A comprehensive survey of the application of swarm intelligent optimization algorithm in photovoltaic energy storage systems

Abstract

With the rapid development of renewable energy, photovoltaic energy storage systems (PV-ESS) play an important role in improving energy efficiency, ensuring grid stability and promoting energy transition. As an important part of the micro-grid system, the energy storage system can realize the stable operation of the micro-grid system through the design optimization and scheduling optimization of the photovoltaic energy storage system. The structure and characteristics of photovoltaic energy storage system are summarized. From the perspective of photovoltaic energy storage system, the optimization objectives and constraints are discussed, and the current main optimization algorithms for energy storage systems are compared and evaluated. The challenges and future development of energy storage systems are briefly described, and the research results of energy storage system optimization methods are summarized. This paper summarizes the application of swarm intelligence optimization algorithm in photovoltaic energy storage systems, including algorithm principles, optimization goals, practical application cases, challenges and future development directions, providing new ideas for better promotion and application of new energy photovoltaic energy storage systems and valuable reference.

Introduction

The "dual carbon" aim has emerged as a new path for global energy development in response to the worsening effects of global warming and ongoing energy structure optimization^1,2,3. In light of current global issues, the creation of new energy and its extensive integration into power systems has emerged as a key strategy for developing new power systems. As the times demand, the idea of a new power system with new energy as the major body has evolved against the backdrop of "dual carbon"^4,5. The new power system's development patterns and directions include aggressively producing new energy and quickening the electrification of terminal energy use. A deterministic one-way power balancing where the "source moves with load" characterizes the conventional power system⁶. The power supply side of the new power system has progressively changed into a high-uncertainty energy supply system with new energy as the primary body as a result of the ongoing development of the penetration rate of new energy^7,8. With demand response incentives, many load types, and entwined evolving energy consumption ideas, the system load side has progressively evolved into a highly unpredictable energy consumption system⁹. A new type of power-energy dynamic balancing with two directions of source and load has been fashioned by the stochastic fluctuating energy supply and consumption system of the new power system, and the system's need for flexible resources has greatly grown^10,11. The power system's operational boundary is lowered when conventional energy is replaced with renewable energy, and the boundary conditions become more complicated due to the interaction between the source and the load. The system's dynamic characteristics have changed significantly as a result of the widespread use of power electronic equipment, and the stability issue has gained more attention^12,13. In addition to improving the link between energy supply and demand, this power structure, which mostly consists of new energy, strives to achieve low-carbon, high-efficiency, and steady supply¹⁴. It also speeds up the transformation of the power grid to electrification and intelligence. However, this human endeavor has also resulted in new issues. The unpredictability of the source side's new energy supply and the load side's variable demand response have combined to raise operational uncertainty, impact the power system's elasticity, and raise the need for robustness^15,16.

As a result of the economy's and society's rapid growth, there is a growing need for power loads, a growing contradiction between sources and loads, and an expanding prominence for energy storage applications^17,18. These factors are primarily represented in: (1) Large-scale grid integration of variable and intermittent renewable power sources produces unprecedented levels of energy security¹⁹. Energy storage is required to increase the consumption capacity of renewable energy power generation due to the significant issues with steady operation and efficient consumption^20,21. Economically developed regions exhibit high energy demand coupled with inadequate power supplies, whereas undeveloped regions display low energy demand coupled with adequate power resources^22,23. Large-capacity, long-distance power energy transmission is the result of this reversal of the distribution of power energy supplies and power demand. The need will persist for a considerable amount of time, and the pace at which transmission lines are built is slower than that of power sources²⁴. Conversely, the urban load is expanding quickly, the power grid's peak-to-valley difference rate is progressively rising, and the issue of distribution network lines and equipment capacity bottlenecks is becoming more and more noticeable^25,26. By delaying the need to replace transmission and distribution lines and equipment, energy storage technology can increase the effectiveness with which network resources and equipment are used^27,28. (3) The control, protection, and operation management of the distribution network are challenged by the grid connection of highly penetration distributed renewable power supply on the user side²⁹. The addition of energy storage will guarantee power supply dependability, enhance user access to dispersed renewable power sources, and satisfy user demands. Achieve user-informed power management by meeting power quality requirements^30,31.

Energy storage technology is playing a bigger and bigger part in the new energy power system^32,33,34. The industry has largely acknowledged the application functions of energy storage technology in all facets of the power system, but the economics of energy storage system applications are now restricted owing to the technological and economic state of energy storage systems^35,36. Energy storage incentive programs have been established one after another to encourage the growth of the energy storage sector. The introduction of energy storage incentive policies is conducive to improving the efficiency of energy storage systems and making investment in energy storage projects economical, thereby attracting investors from all walks of life to enter the energy storage field and promoting Healthy and rapid development of the energy storage industry^37,38. At this stage, the economics of some types of energy storage technologies are limited. Even if the energy storage subsidy policy is introduced, it does not yet have economies of scale³⁹. Capacity allocation is a prerequisite for the promotion and application of energy storage systems. With the improvement of energy storage technology performance and the reduction of cost, the economics of the application of battery energy storage technology with long-life, high-energy conversion efficiency. And low cost has gradually become prominent, and the application of energy storage technology is gradually transforming from engineering demonstration to commercial operation^40,41. Energy storage can not only provide timely, safe and stable power supply, ensure the flexibility and stability of the system in extreme cases, but also provide strong technical support in conventional and unconventional situations⁴². For example, power-type energy storage such as supercapacitors and battery energy storage is suitable for short-term high-power output, while capacity-type energy storage such as pumped storage and hydrogen energy storage is more suitable for long-term continuous power supply^43,44. Hybrid energy storage technology combines the advantages of power-type and capacity-type energy storage, and is suitable for complex and changeable regulation needs⁴⁵. Diversified energy storage systems can meet multi-time-scale responses and provide dual power-energy regulation capabilities. Recovery efficiency plays an indispensable role^46,47.

Although the importance of energy storage technology is gradually being recognized, in actual system planning and management, how to effectively integrate and dispatch energy storage resources, and how to ensure that the power system can withstand extreme event impacts. Meanwhile, quickly restoring its stability and robustness remains an urgent issue to be addressed^48,49. In addition, current research on the intelligent scheduling and planning strategies of energy storage resources in new power systems using swarm intelligence optimization algorithms is not sufficient, and the potential of swarm intelligence optimization algorithms in responding to extreme events and improving system resilience has not been fully explored^50,51.

This review delves into the key role of energy storage technology in the emerging challenges faced by new power systems. In the optimization problem of energy storage systems, swarm intelligence optimization algorithms have become a key technology for solving power scheduling, energy storage capacity configuration, and grid interaction problems in energy storage systems due to their excellent search ability and wide applicability. Especially in photovoltaic energy storage systems, the application of these algorithms not only helps to achieve a balance between power generation and load demand, but also optimizes energy utilization efficiency and reduces operating costs. The article first discusses the main characteristics of new energy grid connection, and then combines a review of various energy storage technologies to analyze their optimization strategies in practical operation. Finally, it is pointed out that research directions are needed to enhance the anti-interference ability of the new power system and improve the system recovery efficiency. Through this research, we aim to promote the understanding of the robustness and resilience of new power systems in academia and industry practice, and further promote the broader exploration and application of swarm intelligence optimization algorithms in the field of energy storage.

Basic knowledge of energy storage systems

A breakthrough for the transformation of the current energy structure has been made possible by the combination of solar power generating technology and energy storage systems. This section attempts to give a basic understanding of photovoltaic energy storage systems, including topics such as the fundamentals of solar power generation, the many kinds and features of energy storage systems, and the general architecture of these systems^52,53.

Principles of photovoltaic power generation technology

With the continuous growth of energy demand and the global emphasis on renewable energy, photovoltaic power generation technology, as an important means of converting solar energy into electric energy, has attracted widespread attention. The core component of photovoltaic power generation is photovoltaic cells. This technology uses the photovoltaic effect of semiconductor materials to directly convert the energy of sunlight into electrical energy. When sunlight hits a photovoltaic cell, the semiconductor material absorbs photon energy to produce electron–hole pairs. Under the action of the built-in electric field, electrons and holes are separated and moved to different sides of the battery to form a voltage. When the battery is connected to an external circuit, a current is generated^54,55.

The electrical properties of photovoltaic cells, such as their maximum power point (MPP), short circuit current (Isc), open circuit voltage (Voc), and photoelectric conversion efficiency, are primarily used to evaluate their performance. The highest potential difference when the load is disconnected is referred to as the open circuit voltage among them, and it is influenced by the operating temperature and the characteristics of the semiconductor material⁵⁶. The greatest current value produced when the external circuit is shorted out is known as the short-circuit current, and it has a direct positive correlation with light intensity. The voltage and current at which a solar cell may produce its maximum power under specific conditions is known as the maximum power point. Efficiency refers to the ability of the photovoltaic cell to effectively convert the incident light energy into electrical energy⁵⁷.

Numerous factors influence how well solar electricity generating performs. Because the carrier activity inside the semiconductor intensifies and the voltage declines as temperature rises, an increase in temperature often results in a loss in efficiency⁵⁸. The quantity of photogenerated carriers is directly influenced by light intensity, which also has an impact on power production efficiency. Furthermore, shadow occlusion may lead certain panels to produce less power, and in extreme circumstances, it may also result in a hot spot effect owing to a local temperature rise, endangering the panels' long-term functionality and safety⁵⁹. The installation angle and direction of photovoltaic panels need to take into account factors such as geographical location, season and sunshine time to obtain the maximum amount of light and optimize power generation efficiency.

Types and characteristics of energy storage systems

Energy storage technology is essential to today's electricity system. It can assist in balancing the grid's supply and demand in addition to increasing energy consumption efficiency and power supply stability⁶⁰. Energy storage systems come in a variety of forms, and each kind of technology has unique properties as well as ideal use cases^61,62. The energy storage system may be classified as mechanical, electrochemical, chemical, electrical, and thermal energy storage systems based on the formation method and materials utilized in the system. Therefore, battery³², compressed air energy storage⁵¹, flywheel energy storage²¹, supercapacitor energy storage³³, superconducting magnetic energy storage⁶³, hydrogen storage⁶⁴ and hybrid energy storage^43,65 are the most commonly used energy storage technologies in photovoltaic energy storage system applications. Various energy storage technologies and their characteristics are shown in Table 1. The performance of photovoltaic power generation is affected by many factors⁴⁸. The increase in temperature usually leads to a decrease in efficiency, because as the temperature increases, the carrier activity inside the semiconductor intensifies and the voltage drops. Light intensity directly determines the number of photogenerated carriers, thus affecting the power generation performance^66,67. In addition, shadow occlusion may reduce the power generation of some panels, and in severe cases, it may also cause a hot spot effect due to local temperature rise, posing a threat to the long-term performance and safety of panels⁶⁸. The installation angle and direction of photovoltaic panels need to take into account factors such as geographical location, season and sunshine time to obtain the maximum amount of light and optimize power generation efficiency.

