hydrothermal system involves the allocation of
generation among the hydroelectric and thermal plants so as to minimize total operation costs of
thermal plants while satisfying the various constraints on the hydraulic and power system network.
In short term scheduling, the total volume of water or power expected to be generated by each
hydro plant over the scheduling period is fixed. It is assumed that the target dam levels at the end
of the scheduling period have been set by a medium term scheduling process that takes into account
river inflow modelling and load predictions. The short term scheduler then allocates this water
(power) to the various time intervals in an effort to minimize thermal generation costs while
attempting to satisfy the various unit and reservoir constraints.
The main constraints include:
Time coupling effect of the hydro sub problem, where the water flow in an earlier time
interval affects the discharge at a later period of time.
the varying system load demand,
the cascade nature of the hydraulic network
hourly reservoir inflows,
reservoir storage and turbine flow rate limits,
dynamic hydraulic flow continuity equations,
Minimum and maximum loading limits of both thermal and hydro plants.
Further constraints could be imposed depending on the particular requirements of a given power
system, such as the need to satisfy activities such as; flood control, irrigation, fishing, water supply
etc. In a hydrothermal power system, apart from replacing the thermal generation which would
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have incurred a given fuel consumption, the hydroelectric power generation is usually responsible
for providing frequency regulation, by taking advantage of its fast load pick up characteristic.
In a hydrothermal power system, the thermal generation is used to supply that part of the load
demand that cannot be supplied by the hydro generation. A mathematical formulation of the
hydrothermal scheduling problem in a multi-reservoir cascaded hydroelectric system with a
nonlinear relationship between water discharge rate, net head and power generation, and water
transport delay is presented in the next section.
2.41 Problem objective function The basic optimal hydrothermal coordination, involves minimizing the thermal cost function, F,
Min F=∑∑ Fi (Psi, t) I ϵ Rs t ϵ T
Subject to a number of unit and power system network equality and inequality constraints. More
advance models account for the power loss in the transmission networks. The thermal unit
commitment is assumed known, and only the unit generation levels are to be determined.
2.42 System constraints
System active load balance The total active power generation must balance the predicted power demand plus losses, at each
time interval over the scheduling horizon.
∑Psi, t + ∑Phi, t = PD, t + PL, t
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Transmission line constraints The power transported by the transmission lines must not violate their maximum loading limits.
Transmission limits constraints are particularly important in systems with major hydro
components, as the hydro generation stations are usually located far from load centers.
Unit constraints In the hydrothermal scheduling problem, both the hydro and thermal units loading levels are
limited by the physical limitations on the generating units. Thus:
i. the thermal plant loading limits must be satisfied,
Psi, t min ≤ Psi, t ≤ Psi, t
max
ii. the hydro plant loading limits must be satisfied,
Phi, t min ≤ Phi, t ≤ Phi, t
max
Hydraulic network constraints The hydraulic operational constraints comprise the water balance (continuity) equations for each
hydro unit (system) as well as the bounds on reservoir storage and release targets. These bounds
are determined by the physical reservoir and plant limitations as well as the multipurpose
requirements of the hydro system. These constraints include;
i) Physical limitations on reservoir storage volumes and discharge rates,
Vhi, t min ≤ Vhi, t ≤ Vhi, t
max
Qhi, t min ≤ Qhi, t ≤ Qhi, t
max
ii) the desired volume of water to be discharged by each reservoir over the scheduling
period,
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Vhi, t t=0 = Vh, i
begin
Vhi, t t=T = Vh, i
end
iii) the continuity equation for the hydro reservoir network,
Vh (i, t) = Vh (i, t-l )+Ih (i, t)-Qh (i, t)+ ∑ [Qh( m,t-τ(i,m ))+Sh( m,t-τ(i,m)) ]
Hydro plant power generation characteristics The power generated from a hydro plant is related to the reservoir characteristics as well as the
water discharge rate. In general, the hydro generator power output is a function of the net hydraulic
head, H, reservoir volume, V, and the rate of water discharge, Q,
Phi, t = f (Q hi, t, Vhi , t) and Vhi , t = f (Hi, t)
Phi, t = [αi, 0 + αi, 1 Hi + αi, 2 Hi2] [βi, 0 + βi, 1Qi + βi, 2Qi
2]
Where αi and βi are constants, representing reservoir and turbine characteristics. The model can
also be written in terms of reservoir volume instead of using the reservoir net head,
Phi, t = C1, i Vhi, t2 + C2, i Q hi, t
2 + C 3, i (Vhi , t) (Q hi, t) + C 4, i Vhi , t + C 5, i Q hi , t + C 6, i
Thermal cost function In setting the generation levels of the thermal plants, a quadratic cost function is frequently used
to model the fuel input / power output characteristic of thermal units;
Fi (Psi, t) = αi + βi Psi, t + γ Psi, t2
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2.5 REVIEW OF HYDROTHERMAL COORDINATION OPTIMIZATION
METHODS The hydrothermal coordination problem is an optimization problem requiring an optimization
technique for its analysis. There are various optimization techniques which can be grouped as
follows:
1. Classical Techniques:
a) Dynamic programming
b) Langragrian relaxation method
c) Quadratic programming method
d) Benders decomposition method
e) Interior point method
2. Heuristic(Artificial intelligence Techniques):
f) Simulated annealing
g) Particle Swarm algorithm
h) Genetic algorithm
i) Tabu search
j) Artificial Neural Networks
k) Fuzzy logic method
l) Ant-Colony method
3. Hybrid techniques.
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2.51 Classical Techniques
Dynamic programming [8]Dynamic programming is a method for solving complex problems by breaking them down into
simple sub problems. This method will examine all possible ways to solve the problem and pick
the best solution. Therefore we can roughly think of dynamic programming as an intelligent brute
force method that enables us to go through all possible solutions to pick the best one. Dynamic
programming has the potential of solving large dynamic planning methods but suffers from the
curse of dimensionality due to the necessity of discretizing the state space of the problem.
