An affine optimization scheduling method for high-load energy park considering wind-solar correlation

Abstract

The present application relates to a kind of high load energy park affine optimization scheduling method considering wind light correlation, belong to energy optimization scheduling field.The steps include: collecting the forecast interval of wind light unit output and load demand in park, construct initial parallelogram correlation model, convert it into multiple constraint affine form model by combining improved adaptive polygon algorithm;Using particle swarm optimization algorithm dynamically adjusts constraint condition, eliminates redundant interval, generates irregular polygon affine constraint that conforms to actual;The deterministic model of electrolytic aluminium, energy storage and thermal power unit is converted into affine form, and an optimization scheduling model containing power balance, equipment operation and cross-period constraint is constructed;With the minimum operating cost as the goal, a mixed integer linear programming solver is used to solve it.The present application reduces the conservatism of uncertainty interval by dynamically correcting wind light correlation area, improves new energy consumption rate, reduces the start-stop cost of thermal power unit, and realizes the collaborative optimization of economy and reliability.

Description

Technical Field

[0001] This invention relates to the field of industrial park optimization scheduling technology, specifically to an affine optimization scheduling method for high-energy-consuming industrial parks that considers the correlation between wind and solar power. Background Technology

[0002] Industrial parks reliant on energy-intensive industries face higher demands for grid stability and energy supply reliability due to their massive electricity needs. With the continuous increase in the penetration rate of new energy sources, industrial parks urgently need to leverage optimized dispatch strategies to resolve supply-demand imbalances. Therefore, for energy-intensive electrolytic aluminum industrial parks, this study utilizes the adjustable characteristics of electrolytic aluminum and energy storage devices to adjust peak and off-peak loads in a short time, coordinating with conventional loads to flexibly adjust demand power, enhance the absorption capacity of renewable energy, reduce carbon emissions, and achieve green and sustainable development goals.

[0003] In the field of traditional power system optimization and dispatching research, various uncertainties exist, such as the intermittency of wind and solar power generation and the random fluctuations in load demand. These factors pose challenges to traditional deterministic optimization methods. Affine optimization dispatching, which considers the uncertainty and correlation of renewable energy unit output, significantly reduces the interval width and conservatism compared to interval optimization. However, it still has shortcomings in considering correlation issues; the correlation region is limited by the correlation coefficient and does not reflect actual operating patterns. Further combining actual production data with affine dispatching that considers the correlation between wind and solar power distribution is of great significance for addressing the challenges of renewable energy fluctuations and obtaining more flexible, economical, and practically tailored optimization dispatching schemes. This can ensure production continuity while improving the overall efficiency of industrial parks. Summary of the Invention

[0004] The purpose of this invention is to provide an affine optimization scheduling method for high-energy-consuming industrial parks that considers the correlation between wind and solar power. By utilizing historical operating data and future forecast data of wind and solar power units, the method ensures the comprehensiveness and continuity of the data, so as to more accurately reflect the uncertain output of new energy units and obtain a more flexible, economical, and practical optimized scheduling scheme. This method can improve the overall efficiency of industrial parks while ensuring production continuity.

[0005] To achieve the above objectives, this invention provides an affine optimization scheduling method for high-energy-consuming industrial parks that considers the correlation between wind and solar power, comprising the following steps:

[0006] (1) Collect the output prediction range and load demand prediction range of wind turbines and photovoltaic units in the industrial park, and construct an initial parallelogram correlation model based on the correlation of historical wind and solar operation data. The model defines the wind and solar output fluctuation range and their correlation coefficients through constraints.

[0007] (2) Based on the cutting line equation and the adaptive polygon algorithm for adaptive correction of irregular convex polygon regions, the initial parallelogram correlation model is transformed into an affine model that includes the fluctuation range of wind and solar power output, correlation coefficient and authenticity constraints.

[0008] (3) The particle swarm optimization algorithm is adopted to minimize the area of ​​the corrected polygon region as the optimization objective. The cutting line slope coefficient and constant coefficient are dynamically adjusted to eliminate redundant intervals and obtain irregular polygon affine constraints that fit the actual operation.

[0009] (4) The deterministic models of electrolytic aluminum equipment, energy storage equipment and thermal power units in the park are transformed into affine models. Combined with the affine constraints in step (3), an affine interval optimization scheduling model for high energy-consuming industrial parks is constructed, which includes power balance constraints, equipment operation constraints and cross-time constraints.

[0010] (5) Using the minimization of park operation costs as the objective function, the Gurobi mixed-integer linear programming solver is used to solve the optimization scheduling model and output the optimization scheduling results.

[0011] Furthermore, the construction of the initial parallelogram correlation model in step (1) includes the following steps:

[0012] Step 1.1 Based on the correlation parallelogram

[0013] |ρ -1 T -1 R -1 D|≤e (1)

[0014] ρ xy = (ba) / (a+b) (2)

[0015] In the formula: a and b are the lengths of the two half-diagonals of the parallelogram, where a is the half-length of the shorter diagonal and b is the half-length of the longer diagonal. Half the length of the diagonal.

[0016] Correlation matrix of two uncertain variables ρ It can be constructed as:

[0017]

[0018] Where T is the correlation matrix; R is the interval matrix, which controls the size of the interval; D is the translation matrix; and e is the identity matrix.

