Dynamic Economic Dispatch Research Articles

Solving the Real Power Limitations in the Dynamic Economic Dispatch of Large-Scale Thermal Power Units under the Effects of Valve-Point Loading and Ramp-Rate Limitations

Few non-traditional optimization techniques are applied to the dynamic economic dispatch (DED) of large-scale thermal power units (TPUs), e.g., 1000 TPUs, that consider the effects of valve-point loading with ramp-rate limitations. This is a complicated multiple mode problem. In this investigation, a novel optimization technique, namely, a multi-gradient particle swarm optimization (MG-PSO) algorithm with two stages for exploring and exploiting the search space area, is employed as an optimization tool. The M particles (explorers) in the first stage are used to explore new neighborhoods, whereas the M particles (exploiters) in the second stage are used to exploit the best neighborhood. The M particles’ negative gradient variation in both stages causes the equilibrium between the global and local search space capabilities. This algorithm’s authentication is demonstrated on five medium-scale to very large-scale power systems. The MG-PSO algorithm effectively reduces the difficulty of handling the large-scale DED problem, and simulation results confirm this algorithm’s suitability for such a complicated multi-objective problem at varying fitness performance measures and consistency. This algorithm is also applied to estimate the required generation in 24 h to meet load demand changes. This investigation provides useful technical references for economic dispatch operators to update their power system programs in order to achieve economic benefits.

Solving dynamic economic and emission dispatch in power system integrated electric vehicle and wind turbine using multi-objective virus colony search algorithm

Climate change and development of today’s power grids have led to unprecedented changes in the old power grid in terms of fossil fuel consumption level and environmental pollution. So, the ancillary power plants and services have found a good position in power systems. In this paper, renewable energy generators such as wind energy units and plug-in electric vehicles (PEVs) are being integrated in the multi-objective dynamic economic emission dispatch (DEED) problem during a day, which minimizes wind-thermal electrical energy cost and emissions obtained by fossil-fueled power generators at the same time. To obtain a real-world problem, consider several practical and nonlinear constraints such as valve-point effect, ramp-up/ramp-down, prohibited zones, and power generation boundaries. Since the proposed multi-objective problem consists of different variables and constrains, the classical mathematic methods cannot guarantee finding the best solution. Therefore, this paper suggested a new multi-objective virus colony search (MOVCS) based on non-dominated sorting theory and fuzzy decision making for finding the best solution among Pareto fronts. Also, PEVs are remarkable and stochastic power demands and, unlike conventional demands, four dissimilar charging scenarios are considered. The efficiency of the proposed method and model is investigated on some test systems with the presence of wind units and electric vehicles during the day and night. The results are evaluated based on appropriate performance criteria. The results obtained from the proposed algorithm are compared with other algorithms, which indicates the efficiency, accuracy, and speed of this algorithm in solving the proposed problem.

Dynamic economic dispatch of wind-storage combined system based on conditional value-at-risk

Wind power's uncertainty is from the intermittency and fluctuation of wind speed, which brings a great challenge to solving the power system's dynamic economic dispatch problem. With the wind-storage combined system, this paper proposes a dynamic economic dispatch model considering AC optimal power flow based on Conditional Value-at-Risk (CVaR). Since the proposed model is hard to solve, we use the big-M method and second-order cone description technique to transform it into a trackable mixed-integer second-order conic programming (MISOCP) model. By comparing the dispatching cost of the IEEE 30-bus system and the IEEE 118-bus system at different confidence levels, it is indicated that CVaR method can adequately estimate dispatching risk and assist decision-makers in making reasonable dispatching schedules according to their risk tolerance. Meanwhile, the optimal operational energy storage capacity and initial/final energy storage state can be determined by analyzing the dispatching cost risk under different storage capacities and initial/final states.

