Combined Economic And Emission Dispatch Using Random Drift Particle Swarm Optimization

134 International Journal for Modern Trends in Science and Technology

Combined Economic And Emission Dispatch Using Random Drift Particle Swarm Optimization

K.Naga Bindu ¹ |K.Kiran Kumar ²

1PG Student, Department of EEE, Sree Vahini Institute of Science and Technology, Tiruvuru, Andhra Pradesh, India

2Associate Professor & Head, Department of Electrical and Electronics Engineering, Tiruvuru, Andhra Pradesh, India.

To Cite this Article

K. Naga Bindu, K. Kiran Kumar, “Combined Economic And Emission Dispatch Using Random Drift Particle Swarm Optimization”, International Journal for Modern Trends in Science and Technology, Vol. 02, Issue 11, 2016, pp. 134-139.

The efficient and optimum economic operations of electric power generation systems have always occupied an important position in the electric power industry. In recent years, this problem area has taken a new direction as the public has become increasingly concerned with environmental matters. The harmful ecological effects caused by the emission of these gaseous pollutants can be reduced by optimal distribution of load between the plants of a power system. However, this leads to a noticeable increase in system operating cost. Therefore both need to be balanced. In this work, three techniques, i.e., one Conventional Technique- Lambda Iteration Technique and two AI Techniques- Particle Swarm Optimization (PSO) and Random Drift Particle Swarm Optimization (RDPSO) Techniques, are investigated to solve Combined Economic and Emission Dispatch (CEED) problem. This multi-objective CEED problem is converted into a single optimization problem using a Price Penalty factor approach. The investigation is carried out on 15- Generating Unit Test Systems with respect to Total Operating Cost, Total Emission, System Losses. Results show that in solving Combined Economic and Emission Dispatch (CEED) problem, Random Drift Particle Swarm Optimization (RDPSO) Technique is superior to other two techniques in terms of reduced operating cost. Therefore, Random Drift Particle Swarm Optimization (RDPSO) Technique is very much suitable and recommended for On-Line application for solving Combined Economic and Emission Dispatch problem of power system operation.

KEYWORDS: optimization, economic load dispatch, emission dispatch, combined economic emission dispatch, generating unit, power system operation

Copyright © 2016 International Journal for Modern Trends in Science and Technology All rights reserved.

I. INTRODUCTION

Highlight a Electric power utilities are always attempting to provide high quality, reliable supply of electrical energy at a reasonable cost. Among the options that are available to the power system operator in choosing how to operate the system, the most significant choice is Economic Load Dispatch (ELD). Economic Load Dispatch is the scheduling of generators to minimize the total operating cost of power system subjected to the

satisfaction of equality and inequality constraints.

The traditional Economic Load Dispatch problem purpose is to determine the most economical schedule of the generating plants or units while satisfying operational constraints and total load demand. This includes allocation real power allocation between the generating units, as the fuel cost is insensitive to the reactive loading of a generator. Economy of a generating unit does not depend upon the manner in which the reactive load of the power station is shared among different ABSTRACT

International Journal for Modern Trends in Science and Technology

ISSN: 2455-3778 http://www.ijmtst.com

135 International Journal for Modern Trends in Science and Technology generating units connected online. Many

techniques have been applied to ELD to obtain better solutions. These include Lambda Iteration Technique, Gradient Decent Technique, Dynamic Programming Technique, Newton-Raphson Technique, Artificial Intelligence Methods etc.

II. COMBINEDECONOMICANDEMISSION DISPATCH(CEED)

Objectives of Economic Load Dispatch and Minimum Emission Dispatch are noticeably different. The Economic Load Dispatch deals with only minimizing the total operating cost of the system without considering pollution constraint.

Whereas Minimum Emission Dispatch deals with only minimizing the total emission of pollutants from the power system to the environment without considering the economic constraints. If the Economic Load Dispatch is done, emission increases. If Emission Dispatch is done, cost increases. Hence an operating point,that strikes a balance between fuel cost and emission need to be determined. This can be attained by Combined Economic and Emission Dispatch.

