A method for optimizing the capacity configuration of a composite energy storage system

Abstract

This invention relates to the field of composite energy storage technology, and more particularly to a method for optimizing the capacity configuration of composite energy storage systems. The technical solution includes the following steps: modal decomposition and reconstruction of the target compensation power data of the composite energy storage system to obtain multiple sets of reference power command combinations corresponding to the superconducting energy storage subsystem and the electrochemical energy storage subsystem, respectively; establishment of a variable lifetime annual cost model for the entire life cycle of electrochemical energy storage; this invention significantly improves the accuracy and engineering reliability of the capacity configuration results of the superconducting-electrochemical composite energy storage system by constructing a refined model that integrates the cycle life decay characteristics of electrochemical energy storage with the operational safety constraints of the superconducting magnet; and establishes a collaborative optimization framework aimed at minimizing the overall comprehensive cost throughout the system's life cycle and minimizing power tracking error, achieving an overall optimal trade-off between the economic efficiency and dynamic compensation performance of the energy storage system.

Description

Technical Field

[0001] This invention relates to the field of composite energy storage technology, and in particular to a method for optimizing the capacity configuration of a composite energy storage system. Background Technology

[0002] Energy storage technology, as a key support for building new power systems, can effectively smooth power fluctuations and improve system inertia and regulation capabilities, which is crucial for ensuring a "clean, low-carbon, safe, and efficient" energy system. However, single forms of energy storage, limited by their own physical characteristics, often cannot simultaneously meet the diverse needs of systems for high power density and high energy density. For example, while electrochemical energy storage (such as lithium-ion batteries) has high energy density, its power response speed is relatively slow, and frequent deep charge-discharge cycles can severely accelerate its cycle life decay. Superconducting magnetic energy storage (SMES) has millisecond-level power response and extremely high power density, but its energy density is relatively low. Furthermore, during frequent high-power charge-discharge cycles, the AC losses generated by the magnet can lead to temperature rise, potentially jeopardizing the stable maintenance of the superconducting state and posing operational safety hazards.

[0003] To leverage the respective advantages of both, composite energy storage systems combining superconducting and electrochemical energy storage are considered an effective way to solve the aforementioned problems. Currently, most studies on capacity configuration for such composite systems simplify the two energy storage elements into ideal, lossless power source and energy pool models for optimization. These methods generally suffer from two main drawbacks: First, they fail to fully consider the nonlinear impact of discharge depth on cycle life during actual variable operating conditions, leading to significant discrepancies between cost models based on fixed lifespan estimates and actual conditions, resulting in distorted economic assessments of the configuration results. Second, they neglect the temperature rise caused by internal AC losses in superconducting magnets when compensating for high-frequency fluctuating power, and the constraints on the magnet's safe operating boundaries (such as critical current). This makes it possible that the configured power and capacity may be physically unsafe to achieve, or require excessive margins, making it extremely uneconomical.

[0004] Existing technologies struggle to achieve precise and synergistic optimization of the overall economic efficiency and dynamic compensation performance of composite energy storage systems while ensuring their safe and reliable operation. This has become one of the key bottlenecks hindering the transition of superconducting-electrochemical composite energy storage technology from theoretical research to practical engineering applications. Therefore, this application proposes a method for optimizing the capacity configuration of composite energy storage systems. Summary of the Invention

[0005] The purpose of this invention is to address the problem in the prior art that it is difficult to achieve synergistic and precise optimization of the economic efficiency and dynamic compensation performance of a composite energy storage system throughout its entire life cycle while ensuring its safe and reliable operation. The invention proposes a method for optimizing the capacity configuration of a composite energy storage system.

[0006] The technical solution of this invention: a method for optimizing the capacity configuration of a composite energy storage system, comprising the following steps:

[0007] S1. Perform modal decomposition and reconstruction on the target compensation power data of the composite energy storage system to obtain multiple sets of reference power command combinations corresponding to the superconducting energy storage subsystem and the electrochemical energy storage subsystem, respectively.

[0008] S2. Establish an annual cost model for the entire life cycle of electrochemical energy storage with varying lifespan, taking into account the impact of depth of discharge on battery cycle life.

[0009] S3. Establish an annual cost model for the entire life cycle of a superconducting magnet. The model is based on optimizing the magnet structure with target compensation power and capacity, and evaluates its operational safety and losses through multi-physics field coupling simulation. Iterative optimization yields magnet parameters and costs that meet safety constraints.

[0010] S4. Construct a multi-objective optimization model with the goals of minimizing the average annual comprehensive cost over the entire life cycle and minimizing the power tracking error. Integrate the cost models and system operation constraints from steps S2 and S3, obtain the Pareto optimal solution set by solving the model, and determine the final capacity and power configuration scheme accordingly.

[0011] Optionally, step S1 specifically includes:

[0012] S1.1 Based on mutual information theory, find the sub-waveform with the highest matching degree with the waveform features of the left or right edge of the signal within the signal sequence composed of the target compensation power data;

[0013] S1.2. Extend the original signal at the boundary using the sub-waveform with the highest matching degree to suppress the endpoint effect;

[0014] S1.3 Perform variational mode decomposition on the extended signal to obtain multiple eigenmode function components arranged according to the center frequency;

[0015] S1.4 Enumerate different high and low frequency power boundary points, and reconstruct the components into high frequency power commands and low frequency power commands respectively to form multiple sets of reference power command combinations, wherein the high frequency power command serves as the reference command for superconducting energy storage and the low frequency power command serves as the reference command for electrochemical energy storage.

[0016] Optionally, in step S1.1, the mutual information value is used as a measure of waveform matching degree, and its calculation adopts the following formula:

[0017] Where MI(X,Y) is the mutual information value between the two signals. and Let X and Y represent the two waveform sequences to be compared, respectively. P(x) and P(y) represent the marginal distributions of sequences X and Y, respectively. P(x,y) is the joint distribution of X and Y, where x is the specific value of each sampling time in waveform sequence X, and y is the specific value of each sampling time in waveform sequence Y.

[0018] Optionally, the construction of the electrochemical energy storage full life cycle variable lifetime average annual cost model in step S2 includes:

[0019] S2.1 Establish a mapping model between battery discharge depth and cycle life, which is represented by the following fitting function:

[0020] in, For the cycle life of energy storage batteries, This refers to the depth of discharge of the energy storage battery.

