A Hybrid Energy Storage Double-Layer Capacity Configuration Method for Microgrids Considering the Three States of Wind and Photovoltaic

Abstract

The present invention provides a two - layer capacity configuration method for a hybrid energy storage system in a micro - grid considering the three - state of wind and light, including the following steps: Step 1, screen the micro - grid data of the area to be configured, select typical days, and establish the output power models of wind turbines and photovoltaic units; Step 2, establish the three - state models of wind turbines and photovoltaic systems; Step 3, within the constraints of the upper and lower limits of the wind and light capacity, select a set of initial values of the wind and light capacity, calculate the deficit power, and randomly sample the output power of wind turbines and photovoltaic units; Step 4, perform Fourier transform and inverse Fourier transform on the deficit power, separate the low - frequency power and high - frequency power, and compensate through the hybrid energy storage system and the tie line; Step 5, establish a configuration model with the minimum total cost of the micro - grid as the objective, perform spectrum analysis on the deficit power within the planning period to determine the output of the hybrid energy storage system and the tie line, transmit the results to Step 3, and obtain the optimal solution of the wind and light capacity through particle swarm algorithm iteration, and output the corresponding capacity and power configuration results.

Description

Technical Field

[0001] The present invention designs a method for optimizing the configuration of a hybrid energy storage system in a microgrid, specifically involving a two-layer capacity configuration method for a hybrid energy storage system in a microgrid considering the three states of wind and light. Background Art

[0002] A microgrid integrates various units such as wind turbines, photovoltaic systems, energy storage systems, diesel engines, and local loads through advanced power electronics technology and control technology to form a small independent power system. Its emergence provides the possibility for the power system to conduct more macroscopic regulation of distributed generation. A microgrid has two operating modes, namely grid-connected operation with the external grid or isolated operation on its own. Existing models are only applicable to islanded microgrids or grid-connected microgrids alone, and there are few models that are applicable to both operating states of a microgrid. Due to the strong uncertainty of wind power output and photovoltaic power output, it is impossible to accurately establish their output models. How to fully consider the uncertainty of distributed power generation output and make full use of local resources to complete the configuration of energy storage and various micro-sources is the key point to be concerned in the microgrid planning stage.

[0003] Currently, in a microgrid, a storage device used to solve the problems of large-capacity electrical energy storage and conversion and act as a backup capacity for distributed generation generally selects a battery. As a representative of energy-type energy storage, the battery has a large energy density and can store energy for a long time. However, for loads with a high fluctuation frequency, the battery is not suitable for frequent charging and discharging. As a representative of power-type energy storage, a supercapacitor can better make up for the defects of the battery. Therefore, it is considered to connect the battery and the supercapacitor to the microgrid together. There are few models that consider the configuration of hybrid energy storage under the condition of multi-state operation of wind power output and photovoltaic power output. Summary of the Invention

[0004] The present invention is made to solve the above problems, and aims to provide a two-layer capacity configuration method for a hybrid energy storage system in a microgrid considering the three states of wind and light.

[0005] The present invention provides a two-layer capacity configuration method for a hybrid energy storage system in a microgrid considering the three states of wind and light, which is used to configure the capacity and power of wind turbines, photovoltaic units, and hybrid energy storage systems in a microgrid in a grid-connected or off-grid state, and has the following characteristics, including the following steps: Step 1, screen the microgrid data of the area to be configured, select a typical day, and establish a wind turbine output model and a photovoltaic unit output model;

[0006] Step 2, establish a three-state model of the wind turbine and the photovoltaic using the Markov process, and the three states include the normal operation state, the derating state, and the fault outage state;

[0007] Step 3: Within the constraints of the upper and lower limits of the wind and light capacity, randomly select a set of initial values of the wind and light capacity, calculate the deficit power, and use the sequential Monte Carlo method to randomly sample the output powers of the wind turbines and photovoltaic units under different states;

[0008] Step 4: Perform Fourier transform and inverse transform on the deficit power, separate the low-frequency power and high-frequency power according to the transformed frequency spectrum diagram, and respectively compensate the low-frequency power and high-frequency power according to the characteristics of the battery and supercapacitor in the hybrid energy storage system and according to whether the microgrid is connected to the main grid through a tie line;

[0009] Step 5: Establish a configuration model with the minimum total cost of the microgrid as the objective, perform spectrum analysis on the deficit power within the planning period according to the Fourier transform and inverse transform in Step 4, separate the low-frequency power and high-frequency power, determine the output of the hybrid energy storage system and the tie line, and transmit the results to Step 3. Repeat Steps 3 - 5. After obtaining the optimal solution of the wind and light capacity through particle swarm algorithm iteration, output the corresponding capacity and power configuration results.

[0010] In the method for double-layer capacity configuration of the hybrid energy storage in the microgrid considering the three states of wind and light provided by the present invention, it may further have the following characteristics: Among them, Step 1 includes the following sub-steps:

[0011] Step 1 - 1: Calculate the output of the wind turbine according to the obtained wind speed data of the typical day, and establish the following wind turbine output model:

[0012]

[0013] Step 1 - 2: Calculate the output of the photovoltaic unit according to the obtained illumination and ambient temperature data of the typical day, and establish the following photovoltaic unit output model:

[0014]

[0015] In formula (1), v out is the cut-out wind speed, v in is the cut-in wind speed, v r is the rated wind speed, P r.wind is the rated power of the wind turbine,

[0016] In formula (2), P SC is the rated output power of the photovoltaic array under standard conditions, G SC is the solar irradiance under standard conditions, G C is the actual solar irradiance at the operating point, k is the power temperature coefficient, T c (t) is the temperature at the operating point at time t, T SC is the temperature under standard conditions, N PV is the number of photovoltaic array units.

[0017] In the method for configuring the double-layer capacity of the hybrid energy storage in the microgrid considering the three states of wind and light provided by the present invention, it may further have the following characteristics: Among them, step 2 includes the following sub-steps:

[0018] Step 2-1, solve the probabilities of the normal operation state, derating state, and fault outage state, and use the Markov principle to obtain the state transition matrix as:

[0019]

[0020] Further solve to obtain:

[0021]

[0022] Step 2-2, adopt the Monte Carlo method for simulation sampling. The continuous operation time of the three states of the wind turbine or photovoltaic unit is obtained by simulating the mean time to failure (MTTF) and the mean time to repair (MTTR). The calculation formula is:

[0023]

[0024]

[0025] In formulas (3) and (4), λ is the failure rate, μ is the repair rate, and P1, P2, and P3 are the probabilities of the wind turbine or photovoltaic unit being in the normal operation state, derating state, and fault state respectively.