[0019] Step 1.2: Define the auxiliary matrix A = ρ -1 T -1 R -1 ;

[0020] Right now

[0021]

[0022]

[0023] Step 1.3: The original parallelogram satisfies the following constraints.

[0024] -1≤ineq1≤1

[0025] -1≤ineq2≥1 (6)

[0026] Further, in step (2), the correlation model of the wind and light parallelogram is transformed into a constraint based on the improved adaptive polygon, and an affine form model considering the uncertainty, correlation and integrity of wind and light is constructed; the irregular convex polygon is subjected to analytical transformation and adaptive correction to unify the parallelogram and convex polygon.

[0027] Step 2.1: Define the equation of the tangent line

[0028] k1ineq1 + k2ineq2 ≤ R3

[0029] k3ineq1+k4ineq2≥R4 (7)

[0030] If k2 and k3 are both set to 1, then when the equation holds true, the expression is represented by two straight lines.

[0031] Step 2.2: Consider the constraints of the multi-dimensional region with correlation.

[0032] Overall constraints:

[0033]

[0034] Step 2.3 According to the formula (6) Know

[0035] -2≤ineq1+ineq2≤2 (10)

[0036] Step 2.4: The value ranges of k1, k2, R3, k4, and R4 are as follows:

[0037]

[0038] If k2 and k3 are both set to 1, and ineq1 and ineq2 are two variables, then equation (8) represents the region enclosed by 6 straight lines.

[0039] Step 2.5, based on the fundamental consideration of the correlation between wind and solar power, rewrites the affine form of wind and solar power output as follows:

[0040]

[0041] Step 2.6: [The formula is missing from the original text.] (12) Transforming into inequality form, we get:

[0042]

[0043] Where inf(·) represents the lower bound of the interval number; sup(·) represents the upper bound of the interval number.

[0044] Step 2.7: Construct k1A i +B i An interval number is obtained by calculating it. Right now:

[0045]

[0046] When two intervals are subtracted in an affine manner and the correlation coefficient is negative, the operation closely approximates the true value. The true transformation region is a mirror image of this. At this point, it can be considered that it is within... Figure 3 The line can represent lines AF and CE; similarly, lines CF and AE can be represented by choosing an appropriate k. 22 Obtain. For the two cuts GH and IJ, also select appropriate k values.

[0047] Step 2.8: The complete constraints of the adaptive polygonal interval affine form considering correlation are as follows:

[0048]

[0049] In the formula,

[0050]

[0051] Further, in step (3), the particle swarm optimization algorithm is used to transform the correlation into the slope coefficient and constant coefficient of the straight line in the inequality constraints for optimization:

[0052] Step 3.1: For area correction, the values ​​of k1, R3, k4, and R4 need to be determined. The slope coefficients and constant coefficients of the two lines are determined by the particle swarm optimization algorithm. The optimization objective is to minimize the area of ​​the cut region.

[0053] Particle velocity update formula:

[0054]

[0055] In the formula Let be the velocity of particle i in d-dimensional space at generation t+1; w be the inertia weight; c1 be the individual learning factor; and r1 and r2 be randomly generated numbers in the range [0,1]. Let represent the velocity and global extremum of generation t, respectively.

[0056] Particle position update formula:

[0057]

[0058] In the formula, Let be the position of particle i in the (t+1)th generation in d-dimensional space.

[0059] Step 3.2: Without considering the effects of correlation or realism, the true range of wind and solar power output is a parallelogram region. However, considering both realism and correlation, the true range of wind and solar power output is an irregular polygonal region. This demonstrates that the proposed method can account for both the correlation between wind and solar power outputs and the realism of wind and solar operation, thus obtaining the affine domain of wind and solar power output from the initial parallelogram region after the first correction. The value of .

[0060] Step 3.3: Obtain the k value that minimizes the region area using the particle swarm optimization algorithm. 33 k 44 R 33 R 44 The value of is determined by removing the excess area, which is represented as a corrected irregular polygonal region that more closely matches the actual operating range, thus helping to obtain affine optimization results with lower conservatism. The particle count is set to 50, the maximum number of iterations to 100, the cognitive factor C1 = 1.4, the social factor C2 = 1.4, and the inertia weight w = 0.7.

[0061] Further, in step (4), the remaining equipment in the park is transformed from a deterministic model into an affine model, and an affine model of the high-energy-consuming industrial park is constructed for optimization and solution.

[0062] Step 4.1: Establish an electrolytic aluminum equipment model:

[0063] Power-current constraint: The output power of the electrolytic aluminum load is controlled by controlling the current of the electrolytic cell. The power-current constraint is as follows:

[0064]

[0065] Power-temperature constraint: Because the electrolytic cell has thermal inertia, changes in power will cause significant fluctuations in the cell's temperature over a short period. The power-temperature constraints for adjacent time points are as follows:

[0066]

[0067]

[0068] In the formula: T t al The production temperature at time t is the load of the electrolytic aluminum. These are the upper and lower temperature limits for the electrolytic aluminum load, typically taken as 970 and 950℃ respectively. al m al These are the specific heat capacity coefficient and mass of the electrolyte, respectively.

