# A new algorithm for combined heat and power dynamic economic dispatch considering valve-point effects

**ABSTRACT** In this study, combined heat and power units are incorporated in the practical reserve constrained dynamic economic dispatch, which minimizes total production costs considering realistic constraints such as ramp rate limits and valve-point effects over a short time span. The integration of combined heat and power units and considering power ramp constraints for these units necessitate an efficient tool to cope with joint characteristics of electricity power-heat. Unlike pervious approaches, the system spinning reserve requirements are clearly formulated in the problem and a novel charged system search algorithm is proposed to solve it. In the proposed algorithm a novel self-adaptive learning framework, adaptive selection operation and repelling force modeling are used in order to increase the population diversity and amend the convergence criteria. The proposed framework is applied for three small, medium and large test systems in order to evaluate its efficiency and feasibility.

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**ABSTRACT:**This paper addresses the unit commitment (UC) in multi-period combined heat and power (CHP) production planning under the deregulated power market. In CHP plants (units), generation of heat and power follows joint characteristics, which implies that it is difficult to determine the relative cost efficiency of the plants. We introduce in this paper the DRDP-RSC algorithm, which is a dynamic regrouping based dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units, sequential commitment of units in small groups. Relaxed states of the plants are used to reduce the dimension of the UC problem and dynamic regrouping is used to improve the solution quality. Numerical results based on real-life data sets show that this algorithm is efficient and optimal or near-optimal solutions with very small optimality gap are obtained.Energy Conversion and Management. 01/2009; - [show abstract] [hide abstract]

**ABSTRACT:**We propose a component model for the scheduling of combined-cycle gas turbine (CCGT) units by mixed-integer programming (MIP) in which combustion turbines (CTs) and steam turbines (STs) are modeled as individual units. The hourly schedule of CCGT based on the component model is compared with that of the mode model. The modeling of modes, which includes a combination of CTs and STs, would require certain approximations for representing fuel input-power output curves, ramping rate limits, minimum operating time limits, etc. The approximations can result in sub-optimal schedules. Furthermore, the commitment and dispatch of CCGTs based on the mode model will require a real-time dispatch to individual CT and ST components of CCGT. In comparison, the mode modeling approximations will no longer be required in the component model as individual CTs and STs are modeled and dispatched. The enhancement tools such as duct burners, foggers, and peak firing for increasing the CCGT output can be easily modeled in the component model. Case studies show that the proposed component model is effective for representing CCGTs, and verify that the proposed component model can potentially save CCGT operating costs. Numerical simulations in this paper also demonstrate the application of the component model of CCGT to schedule a cogeneration unit.IEEE Transactions on Power Systems 06/2009; · 2.92 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**Cities account for approximately two-thirds of global primary energy consumption and have large heat and power demands. CHP (combined heat and power) systems offer significant primary energy-efficiency gains and emissions reductions, but they can have high upfront investment costs and create nuisance pollution within the urban environment. Urban planners therefore need to understand the tradeoffs between limitations on CHP plant size and the performance of the overall energy system. This paper uses a mixed-integer linear programming model to evaluate urban energy system designs for a range of city sizes and technology scenarios. The results suggest that the most cost-effective and energy-efficient scenarios require a mix of technology scales including CHP plants of appropriate size for the total urban demand. For the cities studied here (less than 200,000 people), planning restrictions that prevent the use of CHP technologies could lead to total system cost penalties of 2% (but with significantly different cost structures) and energy-efficiency penalties of up to 24% when measured against a boiler-only business-as-usual case.Fuel and Energy Abstracts 05/2012;

Page 1

A new algorithm for combined heat and power dynamic economic

dispatch considering valve-point effects

Bahman Bahmani-Firouzi, Ebrahim Farjah*, Alireza Seifi

Department of Power and Control Eng., School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran

a r t i c l e i n f o

Article history:

Received 7 August 2012

Received in revised form

31 December 2012

Accepted 3 January 2013

Available online 6 March 2013

Keywords:

Self-adaptive learning charged system

search algorithm

Cogeneration technology

Combined heat and power dynamic

economic dispatch

Ramp rate limit

Spinning reserve constraint

Valve-point effects

a b s t r a c t

In this study, combined heat and power units are incorporated in the practical reserve constrained

dynamic economic dispatch, which minimizes total production costs considering realistic constraints

such as ramp rate limits and valve-point effects over a short time span. The integration of combined heat

and power units and considering power ramp constraints for these units necessitate an efficient tool to

cope with joint characteristics of electricity power-heat. Unlike pervious approaches, the system spin-

ning reserve requirements are clearly formulated in the problem and a novel charged system search

algorithm is proposed to solve it. In the proposed algorithm a novel self-adaptive learning framework,

adaptive selection operation and repelling force modeling are used in order to increase the population

diversity and amend the convergence criteria. The proposed framework is applied for three small, me-

dium and large test systems in order to evaluate its efficiency and feasibility.

? 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Combined Heat and Power (CHP) known as cogeneration has

the ability of creating simultaneous generation of two types of

energy: useful heat and electricity. It improves efficiency and

therefore, is more environmental friendly [1]. It also reduces the

generation cost between 10 and 40% [2]. In Thermal Units (TUs), all

the thermal energy is not converted into electricity and large

quantities of energyare wasted in the form of heat [3]. CHP uses the

heat and canpotentiallyachieve the energyconversion efficiency of

up to 80% [4,5]. This means that less fuel needs to be consumed to

produce the same amount of useful energy.

The objective of the CHP Dynamic Economic Dispatch (CHPDED)

is to find the optimal dispatching of power and heat with minimum

total operation cost while satisfying both heat and electricity load

demands and other various practical constraints over a short time

span. Thus, the CHP units operate in a bounded electricity power

versus heat plane. However, the model of the CHPDED problem

must consider the Spinning Reserve Requirements (SRRs) at the top

of time interval coupling to compensate for the error in largest

generation output and unexpected electric load deviations [6]. In

practice, the change in unit power outputs from one time to

another one is restricted due to the up and down ramp rate con-

straints [6]. Furthermore, opening steam valves of the large steam

turbine for increasing the power output of the TUs leads to a non-

convex fuel cost function. It should be noted that the mutual de-

pendencyof the heat production capacityand electricitygeneration

for CHP units must be considered in the problem [7]. Consequently,

a practical CHPDED problem should include valve-point effects,

ramp rate limits, SRRs and joint characteristic of electricity power-

heat which makes finding the optimal dispatching a challenging

problem. Threeapproaches have beenproposed in the literature: (i)

addressing multi-period economic dispatch, also called DED [8], or

(ii) considering SRRs in DED known as Reserve Constrained DED

(RCDED) [9], and (iii) solving economic dispatch of CHP units [7].

However, no economic dispatch approach incorporating CHP units

in a multi-period optimization framework i.e. RCCHPDED is cur-

rently available in the technical literature.

Currently, the available methods and algorithms for solving the

DED problem can be generally classified into two categories: 1)

optimization-based methods [10] and 2) meta-heuristic-based

methods [11e26]. The optimization-based methods impose no re-

striction on the non-smooth and non-convex characteristics of the

* Corresponding author. Tel.: þ98 917 3116278; fax: þ98 711 2330766.

E-mail addresses: bahman_bah@yahoo.com (B. Bahmani-Firouzi), farjah@

shirazu.ac.ir (E. Farjah), Seifi@shirazu.ac.ir (A. Seifi).

Contents lists available at SciVerse ScienceDirect

Energy

journal homepage: www.elsevier.com/locate/energy

0360-5442/$ e see front matter ? 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.energy.2013.01.004

Energy 52 (2013) 320e332

Page 2

valve-point effects. The major deficiency of these methods is the

“curse of dimensionality” when facing the DED problem especially

in large-scale power systems. Consequently, these methods are not

guaranteed to find the global optimum. Nowadays, the researchers’

interest has been directed toward modern meta-heuristic algo-

rithms. The objectives are to remove most of the inaccuracies in the

family of classic optimization-based approaches.