[0021] S2.2. Based on the charge-discharge curves of electrochemical energy storage in actual operation, the actual discharge amount at different depths of discharge is calculated. The equivalent discharge quantity converted to the standard depth of discharge is calculated using the following formula. :

[0022] in, Indicates the rated depth of discharge The cycle life is below, Indicates the actual depth of discharge The cycle life is below;

[0023] S2.3. Based on the equivalent discharge quantity and rated installed capacity, calculate the actual cycle life of the electrochemical energy storage. ;

[0024] S2.4, Based on the actual cycle life years Rated capacity Rated power The unit capacity cost coefficient, unit power cost coefficient, and operation and maintenance cost coefficient are used to construct the annual average cost model for the entire life cycle using the equal annual value method.

[0025] Optionally, the optimization of the magnet structure based on the target compensation power and capacity mentioned in step S3 specifically means: taking the minimum total length of the superconducting tape as the target, and the inner radius of the magnet as the target. Number of double-sided coils Number of coil turns To optimize variables, while meeting energy storage capacity requirements and operating current... Below the critical current The optimization solution is performed under certain constraints.

[0026] Optionally, the evaluation of operational safety and losses through multiphysics coupling simulation in step S3 specifically includes:

[0027] S3.1 Based on the optimized magnet structure parameters, a multi-physics coupling model of the superconducting magnet, consisting of "electromagnetic-thermal" fields, is established in the finite element simulation software.

[0028] S3.2, EJ characteristic model based on superconducting magnets Calculate the AC loss of the magnet under the reference power command, where E is the local electric field strength (V / m) inside the superconductor. It is the local current density (A / m) inside the superconductor 2 ), E c J represents the characteristic electric field of a superconducting magnet. c Here, B represents the critical current density, and n is an empirical exponent, which is taken as n=31;

[0029] S3.3. Using the AC loss as a heat source, perform heat conduction simulation to obtain the temperature rise distribution of the magnet;

[0030] S3.4 Determine whether the temperature rise causes the magnet's operating temperature to exceed the safe range or the operating current to exceed the critical current. If the temperature rise constraint and critical current constraint of the magnet are not met, return to adjust the magnet's structural parameters or compensation capacity, and repeat the optimization and simulation iteration.

[0031] Optionally, in step S3.1, the optimization of the magnet structure parameters and the multiphysics coupling simulation are achieved through a joint simulation process using MATLAB and COMSOL software.

[0032] Optionally, the two objective functions of the multi-objective optimization model are:

[0033] Objective function 1: Minimize the average annual comprehensive cost of the composite energy storage system over its entire life cycle. ;

[0034] Objective function two: Minimize the sum of squared power tracking errors. ;

[0035] in, This refers to the average annual comprehensive cost of a composite energy storage system over its entire lifecycle. C refers to the sum of squared power tracking errors. HESS This represents the average annual cost over the entire lifecycle of a composite energy storage system. , These are the average annual costs over the entire lifecycle of electrochemical energy storage and superconducting energy storage, respectively. For the cost of power conversion system, For the actual output power of the electrochemical energy storage subsystem, This represents the actual output power of the superconducting energy storage subsystem. For the target reference power of the electrochemical energy storage subsystem, This is the target reference power for the superconducting energy storage subsystem.

[0036] Optionally, in step S4, the constraints of the multi-objective optimization model include: power balance constraints of the composite energy storage system, output limits of each energy storage subsystem, capacity constraints, and state-of-charge (SOC) operating range constraints.

[0037] Optionally, in step S4, a non-dominated sorting genetic algorithm with an elitist strategy is used to solve the multi-objective optimization model to obtain the Pareto optimal solution set.

[0038] Compared with the prior art, this application includes at least one of the following beneficial technical effects:

[0039] By establishing an electrochemical energy storage variable lifetime cost model that takes into account the influence of discharge depth, and a superconducting magnet safe operation constraint model that considers AC loss and temperature rise, the configuration deviation caused by ignoring key physical processes is significantly reduced, making the optimization results more in line with actual operating conditions.

[0040] This invention constructs a multi-objective optimization framework with the goals of minimizing overall cost and power tracking error, and uses an efficient algorithm to solve it. This directly yields a Pareto optimal configuration scheme that balances investment cost and operating performance, thus avoiding the one-sidedness of single-objective optimization.

[0041] The method proposed in this invention outputs specific power / capacity configuration values, magnet structure parameters, and corresponding cost and performance indicators, forming a complete closed loop from system requirements to equipment-level parameters. It can be directly used to guide the engineering design and equipment development of composite energy storage systems.

[0042] In summary, this invention significantly improves the accuracy and engineering reliability of capacity configuration results for superconducting-electrochemical composite energy storage systems by constructing a refined model that integrates the cycle life decay characteristics of electrochemical energy storage with the operational safety constraints of superconducting magnets. Furthermore, by establishing a collaborative optimization framework aimed at minimizing the overall cost throughout the system's lifecycle and minimizing power tracking error, this invention achieves an optimal overall trade-off between the economic efficiency and dynamic compensation performance of the energy storage system. Attached Figure Description

[0043] Figure 1 The waveform diagram of the load power compensated by the composite energy storage;

[0044] Figure 2 Graph of IMFs signal for target compensation power of composite energy storage;

[0045] Figure 3Reference power diagrams for superconducting and electrochemical energy storage compensation under different reconstruction schemes;

[0046] Figure 4 Optimization flowchart for superconducting magnets;

[0047] Figure 5 Optimize the logic structure diagram for co-simulation;

[0048] Figure 6 Flowchart of the method for optimizing the capacity configuration of superconducting-electrochemical composite energy storage;

[0049] Figure 7 Configure Pareto solution set graphs for capacity optimization under different power allocation schemes. Detailed Implementation

[0050] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0051] Example: The present invention proposes a method for optimizing the capacity configuration of a composite energy storage system. The method is described in detail below.

[0052] Step 1: Decomposition of the original power signal and reconstruction of the high and low frequency power of the decomposed signal based on feature matching extended variational mode decomposition (VMD).

