# Combined Heat and Power Economic Dispatch Using Hybrid Constriction Particle Swarm Optimization

DOI : 10.17577/IJERTCONV4IS15015

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#### Combined Heat and Power Economic Dispatch Using Hybrid Constriction Particle Swarm Optimization

Himanshu Anand (Student), EIED Thapar University Patiala, India

Dr. Nitin Narang (Assistant Professor), EIED Thapar University

Patiala, India

Abstract The Combined Heat and Power Economic Load Dispatch (CHPED) is an optimization problem to minimize the cost while ensuring the minimum transmission loss and fulfilling the power and heat demand. This paper presents the hybrid constriction particle swarm optimization (HCPSO) technique to solve CHPED with bounded feasible operating region. The main potential of this technique is that it enhances the balance between global and local search area in comparison to PSO. A comparative analysis of the proposed technique with PSO, evolutionary programming (EP), differential evolution (DE), and classic particle swarm optimization (CPSO) respectively is

so a new factor has been introduced called constriction factor [8]. This paper presents the solution to CHPED problem by HCPSO.

II. PROBLEM FORMULATION OF CHPED

The main aim of CHPED problem is to obtain the optimal scheduling of power and heat with minimum cost while ensuring the heat and power constraints. Mathematically, the problem can be formulated as:

presented.

Min FT= nt

F t,k(p )+ ns

F s,l (hl)+ nco F co,m (p

hm) (1)

k=1

k l=1

m=1 m,

Keywords Combined Heat And Power; Economic Load Dispatch; Hybrid Constriction Particle Swarm Optimization

Cost of thermal units can be defined as:

F (p )=a (p )2+b (p )+c +|d sin (e (pmin-p ))| (2)

t k k k

k k k k

k k k

1. INTRODUCTION

With the rising standard of living being the consumption and dependencies on conventional and non-conventional form of energy is increasing day by day. But the excessive use of non-conventional form of energy is a great matter of concern for the society as it is having hazardous impact on the environment like greenhouse effect etc. This has forced the power industry to make optimal utilization of the fuels. Combined Heat and Power is one of the most efficient and reliable method for generation of heat and power. The generated heat can be efficiently used to support local industry development and thus increasing the overall efficiency of the power plant. In combined heat and power, the heat and power demands are to be met simultaneously which make the CHPED complex. Number of techniques has been evolved in last decades to solve this complex CHPED problem.

Several methods which have been used to find out

Cost of heat only units can be defined as: Fs(hl)=l(hl)2+l(hl)+l (3)

Cost of cogeneration units can be defined as:

Fco(pm, hm)=m(pm)2+m(pm)+m+m(hm)2+m(hm)+m(pm, hm)

(4)

where nt, ns and nco are the number of thermal, heat and cogeneration units respectively. Ft (pk)represent cost of kth thermal units for producing power. ak, bk, ck cost coefficients of kth thermal units. dk, ek are the cost coefficients of kth thermal units including valve point effect. Fs(hl) represent cost of lth for producing heat(hl). l , l , l are cost coefficients of heat only units. Fco(pm,hm) represent cost of mth cogeneration units for producing heat(hm) and power(pm).

CHPED problem is subjected to following constraints:

1. Equality Constraints

Power balance constraints

m=1

m=1

CHPED with constraints are Mixed Integrating Programming, Lagrange Relaxation etc. But all these

nt k=1

p(k) + nco

p(m) =pL+pD

(5)

methods have drawbacks like problems related to constraints handling, convergent problem etc. So, to overcome the above

where pD is electrical power demand, pL is power transmission loss and may be defined as:

mentioned problem of traditional techniques some alternative

p nt

nt p Bij p + nt

nco p

Brs p + nco nco p Bst p

(6)

L= i=1

j=1 i

j r=1

s=1 r

s s=1 t=1 s t

approaches have to be used. These alternative approaches include Genetic Algorithm (GA), PSO, EP, DE, etc [1- 6]. PSO is an active random search technique that traverses good regional solution very quickly. The main problem with PSO

where Bij, Brs, Bst are transmission loss coefficients.

