Optical storage micro-grid capacity configuration method considering battery degradation cost

Abstract

The invention discloses an optical storage micro-grid capacity configuration method considering battery degradation cost. The method comprises the following steps: step 1, establishing a photovoltaic output derating model and a hybrid energy storage system aging dynamic model; step 2, by taking the cost minimization of the capacity configuration of the optical storage micro-grid as a target, constructing a total objective function of the capacity configuration model of the optical storage micro-grid; and step 3, considering a photovoltaic output derating model and a hybrid energy storage system aging dynamic model, and constructing constraint conditions of a capacity configuration model of the optical storage micro-grid. According to the method, challenges caused by battery aging are effectively solved, and the method has excellent economic and technical performance in the aspect of capacity configuration of the optical storage micro-grid.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic and energy storage microgrid capacity configuration, and in particular to a photovoltaic and energy storage microgrid capacity configuration method taking battery degradation costs into consideration. Background Art

[0002] In recent years, with the widespread deployment of distributed renewable energy, energy storage and microgrid technologies in various countries and regions, the global electrification rate has increased significantly.

[0003] The decline in investment costs and the improvement in conversion efficiency have stimulated investment in renewable energy-based electrification projects. However, the construction and operation of these projects are closely related to factors such as regional investment budget, geographical location, climatic conditions, and the policy environment of the installation site. Non-interconnected areas that are not connected to the national grid due to remote geographical locations or economic barriers face significant technical and economic challenges in achieving grid connection. Problems such as insufficient power quality in the existing distribution network can lead to reduced power supply reliability. In addition, the deployment of microgrid projects in these non-interconnected areas is challenging due to the lack of detailed operating data and historical meteorological data from similar projects. Therefore, it is crucial to establish a mathematical model to optimize the capacity of various distributed generation technologies within the microgrid, taking into account the need for uninterrupted power supply to critical loads during independent operation, and to conduct a comprehensive technical and economic feasibility pre-assessment in combination with the economic, technical and environmental conditions of the region.

[0004] Existing optimization configuration methods mainly focus on economy, energy efficiency maximization and power supply reliability, including commonly used mathematical programming, heuristic algorithms, meta-heuristic algorithms and multi-objective optimization methods. These methods have made some progress in the capacity optimization problem of microgrids. Common technical means include linear programming, dynamic programming, genetic algorithm, particle swarm algorithm, etc. However, these studies generally have an important technical shortcoming, that is, they fail to fully consider the degradation cost of energy storage systems. Energy storage systems such as batteries will gradually degrade due to charge and discharge cycles during long-term operation, and their shortened life will bring additional maintenance and replacement costs. However, most existing studies assume that the performance of energy storage systems is constant, ignoring the aging effect of energy storage equipment, resulting in the failure to accurately evaluate the full life cycle cost of energy storage systems in actual operation. This optimization method that ignores the degradation cost of energy storage, although it can optimize system performance in the short term, cannot provide an economically reasonable solution for long-term operation. In addition, existing optimization methods usually only consider a single type of energy storage system (such as batteries), and fail to fully utilize the synergistic advantages of multiple energy storage technologies (such as batteries and supercapacitors). Supercapacitors can reduce the load of batteries and extend battery life under high-power and short-term storage conditions. However, in existing research, the collaborative optimization configuration methods of multiple energy storage systems are relatively scarce, making it difficult to fully utilize the complementary characteristics of different energy storage technologies. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art, thereby providing a photovoltaic storage microgrid capacity configuration method that takes into account the battery degradation cost. By incorporating the degradation cost of the energy storage system into the optimization model, the full life cycle economy of the energy storage system can be more accurately evaluated, avoiding the problem of excessively high long-term operating costs caused by traditional methods that ignore the battery aging effect.

[0006] A method for configuring the capacity of a photovoltaic and energy storage microgrid considering battery degradation costs comprises the following steps:

[0007] Step 1: Establish a PV output derating model and a hybrid energy storage system aging dynamic model;

[0008] Step 2: Taking the cost minimization of the photovoltaic-storage microgrid capacity configuration as the goal, the total objective function of the photovoltaic-storage microgrid capacity configuration model is constructed;

[0009] Step 3: Considering the PV output derating model and the hybrid energy storage system aging dynamic model, construct the constraints of the PV-storage microgrid capacity configuration model.

[0010] The photovoltaic output derating model is:

[0011]

[0012] Where P PV (I T ,T) represents the photovoltaic output, corresponding to the irradiance level I T and ambient temperature T; is the rated power of a single photovoltaic panel under standard conditions; γ PT Represents the power temperature coefficient of the photovoltaic panel; I STC and T STC are the irradiance and ambient temperature under standard test conditions respectively.

