Method for configuring energy storage capacity of wind farm considering carbon benefit and auxiliary frequency modulation

Abstract

The wind farm energy storage capacity configuration method considering carbon benefits and auxiliary frequency modulation comprises the following steps: firstly, a double-layer planning model of energy storage capacity based on model algorithm control is constructed. The upper layer model takes the minimum output of energy storage and charge-discharge balance as the target, and adopts MAC algorithm to solve the output sequence of energy storage for smoothing wind power fluctuation. Then, a multi-scenario coordinated energy storage operation strategy based on SOC is formulated according to the smoothing sequence solved by the upper layer. The lower layer model takes the maximum comprehensive benefit of energy storage as the target, introduces a carbon trading mechanism, takes the energy storage operation strategy as the constraint condition, and adopts Harris eagle intelligent algorithm to solve the optimal energy storage capacity. The wind farm energy storage capacity configuration method considering carbon benefits and auxiliary frequency modulation is proposed. Compared with the traditional energy storage capacity configuration method, the method can not only effectively smooth wind power fluctuation, improve the wind farm grid connection level and improve the flexibility of the power grid, but also optimize the energy storage cost and prolong the service life of the energy storage.

Description

Technical Field

[0001] This invention relates to the field of energy storage optimization configuration technology, specifically to a wind farm energy storage capacity configuration method that considers carbon efficiency and auxiliary frequency regulation. Background Technology

[0002] With the advancement of my country's sustainable development strategy for energy and electricity, by the end of 2022, my country's cumulative installed wind power capacity had reached 395.6 GW, accounting for 39.1% of the global total. my country's wind farms generally operate in maximum wind capture mode, and their volatility and spatiotemporal uncertainties can impact the safe and stable operation of the power grid. Energy storage systems (ESS), as a highly dispatchable technology, can significantly smooth wind power output, effectively reduce wind curtailment, and improve the reliability of large-scale wind power grid connection.

[0003] Domestic and international research on energy storage configurations largely focuses on economic benefits, comprehensively considering the technical and economic indicators of energy storage across different time scales and in single or multiple application scenarios. However, research on the auxiliary frequency regulation benefits and carbon emission benefits of energy storage systems is relatively limited. Currently, research on carbon emissions from energy storage only involves the calculation of direct carbon emissions from energy storage, with less discussion of its potential carbon benefits in optimizing renewable energy utilization and improving grid flexibility.

[0004] Regarding wind power storage (ESS) operation and control strategies, model prediction algorithms, filtering algorithms, and other control algorithms are commonly used to mitigate wind power fluctuations. Current research largely employs single mitigation methods to achieve wind power fluctuation mitigation, without embedding novel control algorithms into existing methods. Much research focuses on ESS applications in single scenarios, making it difficult to adapt to the integrated application of ESS in multiple scenarios such as wind power fluctuation mitigation and frequency regulation in the new context. This results in ESS being idle for certain periods and capacities, failing to fully realize its potential value and causing economic losses.

[0005] Furthermore, the decision variables for energy storage optimization are often continuous variables, pursuing single or multiple objectives. Constraints typically include linear, nonlinear, equality, and inequality constraints, resulting in multi-objective, nonlinear mathematical models. Conventional optimization algorithms are computationally complex, and their computational speed and convergence are insufficient. The Harris Eagle algorithm, proposed in 2019, is a novel swarm intelligence optimization algorithm that exhibits good convergence and robustness in solving highly complex problems, attracting considerable attention from scholars. However, its application in the field of energy storage capacity allocation is currently limited. Summary of the Invention

[0006] To address the challenge that energy storage is ill-suited to the engineering requirements of ESS (Energy Storage System) applications in various scenarios, such as smoothing wind power fluctuations and assisting frequency regulation, under the new circumstances, this invention provides a wind farm energy storage capacity configuration method that considers carbon benefits and assisting frequency regulation. This method can improve the profitability of energy storage entities and more accurately reflect the value of configuring energy storage.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for configuring wind farm energy storage capacity considering carbon efficiency and auxiliary frequency regulation includes the following steps:

[0009] Step 1: Establish a two-layer optimization model for energy storage system capacity configuration. The upper-layer model is a mathematical model that takes into account the minimum output of energy storage and the balance between charging and discharging. The MAC algorithm is used to solve the output sequence of energy storage to smooth wind power fluctuations, providing a reference range for the actual smooth output of energy storage.

[0010] Step 2: Use the uncertainty of the frequency modulation signal to approximate the uncertainty of the frequency modulation demand, and use stochastic differential equations to model the frequency modulation signal;

[0011] Step 3: Based on the energy storage smoothing sequence obtained from the upper-level model in Step 1, formulate a multi-scenario collaborative energy storage operation strategy based on SOC;

[0012] Step 4: Introduce a carbon trading mechanism into the lower-level model to construct an energy storage comprehensive benefit model, an energy storage equivalent cycle life assessment model, and an energy storage full life cycle cost model;

[0013] Step 5: Establish constraints on energy storage capacity and power.

[0014] Step 6: With the goal of maximizing the overall benefits of energy storage, the energy storage operation strategy based on SOC multi-scenario coordination in Step 3 is embedded as a constraint into the Harris Eagle algorithm to solve for the optimal energy storage capacity.

[0015] In step 1, the mathematical model that takes into account the minimum energy storage output and the charge-discharge balance is as follows:

[0016] P g (k+1)=P w (k)+P b (k)(1);

[0017]

[0018] In the formula: P g (k+1) represents the grid-connected power of the wind farm at time k+1; P w (k) represents the actual output power of the wind farm at time k; P b(k) represents the energy storage charge / discharge power; SOC(k) represents the energy storage SOC state at time k; SOC(k+1) represents the energy storage SOC state at time k+1; T, E es These are the energy storage control cycle and the rated capacity, respectively.

[0019] The current output of an energy storage system influences its future output capacity, and different changes in the state of energy (SOC) of the battery determine its future charging and discharging capabilities. This invention introduces changes in the SOC of the energy storage system into the objective function, causing the SOC to tend towards the region of maximum charging and discharging capacity. This ensures that the energy storage battery has the greatest adaptability to future wind power changes, reducing the possibility of adverse effects on the power grid caused by uncertainties in wind power.

[0020] Based on equations (1) and (2), under the premise of ensuring that wind power fluctuations meet grid connection requirements, the objective function of MAC rolling optimization is to minimize energy storage output and balance energy storage charging and discharging:

[0021]

[0022] In the formula: P b (k+i) represents the energy output at time k+i; SOC(k+i) represents the energy storage SOC state at time k+i, where i represents the i-th time; M is the prediction time scale, i.e. the length of the control command sequence.

[0023] Under the MAC rolling optimization constraint, considering its upper and lower limits for charging and discharging, as well as the grid connection fluctuation requirements of wind farms, the constraint conditions are as follows:

[0024] -P max ≤P b (k+i)≤P max (4);

[0025] SOC min ≤SOC(k+i)≤SOC max (5);

[0026]

[0027] In the formula: P max The maximum allowable charge / discharge power of the energy storage system; SOC min SOC max These are the upper and lower limits of the SOC of the energy storage system; P rate δ represents the installed capacity of the wind farm; δ represents the grid connection volatility limit of the wind farm; P g (k+i+1) represents the grid-connected power of the k+i+1 wind farm.

[0028] According to state-space theory, assume that state variables x1 and x2 represent the grid-connected wind power P. gWith the energy storage SOC state, the control input u is the energy storage output P. b Actual power P of wind farm w As a disturbance quantity r, the state-space equation of the wind farm system including energy storage is:

[0029]

[0030] In the formula, x1(k+1) represents the state variable, the grid-connected wind power P. g The predicted output at time k+1; x2(k+1) represents the predicted output of the state variable energy storage SOC at time k+1; x1(k) represents the state variable wind power grid-connected power P. g The actual output at time k; x2(k) represents the state variable of the energy storage SOC at time k. u(k) represents the control input at time k; r(k) represents the disturbance input.