[0026] In formulas (5) and (6), t1 and t2 are the continuous operation time of the operation state and the outage fault repair time respectively, and x1 and x2 are random numbers uniformly distributed within the interval [0, 1].

[0027] In the method for configuring the double-layer capacity of the hybrid energy storage in the microgrid considering the three states of wind and light provided by the present invention, it may further have the following characteristics: Among them, step 3 includes the following sub-steps:

[0028] Step 3-1, set the construction site area as S, the length as L, and the width as W. Then, the wind turbines and photovoltaic units in the microgrid satisfy the following conditions:

[0029]

[0030] Step 3-2, the output powers of the three states of the wind turbine and the photovoltaic unit are:

[0031]

[0032]

[0033] i ∈ [1, i max , j ∈ [1, jmax (10),

[0034] In formulas (8) - (9), represents the state of the wind turbine and the photovoltaic unit at time t, obtained through sequential Monte Carlo sampling, and the calculation formula is as follows:

[0035]

[0036] Step 3 - 3, obtain the deficit power P from the power difference generated by wind power generation, photovoltaic power generation, and load power consumption in the microgrid J , and the calculation formula is as follows:

[0037]

[0038] In formula (7), d is the diameter of the wind turbine rotor, S2, [] are respectively the floor area of a single photovoltaic array, the shading coefficient, and the rounding function,

[0039] In formulas (8) - (10), i max is the maximum number of wind turbines, j max is the maximum number of photovoltaic units, is the power generated by i wind turbines at time t, is the power generated by j photovoltaic units at time t, is whether the i - th wind turbine is introduced at time t, is whether the j - th photovoltaic unit is introduced,

[0040] In formula (12), P L (t) is the load power at time t, and P G (t) is the power generated by the wind turbine and the photovoltaic unit at time t.

[0041] In the method for configuring the double - layer capacity of the hybrid energy storage in the microgrid considering the three - state of wind and light provided by the present invention, it can also have the following characteristics: Among them, step 4 includes the following sub - steps:

[0042] Step 4 - 1, the discrete Fourier transform formula is:

[0043]

[0044]

[0045] Step 4 - 2, substitute the deficit power into formulas (13) - (14) to calculate the amplitude - frequency sequence P J (k), and the amplitude - frequency sequence P J (k) takes the frequency f k = f s / 2 as the axis of symmetry and is expressed as:

[0046]

[0047] Cut off formula (15) at k = n, where n is the break point. Here, [0, n] is the low-frequency part and [n + 1, N / 2] is the high-frequency part. Separate the low-frequency and high-frequency parts to obtain the following formula:

[0048]

[0049] P J.H (k) = {0, …, 0, P J (N - 1), …, P J (N - n - 1), 0, … 0} (17),

[0050] In formula (16) and formula (17), P J.D (k) and P J.H (k) are the low-frequency component and high-frequency component of the deficit power respectively. Substitute formula (16) and formula (17) into formula (14) respectively to obtain the low-frequency power and high-frequency power of the deficit power as follows:

[0051]

[0052]

[0053] Step 4 - 3: Compensate the corresponding low-frequency power and high-frequency power through the hybrid energy storage system and the tie line.

[0054] P J.D (t) = β ES1 P ES1 (t) + αP line (t) (20)

[0055] P J.H (t) = β ES2 P ES2 (t) (21)

[0056] P J (t) = β ES1 P ES1 (t) + β ES2 P ES2 (t) + αP line (t) (22),

[0057] In formula (20) - formula (22), P ES1 (t) is the power compensated by the battery, P ES2 (t) is the power compensated by the supercapacitor, β ES1 is whether to introduce the battery, β ES2For whether to introduce a supercapacitor, α is the grid-connected and islanding coefficient. When it takes 1, it represents grid connection, and when it takes 0, it represents islanding.

[0058] When the grid-connected and islanding coefficient α = 0, the microgrid operates in island mode. The low-frequency power is compensated by the battery, and the high-frequency power is compensated by the supercapacitor.

[0059] When the grid-connected and islanding coefficient α = 1, the microgrid operates in grid-connected mode. The low-frequency power is compensated by the battery and the tie line, and the high-frequency power is compensated by the supercapacitor.

[0060] Step 4-4, the rated power of the hybrid energy storage system is the maximum value of the absolute value of the actual charge and discharge power of the energy storage, and the formula is as follows:

[0061] S ES1 / u1 ≥ max{|P ES1 (t)|} (23)

[0062] S ES2 / u2 ≥ max{|P J.H (t)|} (24);

[0063] Step 4-5, the formula for the initial energy change of the energy storage is as follows:

[0064]

[0065] Step 4-6, the formula for the rated capacity of the energy storage is as follows:

[0066]

[0067] E0 = 0.5S ES (27),

[0068] In formulas (13)-(14), P(k) and p(n) are the principal value sequences of the frequency-domain signal and the time-domain signal respectively, k is the sequence number of different frequency bands,

[0069] In formulas (23)-(24), S ES is the rated capacity of the energy storage, u1 is the ratio of the rated capacity of the battery to the rated power, u2 is the ratio of the rated capacity of the supercapacitor to the rated power,

[0070] In formula (25), E(t) is the energy change of the energy storage relative to the original state at the t-th sampling point, with the unit of kw·h, and T0 represents the sampling period, with the unit of s,

[0071] In formulas (26)-(27), S ES is the rated capacity of the energy storage, E0 is the initial energy of the energy storage, and the initial energy of the energy storage is set to 0.5 times the rated capacity of the energy storage.