A salient feature of this paper is that it studies the DED problem

incorporating CHP units and simultaneously handles the SRRs

constraints, ramp rate limits and other constraints so that both

electric and heat load demands are met. Accordingly, a modified

evolutionary technique based on Charged System Search Algorithm

(CSSA) is applied to solve the RCCHPDED problem in realistic power

system models for which the total production costs of TUs, CHP and

heat-only units are minimized. Recently, CSSA has been effectively

implemented to solve various problems [27]. The CSSA is a novel

population-based meta-heuristic evolutionary algorithm on the

basis of the Coulomb’s law from electrostatics and the Newtonian’s

laws from mechanics [27]. This paper proposes two modifications

in the original CSSA to enhance the performance and capability of

it. Furthermore, in order to enhance the search ability of this

algorithm, a new Self-Adaptive Learning Mechanism (SALM) is

implemented in this paper. Using the proposed SALM, in each stage

of the optimization process, the algorithm self-adaptively recog-

nizes which mutation strategy is more beneficial to focus on. It is

noteworthy that this modified algorithm is called Self-Adaptive

Learning Charged System Search Algorithm (SALCSSA). The per-

formance of the proposed approach is successfully validated by

numerical models. The simulation results show that the new

modified algorithm has the ability of finding better solutions while

Nomenclature

Indices

h

i

ii, jj

j

j0

k

m, n

t

heat-only (H) unit index

thermal unit (TU) index

electricity power generating unit index

Combined Heat and Power (CHP) unit index

linear inequality constraint index

iteration index

charged particle index

time index

Constants

ai, bi, ci, di, ei cost coefficients of thermal unit i

Bii,jj,t

loss coefficient relating the productions of electricity

power generating units ii and jj at time t (MW?1)

B0,ii,t

loss coefficient associated with the production of

electricity power generating unit ii at time t

B00,t

loss coefficient parameter at time t (MW)

DRTU

i

ramp-down rate of thermal unit i (MW/h)

DRCHP

j

ramp-down rate of CHP unit j (MW/h)

DRii

ramp-down rate of electricity power generating unit ii

(MW/h)

HD,t

heat load demand at time t (MWth)

HH

h;max

HH

h;min

HCHP

j;max

heat capacity of CHP unit j (MWth)

HCHP

j;min

kmax

maximum iteration

NCHP

number of CHP units

NCP

number of charged particles

NGnumber of electricity power generating units

NH

number of heat-only units

Nlin

number of linear inequality constraints

NTnumber of time intervals

NTU

number of thermal units

PD,t

electricity load demand at time t (MW)

PCHP

j;max

power capacity of CHP unit j (MW)

PCHP

j;min

PTU

i;max

power Capacity of thermal unit i (MW)

PTU

i;min

Pii,max

power capacity of electricity power generating unit ii,

respectively (MW)

heat capacity of heat-only unit h (MWth)

minimum heat output of heat-only unit h (MWth)

minimum heat output of CHP unit j (MWth)

minimum power output of CHP unit j (MW)

minimum power output of Thermal unit i (MW)

rand($) and randQ($) Q ¼ 1,.,3 random function generator in

the range [0,1]

SRt

URii

10 min spinning reserve requirements at time t (MW)

ramp-up rate of electricity power generating unit ii

(MW/h)

ramp-up rate of CHP unit j (MW/h)

ramp-up rate of thermal unit i (MW/h)

aj,bj,zj,gj,lj,fj cost coefficients of CHP unit j

sh,mh,rh

cost coefficients of heat-only unit h

URCHP

j

URTU

i

Variables

Bestk

F(PHG)

G1ðPTU

G2ðPCHP

G3ðHCHP

HH

h;t

best position among all charged particles in iteration k

total operational costs at time span NT ($)

tÞ total thermal units costs at time t ($)

tt

Þ total CHP units costs at time t ($)

t

Þtotal heat-only costs at time t ($)

heat generation output of heat-only unit h at time t

(MWth)

HCHP

j;t

heat generation output of CHP unit j at time t (MWth)

HCHP

j;t

lower limit of the jth CHP unit output heat at time t

(MWth)

HCHP

j;t

upper limit of the jth CHP unit output heat at time t

(MWth)

HLoss,t

total heat losses at time t (MWth)

H_violatet heat mismatch at time t (MWth)

Meank

mean position of all charged particles in iteration k

PHG

generating unit vector

Pii,t

power generation output of electricity power

generating unit ii at time t (MW)

PLoss,t

total real power losses at time t (MW)

PTU

i;t

power generation output of thermal unit i at time t

(MW)

PTU

i;t

upper limit of the ith thermal unit output power at

time t (MW)

PTU

i;t

upper limit of the ith thermal unit output power at

time t (MW)

PCHP

j;t

power generation output of CHP unit j at time t (MW)

PCHP

j;t

lower limit of the jth CHP unit output power at time t

(MWth)

PCHP

j;t

upper limit of the jth CHP unit output power at time t

(MWth)

P_violatet power mismatch at time t (MW)

Worstk

worstpositionamongallchargedparticlesiniterationk

;HCHP

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

321

Page 3

the convergence of the SALCSSA is considerably improved com-

pared to the CSSA. The main contributions of the paper are as

follows:

a) The electricity power-heat plane and power ramp constraints

are modeled in the multi-period problem for CHP units.

b) The SRRs is modeled and formulated in the problem to over-

come the sudden fault in the system.

c) The RCCHPDED problem including ramp rate limits, valve-

point effect and SRRs is formulated. Moreover, an enhanced

simultaneous constraint-handling scheme is proposed to bias

the optimization toward the feasible region without enforcing

any restrictions on the objective function.

d) A new SALCSSA method which involves some novel meta-

heuristic approaches is proposed to solve the RCCHPDED

problem.

2. Problem formulation

2.1. Objective function

The system’s production cost can be mathematically repre-

sented in the following form:

Min FðPHGÞ ¼

X

X

NT

t ¼1

NT

GðPHtÞ

¼

t ¼1

?

G1ðPTU

tÞ þ G2ðPCHP

t

;HCHP

t

Þ þ G3ðHH

tÞ

?

(1)

where PHG¼ [PH1,...,PHt,...,PHNT] and PHt ¼ ½PTU

can be described in the following equations.

The cost of the TUs, CHP and heat-only units considered in the

problem can be represented as follows:

t;PCHP

t

;HCHP

t

;HH

t?

1) Thermal units (TUs) [28]

G1ðPTU

tÞ ¼

X

NTU

i¼1

?

aiþ biPTU

i;tþ ci

?

?

PTU

i;t

?2þ

???di

? sin

?

ei?

PTU

i;min? PTU

i;t

?????

?

t ¼ 1;.;NT

(2)

where PTU

t

¼ ½PTU

1;t

PTU

2;t

/

PTU

NTU;t?.

2) CHP units

CHP sometimes known as cogeneration is the use of a single

plant to generate both heat and electricity simultaneously. Each

CHP unit has an electricity power-heat Feasible Operation Region

(FOR) shown in Fig.1, which can be presented as a set of Nlinlinear

inequality constraints [2,29]:

xj0;j;tHCHP

j;t

þyj0;j;tPCHP

j;t

?zj0;j;tj0¼1;.;Nlin;j¼1;.;NCHP;t¼1;.;NT

(3)

The curve ABCDEF determines the boundary of the FOR. It is

noteworthy that according to this curve, xj0;j;t, yj0;j;tand zj0;j;tare

specified. Along the boundary curve BC, the heat capacity increases

as the electricity power generation declines and the heat capacity

decreases along the curve CD [7].

These constraints show the joint characteristic technology of

electricity power-heat in CHP units. The operating cost of CHP units

is presented as follows [7]:

G2ðPCHP

t

;HCHP

t

Þ ¼

X

NCHP

j¼1

?

ajþbjPCHP

j;t

þzj

?PCHP

j;t

?2þgjHCHP

HCHP

j;t

j;t

þlj

?HCHP

j;t

?2þ4jPCHP

j;t

?

t ¼ 1;.;NT

(4)

where

HCHP

t

PCHP

t

HCHP

2;t

¼ ½PCHP

/

1;t

HCHP

PCHP

2;t

/

PCHP

NCHP;t?

and

¼ ½HCHP

1;t

NCHP;t?.

3) Heat-only units

The heat-only units are taken into account to add a good flexi-

bility to CHP units in meeting high-heat load demands. The cost

function of heat-only units can be described as [30]:

G3ðHH

tÞ ¼

X

NH

h¼1

?

shþ mhHH

h;tþ rh

?HH

NH;t?.

h;t

?2?

t ¼ 1;.;NT

(5)

where HH

t¼ ½HH

1;t

HH

2;t

/

HH

2.2. Constraints

? Real power and heat balance

X

NG

ii¼1

Pii;t¼ PD;tþ PLoss;t

t ¼ 1;.;NT

(6)

X

NCHP

j¼1

HCHP

j;t

þ

X

NH

h¼1

HCHP

h;t

¼ HD;tþ HLoss;t

t ¼ 1;.;NT

(7)

where PLoss,tis a function of the generation unit power output and

B-loss coefficients that can be expressed as follows [24]:

PLoss;t¼

X

NG

ii¼1

X

NG

jj¼1

Pii;tBii;jj;tPjj;tþ

X

NG

ii¼1

B0;ii;tPii;tþB00;tt ¼ 1;.;NT

(8)

In addition, it should be noted that the heat load demands are

used within a short distance of CHP units and so that the heat losses

HLoss,tt ¼ 1,...,NT are negligible [2].

Electricity power

(MW)

Heat (MWth)

Max. Fuel

Min. Fuel

Max. Heat Extraction

A

B

C

D

E

F

Fig. 1. Electricity power-heat feasible operating region (FOR) for a CHP unit.