[0031] make

[0032] In the energy storage model algorithm control that balances charge and discharge and minimizes energy storage output at time k, the objective function (3) and constraints (4) to (6) can be transformed into the standard form of a quadratic programming problem through numerical calculation:

[0033]

[0034]

[0035]

[0036] In the formula: z=[u(k),x T (k+1),u(k+1),…,u(k+M-1),x T (k+M)] T , where x T (k+1),x T (k+M) represent the transposes of the system state matrix at time k+1 and k+M, respectively; u(k+1) and u(k+M-1) represent the values ​​of the control input at time k+1 and k+M-1, respectively; z T H represents the transpose of matrix z; H represents the quadratic objective term, a matrix composed of the quadratic weights R and Q of the energy storage control sequence and the output level, where R = 2.

[0037] According to formulas (3) to (7), we can obtain:

[0038] B es =[-P max ,P max ,-δ,δ,-SOC min SOCmax ] T ;

[0039] B eq =[-P max ,P max SOC min SOC max ] T

[0040]

[0041] In the formula, A represents the parameter matrix of the state variables in the system state-space equation; B represents the parameter matrix of the control input in the system state-space equation; Ax T (k), Cr(k), and Cr(k+M-1) represent the system's state variables, disturbances, and control inputs from the initial time k to the predicted time k+M. The system state at time k+M is predicted from the control inputs and disturbances at time k+M-1. es A ep B es B eq The matrix form of constraint equations (4) to (6) is represented; M represents the prediction time length.

[0042] Using the quadratic programming method in MATLAB, Equation (8) is optimized and solved in each control cycle. The first value of the optimized sequence obtained in each cycle is taken as the current energy storage output control command. Then, the control command sequence for smoothing wind power fluctuations in energy storage during the day is obtained, [u(k),u(k+1),…,u(k+M-1)]. T .

[0043] In step 2, the uncertainty of frequency modulation (FM) demand is approximated by the uncertainty of the FM signal, and the FM signal is modeled using stochastic differential equations (SDEs).

[0044] SDEs are differential equations typically driven by Brownian motion, which originated in the financial field and is often used to describe phenomena such as continuous stochastic processes like stock price and exchange rate fluctuations. It is now being gradually extended to research on high-proportion renewable energy power systems.

[0045] AGC signal ξ t Modeled as a stochastic differential equation (SDE):

[0046] dξ t =μ(ξ t )dt+σ(ξ t )dW t (9);

[0047] In the formula: ξ t W represents the random variable that needs to be described. t This is a Wiener process, i.e., standard Brownian motion; μ(ξ) t ) represents the drift coefficient, indicating the random variable ξ. t The average rate of change per unit time; σ(ξ) t ) is the scaling factor, representing W t The randomness of ξ t Degree of influence; SDE solution ξ t Known as the Ito process ( StochasticProcess.

[0048] Determine μ(ξ) t ), σ(ξ) t These two coefficients are crucial for constructing the SDE model. The Fokker-Planck equation is used to model the stochastic process ξ defined in the SDE. t The evolution probability density p(ξ) t The characterization is represented by the formula:

[0049]

[0050] In a stationary state, the probability density does not change over time. At this point, σ(ξ) is obtained through two integrations. t ) and μ(ξ t The relationship is:

[0051]

[0052] The autocorrelation function is used to represent the time correlation of random variables, and is defined as:

[0053]

[0054] When R(τ) exhibits exponential decay, the autocorrelation function expression satisfies the following equation:

[0055] R(τ)=e -λτ R(0) (13);

[0056] In the formula, R(0) represents the value of the autocorrelation function when τ=0.

[0057] The drift coefficients of the stochastic differential equation SDE can be expressed as:

[0058] μ(ξ t )=-λ(ξ t -c) (14);

[0059] In the formula: λ represents the time constant of exponential decay, and λ is taken as 0.0107; c is a constant, generally taken as ξ. t The mean of RegD is approximately 0, i.e., μ(ξ) t )=-λξ t ;λ(ξ t -c) represents the formula for calculating the drift term.

[0060] Once the probability density function is known, by appropriately choosing μ(ξ) t ) and σ(ξ t ), capable of constructing ξ t The SDE model.

[0061] Numerical simulation of stochastic differential equation (SDE) models employs stochastic numerical integration methods, such as the Euler-Maryuama algorithm, to calculate the random variable ξ. t Complete time series:

[0062] ξ t+h =ξ t +hμ(ξ t )+σ(ξ t )ζ (15);

[0063] In the formula: h is the sampling step size of the sequence, and ζ~N(0,h) represents a normal distribution with variance h.

[0064] Step 3 includes the following steps:

[0065] 1) Based on the MAC rolling solution results of the upper-level model, obtain the control sequence and first determine the energy storage stabilization period and stabilization domain.

[0066] 2) Taking into account the rechargeable and dischargeable capacity of energy storage, the declared frequency regulation power is calculated and determined as the frequency regulation range;

[0067] First, calculate the current chargeable or dischargeable power P. be Take its rated power P rate The smaller of the two values ​​is used as the declared power. When declaring an upward adjustment to the power at time t, the current chargeable power of the energy storage is determined by the upper limit of the energy storage SOC and the remaining capacity of the energy storage at the previous time. When declaring a downward adjustment to the power at time t, the current dischargeable power of the energy storage is determined by the lower limit of the energy storage SOC and the remaining capacity of the energy storage at the previous time. The expression for the chargeable and dischargeable power at time t is:

[0068]

[0069] In the formula: E bt' (t-△t) represents the remaining capacity of the energy storage device at the previous moment; P be (t) represents the current chargeable or dischargeable power of the stored energy at time t; Erate Indicates the rated capacity of energy storage; S max S min These represent the upper and lower limits of the energy storage state of charge, respectively; Δt represents the time interval.

[0070] The expression for the frequency modulation power declared at time t is:

[0071]

[0072] 3) Calculate the current SOC state:

[0073] When 0.4≤SOC≤0.6, it is the optimal working state of energy storage. When energy storage is in the optimal working state, the control objective of ESS is to track the wind power fluctuation smoothing sequence command U while participating in ancillary services to provide bidirectional frequency regulation services.

[0074] When 0.1≤SOC≤0.4, it is in the priority charging state. In this state, the control objective of ESS is to prioritize tracking the smoothing command U (i.e., U>0) that requires energy storage charging while providing down-frequency regulation services to the ancillary service market. When the smoothing command and the frequency regulation command are both discharge commands, the one with the smaller power will be used.

[0075] When 0.6≤SOC≤0.9, it is a priority discharge state. In this state, the control objective is to prioritize tracking the smoothing command U (i.e., U<0) that requires energy storage discharge while providing up-frequency modulation services to the auxiliary market. When the smoothing command and the frequency modulation command are both charging, the one with the smaller power is selected for operation.

[0076] When SOC < 0.1, it is in over-discharge protection state; in this state, ESS only charges until SOC increases to 0.2 to restore priority charging state.

[0077] When SOC > 0.9, it is in an overcharged state; in this state, the energy storage system only discharges until the SOC drops to 0.8 to resume the priority discharge state.

[0078] In step 4

[0079] The objective function of the lower-level model, representing the comprehensive benefit model of energy storage, is shown in the following equation:

[0080] J = max(I e-sell +I r-sell +I c-sell -C LCC (18);

[0081] In the formula: I e-sell Revenue generated from electricity used for internet access; I r-sell To supplement FM revenue; I c-sell For carbon emission benefits; CLCC This refers to the total lifecycle cost of energy storage.

[0082] To standardize benefit calculations, the present value method is used to convert the costs and benefits of equipment at different times into the average present value for each year. Assuming a total study period of n years and a discount rate of r, a capital discount factor i is introduced. LF :

[0083]

[0084] In step 4, the energy storage benefit model is as follows:

[0085] 1) Revenue from increased electricity generation e-sell for:

[0086]

[0087] In the formula: c e-sell The on-grid electricity price per unit for wind farms; The formula for calculating the average annual increase in power generation at a wind farm after energy storage is configured is as follows:

[0088]

[0089] In the formula: N is the total number of sampling points; The entire life cycle is measured in years; P b (t) represents the power of energy storage output that smooths out fluctuations.

[0090] 2) Benefits of energy storage participating in frequency regulation I r-sell :

[0091] The benefits of energy storage participating in the frequency regulation auxiliary market include both capacity compensation and mileage compensation.

[0092]

[0093] In the formula: t represents the capacity and mileage price for time period t; m represents the average mileage. To report the power involved in frequency modulation.