Enhanced emperor penguin optimization algorithm for dynamic economic dispatch with renewable energy sources and microgrid

In this paper, an enhanced version of the emperor penguin optimization algorithm is proposed for solving dynamic economic dispatch (DED) problem incorporating renewable energy sources and microgrid. Dynamic economic load dispatch optimally shares the power on an hourly basis for a day among the committed generating units to satisfy the feasible load demand. Emission of pollutants from the combustion fossil fuel and gradual depletion of fossil fuel encourages the usage of renewable energy sources. Implementation of renewable energy sources with the reinforcement of green energy transforms the fossil fuel-based plant into a hybrid generating plant. The increase in power production with the increase in electricity demand implicates challenges for economical operation. The proposed algorithm is applied to the DED problem for fossil fuel based and renewable energy system to find economic schedule of generated power among the committed generating units. The proposed optimization algorithm is inspired by the huddling behavior of the emperor penguin. The exploration strategy is enhanced by adapting oppositional based learning. Chaotic mapping is used to maintain a proper balance between exploration and exploitation in the entire search space, which minimizes the cost of generation in the power system.

A Modified Teaching—Learning-Based Optimization for Dynamic Economic Load Dispatch Considering Both Wind Power and Load Demand Uncertainties With Operational Constraints

Dynamic economic load dispatch (DELD), which determines the best generation scheduling for different power plants during the next 24 hours in order to meet the electricity demand as well as minimize the total energy cost, is a highly complex non-linear and non-convex problem. This study proposes an efficient modified teaching-learning-based optimization algorithm, called MTLBO, to effectively solve the DELD optimization problem in a power system containing thermal generations and wind power. The planning problem comprises the total fuel cost function with valve-point loading effect and the transmission power losses. Also, the uncertainties of wind power and load demand along with the various equality and inequality operational constraints such as power generation limits, ramp rate limits, prohibited operating zones and power balance are considered in the problem. Additionally, in the proposed MTLBO algorithm, the learning phase is properly integrated into the teaching phase to improve the convergence characteristic of the original TLBO. Moreover, in order to enhance the feature of local optima avoidance, interaction of up to five students are incorporated into the learning phase to improve the knowledge of each student. To exhibit the effectiveness of the proposed approach, the algorithm is applied into the 14 real test functions. In addition, several cases with 10 and 30 unit test systems are investigated over the planning period. Compared to the main TLBO algorithm which is mostly used optimization algorithms proposed in prior studies, the simulation results demonstrate the efficiency and superiority of the proposed optimization approach in terms of consistency, robustness, convergence rate and finding better plausible optimal solutions.

Integrated solution for optimal generation operation efficiency through dynamic economic dispatch on Software Technological Park of India

The study aimed to identify the contribution made by the STPI units towards Indian GDP and determine the forecasting model. Further, the study investigates the relationship existing between No. of Units and its export contribution. The researchers adopted an analytical research design. Herein data published by STPI were considered. The data analysis was conducted for the period (2002 to 2018). From the analysis performed it was found that over the 17 years (2002–2018) on an average export worth 196305.3529 Crore Rs. Is exported from Software Technological Park (STP) units. Similarly, on an average export worth 8216.2941Crore Rs. Is exported from Electronic Hardware Technological Park (EHTP) units. Also, it is understood that there is a strong positive relationship No. of registered STP and EHTP i.e. when No. of STP units increases correspondingly the No. of EHTP units also increases. Similarly, there is a positive relationship between total export by STP and EHTP i.e. when the export value of STP units increases correspondingly the export value of EHTP units also increases. Furthermore, there is a strong positive relationship No. of registered STPI and Export Value of STPI units i.e. when No. of STPI units increases correspondingly the Export value from STPI units also increases. Among the various foresting regression models, the cubic regression model is found to be best suited to forecast STP total export value. As per the forecast, during the year 2021 and 2022 the STP units will export value worth 462784 Crores Rs. And 498,687 Crores Rs respectively. Similarly, among the various foresting regression models, the power regression model is found to be best suited to forecast EHTP total export value. As per the forecast, during the year 2021 and 2022 the EHTP units will export value worth 15,210 Crores Rs. And 15,905 Crores Rs respectively. It was also perceived that Total Exports by STPI Units influences the GDP of India.

