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Combined heat and power economic dispatch by improved ant colony search algorithm
Abstract
The difficulty of solving combined heat and power (CHP) economic dispatch lies in the constraints imposed by the multi-objectives. The mutual dependencies of heat–power capacity make it hard to find a feasible region, not to mention the optimum. This paper presents a novel ant colony search algorithm (ACSA) approach for this problem. The main characteristics of the ACSA are positive feedback, distributed computation and the use of a constructive greedy heuristic. Positive feedback accounts for the rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps to find acceptable solutions in the early stages of the search process. However, despite the attraction of the ACSA’s potential search ability, there are still some difficulties, such as the handling of constraints and premature convergence. This paper proposes to couple the ACSA with other search techniques to improve its performance. The numerical results reported are encouraging.
... Also, the derivative based approaches are ineffective to solve the non-convex problems with complex search space and computationally expensive cost functions. To overcome the deficiencies of derivative -based approaches, many derivative -free methods namely Evolutionary Algorithms (EA) and Swarm Algorithms (SA) collectively known as Meta-heuristics Algorithms (MAs) [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] have been unveiled to deal with the challenges, which are linked with computationally expensive CHPED problem. MAs [1,[5][6][7][8][9][10][11] did not consider the transmission loss and valve-point effect while solving the CHPED problem whereas the valve-point effect and transmission losses are included in CHPED problem formulation [12][13][14][15][16]. ...
... To overcome the deficiencies of derivative -based approaches, many derivative -free methods namely Evolutionary Algorithms (EA) and Swarm Algorithms (SA) collectively known as Meta-heuristics Algorithms (MAs) [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] have been unveiled to deal with the challenges, which are linked with computationally expensive CHPED problem. MAs [1,[5][6][7][8][9][10][11] did not consider the transmission loss and valve-point effect while solving the CHPED problem whereas the valve-point effect and transmission losses are included in CHPED problem formulation [12][13][14][15][16]. In the Refs. ...
... Step2: Evaluation of Population: Find the current best solution by evaluating the fitness score of each individual from the generated population, taking inverse of its objective function values that can be calculated with Eq. (1), if the individuals are satisfied with all the constraints of the CHPED problem as given in Eqs. (2)- (8). Else objective function of each individual is calculated using adaptive penalty function method as follows: ...
... In recent years, extensive work has been conducted on the coordinated optimization of integrated electric-heat system, the emergence of intelligent algorithms has solved this problem. For example, particle swarm algorithm [11][12][13], genetic algorithm [14], ant colony search algorithm [15], harmonic search algorithm [16] and group search optimizer [17,18] all can be used to solve the coordination and optimization of integrated electric-heat system. However, the common defects of intelligent algorithms are that the computation time is long and it is difficult to use them in real-time applications. ...
... The flow time of hot water in the pipe section of the heating network with length ∆ is shown as follows. (15) where is the density of the fluid, kg/m 3 , ∆ is the length of the pipe section, m , is the inner diameter of the pipe section, m, , is the fluid flow rate inside the pipe section at , kg/h . , , , ...
... Total objective function: (15 ) ...
There are the transmission loss of the electric power network, the delay and loss of the heating network, the insufficient utilization of flexible resources such as energy storage in the integrated electric-heat system, which may lead to the imbalance of supply and demand and energy waste. In this paper, the coordinated dispatch of integrated electric-heat system (IEHS) considering the transmission characteristics of the electric power network and heating network, which is formulated as a convex quadratic program. The strong linkage of electric power and heat supplies can be decoupled to reduce wind power curtailment by exploiting the energy storage and regulation capabilities of the district heating network (DHN), storage batteries, electric boilers (EBs) and heat storage tanks (HSs). The energy storage system works according to the situation division strategy designed in this paper. This paper introduces the wind curtailment boundary power and optimizes dispatch based on the wind curtailment boundary power and unit output, which can make full use of the energy storage capacity and reduce the wind abandonment power. Since the electric power system (EPS) and the distribution heating system (DHS) are controlled separately by different operation organizations, IEHS is solved using double- λ iterative algorithm. The double- λ iterative algorithm, with guaranteed convergence for convex programs, can achieve a fully distributed solution for the IEHS and requires only a small amount boundary information exchange between the EPS and the DHS. At last, one integrated electric-heat system was studied to demonstrate the effectiveness of the proposed method which achieves the effective solution in a moderate number of iterations. This system includes two 10-nodes heating system and one 14-nodes electric power system
... The vast majority of methods focused on metaheuristic optimization approaches, with seemingly endless creativity in using naturally observable phenomena as justification for the merit of new solution approaches. The well-established metaheuristic methods were thoroughly applied to the problem in the years prior to 2010, such as ant colony search [17], the genetic algorithm [18][19][20], and particle swarm optimization [21,22]. In the years since these pioneering works, the imaginativeness of researchers has continued to flourish. ...
... In the early CHP-ED literature the cost functions of all generating units were represented as quadratic functions of heat and/or power [14,[16][17][18][19][20]67]: However, it has long been well-known that the valve-point effects on the cost functions of steam power generators cannot be sufficiently described by smooth quadratic functions. The cost function of the power-only units is obtained by collecting operating data as the generator is varied across its operating region. ...
... The feasible operating region of a set of typical cogeneration units are shown in Figure 2. It can be seen that the feasible operating region of cogeneration units is a potential source of model nonconvexity [17]. ...
Combined heat and power (CHP) systems are attracting increasing attention for their ability to improve the economics and sustainability of the electricity system. Determining how to best operate these systems is difficult because they can consist of many generating units whose operation is governed by complex nonlinear physics. Mathematical programming is a useful tool to support the operation of CHP systems, and has been the subject of substantial research attention since the early 1990s. This paper critically reviews the modeling and optimization work that has been done on the CHP economic dispatch problem, and the CHP economic and emission dispatch problem. A summary of the common models used for these problems is provided, along with comments on future modeling work that would beneficial to the field. The majority of optimization approaches studied for CHP system operation are metaheuristic algorithms. A discussion of the limitations and benefits of metaheuristic algorithms is given. Finally, a case study optimizing five classic CHP system test instances demonstrates the advantages of the using deterministic global search algorithms over metaheuristic search algorithms.
... Also, the derivative based approaches are ineffective to solve the non-convex problems with complex search space and computationally expensive cost functions. To overcome the deficiencies of derivative -based approaches, many derivative -free methods namely Evolutionary Algorithms (EA) and Swarm Algorithms (SA) collectively known as Meta-heuristics Algorithms (MAs) [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] have been unveiled to deal with the challenges, which are linked with computationally expensive CHPED problem. MAs [1,[5][6][7][8][9][10][11] did not consider the transmission loss and valve-point effect while solving the CHPED problem whereas the valve-point effect and transmission losses are included in CHPED problem formulation [12][13][14][15][16]. ...
... To overcome the deficiencies of derivative -based approaches, many derivative -free methods namely Evolutionary Algorithms (EA) and Swarm Algorithms (SA) collectively known as Meta-heuristics Algorithms (MAs) [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] have been unveiled to deal with the challenges, which are linked with computationally expensive CHPED problem. MAs [1,[5][6][7][8][9][10][11] did not consider the transmission loss and valve-point effect while solving the CHPED problem whereas the valve-point effect and transmission losses are included in CHPED problem formulation [12][13][14][15][16]. In the Refs. ...
... Step2: Evaluation of Population: Find the current best solution by evaluating the fitness score of each individual from the generated population, taking inverse of its objective function values that can be calculated with Eq. (1), if the individuals are satisfied with all the constraints of the CHPED problem as given in Eqs. (2)- (8). Else objective function of each individual is calculated using adaptive penalty function method as follows: ...
... ED allocates the demand of load among the list of dedicated power generators most economically while fulfilling the functional and the physical constraints in one area. The primary objective of ED [3][4][5][6][7][8][9][10][11][12][13][14][15][16] is always to minimize the cost of entire generation such that the necessity and restrictions are satisfied, that is, we need to optimally create the concept of power generation. Fig. 1 shows the Economic dispatch problem used in solving the problem based on the reparability of the objective function of the problem. ...