Langragrian Relaxation method [8]It is a relaxation method which approximates a difficult problem of constrained optimization to
a simpler problem. A solution to the relaxed problem is an approximate solution to the original
problem and provides useful information. The method penalizes violations of inequality
constraints using a Lagrange multiplier which imposes a cost on violations. These added costs are
used instead of the strict inequality constraints in the optimization. The problem of maximizing
the lagrangian function of the dual variables is the dual problem.
Quadratic Programming method SQP (sequential quadratic programming) is an iterative method for nonlinear optimization. SQP
methods are used on problems for which the objective function and the constraints are twice
continuous differentiable. These methods solve a sequence of optimization sub problems, each of
which optimizes a quadratic model of the objective subject to a linearization of the constraints. If
the problem is unconstrained, then the method reduces to Newton’s Method of finding a point
where the gradient of the objective vanishes. If the problem has only equality constraints, then the
method is equivalent to applying Newton’s Method to the first order of optimality condition, or a
Karush-Kuhn-Tucker conditions of the problem.
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Benders Decomposition method This is a solution method for solving certain large scale optimization problems. Instead of
considering all decision variables and constraints of a large scale problem simultaneously Bender’s
decomposition partitions the problem into multiple smaller problems. Since computational
difficulty of optimization problems increase significantly with number of variables and constraints
solving this smaller problems iteratively can be more efficient than solving a single large problem.
[18]
Interior point method It is also referred to as barrier method. It is a certain class of algorithms to solve linear and
nonlinear convex optimization problems. [18] The interior point method was invented by John
Von Neumann. Contrary to the simplex method, it reaches an optimal solution by traversing the
interior of the feasible region. Any convex optimization problem can be transformed into
minimizing or maximizing a linear function over a convex set by converting it to the epigraph
form.
2.52 Heuristic Techniques
Simulated Annealing [9]This is a generic probabilistic metaheuristic for the global optimization problem of locating a
good approximation to the global optimum of a given function in a large search space. The name
and inspiration come from annealing in metallurgy, a technique involving heating and controlled
cooling of a material to increase the size of its crystals and reduce their defects. Both are attributes
of the material that depend on its thermodynamic free energy. Heating and cooling the material
affects both the temperature and the thermodynamic free energy. While the same amount of
cooling brings the same amount of decrease in temperature it will bring a bigger or smaller
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decrease in the thermodynamic free energy depending on rate that it occurs with a slow rate
producing a bigger decrease.
Particle Swarm Optimization [10]PSO is a computational method that optimizes a problem by iteratively trying to improve a
candidate solution with regard to a given measure of solution. PSO optimizes a problem by having
a population of candidate solutions (particles) and moving these particles around in the search
space according to simple mathematic formulae over the particle’s position and velocity. Each
movement is influenced by its local best known position but, it is also guided towards the best
known positions in the search space, which are updated as better positions are found by other
particles. This is expected to move the swarm toward the best solution. PSO is a metaheuristic as
it makes few or no assumptions about the problem being optimized and can search very large
spaces of candidate solutions. However, metaheuristic such as PSO do not guarantee an optimal
solution is ever found. More specifically, PSO does not use the gradient algorithm of the problem
being optimized, which means PSO does not require that the optimization problem be
differentiable as is required by classic optimization methods such as gradient descent and quasi-
newton methods. PSO can therefore also be used on optimization problems that are partially
irregular noisy, change over time.
Genetic Algorithms [9,10]GA is a search heuristic that mimics the process of natural selection. This heuristic is used
to generate useful solutions to optimization and search problems. GA belongs to a large class of
evolutionary algorithms which generate solutions to optimization problems using techniques
inspired by natural evolution, such as inheritance, mutation, selection and crossover. In GA, a
population of candidate solutions (called individuals, creatures or phenotypes) to an optimization
problem is evolved towards better solutions. Each candidate solution has a set of properties (its
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chromosomes or genotype) which can be mutated and altered; traditionally, solutions are
represented in binary as strings of 0s and 1s, but other encodings are also possible.
The evolution usually starts from a population of a randomly generated individuals, and is an
iterative process with the population in each iteration called a generation. In each generation, the
fitness of every individual in the population is the evaluated; the fitness is usually the value of the
objective function in the optimization problem being solved. The more fit individual are
stochastically selected from the current population, and each individual’s genome is modified
(recombined and possibly randomly mutated) to form a new generation. The new generation of
candidate solutions is then used in the next iteration of the algorithm. Commonly, the algorithm
terminates when either a maximum number of generation has been produced, or a satisfactory
fitness level has been reached for the population.
Tabu Search Algorithm [9]This is a metaheuristic search method employing local search methods used for mathematical
optimization. Local (neighborhood) searches take a potential solution to a problem and check its
immediate neighbors (that is solutions that are similar except one or two minor details) in the hope
of finding an improved solution. Local search methods have a tendency to become stuck in sub-
optimal regions or on plateaus where many solutions are equally fit. Tabu search enhances the
performance of these techniques by using memory, structures that describe the visited solutions or
user-provided set of rules. If a potential solution has been previously visited within a certain short
term period or if it has violated a rule, it is marked as tabu (forbidden) so that the algorithm does
not consider that possibility repeatedly.
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Artificial Neural Networks [9, 10]ANNs are computational models inspired by human’s central nervous system (in particular
the brain) that are capable of machine learning and pattern recognition. They are usually presented
as systems of interconnected neurons that can compute values from inputs by feeding information
through the network. In ANN, simple artificial nodes called neurons neurodes processing elements
or units are connected together to form a network which mimics a biological neural network. It
consists of a set of adaptive weights i.e. numerical parameters that are trained by a learning
algorithm and are capable of approximating non-linear functions of their inputs. The adaptive
weights are conceptually connection strengths between neurons, which are activated during
training and prediction.
