Short-term Hydrothermal Scheduling Problem Research Articles

Generation cost optimisation of hydrothermal system using arithmetic optimisation algorithm considering transmission loss and valve point loading effect

Hydrothermal scheduling is a crucial issue in the field of power system economics. The goal of short-term hydrothermal scheduling is to reduce the total cost of generation by optimising the hourly output of power generation for specific time intervals. This paper presents a new population-based approach called the arithmetic optimisation algorithm for solving the short-term hydrothermal scheduling problem. To verify the performance of the arithmetic optimisation approach, six different test systems with different cost functions were investigated. It has been observed that the proposed AOA reduced the generation cost by 3.41%. Furthermore, upon considering non-linearity in the fitness function by involving the valve-point effect, AOA diminished the generation cost by 8.54%. An appreciable 25.08% reduction in the algorithm execution time was also observed when the proposed AOA was used as the optimisation tool. Numerical results and non-parametric statistical analysis claim the superiority of the proposed approach.

Optimal scheduling of short-term hydrothermal with integration of renewable energy resources using Lévy spiral flight artificial hummingbird algorithm

Short-term hydrothermal scheduling (STHS) is taking an important consideration in the power system for economics operation. The solution to the STHS problem gives time-varying scheduling of power generation with available hydro and thermal units aims to attain the cost saving of thermal units for a given time period. It is a non-convex optimization problem with a set of inequality and equality constrains such as load balancing, transmission losses as well as valve-point effect to the thermal power units. The permeation of renewable energy is frequently used into the power networks aims to reduce the cost of generation and emissions. The two foremost resources such as wind and photo-voltaic are frequently used in the power networks. In the research, the use of both powers integrated into the STHS problem to reduce the fuel cost ($) by using the modified artificial hummingbird algorithm (MAHA). To modelled the uncertainty in solar irradiance and windspeed, the lognormal and Weibull distribution are used. The novel MAHA is based on two enhancing methods; (1). updating the positions of the hummingbirds in stochastic motion via Lévy flight walk and (2). updating the location of the hummingbirds via pitch adjustment motion. The MAHA is further tested on the four STHS cases such as; four hydro one thermal (non-vple and vple), four hydro three thermal (vple without and with losses), four hydro three thermal with integration of RERs including direct cost only (VPLE without and with losses) and four hydro three thermal with uncertainty of RERs including direct, reverse and penalty costs (vple without losses), respectively. Moreover, for validation the performance of MAHA is further compared to the outcomes of AHA and other state-of-the-arts techniques.

Non-Dominated Sorting-Based Hybrid Optimization Technique for Multi-Objective Hydrothermal Scheduling

Short-term hydrothermal scheduling problem plays an important role in maintaining a high degree of economy and reliability in power system operational planning. Since electric power generation from fossil fired plants forms a major part of hydrothermal generation mix, therefore their emission contributions cannot be neglected. Hence, multi-objective short term hydrothermal scheduling is formulated as a bi-objective optimization problem by considering (a) minimizing economical power generation cost, (b) minimizing environmental emission pollution, and (c) simultaneously minimizing both the conflicting objective functions. This paper presents a non-dominated sorting disruption-based oppositional gravitational search algorithm (NSDOGSA) to solve multi-objective short-term hydrothermal scheduling (MSHTS) problems and reveals that (i) the short-term hydrothermal scheduling problem is extended to a multi-objective short-term hydrothermal scheduling problem by considering economical production cost (EPC) and environmental pollution (EEP) simultaneously while satisfying various diverse constraints; (ii) by introducing the concept of non-dominated sorting (NS) in gravitational search algorithm (GSA), it can optimize two considered objectives such as EPC and EEP simultaneously and can also obtain a group of conflicting solutions in one trial simulation; (iii) in NSDOGSA, the objective function in terms fitness for mass calculation has been represented by its rank instead of its EPC & EEP values by using the NS approach; (iv) an elite external archive set is defined to keep the NS solutions with the idea of spread indicator; (v) the optimal schedule value is extracted by using fuzzy decision approach; (vi) a consistent handling strategy has been adopted to handle effectively the system constraints; (vii) finally, the NSDOGSA approach is verified on two test systems with valve point loading effects and transmission loss, and (viii) computational discussion show that the NSDOGSA gives improved optimal results in comparison to other existing methods, which qualifies that the NSDOGSA is an effective and competitive optimization approach for solving complex MSHTS problems.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

