Carbon-based capacitor and lithium battery energy storage system configuration method for stabilizing wind power fluctuation

Abstract

The invention relates to a configuration method of a carbon-based capacitor and lithium battery energy storage system for stabilizing wind power fluctuation. The carbon-based capacitor and lithium battery energy storage system and a wind power system form a wind storage system, and the wind storage system is connected to a power grid after combined output. The method comprises the steps that according to wind power output of a wind power system at the current moment and a power output smooth value of a wind storage system at the previous moment, the power output value of the wind storage system at the current moment is obtained through a moving weighted average filtering algorithm, and therefore power instructions of a carbon-based capacitor and a lithium battery energy storage system at the current moment are determined; performing power instruction distribution of the lithium battery energy storage system and the carbon-based capacitor energy storage system by using an ensemble empirical mode method; and solving the optimal rated power and rated capacity configuration of the lithium battery energy storage system and the carbon-based capacitor energy storage system according to the average daily minimum cost model. Compared with the prior art, the method has the advantages that wind power fluctuation suppression is achieved, the compensation capacity of the energy storage system is improved, and the consumption cost is reduced.

Description

Technical Field

[0001] The present invention relates to the field of wind power systems, and in particular to a method for configuring a carbon-based capacitor and a lithium battery energy storage system for smoothing wind power fluctuations. Background Art

[0002] As a clean energy, wind power has an increasing installed capacity and penetration rate. However, wind power is an intermittent energy source, and its availability and intensity are affected by many factors, such as wind speed, wind direction, and terrain. The random changes in these factors lead to the randomness, intermittency, and uncertainty of wind power generation, which seriously affect the normal operation of the power system in large-scale wind power grid connection, such as affecting the frequency stability of the power grid, power quality, and grid planning and scheduling. Therefore, the current wind power grid connection power fluctuations are difficult to meet the grid assessment requirements. Summary of the invention

[0003] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations, so as to effectively smooth the instability of wind power generation.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations, wherein the carbon-based capacitor and lithium battery energy storage system and a wind power system form a wind storage system for joint output and then are connected to a power grid, and the carbon-based capacitor and lithium battery energy storage system includes a lithium battery energy storage system and a carbon-based capacitor energy storage system, and the method includes the following steps:

[0006] According to the wind power output of the wind power system at the current moment and the power output smoothing value of the wind storage system at the previous moment, the moving weighted average filtering algorithm is used to obtain the power output value of the wind storage system at the current moment, thereby determining the power instructions of the carbon-based capacitor and lithium battery energy storage system at the current moment;

[0007] By using the ensemble empirical mode method, the power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system are allocated according to the power instructions of the carbon-based capacitor and the lithium battery energy storage system at the current moment;

[0008] Based on the power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system, the optimal rated power and rated capacity configurations of the lithium battery energy storage system and the carbon-based capacitor energy storage system are obtained according to the daily minimum cost model.

[0009] Furthermore, the processing process of the moving weighted average filtering algorithm is specifically as follows:

[0010] For determining the power output value of the wind storage system at each current moment, the wind power output of the wind power system at the current moment and the power output smoothing value of the wind storage system at the previous moment are weighted summed to obtain the smoothing value of the power output value of the wind storage system at the current moment.

[0011] Furthermore, the calculation expression of the smoothed value of the power output value of the wind storage system at the current moment is:

[0012] P Total (t) = λP WP (t)+(1-λ)P Total (t-1),λ∈[0,1]

[0013] Where P Total (t) is the smoothed value of the power output of the wind-storage system at time t, P WP (t) is the wind power output of the wind power system at time t, P Total (t-1) is the smoothed value of the power output of the wind-storage system at time t-1, and λ is the filter coefficient;

[0014] The calculation expression of the power instruction of the carbon-based capacitor and lithium battery energy storage system at the current moment is:

[0015] P HESS (t) = P Total (t)-P WP (t)

[0016] Where P HESS (t) is the power command of the carbon-based capacitor and lithium battery energy storage system at time t.

[0017] Furthermore, the ensemble empirical mode method is specifically:

[0018] In the time-frequency domain, the power instructions of the carbon-based capacitor and lithium battery energy storage system at the current moment are decomposed into n eigenmodes with high to low frequencies and a residual component. The high-frequency component is selected as the power instruction of the carbon-based capacitor energy storage system, and the low-frequency component in the area is selected as the power instruction of the lithium battery energy storage system.