Table 1 Typical energy storage technologies and their characteristics.

Battery energy storage technology is a way of energy storage and release through electrochemical reactions, and is widely used in personal electronic devices to large-scale power storage⁶⁹. Lead-acid batteries are widely used due to their low cost and mature recycling technology, but due to energy density constraints and short cycle life, they are usually limited to small-scale energy storage needs⁷⁰. On the other hand, with the advantages of high energy density and long life, lithium-ion batteries have not only become the core components of mobile electronics and electric vehicles, but also occupy an increasingly important position in large-scale energy storage of power systems. As a special energy storage device, supercapacitors are famous for their excellent power density and rapid charging and discharging capabilities^71,72. They can release huge energy in a very short time, and are especially suitable for energy recovery and rapid acceleration in electric vehicles. However, at the same time, supercapacitors have a low energy density, so they are not suitable for long-term energy storage⁷³.

Due to the randomness of weather changes affecting photovoltaic output, photovoltaic power generation has volatility and uncertainty, and its direct access to the grid will affect the safe and stable operation of the distribution network⁷⁴. Energy storage technology is connected to the photovoltaic power generation side, which can stabilize the fluctuation of photovoltaic output and change the operating state of the traditional power system that needs to balance supply and demand at all times. It is the most important manifestation of the value of energy storage⁷⁵. Its key factor is the time t, that is, the time factor, which is also the most important symbol that it is different from the traditional instant power supply. Energy storage technology can be divided into chemical energy storage, mechanical energy storage, electromagnetic energy storage and phase change energy storage according to different methods of electric energy storage⁷⁶. Chemical energy storage includes lead-acid batteries, sodium-sulfur batteries, flow batteries, lithium batteries, nickel-metal hydride batteries, etc. Mechanical energy storage includes pumped storage, flywheel energy storage, compressed air energy storage, etc. Electromagnetic energy storage includes superconducting energy storage, supercapacitor energy storage, etc.^77,78. Phase change energy storage is realized through heat exchange, in which the heat storage material undergoes phase transformation, and then absorbs or releases potential heat to realize energy storage. Table 2 summarizes the comparison of typical energy storage methods.

Table 2 Characteristics of different energy storage devices.

According to Tables 1 and 2, energy storage can be roughly divided into two categories: energy type and power type from the perspective of function. Energy type energy storage has higher energy density and large capacity, but its discharge time is longer, the cycle life is short, and it can be used as a long-term energy storage device⁷⁹. Power-type energy storage has higher power density, faster response speed, and long cycle life, but unlike energy-type energy storage, it cannot be stored in large capacity and can only be used as a short-term storage device. The application of energy storage technology has a non-negligible impact on the microgrid, and its role is not only reflected in the economy of the microgrid, but also in the reliability of the microgrid⁸⁰. Jabir et al. considered that the influence of random fluctuation of wind power on the system, the moving average method is used to smooth the fluctuation of wind power, so as to achieve the purpose of reducing the impact on the power grid⁸¹. Under different confidence levels and capacities, the smoothing effect of the hybrid energy storage system is analyzed with each parameter of the fluctuation as an index. Starting from the characteristics of renewable energy microgrid technology, Faisal et al.⁸² reviewed the role, classification, design optimization methods, and application of energy storage systems in microgrids, comprehensively evaluating energy density, power density, response time, and rated power. Wu et al.⁸³ analyzed energy storage application planning and related benefit evaluations in different scenarios, listed their advantages and disadvantages, and elaborated on the issues that need to be further considered in energy storage planning and the aspects that should be paid attention to in the future application promotion process.

In addition to battery energy storage and supercapacitors, modern power systems also include a variety of other energy storage technologies, such as pumped storage, compressed air energy storage, flywheel energy storage, and flow batteries⁸⁴. As a mature large-scale energy storage solution, pumped storage stores and generates energy by extracting and releasing water between different heights⁸⁵. Compressed air storage uses electrical energy to compress air and store it underground, releasing air to generate electricity when needed^86,87. Flywheel energy storage technology stores kinetic energy by rotating the flywheel at high speed, and uses the kinetic energy of the flywheel to generate electricity when needed. Flow batteries introduce two electrolytes for chemical reaction to store energy, and their ability to independently adjust energy and power makes them have obvious advantages in specific applications^88,89. The functional application of energy storage technology characteristics at different time scales is shown in Fig. 1. The various application forms of distributed energy storage are shown in Fig. 2.

Figure 1

Functional application of energy storage characteristics.

Figure 2

Multiple application forms of distributed energy storage.

Each energy storage technology has its unique advantages and limitations, so many factors need to be considered in the actual selection, such as cost, capacity, cycle life and environmental impact. If high energy density and long discharge time are required, battery energy storage will be a suitable choice⁹⁰. Conversely, if the application scenario requires high-power output in a short period of time, supercapacitors are more ideal. For scenarios that require large-scale energy storage, such as peak shaving and valley filling of the power grid or providing emergency backup power, large-scale energy storage solutions such as pumped storage play an important role⁹¹.

Structure of photovoltaic energy storage system

Photovoltaic energy storage system is a highly integrated energy solution that converts solar energy into electricity and regulates energy supply through energy storage devices to improve the overall efficiency and reliability of the system. The structure of this system is complex and detailed, involving tight connection and integration of components, precise energy management and intelligent control strategies⁹². Due to the randomness of weather changes affecting photovoltaic output, photovoltaic power generation has volatility and uncertainty, and its direct access to the grid will affect the safe and stable operation of the distribution network. Energy storage technology is connected to the photovoltaic power generation side, which can stabilize the fluctuation of photovoltaic output and change the operating state of the traditional power system that needs to balance supply and demand at all times³⁸. It is the most important manifestation of the value of energy storage. The structure diagram of the photovoltaic energy storage system is shown in Fig. 3.

Figure 3

Structural diagram of photovoltaic energy storage system.

The core of the photovoltaic energy storage system is the photovoltaic array, which is composed of multiple photovoltaic modules and is responsible for capturing sunlight and converting it into direct current. These modules can be connected in series or parallel to achieve the required current and voltage output⁹³. This DC is then fed into energy storage units, usually battery packs or supercapacitors, which store the excess electricity for use during low sunlight or peak power demand. Power electronic devices, such as inverters, play a converting role, converting DC power into AC power that can be directly used by the grid or load. In more advanced system designs, DC/DC converters will be included to further optimize energy transmission and storage efficiency^55,94. The energy management strategy of the system is responsible for the intelligent energy management system (EMS), which monitors the power output of the photovoltaic array, the energy storage status of the energy storage equipment, and the demand of the grid. EMS dynamically adjusts the operating mode of power generation and energy storage based on real-time data and forecasts, aiming to ensure that the economy and reliability of system operation are optimized. In addition, in order to maximize the efficiency of the photovoltaic array, the system will use a maximum power point tracking (MPPT) controller to determine the optimal operating point, and the control of the energy storage equipment includes monitoring the charging and discharging process to prevent overcharging or over discharging, and optimize the service life of the energy storage unit^95,96. The system must also be properly interconnected to the grid to meet the frequency and voltage requirements of the grid in order to maintain stability and provide high-quality power. The multi-objective collaborative regulation model of energy storage for power system is shown in Fig. 4.

Figure 4

Multi objective collaborative regulation model for energy storage in the power system.

Optimization methods for energy storage systems

Optimization of energy storage systems is a multi-level, multi-objective complicated task. Reasonable optimization can increase the energy storage system's stability and dependability in addition to its financial advantages. The main objective of energy management, which forms the basis of energy storage systems, is to optimize energy balance, scheduling, and use. At present, energy management optimization mainly uses model predictive control⁹⁷, dynamic programming⁹⁸, reinforcement learning⁹⁹ and other methods to achieve optimal control and scheduling of energy management. The energy management method based on model predictive control, by predicting and controlling the energy demand of the photovoltaic system and the state of the energy storage system¹⁰⁰. For example, using reinforcement learning algorithms to optimize energy management can gradually realize autonomous control and optimal scheduling of energy storage systems.

Battery management optimization can be regarded as a subtask or component of energy management optimization. Battery management is also an important part of the energy storage system, and its optimization goal is to improve the service life and performance of the battery. At present, battery management optimization mainly uses model predictive control¹⁰¹, state estimation¹⁰², dynamic optimization¹⁰³ and other methods to achieve optimal control and management of batteries. Using the state estimation method to estimate the state of the battery, the real-time monitoring and control of the battery can be realized. At the same time, the optimization of battery management based on dynamic programming and reinforcement learning can effectively prolong the service life and improve the performance of the battery.

Optimization objectives of energy storage systems

Battery energy storage system (BESS) optimization mainly refers to optimizing the size and placement of BESS in anticipation of BESS becoming an alternative source with rapid response, adaptability, controllability, environmental friendliness and geographical independence¹⁰⁴.

The basic idea of BESS optimization includes the following aspects: (1) Clarify the optimization goal. This is a key starting point for the optimization process, because different goals may require different strategies and methods. For example, the pursuit of energy efficiency may involve optimizing the charging and discharging process of the battery, while focusing on cost may require finding more economical equipment and operation methods¹⁰⁵. (2) System modeling. Establishing accurate mathematical models can help understand and predict the behavior of systems. Including the characteristics of the battery, such as capacity, internal resistance, efficiency, etc., as well as the characteristics of components such as power converters¹⁰⁶. (3) Load analysis. In-depth understanding of the system's load demand patterns, such as load peaks and valleys, changing trends, etc. This facilitates the development of more efficient energy management strategies to meet load demand and maximize the benefits of energy storage¹⁰⁷. (4) Energy management strategy. Decide when to charge and discharge, and how to allocate energy storage capacity. For example, smart charging based on electricity price periods, or releasing energy at peak grid loads¹⁰⁸. (5) Economic evaluation. Cost factors such as equipment purchase, operation and maintenance are considered. With optimization, the most economically viable solution can be found¹⁰⁷. (6) Reliability analysis. Ensure that the system can operate reliably under various working conditions, and is not affected by environmental factors such as temperature and humidity. At the same time, factors such as battery aging and failure should be considered to ensure the stability of the system. (7) Model optimization. Use advanced optimization algorithms to optimize the model to find the best parameter settings. This may involve various optimization techniques such as genetic algorithms, simulated annealing, etc.¹⁰⁹. (8) Real-time monitoring and adjustment. Through real-time monitoring of the status and operating data of the system, timely adjustment and optimization strategies. Adjust charging and discharging plans according to actual load changes. (9) Life prediction and maintenance. Based on the life model of the battery, predict the life of the battery and formulate a reasonable maintenance and replacement plan. This can extend the life of the system and reduce operating costs¹¹⁰. (10) Multi-scenario analysis. consider different application scenarios and working conditions, such as different geographical locations, climate conditions, etc. Ensuring that the system can achieve optimal operation under various circumstances¹¹¹.