A New Fast Deterministic Economic Dispatch Method and Statistical Performance Evaluation for the Cascaded Short-Term Hydrothermal Scheduling Problem

The Cascaded Short-Term Hydrothermal Scheduling (CSTHTS) problem is a highly non-linear, multi-modal, non-convex, and NP-hard optimization problem that has been solved by conventional and metaheuristic algorithms in the past. As the CSTHTS problem falls under the category of applied operational research, therefore, the work is still on-going to find new algorithms and variants of the existing algorithms that would better approximate the optimal global solution in a shorter computational time. This article proposes a novel deterministic thermal economic dispatch method embedded with the improved Accelerated Particle Swarm Optimization (APSO) algorithm to infinitesimally reduce the Big O time complexity for the standard benchmark test case of the CSTHTS optimization problem. Then, it discusses and presents the importance of performing standard statistical tests to establish the supremacy of one metaheuristic algorithm over the other one in solving the CSTHTS problem. The results obtained are better than the results of the many state-of-the-art algorithms applied to solve the considered test case of the CSTHTS problem in the literature, and the superiority of the improved APSO algorithm has been established statistically using the parametric independent samples t-test and the non-parametric Mann–Whitney U-test over the other metaheuristic algorithms such as particle swarm optimization in solving the chosen test case of the CSTHTS problem.

Salp swarm algorithm to solve Short-Term hydrothermal scheduling problem

Abstract Hydrothermal scheduling possibility is regarding the possible performance of the power system was suggested in this article. Hydrothermal power production largely relies on constraints, which are unpredictable in reality. To catch the difficulty associated with hydrothermal power to get optimize power production and then to manage the optimization section, a recently improved optimization technique named Salp Swarm Algorithm has been employed. It essentially operates on the style of Salps. A procedure has been tested for supporting the capacity for solving challenges and for checking the outcome of the hydrothermal power system. To approach the problem very practical the valve-point charging outcome has been regarded also.

Introducing Adaptive Machine Learning Technique for Solving Short-Term Hydrothermal Scheduling with Prohibited Discharge Zones

The short-term hydrothermal scheduling (STHTS) problem has paramount importance in an interconnected power system. Owing to an operational research problem, it has been a basic concern of power companies to minimize fuel costs. To solve STHTS, a cascaded topology of four hydel generators with one equivalent thermal generator is considered. The problem is complex and non-linear and has equality and inequality constraints, including water discharge rate constraint, power generation constraint of hydel and thermal power generators, power balance constraint, reservoir storage constraint, initial and end volume constraint of water reservoirs, and hydraulic continuity constraint. The time delays in the transport of water from one reservoir to the other are also considered. A supervised machine learning (ML) model is developed that takes the solution of the STHTS problem without PDZ, by any metaheuristic technique, as input and outputs an optimized solution to STHTS with PDZ and valve point loading (VPL) effect. The results are quite promising and better compared to the literature. The versatility and effectiveness of the proposed approach are tested by applying it to the previous works and comparing the cost of power generation given by this model with those in the literature. A comparison of results and the monetary savings that could be achieved by using this approach instead of using only metaheuristic algorithms for PDZ and VPL are also given. The slipups in the VPL case in the literature are also addressed.

Scenario-Based Fuel Constrained Short-Term Hydrothermal Scheduling

For electric power companies, the economic utilization of existing fossil fuel is currently primary issue because of the diminishing supply of fossil fuel. Thermal power plants have fuel limitations and contractual restrictions that must be adhered to. Therefore this work presented the scenario-based fuel constrained short-term hydrothermal scheduling problem with the incorporation of renewable energy sources. The elephant clan optimization (ECO) approach is offered for short-term hydro-thermal scheduling (STHTS) with thermal generators, cascaded hydro, solar PV plants, wind-turbine-generators (WTG), and pumped-storage-hydro (PSH) with and without demand side management (DSM) for various scenarios. On a typical test system, the suggested approach is shown to be successful. Analysis of the typical test system’s numerical results is compared to those produced via the HPSO-TVAC and grey wolf algorithms (GWO). The comparison shows that the suggested ECO is capable of providing a better solution.

