Battery energy storage optimization method and system based on quantile regression convex constraint learning

Abstract

The application discloses a battery energy storage optimization method and system based on quantile regression convex constraint learning, relates to the technical field of battery energy storage optimization, and comprises the following steps: acquiring battery energy storage environment parameters and battery energy storage operation variables, inputting the battery energy storage environment parameters and the battery energy storage operation variables into a pre-established battery aging convex proxy model based on quantile regression, and outputting battery aging prediction values; based on the battery aging prediction values, the battery aging convex proxy model based on quantile regression is converted into a convex polyhedron constraint set in the form of linear inequalities through convex relaxation transformation, a convex mixed scheduling optimization model is generated based on the convex polyhedron constraint set, the convex mixed scheduling optimization model is solved, and battery energy storage optimization results are obtained, so that the battery energy storage optimization effect can be improved, and the health of the battery can be maintained.

Description

Technical Field

[0001] This invention relates to the field of battery energy storage optimization technology, specifically to a battery energy storage optimization method and system based on quantile regression convex constraint learning. Background Technology

[0002] To achieve a low-carbon transformation of the power system, address the high penetration of renewable energy sources such as photovoltaics on the supply side, and facilitate the rapid growth of large-scale flexible loads such as data centers and electric vehicles on the demand side, battery energy storage systems are being deployed more and more widely in modern power grids. Energy storage systems decouple power generation and consumption in the time dimension, enabling them to provide various grid services such as energy arbitrage, demand response, and grid control. However, the continuous charge-discharge cycles during daily operation of energy storage systems gradually lead to battery capacity degradation, i.e., battery aging. This phenomenon is particularly prominent in electrochemical energy storage technologies represented by lithium iron phosphate (LiFePO4) batteries. Battery aging involves two mechanisms: calendar aging accumulated during idle periods and cyclic aging accompanying each charge-discharge process. Both are exacerbated by high temperatures, high-rate currents, and unfavorable state-of-charge curves.

[0003] Existing battery energy storage optimization methods involve highly nonlinear and non-convex mapping relationships. They often rely on integer programming reconstruction to embed neural networks, which destroys the convexity of the optimization problem, making the optimization problem non-convex and computationally intractable, resulting in poor battery energy storage optimization performance. Summary of the Invention

[0004] To address the shortcomings mentioned in the background section, the present invention aims to provide a battery energy storage optimization method and system based on quantile regression convex constraint learning.

[0005] Firstly, the objective of this invention can be achieved through the following technical solution: a battery energy storage optimization method based on quantile regression convex constraint learning, the method comprising the following steps: The battery energy storage environment parameters and battery energy storage operation variables are obtained. The battery energy storage environment parameters include cumulative charge throughput, cell capacity and temperature variables. The battery energy storage operation variables include energy storage capacity, battery-level charging power and battery-level discharging power. The battery energy storage environment parameters and battery energy storage operation variables are input into a pre-established battery aging convex surrogate model based on quantile regression, and the predicted battery aging value is output. Based on the battery aging prediction values, the convex proxy model of battery aging based on quantile regression is transformed into a convex polyhedral constraint set in the form of linear inequalities through convex relaxation transformation. A convex hybrid scheduling optimization model is generated based on the convex polyhedral constraint set. The convex hybrid scheduling optimization model is solved to obtain the battery energy storage optimization results.

[0006] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the battery aging convex proxy model based on quantile regression is obtained by optimizing and improving the data-driven learning-based battery aging model based on a convex neural network.

[0007] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the aging mapping of the battery aging model reconstructed by data-driven learning. f true aging :( x t , θ t ) → ρ battery t The explicit representation of is: In the formula, x t = ( e t , p dis,t , p cha,t ) represents decision-related variables. e t Indicates the amount of energy stored. p dis,t , p cha,t These represent the absolute values ​​of the discharge and charging power, respectively. i t = ( A , Q , T t () represents the environmental parameters for battery energy storage.

[0008] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the convex proxy model obtained after optimizing and improving the data-driven learning-based battery aging model based on the convex neural network is as follows: ρ̃ battery t = f pcf aging ( x t , θ t : Θ) In the formula, I Represents the trainable parameters of the surrogate model; ρ̃ battery t This represents the aging rate predicted by the surrogate model.

[0009] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the battery aging convex surrogate model based on quantile regression is constructed based on a defined parameterized convex function, wherein... i For input parameters, x The input variable is arbitrarily fixed, and the function is valid for any fixed input variable. i about x t To achieve convexity, a nested variable neural network and a parametric neural network are used. The variable neural network incorporates the decision variables... x t Mapped to aging rate prediction, the parametric neural network receives environmental parameters. i t It also generates the weights and biases of the variable neural network.

[0010] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the design of the variable neural network is as follows: It adopts a ResNet residual network structure with skip connections, consisting of a weight set Oh vnn,t control: z 0 t = x t z l t = σ( W l t z l-1 + V l t x t + ω l t ), l = 1, ..., L -1 z L t = W L t z L-1 + V L t x t + ω L t , ρ̃ battery t =z L t In the formula, W l , V l Indicates the first l Layer weight matrix; oh l Indicates the first l Layer bias; L Represents network depth; residual path V l Inject raw input into each hidden layer x t To enrich the gradient flow; the activation function σ(·) is taken as the rectified linear unit σ( x =max( x , 0), or soft-addition function σ( x ) = log(1 + e x The trainable parameter set of a variable neural network is: Oh vnn,t = { W 2 ,..., W L , V 1 , ..., V L , ω 1 , ..., ω L}; The parametric neural network is designed as follows: A parametric neural network is introduced to... i t Mapped to the complete weight set: Oh vnn,t = f pnn (θ t Ω pnn ), f pnn (·): Θ → R m , m = Σ i=2 L n i n i-1 + Σ i=1 L n i n + Σ i=1L n i In the formula, Oh pnn These represent the trainable parameters of the neural network itself. m This represents the total dimension of the generated weights; n i Indicates the first i Layer width; n The input dimension is represented by , and the generated weights and biases are denoted as . W l t (θ) V l t (θ) oh l t (θ).

[0011] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the training of the battery aging convex surrogate model based on quantile regression employs a two-stage quantile training algorithm to optimize the model parameters, wherein the first stage uses adaptive moment estimation Adam for initial training, the second stage uses the finite memory BFGS algorithm with boundary constraints for secondary refinement, and finally outputs the trained parameters as the parameters of the trained battery aging convex surrogate model based on quantile regression.

