power system operation and control solving economic dispatch problem

1. Power System Operation & Control
OPEN ENDED LAB
PRESENTATION TOPIC:
Gravitational Search Algorithm for Optimal
EconomicDispatch
SUBMITTED BY:
2019-EE-505
2019-EE-506
2019-EE-531
DEPARTMENT OF ELECTRICAL ENGINEERING (RCET)
UNIVERSITY OF ENGINEERING AND TECHNOLOGY, LAHORE

2. INTRODUCTION
 The economic dispatch problem (EDP) is related to the optimum
generation scheduling of available generators in a power system to
minimize total fuel cost while satisfying the load demand and
operational constraints.
 EDP plays an important role in operation planning and control of
modern power systems.
 In order to make numerical methods more convenient for solving
EDPs modern optimization techniques have been successfully
employed to solve the EDPs as a non smooth optimization problem.

3. CONTINUED….
 A number of conventional approaches have been developed for
solving EDPs such as gradient method, linear programming algorithm,
lambda iteration method, non-linear programming algorithm, and
lagrangian relaxation algorithm has been successfully used to solve
EDPs such as genetic algorithm, particle swarm optimization and so
on.
 Recently a new heuristic search algorithm, namely gravitational search
algorithm (GSA) motivated by gravitational law and law of motion
has been proposed by Rashedi et al.

4. GRAVITATIONAL SEARCH ALGORITHM
 We are introducing optimization algorithm which is based on the law
of gravity. In the proposed algorithm, agents are considered as objects
and their performance is measured by their masses.
 In GSA, each mass (agent) has four specifications: position, inertial
mass, active gravitational mass, and passive gravitational mass. The
position of the mass corresponds to a solution of the problem, and its
gravitational and inertial masses are determined using a fitness
function.
 GSA is a memory-less algorithm. However, it works efficiently like
the algorithms with memory.

5. ALGORITHM
The main steps of the GSA can be summarized as:
 Step 1. The algorithm starts by setting the values of
gravitational constant G0,α,ε and the iteration counter t.
 Step 2. The initial population is generated randomly and
consists of N agents, the position of each agent is defined by :
 Step 3. The following steps are repeated until
termination criteria satisfied
Xi(t) = (xi (t),xi (t),. . . ,xi (t), . . . ,xi (t)),
1 2 d n
(1)
i = 1,2,. . . .,N,

6. CONTINUED….
 Step 3.1. All agents in the population are evaluated and the
best, worst agents are assigned.
 Step 3.2. The gravitational constant is updated as shown
in equation 1.
 Step 3.3. When agent j acts on agent i with force, at a
Specific time (t) the force is calculated as following:

7. CONTINUED….
 Step 3.4. At iteration t ,calculate the total force acting on
agent i as following:
Where k best is the set of first k agents with the best fitness
value and biggest mass.
 Step 3.5. C alculate the inertial mass as following:

8. CONTINUED….
 S tep 3.6. The acceleration of agent i is calculated as
following
 S tep 3.7. The velocity and the position of agent i are
computed as above equation
 S tep 3.8. The iteration counter is increased until
termination criteria satisfied.
 Step 4 The best optimal solution is produced.

9. COMPUTATIONAL APPROACH
 The different steps of the proposed algorithm are the following:

10. CONCLUSION
 In recent years, various Meta-Heuristic optimization methods have
been developed. Some of these algorithms are inspired by swarm
behaviors in nature. GSA is constructed based on the law of Gravity
and the motion of mass interactions.
 The GSA method gives better results with reduced computational
time. Hence, the study shows that GSA could be a promising
technique for solving complicated optimization problems in power
systems.