[0069] Step 4.2: Establish an energy storage device model:

[0070] Power constraints:

[0071]

[0072] In the formula These are the upper and lower limits of energy storage capacity, Let t be the energy storage capacity value at time t.

[0073] State unique constraint:

[0074]

[0075] In the formula These represent the energy storage charging and discharging states at time t. The charge / discharge power value at time t is the energy storage power value. Upper and lower limits of charging power. Upper and lower limits of charging power.

[0076] Power-capacity constraints:

[0077]

[0078] In the formula μ bess η is the self-discharge rate of energy storage. bch η bdis This refers to the charging and discharging efficiency.

[0079] Step 4.3: Establish a thermal power unit model:

[0080] Output power upper and lower limit constraints:

[0081]

[0082] In the formula P gmin P gmax This indicates the minimum and maximum output limits of the thermal power unit. This represents the output of the thermal power unit at time t.

[0083] Climbing constraints:

[0084]

[0085] In the formula Indicates the upper and lower limits of the ramp rate for thermal power units. This represents the output of the thermal power unit at time t-1.

[0086] Step 4.4: Construct system power balance constraints

[0087]

[0088] In the formula, For conventional loads other than electrolytic aluminum loads, These are the actual outputs of photovoltaic and wind turbines, respectively.

[0089] Further, in step (5), the interval affine form of demand load is defined, and the constraints of electrolytic aluminum, energy storage equipment and thermal power units are transformed into interval affine form. An affine interval optimization scheduling model for high energy-consuming industrial parks that considers wind and solar uncertainties, correlation and integrity is constructed.

[0090] Step 5.1: Define the affine form of the load

[0091]

[0092] In the formula Let be the affine variable corresponding to the load demand power during time period t; These are the center values ​​of the corresponding affine variables; Obtained from the fluctuation range; The value range is [-1, 1]

[0093] Step 5.2: All equipment constraints in the park are transformed into affine constraints, mainly including three types: equality constraints, inequality constraints, and time-crossing constraints. For equality constraints that do not include decision variables other than state variables, the equality conditions are transformed according to the correspondence between the central values ​​on both sides of the equation and the correspondence between noise elements; for example:

[0094]

[0095] In the formula For the affine form of electrolytic aluminum, The central value of the variable in the affine form for electrolytic aluminum; The noise element coefficient is in the affine form for electrolytic aluminum.

[0096] Step 5.3: The inequality constraints are mainly the upper and lower limits of the output of the park model, which constrain the minimum and maximum values ​​that can be obtained, as shown in equation (32).

[0097]

[0098] Step 5.4: For the campus equipment model with cross-time constraints, the following transformation will be adopted:

[0099]

[0100] In the formula: and These are the affine forms of the power output of energy equipment in the industrial park during time period t and time period t-1, respectively; R down and Rup These are the set lower and upper limits for climbing, respectively; and They are respectively and The center value and noise element coefficient.

[0101] Step 5.4: Optimize the power regulation of energy storage and high-energy-consuming loads in electrolytic aluminum production, taking the park's operating costs as the objective and satisfying various constraints such as thermal power units, wind power, photovoltaic units, energy storage, and load. The objective function of the model is...

[0102] minF total =F G +F BESS (34)

[0103]

[0104]

[0105] Based on the fundamental theory of affine algorithms, the objective function in affine form can be further equivalently transformed, dividing it into two parts: operating cost and central value and affine radius. Therefore, equation (34) can be further defined as follows:

[0106]

[0107] In the formula, F total,0 F total,i F represents the center value of the industrial park's operating costs and the noise element coefficient of the uncertainty factor i, respectively; G,0 F BESS,0 F G,i F BESS,i , , respectively, are the center value of the operating cost of energy storage in the industrial park and the thermal power unit and the noise element coefficient of the uncertain factor i during time period t; ω is the optimization weight, and its value range is [0,1].

[0108]

[0109]

[0110] Step 5.5: Optimize the scheduling model as follows

[0111]

[0112] The affine optimization model of the industrial park shown in equation (40) is a mixed-integer linear programming problem. Equations (19)-(29) are all transformed affine constraint forms.

[0113] The Gurobi solver is used to solve the optimization scheduling model, and the interval affine optimization scheduling results of the high-energy-consuming industrial park are output.

[0114] Compared with existing technologies, it has the following advantages:

[0115] 1. Reduce conservatism and narrow the uncertainty range: By constructing an affine model that considers the correlation between wind and solar power output, and combining it with particle swarm optimization algorithm to dynamically correct the constraint region and eliminate extreme values ​​with extremely low probabilities, the width of the uncertainty range is significantly reduced, thereby reducing the conservatism of the scheduling scheme.

[0116] 2. Improve the renewable energy consumption rate: By flexibly adjusting the electrolytic aluminum load and coordinating the scheduling of energy storage equipment, the fluctuations in wind and solar power output are dynamically matched, reducing the phenomenon of wind and solar curtailment, and the renewable energy consumption rate is significantly improved.

[0117] 3. Optimize economic efficiency: With the goal of minimizing operating costs, this approach combines affine optimization and mixed-integer programming to reduce the central value of operating costs while ensuring production continuity, thus balancing economic efficiency and conservatism.