[0053] 1.1 Target Compensation Power Data Feature Matching Boundary Extension. Based on the energy storage compensation power data required under typical operating conditions in the application scenario, and based on mutual information theory, the target compensation power data is directly obtainable in this field. Essentially, it represents the load power or the power lacking in grid-side power supply, which can be directly obtained through detection and calculation. First, the sub-waveform with the highest feature match to the signal edge waveform is found within the compensation power signal sequence. Then, the original signal boundary is extended based on this sub-waveform to address the endpoint effect problem in the VMD decomposition process, avoiding distortion and jitter in the signal frequency and amplitude of the intrinsic mode functions (IMFs) components obtained from the decomposition at both ends of the signal, thereby improving the accuracy of signal decomposition.

[0054] 1.2 Signal Multimodal Decomposition and High-Low Frequency Reconstruction Based on VMD Algorithm. The obtained extended signal is decomposed using the VMD algorithm to obtain a set of IMFs components arranged sequentially from high to low, containing different center frequencies. Based on the N IMFs obtained from the decomposition, the possible values ​​of the high-low frequency power command boundary point va of the composite energy storage are enumerated (1≤va≤N). According to different power boundary points va, the corresponding combinations of power command curves for different electrochemical energy storage and superconducting energy storage are obtained.

[0055] Step 2: Annual cost model of energy storage battery over its entire life cycle, considering depth of discharge.

[0056] 2.1 Construction of a Quantitative Model for the Cycle Life of Energy Storage Batteries. The cycle life of energy storage batteries is significantly affected by the depth of charge and discharge during actual operation. Generally, the cycle life decreases significantly with increasing depth of discharge. To accurately quantify the impact of electrochemical energy storage cycle life degradation on capacity configuration, the influence of depth of charge and discharge on the cycle life of energy storage components is considered, and a variable life model for energy storage batteries is established. First, based on the cycle life of energy storage batteries at different depths of discharge obtained from laboratory tests, an analytical expression relating the depth of discharge to the cycle life is obtained through data fitting.

[0057] Secondly, since batteries do not always operate at full charge and discharge levels in actual use, their state of charge (SOC) changes and charging / discharging processes differ under different operating conditions, resulting in varying depths of charge and discharge, and consequently, different degrees of battery life degradation. To comprehensively analyze the battery life degradation under different operating processes, the discharge capacity at different depths of discharge is uniformly converted to the equivalent value under the standard depth of discharge, thereby determining the cycle life of the battery in actual use.

[0058] Finally, based on the electrochemical energy storage compensation power charge-discharge curves under typical operating conditions, and combined with the variable cycle life model under different discharge depths mentioned above, an analytical model between the battery's equivalent cycle life and capacity configuration in this application scenario is obtained.

[0059] 2.2 Construction of the Annual Cost Model for Electrochemical Energy Storage under Variable Cycle Life. Based on the full life cycle cost model, considering the initial investment cost, operation and maintenance cost, replacement cost, and residual value of electrochemical energy storage, and combined with the levelized cost of electricity (LCOE) assessment method, an annual cost model for the full life cycle of electrochemical energy storage components under variable cycle life is established.

[0060] Step 3: Lifecycle cost model of superconducting magnets considering operational safety

[0061] 3.1 Magnet Structure Optimization Design Based on Compensation Capacity Requirements. First, based on the rated capacity and rated power generated during the iterative solution process using the NSGA-II optimization algorithm, and combined with the operating voltage parameters of the superconducting magnet converter, the required rated operating current of the superconducting magnet is determined while satisfying the high-frequency power compensation curve, and the required magnet inductance value is calculated accordingly. Second, with the objective of minimizing the total amount of superconducting tape used, an optimization model is established in MATLAB to solve for the optimal magnet structure parameters. , and .in, The inner radius of the magnet winding. The number of double-sided coils, This represents the number of turns in the coil.

[0062] 3.2 Construction of a Multi-Physical Field Coupling AC Loss and Temperature Rise Model for Superconducting Magnets. Based on the magnet structural parameters and critical constraint functions obtained from the optimized design, a simulation model of the superconducting magnet under these parameters is established using COMSOL finite element simulation software. Based on the EJ characteristic equation of the superconducting magnet, the AC loss and temperature rise of the superconducting coil under compensated high-frequency power response conditions are calculated. If the magnet meets the operational requirements and critical current limit, the magnet strip material usage, energy storage capacity, and power parameters are retained and participate in the next optimization iteration. If the requirements are not met, the range of magnet structural parameters is increased, and the processes in 3.1 and 3.2 are repeated until the stable operation requirements are met, and the optimal capacity configuration scheme and magnet structural parameters are output.

[0063] 3.3 Joint Optimization Model Based on MATLAB and COMSOL. Based on the collaborative operation mechanism of MATLAB and COMSOL, and combining the MATLAB magnet structure optimization model in 3.1 and the COMSOL electromagnetic-thermal analysis model in 3.2, the magnet operating losses are considered, and the magnet structure and energy storage capacity are jointly optimized to meet the operational requirements.

[0064] 3.4 Construction of the Annual Average Cost Model for the Entire Life Cycle of Superconducting Energy Storage. Based on the life cycle cost model, considering the initial investment cost of superconducting magnet tape (related to the total length of the magnet tape), cooling, operation and maintenance costs, and residual value, and combined with the levelized electricity cost assessment method, an annual average cost model for the entire life cycle of superconducting energy storage is established.

[0065] Step 4: Optimization solution based on multi-objective optimization algorithm

[0066] 4.1 Construction of a Multi-Objective Optimization Model for Superconducting-Electrochemical Composite Energy Storage. Considering the investment economy and compensation performance of the composite energy storage system, and taking the constraints of composite energy storage power compensation balance, compensation power capacity, and operating SOC, a two-dimensional optimization model is established. The economic optimization objective is to minimize the average annual comprehensive cost of the composite energy storage system throughout its entire life cycle, and the operational optimization objective is to minimize the sum of squares of the difference between the actual output power and the target power output in each sampling period during the energy storage compensation process.

[0067] 4.2 Solving the Multi-Objective Optimization Model. Based on the multi-objective optimization model in 4.1, and combined with the multi-objective optimization algorithm, the Pareto solution set of the optimal configuration scheme of the composite energy storage system is solved. Based on the Pareto solution set results, the optimal capacity configuration scheme is obtained.