... In this system The lower level was used to solve the ELD problems of different units for given heat and power Lambda's, and the upper level helps in updating the lambda's using the coefficients of sensitivity. Diverse challenges occurred in ED [4][5] [17] including multi-area economic load dispatch (MAED), method of economic dispatch with valve point (EDVP), cubic cost function economic dispatch (QCFED), and companied economics of environmental dispatch (CEED). A few researchers' offers to do research by resolving the problem of ED using numerous algorithm is like the Particle Swarm Optimization (PSO), Covariance Matrix Adapted Evolution Strategy (CMAES), Real-coded Genetic Algorithm (RCGA), and Differential Evolution (DE).This technique was repeated before power and heat demands are met. ...
... The technique continues to be tested and further compared to show the effective performance of the system. Y. H. Song, et.al [5] revealed a new ACSA i.e.ant colony search algorithm strategy because of this economic dispatch issue. The primary features of the ACSA include distributed computation, positive feedback, and the constructive greedy heuristic usage. ...
Conserving energy and efficient power systems are very important for us to reduce pollution levels and also reduces wasted fuel resources which are already depleting on the planet. In power operation system, the potential of energy conservation and also much less emission of greenhouse gas because of the wise usage of cleaner non-renewable fuels burned in combined heat and power (CHP) models like the natural gas which provide them benefit from the usual electric power systems. Mixed generator systems have been widely employed by the industry. The industry which requires both power and heat can supply the demands with cogeneration of heat-power systems. Cogeneration (CHP) systems could be constructed in cities and used in the form of distributed electricity sources. To get the optimal usage of CHP devices, economic load dispatch (ED) should be requested more for the process of energy conservation. Economic load dispatch plays a vital role and a large number of different approaches and methods have been used in solving such kind of problems. The methods like lambda-iteration and Gradient are used for finding out the optimized solution of nonlinear problem. The purpose of this thesis is to utilize the algorithmic optimization approaches like particle swarm optimization (PSO), genetic algorithm (GA) and PSO-GA. In this work, the method of PSO-GA Optimization is used to find out the minimized cost at four of the generating units of heat and power. The base of the work is already published where in the loss coefficients are also presented with max-min cost function and power limit. This work is implemented in the MATLAB simulation environment. The work starts by initializing the load/power and then generators load power flow. The generators are allocated to initialize the cost and this cost is optimized by PSO with GA. At the end the experimental results of GA ,PSO and PSO-GA algorithm is equated with each other and it seems better convergence is achieved by PSO-GA Algorithm.
... There are other SI-based algorithms to solve the CHPED optimization issue. For example, the ant colony search algorithm (ACSA), which imitates the real ants' behavior in finding the nearest food sources, was improved and used by Song et al. [83]. The other SI-based solvers for this issue, such as the difference brain storm optimization algorithm, the wild goats algorithm, and the modified bat algorithm were presented in [84][85][86], respectively. ...
... [81] 9257.10 NA Heat and power demands, Capacity limits ACSA [83] 9452.20 NA Heat and power demands, Capacity limits HSA [94] 9257.07 NA Heat and power demands, Capacity limits Based on Table 6 the different algorithms obtained a range of costs, from 8440.50 $ to 9452.20 $. ...
Combined heat and power (CHP) plants are known as efficient technologies to reduce environmental emissions, balance energy costs, and increase total energy efficiency. To obtain a more efficient system, various optimization methods have been employed, based on numerical, experimental, parametric, and algorithmic optimization routes. Due to the significance of algorithmic optimization, as a systematic method for optimizing energy systems, this novel review paper is focused on the meta-heuristic optimization algorithms, implemented in CHP energy systems. By considering the applied objective functions, the main sections are divided into single-objective and multi-objective algorithms. In each case, the units’ combination is briefly detailed, the objective functions are introduced, and analyses are conducted. The main aim of this paper is to gather a database for the optimization of CHPs, demonstrate the effect of the applied optimization methods on the objective functions, and finally, introduce the most efficient methods. The most significant feature of this paper is that it covers all types of CHP optimization issues including scheduling, sizing, and designing problems, finding the extent of each optimization issue in the relevant papers in the last decade. Based on the findings, in the single-objective problems the combined heat and power economic dispatch (CHPED) issue as a subcategory of the scheduling problems is introduced as the most paid topic; the designing issue is known as the lowest paid topic. In the multi-objective problems, working on various types of CHP optimization problems has been conducted with an almost similar share. The combined heat and power economic emission dispatch (CHPEED) problem with the most share, and the sizing issue with the lowest share. The CHP designing and sizing optimization issues could be introduced as topics to work on more in the future. Additionally, the numerical results of CHPED and CHPEED problems solved by various algorithms are presented and compared. In this regard, specified test systems are considered.
... For more details about the ACO algorithm the reader should refer to Dorigo, Maniezzo, and Colorni (1996). ACO handles discrete optimization problems well, but it presents some difficulties in continuous search spaces (Song, Chou and Stonham, 1999). ...
... BPO typically has both, which hinders, for example, the use of ACO. ACO does not cope well with continuous spaces, which forces the user to discretize continuous variables for a more efficient search, such as in Song et al. (1999). Second, several comparative studies show that GAs are consistently able to find near-optimum solutions to complex problems and do so faster than other metaheuristic methods, i.e., they require less cost function evaluations (Wetter and Wright, 2004;Tuhus-Dubrow and Krarti, 2010;Bichiou and Krarti, 2011). ...
The resources involved in the construction and operation of buildings represent nearly 40% of the global emissions of greenhouse gases (GHG), making the building sector one of the primary contributors to global warming. This reality has led to the creation of many prescriptive regulatory and voluntary programs that aim to mitigate the environmental impact of the building sector while ensuring high standards for Indoor Environmental Quality (IEQ), particularly those regarding the thermal and visual comfort of building occupants. Thus, the design of high-performance buildings, i.e., resource- and energy-efficient buildings that yield high levels of IEQ, is a pressing need. This scenario pushes architects to simulate their projects’ environmental performance to better support design tasks in a process referred to as performance-based design.
This dissertation studies the integration of daylighting and Building Energy Simulation (BES) tools into performance-based design supported by computational design (CD) methods, particularly parametric design and Building Performance Optimization (BPO). The assumption is that the early integration of parametric, BES, and daylighting simulation tools can be highly effective in the design, analysis, and optimization of high-performance buildings.
However, the research argues that the current daylighting and Building Energy Simulation (BES) tools pose critical challenges to that desirable integration, thus hindering the deployment of efficient exploratory design methods such as Parametric Design and Analysis (PDA) and BPO. These challenges arise from limitations regarding (i) tool interoperability, (ii) computationally expensive simulation processes, and (iii) problem and performance goal definition in BPO.
The primary objective of the dissertation is to improve the use of daylighting and BES tools in PDA and BPO. To that end, the research proposes and validates five modeling strategies that directly tackle the limitations mentioned above. The strategies are the following: (i) Strategy A: Automatically generate valid building geometry for BES; (ii) Strategy B: Automatically simplify building geometry for BES; (iii) Strategy C: Abstract Complex Fenestration Systems (CFS) for BES; (iv) Strategy D: Assess glare potential of indoor spaces using a time and spatial sampling technique; and (v) Strategy E: Painting with Light - a novel method for spatially specifying daylight goals in BPO.
The research work shows that the strategies address the research problem and current limitations by (i) improving the interoperability between design and BES and daylighting simulation tools (Strategies A, B, and C); (ii) producing quick and adequate feedback on the daylight, thermal, and energy behavior of buildings (Strategies B, C, and D); and (iii) facilitating the spatial definition of performance goals in daylighting BPO workflows (Strategy E). These three important merits of the proposed strategies effectively contribute to improving the efficiency of using daylight and BES tools in the design, analysis, and optimization of high-performance buildings.
Finally, the dissertation discusses the merits and limitations of each strategy, provides useful guidelines and recommendations for their use in building design, and suggests future directions for further research.
... Many existing researches have used quadratic or cubic functions like Eq. (2) as the cost function of a power-only unit [43]. However, for a particular power-only unit, the valve-point loading effect occurs when the steam admission valve opens. ...
