Considering carbon emissions in economic dispatch planning for isolated power systems

Economic Dispatch is an important optimization problem in power system planning. This article presents an overview of the economic dispatch problem, its formulation, and a comparison of addressing the problem between the vertically integrated market and the liberalized market environments.

As global energy demand rises and climate change poses an increasing threat, the development of sustainable, low-carbon energy solutions has become imperative. This study focuses on optimizing shared energy storage (SES) and distribution networks (DNs) using deep reinforcement learning (DRL) techniques to enhance operation and decision-making capability. An innovative dynamic carbon intensity calculation method is proposed, which more accurately calculates indirect carbon emissions of the power system through network topology in both spatial and temporal dimensions, thereby refining carbon responsibility allocation on the user side. Additionally, we integrate user-side SES and ladder-type carbon emission pricing into DN to create a low-carbon economic dispatch model. By framing the problem as a Markov decision process (MDP), we employ the DRL, specifically the deep deterministic policy gradient (DDPG) algorithm, enhanced with prioritized experience replay (PER) and orthogonal regularization (OR), to achieve both economic efficiency and environmental sustainability. The simulation results indicate that this method significantly reduces the operating costs and carbon emissions of DN. This study offers an innovative perspective on the synergistic optimization of SES with DN and provides a practical methodology for low-carbon economic dispatch in power systems.

Dynamic economic dispatch of power system based on DDPG algorithm

In view of uncertainties caused by large-scale wind power integration, energy storage system (ESS) is being considered to stabilize the fluctuation of wind power. In this paper, the influence of ESS on power system operation with wind power is analyzed in detail, and an economic dispatch (ED) model with wind power and ESS is proposed based on scenario set. First, the initial scenario set of wind power output is generated by the Monte Carlo sampling. To overcome the shortcoming of heavy dependence on the initial clustering centers, which usually leads to unstable clustering results, the k-means clustering is improved by combining self-organizing feature map neural network and particle swarm optimization (PSO). Then, the initial scenario set is reduced based on this improved k-means clustering method. Finally, an ED model solved by PSO is used to minimize the comprehensive power generation cost based on the reduced scenario set. Taking IEEE-39 bus system as an example, the scenario-set-based ED model is implemented in this paper. The simulation results show that, when solving the ED problem with wind power and ESS, the proposed method considering scenario reduction makes not only the clustering index better, but also the results of ED more reasonable.

The uncertainty of wind farm power and load both have a certain impact on the economic dispatch of the power system. First, this study deals with the fuzzy processing of power prediction error and load forecasting error of wind farms based on fuzzy random theory. On this basis, a multi-objective fuzzy stochastic dispatch model of a power system with flexible load is established under the carbon trading mechanism. And, the nonlinear cost of flexible load response and the cost of carbon emission compensation is introduced to the multi-objective function of the model. In addition, the fuzzy chance constraint of the spinning reserve is added to the constraint conditions. By introducing the variable, the fuzzy random dispatch model is transformed into a clear equivalent model. Finally, the discrete bacterial colony chemotaxis algorithm is used to process the model, and the optimal solution to the multi-objective function is obtained by a compromise strategy based on a small degree of satisfaction. In the simulation, a classic IEEE10 system and a wind farm are taken as examples. The results show that compared with the other three traditional dispatch models, the total power generation cost is reduced by US$13 670, US$5610 and US$86 010, respectively using the model proposed in this article.

For a successful rollout of electric vehicles (EVs), battery swapping stations (BSSs) become a must. Based on the characteristics of battery swapping station, the mathematical model of BSS under the battery to grid (B2G), grid to battery (G2B), battery to battery (B2B) mode is formulated. The economic dispatch model that aims to minimize the operating cost, carbon emissions and pollution settlement cost with their associated constraints is established, incorporating the BSSs into the power system which is highly penetrated intermittent wind power. While transforming the multiple objectives to a single objective, it is solved by means of mixed integer quadratic programming. A system with 10 thermal units, one large-scale wind farm and four BSSs are selected to verify the proposed method. Simulation results show that the operation cost is vastly reduced with BSSs.

Economic dispatch in wind-integrated power systems is a critical challenge, yet many recent metaheuristics suffer from premature convergence, heavy parameter tuning, and limited ability to escape local optima in non-smooth valve-point landscapes. This study proposes a new hybrid optimization framework, the Fractional Grasshopper Optimization algorithm (FGOA), which integrates fractional-order calculus into the standard Grasshopper Optimization algorithm (GOA) to enhance its search efficiency. The FGOA method is applied to the economic load dispatch (ELD) problem, a nonlinear and nonconvex task that aims to minimize fuel and wind-generation costs while satisfying practical constraints such as valve-point loading effects (VPLEs), generator operating limits, and the stochastic behavior of renewable energy sources. Owing to the increasing role of wind energy, stochastic wind power is modeled through the incomplete gamma function (IGF). To further improve computational accuracy, FGOA is hybridized with Sequential Quadratic Programming (SQP), where FGOA provides global exploration and SQP performs local refinement. The proposed FGOA-SQP approach is validated on systems with 3, 13, and 40 generating units, including mixed thermal and wind sources. Comparative evaluations against recent metaheuristic algorithms demonstrate that FGOA-SQP achieves more accurate and reliable dispatch outcomes. Specifically, the proposed approach achieves fuel cost reductions ranging from 0.047% to 0.71% for the 3-unit system, 0.31% to 27.25% for the 13-unit system, and 0.69% to 12.55% for the 40-unit system when compared with state-of-the-art methods. Statistical results, particularly minimum fitness values, further confirm the superior performance of the FGOA-SQP framework in addressing the ELD problem under wind power uncertainty.

