2. Combustion of fossil fuel
• Upon their complete combustion, the carbon in the fuel is oxidized to
carbon dioxide and the hydrogen to water vapor. The energy made
available in this oxidation is the net amount released when the
carbon and hydrogen atoms are separated from each other and
subsequently combined with oxygen to form carbon dioxide and
water.
• Denoting a hydrocarbon fuel molecule as CnHm, where n and m
denote the number of carbon and hydrogen atoms in a fuel
molecule, the molecular rearrangement accompanying complete
oxidation of the carbon and hydrogen may be represented by the
reaction
2
3. • For each hydrocarbon molecule, n + m/4 diatomic oxygen
molecules are required to convert the carbon and hydrogen
to n molecules of CO2 and m/2 molecules of H2O.
• The ratio of the number of oxygen molecules to the number
of fuel molecules, n + m/4, is called the stoichiometric ratio.
• It may be expressed alternatively as a mass ratio by
multiplying the number of molecules by their molecular
masses, yielding
3
4. Electrical energy generation, transmission, and storage
• The generation and transmission of electric power is a necessary component of
the energy supply of modern nations. Most such power is generated in thermal
plants burning fossil or nuclear fuel, or in hydropower plants. In either case,
steam, gas, or hydro turbines supply mechanical power to electric generators
that feed electric power via transmission and distribution lines to the end
consumer. The electricity generation and distribution process is very efficient,
with overall percentage losses being in the single-digit numbers.
• There is very little electric energy stored in the generation and transmission
system, so electric power must be generated at the same rate as it is consumed
if line voltages and frequencies are to be maintained. The diurnal pattern of
electricity demand requires that the electric power network be capable of
supplying the peak demand, which may be 25% or more above the average
demand. Pumped hydroelectric plants are used to store energy that may be used
to supply daily peak electric power demand.
• Electric energy may be stored for various purposes in storage
batteries,
capacitors, and inductors, but the only significant amount of energy storage of
these types is that of lead-acid batteries in motor vehicles. Cost and weight of
storage batteries has limited their use for primary power in vehicles.
4
5. Energy resources
• Energy is a necessary and significant factor of national economies; energy
expenditures amount to 5–10% of the GDP in industrialized nations. The
availability of adequate energy to enterprises and individuals is a national goal
and is thereby affected by governmental policies.
• Among fossil energy resources, coal appears to be available in abundance for
at least two to three centuries, while the fluid fossil fuels, petroleum and
natural gas, may last for less than a century. The availability of fluid fuel
resources can be extended by manufacturing them from coal by coal gasification
and liquefaction. (The manufactured fluid fuels are called synfuels.) Fluid fuels
can also be obtained from unconventional resources, such as oil shale, tar
sands, geopressurized methane, coal seam methane, and methane hydrates
lying on the bottom of the oceans and under the icecaps.
• The manufacture of synfuels and the exploitation of unconventional fossil fuel
resourceswill be more expensive than the
exploitation of proven reserves, and the manufacturing
and recovery processes will entail more severe environmental effects than those
associated with exploitation of conventional reserves.
5
6. Energy resources
• Electricity is an essential energy component of modern industrialized
societies; its use is increasing worldwide. Electricity is a secondary form of
energy; it has to be generated from primary energy sources. Presently about
two-thirds of the world’s electricity is generated from fossil fuels while the
other third comes from hydroenergy and nuclear energy, with very minor
contributions from wind, biomass, and geothermal sources.
• In 1997, about 17% of the world’s electricity and 6.3% of its energy was
supplied by nuclear power plants. The global resources of the raw material for
nuclear power plants—uranium and thorium—would last centuries, at current
usage rates. These resources can be extended even further in the so-called
breeder reactors, where artificial fissile isotopes can be generated from natural
uranium and thorium. Nuclear power plants are much more complex and
expensive to build and operate than fossil-fueled plants. Also, the real and
perceived hazards of nuclear power plants, including the risks of the entire
nuclear fuel cycle, from mining to refining to radioactive waste disposal,
militates against building new nuclear power plants in many countries. However,
with depleting fossil fuel resources and the associated environmental risks of
fossil-fueled power plants, notably global warming due to CO2 emissions, it is
likely that in the future nuclear power will again assume a substantial share of
the world’s electricity generation. 6
7. • Hydropower is a relatively clean source of electricity, but most of the high-
gradient rivers and streams that are near population centers have already been
dammed up for powering the turboelectric generators. Dammingup more rivers
is encountering increasing public resistance, because of the risk to the watershed
ecology and because it may entail massive population displacement. While
several new hydroelectric power generators are being built or planned, notably
the 18-GW hydroelectric station on the Yangtze River, hydropower is not
expected to increase its share substantially among other sources of electricity.