Ant Colony Optimization Method [10]ACO algorithm is a probabilistic technique for solving computational methods which can be
reduced to finding good paths through graphs. In the natural world, ants (initially) wander
randomly, and upon finding food return to their colony while laying down phenomena trails. If
other ants find such a path, they are likely not to keep travelling at random, but to instead follow
the trail, returning and reinforcing if they eventually find food. When one ant finds a good (short)
path from the colony to a food source, other ants are more likely to follow that path, and positive
feedback eventually leads to all ants following a single path.
2.53 Hybrid Techniques [10]Hybrid approaches are used to solve many difficult engineering problems. The aim of hybrid
methods is to improve the performance of single approaches. The objective is to speed up the
convergence and to get better quality of solution compared with single approaches. Hybrid
algorithms can be grouped into three:
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Stand-alone algorithms
Weak-integration algorithms
Fused algorithms
The main difference between them comes from the number of information exchanges that happen
during the problem solution.
Stand-alone algorithms There is no information exchange between the systems. They operate in a parallel and competitive
way. This system allows comparing results obtained by the techniques regarding both the result
quality and the processing time. An example of this would be the use of genetic algorithms for the
optimization of load-dispatch of a set of hydrothermal power-stations versus a dispatch based on
numerical techniques of optimization driven by a fuzzy system
Weak-integration algorithms In this type of integration, the information exchange happens whether in sequence or in hierarchic
form. In the first case the first techniques provides one result that works as input data for the second
technique to continue the processing of the problem solution. This is the very much used
integration type. A characteristic of this integration type is the information exchange through data
basis, which reduces the total processing speed of the system solution and makes it use unfeasible
for frame where the information exchange is very high.
Fused algorithms They are also called strongly integrated systems. The information exchange between the systems
happens in a very intensive way. Therefore for the system to have a processing time adequate to
user requirements, two integration forms may exist. When this system type uses a hierarchic
system, the information is not exchanged only between the upper level technique and the low level
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technique but also between them. Thus other decision levels may be setup and the information
exchanged between the several techniques.
Examples of hybrid techniques are:
a) Genetic-Tabu algorithm
b) Dynamic-Neural Networks Programming
c) Genetic-Particle swarm optimization
d) Fuzzy logic-Particle swarm optimization
e) Neural-Tabu method
f) Benders-Genetic-Fuzzy programming
g) Hybrid Particle Swarm Optimization
h) Tabu search based Hybrid Particle Swarm method
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2.6 SURVEY OF WORK PREVIOUSLY DONE A method based on the Lagrangian relaxation was presented by Yan et al. in Ref. [11] where the
HTC problem was decomposed into two sub-problems. A method of merit order allocation was
implemented to solve the hydro sub-problem while the thermal sub-problem was solved by
applying a dynamic programming approach. The method was tested using limited water resources
hydro units. The hydraulic coupling among these water resources and the upper and lower
constraints were not considered. The hydro sub-problem was formulated as a linear programming
problem without accounting for the non-linear characteristics. The non-linearity that could be
caused by the startup cost function for the thermal units was not taken into consideration.
A peak-shaving method was presented in [12] to study the influence of the interchange resource
scheduling on the HTC problem. The interchange was formulated as a decomposed sub-problem
with a proposed scheduling strategy to provide a smoother hydro generation profile. The
methodology was claimed to be suitable for practical systems although it was only applied to two
test systems. Results showed that the method was beneficial especially for the systems that could
be augmented by interchange purchases. In [13] a network flow programming based algorithm was
presented to solve the HTC problem of dominantly hydro systems. The hydraulic subsystem was
simulated while the transmission system was modeled as an optimal DC load flow. The
performance of the approach was found efficient when applied to two synthetic test systems. The
tests were performed using amateur codes that made the time of convergence an issue of a concern.
Augmented Lagrangian relaxation is also another decomposition-based method that was presented
in a number of papers such as [14]. In this paper, the augmented Lagrangian decomposition and
coordination technique was applied to the HTC problem instead of the standard Lagrangian
relaxation approach. Reducing the oscillation of the solutions to the sub problems in the standard
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Lagrangian relaxation technique was an objective of the augmented Lagrangian approach. By
applying this method, the linearity and piecewise linearity of the cost functions of the sub-problems
was avoided and hence the oscillation was reduced. Compared to the standard Lagrangian
relaxation, the augmented Lagrangian approach required less computational time with better
convergence characteristics although, oscillation was not eliminated. This lead to a smooth
movement of the solutions to the sub-problems with a slight change of the multipliers. The
approach was tested using a practical system consisting of thermal, hydro and pumped-storage
units with many practical constrains were considered. It should be pointed out that the selection of
the penalty coefficient was not easy, as it could be not fitting for all different units. The oscillations
of the solutions to the sub-problems in the Lagrangian relaxation technique as well as the
singularity of these solutions were also discussed in [15]. In this paper, a non-linear approximation
method was presented. Quadratic non-linear functions were used to approximate linear cost
functions. The algorithm was tested and applied to a practical system and the results demonstrated
its efficiency although compared to the standard Lagrangian relaxation method, no difference in
the computational time was reported.
In [16], a mixed-integer model for hydroelectric systems short term planning was presented. This
model was designed to avoid the problems caused by non-linearity and non-convexity by
considering only the points with good degree of efficiency. The problem was decomposed into
sub-problems with relaxed coupling constraints. The model was tested practically using a power
system consisting of nuclear and hydro generation units with some assumptions were applied and
some constraints were not considered for the sake of simplicity.
Yang and Chen presented a special form of dynamic programming techniques in [17] to solve the
STHTC problem. To improve the performance of dynamic programming and overcome its
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disadvantages, those are the high computational time and large memory storage, a multi-pass
dynamic programming technique was implemented. The algorithm was tested using real data
obtained from a realistic power system containing thermal and hydro units however, some
constraints were not considered. Although the cases tested in this paper did convert to reasonable
solutions, but there was no indication that global optimal solutions were guaranteed. In fact, the
solutions that were reached might be local, especially when we keep in mind that the used
algorithm was an iterative-based process. In [18], a priority-list-based dynamic programming was
used to solve the hydro unit commitment as a part of the HTC problem to reduce the dimension of
the problem. A successive approximation method was employed to obtain better convergence
properties when applied to realistic test systems.