Multi-objective dynamic economic dispatch using Fruit Fly Optimization method

An essential task of the interconnected power system is about how to optimize power plants during operation time which is known as economic dispatch. In this study, the Fruit Fly Optimization method is proposed to solve problems of dynamic economic dispatch in an electrical power system. To measure the performance of the method, a simulation was conducted for two different electric systems of the existing Sulselbar 150 kV thermal power plant system in Indonesia with two objective functions, namely fuel costs and active power transmission losses, as well as the 30-bus IEEE standard system with five objective functions namely fuel costs, transmission losses (active and reactive power), a reactive power reserve margin, and an emission index by considering a power generation limit and ramp rates as the constraints. Under tested cases, the simulation results have shown that the Fruit Fly Optimization method can solve the problems of dynamic economic dispatch better than other existing optimization methods. It is indicated by all values of the objective functions that are lowest for the Fruit Fly Optimization method. Moreover, the obtained computational time is sufficiently fast to get the best solution

Dynamic economic dispatch problem in hybrid wind based power systems using oppositional based chaotic grasshopper optimization algorithm

This article introduces a relatively current method named grasshopper optimization algorithm (GOA) for explaining power system based dynamic economic load dispatch (DELD) problem. However, like other optimization approaches, GOA suffers from premature convergence and a slow convergence rate. Thus, to boost the convergence mobility of GOA, oppositional based learning (OBL) is merged with the GOA approach. Moreover, another improvization, namely, chaotic concept, is also integrated with the GOA to improve its solution quality. The suggested oppositional based chaotic grasshopper optimization algorithm (OCGOA) method is applied to handle the DELD problem in the most efficient manner. Among the renewable energies, intermittent wind energy (WE) is the most sustainable one and remains technically and economically advantageous for electrical energy generation. The thermal and wind based power systems are hybridized, so that power generation is distributed among the operating units in an equivalent manner such that overall cost and loss part are optimized until all practical constraints are fulfilled. The production cost of the unpredictable wind generation power is further incorporated in the operational cost by employing a probability density function (PDF) formula. The precision and performance of the suggested GOA and OCGOA approaches are validated on 6-unit and 10-unit DELD systems for conventional and wind based energy systems. The efficacy and performance of the suggested OCGOA is judged by comparing it with conventional GOA and other presently developed meta-heuristic optimization techniques found in the literature.

Simulated Annealing Algorithm for Dynamic Economic Dispatch Problem in the Electricity Market Incorporating Wind Energy

In this paper, a bid-based dynamic economic dispatch (BBDED) problem is solved in the electricity market system under bidding strategies, including wind energy penetration using simulated annealing (SA) algorithm. The multi-objective dispatch model allows generating companies (GENCOs) and their customers to submit supply and demand bids to a market controller known as the independent system operator (ISO) and follow a bidding strategy. ISO is responsible for the market clearing and settlement to maximize the social profit and benefit for GENCOs and customers during trading periods. To study the effect and advantages of wind energy integration in the BBDED problem, the wind energy generation is computed using the forecasted wind speeds and included in the dispatch model. In this regard, the ISO's dispatch model is formulated as a bilevel nonlinear optimization problem. The higher-level is solving the market-clearing with and without wind energy, and the lower level is maximizing GENCO's social profit. The proposed SA algorithm is evaluated for optimality, convergence, robustness, and computational efficiency tested on an IEEE 30-bus test system. The simulation results are compared with those found using different algorithm-based approaches, considering various constraints like power balancing, generator limits, ramp rate limits, and transmission losses.

