# Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review

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## Abstract

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## 1. Introduction

- We conduct a critical analysis of the existing literature that assesses the performance, advantages, and drawbacks of the algorithms used in prior research studies.
- We establish the current state of the art by providing an up-to-date and innovative classification of EDP formulations, objective functions, and optimization algorithms.
- We synthesize the existing literature to offer a useful starting point for future research work in the field of the EDP.
- We identify gaps in the existing literature and highlight areas that require further investigation.

## 2. Research Methodology

## 3. Evolving Paradigms in Economic Dispatch: From Conventional Techniques to Modern Power System Strategies

#### 3.1. Foundations of Economic Dispatch in Conventional Power Systems

#### 3.2. VPP-Based Economic Dispatch

#### 3.3. MES-Based Economic Dispatch

## 4. Economic Dispatch Problem (EDP) Formulation

#### 4.1. Single Objective Optimization

#### 4.2. Multiobjective Optimization

## 5. EDP Optimization Techniques

#### 5.1. Conventional Mathematical Methods

#### 5.1.1. Newton’s Method

#### 5.1.2. Lambda Iteration Algorithm

#### 5.1.3. Interior Point Method (IPM)

#### 5.1.4. Quadratic Programming (QP)

#### 5.2. Uncertainty Modelling Methods

#### 5.2.1. Stochastic Optimization

#### 5.2.2. Chance Constraint Programming (CCP)

#### 5.2.3. Robust Optimization

#### 5.3. AI-Based Techniques

#### 5.3.1. Artificial Neural Networks (ANNs)

#### 5.3.2. Deep Learning Techniques

#### 5.3.3. Reinforcement Learning (RL)

#### 5.3.4. Fuzzy Approaches

#### 5.3.5. Metaheuristic Algorithms

#### 5.4. Hybrid Algorithms

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

EDPs | Economic Dispatch Problems |

EIA | Energy Information Administration |

kWh | Kilowatt Hours |

PRISMA | Preferred Reporting Items for Systematic Reviews and Meta-Analyses |

AI | Artificial Intelligence |

IPM | Interior Point Method |

QP | Quadratic Programming |

CCP | Chance Constraints Programming |

ANNs | Artificial Neural Networks |

DL | Deep Learning |

RL | Reinforcement Learning |

SVMs | Support Vector Machines |

FL | Fuzzy Logic |

CNNs | Convolutional Neural Networks |

RNNs | Recurrent Neural Networks |

HNNs | Hopfield Neural Networks |

MDP | Markov Decision Process |

MAs | Metaheuristic Algorithms |

EAs | Evolutionary Algorithms |

SI | Swarm Intelligence |

PSO | Particle Swarm Optimization |

GA | Genetic Algorithm |

ABC | Artificial Bee Colony |

ANFIS | Adaptive Neuro-Fuzzy Inference System |

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Generation Source | Billion kWh |
---|---|

Natural Gas | 1689 |

Coal | 828 |

Petroleum (total) | 23 |

Petroleum liquids | 16 |

Petroleum coke | 7 |

Other gases | 12 |

Nuclear | 772 |

Wind | 435 |

Hydropower | 262 |

Photovoltaic | 143 |

Solar thermal | 3 |

Biomass (total) | 53 |

Geothermal | 17 |

Other sources | 11 |

Ref. | Solution Approach | Objectives | Constraints | Case Study |
---|---|---|---|---|

[25] | Alternating Direction Method of Multipliers (ADMMs) | Minimize generation cost | Network power balance | IEEE 30-bus and 300-bus test cases |

[26] | NCS-based attack-robust distributed strategy | Minimize the total cost of generation and privacy breach | Active power output bounds of distributed generations | IEEE 123-bus test feeder |

[27] | ADMMs-based Distributed Algorithm | Minimize cost of generation and maximize the utilities of controllable loads | Network constraints, voltage Limitations | Modified version of a 33-bus system |

[28] | Deep Reinforcement Learning | Minimize VPP operation cost | Power balance among DERs, limits on maximum interruptible load percentage | Offline data sets obtained from [38,39] |

[29] | Model Predictive Control Algorithm | Minimum VPP operation cost | Dynamic lower bound constraints on energy storage, network power balance, voltage limitations | VPP with load, 5G station, PV power, energy storage, control center, connected to grid |

[30] | Distributed Primal–Dual Subgradient Method (DPDSM) | Maximize quality of voltage profile and minimize operation cost | Bus voltage limit constraint, limit on DER current injection from each bus, current flow limit on critical lines at risk of congestion | A 14-bus DC distribution feeder and 6-bus radial DC distribution feeder |

[31] | DPDSM-based Nonideal Communication Network | Minimize operation cost function | Power output constraints of DERs, transmission constraints of power lines | Modified IEEE 34- and IEEE 123-bus test VPP systems |

[32] | Distributed Randomized Gradient-Free Algorithm | Maximize the total income of the VPP | Valve-point loading effects, prohibited operating zones | Modified IEEE-34 bus test system |

[33] | Improved Light Robust Optimization Method | Minimize operation costs | Supply–demand balance, battery capacity change constraints, storage, battery rated capacity limits, natural gas unit power output constraints | Data center–VPP system using HOMER and MATLAB |

[34] | Scenario-Based Robust Optimization and Receding Horizon Optimizations | Maximize VPP profit | Power flow constraints, active and reactive branch power flow are constrained | South Australia network |

[35] | Two-Stage Stochastic Programming, Multiobjective PSO, PSO | Maximizing daily net profit and minimizing daily emissions of VPP | Constraints on DER Operation, thermal capacity limits of distribution lines | A total of 3 scenarios on 4-plant VPP |

