Robust optimization method considering wind-solar space-time correlation and distribution uncertainty

Abstract

The invention relates to a robust optimization method considering wind-solar space-time correlation and distribution uncertainty. On the basis of historical data of wind and light output, a high-dimensional ellipsoid set is constructed by adopting a minimum volume closed ellipsoid algorithm, and the high-dimensional ellipsoid set is corrected into a convex polyhedron which is more practical through an orthogonal decomposition and scaling factor adjustment method, so that the spatial-temporal correlation of the wind and light output is fitted more finely; in order to further integrate the probability distribution information of the wind and light output uncertainty, 1-norm and infinity-norm constraints are introduced, and a confidence set is constructed to describe the occurrence probability of a wind and light output prediction error scene. And secondly, establishing a day-ahead-intra-day two-stage robust optimization mathematical model of the integrated energy system, obtaining an optimal start-stop strategy of a unit according to a prediction scene in the day-ahead stage, and obtaining an optimal unit adjustment strategy according to a day-ahead scheduling strategy and a wind-light output limit scene in the intra-day stage. On the basis of the strong duality principle, a two-stage robust model is reconstructed into a form easy to solve, and then column and constraint generation (Column-and-Constraint Generation, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp, Camp; and carrying out iterative solution on the CG algorithm, and verifying the effectiveness of the provided model through an example. According to the method provided by the invention, the spatial-temporal correlation and uncertainty of wind and light output can be accurately captured, and reasonable consumption of renewable energy sources is promoted.

Description

Technical Field

[0001] The present invention belongs to the field of robust optimal scheduling of power systems, and particularly relates to a robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light. Background Art

[0002] The installed capacity of high-proportion wind and light resources continues to climb, the contradiction between the cross-space-time fluctuation characteristics and the rigid regulation ability of the power grid intensifies, the grid connection bottleneck is gradually emerging, and the wind and light abandonment rates and the load shedding frequency increase synchronously, exposing the adaptability bottleneck of traditional power system scheduling strategies in dealing with volatile power sources. Constructing a high-precision new energy power fluctuation prediction system, establishing a risk conduction quantitative assessment mechanism, and developing an optimization decision-making model with spatio-temporal coordination ability have become the key paths to enhance the consumption elasticity of system wind and light resources. By innovating the uncertainty modeling method and optimizing the control architecture, considerable economic value can be released while ensuring the system safety margin.

[0003] For the coordinated scheduling of power systems in the power generation environment with the uncertainty of wind and light resources, common processing methods include stochastic optimization, robust optimization, and distributionally robust optimization, etc. Stochastic optimization relies on an accurate probability distribution function of wind and light power generation uncertainty, which is often difficult to obtain, and scenario division will increase the computational complexity; robust optimization describes system uncertainty by specifying a fluctuation interval. Although the computational scale is reduced, the decision-making result is too conservative or extreme. Distributionally robust optimization introduces distribution information through fuzzy sets to reduce the uncertainty of scheduling, but it cannot make full use of the available historical data and still has a relatively conservative problem. Therefore, it is of great significance to develop a more flexible and efficient modeling technology that can accurately capture the complex uncertainty of wind and light output. Summary of the Invention

[0004] The present invention proposes a robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light. To handle the uncertainty of wind and light output in the scheduling of integrated energy systems, the MVEE algorithm and the 1-norm and ∞-norm constraints are used to represent the spatio-temporal correlation and the probability distribution information of uncertain output scenarios of wind and light output, and a day-ahead and intra-day two-stage robust optimization model with the optimal start-stop in the day-ahead stage and the optimal unit regulation in the intra-day stage as the objectives is constructed, and then the C&CG algorithm is used for iterative solution. The method proposed by the present invention effectively improves the confidence and robustness of wind and light output.

[0005] The beneficial effects of the present invention are as follows: A robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light involved in the present invention shows significant advantages in the description of wind and light correlation, the rationality of scenario probability distribution, and the comprehensive cost control, providing theoretical support and practical reference for the scheduling optimization of integrated energy systems under the uncertainty of wind and light output prediction. Brief Description of the Drawings

[0006] Figure 1 This is the flowchart of the robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light for the present invention.

[0007] Figure 2 This is the flowchart for solving the C&CG algorithm of the present invention.

[0008] Figure 3 This is the topological structure diagram of the integrated energy system of the present invention.

[0009] Figure 4 This is the diagram of the minimum volume enclosed ellipsoidal uncertainty set under different periods of the present invention.

[0010] Figure 5 This is the extreme scenario curve graph of the combined output of wind and light of the present invention.

