International Journal of Computer Science & Communication Vol. 1, No. 2, July-December 2010, pp.
145-149
Improved Tabu Search Algorithm to Economic Emission Dispatch with
Transmission Line Constraint
K. Senthil1 & K. Manikandan2
1
Department of Electrical and Electronics Engineering, St.Joseph college of Engineering and Technology,
Dar Es Salaam, Tanzania
2
Department of Electrical and Electronics Engineering, S.R.M. University, Chennai, India
Email: 1ksenthil_856@yahoo.co.in, 2starmk2015@yahoo.com
ABSTRACT
Every year the amount paid for one unit power consumption is increasing rapidly. By using Improved Tabu Search
Algorithm (ITS) the cost per unit power consumption is reduced. The money spent by the consumer is reduced to a
greater extent. Thus the economy of the country is improved. Economic load dispatch (ELD) is an important
optimization task in power system. It is the process of allocating generation among the committed units such that the
constraints imposed are satisfied and the energy requirements are minimized. There are three criteria in solving the
economic load dispatch problem. They are minimizing the total generator operating cost, total emission cost and
scheduling the generator units. In this paper the Improved Tabu Search (ITS) solution to economic dispatch problem
is very useful when addressing heavily constrained optimization problem in terms of solution accuracy. In this paper
the allocation of generation for each generator unit is optimized by Improved Tabu Search Algorithm. In thermal
power plants the total cost of the power generation is depends upon fuel cost and emission cost. By the proposed
method the total cost for power generation is enormously reduced. Results obtained from this technique clearly
demonstrate that the algorithm is more efficient in terms of number of evolution to reach the global optimum point.
The result also shows that the solution method is valid for real time applications and it provides challenges and
opportunity to the Engineers to improve the economy of the country.
Keywords: Economic Dispatch, Emission Dispatch, Fuel Cost, Improved Tabu Search
1. INTRODUCTION the base point, the participation factors method and
gradient method are well known for the economic
Energy management has to perform more complicated thermal dispatch of generators. All the methods as well
and timely system control function to operate a large known for the economic dispatch problem as a convex
power system reliably an efficiently. In electric power optimization problem and it assumes the whole of the
system operation, the objective is to achieve the most unit operating limit (Pmin) and the maximum generation
economical generation policy that could supply the local limit (Pmax) is available for operation.
demands without violating constraints. Thermal stations,
during power production, burn fossil fuels that generate This paper work deals with the economic scheduling
toxic gases in their effluent and these become a source of problem namely the economic thermal power dispatch.
pollution for the environment. Lack of planning while In seeking the solution for the economic dispatch problem
generating power puts the economical aspect in jeopardy. (EDP) the main aim is to operate a power system in such
Within a plant, however, there are no transmission loss a way to supply all the loads at the minimum cost. The
units; rather pollution exists due to emission. The cost solution technique which is applied to the economic load
minimum condition corresponds to minimum cost with dispatch is Improved Tabu search (ITS) method. The
considerable amount of emission. Similarly, the emission basic idea of the ITS approach is to use adaptive memory
minimum condition produces minimum emission with structures and associated strategies to explore the search
higher deviation from minimum cost. These two space of feasible solutions by means of a sequence of
conditions cannot be implemented simultaneously. moves. The simplest version of this method only makes
Hence, the feasible optimum corresponds to a small use of its short term memory process. The elements of
deviation in cost with an allowable tolerance in emission the more from the current solution, to its selected
taking into account emission constraints and this has been neighbor are partially or completely recorded in the Tabu
termed emission constrained economic dispatch (ECED). List to forbid reversal of the replacement in future
iterations. Without his assurance, the search would cycle
Economic dispatch is one of the most important between the first encountered local optimum and its
problems to be solved in the operation of power system. neighbor. Considerable success is achieved for short term
The traditional method such as lambda iteration method,
146 International Journal of Computer Science & Communication (IJCSC)
memory, which makes use of frequency information and dispatch [6] is an extension of the conventional economic
more advanced principles. This influences the effective emission dispatch problem that takes into consideration
implementation of Improved Tabu Search. the limits on the ramp rate of the generating units. The
multiobjective problem is converted into a single-
A good deal of literature is available pertaining to
objective optimization by goal-attainment method which
the topic of research considered in this thesis. The
is then handled by particle swarm optimization method.
traditional method of solving economic dispatch
Muralidharan and Srikrishna have studied dynamic
problems such as lambda-iteration and gradient method
programming recursive approach for the Emission
requires the unit input-output curves of generators.
constrained economic dispatch [7] presented a
However, these curves do not increase monotonically
multiobjective and multi stage decision making problem
due to prohibited operating zones. Hence, the traditional
has been solved analytically without the familiar lambda
dispatch algorithms cannot be directly used to optimize
iteration method.