One of the earliest applications of GA to solve the HTC problem was presented in [18]. In this
work, a GA-based method was applied to the 24 h ahead generation scheduling of hydraulically
coupled units. The GA was used to solve the hydro sub-problem considering the water balance as
well as the effects of net head and water travel time delays. A realistic system was employed to
test the method and compare its performance to a dynamic programming approach. Results showed
the good performance with good solution quality and robustness of GA especially for avoiding
local minima as it was theoretically stated. In Ref. [18], a real GA and a binary coded GA method
were applied to solve the HTC problem and compared from a computational efficiency point of
view. The two algorithms solved the problem assuming that the unit commitment was already
solved but the economic dispatch was considered in the problem formulation. Two test cases for
each algorithm were run, in the first, the valve-point loading effects were considered while they
were not in the second. Results supported the superiority of the real coded GA as it showed better
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performance than the binary coded GA; however, the two algorithms were not compared to other
applied methods.
Wong and Wong in their paper [18] presented a sequential SA algorithm to solve the HTC problem
considering various hydro and thermal constraints although some other constraints such as ramp
rates were not included. To evaluate the algorithm it was applied to a test example, however, it
was a small size system consisted of equivalent thermal and hydro-plants without including any
pumped-storage units. Results demonstrated the advantages of the SA techniques such as
simplicity and capability to handle complex objective functions in addition to the insensitivity to
the starting schedule. On the other hand, the well-known drawback of SA, which was the high
computational time required, obviously came into sight. To treat this weakness and improve the
speed of execution, the authors developed another SA algorithm, which was described as a coarse
grained parallel SA algorithm, and presented it in another paper [18]. The same testing system was
employed to apply the developed parallel algorithm and compare it to the previous sequential one.
The parallel SA algorithm showed considerable difference in computational time besides slight
improvement in its performance compared to the sequential SA algorithm. In [18], SA was
implemented to solve the thermal sub-problem while the hydro sub-problem was solved using a
peak-shaving method in order to find the optimal short-term scheduling for hydrothermal power
systems. The proposed method was tested using a modified version of a realistic power system
and was considered robust with good performance and reasonable conversion time although it was
not compared to other optimization approaches.
Umayal and Kamaraj in [18], presented a PSO application to find the short-term optimal generation
schedule as a multi-objective optimization problem. In [18], different PSO versions were
presented, applied to solve HTC problem and compared to each other. According to this reference,
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there were four versions of PSO based on the size of the neighborhood and the formulation of
velocity updating. The algorithms were applied to a test system consisting of a number of hydro
units and an equivalent thermal unit while no pumped-storage units were included.
Naresh and Sharma [18] proposed a two-phase neural network-based method to find the optimal
short-term schedule for hydrothermal systems. In this implementation, the neural network seemed
to be a feed-forward network although its structure was not indicated. The states of the analogue
neurons were employed as scheduled discharge for the hydro units. Several hydro and thermal
constraints taken into consideration including water transportation delay between cascaded
reservoirs and transmission losses although some others were not accounted for such as ramp rates.
The method was applied using a test example consisting of multi-chain cascaded hydro units and
an equivalent thermal unit while no pumped-storage units were included.
J.S.Dhillon, S.C.Parti, D.P.Kothari [18] presented a fuzzy decision-making approach to find the
optimal short-term schedule for fixed-head hydrothermal systems considering a multi-objective
problem. In the formulation for the objective function, not only the cost was to be optimized but
also the gaseous emission should be minimized in order to meet the environmental regulations.
Palacio et al. in [18] proposed a primal-dual IP method to solve the HTC problem and studied the
influence of the bilateral contracts and spot market on the optimal coordination. Transmission
losses of each power transaction were calculated and the effects of the loading order on the
transmission losses allocated to the pool and bilateral loads were studied. To validate the results,
two test systems were used; a 6-bus system and a 27-bus system that was assumed equivalent to a
specific real system.
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3.0 CHAPTER 3
3.1 INTRODUCTION TO TABU SEARCH The word tabu comes from taboo which means a prohibition imposed by a social custom as a
protective measure or of something banned as constituting a risk. The overall approach is to avoid
entrapment in cycles by forbidding or penalizing moves which take the solution in the next
iteration, to points in the solution space previously visited. Tabu search proceeds according to the
supposition that there is no point in accepting a new solution unless it is to avoid a path already
investigated. This ensures new regions of a problem solution space will be investigated in with the
goal of avoiding local minima and ultimately finding the desired solution (global minima). The
role of the memory can change as the algorithm proceeds. At initialization the goal is to make a
coarse examination of the solution space, known as diversification. As candidate locations are
identified the search is more focused to produce local optimal solutions in a process of
intensification.[19,20]
Tabu search has two prominent features [20]:
Adaptive memory
Responsive exploration strategies
3.2 ELEMENTS OF TABU SEARCH 1. Space search procedure and Neighborhood structure
2. Tabu list and tabu conditions
3. Tabu tenure
4. Candidate lists
5. Aspiration criteria
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6. Intensification and diversification
7. Long term memory
8. Stopping memory or termination criterion [19, 23, 24]
3.21 Tabu list and tabu conditions Tabu list maintains a list of solution points that must be avoided (not allowed) or a list of more
attributes that are not allowed. The tabu list is updated based on short term memory. This avoids
cycling.
3.22 Neighborhood structure Many solution approaches are characterized by identifying a neighborhood of a given solution
which contains other so called transformed solutions that can be reached in a single iteration. The
transition from a feasible solution can be reached in a single iteration. A transition from a feasible
solution to a transformed feasible solution is referred to as a move.
3.23 Tabu tenure This is the number of iterations that the move is tabu. It can be divided into two: static tabu tenure
and dynamic tabu tenure.