The basic idea of BESS system optimization is shown in Fig. 5. The common optimization objective function is to determine cost, capacity, lifetime and power quality, as well as load flow.

Figure 5

Basic ideas for optimizing BESS system.

Cost optimization of BESS

Cost optimization is a widely recognized optimization that aims to achieve the highest possible outcome by minimizing costs. In most of the literature, the best cost-effective option is considered the best choice¹¹². The cost function was used as an optimization parameter. BESS scheduling is solved by Mixed Integer Linear Programming (MILP), where the cost function of the thermal generator is defined as follows

$$\sum\limits_{i = 1}^{N} {\sum\limits_{{j = T^{*} }}^{T} {\left\{ {u_{i,j}^{{T^{*} }} \cdot \left( {FC_{i} } \right) \cdot \Delta T + u_{i,j}^{{T^{*} }} \cdot \left( {1 - u_{i,j}^{{T^{*} }} } \right) \cdot SC_{i} } \right\}} }$$

(1)

Among them, parameter N is the total number of thermoelectric generators. T^*represents the scheduling time. T^* = T^pre used for the previous day. T^* = T^cu is used for the current day. △T is the unit time. $u_{i,j}^{{T^{{{\text{bu}}}} }}$ is the starting situation of the generator at time j. FC_i is the fuel cost of generator i. SC_i is the starting cost of generator i. The constraints of the system are divided into three categories, namely the constraints of thermal generators, BESS, and prediction updates. The output constraints of thermal power generation units include maximum and minimum power limits, upward reversal capacity, and load frequency control¹¹³. The constraints of BESS include charging and discharging, as well as the stored energy in the initial and final states. The simulation results show that determining the charging and discharging of BESS based on the actual photovoltaic power (PV) power results can reduce the energy gap of the entire system, improve system reliability, and reduce total cost¹¹⁴.

Capacity and lifespan optimization of BESS

Capacity optimization is another key optimization factor for BESS, which needs to consider the capacity of the power conversion system and battery storage¹¹⁵. In designing efficient BESS, it is necessary to optimize the power rating and battery storage capacity accordingly. By optimizing battery capacity, BESS performance is improved and costs are minimized. The main objective of the BESS capacity optimization model is to maximize the equivalent uniform annual profit.

$$\max_{{{\text{obj}}}} = C^{{{\text{sell}}}} - C^{{{\text{WP}}}} - C^{{{\text{PV}}}} - C^{{{\text{CSP}}}} - C^{{{\text{BESS}}}} - C^{{{\text{OM}}}} - C^{{{\text{tax}}}}$$

(2)

$C^{{{\text{sell}}}}$ is annual income, $C^{{{\text{WP}}}}$,$C^{{{\text{PV}}}}$,$C^{{{\text{CSP}}}}$,$C^{{{\text{BESS}}}}$,$C^{{{\text{OM}}}}$ and $C^{{{\text{tax}}}}$ are the equivalent unified annual costs of wind power, photovoltaics, concentrated solar energy, BESS, operation and maintenance, and annual tax respectively. Transmission line capacity, renewable energy annual abandonment rates, wind power generation, photovoltaic power generation, concentrated solar power generation, BESS operation, and battery state of charge (SoC) restrictions are all considered constraints. Capacity optimization is calculated on an hourly basis over a year, and the experimental results yield profit maximization, ensuring an annual power abandonment rate of less than 5%¹¹⁶.

By optimizing the capacity of BESS to reduce the total system cost, the mixed integer linear problem is represented as follows:

$$c_{{{\text{pv}}}} \cdot K_{{{\text{pv}}}} + c_{{\text{w}}} \cdot K_{{\text{w}}} + c_{{{\text{bat}}}} \cdot K_{{{\text{bat}}}} + c_{{{\text{fc}}}} \cdot K_{{{\text{fc}}}} + H^{{{\text{cost}}}} n_{{{\text{hyd}}}}$$

(3)

Among them, $c_{{{\text{pv}}}}$ is the installed capacity of photovoltaic panels. $c_{{\text{w}}}$ is the installed capacity of turbines. $c_{{{\text{bat}}}}$ is the total storage capacity of the battery. $c_{{{\text{fc}}}}$ is the installed capacity of the fuel cell. $K$ is the corresponding cost. $H^{{{\text{cost}}}}$ is the cost of hydrogen storage replacement. $n_{{{\text{hyd}}}}$ is the number of times hydrogen storage is replaced¹¹⁷.

The lifetime of a battery depends on its structure, operating procedures, and charge–discharge cycles. Many researchers take different approaches to analyzing and optimizing battery life, sometimes combining life with a cost function. Kumar et al.¹¹⁸ allocated battery capacity and power according to the current State of Health (SoH). Degradation rate, corrosion, cycle count and SoH are considered as parameters of the battery management system. Multiple applications of uninterruptible power supply systems extend the life of BESS through higher average SoC and lower Depth of Discharge (DoD). Berecibar et al.¹¹⁹ used a cycle counting based battery life assessment method, where DoD and SoC are two key parameters used in battery control algorithms. The battery life estimation formula is

$$L_{{{\text{BESS}}}} = T/\left( {\sum\limits_{i = 1}^{m} {N_{i} } /CF_{i} } \right)$$

(4)

The parameter T is the simulation duration (in years), N_i is the number of cycles for each DoD, and CF_i is the number of failure cycles for the corresponding DoD. The battery life also depends on temperature and humidity. Optimizing battery capacity and lifespan is essential as it directly affects the operating cost of the entire BESS.

Constraints for optimizing energy storage systems

Charge discharge constraints

The most common operational constraints in developing efficient BESS optimization techniques are charge discharge constraints or SoC constraints. When considering BESS optimization, the degradation rate and service life of the battery should be considered, both of which are directly related to SoC. On the other hand, optimizing BESS capacity, power loss, power balance, control strategy, battery life, and SoC constraints have been taken into consideration. Atia et al.¹²⁰ analyzed the impact of battery constraints on microgrid applications. Dynamic programming is used to optimize costs and SoC, and battery capacity is considered a constraint. The conditions for its definition are as follows

$$0.3 \le {\text{SoC}} (k) \le 0.9$$

(5)

$$- 6{\text{kW}} \le P_{{\text{b}}} (k) \le 6{\text{kW}}$$

(6)

In order to ensure the safety of the system, the battery charging is carried out in the mode of constant current and constant voltage, and the energy cost of the grid with and without the constraint of constant current and constant voltage charging is compared. Kiptoo et al.¹²¹ proposed a MILP-based ESS optimization with flexible demand control, using self-sufficiency index and system self-consumption index to evaluate system performance. In this paper, SoC is considered as a system constraint, and the maximum and minimum charging constants are defined as follows

$$E_{{\text{min }}} = 0.2P_{{\text{stge }}}$$

(7)

$$E_{{\text{max }}} = 0.8P_{{\text{stge }}}$$

(8)

$$0 \le P_{ch}^{t} \le \delta_{ch}^{t} \cdot P_{{\text{stge }}}$$

(9)

$$0 \le P_{dch}^{t} \le \delta_{dch}^{t} \cdot P_{{\text{stge }}}$$

(10)

The discharge time h is the longest duration that the system can discharge the rated power. $P_{{\text{stge }}}$, $P_{ch}^{t}$, and $\delta_{ch}^{t}$ are the rated power of energy storage, charging power, and charging control, respectively. E_min and E_max are the maximum and minimum discharge depths, respectively.

Capacity constraints

The maximum energy that can be extracted from a battery under specific preset conditions is called its capacity. Since the lifespan of a battery depends on the degradation rate, it is important to consider the battery capacity when adjusting the BESS size. Xu et al.¹²² regarded power and energy capacity as BESS constraints, which are defined as follows

$$0 \le P_{i}^{B,d} \le S_{\max }$$

(11)

$$0 \le P_{i}^{B,c} \le S_{\max }$$

(12)

$$\sum\limits_{i = 1}^{24} {P_{i}^{B,d} } \le W_{\max }$$

(13)

Among them, parameters $P_{i}^{B,d}$ and $P_{i}^{B,c}$ are the discharge and charging rates of BESS within the i-th hour. Capacity constraints play a role in balancing cost, performance, and feasibility in optimizing battery energy storage systems. Reference¹²³ achieved cost savings by constraining battery capacity. In reference¹²⁴, battery capacity was considered as the main objective function, where initial charge discharge rate and capacity are considered as the main constraints, which not only meet the periodic demand for energy storage but also avoid unnecessary costs due to the large scale of BESS.

Environmental constraints

Due to the rapid increase in fossil fuel prices and greenhouse gas emissions, an alternative environmentally friendly energy solution is needed. Integrating BESS into renewable energy systems has great potential in addressing global warming issues. Rathod et al.¹²⁵ used a quantum inspired particle swarm optimization method to optimize cost and power consumption capacity. The economic scheduling model is a combination of BESS considering carbon emissions and wind energy, as described below

$$F_{{\text{ods }}} = \sum\limits_{i = 1}^{M} {C_{i,t}^{p} } + \sum\limits_{j = 1}^{N} {C_{j,t}^{w} } + \sum\limits_{i = 1}^{M} {C_{i,t}^{e} } - \sum\limits_{j = 1}^{N} {C_{j,t}^{s} } + \sum\limits_{j = 1}^{N} E \left[ {C_{o,t} \left( {W_{{{\text{oe}}}} } \right)} \right] + \sum\limits_{j = 1}^{N} E \left[ {C_{u,t} \left( {W_{{\text{ue }}} } \right)} \right] + \sum\limits_{i = 1}^{N} {C_{i,t}^{{\text{BESS }}} }$$

(14)

$$\sum\limits_{i = 1}^{M} {C_{i,t}^{e} } = C_{{{\text{Tax}}}} EM_{i} \left( {p_{i} } \right)$$

(15)

$$EM_{i} \left( {p_{i} } \right) = ef_{i} \left( {f_{i} + g_{i} p_{i} + h_{i} p_{i}^{2} } \right)$$

(16)

The parameter j is the wind turbine unit. $C_{i,t}^{p}$, $C_{j,t}^{w}$, $C_{i,t}^{e}$, and $C_{j,t}^{s}$ represent the costs of thermal generators, wind power generation, emissions, and government subsidies, respectively. $E\left[ {C_{o,t} \left( {W_{{{\text{oe}}}} } \right)} \right]$ is the penalty cost for overestimating wind power, which is $E\left[ {C_{u,t} \left( {W_{{\text{ue }}} } \right)} \right]$. It is the average penalty cost for underestimating wind power. $C_{i,t}^{{\text{BESS }}}$ is the operating cost of BESS. $EM_{i} \left( {p_{i} } \right)$ is the carbon emissions of the thermal unit. $ef_{i}$ is the fuel emission factor for CO₂. $C_{{{\text{Tax}}}}$ is the market carbon tax price. The integration of BESS and WP can reduce carbon emissions by up to 20%, including total costs. However, Hu et al.¹²⁶ proposed an optimized plug-in hybrid vehicle integration model that considered the cost and environmental impacts. Das et al.¹²⁷ proposed a multi-objective optimization method, where net present value cost and lifecycle environmental impact are considered as the main objective functions. At the household level, genetic algorithms were used to optimize hybrid renewable energy systems, and the results showed that PV was the most economical system to minimize greenhouse gas emissions in renewable energy supply.