Impact of parameter control on the performance of APSO and PSO algorithms for the CSTHTS problem: An improvement in algorithmic structure and results.

Cascaded Short Term Hydro-Thermal Scheduling problem (CSTHTS) is a single objective, non-linear multi-modal or convex (depending upon the cost function of thermal generation) type of Short Term Hydro-Thermal Scheduling (STHTS), having complex hydel constraints. It has been solved by many metaheuristic optimization algorithms, as found in the literature. Recently, the authors have published the best-achieved results of the CSTHTS problem having quadratic fuel cost function of thermal generation using an improved variant of the Accelerated PSO (APSO) algorithm, as compared to the other previously implemented algorithms. This article discusses and presents further improvement in the results obtained by both improved variants of APSO and PSO algorithms, implemented on the CSTHTS problem.

Backtracking search optimization applied to solve short-term electrical real power generation of hydrothermal plant

This article aims to determine the feasible optimal solution for the short-term hydrothermal scheduling (STHS) problem using the efficient backtracking search optimization technique. The problem formulation for hydrothermal systems is highly complex owing to its nonlinear nature. Hydrothermal scheduling is considered with two decision variables simultaneously: thermal states and water discharge. These two variables are instrumental in determining the optimal hourly schedule of power generation in hydrothermal power plants. The optimum solution is obtained using the backtracking search algorithm (BSA) with two primary operations, namely, mutation and crossover. The BSA is an optimization technique free from high-sensitivity control parameters, because it has only one control parameter for finding the optimal solution. It also has powerful exploration and exploitation capabilities. The simulation results corroborate that BSA is highly efficient compared to existing optimization techniques (e.g. oppositional real coded chemical reaction-based optimization, differential evolution) in terms of overall efficiency and the quality of the solutions.

Short-Term Hydrothermal Scheduling using Imperialist Competitive Algorithm

In this study, the Imperialist Competitive Algorithm (ICA) is proposed to solve a multi-chain Short-Term Hydrothermal Scheduling problem (STHTS). It aims to minimize the generation cost of the thermal plants while satisfying the thermal and hydro plants constraints. In order to evaluate the effectiveness of the ICA, it has been tested on a system having a hydro plant with four-cascaded reservoir and a thermal plant. The results are compared with that obtained by other techniques. The ICA has the good convergence and the better results.

A Rigid Cuckoo Search Algorithm for Solving Short-Term Hydrothermal Scheduling Problem

The key criteria of the short-term hydrothermal scheduling (StHS) problem is to minimize the gross fuel cost for electricity production by scheduling the hydrothermal power generators considering the constraints related to power balance; the gross release of water, and storage limitations of the reservoir, and the operating limitations of the thermal generators and hydropower plants. For addressing the same problem, numerous algorithms were being used, and related studies exist in the literature; however, they possess limitations concerning the solution state and the number of iterations it takes to reach the solution state. Hence, this article proposes using an enhanced cuckoo search algorithm (CSA) called the rigid cuckoo search algorithm (RCSA), a modified version of the traditional CSA for solving the StHS problem. The proposed RCSA improves the solution state and decreases the iteration numbers related to the CSA with a modified Lévy flight. Here, the movement distances are divided into multiple possible steps, which has infinite diversity. The effectiveness of RCSA has been validated by considering the hydrothermal power system. The observed results reveal the superior performance of RCSA among all other compared algorithms that recently have been used for the StHS problem. It is also observed that the RCSA approach has achieved minimum gross costs than other techniques. Thus, the proposed RCSA proves to be a highly effective and convenient approach for addressing the StHS problems

Conventional and Metaheuristic Optimization Algorithms for Solving Short Term Hydrothermal Scheduling Problem: A Review

Short term hydrothermal scheduling (STHTS) is a non-linear, multi-modal and very complex constrained optimization problem which has been solved using several conventional and modern metaheuristic optimization algorithms. A number of research articles have been published addressing STHTS using different techniques. This article presents a comprehensive review of research published for solving the STHTS problem in the last four decades.