[0012] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes: the process of transforming the battery aging convex surrogate model based on quantile regression based on battery aging prediction values ​​into a convex polyhedral constraint set in the form of linear inequalities through convex relaxation transformation, comprising: The trained convex surrogate model is transformed into a polyhedral constraint set applicable to linear programming, replacing the original non-convex aging constraints. A neural network is instantiated using ReLU as the activation function, and a degradation budget constraint is added to obtain the accurate data-driven aging region. ε ≥ ρ battery t r battery t = W L t z L-1 t + V L t x t + ω L t z l+1 = max( W l z l + V l x t + ω l , 0), l = 1, ..., L -1 z 1 t = x t , ( W 2 ,..., W L , V 1 ,..., V L , ω 1 ,...,ω L ) = f pnn (θ t ) In the formula, e Let represent the degenerate budget. Since the max(·) operator makes the region non-convex, relaxing each max to the inequality ≥ yields a set of convex polyhedra: ε ≥ ρ battery t r battery t = W L t z L-1 t + V L t x t + ω L t z l+1 ≥ W l z l + V l x t + ω l ,l = 1, ..., L -1 z l+1 ≥ 0, l = 1, ..., L -1 z 1 t = x t Consider any point that is feasible in the relaxed set ( x t , ρ battery t , z 1 t , ..., z L-1 t ), can be started from the first L -1 layers tighten layer by layer towards 1. z l t until the inequality is equal, since each W l Element-wise non-negative, decrease z l It will only decrease W l z l Therefore, the inequality is preserved, and we finally obtain... Y aging ≥ W L t z L-1 t + V L t x t + ω L t Therefore, each in the convex relaxed set x t It also satisfies the precise aging region, meaning that the convex relaxation is feasible, and the relaxation constraint set is denoted as ( x t , θ t ) ∈ R pcf τ ( Y Aging ), and apply it independently for each charge / discharge period.

[0013] Secondly, in order to achieve the above objectives, this invention discloses a battery energy storage optimization system based on quantile regression convex constraint learning, comprising: The data acquisition module is used to acquire battery energy storage environment parameters and battery energy storage operation variables. The battery energy storage environment parameters include cumulative charge throughput, cell capacity and temperature variables, and the battery energy storage operation variables include energy storage capacity, battery-level charging power and battery-level discharging power. The data processing module is used to input battery energy storage environment parameters and battery energy storage operation variables into a pre-established battery aging convex surrogate model based on quantile regression, and output the battery aging prediction value. The optimized output module is used to transform the convex proxy model of battery aging based on quantile regression into a convex polyhedral constraint set in linear inequality form based on the predicted battery aging values. A convex hybrid scheduling optimization model is generated based on the convex polyhedral constraint set, and the convex hybrid scheduling optimization model is solved to obtain the battery energy storage optimization results.

[0014] The beneficial effects of this invention are: This invention utilizes a parameterized input convex neural network to learn a battery aging surrogate model that maintains convexity regarding operational decision variables from data generated by a semi-empirical aging model. Based on quantile regression (using pinball loss), the surrogate model provides a high-confidence upper bound on the true aging rate with a user-specified confidence probability, thereby transforming the user-defined probability level into an explicit operational safety margin. Furthermore, through convex relaxation with feasibility guarantees, the trained surrogate model is transformed into a set of linear inequality constraints, seamlessly embedded into the day-ahead scheduling model, and constructs a fully convex, computationally tractable hybrid optimization model, thereby improving battery energy storage optimization performance and maintaining battery health. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram of the processing procedure of the present invention; Figure 3 This is a schematic diagram of the system structure of the present invention; Figure 4 This is a schematic diagram of the two-stage training process according to an embodiment of the present invention; Figure 5 This is a schematic diagram comparing the solution time of multiple methods in an embodiment of the present invention; Figure 6 This is a schematic diagram comparing the scheduling costs of multiple methods according to an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the comparison of empirical coverage using multiple methods in an embodiment of the present invention; Figure 8 This is a schematic diagram of the shadow prices of τ=0.90 / 0.95 / 0.99 and mse in the embodiments of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Example 1: like Figure 1 As shown, a battery energy storage optimization method based on quantile regression convex constraint learning includes the following steps: S101: Obtain battery energy storage environment parameters and battery energy storage operation variables, wherein the battery energy storage environment parameters include cumulative charge throughput, cell capacity and temperature variables, and the battery energy storage operation variables include energy storage capacity, battery-level charging power and battery-level discharging power; The process of constructing and collecting battery energy storage environmental parameters and battery energy storage operation variables includes: First, a semi-empirical aging model of the battery is established. The battery consists of several cells, and for an initial capacity of... Q A 0-cell battery has a capacity of Q t The capacity loss decreases monotonically with charge-discharge cycles. The normalized capacity loss and instantaneous cell aging rate are defined as follows: l t = ( Q 0- Q t ) / Q 0, ρ cell t = ( l t+1 - l t ) / Δ t In the formula, l t Indicates normalized capacity loss (e.g.) l t =0.07 corresponds to a 7% capacity loss); rcell t Indicates the instantaneous aging rate of the battery cell; Δt Indicates a time interval; Q 0、 Q t These represent the initial capacity of the battery cell and... t Capacity at a given moment. A cell reaches the end of its life when its capacity decays to a fixed percentage of its initial value (usually 80% or 90%).

[0018] Furthermore, a semi-empirical degradation model of lithium iron phosphate cells is used to characterize the dependence of cell aging rate on complete charge-discharge history and environmental conditions: r cell t = z (Σ s=1 t | b s | Δ t ) z-1 | b t | (α q t / Q t + β) exp((- E a + η| b t | / Q ) / ( R g ( T 0+ T ))) In the formula, z Represents a dimensionless power-law exponent; b t express t Cell current during a given period; α , β This represents the aging coefficient related to instantaneous charging; q t Indicates the cell charge; E a Indicates activation energy; or Indicates the current correlation coefficient; R g Represents the ideal gas constant; T 0、 T These represent the reference temperature and the temperature variable, respectively. The three factors in this formula characterize the accumulated charge, the instantaneous aging rate, and the temperature effect, respectively.

