Combined heat and power economic dispatch problem solution by implementation of whale optimization method

Kepler Algorithm for Large-Scale Systems of Economic Dispatch with Heat Optimization

Combined Heat and Power Units Economic Dispatch (CHPUED) is a challenging non-convex optimization challenge in the power system that aims at decreasing the production cost by scheduling the heat and power generation outputs to dedicated units. In this article, a Kepler optimization algorithm (KOA) is designed and employed to handle the CHPUED issue under valve points impacts in large-scale systems. The proposed KOA is used to forecast the position and motion of planets at any given time based on Kepler's principles of planetary motion. The large 48-unit, 96-unit, and 192-unit systems are considered in this study to manifest the superiority of the developed KOA, which reduces the fuel costs to 116,650.0870 USD/h, 234,285.2584 USD/h, and 487,145.2000 USD/h, respectively. Moreover, the dwarf mongoose optimization algorithm (DMOA), the energy valley optimizer (EVO), gray wolf optimization (GWO), and particle swarm optimization (PSO) are studied in this article in a comparative manner with the KOA when considering the 192-unit test system. For this large-scale system, the presented KOA successfully achieves improvements of 19.43%, 17.49%, 39.19%, and 62.83% compared to the DMOA, the EVO, GWO, and PSO, respectively. Furthermore, a feasibility study is conducted for the 192-unit test system, which demonstrates the superiority and robustness of the proposed KOA in obtaining all operating points between the boundaries without any violations.

Solving the Combined Heat and Power Economic Dispatch Problem in Different Scale Systems Using the Imperialist Competitive Harris Hawks Optimization Algorithm

The aim of electrical load dispatch (ELD) is to achieve the optimal planning of different power plants to supply the required power at the minimum operation cost. Using the combined heat and power (CHP) units in modern power systems, increases energy efficiency and, produce less environmental pollution than conventional units, by producing electricity and heat, simultaneously. Consequently, the ELD problem in the presence of CHP units becomes a very non-linear and non-convex complex problem called the combined heat and power economic dispatch (CHPED), which supplies both electric and thermal loads at the minimum operational cost. In this work, at first, a brief review of optimization algorithms, in different categories of classical, or conventional, stochastic search-based, and hybrid optimization techniques for solving the CHPED problem is presented. Then the CHPED problem in large-scale power systems is investigated by applying the imperialist competitive Harris hawks optimization (ICHHO), as the combination of imperialist competitive algorithm (ICA), and Harris hawks optimizer (HHO), for the first time, to overcome the shortcomings of using the ICA and HHO in the exploitation, and exploration phases, respectively, to solve this complex optimization problem. The effectiveness of the combined algorithm on four standard case studies, including 24 units as a medium-scale, 48, 84, units as the large-scale, and 96-unit as a very large-scale heat and power system, is detailed. The obtained results are compared to those of different algorithms to demonstrate the performance of the ICHHO algorithm in terms of better solution quality and lower fuel cost. The simulation studies verify that the proposed algorithm decreases the minimum operation costs by at least 0.1870%, 0.342%, 0.05224%, and 0.07875% compared to the best results in the literature.

A Multi-Objective Teaching–Learning Studying-Based Algorithm for Large-Scale Dispatching of Combined Electrical Power and Heat Energies