Heat balance constraints

is that it cannot go out of regional optimal solution to reach the global solution [12-13]. The concurrence towards a stable

ns l=1

h(l) + nco

h(m) =hD (7)

m=1

m=1

solution is the primary requirement of any search algorithm

where hD is heat demand.

2. Inequality Constraints

Limits of thermal only units

Randomly generate the power, heat of individual unit.

Randomly generate the power, heat of individual unit.

pmin p pmax (8)

Start

i i i

Limits of heat only units

Randomly generate the power and heat of CHP.

Randomly generate the power and heat of CHP.

(9)

Limits of CHP units

m

m

pmin(hm) pm

(h ) pmax(h ) (10)

m

m

m m

m m

No

m

m

m

m

hmin(p

) hm

(pm

) hmax(p

m

m

m

) (11)

IF feasible operating region

where, pmin and pmax are the minimum and maximum power

i i

Check equality constraints

Check equality constraints

limits of thermal units. hminand hmax are the minimum and

i

maximum limits of heat nly un

i

. hmin(p

) and hmax(p )

o its m m m m

Find the value of K from Eq. 17

Find the value of K from Eq. 17

are the minimum and maximum heat limit of mth CHP which

m

m

are the function of power produced. pmin(hm

) and

m

m

pmax(hm

)are the minimum and maximum power limit of mth

CHP which are the function of heat produced. pm,hm coordinates should lie in the feasible operating region of cogeneration units as shown in Fig.1 and should satisfy the test system equations for two cogeneration units.

Iteration index( itr=1)

Iteration index( itr=1)

Calculate the inertia weight from Eq. (16)

Particle index (i=1)

Particle index (i=1)

Update the velocity of heat , power of individual and CHP from Eq. 14 3.14

Update the velocity of heat , power of individual and CHP from Eq. 14 3.14

Update the position of heat , power of individual and CHP units from Eq. 15 (3.10)

Calculate the objective function of each particle

Calculate the objective function of each particle

Fig.1. Feasible operating region of the cogeneration units

3. Constraints Handling

Power balance constraints in order to determine the actual cost of the system it is necessary to include the transmission losses. So to satisfy the equality constraint criterion for power a decision variable is arbitrarily chosen as dependent generator (d).

IF(i<=PR)

i = i+1

i = i+1

Yes

p = p – p – nt

p – nco p

(12)

k=k+1

k=k+1

d D L k=1,kd k m=1 m

Yes

m=1

m=1

Heat balance constraints to satisfy the equality constraint criterion for heat a decision variable is arbitrarily chosen as dependent generator (d).

itr<=itrmax

hd = hD-

hd = hD-

ns l=1,ld

hl- nco hm

(13)

Output is te global best Position

Output is the global best Position

1. HYBRID CONSTRICTION PARTICLE SWARM

OPTIMIZATION

PSO is population based stochastic search algorithm introduced by Kennedy & Eberhart in 1995[7]. A particle i

FIG.2. IMPLEMENTATION OF HCPSO

The position of the particles keeps on updating by utilizing earlier positions and velocities.

itr

itr

itr

itr

yitr+1=itr+1+yitr(15) (i=1,2,3.PR;j=1,2,3,G;itr=1,2,3.itrmax)

at iteration itr has a position vector yi =(yi1 ,yi2 ,—yin )and a

i,j

i,j

i,j

velocity, uitr=(uitr,uitr,—uitr ). The best known position of ith

The inertia weight (W) can be expresses as:

i i1 i2

in

itr

itr

itr

w=wmax-((wmax-wmin)Ã—k)/itr

(16)

best i

best i

particle is as Pitr =(P

best i1

,Pbest i2

,—P

best in

).The best known

max

position of entire swarm is known as global best Gitr . The

K=2/|2–(2-4)| (17)

velocity of the particle is given by

best

When, 2-40 (=C +C

, >4)