[0118] 4. Dynamically adapt to actual operational needs: Based on historical and predicted data, an adaptive polygon algorithm is used to dynamically correct the model region, making the scheduling scheme more consistent with the actual distribution of wind and solar power output and improving scheduling accuracy.

[0119] 5. Reduce start-up and shutdown costs of thermal power units: By optimizing the synergy between energy storage and electrolytic aluminum load, the load peak-valley difference is smoothed, the frequent peak-shaving needs of thermal power units are reduced, the number of start-ups and shutdowns is reduced, the equipment life is extended, and the operating cost is reduced by about 30%.

[0120] 6. Flexible handling of complex correlations: Breaking through the limitations of traditional rectangular or parallelogram regions, it constructs irregular polygonal affine constraints, which more realistically reflects the nonlinear correlation characteristics between wind and solar power output, and improves the robustness of scheduling schemes. Attached Figure Description

[0121] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0122] Figure 2 This is the predicted range for wind power output according to the present invention;

[0123] Figure 3 This is the predicted range for load demand according to the present invention;

[0124] Figure 4 This is the predicted range for photovoltaic output according to the present invention;

[0125] Figure 5 This is a diagram illustrating the effect of the modification process 1 of the present invention;

[0126] Figure 6 This is a diagram illustrating the effect of the modification process 2 of the present invention;

[0127] Figure 7 This represents the operating cost range for different weights in this invention;

[0128] Figure 8 This is the result of the affine scheduling of electric power in this invention. Detailed Implementation

[0129] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0130] This embodiment uses a two-dimensional planar affine wind-solar correlation model. Based on the correlation and dependence between noise elements, it can effectively eliminate possible values ​​with extremely low probability in the uncertain interval, thereby reducing the conservatism of scheduling.

[0131] The adaptive polygonal affine modeling method proposed in this invention, which considers correlation, dynamically corrects polygonal regions by combining historical wind and solar power output and prediction data, thereby obtaining a scheduling scheme that is closer to reality and providing a high-precision, low-conservatism solution for multi-energy synergistic optimization in industrial parks.

[0132] By introducing high-energy-consuming adjustable electrolytic aluminum loads into industrial parks, the overall efficiency of industrial parks can be improved. While ensuring production continuity, the synergistic interaction between the high-energy-consuming electrolytic aluminum loads and energy storage equipment can increase the renewable energy absorption rate, reduce the start-up and shutdown costs of thermal power units, and improve the renewable energy absorption rate, thus balancing economic efficiency and renewable energy utilization efficiency.

[0133] like Figure 1 The steps shown are as follows:

[0134] S1: Collect the source-load prediction interval of the industrial park and construct an initial parallelogram correlation model.

[0135] S1.1 Based on the correlation parallelogram

[0136] |ρ -1 T -1 R -1 D|≤e (1)

[0137] ρ xy = (ba) / (a+b) (2)

[0138] In the formula: a and b are the lengths of the two half-diagonals of the parallelogram, where a is the half-length of the shorter diagonal and b is the half-length of the longer diagonal. Half the length of the diagonal.

[0139] The correlation coefficient matrix ρ of two uncertain variables can be constructed as follows:

[0140]

[0141]

[0142] Where T is the correlation matrix; R is the interval matrix, which controls the size of the interval; D is the translation matrix; and e is the identity matrix.

[0143] S1.2: Define the auxiliary matrix A = ρ -1 T -1 R -1

[0144] Right now

[0145]

[0146]

[0147] S1.3: The original parallelogram satisfies the following constraints:

[0148] -1≤ineq1≤1

[0149] -1≤ineq2≥1 (6)

[0150] S2: Based on the improved adaptive polygon, the correlation model of the parallelogram of wind and light is transformed into a constraint, and an affine form model considering the uncertainty, correlation and integrity of wind and light is constructed; the irregular convex polygon is subjected to analytical transformation and adaptive correction to unify the parallelogram and convex polygon.

[0151] S2.1: Define the equation of the tangent line

[0152] k1ineq1 + k2ineq2 ≤ R3

[0153] k3ineq1+k4ineq2≥R4 (7)

[0154] If k2 and k3 are both set to 1, then when the equation holds true, the expression is represented by two straight lines.

[0155] S2.2: Constraints on the multivariable region considering correlation

[0156] Overall constraints:

[0157]

[0158] S2.3 According to formula (6) Know

[0159] -2≤ineq1+ineq2≤2 (10)

[0160] S2.4: That is, the ranges of values ​​for k1, k2, R3, k4, and R4 are respectively

[0161]

[0162] If k2 and k3 are both set to 1, and ineq1 and ineq2 are two variables, then equation (8) represents the region enclosed by 6 straight lines.

[0163] S2.5, based on the consideration of wind-solar correlation ， Rewrite the affine form of the wind and light output. ：

[0164]

[0165] S2.6: [The sentence is incomplete and requires more context to be translated accurately.] (12) Transforming into inequality form, we get:

[0166]

[0167] Where inf(·) represents the lower bound of the interval number; sup(·) represents the upper bound of the interval number.

[0168] S2.7: Construct k1A i +B i An interval number is obtained by calculating it. Right now:

[0169]

[0170] When two intervals are subtracted in an affine manner and the correlation coefficient is negative, the operation closely approximates the true value. The true transformation region is a mirror image of this. At this point, it can be considered that it is within... Figure 3 The line can represent lines AF and CE; similarly, lines CF and AE can be represented by choosing an appropriate k. 22 Obtain. For the two cuts GH and IJ, also select appropriate k values.