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

322

Page 4

? Up and down ramp rate limits

These limitations can be formulated as follows:

PTU

i;t? PTU

i;t?1? URTU

i

i ¼ 1;.;NTU; t ¼ 1;.;NT

(9)

PTU

i;t?1? PTU

i;t? DRTU

i

i ¼ 1;.;NTU; t ¼ 1;.;NT

(10)

PCHP

j;t

? PCHP

j;t?1? URCHP

j

j ¼ 1;.;NCHP; t ¼ 1;.;NT

(11)

PCHP

j;t?1? PCHP

j;t

? DRjj ¼ 1;.;NCHP; t ¼ 1;.;NT

(12)

? Power generation limits

According to the pervious discussion, the generation output of

each unit shall be within their lower and upper limits. So that

PTU

i;t? PTU

i;t? PTU

i;t i ¼ 1;.;NTU; t ¼ 1;.;NT

(13)

PCHP

j;t

? PCHP

j;t

? PCHP

j;t

j ¼ 1;.;NCHP; t ¼ 1;.;NT

(15)

? Heat generation limits

The operation of CHP and heat-only units are expressed as

follows:

HCHP

j;t

?PCHP

j;t

??HCHP

h;t? HH

j;t

?HCHP

j;t

?PCHP

h ¼ 1;.;NH; t ¼ 1;.;NT

j;t

?j ¼ 1;.;NCHP; t ¼ 1;.;NT

(17)

(18)

HH

h;min? HH

h;max

? Spinning reserve requirements

The SRRs constraint is formulated as follows [3,6,31]:

?

Dt ¼

X

NG

ii¼1

min

Pii;max? Pii;t;URii

6

?

? SRt

!

? 0

t ¼ 1;.;NT

(19)

This formulation will exactly satisfy the SRR from the spinning

generators in each time within 10 min of being required and its

amount is related to the ramp up rate constraint of electricity

generating unit. For time t to t þ 1, the ramp up rate of unit i is

URi(MW/h) the corresponding amount for 10 min is URi/6 [3,6,31].

3. Self-adaptive learning charged system search algorithm

(SALCSSA)

3.1. Original CSSA

CSSA is a new population-based evolutionary algorithm, in

which searching for the global optimum is inspired by electro-

static and Newtonian mechanics laws between agents named CP.

CSSA consists of a number of CPs (PHG,mm ¼ 1,...,NCP) with dif-

ferent fitness value F(PHG,m). In each iteration, similar to what

occurs in the electrical and mechanical forces procedure between

a network of CPs, the CP with the best fitness function among all

the CPs is selected as Bestk¼ ½bestk

regard, the structure of each CP of the group can be defined as

follows:

1;.;bestk

t;.;bestk

NT?. In this

PHk

G;m¼ ½PHk

In this paper, the output power of the NTUthermal units plus

NCHPcombined heat and power units and output generation heat of

NCHPcombined heat and power units plus NHheat-only units in NT

time horizon represent the CP as shown in Eq. (20).

m;1;.;PHk

m;NT?

m ¼ 1;.;NCP

(20)

Each agent is assumed as a charged sphere with radius a and having

a proper uniform charge density which can insert an electric force

to the other CPs. This charge density for each agent can be for-

mulated as follows [27]:

Qk

m¼

FðPHk

F?Bestk?? F?Worstk?

All these CPs attract each other based on their fitness value and

separation distance. The separation distance between two CPs m

and n is defined as follows [27]:

G;mÞ ? F

?

Worstk?

m ¼ 1;.;NCP

(21)

Rk

m;n¼

kPHk

G;m? PHk

G;nÞ=2 ? Bestk??þ

G;nk

??ðPHk

G;mþ PHk

3

m ¼ 1;.;NCP;

n ¼ 1;.;NCP

(22)

3 is a small positive number to avoid singularities. In the CSSA,

a probability PRk

moving the mth CP toward the nth one and is obtained using the

following function [27]:

m;nhas been defined which is the probability of

PTU

i;t¼ min?PTU

i;max;PTU

i;t?1þ URTU

i

?

i ¼ 1;.;NTU; t ¼ 1;.;NTPTU

i;t¼ max?PTU

i;min;PTU

i;t?1? DRTU

i

?

i ¼ 1;.;NTU; t ¼ 1;.;NT

(14)

PCHP

j;t

¼ min?PCHP

j;max;PCHP

j;t?1þ URCHP

j

?

j ¼ 1;.;NCHP; t ¼ 1;.;NTPCHP

j;t

¼ max?PCHP

j;min;PCHP

j;t?1? DRCHP

j

?

j ¼ 1;.;NCHP; t ¼ 1;.;NT

(16)

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

323

Page 5

This rule means that the respective good and bad CPs are awar-

dedthepotentialofattractionandrepelling,whichwillimprovethe

exploitationexplorationcapabilitiesofthealgorithm[27].Thevalue

of resultant force affecting a CP is calculated as follows [27]:

Forck

m¼Qk

m

X

NCP

n¼1;nsm

Qk

a3Rk

n

m;ni1þ

Qk

n

?

Rk

m;n

?2i2

!

PRk

m;n

?ðPHk

G;n?PHk

G;mÞ

!

m ¼ 1;.;NCP

(24)

where ði1¼ 1; i2¼ 05Rk

In this study, a is assumed to be unity [27]. According to Eq. (24),

the value of the Forck

tional to ðRk

CSSA where the CPs are far from each other. This leads to the high

exploration power because of performing more searches in the first

iterations. It is noteworthy that in the search procedure of the CSSA

the exploitation should be increased and the exploration should be

decreased gradually. When CPs are collected in the optimal space,

the Forck

space more carefully. In addition, according to Eq. (24) a larger

charge magnitude corresponding to a better CP creates a stronger

force, so the tendency of the CPs to be affected by better solutions

are more than worse ones.

The position modification of each element m occurs based on

the attraction or repelling electric and mechanical force to other

elements in the entire search space. Accordingly [27], each CP m

moves toward its new position with the Forck

velocity Vk

m;n< aÞorði1¼ 0; i2¼ 15Rk

m;n? aÞ.

macting on the mth CP is inversely propor-

m;nÞ2between the particles in the early iterations of the

mfollows the first term of Eq. (24) to search the consequent

mand its previous

G;mas follows:

PHk

G;m;new¼PHk

G;mþ rand1?$?kaForck

þ rand2?$?kvVk

m

Mk

m

PHk

G;mDt2

G;mDtm ¼ 1;.;NCP

(25)

Vk

G;m;new¼ ðPHk

Mk

Dtis the step time and is equal to one. kaand kvare the acceleration

and velocity coefficient control the exploration and exploitation

concentration of the CSSA, respectively and selected as follow [27]:

G;m;new? PHk

G;mÞ=Dtm ¼ 1;.;NCP

min this work [27].

(26)

mis the mass of CP m which is equal to Qk

ka ¼ 0:5ð1 ? k=kmaxÞ

(27)

kv ¼ 0:5ð1 þ k=kmaxÞ

Compared to other evolutionary algorithms, CSSA has major

advantages to be used for solving complex non-linear optimization

problems such as the RCCHPDED problem. Some of these advan-

tages are simple concept, easy implementation, higher stability

mechanism and less execution effort. Despite these features, it

often experiences inappropriate convergence local optima, di-

versity losing via the CPs, or slow proceeding of the algorithm

search, which motivates the three major modifications character-

izing our proposed SALCSSA as described next.

(28)

3.2. Adaptive selection operation

In the CSSA, all the CPs are affected on the movement of each CP,

but in the proposed approach only Ngoodnumber of CPs with best

fitness values have the chances to attract or repel each CP. In this

study, the value of Ngoodstarts from NCPand changes adaptively in

the following form:

Ngood¼ roundðð0:2NCP? NCPÞk=kmaxþ NCPÞ

(29)

3.3. Repelling force modeling

It is necessary to note that in Ref. [27], only the attractive force

between the CPs is modeled. In order to consider the repelling

feature of the CPs and improve the exploration capability of the

CSSA, the original CSSA is modified by using a parameter of sign in

Eq. (24) as follows:

Forck

m¼Qk

m

X

NCP

n¼1; nsm

Qk

a3Rk

n

m;ni1þ

Qk

n

?

Rk

m;n

?2i2

G;mÞsign

!

? PRk

m;nðPHk

G;n? PHk

!

m ¼ 1;.;NCP

(30)

where sign determines the type of electrical force and is deter-

mined as follows:

?þ1

sign ¼

if rand ? pr

else

?1

(31)

where, þ1 and ?1 show the attractive or repelling electrical force,

respectively. pr controls the ratio of the two types of the forces. This

parameter is selected 0.8 in this study.

3.4. Self-adaptive learning mechanism (SALM)

The principle of designing a SALM framework is to enhance the

performance or robustness of the original CSSA to obtain good re-

sults in the numerical optimization with effective yet diverse

characteristics. The basic idea is to select adaptively multiple

effective strategies based on their previous experiences of gen-

erating promising solutions and applied to achieve the mutation

operation. It means that at different steps of the optimization

procedure, multiple strategies may be assigned a different proba-

bility based on their success rate in generating improved solutions

within a certain number of previous generations. In this paper, two

mutation strategies are implemented in SALM to diverse the

complex RCCHDED problemwith non-linear, non-smooth and non-

convex nature. These mutation operators can be described as

follows:

Mutation strategy 1:

PHk

G;m;mut1¼PHk

m ¼ 1;.;Nk

G;mþ round

?

1 þ rand

?

$

???

Bestk? Meank?

1

(32)

PRk

m;n¼

8

>

>

>

>

>

>

:

<

1if

FðPHk

FðPHk

else

G;mÞ ? F

G;nÞ ? FðPHk

?

Bestk?