[0019] For by NA grid-scale battery composed of individual cells, assuming that each cell operates in a balanced manner (i.e., current, capacity, and energy storage are equal across all cells at any given moment), can establish a deterministic mapping between cell-level and battery-level quantities. Simultaneously, on the day-ahead dispatch timescale, the cumulative charge throughput... A := Σ s=1 t | b s | Δ t With cell capacity Q t The evolution of [the parameter] is much slower than the scheduling decision, and therefore it is considered a fixed parameter. From this, the conversion relationship between battery level quantity and battery level aging rate is obtained: p cha / dis,t = 3.3 Nb t , e t = 3.3 Nq t , E t = 3.3 NQ t r battery t = zA z-1 | b t | (α e t / Q + β) exp((- E a + η| b t | / Q ) / ( R g ( T 0+ T ))) In the formula, p cha / dis,t Indicates battery-level charging / discharging power; e t Indicates the amount of energy stored; E t Indicates total energy capacity; N Indicates the number of battery cells; A 3 represents the cumulative charge throughput considered as a fixed parameter; 3.3 is the conversion factor for the rated voltage (V) of a single cell.

[0020] Based on this, a day-ahead scheduling model for aging awareness is constructed, constraining the battery aging rate within the user-defined budget: aiming to minimize the sum of conventional unit power generation costs and photovoltaic reduction penalties. min Σ t Σ g C g ( p g,t ) + Σ t Σ pv C p ( p max pv,t - p pv,t ) Consider the following constraints: Node power balance (dual variables) l t ): p pv,t + p g,t - p d,t = B θ t Unit output upper and lower limits: p g min ≤ p g,t ≤ p g max , ∀ g Photovoltaic power output limit: 0 ≤ p pv,t ≤ p max pv,t , ∀pv Line power flow restrictions: | F θ t | ≤ f max Node phase angle constraints: i min ≤ θ t ≤ θ max , θ0= 0 Battery aging constraints: r aging t ≤ Y Aging Aging process (strongly nonlinear, nonconvex): raging t = zA z-1 | b t | (α e t / Q + β) exp((- E a + η| b t | / Q ) / ( R g ( T 0+ T ))) Energy storage power dynamics: e t+1 = e t + η cha p cha,t Δ t - (1 / η dis ) p dis,t Δ t , t = 1, ..., T Charge / discharge power limit: 0 ≤ p dis,t ≤ P max dis , 0 ≤ p cha,t ≤ P max cha Energy storage capacity limit: 0 ≤ e t ≤ E max In the formula, t Indicates the scheduling period (total) T (time period) g PV and PV represent conventional units and photovoltaic units, respectively; C g (·) C p (·) represent the power generation cost function and the photovoltaic reduction penalty function, respectively; B Represents the nodal admittance matrix; F Indicates the line-node transfer distribution factor; f max Indicates the thermal stability limit of the line; it Represents the node voltage phase angle vector; Y Aging This indicates the aging budget set by the user; l t The dual multiplier represents the node power balance constraint, corresponding to the node marginal electricity price; or cha , or dis These represent the charging and discharging efficiencies, respectively. The aging process constraint is a strongly nonlinear and non-convex constraint, making this scheduling model unsolvable by standard solvers.

[0021] S102: Input the battery energy storage environment parameters and battery energy storage operation variables into the pre-established battery aging convex surrogate model based on quantile regression, and output the predicted battery aging value. The convex surrogate model for battery aging based on quantile regression is obtained by optimizing and improving the data-driven learning-based battery aging model using a convex neural network.

[0022] The process of reconstructing the battery aging model using data-driven learning is as follows: To overcome the aforementioned nonconvexity, the battery aging model is reconstructed into a form that facilitates data-driven learning. From a scheduling perspective, the inputs to the aging mapping can be divided into two categories: environmental variables as given parameters and runtime variables as the optimization objects. Based on this, the inputs are separated into parameters. i t = ( A , Q , T t ) and variables x t = ( e t , p dis,t , p cha,t ), and map aging f true aging :( x t , θ t ) → ρ battery t Explicitly represented as: In the formula, x t = ( e t , p dis,t , p cha,t) represents decision-related variables (three-dimensional non-negative real vectors). e t Indicates the amount of energy stored. p dis,t , p cha,t These represent the absolute values ​​of the discharge and charging power, respectively. i t = ( A , Q , T t Let be an environmental parameter (a three-dimensional non-negative real vector). This reconstruction makes the aging rate a decision variable. x t scalar value mapping, for subsequent... x t This lays the foundation for building a convex proxy model for the input.

[0023] The convex surrogate model for battery aging based on quantile regression is as follows: Since the detailed physical parameters in the above formula are often unavailable in practice, and their nonlinearity prevents direct embedding into the scheduling model, this invention constructs a convex surrogate model based on an Input Convex Neural Network (ICNN) and employs quantile regression to provide it with a probability safety margin. The surrogate model is denoted as: ρ̃ battery t = f pcf aging ( x t , θ t : Θ) In the formula, I Represents the trainable parameters of the surrogate model; ρ̃ battery t This represents the aging rate predicted by the surrogate model.

[0024] The key idea is that any data-driven agent model has an approximation error. If mean squared error is used for training and the true aging rate is underestimated, the scheduling scheme will exceed the physical degradation budget. Therefore, this invention uses quantile regression, that is, fitting the conditional quantile of the response variable under a given input instead of the conditional mean, thereby introducing a controllable one-sided bias as an explicit probability safety buffer. For quantile levels τ ∈ (0,1), the conditional quantile function of the aging rate is defined as: Q τ (ρ battery t | x t , θ t) = inf{ r ∈ R : Φ( r | x t , θ t ) ≥ τ} In the formula, Φ(· | x t , θ t ) indicates the aging rate at a given ( x t , θ t The conditional cumulative distribution function (CDF) under ( ). Q τ (·) indicates the first t Conditional quantile function (its subscript) t To distinguish it from cell capacity Q By definition, the first... t Conditional quantiles satisfy: Pr( ρ battery t ≤ Q τ (ρ battery t | x t , θ t ) ) = τ Therefore, training the agent model approximates... t The conditional quantile of 0.95 yields a function that upper bounds the true aging rate with a 95% probability, which is precisely the probabilistic safety margin required for the aging constraint. The conditional quantile is obtained by minimizing the expected pinball loss, defined as: L τ ( y , ŷ) = τ max( y - ŷ, 0) + (1 - τ) max(ŷ - y , 0) = ( y - ŷ)(τ - 1 y<ŷ ) In the formula, y Represents the actual value; ŷ Indicates the predicted value; 1 y<ŷ Indicates when y An indicator function that takes 1 when <ŷ and 0 otherwise. This loss has an asymmetric penalty structure: underestimation (ŷ< y ) is proportional to t The punishment is overestimated. y) is penalized proportionally to (1-τ). When t When the coefficient of performance is 0.95, the penalty for underestimating the aging rate is 19 times that for overestimating it (0.95 / 0.05), thus prompting the surrogate model to systematically provide a conservative upper bound. The bouncing loss is related to the predicted value. ŷ The subgradient is: ∂ L τ ( y , ŷ) / ∂ŷ = τ - 1 (ŷ< y ); [τ-1, τ] (ŷ = y ); τ (ŷ> y ) This gradient is in y The t The quantile being zero indicates that the minimum expected bouncing loss is exactly at the quantile. t Quantiles. Therefore, training the surrogate model can be formulated as a quantile regression problem that minimizes the bouncing loss on the training data: min Θ Σ i=1 N L τ ( f true aging ( x t,i , θ t,i ), f pcf aging ( x t,i , θ t,i : Θ) ) In the formula, N This represents the number of training samples, taken from the aging dataset. D aging ,Right now( x t,i , θ t,i ) i=1 N ∈ D aging .when N → ∞ and assuming the classes are sufficiently rich, this empirical minimum converges to the conditional quantile function.