An agile and intelligent dynamic economic emission dispatcher based on multi-objective proximal policy optimization

The recent development in power systems claims the improvement of the efficiency to solve dynamic economic emission dispatch (DEED) problem. However, the popular pure optimization framework based on evolutionary algorithms only starts the compute-intensive optimization process after receiving the power demand, which causes significant delays To address this limitation, this research defines a novel dynamic economic emission dispatcher (DEEDer) problem and the dispatcher learning framework. It is different from previous research and the most current algorithms in the advantage of transferring the on-line compute-intensive optimization task to off-line. To solve the dispatcher, we model the dispatching process as a conditional deterministic Markov Decision Process (MDP) and propose the multi-objective proximal policy optimization (MOPPO). The Benchmark Test Set with 10,000 different dispatching tasks for 5-unit and 10-unit system is released to evaluate the generalization of the dispatcher. The experiment results indicate that the neural network dispatcher trained with MOPPO is hundreds to thousands of times faster than the state-of-the-art pure optimization algorithms. Meanwhile, the dispatcher not only has comparable performance as the state-of-the-art multi-objective optimization algorithms in standard dispatching task but also shows generalization on generating Pareto optimal solutions given any possible dispatching task. Following the DEEDer framework, the proposed method makes it possible to dispatch power in a more agile way as the timely response to the changing of power demand while still controlling economic and emission.

Teaching-Learning-Based Optimization Algorithm for the Combined Dynamic Economic Environmental Dispatch Problem

The Dynamic Economic Environmental Dispatch Problem (DEEDP) is a major issue in power system control. It aims to find the optimum schedule of the power output of thermal units in order to meet the required load at the lowest cost and emission of harmful gases. Several constraints, such as generation limits, valve point loading effects, prohibited operating zones, and ramp rate limits, can be considered. In this paper, a method based on Teaching-Learning-Based Optimization (TLBO) is proposed for dealing with the DEEDP problem where all aforementioned constraints are considered. To investigate the effectiveness of the proposed method for solving this discontinuous and nonlinear problem, the ten-unit system under four cases is used. The obtained results are compared with those obtained by other metaheuristic techniques. The comparison of the simulation results shows that the proposed technique has good performance.

Solving Bid-Based Dynamic Economic Dispatch in Competitive Electricity Market Using Improved Simulated Annealing Algorithm

Electricity markets are open after the deregulation of power systems due to competition. An optimization problem based on dynamic economic dispatch has recently come up in the new context of deregulated power systems known as bid-based dynamic economic dispatch (BBDED). It is one of the major operations and control functions in the electricity markets used to determine the optimal operations of market participants with scheduled load demands during a specified period. BBDED involves power generation companies (GENCOs) and customers to submit energy and price bids to the independent system operator (ISO) in a day-ahead market. The ISO clears the market with the objective of social profit maximization. In this paper, a BBDED problem is solved using an improved simulated annealing algorithm (ISA), including system constraints with different periods under bidding strategies. The proposed ISA technique is implemented in MATLAB and applied on a 3-unit system, a 6-unit system, and a 40-unit large-scale system. The proposed ISA is evaluated by comparison with relevant methods available in the literature, to demonstrate and confirm its potential in terms of convergence, robustness, and effectiveness for solving the BBDED problem.

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.

Dynamic economic emission dispatch of thermal-wind-solar system with constriction factor-based particle swarm optimization algorithm

