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 Total Downloads : 2903
 Authors : Devendra Bisen, Hari Mohan Dubey
 Paper ID : IJERTV1IS3127
 Volume & Issue : Volume 01, Issue 03 (May 2012)
 Published (First Online): 30052012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Dynamic Economic Load Dispatch with Emission and Loss using GAMS
Devendra Bisen
Department of Electrical Engineering Madhav Institute of Technology and Science Gwalior (M.P), India
Hari Mohan Dubey
Department of Electrical Engineering Madhav Institute of Technology and Science Gwalior (M.P), India
Abstract
Dynamic economic dispatch (DED) is a real time problem of electric power system. DED intends to schedule the online generators outputs with the predicted load demands over a certain period of time in order to operate an electric power system most economically within its security limits. This paper introduces a solution of the dynamic economic dispatch (DED) problem including the loss and emission is participated among all generating units over time interval for a system using General Algebraic Modeling System (GAMS). The objective of the collective problem can be expressed by taking the production cost including emission and losses into account with required constraints for 24 hour time interval of each generating unit. The general algebraic modeling system (GAMS) technique is guarantees the global optimality of the solution due to its look further on capability. To validate practicability and robustness of the GAMS, it is tested on six generating unit system with different cases for determine minimum production cost of individual generating unit over a time period. In test case I only production cost without emission and loss, In test case II production cost with loss, In test case III production cost with including emission and without losses and In test case IV production cost including emission and losses for time interval of 24 hours.
Keyword Dynamic economic dispatch (DED), security limits, general algebraic modeling system (GAMS), production cost etc.

Introduction
Economic dispatch problem is one of the most important proble ms in e lectric power system operation. Energy manage ment has to perform mo re complicated and timely system control function to operate a large power system re liably an effic iently.
Electric utility system is interconnected to accomplish the benefits of min imu m production cost, ma ximu m reliability and superior operating conditions [1]. The economic scheduling is the on line economic dispatch, in which it is required to distribute the load among the co mmitted generating units which are actually paralleled with the system, in such a way as to minimize the total cost of generation without violating constraints [2]. The Dyna mic Economic Dispatch (DED), which is an e xtension of the conventional economic dispatch problem, determines the optima l generation schedule of on line generators, so as to meet the predicted load demand over a time horizon satisfying the constraint.
The intention of economic load dispatch (ELD) is
to work out the optima l a mount of the generated power for the fossilbased generating units in the system by minimizing the fuel cost. So operating at absolute minimu m cost may no longer be the only criterion for dispatching electric power due to increasing concern over the environmental considerations. In fact, the Clean Air Act Amend ments have been applied to reduce poisonous gases emissions from such power plants. Poisonous gases generate during power production in therma l stations by burn fossil fuels, due to poisonous gases (CO, CO2, SO2, NOX etc) effluent and these become a source of pollution for the environment. Lac k of planning while generating power puts the economica l aspect in difficulty. W ithin a plant, however, there is transmission loss ; also pollution e xists due to emission. The cost minimu m condition matchup to minimu m cost with considerable amount of loss and emission. Simila rly, the emission minimu m condition produces minimu m e mission with higher deviation fro m minimu m cost and loss. And also the loss minimu m condition produces minimu m loss with higher deviation from min imu m cost and emission. These three conditions cannot be imple mented simu ltaneously. Hence, the feasible optimu m corresponds to a small deviation in cost with an
allo wable tolerance in loss and emission taking into account emission constraints and this type of economic load dispatch has been termed emission constrained economic d ispatch (ECED) wh ich comes under mult iobjective proble ms[3].
The dynamic econo mic dispatch (DED), where optimization is done with respect to the dispatchable powers of the committed generation units for time particular g iven period and formulated as a minimizat ion problem of the total cost over the dispatch period under some constraints[4]. The development of DED is still going on; it has though
reached a certain level of development in terms of academic thoughts. Various optimizat ion techniques
simu lation studies are discussed in Section 4. Finally, Section 5 presents the conclusions.

