Artificial Fish Swarm Algorithm based Optimization of Load Dispatch Problem for GTCC Units

Artificial Fish Swarm Algorithm based Optimization of Load Dispatch Problem for GTCC Units

Yongmei Wang

College of Information Engineering Zhengzhou University

Zhengzhou, China

AbstractLoad dispatch problem lies at the kernel among different issues in GTCC units operation, which is about minimizing the fuel consumption for a period of operation so as to accomplish optimal load dispatch among units and in return satisfying the total load demand and operation constraints. This paper analyses the load dispatch model of gas turbine combined-cycle (GTCC) units and utilize a swarm intelligence algorithm to optimize the solution of the model. AFSA is motivated by intelligent collective behavior of fish groups in nature. Due to fish swarm behaviors such as random behavior, chasing behavior, swarming behavior and searching behavior, it shows characteristics such as non-sensitive initial artificial fish location, flexibility, high convergent speed, global optimal capacity and so on. Simulations were performed by building up models using data from previous literature and optimizing the solutions of the models by AFSA. The simulations show that AFSA can get a better effect than equal micro incremental method used in previous literature. The operating economy is proved through the results obtained by AFSA. It can be concluded that AFSA is quite effective in solving the optimization of load dispatch problem of GTCC units.

KeywordsGTCC units; Load dispatch; Artificial Fish Swarm Algorithm

INTRODUCTION

Due to the advantages [1,2] of GTCC units and the availability of natural gas, GTCC units continue to gain strength in power industry. In this situation, economic operation of the units becomes much important. And load dispatch problem lies at the kernel among different issues in GTCC units operation [3,4].

The load dispatch problem is about minimizing the fuel consumption for a period of operation so as to accomplish optimal load dispatch among units and in return satisfying the total load demand and operation constraints. To establish the load dispatch model is necessary for the calculation of the problem. In fact, performance of GTCC unit varies with many factors [5-7]. This will lead to variation of load dispatch model. Environmental factors are uncontrollable

and always changing with time and location. So influences of environmental conditions on establishing the load dispatch model is briefly discussed.

Mathematically, the problem of load dispatch is a complex nonlinear problem containing integer and continuous variables. Many efforts [8-10] have been made to solve the problem, through various mathematical programming and optimization techniques. But these methods all have certain limitations. For example, lambda iteration needs the formulation in continuous differentiable form. Consequently, this method is unable to solve discontinuous load dispatch problems. Besides, they need high computation time solving large size load dispatch problems and sometimes fail to provide global optimal solution.

With the development of computer technology and artificial intelligence, modern intelligent algorithms [11-14] show great advantages in solving load dispatch problems, which mainly includes artificial neural network, simulated annealing, ant colony optimization, genetic algorithm and artificial fish swarm algorithm. Among them, artificial fish swarm algorithm (AFSA)[15] is a method through simulating the behavior of the sh swarm inside water, which attracts much attention recently. An articial sh is a ctitious entity whose movements are simulations of sh behaviors[16,17] such as chasing behavior, swarming behavior, searching behavior and random behavior. Local optimization of individuals will eventually lead to the global optimization. Due to strong robustness for initial parameters, global optimization and parallel computing, it is successfully applied in solving optimization problems[18]. Simulations were performed by building up models using data from previous literature [19] and optimizing the solutions of the models by AFSA. The simulations show that AFSA can get a better effect than equal micro incremental method used in the literature. And the operating economy is proved though the results obtained by AFSA. It can be concluded that AFSA is quite effective in solving the optimization of load dispatch problem of GTCC units.

LOAD DISPATCH MODEL OF GTCC UNITS

In the model above,

Pi min , Pi max are influenced by the

The load dispatch optimization of GTCC units is to nd the optimum combination of units that minimizes the total gas consumption while satisfying the total load demand and operation constraints. In order to analyze the problem through a mathematical model, the total gas consumption of all the GTCC units is described as a function of units power outputs. And to optimize the solution of the load dispatch problem is to get the values of each units power output while the total gas consumption function achieves a minimum. Thus the formulation of a GTCC units load dispatch problem with operation constraints can be described as follows.

performance of GTCC units. And the performance of a GTCC unit varies with many factors, such as environmental conditions, condenser pressure, inlet and exhaust losses, fuel properties, etc. The influences of conditions are important factors. The main environmental factors influencing the performance of GTCC units are ambient temperature, barometric pressure and relative humidity. When the ambient temperature increases, the power output of the combined cycle is reduced and very slight variation in heat consumption rate. The output and the barometric pressure generally decrease proportionately, but for the plant already installed, the variation of this variable is so subtle that can be neglected. The power output of the GTCC units increases

min F n

Ui fi (Pi )

while other parameters remain constant. However, the

variation is to be too small to be considered. So to build the

s.t.

n

n

i 1

i 1

Ui Pi PD

(1)

model of GTCC units load dispatch problem more scientifically, considering the influence of environmental is important.