PurposeDynamic economic and emission dispatch (DEED) aims to optimally set the active power generation with constraints in a power system, which should target minimum operation cost and at the same time minimize the pollution in terms of emission when the load dynamically changes hour to hour. The purpose of this study is to achieve optimal economic and emission dispatch of an electrical system with a renewable generation mix, consisting of 3-unit thermal, 2-unit wind and 2-unit solar generators for dynamic load variation in a day. An improved version of a simple, easy to understand and popular optimization algorithm particle swarm optimization (PSO) referred to as a constriction factor-based particle swarm optimization (CFBPSO) algorithm is deployed to get optimal solution as compared to PSO, modified PSO and red deer algorithm (RDA).Design/methodology/approachDifferent model with and without wind and solar power generating systems; with valve point effect is analyzed. The thermal generating system (TGs) are the major green house gaseous emission producers on earth. To take up this ecological issue in addition to economic operation cost, the wind and solar energy sources are integrated with the thermal system in a phased manner for electrical power generation and optimized for dynamic load variation. This DEED being a multi-objective optimization (MO) has contradictory objectives of fuel cost and emission. To get the finest combination of the two objectives and to get a non-dominated solution the fuzzy decision-making (FDM) method is used herein, the MO problem is solved by a single objective function, including min-max price penalty factor on emission in the total cost to treat as cost. Further, the weight factor accumulation (WFA) technique normalizes the pair of objectives into a single objective by giving each objective a weightage. The weightage is decided by the FDM approach in a systematic manner from a set of non-dominated solutions. Here, the CFBPSO algorithm is applied to lessen the total generation cost and emission of the thermal power meeting the load dynamically.FindingsThe efficacy of the contribution of stochastic wind and solar power generation with the TGs in the dropping of net fuel cost and emission in a day for dynamic load vis-à-vis the case with TGs is established.Research limitations/implicationsCost and emission are conflicting objectives and can be handled carefully by weight factors and penalty factors to find out the best solution.Practical implicationsThe proposed methodology and its strategy are very useful for thermal power plants incorporating diverse sources of generations. As the execution time is very less, practical implementation can be possible.Social implicationsAs the cheaper generation schedule is obtained with respect to time, cost and emission are minimized, a huge revenue can be saved over the passage of time, and therefore it has a societal impact.Originality/valueIn this work, the WFA with the FDM method is used to facilitate CFBPSO to decipher this DEED multi-objective problem. The results reveal the competence of the projected proposal to satisfy the dynamic load demand and to diminish the combined cost in contrast to the PSO algorithm, modified PSO algorithm and a newly developed meta-heuristic algorithm RDA in a similar system.

An enhanced multi‐objective differential evolution algorithm for dynamic environmental economic dispatch of power system with wind power

AbstractDynamic environmental economic dispatch (DEED) with wind power is an important extension of the classical environmental economic dispatch (EED) problem, which could provide reasonable scheduling scheme to minimize the pollution emission and economic cost at the same time. In this study, the combined dynamic scheduling of thermal power and wind power is carried out with pollutant emission and economic cost as optimization objectives; meanwhile, the valve‐point effect, power balance, ramp rate, and other constraints are taken into consideration. In order to solve the DEED problem, an enhanced multi‐objective differential evolution algorithm (EMODE) is proposed, which adopts the superiority of feasible solution (SF) and nondominated sorting (NDS) two selection strategies to improve the optimization effect. The suggested algorithm combines the total constraint violation and penalty function to deal with various constraints, due to different constraint techniques could be effective during different stages of searching process, and this method could ensure that each individual in the Pareto front (PF) is feasible. The results show that the proposed algorithm can deal with DEED problem with wind power effectively, and provide better dynamic scheduling scheme for power system.

The Dynamic Economic Dispatch in An Integrated Wind-Thermal Electricity Market Using Simulated Annealing Algorithm

The Dynamic Economic Dispatch in An Integrated Wind-Thermal Electricity Market Using Simulated Annealing Algorithm

A Novel Distributed Dynamic Economic Dispatch Based on Dual ADMM and IPM

This paper presents a novel distributed method for dynamic economic dispatch (DED) problems with cubic fuel cost functions based on the dual alternating direction method of multipliers (D‐ADMM) and interior point method (IPM). This scheme enables us to combine the excellent parallelism of ADMM with the superior convergence properties of the IPM. The idea adopted by the proposed algorithm is that the outer‐loop uses ADMM decoupling, and the inner‐loop uses IPM to solve the cubic polynomial optimization subproblems. When the unit set is divided into multiple partitions, D‐ADMM also has the nice central processing unit (CPU) runtime as the well as the number of iterations. In addition, we use a Decoupling‐Decomposition‐Backtracking and parallel improved multiple centrality corrections decoupling interior point method (DDB‐PIMCCD) to solve the aforementioned larger subproblems more efficiently. Finally, the numerical results, in both serial and parallel modes, on a set of 22 DED cases with the range of units from 8 to 1000 units show that the proposed method is very promising for large scale distributed DED problems. Because it can keep the unit information about each subset in secret to suit the market environment and can obtain high‐quality solutions with reasonable time. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Distributed fixed step-size algorithm for dynamic economic dispatch with power flow limits

