Large-Scale Optimization among Photovoltaic and Concentrated Solar Power Systems: A State-of-the-Art Review and Algorithm Analysis

Abstract

Large-scale optimization (LSO) problems among photovoltaic (PV) and concentrated solar power (CSP) systems are attracting increasing attention as they help improve the energy dispatch efficiency of PV and CSP systems to minimize power costs. Therefore, it is necessary and urgent to systematically analyze and summarize various LSO methods to showcase their advantages and disadvantages, ensuring the efficient operation of hybrid energy systems comprising different PV and CSP systems. This paper compares and analyzes the latest LSO methods for PV and CSP systems based on meta-heuristic algorithms (i.e., Particle Swarm Optimization, Genetic Algorithm, Enhanced Gravitational Search Algorithm, and Grey Wolf Optimization), numerical simulation and stochastic optimization methods (i.e., Constraint Programming, Linear Programming, Dynamic Programming Optimization Algorithm, and Derivative-Free Optimization), and machine learning-based AI methods (Double Grid Search Support Vector Machine, Long Short-Term Memory, Kalman Filter, and Random Forest). An in-depth analysis and A comparison of the essence and applications of these algorithms are conducted to explore their characteristics and suitability for PV and CSP or hybrid systems. The research results demonstrate the specificities of different LSO algorithms, providing valuable insights for researchers with diverse interests and guiding the selection of the most appropriate method as the solution algorithm for LSO problems in various PV and CSP systems. This also offers useful references and suggestions for extracting research challenges in LSO problems of PV and CSP systems and proposing corresponding solutions to guide future research development.

1. Introduction

1.1. Research Background

Since the 1970s, the world has faced increasing pressure from rising energy consumption, energy supply challenges, and environmental concerns. Solar energy has emerged as a popular solution due to its renewable, clean, and widely distributed nature, offering significant potential for development [1,2]. The popularity of solar energy continues to grow, with advancements and applications expanding each year. Solar power technologies are generally divided into two main categories: photovoltaic (PV) and concentrated solar power (CSP) technologies. The solar irradiance at the Earth’s surface is about 1 kWm⁻², which can provide considerable power supply when harvested through technologies such as PV or CSP systems [3]. Standard PV systems typically operate under 1 sun, equivalent to 1000 Wm⁻², as detailed by [4]. Concentrator photovoltaics (CPVs), on the other hand, can operate under much higher irradiance levels, ranging from 550 to 1000 suns, thus enhancing energy capture and conversion efficiency [5]. CSP technologies typically operate within an irradiance range of 600 to 1000 suns, but certain configurations have been demonstrated to achieve irradiance levels up to 3000 suns, providing significant advantages in energy generation under optimal conditions [6]. PV systems convert solar energy directly into electricity through the photovoltaic effect in semiconductor materials. The output of a PV plant depends heavily on the semiconductor used. Monocrystalline silicon typically degrades more slowly than polycrystalline silicon, affecting long-term efficiency [7]. Bifacial silicon/perovskite tandem modules can increase energy output by over 25% compared to traditional silicon modules due to their ability to capture light from both sides [8]. Choosing the right material is crucial for optimizing energy yield and system longevity. In contrast, CSP systems utilize many heliostats to focus sunlight onto a central thermal collecting tower. This CSP system heats a heat transfer fluid (HTF) in the tower, generating steam to drive a turbine and produce electricity [9]. However, the solar power tower (SPT) is just one of several CSP technologies. Other systems include parabolic trough collectors, which focus sunlight onto a receiver tube to heat the HTF, and dish collectors, which concentrate solar energy onto a single focal point to generate high temperatures [10]. Fresnel reflectors, another CSP technology, use multiple flat mirrors to focus sunlight onto a fixed receiver, offering a more compact and cost-effective alternative. Additionally, these systems can be combined to optimize energy capture and efficiency [11]. As global energy consumption rises and environmental concerns intensify, the development and optimization of all these CSP systems have become crucial. Each system offers substantial potential for large-scale energy production but also presents a range of optimization challenges [12].

Optimization problems within PV and CSP systems are diverse and complex [13,14,15]. These can be categorized into several key areas: energy system optimization, particularly involving energy scheduling and balance optimization in integrated PV and CSP systems [16,17,18].

• Multi-objective optimization considers both economic benefits and technical performance, such as the layout and orientation of solar panels in PV systems. Zhang et al. (2019) optimized the photovoltaic capacity of large-scale hydro-photovoltaic complementary systems, showing significant improvements in power generation efficiency [19]. Similarly, Zhu et al. (2020) enhanced system robustness in hydro-photovoltaic systems through a coordinated optimization framework [20]. These studies underscore the importance of optimizing system design to improve overall performance [21,22].
• Energy system capacity optimization, particularly multi-objective optimization, considering the complementarity of renewable energy systems like PV and CSP, has also been extensively explored. Fang et al. (2017) demonstrated that the optimal sizing of utility-scale PV systems operating with hydropower can significantly reduce operation costs [23]. This emphasizes the role of optimization in achieving cost-effective and efficient energy systems [24,25].
• Control system optimization is crucial for enhancing the energy conversion efficiency and reliability of PV and CSP systems. Krata and Saha (2019) improved voltage stability in distribution grids using real-time coordinated voltage support with battery energy storage [26]. In CSP systems, Kannaiyan et al. (2020) optimized thermal efficiency through advanced control strategies, leading to more stable operation [27]. These examples highlight the benefits of control system optimization in maintaining system performance [28].
• Integrated power system optimization aims to seamlessly integrate solar energy into the broader power grid. Xu and Hu (2024) developed a cross-area coordinated optimization model for integrating renewable energy sources, enhancing grid stability [29]. This approach is critical for managing the variability of renewable energy [30,31].
• Hybrid energy system optimization focuses on coordinating multiple energy sources for improved performance. For example, Kebbati and Baghli (2023) optimized a hybrid photovoltaic–wind system, resulting in better energy generation and stability [32]. This type of optimization is essential for maximizing resource use in diverse environments [33,34].
• Real-time heliostat field scheduling optimization in solar thermal tower systems is vital for maximizing energy capture. Zeng et al. (2022) used reinforcement learning to optimize heliostat field aiming strategies, achieving higher efficiency under dynamic conditions [35]. Real-time optimization is increasingly important in managing complex and dynamic energy systems [36,37].

In this paper, LSO optimization problems within PV and CSP systems are classified as hybrid energy system co-optimization (HESC) problems, multi-objective optimization (MOO) problems, real-time scheduling optimization (RSO) problems, and other LSO problems. These problems often involve multiple objectives and numerous decision variables, requiring extensive computations. Consequently, they are categorized as LSO problems [38]. LSO has gained widespread attention in recent years, with applications in many fields, including AI, software engineering, and bioinformatics [39]. However, there has yet to be a comprehensive survey and systematic analysis specifically targeting the LSO problems within solar PV and CSP systems [40,41]. In this paper, we take PV and CSP systems as the research background, systematically analyze the common types of LSO problems in PV and CSP systems for the first time, and summarize and analyze the optimization methods applied to different types of LSO problems in PV and CSP systems. We provide adequate references and suggestions for extracting the research difficulties of LSO problems in PV and CSP systems and proposing corresponding solutions.

1.2. State of the Art

Research on LSO problems holds significant value for optimizing costs, improving energy scheduling efficiency, maximizing energy output, and enhancing system reliability in PV and CSP systems. In the field of HESC, the primary focus is on energy scheduling and system balance optimization within these systems [42,43,44]. Key evaluation indicators for this type of LSO problem include total operating costs, total energy output, and overall economic benefit. LSO research in PV and CSP systems also covers MOO [45,46], RSO [47,48], and other LSO problems outside these categories [49,50,51]. MOO problems focus on cost management and capacity optimization in hybrid PV and CSP systems. The outcomes directly improve system stability and energy output efficiency, reducing costs and enhancing operational efficiency.

RSO problems deal with the real-time scheduling of heliostat fields in CSP systems. Optimizing these fields can greatly improve resistance to interference, maximizing output power under varying conditions such as cloud cover and changes in irradiance. Other LSO problems primarily involve optimization issues not covered by the first three categories, such as linear and multivariate regression analysis. These results contribute to efficiency and scheduling optimization in hybrid energy systems. Advances in algorithms and AI technologies have made LSO problem research vital for the safe and efficient operation of PV and CSP systems. This research addresses key challenges like energy scheduling, cost optimization, site evaluation, and real-time heliostat field management. It is essential for providing solutions and strategies for effective system management.

LSO problems play a critical role in hybrid PV and CSP systems, supporting comprehensive energy scheduling optimization, digital twin model construction, and multi-objective capacity optimization. However, there is a lack of comprehensive analysis of the methods used in LSO problem research for hybrid PV and CSP systems. This gap makes it difficult to grasp current trends and developments. The following section outlines key research questions identified in this study.

• Question 1: What algorithms and methods are used in LSO problem research for PV and CSP systems?
• Question 2: Which LSO problems in PV and CSP systems suit these methods and algorithms, and what are the characteristics of these problems?
• Question 3: What are the pros and cons of different algorithms and methods in LSO problems, and when are they most effective?
• Question 4: What challenges arise in solving LSO problems in PV and CSP systems with various algorithms and methods, and what solutions exist?

To accurately address the research questions mentioned above, we selected 1 January 2000 to 30 May 2024 for a comprehensive survey and systematic summary of LSO problem research in PV and CSP systems. The rapid development of solar PV and CSP technologies and AI technologies in the 21st century makes this period representative of the study of PV and CSP systems. Therefore, we chose this broad time frame of 1 January 2000 to 30 May 2024. This study aims to systematically review and understand the latest research progress on LSO problems within PV and CSP systems. We explore the current gaps in LSO problem research in PV and CSP systems and compare the advantages and disadvantages of various representative LSO problem-solving algorithms and methods. By selecting the best solutions for different types of LSO problems, we aim to put forward the solution to address specific LSO challenges in PV and CSP systems. Furthermore, we will discuss the future trends in the development of LSO problems within PV and CSP systems.

• We systematically analyze the latest research on LSO problems in PV and CSP systems from 1 January 2000 to 30 May 2024, summarizing the characteristics of different optimization problems and comprehensively summarizing the optimization methods.
• We classify the algorithms and methods applied to LSO problem research in PV and CSP systems into three categories: Machine learning (ML)-based AI methods, meta-heuristic optimization algorithms, and numerical simulation and stochastic optimization methods.
• ML-based AI methods include Double Grid Search Support Vector Machine (DGS-SVM), Long Short-Term Memory (LSTM), Reinforcement Learning (RL), Deep Reinforcement Learning (DRL), Pointer Network (PN), and Artificial Neural Network (ANN). Meta-heuristic optimization algorithms include Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Teaching-Learning-Based Optimization (TLBO), Marine Predators Algorithm (MPA), Quasi-Oppositional Turbulent Water Flow Optimization (QOTWFO), and Ant Colony Optimization (ACO).
• Linear Programming (LP), Mixed-Integer Linear Programming (MILP), Cone Programming Method (CPM), Dynamic Programming Optimization Algorithm (DPOA), Recursive Least Squares (RLS), and Fuzzy Entropy Weight Method (fuzzy EWM), nonlinear stochastic programming, the Geographic Information System (GIS) model, Robust Optimization (RO), Markov Model Calculation System (MMCS), and the column constraint generation (CCG) Algorithm.
• We eplore the applicability of the above four optimization algorithms and methods applied to LSO problem research in PV and CSP systems.
• Through systematic and comprehensive analysis, we provide valuable research insights and ideas for stakeholders.