[0013] The aging dynamic model of the hybrid energy storage system is:

[0014] A battery is considered to have reached the end of its useful life when its initial energy capacity has dropped to 80% of its initial value:

[0015]

[0016] In formula (2), E Br Indicates the rated energy capacity of the battery cell, NC B Indicates the maximum possible number of charge and discharge cycles, E av =20% E Br .

[0017] The objective function of the photovoltaic storage microgrid capacity configuration model is expressed as:

[0018]

[0019] Where Z is the total cost to be minimized, The photovoltaic installation node set Ω is summarized PV The costs associated with installing PV systems at all nodes i; represents the initial investment cost of the ith PV system, is the cost of photovoltaic installation, is a binary variable indicating whether the ith node has a PV system installed;

[0020] Summarizes the set Ω B The cost of installing batteries at all nodes j in is the cost of battery installation at the jth node, is a binary variable indicating whether the jth node is equipped with an energy storage system;

[0021] It represents the discount of future costs in the entire life cycle LY of the project, and the discount rate is Where r is the interest rate per period, y is the energy storage operating life, Represents the replacement or degradation cost of a battery during its life cycle, calculated by dividing the battery cost by Divide by its average lifetime energy output Then multiply by a factor representing attenuation or efficiency loss Ω B represents the replacement or degradation cost of a battery over its life cycle; represents the cost of purchasing electricity from the power grid, The electricity purchase price, including the general power grid purchase price P t G and grid-purchased electricity specifically for battery charging Calculate backup power costs, is the backup power cost factor, P t D is the backup power supply power; represents the energy penalty cost for unmet demand, is the penalty coefficient, P t ENS is the unmet demand power; It is the income from selling photovoltaic power to the power grid. is the cost factor of the sale, It is selling power.

[0022] The constraints are:

[0023] Budget constraints:

[0024] The total cost of installing PV systems on all nodes plus the total cost of installing batteries on all nodes should not exceed the predefined maximum budget C budget , expressed as:

[0025]

[0026] Installation constraints for PV modules and batteries:

[0027]

[0028]

[0029]

[0030] Constraint formula (5) determines the installation status of the photovoltaic system at node i Represents the floor function, which means rounding down to the maximum integer not greater than the value. The constraint on the number of PV systems that can be installed is an integer value, represents the maximum photovoltaic installation or capacity at node i, V i OCU refers to the PV occupied volume or space of node i; constraint formula (5) calculates the maximum number of PV systems that can be installed at a location based on space availability, from Inheriting this installation decision, while also complying with the space constraints; the battery at position j By binary decision variables In constraint formula (6), N BattMax Indicates the total maximum volume or capacity of the battery. is the volume or space required for a battery at node j. This equation ensures that the number of installed batteries does not exceed the number that can be physically accommodated at the location. Constraint formula (7) limits the total available area A for photovoltaic installations at all nodes. av , represents the area required to install the PV system at node i;

[0031] Total power balance and photovoltaic power generation balance constraints:

[0032] Total power balancing requires that the sum of all generation must equal the total load demand P at any given time. t L :

[0033]

[0034] Constraint formula (8) represents the overall power balance in each time period t, requiring the power P from the main grid to be t G , Photovoltaic power delivered to the load Battery discharge power Diesel generator standby power P t D Subtract the loss P t NS The sum of must equal the total load demand P at any time t L ;

[0035] Constraint formula (9) specifies the operation of the PV system at each node i and each time period t and its interaction with the battery, ensuring that the PV power delivered to the load is Photovoltaic power delivered to the main grid Power delivered to battery and the abandoned optical power P t PVcurt The sum is equal to the theoretical maximum power generation of the photovoltaic system at that node and time And it is adjusted according to whether a photovoltaic system is installed, expressed as:

[0036]

[0037] in It can be calculated by formula (1);

[0038] Energy trading and availability constraints for backup diesel generators:

[0039]

[0040]

[0041]

[0042] Constraint formula (10) for any time t the power P supplied by the main grid to the load t G and the power supplied by the main grid to the battery energy storage system A limit is set, in other words, the total power from the main grid cannot exceed the maximum grid available power at that moment and grid availability Constraint formula (11) restricts all nodes i in the network to be connected by all photovoltaic systems at time t. The total power generated ensures that the total PV output does not exceed the maximum permitted PV capacity and adjust according to the availability of the power grid; represents the availability of the backup diesel generator in constraint formula (12), where Indicates the maximum power of the standby diesel generator;