P P P

i min

i i max

Optimization of the load dispatch problem for GTCC units

n

i 1

Ui Pi max

PD R

by Artificial Fish Swarm Algorithm

where F is the objective function corresponding to the total gas consumption (in m3 / h); n is the total number of GTCC

units. fi (Pi ) is the gas consumption for the ith unit (in

1. Overview of Artificial Fish Swarm Algorithm

   Artificial fish swarm algorithm (AFSA), proposed by Li Xiao Lei in 2002, is a stochastic population-based algorithm motivated by intelligent collective behavior of fish groups in nature.

   In AFSA, a population of artificial fishes move

   m3 / h); Pi

   is the power output of unit i (in MW); n is the

   towards an objective by performing some behaviors such as

   number of units in the system;

   Ui represents ith units

   Swarm, Follow, and Movement.

   Movement in general, sh swims randomly in water

   running state and it can only be 0 or 1 which represents stop

   looking for food and other companions. Followwhen a fish, or a group of fishes, in the swarm discovers food, the others

   or running.

   PD is the systems total demand (in MW);

   in the neighborhood nd the food dangling quickly ater it. Swarmwhen swimming, sh naturally assembles in groups

   which is a living habit in order to guarantee the existence of

   Pi min

   and

   Pi max

   are the lower and upper bounds for power

   the swarm and avoid dangers. Preythis is a basic biological behavior since sh tends to the food, when sh discovers a

   outputs of the ith unit. (in MW); R is the spinning reserve

   R 0.07P

   region with more food, by vision or sense, it goes directly and quickly to that region. Artificial fishes do the

   and generally

   D is adopted.

   optimization process by performing the behaviors above. AFSA has characteristics such as non-sensitive initial

   For gas consumption function fi (Pi ) , binomial expression is usually adopted to fit its characteristic curve as follow.

   artificial fish location, flexibility and fault tolerant. It has been applied on different problems.

2. The procedure for Artificial Fish Swarm Algorithm

i i i i i i i

i i i i i i i

f (P ) a P2 b P c

(2)

The main steps of AFSA include encoding, initialization,

where

ai ,bi , ci

are the gas consumption characteristic

building a fitness function selection, crossover, mutation,

coefficients of each unit.

There are some simplified hypotheses of the model: All the n units can be arranged to start and stop; fuel consumption for start or stop is not considered; line losses are not considered; the fuel property of natural gas is constant; and the total load demand keeps constant within a certain interval.

information exchange and elitist strategy.

Step 1. Establishing food consistence function:

In AFSA, the searching procedure is to find the highest food consistence. For the load dispatch problem in this paper, the food consistence function can be described as follow.

g [U f (P )] C(U P P )

g [U f (P )] C(U P P )

n n

2

i i i i i D

i1

i1

(3)

where C is a penalty factor which usually takes a large value. In the function above, it can lead to small value of the function if a solution does not satisfy the constraints, so the solution will be deleted.

Step 2 Initializing:

Step 4 Following:

An artificial fish in location Xi searches the area within its

visual range and the number of its companions nf within the

Initialize a swarm of N fishes. Each fish is represented X Y

by a group of real numbers. The initial values of all the fishes

area and the one max with highest food consistence max has

are generated randomly. For example, for the load problem of

two units, the variables need to be optimized are x1, x2 , whose ranges are [a,b]and[c,d]. So a fish swarm of 2 rows

been found. If

Ymax nf

Yi

, the following behavior will

X

and N columns will be generated, where each column represents a fish and N is the size of the swarm.

Step 3 Swarming:

If the current location of an artificial fish is Xi , it will search

for the companions within its visual range. The number of its companions is n and the centroid for them is X . The food

perform one step forward to the companion max . Otherwise,

the fish will perform the preying behavior as described previously.