In literature, various techniques [1]-[10] are proposed to solve Combined Economic and Emission Dispatch (CEED) problem with generator constraints. In this thesis, three techniques i.e., One Conventional technique-Lambda Iteration Technique and Two Artificial Intelligence techniques –Particle Swarm Optimization (PSO)

&Random Drift Particle Swarm Optimization (RDPSO) Techniques are investigated to find their suitability for ON-LINE application to solve CEED problem. These techniques are applied on two test systems (i.e., 6- Generating and 15- Generating Unit Test Systems). CEED problem considers both the economy and emission objectives. This project work aims at solving this bi-objective CEED problem using PSO, RDPSO and compares its results with Conventional Lambda Iterative technique and draw useful conclusions.

Random DriftParticle Swarm

Optimization(RDPSO) is used to Solve Economic Load Dispatch Problem with Generator Constraints is presented in [1]. In this paper, this technique is compared with most of the evolutionary techniques in solving ELD problem.Particle Swarm Optimization (PSO) to Solve Economic Load Dispatch Considering the Possible Generator Constraints is discussed in [2]. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and non-smooth cost functions are considered using the proposed

technique in practical generator operation.

A Widespread coverage of different PSO applications in solving optimization problems in the area of electric power systems given in [3]. It highlighted the PSO key features and advantages over other various optimization algorithms.Comparison and Application of Various Evolutionary Programming Techniques to Combined Economic and Emission Dispatch with Line Flow Constraints is presented in [4]. Economic Load Dispatch and Emission Dispatch have been applied to obtain optimal fuel cost and optimal emission of generating units, respectively.

Combined Economic and Emission Dispatch problem is obtained by considering both the economy and emission objectives. This bi-objective CEED problem is converted into a single objective function using a price penalty factor approach.

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The techniques and applications of engineering optimization in a comprehensive manner discussed in [5].Aspects related to soft computation such as genetic algorithms, evolutionary programming, and particle swarm optimization, and implementation of different evolution procedures for power system applications in [6]. A detailed study regarding Economic Load Dispatch is discussed in [7], [8], [9].A concept for the optimization of nonlinear functions using particle swarm approach is introduced in [10]. The relationship between particle swarm optimization and both artificial life and genetic algorithms are described.

III. RANDOMDRIFTPARTICLESWARM OPTIMIZATIONTECHNIQUE

If you Random Drift Particle Swarm Optimization (RDPSO) is a novel variant of the PSO algorithm.

The RDPSO is motivated by the free electron model in metal conductors in an external electric field, and the motivation of this new variant is to improve the search ability of the Particle Swarm Optimizationalgorithm by primarilyadjusting the velocity update equation of the particle, insteadof by revising the algorithm based on the original equation, which most likely increases thecomplexity and computational cost ofthe algorithm.

The trajectory analysis proved that the convergence ofthe PSO algorithm may be achieved

136 International Journal for Modern Trends in Science and Technology Optimization

if each particle convergesto its local focus, defined by the coordinates

𝑝_𝑖,𝑛^𝑗 = 𝜑_𝑖,𝑛^𝑗 𝑌_𝑖,𝑛^𝑗 + 1 − 𝜑_𝑖,𝑛^𝑗 𝐺_𝑛^𝑗, 𝜑_{𝑖 ,𝑛}^𝑗 ~U(0, 1) …(1) Wher 𝜑_𝑖,𝑛^𝑗 = 𝑐₁𝑟_𝑖,𝑛^𝑗 / 𝑐₁𝑟_𝑖,𝑛^𝑗 + 𝑐₂𝑅_𝑖,𝑛 ^𝑗 . The parameters 𝑟_𝑖,𝑛^𝑗 and 𝑅_𝑖,𝑛 ^𝑗 are the sequences of two different random numbers distributed uniformly on (0, 1), i.e., 𝑟_𝑖,𝑛^𝑗 , 𝑅_𝑖,𝑛 ^𝑗 ~U(0, 1). 𝑐1and 𝑐2 are known as the acceleration coefficients, which both are generally set to be equal, 𝜑_{𝑖 ,𝑛}^𝑗 is asequence of uniformly distributed random numbers on (0, 1).

