 Open Access
 Total Downloads : 1599
 Authors : Lalita Rani, Ms. Manju Mam, Sanjeev Kumar
 Paper ID : IJERTV2IS70111
 Volume & Issue : Volume 02, Issue 07 (July 2013)
 Published (First Online): 08072013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Economic Load Dispatch In Thermal Power Plant Taking Real Time Efficiency As An Additional Constraints
1 Lalita Rani, 2 Ms. Manju Mam, 3 Sanjeev Kumar
Deenbandhu Chhotu Ram University of Science & Technology, Murthal (Sonipat), Haryana. Director National Power Training Institute, Faridabad (Ministry of Power), Govt. of India.
Lect. NCCE, Technical Campus Israna (Panipat).
AbstractThis paper presents a particle swarm optimization (PSO) algorithm for solving economic load dispatch problem in thermal power plants. An additional inequality constraint, called real time efficiency of different generating units has been considered in order to calculate the economical generation shared by all the generating units. The effectiveness of the algorithm is validated by carrying out extensive test on a power system involving 6 and 8 thermal generating units. The results obtained are compared with the same system without taking efficiency in to consideration. The result shows that by taking efficiency as an additional operating constraint, a considerable reduction in total fuel cost is achieved. PSO approach is used as it is easy to implement and there are few parameters to adjust with high computational efficiency and high accuracy.
Keywords Economic Load Dispatch, Total Efficiency in generating units, Particle Swarm Optimization, real time Efficiency.

INTRODUCTION
The economic load dispatch (ELD) is one of the most important optimization problems in power system operation and planning to derive optimal economy. The main objective of economic load dispatch is to determine the optimal combination of all generating units so as to meet the required load demand at minimum cost while satisfying the various operating constraints like energy balance, maxmin generation limits, transmission line constraints, running spare capacity and network security. A station has incremental operating costs for fuel and maintenance and fixed cost associated with the station itself that can be quite considerable for a typical thermal and nuclear power plant for example. Things get even more complicated when utilities try to account for transmission line losses and the seasonal changes associated with hydraulic power plants. Conventionally, the cost function for each unit for ELD problem has been approximately represented by a quadratic equation and is solved by using various mathematical techniques like lambdaiteration method, Lagrange method, Newtons method etc [1][4]. Unfortunately, the realtime cost characteristics of thermal generating units are highly nonlinear because of prohibited operating zones, valve point loading and multi fuel insertion etc. Thus, practical ELD problem is represented as a non linear optimization problem with various equality and inequality constraints, which directly cannot be solved by conventional mathematical techniques. Hence numerous intelligent techniques like BiogeographyBased Optimization
(BBO) [5], genetic algorithm (GA) [6], Differential Evolution (DE) [7], Evolutionary Programming (EP) [8][10], neural network approaches [11][12], etc were introduced to solve complex nonlinear ELD problems over past few years.
In this paper, a new inequality constraint, called real time efficiency is introduced. The effectiveness of this constraint in solving ELD problem is easily evaluated as by considering it, the generation from units with poor efficiency got decreased and same with better efficiency got improved. The efficiency at any thermal power plant is regularly analyzed for various parameters like Total EFFIC, Hot water and ash contents etc before it is fed to furnace for combustion. Each parameter affects the whole generating unit efficiency
i.e. Total EFFIC with heavy ash contents and poor EFFIC produces less useful heat per unit volume compared to same with maximum value of EFFIC and Total EFFIC. A better efficiency is desirable in order to get stable flame intensity in furnace which results in normal power generation with minimum of fuel consumption. In other case, poor efficiency is obtained which results in same power generation with increase of fuel consumption. Hence, generation from the unit is required to decrease with maximum insertion of efficiency which results in higher fuel cost. Therefore, it is desirable to operate the unit at near lower limits in order to maintain the fuel stock. The economical loading is decided by deriving the various parameter of efficiency of each operating unit of respective thermal power plant in to a suitable formulae which gives minimum fuel cost at any load demand.