3.24 Candidate lists It is the set of all possible moves at each iteration (generations).
3.25 Aspiration Criterion Aspiration criteria are introduced in tabu search to determine when tabu activation rules can be
overridden, thus removing a tabu classification otherwise applied to a move. The appropriate move
of such a criteria can be very important for enabling a tabu search method to achieve its best
performance levels. [19]
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Aspiration by default: if all available moves are classified tabu, and are not rendered admissible
by some other aspiration criteria, then a least tabu move is selected.
Aspiration by objective: Global-a move aspiration is satisfied if the move yields a solution better
than the best obtained so far: Regional-a move aspiration is satisfied if the move yields a solution
better than the best found in the region where the solution lies.
Aspiration by search direction: An attribute can be added and dropped from a solution (regardless
of its tabu status), if the direction of the search (improving or non-improving) has not changed.
Aspiration by influence: the tabu status of a low influence may be revoked if a high influence move
has been performed since establishing the tabu status for the low influence move.
3.26 Intensification and Diversification Intensification strategies are based on modifying choice rules to encourage more combinations and
solution features historically found good. They may also initiate a return to attractive regions to
search them more thoroughly. The diversification strategies on the other hand encourage the search
process to examine unvisited regions and to generate solutions that differ in various significant
ways from those seen before. Since elite solutions must be recorded in order to examine their
immediate neighborhoods, explicit memory is closely related to the implementation of
intensification strategies. Here the term “neighbors” has a broader meaning than in the usual
context of “neighborhood search.” That is, in addition to considering solutions that are adjacent or
close to elite solutions by means of standard move mechanisms, intensification strategies generate
“neighbors” by either grafting together components of good solution or by using modified
evaluation strategies that favor the introduction of such components into a current (evolving)
solution. The diversification stage on the other hand encourages the search process to examine
unvisited regions and to generate solutions that differ in various significant ways from those seen
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before. Again, such an approach can be based on generating subassemblies of solution components
that are then “fleshed out” to produce full solutions, or can rely on modified evaluations as
embodied, for example, in the use of penalty / incentive functions. Intensification strategies require
a means for identifying a set of elite solutions as basis for incorporating good attributes into newly
created solutions. Membership in the elite set is often determined by setting a threshold which is
connected to the objective function value of the best solution found during the search. However,
considerations of clustering and “anti-clustering” are also relevant for generating such a set, and
more particularly for generating subsets of solutions that may be used for specific phases of
intensification and diversification. In the following sections, we show how the treatment of such
concerns can be enhanced by making use of special memory structures. The TS notions of
intensification and diversification are beginning to find their way into other meta-heuristics. It is
important to keep in mind that these ideas are somewhat different than the old control theory
concepts of “exploitation” and “exploration,” especially in their implications for developing
effective problem solving strategies. The main difference between intensification and
diversification is that during an intensification stage the search focuses on examining neighbors of
elite solutions. [21,23]
3.27 Stopping or termination criterion These are the conditions under which the search process will terminate. It can terminate if the
number of iterations since the last change of the best solution is greater than a pre specified number
or if the number of iterations reaches a maximum allowable number.
3.28 Long term memory The most common way to incorporate long term memory into the tabu search is to make moves
that have occurred frequently less attractive. Thus a penalty is added based on the frequency that
a move has occurred.
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3.3 ADVANTAGES OF TABU SEARCH 1. Simple and open to the user in that it is not restricted to strict rules formulas.
2. It is deterministic rather than random in that the user is well aware of the neighborhood
being searched. A determined strategic choice can yield better information than a random
choice.
3. TS has short term memory component which SA and GA does not have. The use of
memory is advantageous because:
Use of memory leads to learning (long-term frequency)
Prevents the search from repeating moves.
Explores the unvisited area of the solution space.
3.4 DISADVANTAGES OF TABU SEARCH 1. It is very much dependent on the initial solution. It must be a near optimal solution, if not
the solution will diverge.
2. Tabu search is very sensitive to change in the search parameters.
There are various tabu variations [22] depending on the application being considered and the
elements (above) being used in optimization:
Simple tabu search
Adaptive tabu search
Parallel tabu search
Embedded tabu search
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3.5 IMPLEMENTATION OF SIMPLE TABU SEARCH IN HTC PROBLEM
3.51 Initial solution For simple tabu search to work effectively, the initial solution must be a near optimal solution. It
must be a feasible solution which satisfies the constraints of the optimization problem. The initial
solution is first guessed and improved on to get a near optimal solution. The problem of generating
an initial solution becomes more complicated because of the required water levels at the beginning
and end of the scheduling period. Without a near optimal solution, the solution will diverge instead
of converging. The initial solution is shown in the appendix.
3.52 Search space The search space in the hydrothermal coordination problem is discharge. From the discharge
values, the volumes and powers of different plants are calculated. The limits of discharge, volume
and power have to be obeyed.
3.53 Neighborhood structure and candidate generations The neighbor solutions (candidate solutions) of discharge can be generated by three directional
methods in simple tabu search.
Forward generation
Backward generation
Forward-backward generation
In forward generation (backward generation), simple tabu search searches in a forward direction
(backward generation) with a certain generation sensitivity. The forward generation (backward
generation) sensitivity can be determined by the maximum percentage error obtained from the
violation of required water levels at the start and end of scheduling period.
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In forward-backward generation, both the forward and backward methods are combined to form a
metric of distance referred to as radius of neighborhood. Simple tabu search gets the best neighbor
from the two.
The total number of neighborhood generations (candidate solutions) depend on the types of
generations (discussed above) used.
3.54 No of iterations and stopping criterion This is the number of steps that the whole process repeats itself so that it converges to an optimal
point. The number of steps in our problem is determined from the generation sensitivities of the
various types of generation and the percentage error obtained from the violations of the required
water levels at the beginning and end of the scheduling period. Each type of generation has its
specified number of iterations.
3.55 Tabu conditions These are the conditions that make a move tabu. A move is considered tabu if it violates the above
inequality constraints (limits of variables)
Discharge limits
Volume limits
Power limits
Required water volumes
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3.6 ALGORITHM FOR THE HTC PROBLEM USING TS
Step 1 Data involved in the hydrothermal coordination problem is to be initialized in Matlab. The data
involved include reservoir limits, discharge limits, hydropower generation coefficients, water
inflows, hourly demand, power generation limits and thermal generator coefficients.
