Economic Power Dispatch of Power System with Pollution Control using Multiobjective Ant Colony Optimization

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 57

ECONOMIC POWER DISPATCH OF POWER SYSTEM WITH POLLUTION CONTROL USING

MULTIOBJECTIVE PARTICLE SWARM OPTIMIZATION

Tarek Bouktir, Rafik Labdani and Linda Slimani

Department of Electrical Engineering, University of Larbi Ben M’Hidi, Oum El-Bouaghi, 04000, Algeria, [email protected]

ABSTRACT This paper reports on a particle swarm optimization (PSO) method for

solving the optimal power flow problem (OPF). The objective is to minimize the total fuel cost of generation and environmental pollution caused by fossil based thermal generating units and also maintain an acceptable system performance in terms of limits on generator real and reactive power outputs, bus voltages, shunt capacitors/reactors and power flow of transmission lines. The proposed approach has been evaluated on an IEEE 30-bus test system. The results obtained with the proposed approach are presented and compared favorably with results of genetic algorithm technique.

Keywords: Optimal Power Flow, Power Systems, Pollution Control, NOx emission, Particle Swarm Optimization.

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1. INTRODUCTION

The optimal power flow (OPF) calculation optimizes the static operating condition of a power generation-transmission system. The

Economic Power Dispatch of Power System with Pollution Control Using Multiobjective Particle Swarm Optimization

University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 58

main benefits of optimal power flow are (i) to ensure static security of quality of service by imposing limits on generation-transmission system’s operation, (ii) to optimize reactive-power/voltage scheduling and (iii) to improve economy of operation through the full utilization of the system’s feasible operating range and by the accurate coordination of transmission losses in the scheduling process. The OPF has been usually considered as the minimization of an objective function representing the generation cost and/or the transmission loss. The constraints involved are the physical laws governing the power generation-transmission systems and the operating limitations of the equipment.

The optimal power flow has been frequently solved using classical optimization methods. Effective optimal power flow is limited by (i) the high dimensionality of power systems and (ii) the incomplete domain dependent knowledge of power system engineers [1-3].

The first limitation is addressed by numerical optimization procedures based on successive linearization using the first and the second derivatives of objective functions and their constraints as the search directions or by linear programming solutions to imprecise models [4-7]. The advantages of such methods are in their mathematical underpinnings, but disadvantages exist also in the sensitivity to problem formulation, algorithm selection and usually converge to local minima [8].

The second limitation, incomplete domain knowledge, precludes also the reliable use of expert systems where rule completeness is not possible.

One of the most recent metaheuristic algorithms, the Particle Swarm Optimization (PSO), is a population based stochastic optimization technology [9, 10] by Eberhart and Kennedy in 1995, inspired by social behavior of bird flocking and fish schooling. It is used for optimization of continuous non linear functions [11, 12].

PSO was applied to different areas of power systems. It was used to optimize the reactive power flow in the power system network to minimize real power system losses [13]. Park et al. [14] and Gaing [15]

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 59

adopted PSO to solve the traditional economic dispatch problem. Gaing considers the nonlinear characteristics of a generator such as ramp rate limits and prohibited operating zone for actual power system operation. Naka et al. formed a hybrid technique by combining PSO with other heuristic techniques to improve the performance of a distribution of state estimator in [16]. Kassabalidis et al. integrated PSO with neural networking to identify the dynamic security border of power systems under a deregulated environment [17]. The transmission network optimal planning was treated by PSO in [18]. Ting et al. proposed a hybrid PSO to tackle the unit commitment problem [19]. The HPSO proposed in the paper is a blend of binary particle swarm optimization (BPSO) and real coded particle swarm optimization (RCPSO). The UC problem is handled by BPSO, while RCPSO solves the economic load dispatch problem. Abido is credited with introducing PSO to solve the OPF problem [9]. The proposed approach has been examined and tested on the standard IEEE 30-bus test system with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. Gaing presented an efficient mixed-integer particle swarm optimization (MIPSO) for solving the constrained optimal power flow (OPF) with a mixture of continuous and discrete control variables and discontinuous fuel cost functions [20]. Alrashidi and El-Hawary presented a comprehensive coverage of PSO applications in solving optimization problems in the area of electric power systems [21].