Dispatch Problem Formulation
The objective of solving the dynamic economic dispatch problem in electric power system is to determine the generation levels for all online units which minimize the total fuel cost and minimizing the losses and emission level of the system, while satisfying a set of constraints over a given dispatch period.
It can be formu lated as follows:
have been proposed by many researchers to deal with this multiobject ive programming proble m with varying degree of success. In the recent past,
Minimize FTc
Where
T N
i 1 i 1
FTi
(Pi )
(1)
stochastic search algorithms such as genetic
algorith m (GA) [5], Part icle Swa rm Optimization
FTi (Pi )
Fi (Pi ) hi {Ei (Pi )}
(2)
(PSO) [6], evolutionary programming (EP) [7], simu lated annealing (SA) [8] and Differentia l Evolution (DE) [9] and artific ial immune system [10] methods are proven to be very effective in solving nonlinear DED proble ms and provide a fast, reasonable nearly optima l solution.
In this paper General Algebraic Modeling System (GAMS) approach has been proposed to solve the
FTc = is the total operating cost over the whole dispatch period,
FTi (Pi ) = is the Emission constrained fuel cost of
ith unit at t imet
i i
F (P ) = is the total fuel cost of a ith generating unit
E (P ) = is the total emission of a ith generating unit
objective of the collective problem can be expressed i i
by taking the total production cost, losses and total emission into account with required constraints for 24 hour time interval. General Algebra ic Modeling System (GAMS) is a highlevel mode l development environment that supports the analysis and solution of linear, non linear and mixed integer optimization problems [11]. General Algebra ic Modeling System is especially useful for handling la rge dimension and comple x proble m easily and accurately.
In this paper the effectiveness of the General
Algebraic Modeling System (GAMS) is demonstrated using six generating unit system with diffe rent cases for determine minimu m production cost of individual generating unit over a time period In test case I only production cost without emission and loss, In test case II production cost with loss , In test case III production cost with including emission and without loss and In test case IV production cost
hi = cost penalty factor
i
P = is a function of its real power output of ith at timet.
T = is the number of hours in time horizon,
N = is the number of d ispatch able units,
The fuel cost Fi (Pi ) of generating unit i at any time ntervalt is norma lly e xpressed as a quadratic function.

Objective Functions

Fuel Cost Objecti ve
The classical economic dispatch problem of finding the optima l comb ination of power generation, which minimizes the total fuel cost of a generating unit is usually described by a quadratic function of power output Pi while satisfying the total required demand can be mathe matica lly stated as follows:
2
including emission and loss for time interva l of 24 hours.
Fi (Pi )
Where
ai Pi
bi Pi
c $/Hr (3)
i
The paper is organized as fo llows: Section 2 provides a brief description and mathe matica l formulat ion of DED proble ms. The concept of General A lgebraic Modeling System (GAMS) is discussed in Section 3. The performance of Genera l Algebraic Modeling System (GAMS) and the
ai, bi and ci are the cost coeffic ient of unit i.

Emission Objec ti ve

The minimu m e mission dispatch optimizes the above classical economic dispatch including emission
objective of a generating unit is usually described by a quadratic function of power output Pi as [12]:
Each generating unit is constrained by its lower and upper limits of real power output to ensure stable
Ei (Pi ) di Pi2
ei Pi fi
Kg/Hr (4)
operation. The power generation of unit n should be between its minimu m and ma ximu m limits.
Where
di, ei and fi are the emission coeffic ient of unit i.
Pi min Pi
Where
Pi max
(11)
2.1.2 Emission constrai ne d c ost e quation
: Economic and emission dispatch problem is
Pi min
is the minimu m generation limit of unit i
converted into single optimization proble m by introducing price penalty factor h [13]:
The Emission constrained cost equation can now be formulated as:
Pi max is the ma ximu m generation limit o f unit i


General Algebraic Modeling System (GAMS)
FTi
(P )
i
ai Pi2
bi Pi ci
hi (di Pi2
ei Pi f )
General Algebra ic Modeling System provides a high – level (algebra ic) language for the representation of
$/Hr (5)
Where
large and co mple x mode ls. It a llows for unamb iguous statements of algebraic re lations that define an
hi Fi max (Pi max )
Ei max (Pi max )
(6)
abstract system of variables and equations. It also
F (P
) a P2 b P
c Rs/Hr (7)
provides several mechanisms for data manage ment.
i max
i max
i i max
i i max i
The system performs appropriate data
E (P
) d P2 e P
f Kg/Hr (8)
transformations to create a specific instance of the
i max
i max
i i max
i i max i
The price penalty factor hi unifies the emission with the normal fue l costs and the total operating cost of the system (i.e., the cost of fuel + the imp lied cost of emission). Once the value of price penalty factor is determined, the problem reduces to a simp le economic dispatch problem. By proper scheduling of generating units, comparative reduction is achieved in both total fuel cost and emission.
2.2 Transmission Loss
The transmission losses Pt can be found using Bmn coeffic ients
model. The Genera l Algebraic Modeling System (GAMS) is a highleve l model specially designed for modeling linear, nonlinear and mixed integer optimization proble ms [11]. GAMS can easily handle large and comple x proble ms. It is especially useful for handling large comple x proble ms, which may require much revision to establish an accurate model. Conversion of linear to nonlinear optimization is also very simple. Models can be developed, solved and documented simu ltaneously, maintain ing the same GAM S model file. The basic structure of a mathe matica l mode l coded in GAM S has the
components: sets, data, variable, equation, model and
n n
PL i 1j 1 Pi Bij Pi
n
B P B
i 1 oj i oo
(9)
output [14] and the solution procedure are shown below in Figure 1.
A GAMS model is a collection of statements in
Where
B
,
ij
and
B
oj
Boo are the transmission line
the GAMS language. This statement define the variables of the model, specify the symbolic
coeffic ients
2.3. Constraints
2.3.1 Power Bal ance Constraints
The real power balance between generation and the load must be ma intained at all t imes, while assuming the load at any time to be constant. The total supply must be equal to power de mand.
relationships between them in the form of equations specify data structures and assign values to them and instructs the computer to generate and solve the model. Other GAMS statements are used to handle output [14].
Pi PD PL
Where
(10)
PD is the load demand