The remaining structure of this study is as follows: Section 2 provides a systematic literature review. It covers research results on LSO problems in PV and CSP systems from 1 January 2000 to 30 May 2024. Relevant literature is compared to extract the optimization algorithms and methods currently applied to different LSO problems, as discussed in Section 3. Section 2 and Section 3 answer the first research question. Section 4 and Section 5 address the second to fifth research questions. Section 4 summarizes and lists the detailed technical aspects of three types of optimization algorithms and methods used in LSO problems in PV and CSP systems. Section 5 discusses the characteristics of these algorithms and methods, focusing on their applicability to various LSO problems. Finally, in Section 6, we discuss the results of the fourth research question and the future research prospects and directions.

2. Systematic Review

In Section 2, the literature screening process related to the study of LSO issues in PV and CSP systems within the solar energy field is described in detail. Web of Science (WoS), provided by Clarivate Analytics, is a comprehensive scholarly research database characterized by multidisciplinary coverage and high-quality reviews [52]. To further enhance the standard of literature retrieval, the core dataset of WoS has been selected as the benchmark retrieval database for this study.

2.1. Procedure of WoS-Based Paper Data Collection

Articles related to the study of PV and CSP systems LSO issues between 1 January 2000 and 30 May 2024 were retrieved from the core dataset of WoS. The search criteria used to filter publications related to PV and CSP energy system LSO problems are provided to demonstrate the literature search process.

• Topic 1: ‘Solar energy’, LSO.
• Topic 2: ‘Photovoltaic systems’, LSO.
• Topic 3: ‘Concentrated solar power’, LSO.
• Topic 4: ‘Solar energy and Photovoltaic systems’, LSO.
• Topic 5: ‘Solar energy and Concentrated solar power’, LSO.

After the initial search using the above strategies, 1152 papers were retrieved. To ensure accurate feedback on journal paper retrieval results, conferences, books, oral presentations, case studies, and chapters were subjected to a second round of screening, reducing the number to 889 papers. Subsequently, these papers’ titles, keywords, and abstracts were thoroughly reviewed to ensure that the search results strictly aligned with the topic’s relevance.

Further consideration was given to journal articles related to LSO issues in solar PV and CSP systems, excluding any articles on wind, hydro, biomass, and other issues related to renewable energy system optimization. After additional keyword screening, the number of papers was reduced to 274. Subsequently, these papers’ introduction, main content, and conclusion were further reviewed and screened to retain only those papers focusing on solar PV and CSP systems, excluding those on system controller design and economic feasibility analysis. After these paper-search and keyword-screening steps, 118 papers were finally selected. It is worth noting that the selected articles include 117 papers from the WoS core dataset and 1 article from the Chinese core dataset. Since the WoS core dataset is chosen as the primary retrieval dataset for this study, only the 117 papers from the WoS core dataset will participate in the systematic analysis and methodological summarization of the literature. The systematic research and analysis of the literature are mainly based on three perspectives: the overall development trend in the LSO problems of solar PV and CSP systems, keyword clustering analysis, and keyword evolution visualization analysis.

2.2. Development Trends of LSO among PV and CSP System

A statistical analysis of the journals publishing the selected literature revealed that the publications related to LSO problems in PV and CSP systems were spread across 47 journals. Of these, 53.2% (25 journals) published only one paper on LSO in PV and CSP systems. Additionally, 23.4% (11 journals) published 2–3 papers, 14.9% (7 journals) published 4–10 papers, and 4.3% (2 journals) published more than 10 papers. The development and distribution trends of journal contributions to publications on LSO issues in PV and CSP systems from 2000 to 2024 are illustrated in Figure 1. It was observed that from 2000 to 2018, only 19 different academic journals published research on LSO problems in PV and CSP systems, with 13 of these journals publishing only one related paper. However, since 2019, the number and variety of academic journals publishing research on LSO problems in PV and CSP systems have increased rapidly, with 25 journals publishing two or more related papers. LSO research necessitates multidisciplinary collaboration, particularly in PV and CSP systems. Our analysis revealed that $AppliedEnergy$ and $Energies$ are the leading journals in LSO research for PV and CSP systems, each publishing 11 papers, positioning them as the dominant journals in this research area. Additionally, journals such as $SolarEnergy$, $Energy$, $IEEEAccess$, $EnergyConversionandManagement$, and $Sustainability$ have made significant contributions, with over five publications on LSO problems in PV and CSP systems.

2.3. Development Trends of Algorithms and Methods

Since there is a wide range of current research on the LSO problem for PV and CSP systems and various application methods, this section focuses on algorithms and methods utilizing meta-heuristic algorithms, numerical simulation and stochastic optimization methods, and ML-based AI methods. To illustrate the temporal development of these methods within the research process of the LSO problem in PV and CSP systems, Figure 2 shows the flow of algorithms and methods for LSO problem research in PV and CSP systems in chronological order. The left side indicates the temporal development sequence of meta-heuristic algorithms, while the right side shows the development sequence of methods based on numerical simulation and stochastic optimization methods and ML-based AI methods.

Through comparative analysis, research on LSO problems in PV and CSP systems based on meta-heuristic algorithms began slightly earlier than research based on numerical simulation and stochastic optimization methods and ML-based AI methods. Both approaches have continued to be developed to this day. The chronological distribution of meta-heuristic algorithms is more evenly spread, with publications exceeding five articles each year except for 2024. In contrast, the publication volume of methods based on numerical simulation and stochastic optimization methods and ML-based AI methods have shown an overall increasing trend year by year. For instance, only one related research method was proposed in 2015, but the average publication volume in the other years, except for 2022, exceeds six articles.

A comparative analysis of the trend in the latest year, 2024, shows that two studies are based on meta-heuristic algorithms, while six studies adopt numerical simulation and stochastic optimization methods and ML-based AI methods. The growing importance of numerical simulation and machine learning methods for solving LSO problems in PV and CSP systems is evident. However, considering the overall publication volume, research on LSO problems based on meta-heuristic algorithms remains the leading solution scheme for PV and CSP systems. As demonstrated in Figure 2, 2020 is a critical time node. Subsequent sections will emphasize and analyze the keywords of the literature before and after this time node to provide deeper insights into the evolution of research trends.

2.4. Analysis of Keyword Clustering

To systematically analyze the connections between the keywords of the 117 documents identified in the screening of this paper, these documents were analyzed using Citespace 6.3. R1(64-bit) Basic [53]. The cluster analysis of these interconnected keywords helps scholars in related fields quickly understand how they describe their research areas. It is conducive to discovering the trends in research themes and quickly extracting research topics in different fields [54]. Figure 3 shows the visualization results of the keyword clustering analysis of the 117 documents screened in this study. These keywords can be divided into six major categories: mathematical models, renewable energy sources, partial shading, energy management, and large-scale solar thermal systems. It should be noted that the title of each group in the keyword cluster analysis visualization is the most frequently occurring keyword in each category, highlighted in colored fonts for emphasis. One thing to note is that the metadata information displayed in the top left corner, including software version, analysis date, and data storage path, is automatically generated by the Citespace software and cannot be edited or removed without affecting the clustering results. This information does not impact the interpretation of the clustering analysis but is essential for documenting the analysis process. These metadata have been retained to ensure the accuracy and completeness of the figure.

To assist readers in understanding the visualizations generated by CiteSpace, we recommend viewing the following online demonstrations, which provide a clear and interactive exploration of the software’s capabilities:

• CiteSpace 5.6.R3: Getting Started—A basic introduction to CiteSpace and its features (available at https://www.youtube.com/watch?v=zPZDu0rm9UM).
• How to Get Started with CiteSpace—A detailed tutorial on working with CiteSpace, including interpretation of visualizations (available at https://www.youtube.com/watch?v=zL2oFRqiP6k).
• CiteSpace 6.2.R4 (Advanced): A Brief Walkthrough—An advanced guide for deeper exploration of CiteSpace’s features (available at https://www.youtube.com/watch?v=yMBUdHEPd-Q).

These resources provide a comprehensive guide to using CiteSpace, ensuring that the figures in this paper can be better understood in their full context.

An in-depth keyword clustering analysis of the literature was conducted to further explore the changes in research topics on LSO problems of PV and CSP systems before and after 2020. The results are shown in Figure 4 and Figure 5. The research hotspots after 2020 have shifted to some extent. Before 2020, the research hotspots mainly included the levelized energy cost at the energy system level, large-scale solar thermal system optimization, energy system storage optimization, hybrid energy system scheduling optimization, and solar power plant location optimization. From 2000 to 2020, the research hotspots focused on hybrid system cooperative optimization and multi-objective optimization problems. In terms of optimization methods, before 2020, the studies primarily involved meta-heuristic algorithms, with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) being the most frequently applied. Specifically, 17 studies utilized GA, while 8 studies employed PSO to tackle LSO problems in PV and CSP systems. In addition to GA and PSO, other meta-heuristic algorithms were also employed, such as Differential Evolution (DE), Simulated Annealing (SA), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), and Grey Wolf Optimizer (GWO).

In contrast, the research hotspots from 2021 to 2024 are more extensive, including the real-time scheduling optimization of solar thermal systems, the large-scale scheduling optimization of hybrid energy systems, and the multi-objective optimization of energy system capacity. A comparison between Figure 4 and Figure 5 shows that ML-based AI methods are still widely used, as evidenced by the keywords in #2 solar energy. Notably, the focus has shifted towards more advanced optimization techniques based on machine learning (ML) and AI methods. Our analysis identified at least 15 studies after 2020 that utilized ML techniques such as Neural Networks, Reinforcement Learning, and Model Predictive Control (MPC) for real-time dispatch optimization and multi-objective optimization in PV and CSP systems.

Moreover, other meta-heuristic algorithms continued to gain attention, with the use of Grey Wolf Optimizer (GWO) in at least three studies, Differential Evolution (DE) in two studies, and other methods like Simulated Annealing (SA), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC), Harmony Search (HS), and Firefly Algorithm (FA) being employed across multiple works. Additionally, multi-objective optimization algorithms such as NSGA-II have been increasingly applied in the field, particularly in addressing complex LSO problems. This shift indicates a broader trend in the field, where traditional meta-heuristic approaches are increasingly being complemented or replaced by ML-based methods, reflecting the growing complexity and dynamic nature of LSO problems in modern energy systems. The increasing diversity in optimization algorithms underscores the evolving nature of research in this area, adapting to the new challenges posed by large-scale, dynamic, and multi-objective optimization tasks.

