Power System Economic Dispatch Research Articles

Optimal replacement of coal with wind and battery energy storage

Abstract Electric utilities are considering replacing their coal power plants with renewables and energy storage to reduce emissions. However, they have also expressed concerns about operational changes and system reliability brought by these replacements. Utilities in remote rural areas face more challenges as they also face energy insecurity while having limited interconnections to wider systems and reliance on imported fuels. Therefore, it is critical for remote utilities to understand different coal replacement approaches and their impacts on system expansion, operation and energy security. In this paper, we define and investigate three approaches to replace coal using wind and batteries: 1) replacing exact coal generation, 2) replacing at least coal generation, and 3) replacing total energy provided by coal. We develop a case study inspired by the small remote grid in Fairbanks, Alaska, which has a single limited interconnection with the grid south of it. We utilize a power system expansion and economic dispatch model that co-optimizes the capacities of wind and batteries required for each approach and the hourly dispatch of energy and reserves for one year. We further analyze the operational cost variability under fixed and fluctuating fuel prices. We find that replacing the exact coal generation requires minimal operational changes, but also significantly more wind and battery capacities. In contrast, replacing total energy provided by coal induces more cycling in other resources, challenging grids with limited flexibility-providing resources. However, replacing total energy provided by coal allows more generation variability in response to fuel price fluctuations, enhancing energy security.

Solving power system economic emission dispatch problem under complex constraints via dimension differential learn butterfly optimization algorithm with FDC-based

The economic emission dispatch (EED) aims to minimize the fuel and pollutant emission costs of generator units under various complex constraints. Optimizing the EED problem is of crucial importance for alleviating the current energy and environmental pressures. In this work, nearly all known complex constraints in the EED problem, including the valve-point effect, transmission line power loss, prohibited operating zones, and ramp-rate limits, are taken into account, and an enhanced version of butterfly optimization algorithm (FDCDLBOA) is proposed to solve it. First, a new adaptive fragrance is employed to optimize the instability caused by target differences and improve the convergence performance. Second, the proposed dimension differential learning strategy evolves the position of individuals with the help of superior dimensional information in the population, and this extensive learning exchange can balance global and local search, maintain diversity, and get rid of local optima. Third, the Fitness-Distance-Constraint (FDC) guide selection method is employed for the first time to handle the complex constraints of EED problems, enhancing the ability of individuals to bypass the infeasible search areas. After evaluating the proposed FDCDLBOA on CEC 2022 test suite, it is applied to solve 8 EED cases, encompassing small-, medium- and large-scale systems. Notably, the 280-generator case is the first large-scale test to exceed 200 generators. Compared with 9 representative algorithms, FDCDLBOA performs outstandingly in terms of robustness, improvement index (IF), mean constraint violation (MV), feasibility rate (FR) and Quade multiple comparison, among which IF, MV, FR, and Quade are all employed for evaluating the EED problem for the first time. The presented results confirm that the proposed method effectively enhances the robustness of high-quality solutions and the ability to handle complex constraints, demonstrating strong competitiveness and potential in solving the EED problem.

Security-constrained economic dispatch of power systems with line outage using firefly algorithm

The Security-constrained Economic Dispatch (SCED) problem is the problem of finding the optimal generation dispatch for a power system that minimizes the operating cost while ensuring the security of the system. The security of the system is defined as the ability of the system to withstand disturbances without violating any operational constraints. Line outage is a common disturbance that can affect the security of a power system. The Firefly Algorithm, inspired by the flashing behavior of fireflies in nature, is a metaheuristic optimization technique known for its effectiveness in solving complex and dynamic optimization problems. In this study, the FA is adapted to the SCED problem with a specific focus on enhancing grid resilience during line outage scenarios. The proposed method aims to simultaneously optimize the economic cost of power generation and the system's ability to withstand line outages. To demonstrate the effectiveness of the proposed approach, extensive simulations are conducted on standard IEEE test systems with varying degrees of complexity and network sizes. The results showcase the superior performance of the SCEDL-Firefly Algorithm compared to traditional optimization methods, as it provides a resilient dispatch solution that can effectively adapt to unexpected line outages while maintaining economic efficiency. Overall, this research contributes to the advancement of secure economic dispatch techniques and power system resilience by leveraging the Firefly Algorithm's capabilities. The findings offer valuable insights for power system operators and planners seeking to enhance grid reliability in the presence of line outages, ultimately promoting a more sustainable and resilient energy infrastructure.

