Economic Environmental Power Dispatch Research Articles

Multi‐objective multiperiod stable environmental economic power dispatch considering probabilistic wind and solar PV generation

AbstractThe economic‐environmental power dispatch (EEPD) problem, a widely studied bi‐objective non‐linear optimization challenge in power systems, traditionally focuses on the economic dispatch of thermal generators without considering network security constraints. However, environmental sustainability necessitates reducing emissions and increasing the penetration of renewable energy sources (RES) into the electrical grid. The integration of high levels of RES, such as wind and solar PV, introduces stability issues due to their uncertain and intermittent nature. This article addresses these concerns by formulating and solving the economic environmental and stable power dispatch (EESPD) problem, which includes fixed zonal reserve capacity from conventional thermal generators and uncertain reserves from RES. Uncertainties in RES and load demand are modelled using random variable generation techniques, applying Gaussian, Weibull, and log‐normal probability density functions (PDFs) for load demand, wind velocity, and solar irradiance, respectively. The stochastic EESPD problem extends to multiple periods by replicating the single‐period problem for each interval in the planning horizon, linking periods through intertemporal ramping costs, physical ramp rate, and fixed zonal reserve constraints on dispatch variables. Multi‐objective evolutionary algorithms (MOEAs) have gained prominence for solving complex non‐linear problems involving multi‐objective functions. This article applies the latest MOEAs to tackle the proposed EESPD problem, incorporating stochastic wind and solar PV power sources. Network security constraints, such as transmission line capacities and bus voltage limits, are considered along with constraints on generator capabilities and intertemporal spinning reserves, ramp‐up and ramp‐down constraints for thermal generators. A bidirectional coevolutionary‐based multi‐objective evolutionary algorithm is employed, integrating an advanced constraint‐handling technique to ensure compliance with system constraints. The simulation results show that the proposed formulation achieves a better trade‐off between various conflicting objective functions compared to other state‐of‐the‐art MOEAs.

Optimal economic environmental power dispatch by using artificial bee colony algorithm

<span>Today, most power plants worldwide use fossil fuels such as natural gas, coal, and oil as the primary resource for energy reproduction primarily. The new term for economic environmental power dispatch (EEPD) problems is on the minimum total cost of the generator and fossil fuel emissions to address atmosphere pollution. Thus, the significant objective functions are identified to minimize the cost of generation, most minor emission pollutants, and lowest system losses individually. As an alternative, an Artificial Bee Colony (ABC) swarming algorithm is applied to solve the EEPD problem separately in the power systems on both standard IEEE 26 bus system and IEEE 57 bus system using a MATLAB programming environment. The performance of the introduced algorithm is measured based on simple mathematical analysis such as a simple deviation and its percentage from the obtained results. From the mathematical measurement, the ABC algorithm showed an improvement on each identified single objective function as compared with the gradient approach of using the Newton Raphson method in a short computational time.</span>

A Modified Strength Pareto Evolutionary Algorithm 2 based Environmental /Economic Power Dispatch

A Strength Pareto Evolutionary Algorithm 2 (SPEA 2) approach for solving the multi-objective Environmental / Economic Power Dispatch (EEPD) problem is presented in this paper. In the past fuel cost consumption minimization was the aim (a single objective function) of economic power dispatch problem. Since the clean air act amendments have been applied to reduce SO2 and NOX emissions from power plants, the utilities change their strategies in order to reduce pollution and atmospheric emission as well, adding emission minimization as other objective function made economic power dispatch (EPD) a multi-objective problem having conflicting objectives. SPEA2 is the improved version of SPEA with better fitness assignment, density estimation, and modified archive truncation. In addition fuzzy set theory is employed to extract the best compromise solution. Several optimization run of the proposed method are carried out on 3-units system and 6-units standard IEEE 30-bus test system. The results demonstrate the capabilities of the proposed method to generate well-distributed Pareto-optimal non-dominated feasible solutions in single run. The comparison with other multi-objective methods demonstrates the superiority of the proposed method.