[0068] The following are specific application examples, taking the application of superconducting-electrochemical composite energy storage in the smart microgrid application scenario of coal mines as an example for example to carry out the example analysis.

[0069] 1. High- and low-frequency power decomposition of composite energy storage

[0070] Given typical daily power data for composite energy storage compensation, as follows: Figure 1 As shown.

[0071] By using mutual information (MI) values, a sub-waveform that best matches the waveform characteristics of the signal edge is found within the compensated power signal sequence. This sub-waveform is then used as the basis for extending the original signal boundary to address the endpoint effect problem. The specific extension method is as follows:

[0072] Assuming signal There are N sampled data points, including M maxima and P minima. Let... and This represents the time and signal value corresponding to the i-th maximum point. and Indicates the first The time and signal value corresponding to each minimum point.

[0073] (1) Extract the end sub-waveform. Truncate the left end of the signal. To the second extreme point The waveforms between them are the end sub-waveforms to be matched (i.e., containing one maximum and one minimum point), denoted as... .

[0074] (2) To find a candidate sub-waveform that matches the end sub-waveform E1 within the signal, a matching method based on extreme point alignment is adopted: First, determine the relative position P1 of the first maximum point x(m1) in the end sub-waveform E1 within it (i.e., E1[P1]=x(m1)), and record the length of E1 as L; then, traverse each maximum point x(m1) in the original signal x(n) except x(m1). i (i=2,3,…,N), let its index in the global signal be I. i To maintain waveform alignment, with x(m) i () is the corresponding point, so that it is in the sub-waveform E to be intercepted. i The middle is in the same position as P1, and E is calculated accordingly. i The starting and ending points are used to obtain a sub-waveform E of the same length as E1. i Ultimately, all Ei that meet the conditions form a set of matching sub-waveforms, which are used for subsequent mutual information matching calculations.

[0075] (3) Calculate the local matching waveform and the end sub-waveform. Calculate the end signal accordingly. and the MI value of each segmented local matching waveform As shown in equation (1-1), each MI value is used as a measure of the matching degree between each sub-waveform and the end sub-waveform. The best matching sub-waveform The value is maximized, then the sub-waveform is... Add the given length of data to the original data Left side;

[0076] (1-1)

[0077] (4) Obtain by using the same operation Right-side extension data;

[0078] (5) Perform VMD decomposition on the extended signal. After decomposition, extract the corresponding original signal. The corresponding IMF components.

[0079] Figure 1 The composite energy storage compensation reference power signal in the image is decomposed by characteristic matching extension VMD to obtain six IMF signals arranged from high to low frequency, such as... Figure 2 As shown.

[0080] Based on the IMF signal obtained from the decomposition, va=2, va=3, va=4, and va=5 can be selected as the high- and low-frequency power reconstruction boundary points. A comparative analysis is then conducted with the single electrochemical energy storage compensation scheme (va=0) and the single superconducting energy storage compensation scheme (va=6). The superconducting and electrochemical energy storage reference power waveforms under different reconstruction schemes are shown below. Figure 3 As shown.

[0081] 2. Annual cost model for energy storage batteries with varying lifespan over their entire lifecycle, considering depth of discharge. Typically, battery cycle life decreases significantly with increasing depth of discharge. Based on experimental data provided by the manufacturer, cycle life data for lithium batteries at different depths of discharge at 25°C were obtained using an inverse proportional function fitting method, as detailed in Table 1.

[0082] Table 1. Relationship between depth of discharge and cycle life of lithium batteries

[0083]

[0084] By fitting the data in Table 1, the relationship between the depth of discharge and cycle life is shown in Equation (2-1):

[0085] (2-1)

[0086] In the formula: For the cycle life of energy storage batteries, This refers to the depth of discharge of the energy storage battery.

[0087] Batteries do not operate in a fully charged and discharged state continuously during actual use. Under different operating conditions, their State of Charge (SOC) changes and charging / discharging processes vary, leading to different depths of charge and discharge, and consequently, varying degrees of battery life degradation. To comprehensively analyze battery life degradation during different processes, the discharge capacity at different depths of discharge is uniformly converted to an equivalent value under a standard depth of discharge, thereby determining the battery's cycle life in actual use. The discharge capacity corresponding to each discharge process is then calculated. Equivalent discharge quantity converted to standard depth of discharge The expression is:

[0088] (2-2)

[0089] In equation (2-2), where, This indicates the actual discharge amount during each discharge process. This represents the equivalent discharge quantity at the standard depth of discharge after equivalent conversion. Depth of discharge The cycle life is below; Indicates the rated depth of discharge The cycle life is generally set to the cycle life at 100% depth of discharge.

[0090] For a BESS with a defined configuration capacity, its total discharge capacity at the rated depth of discharge over its cycle life is... It can be represented as:

[0091] (2-3)

[0092] In equation (2-3), This represents the total discharge amount at the rated depth of discharge. For the rated installed capacity of electrochemical energy storage, Indicates the rated depth of discharge Cycle life.

[0093] Assuming BESS discharges daily during its operating cycle Then, the equivalent cycle life of the battery can be obtained as follows:

[0094]

[0095] In equation (2-4), This refers to the actual cycle life of electrochemical energy storage. For the planned operational dates of electrochemical energy storage within the current year, This represents the total discharge amount at the rated depth of discharge, where n represents the count of discharges during the daily operating cycle of the electrochemical energy storage. This refers to the total number of discharges during the daily operating cycle of the electrochemical energy storage.

[0096] In addition to initial investment costs and operation and maintenance costs, the annual average cost model for the entire life cycle of electrochemical energy storage also includes replacement costs for one or more times, which is mainly affected by the cycle life of electrochemical energy storage.

[0097] (1) Initial investment cost

[0098] The initial investment cost of an electrochemical energy storage system mainly includes the cost of the energy storage battery itself, auxiliary facilities, and power conversion unit. It is mainly determined by the rated power and capacity of the electrochemical energy storage system and is proportional to the rated capacity and power of the electrochemical energy storage.

[0099] (2-5)

[0100] This indicates the initial investment cost of electrochemical energy storage, mainly including the investment cost of the energy storage battery itself. Costs of auxiliary equipment such as fire-fighting liquid cooling and power conversion equipment cost .