The PSO is a swarm intelligence algorithm, inspired by the social dynamics and emergent behavior that arises in socially organized colonies. The PSO algorithm exploits a population of individuals to probe promising regions of search space. In this context, the population is called swarm, and the individuals are called particles or agents. Each particle moves with an adaptable velocity within the regions of search space and retains a memory of the best position it ever encountered. The best position ever attained by each particle of the swarm is communicated to all other particles [22].

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University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 60

The concept of PSO originated as a simulation of a simplified social system. This method is based on researches about swarms such as fish schooling and a flock of birds. According to the research results for a flock of birds, birds find food by flocking (not by each individual). According to the observation of behavior of people during a decision process, people utilize two important kinds of information. The first one is their own experience; that is, they have tried the choices and know which state has been better so far, and they know how good it was. The second one is other people’s experiences; that is, they have knowledge of how the other individuals (agents) around them have performed. They know which choices of their neighbors have been found as more positive and also the positiveness of the pattern. Each agent decides the decision using individual experiences and other people’s experiences [23].

In recent years, environmental constraint started to be considered as part of electric system planning. That is, minimization of pollution emission (NOx, SOx, CO2, etc.) in case of thermal generation power plants. However, it became necessary for power utilities to count this constraint as one of the main objectives, which should be solved together with the cost problem. Thus, we are faced with a multi-objective problem.

Spens and Lee [24] solved the economic load dispatch under environmental restrictions in a multi-hour time horizon minimizing fuel consumption cost for SO2 and NOx using an emission ton limit for the first one and an emission rate for the second one.

Fan and Zhang [25] solved a cost minimization problem proposing a solution via quadratic programming, where environmental restrictions are modeled with linear inequalities.

In a previous paper [26], the authors proposed the use of a genetic algorithm with real coding on the optimal power flow problem using as objective function the minimization of the fuel cost and NOx emission control. More than 6 small-sized test cases were used to demonstrate the performance of the proposed algorithm. Consistently acceptable results were observed.

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 61

In a recent paper [27], the authors presented the application of the Particle Swarm Optimization (PSO) method to the Optimal Power Flow problem for a large scale power system. The objective function considers at the same time the cost of the power generation, the transmission loss and the voltage deviation. Numerical results for IEEE 30-bus and IEEE 118-bus test systems show that a PSO technique can generate an efficiently high quality solution and with more stable convergence characteristics than genetic algorithms (GA).

Recently, a comparative study among the Pareto-based multiobjective evolutionary algorithms (MOEA) techniques has been carried out to assess their potential to solve the real-world multiobjective environmental/ economic dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multiobjective optimization problem where fuel cost and environmental impact are treated as competing objectives. The potential of MOEA to handle this problem is investigated and discussed. The MOEA techniques were compared to each other and to classical multiobjective optimization techniques as well. The effectiveness of MOEA to solve the EED problem is demonstrated [28].

In this paper, we solved the bi-objective OPF via an efficient Particle Swarm Optimization (PSO). The bi-objective function to minimize consists of the fuel cost of generation and the environmental pollution caused by fossil based thermal generating units. The bi-objective Environmental/ economic OPF problem was converted to a single objective problem by linear combination of the two objectives as a weighted sum. The feasibility of the proposed method is tested on the IEEE 30 bus system and compared to genetic algorithm. The PSO algorithm was developed in an Object Oriented manner using the C++ programming language. It was integrated in our object-oriented optimal power flow software [29]. The input and output data can communicate with the OPF computing modules via an object-oriented graphical user interface and through an object-oriented database. Additional non-linear objective functions and constraints can be easily added to the developed software package. The implementation of PSO in object-oriented style will not be addressed in this article due to space limitations.

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University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 62

2. PROBLEM FORMULATION

The standard OPF problem can be formulated as a constrained optimization problem as follows:

0)(0)(..

)(min

≤=

xhxgts

xf (1)

where f(x) is the objective function, g(x) represents the equality constraints, h(x) represents the inequality constraints and x is the vector of the control variables such as generator real power Pg, generator voltages Vg, transformer tap setting T, and reactive generations of VAR sources Qc. Therefore, x can be expressed as

[ ]ncntngngT QcQcTTVgVgPgPgx 1111 ,,,= (2)

where ng is the number of generator buses, nt is the number of transformer branches and nc is the number of shunt compensators.