[0094] 3) Carbon emission benefits I c-sell :

[0095] Carbon emission benefits are categorized into positive carbon benefits and negative carbon benefits.

[0096]

[0097] In the formula: c c-sell This refers to the unit price for carbon trading.

[0098] Energy storage has positive carbon benefits for:

[0099]

[0100] After wind farms are equipped with energy storage devices, the fluctuations in wind power output can be smoothed to achieve grid connection rate, increase the amount of electricity generated and connected to the grid, reduce wind curtailment, and thus increase the amount of carbon emission credits that can be sold.

[0101]

[0102] In the formula: γ ess The carbon emission allowance per unit of electricity is taken as 0.57 t / MWh; This is to increase the average annual wind power grid connection volume for energy storage.

[0103] This invention introduces Carbon emission factors and k of thermal power units tp The conversion factor (generally between 0.8 and 1) used to convert frequency regulation power to thermal power unit output is used to calculate the carbon efficiency of auxiliary frequency regulation. The value is taken from the average value of the marginal emission factor of electricity in six major regions of my country in 2019, which is 0.8953 t / (MW·h). When energy storage systems participate in the frequency regulation market, the charging and discharging power in actual operation changes continuously in response to the frequency regulation signal.

[0104]

[0105] Energy storage devices consume electricity and fuel and generate carbon emissions during production, transportation and operation.

[0106] CO2 emissions during production The calculation expression is as follows:

[0107]

[0108] In the formula: k sc The carbon emission coefficient per unit power produced by energy storage equipment is 0.1-0.2 tons / MWh; P rate This refers to the rated power of the energy storage device.

[0109] CO2 emissions during transmission The calculation expression is as follows:

[0110]

[0111] In the formula: k ys S represents the carbon emission factor for transmission; S represents the transmission distance; and H represents the transmission weight.

[0112] CO2 emissions during operation and maintenance phase Generally, 3% of emissions during the production phase is taken. Therefore, negative carbon benefits... for:

[0113]

[0114] In step 4, the energy storage equivalent cycle life assessment model is as follows:

[0115] The cycle life of an energy storage system is affected by various factors, the main ones being the number of charge-discharge cycles and the depth of discharge (DOD). This invention characterizes the cycle life of energy storage using a fourth-order function, namely:

[0116]

[0117] In the formula: D OD N(D) represents the depth of energy storage discharge; OD (i) represents the discharge depth D OD (i) is the cycle life when the discharge depth is 1, and the value is 0 to 1; N(1) is the cycle life when the discharge depth is 1; This formula (30) is cited in the literature: Han Xiaojuan, Cheng Cheng, Ji Tianming, et al. Capacity optimization model of hybrid energy storage system considering battery life [J]. Proceedings of the CSEE, 2013, 33(34): 91-97, 16.

[0118] The equivalent total cycle life y over the entire working cycle is equal to the sum of the equivalent cycle lives of individual cycles, i.e.

[0119]

[0120] In the formula: n is the total number of energy storage working cycles.

[0121] In step 4, the energy storage life-cycle cost model C LCC for:

[0122] C LCC =(C inv +C o&m )×i LF +C res (32);

[0123] 1) Initial investment cost:

[0124] The initial investment cost is directly proportional to the rated power and rated capacity of the energy storage equipment, as calculated using the following formula:

[0125] C inv =(C pinv P rate +C einv E rate (33);

[0126] In the formula: C pinv Cost per unit power; C einvCost per unit capacity; P rate Rated power for energy storage charging and discharging; E rate This refers to the rated capacity of the energy storage.

[0127] 2) Replacement cost:

[0128] When energy storage reaches the end of its lifespan, it needs to be disposed of in a harmless manner and recycled. The revenue obtained from recycling can be used as a subsidy to replace it. The calculation formula is as follows:

[0129]

[0130] In the formula: x is the number of replacements; σ res The residual value rate is 5% in this invention; y is the equivalent total cycle life of energy storage, which is determined by equations (27) to (28).

[0131] 3) Operation and maintenance costs:

[0132] Operation and maintenance costs refer to the funds invested to ensure the normal operation of energy storage throughout its entire lifespan.

[0133] C o&m =c o&m E rate (35);

[0134] In the formula: c o&m Maintenance cost per unit capacity.

[0135] In step 5, the constraints on energy storage power and energy quantity are as follows:

[0136] ①: The actual charging and discharging power of the energy storage system should not exceed the rated power of the ESS, as shown in the following formula:

[0137] P(t)=P b (t)+P r (t) (36);

[0138] -P max ≤P≤P max (37);

[0139] In the formula: P(t) is the total output power of the energy storage system at time t; P b (t) represents the wind power output suppressed by energy storage at time t; P r (t) represents the power of the stored energy participating in auxiliary frequency regulation service at time t.

[0140] The energy storage system at time t has a power constraint for smoothing fluctuations in charge and discharge.

[0141]

[0142] In the formula: P bu(t) represents the charging and discharging power of the energy storage device at time t; u(t) represents the charging and discharging domain of the battery obtained by MAC at time t; η bc η bd These refer to the charging and discharging efficiency of the battery, respectively.

[0143] The power constraint for the energy storage system participating in auxiliary frequency regulation charging and discharging at time t is:

[0144]

[0145] In the formula: ξ t + ξ t - The frequency modulation signals generated for the established SDE model represent the frequency adjustment command at time t and the frequency adjustment command at time t, respectively.

[0146] ②: Power Constraint:

[0147] The rated capacity constraint of the battery is:

[0148]

[0149]

[0150] In the formula: E bs E represents the maximum remaining capacity of the energy storage device during the dispatch cycle. b0 η represents the initial capacity of the energy storage device. bc η bd These represent the charging and discharging efficiencies of the energy storage device, respectively; P b (t) represents the output power of energy storage at time t to mitigate wind power fluctuations; P r (t) represents the output power of the energy storage participating in the auxiliary frequency regulation service at time t; k represents the initial time.

[0151] The multi-scenario coordinated operation strategy based on SOC proposed in this invention already limits the SOC state of ESS to a certain extent. Therefore, only basic check constraints are added here to ensure that the SOC is within the specified upper and lower limits. The SOC constraints are:

[0152] S min ≤S(t)≤S max (42);

[0153] In the formula: S(t) is the SOC value of the energy storage device at time t; S max S minThese represent the upper and lower limits of the energy storage state of charge, respectively. In step 6, the HHO optimization algorithm is a swarm intelligence optimization algorithm that simulates the cooperative predation behavior of the Harris Eagle, comprising three stages: global search, conversion between global search and development, and development. This invention embeds the multi-scenario collaborative energy storage operation strategy based on SOC, formulated at the upper level of the energy storage bi-layer planning model, into the HHO algorithm to solve the lower-level objective function, improving the matching between the control strategy and the configuration method.

[0154] The Harris Eagle algorithm for finding the optimal energy storage capacity consists of three stages: global search, transformation between global search and development, and development. The three stages are as follows:

[0155] 1) Global search phase:

[0156] Harris eagles randomly perch in a location and employ two strategies to find prey:

[0157]

[0158] In the formula, X(t) and X(t+1) are the positions of the Harris Eagle individual in the current and next iterations, respectively, and t is the iteration number; X rand (t) represents the location randomly chosen by an individual Harris Eagle; X rabbit (t) represents the location of the prey; r1, r2, r3, r4, q are random numbers between 0 and 1; q is used to select the random strategy to be adopted; X m (t) represents the average position of an individual Harris Hawk, expressed as:

[0159]

[0160] In the formula, X k (t) represents the position of the k-th individual in the Harris Eagle population, and M represents the population size.

[0161] Global Search and Development Transformation

[0162] The Harris Eagle algorithm defines the escape energy as: based on the prey's escape energy transitioning between search and different exploitation behaviors.

[0163]

[0164] In the formula, E0 is the initial energy of the prey, which is a random number between [-1,1] and is automatically updated in each iteration. t is the number of iterations and T is the maximum number of iterations. When |E|≥1, the search phase is entered and when |E|<1, the development phase is entered.

[0165] Development phase

[0166] Define r as a random number between [0,1] to select different development strategies.

[0167] When 0.5 ≤ |E| < 1 and r ≥ 0.5, a soft encirclement strategy is adopted for position update:

[0168] X(t+1)=△X(t)-E|JX rabbit (t)-X(t)| (46)

[0169] In the formula, △X(t)=X rabbit (t)-X(t) represents the difference between the prey's location and the current location of the Harris Eagle; J is a random number between [0,2].