G;mÞ

> randnFðPHk

G;nÞhFðPHk

G;mÞ m ¼ 1;.;NCP; n ¼ 1;.;NCP

0

(23)

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

324

Page 6

Mutation strategy 2:

PHk

G;m;mut2¼PHk

G;r1þ randð$Þ1

þ randð$Þ2ðPHk

2are the respective number of CPs which choose the

mutation method 1 and 2 in iteration k. In this regard, the vectors

PHk

population in order to uniformly cover the algorithm search

domain. This operation can be implemented for each of the target

vectors in each mutation strategy. In order to improve the solutions

of the proposed large-scale problem and further increase the

population diversity and enhance the globally search capabilities,

the mutation methods (32) and (33) can be implemented. It should

be pointed out that each of the methods, corresponding to the

optimization problem in hand or corresponding to the different

stages of the one particular problem, may be more profitable than

the other one. The algorithm distinguishes the more beneficial one

in parallel. Although this paper uses the SALCSSA to optimize

RCCHPDED problem, it seems this procedure can be helpful for the

other optimization problems but it should be verified in further

studies.

Generally speaking, the criteria of selecting these two strategies

are that they have different characteristics and strengths that cover

diverse conditions. The occurrence of mutation is followed fromthe

requirements of the CSSA search process. All CPs in the population

will have a chance to mutate, controlled by the probability of their

methods of mutating. Based on a probability model, each particle

selects one of these two methods. Denote Prob1

the initial probability of implementing ath mutation strategy. The

Roulette Wheel Mechanism (RWM) selection method is used to

choose the ath method for each of the CP in the population. Probk

updated after the LP iterations according to the following form:

?

Bestk? Worstk?

G;r2? PHk

G;r3Þ

m ¼ 1;.;Nk

2

(33)

Nk

1and Nk

G;r1, PHk

G;r2and PHk

G;r3are selected randomly from the existing

a¼ 0:5; a ¼ 1;2 as

ais

Probk

a¼

SRk

a¼1SRk

a

P2

arepresents the success rate of the trial solutions gen-

erated by the ath mutation strategy and successfully entering the

next step within the previous LP iterations with respect to the kth

iteration. Thus, SRk

a

; a ¼ 1;2(34)

where SRk

acan be formulated as follows:

SRk

a¼

Pk?1

it ¼k?LP

it ¼k?LPnsit

?

aand nfit

a

Pk?1

nsit

aþ nfit

a

?þ d; a ¼ 1;2; k > LP

aare the respective numbers of the trial solutions

generated by the ath mutation strategy which remain or fail in the

selection process in the last LP iterations. The small constant value

d ¼ 0.01 is used to avoid the possible null values for SRk

ensure that the summing of the probabilities of choosing strategies

are always equal toone, Eq. (34) can be used. It can be expected that

the larger the value of the SRk

implementing it to generate the trial solutions at the current iter-

ation k is. To this end, the RWM selection method is applied to

choose the ath mutation strategy for each CP.

After determining the mutant vector for all of the CPs, this

vector was mixed with PHk

(35)

where nsit

a. In order to

ais, the larger the probability of

G;mwhich generated PHk

G;m;novelas:

Pk;TU

m;t;i;novel¼

8

:

<

Pk;TU

m;t;i;muta

Pk;TU

m;t;i

if

?

rand1

?

$

?

? rand2

?

$

??

otherwise

i ¼ 1;.;NTU; m ¼ 1;.;NCP; t ¼ 1;.;NT

(36)

Pk;CHP

m;t;j;novel¼

8

:

<

Pk;CHP

m;t;j;muta

Pk;CHP

m;t;j

if

?

rand1

?

$

?

? rand2

?

$

??

otherwise

j ¼ 1;.;NCHP; m ¼ 1;.;NCP; t ¼ 1;.;NT

8

:

(37)

Hk;CHP

m;t;j;novel¼

<

Hk;CHP

m;t;j;muta

Hk;CHP

m;t;j

if

?

rand1

?

$

?

? rand2

?

$

??

otherwise

j ¼ 1;.;NCHP; m ¼ 1;.;NCP; t ¼ 1;.;NT

8

:

(38)

Hk;H

m;t;h;novel¼

<

Hk;H

m;t;h;muta

Hk;H

m;t;h

if

?

rand1

?

$

?

? rand2

?

$

??

otherwise

h ¼ 1;.;NH; m ¼ 1;.;NCP; t ¼ 1;.;NT

(39)

where rand1,.,3($) are the random function generators in the range

[0,1]. Pk;TU

tth time for the mth CP of the kth iteration. Pk;CHP

generation output of the jth CHP unit in the tth time for the mth CP

of the kth iteration. Hk;CHP

jth CHP unit in the tth time for the mth CP of the kth iteration.

Hk;H

the tth time for the mth CP of the kth iteration.

The new solutions can replace the original solution based on

their fitness functions as follows:

m;t;i;novel, is the power generation output of the ith TU in the

m;t;j;novelis the power

m;t;j;novelis the heat generation output of the

m;t;h;novelis the heat generation output of the hth heat-only unit in

PHkþ1

G;m¼

?PHk

G;m;novel

PHk

if FðPHk

G;m;novelÞ ? FðPHk

m ¼ 1;.;NCP

G;mÞ

G;motherwise

(40)

After determining PHkþ1

pared to FðPHk

replaced.

G;m, the fitness function FðPHkþ1

G;mÞ. If this solution is better than PHk

G;mÞ was com-

G;mthen it is

4. Solution methodology

In this section, firstly approach to implement the SALCSSA will

be developed for solving the RCCHPDED problem. Particularly, an

enhanced constraint-handling will be propose on how to satisfy all

the equality and inequality constraints (6)e(19) of the RCCHPDED

problem. Secondly, some applicable tool usage of the proposed

approach is drawn.

4.1. Application of SALCSSA on the RCCHPDED problem

The process of the SALCSSA can be summarized as follows:

Step 1) Input all required data.

Step 2) Representation: The vector variables chosen for the

RCCHPDED problem are the output power of the NTUTUs plus

NCHPCHP units and output generation heat of NCHPCHP units

plus NHheat-only units in NT time interval. Thus, each indi-

vidual consists of (NTUþ 2NCHPþ NH) ? NT variables as shown in

(20).

Step 3) Initialization: To begin, the CPs of the population are

randomly generated in the range [0,1] and located between the

maximum and minimum operating limits of the unit subjected

to constraints (6)e(19). For handling these constraints the fol-

lowing sub-steps should be taken.

Step 3.1) Simultaneous handling of the SRR and ramp rate

constraints: for each hour, the feasibility of constraints (6)e

(15) and (18) is checked. If these constraints are violated,

the algorithm returns to previous hours and modifies them

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

325

Page 7

in a way that it can reach the desired solution according to

the following backward and forward procedure:

For m ¼ 1 to NCP

For t ¼ 1 to NT

HH ¼ t;

Generate Phm,HHrandomly subject to constraints (13), (15) and

(18). It should be noted that the power output of NTUthermal units,

the power output of NCHPunits and heat output of NHheat-only

units determined Phm,HHas follows:

For satisfying power and heat balance, go to step 3.2 and return.

Then, calculate the value of violation of the SRR constraint using Eq.

(19):

if Dm;HH< 0

Backward procedure: go to the pervious time and subtract Dm,HH

from each of the Pm;HH?1;ii, which are fixed to their maximum

values. Generate Phm,HH?1randomly subject to constraints (13),

(15) and (18), then, compute Dm,HH?1.This procedure continues

until a time interval is reached inwhich the violation is greater than

or equal to zero. Save this time in hh.

Forward procedure: Generate Phm,t, t ¼ hh þ 1 to HH randomly

subject to constraints (13), (15) and (18). Check the heat and power

balance according to step 3.2. Then according to the power output

of the Phm,Hthe value of violation Dm,HHis calculated again. The

backward and forward procedures continue until Dm;HH? 0.

Else

Endfor (refers to index t)

Calculate F(PHG,m) from (1).

Endfor (refers to index m)

Step 3.2) Heat and power balance handling: Generate HCHP

randomly subject to (17). For satisfying the constraints (6)

and (7), the value of power and heat mismatch are calculated

for each PHm,tof vector PHG,mas follows:

m;t

P violatem;t ¼

X

NG

ii¼1

Pm;t;ii? PD;t? Pm;Loss;t

t ¼ 1;.;NT

(42)

H violatem;t¼

X

NCHP

j¼1

HCHP

m;t;jþ

X

NH

h¼1

HH

m;t;h?HD;tt ¼ 1;.;NT

(43)

If P_violatem,t ¼ 0 and H_violatem,t ¼ 0, return.

If P_violatem,ts 0, select one unit PTU

domly and subtract P_violatem,tfrom it. If any unit of the individual

violates constraint (13) or (15), then the position of the unit gen-

eration is fixed to its minimum/maximum power output in the

corresponding time. This procedure continues to reach the zero

value of P_violatem,tand it makes sure that different units will be

selected to compensate for the power mismatch. After this proce-

dure, the minimum/maximum heat output of the CHP units should

be updated according to the change of output power of these units.

