COMPUTATIONAL FRAMEWORK FOR POWER ECONOMIC
DISPATCH USING GENETIC ALGORITHM
Tahir Nadeem Malik
Elect. Engg. Deptt. University of Engg.& Tech., Taxila (Pakistan) Student Member IEEE
Abdul Qudus Abbasi
Department of Computer Science, Quaid-i-Azam University, Islamabad (Pakistan)
Aftab Ahmad
National Power Control Centre WAPDA, Islamabad (Pakistan)
Elect. Engg. Deptt. University of Engg.& Tech., Taxila (Pakistan)
Keywords: Artificial Intelligence (AI), Software Architecture, Framework, Power Economic Dispatch (PED), Genetic
Algorithm (GA), GA Parameters, White-box Reuse.
Abstract: Economic Dispatch Problem (EDP) is the important step in Power System operation and is non-convex
optimization problem. It has been solved comprehensively with mathematical programming approaches.
However, these approaches handle non-convexity with assumption and resulting in an inaccurate dispatch.
Genetic algorithms are potential tools for Economic dispatch solution. Computational framework
“PED_Frame” has been developed which can handle economic dispatch solutions based on mathematical
programming and Genetic Algorithm based approaches independently and in hybrid form. It has been tested
on standard three machine and twenty machine test systems.
1 INTRODUCTION
Power Economic Dispatch (ED) is one of the main
functions
of modem Energy Management System
(EMS) and
vital step in power system operational
planning. It is defined as the process of allocating
generation levels to the generating units in the mix,
so that the system load may be supplied entirely and
most economically (Happ, 1977). It is on-line
function, carried out after every 15-30 minutes or on
request in Power Control Centers.
Economic dispatch is constrained non-convex
optimization problem. The cost functions of multi-
valve thermal machines are non-smooth
discontinuous and non-differentiable. However,
the
generator fuel costs are generally approximated in the
continuously differentiable quadratic form while
solving economic dispatch problem in mathematical
programming approaches.
Consequently, inaccurate
dispatch results. Genetic algorithms (GA) have been
used to solve the economic dispatch problem
independently and in conjunction with other AI tools
and optimization approaches. GA based approaches
have the ability to handle the non-convex economic
dispatch problem efficiently (
Chao-Lung Chiang,
2005) without any restriction on objective function
thus providing potential tool for real economic
dispatch problem.
The concept of power market has brought the
changes in the trend of power industry. The role and
structure of control center is being redefined. Quick
decision-making and fast answers are very
significant in market environment. Flexible and
extensible framework having the ability to
incorporate approaches for Economic Dispatch
solution may be useful tool for industry and
academia.
In this paper effort has been made to develop the
framework PED_Frame for economic Dispatch
using Genetic Algorithm and mathematical
191
Nadeem Malik T., Qudus Abbasi A. and Ahmad A. (2006).
COMPUTATIONAL FRAMEWORK FOR POWER ECONOMIC DISPATCH USING GENETIC ALGORITHM.
In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics, pages 191-194
DOI: 10.5220/0001203601910194
Copyright
c
SciTePress
programming approaches. The paper is organized as
follows: Section II gives the definition of Economic
dispatch problem. Section III covers concepts and
architecture of PED_Frame. Section IV includes the
implementation detail in PED_Frame. Lastly there is
conclusion.
2 ECONMIC DISPATCH
PROBLEM
The Economic Dispatch in its simplest form is
formulated as:
Minimize
=
=
N
1i
iiT
)P(CC
(1)
Subject to equality constraint:
=
=+
N
1i
iLD
PPP (2)
Inequality constraints:
P
i (min)
P
i
P
i (max)
(3)
Where: C
T
Total cost, C
i
generator fuel cost of the
ith generating unit, P
D
total load, P
i(min)
the
minimum generation power, P
i (max)
the maximum
generation power, and P
L
transmission loss given by
∑∑
=
ij
j
j
iiL
PaPP
Where: a
ij
: transmission loss coefficient.