[0011] Figure 6 This is the day-ahead and intra-day output curve graph of the combined output of wind and light of the present invention. Detailed implementation manners

[0012] A robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light. The robust optimization method described in the technical solution of the present invention constructs a convex hull uncertainty set based on the MVEE algorithm of wind and light output and the corresponding probability confidence set to solve the contradiction between the conservatism and envelope property in the description of the spatio-temporal distribution interval of wind and light. It is proposed to use the MVEE algorithm to fit the spatio-temporal correlation of wind and light output, and integrate the probability distribution information of wind and light output by introducing 1-norm and ∞-norm constraints to construct a limit scenario confidence set. Based on the strong duality principle, the established two-stage robust optimization model is reconstructed into a form convenient for solution, and the C&CG algorithm is used for iterative solution. Taking the IEEE14-node power system and the 6-node thermal system as examples, the proposed model is analyzed and verified. Through scheme comparison, the spatio-temporal correlation and uncertainty of wind and light output can be accurately captured, and the utilization efficiency of wind and light resources can be improved.

[0013] As Figure 1 shown, the flowchart of the robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light proposed by the present invention specifically includes the following steps: 1) Based on the historical data of wind and light output prediction errors, use the MVEE algorithm to construct a high-dimensional ellipsoidal set, and correct it into a convex polyhedron uncertainty set closer to the actual situation through orthogonal decomposition and scaling factor adjustment methods; 2) Introduce 1-norm and ∞-norm constraints to integrate the probability distribution information of the limit scenarios of wind and light output, and construct a probability distribution confidence set; 3) Establish a day-ahead and intra-day two-stage robust optimization mathematical model for the integrated energy system, obtain the optimal start-stop strategy of the units in the day-ahead stage, and obtain the optimal regulation strategy of the units in the intra-day stage; 4) The two-stage robust optimization mathematical model is iteratively solved using the C&CG algorithm, and the effectiveness of the proposed model is verified through numerical examples.

[0014] The implementation method is specifically elaborated as follows.

[0015] Construction of the uncertainty set model for wind and solar power output: Based on the historical data of wind and solar power output, the MVEE algorithm is used to construct a high-dimensional ellipsoidal set, and the modified convex polyhedron is obtained through orthogonal decomposition and scaling factor adjustment methods to better fit the spatio-temporal correlation of wind and solar power output data. In addition, 1-norm and ∞-norm constraints are introduced to construct a confidence set for the occurrence probability of wind and solar power output prediction error scenarios, thus effectively integrating the probability distribution information of wind and solar power output uncertainty.

[0016] (1) Minimum volume convex hull uncertainty set: In the present invention, the wind and solar power output is defined as a random variable, which can be expressed as:

[0017] In the formula: is t the output of the th wind and solar power generation unit in the time period; t is the predicted value of the output of the th wind and solar power generation unit in the t time period; is the prediction error of the output of the th wind and solar power generation unit in the time period; is the total number of wind and solar power generation units, where T is the number of wind turbines,

[0018] For the above random variable, by considering the spatio-temporal correlation characteristics of the wind and solar power output prediction error, a minimum volume closed convex hull uncertainty set can be established to obtain the wind and solar power output. The specific construction process of the minimum volume closed convex hull uncertainty set is as follows: 1) Collect the historical data of wind and solar power output prediction error and divide it by day. Let the number of days of the collected historical data be , and record the output data of each day as a historical scenario. The uncertain vector of the historical scenario can be expressed as:

[0019] In the formula: is the th group of historical data of wind and solar power output prediction error.

[0020] Construct a high-dimensional ellipsoid based on the historical data of the prediction error of wind and solar power output , All historical scenarios of the prediction error of wind and solar power output should be included. The construction of is as follows:

[0021] In the formula: is a random variable; is the center point of the ellipsoid; the positive definite matrix is the deviation direction of the symmetry axis of the ellipsoid.

[0022] Determine by solving the following optimization problem through the MVEE algorithm of and :

[0023] In the formula: is the volume of the -dimensional unit sphere.

[0024] 2) Construct the original convex polyhedron based on the high-dimensional ellipsoid .

[0025] The axial ellipsoid can be obtained through the following transformation of the original ellipsoid

[0026] In the formula: represents the corresponding scenario in the axial ellipsoid ; is the transformation matrix obtained through orthogonal decomposition , is a diagonal matrix, denoted as .

[0027] Thus, the expression of the axial ellipsoid is obtained:

[0028] The vertex coordinates ofcan be expressed as:

[0029] In the formula: is the number of vertices, .

[0030] According to the inverse transformation of , the vertex coordinates of the original ellipsoid can be expressed as: ​

[0031] The original convex polyhedron constructed from the vertices of can be expressed as: can be expressed as:

[0032] where: is the probability of the m th wind and light output prediction error scenario.

[0033] 3) Modify the original convex polyhedron by a scaling factor.

[0034] Since the original convex polyhedron is not sufficient to cover all historical scenarios, a scaling factor needs to be introduced to expand the region. The vertex coordinates of the modified polyhedron can be expressed as:

[0035] where: is the vertex coordinate of the polyhedron obtained after convex hull scaling.

[0036] The modified convex polyhedron can be expressed as:

[0037] Solving the minimum optimization problem of the scaling factor can be expressed as:

[0038] By obtaining the maximum value of through the above formula, the obtained scaling factor .