If H_violatem,ts 0, select one unit HH

H_violatem,tfrom it. If any unit of the individual violates constraint

(18), then the position of the unit generation is fixed to its

m;t;ior PCHP

m;t;jof Phm,tran-

m;t;hrandomly and subtract

minimum/maximum power output in the corresponding time. This

procedure continues to reach the zero value of H_violatem,t.

Step 4) Select Ngoodnumber of CPs via adaptive selection operation.

Step 5) Position modification: To modify the position of each CP,

(30), (25) and (26) should be implemented. The new CP set must

satisfy the quality and inequality constraints (6)e(19). To handle

these constraints, steps 3.1 and 3.2 can be applied.

Step 6) Update Bestkand Worstk: the output power of the NTU

thermal units plus NCHPcombined heat and power units and

output generation heat of NCHPcombined heat and power units

plus NHheat-only units in NT time interval represent the posi-

tion of the CP in the movement process of the optimization

problem. The best and worst positions, which have the lowest

and highest objective functions among all the CPs, are taken as

Bestkand Worstkin the current iteration, correspondingly.

Step 7) Use SALM: Select the ath strategy by the RWM based on

section 3.4 for all the existing solutions. The new CP set must

satisfy the quality and inequality constraints (6)e(19). To handle

these constraints, steps 3.1 and 3.2 are applied.

Step 8) Update the probability for each mutation strategy i.e.

Probk

Step 9) Checking the convergence criteria: Go to step 4 for the

next iteration. This loop can be terminated after a predefined

number of iterations and the best CP with the best position is

selected as the best optimal solution.

a;a ¼ 1;2 using (34) and (35).

5. Simulation results

The SALCSSA described above has been implemented over three

test systems to demonstrate the performance of the proposed

method for the RCCHPDED. The first system includes 10 units and

24 periods, and two different scenarios are considered as (i) con-

sidering losses and (ii) neglecting losses. The second system is a 30-

unit test system obtained by tripling the number of units, load

demand and SRRs. The third system is a 150-unit test system

obtained by making fifteen folds the number of units, load demand

and SRRs. The third test system is large enough to address the is-

sues of scaling up. The data for the TUs cost coefficients, TUs power

generation limits, the forecasted electric load demand for 24 h, the

B-loss coefficient vector and TUs ramp rate limits of the system

with valve-point loading are mainly derived from [25]. These test

systems are subsequently modified to incorporate CHP and heat-

only units.

For a better illustration of the effectiveness of the proposed

approach, three case studies are considered as follows:

? Case study I: RCDED without any CHP, heat-only units and heat

load demands.

? Case study II: RCDED considering heat-only units for supplying

the heat load demands (with heat-only units and without

CHP). One, three and fifteen heat-only units are considered in

the 10-unit, 30-unit and 150-unit test systems to satisfy the

heat load demand, respectively.

? Case study III: RCCHPDED (with CHP and heat-only units). In

this case, the 5th and 8th TUs are replaced by one CHP unit,

separately. Thus, the first test system is modified and consists

Phm;HH¼

h

PTU

m;HH;1;.;PTU

m;HH;NTU;PCHP

m;HH;1;.;PCHP

m;HH;NCHP;HH

m;HH;1;.;HH

m;HH;NH

i

(41)

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

326

Page 8

of eight conventional TUs, two CHP units and one heat-only

unit. The second test system is modified to include 24 con-

ventional TUs, six CHP and three heat-only units. The third test

system is changed to comprise 120 conventional TUs, 30 CHP

and fifteen heat-only units. The data for CHP and heat-only

units and the FOR of CHP units are adopted from Refs. [7,30]

and given in Appendix. A typical forecasted hourly heat load

demand is shown as well. It is necessary to note that the

modified 30-unit and 150-unit test system are generated by

making three and fifteen folds of the modified 10-unit test

system including 8 conventional TUs, 2 CHP units and one heat

only unit, respectively.

It should be pointed out that a time period of one day with

hourly time step is considered as the study period for illustrative

purposes. All the test cases include the SRRs constraint. In this

paper, the 10 min SRRs have been used and set to (10/60) ? 5% of

electric load demand in each hour. Also, it should be mentioned

that the B-loss coefficients are functions of the system operating

state [24]. The different load demands at different periods should

have different loss coefficients. For the comparison of results

obtained by other methods in this area, the loss coefficients are

assumed to be the same over the time span. Moreover, as seen in

Eq. (3) the linear inequality constraints and the extreme point in

Fig.1 allow the shape of the joint characteristic of electricity power-

heat FOR tochange hourly due toexternalvariables such as outdoor

temperature [2]. However, the same number of points is assumed

without any change for each hour.

The solution search space of these cases has many local minima,

and the global minimum is hard to obtain. Due to the stochastic

nature of the evolutionary algorithm, 30 independent trial runs are

made to extract the statistical information.

5.1. Case studies

5.1.1. Case study I

In order to study the effectiveness and superiority of the pro-

posed optimization method, the RCDED is implemented. In the 10-

unit test system, firstly, the transmission losses are neglected and

the best total operation cost using SALCSSA is $1,016,797. The

detailed results of the best solution of SALCSSA for 10-TUs test

system neglecting losses is given in Table 1 to check whether the

constraints of the problem are satisfied or not. To demonstrate the

SRRs handling, Dt, t ¼ 1,...,24 are also calculated and added to

Table 1. Secondly, the effect of the transmission losses is measured

and the RCDED problem is evaluated. The total operation cost of the

best dispatch result of the test system in all dispatch periods

obtained by the proposed SALCSSA is $1,037,550. The detailed re-

sults of the best solution of SALCSSA for 10-TUs test system con-

sidering losses is shown inTable 2. The complete comparison of the

results and performance of SALCSSA with respect to the CSSA with

mutation strategy1, CSSAwith mutation strategy2, CSSAwhich uses

two proposed modifications i.e. adaptive selection operation and

repelling force modeling (named CSSA1), original CSSA and those of

the other known methods in two different scenarios (considering

or neglecting losses) is given in Table 3. Note that the best solution

of Ref. [24] is without handling ramp rate limits of units; therefore

[24], was not compared with the proposed method. It can be seen

from the simulation results that the proposed method reveals

better solutions compared to other methods and outperform them.

Also, Fig. 2 shows the variation of the best solution of total cost for

10-TUs neglecting losses with the number of iterations in the

population during search procedure for CSSA, CSSA1, CSSA-

mutation strategy1, CSSA-mutation strategy2 and SALCSSA. The

SALM characteristics of the proposed approach are analyzed using

the candidate strategies in the pool separately to solve the problem.

It should be mentioned that in each generation, the SALCSSA can

produce diverse solution even with a small population and less

maximum iteration number. Besides, the SALCSSA with SALM can

better manage transition from each generation to the next one in

comparison with each separate strategy. The premature conver-

gences of the other methods compared to the SALCSSA degrade

their performances and reduce their search capabilities that lead to

a higher probability toward being trapped in local optima. One

main disadvantage of other methods with respect to SALCSSA for

solving the RCDED problem is their slow and premature con-

vergence to a near-optimal solution. Also, it can be seen from

Tables 4 and 5 that the best total operation cost for respective 30-

Table 1

Best dispatch found by SALCSSA for case I without losses (10-unit).

Hour Load

P1(MW)

150.0000

150.0000

226.6242

303.2484

303.2484

379.8726

379.8726

379.8726

456.4968

456.4968

456.4968

456.4968

456.4968

456.4968

379.8726

303.2484

226.6242

303.2484

379.8726

456.4968

456.4968

379.8726

303.2484

226.6242

P2(MW)

135.0000

135.0000

215.0000

295.0000

309.5720

389.5720

396.7994

396.7994

396.7994

396.7994

396.7994

460.0000

396.7994

396.7994

396.7994

396.7994

396.7994

396.7994

396.7994

460.0000

390.0604

310.0604

230.0604

222.2665

P3(MW)

194.0932

268.0932

309.3355

300.7113

310.2727

301.6485

300.5802

297.4191

297.2972

297.7471

340.0000

307.6724

302.873

294.3467

297.0079

281.4987

289.1209

310.6301

302.1396

312.5859

322.0756

290.8740

241.7798

178.2025

P4(MW)

60.0000

60.0000

60.0000

60.0000

60.0000

60.0000

77.9744

126.7666

176.7666

226.7666

248.1448

291.2715

241.2715

191.2715

172.1139

122.1139

120.4152

120.4152

120.4150

170.4150

120.4150

70.4150

60.0000

60.0000

P5(MW)

122.8666

122.8666

73.0000

73.0000

122.8666

122.8666

172.7331

172.7331

222.5997

222.5997

222.5997

222.5997

222.5997

172.7331

122.8666

73.0000

73.0000

122.8666

172.7331

222.5998

222.5998

172.7333

122.8666

122.8666

P6(MW)

122.4498

122.4498

122.4499

122.4499

122.4499

122.4499

122.4499

150.8188

122.4499

160.0000

160.0000

160.0000

160.0000

122.4500

122.4499

122.4499

122.4499

122.4499

122.4499

160.0000

122.4499

122.4498

122.4499

122.4498

P7(MW)

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

129.5904

P8(MW)

47.0000

47.0000

47.0000

47.0000

47.0000

47.0000

47.0000

47.0000

47.0000

77.0000

85.3118

85.3121

85.3121

85.3121

80.2993

50.2993

47.0000

47.0000

77.0000

85.3121

85.3121

77.0045

47.0045

47.0000

P9(MW)

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

50.0000

52.0571

52.0571

22.0571

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

P10(MW)

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

Dt(MW)

66.7762

66.1596

64.9262

63.6929

63.0762

61.8429

61.2262

60.6096

59.3762

49.8096

35.8596

35.2429

49.8096

59.3762

60.6096

62.4596

63.0762

61.8429

60.6096

36.4762

59.3762

61.8429

64.3096

65.5429

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

1036

1110

1258

1406

1480

1628

1702

1776

1924

2072

2146

2220

2072

1924

1776

1554

1480

1628

1776

2072

1924

1628

1332

1184

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

327

Page 9

unit and 150-unit test systems are $3,048,972 and $15,256,663

which are better than the results of other methods. This is also

important because as the size of the system increases, the differ-

ences between the results of the methods seem to decrease, but the

solution of the SALCSSA is far from the other methods.

