Evolving Paradigms in Economic Dispatch: Comparison
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

1. Introduction

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.
Figure 1. Composition of electricity generation by different sources in percentages.
Table 1. Comparison of Energy Generation 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].

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

The evolution of economic dispatch is discussed, thereby tracing its progression from established conventional power systems to innovative contemporary models. This part begin with an analysis of the traditional economic dispatch, thereby detailing the foundational principles and strategies employed in earlier power system optimization. The focus then shifts to the application of economic dispatch in the realm of virtual power plants (VPPs), thereby emphasizing the transformative role of these technologies in introducing decentralization and advanced management techniques to the field. Finally, the discussion extends to the utilization of economic dispatch within multienergy systems (MESs), thus underscoring the significance of integrating various energy sources to optimize efficiency and promote environmental sustainability. 

2.1. Foundations of Economic Dispatch in Conventional Power Systems

Economic dispatch problems (EDPs) represent a fundamental optimization challenge within traditional power systems. The principal aim of the EDP is to optimize the cost-efficiency of electricity generation, thereby concurrently ensuring adherence to the plethora of constraints associated with power system operations. Achieving this objective requires the formulation of the EDP as an optimization problem that incorporates an objective function and a set of constraints. The EDP in its most fundamental form is commonly known as the classic EDP. The primary objective of this problem is to minimize the generation cost of electricity in a power system, with the cost function typically defined as a quadratic equation. The optimization problem involves constraints related to the generation load balance, power loss, and generation limits for each power plant. The conventional mathematical formulation of the EDP is represented by the following equation [7]:
C t = i = 1 m α i + β i P i + + γ i P i 2 , i = 1 m P i = P d + P l , P i m i n P i P i m a x .
The total generation cost in Equation (1) is represented by 𝐶𝑡, with the cost coefficients for the ith generator denoted by 𝛼𝑖, 𝛽𝑖, and 𝛾𝑖. The electricity demand and loss are denoted by 𝑃𝑑 and 𝑃𝑙, respectively. The output limits for the ith generator are shown as 𝑃𝑖𝑚𝑖𝑛 and 𝑃𝑖𝑚𝑎𝑥. The classical economic dispatch formulation often falls short in real-world scenarios, especially as traditional power systems, once dominated by fossil fuels and thermal generators, have evolved. Modern power networks now incorporate a variety of renewable energy sources, thereby altering system components and necessitating new approaches in economic dispatch problem solving. These changes have spurred advancements in the EDP, with studies proposing innovative objective functions and formulations. Building on this, the next part explores the EDP within VPPs, thereby showcasing advanced solutions for these modern, complex power systems.

2.2. VPP-Based Economic Dispatch

In contrast to traditional power systems, which predominantly consist of conventional thermal generators, contemporary power systems are increasingly inclusive of renewable energy sources dispersed throughout the network. While these renewables offer considerable environmental and economic advantages, their integration into the power system presents a myriad of challenges [8]. These challenges encompass aspects such as grid stability, variable energy output, and demand–supply management. This complex landscape has been a driving force behind the inception of the concept of virtual power plants (VPPs). A virtual power plant (VPP) is comprised of a heterogeneous array of distributed energy resources (DERs) that are controlled in a centralized manner [9]. VPPs represent a strategic response to these challenges, thereby providing an innovative framework for the efficient and effective integration of diverse energy resources into the power grid. This innovative approach reflects the transition from classic power systems to VPPs, thereby signaling a shift towards more decentralized and flexible energy management [10][11][12]. This transformation has led to a notable shift in the economic dispatch problem (EDP), thereby resulting in a significant deviation from traditional EDP approaches. The integration of diverse renewable energy sources within virtual power plants (VPPs) presents unique challenges, thus driving this change. These complexities require redefining traditional EDP strategies to effectively manage the variable and intermittent nature of renewables, thereby ensuring efficient and reliable energy management in a sustainable power generation landscape [13]. The formulation of the EDP for VPPs can be categorized into two distinct approaches: centralized and distributed. In the centralized approach for EDP formulation in VPPs, control and decision making are centralized at one point. All distributed energy resources (DERs) within the VPP network transmit real-time data, including energy generation and constraints, to this central controller. The controller processes this data to solve the EDP, thereby aiming to maximize the overall system efficiency. The formulated dispatch strategy is then communicated back to the DERs for execution. This approach involves the aggregation of data and operational commands from various distributed energy resources (DERs) within the VPP network to a central control unit [14]. This approach facilitates harmonized operations across the network, thereby potentially enhancing the overall system efficiency. However, it necessitates a substantial communication infrastructure due to the continuous exchange of extensive data between the main controller and DERs dispersed over a vast network. Another challenge is maintaining the privacy of DERs owners, as sensitive operational data are transmitted to the central operator. Additionally, the centralized processing model introduces the risk of a single-point failure, which could potentially lead to a systemic collapse [15]. In contrast to the centralized paradigm, the distributed approach to economic dispatch in VPPs represents a fundamentally different strategy. In this methodology, DERs are each equipped with individual intelligence, thereby enabling autonomous decision making. Each DER utilizes real-time data and specific constraints to achieve the most locally optimal operation for its subproblem. This objective is accomplished through communication and information exchange with neighboring units, thereby ensuring a coordinated approach while maintaining individual operational autonomy [16]. The theoretical foundation and practical applications of the distributed approach in VPPs have been explored in recent research [17][18][19][20][21][22][23][24][25][26][27][28]. These studies provide valuable insights into the intricacies of implementing such systems, addressing key challenges such as communication technology requirements, system resilience, and the complex interplay between local and global objectives. Such coordination necessitates advanced communication and control technologies. However, unlike centralized systems, this approach is not prone to single-point failures, as each DER can operate independently, enhancing the system’s overall resilience. While the distributed approach offers these advantages, it faces the complexity of balancing local and global objectives, requiring sophisticated optimization algorithms [29]. A summarized overview of these key research works, including their methodologies, findings, and contributions, is presented in Table 2 for a comprehensive comparative analysis.
Table 2. Comprehensive summary of distributed EDPs in VPPs.
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