[0019] Furthermore, the calculation expression of the power instruction of the lithium battery energy storage system is:

[0020]

[0021] Where P LB (t) is the power command of the lithium battery energy storage system at time t, c i (t) is the i-th eigenmode after decomposition at time t, r n (t) is the residual component after decomposition at time t, j is the high-frequency and low-frequency division point, and n is the total number of eigenmodes;

[0022] The calculation expression of the power instruction of the carbon-based capacitor energy storage system is:

[0023]

[0024] Where P CB (t) is the power command of the carbon-based capacitor energy storage system at time t.

[0025] Furthermore, the method also determines the optimal high- and low-frequency division point j during the process of solving the daily minimum cost model.

[0026] Furthermore, the expressions for the rated power configurations of the lithium battery energy storage system and the carbon-based capacitor energy storage system are:

[0027]

[0028] Where P r,LB is the rated power of the lithium battery energy storage system, P r,CB is the rated power of the carbon-based capacitor energy storage system, t o is the initial time, T is the test time, P LB (t) is the power command of the lithium battery energy storage system at time t, P CB (t) is the power command of the carbon-based capacitor energy storage system at time t, η c,LB and η dc,LB are the charging and discharging efficiency of the lithium battery energy storage system, η c,CB and η dc,CB They are the charging and discharging efficiency of the carbon-based capacitor energy storage system, respectively.

[0029] Furthermore, the expression of the rated capacity configuration of the lithium battery energy storage system is:

[0030]

[0031] In the formula, E r,LB is the rated capacity of the lithium battery energy storage system, SOC 0,LB is the initial state of charge of the lithium battery energy storage system, SOC min,LB and SOC max,LB are the upper and lower limits of the state of charge of the lithium battery energy storage system, P d,LB (t) is the power command of the lithium battery energy storage system after considering the charging and discharging efficiency, η c,LB and η dc,LB are the charging and discharging efficiencies of the lithium battery energy storage system, ΔT is the power command interval, k is the time, P LB (t) is the power command of the lithium battery energy storage system at time t;

[0032] The expression of the rated capacity configuration of the carbon-based capacitor energy storage system is:

[0033]

[0034] In the formula, E r,CB is the rated capacity of the carbon-based capacitor energy storage system, SOC 0,CB is the initial state of charge of the carbon-based capacitor energy storage system, SOC min,CB and SOC max,CB are the upper and lower limits of the state of charge of the carbon-based capacitor energy storage system, P d,CB (t) is the power command of the carbon-based capacitor energy storage system after considering the charging and discharging efficiency, η c,CB and η dc,CB are the charging and discharging efficiency of the carbon-based capacitor energy storage system, P CB (t) is the power command of the carbon-based capacitor energy storage system at time t.

[0035] Furthermore, the objective function of the daily minimum cost model is expressed as:

[0036]

[0037] In the formula, is the average daily total cost, is the average daily investment cost, is the average daily operation and maintenance cost, is the average daily replacement cost, is the average daily scrap cost, E rv It is the residual value of HESS equipment.

[0038] Furthermore, the constraint condition expression of the daily minimum cost model is:

[0039]

[0040] In the formula, SOC LB (t) and SOC CB (t) are the charge states of the lithium battery energy storage system and the carbon-based capacitor energy storage system at time t, SOC min,CB and SOC max,CB They are the upper and lower limits of the state of charge of the carbon-based capacitor energy storage system, SOC min,LB and SOC max,LB are the upper and lower limits of the state of charge of the lithium battery energy storage system, P LB (t) is the power command of the lithium battery energy storage system at time t, P CB (t) is the power command of the carbon-based capacitor energy storage system at time t, P r,LB is the rated power of the lithium battery energy storage system, P r,CBis the rated power of the carbon-based capacitor energy storage system.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] (1) The present invention first configures a carbon-based capacitor and a lithium battery energy storage system for the wind power system to perform joint output, which can effectively smooth out the instability of wind power generation. At the same time, a moving weighted average filtering algorithm is used to obtain the power instructions of the carbon-based capacitor and the lithium battery energy storage system at the current moment according to the wind power output of the wind power system at the current moment and the power output of the historical wind storage system. This achieves fluctuation suppression of the wind storage system at the current moment, solves the problem of weak correlation between the output of the wind storage system before and after, and obtains a more reasonable power instruction of the energy storage system under the condition of meeting the grid assessment requirements.

[0043] (2) The present invention allocates power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system in the carbon-based capacitor and lithium battery energy storage system, and proposes that the lithium battery energy storage system and the carbon-based capacitor energy storage system respectively bear the high and low frequency components in the power instructions of the energy storage system, thereby solving the problem of insufficient compensation capacity of a single energy storage system.