Step 2 The initial solution is generated by trial and error method. In our case since the search space is
discharge then the initial values of discharge are written into Matlab.
Step 3 The reservoir volumes are calculated from the initial discharge solution. The procedure for
calculation of volume for reservoir 1 and 2 are the same but reservoir 3 and 4 are different because
of the fact that downstream reservoirs depend on the upstream reservoirs.
Step 4 Power is calculated from the discharge and volume values. The values obtained are recorded as
the best initial solution.
Step 5 Initial cost of using an equivalent thermal generating unit is calculated.
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Step 6 Candidate solutions are generated from the initial solution (discharge-search space) within a
certain sensitivity (forward and backward generation) or a certain radius (forward-backward
generation).
Step 7 Step 3, 4 and 5 are repeated for the new values of discharge.
Step 8 If the discharge, volume and power values do not obey the equality constraints then the initial
values of discharge remain the same. If the values are better than the initial values then the
discharge, volume and power values are replaced by the new best values.
Step 9 Steps 6, 3, 4, 5 are repeated in that order until the number of generations and iterations reach
maximum value dictated by the simple tabu search method.
Step 10 Stop
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3.7 FLOWCHART
Start
Input of project parameters, Q initialization
Pinit, Vint calculation
Initial cost calculation
Neighborhood
generation of discharge
Is it tabu?
Neighborhood evaluation
P, V calculation
Is it tabu?
Is Pneigh
>Pinitial
Pinit=Pbest
Vinit=Vbest
Qinit=Qbest
Stop
Is S.T
met?
Qnew=Qinit
Vnew calculated
Pnew calculated
Is S.T
met?
Qnew=Qinitial
Vnew calculated
Pnew calculated
Is S.T.
met?
Qnew=Qinit
Vnew calculated
Pnew calculated
FIGURE 3. 1 (FLOWCHART OF SHTC USING TABU SEARCH)
YES
NO
YES NO
NO NO
YES
YES
NO
NO
YES YES
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4.0 CHAPTER 4
4.1 CASE STUDY To verify the feasibility and effectiveness of TS algorithm, the IEEE hydrothermal system
consisting of 4 hydro plants and a composite thermal generator are used. The effects of time delay
between the power plants are included in the data analysis and code generation. An assumption
has been made that there is no spillage in the plant reservoirs. The optimization program has been
written in MATLAB 2013.
FIGURE 3. 2 (IEEE BLOCK DIAGRAM OF HYDRO TEST SYSTEM)
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DEMAND TABLE (MW)
HOUR LOAD HOUR LOAD HOUR LOAD
1 1370 9 2240 17 2130
2 1390 10 2320 18 2140
3 1360 11 2230 19 2240
4 1290 12 2310 20 2280
5 1290 13 2230 21 2240
6 1410 14 2200 22 2120
7 1650 15 2130 23 1850
8 2000 16 2070 24 1590
TABLE 4.1: DEMAND TABLE 1
HYDROGENERATION COEFFECIENTS
PLANT C1 C2 C3 C4 C5 C6
1 -0.0042 -0.42 0.030 0.90 10.0 -50
2 -0.0040 -0.30 0.015 1.14 9.5 -70
3 -0.0016 -0.30 0.014 0.55 5.5 -40
4 -0.0030 -0.31 0.027 1.44 14.0 -90
TABLE 4.2: HYDROGENERATION COEFFECIENTS 1
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HOURLY INFLOWS (×104 m3/hr)
PLANT
HOUR
1 2 3 4 PLANT
HOUR
1 2 3 4
1 10 8 8.1 2.8 13 11 8 4 0
2 9 8 8.2 2.4 14 12 9 3 0
3 8 9 4 1.6 15 11 9 3 0
4 7 9 2 0 16 10 8 2 0
5 6 8 3 0 17 9 7 2 0
6 7 7 4 0 18 8 6 2 0
7 8 6 3 0 19 7 7 1 0
8 9 7 2 0 20 6 8 1 0
9 10 8 1 0 21 7 9 2 0
10 11 9 1 0 22 8 9 2 0
11 12 9 1 0 23 9 8 1 0
12 10 8 2 0 24 10 8 0 0
TABLE 4.3: HOURLY RESERVOIR INFLOWS 1
POWER PLANT LIMITS
PLANT VMIN VMAX VINI VEND QMIN QMAX PMIN PMAX
1 80 150 100 120 5 15 0 500
2 60 120 80 70 6 15 0 500
3 100 240 170 170 10 30 0 500
4 70 160 120 140 13 25 0 500
TABLE 4.4: LIMITS OF THE HYDRO NETWORK 1
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4.2 RESULTS AND ANALYSIS The best tabu parameters of the HTC were determined by calculation of the mean percentage error
of violating the required water volumes at the beginning and end of the scheduling period.
Different types of sensitivities were evaluated for each type of generation.