• Other renewable energy sources, besides hydropower, hold the promise of
occupying an increasing share among electricity generators. Renewable sources
are biomass, geothermal, wind, solar thermal and thermal electric, photovoltaic,
and ocean tidal energy. Biomass and geothermal plants are able to supply
electric power dependably on a daily and annual basis. The other sources of
renewable energy have diurnal and seasonal rhythms that do not necessarily
match the demand for electric power. Because electricity cannot be directly
stored, the renewable generators usually need to be backed up by conventional
power sources. However, when producing electricity, the renewable sources can
displace fossil fuel consumption and reduce air pollutant emissions. Renewable
electricity generators require a greater capital investment than fossil power
plants and are currently not economically competitive with these power plants.
7
8. Regulating the environmental effects of energy use
• the adverse environmental effects of energy use is a social and economic
dilemma.
• A common solution to this social and economic dilemma is government
regulation of pollutant producing activities. Most often this takes the form of
a performance requirement, such as a standard of maximum emissions per
fuel input from energy using sources, or a requirement that certain pollution
reduction technologies be employed. Less often, economic incentives to
abatement are used, such as emission taxes, pollutant fines, or tax
deductions and credits. Except for the case of deductions and credits, the
cost of abatement is borne by the polluter, thereby internalizing the
externality of pollution into the production process.
• In almost all cases of pollution of air, water, or soil, the amounts of toxic
pollutants emitted are only a tiny fraction of the fuel burned or material
processed. In general, the cost of reducing ordinary pollutant emissions is
only a small fraction of the economic value added to the production process,
but the cost per unit of pollution removed is often very high, inevitably
higher than any possible economic use of the sequestered pollutant. It is
exceedingly rare that any pollutant-producing process pays for itself.
8
9. • Surprisingly, increasing the efficiency of energy use plays no direct
role in environmental regulation of urban and regional pollutants
because the degree of abatement needed is very much greater
than can be garnered by the modest energy efficiency gains that
are economical, while the cost of the requisite abatement
technology is moderate.
• Nevertheless, there is some environmental benefit that accrues to
energy efficiency improvement. Reducing electric power
consumption by increasing the efficiency of its use would reduce
the air pollutant emissions from power plants, given any level of
control technology. Process modification could lead to lesser use of
fossil fuels in manufacturing of industrial goods.
• In the commercial and residential sector, fossil energy use, and
thereby pollution abatement, could be achieved by better
insulation in buildings, replacing incandescent with fluorescent
lighting, and using solar or geothermal space and water heating. In
the transportation sector, great savings could be accomplished in
fossil fuel usage and concomitant pollutant emissions by traveling
in small, light vehicles or using either (a) hybrid internal
combustion engines and electric motors for vehicle propulsion or
(b) more efficient fuel-cell-powered electric motors. 9
10. Efficiency
• In a power plant, water is heated to steam in a boiler. Steam is used to turn a
turbine,
which drives a generator.
• This can be simplified to a simple energy balance where energy in has to equal energy
out (energy wasted in the conversion + useful energy) plus energy accumulated in
box. (energy changed in form).
• Efficiency (E %) of process can be calculated as
E
Energy used
x100
Energy in
10
• Energy systems in steady state, defined as no change occurring over time. If there is no
change over time, there cannot be a continuous accumulation of energy, & the equation
mus read
[rate of energy IN] = [rate of energy OUT]
• or if some of the energy out is useful & the rest is wasted,
12. Activity: Efficiency of the power plant
12
A coal-fired power plant uses 1000 Mg (megagrams, or
1000 kg, commonly called a metric tonne) of coal per
day. The energy value of the coal is 28,000 kJ/kg
(kiloJoules/kilogram). The plant produces 2.8x 106 kWh
of electricity each day. What is the efficiency of the
power plant? (1 kWh = 3.6x106 Joule)
13. Solution
Given: coal used = 1000 Mg/day.
coal energy value = 28,000 kJ/kg
electricity produced = 2.8x 106
kWh/day. efficiency of power plant?
Energy In = Energy value * amount of coal
Energy In = (28,000 kJ/kg * 1000,000
kg/day)
= 28 * 109 kJ/day
Useful Energy Out = 2.8 * 106 kWh/day
x (3.6 x 106) J/kWh * 10-3 kJ/J
= 10.1 * 109 kJ/day
Efficiency(%) = Useful energy
out/Energy in Efficiency(%) = (10.1 * 49
= 36% 1
3
14. Thermal balance on a waste-to-energy combustor
14
• A black box is any process or operation into which certain flows
enter & others leave. If all of the flows can be correctly accounted
for, then they must balance.
• A thermal balance on a large combustion unit is difficult because
much of the heat cannot be accurately measured.
• Assume that in this facility the heat is recovered as steam.