To explore the development trend of interconnected keyword evolution over time, CiteSpace was used to visualize and analyze six sets of keyword clusters in 117 publications related to PV and CSP energy system LSO problem studies, as shown in Figure 6. From the keyword time evolution analysis, it can be observed that classical meta-heuristic algorithms (e.g., GA, PSO, and GWO) are widely applied in various types of LSO problems within PV and CSP systems. Furthermore, the visual analysis demonstrates that ML-based AI methods are increasingly utilized in the real-time optimization of mirror field scheduling for PV systems and in the multi-objective optimization of capacity for energy systems, indicating a broad application prospect. Additionally, the emergence of ML-based AI optimization methods and the optimization of multi-dimensional scheduling for large-scale hybrid energy systems represent new directions in the field.

For the purpose of demonstrating the development changes before and after the pivotal year of 2020, Figure 7 and Figure 8 present the results of the visualization and analysis of keyword stratification trends. From the visualization results, it is evident that before 2020, research on LSO problems in PV and CSP systems primarily focused on the co-dispatch optimization of hybrid systems, the optimization of renewable energy plant siting, and the power system optimization problems that integrated PV and CSP systems with other types of renewable energy systems. After 2020, more publications adopted AI approaches based on machine learning (i.e., #0 machine learning, #1 distribution network, and #2 model predictive control) for LSO problems. Although the visual analysis highlights the trends of research topics over different years, a detailed comparative analysis of PV and CSP energy system LSO problem research based on different algorithms and methods is still needed to identify current mainstream research methods and accurately define the trends, which is explained in detail in Section 3.

3. A Comparative Analysis

To further investigate the three most widely used optimization algorithms and methods in studying LSO problems for PV and CSP systems, this section provides a comprehensive comparative analysis based on the statistical analysis of keywords from the literature in Section 2. The analysis covers different perspectives on MI-based AI methods (i.e., DGS-SVM, LSTM, RL, DRL, PN, and ANN), meta-heuristic optimization algorithms (i.e., PSO, GA, TLBO, MPA, QOTWFO, and ACO), and numerical simulation and stochastic optimization methods (i.e., LP, MILP, CPM, DPOA, RLS, fuzzy-EWM, GIS, RO, MMCS, and CCG).

3.1. Definition of the LSO Problem in the PV and CSP Energy System

The study of LSO problems for PV and CSP systems refers to optimization problems involving a large number of variables and complex constraints, where the objective is to improve the performance of the whole system by optimizing specific key performance indicators (e.g., energy output, cost-effectiveness, siting optimization, system stability, and reliability). Due to the large size and complexity of the system, LSO problem studies usually involve four types of optimization problems, which differ in their optimization objectives and applicable methods.

• Hybrid energy system co-optimization (HESC) problems need to deal with optimizing the multivariate energy scheduling and supply balancing of hybrid energy systems, including PV and CSP solar, to ensure the efficient operation and stability of the system [55,56,57].
• Multi-objective optimization (MOO) problems usually involve multiple optimization perspectives. The most common optimization perspectives within PV and CSP systems are trade-offs between economic benefits and technical performance, such as maximizing energy output while minimizing system cost [58,59,60].
• Real-time scheduling optimization (RSO) problems include real-time optimization of heliostat scheduling within a CSP system to maximize solar capture efficiency [35,37] and real-time scheduling optimization for hybrid energy systems [36,48].
• Excluding the above three optimization problems, other LSO problems include stochastic optimization problems under uncertainty for decentralized energy systems and constrained optimization problems for CSP systems with fixed-day mirror fields [39,61].

For the above studies of various LSOs within PV and CSP systems, conventional optimization methods may be difficult to apply effectively to various problems. Therefore, advanced optimization methods such as meta-heuristic algorithms, AI methods based on machine learning, and other advanced optimization methods must be targeted according to the characteristics of the different LSO problems that need to be solved.

Based on the classification of LSO problem studies within PV and CSP systems, a comprehensive analysis of the development overview of LSO problems in different optimization problems is provided. However, due to the varying optimization objectives and constraints of the various optimization problems, the existing screening literature research and analysis focus unevenly on different types of LSO problem research. Consequently, it is challenging to obtain consistent and reliable data about the different types of LSO problem research in PV and CSP systems. Comparatively, common types of LSO problems, such as HESC and MOO problems, have received more attention than other types, such as RSO and other LSO problems that exclude the above three types. In particular, the latter two types of LSO problems have gradually increased in relevant studies since 2020. Therefore, this study uses different evaluation characteristic indexes for on different types of LSO problems to ensure accurate and relevant assessments.

3.2. HESC-Based LSO Problem Development

Categorizing studies chronological order to search 117 studies after screening, we categorized 9 of them as HESC problem studies, and the overall development belongs to the vulnerable categorization in the LSO problem of PV and CSP systems. Therefore, comparing experimental testing and simulation based on natural hybrid energy systems is an effective way to deal with the HSEC problem. The results of the analysis in chronological order are shown in

Table 1. The comparative analysis of hybrid energy system co-optimization-based LSO problem development.

Refs.	Algorithm/Methods	Applications	Experiments	Optimization Target	Evaluation Index	Performance Metrics	Feature
							Simulated Data	Real Data
[13]	GA, and PSO	Optimal size design	Simulation based on a mathematical model and optimization algorithm	Optimal configuration of hybrid system with minimum investment	Annualized cost of system (ACS) and loss of power supply probability (LPSP)	LPSP: 0.0092, ACS: $1200	—	✓
[14]	Modified PSO	Coordinated energy control	Practical experiment based on multi-agent system designed by JADE platform	Maximum economic benefit of the system during the study period	System economic benefit, and operating costs and depreciation costs	Energy Efficiency: +15%, Response Time: −30%	✓	—
[62]	Enhanced gravity search algorithm (EGSA)	Coordinated energy control	A WPBB-PGU in the Zhangbei region of China was simulated	Maximum economic benefit of the system during the study period	Unit generation cost	Curtailment Rate: <5%, Scheduling Cost: −12%	—	✓
[44]	LP	Collaborative optimization of size design and control strategy	The experiment was conducted by simulating a 1.2 MW PV power station located in Navaratudra, Spain	Maximizes economic returns, and charging and discharging strategy of energy storage system	Economic returns, and system cost	System Efficiency: +20%, Daily Revenue: +20%	—	✓
[16]	Improved multi-objective firefly algorithm (IMOFA)	Multi-source-load joint optimal scheduling	Simulation is carried out by IEEE-30 standard system	Maximize renewable energy capacity connected to the grid	System cost, and power discharge	RE Penetration: +18%, Total Cost: −10%	—	✓
[60]	Cuckoo search (CS) and dynamic programming (DP)	Hydropower unit commitment and load scheduling	Longyangxia hydropower—photovoltaic power station in China is simulated	Optimizes the online state and load scheduling scheme of hydropower units	System economic benefit and system robustness	Water Consumption: −1.5% (Scenario II), −1.0% (Scenario III), Extra Profits: +8.4M CNY/year	✓	—
[56]	Latin hypercube sampling and scene simplification (LHSSR) methods and mixed integer programming (MIP)	Multi-source-load joint optimal scheduling	Generate scenes using Latin Hypercube sampling and scene simplification methods	Minimize operating costs, and risks and maximize economic benefits and stable operation during the study period	System cost, and system robustness	Efficiency: +12%, GHG Emissions: −8%	—	✓
[63]	Fuzzy entropy weight method (FEWM)	Hybrid Power system peak cutting solutions	The experiment passed IEEE six-bus test system	Minimize the peak-valley difference of residual load	Residual load peak-valley difference	Generation Cost: −14%, Reliability: +10%	✓	—
[64]	Improved multi-objective sparrow search algorithm (IMOSSA)	Address the volatility of wind, and photovoltaic power generation	The experiment selected hydropower station in Hubei Province as the research object	Minimize the grid-connected volatility index, and minimize the wind–solar-out rate	System economic benefit, and wind–solar-out rate	Energy Utilization: +20%, Operational Cost: −15%	✓	—

, which summarizes in detail the development process of HESC problem research in the cycle of 2000–2024 from seven perspectives—references, optimization methods, specific application scenarios, experimental setups, optimization objectives, performance metrics, and evaluation indexes—and provides important insights into the solution of HESC optimization problems. HESC problems are characterized by multi-energy complementarity, uncertainty management, the maximization of economic benefits, system stability, and environmental friendliness. All HESC problems have the same optimization objective, and advanced meta-heuristic optimization algorithms are commonly used to solve complex LSO problems such as HSEC, in addition to the use of natural hybrid energy systems for experimental and simulation validation is also a major advantage. Nine screened papers focus on the co-scheduling optimization of PV and CSP-related hybrid energy systems. The economic efficiency and operational stability of the system are the focus of the investigation.

Categorizing studies in chronological order to search 117 studies after screening, we categorized 9 of them as HESC problem studies, and the overall development belongs to the vulnerable categorization in the LSO problem of PV and CSP systems. Therefore, comparing experimental testing and simulation based on natural hybrid energy systems is an effective way to deal with the HESC problem. The results of the analysis in chronological order are shown in Table 1, which summarizes in detail the development process of HESC problem research in the cycle of 2000–2024 from seven perspectives—references, optimization methods, specific application scenarios, experimental setups, optimization objectives, evaluation indexes, and performance metrics—and provides important insights into the solution of HESC optimization problems. Additionally, statistics on the performance improvement metrics of the optimization methods among HESC optimization problems in each study are presented and compared clearly in Figure 9.

HESC problems are characterized by multi-energy complementarity, uncertainty management, the maximization of economic benefits, system stability, and environmental friendliness. All HESC problems have the same optimization objective, and advanced meta-heuristic optimization algorithms are commonly used to solve complex LSO problems such as HESC. In addition, the use of natural hybrid energy systems for experimental and simulation validation is also a major advantage. The nine screened papers focus on the co-scheduling optimization of PV and CSP-related hybrid energy systems. The economic efficiency and operational stability of the system are the focus of the investigation.

From Table 1 and Figure 9, the performance metrics derived from these studies highlight the effectiveness of various optimization methods in enhancing system reliability, reducing costs, and improving energy utilization. For example, Crăciunescu et al. (2013) [13] demonstrated a significant reduction in the loss of power supply probability (LPSP) to 0.0092 while maintaining a low annualized cost of 1200 dollars. Wu et al. (2014) [14] achieved a 15% increase in energy efficiency and a 30% reduction in response time through coordinated energy control. Similarly, Wu et al. (2015) [62] reported a curtailment rate of less than 5% and a 12% reduction in scheduling cost, demonstrating the effectiveness of enhanced gravity search algorithms. Other studies, such as those by Saez-de-Ibarra et al. (2016) [44] and Yang et al. (2017) [16], also achieved notable improvements in system efficiency and renewable energy penetration, respectively. The research by Ming et al. (2018) [60] on hydropower unit commitment showed a reduction in water consumption by up to 1.5% and increased profits by CNY 8.4 million per year. Tan et al. (2019) [56] and Fang et al. (2022) [63] further highlighted reductions in greenhouse gas emissions and generation costs, while Zhao et al. (2022) [64] improved energy utilization by 20% and reduced operational costs by 15%.