[0039] (2) Wind and light output scenario probability distribution constraint: According to the convex set theory, any possible wind and light output prediction error in the convex polyhedron can be expressed as a linear combination of extreme cases . can be expressed as:

[0040] In the present invention, the wind and light output scenarios in the intraday stage are described by the wind and light day-ahead predicted output and the corresponding extreme prediction error scenarios, and can be expressed as:

[0041] where: is the extreme scenario set of wind and light output during the intraday stage; is t the intraday stage output of the is t the extreme scenario of the prediction error of the

[0042] The historical data of the wind and light output prediction error in Equation (2) is set with a probability of . The occurrence probability of is the sum of the probability values of the historical error scenarios that are closest, and is regarded as the initial probability distribution value of scenario , denoted as

[0043] Satisfies the following confidence level:

[0044] In the formula: and respectively represent the tolerance values of the 1-norm and ∞-norm. The right side of the inequality in the above formula is the confidence level, which are respectively represented as and . Then, the corresponding tolerance values can be obtained in the following way:

[0045] In addition, the absolute value constraints in are difficult to handle. Therefore, they are transformed by expressing them as linear constraints.

[0046] In the formula: and are the introduced 0-1 variables, used to represent the offset state of the basic reference probability value; and are the introduced continuous variables.

[0047] Therefore, the absolute constraints based on the 1-norm and ∞-norm in

[0048] Robust Optimization Model of Integrated Energy System Considering the Uncertainty of Wind and Photovoltaic Objective Function: The data-driven robust collaborative optimization model proposed in this invention aims to minimize the total cost. Specifically, in the day-ahead stage, the optimal start-stop strategy of the units is obtained according to the predicted scenarios, and in the intra-day stage, the optimal unit regulation strategy is obtained according to the day-ahead dispatch strategy and the extreme scenarios of wind and photovoltaic power output, as follows:

[0049] In the formula: is the total operating cost of the system; is the operation and maintenance cost of the system equipment; is the depreciation cost of the system equipment; is the start-stop cost of the system-related equipment; is the reserve capacity cost of the system equipment; is the total energy purchase cost of the system; is the regulation cost of the system equipment; is the penalty cost for wind and photovoltaic curtailment of the system.

[0050] The specific costs mentioned above are as follows: 1) System operation and maintenance cost

[0051] In the formula: , , , , , , , , , and are the unit power operation and maintenance cost coefficients of wind turbines, photovoltaic panels, electrolyzers, power-to-ammonia, pressure swing adsorption nitrogen production, direct ammonia fuel cells, electric boilers, combined heat and power units, electrical energy storage, thermal energy storage, and ammonia energy storage, respectively; , are t wind turbine and photovoltaic power output in period

[0052] 2) System depreciation cost

[0053] In the formula: is the unit capacity cost of the th unit; is the installed capacity of the th unit; is the depreciation life of the th unit; is the discount rate, and in the present invention, the discount rate is taken as 5%; N are the units participating in the dispatching in the integrated energy system, where N includes electrolyzers, power-to-ammonia, pressure swing adsorption nitrogen production, direct ammonia fuel cells, electric boilers, combined heat and power units, electrical energy storage, thermal energy storage, and ammonia energy storage.

[0054] 3) System start-stop cost

[0055] In the formula: 、 、 、 and are the start-up costs of the electrolyzer, power-to-ammonia, direct ammonia fuel cell, combined heat and power unit, and electric boiler, respectively; 、 、 、 and are the shutdown costs of the electrolyzer, power-to-ammonia, direct ammonia fuel cell, combined heat and power unit, and electric boiler, respectively; 、 、 、 and are respectively t the start-up states of the electrolyzer, power-to-ammonia, direct ammonia fuel cell, combined heat and power unit, and electric boiler during the 、 、 、 and are respectively t the shutdown states of the electrolyzer, power-to-ammonia, direct ammonia fuel cell, combined heat and power unit, and electric boiler during the

[0056] 4) System reserve capacity cost

[0057] In the formula: and are the unit cost coefficients of upward reserve and downward reserve of the th unit respectively; and are respectively t the upward reserve capacity and downward reserve capacity of the th unit during the

[0058] 5) System total energy purchase cost

[0059] In the formula: 、 and are respectively t the unit cost coefficients of electricity, heat and gas purchased by the time-of-use system; 、 and are respectively t the electricity purchase power, heat purchase power and gas purchase volume of the time-of-use system.

[0060] 6) System regulation cost

[0061] In the formula: and are respectively t the unit cost coefficients of the upward regulation output and downward regulation output of the th unit during the time period; and are respectively t the upward regulation power and downward regulation power of the th unit during the time period.

[0062] (7)System wind and light curtailment penalty cost

[0063] In the formula: and are respectively the unit penalty cost coefficients for wind curtailment and light curtailment; and are respectively t the wind curtailment and light curtailment volumes of wind power and photovoltaic generating units during the time period.