Optimization of charging and discharging strategies for energy storage systems

The optimization of charging and discharging strategies for energy storage systems in microgrids is a key research field. Its goal is to improve the performance, stability and economy of energy storage systems through careful planning of energy storage and release methods. Reasonable charging and discharging strategies are crucial to ensure the sustainable operation of microgrids, reduce energy costs, extend the service life of energy storage equipment, and improve the reliability of energy supply.

Hu et al.¹²⁸ comprehensively considered the joint operation mode of bilateral transactions in the power system for energy storage users and new energy peak shaving needs, fully mobilizing the enthusiasm of users to participate in peak shaving, and verified the economic and feasibility of the proposed operation mode based on case analysis. Ruiz et al.¹²⁹ established a mixed integer programming charging and discharging scheduling model with the goal of minimizing the total daily charging and discharging cost. They optimized the capacity planning of energy storage equipment and conducted sensitivity analysis, effectively reducing the total daily charging cost of charging stations and the peak load of the power grid, and prolonging the battery lifetime.

Optimization algorithm of energy storage system–swarm intelligence optimization algorithm

Energy management and control of solar energy storage systems, including the design of the system's capacity, kind, location, and layout, depend heavily on the optimization of its design¹⁷. To achieve the ideal configuration and cooperative control of energy storage systems in photovoltaic energy storage systems, optimization algorithms, mathematical models, and simulation experiments are now the key tools used in the design optimization of energy storage systems¹³⁰. Energy storage system (ESS) integration with renewable energy can improve the grid's stability and flexibility. Real-time optimization of the interplay between renewable energy output, energy storage, and grid operation is a component of collaborative control of the coordinated operation of renewable energy and energy storage¹³¹. In this process, intelligent optimization algorithms are essential because they provide control methods that dynamically modify energy storage and renewable energy scheduling based on system requirements and conditions. In order to maximize the use of renewable energy and storage resources while preserving grid stability, these algorithms take into account variables like changes in energy demand, variability in renewable energy, grid restrictions, and energy storage system capabilities¹³². These algorithms aid in the seamless integration of energy storage and renewable energy sources, easing the shift to more robust and sustainable power networks by continuously adjusting to shifting circumstances and streamlining energy flows¹³³.

Swarm intelligence optimization algorithm is an important branch of computational intelligence. It is derived from the observation and study of some animal behaviors in biology, especially those behaviors that require group cooperation^134,135. These algorithm designs are often inspired by certain species in nature, such as ants, birds, fish, etc. They show how to solve complex problems through simple communication and cooperation between individuals without centralized control^136,137,138. This phenomenon is called swarm intelligence. Typical examples of swarm intelligence optimization include ant colony algorithm (ACO), differential evolution algorithm (DA), genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA) and so on¹³⁹. They are widely used in many fields such as function optimization, path planning, scheduling problems, network design and so on¹⁴⁰. Especially in energy storage system optimization, swarm intelligence algorithm has become a powerful tool to solve optimization problems because of its efficiency and robustness in searching for the global optimal solution^141,142. The optimization algorithms used in different literatures, as well as the optimization objectives, are given in Table 3. In this paper, the algorithm mentioned in the table is briefly explained, and the application of the algorithm in energy storage system optimization is introduced^143,144.

Table 3 Various optimization algorithms and their optimization objectives.

Ant colony optimization

Ant colony optimization (ACO) is a swarm intelligence optimization method that simulates the foraging behavior of natural ants¹⁵⁹. In power system and energy storage system optimization problems, ACO algorithm has been widely used because of its excellent search ability and good parallel computing characteristics¹⁶⁰. The underlying theory of ACO derives from the observed behavior of ants to communicate indirectly via pheromones, specifically how they find the shortest path from their nest to their food source. The algorithm uses a group of artificial ants to search in the solution space, and each ant chooses its path probabilistically according to the concentration of pheromones, leaving pheromones on the path to guide the search direction of subsequent ants¹⁶¹. The updating rules of pheromones usually follow the following formula.

$$\tau_{ij} (t + 1) = (1 - \rho ) \cdot \tau_{ij} (t) + \sum\limits_{k = 1}^{m} \Delta \tau_{ij}^{k}$$

(17)

Among them, $\tau_{ij} (t)$ represents the concentration of pheromones on edge $(i,j)$ at time t, $\rho$ is the volatility of pheromones, and $\Delta \tau_{ij}^{k}$ is the amount of pheromones left by the k-th ant on edge $(i,j)$. Ant colony algorithm has the advantages of global search ability and high parallelism, making it suitable for solving discrete and continuous optimization problems¹⁶². In the energy storage capacity planning problem, ant colony algorithm can find the optimal energy storage capacity by adjusting parameters such as pheromone volatility coefficient and pheromone concentration. For the charging and discharging scheduling problem, the battery status, load demand, etc. can be used as decision variables to optimize the scheduling strategy using ant colony algorithm¹⁶³.

To improve the efficiency and adaptability of ant colony algorithm (ACO) in energy storage system optimization, specific algorithm improvements are needed. The improved methods include: first, dynamically adjusting the pheromone volatilization rate, which allows the algorithm to adapt to the system changes according to the real-time operating state of the energy storage system. Secondly, a heuristic function based on the characteristics of the energy storage system is designed to guide ants to explore the solution space more accurately¹⁶⁴. Then, in order to meet the multiple objectives of cost, efficiency and reliability in the energy storage system, the ACO is improved to make it able to deal with multi-objective optimization problems. In addition, ACO is combined with other methods such as genetic algorithm and particle swarm optimization to give full play to the advantages of different algorithms and improve the quality of solutions and search efficiency. Finally, strengthen the adaptability of ACO to the dynamic changes of the energy storage system network to ensure that it can still maintain excellent performance in time-varying networks¹⁶⁵. Through these targeted improvements, the application of ACO in energy storage system optimization can not only significantly save operating costs, improve system operating efficiency, but also enhance the stability of power supply, fully demonstrating its great potential in complex system optimization¹⁶⁶. Due to the inaccurate results of power bias and network loss obtained by energy storage power control in multi-source distribution network, the power control results are not ideal. Deshun et al.¹⁶⁷ proposed a reasonable control method for energy storage power in multi power distribution networks based on ant colony algorithm and designed an energy storage architecture. Analyze the operational characteristics of energy storage in multi power distribution networks, with the goal of minimizing the total sum of operating costs and resource depreciation costs, construct a reasonable control model for energy storage power in multi power distribution networks, and optimize the model through ant colony algorithm to achieve reasonable control of energy storage power. Arasteh et al.¹⁶⁸ proposed an ant colony algorithm based energy storage capacity optimization configuration method for distributed wind and photovoltaic systems. Starting from the aspects of effectiveness and economy, a multi-objective function is established with the goal of minimizing the load peak valley difference and energy storage capacity configuration cost of the distributed wind and photovoltaic power storage system. Constraint conditions are set to establish an energy storage capacity optimization configuration model for energy storage capacity balance, peak valley difference, and energy storage system power balance constraints. The ant colony algorithm is used to calculate the model, output the optimal configuration decision, and achieve energy storage capacity optimization configuration for distributed wind and photovoltaic power. Taking a 330 MW unit of a certain power plant as the modeling object, with the optimization goal of shorter dynamic response AGC command time and the time delay difference between the heating network system and the steam turbine power generation system as the constraint condition, Nwohu et al.¹⁶⁹ proposed an ant colony algorithm based optimization method for the allocation of thermal and electrical loads within the unit. Kefayat et al.¹⁷⁰ mainly review the research of domestic and foreign scholars in using Ant Colony Optimization (ACO) for capacity allocation optimization in recent years, and summarize and prospect the role of Ant Colony Optimization in capacity allocation optimization.

Differential evolution algorithm

Differential evolution (DE) algorithm provides an effective strategy for solving multimodal and high-dimensional complex optimization problems^171,172. The DE algorithm has been widely applied in fields such as engineering, scientific research, and energy storage system optimization. Its main characteristics lie in concise operating rules and good global search ability¹⁷³. The DE algorithm weights the differences between individuals in the population and merges them into the current population to drive the population to evolve towards the global optimal solution. The main operational steps include initialization, mutation, crossover, and selection. The mutation operation generates experimental individuals by combining the target individual with the difference vector, the crossover operation provides diversity in the exploration solution space, and the selection operation is based on the greedy criterion to determine whether to adopt new experimental individuals¹⁷⁴. The mathematical expression of mutation operation is

$${\mathbf{v}}_{i}^{(g + 1)} = {\mathbf{x}}_{r1}^{(g)} + F \cdot \left( {{\mathbf{x}}_{r2}^{(g)} - {\mathbf{x}}_{r3}^{(g)} } \right)$$

(18)

The parameter ${\mathbf{v}}_{i}^{(g + 1)}$ is the mutation vector, ${\mathbf{x}}_{r1}^{(g)}$, ${\mathbf{x}}_{r2}^{(g)}$, ${\mathbf{x}}_{r3}^{(g)}$ are three randomly selected individuals from the current generation g, and F is the scaling factor. Cross operation can be defined as

$$u_{ij}^{(g + 1)} = \left\{ {\begin{array}{*{20}l} {v_{ij}^{(g + 1)} ,} \hfill & {{\text{ if }}{\text{rand}}_{ij} \le CR{\text{ or }}j = j_{{\text{rand }}} } \hfill \\ {x_{ij}^{(g)} ,} \hfill & {\text{ otherwise }} \hfill \\ \end{array} } \right.$$

(19)

The parameter $u_{ij}^{(g + 1)}$ is the j-dimensional component of the experimental vector, CR is the crossover probability, rand_ij is a uniformly distributed random number within the range of 0 and 1, and $j_{{\text{rand }}}$ is the randomly selected index. Differential evolution algorithm has become an important tool for solving energy storage system optimization problems due to its simplicity and powerful global search ability¹⁷⁵. In terms of capacity planning for energy storage systems, differential evolution algorithms can optimize the capacity and quantity of energy storage systems to minimize system costs or maximize system energy efficiency. In terms of charging and discharging scheduling in energy storage systems, differential evolution algorithms can develop optimal charging and discharging strategies to meet the energy requirements and constraints of the system. In terms of energy management in energy storage systems, differential evolution algorithms can optimize energy scheduling and storage to improve energy utilization efficiency and stability. Das et al.¹⁷⁶ proposed a method for selecting weighting functions in the controller design process using integrated system performance indicators, and solved it using differential evolution algorithm. The robust stability and performance of the controller were verified through calculation results, greatly improving the load frequency stability of microgrid power systems.

