Power System Economic Dispatch Research Articles

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.

Distributed discrete-time optimization over directed networks: A dynamic event-triggered algorithm

Distributed optimization has a wide variety of applications, such as economic dispatch in power systems, social welfare maximization, optimal power flow, where distributed nodes work cooperatively to achieve a minimized global objective function, where the information exchanges among distributed and networked nodes play an important role. However, such information exchanges often suffer from inevitable energy and bandwidth constraints due mainly to their distributed and networked nature. Event-triggered distributed optimization provides an effective means to address this issue. However, designing an event-triggered distributed optimization algorithm with both fast convergence and resource efficiency is challenging. In this paper, a distributed zero-gradient-sum algorithm with a dynamic event-triggered scheme is presented for distributed discrete-time optimization. The triggering threshold is composed of an exponential decaying term and a positive dynamic auxiliary variable. The linear convergence is established theoretically. Finally, this algorithm is applied to an economic dispatch problem to verify the theoretical findings and to demonstrate the effectiveness and superiority of the proposed algorithm.

A Review of Research on Dynamic and Static Economic Dispatching of Hybrid Wind–Thermal Power Microgrids

As fossil energy is increasingly depleted, promoting the integration of renewable energy into the grid and improving its utilization rate has become an irresistible development trend in China’s power industry. However, the volatility of wind power increases the difficulty of economic dispatch in power systems. With the rising participation of wind power in the system, the complexity of traditional microgrid dynamic scheduling problems has increased, transforming into a dynamic economic scheduling problem for wind power thermal power hybrid microgrids. Starting from the concept and research significance of economic dispatch, this article analyzes the current research status of microgrid economic dispatch as well as the impact and influencing factors of wind energy grid connection on it. It summarizes the research performed by scholars in two aspects: scheduling models and solving algorithms in static dispatch, as well as how to deal with wind power randomness in dynamic dispatch and how to balance environmental protection while ensuring economic maximization. Finally, the existing problems in current research were summarized and future development directions were prospected. This research has important application prospects in improving the economy of the system and protecting the ecological environment.

Hybridizing gaining–sharing knowledge and differential evolution for large-scale power system economic dispatch problems

AbstractEconomic dispatch (ED) of thermal power units is significant for optimal generation operation efficiency of power systems. It is a typical nonconvex and nonlinear optimization problem with many local extrema when considering the valve-point effects, especially for large-scale systems. Considering that differential evolution (DE) is efficient in locating global optimal region, while gain-sharing knowledge-based algorithm (GSK) is effective in refining local solutions, this study presents a new hybrid method, namely GSK-DE, to integrate the advantages of both algorithms for solving large-scale ED problems. We design a dual-population evolution framework in which the population is randomly divided into two equal subpopulations in each iteration. One subpopulation performs GSK, while the other executes DE. Then, the updated individuals of these two subpopulations are combined to generate a new population. In such a manner, the exploration and the exploitation are harmonized well to improve the searching efficiency. The proposed GSK-DE is applied to six ED cases, including 15, 38, 40, 110, 120, and 330 units. Simulation results demonstrate that GSK-DE gives full play to the superiorities of GSK and DE effectively. It possesses a quicker global convergence rate to obtain higher quality dispatch schemes with greater robustness. Moreover, the effect of population size is also examined.

Research on the Economic Dispatch of Power Systems with a High Proportion of Renewable Energy based on Improved PSO

The penetration rate of renewable energy sources represented by wind power and photovoltaics in the power grid is increasing, adding complexity to unit dispatch. In this paper, a multi-objective optimization model is established for power systems containing wind power and photovoltaic economic dispatch. Firstly, the power generation cost of traditional units, the emission cost of traditional units, the power generation costs of wind turbines and photovoltaics, and the output characteristics of wind power and photovoltaics are analyzed. Secondly, a multi-objective economic dispatch model with the lowest power generation cost, the smallest emission cost, and the smallest power generation cost of new energy units are established, and the power flow balance constraint, supply and demand balance constraint, unit output constraint, and node voltage constraint are considered. Then the improved particle swarm algorithm is proposed to solve the multi-objective function to obtain better convergence and optimal solution. Finally, the simulation is carried out in the IEEE-30 node system and the HRP-38 system, which compares and illustrates the similarities and differences of the solution results of various algorithms under multi-objective and verifies the effectiveness of the algorithm.