Joint bidding strategy of multi‐virtual power plant operators

AbstractThe distributed generation of new energy can effectively use the local endemic clean new energy and provide green power. However, due to the small scale and scattered layout of distributed generation resources, it is difficult to participate in the economic dispatch of power systems and even the competition of the power market. Virtual Power Plant (VPP) can act as a carrier of Distributed Energy Resource (DER) to manage its internal energy, to carry out combined bidding in the day‐ahead energy market and the regulation market. When virtual power plants coordinate multiple distributed energy resources to participate in electricity market transactions, the degree of disclosure of their internal privacy information will produce different trading strategies. A Stackelberg game model between multiple virtual power plant aggregators and virtual power plant operators is constructed, and the Kriging model is combined to protect the privacy information in the transactions of virtual power plant operators. Energy management for distributed generation is carried out, and the profit situation of virtual power plant operators under different strategies is analyzed.

Application on power system economic dispatch of marine predator algorithm improved by asymmetric information exchange

The solution to the economic dispatch (ED) problem for power systems allows the power sector to reduce operating costs. However, the ED problem is a complex nonlinear and nonconvex optimization problem whose solution requires powerful algorithms. We propose a new version of the Marine Predator Algorithm (MPA), called IMPA, for solving complex ED problems. The algorithm introduces an asymmetric information exchange (AIE) mechanism, which not only accelerates to escape of local optima but also enriches the diversity of search. In this work, 12 benchmark functions were used to test the performance of the proposed algorithm IMPA. Then, the IMPA was used to solve the ED engineering problem of power system containing of 6, 13, 40, and complex 140 units. The minimum and average costs searched by IMPA are 1657962.7265$/h and 1657962.7265$/h, and they are much lower than the results of the MPA and NMPA, which means that our proposed improved IMPA improves the performance of MPA for solving the economic dispatch problem of large-scale power systems. The results show that the solutions obtained by IMPA are more competitive than those of MPA and NMPA, which provides an additional solution for cost reduction of the power system.

Decentralized Multi-Area Economic Dispatch in Power Systems Using the Consensus Algorithm

A multi-area power system requires coordination to enhance reliability and reduce operating costs. Economic dispatch in such systems is crucial because of the uncertainties associated with variable loads and the increasing penetration of renewable energy sources. This paper presents a hierarchical consensus algorithm designed to determine the economic dispatch in a multi-area power system, accounting for the uncertainties in load and renewable generation. The proposed algorithm, which utilizes distributed agents, operates across three levels. Level 1 coordinates all areas, while levels 2 and 3 form a leader–follower consensus algorithm for overall economic dispatch. Breadth-first search is employed to identify the leader agent within each area. To address the uncertainties in loads and renewable generation, Monte Carlo simulations are performed. The efficacy of the proposed method is validated using the IEEE 39-bus and 118-bus systems, as well as a realistic 1968-bus power system in Taiwan. The traditional equal lambda method is employed to verify that the proposed approach is suitable for multi-area power systems using distributed computation.

The Information Security Issues of Distributed Economic Dispatch for New Generation Power Systems—Present Situation and Forecast

With the large scale and high proportion of distributed generation connected to the power grid, the distributed economic dispatch system has attracted more attention because of its significant advantages. However, the distributed economic dispatch system faces more serious information security issues due to the variation of communication topology. Therefore, the purpose of this paper is to review the information security issues that may occur in the distributed economic dispatch system and the defense measures. By summarizing the existing literature on information security issues and defense measures, it can be found that the current research focuses on the cyber-side defense for information security, and lacks consideration of the cyber-physical coupling characteristics. Additionally, the separate cyber-side defense measures still have a defense blind spot and cannot respond in a timely manner to the physical-side actions caused by information security issues. Finally, the establishment of the information security issues model and the construction of the integrated security defense system are discussed from the perspective of the power cyber-physical system. This research will be helpful in the construction of the security defense system for information issues in distributed economic dispatch systems.