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049] Among them, constraint formulas (13)-(18) constrain the operation of photovoltaic cells and grid-connected batteries in the battery storage system in the grid, ensuring that the charging and discharging operations comply with the physical limitations of the batteries; for each battery j connected to the photovoltaic system at the node, in each time period t, these constraints ensure that the battery charging and discharging are properly controlled according to the battery status and capacity; constraint formula (13) represents the total input / output power of all photovoltaic connected batteries at the node The battery's available capacity should not be exceeded Constraint formula (14) indicates that the total power should not exceed the maximum charging rate; is a binary variable, indicating the charging state from photovoltaics; constraint formula (15) ensures that the total power is not less than the maximum reverse discharge rate; constraint formula (16) ensures that the total exchange power of the battery connected to the grid is Subject to its available capacity Constraints; Constraint formula (17) indicates that the power entering the grid battery is limited by the maximum charging rate of the battery, which is represented by a binary variable indicating the charging state Control; Constraint formula (18) ensures that discharge is controlled in a similar manner, allowing discharge when the battery is not scheduled to be charged. In formulas (14)(15)(17)(18), M is usually a large number to ensure that when the binary variable is allowed to charge or discharge, the inequality effectively becomes an equation that reflects the actual restrictions;

[0050]

[0051]

[0052]

[0053]

[0054] Constraint formulas (19)-(22) are the discharge power constraints of the battery. Constraint formula (22) stipulates that in any given time period t, battery j can only be in one of the three states: photovoltaic charging to the battery, grid charging to the battery, and discharging. Represents the self-discharge rate; η ch and η dch Respectively represent the charge / discharge efficiency; is the minimum energy of the battery, Indicates the current capacity of the battery; Indicates the rated energy capacity of the battery cell; SoC init represents the initial coefficient of SoC;

[0055]

[0056]

[0057]

[0058] Constraint formulas (23)-(25) define the state of charge (SoC) dynamics and constraints of the battery in the energy management system. Constraint formula (23) represents the change of SoC over time; constraint formula (24) limits the minimum and maximum levels of SoC; constraint formula (25) defines the initial SoC level;

[0059]

[0060]

[0061]

[0062] Constraints (26)-(28) extend the battery model to account for capacity degradation over time and enforce limits on the total degradation during the battery life. Constraint (26) restates the initial battery capacity setting. Constraint (27) describes the capacity degradation over time. The capacity at each time step t is updated by subtracting the degradation effect caused by battery discharge during that period. The degradation rate is expressed as represents, is a constant; constraint formula (28) ensures that the total battery capacity reduction from the beginning of the analysis period t0 to the end tf does not exceed 20% of its initial capacity divided by the life of the battery system LY, plus a small tolerance

[0063] The proposed method incorporates an energy storage system throughput aging model, which aims to accurately estimate the renewal cost of the energy storage system. The model does this by calculating the additional energy required to compensate for the operational degradation that occurs over time. In addition, the method integrates a hybrid energy storage system that uses supercapacitors to extend the battery life. A photovoltaic power generation performance model is introduced into the classification method to evaluate the technical and economic feasibility of various power generation technologies and select the optimal option. Grid intermittency is considered by predicting the availability curve during microgrid operation, and the dynamic critical load interruption cost is evaluated using the adjusted load curve to evaluate the dynamic criticality of the load. Finally, the proposed microgrid capacity classification method is applied to two case studies to further verify its effectiveness.

[0064] The photovoltaic hybrid energy storage microgrid optimization configuration method proposed in the present invention can more accurately evaluate the economic efficiency of the energy storage system throughout its life cycle by incorporating the degradation cost of the energy storage system into the optimization model, thus avoiding the problem of excessively high long-term operating costs caused by the traditional method of ignoring the battery aging effect. At the same time, the present application reduces the charging and discharging pressure of the battery, slows down its degradation rate, and improves the overall economy and power supply reliability of the system by realizing the coordinated optimization of multiple energy storage technologies, especially by using supercapacitors to undertake high-power, short-term energy storage tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a box plot of climate condition data used in the embodiment of the present invention. DETAILED DESCRIPTION

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, without paying creative labor, other drawings obtained based on these drawings still belong to the scope of the present invention.