... In initiation, for each z i , the decision variables associated with power-only units are stochastically generated by Eq. (41), the decision variables associated with CHP units are stochastically generated by Eq. (42) and Eq. (43), and the decision variables associated with heat-only units are stochastically generated by Eq. (44). ...
In power system operation, the combined heat and power economic dispatch (CHPED) is an attractive and momentous optimization problem where the major objective is to find an optimal generation schedule of heat and power to meet the heat and power demands with the minimum cost, while satisfying various practical operation constraints. This paper puts forward an adaptive cuckoo search with differential evolution mutation (ACS-DEM) for solving the CHPED problem. Compared with the basic cuckoo search (CS), there are three main improvements in the proposed ACS-DEM. The first improvement is that adaptive parameters are employed and therefore no parameter adjustment is required. The second is the incorporation of a Gaussian sampling strategy into the global search phase of the algorithm to increase the exploration capability. The third is the introduction of an improved differential evolution mutation strategy into the local search phase to replace the simple biased random walk in the basic CS, thus discouraging the blindness and enhancing the exploitation capability. The outstanding performance of ACS-DEM is first confirmed through the test suite from the 2017 Conference on Evolutionary Computation and then demonstrated on several CHPED problems. The obtained dispatch schedules from ACS-DEM are feasible and in most cases exhibit a distinct improvement over the results offered by six other CS-based algorithms, one state-of-the-art differential evolution algorithm, as well as recent works in this field.
... To deal with the problem of not being able to handle the complexities, researchers have now started using meta-heuristic methods and have found a rational solution. In earlier literature, some of the methods used were: Ant Colony Optimization (ACO) [6], Gravitational Search Algorithm (GSA) [7], Krill Herd Algorithm (KHA) [8], Particle Swarm Optimization (PSO) [9] and its variants such as Selective PSO [10], Time-Varying Acceleration Coefficients with WOA. Reference [25] suggested WOA focused on the Levy Flight Trajectory to solve the issue of global optimization. ...
... Figure 3 shows graphically the effect of valve-point loading. The fuel cost for the CHP plants is given by [6]: ...
This paper proposes an Exponentially Varying Whale Optimization Algorithm (EVWOA) to solve the single-objective non-convex Cogeneration Units problem. This problem seeks to evaluate the optimal output of the generator unit to minimize a CHP system’s fuel costs. The nonlinear and non-convex characteristics of the objective function demands a powerful optimization technique. The traditional Whale Optimization Algorithm (WOA) is improved by incorporating four different acceleration functions to fine-tune its performance during exploration and exploitation phases. Among the four variants of the proposed WOA, the emphasis is laid on the EVWOA which uses the exponentially varying acceleration function (EVAF). The proposed EVWOA is tested on six different small-scale to large-scale systems. The results obtained for these six test systems, followed by a statistical study highlight the supremacy of EVWOA for finding the best optimal solution and the convergence traits.
... i , i , and i are the cost coefficients of ith conventional thermal unit. The cost function of conventional thermal plants are modelled using quadratic function estimation (2) (Khorram and Jaberipour 2011;Song et al. 1999;Wang and Singh 2008;Esmaeeli et al. 2019). C j P c j , H c j is operation cost of CHP plant j, and a j , b j , c j , d j , e j and f j are the cost coefficients of such plant. ...
... Quadratic and cubic functions are used in most of the reported studies (Song et al. 1999;Su and Chiang 2004). However, the wire drawing effects cause a ripple in generation cost when steam admission valve begins to open. ...
Combined heat and power economic dispatch (CHPED) is an energy management problem that minimizes the operation cost of power and heat generation while a vast variety of operational constraints of the system should be met. The CHPED is a complicated, non-convex and non-linear problem. In this study, a new real-coded genetic algorithm with random walk-based mutation (RCGA-CRWM) is under study, which is effective in solving large-scale CHPED problem with minimum operation cost. In the presented optimization method, a simple approach is introduced to combine the positive features of different probabilistic distributions for the step size of random walk. Using the presented approach, while the genetic algorithm is speeded up, the premature convergence is also avoided. After verifying the performance of the presented method on the benchmark functions, two large-scale and two medium-scale case studies are used for determining the algorithm strength in solving the CHPED problem. Despite the fact that the complexity of the CHPED rises dramatically by increasing its dimensionality, the algorithm has solved the problems accurately. The application of RCGA-CRWM method improves the results of the CHPED problem in terms of both operation cost and convergence speed in comparison with other optimization methods.
... A genetic algorithm (GA) with penalty functions to handle the heat power dependency of CHP units is proposed in [6], improved GA in [7], and self-adaptive GA to solve this problem is proposed in [8]. The greedy heuristics of the ant colony algorithm is used in [9] to find the optimal solutions of the CHPED problem. A explicit formula is developed in [10] to find the direct solution of CHPED problem. ...
... The total fuel cost is represented by f 1 (x) in (2). The optimal solution obtained by solving the CHPED problem will minimize the total fuel production cost given by f 1 (x) and will also satisfy the power balance equality constraint h 1 (x) in (3), heat balance operating constraint in (4), feasible operating region (FOR) inequality constraints given by (5)- (8), and bounds of the thermal units given by (9), and heat only units given by (10). The total power demand in the system is Pd and total heat demand in the system is Hd. ...
Combined heat and power economic dispatch is an important optimization problem in a power system integrated with cogeneration units. In addition to the optimal solution satisfying the power balance equality constraint and the bounds of the thermal units, it must also lie within feasible operating region of the cogeneration units. This increases the complexity of the problem, and a potent meta-heuristic algorithm is required to solve the problem. This paper investigates the optimal solutions of the combined heat and power economic dispatch problem obtained by a recent meta-heuristic salp swarm algorithm. Transmission losses of the power system and valve point loading have been taken into consideration in this work. The algorithm is tested on standard test system available in literature. The results indicate there is scope for improvement of the salp swarm algorithm to solve combined heat and power economic dispatch problem.
... In reality, these FORs are non-convex [6][7][8][9][10][11]. However, in some studies, they have been approximated by convex ones with the aim of simplicity [12,13]. ...
... It is worth mentioning that an analogy made in [23] between HSA and Lagrangian Relaxation (LR) method demonstrated the effectiveness of the HSA in large-scale networks. [9] showed that the Ant Colony Search Algorithm (ACSA) itself has some difficulties in terms of CHPS constraints handling and convergence, and therefore attempted to bridge the gap with the help of Tuba Search (TS) and GA incorporated into the ACSA. To reduce the computational burden of the CHPS problem, the authors in [24] utilized the Bee Colony Optimization Algorithm (BCOA) while its performance was validated by comparing the obtained results with those of Real Coded Genetic Algorithm (RCGA) and PSO. ...
... Hayvanların arama davranışına dayanan bir başka sezgisel optimizasyon yöntemi olan grup arama optimizasyonu Birleşik ısı ve güç ekonomik dağıtımına uygulanmıştır (Basu 2016). Ayrıca arı kolonisi optimizasyon, karınca kolonisi arama ve harmoni arama algoritması gibi bir çok algoritma Birleşik ısı ve güç ekonomik dağıtımına uygulanmıştır (Basu 2011;Song, Chou, ve Stonham 1999;Vasebi, Fesanghary, ve Bathaee 2007). ...
Enerji kaynaklarının artan maliyeti ve çevre sorunları nedeniyle birleşik ısı ve güç birimleri gibi daha yüksek verimlilikte çalışan sistemler daha popüler hale gelmektedir. Birleşik ısı ve güç ünitelerinin doğrusal ve dışbükey olmayan özelliklere sahip olmaları nedeniyle optimum çalışması giderek karmaşıklaşmaktadır. Bahsi geçen bu problemin zorlukları bizi sezgisel ve evrimsel yöntemleri kullanmaya yöneltmektedir. Bu çalışmada, parçacık sürü optimizasyon (PSO) algoritması ve genetik algoritma (GA), birleşik ısı ve güç birimlerinin ekonomik dağıtımına(ED) uygulanmaktadır. ED probleminin temel amacı, toplam üretim maliyeti en aza indirilirken ve sistem operasyonel kısıtlamaları yerine getirilirken her bir ünitenin optimum çıkış gücü ve ısısını elde etmektir. Sonuçlar bu algoritmaların birleşik ısı ve güç sistemlerinin ekonomik dağıtımı problemini çözmedeki yeteneklerinin gösterilmesi ve karşılaştırılmasıdır.