3.3. MOO-Based LSO Problem Development

This section comprehensively examines and analyzes the 117 screened papers on MOO problems for hybrid energy systems from seven perspectives: optimization algorithms and methods, specific application scenarios, experimental setups, optimization objectives, evaluation indexes, performance metrics, and data characteristics. Based on the optimization problem-solving strategy, we classify MOO problems in PV and CSP systems into two categories: meta-heuristic algorithm-based problems and numerical simulation and ML-based problems. Among them, 10 studies focused on MOO problems using meta-heuristic optimization algorithms, primarily aiming to enhance the efficiency and sustainability of energy systems, such as photovoltaic power plants and hybrid energy systems, emphasizing the optimal utilization of renewable energy. However, their focus varies: two articles address the optimization of energy storage systems, while five articles focus on the design of hybrid energy systems, emphasizing generation efficiency and environmentally friendly design. Detailed data is presented in

Table 2. The comparative analysis of Multi-objective optimization-based LSO problems development based on meta-heuristic algorithms.

Refs.	Algorithm/Methods	Applications	Experiments	Optimization Target	Evaluation Index	Performance Metrics	Feature
							Simulated Data	Real Data
[65]	Non-dominated sorting Genetic Algorithm (NSGA-II)	Improve overall hybrid power supply reliability and reduce associated costs	Computational experiment	Minimize power generation costs, Maximize supply reliability, and Maximize average power fill rate	Cost-effectiveness, and power filling rate	Energy Loss: −9.4%, ROI: +3.5%	—	✓
[1]	Hybrid PSO and GA algorithm	Optimization of heliostat field layout	The actual direct solar radiation data of the Lhasa region was used for annual analysis	Maximize ECUC by optimizing the layout of the helioscope field	Annual energy harvesting efficiency, and unit cost energy	Solar Collection: +4.3%, Annual Cost: −2.1%	✓	—
[66]	GA	Determination of optimal photovoltaic capacity in large-scale water-light complementary systems	Experiment through the actual measurement of the photovoltaic power station output data	Optimization of photovoltaic capacity	Complementary guarantee rate (CGR)	ECUC: +3.8%, Efficiency: +6%	—	✓
[58]	Pareto-based immune clone evolutionary algorithm (PICEA)	Independent microgrid based hybrid energy system planning	Simulation studies	Balance economic benefits and system operation risks	Semi-entropy, and semi-entropy	System Risk: −15%, Generation Efficiency: +7.8%	✓	—
[20]	General front modeling-based multi-objective evolutionary algorithm (GFM-MOEA)	Optimize the economic efficiency and operational safety of hydropower and photovoltaic systems	Experiment is conducted in Longyangxia water-light complementary power station in Qinghai, China	Improve the economic benefit, and operation safety of the system	Standard deviation of overgenerated charge and output fluctuation	Generation: +8.2%, Scheduling Cost: −5.7%	✓	—
[67]	Map-reduce-based Genetic Algorithm with a repair operator (MRGAR)	Optimization of solar photovoltaic power station location	GIS data and Genetic Algorithm are used to simulate site selection	Achieve the best geographical location choice for solar power plants	The amount of solar radiation, and the economic cost of site selection	Solar Efficiency: +6%, Computation Speed: +100%	—	✓
[68]	TLBO	Optimization of location and size of EV charging infrastructure in hybrid energy system	Simulation was performed on IEEE 33 and 123 bus systems	Minimize power generation costs, Maximize supply reliability, and maximize average power fill rate	Voltage Stability Index (VSI), and system average interruption frequency index (SAIFI)	Load Balance: +10%, Energy Utilization: +7%	✓	—
[69]	GA	Emphasis on the combination of solar energy and molten salt heat storage technology	Detailed thermodynamic models and economic analyses were used for the systematic evaluation	Optimize energy efficiency and economic efficiency	Energy efficiency, and cost–benefit ratio of the system	Energy Efficiency: +13.5%, GHG Emissions: −10.2%	✓	—
[70]	NSGA-II	Large-scale heating solution for urban or district heating systems	The system performance was simulated with TRNSYS and MATLAB	Achieve high energy efficiency and low operating costs in hybrid energy systems	Heating capacity, and heating cost	Thermodynamic Efficiency: +11.7%, System Stability: +9.3%	✓	—
[71]	Improved PSO	Capacity configuration of energy storage system in photovoltaic power station	Simulation based on improved IEEE 14-bus network	Capacity configuration	The total benefit, and cost–benefit ratio of the system	Storage Efficiency: +14%, Operational Cost: −6%	✓	—

. Additionally, the statistics on the performance improvement metrics of the optimization methods among 10 studies focused on MOO problems using meta-heuristic optimization algorithms in each study, which are presented and compared clearly in Figure 10.

From Table 2 and Figure 10, we observe that the data characteristics used in various articles are closely tied to their research focus. For instance, articles concentrating on power generation efficiency and environmentally optimized hybrid system design often employ simulation experiments, using platforms like MATLAB for algorithm validation and performance testing. The data in these studies are typically extracted from simulation software or historical power generation data from specific regions. Conversely, articles focusing on optimizing energy storage systems for hybrid PV and CSP systems in characteristic areas predominantly use real-time data from those regions. The primary optimization objectives of MOO-based LSO problems are generally consistent, aiming to maximize energy output, minimize costs, and ensure system stability and reliability. The main evaluation indexes include total system production cost and energy efficiency.

Analyzing the performance improvements of various algorithms within these MOO problems, we find that advanced meta-heuristic algorithms like GA, PSO, and NSGA-II play a crucial role in enhancing the efficiency and cost-effectiveness of hybrid energy systems. For example, GA and PSO have been shown to increase energy collection by up to 6% and reduce costs by around 2.1%, as seen in Li et al. (2023) [66]. Similarly, improvements in system reliability and reduction in energy losses were evident in studies using NSGA-II, with Long et al. (2017) [65] reporting a 9.4% reduction in energy loss and a 3.5% increase in return on investment (ROI). Additionally, algorithms like the Pareto-based immune clone evolutionary algorithm (PICEA) have been effective in reducing system risks by 15% while simultaneously improving generation efficiency by 7.8%, highlighting their importance in balancing multiple conflicting objectives in MOO-based LSO problems.

These performance gains underscore the effectiveness of meta-heuristic algorithms in addressing the complexities inherent in multi-objective optimization within large-scale hybrid energy systems. By optimizing key parameters such as energy efficiency, cost reduction, and system stability, these algorithms not only meet the optimization objectives but also enhance the overall reliability and sustainability of the energy systems.

In MOO problem research, other major optimization methods include numerical simulation and stochastic optimization methods, as well as ML-based AI methods. Among the 117 screened articles, 12 papers employed these methods, and detailed statistical information is presented in Table 3. These studies on MOO problems focus more on multivariate optimization calculations in hybrid energy systems, such as hybrid energy management and power load forecasting. Common optimization objectives include minimizing prediction errors, improving system stability, and optimizing resource allocation. Common evaluation metrics include prediction accuracy, system reliability, and operation cost. Additionally, the statistics of the performance improvement metrics of the optimization methods among 10 studies focused on MOO problems using numerical simulation, stochastic optimization methods, and ML-based AI methods in each study are presented and compared clearly in Figure 11.

Unlike studies of MOO problems based on meta-heuristic algorithms, studies based on numerical simulation and stochastic optimization methods typically use deterministic models with relatively low complexity but require more detailed system physical parameters. Consequently, the data used in these types of MOO problem studies are often derived from the real-time data of real-area energy systems, which is also reflected in Table 3 and Figure 11. Specifically, 8 out of 12 studies utilized real-time data from natural hybrid energy systems in different regions of various countries for experimental calculations. In contrast, ML-based AI methods, which can handle high-dimensional data and complex relationships, are capable of dealing with more complex systems and require large amounts of data during the training phase. Therefore, it is often necessary to expand the data volume using simulated data to meet the model’s requirements. Four of the aforementioned articles used simulated data along with historical data.

Further analysis of the performance improvements of the algorithms used in the 12 articles shows that

• ML and AI methods demonstrated significant advantages in improving energy system efficiency and reducing operational costs. For instance, in the study by [72], the optimization algorithms K-means and GA reduced output volatility from 20% to 2%; in [73], the combination of LSTM and ACO improved hydrogen production rates and increased system efficiency to 5.92%.
• These studies have proven the widespread application of ML- and AI-based algorithms in MOO problems, particularly in handling complex systems and large datasets, where the observed performance improvements are substantial. These studies not only enhanced prediction accuracy but also optimized system stability and resource allocation efficiency, which is critical for future hybrid energy system management.

Table 3. Comparative analysis of multi-objective optimization-based LSO problems development based on numerical simulation and stochastic optimization methods and ML-based AI methods.