[0067] The embodiment of the present invention provides a method for configuring the capacity of a photovoltaic microgrid taking into account the battery degradation cost, comprising the following steps:

[0068] 1. Establish a photovoltaic output derating model and a hybrid energy storage system aging dynamic model

[0069] The efficiency of photovoltaic cells is significantly affected by the ambient temperature, and their output power generally decreases with increasing temperature. A simplified formula that approximates this effect is:

[0070]

[0071] Where P PV (I T,T) represents the photovoltaic output, corresponding to the irradiance level I T and ambient temperature T. is the rated power of a single photovoltaic panel under standard conditions; γ PT Represents the power temperature coefficient of the photovoltaic panel. STC and T STC They are the irradiance and ambient temperature under standard test conditions, which are set to 1000W / m 2 and 25℃.

[0072] The ampere-hour flux model is an ideal tool for integrating battery aging effects into energy storage system capacity planning. In our research framework, a battery is considered to have reached the end of its service life when its initial energy capacity drops to 80% of its initial value. Based on this criterion, we can calculate the total energy availability (E av ), and then evaluate the battery degradation rate per unit discharge power. The calculation formula is as follows:

[0073]

[0074] This study focuses specifically on hybrid energy storage systems combining supercapacitors and batteries, and their application in microgrid capacity planning. According to the ampere-hour flux model, the addition of OpZV supercapacitors, which account for only 0.1% of the total energy capacity of the battery pack, can significantly increase the battery life by about 7.7%. This aging estimation model is highly general and flexible, and its parameters are obtained through technical charge and discharge tests, so it is applicable to all types of batteries. Br Indicates the rated energy capacity of the battery cell, NC B Indicates the maximum possible number of charge and discharge cycles, E av =20% E Br .

[0075] 2. Constructing the overall objective function

[0076] Taking the minimization of the cost of photovoltaic and storage microgrid capacity configuration as the goal, the overall objective function of the photovoltaic and storage microgrid capacity configuration model is constructed.

[0077] The main objective of this paper is to propose a resource allocation method that aims to determine the most cost-effective and technically feasible combination of photovoltaic (PV) panels, battery storage units, and supercapacitor (SC) units to configure the capacity of a microgrid within a set investment budget. The method achieves this goal by comparing various PV and energy storage system (ESS) units based on technical and economic factors. The objective function takes into account the initial investment cost and the long-term operating costs, ensuring a holistic economic analysis. Key factors such as load demand variations, meteorological conditions, and energy supply availability are incorporated to ensure a realistic assessment of the microgrid performance and reliability, ultimately aiming to optimize these aspects as well as cost-effectiveness. The end result is a robust and efficient energy management solution that guarantees that the microgrid can reliably and economically meet the energy needs of consumers. The objective function of the proposed MILP model is the cost minimization function that optimizes the size of the microgrid, incorporating various cost components related to photovoltaic (PV) installation, battery installation, grid interaction, backup power, and unsupplied energy. The objective function is expressed as:

[0078]

[0079] In formula (3), Z is the total cost to be minimized. The first term in the first row summarizes the set Ω PV The cost associated with installing a PV system at all nodes i in . Here, may represent the upfront capital cost of the ith PV system, May include any installation specific costs. is a binary variable indicating whether the i-th PV system is installed (1 or 0). The second term in the first row summarizes the set Ω B The cost of installing batteries for all members j in is the cost of the jth battery, is a binary variable, similar to But for batteries. It is the discount of future costs in the entire life cycle LY of the project. The discount rate is Where r is the interest rate per period, y is the energy storage operating life, Represents the replacement or degradation cost of a battery during its life cycle, calculated by dividing the battery cost by Divide by its average lifetime energy output Then multiply by a factor representing attenuation or efficiency loss Ω B represents the replacement or degradation cost of a battery over its life cycle; represents the cost of purchasing electricity from the power grid, The electricity purchase price, including the general power grid purchase price P t Gand grid-purchased electricity specifically for battery charging Calculate backup power costs, is the backup power cost factor, P t D is the backup power supply power; represents the energy penalty cost for unmet demand, is the penalty coefficient, P t ENS is the unmet demand power; It is the income from selling photovoltaic power to the power grid. is the cost factor of the sale, It is selling power.

[0080] 3. Constructing constraints

[0081] Considering the photovoltaic output derating model and the hybrid energy storage system aging dynamic model, the constraints of the photovoltaic storage microgrid capacity configuration model are constructed.