... Throughout the development of intelligent optimization algorithms, the shortfalls of classical optimization strategies have been the starting point for the creation of new algorithms, such as the time-out of Newton's method in the face of complex mathematical processes, so people are paying attention to optimization algorithms inspired by nature. For examples, see the genetic algorithm (GA) [3], the differential evolution algorithm (DE) [4], the immune algorithm (IA) [5], the ant colony algorithm (ACO) [6], the particle swarm algorithm (PSO) [7], the simulated annealing algorithm (SA) [8], etc. In addition, due to the increase in the actual needs of the current society and the improvement of computer computing power, in order to improve the accuracy of the solution, more and more scholars are committed to developing new algorithms based on the existing algorithm solution strategies and extending them to many problems in multidisciplinary optimization. ...
In this article, an improved slime mould algorithm (SMA-CSA) is proposed for solving global optimization and the capacitated vehicle routing problem (CVRP). This improvement is based on the mixed-strategy optimization of Cauchy mutation and simulated annealing to alleviate the lack of global optimization capability of the SMA. By introducing the Cauchy mutation strategy, the optimal solution is perturbed to increase the probability of escaping from the local extreme value; in addition, the annealing strategy is introduced, and the Metropolis sampling criterion is used as the acceptance criterion to expand the global search space to enhance the exploration phase to achieve optimal solutions. The performance of the proposed SMA-CSA algorithm is evaluated using the CEC 2013 benchmark functions and the capacitated vehicle routing problem. In all experiments, SMA-CSA is compared with ten other state-of-the-art metaheuristics. The results are also analyzed by Friedman and the Wilcoxon rank-sum test. The experimental results and statistical tests demonstrate that the SMA-CSA algorithm is very competitive and often superior compared to the algorithms used in the experiments. The results of the proposed algorithm on the capacitated vehicle routing problem demonstrate its efficiency and discrete solving ability.
... In order to overcome these disadvantages of the classical techniques, currently, the use of artificial intelligence algorithms and MHAs has become increasingly common in solving this problem. According to a state-of-the-art literature review, many researchers have attempted to solve the CHPED problem by applying various optimization algorithms such as the HS algorithm (Vasebi et al. 2007), IACSA (Song et al. 1999), SARGA (Subbaraj et al. 2009 Their proposed algorithm focused on solving the problem with thermal generation units that included both the valve point effect and prohibited operating region constraints. The results obtained from the IGSO algorithm were compared to the results of other optimization algorithm presented in the literature and indicated that the IGSO algorithm was effective and applicable in solving this problem (Hagh et al. 2014). ...
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.
... Looking back on the development of algorithms, due to the shortcomings of some classical optimization methods, such as the time-out of Newton's method in the face of complex mathematical processes, researchers are paying increasing attention to optimization algorithms inspired by nature. These algorithms include the genetic algorithm (GA) [3], differential evolution algorithm (DE) [4], immune algorithm (IA) [5], ant colony algorithm (ACO) [6], particle swarm algorithm (PSO) [7] and simulation annealing algorithm (SA) [8]. However, since the accuracy of these algorithms in solving practical problems cannot meet the actual needs of the current society, an increasing number of scholars have focused on the improvement and application of population optimization algorithms inspired by natural biological populations. ...
In order to improve the global search performance of the Komodo Mlipir Algorithm, this paper proposed two adaptive Komodo Mlipir Algorithms with variable fixed parameters (IKMA-1; IKMA-2). Among them, IKMA-1 adaptively controls the parthenogenesis radius of female Komodo dragons to achieve more efficient conversion of global search and local search. Second, IKMA-2 introduces adaptive weighting factors to the “mlipir” movement formula of Komodo dragons to improve the local search performance. Both IKMA-1 and IKMA-2 were tested on 23 benchmark functions in CEC2013 and compared with the other seven optimization algorithms. The Wilcoxon rank-sum test and Friedman rank test were used to compare the performance of different algorithms. Furthermore, IKMA-1 and IKMA-2 are applied to two constrained engineering optimization problems to verify the engineering applicability of the improved algorithm. The results show that both IKMA-1 and IKMA-2 have better convergence accuracy than the initial KMA. In terms of the benchmark function simulation results, IKMA-1 improves the performance by 17.58% compared to KMA; IKMA-2 improves by 10.99%. Both IKMA-1 and IKMA-2 achieve better results than other algorithms for engineering optimization problems, and IKMA-2 outperforms IKMA-1.
... The considered formulations deal with the binary design variable for the location and consider the real representation for sizing of allocated capacitors. (Song et al., 1999) Combined heat and power economic dispatch ...
Optimization has been an active area of research for several decades. As many real-world optimization problems become increasingly complex, better optimization algorithms are always needed. Recently, meta-heuristic global optimization algorithms have become a popular choice for solving complex and intricate problems, which are otherwise difficult to solve by traditional methods. This chapter reviews the recent applications of ant colony optimization (ACO) algorithm in the field of electrical power systems. Also, the progress of the ACO algorithm and its recent developments are discussed. This chapter covers the aspects like (1) basics of ACO algorithm, (2) progress of ACO algorithm, (3) classification of electrical power system applications, and (4) future of ACO for modern power systems application.
... For this reason, various conventional mathematical solutions were presented to solve the CHPED problem such as Lagrangian relaxation (Sashirekha et al., 2013), mixed-integer non-linear programming (Kim and Edgar, 2014), branch and bound algorithm, and benders decomposition (Abdolmohammadi and Kazemi, 2013). However, introducing practical constraints such as prohibited operating zones POZs, valve-point loading effects (VPLEs), and consideration of multiple pollutant emissions have greatly extended the complexity Minimum and the maximum position of each particle in the PSO X k i,j , X k+1 i,j Current and updated position of the particle i with regards to component j To overcome the shortcomings in classical mathematical methods, recently several meta-heuristic based solutions are presented which are more effective in solving the non-convex CHPED problem such as squirrel search algorithm (Basu, 2019), gray wolf optimization (Jayakumar et al., 2016), improved genetic algorithm (Zou et al., 2019), Cuckoo optimization algorithm (Mellal and Williams, 2015), civilized swarm optimization and Powell's pattern search algorithm (Narang et al., 2017), artificial immune system (Basu, 2012), kho-kho optimization algorithm (Srivastava and Das, 2020), deep reinforcement learning approach (Zhou et al., 2020), biogeography-based learning particle swarm optimization and colony search algorithm (Song et al., 1999). However, the meta-heuristic methods are also limited by constraints such as complexity in the derivation of the algorithm in a programming language, number of tuning parameters, and execution time of the algorithm. ...
The ever-growing trend of electricity demand and environmental concerns have mandated the operation of electrical energy grids in a more economical and environmentally friendly manner. In the past few years, the integration of combined heat and power units has offered a promising solution to these concerns, however, at the same time a new challenging problem has revealed itself that is finding a simultaneous optimal solution between two competing criteria of power and heat. Furthermore, this problem will be more complex when the reduction of emission gasses is taken into consideration. Thus, to solve optimal scheduling of combined heat and power units, this study proposes an intelligent sequential algorithm based on the hybridization of teaching and learning-based optimization algorithm and an improved version of particle swarm optimization. The proposed algorithm is uniquely capable of the concurrent minimization of total generation costs and multi-pollutant gasses while several physical, operational, and environmental constraints are considered. Also, to ensure the safe maintenance of systems' constraints, this study employs an adaptive violation constraint handling technique in conjunction with the proposed hybridized optimization algorithm. Finally, the performance of the proposed algorithm is compared to the recently developed methods, in which the proposed algorithm of the study outperforms all the other algorithms and achieves up to 2.2% lower overall costs of operation in most of the studied cases.