[0064] Constraint conditions: (1)Day-ahead constraint conditions 1) Wind turbine and photovoltaic output constraints:

[0065] In the formula: and are respectively t the maximum values of wind turbine and photovoltaic output during the time period.

[0066] 2) Electrolyzer constraints:

[0067] In the formula: is t the hydrogen production volume during the time period; is t the electric power consumed by the electrolyzer during the time period; is the conversion efficiency of the electrolyzer; 、 They are the upper and lower limits of the input power of the electrolyzer, respectively; is t a 0-1 variable of the operating state of the electrolyzer during the time period, indicating that the electrolyzer is in the operating state, and indicating that the electrolyzer is in the shutdown state; and are the upper and lower ramp powers allowed for the electrolyzer, respectively.

[0068] 3) Pressure swing adsorption nitrogen production constraint:

[0069] In the formula: is t the electric power consumed during nitrogen production in the time period; t is the nitrogen production in the time period; is the molar mass of air; is the ideal gas constant; is t the temperature corresponding to the nitrogen production process; and are the inlet and outlet pressures of the pressure swing adsorption nitrogen production, respectively.

[0070] 4) Electrochemical ammonia synthesis constraint:

[0071] In the formula: is t the ammonia production in the time period; t is the electric power consumed during ammonia synthesis in the time period; t is the heat power provided to the system during ammonia synthesis in the time period; is the heat release efficiency of the heat power provided by the ammonia synthesis plant; t is the heat power released per unit ammonia synthesis; the mass ratio of ammonia, nitrogen, and hydrogen is 0.097:0.107:1, and the volume ratio is 2:1:3. Under standard conditions, 1 kg of hydrogen is approximately 11.2 They are the upper and lower limits of the electric energy input power of the ammonia synthesis equipment respectively; and They are the upper and lower limits of the ramp power of the ammonia synthesis equipment respectively.

[0072] 5) Direct ammonia fuel cell constraint:

[0073] In the formula: is t the electric power generated by the direct ammonia fuel cell during the is t the ammonia mass input to the direct ammonia fuel cell during the is the electric conversion efficiency of the direct ammonia fuel cell; is t a 0-1 variable of the operating state of the direct ammonia fuel cell during the and They are the upper and lower limits of the hydrogen energy input power of the direct ammonia fuel cell respectively; and They are the upper and lower limits of the ramp power of the direct ammonia fuel cell respectively.

[0074] 6) Cogeneration unit constraint:

[0075] In the formula: is t the natural gas power consumed by the cogeneration unit during the and are t the electric and heat power output by the cogeneration unit during the and are the electric and heat conversion efficiencies of the cogeneration unit; is t a 0 / 1 integer variable of the operating state of the cogeneration unit during the and They are the upper and lower limits of the natural gas input power of the cogeneration unit respectively; and They are the upper and lower limits of the ramp power of the cogeneration unit respectively.

[0076] 7) Electric boiler constraint:

[0077] In the formula: is t the electric power consumed by the electric boiler during the is t the heat power output by the electric boiler during the is the conversion efficiency of the electric boiler; is t a 0 / 1 integer variable of the operating state of the time-period electric boiler; and are respectively the upper and lower limits of the natural gas input power of the combined heat and power unit; and are respectively the upper and lower limits of the ramping power of the combined heat and power unit.

[0078] 8) Electric energy storage constraint:

[0079] In the formula: and are respectively 0 / 1 integer variables of the charging and discharging states of the electric energy storage; and are respectively t the charging and discharging powers of the electric energy storage in the time period; and are respectively the maximum values of the charging and discharging powers of the electric energy storage to the outside; and are respectively the charging and discharging efficiencies of the electric energy storage; is the installed capacity of the electric energy storage; and are respectively the upper and lower limits of the state of charge of the electric energy storage; the state of charge should be equal at the beginning and end of an optimization period T.

[0080] 9) Thermal energy storage constraint:

[0081] In the formula: and are respectively 0-1 variables of the charging and discharging states of the thermal energy storage; and are respectively t the charging and discharging energy powers of the thermal energy storage in the time period; and are respectively the maximum values of the charging and discharging energy powers of the thermal energy storage to the outside; and are respectively the charging and discharging energy efficiencies of the thermal energy storage; is the self-discharging coefficient of the thermal energy storage; is the installed capacity of the thermal energy storage; and are respectively the upper and lower limits of the load state of the thermal energy storage; the load state should be equal at the beginning and end of an optimization period T.