[0101] 1) Cost of the energy storage battery itself

[0102] (2-6)

[0103] In equation (2-6), Investment cost of the energy storage battery itself; This is the unit capacity cost coefficient for electrochemical energy storage; The unit power cost coefficient for electrochemical energy storage; , The rated capacity and power are configured for electrochemical energy storage, respectively.

[0104] 2) Investment cost of auxiliary facilities :

[0105] (2-7)

[0106] In equation (2-7), This refers to the unit capacity cost coefficient for auxiliary facilities. This is the unit power cost coefficient for auxiliary facilities.

[0107] 3) Cost of electrochemical energy storage power conversion equipment

[0108] The cost of the energy storage power conversion unit depends on the rated power of the BESS, and its cost can be approximately linearly equivalent to the rated power.

[0109] (2-8)

[0110] In equation (2-8), This indicates the cost of electrochemical energy storage power conversion equipment. The unit power cost coefficient for the power conversion unit. This indicates the rated power of the electrochemical energy storage.

[0111] (2) Operation and maintenance costs of electrochemical energy storage systems :

[0112] (2-9)

[0113] In equation (2-9), This represents the unit power operation and maintenance cost coefficient for electrochemical energy storage; This represents the unit capacity operation and maintenance cost coefficient for electrochemical energy storage.

[0114] (3) Lifecycle replacement cost

[0115] Since the cycle life of superconducting energy storage is much longer than that of electrochemical energy storage, the operation of composite energy storage systems also involves the replacement of energy storage components. Combining the impact of discharge depth on the cycle life of electrochemical energy storage in the annual cost model of the entire life cycle of electrochemical energy storage, the replacement cost of electrochemical energy storage can be obtained as shown in the following formula:

[0116] (2-10)

[0117] In the formula, Cost of replacing electrochemical energy storage; The number of times the battery energy storage system can be replaced throughout the entire life cycle of the hybrid energy storage system; The system discount rate is m = Y / Yb, derived from the superconducting cycle life. and actual battery cycle life A joint decision.

[0118] (4) The total life cycle cost of electrochemical energy storage

[0119] To reflect the time value of investment, an annual cost model for the entire life cycle of electrochemical energy storage components is established using the equal annual value method, as shown in equation (2-11).

[0120] (2-11)

[0121] 3. Lifecycle cost model for superconducting magnets considering operational safety

[0122] 3.1 Magnet Structure Optimization Design Based on Compensation Capacity Requirements

[0123] like Figure 4 In the magnet parameter design process, based on the superconducting compensation capacity and power requirements of capacity optimization configuration, the minimum operating current and inductance value of the magnet can be obtained. A magnet structure optimization model is designed with the goal of minimizing the length of the superconducting tape used, and the required tape length is calculated using formula (3-1), establishing an optimization model for the superconducting energy storage magnet structure parameters. Simultaneously, its inductance value is estimated based on formulas (3-2) and (3-3).

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] in This represents the required strip length. The number of double-sided coils. To wind the inner diameter of the magnet, To wind the outer diameter of the magnet, Where is the number of turns of the coil, th is the thickness of the selected strip, L is the inductance of the wound magnet, and h represents the half-height of the magnet. Indicates the energy storage capacity of the magnet. Indicates the operating current of the magnet. is the Nagaoka coefficient (also known as the inductance coefficient), which is a dimensionless value.

[0130] The optimization constraints for the given magnet are as follows:

[0131] (3-4)

[0132] In the formula This indicates the minimum inner diameter of the magnet. This indicates the maximum inner diameter of the magnet. This indicates the minimum number of double-coil coils in the magnet. Indicates the maximum number of double-coil coils in the magnet. This represents the actual energy storage capacity of the magnet. This represents the superconducting energy storage capacity parameters generated by the NSGA-II algorithm. Indicates the operating current of the magnet. This is the critical current of the magnet.

[0133] In this embodiment, BESS stands for Battery Energy Storage System; SMES stands for Superconducting Magnetic Energy System.

[0134] 3.2 Construction of a Multi-Physics Coupled AC Loss and Temperature Rise Model for Superconducting Magnets. Based on the determined magnet structural parameters, combined with the finite element analysis method and the magnet's EJ characteristic model, the AC loss during magnet operation can be solved (by establishing a finite element model of the magnet using COMSOL simulation software), thus obtaining the temperature rise during operation. Based on the required rated energy storage capacity and power parameters of the superconducting magnet, the magnet structural parameters are designed, and an AC loss model of the magnet is established to analyze the magnet's temperature rise. The magnet's EJ characteristic equation is shown below:

[0135] (3-5)

[0136] 3.3 Joint Simulation Optimization Based on MATLAB and COMSOL. Based on the collaborative operation mechanism of MATLAB and COMSOL, combining the MATLAB magnet structure optimization model in 3.1 and the COMSOL electromagnetic-thermal analysis model in 3.2, considering magnet operating losses and temperature rise, the magnet structure and energy storage capacity are jointly optimized. The simulation optimization logic is as follows: Figure 5 As shown.

[0137] 3.4 Life Cycle Cost Model of Superconducting Energy Storage. The life cycle cost of a superconducting energy storage system can be divided into initial investment cost, operation and maintenance cost, and residual value. The initial investment cost of superconducting magnetic energy storage mainly includes the cost of energy storage magnet tape, cooling and power conversion units; the operation and maintenance cost mainly includes the cooling cost of the magnet during daily operation and the equipment operation and maintenance cost; the residual value is the recovery value at the end of the energy storage system's life cycle.

[0138] (1) Initial investment cost of SMES

[0139] The initial investment cost of SMES is divided into three aspects: the cost of superconducting magnet tape and winding, the cost of auxiliary equipment such as cooling and vacuum, and the cost of power conversion unit.

[0140]

[0141] This indicates the initial investment cost of SMES. This indicates the initial investment cost for constructing a superconducting energy storage magnet. This indicates the investment cost of the cooling equipment for magnet operation. This indicates the equipment cost required for power conversion of energy storage magnets.

