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Improvement of the Fitness-Distance Balance-Based Supply–Demand Optimization Algorithm for Solving the Combined Heat and Power Economic Dispatch Problem

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Abstract

The CHPED scheduling problem involving a limited feasible operation region is considered to be one of the most basic nonlinear planning and operation problems in modern power systems. In this study, the aim was to minimize the total fuel cost of the system by simultaneously modeling the cost of the cogeneration units, and the fossil fuel thermal generation units. The study presents a chaotic map-based supply–demand optimization (SDO) algorithm including the fitness-distance balance (FDB) selection method (CFDBSDO) to solve the CHPED problem. In the FDB supply–demand optimization, chaotic maps are used to increase the convergence performance of the algorithm to the global solution and to find the global solution in the solution search space. The proposed CFDBSDO algorithm was used in two experimental studies. In the first, the performance of ten different chaotic map-based FDBSDO variants was investigated for solving the CEC benchmark functions. The second experimental study demonstrated the performance and effectiveness of CFDBSDO algorithm in optimizing the objective function of the CHPED problem in four different test systems. According to the results from both experimental studies, by using the proposed approach, the exploration, exploitation, and balanced search capability of the algorithm was further improved compared to other algorithms.

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Abbreviations

CHPED:

Combined heat and power economic dispatch

SDO:

Supply–demand optimization

FDB:

Fitness-distance balance

CFDBSDO:

Chaotic fitness-distance balance-based supply–demand optimization

FDBSDO:

Fitness-distance balance-based supply–demand optimization

CEC:

Congress on evolutionary computation

CHP:

Combined heat and power

MHAs:

Metaheuristic approaches

HS:

Probability density function

IACSA:

Improved ant colony search algorithm

SARGA:

Self-adaptive real-coded genetic algorithm

BCO:

Bee colony optimization

AIS:

Artificial immune system

TVAC-PSO:

Novel time varying acceleration coefficients particle swarm optimization

IGSO:

Improved group search optimization

OGSO:

Opposition-based group search optimization

EMA:

Exchange market algorithm

GWO:

Grey wolf optimization

TVAC-GSA-PSO:

Hybrid gravitational search algorithm-particle swarm optimization with time varying acceleration coefficients

MHS:

Meta-heuristic search

FA:

Firefly algorithm

GSA:

Gravitational search algorithm

CPSO:

Classic particle swarm optimization

IGA-NCM:

Improved genetic algorithm using novel crossover and mutation

MGSO:

Modified group search optimizer

IWO:

Invasive weed optimization algorithm

MRFOA:

Manta ray foraging optimization algorithm

WVO:

Weighted vertices-based optimizer

WVO-PSO:

Weighted vertices-based optimizer and particle swarm optimization algorithm

BLPSO:

Biogeography-based learning particle swarm optimization

EP:

Evolutionary programming

DE:

Differential evolution

AIS:

Artificial immune system

CSO-PPS:

Civilized swarm optimization and powell’s pattern search

LCA:

Line-up competition algorithm

BCO:

Bee colony optimization

TLBO:

Teaching learning-based optimization

OTLBO:

Oppositional teaching learning-based optimization

HTS:

Heat transfer search

GSO:

Group search optimization

CSO:

Crisscross optimization

GWO:

Grey wolf optimization

RCGA-IMM:

Real coded genetic algorithm with improved Mühlenbein mutation

WOA:

Whale optimization algorithm

CSA:

Cuckoo search algorithm

TFC:

The total fuel cost of the system

cost t,i :

The fuel cost of the i-th traditional power generation unit

cost c,j :

The j-th CHP unit

cost h,k :

The k-th heat generation unit

Nt :

The number of traditional thermal generation units

Nc :

The number of CHP generation units

Nh :

The number of heat generation units

P i t :

The output power of the i-th thermal generation unit

P j c, H j c :

The active power and heat outputs of the j-th CHP generation unit

H k h :

The heat output of the k-th heat generation unit

a i, b i, c i, d i, and e i :

The cost coefficients of the i-th thermal generation unit

a j, b j, c j, d j, e j, and f j :

The cost coefficients of the j-th CHP generation unit

a k, b k, and c k :

The cost coefficients of the k-th heat generation unit

P dm :

The active power demand

P ls :

The active power losses of the test system

B ij, B 0i, and B 00 :

The coefficients of the B-loss matrix

H dm :

The total heat demand value of the test system

P i t,min, P i t,max :

The limit values of the i-th thermal generation unit

P j c,min ( H j c ), P j c,max ( H j c ) :

The lower and upper limits of the j-th CHP generation unit and are related to the Hjc value

H j c,min ( P j c ), H j c,max ( P j c ) :

The limit values of the j-th CHP generation unit and are related to the Pjc value

H k h,min, H k h,max :

Limit values of the k-th heat generation unit

Fitx :

The price of a commodity representing the value of the fitness function in the search space

Fity :

The quantity of a commodity representing the value of the fitness function in the search space

x 0 :

The equilibrium cost

y 0 :

The equilibrium quantity

Qt, Cst :

The coefficients to be used for the roulette wheel selection method

Ni :

Calculated value based on the quantity of a commodity to determine the Qt coefficient

Mi :

Calculated value based on the price of a commodity to determine the Cst coefficient

x i (t), y i (t) :

The i-th commodity cost and commodity quantity at the iteration t

α, β :

The supply and demand weight coefficients

T :

The number of maximum iterations

r :

The random number or random vector between [0,1]

p best :

The best solution candidate

P :

The vector of solution candidates

F :

The fitness value vector of these candidates

p i :

The Euclidean distance of the i-th solution candidate

D p :

The distance vector

S P :

The FDB values of the solution candidates

normF :

The normalized fitness values

normD p :

The normalized distance values

w :

The weight coefficient

x fdb :

The parameter used instead of y0

y fdb :

The parameter used instead of y0

Ch i norm :

The normalized chaotic map value at the kth iteration for all chaotic maps

C i :

The chaotic map

[a, b]:

The limits of the chaotic maps

Vk :

The value calculated by normalizing the effect of the chaotic map according to the determined limits

[Max, Min]:

The limit values of the chaotic effect

C fc :

The coefficient calculated according to the normalized chaotic maps

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Authors and Affiliations

  1. Electrical Engineering, Engineering and Natural Sciences Faculty, Bandirma Onyedi Eylul University, Bandirma, 10200, Turkey

    Serhat Duman, Harun Ozbay, Emre Celik, Serhat Berat Efe & Evren Isen

  2. Turkish Aerospace, 06980, Ankara, Turkey

    Berk Duman

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  1. Serhat Duman
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  2. Harun Ozbay
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Correspondence to Serhat Duman.

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Duman, S., Ozbay, H., Celik, E. et al. Improvement of the Fitness-Distance Balance-Based Supply–Demand Optimization Algorithm for Solving the Combined Heat and Power Economic Dispatch Problem. Iran J Sci Technol Trans Electr Eng 47, 513–548 (2023). https://doi.org/10.1007/s40998-022-00560-y

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