5.1.2. Case study II

In this case, we have considered that only 10-TUs are employed

to supply electric load demands and one heat-only unit to meet

heat load demands in the case of RCDED with heat demands for the

first test system. In this regard, the best total system production

costs are equal to $1,246,561 and $1,267,314 for neglecting or

considering transmission losses, respectively. Also, 30-TUs and

three heat-only units and 150-TUs and 15 heat-only units are used

to supplyelectricity powerand heat load demand in the second and

third test system, respectively. In these test system, the best total

operation costs using SALCSSA are $3,738,264 and $18,703,123,

respectively.

5.1.3. Case study III

To better illustrate the effects of CHP units in the scheduling

results, the entire test systems are modified as mentioned above.

The results obtained by SALCSSA have been compared with those

obtained by CSSA. Table 6 lists the best, the worst, and the average

solutionsattainedbyeachmethodaswellastheaveragecomputing

time in the case of RCCHPDED for the first test system in both

Table 3

Results obtained by different methods for case I (10-unit).

Solution

technique

Total cost ($)Scaled CPU

time (min)

Best valueMean value Worst value

Without losses

SQP [23]

EP [23]

EP-SQP [23]

MDE [13]

HQPSO [26]

PSO-SQP [9]

MHEP-SQP [25]

PSO-SQP (C) [9]

IPSO [17]

ICPSO [19]

CSAPSO [20]

CSSA

CSSA1

CSSA-mutation

strategy2

CSSA-mutation

strategy1

SALCSSA

With losses

EP [25]

EP-SQP [25]

MHEP-SQP [25]

IPSO [17]

CSAPSO [20]

CSSA

SALCSSA

1,051,163

1,048,638

1,031,746

1,031,612

1.031,559

1,030,773

1,028,924

1,027,334

1,023,807

1,019,072

1,018,767

1,019,572

1,018,930

1,017,697

NA

NA

1,035,748

1,033,630

1,033,837

1,031,371

1,031,179

1,028,546

1,026,863

1,020,027

1,019,874

1,020,056

1,019,447

1,018,052

NA

NA

NA

NA

1,036,681

1,053,983

NA

1,033,983

NA

NA

NA

1,020,683

1,019,912

1,018,418

0.421

15.049

7.264

4.417

0.773

6.364

21.23

7.219

0.050

0.350

0.350

0.109

0.114

0.174

1,017,1641,017,3311,017,5360.156

1,016,7971,017,0111,017,2050.139

1,054,685

1,052,668

1,050,054

1,046,275

1,038,251

1,040,541

1,037,550

1,057,323

1,053,771

1,052,349

1,048,154

1,039,543

1,041,319

1,038,044

NA

NA

NA

NA

NA

1,042,405

1,038,696

47.23

27.53

24.33

0.150

NA

0.164

0.242

NA: Not available in the literature. The bold values represent the minimum values of

objective functions obtained by the proposed algorithm.

Fig. 2. Convergence characteristics of SALCSSA, CSSA-mutation strategy1, CSSA-

mutation strategy2, CSSA1 and original CSSA for case I (10-unit without losses).

Table 2

Best dispatch found by SALCSSA for case I with losses (10-unit).

Hour Load

P1(MW)

150.0000

150.0000

226.6255

303.2483

379.8726

379.8731

379.8717

456.5033

456.4985

456.5022

456.5303

456.4970

456.4967

456.3027

379.8686

303.2143

226.6191

303.2089

379.8739

456.638

456.4913

379.8720

303.2504

226.6236

P2(MW)

135.0000

135.0000

139.9780

219.9780

222.2664

302.2664

309.5256

309.5338

389.5338

396.7974

396.7995

460.0000

396.8000

316.8000

308.8123

228.8123

308.8123

309.5289

310.0074

390.0074

389.1114

309.1114

229.1114

222.2653

P3(MW)

206.2298

282.7918

302.5180

299.5342

297.3956

291.4321

300.8194

300.1723

297.6970

323.9295

340.0000

325.0791

306.4636

310.4387

296.2141

284.6540

308.6420

296.9019

305.5787

340.0000

308.3274

284.857

204.8571

184.9410

P4(MW)

60.0001

60.0000

60.0064

60.0000

60.0000

60.9896

110.9896

160.9896

191.1273

241.1273

291.1273

299.9999

291.6450

241.6450

191.6453

176.6549

126.6677

163.1842

180.8305

230.8305

180.8501

130.8510

119.1125

120.0880

P5(MW)

122.8666

122.8667

172.7360

172.7320

172.7330

222.4980

222.5870

172.7331

222.6006

222.5994

227.8976

222.5996

222.5995

222.6002

222.5832

172.7212

122.8602

172.7148

222.6193

222.8436

222.6057

172.7351

122.8336

73.0000

P6(MW)

122.4500

122.4499

122.4814

122.4662

122.4496

122.4540

122.4595

122.4710

122.4582

159.9999

160.0000

160.0000

122.4692

122.4808

122.4257

122.4396

122.5624

122.4435

122.6200

160.0000

122.4638

123.0930

122.4498

122.4499

P7(MW)

129.5905

129.5905

129.5905

129.5905

129.5904

129.5909

129.5931

129.5906

129.5905

129.5890

129.6055

129.5905

129.5905

129.5985

129.5901

129.5906

129.5904

129.5899

129.5906

129.5908

129.5925

129.5907

129.5903

129.5906

P8(MW)

47.0000

47.0000

47.0000

47.0000

47.0000

77.0000

85.3122

85.3077

85.4707

115.4707

120.0000

120.0000

120.0000

90.0000

85.3113

85.3056

85.3123

85.3119

85.3138

115.3138

85.3138

55.3287

47.0000

47.0000

P9(MW)

20.0000

20.0000

20.0000

20.0001

20.0000

20.0000

20.0000

20.0000

20.0000

20.0045

20.0016

50.0016

20.0018

20.0000

20.0000

20.0000

20.0005

20.0000

20.0000

20.0000

20.0000

20.0000

20.0000

20.0001

P10(MW)

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

PLoss(MW)

12.1369

14.6989

17.9357

23.5494

26.3077

33.1042

34.1581

36.3013

45.9766

49.0199

50.9618

58.7676

49.0663

40.8661

35.4506

24.3925

26.0669

29.8839

35.4342

48.2240

45.7559

32.4389

21.2051

16.9586

Dt(MW)

66.7762

66.1595

64.9262

63.6928

63.0762

61.8424

61.2236

60.6094

59.3762

49.3403

30.8445

21.9096

53.1428

59.3681

60.6099

62.4594

63.0763

61.8435

60.6093

36.1620

59.3742

61.8426

64.3097

65.5427

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

1036

1110

1258

1406

1480

1628

1702

1776

1924

2072

2146

2220

2072

1924

1776

1554

1480

1628

1776

2072

1924

1628

1332

1184

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

328

Page 10

different scenarios (with and without losses). From these results, it

can be seen that the proposed SALCSSA provides lower total oper-

ation cost forall the above mentioned methods. Therefore, SALCSSA

is effective in providing better solutions and shows a more robust

performance. The detailed results of the best solution of SALCSSA

neglecting and considering losses are shown in Tables 7 and 8 as

well as Tables 9 and 10, respectively. The total cost of RCDED with

heat load demands in the previous case study is higher than the

total cost of RCCHPDED for the first scenario i.e. neglecting losses

($1,246,561 opposed to $1,225,447) for the reason that the CHP

units have the capability to produce two types of energy in lower

cost. Therefore, the total operation cost is significantly reduced due

to using CHP units. The difference in the total cost can be accounted

for CHP units’ installations for future expansion planning of the

system. The same justification can be used for the second scenario,

which considers losses. Also, the results and performance of SAL-

CSSA are completely compared with CSSA for the second and third

test system as shown in Table 11. The total cost of RCDED with heat

loaddemandsinthepreviouscasestudyishigherthanthetotalcost

Table 7

Best electricity power dispatch found by SALCSSA for case III without losses (first test system).