Hierarchical deep reinforcement learning for self-adaptive economic dispatch

It is challenging to accurately model the overall uncertainty of the power system when it is connected to large-scale intermittent generation sources such as wind and photovoltaic generation due to the inherent volatility, uncertainty, and indivisibility of renewable energy. Deep reinforcement learning (DRL) algorithms are introduced as a solution to avoid modeling the complex uncertainties and to adapt the fluctuation of uncertainty by interacting with the environment and using feedback to continuously improve their strategies. However, the large-scale nature and uncertainty of the system lead to the sparse reward problem and high-dimensional space issue in DRL. A hierarchical deep reinforcement learning (HDRL) scheme is designed to decompose the process of solving this problem into two stages, using the reinforcement learning (RL) agent in the global stage and the heuristic algorithm in the local stage to find optimal dispatching decisions for power systems under uncertainty. Simulation studies have shown that the proposed HDRL scheme is efficient in solving power system economic dispatch problems under both deterministic and uncertain scenarios thanks to its adaptation system uncertainty, and coping with the volatility of uncertain factors while significantly improving the speed of online decision-making.

Power Load Forecast Based on CS-LSTM Neural Network

Load forecast is the foundation of power system operation and planning. The forecast results can guide the power system economic dispatch and security analysis. In order to improve the accuracy of load forecast, this paper proposes a forecasting model based on the combination of the cuckoo search (CS) algorithm and the long short-term memory (LSTM) neural network. Load data are specific data with time series characteristics and periodicity, and the LSTM algorithm can control the information added or discarded through the forgetting gate, so as to realize the function of forgetting or memorizing. Therefore, the use of the LSTM algorithm for load forecast is more effective. The CS algorithm can perform global search better and does not easily fall into local optima. The CS-LSTM forecasting model, where CS algorithm is used to optimize the hyper-parameters of the LSTM model, has a better forecasting effect and is more feasible. Simulation results show that the CS-LSTM model has higher forecasting accuracy than the standard LSTM model, the PSO-LSTM model, and the GA-LSTM model.

A Review on Economic Dispatch of Power System Considering Atmospheric Pollutant Emissions

The environmental/economic dispatch (EED) of power systems addresses the environmental pollution problems caused by power generation at the operational level, offering macroscopic control without requiring additional construction and remediation costs, garnering widespread attention in recent years. This paper undertakes a comprehensive review of existing EED models, categorizing them according to the control of atmospheric pollutants into total air pollutant control (TAPC) and control considering the spatial and temporal diffusion (STD) of atmospheric pollutants. In addition, various methods employed to address the EED problems, as well as the current state of research on multi-area EED models, are presented. Finally, this paper analyzes and summarizes the literature on existing EED models, highlighting the deficiencies of the current work and future research directions. Through these explorations, the authors find that controlling the EED model by considering TAPC is more suitable for general macro planning, whereas the EED model considering the STD of air pollutant emissions enables more precise and effective control. Summarizing such models and techniques is conducive to developing dispatch plans adapted to local conditions, which is significantly beneficial for public welfare and government management, promoting sustainable and environmentally friendly power system dispatch methods.

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Low-carbon economic dispatch of power systems considering synergistic operation of carbon capture and electric hydrogen production

Low-carbon economic dispatch of power systems considering synergistic operation of carbon capture and electric hydrogen production

Quantum‐Behaved Particle Swarm Optimization Based on Concentration Selection Probability Assignment Weights for Power System Economic Dispatch

The economic dispatch (ED) problem is very important in the economics of power systems, and a suitable dispatch algorithm can help power plants save huge amounts of money and use energy efficiently. To ensure the economics of the power system dispatch strategy, this paper proposes a quantum‐behaved particle swarm improvement algorithm for solving the ED problem. First, the algorithm addresses the problem that the classical quantum‐behaved particle swarm optimization (QPSO) tends to be premature and falls into local optimality. We propose a method to calculate the mean best position by assigning weights to different particles, by adopting the idea of concentration selection in the immune concentration regulation mechanism, and designing a Weight‐Concentration selection probability function, so that those particles located outside the local optimal solution region but with smaller fitness value and better evolutionary trend can be retained. Second, to make the algorithm focus on global search at the beginning of the iteration and more focused search at the end to enhance the neighborhood search capability at the later stage, a decreasing function of the slope K in the Weight‐Concentration selection probability function is designed so that the influence of the weighting term on the calculation of the mean best position decreases gradually. The algorithm is evaluated with four power systems, and the results show that the overall performance of the improved algorithm is better than other algorithms in solving the ED problem in terms of minimum solution, convergence, and stability. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