Research on the environment & economic indicators for electricity trading

In this paper, the environmental and economic indicators based on the reactive power pricing are proposed so as to formulate the novel environmental economic power dispatch (NEED) problems for electricity trading. Here, a new way of calculating total cost is proposed based on the reactive power pricing instead of the pure fuel cost, which leads to the NEED problems. In addition, an improved tunicate swarm algorithm (ITSA) is proposed to deal with the NEED problems. Different from the original tunicate swarm algorithm (TSA), adaptive weight parameter and mutation process are used to improve the disadvantages of TSA which converges too fast and easily falls into local optimum. In combination with the Pareto dominance rule, the ITSA can be more effective in dealing with the NEED problems. In order to examine the performance of the ITSA, simulation tests of ITSA, TSA, and particle swarm optimization (PSO) are conducted in IEEE30 node system. During the experimental process, optimized objective functions include total cost considering reactive cost, pollution emission and power loss. The final comparison results show that the ITSA is able to get better distributed Pareto front (PF) and superior best compromise solution (BCS), which proves the high efficiency of the ITSA in dealing with the NEED problems.

Pareto-based Multi-objective Firefly Algorithm with Hierarchical Clustering for Environmental-Economic Power Dispatch Problem

This paper proposes a multi-objective firefly algorithm (MOFFA) to solve the environmental-economic power dispatch (EEPD) problem. Also, it presents a modified firefly algorithm (FFA) to solve the economic power dispatch (EPD) and the emission dispatch (ED) problems as single goals. The modifications proposed on the traditional FFA aim to improve its exploration and ensure the feasibility of the obtained solutions. The proposed MOFFA uses an external Pareto set to keep the non-dominated solutions, where a hierarchical clustering algorithm is used to get a representative and controlled set of Pareto-optimal solutions. The best compromise solution is also extracted from the Pareto set using an approach based on the fuzzy set theory. The constraints of EEPD, EPD, and ED problems are power balance constraint, generation limits constraint, and transmission power losses. To verify the effectiveness of the proposed algorithms, two methodologies are adopted and tested on the IEEE 30-bus test and the 10-unit test system with valve-point loading. In methodology 1, the EPD problem and the ED problem are solved separately using the modified FFA. In methodology 2, the EEPD is solved as a true multi-objective optimization problem using the proposed MOFFA. The simulation results and the statistical analysis ensure the high-quality solutions of the proposed algorithms and prove the ability of the MOFFA to produce well-distributed Pareto-optimal solutions.

A Multiagent Fuzzy Reinforcement Learning Approach for Economic Power Dispatch Considering Multiple Plug-In Electric Vehicle Loads

Economic/environmental power dispatch goals were to determine the optimal power generation from thermal plants to satisfy the given demand while diminishing operational costs and also minimizing emissions due to burning of fossil fuels. In this paper, economic and environmental scheduling problems are mathematically formulated by considering various system constraints like the valve point loading effect, ramp rate constraints, plug-in electric vehicle charging constraints, and generator’s capacity constraints. In this work, multiagent fuzzy reinforcement learning (MAFRL) is implemented for an effective elucidation for the economic/environmental power dispatch (EEPD) problem with multiple charging scenarios of plug-in electric vehicle and valve point loading of concern thermal power generators. Here, the EEPD is framed as a multiagent fuzzy reinforcement learning (MAFRL) tasks in which specific plug-in electric vehicles and power generating units act as multiple players for minimizing emissions due to fossil fuels and costs of power generation also satisfying charging constraints of plug-in electric vehicles and several thermal unit’s constraints. To prove the superiority of multiagent fuzzy RL, two standard test functions containing five and fifteen thermal generating units integrated with multiple charging scenarios of plug-in electric vehicles have projected. Numerical consequences and assessment with a numerous current solution methodologies show the potentiality of multiagent fuzzy reinforcement learning method in solving the EEPD problem.