[36] | DLs Aggregation-Based Multi-Timescale Strategy | Minimizing operational cost | Power flow and network constraints, limits on DERs, storage systems, and reserve balance, aggregator constraints | Southern China distribution system |

Ref. | Objective | Utilized Method | Performance Indicator | Case Study |
---|---|---|---|---|

[46] | Minimize generation cost | Lambda Iteration Algorithm, ANN, Levenberg Marquardt | Percentage error in lambda | A 9-generating-unit system |

[47] | Minimize generation cost | Hybrid PSO and Termite Colony Optimization | Average execution time and cost function value | Total of 5-, 10-, and 30-unit power systems |

[48] | Minimize generation cost | Memory-Based Gravitational Search Algorithm | Cost function value versus iterations | IEEE 37-bus system |

[49] | Minimize generation cost | Hybrid Mixed-Integer Linear Programming and IPM | Cost function value and CPU time | Total of 5- and 10-unit power systems |

[50] | Minimize generation cost | Macroscopically Semiempirical Degradation Cost Modeling | - | Zimbabwe and Northern Ireland power systems |

[51] | Minimize generation cost | PSO | Cost reduction | Two microgrids, including RES and 4 generators |

[52] | Minimize generation and carbon emission cost | Very relaxed ADMM | Convergence speed and Cost reduction | A 6-bus system and IEEE 118-bus system |

[53] | Minimize operational cost and emission levels | Improved mayfly algorithm | Convergence speed and Cost reduction | Microgrid comprising three conventional generators, solar, and wind units |

[54] | Minimize the total operation, carbon tax-based emission, and energy balance cost | CCP-based two-stage stochastic programming | Allocation of carbon quota and cost reduction | Six-bus power system and six-node natural gas system |

[55] | Minimize thermal and CCPP generation cost and produced CO${}_{2}$ emission | Fuzzy decision making | Minimum fuzzy membership degrees | Modified IEEE 24-bus test system |

[56] | Minimize operation cost and emission | Improved TLBO algorithm | Mutation probability and cost reduction | Total of 6 and 400 thermal units, as well as a system of thirteen solar units, forty wind turbines, six thermal units |

[57] | Minimize operational cost of IENGSs | Mixed-integer linear programming | Permissible emission limit and CO${}_{2}$ price | A 6-bus power system and 7-node natural gas system; Jing–Jin–Ji economic circle |

[58] | Minimize cost and flue gas emission | Game theory | Deregulation and cost reduction | A 62-bus system of Indian utility |

[59] | Minimizing total system failure | Reliability assessment using ETAP | Failure, hazard rate, and reliability parameters | Power system of Tehran metro |

[60] | Minimize cost | Comparative and analytical study of approximation errors | Dispatch approximation error and cost reduction | Total of 2-bus and 2383-bus test systems |

[61] | Minimize cost | Mixed-integer linear programming | CPU time and cost reduction | Total of 6-, 13-, 20-, 40-, and 140-bus power systems |

[62] | Minimize total fuel cost | Improved competitive swarm optimization algorithm | CPU time and cost reduction | Total of 10-, 40-, and 120-unit systems |

[63] | Minimize cost | Discrete dynamic programming | Computational efficiency and cost reduction | Total of 15- and 53-generating-unit systems |

[64] | Minimize cost | IL-SHADE algorithm | Wilcoxon sign rank test and cost reduction | IEEE 6-, 40-, and 140-unit test systems |

Ref. | Objective | Utilized Method | Performance Indicator | Case Study |
---|---|---|---|---|

[65] | Minimize cost and emission | Improved shuffled frog leaping algorithm | IGD index | IEEE 30-bus test system |

[66] | Minimize cost and emission | Lagrangian duality | Normalized diversity metric | Six-generating-unit system |

[67] | Minimize cost and emission level | Multiobjective Harris hawks optimization | Crossover rate and mutation factor | IEEE 30-bus system |

[68] | Minimize cost and total amount of pollutants | Niching penalized chimp algorithm | p value and RMSE | IEEE 30-bus with six generators and a ten-unit system |

[69] | Minimize cost and total quantity of emissions | Duality theory approach | Normalized diversity metric | Total of 6-, 11-, and 40-generator-unit systems |

[70] | Minimize fuel and emission cost | Hybrid FA-GA multiobjective algorithm | Voltage stability index | A 39-bus IEEE system |

[71] | Minimize cost and emission | Multiobjective gray prediction evolution algorithm | Average satisfactory degree | IEEE 30-bus 6-generator-unit test system |

[72] | Minimize cost and emission | PSO | Loss of power supply probability, cost of electricity, renewable factor, and capital recovery factor | Sweden electricity network |

[73] | Minimize total cost and fluctuation of the interaction power | Multiobjective seeker optimization algorithm | Overall satisfactory degree | China microgrid |

[74] | Minimize cost and composite demand peak | Probabilistic models | Loss of load probability and expected unserved energy | Texas power system |

[75] | Minimize cost and water consumption | Whale optimization algorithm | CPT time and cost reduction | IEEE 40-unit test system |

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## Share and Cite

**MDPI and ACS Style**

Marzbani, F.; Abdelfatah, A.
Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review. *Energies* **2024**, *17*, 550.
https://doi.org/10.3390/en17030550

**AMA Style**

Marzbani F, Abdelfatah A.
Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review. *Energies*. 2024; 17(3):550.
https://doi.org/10.3390/en17030550

**Chicago/Turabian Style**

Marzbani, Fatemeh, and Akmal Abdelfatah.
2024. "Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review" *Energies* 17, no. 3: 550.
https://doi.org/10.3390/en17030550