The essence of the optimal power flow problem resides in reducing the objective function and simultaneously satisfying the load flow equations (equality constraints) without violating the inequality constraints

Objective Function

Economic objective function

The most commonly used objective in the OPF problem formulation is the minimization of the total operation cost of the fuel consumed for producing electric power within a schedule time interval (one hour). The individual costs of each generating unit are assumed to be function, only, of real power generation and are represented by quadratic curves of

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 63

second order. The objective function for the entire power system can then be expressed as the sum of the quadratic cost model at each generator [2, 3].

( ) ( )∑=

++=ng

iiiiiiec PgcPgbaxF

1

2 $/h (3)

where ai , bi and ci are the cost coefficients of generator at bus i.

Emission objective function

The emission control cost results from the requirement for power utilities to reduce their pollutant levels bellow the annual emission allowances assigned for the affected fossil units. The total emission can be reduced by minimizing the three major pollutants: oxides of nitrogen (NOx), oxides of sulphur (SOx) and carbon dioxide (CO2). The objective function that minimizes the total emissions can be expressed in a linear equation as the sum of all the three pollutants resulting from generator real power Pgi [30].

In this study, Nitrogen-Oxide (NOx) emission is taken as the index from the viewpoint of environment conservation. The amount of NOx emission is given as a function of generator output (in Ton/hr), that is, the sum of quadratic and exponential functions [31].

( )( )∑=

+++=ng

iiiiiiiiiE PgedPgcPgbaF

1

2 exp Ton/hr (4)

where ai, bi,ci, di, and ei are the coefficients of generator emission characteristic.

The pollution control cost (in $/h) can be obtained by assigning a cost factor to the pollution level expressed as

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University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 64

Epc FwF ⋅= $/h (5)

where w is the emission control cost factor in $/Ton [32].

Total objective function

The total objective function considers at the same time the cost of the generation and the cost of pollution level control. These objectives have complicated natures and conflict in some points (the minimization of the generation cost can maximize the emission cost and vice versa). However, the solutions may be obtained in which fuel cost and emission are combined in a single function with a difference weighting factor. This objective function is described by [33]:

( ) pcFecFF ⋅−+⋅= αα 1min (6)

where α is a weighting factor that satisfies 10 ≤≤α . The boundary values α=1 and α=0 give the conditions for the pure minimization of the fuel cost function and the pure minimization of the pollution control level.

Types of equality constraints

While minimizing the objective function, it is necessary to make sure that the generation still supplies the load demands plus losses in transmission lines. The equality constraints are the power flow equations describing bus injected active and reactive powers of the i th bus.

where active and reactive power injection at bus i are defined in the following equation:

( )∑=

+=−=nb

jijijijijjiiii bgVVPdPgP

1sincos θθ (7)

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 65

( )∑=

−=−=nb

jijijijijjiiii bgVVQdQgQ

1cossin θθ (8)

where Qgi is the reactive power generation at bus i; Pdi, Qdi are the real and reactive power demands at bus i; Vi, Vj, the voltage magnitude at bus i, j, respectively; θij is the admittance angle, bij and gij are the real and imaginary part of the admittance and nb is the total number of buses.

Types of inequality constraints

The inequality constraints of the OPF reflect the limits on physical devices in the power system as well as the limits created to ensure system security. The most usual types of inequality constraints are upper bus voltage limits at generations and load buses, lower bus voltage limits at load buses, var. limits at generation buses, maximum active power limits corresponding to lower limits at some generators, maximum line loading limits and limits on transformer tap setting.

The inequality constraints on the problem variables considered include:

• Upper and lower bounds on the active generations at generator buses Pgi

min≤ Pgi ≤ Pgimax , i = 1, ng.

• Upper and lower bounds on the reactive power generations at generator buses Qgi

min≤ Qgi≤ Qgimax , i = 1, ng

• Upper and lower bounds on reactive power injection at buses with VAR compensation Qci

min≤ Qci≤ Qcimax, i= 1, nc

• Upper and lower bounds on the voltage magnitude at the all buses. Vi

min≤ Vi ≤ Vimax , i = 1, nb.