... Many effective meta-heuristic or heuristic algorithms are implemented to search the optimal solution for the CHPED optimization problem [1]. The metaheuristic algorithms applied in CHPED optimization problem from the literatures include Genetic Algorithm (GA) [8][9], Particle Swarm Optimization (PSO) algorithm [10][11], Ant Colony Optimization (ACO)algorithm [12], Bee Colony Optimization (BCO) [13], Cuckoo Search (CS)algorithm [14], Grey Wolf Optimization (GWO) algorithm [15], Artificial Immune System (AIS) algorithm [16], Firefly Algorithm (FA) [17], Harmony Search(HS) [18] , Differential Evolution (DE) [19] , Fish School Search (FSS) [20], Invasive Weed Optimization(IWO) algorithm [21], Group Search Optimization(GSO) [22] and Teaching Learning Based Optimization (TLBO) [23]. Although the above swarm intelligence optimization algorithms have had acceptable results to solve the CHPED optimization problem, the global optimization solution and its global convergence are usually difficult to be guaranteed. ...
Combined Heat and Power Economic Dispatch (CHPED) problem is a sophisticated constrained nonlinear optimization problem in a heat and power production system for assigning heat and power production to minimize the production costs. To address this challenging problem, a novel Social Cognitive Optimization
algorithm with Tent map (TSCO) is presented for solving the CHPED problem. To handle the equality constraints in heat and power balance constraints, Adaptive Constraints Relaxing (ACR) rule is adopted in constraint processing. The novelty of our work lies in the introduction of a new powerful TSCO algorithm to solve the CHPED issue. The
effectiveness and superiority of the presented algorithm is validated by carrying out two typical CHPED cases. The numerical results show that the proposed approach has better convergence speed and solution quality than all other existing state-of-the-art algorithms.
... The successful implementation of an Evolutionary Algorithm (EA) in solving many complex engineering problems made many researchers implement these stochastic algorithms to solve the complicated CHPED problem. The Gravitational Search Algorithm [16], Gray Wolf Optimization [17], improved Genetic Algorithm [18], real coded genetic algorithm [19,20], Cuckoo Optimization Algorithm [21], Civilized Swarm Optimization [22], Exchange Market Algorithm [23], Harmony Search Algorithm [24], Differential Evolution [25], Bee Colony Optimization [26], Artificial Immune System [27], Oppositional Teaching Learning based Optimization [28], Ant Colony Optimization [29], MLCA algorithm [30], Group search optimization [31] and PSO based hybrid algorithm [32], hybrid Bat-ABC algorithm [33] have been applied to solve the CHPED problem. These single optimization-based approaches only optimize the schedules of the thermal generators to minimize fuel cost but do not minimize the pollutant gases from them. ...
This study implements a potent Multiobjective Multi-Verse Optimization algorithm to solve the high complicated combined economic emission dispatch and combined heat and power economic emission dispatch problems. Solving these problems operates the power system integrated with cogeneration plants economically and reduces the environmental impacts caused by the pollutants of fossil fuel-fired power plants. A chaotic opposition based strategy is proposed to explore the search space extensively and to generate the initial populations for the multiobjective optimization algorithm. An effective constraint handling mechanism is also proposed to enable the population to remain within the bounds and in the feasible operating region of the cogeneration plants. The algorithm is applied to standard test functions, four test systems including a large 140 bus system considering valve-point effects, ramp limits, transmission power losses, and the feasible operating region of cogeneration units. The Pareto optimal solutions obtained by the algorithm are well spread and diverse when compared with other optimization algorithms. The statistical analysis and various performance metrics used indicate the algorithm converges to true POF and is a viable alternative to solve the highly complicated combined economic emission dispatch and combined heat and power economic emission dispatch problems.
... In improved ant colony search (IACS) algorithm (Song et al. 1999), cooperation and several search techniques have been recommended that lead to the fast search of optimal solution. However, in this method there is a tendency to find solution near to global optimal solution, even if it runs in small scales and CHPED simple problems. ...
Economic dispatch is the optimal scheduling for generating units with technical constraints. Combined heat and power economic dispatch (CHPED) refers to minimization of the total energy cost for generating electricity and heat supply to load demand. This planning model integrates heat and power energy to balance energy supply and demand, mitigate climate change and improve energy efficiency of sustainable cities and green buildings. In this paper for the first time, self-regulating particle swarm optimization (SRPSO) algorithm is utilized for solving the CHPED problem by considering valve point effects and prohibited zones on fuel cost function of pure generation units and electrical power losses in transmission systems. The main advantage of SRPSO algorithm to PSO algorithm is the inertia weight flexibility with respect to search conditions. In this algorithm, unlike PSO algorithm that inertia weight reduces in each iteration, this value increases or reduces proportional to particles’ positions, which will lead particles to achieve optimal value with higher speed. The capability and effectiveness of the proposed algorithm are evaluated on a large-scale energy system using MATLAB environment. The results obtained by SRPSO algorithm are outperformed by other optimization methods from the economic, sustainable energy and time consumption point of view.
... Mathematically, problem is formulated as "(1)" [10]- [11], [12]: ...
Abstract: The Harmony Search (HS) algorithm is a population-based meta-heuristic optimization
algorithm. This algorithm is inspired by the music improvisation process in which the musician
searches for harmony and continues to polish the pitches to obtain a better harmony. Although
several variants of the HS algorithm have been proposed, their effectiveness in dealing with
diverse problems is still unsatisfactory. The performances of these variants mainly depend on
the selection of different parameters of the algorithm. This paper develops an improved harmony
search (IHS) algorithm for solving optimization problems. IHS employs a novel method for
generating new solution vectors that enhances accuracy and convergence rate of harmony search
(HS) algorithm. The IHS algorithm has been successfully applied to various benchmarking and
standard engineering optimization problems. The optimal utilization of multiple combined heat
and power (CHP) systems is a complicated problem that needs powerful methods to solve. This
paper presents an improved harmony search (IHS) algorithm to solve the combined heat and
power economic dispatch (CHPED) problem. In this paper the impacts of constant parameters
on harmony search algorithm are discussed and a strategy for tuning these parameters is
presented. Numerical results reveal that the proposed algorithm can find better solutions when
compared to HS and other heuristic or deterministic methods where IHS algorithm is a powerful
for will be effective in the problems of CHPED.
... Buoro et al. [21] put forward a mixed-integer linear programming model to optimise the operation strategy of integrated power and thermal system consisting of a CHP plant, a district heating network and other conventional components such as boilers and compression chillers. In addition, in order to search for the optimal solutions effectively, other researchers developed several advanced algorithms to solve the dispatch models, such as Lagrangian relaxation with surrogate subgradient multiplier updates [23], harmony search algorithm [24], genetic algorithmbased penalty function method [25], improved ant colony search algorithm [26], and chance-constrained programming and particle swarm optimisation [27]. The aforementioned optimisation models and algorithms for the dispatch of integrated power and thermal systems presented remarkable effects of increasing renewable energy penetration [28][29][30][31][32]. ...
Heat storage (HS) instalment in combined heat and power (CHP) plants is a promising solution to increase the adjustability of CHP plants and reduce renewable energy curtailment. Despite the proposed optimisation models and algorithms, it still lacks a dispatching framework for HS facilities to integrate with the existing dispatching system of power grids. This study integrates a coordination control system (CCS) and a plant‐level energy management system (PEMS) into the existing dispatching system and proposes the corresponding scheduling method to ensure the rationality, veracity, and timeliness of scheduling. The CCS generates power and thermal generation schedules in multi‐time scales, while the PEMS operates as the bridge between the HS facilities and the CCS. Meanwhile, taking into account the actual scheduling requirements, the authors propose a downward spinning reserve capacity (DSRC) preservation method for the dispatch of CHP plants, develop multi‐level coordination and progressive refinement strategy for schedules and apply the DSRC as a criterion to obtain the day‐ahead, the rolling and the real‐time schedules in sequence. Finally, the dispatch simulation results show that the newly proposed CHP dispatching framework can schedule the HS facilities in CHP plants effectively and achieve the desired effect of wind power accommodation.
