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

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)×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[w×V k+ C1×rand()×(ybest-yitr)+C2×rand()×(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=w×V k+ C ×rand()×(ybest-yitr)+C ×rand()× (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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