HourLoad

PTU

1;t(MW)

150.0146

150.0000

226.8191

303.3769

379.4615

456.4160

456.6620

457.1691

456.5828

456.3768

456.4900

464.1493

456.4964

456.5248

380.0211

303.3134

226.6511

303.0727

379.9923

456.7139

456.2082

379.6059

302.7469

227.1612

PTU

2;t(MW)

135.0000

135.0000

215.0000

222.4307

302.4307

309.6805

389.6805

396.8375

396.9396

460.0000

460.0000

460.0000

396.8000

396.8335

396.3981

316.3981

309.6501

389.6501

396.8494

460.0000

396.8605

389.8111

309.8111

229.8267

PTU

3;t(MW)

202.2253

282.2186

297.6844

301.9303

290.0734

297.0540

297.2707

296.2320

307.3350

332.8533

339.9241

340.0000

332.8418

297.5478

297.0155

297.4554

297.2376

297.4398

297.8134

340.0000

340.0000

279.6125

199.6125

185.2120

PTU

4;t(MW)

60.0000

60.0000

60.0000

60.0128

60.0000

60.0664

110.0664

151.5608

191.1874

241.1874

291.1874

300.0000

300.0000

250.0229

238.7797

188.7797

180.8294

179.7331

180.9971

230.9648

180.9764

130.9764

80.9764

60.0000

PCHP

1;t

121.3434

115.5604

91.3910

151.1265

81.1265

137.3287

81.0000

107.1835

167.2442

146.9096

161.5835

219.1995

149.2223

153.9837

97.1005

81.0000

98.0572

91.4778

153.2223

149.7313

145.4204

81.0243

81.0000

114.8943

(MW)

PTU

5;t(MW)

122.8239

122.4854

122.4634

122.4537

122.3120

122.8522

122.7149

122.0043

160.0000

160.0000

159.9559

160.0000

160.0000

122.4349

122.4576

122.4788

122.8942

122.1409

122.5115

160.0000

160.0000

122.3517

113.2641

122.3153

PTU

6;t(MW)

129.5923

129.7341

129.6421

129.6691

129.5960

129.5900

129.6055

129.7192

129.7026

129.6729

129.7106

129.5932

129.5891

129.5912

129.2274

129.5744

129.6805

129.4857

129.6134

129.5894

129.4797

129.6180

129.5889

129.5795

PCHP

2;t

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

(MW)

PTU

7;t(MW)

20.0006

20.0016

20.0000

20.0000

20.0000

20.0122

20.0000

20.2935

20.0085

50.0000

52.1484

52.0580

52.0503

22.0613

20.0000

20.0000

20.0000

20.0000

20.0006

50.0006

20.0548

20.0000

20.0000

20.0109

PTU

8;t(MW)

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

Dt(MW)

73.4410

72.6826

71.5412

70.2809

69.7373

68.5100

67.8778

66.6450

57.5974

36.8738

29.1927

12.7575

41.9691

66.0421

67.6393

69.1423

69.6528

68.6143

67.2533

29.7634

44.4870

68.4820

70.978

72.2205

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

1036

1110

1258

1406

1480

1628

1702

1776

1924

2072

2146

2220

2072

1924

1776

1554

1480

1628

1776

2072

1924

1628

1332

1184

Table 8

Best hest dispatch found by SALCSSA for case III without losses (first test system).

HourHeat load (MWth)

HCHP

1;t

127.3404

123.7369

110.3319

143.9638

104.8625

136.3579

104.8000

118.4824

152.9939

141.7409

149.9740

156.3629

143.0787

145.7350

112.5391

104.8000

114.3244

110.6730

145.2789

142.9997

139.7594

104.7779

104.8000

123.7946

(MWth)

HCHP

2;t

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

(MWth)

HH

1;t(MWth)

198.6596

208.2631

231.6681

212.0362

258.1375

238.6421

275.2000

268.5176

244.0061

257.2591

253.0260

251.6371

255.9213

249.2650

274.4609

263.2000

248.6756

264.3270

241.7211

256.0003

253.2406

269.2221

250.2000

215.2054

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

401

407

417

431

438

450

455

462

472

474

478

483

474

470

462

443

438

450

462

474

468

449

430

414

Table 4

Results obtained by different methods for case I (30-unit).

Solution

technique

Total cost ($)Scaled CPU

time (min)

Best valueMean valueWorst value

IPSO [17]

CSAPSO [20]

ICPSO [19]

CSSA

3,090,570

3,066,907

3,064,497

3,068,556

3,071,588

3,075,023

3,071,588

3,074,784

NA

NA

NA

3,084,861

0.142

NA

0.773

0.198

SALCSSA 3,048,972 3,050,7693,051,6220.276

NA: Not available in the literature. The bold values represent the minimum values of

objective functions obtained by the proposed algorithm.

Table 5

Results obtained by different methods for case I (150-unit).

Solution

technique

Total cost ($)Scaled CPU

time (min)

Best valueMean value Worst value

CSSA

SALCSSA

15,287,904

15,256,663

15,291,148

15,257,981

15,296,169

15,260,231

1.380

2.125

NA: Not available in the literature. The bold values represent the minimum values of

objective functions obtained by the proposed algorithm.

Table 6

Results obtained by different methods for case III (first test system).

Solution

technique

Total cost ($)Average CPU

time (min)

Best valueMean value Worst value

Without losses

CSSA

SALCSSA

1,228,766

1,225,447

1,229,430

1,225,913

1,229,979

1,226,604

0.219

0.256

With losses

CSSA

SALCSSA

1,256,142

1,252,462

1,257,281

1,253,032

1,258,061

1,253,883

0.296

0.371

The bold values represent the minimum values of objective functions obtained by

the proposed algorithm.

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

329

Page 11

of RCCHPDED ($3,738,264 opposed to $3,684,107) and ($18,703,123

apposed to $18,422,610) for the aforementioned reason of using

CHP units for second and third test system, respectively.

5.2. Population size efficiency of SALCSSA e.g. in case study 1 for

10-unit test system

The optimum population size of each algorithm is related to the

search space dimension and complexity of the problem. Too large

or very small populations may not be able to reach the optimal

solution, especially in non-convex complex multidimensional

problems. In this study, different population sizes are selected and

the RCDED problem is carried out in 30 independent runs

neglecting losses to evaluate the effect of each population size on

the performance of SALCSSA. The statistical information of the total

cost as well as the average CPU time and frequency of convergence

for 25, 50, 100 and 150 population sizes are shown in Table 12. A

population size of 50 resulted in less CPU execution time.

5.3. Comparison study in case study 1 for 10-unit test system

5.3.1. Solution quality

The convergence characteristics of CSSA and SALCSSA are com-

pared in Table 3 by calculating the statistical information of the so-

lutions in 30 independent runs. It should be stressed that the worst

valueofthetotalcostobtainedbytheproposedmethodisbetterthan

the best solutions of all other methods in two scenarios. By compar-

ison of the best values in this table, the effectiveness of the proposed

method is clearly specified. Also, comparing the mean values dem-

onstratestheSALCSSA’sbetterconvergencecharacteristics.Table13is

provided to compare the computational cost of the proposed

approach and other recent methods such as ICPSO [19], CSAPSO [20]

and HQPSO [26]. This table shows that the proposed method reaches

to a lower total cost than the ICPSO ($1,016,797 opposed to

$1,019,072)[19], CSAPSO($1,016,797 opposed to $1,018,767)[20]and

($1,016,797 apposed to $1,031,559) [26] in less number of iterations,

population size, power mismatch and computational effort.

5.3.2. Computational efficiency

Computational burden of each optimization method is a critical

factor for its applicability to real-time and real-size systems. The

Average CPUtime is highly dependentonthecomputer system used

Table 9

Best electricity power dispatch found by SALCSSA for case III with losses (first test system).

HourLoad

PTU

1;t(MW)

150.2159

230.1240

302.3702

382.3702

381.8825

376.6634

454.5445

458.8557

457.5538

458.6825

470.0000

470.0000

456.8795

461.4903

381.4903

301.4903

224.3733

304.3733

376.8072

456.8072

456.1022

383.4385

381.7947

301.7947

PTU

2;t(MW)

135.0101

135.0000

135.0000

215.0000

221.4975

301.4975

309.3419

389.3419

397.9894

460.0000

460.0000

460.0000

396.9273

396.3539

393.1218

313.1218

310.4489

388.0404

458.4681

460.0000

383.2863

309.8913

229.8979

220.7384

PTU

3;t(MW)

186.9512

199.6969

277.8755

320.5508

288.7401

297.4439

310.2957

299.1485

299.3375

296.2912

340.0000

340.0000

339.9999

300.1891

311.8332

293.4889

289.9599

295.2662

319.9151

340.0000

320.1283

298.6239

223.8443

180.6968

PTU

4;t(MW)

60.0888

60.4424

60.0000

60.0000

110.0000

124.9736

134.7851

184.7851

234.7851

284.7851

300.0000

300.0000

300.0000

300.0000

250.0000

204.6502

181.3402

180.1987

180.0394

230.0394

233.8726

183.8726

136.0187

115.9471

PCHP

1;t

143.2162

125.2561

125.1491

86.7938

128.4478

153.2227

124.3162

120.5205

177.0597

195.2529

171.1017

216.3632

194.4893

141.7551

109.7806

100.4493

131.5572

102.1167

81.0000

151.0000

164.8877

132.5951

81.0000

81.5798

(MW)