such non-linear cost function. Wong suggested the
Evolutionary programming based algorithm for The optimization algorithm has been developed with
environmentally constrained economic dispatch [1] to a sequential dynamic programming model. The salient
solve the highly non linear economic dispatch problem feature of this technique is that all the former
without restrictions on the shape of the fuel cost conventional procedures have been avoided completely.
functions. These applications involved a large number Whei-Min Lin and Fu-Sheng Cheng implemented an
of iterations and susceptible to the related control Improved Tabu Search Algorithm [8] for economic
parameters. Park analyzed the adaptive learning dispatch with non continuous and non smooth cost
approach in the Hopfield Neural Network [2] using the functions. Modified Tabu Search generates new
slope adjustment and has adjustment methods for population from one candidate and usually converges
application to economic load dispatch. These methods to local optimum very quickly, for ITS vectors with fitness
reduce transient period drastically. The adaptive learning
score good enough would be used as candidates to create
in both methods gives better response compared to fixed
new solutions regardless of Tabu restrictions. The theory
learning rate. The bias adjustment method gives good
of tabu Search has been well developed an Improved
response especially in the beginning of the process. Both
Tabu Search Algorithm (ITS) to make tabu Search more
methods reduced the number of iterations to one half of
the traditional Hopfield neural network. When the practicable in real valued systems.
momentum is introduced to all methods in either input
or gain, the number of iterations and the computation 2. PROBLEM FORMULATION
time are reduced in the order of magnitude. Sewothul The objective of solving the economic dispatch problem
and Rughooputh have studied genetic algorithm for in electric power system is to determine the generation
economic dispatch with valve point effect [3] develops levels for all on-line units which minimize the total fuel
four genetic algorithms: simple genetic algorithm, Simple cost and minimizing the emission level of the system,
genetic algorithm with generation-apart elitism, Simple while satisfying a set of constraints. It can be formulated
genetic algorithm with atavism and atavistic genetic as follows:
algorithm for non monotonically increasing cost
functions. The economic dispatch problem can be modeled by
Basu analyzed the interactive fuzzy satisfying-based
simulated annealing technique [4] for economic emission Minimize FT = F
i
i ( P ) Rs/hr
i
(1)
load dispatch with non smooth fuel cost and emission
level functions treats economic and emission as Where
competing objectives for optimal dispatch, which FT is the total fuel cost
requires some form of conflict resolution to arrive at a
solution. Assuming that the decision maker has imprecise Fi(Pi) is the fuel cost of generating unit i
or fuzzy goals for each of the objective functions, the
multiobjective problem is transformed into a minimax A. Fuel Cost Function
problem, which is then handled by the simulated
The fuel cost function of a generating unit is usually
annealing technique. Khamsawang and Pothiya have
described by a quadratic function of power output Pi as:
suggested a novel method on simple Tabu search
algorithm (TSA) to solve economic dispatch (ED) Fi(Pi) = ai P2i + biPi + ci Rs/hr (2)
problem for thermal power plants, which we call
Distributed Tabu Search algorithm (DTSA) [5]. It consists Where
of thirteen generating units with valve point effect fuel ai, bi and ci are the cost co-efficient of unit i.
functions. Basu analyzed the dynamic economic emission
Improved Tabu Search Algorithm to Economic Emission Dispatch with Transmission Line Constraint 147
B. Emission Equation whose operations produce a sequence of moves that lead
The Emission equation of a generating unit is usually from one trail solution to another. Each move is obtained
described by a quadratic function of power output Pi as: from a set of available alternatives that are be evaluated
by one or more functions that measure their
Fi(Pi) = diP2i + ei Pi + fi Kg/hr (3) attractiveness in some local sense. Applying to the
Where optimization problems, the ITS starts at some initial
solution and then moves to a neighboring solution. A
di, ei and fi are the emission co-efficient of unit i. neighboring solution is generated by a set of admissible
moves. At each iteration the method moves to the best
C. Emission Constrained Cost Equation solution in the neighborhood of the current solution. The
The Emission constrained cost equation can now be best solution of all stages is sorted as the new best
formulated as: solution and used as forward initial solution for every
stage. Finally, the searching of all stages has completed
Fi(Pi) = (aiPi2 + biPi + ci) + their solutions, applying the global updating to select
+ hi (di P2i + eiPi + fi) Rs/hr (4) the best solution. The details of the ITS is applied to ED
problem are given in the following Algorithm:
Where
Set initial solution of stage i to be current
hi = Fimax/Eimax (5) solution.
Fimax = aiPi2max + biPimax + ciRs/hr (6) S iO = (P 1 P 2..P N) where P 1 P 2..P N =
Ei max = diPi2max + eiPimax + fiKg/hr (7) Output power of Generating unit.