ERROR DETERMINATION (FORWARD-BACKWARD) (SENSITIVITY-0.0001)
ITERATIONS MEAN % ERROR CPU TIME (sec) THERMAL COST
(×105 dollars)
5 1.8911 29 9.3278
10 3.76165 59 9.3141
15 5.5233 104 9.3045
20 7.131 132 9.2980
25 8.6572 169 9.2942
TABLE 4.5: ERROR DETERMINATION 1.1 (FORWARD-BACKWARD-0.0001)
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ERROR DETERMINATION (FORWARD-BACKWARD) (SENSITIVITY-0.00001)
ITERATIONS MEAN % ERROR CPU TIME (sec) THERMAL COST
(×105 dollars)
5 0.1911 32 9.3435
10 0.3811 66 9.3416
15 0.5695 97 9.3398
20 0.758 145 9.3379
60 2.2714 378 9.3247
100 3.7613 719.366 9.3141
200 7.1305 1439.206 9.2980
TABLE 4.6: ERROR DETERMINATION 1.2 (FORWARD-BACKWARD-0.00001)
ERROR DETERMINATION (BACKWARD) (SENSITIVITY-0.0001)
ITERATIONS MEAN % ERROR CPU TIME (sec) THERMAL COST
(×105 dollars)
5 0.0868 19 9.3399
10 0.1711 40 9.3357
20 0.3331 77 9.3306
35 0.56 148 9.3294
TABLE 4.7: ERROR DETERMINATION 1.3 (BACKWARD SENSITIVITY-0.0001)
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ERROR DETERMINATION (BACKWARD) (SENSITIVITY-0.00001)
ITERATIONS MEAN % ERROR CPU TIME (sec) THERMAL COSTS
(×105 dollars)
5 0.00875 17 9.3448
20 0.034975 81 9.3431
40 0.0696 147 9.3409
100 0.1712 374 9.3357
200 0.3331 747 9.3306
350 0.5599 1468 9.3294
TABLE 4.8: ERROR DETERMINATION 1.4 (BACKWARD SENSITIVITY-0.00001)
ERROR DETERMINATION (FORWARD) (SENSITIVITY-0.0001)
ITERATIONS MEAN % ERROR CPU TIME (sec) THERMAL COST
(×105 dollars)
5 1.4516 27 9.3423
10 2.81175 53 9.3415
11 3.1010 54 9.3414
TABLE 4.9: ERROR DETERMINATION 1.5 (FORWARD SENSITIVITY-0.0001)
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ERROR DETERMINATION (FORWARD) (SENSITIVITY-0.00001)
ITERATIONS MEAN % ERROR CPU TIME (sec) THERMAL COST
(×105 dollars)
5 0.1449 23 9.3450
10 0.2883 43 9.3446
20 0.57645 91 9.3440
40 1.1583 183 9.3428
80 2.277 366 9.3417
110 3.080 511 9.3415
TABLE 4.10: ERROR DETERMINATION 1.6 (FORWARD SENSITIVITY-0.00001)
TABU PARAMETERS
CANDIDATE SOLUTIONS 10
ITERATIONS (FORWARD) 110
ITERATIONS (BACKWARD) 35
ITERATIONS (COMBINED) 100
SENSITIVITY (BACKWARD) 1×10-4
INITIAL THERMAL COST (dollars) 9.3454×105
BEST COST 9.3294×105 (BACKWARD)
MEAN % ERROR 0.56
TABLE 4.11: TABU PARAMETERS 1
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FIGURE 4. 1 (MATLAB EXCEL WORKSHEET RESULTS)
FIGURE 4. 2 (CONVERGENCE CHARACTERISTICS)
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FIGURE 4. 3 (VOLUME AND DISCHARGE LEVELS)
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COMPARISON OF TOTAL THERMAL COST
OPTIMIZATION
TECHNIQUE
TOTAL
THERMAL
COST (dollars)
CPU TIME
(seconds)
MEAN % ERROR
T.S 932940 148 0.56000
H.P.0.N.N [25] 926700 258.84 2.79275
G.A [26] 936451 1200 3.41152
TABLE 4.12: COST COMPARISON 1
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IMPROVING THE SOLUTION BY CHANGING THE INITIAL SOLUTION The initial solution was changed after observing the behavior of simple tabu on the plant volumes.
The initial plant discharges of hour 24 were changed to 10, 7, 21.2, and 13.5 for plant1, plant2,
plant3 and plant4. It required 20 iterations with a sensitivity of 0.0001 to obtain the final cost of
933190 dollars from an initial cost of 935050 dollars. The percentage error in violation of volume
at the start and end of scheduling period improved to 0.07%.
FIGURE 4. 4 (MATLAB EXCEL WORKSHEET-IMPROVED RESULTS)
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FIGURE 4. 5 (CONVERGENCE CHARACTERISTICS, VOLUME AND DISCHARGE LEVELS)
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5.0 CONCLUSION AND RECOMMENDATION FOR FURTHER
WORK
5.1 CONCLUSION Tabu search has been successfully implemented to solve the HTC problem with the inclusion of
hydraulic network constraints and also considering the dynamic nature of the flow of water in the
reservoirs. From the results, it is clear that TS has the ability to find a better solution and has better
convergence characteristics, computational efficiency and less CPU processing time when
compared to GA. The tabu search optimization technique strongly depends on the initial solution
in that it must be a near optimal solution. The no of iterations are governed by the error in violation
of the required water levels at the beginning and end of the scheduling period. It should also be
noted that the convergence of TS in HTC increases with the number of iterations till a certain
minimum where it diverges from the best solution (dependent on the function being optimized).
This is because of the dynamic nature of the HTC problem. The thermal costs found with TS are
found to be less than the thermal costs found by GA and with minimal error. Numerical thermal
costs found by HPONN are found to be better than TS but with great compromise in mean
percentage error in volume violations.
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5.2 RECOMMENDATION FOR FURTHER WORK 1) Hybrid optimization can be used to solve the HTC problem by using another optimization
technique such as ANN to generate an initial solution and TS to be used to improve the
quality of the initial solution.
2) Various forms of TS (ATS, PTS and ETS) to be exploited to solve the HTC problem.
Regarding the results obtained, SHTC should be correlated with MHTC for volume at the
end of the scheduling period of plant 3 and plant 4.
3) The effect of inclusion of water spillage data in the water balance dynamic equation can be
investigated. Also, the effect of more downstream plants can also be investigated and the
relationship between the most upstream plant and most downstream plant obtained.
4) There should be more linkage between the University and Kengen so that data requested
is understandable to the organization Engineering Department. The theoretical aspects
should be correlated with the practical aspects.
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REFERENCES [1] Hossein Seifi and Mohammed Sadegh Sepasian, Electric Power Systems Planning: Issues,
Algorithm and Solutions.
[2] Al Raston, Director, Operations Planning, May 5 2010, Preliminary Technical Conference-
Work in progress.
