Please note this is a comparison between Version 2 by Fanny Huang and Version 3 by Fanny Huang.

Economic Dispatch Problems (EDP) refer to the process of determining the power output of generation units such that the electricity demand of the system is satisfied at a minimum cost while technical and operational constraints of the system are satisfied. This procedure is vital in the efficient energy management of electricity networks since it can ensure the reliable and efficient operation of power systems. As power systems transition from conventional to modern ones, new components and constraints are introduced to power systems, making the EDP increasingly complex. This highlights the importance of developing advanced optimization techniques that can efficiently handle these new complexities to ensure optimal operation and cost-effectiveness of power systems.

- economic dispatch
- Economic Dispatch Problems (EDP)
- conventional optimization
- probabilistic algorithms
- artificial intelligence
- metaplastic algorithms
- hybrid approaches

Power grids, involving conventional thermal power plants that run on fossil fuels, play a vital role in energy generation. They are responsible for producing a significant proportion of the electricity energy mix. This is despite the fact that several alternative energy sources such as renewable energies are available to power system operators. Two main characteristics of thermal power plants, namely, reliability and affordability, cause thermal plants to hold a prominent position among other sources of electricity in electricity generation.

According to the U.S. Energy Information Administration (EIA) ^{[1]}, fossil fuels have been the largest sources of energy for electricity generation from 1950 to 2021. **Table 1**, depicts the contribution of various energy sources in billions of kilowatt hours (kWh), thereby showcasing the significant role of fossil fuels in meeting the electricity demand in the United States. Natural gas and coal were shown to constitute about 38% and 22% of the total generation, respectively, and were reported as the two largest sources of electricity generation in the U.S. in 2021. Additionally, thermal plants powered by fossil fuels have generated about 60% of the total electricity generation in 2022 ^{[1]}. The data of US energy sources in 2022 ^{[1]}, have been utilized to create **Figure 1**, illustrating the distribution of these energy sources.

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 |

Population and urbanization growth, along with the growth of industries, have contributed to continuous increments in electricity consumption. The scarcity of fossil fuels and the adverse environmental impacts of thermal power plants are the major driving forces with respect to efficiently managing the power network and obtaining the optimal power generation schedule for the power system. It is noteworthy that power networks are vast in size and include multiple generators and transmission networks that span huge geographical areas. Hence, the management of the electricity grid is a complex task that involves several challenges ^{[2]}. One of the major challenges that power system operators face when managing the electricity grid is maintaining the balance between electricity demand and generation. It is a technically difficult task to store electricity on a large scale; therefore, it is highly significant to retain the supply and demand equilibrium in the power networks.

Moreover, in order to have an economically feasible power system, the network must meet the electricity demand while minimizing the operation cost. The economic challenge stems from the fact that the generation cost varies from one generator to another one. This is because the cost of generated electricity at a specific generator is affected by several factors such as local fuel cost, the availability of the generator, and the plant’s maintenance cost ^{[3]}. Hence, to efficiently run the power system, it is vital to address the above-mentioned techno-economic constraints while operating electricity grids.

The EDP refers to the process of calculating the output power of each available generator to meet the total network demand while minimizing operation costs and/or generators’ carbon dioxide emissions ^{[4]}. Essentially, the EDP involves identifying the most efficient scheduling of generators while considering various economic and technical limitations associated with both the committed generators and the power grid. The primary concept in the EDP is to prioritize the generators with the lowest marginal costs for operation, and the marginal cost of the overall system is determined by the generator with the highest cost.

Economic dispatch offers several advantages, including lower operating costs, increased efficiency, and reduced emissions. By optimizing the output of each generator, economic dispatch can help to minimize the overall cost of electricity production. Additionally, it can help to maximize the efficiency of the power system and reduce its negative environmental impact by utilizing the most cost-effective and least-polluting generators first.

The assistance of economic dispatch greatly facilitates the optimization of electricity network operation, thereby making it an essential tool for achieving efficient operation of the power grid. System operators can reap a multitude of benefits from economic dispatch, including economic, technical, health, and climate advantages ^{[5]}. By enhancing system efficiency and reducing greenhouse gas emissions, economic dispatch can have a positive impact on health and the climate. Additionally, it can lead to increased reliability and more effective utilization of power sources for the electricity grid. Therefore, it is of utmost importance to define and solve the EDP precisely.