[0142] 1) SMES Energy Storage Magnet. The cost of the magnet itself includes the cost of the superconducting tape and winding, as well as the cost of cold components such as the Dewar, current leads, and insulation support structure. In the modeling process, the cost of the superconducting energy storage magnet can be simplified as being proportional to its rated energy storage capacity and power. However, considering the impact of temperature rise on the magnet's critical operating conditions during operation, a safety margin of approximately 30% should be reserved when designing the rated energy storage capacity of the superconducting energy storage magnet. This is to prevent quench failure caused by a decrease in critical current due to temperature rise during charging and discharging. This yields the initial investment cost for constructing the superconducting magnet. for:

[0143] (3-8)

[0144] In equation (3-8), and These represent the capacity cost coefficient and power cost coefficient of superconducting magnetic energy storage, respectively. This refers to the rated installed capacity of superconducting energy storage. This is the rated operating power for superconducting capacity.

[0145] 2) SMES Cooling Costs. Since superconducting magnets must operate in a cryogenic environment to maintain their superconducting state, and the current inside the superconducting energy storage magnet changes during power exchange with the grid, these changes cause excitation and demagnetization within the magnet, leading to Joule heat loss. This increases the magnet's operating temperature, affecting its current-carrying capacity and reducing its output capacity, thus impairing the compensation performance of the superconducting energy storage. Therefore, the cooling power of the cooling mechanism must be considered during magnet operation to maintain stable operation. Currently, the cooling devices used in superconducting magnets are commercially available, and the relationship between the cost of the cooling system and its cooling capacity can be modeled using data fitting methods.

[0146] (3-9)

[0147] In equation (3-9), For refrigeration costs; This refers to the heat load during SMES power exchange. The operating temperature range set for the magnet.

[0148] During SMES operation, the heat load varies under different power exchanges. To ensure the safe and stable operation of the magnet, the design heat load value is the maximum heat load value under constant rated operating power. The cooling investment cost of the magnet can be simplified as follows:

[0149] (3-10)

[0150] In equation (3-10) This represents the refrigeration cost coefficient related to the rated operating power. This indicates the cost of the cooling equipment required for the magnet to operate. Configure the magnet with rated power.

[0151] 3) Cost of power conversion equipment

[0152] The cost of the power conversion unit depends on the rated power of the SMES, and its cost can be approximately linearly equivalent to the rated power.

[0153] (3-11)

[0154] In equation (3-11) This represents the cost factor of the power conversion unit related to the rated operating power. This represents the rated operating power of the magnet.

[0155] (2) SMES operation and maintenance costs

[0156] It mainly consists of cooling costs and maintenance costs.

[0157] (3-12)

[0158] This indicates the operation and maintenance costs of superconducting energy storage, including Refrigeration costs and Operation and maintenance costs.

[0159] 1) Refrigeration cost

[0160] Since the refrigerator needs to operate continuously to maintain the stable operating temperature of the magnet, regardless of whether the magnet exchanges power with the outside world, the annual power consumption cost of the SMES refrigeration system can be calculated using the following formula:

[0161]

[0162] In equation (3-13), For the refrigeration power of the refrigeration unit; The unit represents the electricity cost, i.e., the price per kilowatt-hour, expressed in yuan. T represents the operating time of the chiller in a day, expressed in hours. To ensure the stable operation of the magnet, the chiller typically operates 24 hours a day. This indicates the operating cost of magnet cooling. This indicates the refrigeration efficiency of the refrigeration system.

[0163] 2) Operation and maintenance costs

[0164] The operation and maintenance costs of an energy storage system mainly consist of fixed costs and variable costs. Fixed costs include daily operating labor and maintenance costs, which are related to the system's operating time and capacity. Variable costs mainly refer to maintenance costs incurred due to system failures caused by internal or external factors. Since operation and maintenance costs only account for a small portion of the total cost of an energy storage system (SMES), it can be assumed that maintenance costs are proportional to the cost of rated operating power.

[0165] (3-14)

[0166] In equation (3-14), The cost of operation and maintenance is expressed in ten thousand yuan per year. This represents the unit capacity operation and maintenance cost coefficient for superconducting energy storage. This represents the unit power operation and maintenance cost coefficient for superconducting energy storage.

[0167] (3) Total life cycle cost of superconducting energy storage

[0168] To reflect the time value of investment, an annual cost model for the entire life cycle of electrochemical energy storage components is established using the equal annual value method, as shown in equation (3-15):

[0169] (3-15)

[0170] Among them, C SMES_LCOE This represents the average annual cost over the entire lifecycle of superconducting energy storage.

[0171] 4. Optimization Solution Based on Multi-Objective Optimization Algorithm

[0172] 4.1 Construction of a Multi-Objective Optimization Model for Superconducting-Electrochemical Composite Energy Storage

[0173] (1) Objective function

[0174] Objective function 1: Minimize the average annual comprehensive cost of the composite energy storage system throughout its entire life cycle as the economic optimization objective.

[0175] (4-1)

[0176] in, This represents the total annual comprehensive cost of the entire lifecycle of the composite energy storage system. This represents the average annual comprehensive cost over the entire lifecycle of an electrochemical energy storage system. This represents the average annual comprehensive cost of a superconducting energy storage system throughout its entire lifecycle.

[0177] Objective function 2: Minimize the sum of squares of the difference between the actual output power and the target power output in each sampling period during the energy storage compensation process as the operation optimization objective.

[0178] (4-2)

[0179] This represents the compensation power signal that is actually output by the superconducting energy storage. This represents the compensation power signal that is actually output by the electrochemical energy storage. This represents the desired electrochemical energy storage output compensation power signal. This represents the desired superconducting energy storage output compensation power signal.

[0180] (2) Operational constraints of the composite energy storage system

[0181] 1) Power balance constraints of composite energy storage systems

[0182] The power and compensation power at any sampling moment during the operation of the composite energy storage system should remain in balance;

[0183] (4-3)

[0184] express Battery output power at all times express The output power of the superconducting magnet at all times Let t be the total power that the composite energy storage system needs to compensate at time t.

[0185] 2) Output limitations of energy storage systems

[0186] Both types of energy storage elements must have their output power within the rated power range:

[0187] (4-4)

[0188] and These represent the minimum power of the battery and the superconductor, respectively. and These represent the rated output power of the battery and the superconducting energy storage, respectively.