The particle’s directional movement toward is similar to the electron’sdrift motion in a metal conductor, which is placed inan external electric field. However, according to the free electron model [28], the electron is also in thermal motion,along with above mentioned drift motion caused by the electricfield, which appears to bea random movement. The overall effect of the movement of the electron is that the electron traversesin the direction of the minimumpotential energylocation.

It is noticeablethat the movement of theelectron is analogous to the process of finding the minimum solution of the problem, if the electron’s position is considered asa candidate solution and the potential energy function as the objective function.

Inspired by the above facts, we assume that the particle in theRDPSO behaves like an electron moving in a metal conductorplaced in an external electric field. Therefore, the movementof the particle is the superposition of the thermal motion andthe drift motiontowards𝑝𝑖,𝑛. Hence, the particle velocitycan be characterized as

𝑉_𝑖,𝑛^𝑗 = 𝑉𝑅_𝑖,𝑛^𝑗 + 𝑉𝐷_𝑖,𝑛^𝑗 …(2)

Where𝑉𝐷_𝑖,𝑛^𝑗 and𝑉𝑅_𝑖,𝑛^𝑗 represent the velocities of the drift motiontoward 𝑝𝑖,𝑛 and thethermal motion, respectively. Here, we adoptthe following expressions for 𝑉𝑅_𝑖,𝑛^𝑗 and 𝑉𝐷_𝑖,𝑛^𝑗 :

𝑉𝑅_𝑖,𝑛^𝑗 = 𝜎_𝑖,𝑛^𝑗 𝜆_𝑖,𝑛^𝑗 …(3)

𝑉𝐷_𝑖,𝑛^𝑗 = 𝛽 ( 𝑝_𝑖,𝑛^𝑗 − 𝑋_𝑖,𝑛 ^𝑗 ) …(4)

In (5.3),𝜆_𝑖,𝑛^𝑗 is a random number with a standard normal distribution, 𝜎_𝑖,𝑛^𝑗 andis the standard deviation of a Gaussian distribution, whose value is determined adaptively as

𝜎_𝑖,𝑛^𝑗 = 𝛼 | 𝐶_𝑛^𝑗− 𝑋_𝑖,𝑛 ^𝑗 | …(5)

where 𝐶_𝑛^𝑗 = (1/𝑀) ^𝑀_𝑖=1𝑌_𝑖,𝑛^𝑗 , ( 1 ≤ j ≤ N) and is called the mean best position. In (5.4),𝑝_𝑖,𝑛^𝑗 is defined by (5.1). In (5.4) and(5.5), 𝛼 and 𝛽 are two positive real numbers called the thermalcoefficient and the drift coefficient, respectively. It is obvious that the

velocity of thermal motion 𝑉𝑅_𝑖,𝑛^𝑗 follows the Maxwellvelocity distribution law. It can also be seen from (5.4) that theeffect of the drift velocity 𝑉𝐷_𝑖,𝑛^𝑗 leads the particle to make amovement toward 𝑝_𝑖,𝑛^𝑗 at eachiteration. With the above specifications, we have the particle update equation in the RDPSO as follows:

𝑉_𝑖,𝑛+1^𝑗 = 𝛼 | 𝐶_𝑛^𝑗− 𝑋_𝑖,𝑛 ^𝑗 |𝜆_𝑖,𝑛^𝑗 + 𝛽 ( 𝑝_𝑖,𝑛^𝑗 − 𝑋_𝑖,𝑛 ^𝑗 )

…(6)

𝑋_{𝑖,𝑛 +1}^𝑗 = 𝑋_𝑖,𝑛^𝑗 + 𝑉_{𝑖,𝑛 +1}^𝑗 . …(7)