In this study, a discrete-time distributed algorithm is proposed for solving the dynamic economic dispatch problem with active power flow limits and transmission line loss. To avoid the communication burden and implement the algorithm in a favorably distributed manner, the splitting method is used to bypass the centralized updating of the algorithms parameters, which is unavoidable when implementing conventional Lagrangian methods. The use of a fixed step-size and distributed update enhances the applicability of the algorithm. The performance and effectiveness of the proposed distributed algorithm are verified via numerical studies on the IEEE 14-bus system.

Reserve constrained dynamic economic dispatch in multi-area power systems: An improved fireworks algorithm

The multi-area economic dispatch (MAED) plays a major role in an interconnected power system to determine the generation dispatch strategy and satisfy the load demands as well as the technical constraints. Tie-line capacity between different areas, upper/lower generation limits, generator ramp rates, transmission losses, valve point effect, disjoint prohibited zones as well as spinning reserve are considered as the MAED problem constraints. Due to hourly load variations, the MAED problem should be solved dynamically to coincide the realistic conditions which build up the multi-area dynamic economic dispatch (MADED) problem. Considering these constraints besides the intertemporal constraints which depends to the optimal conditions of each hour with respect to other time steps may increase the problem complexity. In this regard, an improved version of fireworks algorithm which is equipped with two effective cross-generation mutation strategies is deployed to handle the non-linear, non-smooth, non-convex, multi-dimensional and multi-constraints MADED problem. Furthermore, a new constraint handling scheme is developed to correct the potential solutions in feasible search space. Finally, two small and large systems are used to investigate the capability of the developed algorithm in finding the global or near-global optima.

A novel disruption based symbiotic organisms search to solve economic dispatch

Economic dispatch (ED) is one of the vital prospects in the energy management system for determining the optimal power generation distribution among several committed power generating units. The objective of ED is to generate the electric power to meet the load demand by minimizing the total operating cost subjected to various equality and inequality constraints. This ED problem is generally solved using conventional techniques such as a gradient method by assuming the objective function as linear and convex. However, in general, the ED problem is constrained, non-convex, large scale, multimodal and highly nonlinear optimization problem. In order to overcome this drawback, various heuristic techniques have been introduced in the literature. Symbiotic organism search (SOS) is one of the emerging nature-inspired meta-heuristic algorithms. Due to simple in implementation and free from algorithm-specific control parameters, the SOS algorithm has gained a reputation among the researchers. The SOS technique mimics the biological interaction between two distinct species to survive and proliferate in the ecosystem. To evade the suboptimal solution and to enhance the exploration and exploitation of the SOS algorithm, the disruption operator is integrated with the basic SOS to form a novel disruption based SOS (DSOS) algorithm. The disruption strategy is originated from astrophysics and has the ability to shift between exploration and exploitation during the process of finding an optimum solution. To illustrate the effectiveness of the proposed method, it is applied on various test systems such as 3-unit, 5-unit, 6-unit, 13-unit, 20-unit, 38-unit, and 110-unit systems to solve different ED problems, namely, without transmission losses (TL), with transmission losses, by simultaneously considering valve point loading (VPL) effect along with TL, by simultaneously considering the effect of ramp rate limits (RRLs), prohibited operating zones (POZs) and TLs, and dynamic economic load dispatch by considering RRLs, POZs, VPL, and TL. The comparison of DSOS based simulation results with other methods reveal the efficiency and robustness of the proposed method to provide minimum total generation cost in all the cases with better convergence rate and less computational time.