[0082] Budget constraints:

[0083] It states that the total cost of installing photovoltaic (PV) systems on all nodes plus the total cost of installing batteries on all j nodes should not exceed a predefined maximum budget

[0084]

[0085] Installation constraints for PV modules and batteries:

[0086] Constraint (5) determines the installation status of the photovoltaic system at node i Floor Function Points to round down, taking the value as the largest integer not greater than the number, floor function The constraint represents the number of PV systems that can be installed as an integer value. represents the maximum PV installation or capacity that can be considered strategic at node i, V i OCU refers to the occupied volume or space of node i. Therefore, constraint (5) calculates the maximum number of PV systems that can be installed at a location based on space availability, from Inheriting this placement decision, we must also respect the space constraints. Similarly, the battery at position j By binary decision variables Determined in constraint (6). N BattMax Indicates the total maximum volume or capacity of the battery. is the volume or space required for one battery at location j. This equation ensures that the number of batteries installed does not exceed the number that can be physically accommodated at the location. Constraint (7) limits the total available area A for all node PV installations. Av . represents the area required to install the PV system at node i. The sum of all i ensures that the total area allocated does not exceed the available area.

[0087]

[0088]

[0089]

[0090] Total power balance and photovoltaic power generation balance constraints:

[0091] Constraint formula (8) represents the overall power balance in each time period t, which requires that the power P from the main grid t G , Photovoltaic power delivered to the load Battery discharge power Diesel generator standby power P t D Subtract the loss P t NS The sum of must equal the total load demand P at any time t L ; Constraint (9) specifies the operation of the PV system at each node i and each time period t and its interaction with the battery, ensuring that the PV power delivered to the load is Photovoltaic power delivered to the main grid Power delivered to battery and the abandoned optical power P t PVcurt The sum is equal to the theoretical maximum power generation of the photovoltaic system at that node and time And it is adjusted according to whether a photovoltaic system is installed, expressed as:

[0092]

[0093]

[0094] Energy trading and availability constraints for backup diesel generators:

[0095] Constraint (10) limits the load P at any time t t G and battery energy storage systemsBattery energy storage systems In other words, the total power from the mains cannot exceed the maximum grid power available and the grid availability during that time period Constraint (11) restricts all nodes i in the network to be connected to all photovoltaic systems at any time t. The total power generated. It ensures that the total PV output does not exceed the maximum permitted PV capacity adjusted for grid availability. parameter represents the availability of the backup diesel generator in constraint (12).

[0096]

[0097]

[0098]

[0099] Constraints (13)-(18) constrain the operation of the battery storage system (including photovoltaic cells and grid-connected batteries) in the grid, ensuring that the charging and discharging operations comply with the physical limitations of the battery. For each battery j connected to the photovoltaic system at the node, at each time period t, these constraints ensure that the battery charging and discharging are properly controlled according to the battery state and capacity.

[0100] Constraint formula (13) represents the total input / output power of all photovoltaic connected batteries at the node The battery's available capacity should not be exceeded Constraint formula (14) indicates that the total power should not exceed the maximum charging rate is a binary variable, indicating the charging state from photovoltaics; constraint formula (15) ensures that the total power is not less than the maximum reverse discharge rate; constraint formula (16) ensures that the total exchange power of the battery connected to the grid is Subject to its available capacity Constraints; Constraint formula (17) indicates that the power entering the grid battery is limited by the maximum charging rate of the battery, which is represented by a binary variable indicating the charging state Control; Constraint formula (18) ensures that discharge is controlled in a similar manner, allowing discharge when the battery is not scheduled to be charged. In formulas (14)(15)(17)(18), M is usually a large number to ensure that when the binary variable is allowed to charge or discharge, the inequality effectively becomes an equation that reflects the actual restrictions;

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] Constraint formulas (19)-(22) are the discharge power constraints of the battery. Constraint formula (22) stipulates that in any given time period t, battery j can only be in one of the three states: photovoltaic charging to the battery, grid charging to the battery, and discharging. Represents the self-discharge rate; η ch and η dch Respectively represent the charge / discharge efficiency; is the minimum energy of the battery, Indicates the current capacity of the battery; Indicates the rated energy capacity of the battery cell; SoC init represents the initial coefficient of SoC;

[0108]

[0109]

[0110]

[0111]

[0112] Constraints (23) - (25) define the state of charge (SoC) dynamics and constraints of the battery in the energy management system, in particular to optimize the use of the battery in interaction with renewable energy sources and the grid. The evolution of SoC over time is shown in (23). Constraint (24) limits the minimum and maximum levels of SoC. Constraint (25) defines the initial SoC level.