2.3. MES-Based Economic Dispatch

Building upon the advancements presented in VPPs, the concept of multienergy systems (MESs), also known as integrated energy systems, emerges as an even more integrative approach in modern energy management. These systems integrate a diverse array of energy carriers, such as electricity, heat, and gas, into a unified framework, thus resulting in a significant advancement in creating a more efficient energy system [32][33]. In this context, the EDP for MESs plays a crucial role in optimizing the allocation of various energy resources, thereby ensuring the most efficient use of the integrated energy mix. The literature reveals extensive research on economic dispatch planning—EDP—for MESs. In the following paragraphs, the key and most influential papers among these are briefly discussed, particularly focusing on those which have garnered 80 or more citations. This approach allows us to highlight the most significant contributions and emerging trends in the realm of the EDP for MESs, thereby emphasizing studies that have had a substantial impact and recognition in the field. The concept of economic emission dispatch for an MES comprising combined heat and power has been explored in [34]. This study introduces a two-stage technique to address EDP challenges within this system. Initially, a novel metaheuristic algorithm, the 𝜃 Dominance-Based Evolutionary Algorithm (𝜃-DEA), was employed to tackle the multiobjective problem. Subsequently, fuzzy C-Means (FCM) clustering was applied to the Pareto optimal solutions, followed by the use of a gray relation projection (GRP) on these clusters to identify the most balanced compromise solutions. This proposed methodology was tested across three distinct case studies of varying complexity, wherein the results underscore its effectiveness and efficiency. The optimal scheduling of a comprehensive regional integrated system in Tianjin, China was examined in [35]. This system encompasses a variety of components, including combined cooling, heating, and power (CCHP), thermal energy storage, electric energy storage, electric boilers, wind turbines, and photovoltaic systems. The study considered constraints like energy balance and external network transmission power, with the primary goal of minimizing the system’s total cost. This included energy transaction costs, operational expenses, energy storage costs, and environmental impact costs. To solve this EDP, the fruit fly optimization algorithm was employed. The study explored three different operational modes: “Following Power Load”, “Following Heat Load”, and an “Optimal Scheduling” mode—which integrates both power and heat loads. The findings indicate that the optimal scheduling solution significantly outperformed the scenarios focusing solely on either heat or power load. The study in [36] investigated the impact of various storage technologies, including lithium-ion, vanadium redox, ice, and phase change material thermal storage, on multienergy systems (MESs). Utilizing mixed integer quadratic programming, it conducted a sensitivity analysis for optimal dispatch problems (ODPs) in MESs and also determined the optimal dispatch strategy using the in-house developed simulation tool known as ©E-OPT. This methodology was applied to two distinct case studies: the first connected to the national electricity network and the second operating in island mode. The case studies catered to electricity and peak cooling demands of 1600 kWe and 3000 kWc, respectively. The results indicate that the island mode, particularly due to higher fuel prices, benefits significantly from incorporating energy storage technologies, thereby achieving a 23% reduction in CO22 emissions. In [37], a novel multiplayer harmony search (MPHS) algorithm was developed to address nonconvex, nonlinear, large-scale EDPs for combined heat and power (CHP) systems. The core principle of the proposed MPHS method involves improvising harmonies through the collective experiences of multiple players to achieve the optimal solution for the CHPED. This approach was tested on two case studies: a 24-unit case study and an 84-unit case study, thus representing a large-scale scenario. The results demonstrate significant cost savings amounting to over 17 million dollars annually and exhibited superior performance compared to other algorithms such as the gravitational search algorithm, improved group search optimization, cuckoo optimization algorithm, crisscross optimization algorithm, and improved PSO.

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