In the optimization application of energy storage systems, the efficiency of differential evolution (DE) algorithm can be significantly improved through a series of improvement methods. Firstly, by dynamically adjusting the algorithm parameters, such as updating the scaling factor and crossover probability in real-time based on the population evolution state, the convergence speed and solution accuracy of the algorithm can be optimized. Secondly, adopting a hybrid strategy and integrating local search can enhance the algorithm's local search ability, thereby improving the overall efficiency of energy storage system optimization. Furthermore, extending the DE algorithm to make it applicable to multi-objective optimization to comprehensively consider the cost-effectiveness, reliability, and sustainable development of energy storage systems. De et al.¹⁷⁷ constructed a coordinated dynamic economic scheduling model for wind and solar energy storage systems and proposed a competitive mechanism based multi strategy multi-objective differential evolution algorithm. Simulation calculations were conducted on 10 and 15 test systems with wind power, optoelectronics, and energy storage units. The effectiveness of the improved DE algorithm in solving dynamic economic scheduling problems was demonstrated, and the constraint handling method has good feasibility. A capacity configuration model was constructed for the independent microgrid of wind, solar, and diesel storage, considering economic, environmental, and system reliability requirements, with the goal of minimizing total cost. Ramli et al.¹⁷⁸ proposed an improved differential evolution algorithm. Applying the proposed method to microgrid capacity optimization configuration, the improved differential evolution algorithm has broader application value. Li et al.¹⁷⁹ designed a capacity optimization algorithm for photovoltaic energy storage and generation systems. Construct capacity optimization objectives and constraints based on the principle of electricity balance. Then, combining differential evolution algorithm for mutation, crossover, and selection operations, by analyzing data such as component configuration quantity and load shortage rate. The discovery that this algorithm significantly improves economic benefits while ensuring power supply reliability indicates that it has significant optimization advantages and great potential for trial operation.

Genetic algorithm

Genetic algorithm (GA) is a search heuristic algorithm developed by simulating natural selection and genetic principles in biological evolution¹⁸⁰. Since John proposed genetic algorithm, it has become a very popular method for solving optimization problems, especially in energy storage system design and operation optimization¹⁸¹. The core mechanisms of genetic algorithms include fitness evaluation, selection, crossover (also known as "hybridization"), and mutation. Each individual in the population represents a potential solution in the problem space and is encoded through its "chromosome" (usually a string of binary sequences). The algorithm iteratively selects individuals with high fitness in the current population, generates new individuals through crossover and mutation, and simulates reproduction and genetic variation in biological evolution¹⁸². In genetic algorithms, the fitness function is used to evaluate an individual's adaptability, and the selection process can use methods such as roulette wheel selection or tournament selection. The roulette wheel selection method is represented as follows.

$$P(x) = \frac{f(x)}{{\sum\limits_{i = 1}^{N} f \left( {x_{i} } \right)}}$$

(20)

The parameter P(x) represents the probability of individual x being selected, and N is the size of the population. Cross operation is expressed by the following formula.

$$C = {\text{crossover}} (A,B)$$

(21)

The parameter C represents the offspring generated by the parent individuals A and B, randomly selected at the intersection. Mutation operations can prevent premature convergence of algorithms, and a common mutation operation is represented as

$$M = {\text{mutate}} (C)$$

(22)

The parameter M represents the individual after gene mutation. The advantages of GA algorithm are its global search ability, good robustness, and ease of parallel implementation. Meanwhile, the GA algorithm does not require solving the derivative of the objective function, nor is it limited by the nonlinearity and non-convexity of the function, and can be applied to various types of optimization problems¹⁸³. However, the GA algorithm also has some drawbacks, such as being prone to getting stuck in local optima, slow convergence speed, and parameter settings having a significant impact on the results. In the optimization problem of energy storage systems, the GA algorithm can be applied to energy storage capacity planning, charge and discharge scheduling, energy management, and other aspects¹⁸⁴.

To enhance the efficiency and accuracy of genetic algorithm in energy storage system optimization, researchers have proposed a series of improvements. One of the key improvements is the development of multi-objective genetic algorithm (MOGA), which can comprehensively deal with multiple conflicting optimization objectives such as cost, efficiency, and reliability¹⁸⁵. In addition, combined with other optimization techniques such as particle swarm optimization or simulated annealing algorithm, the unique advantages of these algorithms can be used to improve the quality of solutions and search efficiency. For the improvement of the algorithm coding mechanism, the application of real coding or other advanced coding strategies is better in line with the reflection of the energy storage system attributes. At the same time, the adaptive adjustment of the crossover rate and mutation rate in the algorithm can better adapt to the evolutionary dynamics of the population, and increase the robustness and adaptability of the algorithm. The introduction of local search algorithms, such as hill-climbing algorithm, can also significantly enhance the local search ability of genetic algorithms in the solution space. In view of the flexibility and robustness of genetic algorithm, its application in energy storage system optimization is considered to have broad prospects. In response to the current situation where the maximum power point tracking process of distributed photovoltaic energy storage output is affected by multi peak characteristics, Yousri et al.¹⁸⁶ proposed an improved chaotic genetic algorithm based method for tracking the maximum power point of distributed photovoltaic energy storage output. It can effectively track the maximum power output point of distributed photovoltaic energy storage under different environmental temperatures and light intensities, and the application effect is significant. Peng et al.¹⁸⁷ proposed a dual layer optimization strategy for frequency regulation power scheduling in a fire multi storage system based on ensemble empirical mode decomposition (EEMD) and multi-objective genetic algorithm (MOGA), targeting the problem of multiple energy storage power stations distributed at different network nodes in the regional power grid participating in frequency regulation power scheduling. The proposed strategy can enhance the frequency regulation effect of the regional power grid and reduce the frequency regulation cost, balance the frequency regulation cost and SOC of multiple energy storage stations, and enhance the enthusiasm and sustainability of energy storage stations participating in frequency regulation. In order to improve the power quality of the distribution network and achieve load level regulation, Grisales et al.¹⁸⁸ proposed a distributed photovoltaic distribution network energy storage optimization configuration method based on genetic algorithm, which can achieve peak shaving of various loads and has the effect of peak shaving and valley filling.

Particle swarm optimization

Particle swarm optimization (PSO) is an important algorithm in the field of swarm intelligence optimization¹⁸⁹. It was proposed by Eberhart and Kennedy based on the social behavior patterns of bird flocks. It is suitable for a variety of continuous optimization problems, and is widely used in the design and management optimization of energy storage systems due to its simplicity and effectiveness¹⁹⁰. In the PSO algorithm, each solution is treated as a flying "particle" in the solution space. These particles adjust their position by tracking the best position in individual experience (individual cognition) and the best position in group experience (social cognition) to find a global optimal solution. The movement of particles is determined by speed, which is constantly updated according to the optimal solution of individuals and groups¹⁹¹. The particle position and velocity updates follow the following formula.

$$v_{i}^{(t + 1)} = w \cdot v_{i}^{(t)} + c_{1} \cdot r_{1} \cdot \left( {p_{i} - x_{i}^{(t)} } \right) + c_{2} \cdot r_{2} \cdot \left( {g - x_{i}^{(t)} } \right)$$

(23)

$$x_{i}^{(t + 1)} = x_{i}^{(t)} + v_{i}^{(t + 1)}$$

(24)

Among them, $x_{i}^{(t)}$ and $v_{i}^{(t)}$ respectively represent the position and velocity of the i-th particle at time t. p_i is the optimal position discovered by the particle so far, g is the current global optimal position, w is the inertia weight, c₁ and c₂ are acceleration constants, and r₁ and r₂ are both random numbers in the [0,1] interval. The advantages of PSO algorithm are its global search ability, fast convergence speed, and relatively simple parameter settings¹⁹². Meanwhile, the PSO algorithm does not require solving the derivative of the objective function, nor is it limited by the nonlinearity and non convexity of the function, and can be applied to various types of optimization problems¹⁹³. Liu et al.¹⁹⁴ proposed a hybrid particle swarm optimization algorithm that combines random weight balanced particle swarm optimization and immune mechanism, and improves the algorithm's optimization ability and convergence speed by introducing nonlinear weights and sub gradient optimization techniques. Li et al.¹⁹⁵ used an improved particle swarm optimization algorithm with adaptive inertia weights to optimize the energy storage configuration of microgrids.

When solving the problem of energy storage system optimization, the performance improvement of particle swarm optimization (PSO) algorithm can be achieved by implementing a series of innovative improvement strategies¹⁹⁶. First of all, dynamically adjusting the inertia weight can form a balance between the global exploration and local search capabilities of the algorithm. In addition, the multi-group strategy allows parallel search in different regions of the solution space, thereby increasing the diversity of solutions and improving the global search capability. Combining PSO with other algorithms such as genetic algorithm or simulated annealing will also help to synthesize the high-efficiency characteristics of their respective algorithms to improve the overall performance of the solution¹⁹⁷. The local search mechanism is introduced to search the region near the individual optimal solution or the global optimal solution in detail, so that the solution is more accurate. Finally, for the special constraints in the energy storage system, it is very important to develop an efficient constraint processing technology, which ensures the feasibility and practicability of the optimization results. Through the comprehensive implementation of these strategies, the ability of PSO algorithms to solve energy storage system optimization problems can be significantly improved, and the efficiency of design and management can be improved¹⁹⁸. On the basis of comprehensively considering various economic factors such as photovoltaic power generation cost, electricity purchase cost, and energy storage cost, an economic operation model of the "source grid load storage" multi energy complementary system is established. Ju et al.¹⁹⁹ proposed an energy scheduling optimization scheme for the multi energy complementary system based on particle swarm optimization algorithm. The effectiveness of the scheduling scheme based on particle swarm optimization algorithm can not only reduce system development and operation costs, but also be promoted and applied to military island and reef multi energy complementary microgrid systems, fully leveraging the flexible and efficient application characteristics of distributed power sources. By utilizing the linkage between thermal and electrical loads in microgrids to mitigate the volatility of wind power generation, Li et al.²⁰⁰ established a particle swarm optimization scheduling model for cogeneration microgrids considering the impact of wind power generation. Martinez et al.²⁰¹ used particle swarm optimization algorithm with the goal of maximizing economic benefits, selected the optimal ratio of wind and solar energy storage capacity, and conducted economic analysis using data collected from the demonstration project of smart microgrid construction in energy-saving office and residential areas. This can provide a theoretical and data basis for the energy-saving transformation of smart microgrids. The energy storage system plays a crucial role in maintaining energy balance and improving the quality of distribution network power supply, and can effectively suppress power fluctuations, reduce wind and solar curtailment rates, and improve power quality. Subramanian et al.²⁰² comprehensively considered the constraints on the safe operation of distributed power sources, energy storage devices, and distribution networks, and established an optimization configuration model for distribution network energy storage based on energy storage cost, network loss rate, and voltage stability as optimization indicators. Taking the IEEE33 node distribution network as an example, the model was solved using the niche multi-objective particle swarm optimization algorithm, and the effectiveness of the model and algorithm was verified.