• Upper and lower bounds on the bus voltage phase angles θimin≤ θi

≤ θimax , i = 1, nb.

• For secure operation, the transmission line loading Sl is restricted by its upper limit as:

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Sli≤ Slimax , i = 1, nl, where Sli, Sli

max are stand for the power of transmission line and limit of transfer capacity of transmission line. nl is the number of transmission lines.

It can be seen that the generalized objective function F is a non-linear, the number of the equality and inequality constraints increase with the size of the power distribution systems. Applications of a conventional optimization technique such as the gradient-based algorithms to a large power distribution system with a very non-linear objective functions and great number of constraints are not good enough to solve this problem, because it depends on the existence of the first and the second derivatives of the objective function and on the efficient computing of these derivatives in a large search space.

3. PARTICLE SWARM OPTIMIZATION IN OPTIMAL POWER FLOW

Description of Particle Swarm Optimization method

The particle swarm optimization works by adjusting trajectories through manipulation of each coordinate of a particle. Let ix and iv denote the positions and the corresponding flight speed (velocity) of the particle i in a continuous search space, respectively. The particles are manipulated according to the following equations.

( ) ( ) ( ) ( )( ) ( ) ( )( )ti

tipbest

ti

tgbest

ti

ti xxrcxxrcvwv −+−⋅⋅+=+ **. 2211

1 (9)

( ) ( ) ( )11 ++ += ti

ti

ti vxx (10)

Where:

t: pointer of iterations (generations).

w: inertia weight factor.

c1, c2: acceleration constant.

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 67

r1, r2: uniform random value in the range (0,1). ( )tiv : velocity of particle i at iteration t. ( )tix : current position of particle i at iteration t. ( )tipbestx : previous best position of particle i at iteration t. ( )tgbestx : best position among all individuals in the population at

iteration t. ( )1+tiv : new velocity of particle i. ( )1+tix : new position of particle i.

PSO applied to optimal power flow

Our objective is to minimize the objective function of the OPF defined by (6), taking into account the equality constraints and the inequality constraints.

The cost function implemented in PSO is defined as:

( ) ( )

( ) ( )( )⎥⎥⎦

⎤

⎢⎢⎣

⎡+++⋅⋅−

+⎥⎥⎦

⎤

⎢⎢⎣

⎡++⋅=

∑

∑

=

=

ng

igiiiiiii

ng

iiiiii

iPedPgcPgbaw

PgcPgbaxF

1

2

1

2

exp1 α

α

(11)

To minimize F is equivalent to getting a maximum fitness value in the searching process. The particle that has lower cost function should be assigned a larger fitness value.

The objective of OPF has to be changed to the maximization of fitness to be used as follows:

Fffitness max= (12)

Economic Power Dispatch of Power System with Pollution Control Using Multiobjective Particle Swarm Optimization

University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 68

where:

maxf : the maximum of F, ( maxgigi pp = ).

The search of the optimal control vector is performed using into account the real power flow equation defined by (7) which present the system transmission losses (Ploss). These losses can be approximated in terms of B coefficients as [34]:

∑∑= =

⋅⋅=ng

i

ng

jjijiloss PgBPgP

1 1 (13)

The Bij coefficients are obtained from a power flow solution. These losses are introduced in the represented as a penalty vector given by:

1)1( −

∂∂

−=Pg

PPf loss (14)

In this method only the inequality constraints on active powers are handled in the cost function. The other inequality constraints are scheduled in the load flow process. Because the essence of this idea is that the inequality constraints are partitioned in two types of constraints, active constraints that affect directly the objective function are checked using the PSO-OPF procedure and the reactive constraints are updating using an efficient Newton-Raphson Load flow (NR) procedure.

Our objective is to search (Pgi) set in their admissible limits to achieve the optimization problem of OPF. At initialization phase, (Pgi) is selected randomly between Pgi

min and Pgimax.