The EDP has been a persistent issue in the literature since 1920, thereby leading to extensive research in this area ^{[6]}.

$$\begin{array}{cc}\hfill {C}_{t}& =\sum _{i=1\underset{}{\overset{}{m}}{\alpha}_{i}+{\beta}_{i}{P}_{i+{}_{}+{\gamma}_{i}{P}_{i}^{2},}}^{}\hfill \\ \hfill \sum _{i=1\underset{}{\overset{}{m}}{P}_{i}}^{}& ={P}_{d}+{P}_{l},\hfill \\ \hfill {P}_{i}& \le {P}_{i}\le {P}_{i}\hfill \end{array}$$

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

^{[17]} |
Alternating Direction Method of Multipliers (ADMMs) | Minimize generation cost | Network power balance | IEEE 30-bus and 300-bus test cases |

^{[18]} |
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 |

^{[19]} |
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 |

^{[20]} |
Deep Reinforcement Learning | Minimize VPP operation cost | Power balance among DERs, limits on maximum interruptible load percentage | Offline data sets obtained from ^{[30]}^{[31]} |

^{[21]} |
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 |

^{[22]} |
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 |

^{[23]} |
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 |

^{[24]} |
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 |

^{[25]} |
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 |

^{[26]} |
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 |

^{[27]} |
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 |

^{[28]} |
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 |

- U.S. Energy Information Administration. How Much Carbon Dioxide Is Produced When Different Fuels Are Burned? Available online: https://www.eia.gov/tools/faqs/faq.php?id=427&t=3 (accessed on 15 May 2023).
- Liu, Y.; Yang, C.; Jiang, L.; Xie, S.; Zhang, Y. Intelligent Edge Computing for IoT-Based Energy Management in Smart Cities. IEEE Netw. 2019, 33, 111–117.
- Durvasulu, V.; Hansen, T.M. Market-based generator cost functions for power system test cases. IET Cyber-Phys. Syst. Theory Appl. 2018, 3, 194–205.
- Kunya, A.B.; Abubakar, A.S.; Yusuf, S.S. Review of economic dispatch in multi-area power system: State-of-the-art and future prospective. Electr. Power Syst. Res. 2023, 217, 109089.
- Qu, B.; Zhu, Y.; Jiao, Y.; Wu, M.; Suganthan, P.; Liang, J. A survey on multi-objective evolutionary algorithms for the solution of the environmental/economic dispatch problems. Swarm Evol. Comput. 2018, 38, 1–11.
- Happ, H.H. Optimal power dispatch—A comprehensive survey. IEEE Trans. Power Appar. Syst. 1977, PAS-96, 841–854.
- Al Farsi, F.N.; Albadi, M.H.; Hosseinzadeh, N.; Al Badi, A.H. Economic Dispatch in power systems. In Proceedings of the 2015 IEEE 8th GCC Conference & Exhibition, Muscat, Oman, 1–4 February 2015; pp. 1–6.
- Ang, T.Z.; Salem, M.; Kamarol, M.; Das, H.S.; Nazari, M.A.; Prabaharan, N. A comprehensive study of renewable energy sources: Classifications, challenges and suggestions. Energy Strategy Rev. 2022, 43, 100939.
- Wang, X.; Liu, Z.; Zhang, H.; Zhao, Y.; Shi, J.; Ding, H. A Review on Virtual Power Plant Concept, Application and Challenges. In Proceedings of the 2019 IEEE Innovative Smart Grid Technologies—Asia (ISGT Asia), Chengdu, China, 21–24 May 2019; pp. 4328–4333.
- Zheng, Y.; Wang, Z.; Ju, P.; Wu, H. A Distributed Two-Stage Economic Dispatch for Virtual Power Plant Based on an Improved Exact Diffusion Algorithm. Front. Energy Res. 2021, 9, 734801.
- Oladimeji, O.; Ortega, A.; Sigrist, L.; Rouco, L.; Sánchez-Martin, P.; Lobato, E. Optimal Participation of Heterogeneous, RES-based Virtual Power Plants in Energy Markets. arXiv 2021, arXiv:2112.02200.
- Iria, J.; Coelho, A.; Soares, F. Network-secure bidding strategy for aggregators under uncertainty. Sustain. Energy Grids Netw. 2022, 30, 100666.
- Naval, N.; Yusta, J.M. Virtual power plant models and electricity markets—A review. Renew. Sustain. Energy Rev. 2021, 149, 111393.
- Espín-Sarzosa, D.; Palma-Behnke, R.; Núñez-Mata, O. Energy Management Systems for Microgrids: Main Existing Trends in Centralized Control Architectures. Energies 2020, 13, 547.
- Gao, H.; Jin, T.; Feng, C.; Li, C.; Chen, Q.; Kang, C. Review of virtual power plant operations: Resource coordination and multidimensional interaction. Appl. Energy 2024, 357, 122284.