Implementation of APSO and Improved APSO on Non-Cascaded and Cascaded Short Term Hydrothermal Scheduling

Short-term hydrothermal scheduling (STHTS) is a highly non-linear, multi-model, non-convex, and multi-dimensional optimization problem that has been worked upon for about 5 decades. Many research articles have been published in solving different test cases of STHTS problem, while establishing the superiority of one type of optimization algorithm over the type, in finding the near global best solution of these complex problems. This paper presents the implementation of an improved version of a variant of the Particle Swarm Optimization algorithm (PSO), known as Accelerated Particle Swarm Optimization (APSO) on three benchmark test cases of STHTS problems. The adaptive and variable nature of the local and global search coefficients for the proposed APSO significantly improve its performance in obtaining the optimal solution for the STHTS test cases. Two of these cases are non-cascaded cases of STHTS problem (NCSTHTS) and one case is cascaded case of STHTS problem (CSTHTS). The results are compared with the results of the previous implementations of the other algorithms as presented in the literature. Due to the stochastic nature of the meta-heuristic algorithms, the parametric and non-parametric statistical tests have been implemented to establish the superiority of results of one type of algorithm over the results of the other type of algorithms.

Convex Relaxations of the Short-Term Hydrothermal Scheduling Problem

This paper concerns the assessment of two methods for convex relaxation of the short-term hydrothermal scheduling problem. The problem is originally formulated as a mixed integer programming problem, and then approximated using both Lagrangian and Linear relaxation. The two relaxation methods are quantitatively compared using a realistic data description of the Northern European power system, considering a set of representative days. We find that the Lagrangian relaxation approximates system operational costs in the range 55-81% closer to the mixed integer programming problem solution than the Linear relaxation. We show how these cost gaps vary with season and climatic conditions. Conversely, the differences in both marginal cost of electricity and reserve capacity provided by the Lagrangian and Linear relaxation are muted.

Scheduling of Hydrothermal System Considering Variable Nature of Water Transportation Delay

This paper presents solution of short-term hydrothermal scheduling problem using an algorithm called Grasshopper optimization. The objective of hydrothermal scheduling is to reduce the total cost of generation by optimizing the output of power generation of different thermal and hydro plants for a certain time interval. A non-linear relationship between hydropower generation, net head and rate of water discharge is considered here. The complicated head-sensitive water-to-power conversion and piecewise output limit is also considered. To investigate the performance of this new technique, two test systems have been considered. The simulation results are compared with some well-known optimization methods such as Genetic algorithm, Biogeography based optimization, hybrid Differential evolution with Biogeography based optimization and Grey wolf optimizer algorithm. The simulation results show the superiority of this technique as compared to other well-known optimization methods.

Optimal short-term hydro-thermal scheduling using multi-function global particle swarm optimization

<p>An optimal short-term hydro-thermal scheduling (ST-HTS) problem is solved in this paper using the multi-function global particle swarm optimization (MF-GPSO). A multi-reservoir cascaded hydro-electric system with a non-linear relationship between water discharge rate, power generation and net head is considered in this paper. The ST-HTS problem determines the optimal power generation of hydro and thermal generators which is aimed to minimize total fuel cost of thermal power plants during a determined time period. Effects of valve point loading and prohibited operating zones in the fuel cost function of the thermal power plants is examined. Power balance, reservoir volume, water balance and operation constraints of hydro and thermal plants are considered. The effectiveness and feasibility of MF-GPSO algorithm is examined on a standard test system, and the simulation results are compared with other algorithms presented in the literature. The results show that the MF-GPSO algorithm appears to be the best in terms of convergence speed and optimal cost compared with other techniques reported in the literature.</p>