... In order to overcome the limitations of conventional mathematical methods, many researchers focus on heuristic intelligence optimization algorithms including swarm intelligence algorithms that simulate the behavior of biological swarms, evolutionary algorithms that simulate the evolution of biological organisms and simulated ecosystem algorithms. In recent years, some researchers have used these heuristic algorithms to solve ED problems, such as differential evolution algorithm (DE) [5], particle swarm optimization (PSO) [6], ant colony optimization algorithm (ACO) [7], genetic algorithm (GA) [8], simulated annealing (SA) [9], Hopfield neural network (HNN) [10], tabu search (TS) [11], bacterial foraging (BF) [12], cuckoo search algorithm (CS) [13], bee colony optimization (BCO) [14], and bio-geography based optimization (BBO) [15]. For the purpose of improving the global optimization ability and search efficiency, many researchers developed a variety of modification and hybridization of these intelligent methods. ...
Economic dispatch (ED) problem with valve-point effects of generation units is a non-smooth and non-convex problem. This paper presents a differential evolution algorithm based on multi-population (MPDE) to solve economic dispatch problems with valve-point effects. The proposed MPDE algorithm employs the evolutional methodology of multiple populations to overcame the limitations of the traditional differential evolution algorithm. In multiple populations, each population has its own mutation strategy and parameters to enhance the searching ability. Moreover, information exchange among multiple populations to increase the diversity of individuals in the single population. In addition, the algorithm also introduces the normal distribution function to dynamically adjust the scaling factor and crossover rate to accelerate convergence speed. The proposed algorithm is tested on the 13-, 40-, 80-and 140- unit test systems. Simulation results show that the MPDE algorithm can achieve much smaller variances compared with other intelligent algorithms. The proposed algorithm has significant performance in accuracy for solving economic dispatch problems with valve-point effects.
Combined heat and power economic dispatch (CHPED) can enhance energy efficiency compared with conventional economic dispatch (ED). From the optimization standpoint, the CHPED problem usually involves the nonlinear products of heat and power generation variables, nonconvex objective functions, and nonconvex feasible operating range. Thus, its solution method should be able to cope with the problematic nonconvex problem since finding a poor solution for the CHPED implies reducing the maximum achievable efficiency. This paper presents an effective method utilizing several mathematical transformations to cope with the nonlinear, nonconvex terms. The method transforms the nonconvex regions and nonlinear functions into convex polyhedrons and segments. Then, the method formulates the polyhedrons and segments with integer variables, logical constraints, and combinatorial restrictions. Thus, we derive a mixed integer model, which optimization software can better solve. Simulation results illustrate the effectiveness of the method presented and its advantages compared with existing CHPED solution techniques in the literature.
Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates. Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.
The design of buildings has become a complex and multidisciplinary problem involving multiple conflicting objectives as architects and designers address competing technical, economic, environmental, and societal concerns. This has been driving research in Architecture, Engineering, and Construction (AEC) toward rigorous multidisciplinary decision-making frameworks that generate and evaluate numerous design alternatives using multi-objective optimization in concert with simulation and analysis models of varying fidelity and computational expense. While such frameworks are well known and widely employed in the aerospace and systems engineering domains, efforts by design professionals and researchers in the AEC field are scattered at best. In this paper, we provide a detailed review of recent developments in optimization frameworks in the AEC field and subsequently highlight how such developments are largely compartmentalized into separate domains such as structural, energy, daylighting, and other performance factors. We further discuss the technical challenges involved in concurrent coupled multidisciplinary design optimization (MDO) in the AEC field such as interoperability issues between Building Information Modeling (BIM) environments, analysis/simulation tools, and optimization frameworks. We conclude by outlining research needed for more unified modeling and simulation-based optimization frameworks to aid in complex and multidisciplinary building design processes. We also highlight the need for the identification and development of multi-fidelity simulation tools for use across multiple design phases. As such, this paper contributes a novel roadmap to leverage aerospace and systems engineering research in MDO into the field of AEC, along with a call for researchers in the MDO community to seek collaborations in AEC field.
In recent years, one of the most important and promising research fields has been metaheuristics to find optimal or near-optimal solutions for NP-hard combinatorial optimization problems. Improving the quality of the solution or the solution time is basic research area on metaheuristics. Modifications of the existing ones or creation of hybrid approaches are the focus of these efforts. Another area of improving the solution quality of metaheuristics is finding the optimal combination of algorithm control parameters. This is usually done by design of experiments or one-at-a-time approach in genetic algorithms, simulated annealing and similar metaheuristics. We observe that, in studies which use Ant Colonies Optimization (ACO) as an optimization technique; the levels of control parameters are determined by some non-systematic initial experiments and the interactions of the parameters are not studied yet.In this study, the parameters of Ant System have been investigated on different sized and randomly generated job-shop scheduling problems by using design of experiments. The effects and interactions of the parameters have been interpreted with the outputs of the experiments. Referring to the statistical analysis it is observed that none of the interactions between the Ant System parameters has a significant effect on makespan value. A specific fractional experimental design is suggested instead of the full factorial design. Depending on the findings from the benchmark problems it will be a reliable approach to use the suggested design for saving time and effort in experiments without sacrificing the solution quality.
Combined heat and power economic dispatch (CHPED) is a critical, non-linear, non-convex, non-differential, and constrained optimization problem in power systems that aims to minimize the total fuel cost and provide precise power and heat demands. In this paper, a novel optimization algorithm, namely social network search algorithm (SNS), is applied to solve the challenging CHPED problem. SNS mimics social network users’ behavior to increase popularity by modeling the different decision moods in expressing their views. The performance of SNS is investigated on five test systems considering valve-point loading effects, prohibited operating zones, and transmission power losses. The simulation results of SNS are compared with those of driving training-based optimization (DTBO), egret swarm optimization algorithm (ESOA), manta ray foraging optimization algorithm (MRFO), particle swarm algorithm (PSO), crow search algorithm (CSA), and various reported algorithms. The comparison results show that the SNS algorithm outperforms the other algorithms in terms of solution quality and provides better than or as well as the best-reported solution, resulting in enormous annual cost savings and significant economic benefits for the power systems while satisfying consumers demands of heat and power, which confirms the effectiveness of the proposed SNS algorithm in solving different CHPED problems.
Synopsis
This chapter presents a comprehensive presentation of different formulation of economic dispatch problems. These problems include dynamic/economic/emission dispatch and multi area-dynamic/economic/emission dispatch. In this regard explanations about these problems are presented based on in-depth literature review. This review considers different problem formulations, optimization methodologies, problem constraints and test systems. After that, the problem formulations of the above-mentioned problems are in details presented. Finally, a set of useful data from different test systems are gathered.
Combined heat and power economic dispatch (CHPED) is a challenging important optimization task in the economic operation of power systems that aims to minimize the production cost by scheduling the generation and heat outputs to committed units. The interdependency of heat and power production of the CHPED task exhibits non-convexity and non-linear natures in its modeling and optimization. Therefore, this paper introduces a novel hybrid approach comprising chameleon swarm algorithm (CSA) and mayfly optimization (MO), named CSMO, for solving the CHPED problem. The proposed CSMO algorithm has a better capability to evade from the trapping in local optima with faster rate of convergence pattern than the traditional CSA. Also the proposed CSMO algorithm employs the MO’ phase to assist the CSA to search based on deeper exploration/exploitation capabilities as MO utilizes two populations of male and female mayflies with crossover-based matting process. The effectiveness of the proposed CSMO algorithm is validated on CEC 2017 benchmark functions and two systems of the CHPED problem. The obtained results are compared with some successful optimizers. The simulation outcomes are portrayed based on the number of occasions where CSMO performs superior/equal/inferior to the other optimizers by considering the smaller mean values obtained by each algorithm for all test suites. Accordingly, it is exposed that the occasions achieved by the proposed CSMO are 29/1/0, 30/0/0, 30/0/0, 28/2/0, and 30/0/0 against some implemented algorithms, i.e., ISA, GOA, GBO, EO, and the original CSA. Similarly, the number of occasions achieved by the proposed CSMO are 30/0/0, 30/0/0, 30/0/0, 30/0/0, 30/0/0, 29/1/0, and 22/2/6 when the simulations are portrayed against some competitors from literature including the PSO, FA, FFPSO, HPSOFF, HFPSO, HGSO, and Q-SCA, respectively. Furthermore, the results of total cost found by CSMO are 9257.07 $/h for system 1 and 10094.25 $/h for system 2 of the CHPED problem, with percentage of improvement 0.02% and 14.42% on the original CSA, respectively. In addition, further assessments based on the Wilcoxon test, and convergence characteristic are reported. Based on the recorded results, it is portrayed that the CSMO can efficiently deal with the CEC 2017 benchmark functions and CHPED problem.