After the search goal is achieved, or an allowable generation is attained by the PSO algorithm. It is required to performing a load flow solution in order to make fine adjustments on the optimum values

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 69

obtained from the PSO-OPF procedure. This will provide updated voltages, angles and points out generators having exceeded reactive limits. to determining all reactive power of all generators and to determine active power that should be given by the slack generator taking into account the deferent reactive constraints. Examples of reactive constraints are the min and the max reactive rate of the generators buses and the min and max of the voltage levels of all buses. All these require a fast and robust load flow program with best convergence properties. The developed load flow process is based upon the NR algorithm using the optimal multiplier technique [35, 36].

Optimal setting of PSO parameters in OPF case

The role of the inertia weight iw , in Equation (9), is considered critical for the PSO’s convergence behavior. The inertia weight is employed to control the impact of the previous history of velocities on the current velocity. In this way, the parameter iw regulates the trade-off between the global (wide-ranging) and local (nearby) exploration abilities of the swarm. A large inertia weight facilitates global exploration (searching new areas); while a small one tends to facilitate local exploration, i.e. fine-tuning the current search area. A suitable value for the inertia weight iw usually provides balance between global and local exploration abilities and consequently results in a reduction of the number of iterations required to locate the optimum solution. Initially, the inertia weight was constant. However, experimental results indicated that it is better to initially set the inertia to a large value in order to promote global exploration of the search space, and gradually decrease it to get more refined solutions. The experimental results can consider 0.6 a good choice for iw . The parameters 1c and 2c , in Equation (9), are not critical for PSO’s convergence. However, proper fine-tuning may result in faster convergence and alleviation of local minima. An extended study of the acceleration parameter in PSO is given in [11, 12]. The experimental results indicate that ( 121 == cc ) might provide even better results. The random numbers ( )21,rr are used to maintain the diversity of the population, and they are uniformly distributed in the range (0, 1).

Economic Power Dispatch of Power System with Pollution Control Using Multiobjective Particle Swarm Optimization

University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 70

The PSO algorithm applied to OPF can be described in the following steps.

Step 1: Input parameters of system, and specify the lower and upper boundaries of each control variable.

Step 2: The particles are randomly generated between the maximum and minimum operating limits of the generators.

Step 3: Calculate the evaluation value of each particle using the objective function.

Step 4: Calculate the fitness value of objective function of each particle using (12). xibest is set as the i th particle’s initial position; xgbest is set as the best one of xibest. The current evolution is t =1.

Step 5: Initialize learning factors c1, c2, inertia weight w and the initial velocity v1.

Step 6: Modify the velocity v of each particle according to (9).

Step 7: Modify the position of each particle according to (10). If a particle violates its position limits in any dimension, set its position at the proper limits. Calculate each particle’s new fitness; if it is better than the previous xgbest, the current value is set to be xgbest.

Step 8: To each particles of the population, employ the Newton-Raphson method to calculate power flow and the transmission loss.

Step 9: Update the time counter t=t+1.

Step 10: If one of the stopping criteria is satisfied then go to step 11. Otherwise go to step 6.

Step 11: The particle that generates the latest pgbest is the global optimum.

4. APPLICATION STUDY

The OPF using particle swarm optimization method (PSO) has been developed by the use of Borland C++ Builder version 5 tested with P4 1.5 GHz, 128MO. consistently acceptable results were observed. The IEEE 30-bus system with 6 generators is presented here. The total load was 283.4 MW.

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June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 71

Upper and lower active power generating limits and the unit costs of all generators of the IEEE 30-bus test system are presented in Table 1. The NOx emission characteristics of generators are grouped in Table 2. The emission control cost factor for 30-bus system was taken as 550.66 $/Ton.

Table 1. Power generation limits and cost coefficients for IEEE 30-bus system.

Bus Pgmin (MW) Pgmax (MW) a ($/hr)

b ($/MW.hr)

c.10-4 ($/MW².hr)

01 50.00 200.00 0 2.00 037.5 02 20.00 080.00 0 1.75 175.0 05 15.00 050.00 0 1.00 625.0 08 10.00 035.00 0 3.25 083.0 11 10.00 030.00 0 3.00 250.0 13 12.00 040.00 0 3.00 250.0

The results including the generation cost, the emission level and power losses are shown in Table 3. This table gives the optimum generations for minimum total cost in three cases: minimum generation cost without using into account the emission level as the objective function (α=1), an equal influence of generation cost and pollution control in this function and at last a total minimum emission is taken as the objective of main concern (α=0). The active powers of the 6 generators as shown in this table are all in their allowable limits. We can observe that the total cost of generation and pollution control is the highest at the minimum emission level (α=0) with the lowest real power loss (3,749 MW).