A Novel Approach for Solving a Fully Rough Multi-Level Quadratic Programming Problem and Its Application

The most widely used actions and decisions of the real-world tasks frequently appear as hierarchical systems. To deal with these systems, the multi-level programming problem presents the most flourished technique. However, practical situations involve some the impreciseness regarding some decisions and performances; RST provides a vital role by considering the lower and upper bounds of any aspect of uncertain decision. By preserving the advantages of it, in the present study, solving fully rough multi-level quadratic programming problems over the variables, parameters of the objective functions, and the constraints such as rough intervals are focused on. The proposed approach incorporates the interval method, slice-sum method, Frank and Wolfe algorithm, and the decomposition algorithm to reach optimal values as rough intervals. The proposed is validated by an illustrative example, and also environmental-economic power dispatch is investigated as a real application. Finally, the proposed approach is capable of handling the fully rough multi-level quadratic programming models.

Multi‐objective squirrel search algorithm to solve economic environmental power dispatch problems

Multi‐objective squirrel search algorithm to solve economic environmental power dispatch problems

Environmental Economic Power Dispatch Using Bat Algorithm with Generalized Fly and Evolutionary Boundary Constraint Handling Scheme

This article intends to resolve the evolving environmental economic power dispatching problem (EED) using an enhanced version of the bat algorithm (BA) which is the Bat Algorithm with Generalized Fly (BAG). A good solution based on the Evolutionary Boundary Constraint Handling Scheme rather than the well-known absorbing technique and a good choice of the bi-objective function are provided to maintain the advantages of such algorithms on this problem. In the first stage, an individual economic power dispatch problem is considered by minimizing the fuel cost and taking into account the maximum pollutant emission. In the second stage and after weighting soft constraints satisfaction maximization and hard constraints abuse penalties, the proposed approach of the bi-objective environmental and economic load dispatch was built on a pareto function. The approach was tested on a thermal power plant with 10 generators and an IEEE30 power system of 6 generators. The results on the two datasets compared to those of other methods show that the proposed technique yields better cost and pollutant emissions.

Solution of Economic and Environmental Power Dispatch Problem of an Electrical Power System using BFGS-AL Algorithm

Abstract This paper presents a deterministic optimization strategy to solve the economic-environmental power dispatch (EEPD) problem of an electrical power system, using a Broyden Fletcher Goldfarb Shanno based on the augmented Lagrangian (BFGS-AL) algorithm. This problem is a nonlinear constrained multi-objective optimization. The objectives of this optimization are minimized the total fuel cost and emission amount for thermal generators while satisfying electric power systems equality and inequality constraints. The proposed approach is applied on the standard IEEE 30 bus test system, where the power transmission losses are taken into account. Simulation results proved that the proposed approach gives better-quality solution in terms of accuracy and convergence to the best compromise solution compared to other deterministic and meta-heuristic optimization techniques.

Many-Objective Optimal Power Dispatch Strategy Incorporating Temporal and Spatial Distribution Control of Multiple Air Pollutants

Traditional economic/environment dispatch usually aims to reduce emission, but neglects air pollutant dispersion and lacks target-oriented control. This paper proposes a many-objective optimal power dispatch (MaOOPD) strategy incorporating temporal and spatial distribution (TSD) control of multiple air pollutants. Ground level concentration, i.e., the TSD, of air pollutant is estimated by a novel air pollutant dispersion model specifically constructed for thermal power plants. A MaOOPD model is developed to cut generation cost, reduce CO2 emission, and control the TSD of PM2.5, SO2, and NO2 simultaneously. To determine a compromise solution, a decision-making method which exploits atmospheric environmental capacity margin is employed, so that actual needs of atmospheric environmental protection are captured. Case studies indicate that not only can the strategy reduce air pollution effectively, but also it can achieve a dynamic tradeoff among the objectives as weather conditions and background pollution vary, leading to an authentic economic environmental power dispatch.