[0044] (3) The present invention takes the daily average minimum cost as the target value to obtain the rated power and rated capacity of the carbon-based capacitor energy storage system and the lithium battery energy storage system. This algorithm is more suitable for practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A schematic diagram of the structure of a wind storage system provided in an embodiment of the present invention;

[0046] Figure 2 A schematic flow chart of a method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations provided in an embodiment of the present invention;

[0047] Figure 3 The present invention is a schematic diagram of an iterative solution process of a method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0049] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0051] Some of the terms in this article are explained as follows:

[0052] Hybrid energy storage system (HESS)

[0053] Lithium battery storage system (LBSS)

[0054] Carbon based capacitor storage system (CBCSS)

[0055] Example 1

[0056] like Figure 2 As shown, this embodiment provides a configuration method of a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations. The carbon-based capacitor and lithium battery energy storage system and the wind power system form a wind storage system for joint output and then connect to the power grid. The carbon-based capacitor and lithium battery energy storage system includes a lithium battery energy storage system and a carbon-based capacitor energy storage system. Figure 1 As shown, P WP For wind power output, P HESS is the power command of the hybrid energy storage system, P LB is the power instruction of the lithium battery energy storage system, P CB is the power instruction of the carbon-based capacitor energy storage system, P Total Combined contribution to wind and storage systems.

[0057] The above method specifically comprises the following steps:

[0058] S1: According to the wind power output of the wind power system at the current moment and the power output smoothing value of the wind storage system at the previous moment, the moving weighted average filtering algorithm is used to obtain the power output value of the wind storage system at the current moment, thereby determining the power instructions of the carbon-based capacitor and lithium battery energy storage system at the current moment;

[0059] The processing process of the moving weighted average filtering algorithm is as follows:

[0060] For determining the power output value of the wind storage system at each current moment, the wind power output of the wind power system at the current moment and the power output smoothing value of the wind storage system at the previous moment are weighted summed to obtain the smoothing value of the power output value of the wind storage system at the current moment.

[0061] That is, due to the strong volatility of wind power, which leads to unstable output, a moving weighted average filtering algorithm is adopted to obtain the smoothed value of the current moment by weighted summing up the smoothed value processed by the algorithm at the previous moment and the data at the current moment, so as to suppress the power output fluctuation of the wind power system.

[0062] The calculation expression of the smoothed value of the power output value of the wind storage system at the current moment is:

[0063] P Total (t) = λP WP (t)+(1-λ)P Total (t-1),λ∈[0,1] (1)

[0064] Where P Total (t) is the smoothed value of the power output of the wind-storage system at time t, P WP (t) is the wind power output of the wind power system at time t, P Total (t-1) is the smoothed value of the power output value of the wind storage system at time t-1, and λ is the filtering coefficient; when λ=1, there is no filtering effect. After filtering, P that meets the wind power fluctuation limit standard is obtained. Total (t), and wind power output P WP (t), and obtain the power command of HESS at time t:

[0065] P HESS (t) = P Total (t)-P WP (t) (2)

[0066] Where P HESS (t) is the power command of the carbon-based capacitor and lithium battery energy storage system at time t. Total (t)>P WP At (t), HESS discharges, i.e., P HESS (t)>0; when P Total (t)<P WP At (t), HESS is charged, i.e., P HESS (t)<0, so as to achieve the purpose of stabilizing wind power output.

[0067] S2: using the ensemble empirical mode method, according to the power instructions of the carbon-based capacitor and the lithium battery energy storage system at the current moment, the power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system are allocated;

[0068] The specific content of the ensemble empirical mode method is:

[0069] In the time-frequency domain, the power command P of the carbon-based capacitor and lithium battery energy storage system at the current moment is HESS (t) is decomposed into n eigenmodes with high to low frequencies and a residual component. The high-frequency component is selected as the power instruction of the carbon-based capacitor energy storage system, and the low-frequency component in the region is selected as the power instruction of the lithium battery energy storage system. The specific expression is:

[0070]

[0071] Where P LB (t), P CB (t) represents the power instructions assigned to LBSS and CBCSS at time t. i (t) is the i-th eigenmode after decomposition, r n (t) is the residual component after decomposition. j is the high-low frequency division point. The sum of the eigenmode components less than j is the high-frequency component, which is smoothed by CBCSS; the sum of the eigenmode components greater than j and the residual components is the low-frequency component, which is smoothed by LBSS.