3 PROPOSED
FRAMEWORK - “PED_Frame”
Framework is a set of cooperating classes that
makeup reusable design for a specific class of
software and defines overall structure of application,
it’s partitioning in classes and objects (Gamma,
1995). A framework can be customized to a
particular application by creating application
specific subclasses of abstract classes targeting a
specific group of applications, which have similar
architecture design. A fairly large number of useful
frameworks are available for application builders.
One of these frameworks is Microsoft’s Document-
View architecture.
The proposed framework “PED_Frame” targets
power economic dispatch software application
development. It provides white-box reuse
mechanism for incorporating new algorithms. All
inputs and outputs are handled through a grid.
PED_Frame provides extremely efficient component
for status visualization.
Standard Template Library (STL) is used as base
for the development of the vector-matrix library.
This library gives efficient algorithm
implementation for vectors and matrices. Document-
View Architecture acts as container for PED_Frame
and provides base services. These are primarily in
the form of messaging mechanisms, and threading
support. The class diagram of PED_Frame is shown
in figure 1.
3.1 Input/Output Using Grid
CPEDGrid class acts as interface for grid, which
provides functionality like input, formatted output,
print and data validation checks. It extends grid
functionality to link its services with other parts of
the PED_Frame. These are:
a. Data present in Grid is transferred to a matrix,
which can act as data communicator.
b. Data present in matrix is formatted in grid for
display and printing purposes.
c. Data editing and data validation checks.
PED_Frame creates three instances for grid class -
-- Machine data, B-Coefficients and output.
3.2 Analysis Status Visualization
Analysis status visualization is implemented in class
CPEDAnalysisStatus derived from CDialog class of
MFC. This dialog window contains progress
indicators showing current state of convergence,
iteration count, and time elapsed.
3.3 Analysis
This part of the framework is responsible for actual
implementation of algorithm. The analysis is
accomplished through following classes:
a. CPEDAnalysisBase class is derived from
CWinThread so acting as independent thread of
execution. It contains references to matrices for
input, B-Coefficient and output, Machines
count, maximum iterations count, power
demand and error tolerance. It also provides
virtual functions for start analysis,
communicating status information and
formatting output.
b. CPEDGABased is derived from
CPEDAnalysisBase and works as base for
implementation of genetic algorithm. This class
contains information for Genetic Algorithm
(GA) parameters. A new class can be derived
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192
from this class to implement any GA based
solution for Economic dispatch.
c. CPEDCABase is also derived from
CPEDAnalysisBase and works as base for
conventional algorithm implementation. It
contains information like initial start and step
length. A new class can also be derived from
this class to implement any mathematical
programming based solution for Economic
dispatch.
3.4 Vector-Matrix Library
This library includes template based CPEDVector
and CPEDMatrix classes. CPEDVector is derived
from vector<class T> and it implements
functionality for initialization, resizing, addition,
multiplication, searching, sorting and debugging
routines.
CPEDMatrix class is derived from CPEDVector
< CPEDVector <calss T> > and it implements
functionality for initialization, resizing, and matrix
algebra operations.
3.5 MFC Document-View
Architecture
PEDFramework is primarily based upon doc-view
architecture of MFC. CPEDApp is derived from
CWinApp, CMainFrame is derived from
CFrameWnd, CPEDView is derived from
CScrollView and CPEDDoc is derived from
CDocument class. CPEDView contains grid objects
and manages their functionality. CPEDDoc contains
instances of matrix class for input matrix, B-
Coefficient matrix and output matrix. The reference
of these matrices is passed to respective
CPEDAnaslysisBase derived class, which performs
analysis by using these matrices and updates output
matrix.
4 IMPLEMENTATION USING
PED_FRAME
4.1 Economic Dispatch using
Mathematical Programming
based Approach
It can be implemented as follows:
a. Derive a class from “CPEDCABase”and
declare algorithm specific parameters in it.
b. Write code for new algorithm in StartAnalyse
function, which is in overridden form.
c. Call UpdateStatus with error value and current
iteration.
d. Override “FormatResults” to transfer results
from analysis structure to output matrix.
e. Create a new menu item and write its message
handler in CPEDDoc. Create an object of
Derived class and set parameters.
f. Create an object of CPEDAnalysisStatus and
pass this object to it; calling its DoModal().