1 2

itr+1=K[wÃ—V k+ C1Ã—rand()Ã—(ybest-yitr)+C2Ã—rand()Ã—(Gbest -yitr)]; Constriction factor is taken into account when PSO struck

i,j

i,j

i,j

i,j

j i,j

into local optimum[8-10]. To improve the quality of solution,

itr+1=

(C factor>k) and (FT(k-1)=FT(k-N))

these acceleration coefficient[14] are updated in a way that

i,j

itr+1=wÃ—V k+ C Ã—rand()Ã—(ybest-yitr)+C Ã—rand()Ã— (Gbest-yitr) ;

i,j

i,j 1

i,j

i,j 2

j i,j

rate of convergence increases and give better results.

{ ( k>0) and (FT(k-1)FT(k-N)) (14)

2. RESULTS AND DISCUSSIONS

In order to show the effectiveness of the proposed method two test systems are considered for simulation study. Results obtained from this HCPSO method have been compared with PSO, EP, DE, RCGA, BCO and CPSO. This paper, proposes a HCPSO based CHPED problem which is implemented using FORTRAN 90 on a computer system. Proposed method has been applied on two test systems named test system 1 and test system 2. The feasible operating regions of different CHP units of different test systems are shown in Fig3-6.

Fig.3. Feasible operating region of CHP (5 of test case 1)

To find the stable and optimal solution, program is run for different value of C1 , C2, C3, C4, wmax , wmin , itrmax and S. After 50 trials of run following parameter set mentioned as: Table 1 Set of Parameters gives the optimal results.

 PR itrmax wmax wmin C1 C2 C3 C4 S 50 300 .9 .4 2 2 2.05 2.05 70

Fig.4. Feasible operating region of CHP units ( 6 of test case 1)

Fig.5. Feasible operating region of CHP units (18 of test case 2)

Fig.6. Feasible operating region of CHP units (18 of test case 2)

Test System 1

this test system there are total seven units as shown in Table2 out of which the four power only units, two cogeneration units and one heat only unit. The feasible operating region of cogeneration units are shown in fig3 and fig4 respectively. The total demand of heat and power for the test system is 150MWth and 600MW respectively. The simulation results of the proposed HCPSO are shown in Table3. It is observed from Table 3 that the cost(\$/h) obtained by applying the proposed technique HCPSO (10225) is much less in comparison to previously proposed techniques like PSO (10613), EP (10390), DE (10317),RCGA (10667), BCO

(10317), CPSO (10325). Moreover, proposed technique HCPSO is not only cost efficient but also it gives better results in terms of average fuel cost, computational time and power loss as shown in Table 4.

Convergence Behavior

Convergence characteristics of fuel costs obtained by the proposed technique HCPSO for test system 1 and test system 2 are shown in fig7- fig10. From the convergence curve, it is observed that the fuel cost values converge smoothly for proposed technique HCPSO without any abrupt oscillations in comparison with PSO. Thus, ensuring convergence reliability as well results are obtained in lesser iteration

PSO EP

DE RCGA BCO CPSO HCPSO

PSO EP

DE RCGA BCO CPSO HCPSO

C.P.U(sec)

COST(K\$/h)

LOSS(MW)

C.P.U(sec)

COST(K\$/h)

LOSS(MW)

Fig.7. Optimal cost, Computational time and Power losses for different techniques

Table 2: System data of test case 1

 Unit Pmin(MW) Pmax(MW) a(\$/MW2) b(\$/MW) c (\$) d(\$) e(rad/MW) Power only units: 1 10 75 0.008 2 25 100 0.042 2 20 125 0.003 1.8 60 140 0.04 3 30 175 0.0012 2.1 100 160 0.038 4 40 250 0.001 2 120 180 0.037 Feasible operating coordinates a(\$/MW2) b(\$/MW) c (\$) d(\$/MWtp) e(\$/MWth) f(\$/MW MWth) CHP unit: 5 [98.8,0],[81,104.8],[215,180], [247,0] 0.0345 14.5 2650 0.03 4.2 0.031 6 [44,0],[44,15.9], [40,75], [110.2,135.6], [125.8,32.4], [125.8, 0] 0.0435 36 1250 0.027 0.6 0.11 hmin(MWth) hmax(MWth) a(\$/MWtp) b(\$/MWth) c(\$) hmin(MWth) Heat only unit: 7 0 2695.20 0.038 2.0109 950 7 0