FORMULATION OF ELD PROBLEM

Classical ELD problem
The ELD problem is to find the optimal combination of power generations that minimizes the total generation cost while satisfying an equality constraint and inequality constraints. The most simplified cost function of each generator can be represented as a quadratic function as given in (2).
.(1)
.(2)
Where
is the total fuel cost.
is the cost function of generator . is electrical output of generator .
are the cost coefficients of generator .
..(6)
..(7)
While minimizing the total generation cost, the total generation should be equal to the total system demand plus the transmission network loss. However, the network loss is not considered in this paper as all the operating units of a power plant are on single bus. This gives the equality constraint
.(3)
Where is the total power demand. The maximum
And
Where
operating units.
….(8)
is the total efficiency for unit.
is the maximum value of efficiency of n
active power generation of a source is limited again by thermal consideration and also minimum power generation is limited by the flame instability of a boiler. If the power output of a generator for optimum operation of the system is less than
is the %age ash contents for unit.
is the maximum value of ash contents of n operating units.
is the %age of hot water for unit.
is the minimum value of hot water of n operating
a prespecified value , the unit is not put on the bus bar because it is not possible to generate that low value of power
units.
is the Penalty Factor associated with total efficiency
from the unit. Hence the generator power P cannot be outside the range stated by the inequality
…(4)
Where , is the minimum, maximum output of generator .

ELD problem with efficiency as an additional inequality constraint
It is estimated that, if a whole generating Unit worked as running smoothly, then the whole units to calculate the turbine, boiler and generator efficiency. In a thermal power Plant, efficiencies are calculated every day from the bunkers of respective operating Units and are tested for various contents (like hot water, Total EFFIC, ash contents etc).
Suppose on a particular day, the EFFIC is as under
Similarly
Now
..(5)
for operating unit.
is the Penalty Factor associated with ash contents of efficiency for operating unit.
is the Penalty Factor associated with hot water in efficiency for operating unit.
is the gross Penalty Factor for operating unit.
The generation from each unit obtained by applying PSO will be modified by multiplying the individual penalty factors with respective generating unit as given in eq. (9)
(9)
For a particular amount of load demand, after considering the effect of penalty factors, it is sometimes posible that the generation from any (or more than one) unit violate the maximum or minimum limits. In that case, it is recommended that the additional amount (after settling the maximum or minimum limits) will be proportionally distributed among the remaining units.


IMPLEMENTATION OF PSO AS ELD PROBLEM

Overview Of PSO
In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. The system is initialized with a population of random solutions and searches for optima by updating generations.
PSO is initialized with a group of random particles (solutions) and then searches for optima by updating generations. In every iteration, each particle is updated by following two "best" values. The first one is the best solution (fitness) it has achieved so far. (The fitness value is also stored.) This value is called . Another "best" value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the population. This best value is a global best and called . When a particle takes part of the population as its topological neighbors, the best value is a local best and is called . After finding the two best values, the particle updates its velocity and positions with following equation (10) and (11) as
(10) …(11)
In the above equation,

The term is called
particle memory influence

The term is called swarm influence.
is the velocity of particle at iteration u
and are constants which pulls each particle towards pbest and gbest positions.
is the inertia weight provides a balance between global and local explorations, thus requiring less iteration on average to find a sufficiently optimal solution. It is set according to the following equation,


ELD using PSO
When any optimization process is applied to the ELD problem, some constraints are considered. In this work three different constraints are considered. Among them the equality constraint is summation of all the generating power must be equal to the load demand and the inequality constraint is the powers generated must be within the limit of maximum and minimum active power of each unit. The additional constraint is the real time efficiency. The sequential steps of the proposed PSO method are given below.
Step 1) The individuals of the population are randomly initialized according to the limit of each unit including individual dimensions. The velocities of the different particles are also randomly generated keeping the velocity within the maximum and minimum value of the velocities. These initial individuals must be feasible candidate solutions that satisfy the practical operation constraints.
Step 2) Each set of solution in the space should satisfy the equality constraints. So equality constraints are checked. If any combination doesnt satisfy the constraints then they are set according to the power balance equation.
Step 3) The evaluation function of each individual is calculated in the population using the evaluation function (2). The present value is set as the value.
Step 4) Each values are compared with the other values in the population. The best evaluation value among the is denoted as .
Step 5) The member velocity v of each individual Pg is modified according to the velocity update equation (10).
Step 6) The velocity components constraint occurring in the limits from the following conditions are checked.
Where
.(12)
– maximum value of weighting factor. – minimum value of weighting factor.
Step 7) The position of each individual is modified according to the position update equation (11).
Step 8) If the evaluation value of each individual is better than
A. Flow chart
previous , the current value is set to be . If the
best is better than , the value is set to be
.
Step 9) If the number of iterations reaches the maximum, then go to step 10.Otherwise, go to step 2.
Step 10) The individual that generates the latest is the optimal generation power of each unit with the minimum total generation cost.
IJERTV2IS70111
www.ijert.org
302