[0072] In the method for configuring the double-layer capacity of the hybrid energy storage in the microgrid considering the three states of wind and light provided by the present invention, the following features may also be included: Among them, step 5 includes the following sub-steps:

[0073] Step 5-1, when establishing the configuration model, the total cost of the microgrid includes the equivalent annual investment cost of the equipment and the operation and maintenance costs of each component. The formula is as follows:

[0074] minF m = min(f am + f bm ) (28),

[0075] In formula (28), f am is the equivalent annual investment cost of the equipment, and f bm is the operation and maintenance costs of each component;

[0076] Step 5-2, the calculation formula for the equivalent annual investment cost of the equipment is as follows:

[0077] f am = f cr (f wind.am S wind + f PV.am S PV + f ES1.am S ES.1 + f ES2.am S ES.2 ) (29)

[0078]

[0079] In formula (29) - formula (30), f wind.am , f PV.am , f ES1.am , f ES2.am are respectively the initial investment costs per unit capacity of wind power, photovoltaic, battery, and supercapacitor. S k is the rated capacity of the Kth component, f cr is the annual capital recovery factor, L f is the engineering planning service life, and r is the discount rate;

[0080] Step 5-3, the calculation formula for the operation and maintenance costs of each component is as follows:

[0081] f bm = f wind.bm S wind + f PV.bm S PV + f ES1.bm S ES.1 + f ES2.bm S ES.2 (31),

[0082] In formula (31), f wind.bm , f PV.bm , f ES1.bm , f ES2.bm are the maintenance cost coefficients of the wind power generation unit, photovoltaic power generation array, storage battery, and supercapacitor, respectively;

[0083] Step 5-4: Establish the constraint conditions that need to be satisfied for the configuration model with the minimum total cost of the microgrid as the objective, including power balance constraint, system and grid power exchange constraint, tie line utilization rate constraint, tie line power fluctuation constraint, and energy storage system state of charge constraint;

[0084] Step 5-5: According to the Fourier transform and inverse transform in Step 4, perform spectral analysis on the power deficit during the planning period, separate the low-frequency power and high-frequency power, determine the output of the hybrid energy storage system and the tie line, and transmit the results to Step 3. Repeat Steps 3-5. After obtaining the optimal solution of the wind-solar capacity through particle swarm algorithm iteration, output the corresponding capacity and power configuration results. The update speed and update position of the particles in the particle swarm algorithm are as follows:

[0085]

[0086]

[0087] In formulas (32)-(33), i is the i-th particle, k is the number of algorithm iterations, c1 and c2 are learning factors, w is the inertia weight coefficient, r1 and r2 are random numbers between [0,1], v represents the update speed, x is the update position, p g is the global historical optimal position, and p best is the individual historical optimal position.

[0088] In the method for configuring the double-layer capacity of the hybrid energy storage of the microgrid considering the three states of wind and light provided by the present invention, it may also have the following characteristics: Among them, Step 5-4 includes the following sub-steps:

[0089] Step 5-4-1: The power balance constraint is as follows:

[0090] P J.D (t) = β ES1 P ES1 (t) + αP line (t) (34)

[0091] P J.H (t) = β ES2 P ES2 (t) (35),

[0092] In Formulas (34) - (35), β is the introduction coefficient. Taking 1 indicates the introduction of the corresponding component in the model, and vice versa taking 0. α is the grid-connected and islanded operation coefficient, which is a 0 - 1 variable. When α = 1, the microgrid operates in grid-connected mode, and when α = 0, the microgrid operates in islanded mode;

[0093] In step 5 - 4 - 2, the power exchange constraint between the system and the grid is that the power exchange P between the wind - solar - storage system of the microgrid and the grid line needs to meet the following requirements:

[0094] αP line.min ≤P line (t)≤αP line.max (36),

[0095] In Formula (36), P line.min 、P line.max are respectively the minimum and maximum powers allowed for the microgrid to exchange with the main grid, and this value is determined according to the supply - demand agreement reached between the microgrid and the main grid;

[0096] In step 5 - 4 - 3, the utilization rate constraint of the tie line is as follows:

[0097] αU line ≥αU line.min (37)

[0098]

[0099] In Formulas (37) - (38), U line.min is the lower limit of the tie - line utilization rate, U line is the tie - line utilization rate, P line.in is the power transmitted from the main grid to the microgrid, P line.out is the power fed back from the microgrid to the main grid, E line is the power quantity transmitted under the rated power of the tie line, P line,0 (t) is the rated power of the tie line;

[0100] In step 5 - 4 - 4, the power fluctuation constraint of the tie line uses the power standard deviation to represent the magnitude of the tie - line power fluctuation. The smaller the value of the power standard deviation, the smaller the tie - line power fluctuation. The formula is as follows:

[0101]

[0102] D sd ≤δ g (40),

[0103] In Formulas (39) - (40), D sd is the power standard deviation, δ g is the maximum power change rate of the main grid, is the average value of the tie-line power;

[0104] Step 5-4-5, the state of charge constraint of the energy storage system is as follows:

[0105] SOC imin ≤SOC i (t) ≤ SOC imax (41),

[0106] In formula (41), SOC imin and SOC imax are the upper and lower limits of the SOC of the i-th energy storage system respectively, and SOC i (t) is the SOC value of the energy storage system at stage t.

[0107] Functions and effects of the invention

[0108] According to a dual-layer capacity configuration method for a microgrid hybrid energy storage considering the three states of wind and light involved in the present invention, by establishing a three-state model of a wind turbine and a photovoltaic system, and using the sequential Monte Carlo method to randomly sample the output powers of the wind turbine and the photovoltaic units in different states, the output powers of the wind turbine and the photovoltaic units can be obtained more accurately; moreover, by dividing the deficit power into low-frequency power and high-frequency power, and compensating the low-frequency power and the high-frequency power through a hybrid energy storage system composed of a battery and a supercapacitor and a tie-line, the optimal configuration of the hybrid energy storage can be carried out while considering the multi-state operation of wind power output and photovoltaic power output; in addition, by setting the introduction coefficient and the grid-connected and off-grid coefficients, the selection and combination of whether to introduce a battery or a supercapacitor and the grid-connected and off-grid of the microgrid can be flexibly carried out, which is very user-friendly in terms of user interaction and can be applied to both the island and grid-connected scenarios of the microgrid. Description of the drawings

[0109] Figure 1 is a flowchart of a dual-layer capacity configuration method for a microgrid hybrid energy storage considering the three states of wind and light in an embodiment of the present invention;

[0110] Figure 2 is a schematic diagram of a three-state model of a wind turbine and a photovoltaic system in an embodiment of the present invention;

[0111] Figure 3 is a schematic diagram of the results of sampling and simulating the states and durations of a wind turbine and a photovoltaic unit according to the three-state model of the wind turbine and the photovoltaic system in an embodiment of the present invention;

[0112] Figure 4 is a schematic diagram of high-frequency power in an embodiment of the present invention;

[0113] Figure 5 is a schematic diagram of low-frequency power in an embodiment of the present invention;

[0114] Figure 6 It is a schematic diagram of the tie-line power in the embodiments of the present invention. Specific Embodiments

[0115] In order to make the technical means and effects achieved by the present invention easy to understand, the present invention will be specifically described below in conjunction with embodiments and the accompanying drawings.