Table 3: Results obtained by different techniques for test system1

 Control variables PSO EP DE RCGA BCO CPSO HCPSO P1 18.4626 61.361 44.2118 74.6834 43.9457 75 10 P2 124.2602 95.1205 98.5383 97.9578 98.5888 112.38 101.8 P3 112.7794 99.9427 112.6913 167.2308 112.932 30 175.32 P4 209.8158 208.7319 209.7741 124.9079 209.7719 250 173.2 P5 98.814 98.8 98.8217 98.8008 98.8 93.2701 99.28584 P6 44.0107/p> 44 44 44.0001 44 40.1585 41.26551 H5 57.9236 18.0713 12.5379 58.0965 12.0974 32.5655 1.18241 H6 32.7603 77.5548 78.3481 32.4116 78.0236 72.6738 56.30214 H7 59.3161 54.3739 59.1139 59.4919 59.879 44.7606 92.51544 COST(\$) 10,613 10,390 10,317 10667 10317 10325 10225

Table 4: Comparison of optimal costs obtained by different techniques after 50 trials for test system

 Algorithms Best fuel cost(\$) Average fuel cost(\$) Average CPU time P LOSS PSO 10613 – 5.3844 8.1427 EP 10390 – 5.275 7.9561 DE 10317 – 5.2563 8.0372 RCGA 10667 6.4723 7.5808 BCO 10317 5.1563 8.0384 CPSO 10325 3.29 .8086 HCPSO 10225 10244.53 3.37 .76651

HCPSO

CPSO

25

20

15

10

5

0

HCPSO

CPSO

25

20

15

10

5

0

0 50 100 150 200

Iteration

0 50 100 150 200

Iteration

Cost(K\$/h)

Cost(K\$/h)

Fig.8. Convergence curve of HCPSO and PSO

Table 6: Simulation results obtained by different techniques for test case2.

 CPSO HPSO CPSO HPSO P1 (MW) 680.00 567.8467 P16 (MW) 117.4854 81 P2 (MW) 0.00 325.7905 P17 (MW) 45.9281 40 P3 (MW) 0.00 345.7023 P18 (MW) 10.0013 10 P4 (MW) 180.00 105.8591 P19 (MW) 42.1109 35 P5 (MW) 180.00 105.6171 H14 (MWth) 125.2754 104.8 P6 (MW) 180.00 105.5029 H15 (MWth) 80.1175 75 P7 (MW) 180.00 105.3421 H16 (MWth) 125.2754 104.8 P8 (MW) 180.00 105.6443 H17 (MWth) 80.1174 75 P9 (MW) 180.00 105.6949 H18 (MWth) 40.0005 40 P10 (MW) 50.5304 40 H19 (MWth) 23.2322 20 P11 (MW) 50.5304 40 H20 (MWth) 415.9815 470.4 P12 (MW) 55.00 55 H21 (MWth) 60.00 60 P13 (MW) 55.00 55 H22 (MWth) 60.00 60 P14 (MW) 117.4854 81 H23 (MWth) 120.00 120 P15 (MW) 45.9281 40 H24 (MWth) 120.00 120 Cost(\$/hr) 59736.2635 57998.77

Table 5: System data of test case2.