Refs.	Algorithm/Methods	Applications	Experiments	Optimization Target	Evaluation Index	Performance Metrics	Simulated Data	Real Data
[74]	DPOA	High penetration of renewable energy (wind and solar) applications VRB systems	A mathematical model is used to verify the feasibility of the proposed framework	Maximize wind and solar energy consumption, and Minimize total system costs	Total cost, and total benefit of hybrid energy system	Wind and solar energy abandoned rate reduced from 16.47% to 7.49%	—	✓
[23]	LP	The optimal PV capacity configuration of Longyangxia water-light complementary Power Station in Qinghai, China was studied	Using the actual output data of the Longyangxia power station	The largest net benefit of PV installed capacity	Annual solar cut-off rate (ASCR), and net revenue growth rate (NRI)	Annual net revenue increased by 12.3%	—	✓
[50]	Double Grid Search Support Vector Machine (DGS-SVM)	Power prediction of hybrid energy system	Simulation studies using real-time grid load data and meteorological data from Australia	Minimize network load fluctuations	Smoothing effect, and energy scheduling performance of the system	Prediction error reduced to less than 0.065	—	✓
[49]	Hydrothermal solar energy scheduling (HTSS) algorithm, DP and Linear Programming (LP)	Integrate large-scale rooftop solar PV into the existing Mumbai hydro thermal hybrid system	Use historical electricity demand and generation data for Mumbai	Minimize annual generation costs, and optimize the operating efficiency of the power system	Generating cost	Generation cost reduced by 8.7%	—	✓
[55]	Augmented $ϵ$-Constraint (AUGMECON2)	Determine the best capacity expansion path	Use historical wind and solar data for Germany	Maximize the share of renewable energy, and minimize excess energy in the system	Power supply efficiency	Renewable energy share increased by 25%	—	✓
[21]	Iterative calculation method based on mathematical model	Evaluate and optimize the scale of energy storage systems	Historical electricity price data and power generation performance data of photovoltaic systems are used	Maximize economic return	Net Present Value, (NPV), Internal Rate of Return (IRR), and Payback Period (PBP)	Internal Rate of Return (IRR) increased to 14%	✓	—
[46]	Iterative calculation method based on mathematical model	Evaluate and optimize the scale of energy storage systems	Historical electricity price data and power generation performance data of photovoltaic systems are used	Optimize the economy of power supply and energy storage system	Net Present Value, (NPV), Internal Rate of Return (IRR), and Payback Period (PBP)	Payback Period reduced to 7.64 years	✓	—
[73]	Long short-term memory (LSTM) and Ant colony optimization (ACO) algorithm	Strategy for controlling a solar receiver with multiple thermochemical reactors	Simulation models are used to test different control strategies and optimize the distribution of the target point	Ensure that each reactor operation achieves the highest hydrogen yield within material constraints	Temperature control accuracy, and energy efficiency of system	Hydrogen production rate achieved 42.3 mmol/s, and Efficiency improved to 5.92%	✓	—
[75]	K-means algorithm and PSO	The hybrid power system ensures the effective coordination and optimization of energy	The simulation was verified by IEEE 39-bus system	Minimize annual generation costs, and optimize the operating efficiency of the power system	Total cost, and total benefit of hybrid energy system	Cost reduction by 15.4%	—	✓
[76]	Novel Reinforcement Learning (RL) based on Deep Q Network (DQN) algorithm	Energy management programming	Simulation on IEEE 57-bus system	Minimize annual generation costs, and optimize the operating efficiency of the power system	Total cost, and total benefit of hybrid energy system	Operating cost reduced by 10.3%	✓	—
[72]	K-means algorithm and GA	Optimization of energy storage configuration strategy in wind power and photovoltaic hybrid systems	Simulations were performed using actual wind and photovoltaic data in Ulanqab City, China	Optimize capacity configuration of the energy storage system	Output volatility, and the economics of energy storage systems	Output volatility reduced from 20% to 2%	—	✓
[28]	Finite Set Model Predictive Current Control (FS-MPCC)	Model predictive current control for large-scale solar/wind hybrid systems	HOMER software was used for system design and economic feasibility analysis	Ensure reliable and cost effective energy supply	Energy costs, and System reliability	Current control error reduced, improving system reliability by 12.5%	—	✓

Table 3. Comparative analysis of multi-objective optimization-based LSO problems development based on numerical simulation and stochastic optimization methods and ML-based AI methods.

Refs.	Algorithm/Methods	Applications	Experiments	Optimization Target	Evaluation Index	Performance Metrics	Simulated Data	Real Data
[74]	DPOA	High penetration of renewable energy (wind and solar) applications VRB systems	A mathematical model is used to verify the feasibility of the proposed framework	Maximize wind and solar energy consumption, and Minimize total system costs	Total cost, and total benefit of hybrid energy system	Wind and solar energy abandoned rate reduced from 16.47% to 7.49%	—	✓
[23]	LP	The optimal PV capacity configuration of Longyangxia water-light complementary Power Station in Qinghai, China was studied	Using the actual output data of the Longyangxia power station	The largest net benefit of PV installed capacity	Annual solar cut-off rate (ASCR), and net revenue growth rate (NRI)	Annual net revenue increased by 12.3%	—	✓
[50]	Double Grid Search Support Vector Machine (DGS-SVM)	Power prediction of hybrid energy system	Simulation studies using real-time grid load data and meteorological data from Australia	Minimize network load fluctuations	Smoothing effect, and energy scheduling performance of the system	Prediction error reduced to less than 0.065	—	✓
[49]	Hydrothermal solar energy scheduling (HTSS) algorithm, DP and Linear Programming (LP)	Integrate large-scale rooftop solar PV into the existing Mumbai hydro thermal hybrid system	Use historical electricity demand and generation data for Mumbai	Minimize annual generation costs, and optimize the operating efficiency of the power system	Generating cost	Generation cost reduced by 8.7%	—	✓
[55]	Augmented $ϵ$-Constraint (AUGMECON2)	Determine the best capacity expansion path	Use historical wind and solar data for Germany	Maximize the share of renewable energy, and minimize excess energy in the system	Power supply efficiency	Renewable energy share increased by 25%	—	✓
[21]	Iterative calculation method based on mathematical model	Evaluate and optimize the scale of energy storage systems	Historical electricity price data and power generation performance data of photovoltaic systems are used	Maximize economic return	Net Present Value, (NPV), Internal Rate of Return (IRR), and Payback Period (PBP)	Internal Rate of Return (IRR) increased to 14%	✓	—
[46]	Iterative calculation method based on mathematical model	Evaluate and optimize the scale of energy storage systems	Historical electricity price data and power generation performance data of photovoltaic systems are used	Optimize the economy of power supply and energy storage system	Net Present Value, (NPV), Internal Rate of Return (IRR), and Payback Period (PBP)	Payback Period reduced to 7.64 years	✓	—
[73]	Long short-term memory (LSTM) and Ant colony optimization (ACO) algorithm	Strategy for controlling a solar receiver with multiple thermochemical reactors	Simulation models are used to test different control strategies and optimize the distribution of the target point	Ensure that each reactor operation achieves the highest hydrogen yield within material constraints	Temperature control accuracy, and energy efficiency of system	Hydrogen production rate achieved 42.3 mmol/s, and Efficiency improved to 5.92%	✓	—
[75]	K-means algorithm and PSO	The hybrid power system ensures the effective coordination and optimization of energy	The simulation was verified by IEEE 39-bus system	Minimize annual generation costs, and optimize the operating efficiency of the power system	Total cost, and total benefit of hybrid energy system	Cost reduction by 15.4%	—	✓
[76]	Novel Reinforcement Learning (RL) based on Deep Q Network (DQN) algorithm	Energy management programming	Simulation on IEEE 57-bus system	Minimize annual generation costs, and optimize the operating efficiency of the power system	Total cost, and total benefit of hybrid energy system	Operating cost reduced by 10.3%	✓	—
[72]	K-means algorithm and GA	Optimization of energy storage configuration strategy in wind power and photovoltaic hybrid systems	Simulations were performed using actual wind and photovoltaic data in Ulanqab City, China	Optimize capacity configuration of the energy storage system	Output volatility, and the economics of energy storage systems	Output volatility reduced from 20% to 2%	—	✓
[28]	Finite Set Model Predictive Current Control (FS-MPCC)	Model predictive current control for large-scale solar/wind hybrid systems	HOMER software was used for system design and economic feasibility analysis	Ensure reliable and cost effective energy supply	Energy costs, and System reliability	Current control error reduced, improving system reliability by 12.5%	—	✓

In conclusion, the 12 articles in Table 3 and Figure 11 demonstrated through real-world applications and the integration of simulated data that ML- and AI-based algorithms are widely used in MOO problems, showing great potential in optimizing the multi-objective performance of energy systems.

3.4. RSO-Based LSO Problem Development

Compared with HESC- and MOO-based LSO problem research, RSO-based is a new LSO problem research direction that emerged around 2020. Therefore, there are fewer research results and 5 RSO-based LSO problem studies among the 117 articles screened. These five articles mainly focus on the real-time scheduling optimization of energy systems, including PV and CSP, and the articles generally focus on the operational efficiency and stability of energy systems, so real-time system scheduling is a vital reference index. In addition to the system stability, the output energy efficiency is another commonly used evaluation index in the research on RSO-based LSO problems. RSO brings significant challenges to the algorithms. In order to solve this challenge, improved meta-heuristic algorithms and AI methods based on ML have been applied to the research of this problem, in which the improved meta-heuristic algorithms can be improved by adaptation to obtain a more efficient solution efficiency from the real-time requirements. The ML-based AI methods can be improved through a large amount of high-quality data and training to obtain a high-accuracy system-scheduling model, thus realizing the real-time scheduling optimization of the hybrid energy system. Detailed RSO-based LSO problem study information is shown in

Table 4. A comparative analysis of real-time scheduling optimization-based LSO problem development.

Refs.	Algorithm/Methods	Applications	Experiments	Optimization Target	Evaluation Index	Performance Metrics	Simulated Data	Real Data
[26]	Newton–Raphson algorithm numerical simulation method, MPC model prediction controller	Real-time voltage coordination in the distribution network of photovoltaic power generation	The model test was carried out on the digital real-time simulator (RTDS) of the real power grid	Optimize control measures and coordinate regulatory actions for BESS and other grid devices	Global voltage stability	Voltage deviation reduced by 15%, total system losses reduced by 12%, overall system efficiency improved by 9%	—	✓
[35]	Reinforcement learning (RL), and pointer network (PN)	Heliostat field real-time aiming strategy optimization	A Crescent-dune-style SPT case study was used	Maximize thermal power output while maintaining safe operating limits	Thermal power output	Thermal power output increased by 16%, optimization time reduced by 70%	—	✓
[36]	DP	Real-time scheduling strategy of water-light hybrid system	Simulate the behavior of hybrid systems under different solar outputs to verify the methodology	Improve the overall efficiency of energy use	Reliability and economic efficiency of power generation systems	Overall energy efficiency improved by 12.5%, operation cost reduced by 10.7%	—	✓
[37]	Improved PSO	Heliostat field real-time aiming strategy optimization	Verify by simulating the environment	Improve heliostat interception efficiency, system robustness, and reduce optimization time	Interception efficiency, system stability, and time required for optimization	Interception efficiency improved by 11.3%, optimization time reduced by 20%	—	✓
[48]	Dynamic Real-Time Optimization with Rolling Time Horizon	Non-concentrating solar thermal power plant dynamic real-time optimization	Online testing methods through detailed simulation models	Economically optimal operation to improve the reliability of energy supply	Percentage of energy provided, and operating cost, system stability	Storage system efficiency improved by 14%, operating cost reduced by 6%	—	✓

and Figure 12.

From Table 4 and Figure 12, it is evident that while all the studies are within PV and CSP systems, their specific application scenarios differ. Two articles focus on real-time voltage control in hybrid energy systems, aiming for voltage stability and reliability, a complex process due to the intermittent and unpredictable nature of PV outputs. Another two articles concentrate on the real-time optimization of heliostat aiming strategies, adjusting the angle and position of heliostats in CSP systems to maximize solar energy capture and thermal energy output.

In terms of performance improvement, the studies demonstrate significant advancements. In Krata et al. (2019) [26], voltage deviation was reduced by 15%, total system losses were reduced by 12%, and overall system efficiency improved by 9%. This highlights the effectiveness of the applied real-time optimization algorithms in enhancing voltage stability and reducing losses in hybrid energy systems. In Wang et al. (2023, 2024) [36,37], for heliostat field optimization, thermal power output increased by 16%, and interception efficiency improved by 11.3%. Additionally, the optimization time was significantly reduced, with reductions of up to 70% in some cases. These improvements underscore the importance of real-time optimization in CSP systems, where precise heliostat control is critical for maximizing energy capture. In Untrau et al. (2024) [48], in storage management for solar thermal power plants, storage system efficiency improved by 14%, and operating costs were reduced by 6%. This demonstrates the potential of real-time optimization in enhancing the economic and operational efficiency of energy storage systems.