Figure 1 Flowchart of RDPSO

IV. RESULTS OF ELD WITH LOSSES FOR A

6-GENERATING UNIT TEST SYSTEM Table 1

Result of ELD for 6- Generating Unit Test System for a power demand of 900 MW

Power Demand

(PD) in MW

Description Conventional Lambda

Technique PSO RDPSO

900

Total Cost (Rs./hr)

46995.82 46900.8 46783.6

Loss (MW)

28.98 24.59 19.59

137 International Journal for Modern Trends in Science and Technology

Table 2

Unit Generation in MW for ELD with losses for a power demand of 900MW

Power Demand

(PD) in MW

Generati ng Unit Number

Convent ional Lambda Techniq

ue

PSO RDPSO

900

PG1 45.46 74.88 40.25 PG2 29.43 41.07 12.86 PG3 129.42 221.59 192.31 PG4 160.34 154.04 112.77 PG5 249.30 126.09 303.20 PG6 315.00 301.82 263.16

4.1 Results of MED with losses for a 6- Generating Unit Test System

Table 2

Result of MED for 6- Generating Unit Test System for a power demand of 900 MW

Power Demand

(PD) in MW

Description Conventional Lambda

Technique PSO RDPSO

900

Total Emission

(lb/hr) 698.99 692.75 683.98 Loss (MW) 28.14 26.55 24.49

Table 2

Unit Generation in MW for MED with losses for a power demand of 900MW

Power Demand

(PD) in MW

Generating Unit Number

Conventional Lambda

Technique PSO RDPSO

900

PG1 125.0 79.90 117.06

PG2 123.12 108.08 92.24

PG3 134.62 175.48 153.40

PG4 140.74 153.47 150.91

PG5 197.65 215.95 229.35

PG6 207.01 191.58 183.57

4.3 Results of CEED with losses for a 6- Generating Unit Test System

Table 3

Result of CEED for 6- Generating Unit Test System for a power demandOf 900 MW

Power nd (PDema

D) in MW

Price Penal

ty Facto

r (h) in Rs./K

g

Descripti on

Conventio nal Lambda Technique

PSO RDPSO

900 9.192 8

Total Cost (Rs./hr)

54518.77 5

4181.3 2

5 4012.3

5 Loss

(MW) 28.98 2

3.53 2

3.13 Table 4

Unit Generation in MW for CEED with losses for a power demand of 900MW

Power Demand

(PD) in MW

Generating Unit Number

Conventional Lambda Technique

PSO RDPSO

900

PG1 45.46

54.23 44.36 P_G2

29.43 55.52 63.19

PG3 129.42 207.00 164.89 PG4 160.34 173.95 130.87 PG5 249.31 215.64 273.32 PG6 315.00 217.16 248.48

4.3 Results of ELD with losses for a 15- Generating Unit Test System

Table 5

Result of ELD for 15- Generating Unit Test System for a power demand of 2630 MW

Power Demand

(PD) in MW

Descripti on

Conventi onal Lambda Techniqu

e

PSO RDPSO

2630

Fuel Cost

(Rs./hr) 32482.55 32400.82 32062.98 Loss (MW) 19.81 19.91 19.08

Table 6

Unit Generation in MW for ELD with losses for a power demand of2630MW

Power Demand (PD) in MW

Generating Unit Number

Conventio nal Lambda

Technique

PSO RDPSO

2630

PG1 455 452.8 447.03

PG2 363.01 294.0 455.00

PG3 130 95.09 96.44

PG4 130 99.91 80.75

PG5 383.97 170.0 413.76

PG6 460 455.0 305.41

PG7 465 430.0 370.08

PG8 60 98.65 65.81

PG9 25 147.9 46.30

PG10 25 144.1 81.78 PG11 41.73 80.00 79.53

138 International Journal for Modern Trends in Science and Technology Optimization

PG12 56.09 51.65 80.00 PG13 25 58.73 41.98 PG14 15 35.52 47.71 PG15 15 50.14 38.86

4.4 Results of MED with losses for a 15- Generating Unit Test System

Table 7

Result of MED for 15- Generating Unit Test System for a power demandof 2630 MW

Power Demand

(PD) in MW

Descripti on

Conventi onal Lambda Techniqu

e

PSO RDPSO

2630

Total Emission (lb/hr)