Modified Social Group Optimization—a meta-heuristic algorithm to solve short-term hydrothermal scheduling

Social Group Optimization (SGO), developed by Satapathy et al. in the year 2016, is a class of meta-heuristic optimization inspired by social behavior. It has two phases: improving phase and acquiring phase. In the improving phase, each individual improves its knowledge by interacting with the best person/solution and in acquiring phase, the individuals interact with randomly selected individuals and the best person simultaneously to acquire knowledge. Modified Social Group Optimization (MSGO) is the improved version of SGO, where the acquiring phase is modified. A self-awareness probability factor is added in the acquiring phase, which enhances the learning capability of an individual from the best-learned person in the societal setup. It is observed that this modification has improved both exploration and exploitation abilities in comparison with the conventional SGO. To analyze the performance of the MSGO, an exhaustive performance comparison is made with GA, PSO, DE, ABC, and a few newer algorithms of the years 2010–2019. The results are tabulated in six experiments. Later, MSGO is applied to solve the short-term hydrothermal scheduling (HTS) problem. The central objective of the HTS problem is to ascertain the optimal plan of action for hydro and thermal generation minimizing the fuel cost of thermal plants and, at the same time satisfying various operational and physical constraints. The valve point loading effect related to the thermal power plants, transmission loss, and other constraints lead HTS as a complex non-linear, non-convex, and non-smooth optimization problem. Simulation results clearly show that the MSGO method is capable of obtaining a better solution.

Lightning attachment procedure optimization algorithm for nonlinear non-convex short-term hydrothermal generation scheduling

Short-term hydrothermal scheduling (STHS) is considered an important problem in the field of power system economics. The solution of this problem gives the hourly output of power generation schedule of the available hydro and thermal power units, which leads to minimization of the total fuel cost of thermal units for a given period of a time. The optimal generation of STHS is considered as a complicated and nonlinear optimization problem with a set of equality and inequality constraints such as the valve point loading effect of thermal units, the power transmission loss and the load balance. This paper proposes lightning attachment procedure Optimization (LAPO) algorithm for solving the nonlinear non-convex STHS optimization problem in order to minimize the operating fuel cost of thermal units with satisfying the operating constraints of the system. The performance of LAPO algorithm is validated using three different test systems considering the valve point loading effects of thermal units and the power transmission losses. The obtained results prove the effectiveness and superiority of LAPO algorithm for solving the STHS problem compared with other well-known optimization techniques.

Performance Analysis of APSO and Firefly Algorithm for Short Term Optimal Scheduling of Multi-Generation Hybrid Energy System

This paper presents a modified and novel form of the conventional short-term hydrothermal scheduling problem by incorporating the effects of adding the photovoltaic energy source to the conventional grid. A photovoltaic energy source is intermittent in nature, therefore, to determine the optimal power contribution of the photovoltaic source towards the economic dispatch problem, a detailed strategy is presented in this paper. The proposed design method includes the forecasting of the photovoltaic system’s parameters using the Auto-Regressive Integrated Moving Average (ARIMA) model. The analytical model is developed based on the fractional integral polynomials for studying the characteristics of the single photovoltaic module. The optimization of power allocation in the system consisting of conventional and non-conventional energy sources is highly non-linear and classical deterministic methods can not be guaranteed to determine the optimal solution for economic power dispatch. The global optima of such non-linear and non-convex problems can be determined using swarm-based intelligence techniques. This paper presents accelerated particle swarm optimization and the firefly algorithm to determine a solution for short-term non-linear scheduling problems. The multiple test cases have been presented to demonstrate the effectiveness of the proposed solution over classical methods. The overall generation cost of the selected hybrid system is reduced using the proposed methods while meeting the generation constraints of each energy source. Moreover, due to the stochastic nature of the meta-heuristic techniques, a comprehensive statistical comparison, based on the independent T-test results, is also presented to highlight the algorithm which performs better for selected scheduling problems. It has been demonstrated that accelerated particle swarm optimization gives lower mean generation cost of the system whereas the execution time of the firefly algorithm is better compared to its counterpart.