[0171] S2.8: The complete constraints of the adaptive polygonal interval affine form considering correlation are as follows:

[0172]

[0173] In the formula,

[0174]

[0175] S3. Use the particle swarm optimization algorithm to transform the correlation into the slope coefficient and constant coefficient of the straight line in the inequality constraints for optimization;

[0176] S3.1: For area correction, the values ​​of k1, R3, k4, and R4 need to be determined. The slope coefficients and constant coefficients of the two lines are determined by the particle swarm optimization algorithm. The optimization objective is to minimize the area of ​​the cut region.

[0177] Particle velocity update formula:

[0178]

[0179] In the formula Let be the velocity of particle i in d-dimensional space at generation t+1; w be the inertia weight; c1 be the individual learning factor; and r1 and r2 be randomly generated numbers in the range [0,1]. Let represent the velocity and global extremum of generation t, respectively.

[0180] Particle position update formula:

[0181]

[0182] In the formula, Let be the position of particle i in the (t+1)th generation in d-dimensional space.

[0183] S3.2: Without considering the effects of correlation, the true range of wind and solar power output is a parallelogram region. However, considering both realism and correlation, the true range of wind and solar power output is an irregular polygonal region. This demonstrates that the proposed method can account for both the correlation between wind and solar power outputs and the realism of wind and solar operation, thus obtaining the affine domain of wind and solar power output from the initial parallelogram region after the first correction. The value of .

[0184] S3.3: Obtain the k value that minimizes the region area using the particle swarm optimization algorithm. 33 k 44 R 33 R 44 The value of is determined by removing the excess area, which is represented as a corrected irregular polygonal region that more closely matches the actual operating range, thus helping to obtain affine optimization results with lower conservatism. The particle count is set to 50, the maximum number of iterations to 100, the cognitive factor C1 = 1.4, the social factor C2 = 1.4, and the inertia weight w = 0.7.

[0185] S4: The remaining equipment in the park is transformed from a deterministic model into an affine model, and an affine model of the high-energy-consuming industrial park is constructed for optimization and solution.

[0186] S4.1: Establish an electrolytic aluminum equipment model:

[0187] Power-current constraint: The output power of the electrolytic aluminum load is controlled by controlling the current of the electrolytic cell. The power-current constraint is as follows:

[0188]

[0189]

[0190]

[0191] Power-temperature constraint: Because the electrolytic cell has thermal inertia, changes in power will cause significant fluctuations in the cell's temperature over a short period. The power-temperature constraints for adjacent time points are as follows:

[0192]

[0193]

[0194] In the formula: T t al The production temperature at time t is the load of the electrolytic aluminum. These are the upper and lower temperature limits for the electrolytic aluminum load, set to 970℃ and 950℃ respectively. al m al These are the specific heat capacity coefficient and mass of the electrolyte, respectively.

[0195] S4.2: Establish an energy storage device model:

[0196] Power constraints:

[0197]

[0198] In the formula These are the upper and lower limits of energy storage capacity, Let t be the energy storage capacity value at time t.

[0199] State unique constraint:

[0200]

[0201]

[0202]

[0203] In the formula These represent the energy storage charging and discharging states at time t. The charge / discharge power value at time t is the energy storage power value. Upper and lower limits of charging power. Upper and lower limits of charging power.

[0204] Power-capacity constraints:

[0205]

[0206] In the formula μ bess η is the self-discharge rate of energy storage. bch η bdis This refers to the charging and discharging efficiency.

[0207] S4.3: Establish a thermal power unit model:

[0208] Output power upper and lower limit constraints:

[0209]

[0210] In the formula P gmin P gmax This indicates the minimum and maximum output limits of the thermal power unit. This represents the output of the thermal power unit at time t.

[0211] Climbing constraints:

[0212]

[0213] In the formula Indicates the upper and lower limits of the ramp rate for thermal power units. This represents the output of the thermal power unit at time t-1.

[0214] S4.4: Constructing system power balance constraints:

[0215]

[0216] In the formula, For conventional loads other than electrolytic aluminum loads, These are the actual outputs of photovoltaic and wind turbines, respectively.

[0217] S5: Define the interval affine form of demand load, transform the constraints of electrolytic aluminum, energy storage equipment, and thermal power units into the interval affine form, and construct an affine interval optimization scheduling model for high energy-consuming industrial parks that considers the uncertainty, correlation, and integrity of wind and solar power.

[0218] S5.1: Define the affine form of the load

[0219]

[0220] In the formula Let be the affine variable corresponding to the load demand power during time period t; These are the center values ​​of the corresponding affine variables; Obtained from the fluctuation range; The value range is [-1, 1]

[0221] S5.2: All equipment constraints in the park are transformed into affine constraints, mainly including three types: equality constraints, inequality constraints, and time-crossing constraints. For equality constraints that do not include state variables and other decision variables, the equality conditions are transformed according to the correspondence between the central values ​​on both sides of the equation and the correspondence between noise elements. For example:

[0222]

[0223] In the formula For the affine form of electrolytic aluminum, The central value of the variable in the affine form for electrolytic aluminum; The noise element coefficient is in the affine form for electrolytic aluminum.