N = Number of total generating unit in this
D. Transmission Loss system.
The transmission losses P t can be found using B mn Set, Iteration count K = 0.
coefficients
Tabu list as empty.
n n
PL = B
i =1 i =1
ij Pj P i (8)
Where
Bij is the transmission line coefficients
E. Power Balance Constraints
Power Balance Constraints: The total generation must
supply the demand
(Pi) = PD (9)
Where
PD is the load demand
F. Generator Limit Constraints
The power generation of unit n should be between its
minimum and maximum limits.
Pnmin < Pn < Pn max (10)
Where
Pi min is the minimum generation limit of unit i
Pi max is the maximum generation limit of unit i
3. IMPROVED TABU SEARCH ALGORITHM
An Improved Tabu Search (ITS) search is a higher-level
Fig. 1: Flow Chart for Improved Tabu Search Application
method or strategy for solving optimization problems. to Economic Load Dispatch
The ITS approach can be imposed on any procedure
148 International Journal of Computer Science & Communication (IJCSC)
Calculate the total fuel cost function of each stage Stop if the termination criterion is satisfied and
FT(SiO). global updating solution else go to step 5.
Set best solution (Sib) = current solution SiO and
4. EXPIREMENTS AND RESULTS
FT(SiO) = FT(Sib).
The power system economic dispatch problem based on
Find as set of neighbors solution Sineighbour of (Sib). the concept of Improved Tabu Search method has been
Calculate total fuel cost function FT tested on 3-generator system. Multiple generator limits
(Sineighbour). and total operating cost of the system is simulated in
order to evaluate the correctness as well as accuracy of
If FT (Sineighbour) < FT (Sib), update solution. this method. The test system consists of 3-generating
Set (Sib) = (Sineighbour), else do not update units with various demand of 300-700 MW. The cost
solution. coefficient, emission coefficient and generating limits of
the 3-generator system are shown in table (I).
Update tabu list, i.e, regency frequency & move
direction are update. The Loss Coefficient Matrix of 3- Generator System
Check the condition of interchange solutions. If 0.000071 0.000030 0.000025
reaches the appropriate point, inter change
solutions between stages; the best solution of all Bmn = 0.000030 0.000069 0.000032
stages is sorted as the new best solution and used 0.000025 0.000032 0.000080
as forward initial solution for every stage. Set
iteration counter K = K+1 and go to Step 5.
Table I
Cost Coefficients, Emission Coefficients and Power Limits for Three Generator System
Generator ai bi ci di ei fi Pmin Pmax
1 0.03546 38.30553 1243.5311 0.00683 -0.54 551 40.26690 20 200
2 0.02111 36.32782 1658.5696 0.00461 -0.51160 42.89553 15 150
3 0.01799 38.27041 1356.6592 0.00461 -0.51160 42.89553 18 180
5. SIMULATION TEST RESULTS
total fuel cost and emission level is minimum in
The Improved Tabu Search Algorithm is used to solve Improved Tabu Search Algorithm compared to other
the Economic Dispatch problem for 3-generator test techniques with considering fuel cost functions, emission
system. The simulation is carried out using Mat Lab 7.0 equations, emission constrained cost equation,
software. The total operating cost, emission level and transmission line constraints, power balance constraints
transmission loss of the system are minimized. The and generator limit constraints. In comparison of the test
computational results of table (II) consists of three system, it can be seen that when a large scale problem,
generator test system, shows that ITS fuel cost function, ITS can clearly obtain solution better than other methods
emission level & Transmission loss are less than and converges to near global minimum with less search
conventional methods. The test system data produce the account.
better result for 3-generating units. It concludes that the
Table II
Fuel Cost, Emission and Transmission Loss Values for 3-Generator System Under Various Load Conditions
Sl.no Power P1(MW) P2(MW) P3(MW) Ploss(MW) Fuel Cost Emission
demand (mw) (Rs/hr) Release(kg/hr)
1 300 76.5863 115.2465 112.2969 4.1296 16392 127.2929
2 350 89.5245 134.4453 131.6782 5.6480 18589 159.0743
3 400 104.0372 150.0000 153.3721 7.4093 20845 200.1917
4 450 129.3902 150.0000 180.0000 9.3902 23204 254.0819
5 500 181.4774 150.0000 180.0000 11.4774 25774 336.2607
6 550 211.3118 161.3118 191.3118 13.9354 28326 424.0469
7 600 228.8856 178.8856 208.8856 16.6568 30837 509.2984
8 650 246.5455 196.5455 226.5455 19.6366 33407 604.9546
9 700 264.2929 214.2929 244.2929 22.8788 36037 711.1699
10 750 282.1291 232.1291 262.1291 26.3872 38727 828.1029
Improved Tabu Search Algorithm to Economic Emission Dispatch with Transmission Line Constraint 149
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[8] Whei-Min Lin, Fu-Sheng Cheng and Min-Tong Tsay, An
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