NUMERICAL STUDIES
The proposed method is used to solve two case studies involving 6 and 8 generating units. The initial particles are randomly generated within the feasible range. The parameters and inertia weight are selected for best convergence characteristic. Here = = 2.0 The maximum value of w is chosen 0.9 and minimum value is chosen 0.4. The
velocity limits are selected as and the
minimum velocity is selected as . There are 10 no of particles selected in the population. The algorithm is implemented in MATLAB 7.10.0(R2010a).

Case Study 1
This test case comprise of 6 generating units [12] with quadratic cost functions and penalty factors as shown in Table
I. The results obtained with load demand 1050 MW are compared in Table II for both approaches i.e. i) without taking efficiency ii) with taking efficiency
TABLE 1
GENERATION CHRACTISTICS OF 6GENERATING UNIT SYSTEM
Unit
Penalty Factor
P1
10
125
0.152
38.54
756.80
0.8806
P2
10
150
0.106
46.16
451.32
0.9431
P3
35
225
0.028
40.40
1050.0
0
1.9886
P4
35
210
0.035
38.21
1243.5
3
0.9438
P5
130
325
0.021
36.32
8
1658.5
7
1.9998
P6
125
315
0.018
38.27
1356.6
6
1.9413
TABLE 2
COMPARISON OF FUEL COSTS FOR 6GENERATOR SYSTEM WITH
PD = 1050MW
Li
Units
Load Demand (1050MW)
Output (W/o EFFIC)
Output (With EFFIC)
0.8806
P1
73.20
76.03
0.9431
P2
175.75
175.30
1.9886
P3
170.09
188.47
0.9438
P4
172.51
170.07
1.9998
P5
182.16
221.72
1.9413
P6
259.24
329.45
Fuel Cost (Rs)
15598.557
15418.024

Case Study II
This test case comprises of 8 generating units with quadratic cost functions and penalty factors as shown in Table

The load demand in the system is taken as 1000 MW. The transmission loss is assumed to be zero. The output obtained is shown in Table IV.
TABLE 3
GENERATION CHRACTISTICS OF 8GENERATING UNIT SYSTEM
Unit
Penalty Factor
P1
62
101
0.3167
10.94
102.8
0.1351
P2
55
85
0.3463
7.586
100.6
1.0003
P3
53
78
0.6362
23.52
104.6
0.0113
P4
52
82
0.5263
16.15
109.6
1.0573
P5
115
183
0.08842
2.344
63.7
0.0002
P6
110
182
0.08394
4.138
77.77
1.0624
P7
168
240
0.08638
5.496
98.7
1.000
P8
168
245
0.09525
6.382
58.44
0.0165
TABLE 4
COMPARISON OF FUEL COSTS FOR 8GENERATOR SYSTEM 1000 MW
Li
Units
Load Demand (1000MW)
Output (W/o EFFIC)
Output (With EFFIC)
0.1351
P1
69.99
68.54
1.0003
P2
71.76
72.50
0.0115
P3
66.97
66.26
1.0573
P4
68.76
71.38
0.0002
P5
153.00
152.66
1.0624
P6
150.23
150.51
1.000
P7
208.23
205.37
0.0165
P8
211.03
211.59
Fuel Cost (in Thousand Rs)
13877.947
13721.500