[0170] When |E|≤0.5 and r≥0.5, a hard siege strategy is adopted for position update:

[0171] X(t+1)=X rabbit (t)-E|△X(t)| (47)

[0172] When 0.5 ≤ |E| < 1 and r < 0.5, a soft encirclement strategy of asymptotic rapid dive is adopted for position update:

[0173]

[0174] Y = X rabbit (t)-E|JX rabbit (t)-X(t)| (49)

[0175] Z=Y+S*LF(2) (50)

[0176] In the formula, f() is the fitness function, S is a 2-dimensional random vector with elements being random numbers between [0,1], and LF() is the mathematical expression for Levi's flight.

[0177] When |E| < 0.5 and r < 0.5, a gradual, rapid dive-type hard-siege strategy is adopted for position update:

[0178]

[0179] Y = X rabbit (t)-E|JX rabbit (t)-X m (t)| (52)

[0180] Z=Y+S*LF(2) (53)

[0181] The specific steps to solve this problem are as follows:

[0182] Step 1: Population initialization: Initialize each individual based on the upper and lower bounds of each dimension of the search space.

[0183] Step 2: Calculate the initial fitness: Set the position of the individual with the best fitness as the current prey position.

[0184] Step 3: Position Update: First, update the prey's escape energy, and then execute the corresponding position update strategy in the search or development behavior based on the escape energy and the generated random number.

[0185] Step 4: Calculate fitness: Calculate the individual's fitness after the position update and compare it with the prey's fitness value. If the individual's fitness value after the position update is better than the prey's, then the position of the individual with the better fitness value is used as the new prey position. Step 5: Repeat Step 3 and Step 4 until the algorithm reaches its maximum iteration count. Output the current prey position as the estimated target position.

[0186] This invention provides a method for configuring energy storage capacity in wind farms that considers carbon efficiency and auxiliary frequency regulation. The technical effects are as follows:

[0187] 1) The wind farm energy storage capacity configuration method of the present invention is designed for multiple application scenarios such as wind power fluctuation and participation in auxiliary frequency regulation services. It constructs a two-level planning model based on model algorithm control, which ensures economy while enabling energy storage to achieve better control effect.

[0188] 2) This invention designs a SOC-based energy storage operation strategy for coordination across multiple application scenarios, thus mitigating the impact on energy storage lifespan.

[0189] 3) This invention introduces a carbon trading mechanism, which makes full use of the advantage of the extremely low carbon emissions of the ESS itself, and takes into account the carbon revenue indirectly generated during the process of new energy consumption and auxiliary frequency regulation, so as to obtain a considerable carbon revenue.

[0190] 4) This invention proposes a wind farm energy storage capacity configuration method that considers carbon benefits and auxiliary frequency regulation. It can not only improve the grid connection level of wind farms, increase grid flexibility, optimize energy storage costs and service life, but also meet the needs of energy storage to participate in multiple application scenarios at the same time. Attached Figure Description

[0191] Figure 1 This is a schematic diagram of the power system structure and energy flow.

[0192] Figure 2 Active power output control target diagram for energy storage system

[0193] Figure 3(a) shows the mean and variance of the RegD signal;

[0194] Figure 3(b) shows the probability density distribution of the RegD signal on a certain day;

[0195] Figure 3(c) shows the autocorrelation function of the RegD signal on a certain day.

[0196] Figure 4 This is a schematic diagram of a carbon trading market for wind farms.

[0197] Figure 5(a) is a comparison diagram of the characteristics (probability density distribution) of the SDE analog signal and the actual signal;

[0198] Figure 5(b) is a comparison of the characteristics of the SDE analog signal and the actual signal (autocorrelation function).

[0199] Figure 6 The graph shows the power fluctuation curves of the wind farm before and after smoothing out the grid-connected power of the wind farm before and after the method proposed in this invention and the traditional method.

[0200] Figure 7(a) is a comparison chart of economic indicators between the method proposed in this invention and other methods (example);

[0201] Figure 7(b) is a comparison chart of the economic indicators of the method proposed in this invention and other methods (Comparative Example 1);

[0202] Figure 7(c) is a comparison chart of the economic indicators of the method proposed in this invention and other methods (Comparative Example 2);

[0203] Figure 7(d) is a comparison chart of the economic indicators of the method proposed in this invention with other methods (Comparative Example 3). Detailed Implementation

[0204] This paper proposes a method for configuring energy storage capacity in wind farms, considering carbon benefits and auxiliary frequency regulation. First, a two-layer planning model for energy storage capacity based on model-algorithm control is constructed. The upper-layer model aims to minimize energy storage output and achieve charge-discharge balance, using the MAC algorithm to solve for the energy storage output sequence that mitigates wind power fluctuations. Then, based on the mitigation sequence solved in the upper layer, a multi-scenario collaborative energy storage operation strategy based on SOC is formulated. The lower-layer model aims to maximize the overall energy storage benefit, introducing a carbon trading mechanism and using the energy storage operation strategy as a constraint, employing the Harris Eagle algorithm to solve for the optimal energy storage capacity. Finally, four scenarios based on different operation strategies are established, discussing the impact of different operation strategies on energy storage lifetime and the impact of feed-in tariffs, carbon trading prices, frequency regulation mileage prices, and energy storage investment costs on the optimal energy storage capacity and overall benefits, thus verifying the effectiveness of the proposed configuration method.

[0205] The preferred embodiments are described in detail below with reference to the accompanying drawings:

[0206] 1. Figure 1 For power system structure:

[0207] In this system, the load power PL is mainly provided by the output power of the traditional power plant PT and the output power of the wind farm Pw. The energy storage system smooths out wind power fluctuations in output Pb, while providing frequency regulation services Pr to the ancillary services market.

[0208] 2. The operation of the AGC system constructed in this invention is divided into two stages:

[0209] Day-ahead and real-time. In the day-ahead phase, the AGC system predicts the frequency regulation power for the following day based on existing market rules and scheduling. The AGC system decouples the frequency regulation power distributed between ESS and traditional units. Traditional frequency regulation commands (RegA) are issued to traditional units, and the output curve of traditional units for the following day is determined by this command. In the real-time phase, 15 minutes before the next control cycle, the AGC system performs ultra-short-term predictions of the area control error (ACE) based on the state parameters of the entire network and determines the demand for rapid regulation. Large-capacity energy storage stations should, based on feedback information from energy storage, built-in bidding mechanisms, scheduling strategies, etc., declare their maximum available frequency regulation capacity and electricity price curve 5 minutes before the next control period. The AGC system determines the clearing price and frequency regulation capacity of each energy storage station and delivers it quickly. Small-capacity energy storage stations have limited impact on the clearing price of the entire market in market bidding and are generally considered price takers in the real-time market.

[0210] 3. By Figure 1 It can be seen that during the process of using energy storage systems to smooth the grid connection of wind farms, the original wind power P w Energy storage output power P b Wind power grid-connected power P g And the relationship between the state of charge (SOC) and the state of charge (SOC):

[0211] P g (k+1)=P w (k)+P b (k) (1);

[0212]

[0213] In the formula: P g (k+1) represents the grid-connected power of the wind farm at time k+1; P w (k) represents the actual output power of the wind farm at time k; P b (k) represents the energy storage charge / discharge power; SOC(k+1) represents the energy storage SOC state at time k+1; T, E es This refers to the energy storage control cycle and rated capacity.

[0214] 4. Under the premise of ensuring that wind power fluctuations meet grid connection requirements, the objective function for MAC rolling optimization is to minimize energy storage output and balance energy storage charging and discharging:

[0215]

[0216] In the formula: P b(k+i) represents the energy output at time k+i; S(k+i) represents the SOC state of the energy storage at time k+i; M represents the prediction time scale, i.e., the length of the control command sequence.

[0217] 5. In the MAC rolling optimization, the upper and lower limits of energy storage charging and discharging power, the upper and lower limits of SOC, and the grid connection fluctuation requirements of wind farms are considered. The constraints are as follows:

[0218] -P max ≤P b (k+i)≤P max (4);

[0219] S min ≤S(k+i)≤S max (5);

[0220]

[0221] In the formula: P max The maximum allowable charge / discharge power of the energy storage system, i.e., the rated power; S min S max These are the upper and lower limits of the SOC of the energy storage system; P rated δ represents the installed capacity of the wind farm; δ represents the limit value for the grid connection volatility of the wind farm.