The significance and purpose of this multi-objective Combined Heat and Power Economic Emission Dispatch (MO-CHPEED) problem aims to determine the optimal generator output of the co-generation systems, in which two conflicting objectives of the fuel cost and mass of emissions are to be simultaneously minimized. The nonlinear and nonconvex nature of the objective functions needs a good optimization technique to handle it. This paper proposes a Dynamically Controlled Whale Optimization Algorithm (DCWOA) to solve the multi-objective non-convex MO-CHPEED problem in fuzzy environment. The proposed DCWOA is an improved variant of the traditional WOA method by adding dynamically controlled constriction function. Both the conflicting objectives of fuel cost and mass of emissions are handled using Fuzzy Framework. To highlight the performance of the proposed technique, it is tested on the latest CEC test functions and three different MO-CHPEED case studies. The results obtained by proposed DCWOA after 100 independent trails on latest CEC test functions and compared with latest different published methods show the effectiveness and robustness of the proposed method for getting better average and STD values. Moreover, proposed DCWOA is also tested on different dimensioned MO-CHPEED test functions after 100 independent trails and compared with latest techniques. Again the most compromise results given by proposed DCWOA highlights the supremacy of the proposed method in terms of the getting better fitness and best compromise solution obtained and the convergence traits of the MO-CHPEED problem.
Combined heat and power systems are known for their high efficiency. On the other hand, economic dispatching of these systems is very important in terms of total efficiency and reliability of the power system. The novelty of this study is to use the Filled Function Method (FFM) to solve this optimization problem in a way different from that to be found in the literature. Moreover, the Taguchi method is combined with the FFM for the first time to obtain the best initial parameters. So the proposed hybrid deterministic optimization algorithm is called the Taguchi-based Filled Function Method (TFFM). The most important advantage of the suggested TFFM is that it always gives the same result for the same inputs and all the solutions are in the feasible region. The method is applied to four different test systems and the results obtained are compared with those of recent powerful optimization algorithms. With the proposed optimization method, a significant performance increase of 5.676% was achieved. Online supplemental data for this article can be accessed at https://doi.org/10.1080/0305215X.2022.2034802.
The authors in this paper formulated mathematical equations of Multi-area Economic load dispatch in conventional approach. Multi-area Economic load dispatch problem is a vital issue in power system scheduling, processing, organizing and managing. MAELD issue in power system is explored with the combination of electric utilities of various different regions. The mathematical formulation of multi area dynamic dispatch problem in view of real power and tie-line limits have been explained in this paper. This work of mathematical formulation will be useful for the research work on multi-area economic load dispatch problems with electric vehicles (EVs) and Renewable Energy Sources (RES).
The article considers a system for monitoring the state of hydrolytospheric processes in the region. The results of pilot filtration work (PFW) at the field under consideration are presented. Based on PFW, a methodology for determining the parameters of a link approximating the static coefficients of mutual influence of producing wells is shown. Using the obtained link, the procedure for determining the optimal number of producing wells located on a given size section is shown. Using the results of PFW, the parameters of the discrete mathematical model of the hydrolyte-sphere processes of the field were verified. The technique of designing a distributed network for controlling the flow rate of producing wells of a given field is shown. Using a verified mathematical model of the hydrolyte-sphere process, the operation of a closed control system was simulated.
Increasing fuel cost and environmental issues force power producers to use high efficiency methods with low pollutant gas emission for power generation as in combined heat and power (CHP) generators. Non-linearity, non-convexity and complication of CHP generators turn combined heat and power economic emission dispatch (CHPEED) setback to an intricate maximization procedure. Because of inability of conventional methods in solving CHPEED problem, heuristic and evolutionary algorithms are needed to solve. The CHPEED problem is a multi-objective maximization setback where production cost and emission are the two competing objective functions. In this paper, the challenges of multi-objective CHPEED is regarded as a single objective optimization problem by utilizing weighting coefficients. Application of exchange market algorithm (EMA) is necessitated to resolve this setback and also find compromise solutions. In view of selecting the optimal accommodating solution, fuzzy satisfying method is applied.
The Multi-objective Non-convex Combined Heat and Power (CHP) scheduling problem of the systems is a complex and arduous problem. This is due to the nonconvex and nonlinear nature of the objective functions involved. This problem aims to simultaneously minimize two vital but conflicting objectives i.e. cost and emission. As the number of operational units and the constraints increase, regular mathematical algorithms are not able to provide a satisfactory solution to the problem. The non-convexity and nonlinearity of these objectives require a good optimization technique to handle it. In this chapter, a comparative analysis of Particle Swarm Optimization (PSO) and Whale Optimization Algorithm (WOA) is presented which is used to provide a compromise solution to this Multi-objectives CHP Economic and Emission Dispatch (MOCHPEED) problem. Both objectives of the CHPEED problem are solved using the fuzzy framework. Later, this framework is used to obtain the compromised solution between the both the objectives. The PSO and WOA techniques are tested on three different test systems. In these test systems, valve-point loading and transmission losses are also considered. To highlight the accomplishments of both the techniques, a comparative analysis is done with the results obtained using the latest literature. Statistical data related to costs and emission, and fitness function are included in this chapter which is obtained after simulating the test systems for 100 different unbiased trials. A detailed investigation on various test generating systems shows supremacy of WOA over PSO and other recently established techniques.
The objective of Multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas that minimize fuel costs, while satisfying power balance and generating limit and transmission constraints. If an area with excess power is not adjacent to a power deficient area, or the tie-line between the two areas is at transmission limit, it is necessary to find an alternative path between these two areas to transmit additional power. When a MAED problem is solved with spinning reserve constraints, the problem becomes further complicated. The power allocation to each unit is done in such a manner that after supplying the total load, some specified reserve is left behind. In this paper, the authors compare classic PSO and DE strategies and their variants for reserve constrained MAED. The superior constraint handling capability of these techniques enables them to produce high quality solutions. The performance is tested on a 2-area system having 4 generating units and a 4-area, 16-unit system.
It is well accepted that combined heat and power (CHP) generation can increase theefficiency of power and heat generation at the same time. With the increasing penetration of CHPs, determination of economic dispatch of power and heat becomes more complex and challenging.The CHP economic dispatch (CHPED) problem is a challenging optimization problem due to non-linearity and non-convexity in both objective function and constraints. Hence, in this paper a novel meta-heuristic algorithm, namely improved artificial bee colony (IABC) algorithm is proposed to solve the CHPED problem. The valve-point effects, power losses as well as the feasible operation region of CHP units are taken into account in the proposed CHPED problem model and the optimaldispatch of power/heat outputs of CHP units is determined via the proposed IABC algorithm. The proposed algorithm is applied on three test systems, in which two of them are large-scale CHPED benchmarks. The obtained results and comprehensive comparison with available methods, demonstrate the superiority of the proposed algorithm for dealing with non-convex and constrained CHPED problem.
One of the most important issues in the energy generation scheduling is the determination of the operating points of the electric and thermal energy resources. In the real conditions, there are different types of energy resources available for fulfilling the electrical and thermal load demands. The power plants (thermal generating units), boilers, as well as Combined Heat and Power (CHP) units are the most common technologies to serve this purpose. The main objective beyond solving the generation scheduling problem here is to determine the optimal operating points of these units to meet the electrical and thermal load demands. Since the determination of the optimal operating points of each generating unit to meet the load demand depends upon the technical and thermodynamic conditions of each unit, it is necessary to adopt an optimization problem to derive the optimal utilization pattern. In this chapter, the state of the art of the generation scheduling problem, as well as the mathematical expression regarding this problem, is investigated. In order to solve the aforementioned problem, the modified fireworks algorithm is adopted in this paper to solve the mentioned problem, and its performance is verified through comparing the results with those reported by other optimization algorithms by simulating the Economic Load Dispatch (ELD) and the combined heat and power scheduling (CHPS) problems.