This will start analysis.
g. On completion of analysis just call
“UpdateAllViews”, this will update grid
control with results.
4.2 Economic Dispatch using GA
a. Derive a class from “CPEDGABase”.
b. Remaining steps are same as those in
Conventional Approach.
4.3 Economic Dispatch in
PED_Frame
In PED_frame following algorithms have been
implemented:
Lamda iteration algorithm with and without loss,
Simple Genetic Algorithm with typical reproduction,
crossover and mutation operators, and Sequential
hybrid approach, which after fixed number of
generation, passes control to Lambda iteration
algorithm.
The transmission loss has been calculated using
B-Coefficients. The inputs are standard machine cost
curves, B-coefficients, power demand. Genetic
algorithm solution involves GA parameter settings.
The software has been tested on 3 and 20 machine
systems (
Ching-Tzong Su, 2000) and several other
standard test systems. However, in the paper three
machine system results have been given in Table 1.
Table 1: Computational Results Using PED_Frame.
Unit Out
put (MW)
Lambda
Iteration
Genetic
Algorithm
Hybrid
P
1
73.6600 50.0000 73.6600
P
2
69.9850 75.7173 69.9850
P
3
75.1803 93.0189 75.1803
P
total
218.8253 218.7362 218.8253
P
L
(MW) 8.8254 8.7362 8.8254
P
D
210.0 210 210.0
Generation
Cost ($/h)
3164.5664 3155.0181 3164.5664
COMPUTATIONAL FRAMEWORK FOR POWER ECONOMIC DISPATCH USING GENETIC ALGORITHM
193
5 CONCLUSIONS
Economic dispatch is online function and vital step
in power system operational planning. It forms an
important part of energy management system. It has
been solved comprehensively in mathematical
programming environment by approximating cost
curves. However, genetic algorithm based
approaches ca handle actual non-convex cost curves
effectively. In this paper a framework has been
developed which can handle economic dispatch
using classical optimization and Genetic Algorithm
based approaches independently and in hybrid form.
It has been tested for on 3 machine, 20 machine
systems and several other standard test systems. It is
the platform, which is flexible, extensible and useful
for many individuals. Step by step transition of
PED_Frame to the computational framework
“Power System Master (PSM)” would be the future
activities to achieve the goal of developing the
software package for Power System Operational
Planning.
REFERENCES
Happ H.H, 1997. Optimal power dispatch -- A
comprehensive survey. In IEEE Transactions on PAS,
vol. PAS-96, no.3, pp.841-854.
Chiang Chao-Lung, 2005. Improved genetic algorithm for
power economic dispatch of units with valve-point
effects and multiple fuels. In IEEE Transactions on
Power System, vol. 20, no. 4, pp. 1690 –1699.
Gamma, Helm, Johnson, Vlissides, 1995. Design Patterns
Catalog of Design Patterns, Addison-Wesley.
Desktop Application with Visual C++ 6.0, MCSD Series
Microsoft Press.
Chowdhury B.H. & Rahman Salfur 1990. A review of
recent advances in economic dispatch. In IEEE
Transactions on Power Systems,vol.5, no.4, pp.148-
1259.
Su Ching-Tzong & Lin Chien-Tung, 2000. New approach
with a Hopfield modeling framework to economic
dispatch. In IEEE Transactions on Power Systems,
vol.15, no.2, pp. 541 -545.
CPEDApp CPEDView CPEDDoc CFrameWnd
CWinThread CDialog
CPEDGrid CPEDAnalysisisBase CPEDAnalysisStatus
CPEDGABase CPEDCABase CPEDMatrix CPEDVector
Derived From
Contained in
Figure 1: Class Diagram for PED_Frame
Figure 1: Class Diagram for PED_Frame.
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194