[0224] S5.3: Inequality constraints are mainly the upper and lower limits of the output of the park model, which constrain the minimum and maximum values ​​that can be obtained, as shown in equation (32).

[0225]

[0226] S5.4: For campus equipment models with cross-time constraints, the following transformation will be adopted:

[0227]

[0228] In the formula: and These are the affine forms of the power output of energy equipment in the industrial park during time period t and time period t-1, respectively; R down and R up These are the set lower and upper limits for climbing, respectively; and They are respectively and The center value and noise element coefficient.

[0229] S5.4: Optimizing the power regulation of energy storage and high-energy-consuming loads in electrolytic aluminum production, with the objective of controlling park operating costs while satisfying various constraints such as thermal power units, wind power, photovoltaic units, energy storage, and load. The objective function of the model is...

[0230] minF total =F G +F BESS (34)

[0231]

[0232]

[0233] Based on the fundamental theory of affine algorithms, the objective function in affine form can be further equivalently transformed, dividing it into two parts: operating cost and central value and affine radius. Therefore, equation (34) can be further defined as follows:

[0234]

[0235] In the formula, F total,0 F total,i F represents the center value of the industrial park's operating costs and the noise element coefficient of the uncertainty factor i, respectively; G,0 F BESS,0 F G,i F BESS,i, , are the center value of the operating cost of energy storage in the industrial park and thermal power unit and the noise element coefficient of uncertain factor i, respectively, during time period t; ω is the optimization weight, with a value range of [0,1].

[0236]

[0237]

[0238] S5.5: The optimized scheduling model is as follows:

[0239]

[0240] The affine optimization model of the industrial park shown in equation (40) is a mixed-integer linear programming problem. Equations (19)-(29) are all transformed affine constraint forms.

[0241] S6: The Gurobi solver is used to solve the optimal scheduling model, and the interval affine optimization scheduling results of the high-energy-consuming industrial park are output.

[0242] The predicted source load values ​​for the industrial park within 24 hours are as follows: Figure 2 , Figure 3 and Figure 4 As shown, the fluctuation range for wind turbine and photovoltaic output is set at 10% of the predicted value, and the fluctuation range for electrical load is set at 5% of the predicted value. For an electrolytic aluminum plant with a rated power of 600MW, the current regulation range is set at 5%-10% above the rated value and 25%-30% below the rated value. For a 500MW thermal power unit that only performs routine peak shaving, the regulation range is set at 10% of the rated power. For a 100MW energy storage unit, the charging and discharging power is set at 20%-80% of its capacity, with the remaining 20% ​​of the rated capacity as the limit for regulation fluctuation.

[0243] Figure 5 , Figure 6 These are schematic diagrams of the correlation region after the first correction and the second correction, respectively.

[0244] To demonstrate the advantages of affine optimization and to consider the correlation between wind and solar power, the following three methods are compared, and the operating cost ranges of the three methods are shown in Table 1.

[0245] Method 1: Interval affine optimization algorithm that does not consider the correlation between wind and light;

[0246] Method 2: Interval affine optimization algorithm considering wind-solar correlation (ρ xy =-0.5);

[0247] Method 3: An adaptive polygon interval affine optimization scheduling method considering correlation and realism;

[0248] Table 1. Operating cost range for different methods

[0249]

[0250] Because the affine optimization method does not consider correlation, the interval values ​​are taken as the entire rectangle, resulting in a strong conservatism that easily leads to extreme cases. Therefore, as shown in Table 1 above, Method 1's operating cost interval completely covers that of Methods 2 and 3, exhibiting the greatest conservatism. Method 2, by using the PM model to narrow the fluctuation range of new energy units, achieves a narrower operating cost interval than the interval optimization method. Furthermore, Method 3, considering the realism of wind and solar power output, eliminates redundant value regions by considering correlation in the PM model, thereby further narrowing the operating cost interval.

[0251] The different correlation coefficient values ​​for Method 2 are as follows, from Figure 6 It can be seen that the closer the correlation coefficient is to -1, the smaller the parallelogram region, and the less conservative it is. Since the central value of operating costs represents the deterministic optimization result, the interval width represents the degree of fluctuation in operating costs considering uncertainty. Method 3 takes into account the realism of wind and solar operation, and its interval width can be compared with ρ in Method 2. xy The results for the operating cost range of -0.8 are similar, and the median operating cost of Method 3 is similar to that of Method 2. xy = -0.9 is closer. Its result is closer to the deterministic operation result, while also having an appropriate interval width to adapt to the uncertain output on the source load side.

[0252] Table 2. Operating cost ranges for different correlation coefficients in Method 2.

[0253]

[0254] Setting different weight values ​​in the objective function will shift the optimization scheduling scheme towards either an economical or conservative approach. For example... Figure 7 As shown, when the weight When the weights are large, the results tend to be conservative, resulting in a wider interval. At that time, the interval width increased significantly, and the central value of operating costs and The differences are not significant, combining good economic efficiency with conservatism.

[0255] like Figure 7 By setting different weight values ​​in the objective function shown, the optimized scheduling scheme will shift towards either an economical or conservative approach. For example... Figure 7 As shown, when the weight When the weights are large, the results tend to be conservative, resulting in a wider interval. At that time, the interval width increased significantly, and the central value of operating costs and The differences are not significant, combining good economic efficiency with conservatism.