[0025] Furthermore, paired training t upper and t lower Two quantile proxy models can be constructed with a nominal coverage of (τ) upper - τ lowerThe prediction interval (PI): PI t = [ f pcf aging,τlower ( x t , θ t ), f pcf aging,τupper ( x t , θ t ) ] Its empirical coverage probability (ECP) is assessed as follows: ECP = (1 / N test ) Σ i=1 Ntest 1{ ρ battery t,i ∈ PI t,i} In the formula, N test Indicates the number of test samples. (Take...) t upper =0.95、 t lower When the value is 0.05, the nominal coverage rate is 90%. In safe scheduling, the upper quantile surrogate model is substituted into the aging constraint; the interval width can also be used as a diagnostic measure of the uncertainty of the surrogate model. By adjusting... t The operator can directly control the trade-off between constraint conservatism and economy. Since real-world aging data is usually unavailable, training labels are generated by evaluating the semi-empirical model at the sampled input, i.e., a "model-guided, data-driven" learning paradigm. It should be noted that, because the bouncing loss is a convex piecewise linear function of the residuals, replacing it with any other convex training loss will not affect the surrogate model's... x t Since the convexity of the τ is such that all the following convexity and feasibility guarantees hold for any τ ∈ (0,1).

[0026] Implementing the above convex proxy model requires a concept of... x It can be proven that it is convex, and at the same time about i To maintain a flexible network architecture, a parametric convex function (PCF) is defined. f pcf aging ( x t , θt ),in i For input parameters, x The input variable is arbitrarily fixed, and the function is valid for any fixed input variable. i about x t The model is convex. This surrogate model is implemented by two nested sub-networks: a variable neural network that handles the decision variables... x t Mapped to aging rate prediction; parametric neural network receives environmental parameters. i t And generate the weights and biases of the variable neural network, thereby maintaining the relationship with respect to... x t While maintaining convexity, it also enables the surrogate model to adapt to operating conditions.

[0027] 1) Variable Neural Network Design: A Residual Network (ResNet) structure with skip connections is adopted, consisting of a weight set... Oh vnn,t control: z 0 t = x t z l t = σ( W l t z l-1 + V l t x t + ω l t ), l = 1, ..., L -1 z L t = W L t z L-1 + V L t x t + ω L t , ρ̃ battery t = z L t In the formula, W l , V l Indicates the first l Layer weight matrix; oh l Indicates the first l Layer bias; L Represents network depth; residual path V l Inject raw input into each hidden layer x t To enrich the gradient flow; the activation function σ(·) is taken as the rectified linear unit (ReLU) σ( x ) = max( x , 0), or the soft-plus function σ( x ) = log(1 + e x The trainable parameter set of a variable neural network is: Oh vnn,t = { W 2 , ..., W L , V 1 , ..., V L , ω 1 , ...,ω L}

[0028] 2) Parametric Neural Network Design: To make the variable neural network dependent on environmental parameters i t Introducing a parametric neural network will i t Mapped to the complete weight set: Oh vnn,t = f pnn (θ t Ω pnn ), f pnn (·): Θ → R m , m = Σ i=2 L n i n i-1 + Σ i=1 Ln i n + Σ i=1 L n i In the formula, Oh pnn These represent the trainable parameters of the neural network itself. m This represents the total dimension of the generated weights; n i Indicates the first i Layer width; n Indicates the input dimension. The generated weights and biases are denoted as... W l t (θ) V l t (θ) oh l t (θ).

[0029] 3) Convexity condition and application method: Since σ(·) is a non-decreasing convex activation function, as long as the inter-layer weight matrix is ​​restricted to be element-wise non-negative, the output of the variable neural network can be guaranteed to be convex with respect to the convexity condition. x For convexity: W l t (θ t ) ≥ 0, ∀θ t , in W l t ∈ Ω vnn,t The sufficiency of this condition is proved as follows (by mathematical induction): The independent variable activated at each layer is... W l t z l-1 t + V l t x t +ω l t .when l When =1, z 1 = σ( W 1 t z 0 t + V 1t x t + ω 1 t ) about x It is convex. Inductive hypothesis z l-1 t about x If it is convex, then by W l t ≥0, the pre-activation term is a non-negative combination of convex functions plus an affine term, and is still convex. For z l t about x t Find the second derivative: ∂ 2 z l t / ∂ x 2 t = (∂ 2 σ / ∂ t 2 )(∂( W l t z l-1 t + V l t x t + ω l t ) / ∂ x t ) 2 + (∂σ / ∂ t (∂) 2 ( W l t z l-1 t + V l t x t +ω l t ) / ∂ x 2 t ) because s Non-decreasing and convex, its first and second derivatives are both non-negative; combined with the non-negative weight constraint, the pre-activation term has... xThe Hessian matrix is ​​positive semi-definite, therefore z l t The Hessian matrix is ​​also positive semi-definite, i.e., ∂ 2 z l t / ∂ x 2 t ≥ 0. Convexity is determined by z 1 t propagating layer by layer to z L t Thus establishing the proxy model output ρ̃ battery t about x t convexity.