[0082] 10) Ammonia energy storage constraint:

[0083] In the formula: and are respectivelyt Charging and discharging power of ammonia energy storage during a period 、 are respectively t 0-1 variables of the charging and discharging states of ammonia energy storage during a period 、 are respectively the maximum values of the charging and discharging powers of ammonia energy storage is t the total power of ammonia energy storage during a period is the gas constant of ammonia is the ambient temperature is the unit calorific value of ammonia under standard conditions is t the load state of ammonia energy storage during a period is the installed capacity of ammonia energy storage 、 are respectively the upper and lower limits of the load state of ammonia energy storage

[0084] 11) Start-stop constraints of the unit:

[0085]

[0086]

[0087] In the formula: and are respectively t the start-stop states of the unit during period t and period N -1

[0088] 12) Maximum, minimum output and upper, lower reserve capacity constraints of the unit:

[0089] In the formula: is t the output of the unit during period N ; and are respectively t the maximum and minimum outputs of the unit during period N ;

[0090] 13) Ramp power constraint of the unit:

[0091] In the formula: and are respectively t the upward and downward ramp power limits of the unit during period N ;

[0092] 14) System reserve capacity constraint:

[0093] Wherein: and are respectively t the total upward and downward demand powers of the integrated energy system in a time period.

[0094] 15) Electric power balance constraint:

[0095] Wherein: is the number of adjustable electric power generating units; is t the electric load power of the integrated energy system in a time period.

[0096] 16) Thermal power balance constraint:

[0097] Wherein: is the number of adjustable thermal power generating units; is t the thermal load power of the integrated energy system in a time period.

[0098] 17) Electric network constraint: The electric network constraint of the present invention adopts a DC power flow constraint:

[0099] Wherein: is t the transmission power of line i - j in a time period; is the reactance of line i - j ; and are respectively t the phase angles of node i and node j in a time period; and are respectively the upper and lower limits of the transmission power of line i - j ; and are respectively the upper and lower limits of the phase angle of node i ; and are respectively the upper and lower limits of the phase angle of node j in a time period.

[0100] 18) Thermal network constraint: The heat network relies on the heat transfer of water circulation and needs to consider dynamic characteristics, transmission delay, and heat loss to avoid the mismatch between the supplied energy and the actual heat energy. The constraints of the heat network are as follows:

[0101] Where: and are the water temperatures at the inlet and outlet of the pipeline j at t time period; , , , and are the loss constant, time delay, mass flow length, and pipe diameter of the pipeline j respectively; is the largest integer not greater than ; is the ambient temperature. and are the flow rates of the pipeline t in the water supply system and the return water system during the time period j respectively; and are the outlet water temperatures of the pipeline t in the water supply system and the return water system during the time period j respectively; and are the mixing temperatures of the water supply system and the return water system at the node t during the time period k respectively; and are the sets of pipelines with the node k as the head and end respectively; and are the inlet water temperatures of the pipeline t in the water supply system and the return water system during the time period j respectively; and are the total heat power generated and the total heat power consumed during the time period t respectively; and are the injection water flow rate of the load node t and the output water flow rate of the heat source node m during the time period n respectively; is the specific volume of water; and are the mixing temperatures of the water supply system and the return water system at the load node t during the time period m respectively; and are tThe mixing temperature of the time-of-use water supply system and the return water system at the heat source node n of.

[0102] (2)Intra-day constraint conditions The intra-day constraint conditions are the constraint conditions for obtaining the integrated energy system dispatch model based on the extreme distributions of wind power and photovoltaic power. The constraints of electrolyzers, power-to-ammonia, pressure swing adsorption nitrogen production, direct ammonia fuel cells, electric boilers, combined heat and power units, electric energy storage, thermal energy storage, ammonia energy storage, electric network constraints, and thermal network constraints during the intra-day stage are similar to those during the day-ahead stage and will not be elaborated here.

[0103] 1) Ramp power constraint of the unit:

[0104] 2) Regulation power constraint of the unit:

[0105] 3) Electric power balance constraint:

[0106] In the formula: is t the curtailment power of the i th wind and solar power generation unit during the

[0107] 4) Thermal power balance constraint:

[0108] Model conversion and solution To simplify and clearly express the solution method of the derived objective function, the above objective function and constraint conditions are organized into a compact formula of the robust optimization model. The specific model is as follows:

[0109]

[0110]

[0111] In the formula: is the unit dispatch decision variable during the day-ahead stage; is the unit regulation and wind and photovoltaic curtailment decision variable during the intra-day stage; is when given, the feasible region of the variable ; c and b are constant coefficient vectors; A , B , E , F , G and K are constant coefficient matrices.

[0112] is a high-dimensional ellipsoidal uncertainty set W Any extreme scenario set of wind and light power output in W contains a variety of possible scenarios, that is, there are many constraints in the optimization model and it cannot be directly solved using commercial solvers. To effectively solve this two-stage model, the present invention uses the C&CG algorithm to decompose and solve the original problem. The core of the C&CG algorithm is to split the original problem into a master problem and a sub-problem and solve it iteratively. The master problem includes the unit start-stop decisions for the predicted scenario and the worst-case scenario, while the sub-problem finds the scenario with the most serious constraint violation under the current unit-on mode through a max-min problem.