[0113]

[0114]

[0115]

[0116] Constraints (26)-(28) extend the battery model to account for capacity degradation over time and enforce limits on the total degradation over the battery life. Constraint (26) restates the initial battery capacity setting, where is the capacity at the beginning of the analysis period (t0), determined by the battery’s binary presence and its nominal energy capacity. Constraint (27) describes the degradation of the capacity over time. Here, the capacity at each time step t is updated by subtracting the degradation effect caused by the battery discharge during that period. The degradation rate is given by It can be a constant or a function that takes into account factors such as cycle frequency, depth of discharge and temperature. Constraint (28) ensures that the total battery capacity reduction from the beginning t0 to the end tf of the analysis period does not exceed 20% of its initial capacity divided by the life of the battery system LY, plus a small tolerance This model places practical limits on how much the battery capacity can degrade over its useful life, allowing for small deviations. Together, these limits form a comprehensive battery capacity management model that includes the effects of degradation over time, as well as setting limits to ensure that the battery remains useful over its expected lifetime.

[0117]

[0118]

[0119]

[0120] Example

[0121] Parameter settings

[0122] In the examples, three different photovoltaic (PV) module technologies and two mainstream battery technologies were included in the simulation. In addition, the impact of the integration of supercapacitors (SCs) on each technology and case study was evaluated. The relevant parameters used in the simulation are detailed in Tables 1 and 2. The climate condition data used in the examples are as follows: Figure 1 As shown, Figure 1 (a) shows the wind speed data box plot, Figure 1 (b) shows the box plot of solar irradiance data and Figure 1 (c) in the figure shows a box plot of temperature data. In addition, Set to 1200kW, Set to 72kW. Interest rate set to 6% and life cycle to 25 years. Budget C budget It is 25,000 US dollars.

[0123] Table 1 Technical parameters of candidate photovoltaic modules

[0124]

[0125]

[0126] *Poly, Mono1 and Mono2 refer to three types of PV module technologies, namely polycrystalline silicon, monocrystalline silicon 1 and monocrystalline silicon 2.

[0127] Table 2. Candidate energy storage parameters

[0128]

[0129] In the embodiment, It is set to fluctuate with load changes during the day. During the peak load period (6:00 to 18:00), the unsupplied energy cost coefficient and marginal cost However, during other off-peak hours, the unsupplied energy cost is set to one-tenth of the marginal cost because the economic losses caused by energy service interruption are significantly reduced.

[0130] We compare two scenarios: Case A uses the proposed capacity configuration model, while Case B assumes that the battery energy storage system has no degradation. This means that the impact of integrating supercapacitors into the hybrid energy storage system to extend the battery life is not considered, the linear degradation in the battery degradation model is not considered, and the estimation of energy storage replacement units based on equipment degradation is omitted. Therefore, the objective function (5) omits In this case, constraints (24) and (25) are omitted, and constraint (23) is replaced by Therefore battery degradation and replacement units in capacity configuration are no longer modeled.

[0131] The capacity configuration results and economic indicators of the two scenarios are given in Tables 3 and 4, respectively. In Case A, the system includes Mono2-type PV panels and a hybrid energy storage system with 5 VRLA+SC units. Due to the low cost of ENS, battery replacement is not considered, and energy export to the main grid is allowed.

[0132] Table 3. Capacity allocation results

[0133]

[0134] Table 4. Economic indicators

[0135] Case Case A Case B Photovoltaic investment cost 22912.00 22400.00 Energy storage system investment cost 4324.95 6130.00 Energy storage system maintenance costs 0.00 0.00 Power purchase cost 35144.75 25693.01 Backup energy costs 0.00 0.00 Unsupplied energy costs 30676.91 15811.63 Electricity sales cost -42934.61 -31219.84 Objective Function 50123.99 38814.80

[0136] Comparing the results in Tables 3 and 4, in Case B, battery aging and replacement are not considered, the number of ESS units increases, the technology composition changes, and supercapacitor coupling is not considered in the ESS BESS. However, the addition of the ESS BESS option in Case B does not affect the battery life, and the results show that supercapacitors are excluded from the capacity configuration results. Ignoring the ESS BESS degradation underestimates the advantages of supercapacitor coupling, resulting in higher operating costs when implementing the microgrid. Therefore, excluding the ESS BESS degradation model in Case B leads to optimistic estimates of the expected unsupplied energy and the interaction of the microgrid with the main grid, underestimating the advantages of supercapacitor coupling.

[0137] Comparing the results in Tables 3 and 4, Case B shows that ignoring battery aging and replacement has important implications for the design and operation of the BESS in the microgrid. In Case B, these factors are not considered, the number of storage units increases, the technology mix changes, and especially the integration of supercapacitors with the BESS. This omission underestimates the benefits of integrating supercapacitors into the BESS, leading to higher operating costs in real-world implementations. In fact, supercapacitors may significantly reduce the frequency of battery replacement and maintenance requirements, thereby reducing overall operating expenses. In addition, ignoring BESS degradation leads to overly optimistic expectations for unsupplied energy in Case B, as well as overly optimistic interactions between the microgrid and the main grid. This optimistic perspective fails to consider potential challenges caused by battery aging, such as increased unreliability and reduced available energy during peak demand. As a result, the role of supercapacitor coupling in improving microgrid performance, reliability, and cost-effectiveness is underestimated.