Determining the optimal operating point of generating units in the optimal combined heat and power scheduling is an economic optimization problem aimed at minimizing the total operating costs. The generation cost would nonlinearly increase with the increase in the power generation of fossil fuel thermal units. On the other hand, in combined heat and power (CHP) units, the amounts of power and heat generation are highly mutually dependent. Therefore, the determination of the optimal operating points of such units would be much more difficult compared to electric power or heat-only generating units. Obviously, the aim beyond implementing the day-ahead generation scheduling (GS) problem is to determine the optimal operating points of generating units. In this regard, the power outputs of the units are specified such that the total operating costs of the system are minimized taking into consideration the technical and economic constraints. This paper solves the GS problem in the presence of CHP units with nonconvex feasible operating regions (FORs). This paper investigates the problem of optimal operating point determination of CHP units along with electrical and heat-only units.
Variations in energy demands require combined heat and power (CHP) systems to be more flexible in adjusting its operations. However, high flexibility is often achieved at the expense of other aspects. In other words, increasing flexibility of a CHP system would require large number of equipment to start-up or shutdown. This would lead to potentially high emissions and high start-up/shutdown costs due to sub-optimal fuel choices and poor selection of technologies respectively. In this respect, it would be challenging to determine the optimal CHP operation with high flexibility, low emissions and low start-up/shutdown costs. To address this challenge, operational optimisation must be considered. In this paper, a multi-objective fuzzy optimisation model was developed to optimise system flexibility, fuel emissions, equipment start-up and shutdown costs for a CHP system operation to meet varying energy production requirements. Essentially, fuzzy optimisation is used to maximise the degree of satisfaction among the three mentioned objectives. To demonstrate the proposed approach, a multi-fuel CHP case study consisting of several scenarios was solved. Results from the case study show that a trade-off CHP operation was determined for increased production. The trade-off operation had the degree of satisfaction of 35 % for each objective. The obtained degree of satisfaction indicates that a balance between flexibility, emissions and costs was achieved. In addition, chosen technologies and fuels were analysed and classified under categories such as “must have”, “optional” and “must avoid”.
This paper suggests heat transfer search (HTS) algorithm for solving complicated combined heat and power economic dispatch (CHPED) problem. The valve point effect, prohibited operating zones of conventional thermal generators and transmission loss are taken into consideration. The main objective of the CHPED problem is to minimize the total fuel cost for producing electricity and heat supplying to a load demand. HTS is a novel meta-heuristic optimization algorithm that is based on the law of thermodynamics and heat transfer. The efficiency of the suggested HTS algorithm has been confirmed on four test systems. Test results of the suggested HTS algorithm have been compared with those achieved by other evolutionary algorithms. It has been observed from the comparison that the suggested HTS algorithm has the ability to offer superior solution.
In this paper, the performance of CCHP with optimal operation were investigated, and theimpact of the time-use-price were analyzed. The results shown that the operation cost can beobviously save with optimal operation strategy than the HET strategies. The main reason to reduceconst is more power generation by the generator, it means that the generator efficiency is higher, sothe primary energy ratio got obvious improvement and carbon dioxide emissions are also reduced inoptimal operation. The TOU can reduce the operation cost, and induce more purchasing electricity ofCCHP in peak-off period. But the primary energy ratio almost did not improve, and carbon dioxideemissions increased in the TOU case.
An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call ant system (AS). We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation, and the use of a constructive greedy heuristic. Positive feedback accounts for rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps find acceptable solutions in the early stages of the search process. We apply the proposed methodology to the classical traveling salesman problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the ant system (AS) can be applied to other optimization problems like the asymmetric traveling salesman, the quadratic assignment and the job-shop scheduling. Finally we discuss the salient characteristics-global data structure revision, distributed communication and probabilistic transitions of the AS.
This paper introduces the ant colony system (ACS), a distributed
algorithm that is applied to the traveling salesman problem (TSP). In
the ACS, a set of cooperating agents called ants cooperate to find good
solutions to TSPs. Ants cooperate using an indirect form of
communication mediated by a pheromone they deposit on the edges of the
TSP graph while building solutions. We study the ACS by running
experiments to understand its operation. The results show that the ACS
outperforms other nature-inspired algorithms such as simulated annealing
and evolutionary computation, and we conclude comparing ACS-3-opt, a
version of the ACS augmented with a local search procedure, to some of
the best performing algorithms for symmetric and asymmetric TSPs
In recent years, there has been growing interest in algorithms
inspired by the observation of natural phenomena to define computational
procedures that can solve complex problems. We describe a distributed
heuristic algorithm that was inspired by the observation of the behavior
of ant colonies, and we propose its use for the quadratic assignment
problem. The results obtained in solving several classical instances of
the problem are compared with those obtained from other evolutionary
heuristics to evaluate the quality of the proposed system
This paper presents a new cooperative agent search approach for solving power economic dispatch problems. One of the main objectives of this paper is to investigate the applicability of an alternative agent search method in power system optimization. The proposed Artificial Ant Colony Search Algorithm (ACSA) is based on the results of real ant trail formation and foraging obtainedfrom theoretical biology science. A new encoding technique is proposed to overcome the difficulties of applying ACSA in a continuous search space, such as economic dispatch problems. An object-oriented ACSA system is developed and programmed. The effectiveness of the proposed technique has been demonstrated on a number of systems, which include an actual utility system of up to 40 units. Comparison with conventional genetic algorithms is presented. The outcome of the study shows that an emergent collective search ability resulted from the massive parallel fashion and positive feedback of ant colony is particularly attractive in addressing some difficult engineering problems; however, it should be observed that current research of Ant Colony Search Algorithm in power system is relatively new and still at a feasibility stage. More potentially beneficial work remains to be done.
This paper presents a new genetic approach for solving combined heat and power (CHP) economic dispatch problems. The complication of CHP dispatch lies in the constraints imposed by the multi-demand and heat-power capacity mutual dependencies. The paper proposes improved penalty function formulation for Genetic Algorithms (GAs) to effectively handle constraints. The method has been tested and compared to demonstrate its effectiveness
This paper describes a form of dynamical computational system—the ant colony—and presents an ant colony model for continuous space optimisation problems. The ant colony metaphor is applied to a real world heavily constrained engineering design problem. It is capable of accelerating the search process and finding acceptable solutions which otherwise could not be discovered by a GA. By integrating the Pareto optimality concept within the selection mechanism in GAs and Ant Colony it is possible to treat both hard and soft constraints. Hard constraints participate in a penalty term while soft constraints become part of a multi-criteria formulation of the problem.
This paper presents a new algorithm for combined heat and power
(CHP) economic dispatch. The CHP economic dispatch problem is decomposed
into two sub-problems: the heat dispatch; and the power dispatch. The
sub-problems are connected through the heat-power feasible region
constraints of cogeneration units. The connection can be interpreted by
the unit heat-power feasible region constraint multipliers in the
Lagrangian function, and the interpretation naturally leads to the
development of a two-layer algorithm. The outer layer uses the
Lagrangian relaxation technique to solve the power dispatch iteratively.
In each iteration, the inner layer solves the heat dispatch with the
unit heat capacities passed by the outer layer. The binding constraints
of the heat dispatch are fed back to the outer layer to move the CHP
economic dispatch towards a global optimal solution
A genetic-based algorithm is used to solve a power system economic
dispatch (ED) problem. The algorithm utilizes payoff information of
perspective solutions to evaluate optimality. Thus, the constraints of
classical LaGrangian techniques on unit curves are eliminated. Using an
economic dispatch problem as a basis for comparison, several different
techniques which enhance program efficiency and accuracy, such as
mutation prediction, elitism, interval approximation and penalty
factors, are explored. Two unique genetic algorithms are also compared.
The results are verified for a sample problem using a classical
technique
This paper presents an efficient algorithm for the solution of the
economic dispatch of co-generation systems. The key lies in the
exploitation of the high degree of separability of the cost function and
the constraints. Test results show that for medium size systems (40
units) the method is more than 20 times faster than a conventional
procedure based on quadratic programming. Specific implementation
details are given in an appendix
Ant-Tabu approach to power economic dispatch
- C S Chou
- Y H Song
C.S. Chou, Y.H. Song, Ant-Tabu approach to power economic dispatch, Proc UPEC, UMIST, UK, 1997.