[3] K.P. Dahal, J.R. Mcdonald and G.M. Burt, “Modern heuristic techniques for scheduling
generator mantainance in power systems,” Transactions of the institute of Measurement and
Control 22, 2 (2000) pp. 179-194.
[4] Mohammed Sadegh Jaradi, Ali Esmaeelhejad, Rahmat Azam, Amin Jaradinasab and Ghasem
Hematipour, “Generation Mantainance Scheduling considering Short term Operational
Constraints,” International Journal of Multidiscplinary Science and Engineering, Vol.2 No.8,
Nov.2011.
[5] R.F. Rajput, A Textbook of Power System Engineering; Laxmi Publications (p) Ltd 5th Edition
2011.
[6] C.L.Wadhwa, Electrical Power Systems; New Age International Publishers 6th Edition 2012.
[7] Shadrack Orero Otieno, “Power Systems Generation Scheduling and Optimization using
Evolutionary Computation Techniques; thesis,” Department of Electrical and Electronics
Engineering, Brunel University.
[8] A.J.Wood, B.F.Wollenberg, Power Generation Operation and Control, 2nd Ed.
John Wiley & Sons, Inc, New York, USA, 1996.
F17/28658/2009
59
[9] D.T. Pham and D.Karaboga, Intelligent Optimization Techniques (Genetic Algorithms, Tabu
Search, Simulated Annealing and Neural Networks), 1st Edition.
[10] Kwang Y. Lee, Mohammed A. El-Sharkawi, Modern Heuristic Optimization Techniques:
Theory and Applications to Power Systems. IEEE press, A John Wiley and Sons Publication.
[11] H. Yan Luh x. Guan, P.M.Rogan, “Scheduling of Hydrothermal Power Systems,” IEEE
Transactions on Power Systems Vol 8 1993 pp 1358-1365
[12] R.N.Wu, T.H. Lee, E.F. Hill, “Effect of interchange on short-term hydro-thermal scheduling,”
IEEE Transactions on Power Systems 6 (1991) 1217–1223.
[13] T. Ohishi, S. Soares, M.F. de Carvalho, “A short term hydrothermal scheduling approach for
dominantly hydro systems,” IEEE Transactions on Power Systems 6 (1991) 637–643.
[14] H. Yan, P.B. Luh, L. Zhang, “Scheduling of hydrothermal power systems using the
augmented Lagrangian decomposition and coordination technique,” in: American Control
Conference, 1994, vol. 2, 1994, pp. 1558–1562.
[15] Xi. Guan, P.B. Luh, L. Zhang, “Nonlinear approximation method in Lagrangian relaxation-
based algorithms for hydrothermal scheduling,” IEEE Transactions on Power Systems 10 (1995)
772–778.
[16] O. Nilsson, D. Sjelvgren, “Mixed-integer programming applied to short-term planning of a
hydro-thermal system,” IEEE Transactions on Power Systems 11 (1996) 281–286.
[17] J.-S. Yang, N. Chen, “Short term hydrothermal coordination using multipass dynamic
programming,” IEEE Transactions on Power Systems 4 (1989) 1050–1056.
F17/28658/2009
60
[18] I.A. Farhat, M.E El-Hawary, “Optimization Methods Applied for Solving the Short-Term
Hydrothermal Coordination Problem,” Electric Power System Research 79 (2009) pp. 1308-1320.
[19] Fred Glover and Manuel Laguna, Tabu Search (University of Colarado, USA). Kluwer
Academic Publishers, 1st Edition, 1997.
[20] Fred Glover, A Tutorial on Tabu search Interfaces 20, 1990 pp. 77-94.
[21] Zebo Peng, Tabu Search-Basic Principle and Algorithm, Embedded System Laboratory
(ESLAB) Linkoping University.
[22] Manuel Laguna, A Guide to implementing Tabu Search, Vol.4. No.1. April 1994.
[23] Allain Hertz, Eric Taillard, Dominique de Werra, A tutorial on Tabu Search.
[24] Hillier F.S and Lieberman G.J, 2005, Introduction to Operations Research, New York, Mc-
Graw Hill 8th Edition.
[25] V. Sharma, R. Naresh, Sushil and Deepika Yadav, “Optimal Hydro-Thermal Generation
Scheduling Using an Efficient Feedback Neural Network Optimization Model,” Research Journal
of Applied Sciences, Engineering and Technology 3(8): 770-778, 2011.
[26] S.O. Orero, M.R. Irving, “A genetic algorithm modelling framework and solution technique
for short term optimal hydrothermal scheduling,” IEEE Transactions on Power Systems 13 (1998)
501–518.
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APPENDIX A (initial discharge solution)
H
R
PLANT
1
PLANT
2
PLANT
3
PLANT
4
H
R
PLANT
1
PLANT
2
PLANT
3
PLANT
4
1 6 6 23 22 13 10 6 25 19
2 9 9 26 13 14 7 9 11 19
3 13 13 24 13 15 11 8 10 15
4 6 6 24 13 16 8 8 14 15
5 5 6 12 14 17 10 8 12 14
6 8 6 16 14 18 5 11 17 13
7 6 6 22 13 19 6 11 11 13
8 10 6 17 14 20 5 11 20 13
9 13 6 19 15 21 7 8 20 14
10 10 13 21 15 22 6 13 15 13
11 10 7 19 17 23 5 10 10 14
12 5 6 10 18 24 10 7 19.2 15
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APPENDIX B: Matlab code (forward-backward generation)
Initial1-initial volume
Initial2-initial discharge
Initial3-neighborhood discharge
Initial4-neighborhood discharge
Initial5-neighborhood volume
Initial6-neighborhood volume
Power-initial power
Power1-neighborhood power
Power2-neighborhood power
Table3-inflows
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APPENDIX C Matlab code (forward/backward generation)
Initial1-initial volume
Initial2-initial discharge
Initial3-neighborhood volume
Initial4-neighborhood disharge
Power-initial power
Power1-neighborhood power
Table3-inflows
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