An innovative interpretable combined learning model for wind speed forecasting

Wind energy is taken as one of the most potential green energy sources, whose accurate and stable prediction is important to improve the efficiency of wind turbines as well as to guarantee the power balance and economic dispatch of power systems and equipment safety. However, the random and fluctuating nature of wind speed poses a great risk to wind power grid connections. To address the issues of low prediction performance and lack of interpretable analysis in most past studies, this research proposes an interpretable combined learning model for wind speed time series prediction by combining linear models, different neural networks, and deep learning by introducing interpretable TFT models. To test the effectiveness of the forecasting models, the presented combined model is verified using eight wind speed datasets covering four seasons collected from two wind farms in Shaanxi, China. The experimental results show that the average root mean squared error of the one-step, two-step, and three-step predictions on the eight datasets for proposed model are 0.3448, 0.4586 and 0.6164, respectively, which are much better than the six single models and the six combined models with different strategies. And proposed model outperforms the single model and combined model in most cases, with 86.80% and 92.01% of the DM values greater than the corresponding critical values when the significance level is set to 0.01 and 0.1, respectively. Finally, the proposed model is discussed and analyzed in depth through interpretability analysis of the combined model, which further validates the potential of the model and also provides a reference for other time series forecasting studies.

Parallel Dual-DQAM for Multi-Scenario Stochastic Economic Dispatch Model by Temporal and Scenario Decompositions

Large-scale multi-scenario stochastic economic dispatch (SED) is hard to directly solve due to the huge number of variables and constraints. To reduce the computational burden, a nested dual-DQAM (Diagonal Quadratic Approximation Method) is proposed in this paper to decouple the SED problem in both scenarios and time periods, where each subproblem only contains one time period and one scenario. Moreover, these subproblems can be handled in parallel, such that the computational performance can be significantly improved. Besides, we have investigated the optimal policy to select the best parallel structure of the proposed dual-DQAM, and the theorical convergence performance is proved. Numerical results on several test systems show the effectiveness of the proposed dual-DQAM. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Nowadays, the safe operation and economic dispatch in power system are greatly challenged by the high penetration of renewable energy. Although the uncertainty of renewable energy can be well modeled by stochastic programming, the solution complexity will seriously increase due to the large number of typical scenarios. For this problem, the parallel solution using decomposition methods is the state-of-the-art strategy. In this paper, we propose an efficient solution to the multi-scenario SED problem by temporal and scenario decompositions. It realizes an important innovation in both reducing the computational burden and improving the solving efficiency, which greatly promotes the application of SED in large-scale systems. To better use this method, the following two properties should be highlighted: i) the proposed method has a convergence guarantee and works especially well on SED due to the sparsity property of linking constraint matrices. ii) the computational efficiency of the proposed method becomes more significant as the number of time periods and scenarios grows and can be further improved under a fast ramp rate.

Multimodal hierarchical distributed multi-objective moth intelligence algorithm for economic dispatch of power systems

The issue of economic dispatch in the context of environmental sustainability is more challenging with the integration of clean energy into the grid and the increase in the size of power systems. Power engineers have a responsibility to seek a novel algorithm that can hierarchically simplify the problem, enhance the diversity of solutions, balance economic and environmental goals, reduce the environmental footprint, and increase economic efficiency. In this paper, a multimodal hierarchical distributed multi-objective moth intelligence algorithm is proposed, combines the hierarchical distributed method with the moth algorithm, introduces the loose equivalence of multimodality, and adopts the Pareto curve partition processing and the extraction of objective points. The proposed method converts the information exchange of the adjacent regions of each layer and the optimization of each layer to be performed in the bottom layer, achieving the coordinated optimization of the whole system through the parallel optimization of the bottom layer regions. The simulation results show that: (1) the computational efficiency is improved. In the 118-bus system, the proposed algorithm reduces 0.13% cost and 5.76% carbon emission than distributed optimization; the proposed algorithm reduces 0.53% cost and 3.81% carbon emission than centralized optimization; (2) the speed of computation is accelerated. In the 1139-bus system, three-layer distributed optimization and two-layer distributed optimization of the proposed algorithm reduce the time by 62.64% and 37.22% than distributed optimization, respectively; (3) the performance metrics of the proposed method demonstrate superiority.