[0030] To satisfy the above non-negativity requirement, the parametric neural network is instantiated as a fully connected network, and its output is divided into three branches: z 0 = θ t z l = σ( A l z l-1 + β l ), l = 1, ..., L -1 Oh W vnn,t = ReLU( A L z L-1 + β L ) := { W 2 , ..., W L} Oh V vnn,t = A L z L-1 + β L := { V 1 , ..., V L} Ohω vnn,t = A L z L-1 + β L := {ω 1 , ..., ω L} In the formula, A l , β l The weights and biases of a parametric neural network (denoted as ) Oh pnn ). Among them, the generation W The branches are processed by ReLU thresholding to ensure element-wise non-negativity, thus satisfying the convexity condition; generating V and oh The branches employ linear activation to preserve approximation capability. Thus, the composite variable neural network and the parametric neural network yield the convex surrogate model for battery aging. f pcf aging ( x t , θ t ), and environmental parameters i t = ( A , Q , T Each value of ) guarantees that with respect to the decision variable x t = ( p cha,t , p dis,t , e t ) is convex.

[0031] The training of the battery aging convex surrogate model based on quantile regression employs a two-stage quantile training algorithm to optimize the model parameters. In the first stage, the adaptive moment estimation algorithm Adam is used for initial training, and in the second stage, the finite memory BFGS algorithm with boundary constraints is used for secondary refinement. Finally, the trained parameters are output as the parameters of the trained battery aging convex surrogate model based on quantile regression.

[0032] Specifically, the training process includes: To solve the aforementioned training problem with convexity constraints with high accuracy, a two-stage training strategy is adopted, and specific training is performed for each target quantile. t Execute independently.

[0033] 1) First stage (Adam initialization training): The Adaptive Moment Estimation (Adam) optimizer is used to minimize the bouncing loss without imposing convexity constraints, in order to obtain robust initial parameter estimates. min Ωpnn Σ i=1 N L τ (ρ battery t,i , ρ̃ battery t,i ) 2) Second Stage (Boundary Constraint Refinement): Due to the nested network structure making Adam difficult to converge with high precision, a second-order refinement is performed using the Limited-memory Broyden–Fletcher–Goldfarb–Shannowith Box constraints (L-BFGS-B) algorithm. A secondary penalty term for negative weights is added to the objective function to force... W l t (θ t ) ≥ 0: min Ωpnn Σ i=1 N L τ (ρ battery t,i , ρ̃ battery t,i ) + ρ h Σ Wlt∈ Ωvnn max(- W l t , 0) 2 In the formula, r h This indicates a larger penalty coefficient. If negative weights still exist after optimization, then increase it. r h Solve again. This two-stage strategy fully combines the stable early convergence characteristics of Adam with the fast local convergence characteristics of L-BFGS-B utilizing curvature information. The complete process is summarized as follows: Algorithm 1: Two-stage training of the battery aging convex surrogate model Input: Training dataset D aging = {( x t,i , θ t,i , ρbattery t,i )} i=1 N ; Quantile level τ ∈ (0,1).

[0034] Initialization: Constructing variable neural networks and parameter neural networks.

[0035] Phase 1 (Adam training, used for model initialization): For epoch=1 to N adam For each small batch B Calculate in sequence Oh vnn,i = f pnn (θ t,i Ω pnn ), predict ρ̃ battery t,i = f vnn ( x t,i Ω vnn,i ), ball loss L reg = (1 / | B |)Σ i∈B L τ (ρ battery t,i , ρ̃ battery t,i ), and calculate its relation to Oh pnn The gradient is updated using the Adam optimizer. Oh pnn .

[0036] Phase 2 (L-BFGS-B refinement, used to apply boundary constraints): Define the objective function L box = Σ i=1 N L τ (ρ battery t,i , ρ̃ battery t,i ) + ρ h Σ Wlt∈ Ωvnn max(- W l t , 0) 2 Using the solution from stage 1 as the initial value, the objective is minimized using L-BFGS-B to optimize. Oh pnn .

[0037] Output: The trained parameterized input convex neural network f pcf aging and its optimal parameters Oh pnn .

[0038] S103: Based on the battery aging prediction value, the convex proxy model of battery aging based on quantile regression is transformed into a convex polyhedral constraint set in the form of linear inequalities through convex relaxation transformation. A convex hybrid scheduling optimization model is generated based on the convex polyhedral constraint set. The convex hybrid scheduling optimization model is solved to obtain the battery energy storage optimization results.

[0039] The process of transforming a convex surrogate model of battery aging based on quantile regression into a convex polyhedral constraint set in linear inequality form, based on predicted battery aging values, includes: The trained convex surrogate model is transformed into a polyhedral constraint set that can be used for linear programming (LP) to replace the original non-convex aging constraints. A variable neural network is instantiated using ReLU as the activation function, and a degradation budget constraint is added to obtain the accurate data-driven aging region. ε ≥ ρ battery t r battery t = W L t z L-1 t + V L t x t + ω L t z l+1 = max( W l z l + V l x t + ω l , 0), l = 1, ..., L -1 z 1 t = xt , ( W 2 ,..., W L , V 1 ,..., V L , ω 1 ,...,ω L ) = f pnn (θ t ) In the formula, e This represents the degenerate budget. Since the max(·) operator keeps the region non-convex, relaxing each max to the inequality ≥ yields a set of convex polyhedra: ε ≥ ρ battery t r battery t = W L t z L-1 t + V L t x t + ω L t z l+1 ≥ W l z l + V l x t + ω l , l = 1, ..., L -1 z l+1 ≥ 0, l = 1, ..., L -1 z 1 t = x t Proof of feasibility guarantee: Consider any point that is feasible in the relaxed set ( x t , ρ batteryt , z 1 t , ..., z L -1 t ), can be started from the first L -1 layers tighten layer by layer towards 1. z l t , until the above inequalities are satisfied. Since each W l Element-wise non-negative, decrease z l It will only decrease W l z l Therefore, the inequality is preserved, and we finally obtain... Y aging ≥ W L t z L-1 t + V L t x t + ω L t Therefore, each in the convex relaxed set x t It also satisfies the precise aging region, meaning that the convex relaxation is feasible. This relaxation constraint set is denoted as ( x t , θ t ) ∈ R pcf τ ( Y Aging ), and apply it independently for each charge / discharge period.

[0040] Replacing the original non-convex aging constraints with polyhedral relaxation constraints yields a tractable convex hybrid scheduling model: the objective is to minimize the sum of generation cost and photovoltaic reduction penalty, considering node power balance (dual variables). l t ), unit and photovoltaic output limitations, line power flow and node phase angle constraints, dynamic equations for energy storage capacity, charging and discharging power and energy storage capacity limitations, and convex aging polyhedron constraints ( x t , θ t ) ∈ R pcf τ (ε), wherex t = ( p cha,t , p dis,t , e t ), i t = ( A , Q , T ), t =1,..., T .