[0222] 6. The state-space equations of a wind farm system including energy storage are:

[0223]

[0224] make

[0225] In the energy storage model algorithm control that balances charge and discharge and minimizes energy storage output at time k, the objective function (3) and constraints (4)-(6) can be transformed into a quadratic standard optimization model through numerical calculation:

[0226]

[0227]

[0228] In the formula: z=[u(k),x T (k+1),u(k+1),…,u(k+M-1),x T (k+M)] T H is a matrix composed of the quadratic weights R and Q of the energy storage control sequence and the output level. R = 2.

[0229] According to formulas (3) to (7), we can obtain

[0230] B es =[-Pmax ,P max ,-δ,δ,-SOC min SOC max ] T

[0231] B eq =[-P max ,P max SOC min SOC max ] T

[0232]

[0233] Using the quadratic programming method in MATLAB, Equation (8) is optimized and solved in each control cycle. The first value of the optimized sequence obtained in each cycle is taken as the current energy storage output control command. Then, the control command sequence for smoothing wind power fluctuations in energy storage during the day is obtained, [u(k),u(k+1),…,u(k+M-1)]. T .

[0234] 7. Active power output control targets for energy storage systems, such as... Figure 2 As shown:

[0235] This invention assumes that the configured energy storage acts as a price taker and a high-quality frequency regulation resource, and that all reported frequency regulation capacity is accepted by the grid dispatching agency, with a frequency regulation service cycle and settlement period of 15 minutes. A new operation model for wind farm-side energy storage is proposed:

[0236] 1) Using the MAC algorithm, calculate the energy storage control command sequence for a future period of time based on the current actual output value of the wind farm and the energy storage SOC state variable value;

[0237] 2) Apply the first value of the control command sequence to the energy storage control system;

[0238] 3) If the sequence value is small or 0, the energy storage will be arranged to report its idle capacity to the dispatch center; otherwise, frequency regulation service will not be provided.

[0239] 4) Roll to the next time step, update the SOC state variable value and grid-connected power value, and repeat the above process.

[0240] 8. Statistical characteristics of PJM market dynamic adjustment signals are shown in Figures 3(a), 3(b), and 3(c):

[0241] This invention approximates the uncertainty of frequency modulation (FM) demand by using the uncertainty of FM signals, and models the FM signals using stochastic differential equations. Historical data selected is the dynamic FM signal of the PJM market in 2022, which is a normalized time series command representing the ratio of energy storage power transfer (increase or decrease) to its declared FM capacity.

[0242] AGC signal ξ t Modeled as SDE:

[0243] dξ t =μ(ξ t )dt+σ(ξ t )dW t (9);

[0244] In the formula: ξ t W represents the random variable that needs to be described. t This is a Wiener process, i.e., standard Brownian motion; μ(ξ) t ) represents the drift coefficient, indicating the random variable ξ. t The average rate of change per unit time; σ(ξ) t ) is the scaling factor, representing W t The randomness of ξ t Degree of influence. The solution ξ of SDE t Known as the Itoh Process

[0245] Determine μ(ξ) t ), σ(ξ) t These two coefficients are crucial for constructing the SDE model. The Fokker-Planck equation is used to model the stochastic process ξ defined in the SDE. t The evolution probability density p(ξ) t The characterization is represented by the formula:

[0246]

[0247] In a stationary state, the probability density does not change over time. At this point, σ(ξ) is obtained through two integrations. t ) and μ(ξ t The relationship is:

[0248]

[0249] The autocorrelation function is used to represent the time correlation of random variables, and is defined as:

[0250]

[0251] When R(τ) exhibits exponential decay, the autocorrelation function expression satisfies the following equation:

[23] :

[0252] R(τ)=e -λτ R(0) (13);

[0253] The drift coefficient of SDE can be expressed as:

[0254] μ(ξ t )=-λ(ξ t -c) (14);

[0255] In the formula: λ is taken as 0.0107; c is a constant, generally taken as ξ. t The mean of RegD is approximately 0, i.e., μ(ξ). t )=-λξ t .

[0256] Once the probability density function is known, by appropriately choosing μ(ξ) t ) and σ(ξ t ), can construct ξ t The SDE model.

[0257] The numerical simulation of the SDE model uses stochastic numerical integration methods, such as the Euler-Maryuama algorithm, to calculate the random variable ξ. t Complete time series:

[0258] ξ t+h =ξ t +hμ(ξ t )+σ(ξ t )ζ (15);

[0259] In the formula: h is the sampling step size of the sequence, and ζ ~ N(0,h) is a normal distribution with variance h.

[0260] 9. The specific steps of the energy storage operation strategy based on SOC multi-scenario coordinated control are as follows:

[0261] 1) Obtain the upper-layer MAC rolling solution results to obtain the control sequence and first determine the energy storage stabilization period and stabilization domain.

[0262] 2) Taking into account the rechargeable and dischargeable capacity of energy storage, the declared frequency regulation power is determined as the frequency regulation range. First, the current rechargeable or dischargeable power P is calculated. be Take its rated power P rate The smaller of the two values ​​is used as the declared power. When declaring an upward adjustment to the power at time t, the current chargeable power of the energy storage is determined by the upper limit of the energy storage SOC and the remaining capacity of the energy storage at the previous time. When declaring a downward adjustment to the power at time t, the current dischargeable power of the energy storage is determined by the lower limit of the energy storage SOC and the remaining capacity of the energy storage at the previous time. The expression for the chargeable and dischargeable power at time t is:

[0263]

[0264] In the formula: E bt' (t-△t) represents the remaining capacity of the energy storage device at the previous moment.

[0265] The expression for the declared frequency modulation power at time t is:

[0266]

[0267] 3) Calculate the current SOC state. When 0.4 ≤ SOC ≤ 0.6, it represents the optimal operating state for energy storage. When energy storage is in its optimal operating state, the ESS's control objective is to track the wind power fluctuation smoothing sequence command U while simultaneously providing bidirectional frequency regulation services to the ancillary services market. When 0.1 ≤ SOC ≤ 0.4, it is in a priority charging state. In this state, the ESS's control objective is to prioritize tracking the smoothing command U (i.e., U > 0) that requires energy storage charging while providing downward frequency regulation services to the ancillary services market; when both the smoothing command and the frequency regulation command are discharging, the command with the lower power output will operate. When 0.6 ≤ SOC ≤ 0.9, it is in a priority discharging state. In this state, the control objective is to prioritize tracking the smoothing command U (i.e., U < 0) that requires energy storage discharging while providing upward frequency regulation services to the ancillary services market; when both the smoothing command and the frequency regulation command are charging, the command with the lower power output will operate. SOC < 0.1 indicates an over-discharge protection state. In this state, the ESS only charges until the SOC increases to 0.2 to restore the priority charging state. A SOC greater than 0.9 indicates an overcharge state. In this state, the energy storage system only discharges until the SOC drops to 0.8 to resume the priority discharge state.

[0268] 10. The objective function of the lower-level model, the comprehensive benefit model of energy storage, is shown in the following equation:

[0269] J = max(I e-sell +I r-sell +I c-sell -C LCC (18);

[0270] In the formula: I e-sell Revenue generated from electricity used for internet access; I r-sell To supplement FM revenue; I c-sell For carbon emission benefits; C LCC This refers to the total lifecycle cost of energy storage.

[0271] To standardize benefit calculations, the present value method is used to convert the costs and benefits of equipment at different times into the average present value for each year. Assuming a total study period of n years and a discount rate of r, a capital discount factor i is introduced. LF .

[0272]

[0273] 11. The energy storage benefit models are as follows:

[0274] 1) Revenue from increased electricity generation e-sell for

[0275]

[0276] In the formula: c e-sell The on-grid electricity price per unit for wind farms; The formula for calculating the average annual increase in power generation at a wind farm after energy storage is configured is as follows:

[0277]

[0278] In the formula: N is the total number of sampling points; The entire life cycle is measured in years.

[0279] 2) Energy storage participation in frequency regulation revenue I r-sell

[0280] The benefits of energy storage participating in the frequency regulation auxiliary market include both capacity compensation and mileage compensation.