Ge nerator limit Constr aints
Figure 1. GAM S modeling and solution procedure STEPS FOR PROBLEM Formu lation WITH GAM S
GAM S formu lation follows the basic format as given below:

SETS
Decla ration
Assignment of me mbers

Data (PARAM ETERS, TABLES, SCA LA RS)
Decla ration
Assignment of values

VA RIABLES Decla ration
Assignment of type
Assignment of bounds and/or initia l va lues (optional)

EQUATIONS Decla ration
Definition

MODEL and SOLVE statements

DISPLA Y statements (optional)


Result and Discussion
The GAMS approach has been tested on four diffe rent test cases of a single six unit system of the dynamic economic dispatch problem. In test case I only production cost without taking loss and emission, In test case II production cost with loss and without e mission, In test case III production cost with including e mission and without loss and In test case IV total production cost including e mission and loss for hourly time interval of 24 hours . The imple mentation model on GAMS with system configuration Core 2 Duo processor and 3GB RAM.
Table I. Cost and emission coefficient of six unit system
Linear Coeffic ient of B losses are:
B0j = [0.00003, 0.00009, 0.00012, 0.00007, 0.000085,
0.00011]

Test case I
The generator cost coefficients and generation limits of six units system are taken fro m Table I. For this test case emission coeffic ients and losses coefficients are not considered. In this test case production cost of sixunit system is calculated at different power demand over time period of 24 hours using GAMS. Table II shows the optimal solution of power output and production cost of each generator at different power demand over time period of 24 hours obtained using GAMS.
Table II. The optimal solution of total generation cost of each unit

Test case II
The generator cost coefficients, loss coefficients and generation limits of six units system are taken fro m Table I of sixunit system. For this test case emission coeffic ients are not considered. In this test case production cost with losses of sixunit system is calculated at different power de mand over time period of 24 hours using GAMS. Tab le III shows the optima l solution of power output and production cost of each generator at different power demand over time period of 24 hours obtained using GAMS.
Table III. The optima l solution of total generation cost with power loss of each unit

Test case III
The generator cost coefficients, emission coefficients and generation limits of six un its system are taken fro m Table I of sixunit system. For this test case loss coefficients are not considered. In this test case production cost including emission of sixunit system is calculated at different power demand over time
period of 24 hours using GAMS. Table VI shows the optima lsolution of power output and production cost of each generator at different power demand over time period of 24 hours obtained using GAMS.
Table IV. The optimal solution of total generation cost including e mission of each unit

Test case IV
The generator cost coefficients, loss coeffic ients, emission coefficients and generation limits of six units system are taken fro m Table I of sixunit system. In this test case production cost including emission with power losses of sixunit system is calculated at different power de mand over time period of 24 hours using GAMS. Table V shows the optima l solution of power output and production cost of each generator at different power demand over time period of 24 hours obtained using GAMS.


Conclusion
In this paper, General Algebraic Modeling System (GAMS) for optimization have been used for solving
Table V. The optima l solution of total generating cost including emission and power loss of each unit
dynamic power d ispatch problems. Three different test cases of a single six unit system of the dynamic economic d ispatch problem are taken. In test case I only production cost without emission and loss, In test case II production cost with loss, In test case III production cost with including emission and without loss and In test case IV production cost including emission and loss for time interval o f 24 hours.
An effic ient economic dispatch algorithm for dealing with nonlinear functions such as the thermal cost, transmission loss and emission constraint is developed. The quality of the solutions generated by the General Algebra ic Modeling System (GAMS) offers e xcellent approach to solve the dynamic therma l power dispatch problem. The solution is analytic in nature with high accuracy and it is used for any online application. The result shows that GAM S performs better so far for the above
mentioned test cases. The GAMS algorith m has superior features, including quality of solution and good computational effic iency. Therefore, this results shows that GAMS is a promising technique for solving complicated proble ms in power system.
Acknowledgme nt
The authors are thankful to Director, Madhav Institute of Technology & Science, Gwa lior (M .P) India for prov iding support and facilities to carry out this research work
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