[0072] S3: Based on the power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system, the optimal rated power and rated capacity configuration of the lithium battery energy storage system and the carbon-based capacitor energy storage system are solved according to the daily minimum cost model.

[0073] Specifically, for the configuration of rated power, the rated power configuration of LBSS and CBCSS is allowed to meet the maximum absorption or release power that HESS should compensate to the wind storage system during the assessment time, as shown in the following formula:

[0074]

[0075] Where P r,LB , P r,CB are the rated powers of LBSS and CBCSS respectively, t o is the initial time, T is the test time, η c,LB , η dc,LB are the charge and discharge efficiency of LBSS, η c,CB , η dc,CB are the charge and discharge efficiency of CBCSS respectively.

[0076] For the configuration of rated capacity, the rated capacity configuration of LBSS needs to satisfy the following expression:

[0077]

[0078] Among them, E r,LBis the rated capacity of LBSS, SOC 0,LB is the initial state of charge of LBSS, SOC min,LB , SOC max,LB are the upper and lower limits of the state of charge of LBSS, P d,LB (t) is the LBSS power command after considering the charging and discharging efficiency, ΔT is the power command interval, and k represents the kth moment.

[0079] The rated capacity configuration of CBCSS must satisfy the following expression:

[0080]

[0081] Among them, E r,CB is the rated capacity of CBCSS, SOC 0,CB is the initial state of charge of CBCSS, SOC min,CB , SOC max,CB are the upper and lower limits of the state of charge of LBSS, P d,CB (t) is the CBCSS power command after considering the charging and discharging efficiency.

[0082] For the HESS daily average cost model, the objective function is the minimum daily average cost during the operation period, as shown in the following formula:

[0083]

[0084] in is the average daily total cost, is the average daily investment cost, is the average daily operation and maintenance cost, is the average daily replacement cost, is the average daily scrap cost, E rv It is the residual value of HESS equipment.

[0085]

[0086] where ρ co is the daily average cost coefficient, d is the discount rate, L is the total number of years of operation, T d is the total number of days in a year. p,LB , β p,CB are the unit power investment costs of LBSS and CBCSS, respectively, E,LB , β E,CB They are the unit capacity investment costs of LBSS and CBCSS respectively.

[0087]

[0088] Among them, C m,LB , C m,CBThey are the unit operation and maintenance costs of LBSS and CBCSS respectively.

[0089]

[0090] Where D p,LB , D p,CB are the unit power scrapping costs of LBSS and CBCSS, respectively, E,LB , D E,CB They are the unit capacity scrapping costs of LBSS and CBCSS respectively.

[0091]

[0092] where η rv is the residual value recovery rate.

[0093] The HESS daily cost model has the following constraints:

[0094]

[0095] Among them, SOC LB (t), SOC CB (t) represent the charge state of LBSS and CBCSS at time t respectively.

[0096] like Figure 3 As shown, in the process of configuring the optimal rated power and rated capacity, the above method also solves the optimal high- and low-frequency division point j through a cyclic iteration.

[0097] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations, characterized in that: The carbon-based capacitor and lithium battery energy storage system and the wind power system form a wind storage system for joint output and then connect to the power grid. The carbon-based capacitor and lithium battery energy storage system includes a lithium battery energy storage system and a carbon-based capacitor energy storage system. The method includes the following steps: According to the wind power output of the wind power system at the current moment and the power output smoothing value of the wind storage system at the previous moment, the moving weighted average filtering algorithm is used to obtain the power output value of the wind storage system at the current moment, thereby determining the power instructions of the carbon-based capacitor and lithium battery energy storage system at the current moment; By using the ensemble empirical mode method, the power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system are allocated according to the power instructions of the carbon-based capacitor and the lithium battery energy storage system at the current moment; Based on the power instructions of the lithium battery energy storage system and the carbon-based capacitor energy storage system, the optimal rated power and rated capacity configurations of the lithium battery energy storage system and the carbon-based capacitor energy storage system are obtained according to the daily minimum cost model.

2. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 1, characterized in that: The processing process of the moving weighted average filtering algorithm is specifically as follows: For determining the power output value of the wind storage system at each current moment, the wind power output of the wind power system at the current moment and the power output smoothing value of the wind storage system at the previous moment are weighted summed to obtain the smoothing value of the power output value of the wind storage system at the current moment.

3. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 2, characterized in that: The calculation expression of the smoothed value of the power output value of the wind energy storage system at the current moment is: P Total (t)=λP WP (t)+(1-λ)P Total (t-1),λ∈[0,1] Where P Total (t) is the smoothed value of the power output of the wind-storage system at time t, P WP (t) is the wind power output of the wind power system at time t, P Total (t-1) is the smoothed value of the power output of the wind-storage system at time t-1, and λ is the filter coefficient; The calculation expression of the power instruction of the carbon-based capacitor and lithium battery energy storage system at the current moment is: P HESS (t)=P Total (t)-P WP (t) Where P HESS (t) is the power command of the carbon-based capacitor and lithium battery energy storage system at time t.

4. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 1, characterized in that: The ensemble empirical mode method is specifically: In the time-frequency domain, the power instructions of the carbon-based capacitor and lithium battery energy storage system at the current moment are decomposed into n eigenmodes with high to low frequencies and a residual component. The high-frequency component is selected as the power instruction of the carbon-based capacitor energy storage system, and the low-frequency component in the area is selected as the power instruction of the lithium battery energy storage system.

5. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 4, characterized in that: The calculation expression of the power instruction of the lithium battery energy storage system is: Where P LB (t) is the power command of the lithium battery energy storage system at time t, c i (t) is the i-th eigenmode after decomposition at time t, r n (t) is the residual component after decomposition at time t, j is the high-frequency and low-frequency division point, and n is the total number of eigenmodes; The calculation expression of the power instruction of the carbon-based capacitor energy storage system is: Where P CB (t) is the power command of the carbon-based capacitor energy storage system at time t.

6. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 5, characterized in that: The method also determines the optimal high- and low-frequency division point j during the process of solving the daily minimum cost model.

7. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 1, characterized in that: The expressions for the rated power configurations of the lithium battery energy storage system and the carbon-based capacitor energy storage system are: Where P r,LB is the rated power of the lithium battery energy storage system, P r,CB is the rated power of the carbon-based capacitor energy storage system, t o is the initial time, T is the test time, P LB (t) is the power command of the lithium battery energy storage system at time t, P CB (t) is the power command of the carbon-based capacitor energy storage system at time t, η c,LB and η dc,LB are the charging and discharging efficiency of the lithium battery energy storage system, η c,CB and η dc,CB They are the charging and discharging efficiency of the carbon-based capacitor energy storage system, respectively.

8. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 1, characterized in that: The expression of the rated capacity configuration of the lithium battery energy storage system is: In the formula, E r,LB is the rated capacity of the lithium battery energy storage system, SOC 0,LB is the initial state of charge of the lithium battery energy storage system, SOC min,LB and SOC max,LB are the upper and lower limits of the state of charge of the lithium battery energy storage system, P d,LB (t) is the power command of the lithium battery energy storage system after considering the charging and discharging efficiency, η c,LB and η dc,LB are the charging and discharging efficiencies of the lithium battery energy storage system, ΔT is the power command interval, k is the time, P LB (t) is the power command of the lithium battery energy storage system at time t; The expression of the rated capacity configuration of the carbon-based capacitor energy storage system is: In the formula, E r,CB is the rated capacity of the carbon-based capacitor energy storage system, SOC 0,CB is the initial state of charge of the carbon-based capacitor energy storage system, SOC min,CB and SOC max,CB are the upper and lower limits of the state of charge of the carbon-based capacitor energy storage system, P d,CB (t) is the power command of the carbon-based capacitor energy storage system after considering the charging and discharging efficiency, η c,CB and η dc,CB are the charging and discharging efficiency of the carbon-based capacitor energy storage system, P CB (t) is the power command of the carbon-based capacitor energy storage system at time t.

9. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 1, characterized in that: The objective function of the daily minimum cost model is expressed as: In the formula, is the daily average total cost, is the average daily investment cost, is the average daily operation and maintenance cost, is the average daily replacement cost, is the average daily scrap cost, E rv It is the residual value of HESS equipment.

10. A method for configuring a carbon-based capacitor and lithium battery energy storage system for smoothing wind power fluctuations according to claim 9, characterized in that: The constraint expression of the daily minimum cost model is: In the formula, SOC LB (t) and SOC CB (t) are the charge states of the lithium battery energy storage system and the carbon-based capacitor energy storage system at time t, SOC min,CB and SOC max,CB They are the upper and lower limits of the state of charge of the carbon-based capacitor energy storage system, SOC min,LB and SOC max,LB are the upper and lower limits of the state of charge of the lithium battery energy storage system, P LB (t) is the power command of the lithium battery energy storage system at time t, P CB (t) is the power command of the carbon-based capacitor energy storage system at time t, P r,LB is the rated power of the lithium battery energy storage system, P r,CB is the rated power of the carbon-based capacitor energy storage system.

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