 Unit Pmin (MW) Pmax (MW) a (\$/MW2) b (\$/MW) c (\$) d (\$) e (rad/MW) Power only units 1 0 680 0.00028 8.1 550 300 0.035 2 0 360 0.00056 8.1 309 200 0.042 3 0 360 0.00056 8.1 309 200 0.042 4 60 180 0.00324 7.74 240 150 0.063 5 60 180 0.00324 7.74 240 150 0.063 6 60 180 0.00324 7.74 240 150 0.063 7 60 180 0.00324 7.74 240 150 0.063 8 60 180 0.00324 7.74 240 150 0.063 9 60 180 0.00324 7.74 240 150 0.063 10 40 120 0.00284 8.6 126 100 0.084 11 40 120 0.00284 8.6 126 100 0.084 12 55 120 0.00284 8.6 126 100 0.084 13 55 120 0.00284 8.6 126 100 0.084 Feasible operating coordinates a(\$/MW2) b(\$/MW) c (\$) d(\$/MWtp) e(\$/MWth) f(\$/MW MWth) CHP unit 14 [98.8, 0], [81, 104.8], [215,180], [247,0] 0.0345 14.5 2650 0.03 4.2 0.031 15 [44, 0], [44, 15.9], [40, 75], [110.2, 135.6], [125.8, 32.4], [125.8, 0] 0.0435 36 1250 0.027 0.6 0.011 16 [98.8, 0], [81, 104.8],[215, 180], [247,0] 0.0345 14.5 2650 0.03 4.2 0.031 17 [44, 0], [44, 15.9], [40, 75], [110.2,135.6], [125.8, 32.4], [125.8, 0] 0.0435 36 1250 0.027 0.6 0.011 18 [20, 0], [10, 40], [45, 55], [60, 0] 0.01035 34.5 2650 0.025 2.203 0.051 19 [35, 0], [35, 20], [90, 45], [105, 0] 0.072 20 1565 0.02 2.34 0.04 hmin(MWth) hmax(MWth) a(\$/MWtp) b(\$/MWth) c(\$) Heat only unit 20 0 2695.20 0.038 2.0109 950 21 0 60 0.038 2.0109 950 22 0 60 0.038 2.0109 950 23 0 120 0.052 3.0651 480 24 0 120 0.052 3.0651 480

Test case2

In this test system there total of 24 units, out of which 13 are power only units, 6 cogeneration units and 5 heat only units. The full system data along with cost coefficients and operating limits of power only units and heat only units are taken as shown in Table 5 Total demand of power and heat are respectively. The feasible operating regions of 6 cogenerations unit are shown in fig3-6. The simulation results of the proposed HCPSO are shown in Table 6 and their results are compared with the results obtained using CPSO. It is clear from the results that the proposed HCPSO can avoid the shortcomings of premature convergence and can obtain better results. The obtained optimum power and heat generated by all the units are well within the limits.

49 14 15 15 20 25

14 45 16 20 18 19

dispatch, International Journal of Electrical and Electronics Engineering, vol. 7, no. 1, January2015.

1. Zhisheng, Zhang., Quantum-behaved particle swarm optimization algorithm for economic load dispatch of power system, Expert systems with applications, vol. 37, no. 2, pp: 1800-1803, March 2010.

2. Dos, Leandro.; Coelho, Santos.; Lee, Chu-Sheng., Solving economic load dispatch problems in power systems using chaotic and gaussian particle swarm optimization approaches, International journal of electrical power & energy systems, vol. 30, no. 5, pp: 297-307, June 2008.

3. Hosseinnezhad, Vahid.; Babaei, Ebrahim., Economic load dispatch using -PSO, International journal of electrical power & energy systems, vol. 49, pp: 160-169, july 2013.

4. Chaturvedi, K.T.; Pandit, Manjaree.; Srivastava, Laxmi., Particle swarm optimization with time varying acceleration coefficient for non- convex economic power dispatch, International journal of electrical power & energy systems, vol. 31, no. 6, pp: 249-257, July 2009.

B= 15 16 39 10 12 15 X10-7

15 20 10 40 14 11

20 18 12 14 35 17

[ 25 19 15 11 17 39]
3. CONCLUSION

This paper proposes a new technique HCPSO for solving CHPED problems. All the complications present in CHPED problems can be handled effectively by HCPSO. The results clearly illustrate its effectiveness. Proposed technique HCPSO

is not only cost efficient but also it gives better results in terms of average fuel cost, computational time and power loss.

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