- Qiu, H.; Vinod, A.; Lu, S.; Gooi, H.B.; Pan, G.; Zhang, S.; Veerasamy, V. Decentralized mixed-integer optimization for robust integrated electricity and heat scheduling. Appl. Energy 2023, 350, 121693.
- Wasti, S.; Ubiratan, P.; Afshar, S.; Disfani, V. Distributed Dynamic Economic Dispatch using Alternating Direction Method of Multipliers. arXiv 2020, arXiv:2005.09819.
- Li, P.; Liu, Y.; Xin, H.; Jiang, X. A Robust Distributed Economic Dispatch Strategy of Virtual Power Plant under Cyber-Attacks. IEEE Trans. Ind. Inform. 2018, 14, 4343–4352.
- Lu, Q.; Yang, Y.; Zhu, Y.; Xu, T.; Wu, W.; Chen, J. Distributed Economic Dispatch for Active Distribution Networks with Virtual Power Plants. In Proceedings of the 2019 IEEE Innovative Smart Grid Technologies—Asia (ISGT Asia), Chengdu, China, 21–24 May 2019; pp. 328–333.
- Lin, L.; Guan, X.; Peng, Y.; Wang, N.; Maharjan, S.; Ohtsuki, T. Deep Reinforcement Learning for Economic Dispatch of Virtual Power Plant in Internet of Energy. IEEE Internet Things J. 2020, 7, 6288–6301.
- Ye, H.; Huang, H.; He, Y.; Xu, M.; Yang, Y.; Qiao, Y. Optimal Scheduling Method of Virtual Power Plant Based on Model Predictive Control. In Proceedings of the 2023 3rd International Conference on Energy, Power and Electrical Engineering (EPEE), Wuhan, China, 15–17 September 2023; pp. 1439–1443.
- Liu, Y.; Li, Y.; Wang, Y.; Zhu, J.; Gooi, H.B.; Xin, H. Distributed Real-Time Multi-Objective Control of a Virtual Power Plant in DC Distribution Systems. IEEE Trans. Power Deliv. 2022, 37, 1876–1887.
- Cao, C.; Xie, J.; Yue, D.; Huang, C.; Wang, J.; Xu, S.; Chen, X. Distributed Economic Dispatch of Virtual Power Plant under a Non-Ideal Communication Network. Energies 2017, 10, 235.
- Xie, J.; Cao, C. Non-Convex Economic Dispatch of a Virtual Power Plant via a Distributed Randomized Gradient-Free Algorithm. Energies 2017, 10, 1051.
- Wu, X.; Xiong, H.; Li, S.; Gan, S.; Hou, C.; Ding, Z. Improved Light Robust Optimization Strategy for Virtual Power Plant Operations with Fluctuating Demand. IEEE Access 2023, 11, 53195–53206.
- Naughton, J.; Wang, H.; Cantoni, M.; Mancarella, P. Co-Optimizing Virtual Power Plant Services Under Uncertainty: A Robust Scheduling and Receding Horizon Dispatch Approach. IEEE Trans. Power Syst. 2021, 36, 3960–3972.
- Hadayeghparast, S.; SoltaniNejad Farsangi, A.; Shayanfar, H. Day-ahead stochastic multi-objective economic/emission operational scheduling of a large scale virtual power plant. Energy 2019, 172, 630–646.
- Yi, Z.; Xu, Y.; Gu, W.; Wu, W. A Multi-Time-Scale Economic Scheduling Strategy for Virtual Power Plant Based on Deferrable Loads Aggregation and Disaggregation. IEEE Trans. Sustain. Energy 2020, 11, 1332–1346.
- Setiawan, E.A. Concept and Controllability of Virtual Power Plant; Kassel University Press GmbH: Kassel, Germany, 2007.
- Open Energy Information. Main Page. 2017. Available online: http://en.openei.org/wiki/Main_Page (accessed on 12 February 2017).
- NREL. Home Page. 2017. Available online: http://www.nrel.gov/midc (accessed on 14 February 2017).
- Liu, J.; Song, C.; Tao, R.; Wang, X. Cooperative Operation for Integrated Multi-Energy System Considering Transmission Losses. IEEE Access 2020, 8, 96934–96945.
- Byeon, G.; Van Hentenryck, P. Unit Commitment With Gas Network Awareness. IEEE Trans. Power Syst. 2020, 35, 1327–1339.
- Li, Y.; Wang, J.; Zhao, D.; Li, G.; Chen, C. A two-stage approach for combined heat and power economic emission dispatch: Combining multi-objective optimization with integrated decision making. Energy 2018, 162, 237–254.
- Wang, Y.; Wang, Y.; Huang, Y.; Yang, J.; Ma, Y.; Yu, H.; Zeng, M.; Zhang, F.; Zhang, Y. Operation optimization of regional integrated energy system based on the modeling of electricity-thermal-natural gas network. Appl. Energy 2019, 251, 113410.
- Mazzoni, S.; Ooi, S.; Nastasi, B.; Romagnoli, A. Energy storage technologies as techno-economic parameters for master-planning and optimal dispatch in smart multi energy systems. Appl. Energy 2019, 254, 113682.
- Nazari-Heris, M.; Mohammadi-Ivatloo, B.; Asadi, S.; Geem, Z.W. Large-scale combined heat and power economic dispatch using a novel multi-player harmony search method. Appl. Therm. Eng. 2019, 154, 493–504.

More