[0256] Electrolytic aluminum loads, through coordinated scheduling with energy storage devices, significantly improve system flexibility. For example... Figure 8 As shown in (a), during the period when wind turbine output is high and photovoltaic output is low (0:00–1:00), the electrolytic aluminum load actively reduces its power. During the period from 3:00 to 4:00, wind turbine output increases, electrolytic aluminum output increases, and energy storage devices charge, ensuring that thermal power units operate at minimum power without shutting down, thus reducing start-up and shutdown costs. During the period from 9:00 to 17:00, wind turbine output fluctuates drastically, and photovoltaic units gradually reach their peak output for the day before gradually decreasing. The remaining power supplied to this portion of the load is rationally allocated by the energy storage system. This reduces part of the peak-to-valley difference in net load during this period. Figure 8 (c) Curve 1. During the period from 18:00 to 23:00, the output of wind turbines gradually increases, while the output of photovoltaic units is almost zero. At this time, the output of electrolytic aluminum decreases. Throughout the process, the electrolytic aluminum follows the principle of production constraints to adjust power and coordinates energy storage scheduling to enhance the consistency of supply and demand in the park. This strategy improves the renewable energy consumption rate and reduces the start-up and shutdown costs of thermal power units. Figure 8 (b) indicates that under the condition of source load fluctuation, the scheduling range of the other equipment in the park can be adjusted according to the uncertainty of the output of the new energy unit to obtain the optimal scheduling range. It can be seen that the electrolytic aluminum supply scheduling personnel have sufficient scheduling margin.

Claims

1. An affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation, characterized in that, Includes the following steps: (1) Collect the output prediction range and load demand prediction range of wind turbine and photovoltaic units in the industrial park, and construct an initial parallelogram correlation model based on the correlation of historical wind and solar operation data. The model defines the wind and solar output fluctuation range and their correlation coefficient through constraints. (2) Based on the tangent line equation and the adaptive polygon algorithm for adaptive correction of irregular convex polygon regions, the initial parallelogram correlation model is transformed into an affine model containing the fluctuation range of wind and solar power output, correlation coefficient and authenticity constraints. (3) The particle swarm optimization algorithm is adopted to minimize the area of ​​the corrected polygon region as the optimization objective. The cutting line slope coefficient and constant coefficient are dynamically adjusted to eliminate redundant intervals and obtain irregular polygon affine constraints that fit the actual operation. (4) The deterministic models of electrolytic aluminum equipment, energy storage equipment and thermal power units in the park are transformed into affine models. Combined with the affine constraints in step (3), an affine interval optimization scheduling model for high energy-consuming industrial parks is constructed, which includes power balance constraints, equipment operation constraints and cross-time constraints. (5) Using the minimization of park operation costs as the objective function, the Gurobi mixed-integer linear programming solver is used to solve the optimization scheduling model and output the optimization scheduling results; Step (2) in generating the affine form model includes the following steps: Step 2.1: Define the equation of the tangent line: The formula will make , When all values ​​are 1, the equation is true and the expression is represented by two straight lines. Step 2.2: Consider the constraints of the polymorphic region with correlation: Overall constraints: Step 2.3 According to equation (6): Step 2.4: The range of values ​​for are as follows: Will , All values ​​are 1, when When there are two variables, then equation (8) represents the region enclosed by six straight lines; Step 2.5, based on the fundamental consideration of wind-solar correlation, rewrites the affine form of wind-solar output as a linear expression including correlation coefficients: Step 2.6: Transform equation (12) into inequality form to obtain expression (13): in Represents the lower bound of the interval number; Represents the upper bound of the interval number; Step 2.7: Construction An interval number is obtained by calculating it. : Step 2.8: The complete constraints of the adaptive polygonal interval affine form considering correlation are as follows: In the formula, (16)。 2. The affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation as described in claim 1, characterized in that, The construction of the initial parallelogram correlation model in step (1) includes the following steps: Step 1.1: Based on the correlation coefficients of historical wind and solar power output data, construct a parallelogram model that satisfies the following constraints; In the formula: and These are the lengths of the two half-diagonals of the parallelogram. It is half the length of the shorter diagonal. It is half the length of the long diagonal; Correlation matrix of uncertain variables It can be constructed as: in, This is a correlation matrix; Let be an interval matrix, controlling the size of the interval; D is the translation matrix; and e is the identity matrix. Step 1.2: Define the auxiliary matrix , used to calculate the joint fluctuation range of wind and solar power output; Step 1.3: Verify whether the constraints of the parallelogram model satisfy the correlation distribution of historical wind and solar power output data: (6)。 3. The affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation as described in claim 1, characterized in that, Step (3) involves the following steps in the affine constraint of the irregular polygon: Step 3.1: Area correction needs to be determined. The value is determined by using the particle swarm optimization algorithm, with the minimum area of ​​the region as the optimization objective, and the slope coefficients and constant coefficients of the two straight lines are determined. During the optimization process, the particle position is continuously iterated according to the particle velocity update formula and the particle position update formula. Particle velocity update formula: In the formula For particles exist In 3D space, the first The speed of generation; Inertial weights; For individual learning factors; A randomly generated number within the range [0,1]. , They represent the first The speed and global extremum of the generation; Particle position update formula: In the formula, For particles exist In 3D space, the first The position of the generation; Step 3.2: Without considering the effects of correlation or realism, the true range of wind and solar power output is a parallelogram region; however, considering both realism and correlation, the true range is an irregular polygonal region. This demonstrates that the proposed method can account for both the correlation between wind and solar power outputs and the realism of wind and solar operation, allowing the affine range of wind and solar power output to be obtained from the initial parallelogram region after the first correction. The possible values ​​of ; Step 3.3: Obtain the minimum area of ​​the region using the particle swarm optimization algorithm. The value of is used to remove excess area, which is represented as a corrected irregular polygonal region that more closely matches the actual operating range, helping to obtain affine optimization results with lower conservatism; the particle number is set to 50, the maximum number of iterations is 100, and the cognitive factor is... Social factors Inertial weight .