Weighted fully-connected regression networks for one-day-ahead hourly photovoltaic power forecasting

Accurate photovoltaic power forecasting can provide a basis for low-carbon economic dispatch of power systems with a high proportion of renewable energy. Regression networks with many times training based on multi-group multi-configuration still cannot resist the randomness of training processes, resulting in the accuracy of photovoltaic power prediction needs to be improved. This work proposes a weighted fully-connected regression network, including a feature input layer, deep fully-connected layers, particle swarm optimization, and a regression output layer. The proposed model automatically selects two networks from multi-group multi-configuration well-trained regression networks to effectively reduce photovoltaic power prediction errors without additional sensors and data sources. The errors of these two chosen well-trained networks exactly neutralize each other by fixed and simple weights. The results under the one-day-ahead hourly photovoltaic power forecasting of Natal of Brazil show that the proposed method can reduce photovoltaic power prediction errors with at least 75.9954% smaller mean absolute error than the state-of-art methods and 68.2937% than other 18 famous convolutional neural networks methods.

A fast sequential transient stability preventive control approach driven by model interpretation

Transient stability preventive control (TSPC), regarded as generation rescheduling, plays an important role in maintaining secure and economic dispatch of power systems. To accommodate the increasing uncertainty of operation conditions, online TSPC is urgently required in real power systems. To this end, a new sequential online TSPC strategy driven by transient stability assessment (TSA) model interpretation is proposed in this paper. In this strategy, two data-driven TSA models, namely full-feature-trained and controllable-feature-trained models, are deployed for online TSA and generation rescheduling, respectively. To identify the control generators for TSPC, an instance-based model interpretation tool, Local Interpretable Model-agnostic Explanations (LIME), is introduced to interpret the unstable operation detected by online TSA. In addition, a pair-wise generator regulation strategy and a continual prediction method are used to quickly search the TSPC operating point while ensuring the power shift balance of the system during regulation. The adaptability of the strategy to the online applications is demonstrated on the IEEE 3-machine 9-bus system and the IEEE 10-machine 39-bus system. • Sequential framework speeds up transient stability preventive control (TSPC). • TSA model trained by controllable features locates the origin of system instability. • Model interpretation breaks up the opacity of TSA model’s predictions.

Marginal utility of battery energy storage capacity for power system economic dispatch

The battery energy storage (BES) is recognized as a key resource for the power fluctuations smoothing, peak load shaving and frequency regulation, and its performance depends heavily on the available capacity. It is meaningful to investigate the influence of the BES capacity on the power system operation cost. This paper focuses on the marginal utility of BES capacity in the day-ahead power system operation cost. Firstly, the day-ahead economic dispatch problem is formulated as a constrained quadratic programming problem, with the consideration of the BES degradation cost. Then, the relationship between the BES-related shadow prices and the marginal electricity price is derived from the KKT conditions of the dispatch problem. Based on it, the marginal utility of BES capacity is modeled to evaluate the effect of BES capacity on the system day-ahead operation cost. Finally, the numerical results demonstrate that the proposed marginal utility can manifest the influence of BSS capacity on the power system operation.

Scenario-oriented hybrid particle swarm optimization algorithm for robust economic dispatch of power system with wind power

An economic dispatch problem for power system with wind power is discussed. Using discrete scenario to describe uncertain wind powers, a threshold is given to identify bad scenario set. The bad-scenario-set robust economic dispatch model is established to minimize the total penalties on bad scenarios. A specialized hybrid particle swarm optimization (PSO) algorithm is developed through hybridizing simulated annealing (SA) operators. The SA operators are performed according to a scenario-oriented adaptive search rule in a neighborhood which is constructed based on the unit commitment constraints. Finally, an experiment is conducted. The computational results show that the developed algorithm outperforms the existing algorithms.