Table 2. Pollution coefficients for IEEE 30-bus system

Bus a.10-2 b.10-4 c.10-6 d.10-4 e.10-2

1 4.091 -5.554 6.490 02.00 2.857 2 2.543 -6.047 5.638 05.00 3.333 5 4.258 -5.094 4.586 00.01 8.000 8 5.326 -3.550 3.380 20.00 2.000 11 4.258 -5.094 4.586 00.01 8.000 13 6.131 -5.555 5.151 10.00 6.667

As seen by the optimal results shown in the table 3, there is a trade-off between the fuel cost minimum and emission level minimum. The

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University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 72

difference in generation cost between these two cases (801,942 $/hr compared to 937,123 $/hr), in real power loss (9,428 MW compared to 3,749 MW) and in emission level (0,368 Ton/hr compared to 0.218 Ton/hr) clearly shows this trade-off.

Table 3. Results of minimum total cost for IEEE 30-bus system in three cases (α=1, α=0.5 and α=0).

Variable Generation cost minimum

Generation cost + Emission minimum Emission minimum

Pg01(MW) 176,928 129,984 66,760 Pg02(MW) 49,038 57,065 73,626 Pg05(MW) 21,414 25,471 50,000 Pg08(MW) 21,382 35,000 35,000 Pg11(MW) 12,074 22,148 30,000 Pg13(MW) 12,000 20,304 31,762 Generation cost ($/hr) 801,942 820,033 937,123 Emission (ton/h) 0,368 0,270 0,218 Total cost ($/h) 1004,492 968,917 1056,966 Power Loss (MW) 9,428 6,570 3,749

Figure 1. The results of the voltage magnitude by the different values of α (α=0, α=0.5, α=1).

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June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 73

To decrease the generation cost, one has to sacrifice some environmental constraint. The minimum total cost is at α=0.5 of the order of 968.917 $/h. The security constraints are also checked for voltage magnitudes, angles and branch flows.

The voltage magnitudes and the angles are between their minimum and the maximum values. The results including the voltage magnitude of the different values of α (α=0, α=0.5, α=1) shown in (Fig. 1). The transmission lines loading do not exceed their upper limits. In addition, it is important to point out that this algorithm converges in an acceptable time. For this test system it was approximately 2 seconds.

Table 4 shows a comparison between the PSO and Genetic Algorithm with real code [29]. The PSO is superior on GA in the two first cases: the generation cost minimum and the simultaneous minimization of fuel cost and emission cases, but in the case of the pure emission minimization GA gives slightly better values.

Table 4. Comparison between GA and PSO results for IEEE 30 bus system.

Generation cost minimum

Generation cost + Emission minimum Emission minimum

GA PSO GA PSO GA PSO Generation Cost ($/hr) 803.106 801.942 824.988 820.033 943.1 937.12

Emission (ton/h) 0.3771 0.368 0.266 0.270 0.205 0.218

Total cost ($/h) 1010.7 1004.5 971.4 968.9 1056.1 1056.9

5. CONCLUSION

This paper introduces a Particle Swarm Optimization algorithm to solve the economic power dispatch of power system with pollution control. The fuel cost and emission are combined in a single function with a difference weighting factor. The main advantage of PSO over other modern heuristics is modeling flexibility, sure and fast convergence, less computational time than other heuristic methods. PSO

Economic Power Dispatch of Power System with Pollution Control Using Multiobjective Particle Swarm Optimization

University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 74

requires only a few parameters to be tuned, which makes it attractive from an implementation viewpoint. The feasibility of the proposed algorithm is demonstrated on an IEEE 30-bus system. The results show that the proposed algorithm is applicable and effective in the solution of OPF problems that consider nonlinear characteristics of power systems with different objective functions. PSO can generate an efficiently high quality solution and with more stable convergence characteristics than Genetic Algorithm.