Multi‐stage stochastic dual dynamic programming to low‐carbon economic dispatch for power systems with flexible carbon capture and storage devices

AbstractThe carbon capture and storage (CCS) technique gains much attention due to its role in reducing CO2 emissions. By introducing flexible CCS devices into conventional power plants, the low‐carbon economic operation of the power system can be achieved. However, the uncertainty of renewable energy makes it hard to obtain an optimal operation policy. First, the detailed model of CCS consisting of bypass venting stacks, solvent storage tanks, absorber, and stripper is described. Then, a low‐carbon economic dispatch model of the power system with CCS is proposed to minimize the total operation and renewable energy abandonment penalty costs. Next, the problem is reformulated as multi‐stage stochastic programming, and the stochastic dual dynamic programming (SDDP) method is applied to relieve the computation burden. To control the probability of stopping the algorithm prematurely, a new stopping criterion based on a two‐sided hypothesis test is proposed. Finally, the effectiveness of the proposed model and the new stopping criterion is demonstrated by case studies on a practical power system.

Economy-carbon coordination in integrated energy systems: Optimal dispatch and sensitivity analysis

The acceleration of low carbon development and carbon emission reduction (CER) policies have compelled power systems to act and consider carbon emissions in their dispatches. To realize CER, power system economic dispatch has become more challenging. The integrated energy system (IES) can significantly reduce the production of carbon emissions. In light of this, this paper proposes a bi-objective optimization model to coordinate the operating cost and carbon emission of the IES and a sensitivity analysis approach to evaluate the impact of CER. First, the coupling relationship between energy and carbon in the IES is analyzed. Second, the bi-objective optimization model of the IES is proposed, in which the thermal inertia is embedded to provide operational flexibility. Third, three sensitivity metrics and the corresponding models are proposed to quantify the impact of global/local CER of IES, including the cost of global CER, the cost of local CER, and the sensitivity of local CER. Finally, the dispatch procedure and algorithm are introduced. Case studies demonstrate the effectiveness of the proposed method, in which the impact of thermal inertia and battery capacity on dispatch results and CER sensitivity is analyzed.

Modeling the Reserve Capacity of Wind Power and the Inherent Decision-Dependent Uncertainty in the Power System Economic Dispatch

The ever-increasing penetration of renewable generation is demanding additional flexibility for the operation of power systems. In this sense, it has been proved that wind power generators (WPGs) can provide part of the required operating reserve through pitch angle control (PAC) under a deloaded strategy. Unlike conventional operating reserve sources, however, the operating reserve provided by WPGs can't always be considered reliable, which renders the power system dispatch more challenging. In this research, the reserve capacity of the WPGs is modeled considering the decision-dependent uncertainty (DDU). The random wind speed introduces uncertainty to the available reserve capacity of the WPGs while the decisions on the deloading degrees of the WPGs directly affect their coefficients between wind speed and usable wind power, making the uncertainty decision-dependent. Moreover, the operational technical limits of the WPGs and the multiple possible wind speed scenarios are also considered in the wind power reserve capacity modeling. Then, a two-stage reliability constrained stochastic economic dispatch model with WPGs' reserve provision (SED-WRP) is developed to jointly dispatch the generation and reserve. A group-based multi-cut Benders decomposition method is applied to improve the convergence performance of the solution algorithm. Case studies are solved to quantify the impact of considering the reserve provision of WPGs and the inherent DDU in power system dispatch decisions.

Multi-energy Complementary Power System Economic Dispatch Considering Carbon Emission and Regional User Coordination

The integration of multi-energy complementarity and source-grid-load-storage is an important initiative to promote energy transformation and the high-quality development of power systems. This paper proposes a two-tier day-ahead multi-energy complementary power system economic dispatch model from the perspective of clean and low-carbon, taking into account carbon emissions and multi-regional user synergy. The model optimises the production and purchase of electricity through different decisions between the upper generation side and the lower user side, which minimises the energy production cost in the upper tier and the energy purchase cost in the lower tier, and achieves mutual benefits between the upper and lower tiers. This paper validates the algorithm and model with an improved IEEE 39-node system.