[0138] The advantages of Case A over Case B are mainly reflected in the economic aspect. First, the investment cost of the energy storage system in Case A is lower (4324.95 vs. 6130.00), which is more economically advantageous in the initial investment of the energy storage system. In addition, the objective function value of Case A is higher (50123.99 vs. 38814.80), showing that it is better in optimizing the target. At the same time, the unsupplied energy cost of Case A is lower (30766.91 vs. 15811.63), which may indicate that it has achieved a better balance between system cost and power supply reliability. In addition, the electricity purchase cost of Case A is lower (35144.75 vs. 25693.01), further highlighting its cost advantage in power supply. Overall, Case A shows better cost performance in terms of initial investment and operation and maintenance costs.

Claims

1. A method for configuring the capacity of a photovoltaic and energy storage microgrid considering battery degradation costs, characterized in that: The following steps are involved: Step 1: Establish a PV output derating model and a hybrid energy storage system aging dynamic model; Step 2: Taking the cost minimization of the photovoltaic-storage microgrid capacity configuration as the goal, the total objective function of the photovoltaic-storage microgrid capacity configuration model is constructed; Step 3: Considering the PV output derating model and the hybrid energy storage system aging dynamic model, construct the constraints of the PV-storage microgrid capacity configuration model.

2. A method for configuring the capacity of a photovoltaic microgrid taking into account battery degradation costs according to claim 1, characterized in that: The photovoltaic output derating model is: Where P PV (I T ,T) represents the photovoltaic output, corresponding to the irradiance level I T and ambient temperature T; is the rated power of a single photovoltaic panel under standard conditions; γ PT Represents the power temperature coefficient of the photovoltaic panel; I STC and T STC are the irradiance and ambient temperature under standard test conditions respectively.

3. A method for configuring the capacity of a photovoltaic microgrid taking into account battery degradation costs according to claim 1, characterized in that: The aging dynamic model of the hybrid energy storage system is: A battery is considered to have reached the end of its useful life when its initial energy capacity has dropped to 80% of its initial value: In formula (2), E Br Indicates the rated energy capacity of the battery cell, NC B Indicates the maximum possible number of charge and discharge cycles, E av =20% E Br .

4. A method for configuring the capacity of a photovoltaic microgrid taking into account battery degradation costs according to claim 1, characterized in that: The objective function of the photovoltaic storage microgrid capacity configuration model is expressed as: Where Z is the total cost to be minimized, The photovoltaic installation node set Ω is summarized PV The costs associated with installing PV systems at all nodes i; represents the initial investment cost of the ith PV system, is the cost of photovoltaic installation, is a binary variable indicating whether the ith node has a PV system installed; Summarizes the set Ω B The cost of installing batteries at all nodes j in is the cost of battery installation at the jth node, is a binary variable indicating whether the jth node is equipped with an energy storage system; It represents the discount of future costs in the entire life cycle LY of the project, and the discount rate is Where r is the interest rate per period, y is the energy storage operating life, Represents the replacement or degradation cost of a battery during its life cycle, calculated by dividing the battery cost by Divide by its average lifetime energy output Then multiply by a factor representing attenuation or efficiency loss Ω B represents the replacement or degradation cost of a battery over its life cycle; represents the cost of purchasing electricity from the power grid, The electricity purchase price, including the general power grid purchase price P t G and grid-purchased electricity specifically for battery charging Calculate backup power costs, is the backup power cost factor, P t D is the backup power supply power; represents the energy penalty cost for unmet demand, is the penalty coefficient, P t ENS is the unmet demand power; It is the income from selling photovoltaic power to the power grid. is the cost factor of the sale, It is selling power.