• The heat input to this black box is from heat value in the fuel & the
heat in the water entering the water-wall pipes.
• The output is the sensible heat in the stack gases, the latent heat of
water, the heat in the ashes, the heat in the steam, & the heat lost due
to radiation.
• If the black box is thought of in dynamic terms, the balance would
be If the process is in a steady state, the first term (accumulation) is
zero, & the equation can be balanced.
17. Energy flow in a combustor
To stack = mass*temperature*specific heat of air
To steam
To vaporization =
mass*
%water*latent
heat of
vaporization
From water
To radiation =
from
combustion*%to
radiation
Rate of heat
accumulation
From fuel = mass*
%organics*heat
value of fuel
To ash = (mass inerts+unburned)*
%organics*temperature* specific heat
of ash
20. 2
0
Benefits of Multi Objective Optimization Problems
Examples:
1. Purchase of Car with minimizing the cost and Maximizing the comfort.
2. Maximizing the profit and minimizing the usage of resources in an industry.
3. Maximizing the portfolio returns and minimizing the risk in stock market.
4. Maximizing the performance and minimizing the cost.
5. In mobile networks, maximizing the coverage area and maximizing the data
rates.
6. Generator dispatch, minimizing the production cost and minimizing the
emissions.
7. In Installation distributed generators, minimization of losses and
minimization of distortions.
21. As shown in Fig. (1), multi-objective methods are divided into two sub-
groups – a posteriori methods using the scalarization approach and a
posteriori methods using the multi-objective approach, for two reasons
(Rangaia 2009).
21
22. Multi-Objective Optimization Problems (MOPs)
• Multiple, often competing objectives.
• In the case of a commensurable variable
space, can often be reduced to a single
objective function (or sequence thereof)
and solved using standard methods.
• Some problems cannot be reduced and
must be solved using pure MO
techniques.
22 2
2
23. Three General
Approaches
23
• Preemptive Optimization
• Sequential optimization of individual
objectives (in order of priority).
• Composite Objective Function
• Weighted sum of objectives.
• Purely Multi-Objective
• Population-Based.
• Pareto-Based. 2
3
24. Preemptive Optimization
Steps
24
1. Prioritize objectives according to
predefined criteria (problem-specific).
2. Optimize
function.
3. Introduc
e
highest-priority objective
new constraint based on
optimum value just obtained.
4. Repeat steps 2 & 3 for
everyother objective function, in
succession. 2
4
25. Composite Objective
Functions
25
1.Assign weights to each function
according to predefined criteria
(problem-specific)
• MAX and MIN objectives receive opposite
signs
2.Sum weighted functions to create
new composite function
3.Solve as a regular, single-objective
optimization problem 2
5
26. Transformation
Approaches
26
• Advantages:
• Easy to understand and formulate
• Simple to solve (using standard techniques)
• Disadvantages:
• A priori prioritization/weighting can end up
being arbitrary (due to insufficient
understanding of problem): oversimplification
• Not suited to certain types of MOPs
2
6
27. Pure MOPs: Population-Based Solutions
• Allow for the investigation of tradeoffs
between competing objectives.
• Genetic algorithm (Gas) are well suited
to solving MOPs in their pure, native
form.
• Such techniques are very often based
on the concept of Pareto optimality.
27 2
7
28. Pareto Optimality
28
• MOP tradeoffs between
competing objectives
• Pareto approach exploring the tradeoff
surface, yielding a set of possible
solutions
• Also known as Edgeworth-Pareto optimality
2
8
29. Pareto Optimum:
Definition
29
• A candidate is Pareto optimal if:
• It is at least as good as all other candidates for
all objectives, and
• It is better than all other candidates for at least
one objective.
• We would say that this candidate
dominates
all other candidates.
2
9
32. Activity
• Consider purchase of car with objectives of reducing cost and
minimizing emissions coming out with the exhaust
Cost
Emission Pareto front
32
33. Non-dominating front
3 is better than 1, 3 is dominating solution over
1
Compare 3 & 5 (non-dominating) 33
34. Example Dominance Test
• 1 Vs 2: 1 dominates 2
• 1 Vs 5: 5 dominates 1
• 1 Vs 4: Neither solution dominates
34
35. 35
Number of function evaluations
• In MOO, performance metrics are used to characterize the quality of
the obtained non-dominated solutions using a given
method/program, and to compare
performance of different
algorithms quantitatively.
• Some of them are used to check the convergence of the non-
dominated solutions to the known/true Pareto-optimal front (i.e.,
closeness of the two fronts) while some others are used to check the
spread of the non-dominated solutions obtained.
• Some other performance metrics can be used to evaluate both
convergence and spread of the non-dominated solutions obtained
(Sharma and Marechal 2017)
• Number of function evaluations at every iteration is 3n, where n is
the number of variables.