[0116] <Embodiment>

[0117] Figure 1 It is a flowchart of a method for double-layer capacity configuration of a hybrid energy storage system in a microgrid considering the three states of wind and light in the embodiments of the present invention.

[0118] As Figure 1 shown, a method for double-layer capacity configuration of a hybrid energy storage system in a microgrid considering the three states of wind and light in this embodiment is used to perform capacity and power configuration on the wind turbines, photovoltaic units, and hybrid energy storage systems in the microgrid in the grid-connected or off-grid state, and includes the following steps: Step 1, screen the microgrid data of the area to be configured, select a typical day, and establish a wind turbine output power model and a photovoltaic unit output power model.

[0119] The following sub-steps are included in Step 1:

[0120] Step 1-1, calculate the output power of the wind turbine according to the wind speed data obtained on the typical day, and establish the wind turbine output power model as follows:

[0121]

[0122] Step 1-2, calculate the output power of the photovoltaic unit according to the illumination and ambient temperature data obtained on the typical day, and establish the photovoltaic unit output power model as follows:

[0123]

[0124] In formula (1), v out is the cut-out wind speed, v in is the cut-in wind speed, v r is the rated wind speed, P r.wind is the rated capacity of the wind turbine,

[0125] In formula (2), P SC is the rated output power of the photovoltaic array under standard conditions, G SC is the solar irradiance under standard conditions, G C is the actual solar irradiance at the operating point, k is the power temperature coefficient, T c (t) is the temperature at the operating point at time t, T SC is the temperature under standard conditions, N PV is the number of photovoltaic array units.

[0126] Figure 2 It is a schematic diagram of the fan and the photovoltaic three-state model in the embodiments of the present invention.

[0127] As Figure 2 shown, in step 2, a Markov process is used to establish a three-state model of the fan and the photovoltaic, and the three states include the normal operation state, the derating state, and the fault outage state.

[0128] The following sub-steps are included in step 2:

[0129] In step 2-1, the probabilities of the normal operation state, the derating state, and the fault outage state are solved, and the state transition matrix is obtained by using the Markov principle as:

[0130]

[0131] By further solving, we get:

[0132]

[0133] In step 2-2, the Monte Carlo method is used for simulation sampling, and the three-state continuous operation time of the fan or the photovoltaic unit is obtained by simulating the mean time to failure MTTF and the mean time to repair MTTR. The calculation formula is:

[0134]

[0135]

[0136] In formulas (3) and (4), λ is the failure rate, μ is the repair rate, and P1, P2, and P3 are the probabilities that the fan or the photovoltaic unit is in the normal operation state, the derating state, and the fault state respectively.

[0137] In formulas (5) and (6), t1 and t2 are the continuous operation time of the operation state and the outage fault repair time respectively, and x1 and x2 are random numbers uniformly distributed within the interval [0, 1].

[0138] In step 3, within the constraints of the upper and lower limits of the wind and light capacity, a set of initial values of the wind and light capacity are randomly selected, the deficit power is calculated, and the output powers of the fan and the photovoltaic unit in different states are randomly sampled by using the sequential Monte Carlo method.

[0139] The following sub-steps are included in step 3:

[0140] In step 3-1, it is set that the construction site area is S, the length is L, and the width is W. Then, the fans and photovoltaic units in the microgrid meet the following conditions:

[0141]

[0142] Step 3-2, the output powers of the fan and the photovoltaic unit in three states are as follows:

[0143]

[0144]

[0145] i ∈ [1, i max , j ∈ [1, j max (10)

[0146] In formula (8) - formula (9), represents the state of the fan and the photovoltaic unit at time t, obtained through sequential Monte Carlo sampling, and the calculation formula is as follows:

[0147]

[0148] Step 3-3, the deficit power P is obtained from the power difference generated by wind power generation, photovoltaic power generation, and load power consumption in the microgrid J , and the calculation formula is as follows:

[0149]

[0150] In formula (7), d is the diameter of the fan rotor, S2, [ ] points are the floor area of a single photovoltaic array, the shading coefficient, and the rounding function respectively,

[0151] In formula (8) - formula (10), i max is the maximum number of fans, j max is the maximum number of photovoltaic units, is the power generated by i fans at time t, is the power generated by j photovoltaic units at time t, is whether the i-th fan is introduced at time t, is whether the j-th photovoltaic unit is introduced,

[0152] In formula (12), P L (t) is the load power at time t, and P G (t) is the power generated by the fan and the photovoltaic unit at time t.

[0153] Step 4, perform Fourier transform and inverse transform on the deficit power, separate the low-frequency power and high-frequency power according to the transformed frequency spectrum diagram, and compensate the low-frequency power and high-frequency power respectively according to the characteristics of the battery and the supercapacitor in the hybrid energy storage system and according to whether the microgrid is connected to the main grid through the tie line.

[0154] Step 4 includes the following sub-steps:

[0155] Step 4-1, the discrete Fourier transform formula is:

[0156]

[0157]

[0158] Step 4-2, substitute the deficit power into formulas (13)-(14) to calculate the amplitude-frequency sequence P J (k). The amplitude-frequency sequence P J (k) is symmetric about the frequency f k = f s / 2, and is expressed as:

[0159]

[0160] Cut off formula (15) at k = n, where n is the break point. Among them, [0, n] is the low-frequency part, and [n + 1, N / 2] is the high-frequency part. Separate the low-frequency and high-frequency parts to obtain the following formula:

[0161]

[0162] P J.H (k) = {0,…,0, P J (N - 1),…, P J (N - n - 1), 0,…0} (17),

[0163] In formulas (16) and (17), P J.D (k) and P J.H (k) are the low-frequency component and high-frequency component of the deficit power respectively. Substitute formulas (16) and (17) into formula (14) respectively to obtain the low-frequency power and high-frequency power of the deficit power as:

[0164]

[0165]

[0166] Step 4-3, compensate the low-frequency power and high-frequency power correspondingly through the hybrid energy storage system and the tie line.