ACKNOWLEDGEMENT

Dr. Tarek Bouktir acknowledges support from MESRS (Algeria), grant number J0401/52/05.

REFERENCES [1] M. Huneault, F. D. Galiana, (1991). A survey of the optimal power

flow literature, IEEE Trans. Power Syst., Vo1. 6 (2) (pp. 762-770). [2] A. Momoh, M. E. El-Hawary and R. Adapa, A (1999). Review of

Selected Optimal Power Flow Literature to 1993 Part I: Nonlinear and Quadratic Programming Approaches, IEEE Trans. Power Syst., Vol. 14 (1) (pp. 96-104).

[3] A. Momoh, M. E. El-Hawary and R. Adapa, (1999). A Review of Selected Optimal Power Flow Literature to 1993 Part II: Newton, Linear Programming and Interior Points Methods, IEEE Trans. Power Syst., Vol.14 (1) (pp. 105-111).

[4] H. W. Dommel, W. F. Tinney, (1968). Optimal Power Flow Solutions, IEEE Trans. on power apparatus and systems, Vol. PAS-87 (10) (pp. 1866-1876).

[5] K. Y. Lee, Y. M. Park, and J. L. Ortiz, (1985). A United Approach to Optimal Real and Reactive Power Dispatch, IEEE Trans. Power Syst., Vol. PAS-104 (pp. 1147-1153).

[6] M. Sasson, (1969). Non linear Programming Solutions for load flow, minimum loss, and economic dispatching problems, IEEE Trans. On power apparatus and systems, Vol. PAS-88 (4) (pp. 399-409).

[7] T. Bouktir, M. Belkacemi, K. Zehar, (2000). Optimal power flow using modified gradient method, In: Proc. of ICEL’2000, U.S.T.O, Algeria, Vol. 02 (pp. 436-442).

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 75

[8] R. Fletcher, (1986). Practical Methods of Optimisation, New York, John Wiley & Sons.

[9] M. A. Abido, (2002). Optimal power flow using particle swarm optimization, Electrical power and energy systems, Vol. 24 (pp. 563-571).

[10] J. Kennedy and R. Eberhart, (1995). A Particle Swarm Optimization, In: Proc. of IEEE International conference on Neural Networks, Vol. 4, Perth, Australia (pp. 1942-1948).

[11] I. C. Trelea, (2003). L’essaim de particule vu comme un système dynamique: convergence et choix des paramètres, In: Proc. of Séminaire: L’optimisation par essaim de particules, Paris.

[12] M. Clerc et P. Siarry, (2003). Une nouvelle métaheuristique pour l’optimisation difficile: la méthode des essaims particulaires, In: Proc. of Séminaire: L’optimisation par essaim de particules, Paris.

[13] H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama, and Y. Nakanishi, (2000). A particle swarm optimization for reactive power and voltage control considering voltage security assessment, IEEE Trans. Power Syst., Vol. 15 (4) (pp. 1232-1239).

[14] J.-B. Park, K.-S. Lee, J.-R. Shin, and K. Y. Lee, (2005). A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Trans. Power Syst., Vol. 20 (1), (pp. 34–42).

[15] Zwe-Lee Gaing, (2003). Particle swarm optimization to solving the economic dispatch considering the generator constraints, IEEE Trans. Power Syst., Vol. 18 (3) (pp. 1187-1195).

[16] S. Naka, T. Genji, T. Yura, and Y. Fukuyama, (2003). A hybrid particle swarm optimization for distribution state estimation, IEEE Trans. Power Syst., Vol. 18 (1) (pp. 60-68).

[17] N. Kassabalidis, M. A. El-Sharkawi, R. J. Marks, L. S. Moulin, and A. P. Alves da Silva, (2002). Dynamic security border identification using enhanced particle swarm optimization, IEEE Trans. Power Syst., Vol. 17 (3) (pp. 723-729).

[18] P. Ren, L. Q. Gao, N. Li, Y. Li and Z. L. Lin, (2005). Transmission network optimal planning using the particle swarm optimization method, In: Proc. of the IEEE fourth International Conference on Machine Learning and Cybernetics, Guangzhou, Vol. 7 (pp. 4006-4011).

