 Open Access
 Total Downloads : 26
 Authors : Himanshu Anand, Dr. Nitin Narang
 Paper ID : IJERTCONV4IS15015
 Volume & Issue : ACMEE – 2016 (Volume 4 – Issue 15)
 Published (First Online): 24042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
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 (pminp )) (2)
t k k k
k k k k
k k k

INTRODUCTION
With the rising standard of living being the consumption and dependencies on conventional and nonconventional form of energy is increasing day by day. But the excessive use of nonconventional 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:

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 [1213]. 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.

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

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

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((wmaxwmin)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–(24) (17)
velocity of the particle is given by
best
When, 240 (=C +C
, >4)
1 2
itr+1=K[wÃ—V k+ C1Ã—rand()Ã—(ybestyitr)+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[810]. To improve the quality of solution,
itr+1=
(C factor>k) and (FT(k1)=FT(kN))
these acceleration coefficient[14] are updated in a way that
i,j
itr+1=wÃ—V k+ C Ã—rand()Ã—(ybestyitr)+C Ã—rand()Ã— (Gbestyitr) ;
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(k1)FT(kN)) (14)

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 Fig36.
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 fig36. 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
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B= 15 16 39 10 12 15 X107
15 20 10 40 14 11
20 18 12 14 35 17
[ 25 19 15 11 17 39] 

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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