[0041] This model is a convex quadratic programming problem, which can be efficiently solved by a general solver, while supporting sustainable energy storage scheduling and market clearing that accounts for aging. When the proxy model is at high quantiles (e.g., t =0.95) During training, polyhedral constraints R pcf τ (ε) Provides probabilistic safety guarantees: the resulting scheduling scheme guarantees at least t The confidence level meets the true physical aging limit. e This ensures battery health without compromising computational tractability. Since the complete hybrid model maintains convexity, the marginal charge of the aging-sensing node can be determined by the dual multiplier corresponding to the node power balance constraint. l t Direct acquisition, thereby enabling price formation that takes aging into account.

[0042] Specifically, the present invention will be further illustrated below through embodiments: The present invention further achieves this through: (1) Data-driven reconstruction of semi-empirical battery aging model.

[0043] Separate the inputs of battery aging mapping into environmental parameters. i t = ( A , Q , T t ) and operational decision variables x t = ( e t , p dis,t , p cha,t ), and explicitly express the battery-level aging rate as about x t Scalar value mapping: r battery t = ftrue aging ( x t , θ t ) = zA z-1 (( p dis,t + p cha,t ) / (3 N )) (α e t / (3 NQ ) + β) exp((- E a + η ( p dis,t + p cha,t ) / (3 NQ )) / ( R g ( T 0+ T t ))) The meanings of the variables in the formula are the same as before.

[0044] (2) Construct a convex proxy model for battery aging based on quantile regression.

[0045] Constructing a proxy model ρ̃ with conditional quantile as the target battery t = f pcf aging ( x t , θ t : Θ), where the first t Conditional quantiles satisfy Pr(ρ) battery t ≤ Q τ (ρ battery t | x t , θ t )) = τ; Training is performed using bouncing loss: L τ ( y , ŷ) = τ max( y - ŷ, 0) + (1 - τ) max(ŷ - y , 0) = ( y - ŷ)(τ - 1 y<ŷ ) In the formula, y , ŷ Representing the actual value and the predicted value respectively, 1 y<ŷ For indicator functions. High quantiles (e.g.) t =0.95) enables the surrogate model to provide a high-confidence upper bound on the true aging rate with a specified probability, forming an explicit probability safety margin; the training objective is to minimize the bouncing loss on the dataset: min Θ Σ i=1 N L τ ( f true aging ( x t,i , θ t,i ), f pcf aging ( x t,i , θ t,i : Θ) ) And can be by t upper , t lower Constructing the prediction interval PI using the quantile model t Its empirical coverage probability (ECP) is used for uncertainty assessment.

[0046] (3) Parameterized input convex neural network architecture and its convexity application mechanism.

[0047] The surrogate model is a combination of a variable neural network and a parametric neural network. The variable neural network uses a residual structure. z 0 t = x t z l t = σ( W l t z l-1 + V l t x t + ω l t ), l = 1, ..., L -1 z L t =W L t z L-1 + V L t x t + ω L t , ρ̃ battery t = z L t Parametric neural networks map environmental parameters to the total weights and biases of the variable neural network. Oh vnn,t = f pnn (θ t :Ω pnn Its output is divided into three branches, and it generates inter-layer weights. W Apply a ReLU threshold to the branch to ensure element-wise non-negativity: z 0 = θ t z l = σ( A l z l-1 + β l ), l = 1, ..., L -1 Oh W vnn,t = ReLU( A L z L-1 + β L ) := { W 2 , ..., W L} Oh V vnn,t = A L z L-1 + β L := { V 1 , ..., V L} Oh ω vnn,t = A L z L-1 + β L := {ω 1 , ..., ω L} Convexity condition is W l t (θ t ) ≥ 0(∀θ t ).Depend on s The surrogate model is non-decreasing and convex, with element-wise non-negative weights. Through layer-by-layer induction, it can be proven that the output of the surrogate model is related to... x t It is convex, that is, for any fixed i t , f pcf aging ( x t , θ t ) about x t = ( p cha,t , p dis,t , e t ) is convex.

[0048] (4) Two-stage quantile training algorithm.

[0049] The first stage uses the Adam optimizer to minimize the bouncing loss to obtain robust initial values; the second stage refines the values ​​using L-BFGS-B and adds a quadratic penalty term for negative weights to impose non-negativity constraints. min Ωpnn Σ i=1 N L τ (ρ battery t,i , ρ̃ battery t,i ) + ρ h Σ Wlt∈ Ωvnn max(- W l t , 0) 2 In the formula, r h This is the penalty coefficient; if negative weights still exist, it increases. r hResolve. This algorithm applies to each quantile. t Execute independently.

[0050] (5) Convex transformation and polyhedral encoding with feasibility guarantee.

[0051] After obtaining the precise aging region by instantiating a variable neural network using ReLU, each max(·) operator is relaxed to the inequality ≥, resulting in a convex polyhedron constraint set: ε ≥ ρ battery t r battery t = W L t z L-1 t + V L t x t + ω L t z l+1 ≥ W l z l + V l x t + ω l , l = 1, ..., L -1 z l+1 ≥ 0, l = 1, ..., L -1 z 1 t = x t Because the inter-layer weights are non-negative element by element, they tighten layer by layer. z l Since all inequalities hold, each feasible point in the convex relaxation set satisfies the precise aging region, meaning the convex relaxation has a feasibility guarantee, denoted as ( x t , θ t ) ∈ R pcf τ (ε).

[0052] (6) Convex hybrid aging sensing day-ahead scheduling model and calculation of marginal electricity price of aging sensing node.

[0053] Relaxing constraints with polyhedra ( x t , θ t ) ∈ R pcf τ (ε) Replaces the original non-convex aging constraints, and together with node power balance, unit and photovoltaic output limits, line power flow and phase angle constraints, energy storage dynamics, and power / energy limits, forms a fully convex hybrid scheduling model that can be efficiently solved by a general solver; during high quantile training, this model achieves at least t The confidence level meets the physical aging limit. e ; and dual multipliers constrained by nodal power balance l t The marginal electricity price of aging sensing nodes is calculated directly.