This paper proposes a multi-objective teaching–learning studying-based algorithm (MTLSBA) to handle different objective frameworks for solving the large-scale Combined Heat and Power Economic Environmental Dispatch (CHPEED) problem. It aims at minimizing the fuel costs and emissions by managing the power-only, CHP and heat-only units. TLSBA is a modified version of TLBA to increase its global optimization performance by merging a new studying strategy. Based on this integrated tactic, every participant gathers knowledge from someone else randomly to improve his position. The position is specified as the vector of the design variables, which are the power and heat outputs from the power-only, CHP and heat-only units. TLSBA has been upgraded to include an extra Pareto archiving to capture and sustain the non-dominated responses. The objective characteristic is dynamically adapted by systematically modifying the shape of the applicable objective model. Likewise, a decision-making approach based on the fuzzy concept is used to select the most suitable CHPEED solution for large-scale dispatching of combined electrical power and heat energies. The proposed MTLSBA is assigned to multiple testing of 5-unit, 7-unit and 96-unit systems. It is contrasted with other reported techniques in the literature. According to numerical data, the suggested MTLSBA outperforms the others in terms of effectiveness and robustness indices. For the 5-unit system, the proposed MTLSBA achieves improvement in the fuel costs of 0.6625% and 0.3677% and reduction in the emissions of 2.723% and 7.4669% compared to non-dominated sorting genetic algorithm (NSGA-II) and strength Pareto evolutionary algorithm (SPEA 2), respectively. For the 7-unit system, the proposed MTLSBA achieves improvement in the fuel costs of 2.927% and 3.041% and reduction in the emissions of 40.156% and 40.050% compared to NSGA-II and SPEA 2, respectively.

An Enhanced Slime Mould Optimizer That Uses Chaotic Behavior and an Elitist Group for Solving Engineering Problems

This article suggests a novel enhanced slime mould optimizer (ESMO) that incorporates a chaotic strategy and an elitist group for handling various mathematical optimization benchmark functions and engineering problems. In the newly suggested solver, a chaotic strategy was integrated into the movement updating rule of the basic SMO, whereas the exploitation mechanism was enhanced via searching around an elitist group instead of only the global best dependence. To handle the mathematical optimization problems, 13 benchmark functions were utilized. To handle the engineering optimization problems, the optimal power flow (OPF) was handled first, where three studied cases were considered. The suggested scheme was scrutinized on a typical IEEE test grid, and the simulation results were compared with the results given in the former publications and found to be competitive in terms of the quality of the solution. The suggested ESMO outperformed the basic SMO in terms of the convergence rate, standard deviation, and solution merit. Furthermore, a test was executed to authenticate the statistical efficacy of the suggested ESMO-inspired scheme. The suggested ESMO provided a robust and straightforward solution for the OPF problem under diverse goal functions. Furthermore, the combined heat and electrical power dispatch problem was handled by considering a large-scale test case of 84 diverse units. Similar findings were drawn, where the suggested ESMO showed high superiority compared with the basic SMO and other recent techniques in minimizing the total production costs of heat and electrical energies.

Techno-Economic Power Dispatching of Combined Heat and Power Plant Considering Prohibited Operating Zones and Valve Point Loading

Co-generation units (i.e., combined heat and power plants—CHPs) are playing an important role in fulfilling the heat and power demand in the energy system. Due to the depletion of fossil fuels and rising carbon footprints in the environment, it is necessary to develop some alternatives as well as energy efficient operating strategies. By utilising the waste heat from thermal plants, cogeneration units help to decrease energy generation costs as well as reduce emitted pollutants. The combined heat and power economic dispatch (CHPED) operation strategy is becoming an important optimisation task in the energy efficient operation of a power system. The optimisation of CHPED is quite complex due to the dual dependence of heat and power in the cogeneration units. The valve point loading effect and prohibited operating zones of a thermal power unit make the objective function non-linear and non-convex. In this work, to address these issues more effectively, the viable operational area of the CHP and power system network losses are considered for the optimal allocation of power output and heat generation. A metaheuristic optimisation algorithm is proposed to solve the CHPED to minimize the fuel supply, thus satisfying the constraints. To handle equality and inequality constraints, an external penalty factor-based constraint handling technique is used. The success of the proposed CHPED algorithm is tested on three considered cases. In all the cases, the results show the effectiveness in terms of solution accuracy and better convergence.

