The document discusses using the whale optimization algorithm to solve the multiobjective load flow problem. The multiobjective load flow problem aims to minimize generating cost, transmission losses, and power plant emissions while satisfying operational constraints. The whale optimization algorithm is inspired by humpback whales' bubble-net feeding strategy and is used to find optimal solutions to the non-linear, constrained multiobjective load flow problem. The algorithm updates potential solutions based on either the best solution found so far or a randomly selected potential solution to balance exploration and exploitation in finding optimal results.

1. MULTIOBJECTIVE LOAD FLOW
PROBLEM
WITH WHALE OPTIMIZATION
PRESENTED BY:-
ROHIT VIJAY
BE EEE
M.TECH (ICE)
(PROPOSED)

2. CONTENT
1. INTRODUCTION
2. POWER FLOW PROBLEM
3. MATHMATICAL DISCRIPTION
4. WHALE OPTIMIZATION
5. ALGORITHM OF WOA
6. REFERENCES
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3. PROBLEM :- MULTIOBJECTIVE LOAD FLOW
OBJECTIVE FUNCION
 MINIMIZING GENERATING COST
 MINIMIZING TRANSMISSION LOSS
 MINIMIZING POWER PLANT EMISSION
TECHNIQUE :-
WHALE OPTIMIZATION ALGORITHM
INTRODUCTION
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4. LOAD (POWER) FLOW PROBLEM
Optimal power flow is a static nonlinear programming
problem which optimizes a certain objective function
while satisfying a set of physical and operational
constraints imposed by equipment limitation and
security requirements.
OPF = large dimension
nonlinear
highly constrained problem
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5. The objective like minimization of cost , losses and
emission may be conflicting and thus the decision has
to be based on robust multi-objective optimization.
Optimal Power Flow problem is one of the
fundamental issues of power system operation,
designed and planning.
The main purpose of an OPF algorithm is to find
steady state operation point which minimizes
objective function, while satisfying various operating
constraints
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6. Mathematically
Min [F1(x,u), F3(x,u), e(x,u)]
Subject to: g(x,u) = 0
h (x,u) ≤ 0
Where
x =vector of dependent variables or state variables
u=vector of independent variables or control variables
F=objective function to be optimized
g=equality constraints representing nonlinear load
flow Equations
h=inequality constraints representing system
operating constraints.
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7. State Variables
• 1. Slack bus generated active power .
• 2. Load (PQ) bus voltage .
• 3. Generator reactive power output .
• 4. Transmission line loading (line flow)
Where NL,NG and NL are denote the number of load
buses, the number of generators unit and the number of
transmission lines, respectively
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8. Control Variables
1. Generator active power output except at slack bus .
2. Generator bus voltage .
3. Transformer taps setting .
4. Shunt VAR compensation .
Where NG, NT and NC are denote the number of
generators unit, the number of regulating
transformers and the number of shunt VAR
compensators, respectively.
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9. Objective function
1.Minimization of total fuel cost
Rs/hr
Rs/hr
generator
2.Minimization of total transmission losses
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10. 3.Objective of emission
The environmental pollutants such as sulphur oxides
(SOX) and nitrogen oxides (NOX) caused by fossil-fuel
units can be modelled separately. However, for
comparison purposes, the total ton/h emission e(x; u) of
these pollutants can be expressed as follows.
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11. Constraints
1. Equality Constraints
a. Real Power Constraints
b. Reactive Power Constraints
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12. 2. Inequality Constraints
a. Generator Constraints
b.Transformer Constraints
c. Security Constraints
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13. OPF problem is a highly non-linear and a multi-
modal optimization problem Hence, conventional
optimization techniques are not suitable for such a
problem and conventional optimization methods that
make use of derivatives and gradients are in general
not able to locate or identify the global optimum.
. Complex constrained optimization problems have
been solved by many evolutionary computational
optimization techniques in the recent years. These
techniques have been successfully applied to non-
convex, non-smooth and non-differentiable
optimization problems.
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14. WHALE OPTIMIZATION ALGORITHM
Whale Optimization Algorithm (WOA) is a novel
nature-inspired meta-heuristic optimization algorithm
proposed by Seyedali Mirjalili and Andrew Lewis
(2016), which mimics the social behaviour of
humpback whales.
The algorithm is inspired by the bubble-net hunting
strategy. The WOA algorithm starts with a set of
random solutions. At each iteration, search agents
update their positions with respect to either a
randomly chosen search agent or the best solution
obtained so far.
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15. HUNTING STRATEGY
Humpback whale use a special unique hunting method
called bubble net feeding method. in this method
they swim around the prey and create a distinctive
bubbles along circle or 9 shaped path.
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16. MATHEMATICAL MODEL
The mathematical model of WOA is described in the
following sections
1. encircling prey
2. bubble net hunting method
3. search the prey
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17. 1.Encircling prey
= coefficient vector
=current iteration
=position vector of best solution
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18. 2. Bubble-net attacking method (exploitation phase)
a. Shrinking encircling mechanism
b. Spiral updating position
Encircling
spiral
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19. 3. Search for prey (exploration phase)
In contrast to the exploitation phase, we update the
position of a search agent in the exploration phase
according to a randomly chosen search agent instead
of the best search agent found so far. This mechanism
and | A | > 1 emphasize exploration and allow the
WOA algorithm to perform a global search. The
mathematical model is as follows:
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20. The WOA algorithm starts with a set of random
solutions. At each iteration, search agents update their
positions with respect to either a randomly chosen
search agent or the best solution obtained so far. The
a parameter is decreased from 2 to 0 in order to
provide exploration and exploitation, respectively. A
random search agent is chosen when | A | > 1, while
the best solution is selected when | A | < 1 for
updating the position of the search agents. De-
pending on the value of p , WOA is able to switch
between either a spiral or circular movement. Finally,
the WOA algorithm is terminated by the satisfaction
of a termination criterion.
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21. ALGORITHM
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22. REFERENCES
1. Mirjalili, S. (2016). The whale optimization
algorithm. Advances in Engineering Software, 95,
51–67.
2. M.A. Abido, “Multiobjective optimal power flow
using strength pareto evolutionary algorithm," 39th
International Universities Power Engineering
Conference 2004, UPEC 1, 2004, pp. 457 -461
3. Dommel, H. W. and W. F. Tinney (1968). Optimal
power flow solutions. IEEE Trans on Power
Apparatus and System, PAS-87(10), 1866–1876.
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