This study proposes a novel prediction model for uni‐ and multi‐variable forecast, where error feedback is added to the original forecast value predicted using the persistence model. The error feedback mechanism is constructed to find out the relationship between the errors and the original forecast values. Simulation studies are carried out using wind power data obtained from two databases, and the results demonstrate that the proposed model provides a more accurate and stable forecast compared to other methods. Based on this, the economic benefit of accurate wind power forecast has been analysed for power system dispatch, which aims to minimise the operation cost. The dispatch results of two scenarios have shown that accurate forecast result decreases the cost of reserve capacity, balancer set invoking capacity and the possibility of wind curtailment, which leads to more economic dispatch of power systems.

The paper proposes a fully distributed approach for economic dispatch problem (EDP) in power systems. The goal is to determine the output power to meet the load demand economically. In this paper, a simple algorithm is proposed to solve EDP under capacity constraint. The proposed method only needs its local cost parameters and the local predicted load. Simulation studies show the effectiveness of the approach.

In order to coordinate the impact of the integration of electric vehicles and wind power on the economic dispatch of power systems, a multi-objective dispatch model for the environmental economy of wind farms with PHEVs connected to the grid was constructed. The uncertain factors of wind power generation and load will increase the difficulty of dispatching. The fuzzy theory will be used to realize the fuzzy modelling of the coordinated connection of wind power and electric vehicles. The satisfaction index will be used to transform the multi-objective problems of deterministic environment and economy into single For the objective optimization problem, based on the improvement of the traditional particle swarm optimization algorithm using linear descent search ideas and the particle information sharing method considering boundary constraints, the improved PSO algorithm is used to solve the proposed dynamic environment and economic dispatch model. From the grid operation and vehicle owners from the perspective of demand, the constraints of the system’s rotation reserve and the daily travel of the owner are considered. The comparison and analysis of the simulation of algorithms and calculation examples and multiple scheduling schemes in different scenarios verify the rationality of the model and the superiority of the improved PSO algorithm for solving such dynamic scheduling problems.

This paper presents using the Bees algorithm approach to multi-objective optimal economic dispatch of electrical power systems. The generation of electricity from the fossil fuel releases several contaminants, such as sulfur oxides, nitrogen oxides and carbon dioxide, into the atmosphere. Genetic algorithmic approach to power system optimization, as reported here for a case of economic power dispatch, consists essentially of minimizing the objective function while gradually satisfying the constraint relations. In the Multi-objective problem formulation, four important non-commensurable objectives in an electrical thermal power system are considered. These are economy and environmental impacts because of NOx, SO2, CO2 emissions. The suitability of the proposed approach is described to multiobjective optimal economic dispatch of electrical power systems.

This paper proposes Firefly Algorithm (FA) with fuzzy approach for solving combined economic-emission load dispatch (CEELD) problem in power generation. The main objective of the CEELD problem is to determine the optimal cost and emission level of power generation and fulfill the load demand and operational constraints. The CEELD problem used weighted sum method to combine two objective functions (cost and emission) into single objective. Then, the Fuzzy-based mechanism approach is integrated in FA to find the best compromise solution for both conflicting cost and emission level. The FA has been tested on IEEE 118-bus 14-unit test system for minimization both cost of power generation and emission level. The performance of FA for solving CEELD problem has been investigated in terms of optimal solution, convergence characteristics and Pareto front solution. From the comparison of the CEELD solutions, it found that FA can provide significant cost and emission reduction compared to other methods. Thus, it can be used as alternative approach for solving any optimization problems.

Economic Power Dispatch is a critical component of the power system network (EPD). It assigns required load to online producing units while accounting for system constraints. The fundamental purpose of EPD is to lower overall power generation costs. For example, the bi-objective Combined Emission- Economic Dispatch (CE-ED) problem addresses the environmental impacts of fossil fuel power plant emissions. The bi-objective challenge reduces both fuel costs and emissions. Generators are simulated using quadratic cost functions to match their output restrictions. The non-linear, non-convex objective functions and equality and inequality requirements make the EPD issue more feasible. Recent evolutionary algorithms have improved results, especially for complex optimization problems. These methods identify global optimum solutions in non-convex and large solution domains. Recent algorithms search the solution space at random utilising numerous candidate solutions. Evolving algorithms must be able to get answers by exploring the feasible zone rather than researching the complex region. So the optimization process is speedier and consumes less calculation time while still finding the global optimum. The traditional technique fails due to premature convergence.

This paper presents a model and a solution scheme for optimisation and control of an economic and secure dispatch system for power systems. The formulation caters for loading and deloading rates, limits on generators outputs, spinning reserve requirements and group power import-export limits. The modelling strategy and solution techniques employed are based on the Dantzig-Wolfe Decomposition principle, which produces a master problem solved by the revised simplex method and a capacitated transshipment subproblem solved by the network flow algorithm. The computational efficiency of the algorithm was achieved and this makes it suitable for an on-line dispatch. >

Differential Evolution (DE), a vector population based stochastic optimization method has been introduced to the public in 1995. During the last 25 years research on and with DE has reached an impressive state, yet there are still many open questions, In this paper ,An improved differential evolution (IDE) algorithm was presented for power system Dynamic economic dispatch(IDED), Dynamic economic dispatch (DED), an extension of the economic dispatch problem, is a method of scheduling the online generators with a predicted load demand over acertain period of time taking into account the various constraints imposed on the system operation. The results indicate that IDE algorithm outperforms GA ,PSO and DE algorithms in solving DED problems.