Simulated annealing algorithm

Simulated annealing (SA) is a population intelligent random search method, which is inspired by the annealing process in solid state physics²⁰³. This algorithm has been proved to be particularly effective in many optimization problems, including the optimization of energy storage systems. Simulated annealing algorithm simulates the physical process of the metal cooling slowly after heating, so that the system has a probability of accepting a solution that is slightly worse than the current solution, and thus avoids falling into the local minimum prematurely²⁰⁴. The algorithm accepts the difference solution with a certain probability, which decreases with the decrease of the "temperature" parameter. In this way, the SA algorithm can jump out of the local optimal solution with a large jump in the global search, and finally converge to the global optimal solution or the approximate optimal solution²⁰⁵. The iterative process of simulated annealing involves probabilistic acceptance of new solutions, which can be described as

$$P(\Delta E) = \exp ( - \Delta E/(k \cdot T))$$

(25)

Among them, $\Delta E$ represents the energy difference between the new solution and the current solution, the parameter k is the control parameter, usually the Boltzmann constant, and T is the current temperature. The temperature reduction strategy is the key to the cooling process, and it usually follows the following formula.

$$T_{n + 1} = \alpha \cdot T_{n}$$

(26)

T_n is the current temperature and $\alpha$ is the cooling coefficient, satisfying 0 < $\alpha$ < 1. In energy storage system optimization, simulated annealing algorithm can be used to solve problems such as energy storage capacity scaling, charging and discharging strategies, charging efficiency, and energy storage system configuration. The algorithm gradually optimizes the objective function by searching and state transitions in the solution space, to find the optimal solution or a solution close to the optimal solution. By using simulated annealing algorithm for energy storage system optimization, good performance and effectiveness can be achieved²⁰⁶. However, for complex large-scale problems, the computational complexity of simulated annealing algorithms may be high, and other optimization methods or heuristic algorithms need to be combined to improve solution efficiency.

When dealing with energy storage system optimization problems, simulated annealing algorithm (SA) can improve its performance through a series of innovative improvement strategies. Among them, the adaptive cooling plan dynamically adjusts the cooling rate of the algorithm to adapt to the improvement of the search schedule and reconciliation, rather than simply relying on a fixed cooling rate²⁰⁷. In addition, a multi-stage annealing strategy is adopted, that is, a higher temperature is set at the initial stage of the search process to quickly jump out of the local optimal solution, and the temperature is gradually reduced as the process deepens, so as to conduct a more accurate search. Hybrid local search techniques, such as introducing gradient descent algorithm in key stages, can enhance the search accuracy of the algorithm in a specific area. The real variable coding method is more consistent with the continuous variable characteristics of the energy storage system. In addition, the constraint management technology for the operation of the energy storage system ensures the compliance and safety of the optimization process. Through the comprehensive application of these strategies, simulated annealing algorithm can find the optimal or near optimal solution in energy storage system optimization²⁰⁸. For the integration of a large number of distributed power sources and energy storage systems into the power grid, in order to effectively configure the distribution network system and achieve its optimized economic operation, Hannan et al.²⁰⁹ proposed an optimal configuration method for battery energy storage systems and distributed generators in the distribution system. They used a simulated annealing algorithm with a defined neighborhood structure and proposed a decomposition method to solve the operation status problem of the energy storage system, ensuring a near global optimal solution with lower computational complexity. Kumar et al.²¹⁰ used an improved genetic simulated annealing algorithm to search for the optimal location and capacity of photovoltaic power plants, used supercapacitors to smooth out output fluctuations in distributed photovoltaic power generation, optimized the charging and discharging power curve of energy storage devices with the goal of minimizing capacity, and then determined the storage location and capacity. The location and capacity of energy storage stations connected to the distribution network directly affect the safety of the distribution network system operation, and are a key link in the optimization planning of the distribution network. Mohseni et al.²¹¹ proposed the simulated annealing moth to flame algorithm for optimization and solution, determining the location and scale of energy storage stations in the distribution network. The results indicate that the proposed algorithm has a faster iteration speed and stronger ability to seek optimal solutions compared to traditional moth to flame algorithms.

Grey wolf optimizer

Grey Wolf Optimizer (GWO) is a swarm intelligence optimization algorithm based on natural phenomena proposed by Seyedali Mirjalili²¹². The algorithm is inspired by the high degree of cooperation, social hierarchical structure and flexible strategies exhibited by gray wolf populations during the predation process in the wild, and is used to solve various complex numerical optimization problems²¹³. GWO simulates the leading and following behaviors in gray wolf groups, and forms a search group with a clear social hierarchy by simulating the roles of α (alpha), β (beta), and δ (delta) leading wolves, as well as the roles of ω (omega) ordinary wolves. α, β, and δ wolves represent the best, second-best, and third-best solutions in the current search space, and they guide the entire wolf pack to converge to the optimal solution region. The omega wolf imitates the rest of the members, follows the decisions of the leader wolf and gradually adjusts its position to approach the optimal solution^214,215. Grey wolves will use strategies such as encircling, chasing, and attacking during predation. These strategies are transformed into mathematical formulas in the algorithm, which are used to update the position (that is, the solution) of the individual, so that the search process has the ability of both global exploration and local fine search. With the progress of iteration, the algorithm can explore the solution space extensively in the early stage (global search), and gradually turn to the fine search of the optimal solution region (local search), which reflects good convergence and the ability to avoid premature²¹⁶. Because of its simple and effective design and excellent optimization performance, GWO is widely used in various engineering optimization problems, machine learning parameter optimization, function optimization, multi-objective optimization, neural network training, UAV path planning, power system dispatching and other fields. The mathematical model of GWO mainly includes the following key components, initialization and social hierarchy establishment. A set of solutions (i.e. gray wolf individuals) is randomly generated within the search space, and each solution represents a candidate solution to be evaluated²¹⁷. Calculate the fitness value of each individual according to the objective function, that is, the function value of the objective function at the solution. The smaller the fitness value, the better the quality of the solution. According to the size of fitness values, individuals are divided into four categories: α, β, δ and ω. The alpha, beta and delta wolves correspond to the three individuals with the highest fitness respectively, and the rest are omega wolves²¹⁸. In each generation (iteration), all individuals (including lead wolves and regular wolves) update their positions according to the following formula.

$$X_{i}^{t + 1} = X_{i}^{t} + A \cdot D \cdot (C_{{1}} \cdot r_{{1}} \cdot (X_{\alpha } \, - \,X_{i} )\, + \,C_{{2}} \cdot r_{{2}} \cdot (X_{\beta } \, - \,X_{i} )\, + \,C_{{3}} \cdot r_{{3}} \cdot (X_{\delta } \, - \,X_{i} ))$$

(27)

The parameter $X_{i}^{t}$ is the position of the i-th individual in the t-th generation. X_α​, X_β, and X_δ​ respectively are the positions of α, β, and δ wolves in the current iteration (that is, the optimal, suboptimal, and third optimal solution). The parameter A is the decay factor that decreases with increasing iterations, ensuring a gradual transition from global to local search. The parameter D is the distance vector between the individual and the leading wolf, reflecting the relative positional relationship between the following wolf and the leading wolf. The parameters C₁, C₂, C₃ are weight coefficients, which usually take values as a linearly decreasing function to simulate different phases of the surrounding behavior. The parameters r₁, r₂ and r₃ are random numbers between [0, 1], introducing randomness to enhance the flexibility of the search. This position update formula imitates the surrounding, chasing, and attacking behaviors when gray wolves prey. By following the leading wolf and combining with random factors, the individuals move in the search space and gradually converge to the vicinity of the optimal solution. The algorithm runs until the preset maximum number of iterations is reached or specific convergence criteria are met. Finally, the optimal solution (that is, the position of the α wolf) is output as an approximate global optimal solution to the problem.

By continuously adjusting the location of the gray wolf, the gray wolf optimization algorithm can gradually approach the optimal solution of the problem. In each iteration, the algorithm updates the location of the gray wolf based on the current location of the gray wolf and the location of the prey until the optimal solution that meets the requirements is found²¹⁹. To sum up, the gray wolf optimization algorithm builds a concise and efficient mathematical model to solve various optimization problems by simulating the social hierarchy structure and predation strategy of the gray wolf population. By dynamically adjusting the individual position, the model skillfully balances the global search and local search capabilities, showing good optimization performance and application potential.

The optimized configuration of distributed power sources is crucial for the cost of microgrids, meeting load demands, and adapting to local renewable energy consumption. Zhang et al.²²⁰ proposed an optimization configuration method for microgrid source network load storage considering demand response, using the Grey Wolf algorithm for solution analysis, which is an effective means to solve the imbalance between energy supply and demand. Optimizing configuration strategies can maximize the performance and efficiency of energy storage systems. However, the original grey wolf algorithm still has problems such as slow convergence speed and susceptibility to local optima. Abbas et al.²²¹ introduced adaptive parameter adjustment and multi-objective weighting techniques, and applied the improved grey wolf algorithm to the optimization configuration problem of energy storage in distribution networks. Guo et al.²²² took the energy storage bidirectional converter as the research object and used the improved grey wolf optimization algorithm (IGWO) to tune the control parameters of the energy storage bidirectional converter to achieve optimal performance. Aiming at the limitations of traditional linear control strategies, a composite control strategy based on IGWO-PID and improved model prediction is proposed. In response to the problem of reducing the grid's absorption level of wind power fluctuations, Zhou et al.²²³ designed a power allocation strategy for hybrid energy storage systems using a Grey Wolf algorithm optimized and improved adaptive noise integrated empirical mode decomposition. Based on the state of charge of supercapacitors, fuzzy control is used to correct the power of batteries and supercapacitors, achieving secondary power allocation of hybrid energy storage systems.