[0167] P J.D (t) = β ES1 P ES1 (t) + αP line (t) (20)

[0168] P J.H (t) = β ES2 P ES2 (t) (21)

[0169] PJ P(t) = β ES1 P ES1 (t) + β ES2 P ES2 (t) + αP line (t) (22),

[0170] In formulas (20) - (22), P ES1 (t) is the power compensated by the battery, P ES2 (t) is the power compensated by the supercapacitor, β ES1 is whether to introduce the battery, β ES2 is whether to introduce the supercapacitor, α is the grid-connected / off-grid coefficient, taking 1 represents grid connection, and taking 0 represents off-grid;

[0171] When the grid-connected / off-grid coefficient α = 0, the microgrid operates in island mode, and the low-frequency power is compensated by the battery, and the high-frequency power is compensated by the supercapacitor;

[0172] When the grid-connected / off-grid coefficient α = 1, the microgrid operates in grid-connected mode, and the low-frequency power is compensated by the battery and the tie line, and the high-frequency power is compensated by the supercapacitor;

[0173] Step 4-4, the rated power of the hybrid energy storage system is the maximum value of the absolute value of the actual charge and discharge power of the energy storage, and the formula is as follows:

[0174] S ES1 / u1 ≥ max{|P ES1 (t)|} (23)

[0175] S ES2 / u2 ≥ max{|P J.H (t)|} (24);

[0176] Step 4-5, the formula for the initial energy change of the energy storage is as follows:

[0177]

[0178] Step 4-6, the formula for the rated capacity of the energy storage is as follows:

[0179]

[0180] E0 = 0.5S ES (27),

[0181] In formulas (13) - (14), P(k) and p(n) are the principal value sequences of the frequency-domain signal and the time-domain signal respectively, and k is the sequence number of different frequency bands,

[0182] In formulas (23) - (24), S ESLet \(E_{rated}\) be the rated capacity of the energy storage, \(u_1\) be the ratio of the rated capacity to the rated power of the battery, and \(u_2\) be the ratio of the rated capacity to the rated power of the supercapacitor.

[0183] In formula (25), \(E(t)\) is the change in the energy storage relative to the original state at the \(t\)-th sampling point, with the unit of \(kW\cdot h\), and \(T_0\) represents the sampling period, with the unit of \(s\).

[0184] In formulas (26) - (27), \(S\) ES is the rated capacity of the energy storage, \(E_0\) is the initial energy of the energy storage, and the initial energy of the energy storage is set to 0.5 times the rated capacity of the energy storage.

[0185] Step 5: Establish a configuration model with the goal of minimizing the total cost of the microgrid. Perform spectral analysis on the power deficit within the planning period according to the Fourier transform and inverse transform in Step 4 to separate the low-frequency power and high-frequency power, determine the output of the hybrid energy storage system and the tie line, and transmit the results to Step 3. Repeat Steps 3 - 5. After obtaining the optimal solution of the wind and solar capacity through particle swarm algorithm iteration, output the corresponding capacity and power configuration results.

[0186] Step 5 includes the following sub-steps:

[0187] Step 5 - 1: When establishing the configuration model, the total cost of the microgrid includes the equivalent annual investment cost of the equipment and the operation and maintenance costs of each component. The formula is as follows:

[0188] \(\min F\) m \(=\min(f\) am + \(f\) bm \()\) (28),

[0189] In formula (28), \(f\) am is the equivalent annual investment cost of the equipment, and \(f\) bm is the operation and maintenance costs of each component;

[0190] Step 5 - 2: The calculation formula for the equivalent annual investment cost of the equipment is as follows:

[0191] \(f\) am \(=f\) cr \((f\) wind.am \(S\) wind + \(f\) PV.am \(S\) PV + \(f\) ES1.am \(S\) ES.1 + \(f\) ES2.am \(S\) ES.2 ) (29)

[0192]

[0193] In formulas (29) - (30), \(f\) wind.am 、\(f\)PV.am , f ES1.am , f ES2.am are the initial investment costs per unit capacity of wind power, photovoltaic, battery, and supercapacitor respectively. S k is the rated capacity of the Kth component, f cr is the annual capital recovery factor, L f is the project planning service life, and r is the discount rate;

[0194] Step 5-3, the calculation formulas for the operation and maintenance costs of each component are as follows:

[0195] f bm = f wind.bm S wind + f PV.bm S PV + f ES1.bm S ES.1 + f ES2.bm S ES.2 (31),

[0196] In formula (31), f wind.bm , f PV.bm , f ES1.bm , f ES2.bm are the maintenance cost coefficients of the wind turbine generator set, photovoltaic power generation array, battery, and supercapacitor respectively.

[0197] Step 5-4, establish the constraint conditions that need to be satisfied for the configuration model with the minimum total cost of the microgrid, including power balance constraint, system and grid power exchange constraint, tie line utilization rate constraint, tie line power fluctuation constraint, and energy storage system state of charge constraint.

[0198] Step 5-4 includes the following sub-steps:

[0199] Step 5-4-1, the power balance constraint is as follows:

[0200] P J.D (t) = β ES1 P ES1 (t) + αP line (t) (32)

[0201] P J.H (t) = β ES2 P ES2 (t) (33),

[0202] In formulas (32)-(33), β is the introduced coefficient. Taking 1 means introducing the corresponding component in the model, and vice versa taking 0. α is the grid-connected and islanding coefficient, which is a 0-1 variable. When α = 1, the microgrid operates in grid-connected mode, and when α = 0, the microgrid operates in islanding mode;

[0203] Step 5-4-2, the power exchange constraint between the system and the power grid: The exchanged power P between the wind-solar-storage system of the microgrid and the power grid line shall meet the following requirements:

[0204] αP line.min ≤P line (t)≤αP line.max (34),

[0205] In formula (34), P line.min and P line.max are respectively the minimum and maximum powers allowed for the exchange between the microgrid and the main grid, and this value is determined according to the supply and demand agreement reached between the microgrid and the main grid;

[0206] Step 5-4-3, the constraint on the utilization rate of the tie line is as follows:

[0207] αU line ≥αU line.min (35)

[0208]

[0209] In formulas (35)-(36), U line.min is the lower limit of the utilization rate of the tie line, U line is the utilization rate of the tie line, P line.in is the power transmitted from the main grid to the microgrid, P line.out is the power fed back from the microgrid to the main grid, E line is the power transmitted under the rated power of the tie line, P line,0 (t) is the rated power of the tie line (a fixed value);

[0210] Step 5-4-4, the power fluctuation constraint of the tie line: The power standard deviation is used to represent the magnitude of the power fluctuation of the tie line. The smaller the value of the power standard deviation, the smaller the power fluctuation of the tie line. The formula is as follows:

[0211]

[0212] D sd ≤δ g (38),

[0213] In formulas (37)-(38), D sd is the power standard deviation, δ g is the maximum power change rate of the main grid (δ g is less than 10% of the installed capacity), is the average value of the tie line power;

[0214] Step 5-4-5, the state of charge constraint of the energy storage system is as follows:

[0215] SOC imin ≤SOC i (t)≤SOC imax (39),

[0216] In formula (39), SOC imin and SOC imax are respectively the upper and lower limit values of the SOC of the i-th energy storage system, and SOC i (t) is the SOC value of the energy storage system at stage t.