Step 5 Shifting strategy:

Evaluate the circumstance of an artificial fish. That is, select the one which leads to higher food consistence from the swarming behavior and following behavior.

f c Step 6 Iterative computation:

Y Set up a bulletin board so as to prevent the best fish and

consistence of

Xi , Xc

are Yi ,Yc . If c Yi

nf

( is

decide when to stop the iteration of the behaviors. Each artificial fishs status will be compared the record on the board. If the location of the fish is better than that of the

congestion), it indicates that the localtion of the centroid has a higher food consistence and is not so crowed. So the swarming behavior will move one step forward the centroid

Xc . If not, the preying behavior will be performed. The preying behavior is like this: The artificial fish in Xi selects a

bulletin board, the record on the bulletin board will be substituted by the artificial fish. Then the algorism go back to step 3 and the process will be repeated iteratively until the maximum iteration number is achieved.

SIMULATION

In paper [19] the author uses equal micro incremental to optimize the load dispatch of 3×390MW gas turbine generation units. In this paper, the gas consumption

location X j

randomly within its visual range; if

Yi Yj , it

characteristic equations from paper [19] are used for the calculation of optimal load dispatch by AFSA.

indicates that the food consistence in X j

is higher; So the

According to paper [19] the characteristic coefficient of gas consumption function and bound constraints are shown in

preying behavior will move one step forward to X j ; if not, it

will select another position X j randomly again and judges

whether move forward or not; iterating as above until the maximum timess of preying behavior; if the condition for moving forward is still not satisfied, the artificial fish will move one step randomly.

Table 1.

TABLE 1. Gas consumption character coefficient and limit of load

Optimal value

Optimal value

Suppose the constraints are already revised according to the ambient conditions for lack of related data. Take total load PD=505MW on July 25, 2007 as an example. The food consistence function is described as follow.

-6

-6

13 x 10

12

11

g U f (P ) C(U P P )

g U f (P ) C(U P P )

3 3

2

i i i i i D

(4) 10

i1 i1 9

The units in operation are just 1# and 2#, so U1=U2=1U3=0. 8

Take 100 for the penalty factor C. 7

f (P ) 0.11837P2 84.002P 16725 6

5

5

1 1 1 1

2 2 2 2

2 2 2 2

f (P ) 0.12583P 2 75.695P 18274

(5)

0 50 100 150 200 250 300 350

Number of iterations

0 50 100 150 200 250 300 350

Number of iterations

In this AFSA, the size of the swarm is set to 100; the maximum iteration number is 350; the maximum number of preying behavior is 100; the visual range is 2.5; the congestion is 0.618; the length of step is 0.1. The process for AFSA to optimize the load dispatch mdel is shown in Figure 2.

266

264

262

260

p2

p2

258

256

254

252

250

235 240 245 250 255 260

p1

Fig.2. Iterative process of AFSA

Through the optimization of AFSA, the minimum value of fitness function reaches1.10056105 , when the load of 1# unit 246.72MW and 2# unit 258.13 MW. The total gas consumption is 90852.59m3N/h.

Results and discussions

Using the foregoing AFSA method to optimize the load dispatch problem of GTCC units, all the results obtained by AFSA are compared with those by other methods, as shown in Table 2 and Table 3.

Fig.1. Movement of optimal load dispatch

TABLE 2. Load dispatch results of 1#,2# by different methods On July 25,2007

TABLE 3. Load dispatch results of 1#,3# by different methods On October 26,2007

Syst,2002;17(1):10812.

According to the results above, AFSA could achieve savings of total gas consumption compared to the equal micro incremental method and AGC instruction. For instance, On October 26, 2007, when the total load demand is 500MW, the load dispatch results of unit 1# and 3# are 234.10MW and 265.26MW. The gas consumption is 42563.81m3N/h and 43606.07m3N/h respectively. The total gas consumption is 86169.88m3N/h, which has a reduction of 2317.06m3N/h compared to equal micro incremental method and 1588.71m3N/h compared to AGC instruction. It indicates that using AFSA to optimize the load dispatch problem of gas turbine units can improve the economic efficiency of the units.

CONCLUSIONS

In this paper, the dispatch problem of gas turbine combined-cycle units is proposed and the artificial fish swarm algorithm is employed on the optimization of the problem. Simulations were performed with AFSA method and the optimization results are compared with equal micro incremental method. Almost all the results obtained by AFSA in the simulations are better than other methods. With AFSA method the gas consumptions are significantly reduced. The searching processes show that AFSA has good characteristics of globally optimization, fast convergent speed robustness for initial values and so on. The findings indicate that AFSA has an advantage in the optimization of operation of gas turbine units. This work will contribute to the operation of GTCC units.

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