Additionally, all five RSO-based LSO studies utilized simulation data for experimental validation. Simulation data allow for the precise control of experimental variables, facilitating the development and testing of optimization algorithms. It also overcomes the limitations of real data access and privacy concerns by providing a complete and reproducible testing environment without privacy issues. This enables researchers to systematically evaluate algorithm performance under ideal conditions, effectively advancing the early-stage development and optimization of algorithms. The combined analysis of these studies reveals that real-time optimization plays a crucial role in improving the performance, stability, and efficiency of PV and CSP systems, with significant advancements being made in both voltage control and heliostat optimization. The use of simulation data in these studies further enhances the reliability and scalability of the optimization algorithms being developed.

3.5. Development of the Other LSO Problems Excluding the above Three Problems

In the study of LSO problems for PV and CSP systems, in addition to the three types of optimization problems, HESC, MOO, and RSO, some studies do not belong to the characteristics of the above three types of optimization problems but still belong to the category of LSO problems. This optimization problem can be categorized as the stochastic optimization of PV and CSP systems, uncertainty optimization, etc. The main optimization objective is still to improve the economic efficiency of PV and CSP systems. In contrast, energy utilization and system reliability vary according to the research focus of different articles. Among the 117 articles screened, we selected 13 articles for comparative information analysis. The detailed comparative information is shown in

Table 5. A comparative analysis of other LSO problems excluding the above three problems.

Refs.	Algorithm/Methods	Applications	Experiments	Optimization Target	Evaluation Index	Performance Metrics	Simulated Data	Real Data
[39]	GA	Optimization of heliostat layout in solar tower power station	Simulation	Optimize the heliostat layout to maximize energy collection on the receiver	Energy harvesting efficiency, and calculation speed	Energy collection efficiency increased by 18%	✓	—
[57]	Stochastic optimization (SO)	Stochastic optimal scheduling of integrated CSP and wind farms	Simulation experiments, using case studies to verify the validity of the model	Optimize energy output and reduce system uncertainty	Economic benefits of the system	Economic benefits increased by 12.8%	✓	—
[77]	Meta-heuristic algorithm	Bringing renewable energy sources like wind and solar to Saudi Arabia	Simulation	Improve the economic efficiency and sustainability of the energy system	Cost-effectiveness of energy systems, and utilization of renewable energy sources	System costs reduced by 15%, economic benefits increased by 13.5%	✓	—
[78]	Competitive swarm optimizer (CSO), and DP	Optimization of daily operation of photovoltaic - cell hybrid systems	Validate with historical data or generated data	Minimize costs and maximize energy efficiency	Cost-effective and energy-efficient	System energy efficiency increased by 11.7%, operating costs reduced by 9.3%	✓	—
[79]	MILP	Large-scale renewable energy hybrid distributed power generation system applied in distributed network system	The experiment is based on climate data and actual load demand data from the KwaZulu-Natal region of South Africa	Maximize the penetration of renewable energy generation and minimize the total cost	Total system cost, and net present value (NPV)	Energy penetration increased by 15%, system cost reduced by 10.2%	—	✓
[80]	MILP	Improve the reliability and economy of the power system	A case study based on actual data from Punjab power corporation (PSPCL)	Minimize the total cost of the energy system	Total annual energy cost, peak load reduction, economic benefits of the system	System reliability improved by 7.8%, cost reduced by 8%	—	✓
[81]	Marine predators algorithm (MPA)	Reconstruction of large-scale photovoltaic arrays	Experiment with simulation data	Maximize the output power of the photovoltaic array while minimizing power loss	Fill factor (FF), and mismatch power loss	System efficiency improved by 14.5%, reliability increased by 10.4%	✓	—
[82]	Marine predators algorithm (MPA)	Accurate electrical modeling of photovoltaic modules	Real data from two common PV modules in the market (Kyocera KC200GT and Solarex MSX-60)were used for simulation validation	Minimum current error	Fill factor (FF), mismatch power loss, power loss percentage (%Ploss), and mean execution time (Mean Execution Time)	Parameter identification accuracy increased by 13.2%, optimization speed improved by 18%	✓	—
[83]	MILP	Management strategies to minimize system operating costs	The simulation is based on actual data from central Italy, including solar radiation data and market price data	Minimize system operating costs	Total operating cost of the system, and performance of the energy storage system	Operating cost reduced by 17.8%, energy utilization efficiency increased by 12.7%	✓	—
[84]	MILP	Integrate wind, photovoltaic and high-capacity hydropower into the grid	A case study based on the actual data of a provincial power grid in southwest China	Maximize the total profit of a hybrid energy system	Total system operating cost, and total profit	Profit increased by 14.2%, system stability improved by 8%	✓	—
[85]	GA	Optimize cleaning strategies for large-scale photovoltaic power plants	A case study was conducted based on the actual data of a 100 MWp photovoltaic power station in Xinjiang	Minimize the total economic loss of the system	Total economic losses (including power losses, cleaning team costs and travel costs)	Power generation efficiency increased by 10.8%, cleaning cost reduced by 15.4%	✓	—
[86]	Coronavirus herd immunity optimizer (CHIO)	Efficiently configure and scale facade thermal PV systems	A 295-bus system based on the interconnection of IEEE 141-bus, IEEE 85-bus and IEEE 69-bus subsystems is simulated	Minimize system operating costs	Total cost, voltage deviation, and power loss	Energy efficiency improved by 12.7%, structural integrity increased by 9.5%	—	✓
[29]	Alternating direction method of multipliers (ADMM)	Increase the utilization rate of wind power, photovoltaic and solar thermal systems	Based on a regional power grid development planning data	Minimize system operating costs	Total operating cost, and transaction power	System operating cost reduced by 14.2%, system utilization rate improved by 8%	—	✓

. Additionally, the statistics of the performance improvement metrics of the optimization methods, among other LSO problems, excluding the above three problems, in each study are presented and compared clearly in Figure 13.

As shown in Table 5 and Figure 13, analyzing the research background of these 13 articles shows that there are three main types of problems: PV array reconfiguration, energy system reliability optimization, and cross-regional energy system coordination. The optimization algorithms applied in these studies vary depending on the specific attributes of the optimization problems, such as hybrid energy system optimization in cross-regional energy coordination, which involves a hybrid optimization problem with both discrete and continuous variables.

MILP (Mixed-Integer Linear Programming) is widely used in these cases due to its strong modeling capability, high solution efficiency, and good flexibility and robustness. Notably, 5 out of the 13 articles adopted the MILP method, demonstrating its effectiveness in solving complex optimization problems in energy systems. On the other hand, meta-heuristic algorithms like MPA (Marine Predators Algorithm) and CHIO (Coronavirus Herd Immunity Optimizer), known for their strong balance of local and global search capabilities, are primarily applied to PV array modeling and reconfiguration optimization problems. Two articles employed the MPA algorithm, while one utilized the CHIO algorithm. These algorithms showed significant improvements in performance metrics, such as enhancing system efficiency, reducing power losses, and improving the accuracy of parameter identification. Furthermore, the experimental data used in these studies primarily focus on parameter-identification problems within the PV system field. These problems necessitate the use of actual PV module data to ensure that the identified parameters are accurate under real-world conditions, thereby increasing the practical applicability of the models. Among the 13 articles, four utilized real-world data to validate their models.

In terms of performance improvements, the algorithms applied in these studies have demonstrated substantial enhancements across various metrics. For instance,

• Energy collection efficiency increased by 18% in PV array reconfiguration studies using GA;
• Economic benefits in energy system optimization were improved by 12.8% with stochastic optimization methods;
• System costs were reduced by 15%, and economic benefits increased by 13.5% in studies applying meta-heuristic algorithms like MPA and CHIO;
• Energy efficiency in hybrid energy systems was improved by 11.7%, and operating costs were reduced by 9.3% using CSO;
• Energy efficiency in hybrid energy systems was improved by 11.7%, and operating costs were reduced by 9.3% using CSO.

These findings highlight the effectiveness of various optimization algorithms in enhancing the performance of PV and CSP systems across different types of large-scale optimization problems, excluding HESC, MOO, and RSO issues. In summary, the research focus of the study of LSO problems for PV and CSP systems has undergone a shift from hybrid system co-optimization and multi-objective optimization to real-time scheduling optimization of energy systems. Optimization tools also experienced a shift from meta-heuristic algorithms as the main optimization tools to ML-based AI methods along with the change in research focus. In addition, the research on LSO problems of PV and CSP systems has increasingly shown a growing trend of multidisciplinary cooperation.

4. LSO Methods

To further enhance the understanding of the three types of optimization algorithms and methods commonly used in the study of LSO problems for PV and CSP systems, thereby facilitating the progress of LSO research, this section provides a detailed description and analysis of three types of optimization approaches: meta-heuristic algorithms, numerical simulation and stochastic optimization methods, and ML-based AI algorithms. These methods address various LSO problems, as discussed in Section 3. The objective is to establish benchmark criteria for studying different LSO problems, aligning them with appropriate optimization methods, and supporting their application in future LSO research for PV and CSP systems. This section briefly summarizes the key features of two types of numerical simulation and stochastic optimization methods, two types of MI-based AI methods, and four meta-heuristic algorithms. The main contributions of this section include:

• Applying each kind of algorithm and method within each type of LSO problem among PV and CSP systems,
• Consolidating information on various methods and establishing common evaluation criteria as a basis for applying these methods to study various LSO problems in PV and CSP systems.

Finally, the algorithmic characteristics of the various types of algorithms and the peculiar advances in applications and LSO problems are summarized. The comparison results and detailed information are shown in Figure 14.

In Figure 14, the lower part indicates the times when different types of optimization methods and algorithms were first proposed. In contrast, the upper part indicates when these optimization algorithms and methods were first applied to studying LSO problems in PV and CSP systems. It is observed that numerical simulation optimization methods such as MILP and DP were proposed before 1960, while GA and RL were introduced before 1980. PSO, Differential Evolution (DE), and LSTM were proposed before 2000, and only one, CHIO, was proposed in 2020 due to the spread of the novel coronavirus. The first application of these three optimization methods to the LSO problems of PV and CSP systems occurred after 2010. Initially, numerical simulation methods like MILP and DP were applied, and since 2013, meta-heuristic algorithms have been widely used. Around 2020, with increasing emphasis and research on real-time scheduling problems, AI methods based on machine learning have gradually been applied.

4.1. LSO Methods Based on Numerical Simulation and Stochastic Optimization Methods

4.1.1. Mixed-Integer Linear Programming Method

The MILP method is widely used in optimization problems and is a mathematical optimization algorithm combining discrete and continuous variables [87,88,89]. The essence of MILP is to solve an optimization problem with linear constraints and an objective function through modeling to solve optimization problems with mixed integer (0–1 variables) and continuous variables. In the study of LSO problems for PV and CSP systems, the MILP method can find the optimal system configuration and operation strategies by modeling the complex energy system decision problem [90,91].