[0217] Step 5-5: According to the Fourier transform and inverse transform in Step 4, perform spectral analysis on the deficit power during the planning period, separate the low-frequency power and high-frequency power, determine the output of the hybrid energy storage system and the tie line, and transmit the results to Step 3. Repeat Steps 3-5. After obtaining the optimal solution of the wind and light capacity through particle swarm algorithm iteration, output the corresponding capacity and power configuration results. The update speed and update position of the particles in the particle swarm algorithm are as follows:

[0218]

[0219]

[0220] In formulas (40)-(41), i is the i-th particle, k is the number of algorithm iterations, c1 and c2 are learning factors, w is the inertia weight coefficient, r1 and r2 are random numbers between [0,1], v represents the update speed, x is the update position, and p g is the global historical optimal position, and p best is the individual historical optimal position.

[0221] In this embodiment, a method for configuring the double-layer capacity of a hybrid energy storage system in a microgrid considering the three states of wind and light of the present invention is used to configure a certain independent microgrid, specifically as follows:

[0222] Step 1: Select typical day data for the independent microgrid to be configured, establish a fan output model and a photovoltaic unit output model. The sampling time is 2 min, the total number of samples is N = 720, the cut-in wind speed of the fan is 3 m / s, the cut-out wind speed is 25 m / s, the rated wind speed is 15 m / s, the initial rated capacity of the fan is 100 kW, and the rated capacity of the photovoltaic is 50 kW.

[0223] Step 2: Use the Markov process to establish a three-state model for the fan and photovoltaic. The failure rate and repair rate values of the fan and photovoltaic units are: λ 12 = 5.84 times / year, λ 13 = 7.89 times / year, λ 23 = 10.84 times / year, μ 21 = 48.3 times / year, μ31 = 58.4 times / year, μ 32 = 48.3 times / year.

[0224] Step 3: Randomly select a wind turbine and a photovoltaic unit, calculate the deficit power, and sample and simulate the states and durations of the wind turbine and the photovoltaic unit according to the established three-state models of the wind turbine and the photovoltaic. Figure 3 It is a schematic diagram of the results of sampling and simulating the states and durations of the wind turbine and the photovoltaic unit according to the three-state models of the wind turbine and the photovoltaic in the embodiment of the present invention.

[0225] As Figure 3 shown, sampling and simulating the states and durations of the wind turbine and the photovoltaic unit according to the three-state models of the wind turbine and the photovoltaic can obtain the states and durations of the wind turbine and the photovoltaic unit, and then the output powers of the wind turbine and the photovoltaic unit can be correspondingly obtained according to the wind turbine output power model and the photovoltaic unit output power model.

[0226] Step 4: Perform Fourier transform and inverse transform on the deficit power. According to the transformed frequency spectrum diagram, obtain the breakpoint n = 256, and separate the high-frequency power as Figure 4 shown and the low-frequency power as Figure 5 shown. When the grid connection and disconnection coefficient α = 0, the microgrid operates in island mode, the low-frequency power is compensated by the battery, and the high-frequency power is all compensated by the supercapacitor.

[0227] Step 5: Establish a configuration model with the goal of minimizing the total cost of the microgrid. After determining the output of the hybrid energy storage system according to that the low-frequency power is compensated by the battery and the high-frequency power is all compensated by the supercapacitor, return the result to Step 3, and repeat Steps 3 - 5. After continuously iterating through the particle swarm algorithm to obtain the optimal solution of the wind and light capacity, output the corresponding capacity and power configuration results, as shown in Table 1:

[0228] Table 1: Configuration results without considering the tie line

[0229]

[0230]

[0231] In this embodiment, when the grid connection and disconnection coefficient α = 1 in Step 4, the microgrid operates in grid-connected mode, the utilization rate of the tie line is 52.622%, and the tie line power is as Figure 6 shown. At this time, the low-frequency power of the deficit power is compensated jointly by the battery and the tie line, and the high-frequency power is compensated by the supercapacitor. After determining the output of the hybrid energy storage system and the tie line, return the result to Step 3, and repeat Steps 3 - 5. After continuously iterating through the particle swarm algorithm to obtain the optimal solution of the wind and light capacity, output the corresponding capacity and power configuration results, as shown in Table 2:

[0232] Table 2: Configuration results considering tie lines

[0233]

[0234] In summary, the dual-layer capacity configuration method for hybrid energy storage in a microgrid considering the three states of wind and light in this embodiment can be applied to both the islanding and grid-connected scenarios of the microgrid, and can optimize the configuration of the hybrid energy storage system while considering the multi-state operation of wind power output and photovoltaic power output.

[0235] Functions and effects of the embodiment

[0236] According to the dual-layer capacity configuration method for hybrid energy storage in a microgrid considering the three states of wind and light involved in this embodiment, by establishing a three-state model of the fan and photovoltaic, and using the sequential Monte Carlo method to randomly sample the output power of the fan and photovoltaic units in different states, the output power of the fan and photovoltaic units can be obtained more accurately; moreover, in this embodiment, by dividing the deficit power into low-frequency power and high-frequency power, and compensating the low-frequency power and high-frequency power correspondingly through a hybrid energy storage system composed of a battery and a supercapacitor and a tie line, the optimization configuration of the hybrid energy storage can be carried out simultaneously while considering the multi-state operation of wind power output and photovoltaic power output; in addition, in this embodiment, by setting the introduction coefficient and the grid-connected and islanding coefficient, the selection and combination of whether to introduce a battery or a supercapacitor and the grid-connected and islanding of the microgrid can be flexibly carried out, which is very user-friendly and can be applied to both the islanding and grid-connected scenarios of the microgrid.

[0237] The above embodiments are preferred cases of the present invention and are not used to limit the protection scope of the present invention.