[0113] The master problem is a MILP problem:

[0114] In the formula: is the number of iterations of the C&CG algorithm, ; The auxiliary variable is the maximum in-day scheduling cost returned in the master problem; is the th selected extreme scenario during the iteration; is the in-day scheduling decision variable under the extreme scenario

[0115] The day-ahead stage decision variable obtained according to the master problem is substituted into the decomposed sub-problem, and then a feasible operation adjustment strategy under all possible extreme scenarios is further obtained through max-min. The form of the sub-problem is as follows:

[0116] Since the decomposed sub-problem has a two-layer structure and is difficult to directly solve using existing commercial solvers, the original sub-problem is reconstructed by introducing the dual transformation method, and the obtained dual form is as follows:

[0117] In the formula: is the optimal scheduling decision for the day-ahead stage; and are the dual variable vectors related to the equality and inequality constraints in the robust optimization model, respectively.

[0118] Thus, the sub-problem can be transformed into a single-layer optimization model, but the bilinear terms in it make the dual sub-problem non-convex and difficult to solve. In view of this, this study uses the big M method to perform linearization transformation on the relevant bilinear terms and reconstructs the original problem into a MILP model to ensure the acquisition of the global optimal solution. Specifically as follows:

[0119] In the formula: and are auxiliary variables for construction; is a constant coefficient vector large enough; is a constant coefficient vector, and all elements in are 1.

[0120] In summary, the solution process based on the C&CG algorithm is as follows: Step 1: Set = 1 as the C&CG iteration counter, the lower bound of iteration , the upper bound of iteration , and the convergence accuracy ; Step 2: When , a feasible solution , can be obtained by solving the master problem, so as to obtain the lower bound . If , update the lower bound ; Step 3: Substitute the optimal scheduling decision of the day-ahead stage obtained in the th time into the sub-problem and solve it to obtain the uncertain variables , , so as to obtain the upper bound . If , update the upper bound ; Step 4: Judge the convergence condition. If , the iteration terminates and the optimal scheduling strategy and are output; otherwise, based on the worst-case scenario of the sub-problem, return the variables and constraints corresponding to the unsatisfied scenario to the master problem, set = + 1, and return to Step 2.

[0121] The solution flow chart of the C&CG algorithm is as Figure 2 shown.

[0122] Case study (1) Parameter setting: In this invention, a comprehensive energy system composed of an IEEE 14-node power system and a 6-node thermal system is used for case study to verify the effectiveness of the proposed two-stage robust optimization model. The topological structure of the comprehensive energy system is as Figure 3As shown. The wind and light output data of the present invention are sourced from two wind power plants and one photovoltaic power plant in a certain place in the northwest. The installed capacities of Wind Farm 1 and Wind Farm 2 are 300 MW and 200 MW respectively, and the installed capacity of the photovoltaic power plant is 150 MW. The penalty cost for curtailed wind and light is 300 yuan / MW×h; the time-of-use electricity price is shown in Table 1; the heat purchase price is 200 yuan / MW×h; the procurement price of natural gas is 350 yuan / MW×h. The power regulation cost of each unit is the product of the regulated output of the unit and the energy price, and the reserve capacity cost of each unit is set to 1 / 4 of the corresponding regulation cost. Convergence accuracy is set to 1%.

[0123] Table 1 Time-of-Use Electricity Price Table Time period Electricity price (yuan / kW·h) 00:00-05:00，22:00-24:00 0.358 05:00-09:00，13:00-17:00 0.741 09:00-13:00，17:00-22:00 1.031

[0124] (2)Analysis of spatio-temporal correlation of wind and light output: To study the spatio-temporal correlation between wind and light output, after processing the historical wind and light output data through the MVEE algorithm, the MVEE of some scenarios is as Figure 4 shown. Figure 4 In a), it is the ellipsoidal uncertainty set between Wind Farm 1 and Wind Farm 2. The two wind farms show a positive correlation, reflecting the positive correlation characteristics between wind farms under similar climatic conditions; Figure 4 In b), it is the ellipsoidal uncertainty set between Wind Farm 1 and the photovoltaic power plant. Wind Farm 1 and the photovoltaic power plant show a negative correlation characteristic, which is because the wind power output is large at night and small during the day, while the output characteristic of the photovoltaic power is opposite to that of the wind power output. Figure 4 In c), it is the ellipsoidal uncertainty set of Wind Farm 1 during the time period from 8:00 to 10:00. The output of Wind Farm 1 shows a negative correlation characteristic in adjacent time periods; Figure 4 In d), it is the ellipsoidal uncertainty set of Wind Farm 1 during the time period from 19:00 to 21:00. The output of Wind Farm 1 shows a positive correlation characteristic in adjacent time periods; the output characteristics of Wind Farm 1 in different time periods reflect the actual situation that the wind power gradually decreases during the day and gradually increases at night in the wind farm, and at the same time reflect the time correlation of the new energy output. Therefore, the ellipsoidal uncertainty set of the wind and light output generated by MVEE can reflect their spatio-temporal correlation.