The MILP method is a powerful optimization tool capable of handling multiple constraints and objectives and providing globally optimal solutions. The method applies to energy systems containing multiple decision variables and complex constraints, such as power scheduling, capacity planning, and system configuration problems. MILP is able to efficiently optimize the system performance in different energy scenarios to improve economic efficiency and energy utilization [92,93]. Its algorithmic features include strong mathematical modeling capability, high solution efficiency, flexibility, and adaptability. It can accurately describe the discrete and continuous decision problems in complex energy systems and has an efficient solving ability for LSO problems; in addition, it can flexibly introduce a variety of linear constraints to adapt to different optimization objectives and scenarios. In the study of LSO problems in PV and CSP systems, the types of optimization problems adapted by MILP include the following:

• Capacity configuration and dispatch optimization of energy systems: determining the optimal equipment capacity and operation strategy to minimize total system cost and improve system reliability.
• Cross-regional energy system coordination: optimizing te energy transmission and dispatch between different regions to improve overall energy use efficiency.
• Cross-regional energy system coordination: optimizing the energy transmission and dispatch between different regions to improve overall energy use efficiency.

The accuracy of MILP depends on the accuracy of the mathematical model [94,95], the parameter settings, and the solver’s performance. Therefore, in the LSO problem of PV and CSP systems, it is necessary to establish appropriate mathematical models according to the specific situation and ensure correct initialization and parameter adjustment to obtain accurate and reliable optimization results. Through effective modeling and solving, MILP can significantly improve energy systems’ economic and operational efficiency.

4.1.2. Dynamic Programming Method

DP is widely used for multi-stage decision-making problems and is an algorithm that solves complex optimization problems by recursively solving subproblems [96,97,98]. The essence of DP is to decompose the original problem into a series of interrelated subproblems, using the optimal solutions to construct the solution for the entire problem. In the study of LSO problems in PV and CSP systems, DP can optimize the long-term operational strategies of energy systems through staged decision-making and recursive computation [99,100,101]. DP is a powerful tool for handling multi-stage decision-making problems, especially those with time series characteristics. Its algorithm features include staged decision-making, recursive relationships, and global optimal solutions. In the study of LSO problems in PV and CSP systems, the types of optimization problems suitable for DP include the following.

• Long-term energy scheduling and planning: optimizing the operational strategies of energy systems over multiple periods, such as seasonal storage scheduling and multi-year energy planning.
• Charging and discharging optimization of energy storage systems: determining the optimal charging and discharging strategies of energy storage systems at different periods to balance energy supply and demand.
• Multi-stage resource allocation problems: collaborative optimization of PV and CSP systems across seasons to maximize the overall benefits of the system.

DP’s accuracy and efficiency depend on the state space’s definition and the precision of recursive calculations [102,103]. In the LSO problems of PV and CSP systems, it is crucial to properly define the state space and decision variables and ensure the correctness of the recursive relationships to obtain accurate optimal solutions. Using staged decision-making and recursive solving, DP can effectively handle complex long-term optimization problems, providing a powerful optimization tool for energy systems’ long-term planning and operation. Through DP, researchers can optimize the long-term strategies of energy systems, balance energy supply and demand across different periods, and improve the systems’ economic benefits and operational efficiency. Such an approach is crucial in the optimization research of PV and CSP systems, especially when dealing with complex problems that have time-series characteristics. DP offers a systematic solution for effectively addressing these challenges.

4.2. LSO Methods Based on ML-Based AI Methods

4.2.1. Long Short-Term Memory (LSTM)

LSTM [104,105] is a particular type of recurrent neural network (RNN) designed explicitly for handling and predicting time series data. With its unique memory cells and gating mechanisms, LSTM can capture long-term dependencies, avoiding the vanishing and exploding gradient problems in traditional RNNs. The main features of LSTM include memory cells: An LSTM unit contains a cell state and three gates (input gate, forget gate, and output gate) [106,107,108]. These gates control the flow of information in and out, determining which information needs to be remembered and which should be forgotten. They also handle long-term dependencies: LSTM can effectively capture and utilize long-term dependencies in time series data, making it suitable for sequence prediction problems with long-term dependency characteristics. In addition, they also have stable gradients: through its gating mechanism, LSTM addresses the vanishing and exploding gradient issues of traditional RNNs, allowing the network to maintain a stable training process over long time series data. The three basic RNN model diagrams are shown in Figure 15.

In LSO problems, LSTM networks can provide accurate predictions of future states by learning and forecasting time series data, such as historical power generation and weather data for PV and CSP systems. This predictive capability can significantly enhance the efficiency and effectiveness of optimization algorithms. The essence of applying LSTM to solve LSO problems lies in its powerful modeling and forecasting capabilities for time series data, enabling it to capture dynamic changes and long-term trends in system operations. It provides crucial support information for optimization decisions. The optimization problem types suited for LSTM in PV and CSP systems include the following.

• Energy production forecasting: forecasting the power production of PV and CSP systems for future periods, helping to optimize scheduling and resource allocation.
• Load forecasting: forecasting future power demand to provide a basis for optimal scheduling of energy systems.
• Energy management optimization: optimizing the charging and discharging strategy of the energy storage system by combining the prediction results of LSTM to improve the system’s economic and operational efficiency.
• Multi-stage resource allocation problem: synergistic optimization of cross-seasonal PV and CSP systems to maximize the overall benefits of the system.

With its powerful time series data modeling and prediction capabilities, the LSTM network can significantly improve the optimization of the system in the LSO problem of PV and CSP systems. By accurately predicting future energy production and load demand, LSTM provides essential support information for optimization decisions and applies to various optimization problem types, such as energy production forecasting, load forecasting, and energy management optimization. The solution process of LSTM, which involves data preprocessing, network construction, model training and validation, and the combination of prediction and optimization, offers powerful tools.

4.2.2. Reinforcement Learning

RL is a machine learning method that learns optimal strategies to maximize cumulative rewards by interacting with the environment [109,110,111]. Its main features include interactive learning: the RL algorithm adjusts its strategy based on feedback signals (rewards or penalties) by continuously interacting with the environment; the balance between exploration and exploitation: in finding the optimal policy, RL algorithms must find a balance between exploring unknown policies and exploiting the best-known ones; and time-delayed rewards: RL can deal with reward problems with time delays—i.e., the effect of the current action may manifest after multiple steps in the future.

In LSO problems, RL finds optimal strategies that maximize system benefits through continuous experimentation and learning [35,76]. The essence of applying RL to solve LSO problems lies in its adaptability and intelligent decision-making capabilities, allowing it to gradually optimize strategies in complex and dynamic environments to meet the system’s changing demands [112]. The types of optimization problems suitable for RL in PV and CSP systems LSO problems include the following

• Energy scheduling optimization: determining the optimal generation scheduling strategy for PV and CSP systems to maximize efficiency and economic benefits.
• Energy storage system management: optimizing the charging and discharging strategies of the energy storage system to balance energy supply and demand and improve system stability and economic efficiency.
• Load management: optimizing power consumption and improving energy efficiency through intelligent scheduling and load management.
• Multi-energy system integration: optimizing the synergistic operation strategy of multi-energy systems (e.g., photovoltaic, wind, and energy storage systems) to achieve the overall optimal benefits.

RL can significantly improve the optimization of PV and CSP systems in LSO problems through its adaptive and intelligent decision-making capabilities. RL applies to a wide range of optimization problem types, such as energy scheduling optimization, storage system management, load management, and multi-energy system integration. By defining the environment, state space, action space, and reward function, the RL algorithm can learn the optimal strategy step by step in complex and changing environments to achieve efficient operation and the optimization of energy systems. The solution process of RL includes interactive learning, strategy evaluation, and optimization, which provides a flexible and intelligent optimization solution for energy systems.

4.3. LSO Methods Based on Meta-Heuristic Algorithms

4.3.1. Swarm Intelligence Algorithms

Swarm intelligence (SI) algorithms solve complex optimization problems by simulating natural group behaviors (e.g., birds foraging in flocks, fish swimming in schools, wolves foraging in packs, etc.) [113,114,115]. Through collaboration and information sharing among individuals, SI algorithms can efficiently explore and develop the search space to find the global optimal solution [116,117,118,119]. PSO, as the most typical SI algorithm, with the characteristics of group search, fast convergence, and simple implementation, has been widely used in the study of LSO problems in PV and CSP systems. The types of optimization problems that PSO is adapted to in PV and CSP systems are summarized as follows:

• Energy system configuration optimization: e.g., configuration optimization of PV arrays and CSP systems to improve the energy output and efficiency of the system.
• Scheduling optimization: optimizing the energy system’s real-time scheduling strategy to improve the system’s economy and reliability.
• Parameter optimization: e.g., PV model parameter identification and CSP system operation parameter optimization to improve system model accuracy and operational efficiency.

CHIO is a newly developed SI algorithm inspired by the novel coronairus in 2020. CHIO continuously optimizes the fitness of the swarm by simulating the virus infection and the swarm immunity process. CHIO continuously optimizes the fitness of the swarm by simulating the viral infection and the swarm immunity process. The essence of CHIO in solving the LSO problem lies in its dynamic adaptability and its efficient global search ability to find the optimal solution in a complex search space to find the optimal solution. The types of fitness optimization problems of CHIO in LSO problems of PV and CSP systems are summarized as follows.

• System configuration optimization: optimizing the configuration of PV and CSP systems to improve the energy output and efficiency of the system.
• Dynamic dispatch optimization: optimizing the real-time dispatch strategy of complex energy systems to improve the system’s economic efficiency and operational stability.

SI algorithms, such as PSO and CHIO, have broad applicability and flexibility in LSO problems [120,121,122,123]. PSO, which simulates the movement of particles in the search space and information sharing, is characterized by fast convergence and simple implementation. It is well suited for energy system configuration, scheduling optimization, and parameter optimization. Conversely, CHIO simulates virus infection and population immunity mechanisms, offering dynamic adaptability and efficient global search capabilities. This makes it suitable for system configuration, multi-objective, and dynamic scheduling optimization. Both algorithms find near-optimal solutions to optimization problems by initializing the population, evaluating fitness, and updating the state and position to gradually improve the population’s fitness.

4.3.2. Evolutionary Algorithms

Evolutionary algorithms are a class of optimization algorithms inspired by the natural evolutionary process [124,125,126], which find optimal solutions to complex optimization problems by simulating the mechanisms of selection, crossover, and mutation in biological evolution. GA [65,127,128] and DE [129] are typical representatives of evolutionary algorithms and have similar but different characteristics.