Claims

1. A two - layer capacity configuration method for hybrid energy storage in a micro - grid considering the three - state of wind and light, which is used to configure the capacity and power of wind turbines, photovoltaic units and hybrid energy storage systems in a micro - grid in grid - connected or off - grid states. It is characterized in that, It includes the following steps: Step 1: Screen the microgrid data of the area to be configured, select a typical day, and establish a wind turbine output model and a photovoltaic unit output model; Step 2: Use the Markov process to establish a three-state model for the wind turbine and the photovoltaic, and the three states include the normal operation state, the derating state, and the fault outage state; Step 3: Randomly select a set of initial values of the wind and light capacity within the upper and lower limits of the wind and light capacity, calculate the deficit power, and use the sequential Monte Carlo method to randomly sample the output power of the wind turbine and the photovoltaic unit in different states; Step 4: Perform Fourier transform and inverse transform on the deficit power, separate the low-frequency power and the high-frequency power according to the transformed spectrogram, and compensate the low-frequency power and the high-frequency power respectively according to the characteristics of the battery and the supercapacitor in the hybrid energy storage system and according to whether the microgrid is connected to the main grid through a tie line; Step 5: Establish a configuration model with the minimum total cost of the microgrid as the goal, perform spectral analysis on the deficit power within the planning period according to the Fourier transform and inverse transform in Step 4, separate the low-frequency power and the high-frequency power, determine the output of the hybrid energy storage system and the tie line, and transmit the results to Step 3. Repeat Steps 3 - 5. After obtaining the optimal solution of the wind and light capacity through particle swarm algorithm iteration, output the corresponding capacity and power configuration results, Among them, Step 1 includes the following sub-steps: Step 1-1: Calculate the output of the wind turbine according to the wind speed data of the obtained typical day, and establish the wind turbine output model as follows: Step 1-2: Calculate the output of the photovoltaic unit according to the obtained illumination and ambient temperature data of the typical day, and establish the photovoltaic unit output model as follows: In formula (1), v out is the cut-out wind speed, v in is the cut-in wind speed, v r is the rated wind speed, P r.wind is the rated power of the wind turbine. In formula (2), P SC is the rated output power of the photovoltaic array under standard conditions, G SC is the solar irradiance under standard conditions, G C is the actual solar irradiance at the operating point, k is the power temperature coefficient, T c (t) is the temperature at the operating point at time t, T SC is the temperature under standard conditions, N PV is the number of photovoltaic array units. Step 2 includes the following sub-steps: Step 2-1: Solve the probabilities of the normal operation state, the derating state, and the fault outage state, and use the Markov principle to obtain the state transition matrix as: Further solve to obtain: Step 2-2: Use the Monte Carlo method for simulation sampling. The continuous operation time of the three states of the wind turbine or the photovoltaic unit is simulated by the mean time to failure MTTF and the mean repair time MTTR, and the calculation formula is: In Formula (3) and Formula (4), λ is the failure rate, μ is the repair rate, and P1, P2, and P3 are the probabilities that the wind turbine or the photovoltaic unit is in the normal operation state, the derating state, and the fault state respectively, In Formula (5) and Formula (6), t1 and t2 are the continuous operation time of the operation state and the outage fault repair time respectively, and x1 and x2 are random numbers uniformly distributed within the interval [0,1], Step 5 includes the following sub-steps: Step 5-1: When establishing the configuration model, the total cost of the microgrid includes the equivalent annual value investment cost of the equipment and the operation and maintenance costs of each component. The formula is as follows: minF m = min(f am + f bm ) (28), In formula (28), f am is the equivalent annual investment cost of the device, and f bm is the operation and maintenance cost of each component; Step 5-2: The calculation formula of the equivalent annual value investment cost of the equipment is as follows: f am = f cr (f wind.am S wind + f PV.am S PV + f ES1.am S ES.1 + f ES2.am S ES.2 )(29) In Formula (29) - Formula (30), f wind.am , f PV.am , f ES1.am , f ES2.am are respectively the initial investment costs per unit capacity of wind power, photovoltaic, storage battery and supercapacitor, S k is the rated capacity of the Kth component, f cr is the annual capital recovery factor, L f is the project planning service life, and r is the discount rate; Step 5-3: The calculation formula of the operation and maintenance costs of each component is as follows: f bm = f wind.bm S wind + f PV.bm S PV + f ES1.bm S ES.1 + f ES2.bm S ES.2 (31), In formula (31), f wind.bm , f PV.bm , f ES1.bm , f ES2.bm are the maintenance cost coefficients of the wind turbine generator set, the photovoltaic power generation array, the storage battery, and the supercapacitor, respectively; Step 5-4: Establish the constraint conditions that need to be satisfied for the configuration model with the minimum total cost of the microgrid as the objective, including power balance constraint, system and grid power exchange constraint, tie-line utilization rate constraint, tie-line power fluctuation constraint, and energy storage system state of charge constraint; Step 5-5: According to the Fourier transform and inverse transform in Step 4, perform spectral analysis on the deficit power within the planning period, separate the low-frequency power and the high-frequency power, determine the output of the hybrid energy storage system and the tie-line, and transmit the results to Step 3. Repeat Steps 3-5. After obtaining the optimal solution of the wind-solar capacity through particle swarm algorithm iteration, output the corresponding capacity and power configuration results. The update speed and update position of the particles in the particle swarm algorithm are as follows: In formulas (32)-(33), i is the i-th particle, k is the number of algorithm iterations, c1 and c2 are learning factors, w is the inertia weight coefficient, r1 and r2 are random numbers between [0, 1], v represents the update speed, x is the updated position, p g is the globally historically optimal position, p best is the historically optimal position of the individual.

2. The method for configuring the double-layer capacity of the hybrid energy storage of the microgrid considering the three states of wind and light according to claim 1, wherein: Among them, Step 3 includes the following sub-steps: Step 3-1: Set the construction site area as S, the length as L, and the width as W. Then, the wind turbines and photovoltaic units in the microgrid satisfy the following conditions: Step 3-2: The output powers of the wind turbines and photovoltaic units in the three states are: i ∈ [1, i max , j ∈ [1, j max (10), In Formula (8) - Formula (9), represents the state of the fan and the photovoltaic unit at time t, which is obtained through sequential Monte Carlo sampling. The calculation formula is as follows: Step 3-3: Obtain the deficit power P from the power difference generated by wind power generation, photovoltaic power generation, and load power consumption in the microgrid J , and the calculation formula is as follows: In formula (7), d is the diameter of the fan rotor, and S2, [] are respectively the floor area of a single photovoltaic array, the shading coefficient, and the rounding function, In Formulas (8) - (10), i max is the maximum number of wind turbines, j max is the maximum number of photovoltaic units, is the power generated by i wind turbines at time t, is the power generated by j photovoltaic units at time t, indicates whether the i-th wind turbine is introduced at time t, indicates whether the j-th photovoltaic unit is introduced. In formula (12), P L (t) is the load power at time t, and P G (t) is the power generated by the wind turbine and the photovoltaic unit at time t.