4. The affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation as described in claim 1, characterized in that, Step (4) involves constructing an affine interval optimization scheduling model for high-energy-consuming industrial parks, which includes the following steps: Step 4.1: Establish an electrolytic aluminum equipment model: Power-current constraint: The output power of the electrolytic aluminum load is controlled by controlling the current of the electrolytic cell. The power-current constraint is as follows: Power-temperature constraints: The power-temperature constraints for adjacent time intervals are as follows: In the formula: For electrolytic aluminum load The production temperature at any given moment; These are the upper and lower temperature limits for the electrolytic aluminum load, respectively, and the temperatures are set as follows: ; These are the specific heat capacity coefficient and mass of the electrolyte, respectively. Step 4.2: Establish an energy storage device model: Power constraints: In the formula , These are the upper and lower limits of energy storage capacity, For energy storage Capacity value at any given time; State unique constraint: In the formula , These represent the energy storage charging and discharging operating states at time t; , For energy storage Constant charging and discharging power values; , Upper and lower limits of charging power; , Upper and lower limits of charging power; Power-capacity constraints: In the formula For energy storage self-discharge rate, , For charging and discharging efficiency; Step 4.3: Establish a thermal power unit model: Output power upper and lower limit constraints: In the formula This indicates the minimum and maximum output limits of the thermal power unit. express The output of thermal power units at any given moment; Climbing constraints: In the formula Indicates the upper and lower limits of the ramp rate for thermal power units. express The output of thermal power units at any given moment; Step 4.4: Construct system power balance constraints: In the formula, For conventional loads other than electrolytic aluminum loads, These are the actual outputs of photovoltaic and wind turbines, respectively.

5. The affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation as described in claim 1, characterized in that, Step (5) involves constructing the affine form model, which includes the following steps: Step 5.1: Define the affine form of the load: In the formula for Affine variables corresponding to time-period load demand power; These are the center values ​​of the corresponding affine variables; Obtained from the fluctuation range; The range of values ​​is ; Step 5.2: All equipment constraints in the park are transformed into affine constraints, including three types of constraint transformations: equality constraints, inequality constraints, and cross-time constraints. For equality constraints that do not include state variables and other decision variables, equality constraint transformation is performed according to the correspondence between the central values ​​on both sides of the equation and the correspondence between noise elements. In the formula For the affine form of electrolytic aluminum, The central value of the variable in the affine form for electrolytic aluminum; The noise element coefficient in the affine form for electrolytic aluminum; Step 5.3: Inequality constraints are applied to the upper and lower limits of the output of the park model, constraining the minimum and maximum values ​​obtained: Step 5.4: For the campus equipment model with cross-time constraints, the following transformation will be adopted: (33) In the formula: and Energy equipment in the industrial park Time period and Affine form of time-phase output; and These are the set lower and upper limits for climbing, respectively; , and , They are respectively and The center value and noise element coefficient; Step 5.4: Taking the park's operating costs as the objective, and satisfying the constraints of thermal power units, wind power, photovoltaic units, energy storage, and load, optimize the power regulation of energy storage and high-energy-consuming loads of electrolytic aluminum; the objective function of the model is: Based on the fundamental theory of affine algorithms, the objective function in affine form can be further equivalently transformed into two parts: operating cost and central value and affine radius; therefore, equation (34) can be further defined as follows: In the formula, , These represent the center value and uncertainties of the industrial park's operating costs. The noise element coefficient; , , , , representing the median and uncertainties of the operating costs of energy storage and thermal power units in the industrial park during time period t. The noise element coefficient; To optimize the weights, their values ​​range from [0,1]. Step 5.5: Optimize the scheduling model as follows: (40)。 6. The affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation as described in claim 1, characterized in that, The scheduling results output in step (5) include wind and solar power output ranges, energy storage charging and discharging plans, electrolytic aluminum load adjustment ranges, and thermal power unit output ranges.

7. The affine optimization scheduling method for high-energy-consuming industrial parks considering wind-solar correlation according to any one of claims 1-6, characterized in that, The method achieves dynamic matching with wind and solar power output by constraining the power-current of the electrolytic aluminum load and the charging and discharging power of the energy storage device, thereby improving the renewable energy absorption rate and reducing the start-up and shutdown costs of thermal power units.

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