[0054] To verify the beneficial effects of the method of the present invention, a comparative experimental case is presented below. The implementation process includes five steps in sequence: building a simulation case, surrogate model accuracy, probabilistic safety margin, multi-method comparison and verification, and market clearing application.

[0055] 1) Construction of simulation examples A simulation example was built on the IEEE 30-node system for verification: the scheduling cycle is 24 hours and the time step is 1 hour; both the photovoltaic unit and the energy storage system are connected to node 24. The rated power of the energy storage system is 30 MW and the rated capacity is 300 MWh. The initial state of charge is 0.8 and the state of charge range is [0.2, 1.0]. The charging and discharging efficiency is 0.9. The scheduling model is based on CVXPY modeling and solved by the MOSEK solver.

[0056] 2) Quantile Agent Training The variable neural network adopts a two-layer fully connected structure of [5, 5], and the parametric neural network adopts a single-layer fully connected structure of

[10] . The training dataset is generated by evaluating 1000 sets of randomly sampled environmental parameters and grid-sampled running variables using a semi-empirical aging model. The training is divided into two stages: the first stage uses Adam iteration for 2×10³ rounds for coarse convergence, and the second stage uses L-BFGS-B iteration for 1×10³ rounds. 4 High-precision refinement is performed in one round, with a learning rate of 10⁻³. A PICNN agent is trained independently at the three quantile levels τ∈{0.05,0.50,0.95}.

[0057] 3) Verification by multiple methods.

[0058] Within the scanning range of the degraded budget ε∈[0.15, 5.8], the method of this invention (τ takes values ​​of 0.90, 0.95, and 0.99 respectively) is compared with the mean squared error point estimation surrogate model, the conformal quantile regression method, and the exact mixed-integer ReLU reconstruction method based on the big M method in the same scheduling model. As shown in the figure, the average empirical coverage of the mean squared error point estimation baseline is only 0.601, and it fluctuates drastically between 0.40 and 0.77 under different degraded budgets, lacking a stable safety margin; the conformal quantile regression method has an average coverage of 0.951, but because its calibration method is global calibration rather than local calibration, its coverage stability is weaker than that of the method of this invention in the budget tightening scenario; the exact mixed-integer ReLU reconstruction method repeatedly fails to converge within the 150-second solution time limit, and can only return suboptimal and insufficiently covered solutions, and cannot provide dual variables for market clearing due to the introduction of integer variables. In contrast, the method of this invention achieves empirical coverage of 0.950, 0.986, and 0.990 at τ=0.90, 0.95, and 0.99, respectively, all reaching or exceeding the corresponding nominal confidence levels. Moreover, the scheduling cost is basically consistent with other convex methods (approximately $1315 per hour), and the average solution time is only about 1.9 to 2.0 seconds. This verifies that the convex relaxation strategy proposed in this invention can significantly improve computational efficiency while ensuring probabilistic safety margins compared to exact mixed integer programming reconstruction.

[0059] 5) Verification of marginal electricity price at aging sensing nodes.

[0060] Thanks to the complete convexity of the hybrid scheduling model, the dual variables corresponding to the node power balance constraints can be directly used to calculate the node marginal price taking into account aging constraints. In the IEEE 118-node example, the dual variables of the aging budget constraint are extracted and analyzed: their binding time mean monotonically increases with the increase of the quantile level τ, and at τ=0.90, 0.95, and 0.99, they are $17.22, $18.66, and $20.97 per unit, respectively, all higher than the mean square error point estimation baseline of $16.65 per unit; this shadow price is close to zero when energy storage is idle, and rises rapidly to more than $50 per unit during the charge-discharge arbitrage period, which can accurately identify the period when the aging budget plays an economic constraint role; the average marginal price of energy storage access nodes ($35.70 per MWh) is lower than the system average marginal price ($37.00 per MWh), reflecting the moderating effect of energy storage on local node prices. The above results show that the method of the present invention can provide an aging pricing signal with clear physical meaning for the electricity market while maintaining the convexity of the model. This capability is difficult to achieve in non-convex aging models without dual variables or in exact mixed integer reconstruction methods.

[0061] In summary, the above simulation examples, from multiple dimensions such as surrogate model accuracy, probabilistic safety margin, multi-method comparison and verification, and market clearing application, verify the effectiveness and practicality of the battery energy storage optimization method and system based on quantile regression convex constraint learning proposed in this invention. It can provide an aging-aware scheduling scheme for battery energy storage systems that combines safety and economy while maintaining the complete convexity of the model and computational tractability.

[0062] Example 2: To achieve the above objective, such as Figure 3 As shown, based on Embodiment 1, this invention discloses a battery energy storage optimization system based on quantile regression convex constraint learning, comprising: The data acquisition module 11 is used to acquire battery energy storage environment parameters and battery energy storage operation variables. The battery energy storage environment parameters include cumulative charge throughput, cell capacity and temperature variables. The battery energy storage operation variables include energy storage capacity, battery-level charging power and battery-level discharging power. Data processing module 12 is used to input battery energy storage environment parameters and battery energy storage operation variables into a pre-established battery aging convex proxy model based on quantile regression, and output the battery aging prediction value. The optimized output module 13 is used to transform the convex proxy model of battery aging based on quantile regression into a convex polyhedral constraint set in the form of linear inequalities based on the predicted battery aging values. Based on the convex polyhedral constraint set, a convex hybrid scheduling optimization model is generated. The convex hybrid scheduling optimization model is solved to obtain the battery energy storage optimization results.

[0063] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0064] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0065] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0066] The foregoing has shown and described the basic principles, main features, and advantages of this disclosure. Those skilled in the art should understand that this disclosure is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this disclosure. Various changes and modifications can be made to this disclosure without departing from its spirit and scope, and all such changes and modifications fall within the scope of this disclosure as claimed.

Claims

1. A battery energy storage optimization method based on quantile regression convex constraint learning, characterized in that, The method includes the following steps: The battery energy storage environment parameters and battery energy storage operation variables are obtained. The battery energy storage environment parameters include cumulative charge throughput, cell capacity and temperature variables. The battery energy storage operation variables include energy storage capacity, battery-level charging power and battery-level discharging power. The battery energy storage environment parameters and battery energy storage operation variables are input into a pre-established battery aging convex surrogate model based on quantile regression, and the predicted battery aging value is output. Based on the battery aging prediction values, the convex proxy model of battery aging based on quantile regression is transformed into a convex polyhedral constraint set in the form of linear inequalities through convex relaxation transformation. A convex hybrid scheduling optimization model is generated based on the convex polyhedral constraint set. The convex hybrid scheduling optimization model is solved to obtain the battery energy storage optimization results.

2. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 1, characterized in that, The battery aging convex surrogate model based on quantile regression is obtained by optimizing and improving the data-driven learning-based battery aging model based on convex neural networks.

3. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 2, characterized in that, The aging mapping of the battery aging model reconstructed by data-driven learning f true aging :( x t , θ t ) →ρ battery t The explicit representation of is: In the formula, x t = ( e t , p dis,t , p cha,t ) represents decision-related variables. e t Indicates the amount of energy stored. p dis,t , p cha,t These represent the absolute values ​​of the discharge and charging power, respectively. θ t = ( A , Q , T t () represents the environmental parameters for battery energy storage.

4. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 3, characterized in that, The convex proxy model obtained after optimizing and improving the data-driven learning-based battery aging model based on convex neural networks is as follows: r̃ battery t = f pcf aging ( x t , θ t : I) In the formula, Θ Represents the trainable parameters of the surrogate model; ρ̃ battery t This represents the aging rate predicted by the surrogate model.

5. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 4, characterized in that, The battery aging convex surrogate model based on quantile regression is constructed by defining a parameterized convex function, wherein... θ For input parameters, x The input variable is arbitrarily fixed, and the function is valid for any fixed... θ about x t To achieve convexity, a nested variable neural network and a parametric neural network are used. The variable neural network incorporates the decision variables... x t Mapped to aging rate prediction, the parametric neural network receives environmental parameters. θ t It also generates the weights and biases of the variable neural network.

6. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 5, characterized in that, The design of the variable neural network is as follows: Employing a ResNet residual network structure with skip connections, consisting of a weight set Ω vnn,t control: z 0 t = x t z l t = σ( W l t z l-1 + V l t x t + oh l t ), l = 1, ..., L -1 z L t = W L t z L-1 + V L t x t + oh L t , r̃ battery t = z L t In the formula, W l , V l Indicates the first l Layer weight matrix; ω l Indicates the first l Layer bias; L Represents network depth; residual path V l Inject raw input into each hidden layer x t To enrich the gradient flow; the activation function σ(·) is taken as the rectified linear unit σ( x ) = max( x , 0), or soft-addition function σ( x ) = log(1 + e x The trainable parameter set of a variable neural network is: Ω vnn,t ={ W 2 , ..., W L , V 1 , ..., V L , ω 1 , ..., ω L }; The parametric neural network is designed as follows: A parametric neural network is introduced to... θ t Mapped to the complete weight set: Ω vnn,t = f pnn (i t : Oh pnn ), f pnn (·): Θ → R m , m = S i=2 L n i n i-1 + S i=1 L n i n + S i=1 L n i In the formula, Ω pnn These represent the trainable parameters of the neural network itself. m This represents the total dimension of the generated weights; n i Indicates the first i Layer width; n The input dimension is represented by , and the generated weights and biases are denoted as . W l t (θ) V l t (θ) ω l t (θ).

7. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 1, characterized in that, The training of the battery aging convex surrogate model based on quantile regression employs a two-stage quantile training algorithm to optimize the model parameters. In the first stage, the adaptive moment estimation algorithm Adam is used for initial training, and in the second stage, the finite memory BFGS algorithm with boundary constraints is used for secondary refinement. Finally, the trained parameters are output as the parameters of the trained battery aging convex surrogate model based on quantile regression.

8. The battery energy storage optimization method based on quantile regression convex constraint learning according to claim 1, characterized in that, The process of transforming the convex surrogate model of battery aging based on quantile regression into a convex polyhedral constraint set in linear inequality form based on predicted battery aging values ​​includes: The trained convex surrogate model is transformed into a polyhedral constraint set applicable to linear programming, replacing the original non-convex aging constraints. A neural network is instantiated using ReLU as the activation function, and a degradation budget constraint is added to obtain the accurate data-driven aging region. e ≥ p battery t ρ battery t = W L t z L-1 t + V L t x t + oh L t z l+1 = max( W l z l + V l x t + oh l , 0), l = 1, ..., L -1 z 1 t = x t ,( W 2 ,..., W L , V 1 ,..., V L , oh 1 ,...,oh L ) = f pnn (i t ) In the formula, ε Let represent the degenerate budget. Since the max(·) operator makes the region non-convex, relaxing each max to the inequality ≥ yields a set of convex polyhedra: e ≥ p battery t ρ battery t = W L t z L-1 t + V L t x t + oh L t z l+1 ≥ W l z l + V l x t + oh l , l = 1, ..., L -1 z l+1 ≥ 0, l = 1, ..., L -1 z 1 t = x t Consider any point that is feasible in the relaxed set ( x t , ρ battery t , z 1 t , ..., z L-1 t ), can be started from the first L -1 layers tighten layer by layer towards 1. z l t until the inequality is equal, since each W l Element-wise non-negative, decrease z l It will only decrease W l z l Therefore, the inequality is preserved, and we finally obtain... Y aging ≥ W L t z L-1 t + V L t x t + ω L t Therefore, each in the convex relaxed set x t It also satisfies the precise aging region, meaning that the convex relaxation is feasible, and the relaxation constraint set is denoted as ( x t , θ t )∈ R pcf τ ( Y Aging ), and apply it independently for each charge / discharge period.

9. A battery energy storage optimization system based on quantile regression convex constraint learning, employing the battery energy storage optimization method based on quantile regression convex constraint learning as described in any one of claims 1 to 8, characterized in that, include: The data acquisition module is used to acquire battery energy storage environment parameters and battery energy storage operation variables. The battery energy storage environment parameters include cumulative charge throughput, cell capacity and temperature variables, and the battery energy storage operation variables include energy storage capacity, battery-level charging power and battery-level discharging power. The data processing module is used to input battery energy storage environment parameters and battery energy storage operation variables into a pre-established battery aging convex surrogate model based on quantile regression, and output the battery aging prediction value. The optimized output module is used to transform the convex proxy model of battery aging based on quantile regression into a convex polyhedral constraint set in linear inequality form based on the predicted battery aging values. A convex hybrid scheduling optimization model is generated based on the convex polyhedral constraint set, and the convex hybrid scheduling optimization model is solved to obtain the battery energy storage optimization results.

10. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program that can run on the processor. When the processor loads and executes the computer program, it employs the battery energy storage optimization method based on quantile regression convex constraint learning as described in any one of claims 1 to 8.

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