3. The method for configuring the double-layer capacity of the hybrid energy storage of the microgrid considering the three states of wind and light according to claim 1, wherein: Among them, Step 4 includes the following sub-steps: Step 4-1: The discrete Fourier transform formula is: Step 4-2: Substitute the deficit power into Formula (13) - Formula (14) to calculate the amplitude-frequency sequence P J (k), where the amplitude-frequency sequence P J (k) is symmetric about the frequency f k = f s / 2, and is expressed as: Cut off the formula (15) at k = n, where n is the break point. Among them, [0, n] is the low-frequency part, and [n + 1, N / 2] is the high-frequency part. Separate the low-frequency and high-frequency parts to obtain the following formula: P J.H (k) = {0, L, 0, P J (N - 1), L, P J (N - n - 1), 0, L 0} (17), In Formulas (16) and (17), P J.D (k) and P J.H (k) are respectively the low-frequency component and the high-frequency component of the deficit power. Substituting Formulas (16) and (17) into Formula (14) respectively, the low-frequency power and the high-frequency power of the deficit power are obtained as follows: Step 4-3: Compensate the low-frequency power and the high-frequency power correspondingly through the hybrid energy storage system and the tie-line. P J.D P(t) = β ES1 P ES1 P(t) + αP(t) (20) line ​ P J.H P(t) = β ES2 P ES2 P(t) (21) P J P(t) = β ES1 P ES1 P(t) + β ES2 P ES2 P(t) + αP line P(t) (22), In formulas (20) - (22), P ES1 (t) is the power compensated by the storage battery, P ES2 (t) is the power compensated by the supercapacitor, β ES1 is whether to introduce the storage battery, β ES2 is whether to introduce the supercapacitor, α is the grid connection / disconnection coefficient, taking 1 represents grid connection, and taking 0 represents off-grid; When the grid connection and islanding coefficient α = 0, the microgrid operates in island mode. The low-frequency power is compensated by the battery, and the high-frequency power is compensated by the supercapacitor. When the grid connection and islanding coefficient α = 1, the microgrid operates in grid-connected mode. The low-frequency power is compensated by the battery and the tie-line, and the high-frequency power is compensated by the supercapacitor. Step 4-4: The rated power of the hybrid energy storage system is the maximum value of the absolute value of the actual charge and discharge power of the energy storage. The formula is as follows: S ES1 / u1≥max{|P ES1 (t)|} (23) S ES2 / u2 ≥ max{|P J.H (t)|} (24); Step 4-5: The formula for the initial energy change of the energy storage is as follows: Step 4-6: The formula for the rated capacity of the energy storage is as follows: E0 = 0.5S ES (27), In formulas (13)-(14), P(k) and p(n) are the principal value sequences of the frequency-domain signal and the time-domain signal respectively, and k is the sequence number of different frequency bands. In Formula (23) - Formula (24), S ES is the rated capacity of energy storage, u1 is the ratio of the rated capacity to the rated power of the battery, and u2 is the ratio of the rated capacity to the rated power of the supercapacitor. In formula (25), E(t) is the energy change of the energy storage relative to the original state at the t-th sampling point, with the unit of kw·h, and T0 represents the sampling period, with the unit of s. In Formula (26) - Formula (27), S ES is the rated capacity of the energy storage, and E0 is the initial energy of the energy storage. The initial energy of the energy storage is set to 0.5 times the rated capacity of the energy storage.

4. The method for configuring the double-layer capacity of the hybrid energy storage of the microgrid considering the three states of wind and light according to claim 1, wherein: Among them, Step 5-4 includes the following sub-steps: Step 5-4-1: The power balance constraint is as follows: P J.D P(t) = β ES1 P ES1 P(t) + αP(t) (34) line (t) (34) P J.H P(t) = β ES2 P ES2 P(t) (35), In Formula (34) - Formula (35), β is the introduction coefficient. Taking 1 means that the corresponding component is introduced into the model, and vice versa taking 0. α is the grid-connected and islanding coefficient, which is a variable between 0 and 1. When α = 1, the microgrid operates in grid-connected mode, and when α = 0, the microgrid operates in islanding mode; Step 5-4-2, the power exchange constraint between the system and the power grid is the exchange power P between the wind-solar-storage system of the microgrid and the power grid line which needs to meet the following requirements: αP line.min ≤P line (t)≤αP line .max (36), In formula (36), P line.min and P line.max are respectively the minimum power and the maximum power allowed to be exchanged between the microgrid and the main grid, and this value is determined according to the supply and demand agreement reached between the microgrid and the main grid; Step 5-4-3, the utilization rate constraint of the tie line is as follows: αU line ≥αU line.min (37) In Formula (37) - Formula (38), U line.min is the lower limit of the utilization rate of the tie line, and U line is the utilization rate of the tie line. P line.in is the power transmitted from the main power grid to the microgrid, and P line.out is the power fed back from the microgrid to the main power grid. E line is the amount of electricity transmitted under the rated power of the tie line, and P line,0 (t) is the rated power of the tie line; Step 5-4-4, the power fluctuation constraint of the tie line uses the power standard deviation to represent the magnitude of the tie line power fluctuation. The smaller the value of the power standard deviation, the smaller the power fluctuation of the tie line. The formula is as follows: D sd ≤δ g (40), In Formula (39) - Formula (40), D sd is the standard deviation of power, and δ g is the maximum power change rate of the main power grid, is the average value of the tie-line power; Step 5-4-5, the state of charge constraint of the energy storage system is as follows: SOC imin ≤ SOC i (t) ≤ SOC imax (41), In formula (41), SOC imin and SOC imax are respectively the upper and lower limit values of the SOC of the i-th energy storage system, and SOC i (t) is the SOC value of the energy storage system at stage t.

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