Sparrow search algorithm

Sparrow search algorithm (SSA) is a new swarm intelligence optimization algorithm, which was proposed in 2020²²⁴. The algorithm is mainly inspired by the foraging behavior and anti-predation behavior of sparrows, and aims to simulate the intelligent behavior of sparrows to solve the optimization problem²²⁵. In the process of feeding, the overall population of sparrows can be divided into two categories: discoverers and followers. Finders are responsible for finding food and providing foraging areas and directions for the entire sparrow population²²⁶. While the followers rely on the discoverer for food. In addition, a certain proportion of individuals will be selected in the population for investigation and early warning. Once danger is found, they will choose to give up food to ensure safety. This foraging mechanism reflects the intelligence and coordination ability of sparrows, and provides an effective solution to the optimization problem²²⁷.

The mathematical model of the sparrow optimization algorithm is mainly based on the discoverer-follower model, and a detection and early warning mechanism is added. In the model, each individual sparrow has only one attribute²²⁸. Individual sparrows may have three state changes: as a discoverer, they lead the population to find food. As a follower, follow the discoverer to forage. Or have a vigilance mechanism, and give up foraging when they find danger. Finders usually have high energy reserves and are responsible for searching areas with abundant food throughout the population, providing areas and directions for all followers to forage. In the establishment of the model, the level of energy reserve depends on the Fitness Value (Fitness Value) of the sparrow individual²²⁹. Once the sparrow has spotted the predator, the individual starts chirping as an alarm signal. When the alarm value is greater than the safe value, the discoverer will take the followers to other safe areas for foraging. The identities of discoverers and followers are dynamic. If a better source of food can be found, each sparrow can become a discoverer, but the proportion of discoverers and followers in the entire population remains the same. The lower their followers' energy, the poorer their foraging position in the population²³⁰. Some lower-energy followers are more likely to fly to other places to forage for more energy.

The sparrow optimization algorithm can effectively solve the optimization problem by simulating the intelligent behavior of the sparrow group. The algorithm has the characteristics of high efficiency, flexibility, low memory usage and easy implementation, and is especially suitable for large-scale search problems²³¹. At the same time, because the algorithm pays more attention to the local optimal solution, it overcomes the limitations of other optimization algorithms to a certain extent. In a word, the sparrow optimization algorithm is an optimization algorithm based on the intelligent behavior of sparrows. By simulating the foraging behavior of discoverers and followers and the detection and early warning mechanism, it can effectively solve the optimization problem.

Dong et al.¹⁵⁸ proposed an energy storage optimization configuration and scheduling strategy that comprehensively considers the randomness and uncertainty of wind, solar, and water distributed renewable energy generation systems. They used an improved sparrow algorithm to solve the problem and combined it with the complementary characteristics of wind, solar, and water in the actual power grid for optimization configuration calculation. Based on small sample data of energy storage system operation, Yan et al.²³² proposed an energy storage loss calculation model that combines Logistic chaotic sparrow optimization algorithm and convolutional neural network. Zhao et al.²³³ proposed an optimization model for the sparrow optimization algorithm of an electric thermal gas hydrogen integrated energy system that takes into account demand response, addressing issues such as carbon emissions and new energy consumption. Introducing a carbon capture multi-stage electric to gas operation framework, exploring the low-carbon potential of hydrogen energy in electric to gas technology, utilizing hydrogen fuel cells and hydrogen storage tanks, improving the flexibility of system resource scheduling, considering demand response on the load side, and coordinating the optimization of both source and load sides. Qiao et al.²³⁴ comprehensively considered the impact and significance of cold, heat, and power combined energy storage microgrids on economic and environmental issues, and established an economic and environmental optimization scheduling model for cold, heat, and power combined microgrids. The optimization objective is to minimize the operating cost and environmental pollution cost of each micro power source, and the sparrow optimization algorithm is used for optimization and solution of the scheduling model.

The comparison of the characteristics of the seven intelligent optimization algorithm is shown in Table 4. The comparison of seven intelligent optimization algorithms is shown in Table 5.

Table 4 Comparison of characteristics of intelligent optimization algorithms.

Table 5 Comparison of seven intelligent optimization algorithms.

Typical examples of swarm intelligence optimization include ant colony algorithm (ACO), differential evolution algorithm (DA), genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA) and so on. They are widely used in many fields such as function optimization, path planning, scheduling problems, network design and so on. Especially in energy storage system optimization, swarm intelligence algorithm has become a powerful tool to solve optimization problems because of its efficiency and robustness in searching for the global optimal solution.

Application of swarm intelligence optimization algorithm in energy storage systems

In the optimization problem of energy storage system, swarm intelligence optimization algorithm has become the key technology to solve the problems of power scheduling, energy storage capacity configuration and grid interaction in energy storage system because of its excellent search ability and wide applicability. Especially in photovoltaic energy storage systems, the application of these algorithms not only helps to achieve the balance between power generation and load demand, but also optimizes energy utilization efficiency and reduces operating costs.

Application of power dispatch in photovoltaic energy storage system

In photovoltaic energy storage systems, the key to power scheduling is to maximize energy efficiency and minimize the total cost. Swarm intelligent optimization algorithms such as particle swarm optimization (PSO) and ant colony optimization (ACO) play a key role in the global optimal solution search. They effectively manage energy storage systems by automatically adjusting charging and discharging schedules, combined with multiple factors such as energy market prices, weather forecasts, photovoltaic power generation, and changes in user needs. The basic research framework for flexible regulation of diversified distributed energy storage is shown in Fig. 6.

Figure 6

The flexible regulation of multi-dimensional distributed energy storage.

Specifically, the swarm intelligent optimization algorithm adjusts the charging and discharging time of the energy storage system to fill valleys and peaks, responds to market signals to adapt to dynamic changes in the energy market, and optimizes the charging and discharging strategy to prolong the service life of the energy storage system. Accurate power scheduling is achieved in the energy storage system. The PSO algorithm is used to generate an efficient charge and discharge cycle, while the ACO optimizes the energy flow strategy between the photovoltaic array and the energy storage unit, all of which significantly improve the comprehensive utilization rate of energy and contribute to the stable operation of the power system.

Optimizing the charging and discharging strategy of the energy storage system through intelligent algorithms can realize the economic dispatch of the microgrid and distribution network. For example, Ma et al.²³⁵used particle swarm optimization to optimize the economic dispatch in the microgrid, while considering cost and environmental impact. In hybrid energy storage systems, such as electric hydrogen hybrid energy storage and gravity-battery hybrid energy storage systems, intelligent algorithms are applied to carry out life cycle cost analysis and capacity optimization to consider the economy and environmental protection of the energy storage system, and at the same time meet the needs of the system. The demand for peak load adjustment, peak shaving and valley filling, and compensation for intermittent new energy output fluctuations. In microgrid economic dispatching, intelligent algorithms such as improved particle swarm optimization can help microgrids optimize the charging and discharging strategies of energy storage devices in real time to ensure that renewable energy is fully utilized, power purchase costs are reduced, and system losses are reduced while meeting load requirements., and ensure the reliability of system operation by improving power quality.

Application of energy storage capacity configuration

In solar energy storage systems, power scheduling plays a vital role with the primary goal of maximizing energy consumption efficiency and minimizing costs. Swarm intelligent optimization methods, including ant colony optimization (ACO) and particle swarm optimization (PSO), offer an efficient method for locating the global optimal solution in order to accomplish this aim. These algorithms can carry out precise management of energy storage systems by intelligently modifying the plans for charging and discharging energy storage equipment in conjunction with energy market pricing, weather prediction data, solar power generating output, and fluctuating user demands.

Intelligent algorithms, like the simulated annealing algorithm, genetic algorithm, improved lion swarm algorithm, particle swarm algorithm, differential evolution algorithm, and others, are used in the active distribution network environment to optimize the capacity configuration and access location of distributed energy storage systems. Achieve peak shaving and valley filling, raise active power regulation capabilities, save costs, and improve power quality. Intelligent algorithms are frequently employed in distributed energy storage systems to optimize energy storage system setup in distribution networks. For example, particle swarm optimization (PSO) can be used for the dual optimization of energy storage capacity and location in microgrids, while the improved whale algorithm, swarm intelligence algorithms such as Harris eagle optimization algorithm and gray wolf algorithm are also used to solve complex nonlinear and multi-objective optimization problems, and find the best energy storage capacity, location and combined configuration, so as to maximize the operation of microgrids economy and stability. The swarm intelligent optimization algorithm is especially good at optimizing the charging and discharging time, so as to implement an efficient valley-peak filling strategy, which not only responds to market signals to adapt to fluctuations in energy prices, but also extends energy storage by formulating a reasonable charging and discharging strategy. The service life of the system. For example, the particle swarm optimization algorithm can construct an efficient charge–discharge cycle plan, while the ant colony optimization algorithm can optimize the energy conversion strategy between the photovoltaic array and the energy storage unit. The application of these strategies has greatly improved the overall energy utilization rate and made a significant contribution to the stable operation of the power system.

Overall, in photovoltaic energy storage systems, the application of swarm intelligent optimization algorithms not only makes the power scheduling process more accurate and efficient, but also promotes the comprehensive utilization of renewable energy and the improvement of the cost efficiency of energy storage systems. With the continuous optimization of algorithms and the advancement of computing technology, it is expected that swarm intelligent optimization algorithms will play an increasingly important role in the field of power scheduling of photovoltaic energy storage systems, and contribute to the realization of green, efficient and balanced power systems.

Interactive application with the power grid

The interaction between photovoltaic energy storage system and grid is very important for modern power system, and it helps to improve energy efficiency and load balance of grid through swarm intelligent optimization algorithm. For example, during peak hours of the grid, these algorithms help prevent overload, while optimizing the frequency and voltage regulation of the grid, improving the overall operating efficiency of the grid.

Swarm intelligent optimization algorithm, especially particle swarm optimization algorithm, ensures the best state of photovoltaic system output by capturing energy market signals in real time, such as demand response procedures, and optimizing grid operating parameters, thereby promoting the sustainable and stable operation of the grid. Through these methods, the swarm intelligent optimization algorithm can significantly improve the interaction performance between the photovoltaic energy storage system and the grid, make the system more intelligent and automated, and promote the sustainable and stable operation of the grid. With the continuous progress of technology, the application of swarm intelligence optimization algorithm in power grid interaction will become more extensive and effective.