[0281]

[0282] In the formula: t represents the capacity and mileage price for time period t; m represents the average mileage. To report the power involved in frequency modulation.

[0283] 3) Carbon emission benefits I c-sell

[0284] This method categorizes carbon emission benefits into positive carbon benefits and negative carbon benefits.

[0285]

[0286] In the formula: c c-sell This refers to the unit price for carbon trading.

[0287] Energy storage has positive carbon benefits for

[0288]

[0289] After wind farms are equipped with energy storage devices, the fluctuations in wind power output can be smoothed to achieve grid connection rate, increase the amount of electricity generated and connected to the grid, reduce wind curtailment, and thus increase the amount of carbon emission credits that can be sold.

[0290]

[0291] In the formula: γ ess The carbon emission allowance per unit of electricity is taken as 0.57 t / MWh; This is to increase the average annual wind power grid connection volume for energy storage.

[0292] This invention introduces Carbon emission factors and k of thermal power units tp The conversion factor (generally between 0.8 and 1) used to convert frequency regulation power to thermal power unit output is used to calculate the carbon efficiency of auxiliary frequency regulation. The value is taken from the average value of the marginal emission factor of electricity in six major regions of my country in 2019, which is 0.8953 t / (MW·h). When energy storage systems participate in the frequency regulation market, the charging and discharging power in actual operation changes continuously in response to the frequency regulation signal.

[0293]

[0294] Energy storage devices consume electricity and fuel and generate carbon emissions during production, transportation and operation.

[0295] CO2 emissions during production The calculation expression is as follows:

[0296]

[0297] In the formula: k sc Carbon emission coefficient per unit power produced by energy storage equipment (0.1-0.2 tons / MWh); P rate This refers to the rated power of the energy storage device.

[0298] CO2 emissions during transmission The calculation expression is as follows:

[0299]

[0300] In the formula: k ys S represents the carbon emission factor for transmission; S represents the transmission distance; and H represents the transmission weight.

[0301] CO2 emissions during operation and maintenance phase Generally, 3% of emissions during the production phase is taken. Therefore, negative carbon benefits... for

[0302]

[0303] 12. The equivalent cycle life assessment model for energy storage is as follows:

[0304] The cycle life of an energy storage system is affected by various factors, the main ones being the number of charge-discharge cycles and the depth of discharge (DOD). This invention characterizes the energy storage cycle life using a fourth-order function, namely...

[0305]

[0306] Where: N(D) OD (i) represents the discharge depth D OD The cycle life at (i) is 0 to 1; N(1) is the cycle life at a depth of discharge of 1.

[0307] The equivalent total cycle life y over the entire working cycle is equal to the sum of the equivalent cycle lives of individual cycles, i.e.

[0308]

[0309] In the formula: n is the total number of energy storage working cycles.

[0310] 13. Energy Storage Life Cycle Cost Model C LCC for:

[0311] C LCC =(C inv +C o&m )×i LF +C res (32);

[0312] 1) Initial investment cost

[0313] The initial investment cost is directly proportional to the rated power and rated capacity of the energy storage equipment, as calculated using the following formula:

[0314] C inv =(C pinv P rate +C einv E rate (33);

[0315] In the formula: C pinv Cost per unit power; C einv Cost per unit capacity; P rate Rated power for energy storage charging and discharging; E rate This refers to the rated capacity of the energy storage.

[0316] 2) Replacement cost

[0317] When energy storage reaches the end of its lifespan, it needs to be disposed of in a harmless manner and recycled. The revenue obtained from recycling can be used as a subsidy to replace it. The calculation formula is as follows:

[0318]

[0319] In the formula: x is the number of replacements; σ res The residual value rate is 5% in this invention; y is the equivalent total cycle life of energy storage, which is determined by equations (27)-(28).

[0320] 3) Operation and maintenance costs

[0321] Operation and maintenance costs refer to the funds invested to ensure the normal operation of energy storage throughout its entire lifespan.

[0322] C o&m =c o&m E rate (35);

[0323] In the formula: c o&m Maintenance cost per unit capacity

[0324] 14. The constraints on energy storage capacity and power are as follows:

[0325] 1) The actual charging and discharging power of the energy storage system should not exceed the rated power of the ESS, as shown in the following formula:

[0326] P(t)=P b (t)+P r (t) (36);

[0327] -P max ≤P≤P max (37); where: P(t) is the total output power of the energy storage system at time t; P b (t) represents the wind power output suppressed by energy storage at time t; P r (t) represents the power of the stored energy participating in auxiliary frequency regulation service at time t.

[0328] The energy storage system at time t has a power constraint for smoothing fluctuations in charge and discharge.

[0329]

[0330] In the formula: P b u(t) represents the charging and discharging power of the energy storage device at time t; u(t) represents the charging and discharging domain of the battery obtained by MAC at time t; η bc η bd These refer to the charging and discharging efficiency of the battery, respectively.

[0331] The power constraint for the energy storage system participating in auxiliary frequency modulation charging and discharging at time t is:

[0332]

[0333] In the formula: ξ t + ξ t - The frequency modulation signals generated based on the SDE model established in Section 2.3 are the frequency adjustment command at time t and the frequency adjustment command at time t, respectively.

[0334] 2) Power Constraint

[0335] Battery rated capacity constraint is

[0336]

[0337]

[0338] In the formula: E bs E represents the maximum remaining capacity of the energy storage device during the dispatch cycle. b0 This represents the initial capacity of the energy storage device.

[0339] The multi-scenario coordinated operation strategy based on SOC proposed in this invention already limits the SOC state of ESS to a certain extent. Therefore, only basic check constraints are added here to ensure that the SOC is within the specified upper and lower limits. The SOC constraints are as follows:

[0340] S min ≤S(t)≤S max (42);

[0341] In the formula: S(t) is the SOC value of the energy storage device at time t.

[0342] 15. Solve for the optimal energy storage capacity:

[0343] The HHO optimization algorithm is a swarm intelligence optimization algorithm that simulates the cooperative predation behavior of Harris eagles. It includes three stages: global search, conversion between global search and development, and development. This invention embeds the multi-scenario collaborative energy storage operation strategy based on SOC, formulated in the upper layer of the energy storage two-layer planning model, into the HHO algorithm to solve the lower-layer objective function, thereby improving the matching between control strategy and configuration method.

[0344] Figure 4 This is a schematic diagram of the carbon trading market for wind farms. It can be seen that wind power, photovoltaic power, and other new energy power plants, as clean energy sources, are the main entities selling carbon emission credits. Therefore, the carbon benefits brought about by configuring energy storage can be converted into profits from carbon emission credits, proving the rationality of this invention's consideration of carbon benefits.

[0345] Figures 5(a) and 5(b) show a comparison of the characteristics of a set of analog FM signals generated by the present invention and actual signals. It can be seen that the sequence generated by the SDE model of the present invention can match the actual signal well and can accurately characterize its probability density distribution and autocorrelation. The SDE model can be used to quantify the randomness of the FM signal to describe the FM requirements.

[0346] Example:

[0347] The following specific embodiment is provided to further illustrate the control effect of the wind farm energy storage capacity configuration method that takes into account carbon efficiency and auxiliary frequency regulation provided by the present invention.

[0348] This embodiment uses a typical daily power output curve of a 100MW wind farm in northern China and the lithium battery system, which currently has the largest installed capacity, as an example for simulation. The basic parameters are shown in Table 1.

[0349] Table 1. Relevant Prices and Basic Parameters

[0350]

[0351] Figure 6 The figures show the power fluctuation curves of wind farms before and after smoothing using the method proposed in this invention, compared to traditional methods. It can be seen that adding an energy storage system to the wind farm significantly reduces the time when the wind power grid connection fails to meet fluctuation limits. The maximum fluctuation rates after smoothing using the two methods are 8% and 10%, respectively, meeting the allowable grid connection requirements. Compared to the fluctuation rate of the direct grid connection curve for wind power, the smoothed fluctuation rates are reduced by 16% and 14%, respectively. The smoothing effect of the method proposed in this invention is slightly inferior to the MAC method (minimum output of energy storage), because the output performance of energy storage is limited by the State of Charge (SOC) state; when the energy storage is in a non-optimal operating state, it will choose not to output or output less. However, thanks to the optimization of energy storage by SOC control, the energy storage life is extended, and more benefits are obtained.