3588.45 3587.00 3586.24

Loss (MW) 61.66 41.83 34.92

Table 8

Unit Generation in MW for MED with losses for a power demand of2630MW

Power Demand

(PD) in MW

Generatin g Unit Number

Conventi onal Lambda Techniqu

e

PSO RDPSO

2630

PG1 455.00 437.15 482.23

PG2 395.35 260.10 413.41

PG3 47.94 104.83 113.92

PG4 130.00 130.00 88.49

PG5 150.00 150.00 286.27

PG6 135.00 460.00 216.92

PG7 401.36 404.96 465.00

PG8 300.00 160.00 193.52

PG9 162.00 162.00 81.54

PG10 160.00 160.00 134.99

PG11 80.00 63.00 53.45

PG12 80.00 45.16 47.64

PG13 85.00 46.76 78.94

PG14 55.00 55.00 33.23

PG15 55.00 32.03 29.30

4.5 Results of CEED with losses for a 15- Generating Unit Test System

Table 9

Result of CEED for 15- Generating Unit Test System for a power demandOf 2630 MW

Power Deman d (PD) in

MW

Price Penalty

Factor (h) in Rs./Kg

Descrip tion

Conven tional Lambda

Techni que

PSO RDPSO

2630 4.19

Fuel Cost

(Rs./hr) 106005.

77 69647.3

9 61160.3

7 Loss

(MW) 19.811 19.80 19.08 Table 10

Unit Generation in MW for CEED with losses for a power demand of2630 MW

Power Demand

(PD) in MW

Generatin g Unit Number

Conventi onal Lambda Techniqu

e

PSO RDPSO

2630

PG1 455.00 365.93 426.23

PG2 363.01 380.00 363.89

PG3 130.00 130.00 109.91

PG4 130.00 126.35 92.80

PG5 383.97 150.00 223.06

PG6 460.00 425.00 272.15

PG7 465.00 430.00 465.00

PG8 60.00 78.73 178.06

PG9 25.00 124.40 84.81

PG10 25.00 133.78 80.29

PG11 41.73 61.18 57.99

PG12 56.09 80.00 64.23

PG13 25.00 85.00 73.84

PG14 15.00 52.94 32.27

PG15 15.00 40.76 27.66

The output of CEED With Losses for a Power demand of 2630 MW showthat for a practical operating situation (where emission constraint and system losses are considered), RDPSO technique is recommended as this technique is comparatively better in terms of minimizing total operating cost, minimizing emission level than the other two techniques. The operating cost is reduced by 30.0%

when compared with λ technique and 3.22 % when compared with PSO technique.

V. CONCLUSION

In this work, three techniques i.e., One Conventional Technique- Lambda Iteration Technique and Two Artificial Intelligence Techniques- Particle Swarm Optimization (PSO)

139 International Journal for Modern Trends in Science and Technology and Random Drift Particle Swarm Optimization

(RDPSO) are investigated to find the suitability for ON-LINE application to solve ELD, MED and CEED problems. Investigation study of ELD, MED and CEED problems for 15-Gen Unit Test Systems using the three techniques is carried out with respect to Total Operating Cost, Total Emission, System Losses and Computation Time.

The results of case studies show that for solving CEED problem, Random Drift Particle Swarm Optimization Technique gives better results than Conventional Lambda Iteration Technique and Particle Swarm Optimization Technique in terms of Total Operating Cost, Minimum Emission, reduced System Losses and is fast in Computation.Hence, Random Drift Particle Swarm Optimization Technique is recommended for ON-LINE application to solve Combined Economic and Emission Dispatch (CEED) problem of power system operation.

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