A Pareto Optimal Solution for Environmental/Economic Power Dispatch using Multi-objective Genetic Algorithm

The aim of this paper is to apply genetic algorithm (GA) to the solution of the environmental economic power dispatch problem. The environmental economic power dispatch is a multi-objective optimization problem. Fuel cost is considered as one of the objectives. The other objective is emissions such as SO2 or NOx or a combination of both. A trade-off relation between fuel cost and emissions can be formed through a pareto optimal front. Valve point opening and prohibited operating zones add non-smoothness and non-convexities to the objective functions. Evolutionary algorithms can efficiently solve such non-smooth and non-convex problems. Solutions need to be diversified and distributed among the whole range of the pareto optimal front. This allows operators to trade-off between fuel cost and emissions in feasible optimal regions. Applying genetic algorithm with diversity enhancement proves its effectiveness. Application of the algorithm on three and six unit systems is demonstrated

Security-Constrained Unit Commitment Considering Differentiated Regional Air Pollutant Intensity

Conventional environmental-economic power dispatch methods constrain the total amount of emissions of power plants, and they succeed in reducing emissions from the power sector. However, they fail to address the mismatch between emission reductions and the resulting changes in regional air quality. This paper proposes an ecology- and security-constrained unit commitment (Eco-SCUC) model considering the differentiated impacts of generation-associated emissions on regional air quality. A Gaussian puff dispersion model is applied to capture the temporal-spatial transport of air pollutants. Additionally, an air pollutant intensity (API) index is defined for assessing the impacts of emissions on the air quality in regions with differentiated atmospheric environmental capacities. Then the API constraints are formulated based on air quality forecast and included in SCUC model. Moreover, the stochastic optimization is employed to accommodate wind power uncertainty, and the Benders decomposition technique is used to solve the formulated mixed-integer quadratic programming (MIQP) problem. Case studies demonstrate that the Eco-SCUC can cost-effectively improve air quality for densely-populated regions via shifting generation among units and can significantly reduce the person-hours exposed to severe air pollution. Furthermore, the benefits of wind power for air quality control are investigated.

Coordinated consensus for smart grid economic environmental power dispatch with dynamic communication network

Combined economic environmental dispatch problem (CEEDP) is one of the greatest challenges of the future smart grids. It aims at reducing the total cost during the power production process considering the growing environmental impact due to the emission of gaseous pollutants of fossil fuels. This study develops a robust distributed algorithm based on consensus protocols in multi-agent systems, to solve the smart grid CEEDP with a practical communication network consisting of a dynamic communication network, randomly communication failure, transmission delay and noise in communication channels. The proposed algorithm is fully distributed and cooperative in such a way that it eliminates the need for a central energy-management unit, or a leader. The performance of the fully decentralised consensus protocol was evaluated on the IEEE 30-bus and the IEEE 118-bus test system. A comparison with previous consensus algorithms proves the supremacy of the proposed approach in terms of its robustness under dynamic communication network with randomly link failure.

Chaotic crow search algorithm for fractional optimization problems

This paper presents a chaotic crow search algorithm (CCSA) for solving fractional optimization problems (FOPs). To refine the global convergence speed and enhance the exploration/exploitation tendencies, the proposed CCSA integrates chaos theory (CT) into the CSA. CT is introduced to tune the parameters of the standard CSA, yielding four variants, with the best chaotic variant being investigated. The performance of the proposed CCSA is validated on twenty well-known fractional benchmark problems. Moreover, it is validated on a fractional economic environmental power dispatch problem by attempting to minimize the ratio of total emissions to total fuel cost. Finally, the proposed CCSA is compared with the standard CSA, particle swarm optimization (PSO), firefly algorithm (FFA), dragonfly algorithm (DA) and grey wolf algorithm (GWA). Additionally, the efficiency of the proposed CCSA is justified using the non parametric Wilcoxon signed-rank test. The experimental results prove that the proposed CCSA outperforms other algorithms in terms of quality and reliability.