36. General Form of MOOP
Mathematically
min/max
fm(x), m = 1, 2,…, M
Where:
f(x) = scalar
objective
function
(1)
xn = vector of decision of M decision variables (continuous and/or
discontinuous) with lower (xj) and upper (xj) bounds, J and K.
𝑔i (𝑥) 𝑖 = 1,…, n inequality constraint functions
ℎj(𝑥) 𝑖 = 1,…,𝑚 equality constraint functions
n = the number of objective functions to be simultaneously optimized
Equation (1) is subject to set of equations (2).
gj(x), j = 1, 2,…, J
hk(x), k = 1, 2,…, K
(2a)
(2b)
(2c)
The feasible space, F is the set of vectors x that satisfy all the constraints and bounds in
Equation (2).
Constraints may be hard or soft. Hard constraints can’t be violated and may be too
restrictive. Soft constraints are used to represent such goals or targets one like to achieve .
36
37. MOO aids
• In MOO aids determining the set of values of x that yields the
best compromise solutions for all the specified objective
functions.
• A single solution that simultaneously optimizes conflicting
objectives is not feasible. Instead, a set of solutions is found with
the following characteristic: improvement of any one of the
objectives is not possible without worsening one or more of
other objectives in the optimization problem.
• These optimal solutions are referred to as the
Pareto-optimal solutions (named after Italian
economist, Vilfredo Pareto).
• They provide quantitative tradeoffs among the
objectives
Involved.
https://www.econlib.org/library/Enc/bios/Pareto.html
37
38. Dominance:
Definition
Given the vector of objective functions 1
k
→ → → →
f ( x) ( f ( x),… , f
( x))
, (i.e. ) if:
we say that candidate x
→
dominates
x
→
1 2 1
2
x
x
→
→
and
f (x
i 1 i
2
i
2
i
1
→
→
→
→
) f (x
)
i {1,…, k}: f
(x
) i {1,…, k}
) f (x
(assuming we are trying to minimize the objective functions).
(Coello Coello 2002)
22 3
8
39. 39
Dominance
•In the single-objective
optimization problem, the
superiorityof a solution
determined by comparing
over other solutions is easily
their
objective function values.
•In multi-objective optimization problem,
the goodness of a solution is
determined by the dominance.
40. Definition of Dominance
•Dominance Test
•x1 dominates x2, if
•Solution x1 is no worse than x2 in all
objectives
•Solution x1 is strictly better than x2
in at least one objective
•x1 dominates x2 x2 is dominated by
x1
40
41. Pareto Non-Dominance
41
• With a Pareto set, we speak in terms of non-
dominance.
• There can be one dominant candidate
at most.No accommodation for “ties.”
• We can have one or more candidates if we
define the set in terms of non-dominance.
4
1
42. Activity
a)Name a Pareto
set.
b)Identify the most
appropriate Pareto
front. State your
reasons.
C) sugget suitable
functions for
your selected
Pareto front
1
42
2
3
4
5
6
7
8
0
0 1 2 3 4 5 6 7
4
2
43. 43
How to Draw A Pareto Chart
https://www.youtube.com/watch?
v=mk1LvUGpvUc
4
3
44. Activity (4) min-max problem
Considering a car cost and comfort depicted in the figure and table,
outline domination.
Design Cost Comfort
A 25K 65%
B 45K 80%
3 55K 50%
4
4
46. Summary
• There are multiple approaches to MOPs.
• GAs are well suited to exploring a
multi- objective solution space.
• They provide insight into the tradeoffs
associated with MOPs, not necessarily a
particular solution.
5 4
6
47. Activity (): Pareto optimal solution
• Consider the 9 types of air tickets
with different time and cost details.
• Form the non-dominating set.
• How many non-dominating sets can
you identify?
• Identify the Pareto optimal solutions.
• Choose from them with objective
functions of minimum cost and
minimum time.
• Outline a feasible objective space.
• Comment on the data and the results.
https://www.youtube.com/watch?
v=Hm2LK4vJzRw&t=610s
47
![Efficiency
• In a power plant, water is heated to steam in a boiler. Steam is used to turn a
turbine,
which drives a generator.
• This can be simplified to a simple energy balance where energy in has to equal energy
out (energy wasted in the conversion + useful energy) plus energy accumulated in
box. (energy changed in form).
• Efficiency (E %) of process can be calculated as
E
Energy used
x100
Energy in
10
• Energy systems in steady state, defined as no change occurring over time. If there is no
change over time, there cannot be a continuous accumulation of energy, & the equation
mus read
[rate of energy IN] = [rate of energy OUT]
• or if some of the energy out is useful & the rest is wasted,](https://image.slidesharecdn.com/07b08-final-250314094744-403a869d/85/FINAL-Slides-for-the-energy-and-environment-10-320.jpg)