[0189] 3) Energy storage system capacity constraints

[0190] (4-5)

[0191] and This represents the remaining capacity of the battery and superconducting energy storage at time t. and These represent the rated installed capacity of the battery and the superconducting energy storage, respectively.

[0192] 4) SOC constraints of energy storage systems

[0193] To avoid overcharging and over-discharging of energy storage devices, the state of charge (SOC) of the energy storage should be maintained within a safe range.

[0194] (4-6)

[0195] and These represent the state of charge (SOC) of the battery and the superconducting magnet at time t, respectively. and These represent the lower boundary of the State of Charge (SOC) for safe operation of the battery and the superconducting magnet, respectively. and These represent the upper boundary of the State of Charge (SOC) for safe operation of the battery and the superconducting magnet, respectively.

[0196] 4.2 Solving the Capacity Optimization Configuration Model Based on the NSGA-II Optimization Algorithm

[0197] To simultaneously optimize both the system's operational status and investment economics after energy storage compensation, the classic NSGA-II algorithm is employed. The NSGA-II algorithm utilizes a fast non-dominated sorting method to find the non-dominated solution set for the multi-objective problem. Through multiple iterations, it ultimately solves for the Pareto front of the available multi-objective capacity configuration model. The basic process of the NSGA-II algorithm is as follows:

[0198] Step 1: Initialize algorithm parameters by randomly generating N initial populations within the optimization variable solution space. And use it as the parent population;

[0199] Step 2: By analyzing the parent population Perform selection, crossover, and mutation operations to produce the next generation of the population. and will As a progeny population;

[0200] Step 3: Transfer the parent population and offspring population Merging to form new populations The number of its individuals is 2N, and it is related to... Perform fast non-dominated sorting and crowding calculation;

[0201] Step 4: Based on the individual's non-dominant hierarchy number and their crowding distance, from Select the N best individuals to serve as the parent population for the next generation of evolutionary operations. ;

[0202] Step 5: Iterate the algorithm according to Step 2 and Step 3 above until the maximum number of iterations is reached.

[0203] Based on the above analysis steps, a flowchart of the proposed superconducting-electrochemical composite energy storage capacity optimization configuration method can be obtained, as follows: Figure 6 As shown.

[0204] The relevant parameters for the superconducting-electrochemical composite energy storage capacity configuration model are shown in Table 2 below.

[0205] Table 2 Capacity Configuration Related Parameters

[0206]

[0207]

[0208] Setting the lifespan of the superconducting-electrochemical composite energy storage to 20 years, the target compensation power and capacity configuration parameters are substituted into the optimization configuration model, and the NSGA-II algorithm is used for solving. The resulting Pareto solution sets under different power allocation schemes are as follows: Figure 7 As shown in the figure above, when m=4, the composite energy storage system exhibits optimal economic efficiency and compensation performance. Under this power allocation scheme, the composite energy storage system effectively combines the complementary technical characteristics of superconducting energy storage's power response and electrochemical energy storage's energy support. The electrochemical energy storage composite is responsible for compensating for relatively slow-changing, high-amplitude power commands; while the superconducting energy storage is responsible for rapidly changing fluctuating power signals, reducing the number of charge-discharge cycles for the electrochemical energy storage. This allocation also aligns with the technical characteristics of both energy storage devices.

[0209] based on Figure 7 A magnified view of the Pareto solution set under different power allocation schemes, with the square of the power output tracking error set as the condition. The optimal capacity configuration results under different power allocation schemes that take into account both the investment economy and compensation performance of the composite energy storage system are shown in Table 3. As can be seen from Table 3, by reasonably allocating the compensation power command and capacity of the composite energy storage system, the annual comprehensive cost of the composite energy storage system can be reduced by 12.2% compared with the single-cell energy storage system, and the power tracking error of the energy storage system can be reduced from 3.23 to 2.73.

[0210] Table 3 Optimal capacity configuration results under different power allocation schemes

[0211]

[0212] Therefore, a composite energy storage system consisting of electrochemical energy storage and superconducting energy storage can effectively combine the complementary characteristics of the two through reasonable capacity configuration, thereby reducing the configuration capacity of the composite energy storage system, lowering the system investment cost, and improving the compensation performance of the composite energy storage system, which is in line with the theoretical analysis results.

[0213] Under this optimization scheme, the magnet design parameters obtained from the joint simulation optimization are shown in Table 4 below.

[0214] Table 4 Magnet Optimization Design Parameters

[0215]

[0216] This invention significantly improves the physical realism and computational accuracy of capacity configuration models by constructing an electrochemical energy storage variable lifetime cost model that considers the influence of discharge depth, and a superconducting energy storage safety operation constraint model that integrates magnet AC loss and temperature rise simulation. This method effectively overcomes the configuration deviations caused by traditional idealized models that neglect battery lifetime degradation and superconducting magnet thermal stability limitations. It enables the optimization results to simultaneously reflect lifetime degradation and safety boundaries in actual operation, providing a reliable design basis for engineering implementation.

[0217] Furthermore, this invention establishes a collaborative optimization framework aimed at minimizing the overall cost throughout the entire lifecycle and minimizing power point tracking error, and employs a multi-objective optimization algorithm for solution. This enables comprehensive optimization of economy, reliability, and dynamic response performance while strictly meeting system operational constraints. This method not only outputs a complete configuration scheme including power, capacity, and specific magnet structural parameters, but also provides corresponding cost and performance quantitative assessments. This allows for the identification of the technically and economically optimal configuration point during the system planning stage, reducing investment and operational risks and improving the overall application efficiency of the composite energy storage system.

[0218] The above specific embodiments are merely several optional embodiments of the present invention. Based on the technical solutions of the present invention and the relevant teachings of the above embodiments, those skilled in the art can make various alternative improvements and combinations to the above specific embodiments.