Multiobjective economic-environmental power dispatch with stochastic wind-solar-small hydro power

Economic-environmental power dispatch is one of the most popular bi-objective non-linear optimization problems in power system. Classical economic power dispatch problem is formulated with only thermal generators often ignoring security constraints of the network. But importance of reduction in emission is paramount from environmental sustainability perspective and hence penetration of more and more renewable sources into the electrical grid is encouraged. However, most common forms of renewable sources are intermittent and uncertain. This paper proposes multiobjective economic emission power dispatch problem formulation and solution incorporating stochastic wind, solar and small-hydro (run-of-river) power. Weibull, lognormal and Gumbel probability density functions are used to calculate available wind, solar and small-hydro power respectively. Some conventional generators of the standard IEEE 30-bus system are replaced with renewable power sources for study purpose. Network security constraints such as transmission line capacities and bus voltage limits are also taken into consideration alongwith constraints on generator capabilities and prohibited operating zones for the thermal units. Decomposition based multiobjective evolutionary algorithm and summation based multiobjective differential evolution algorithm are applied to the problem under study. An advanced constraint handling technique, superiority of feasible solutions, is integrated with both the multiobjective algorithms to comply with system constraints. The simulation results of both the algorithms are summarized, analyzed and compared in this study.

A nonlinear fractional programming approach for environmental–economic power dispatch

Abstract A nonlinear fractional programming approach is provided for addressing the environmental–economic power dispatch problems in the thermal power dispatch systems. The objective of this study is to simultaneously minimize the total fuel cost and total emissions of the power dispatch systems, which is realized by two simultaneous models with nonlinear constraints. The first model is to minimize the quotient of two competing and conflicting functions (i.e. [total emission function]/[total fuel cost function]), and the second one is to minimize the total fuel cost expressed by a quadratic objective function. In particular, the process of solving the first model uses Dinkelbach’s algorithm to convert the minimization problem with the nonlinear fractional objective function into a sequence of non-fractional minimization problems. The effectiveness of this approach is demonstrated through applying to the standard IEEE 30-bus test system. Comparison between the present approach and other existing approaches shows that the proposed approach can generate superior decision alternatives from the view point of realizing a more environmentally friendly and cost-effective scheme and/or considering the power transmission loss rate in the power dispatch systems.

Backtracking search optimization based economic environmental power dispatch problems

Abstract This paper presents the solution for a nonlinear constrained multi objective of the economic and emission load dispatch (EELD) problem of thermal generators of power systems by means of the backtracking search optimization technique. Emission substance like NO X, power demand equality constraint and operating limit constraint are considered here. The aim of backtracking search optimization (BSA) is to find a global solution under the influence of two new crossover and mutation operations. BSA has capability to deal with multimodal problems due to its powerful exploration and exploitation capability. BSA is out of excessive sensitivity to control parameters as it has single control parameter. The performance of BSA is compared with existing newly developed optimization techniques in terms quality of solution obtained, computational efficiency and robustness for multi objective problems.

Opposition-based gravitational search algorithm applied to economic power dispatch problems consisting of thermal units with emission constraints

In this study, a multiobjective environmental economic power dispatch problem has been converted into a single-objective optimization problem using the weighted sum method. For the solution of the converted problem, the gravitational search algorithm (GSA), which is one of the latest algorithms, has been used. In order to increase the performance of the GSA, opposite positioning quality has been added to the structure of the algorithm (OGSA). The obtained results show that the proposed algorithm has obtained better results and has provided a faster convergence. The 30-bus 6-generator test system has been selected for application of the OGSA. The transmission line losses have been added to the problem by using a B loss matrix. Optimum solutions of the problem have been obtained for different weights and the results have been veried.

Probabilistic economic/environmental power dispatch of power system integrating renewable energy sources

The study of different integration aspects of renewable energy sources (RES) becomes very important to overcome problems caused by their variability or uncertainty. This paper treats the economic environmental power dispatch as a probabilistic multiobjective problem. The operation cost is considered as the sum of deterministic part and probabilistic one. First, the problem is solved based on expected values of generated RES power. Then, using the cumulative distribution function (CDF) of each RES, the CDF of the required reserve to compensate RES power variability is developed. After that, respecting to the reserve contribution of each thermal generator, the probabilistic part of the global generation cost as well as its CDF are developed. In order to solve the proposed multiobjective problem, a new computation approach based on particle swarm is investigated. Finally, the proposed approach is applied to solve the active power dispatch problem of IEEE 30-bus test system in two cases with and without RESs. The simulation results show that the proposed approach allows to get the complete information about the cumulative distribution function of the actual global cost of the system operation.