On the issue of energy storage systems stabilizing new energy fluctuations, Some scholars have studied the optimization of capacity allocation of electric-hydrogen hybrid energy storage microgrids, discussed the complementarity between hydrogen energy storage and other energy storage technologies, and optimized the system through intelligent algorithms structure to improve the operating efficiency and stability of the entire microgrid. Researchers use intelligent algorithms to optimize the effect of the energy storage system on stabilizing fluctuations in the output of new energy sources such as photovoltaics. By accurately predicting changes in natural conditions such as wind speed and light intensity, intelligent algorithms can guide the energy storage system to charge and discharge in a timely manner, reducing the pressure on power grid peak regulation, Improve the acceptance rate of new energy power. In the energy storage configuration in specific scenarios, such as the building photovoltaic energy storage system, the intelligent algorithm can realize the best match between energy storage capacity and photovoltaic capacity according to the energy demand characteristics of the building and the photovoltaic output characteristics of the roof, ensuring the most economical In a reasonable state, functions such as self-production and self-use, surplus electricity grid connection, etc. can be realized.

The challenges faced by energy storage systems

In order to achieve high energy conversion efficiency, lower operating costs, and increase overall system dependability, energy storage systems are essential. For the design and operation of energy storage systems, intelligent algorithms—particularly swarm intelligent optimization algorithms—offer a number of advantages and benefits. These include enhanced reliability, reduced response times, improved demand forecasting, and optimized resource allocation, among other benefits. However, a number of difficult and challenging technological issues, including data quality, algorithm complexity, and real-time requirements, arise when intelligent algorithms are used to energy storage system optimization.

Technical challenges for the application of intelligent algorithms

In the process of integrating intelligent algorithms to optimize energy storage systems, researchers usually face a set of complex technical problems. Among them, the implementation of algorithm performance is highly dependent on the quality of the data used. Imprecise or incomplete data often hinder the performance of advanced algorithms, resulting in unreliable optimization results. Data flaws, such as incorrect inputs, record omissions, and the influence of environmental noise, may cause algorithms to make choices that deviate from optimal decisions. Another concomitant challenge is the management of algorithm complexity. Effective optimization algorithms often require a large amount of computational resources, which is particularly challenging in the response time required for real-time or near-real-time decisions. Algorithms must give solutions in a short period of time, and at the same time need to adapt to changing operating conditions and emergencies that occur from time to time to ensure stable operation in situations such as energy demand fluctuations, market changes, or equipment failures. In order to overcome these challenges, it is first necessary to clean and preprocess the data to ensure its reliability and integrity. The focus of further research should be on the development of algorithms that are suitable for real-time operations and have strong adaptability, and at the same time apply technologies such as cloud computing and edge computing to reduce the computational burden of algorithms. Coupled with the improvement of the self-adaptability of the algorithm and the introduction of the self-learning mechanism, it helps the algorithm to cope with changes in the environment and data. For algorithms that rely on predictive models, it is also crucial to continuously improve the models to enhance their predictive accuracy and credibility.

Through these continuous efforts and innovations, the application challenges of intelligent algorithms in energy storage systems can be effectively dealt with, so that energy storage systems can enter a mature stage in terms of providing safe power supply, optimizing energy utilization, and reducing operating costs. Looking forward to the future, with the further development of technology, the application of intelligent algorithms in energy storage systems is expected to become more efficient, automated and accurate, which will significantly promote the development of energy systems towards a more sustainable and intelligent direction.

The application of swarm intelligence optimization algorithm in photovoltaic energy storage system may have the following limitations: premature convergence: swarm intelligence optimization algorithm may converge to the local optimal solution prematurely during the search process, and cannot find the global optimal solution. This may result in the configuration of the energy storage system being not ideal enough to give full play to its performance. Limited search capability: The search capability of swarm intelligence optimization algorithms may be limited to some extent, especially when dealing with complex photovoltaic energy storage system problems. This may cause the algorithm to fail to find a better solution. Parameter sensitivity: The performance of swarm intelligence optimization algorithms may be sensitive to the choice of parameters. Different problems may require different parameter settings, which requires a lot of experiments and adjustments, which increases the complexity of the application. High computational cost: Some swarm intelligence optimization algorithms may require high computational cost when dealing with large-scale photovoltaic energy storage system problems. This may limit its feasibility in practical applications, especially for systems that require high real-time performance. Lack of theoretical basis: The theoretical basis of swarm intelligence optimization algorithm is relatively weak, and there is a lack of in-depth understanding of the performance and convergence of the algorithm.

Coping strategies and solutions

In the process of adopting intelligent algorithms in energy storage systems, the technical challenges faced require the industry to adopt effective response strategies to ensure the operation effect of algorithms and the stability of systems. A series of solution strategies are proposed below, aiming to optimize the performance of intelligent algorithms and ensure the efficient and stable operation of energy storage systems.

• (1) Improve data quality and integrity. Accurate and reliable data is the cornerstone of the optimality of intelligent algorithms. The first steps to improve data quality include enhancing the accuracy of the data collection process, using precision sensors, and establishing a data redundancy mechanism and regular review process. In addition, the quality of the input data of the algorithm can be significantly improved by applying data cleaning technology to remove outliers and noise, and using data interpolation to repair incomplete records.

• (2) Optimize the complexity of the algorithm. The computational load of the algorithm can be reduced by optimizing its internal structure and reducing the number of parameters. Furthermore, the development of an efficient version of the algorithm and the use of approximate solutions and heuristic methods can speed up the algorithm while ensuring quality. The application of parallel computing and distributed architecture can also improve the processing power of the algorithm.

• (3) Guarantee real-time requirements. In order to meet the needs of rapid response, the design of lightweight algorithms is very important. Optimizing the iterative process of the algorithm and preset a response mechanism to deal with common problems can improve efficiency while reducing calculation delay and ensure that the algorithm meets the needs of high-speed response.

• (4) Improve the adaptability and robustness of the algorithm. The development of adaptive algorithms is crucial, as they can automatically adjust parameters based on changes in system state and external environment. By adopting reinforcement learning and online updating mechanisms, algorithms can continuously learn and improve in practice to enhance adaptability and robustness.

In summary, when applying intelligent algorithms in energy storage systems, it is necessary to face and solve a series of technical challenges, and prepare solutions for more potential problems that may arise in the future. The implementation of these strategies not only enhances the reliability and economy of the system, but also contributes to achieving the goal of sustainable energy. With the continuous integration of new technologies and in-depth exploration of research directions, it is expected that intelligent algorithms will provide more effective support for the optimization and upgrading of energy storage systems.

Future research directions

Enhancing system flexibility, optimizing performance, and increasing algorithm efficiency are the primary goals of applying swarm intelligence optimization algorithms to energy storage systems. In order to offer viable answers to current problems, this study delineates a number of distinct research avenues.

• (1) Integrating advanced predictive technologies. With the continuous advancement of machine learning and big data analysis technologies, it is possible to strengthen the application of these technologies in energy storage system optimization. In particular, the in-depth learning model has excellent capabilities in processing and interpreting highly complex and unstructured data sets, providing accurate and efficient input data for the optimization of energy storage systems.

• (2) Improvement of algorithm performance and real-time performance. The optimization algorithm must simplify its calculation process and reduce calculation complexity while maintaining or improving quality, especially for scenarios that require fast decision-making. It is becoming more and more important to develop new algorithms or improve existing algorithms to complete data processing and give accurate judgments in a relatively short period of time.

• (3) Self-adaptation and self-learning ability strengthening of the algorithm. In order to improve the adaptability and robustness of the algorithm, it is particularly necessary to develop and apply self-adjusting intelligent algorithms. Such algorithms should have the ability to automatically optimize parameters based on environmental changes, and rely on reinforcement learning and online update mechanisms to enhance their self-learning capabilities to cope with changing operating environments and data states.

• (4) Exploration of interdisciplinary methods. Combining knowledge in the fields of geographic information, meteorology, and market economics to promote algorithmic research related to photovoltaic energy storage systems, for example, integration with climate models can improve the prediction of photovoltaic power generation, and optimize the operation of energy storage systems accordingly.

• (5) Meta-heuristic and hybrid intelligent algorithm. By combining multi-population intelligent optimization technology, hybrid algorithm and meta-heuristic method are developed to improve search efficiency and obtain better results in more complex optimization problems.

Based on the research and analysis conducted in the aforementioned areas, it is projected that the energy storage system of the future will evolve into a crucial intelligent component. Intelligent algorithms are efficient and economical, but as they continue to be developed, the energy industry will see more innovation and the field of energy storage technology will advance toward maturity and intelligence. Intelligent algorithms will be able to more successfully enable energy storage system updates and optimization when new technologies are included. Additionally, this will strongly promote the advancement of sustainable energy systems.

Conclusions

As the world's energy structure changes, solar energy storage devices are becoming a more important part of contemporary power networks. The process of transforming energy involves the use of intelligent algorithms. It delivers steady and effective operation to the power system in addition to greatly increasing the efficiency of solar energy consumption. Intelligent algorithms have the potential to optimize energy management systems and have demonstrated significant benefits in power scheduling, energy storage capacity design, and grid integration. PV energy storage systems may successfully save costs, minimize waste, and use energy more efficiently in an unpredictable electricity market by implementing precise power scheduling. The energy storage capacity arrangement that makes use of clever algorithms improves the system's ability to respond to shifting demands. Simultaneously, clever algorithms optimize frequency control and load balancing in grid interaction, increasing the overall grid's elasticity and dependability. It is anticipated that intelligent algorithms will become more thoroughly integrated with these technologies due to advancements in artificial intelligence and computer technology. More sophisticated data processing and flexibility for intelligent algorithms will be made possible by the development of artificial intelligence and machine learning technologies. Comprehensive intelligent optimization algorithms will be able to process and optimize a variety of energy sources and demands in the context of hybrid energy systems in order to guarantee the optimal combination and efficiency of energy.

Subsequent investigations will concentrate on enhancing the precision and instantaneous performance of the algorithm, along with merging the algorithm with sophisticated prediction models, like deep learning-based time series analysis, to enable the algorithm to forecast future energy production and consumption trends with greater accuracy. Simultaneously, as the size of energy storage expands, so do the demands on the algorithm's stability and dependability. To address these issues, it is advised that interdisciplinary collaboration be encouraged amongst many disciplines, including data analysis, computer science, and energy science, in order to collaboratively study and create next-generation intelligent algorithms. Encouraging collaboration between academics and industry, converting theoretical breakthroughs into real-world applications, and developing personnel with dual backgrounds in data and energy systems are also vital. In conclusion, intelligent algorithms have made significant progress in the field of solar energy storage applications. They will also keep producing brilliant works powered by artificial intelligence, advance the advancement of solar energy storage technology, and help to create a more independent and sustainable system. significant input into the energy system.