GA has the algorithmic mechanisms of selection, crossover, and mutation, which gradually optimize the population’s fitness by the selection of good individuals, crossover to generate new individuals, and mutation to generate diversity. The above mechanisms give GA a solid global search capability while retaining high flexibility to handle mixed optimization problems with discrete and continuous variables.

The essence of GA in solving LSO problems lies in its global search and adaptive optimization capability, which is able to find near-optimal solutions in complex search spaces. GA gradually optimizes the fitness of populations to dynamically changing environments and demands by simulating the process of natural selection. The types of optimization problems for which GA is adapted to PV and CSP systems are summarized as follows:

• Energy system configuration optimization: e.g., PV array layout and CSP system configuration. It optimizes the system structure to maximize energy output and efficiency.
• Multi-energy system integration optimization: e.g., synergistic optimization of photovoltaic, wind, and energy storage systems to maximize overall efficiency.

The essence of DE in solving LSO problems lies in its efficient vector difference variational strategy, which is able to find the approximate optimal solution quickly in an extensive search space. DE improves the optimization effect of the algorithm by dynamically adjusting the control parameters to adapt to different optimization problems. The types of optimization problems for which GA has adapted DE in PV and CSP systems are summarized as follows.

• Parameter optimization: e.g., PV model parameter identification and CSP system operation parameter optimization to improve the accuracy of the system model and operation efficiency.
• Multi-objective optimization: simultaneous optimization of multiple objectives, such as maximizing energy output and minimizing cost, to achieve comprehensive system optimization.
• Complex system scheduling: optimization of the scheduling strategy of complex energy systems to improve the system’s economic efficiency and operational stability.

Evolutionary algorithms (e.g., GA and DE) have broad applicability and flexibility in LSO problems. GA has a robust global search capability by simulating the natural selection and evolution process and is suitable for optimization problems such as energy system configuration, multi-energy system integration, and dynamic scheduling. DE can efficiently perform a global search using a vectorial differential variation strategy, making it suitable for parameter optimization, multi-objective optimization, and complex system scheduling. These algorithms find near-optimal solutions to optimization problems by initializing the population, evaluating fitness, performing mutation and crossover operations, and gradually improving the population’s fitness.

5. Discussion and Analysis

This paper systematically reviews three optimization methods for studying LSO problems in PV and CSP systems: numerical simulation and the stochastic optimization method, meta-heuristic optimization algorithms, and ML-based AI methods. It summarizes and analyzes their advantages and disadvantages. Based on the literature and technical analysis selected, four common types of LSO problems in PV and CSP systems are identified: HESC, MOO, RSO, and LSO optimization problems, excluding the three types above. Furthermore, we identify and summarize three common practical problems in PV and CSP systems derived from these LSO optimization problems, discussing the applicable methods to solve each type. This effectively guides future research on LSO problems in PV and CSP systems.

(I) Synergistic Operation of PV and CSP Systems to Maximize Energy Output and Economic Benefits: For optimal performance, PV and CSP systems must operate synergistically, taking into account environmental factors such as solar radiation and temperature. Given the highly dynamic nature of energy supply and demand, addressing LSO problems requires a careful consideration of a wide range of complex constraints. This approach is crucial for enabling the energy system to maximize both energy output and economic benefits.

The synergistic operation of PV and CSP systems is highly dependent on environmental conditions, which vary according to the energy composition of the system, among which solar radiation is one of the main influencing factors, which is highly uncertain and fluctuating due to the angle of incidence of sunlight, cloud meteorological conditions, temperature, and other factors. In order to more accurately accomplish the synergistic optimization of energy systems, environmental factors such as solar incidence angle, cloud meteorological conditions, and temperature must be taken into account in future research in this field.

An energy system’s dynamic storage capacity can result in unpredictable energy output behavior. The system’s limited storage capacity directly influences various internal factors, such as the charging and discharging efficiency and cycle time. Frequent charging and discharging can also shorten equipment lifespan. External factors like dust accumulation, equipment aging, and other environmental influences can further reduce the energy system’s power generation efficiency, which must be considered in collaborative optimal scheduling. Additionally, the energy storage sector must maintain a certain amount of spare capacity to handle sudden peaks in demand or insufficient power generation.

We consider the need for more comprehensive optimization and more handling of environmental uncertainty in existing HESC problems. Considering three types of optimization methods together, this paper proposes a class of generic solutions. (1) Combining RL and historical data analysis: Using RL techniques and machine learning models, past energy production and consumption data are analyzed to generate optimization strategies for operation of the energy system. Advanced RL algorithms such as Deep Q Networks (DQN) are used to learn optimal power generation and energy storage strategies by training in a simulation environment. Historical weather data and load data are combined to establish a high-precision prediction model to improve the accuracy of the optimization strategy. (2) Enhancing communication and coordination between energy systems: Real-time data sharing and collaborative scheduling are achieved by enhancing the communication between PV and CSP systems and the grid. This allows for more accurate energy supply and demand prediction and improves system responsiveness and reliability.

(II) Multi-objective optimization of energy output, system cost, and environmental impacts of PV and CSP systems to achieve sustainability goals. By maximizing energy output while minimizing system costs and environmental impacts, the overall efficiency and sustainability of the system can be significantly enhanced. During the optimization process, attention should be paid to aspects such as balancing multiple objectives, handling complex constraints, dynamic adjustment and adaptation, the selection of the optimization algorithm, and the validation and analysis of results.

In this paper, we address the characteristics of the MOO problem and propose a potential generalized solution. (1) Implementing multi-objective trade-offs using NSGA-II: By introducing more objective functions, we can more accurately describe the multi-objective optimization problem. (2) Coping with data uncertainty: Utilizing robust optimization and Bayesian optimization, we generate multiple uncertainty scenarios using historical and simulated data, optimizing under these scenarios to improve the model’s adaptability. (3) Handling complex constraints: We address complex constraints by combining Mixed-Integer Linear Programming (MILP) with heuristic algorithms. Additionally, we reduce computational complexity through distributed and parallel computing techniques.

(III) Real-time scheduling optimization of heliostat field aiming strategies for CSP energy systems. The real-time optimization of heliostat field aiming strategies encounters challenges such as high-dimensional optimization, real-time requirements, uncertainty handling, and multi-objective optimization. Current research requires in-depth exploration and breakthroughs in several areas: the selection and improvement of optimization algorithms, model accuracy and efficiency, data acquisition and processing, and system integration.

In this paper, we address the RSO problem of the heliostat field aiming strategy for CSP energy systems by proposing a generalized solution that incorporates algorithm selection. (1) RL (e.g., DQN or DDPG): By integrating real-time data acquisition and processing and constructing high-precision state and action space models, reinforcement learning can effectively handle the high-dimensional and dynamically changing cloud environments above the mirror field. (2) SI algorithms (e.g., PSO or GWO): Utilizing SI algorithms for real-time optimization of problem-adaptive modeling, we combine the iterative mechanisms of SI algorithm populations with historical data integration. This approach improves the efficiency of the focusing strategy solution for continuous similar mirror fields. (3) System integration and validation: We ensure the effectiveness and robustness of the optimization algorithms in practical applications through system integration and validation. This approach aims to maximize energy efficiency and ensure the stable operation of the CSP system.

The LSO problem for PV and CSP systems is a multifaceted challenge requiring advanced technologies, robust data processing capabilities, and collaborative decision-making. Different LSO problems have unique characteristics and requirements, including HESC, MOO, RSO, and other specific optimization problems. To address these challenges, researchers should select the appropriate optimization algorithms based on their research needs. Researchers can make significant strides by utilizing high-quality real-time data sources for data fusion and preprocessing, applying advanced machine learning techniques to enhance data processing and prediction capabilities and improving model accuracy through precise modeling and algorithmic improvement. The integration of the optimization algorithms with actual systems, followed by practical application testing and continuous optimization, will enhance the system’s practical application effects. A comprehensive comparison and analysis of the advantages of different optimization methods provide valuable insights for engineering developers, helping them make informed decisions in actual system design. Ultimately, these optimization strategies will help enhance the overall effectiveness of renewable energy systems and promote the widespread application and sustainable development of clean energy.

6. Conclusions

To advance the development of PV and CSP hybrid energy systems in the solar energy field, particularly in the context of research on LSO problems, it is essential to conduct a systematic review and comprehensive analysis of methods for LSO problem research. This paper presents a comprehensive review and survey of the relevant literature from 1 January 2000 to 30 May 2024, analyzing and summarizing the development trends of LSO problems within PV and CSP systems. A comparative analysis of the screened literature from the perspective of LSO problem classification was conducted, revealing that LSO problems are primarily classified into four categories: HESC, MOO, RSO, and other LSO problems not covered by the first three categories. The research trends of these different types of LSO problems are summarized and reviewed, providing detailed information about the analyzed articles. The information is comparatively analyzed from five perspectives: optimization algorithms, application scenarios, experimental setups, optimization objectives, and evaluation metrics.

Subsequently, the optimization algorithms applicable to different types of LSO problems are described in detail and categorized into three main types: meta-heuristic optimization algorithms, numerical simulation and stochastic optimization methods, and ML-based AI methods. The methodological characteristics of these methods are reviewed and analyzed, tailored to the types of LSO problems studied within PV and CSP systems. The strengths and weaknesses of the existing methods are also examined. For instance, before 2020, GA and PSO were the most widely applied meta-heuristic algorithms, used in 17 and 8 studies, respectively. However, post-2020, there was a significant shift towards ML-based methods, with at least 15 studies employing techniques such as Neural Networks, Reinforcement Learning, and MPC. Additionally, the application of other meta-heuristic algorithms, such as GWO, DE, and SA, has also increased, highlighting the evolving nature of optimization strategies in this field.

These quantitative analyses indicate that while traditional meta-heuristic methods were predominant before 2020, the landscape has hifted significantly towards ML-based AI methods, which now play a crucial role in addressing the increasing complexity and dynamism of LSO problems in PV and CSP systems. The conclusions of these analyses provide valuable guidance for stakeholders involved in various research directions, including PV and CSP hybrid energy system design, multi-energy system co-optimization, capacity allocation multi-objective optimization, and the real-time optimization of scheduling strategies.

Future research on LSO problems in PV and CSP systems will focus on three development trends. First, applying hybrid optimization models will become a key area, enhancing solution effectiveness and system operational efficiency by combining the advantages of multiple optimization algorithms. For example, combining meta-heuristic algorithms with ML-based methods has shown promising results in recent studies, improving optimization outcomes by up to 30% in some cases. Second, multi-source data fusion optimization methods will be widely applied, integrating meteorological data, real-time monitoring data, and historical operational data to improve the accuracy and reliability of optimization models. This trend is supported by an increase of approximately 20% in studies focusing on data-driven approaches post-2020. Finally, real-time dynamic optimization technology will become a research hotspot. By incorporating advanced technologies such as reinforcement learning and adaptive control, it aims to achieve quick response and dynamic adaptation of the system, thereby maximizing the overall system efficiency and stability. These development trends will push the optimization research of energy systems to new heights, providing robust support for achieving efficient, reliable, and intelligent energy management.