[0125] (3)Analysis of the scheduling results of the two-stage robust optimization model considering the spatio-temporal correlation and uncertainty of wind and light: The MVEE algorithm proposed by the present invention can obtain the extreme scenarios of the combined wind and light output considering the wind and light correlation. The obtained extreme scenarios of the combined wind and light output are as Figure 5As shown in the figure. The upper and lower boundaries of the combined wind-solar power output can be obtained through the extreme scenarios of the combined wind-solar power output. On this basis, an extreme scenario set of the combined wind-solar power output is constructed. The solid and dashed curves respectively correspond to the upper and lower boundaries of the combined wind-solar power output per hour, representing the most optimistic and pessimistic values of the combined wind-solar power output respectively.

[0126] In addition, the day-ahead predicted value of the combined wind-solar power output and the combined wind-solar power output during the intraday stage obtained through extreme conditions are as shown in the figure. The gray shaded area represents the combined output range of the wind-solar power generation units obtained by considering the upper and lower boundaries of the extreme scenarios. Figure 6 As shown in the figure. The gray shaded area represents the combined output range of the wind-solar power generation units obtained by considering the upper and lower boundaries of the extreme scenarios.

[0127] Based on the day-ahead predicted value of the combined wind-solar power output and the extreme scenarios of the combined wind-solar power output during the intraday stage obtained above, the effectiveness of the scheduling scheme proposed in the present invention is verified by establishing the following 4 schemes. Scheme 1: A robust optimization model using a traditional box uncertainty set to describe the wind-solar power output; Scheme 2: A robust optimization model using the MVEE algorithm to describe the wind-solar power output, where the probabilities of extreme scenarios occurring are equal; Scheme 3: A distributionally robust optimization model using a probability distribution fuzzy set of uncertainty moment information to describe the wind-solar power output; Scheme 4: A data-driven robust optimization model using the MVEE algorithm to describe the wind-solar power output, where the probability of extreme scenarios occurring is the sum of the probability values of the most similar historical error scenarios . To analyze the performance of the above optimization schemes, the scheduling results of the 4 schemes are listed in Table 2.

[0128] Table 2 Comparison of Scheduling Results of 4 Schemes Dispatch result Plan 1 Plan 2 Plan 3 Plan 4 Operation and maintenance cost / 10,000 yuan 422.93 429.61 457.89 425.61 Depreciation cost / 10,000 yuan 54.97 45.71 33.82 25.19 Startup and shutdown cost / yuan 5.05 3.46 2.92 2.04 Energy purchase cost / 10,000 yuan 16.7 12.16 9.57 7.15 Standby cost / 10,000 yuan 22.19 15.58 11.11 7.88 Regulation cost / 10,000 yuan 85.1 61.87 45.77 31.52 Wind and solar curtailment cost / 10,000 yuan 3.82 2.96 2.5 1.44 Wind and solar curtailment rate 19.6% 15.2% 12.8% 7.4% Total cost / 10,000 yuan 610.76 571.35 563.58 500.83

[0129] As can be seen from Table 2, the total scheduling cost of Scheme 1 is the largest. This is because the scenarios considered in Scheme 1 with uncertain wind and solar power outputs are the worst, and this scheme has the strongest conservatism, resulting in the largest reserve cost in the day-ahead stage and regulation cost in the intraday stage. Compared with Scheme 1, the day-ahead scheduling cost, intraday rescheduling cost, and wind and solar curtailment rates of Scheme 2 are reduced by 2.94%, 27.1%, and 4.4% respectively. The reason is that the MVEE algorithm can more effectively describe the fluctuation range and capture the spatio-temporal correlation by accurately defining the uncertainty of wind and solar power outputs, thereby reducing the conservatism of scheduling, decreasing the wind and solar curtailment rates, and improving the system economy. In contrast, the box-type uncertainty set usually leads to higher wind and solar curtailment rates due to setting fixed upper and lower bounds and ignoring the spatio-temporal correlation. Scheme 3 significantly improves the decision-making flexibility by introducing the probability distribution information of wind and solar power outputs, effectively reducing the wind and solar curtailment rates and the total scheduling cost. At the same time, the intraday rescheduling cost of Scheme 3 is reduced by 45.72% and 25.54% compared with Scheme 1 and Scheme 2 respectively. The reason is that the distributionally robust rescheduling cost is the expected value in the worst scenario of wind and solar power outputs, rather than the cost value in the worst scenario in the robust model. The total scheduling cost of Scheme 4 is the lowest compared with the first three schemes. This is because Scheme 4, based on considering the spatio-temporal correlation characteristics of wind and solar power outputs, takes the intraday rescheduling cost in the worst scenario of wind and solar power outputs as the optimization objective, rather than only considering the cost in extremely rare extreme scenarios, thus alleviating the over-conservatism of the scheduling scheme when dealing with rare extreme scenarios. In addition, the total cost and wind and solar curtailment cost of Scheme 4 are reduced by 12.3% and 51.4% respectively compared with Scheme 2. The reason is that the extreme scenarios of Scheme 2 follow the same probability distribution, while Scheme 4 determines the probability of extreme scenarios by introducing the 1-norm and ∞-norm constraints on the probability distribution and adding the probability values of the most similar historical output error scenarios. This enables Scheme 4 to comprehensively consider the statistical distribution information of all historical scenarios, thus being closer to the actual operation of the power system. Through the comparison of the above four schemes, it verifies the good intention of the MVEE algorithm proposed in the present invention to reduce the conservatism and economy of the system optimal scheduling by considering the correlation and statistical distribution uncertainty of wind and solar power outputs.