CONCLUSION
This paper presents a new approach of considering real time efficiency as an inequality constraint to solve the economical load dispatch problem in thermal power plants. The efficiency of individual operating units is formulated as Penalty Factors ( ) of respective units. These penalty factors are utilized to economically distribute the total power demand ( ) among individual operating units in order to achieve minimum fuel cost. A comparison analysis has been done on two different test systems comprises 6 and 8 generating units for two cases i.e. i) without taking efficiency and ii) with taking efficiency. Table II and IV shows the comparison between fuel costs obtained for above two cases. From the respective tables, it is seen that if efficiency is taken in to consideration, the power generation from individual operating units are improved proportional to penalty factors (which are calculated through turbine, boiler and generator efficiencies of respective operating units). From Table II and
IV, it is seen that taking efficiency in to consideration results in net saving (in terms of rupees) to the plant as a whole but it is not always possible. In some of the cases, by taking efficiency as an operating constraint, the total fuel cost may get increased by a small amount but this small increase in fuel cost is justified as at the same time the generation from various operating units are improved (i.e. if efficiency of any unit is poor, contribution from that unit is decreased accordingly and viceversa). If a unit is operating at normal loading with poor efficiency, it results in high rejection from fuel, unstable flame condition, high amount of flyash particles in furnace and increase in loading on PA fans etc which causes sudden tripping and reduces the useful life an efficiency of various boiler auxiliaries and the plant as a whole. Therefore, it is desirable to operate the unit with poor efficiency at near lower limits in order to maintain the fuel stock and efficiency of the power plant.

REFERENCES


P. Aravindhababu and K.R. Nayar, Economic dispatch based on optimal lambda using radial basis function network, Elect. Power Energy Syst,. 24 (2002), pp. 551556.

Happ H. H., Optimal power dispatch a comprehensive survey. IEEE Transection on Power Apparatus and Systems, Vol PAS96. No. 3, MayJune, 1977.

Ramanathan R., Fast economic dispatch based on the penalty factors from Newtons method, IEEE Transection on Power Apparatus and Systems, Vol PAS104. No. 7, July 1985.

E. H. Chowdhury, Saifur Rahrnan, A review of recent advances in economic dispatch, IEEE Transactions on Power Systems, Vol. 5, No. 4, November 1990.

Aniruddha Bhattacharya, Member, IEEE, and Pranab Kumar Chattopadhyay, BiogeographyBased Optimization for Different Economic Load Dispatch Problems, IEEE Transactions on Power Systems, Vol. 25, no. 2, May 2010.

Yalcinoz T. and Altun H., Environmentally constrained economic dispatch via a genetic algorithm with Arithmetic crossover, IEEE 6th Africon Conference in Africa 2002, vol. 2, pp. 923 928, 2002.

Leandro dos Santos Coelho and Viviana Cocco Mariani, Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization With ValvePoint Effect, IEEE Transactions on Power Systems, vol. 21, no. 2, May 2006 989.

Nidul Sinha, R. Chakrabarti, and P. K. Chattopadhyay,
Evolutionary Programming Techniques for Economic Load Dispatch IEEE Transactions on Evolutionary Computation, vol. 7, no. 1, February 2003

Y. M. Park, J. R. Won, and J. B. Park, A new approach to economic load dispatch based on improved evolutionary programming, Eng. Intell. Syst. Elect. Eng. Comm., vol. 6, no. 2, pp. 103110, June 1998.

H. T. Yang, P. C. Yang, and C. L. Huang,
Evolutionary programming based economic dispatch for units with nonsmooth fuel cost functions, IEEE Trans. Power Syst., vol. 11, no. 1, pp. 112118, Feb. 1996.

K.Senthil and K.Manikandan, Economic Thermal Power Dispatch with Emission Constraint and Valve Point Effect loading using Improved Tabu Search Algorithm, International Journal of Computer Applications (0975 8887) Volume 3 No.9, July 2010.

S. Muthu Vijaya Pandian and K. Thanushkodi,
Solving Economic Load Dispatch Problem Considering Transmission Losses by a Hybrid EP EPSO Algorithm for Solving both Smooth and Non Smooth Cost Function International Journal of Computer and Electrical Engineering, Vol. 2, No. 3, June, 2010 17938163
———