Claims

1. A method for optimizing the capacity configuration of a composite energy storage system, characterized in that, Includes the following steps: S1. Perform modal decomposition and reconstruction on the target compensation power data of the composite energy storage system to obtain multiple sets of reference power command combinations corresponding to the superconducting energy storage subsystem and the electrochemical energy storage subsystem, respectively. S2. Establish an annual cost model for the entire life cycle of electrochemical energy storage with varying lifespan, taking into account the impact of depth of discharge on battery cycle life. S3. Establish an annual cost model for the entire life cycle of a superconducting magnet. The model is based on optimizing the magnet structure with target compensation power and capacity, and evaluates its operational safety and losses through multi-physics field coupling simulation. Iterative optimization yields magnet parameters and costs that meet safety constraints. S4. Construct a multi-objective optimization model with the goals of minimizing the average annual comprehensive cost over the entire life cycle and minimizing the power tracking error. Integrate the cost models and system operation constraints from steps S2 and S3, obtain the Pareto optimal solution set by solving the model, and determine the final capacity and power configuration scheme accordingly.

2. The method for optimizing the capacity configuration of a composite energy storage system according to claim 1, characterized in that, Step S1 specifically includes: S1.1 Based on mutual information theory, find the sub-waveform with the highest matching degree with the waveform features of the left or right edge of the signal within the signal sequence composed of the target compensation power data; S1.

2. Extend the original signal at the boundary using the sub-waveform with the highest matching degree to suppress the endpoint effect; S1.3 Perform variational mode decomposition on the extended signal to obtain multiple eigenmode function components arranged according to the center frequency; S1.4 Enumerate different high and low frequency power boundary points, and reconstruct the components into high frequency power commands and low frequency power commands respectively to form multiple sets of reference power command combinations, wherein the high frequency power command serves as the reference command for superconducting energy storage and the low frequency power command serves as the reference command for electrochemical energy storage.

3. The method for optimizing the capacity configuration of a composite energy storage system according to claim 2, characterized in that, In step S1.1, the mutual information value is used as a measure of waveform matching degree, and its calculation uses the following formula: Where MI(X,Y) is the mutual information value between the two signals. and Let X and Y represent the two waveform sequences to be compared, respectively. P(x) and P(y) represent the marginal distributions of sequences X and Y, respectively. P(x,y) is the joint distribution of X and Y, where x is the specific value of each sampling time in waveform sequence X, and y is the specific value of each sampling time in waveform sequence Y.

4. The method for optimizing the capacity configuration of a composite energy storage system according to claim 1, characterized in that, The construction of the electrochemical energy storage full life cycle variable lifetime average annual cost model in step S2 includes: S2.1 Establish a mapping model between battery discharge depth and cycle life, which is represented by the following fitting function: in, For the cycle life of energy storage batteries, This refers to the depth of discharge of the energy storage battery. S2.

2. Based on the charge-discharge curves of electrochemical energy storage in actual operation, the actual discharge amount at different depths of discharge is calculated. The equivalent discharge quantity converted to the standard depth of discharge is calculated using the following formula. : in, Indicates the rated depth of discharge The cycle life is below, Indicates the actual depth of discharge The cycle life is below; S2.

3. Based on the equivalent discharge quantity and rated installed capacity, calculate the actual cycle life of the electrochemical energy storage. ; S2.4, Based on the actual cycle life years Rated capacity Rated power The unit capacity cost coefficient, unit power cost coefficient, and operation and maintenance cost coefficient are used to construct the annual average cost model for the entire life cycle using the equal annual value method.

5. The method for optimizing the capacity configuration of a composite energy storage system according to claim 1, characterized in that, Step S3, which involves optimizing the magnet structure based on the target compensation power and capacity, specifically means: minimizing the total length of the superconducting tape and minimizing the internal radius of the magnet. Number of double-sided coils Number of coil turns To optimize variables, while meeting energy storage capacity requirements and operating current... Below the critical current The optimization solution is performed under certain constraints.

6. The method for optimizing the capacity configuration of a composite energy storage system according to claim 5, characterized in that, Step S3, which describes evaluating operational safety and losses through multiphysics coupling simulation, specifically includes: S3.1 Based on the optimized magnet structure parameters, a multi-physics coupling model of the superconducting magnet, involving "electromagnetism and heat", is established in the finite element simulation software. S3.2, EJ characteristic model based on superconducting magnets Calculate the AC loss of the magnet under a reference power command, where E is the local electric field strength within the superconductor. It is the local current density within the superconductor, E c J represents the characteristic electric field of a superconducting magnet. c Let B represent the critical current density, B represent the magnetic field strength, ε represent the magnet strain, and n be an empirical exponent, taken as n=31; S3.

3. Using the AC loss as a heat source, perform heat conduction simulation to obtain the temperature rise distribution of the magnet; S3.4 Determine whether the temperature rise causes the magnet's operating temperature to exceed the safe range or the operating current to exceed the critical current. If the temperature rise constraint and critical current constraint of the magnet are not met, return to adjust the magnet's structural parameters or compensation capacity, and repeat the optimization and simulation iteration.

7. The method for optimizing the capacity configuration of a composite energy storage system according to claim 1, characterized in that, In step S3.1, the optimization of the magnet structure parameters and the multiphysics coupling simulation are achieved through a joint simulation process using MATLAB and COMSOL software.

8. The method for optimizing the capacity configuration of a composite energy storage system according to claim 1, characterized in that, The two objective functions of the multi-objective optimization model are: Objective function one: Minimize the average annual comprehensive cost of the composite energy storage system over its entire life cycle. ; Objective function two: Minimize the sum of squared power tracking errors. ;in, This refers to the average annual comprehensive cost of a composite energy storage system over its entire lifecycle. C refers to the sum of squares of power tracking errors. HESS This represents the average annual cost over the entire lifecycle of a composite energy storage system. , These are the average annual costs over the entire lifecycle of electrochemical energy storage and superconducting energy storage, respectively. For the cost of power conversion system, For the actual output power of the electrochemical energy storage subsystem, This represents the actual output power of the superconducting energy storage subsystem. For the target reference power of the electrochemical energy storage subsystem, This is the target reference power for the superconducting energy storage subsystem.

9. The method for optimizing the capacity configuration of a composite energy storage system according to claim 8, characterized in that, In step S4, the constraints of the multi-objective optimization model include: power balance constraints of the composite energy storage system, output limits of each energy storage subsystem, capacity constraints, and state-of-charge (SOC) operating range constraints.

10. The method for optimizing the capacity configuration of a composite energy storage system according to claim 1, characterized in that, In step S4, a non-dominated sorting genetic algorithm with an elitist strategy is used to solve the multi-objective optimization model to obtain the Pareto optimal solution set.

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