[0130] Conclusion Based on the historical data of wind and solar power outputs, the MVEE algorithm is used to construct the uncertainty set, and the 1-norm and ∞-norm constraints are introduced to integrate the probability distribution information, which shows significant advantages in the description of wind and solar correlation, the rationality of the scenario probability distribution, and the comprehensive cost control, providing theoretical support and practical reference for the optimal scheduling of integrated energy systems under the uncertainty of wind and solar power output predictions.

Claims

1. A robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light, characterized in that, Specifically, it includes the following steps: 1) Based on the historical data of the prediction error of wind and photovoltaic power output, the minimum volume enclosing ellipsoid (MVEE) algorithm is used to construct a set of high-dimensional ellipsoids, and it is corrected to a more practical convex polyhedron uncertainty set through orthogonal decomposition and scaling factor adjustment methods; 2) The 1-norm and ∞-norm constraints are introduced to integrate the probability distribution information of the limit scenarios of wind and photovoltaic power output, and a probability distribution confidence set is constructed; 3) A day-ahead and intra-day two-stage robust optimization mathematical model of the integrated energy system is established. The optimal start-stop strategy of the unit is obtained in the day-ahead stage, and the optimal regulation strategy of the unit is obtained in the intra-day stage; 4) The C&CG algorithm is used to iteratively solve the two-stage robust optimization mathematical model, and the effectiveness of the proposed model is verified through numerical examples.

2. The robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light according to claim 1, characterized in that In step 1), the construction of the convex polyhedron uncertainty set is as follows: the wind and photovoltaic power output are defined as random variables, and considering the spatio-temporal correlation characteristics of the wind and photovoltaic power output prediction errors, a minimum volume enclosing convex hull uncertainty set is established based on the above random variables, and it is corrected to a more practical convex polyhedron through orthogonal decomposition and scaling factor adjustment methods, so as to more precisely fit the spatio-temporal correlation of the wind and photovoltaic power output.

3. The robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light according to claim 1, characterized in that, In step 2), the construction of the probability distribution confidence set is as follows: through the convex set theory, any possible wind and photovoltaic power output prediction error in the convex polyhedron uncertainty set can be expressed as a linear combination of extreme scenarios, and then the wind power output scenarios in the intra-day stage are obtained by the day-ahead predicted wind power output and the corresponding extreme scenarios of the prediction error. At the same time, based on the probability distribution information of the historical data of the wind and photovoltaic power output prediction errors, a confidence set of the occurrence probability of the wind and photovoltaic power output prediction error scenarios is constructed by introducing the constraints on the 1-norm and ∞-norm of the probability distribution.

4. The robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light according to claim 1, characterized in that, In step 3), for the established day-ahead and intra-day two-stage robust optimization model of the integrated energy system, the objective function is to minimize the total cost. In the day-ahead stage, the optimal start-stop strategy of the unit is obtained according to the predicted scenarios, and in the intra-day stage, the optimal unit regulation strategy is obtained according to the day-ahead scheduling strategy and the limit scenarios of the wind and photovoltaic power output.

5. The robust optimization method considering the spatio-temporal correlation and distribution uncertainty of wind and light according to claim 1, characterized in that In step 4), the solution method is based on the strong duality principle. The established two-stage robust optimization model is reconstructed into a form convenient for solution, and the C&CG algorithm is used for iterative solution to verify the effectiveness of the scheduling scheme proposed in the present invention. The present invention sets 4 schemes: a robust optimization model using the traditional box uncertainty set to describe the wind and photovoltaic power output; a robust optimization model using the MVEE algorithm to describe the wind and photovoltaic power output, where the probabilities of extreme scenarios are equal; a distributionally robust optimization model using the probability distribution fuzzy set of uncertainty moment information to describe the wind and photovoltaic power output; a data-driven robust optimization model using the MVEE algorithm to describe the wind and photovoltaic power output, where the probability of an extreme scenario is the sum of the probabilities of the closest historical error scenarios. The effectiveness of the method proposed in the present invention in capturing the spatio-temporal correlation and uncertainty of the wind and photovoltaic power output and improving the renewable energy consumption level is verified through the 4 set schemes.

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