An Innovative Hybrid Heap-Based and Jellyfish Search Algorithm for Combined Heat and Power Economic Dispatch in Electrical Grids

This paper proposes a hybrid algorithm that combines two prominent nature-inspired meta-heuristic strategies to solve the combined heat and power (CHP) economic dispatch. In this line, an innovative hybrid heap-based and jellyfish search algorithm (HBJSA) is developed to enhance the performance of two recent algorithms: heap-based algorithm (HBA) and jellyfish search algorithm (JSA). The proposed hybrid HBJSA seeks to make use of the explorative features of HBA and the exploitative features of the JSA to overcome some of the problems found in their standard forms. The proposed hybrid HBJSA, HBA, and JSA are validated and statistically compared by attempting to solve a real-world optimization issue of the CHP economic dispatch. It aims to satisfy the power and heat demands and minimize the whole fuel cost (WFC) of the power and heat generation units. Additionally, a series of operational and electrical constraints such as non-convex feasible operating regions of CHP and valve-point effects of power-only plants, respectively, are considered in solving such a problem. The proposed hybrid HBJSA, HBA, and JSA are employed on two medium systems, which are 24-unit and 48-unit systems, and two large systems, which are 84- and 96-unit systems. The experimental results demonstrate that the proposed hybrid HBJSA outperforms the standard HBA and JSA and other reported techniques when handling the CHP economic dispatch. Otherwise, comparative analyses are carried out to demonstrate the suggested HBJSA’s strong stability and robustness in determining the lowest minimum, average, and maximum WFC values compared to the HBA and JSA.

Optimal Scheduling of Non-Convex Cogeneration Units Using Exponentially Varying Whale Optimization Algorithm

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.

Combined Heat and Power Dynamic Economic Emissions Dispatch with Valve Point Effects and Incentive Based Demand Response Programs

In this paper, the Combined Heat and Power Dynamic Economic Emissions Dispatch (CHPDEED) problem formulation is considered. This problem is a complicated nonlinear mathematical formulation with multiple, conflicting objective functions. The aim of this mathematical problem is to obtain the optimal quantities of heat and power output for the committed generating units which includes power and heat only units. Heat and load demand are expected to be satisfied throughout the total dispatch interval. In this paper, Valve Point effects are considered in the fuel cost function of the units which lead to a non-convex cost function. Furthermore, an Incentive Based Demand Response Program formulation is also simultaneously considered with the CHPDEED problem further complicating the mathematical problem. The decision variables are thus the optimal power and heat output of the generating units and the optimal power curbed and monetary incentive for the participating demand response consumers. The resulting mathematical formulations are tested on four practical scenarios depicting different system operating conditions and obtained results show the efficacy of the developed mathematical optimization model. Obtained results indicate that, when the Incentive-Based Demand Response (IBDR) program’s operational hours is unrestricted with a residential load profile, the energy curtailed is highest (2680 MWh), the energy produced by the generators is lowest (38,008.53 MWh), power losses are lowest (840.5291 MW) and both fuel costs and emissions are lowest.

Optimal Operation of Multi-Carrier Energy Networks Considering Uncertain Parameters and Thermal Energy Storage

The coordination of energy carriers in energy systems has significant benefits in enhancing the flexibility, efficiency, and sustainability characteristics of energy networks. These benefits are of great importance for multi-carrier energy networks due to the complexity of obtaining optimal dispatch, considering the non-convex nature of their energy conversion. The current study proposes a robust operation model for the coordination of multi-carrier systems, including electricity, gas, heat, and water carriers concerning thermal energy storage technology. Thermal energy storage is for storing extra heat generated by combined heat and power (CHP) plants and boilers in time intervals with low heat demand on the system and discharging it when required. Energy network operators should have the capability to manage uncertain energy loads to study the impact of load variation on the decision-making process in network operation. Accordingly, this study employs an information gap decision theory (IGDT) method to model the uncertainty of the power demand in optimal system operation. By applying the IGDT approach, the operator of the energy system can use the appropriate methodology to obtain a robust optimal operation. Such a modeling approach helps the operator to make suitable decisions about probable variations in power load. The introduced model is applied in a test system for evaluating the performance and effectiveness of the introduced scheme.

A Critical Review of the Modeling and Optimization of Combined Heat and Power Dispatch

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.