[19] T. O. Ting, M. V. C. Rao and C. K. Loo, (2006). A novel approach for unit commitment problem via an effective hybrid particle

Economic Power Dispatch of Power System with Pollution Control Using Multiobjective Particle Swarm Optimization

University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 June 2007 76

swarm optimization, IEEE Trans. Power Syst., Vol. 21 (1) (pp. 411- 418).

[20] Zwe-Lee Gaing, (2005). Constrained optimal power flow by mixed-integer particle swarm optimization, In Proc. IEEE Power Engineering Society General Meeting, Vol. 1 (pp. 243-250).

[21] M. R. Alrashidi and M. E. El-Hawary, (2006). A Survey of Particle Swarm Optimization Applications in Power System Operations, Electric Power Components and Systems, 34:12, (pp. 1349-1357).

[22] X. Hu, R. C. Eberhart and Y. Shi, (2003). Engineering optimization with particle, In Proc: IEEE Swarm Intelligence Symposium, (pp. 53-57).

[23] Zhiwei Wang, Gregory L. Durst, Russell C. Eberhart, Donald B. Boyd and Zina Ben Miled, (2004). Particle Swarm Optimization and Neural Network Application for QSAR, In: Proc. 18th Int. Parallel and Distributed Processing Symposium (IPDPS'04) - Workshop 9 (p. 194).

[24] W. Y. Spens and F. N. Lee, (1997). Interactive search Approach to Emission Constrained Dispatch, IEEE Trans. Power Syst., Vol. 12 (2) (pp. 811-817).

[25] Y. J. Fan and L. Zhang, (1998). Real Time Dispatch with Line Flow and Emission Constraints Using Quadratic Programming, IEEE Trans. Power Syst., Vol. 13 (2) (pp. 320-325).

[26] T. Bouktir and L. Slimani, (2004). Economic Power Dispatch of Power Systems with a NOx emission Control via an Evolutionary Algorithm, WSEAS Trans. Syst., Vol. 3 (2) (pp. 849-854).

[27] T. Bouktir, L. Slimani and R. Labdani, (2006). Optimal Power Flow for Large Scale Power System using Particle Swarm Optimization, In: Proc. of META’06, Hammamet, Tunisia.

[28] M. A. Abido, (2006). Multiobjective Evolutionary Algorithms for Electric Power Dispatch Problem, IEEE Trans. on Evolutionary Computation, Vol. 10 (3) (pp. 315-329).

[29] T. Bouktir and M. Belkacemi, (2003). Object-Oriented Optimal Power Flow, Electric Power Components and Systems, Vol. 31 (6) (pp. 525-534).

[30] J. H. Talaq, F. El-Hawary and M. E. El-Hawary, (1994). A summary of environmental economic dispatch algorithms, IEEE Trans. Power Syst., Vol. 9 (3) (pp. 1508-1516).

Tarek Bouktir, Rafik Labdani and Linda Slimani (57-77)

June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2 77

[31] R. Yokayama, S. H. Bae, T. Morita and H. Sasaki, (1998). Multi-objective optimal generation dispatch based on probability security criteria, IEEE Trans. Power Syst., Vol. 13 (1) (pp. 317-324).

[32] D. L. Scott, (1973). Pollution in the electric power industry, Lexington and London, D. C. Heath.

[33] J. Nanda, L. Hara and M. L. Khothari, (1994). Economic emission load dispatch with line flow constraints using a classical technique, IEE Proc. Gener. Transm. Distrib., Vol. 141 (1) (pp. 1-10).

[34] A. J. Wood and B. F. Wollenberg. (1996). Power Generation, Operation and Control, 2nd Edition, New York, John Wiley.

[35] Glenn W. Stagg, Ahmed H. El Abiad. (1981). Computer methods in power systems analysis, McGraw-Hill.

[36] S. Kumar and R. Billinton, (1987). Low bus voltage and ill-conditioned network situation in a composite system adequacy evaluation, IEEE Trans. Power Syst., Vol. PWRS-2 (3) (pp. 652-659).