5. The method for configuring the capacity of a photovoltaic microgrid taking into account battery degradation costs according to claim 1, characterized in that: The constraints are: Budget constraints: The total cost of installing PV systems on all nodes plus the total cost of installing batteries on all nodes should not exceed the predefined maximum budget C budget , expressed as: Installation constraints for PV modules and batteries: Constraint formula (5) determines the installation status of the photovoltaic system at node i Represents the floor function, which means rounding down to the maximum integer not greater than the value. The constraint on the number of PV systems that can be installed is an integer value, represents the maximum photovoltaic installation or capacity at node i, V i OCU refers to the PV occupied volume or space of node i; constraint formula (5) calculates the maximum number of PV systems that can be installed at a location based on space availability, from Inheriting this installation decision, while also complying with the space constraints; the battery at position j By binary decision variables In constraint formula (6), N BattMax Indicates the total maximum volume or capacity of the battery. is the volume or space required for a battery at node j. This equation ensures that the number of installed batteries does not exceed the number that can be physically accommodated at the location. Constraint formula (7) limits the total available area A for photovoltaic installations at all nodes. av , represents the area required to install the PV system at node i; Total power balance and photovoltaic power generation balance constraints: Total power balancing requires that the sum of all generation must equal the total load demand P at any given time. t L : Constraint formula (8) represents the overall power balance in each time period t, requiring the power P from the main grid to be t G , Photovoltaic power delivered to the load Battery discharge power Diesel generator standby power P t D Subtract the loss P t NS The sum of must equal the total load demand P at any time t L ; Constraint formula (9) specifies the operation of the PV system at each node i and each time period t and its interaction with the battery, ensuring that the PV power delivered to the load is Photovoltaic power delivered to the main grid Power delivered to battery and the abandoned optical power P t PVcurt The sum is equal to the theoretical maximum power generation of the photovoltaic system at that node and time And it is adjusted according to whether a photovoltaic system is installed, expressed as: in It can be calculated by formula (1); Energy trading and availability constraints for backup diesel generators: Constraint formula (10) for any time t the power P supplied by the main grid to the load t G and the power supplied by the main grid to the battery energy storage system A limit is set, in other words, the total power from the main grid cannot exceed the maximum grid available power at that moment and grid availability Constraint formula (11) restricts all nodes i in the network to be connected by all photovoltaic systems at time t. The total power generated ensures that the total PV output does not exceed the maximum permitted PV capacity and adjust according to the availability of the power grid; represents the availability of the backup diesel generator in constraint formula (12), where Indicates the maximum power of the standby diesel generator; Among them, constraint formulas (13)-(18) constrain the operation of photovoltaic cells and grid-connected batteries in the battery storage system in the grid, ensuring that the charging and discharging operations comply with the physical limitations of the batteries; for each battery j connected to the photovoltaic system at the node, in each time period t, these constraints ensure that the battery charging and discharging are properly controlled according to the battery status and capacity; constraint formula (13) represents the total input / output power of all photovoltaic connected batteries at the node The battery's available capacity should not be exceeded Constraint formula (14) indicates that the total power should not exceed the maximum charging rate; is a binary variable, indicating the charging state from photovoltaics; constraint formula (15) ensures that the total power is not less than the maximum reverse discharge rate; constraint formula (16) ensures that the total exchange power of the battery connected to the grid is Subject to its available capacity Constraints; Constraint formula (17) indicates that the power entering the grid battery is limited by the maximum charging rate of the battery, which is represented by a binary variable indicating the charging state Control; Constraint formula (18) ensures that discharge is controlled in a similar manner, allowing discharge when the battery is not scheduled to be charged. In formulas (14)(15)(17)(18), M is usually a large number to ensure that when the binary variable is allowed to charge or discharge, the inequality effectively becomes an equation that reflects the actual restrictions; Constraint formulas (19)-(22) are the discharge power constraints of the battery. Constraint formula (22) stipulates that in any given time period t, battery j can only be in one of the three states: photovoltaic charging to the battery, grid charging to the battery, and discharging. Represents the self-discharge rate; η ch and η dch Respectively represent the charge / discharge efficiency; is the minimum energy of the battery, Indicates the current capacity of the battery; Indicates the rated energy capacity of a battery cell; SoC init represents the initial coefficient of SoC; Constraint formulas (23)-(25) define the state of charge (SoC) dynamics and constraints of the battery in the energy management system. Constraint formula (23) represents the change of SoC over time; constraint formula (24) limits the minimum and maximum levels of SoC; constraint formula (25) defines the initial SoC level; Constraints (26)-(28) extend the battery model to account for capacity degradation over time and enforce limits on the total degradation during the battery life. Constraint (26) restates the initial battery capacity setting. Constraint (27) describes the capacity degradation over time. The capacity at each time step t is updated by subtracting the degradation effect caused by battery discharge during that period. The degradation rate is expressed as represents, is a constant; constraint formula (28) ensures that the total battery capacity reduction from the beginning of the analysis period t0 to the end tf does not exceed 20% of its initial capacity divided by the life of the battery system LY, plus a small tolerance

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