[0352] Comparative example:

[0353] Three different control strategies were used as comparative examples: Comparative Example 1, energy storage fully tracks the smoothing sequence and participates in the ancillary frequency regulation market based on SOC; Comparative Example 2, energy storage tracks the smoothing sequence based on SOC and considers carbon trading, but does not participate in the ancillary frequency regulation market; Comparative Example 3, energy storage tracks the smoothing sequence based on SOC and participates in the ancillary frequency regulation market, but does not consider carbon trading. The simulation results are shown in Table 2, with the revenue and cost for each part presented in the form of a waterfall chart. Figures 7(a) to 7(d) According to the results, the configuration method proposed in this invention achieved the highest profit. The analysis of the optimization results is as follows:

[0354] The embodiment, by tracking and smoothing sequence commands based on SOC, can increase the overall benefits of energy storage to a certain extent. Compared with Comparative Example 1, although some smoothing effect is sacrificed while meeting grid connection requirements, the ESS lifespan is extended by 14.81% thanks to the optimization of SOC control over the energy storage state, giving it more opportunities to participate in auxiliary frequency regulation services and obtain more profits.

[0355] Comparing the embodiment and Comparative Example 2, ESS participation in SOC-based AGC frequency regulation significantly increases overall revenue. Under the operational strategy of the embodiment, the ESS can not only optimize its SOC state through frequency regulation services but also obtain higher revenue. It is noteworthy that if the ESS cannot generate revenue from frequency regulation services, the optimal energy storage capacity of Comparative Example 2 is 25.02% lower than the optimal capacity of the embodiment. This demonstrates that excessive energy storage capacity only leads to a decrease in overall efficiency.

[0356] By comparing the examples, Comparative Example 2, and Comparative Example 3, the annual revenue of the example increased by RMB 596,300 (approximately 2.78 times) compared to Comparative Example 2 alone, and by RMB 155,200 (approximately 1.2 times) compared to Comparative Example 3. In scenarios where ESS is only used to smooth out fluctuations, the carbon benefits have a relatively small impact on the overall benefits of energy storage, and the low-carbon benefits of energy storage are difficult to fully demonstrate their advantages in this single application scenario. Considering the participation of ESS in auxiliary frequency regulation reduces the frequent start-stop operations of traditional generating units participating in auxiliary frequency regulation services, further improving the low-carbon benefits of energy storage and thus increasing the overall benefits of energy storage.

[0357] Table 2. Calculation results of simulations for four different operating strategies

[0358]

[0359] As can be seen from Table 2, after optimizing the energy storage capacity, the present invention can further improve the grid connection level of wind farms, energy storage life and comprehensive benefits, and enable energy storage to meet the needs of participating in multiple application scenarios at the same time.

Claims

1. A method for configuring energy storage capacity in wind farms considering carbon efficiency and auxiliary frequency regulation, characterized in that... Includes the following steps: Step 1: Establish a two-layer optimization model for energy storage system capacity configuration. The upper-layer model is a mathematical model that takes into account the minimum output of energy storage and the balance between charging and discharging. The MAC algorithm is used to solve the output sequence of energy storage to smooth wind power fluctuations. Step 2: Use the uncertainty of the frequency modulation signal to approximate the uncertainty of the frequency modulation demand, and use stochastic differential equations to model the frequency modulation signal; Step 3: Based on the energy storage smoothing sequence obtained from the upper-level model in Step 1, formulate a multi-scenario collaborative energy storage operation strategy based on SOC; Step 4: Introduce a carbon trading mechanism into the lower-level model to construct a comprehensive energy storage benefit model, an energy storage equivalent cycle life assessment model, and an energy storage full life cycle cost model; Step 5: Establish constraints on energy storage capacity and power; Step 6: With the goal of maximizing the overall energy storage benefits, the energy storage operation strategy based on SOC multi-scenario coordination in Step 3 is embedded as a constraint into the Harris Eagle algorithm to solve for the optimal energy storage capacity. In step 1, the mathematical model considering minimum energy storage output and charge-discharge balance uses minimum energy storage output and energy storage charge-discharge balance as the MAC rolling optimization objective function: （3）； In the formula: for Energy is stored and output at all times; for Energy storage at all times status, in which Indicates the time of the i-th moment; For the time scale of prediction; Under the MAC rolling optimization constraint, considering its upper and lower limits for charging and discharging, as well as the grid connection fluctuation requirements of wind farms, the constraint conditions are as follows: （4）； （5）； （6）； In the formula: This refers to the maximum allowable charge and discharge power of the energy storage system. , energy storage system Upper and lower limits; For wind farm installed capacity; This is the limit value for the grid connection volatility of wind farms; Indicates in Grid-connected power of wind farms; Let the state variable be... , For wind power grid connection power and energy storage Status, control input quantity Contributing to energy storage Actual power of wind farm As a disturbance State-space equations for a wind farm system including energy storage are set. In the energy storage model algorithm control that balances charging and discharging and minimizes energy storage output at time k, the objective function (3) and constraints (4) to (6) are transformed into the standard form of quadratic programming through numerical calculation. In step 2, the uncertainty of frequency modulation (FM) demand is approximated by the uncertainty of the FM signal, and the FM signal is modeled using stochastic differential equations (SDEs). AGC signal Modeled as a stochastic differential equation SDE, the stochastic process defined by the Fokker-Planck equation is used. Evolutionary probability density Characterized by the fact that, under stationary conditions, the probability density does not change over time. At this point, the result is obtained through two integrations. and Relationship; The autocorrelation function is used to represent the time correlation of random variables. Once the probability density function is known, it can be appropriately selected. and It can build The SDE model; the numerical simulation of the stochastic differential equation SDE model uses the stochastic numerical integration method to calculate the random variables. The complete time series; Step 3 includes the following steps: 1) Based on the MAC rolling solution results of the upper-level model, obtain the control sequence, and first determine the energy storage stabilization period and stabilization domain; 2) Taking into account the rechargeable and dischargeable capacity of energy storage, the declared frequency regulation power is determined as the frequency regulation range; 3) Calculate the current SOC state.

2. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 1, the mathematical model that takes into account the minimum energy storage output and the charge-discharge balance is as follows: （1）； （2）； In the formula: for Grid-connected power of wind farms at all times; for The actual output power of the wind farm at any given time; For energy storage charging and discharging power; for Energy storage that can be stored at any time state; for Energy storage at all times state; , These are the energy storage control cycle and rated capacity, respectively. Based on equations (1) and (2), under the premise of ensuring that wind power fluctuations meet grid connection requirements, the objective function of MAC rolling optimization is to minimize energy storage output and balance energy storage charging and discharging. The state-space equations for a wind farm system with energy storage are as follows: （7）； In the formula, Represents the state variable: wind power grid-connected power. exist Predicted output at time step; Represents the energy storage of the state variable at time. Status in The predicted output; Represents the state variable: wind power grid-connected power. exist The actual output at any given moment; Indicates in Energy storage at all times The state variable of the state; This represents the control input at time k; Indicates the amount of interference input; make: , , ; In the energy storage model algorithm control that balances charge and discharge and minimizes energy storage output at time k, the objective function (3) and constraints (4)~(6) can be transformed into the standard form of a quadratic programming problem through numerical calculation: （8）； ； ； In the formula: ,in, , These represent the transposes of the system state matrices at time k+1 and k+M, respectively. , These represent the values ​​of the control input at times k+1 and k+M-1, respectively. Representation matrix transpose; H The quadratic objective term is represented by the quadratic weights of the energy storage control sequence and the output level. and The matrix formed , ; According to formulas (3) to (7), we can obtain: ； ； ； In the formula, A represents the parameter matrix of the state variables in the system state-space equation; B represents the parameter matrix of the control input in the system state-space equation. , , This represents the system's state variables, disturbances, and control inputs from the initial time k to the predicted time k+M. The system state at time k+M is predicted from the control inputs and disturbances at time k+M-1. , , , The matrix form of the constraint equations (4) to (6) represents the prediction time length.

3. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 2, characterized in that: Using the quadratic programming method in MATLAB, equation (8) is optimized and solved in each control cycle. The first value of the optimized sequence obtained in each cycle is taken as the current energy storage output control command. Then, the control command sequence for smoothing wind power fluctuations in energy storage is obtained. .

4. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 2, the uncertainty of frequency modulation (FM) demand is approximated by the uncertainty of the FM signal, and the FM signal is modeled using stochastic differential equations (SDEs). AGC signal Modeled as a stochastic differential equation (SDE): （9）； In the formula: For the random variables that need to be described; For Wiener process; The drift coefficient represents the random variable. The average rate of change per unit time; The scaling factor represents... randomness Degree of impact; Stochastic processes defined by SDE using the Fokker-Planck equation Evolutionary probability density The characterization, the formula is: （10）； In a stationary state, the probability density does not change over time. At this point, the result is obtained through two integrations. and The relationship is: （11）； The autocorrelation function is used to represent the time correlation of random variables, and is defined as: （12）； when When the autocorrelation function exhibits exponential decay, it satisfies the following equation: （13）； In the formula, express When = 0, the value of the autocorrelation function; The drift coefficients of the stochastic differential equation SDE are expressed as: （14）； In the formula: This represents the time constant for exponential decay; Let be a constant, take The average value of RegD; the mean of RegD is approximately 0, i.e. ; The formula for calculating the drift term; Once the probability density function is known, it can be selected appropriately. and It can build The SDE model; Numerical simulation of the stochastic differential equation (SDE) model employs the stochastic numerical integration method to calculate the random variables. Complete time series: （15）； In the formula: The sampling step size of the sequence. The variance is It follows a normal distribution.

5. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: Step 3 includes the following steps: 1) Based on the MAC rolling solution results of the upper-level model, obtain the control sequence, and first determine the energy storage stabilization period and stabilization domain; 2) Taking into account the rechargeable and dischargeable capacity of energy storage, the declared frequency regulation power is determined as the frequency regulation range; First, calculate the current chargeable or dischargeable power. Take its rated power The smaller of the two values ​​is used as the declared power; when declaring an upward adjustment of power at time t, the current chargeable power of the energy storage is determined by the upper limit of the energy storage SOC and the remaining capacity of the energy storage at the previous time; when declaring a downward adjustment of power at time t, the current dischargeable power of the energy storage is determined by the lower limit of the energy storage SOC and the remaining capacity of the energy storage at the previous time. The expression for the chargeable / dischargeable power at time t is: （16）； In the formula: This represents the remaining capacity of the energy storage device at the previous moment. express t It can store the current chargeable or dischargeable power at all times. Indicates the rated capacity of energy storage; , These represent the upper and lower limits of the energy storage state of charge, respectively. Indicates a time interval; t The expression for the frequency modulation power declared at any time is: （17）； 3) Calculate the current SOC state: when When the energy storage is in its optimal operating state, the control objective of the ESS is to track the wind power fluctuation smoothing sequence command U while participating in ancillary services to provide bidirectional frequency regulation services. when When the ESS is in the priority charging state, the control objective of the ESS is to prioritize tracking the easing command U that requires energy storage charging, i.e., U>0, while providing down-frequency modulation service to the ancillary service market; when the easing command and the frequency modulation command are both discharging, the one with the smaller power will be used. when When the discharge is in priority mode, the control objective is to prioritize tracking the smoothing command U that requires energy storage discharge, i.e., U<0, while providing up-frequency modulation service to the auxiliary market; when the smoothing command and the frequency modulation command are both charging, the one with the smaller power is selected for operation. when When the SOC increases to 0.2, it is in over-discharge protection state; in this state, the ESS only charges until the SOC increases to 0.2 to resume priority charging state. when When the SOC drops to 0.8, it is in an overcharged state; in this state, the energy storage system only discharges until the SOC drops to 0.8 to resume the priority discharge state.

6. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 4, the comprehensive benefit model of energy storage, which is the objective function of the lower-level model, is shown in the following equation: （18）； In the formula: Revenue generated from electricity used for internet access; To supplement FM revenue; For carbon emission benefits; Cost of energy storage over its entire life cycle; To standardize benefit calculations, the present value method is used to convert the costs and benefits of equipment at different times into the average present value for each year. The total study period is set as follows: Year, discount rate Introducing a capital conversion factor : （19）。 7. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 4, the energy storage benefit model is as follows: 1) Revenue from increased electricity supply for: （20）； In the formula: The on-grid electricity price per unit for wind farms; The formula for calculating the average annual increase in power generation at a wind farm after energy storage is configured is as follows: （21）； In the formula: This represents the total number of sampling points; The entire life cycle is measured in years. This indicates the power of energy storage output in smoothing out fluctuations. 2) Benefits of energy storage participating in frequency regulation : The benefits of energy storage participating in the frequency regulation auxiliary market include both capacity compensation and mileage compensation. （22）； In the formula: , They are respectively Time-of-use capacity and mileage pricing; Average mileage; To report the power participating in frequency modulation; 3) Carbon emission benefits : Carbon emission benefits are categorized into positive carbon benefits and negative carbon benefits. （23）； In the formula: The unit price for carbon trading; Energy storage has positive carbon benefits for: （24）； After wind farms are equipped with energy storage devices, the fluctuations in wind power output can be smoothed to achieve grid connection rate, increase the amount of electricity generated and connected to the grid, reduce wind curtailment, and thus increase the amount of carbon emission credits that can be sold. （25）； In the formula: Carbon emission allowance per unit of electricity; This is to increase the average annual wind power grid connection volume for energy storage.

8. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 4, the energy storage equivalent cycle life assessment model is as follows: The energy storage cycle lifetime is characterized by a fourth-order function, namely: （30）； In the formula: Indicates the depth of energy storage discharge; For the depth of discharge is The cycle life at that time is taken as a value. ; This represents the cycle life at a depth of discharge of 1. Equivalent total cycle life over the entire working cycle It equals the sum of the equivalent cycle lifetimes of a single cycle, i.e. （31）； In the formula: This represents the total number of energy storage operating cycles.

9. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 4, the energy storage life-cycle cost model for: （32）； 1) Initial investment cost: The initial investment cost is directly proportional to the rated power and rated capacity of the energy storage equipment, as calculated using the following formula: （33）； In the formula: Cost per unit power; Cost per unit capacity; Rated power for energy storage charging and discharging; This refers to the rated capacity of the energy storage. 2) Replacement cost: When energy storage reaches the end of its lifespan, it needs to be disposed of in a harmless manner and recycled. The revenue obtained from recycling can be used as a subsidy to replace it. The calculation formula is as follows: （34）； In the formula: Number of replacements; The recovery residual value rate; The equivalent total cycle life of energy storage is determined by equations (27) to (28); 3) Operation and maintenance costs: Operation and maintenance costs refer to the funds invested to ensure the normal operation of energy storage throughout its entire lifespan; （35）； In the formula: Maintenance cost per unit capacity.

10. The wind farm energy storage capacity configuration method considering carbon efficiency and auxiliary frequency regulation according to claim 1, characterized in that: In step 5, the constraints on energy storage power and energy quantity are as follows: ①: The actual charging and discharging power of the energy storage system should not exceed the rated power of the ESS, as shown in the following formula: （36）； （37）； In the formula: for Total output power of the energy storage system at any given time; for Continuous energy storage to stabilize wind power output; for Energy storage is constantly used to participate in auxiliary frequency regulation service power; Energy storage system Constantly smoothing out fluctuations in charge and discharge power constraints （38）； In the formula: For energy storage devices Constant charging and discharging power; for time The desired charge / discharge range of the battery; , These refer to the charging and discharging efficiency of the battery, respectively. Energy storage system The power constraint for participating in auxiliary frequency modulation charging and discharging at all times is... （39）； In the formula: , These represent the frequency adjustment command to increase and the frequency adjustment command to decrease at time t, respectively. ②: Power Constraint: The rated capacity constraint of the battery is: （40）； （41）； In the formula: This represents the maximum remaining capacity of the energy storage device during the scheduling cycle. This represents the initial capacity of the energy storage device. , These represent the charging and discharging efficiencies of the energy storage device, respectively. This represents the output power of energy storage at time t to mitigate wind power fluctuations. This represents the output power of the energy storage participating in the auxiliary frequency regulation service at time t; k Indicates the initial time; The SOC constraint is: （42）； In the formula: for Real-time energy storage devices value; , These represent the upper and lower limits of the energy storage state of charge, respectively.

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