PTU

5;t(MW)

127.9244

127.9901

129.4330

117.8186

129.4834

160.0000

160.0000

120.5139

160.0000

160.0000

160.0000

160.0000

159.3334

124.9065

124.7028

124.7884

125.9830

146.6041

159.6145

160.0000

134.6914

104.5273

57.0000

57.0000

PTU

6;t(MW)

130.0000

130.0000

130.0000

130.0000

130.0000

130.0000

130.0000

130.0000

129.5853

129.9404

130.0000

130.0000

129.7589

129.0591

130.0000

130.0000

128.7408

129.6626

129.9993

130.0000

130.0000

129.2739

130.0000

129.5793

PCHP

2;t

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

(MW)

PTU

7;t(MW)

20.0754

20.1239

20.5447

22.3786

20.3386

21.9503

20.0113

20.0177

20.4126

49.7017

79.7017

80.0000

52.1160

22.1187

20.0000

20.0000

20.0375

22.2882

20.0000

50.0000

52.7500

22.7500

20.1603

20.0000

PTU

8;t(MW)

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

55

PLoss(MW)

12.4820

13.6334

17.3725

23.9120

25.3899

32.7514

36.2947

42.1833

47.7234

57.6538

59.8034

31.3632

52.5043

46.8727

39.9287

28.9889

27.4408

35.5502

44.8436

0.8466

46.7185

31.9726

22.7159

18.3361

Dt(MW)

73.0333

72.4167

71.1833

69.9500

69.3333

59.7666

59.1500

64.6776

56.8276

40.7771

2.4150

1.5000

35.0950

53.4173

66.8667

68.7167

70.5925

68.4374

47.1181

29.2595

65.6333

68.8261

70.5667

72.2207

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

1036

1110

1258

1406

1480

1628

1702

1776

1924

2072

2146

2220

2072

1924

1776

1554

1480

1628

1776

2072

1924

1628

1332

1184

Table 10

Best hest dispatch found by SALCSSA for case III with losses (first test system).

Hour Heat load (MWth)

HCHP

1;t

118.2766

128.8679

122.2863

104.8000

126.1792

138.9248

127.4483

126.2187

147.8915

159.1461

154.9720

33.4589

162.2306

137.4720

119.4252

113.2934

130.7072

116.5573

104.8000

143.7558

148.9915

129.2464

104.8000

104.7999

(MWth)

HCHP

2;t

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

75

(MWth)

HH

1;t(MWth)

207.7234

203.1321

219.7137

251.2000

236.8208

236.0752

252.5517

260.7813

249.1085

239.8539

248.0280

374.5411

236.7694

257.5280

267.5748

254.7066

232.2928

258.4427

282.2000

255.2442

244.0085

244.7536

250.2000

234.2001

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

401

407

417

431

438

450

455

462

472

474

478

483

474

470

462

443

438

450

462

474

468

449

430

414

Table 11

Results obtained by different methods for case III (second and third test systems).

Solution

technique

Total cost ($)Average CPU

time (min)

Best value Mean valueWorst value

Second test system

CSSA

SALCSSA

3,705,962

3,684,107

3,712,180

3,689,544

3,724,378

3,697,196

0.711

0.853

Third test system

CSSA

SALCSSA

18,495,931

18,422,610

18,541,129

18,432,783

18,592,183

18,451,167

2.414

3.729

The bold values represent the minimum values of objective functions obtained by

the proposed algorithm.

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

330

Page 12

in implementing other methods and therefore, cannot be directly

compared for different techniques. Hence, the scaled CPU time is

calculated by the per-unit CPU speed multiplied by the given Aver-

age CPU time for each of the referred solution techniques [13]. The

per-unit base speed is 2.4 GHz and the scaled CPU time is as follows:

scaled CPU time ¼given CPU speed

2:4 GHz

? given average CPU time

(44)

Table 3 shows less scaled CPU time for the proposed SALCSSA

than the other methods except for IPSO [17]. In other words, the

new proposed algorithm is capable of providing a better solution

with less execution time as well as handling all of the constraints of

the problem, which suggests that the SALCSSA may be appropriate

and favorable for real-time and real-size applications without any

restriction.

5.3.3. Robustness

The performance of meta-heuristic search based optimization

algorithms is judged based on many trials with different initial

populations to study the robustness of SALCSSA. It can be seen from

Tables 3e6 and 11e13 that SALCSSA method produces the lowest

cost most consistently. It is clear that the worst, mean and best

solutions of the SALCSSAare veryclose to each otherconfirming the

robustness of the proposed method.

5.3.4. Performance of inclusion SRRs constraint

Inclusion of SRRs constraint increases complexity and average

CPU time. In this paper, the SRRs constraint incorporating the ramp

rate limits are handled simultaneous without any restriction on the

objective function. Although the ICPSO [19], CSAPSO [20] and

HQPSO [26] do not model this constraint, the result obtained by the

SALCSSA is superior according to Table 13.

6. Conclusion

In this paper, a new optimization algorithm called SALCSSA for

solvingcomplex, non-convex,non-smooth andnon-linear

RCCHPDED was presented for the first time. Moreover, in order to

simultaneously handle the SRRs, electricity power and heat bal-

ance, transmission losses, mutual dependency of electricity power-

heat and ramping rate constraints, a constraints handling are

embedded into the recommended framework. The results showed

that the proposed modification technique improved the perfor-

mance of the original CSSA greatly. Moreover, the proposed SAL-

CSSA were compared with the other algorithm in this area and

found to be superior. The proposed framework has the following

advantages:

? A precise modeling of the joint characteristics of electricity

power-heat and power ramp constraints for CHP units is

important to schedule these units and their generation costs.

This leads to a more efficient utilization of CHP units and per-

mits the system operator to more efficiently use these units in

schedule programming.

? The total operation costs of the systems can be significantly

reduced due to implementation of CHP units.

? The proposed framework is efficient for solving non-convex,

non-smooth, non-linear, high dimension, and high constraint

optimization problem.

However, the CSSA suffers from the problem of being trapped in

local optima. This shortcomings call for the SALM, adaptive selec-

tion operation and repelling forcemodeling suggestedin this paper.

It is evident from the simulations and comparisons that the pro-

posed approach has a better performance in terms of optimal dis-

patching, speed of convergence, consistency and computational

cost. Consequently, the proposed approach can be a good candidate

for real-time and real-size applications.

Furthermore, it should be noted that the research work is under

way in order to incorporate uncertainty of the heat and load de-

mands using stochastic RCCHPDED problem as well as considering

emission objective function.

Appendix

The electricity power-heat FORs of the CHP units are illustrated

in Figs. 3 and 4.

The CHP and Heat-only units data is listed in Tables 14 and 15,

respectively. Also, the typical heat load demand for 24 h is shown in

Table 16.

Electricity power

(MW)

Heat (MWth)

A

B

C

D

247

215

98.8

81

104.8

180

Fig. 3. Electricity power-heat feasible operating region (FOR) for CHP unit 1.

Table 12

Effect of population size on SALCSSA for case I (10-unit without losses).

Population

size

No. of this to

($1,017,400e

$1,016,900)

Total fuel cost ($)Average

CPU time

(min)

Best valueMean valueWorst value

25

50

100

150

18

30

30

30

1,017,214

1,016,797

1,016,797

1,016,797

1,017,398

1,017,011

1,016,986

1,016,951

1,017,711

1,017,205

1,017,165

1,017,128

0.080

0.139

0.381

0.429

The bold values represent the minimum values of objective functions obtained by

the proposed algorithm.

Table 13

Performance comparison of ICPSO, CSAPSO, HQPSO and SALCSSA for case I (10-unit

without losses).

MethodBest

solution ($)

Population

size

Maximum

iteration

Power

mismatch

(MW)

SRRScaled CPU

time (min)

ICPSO [19] 1,019,0721001200 0.00178Not

model

Not

model

Not

model

Model 0.139

0.350

CSAPSO [20] 1,018,76710012000.001000.350

HQPSO [26] 1,031,55950150 0.500000.773

SALCSSA1,016,79750 1500.00000

The bold values represent the minimum values of objective functions obtained by

the proposed algorithm.

B. Bahmani-Firouzi et al. / Energy 52 (2013) 320e332

331

Page 13

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135.6

Electricity power

(MW)

Heat (MWth)

A

B

C

D

E

F

75 32.4

15.9

40

44

110.2

125.8

Fig. 4. Electricity power-heat feasible operating region (FOR) for CHP unit 2.

Table 14

Data of the two incorporated CHP units [7,30].

CHP units

abzglf

DRUR

1

2

2650

1250

14.5

36

0.0345

0.0435

4.2

0.6

0.03

0.027

0.031

0.011

70

50

70

50

Table 15

Data of the one incorporated heat-only units [30].

smr

9502.01090.038

Table 16

Typical heat load demand data.

Hour12345678910 1112

Heat load

(MWth)

401407 417431438450455 462472474478 483

Hour 1314 1516 1718 192021 2223 24

Heat load

(MWth)

474 470462 443 438450462 474468449430414

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