Two-stage robust planning method for demand-side capacity considering cost and flexibility resources

Abstract

This invention relates to a two-stage robust planning method for demand-side capacity that considers both cost and flexibility resources, belonging to the field of power system operation and maintenance technology. By introducing an uncertainty adjustment parameter, this invention constructs a box-shaped uncertainty set with flexibly adjustable conservatism, effectively mitigating the inherent drawbacks of overly conservative traditional robust optimization methods. This allows the model to dynamically adjust the boundary of the uncertainty set according to the different risk tolerances of the actual system, thus achieving a refined trade-off between economy and reliability during the planning stage. The two-stage robust optimization model constructed in this invention, considering the electricity-carbon coupling mechanism, incorporates carbon trading costs as an important component of operating costs into the objective function, effectively responding to the needs of the national green and low-carbon energy strategy. The improved column generation and interior point hybrid algorithm designed in this invention proposes an adaptive scenario selection mechanism and a gradient-guided initialization strategy, significantly shortening the solution time while ensuring the global optimality of the solution.

Description

Technical Field

[0001] This invention belongs to the field of power system operation and maintenance technology, and in particular relates to a two-stage robust planning method for demand-side capacity that takes into account both cost and flexibility resources. Background Technology

[0002] With the increasing penetration of renewable energy sources such as wind and solar power into the power system, the uncertainty and complexity of power system operation have significantly increased. The intermittency and volatility of wind and solar power output, as well as the diversification and random fluctuations of load demand, have brought unprecedented challenges to the planning and operation of the power system. Against this backdrop, while the introduction of electricity market mechanisms has guided resource optimization through price signals to some extent, it has also brought new uncertainties such as electricity price fluctuations and market return risks. Traditional power system planning methods are mostly based on deterministic models or single-scenario optimization, making it difficult to effectively address the risks arising from the superposition of multiple uncertainties on both the source and load sides and in the market. Especially under the combined effect of high-proportion renewable energy integration and deepening electricity market reforms, the limitations of traditional planning methods are becoming increasingly apparent. Their planning results are often overly optimistic or conservative, making it difficult to comprehensively consider the system's economic efficiency, reliability, and market adaptability.

[0003] The closest existing technologies mainly include power capacity planning methods based on stochastic programming or traditional robust optimization. Stochastic programming methods rely on probability distributions to describe uncertainty, requiring high accuracy in the probability distributions of random variables such as wind and solar power output, load, and market electricity prices. However, accurately obtaining the joint probability distribution of multi-dimensional uncertainties is extremely difficult in practice, and the generation of random scenarios easily leads to the curse of dimensionality, with computational complexity increasing sharply with the number of scenarios, thus limiting its engineering applicability. Traditional robust optimization methods, while not requiring probability distributions and using bounded uncertainty sets to describe the fluctuation range, can handle worst-case optimization problems. However, they often over-rely on extremely conservative scenarios, ignoring the statistical characteristics of most scenarios and the mild fluctuations in the market in actual operation. This results in poor economic efficiency, low investment efficiency, and resource allocation that fails to meet the actual operational needs of the electricity market. Furthermore, most existing studies have failed to integrate the carbon-electricity coupling mechanism and electricity market transaction costs into the planning model, lacking joint optimization of operating costs such as carbon trading costs, market electricity purchase costs, and ancillary service fees. This fails to accurately reflect the true operational economics of the system under low-carbon policy guidance and is also difficult to adapt to the planning requirements of new power systems in the electricity market environment.

[0004] Therefore, existing technologies suffer from problems such as insufficient model adaptability, difficulty in balancing economic efficiency and reliability, and insufficient consideration of the synergy between carbon emissions and market mechanisms when dealing with multiple uncertainties in a high proportion of renewable energy and electricity market environment. There is an urgent need to develop an efficient power capacity planning method that can simultaneously take into account system operational reliability, investment economy, low carbon benefits, and market adaptability to solve the above problems. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a two-stage robust planning method for demand-side capacity that takes into account both cost and flexibility resources, in order to address the technical problems of insufficient model adaptability, difficulty in balancing economy and reliability, and insufficient consideration of the synergy between carbon emissions and market mechanisms in existing technologies.

[0006] A two-stage robust planning method for demand-side capacity that considers both cost and flexibility resources includes the following steps, performed sequentially:

[0007] Step 1: Construct a multi-uncertainty model

[0008] This includes uncertainties in photovoltaic power, wind power, and load.

[0009] Step 2: Construct a two-stage robust planning model for power supply capacity that considers multiple uncertainties.

[0010] The first-stage robust programming model is based on the capacity of the units to be installed, namely the configuration capacity of wind power, photovoltaic, thermal power and energy storage, given in the absence of an unknown uncertainty set, with the objective function being to minimize the sum of the investment cost and maintenance cost of the units.

[0011] The second-stage robust programming model adjusts the decisions of the first stage based on the actual system operation results after the uncertainty set is obtained, in order to minimize the additional costs or losses caused by uncertain factors, i.e., minimize the system operation cost.

[0012] Step 3: Solve the two-stage robust programming model. The output results include the optimal power capacity configuration scheme, i.e., the specific installed capacity of thermal power, wind power, photovoltaic power, and energy storage, the objective function values ​​of each stage, the operating state parameters under key uncertainty scenarios, and the algorithm convergence curve.

[0013] The photovoltaic uncertainty model is shown in the following equation:

[0014] ;

[0015] In the formula: For photovoltaic units t Constant output power; t Take 24 moments at equal time intervals within a 24-hour period; For photovoltaic units t Predicted power values ​​at any given time; For photovoltaic units t The maximum uncertainty of the output power at any given moment; For the photovoltaic unit, there is a positive uncertain binary variable, taking the value [0,1]. express t At any given time, the actual output of the photovoltaic units did not exceed the predicted value and did not reach the maximum uncertainty value. express t The actual output of the photovoltaic unit at that time was higher than the predicted value and the output deviation reached the maximum uncertainty value; This is a negative, uncertain binary variable for the photovoltaic unit, taking values ​​[0,1]. This indicates that at time t, the actual output of the photovoltaic unit did not fall below the predicted value and did not reach the maximum uncertainty value. express t The actual output of the photovoltaic unit was lower than the predicted value and the output deviation reached the maximum uncertainty value. For photovoltaic power output power uncertainty adjustment parameters, it means the maximum number of hours in a 24-hour period where the actual output of the photovoltaic unit reaches the maximum positive or negative uncertainty deviation is not allowed to exceed.

[0016] The wind power uncertainty model is shown in the following equation:

[0017] ;

[0018] In the formula: For wind turbines t Constant output power; For wind turbines t Predicted power values ​​at any given time; For wind turbines t The maximum uncertainty of the output power at any given moment; This is a positively indeterminate binary variable for the wind turbine, taking values ​​[0,1]. express t At any given time, the actual output of the wind turbines did not exceed the predicted value and did not reach the maximum uncertainty value. express t At any given moment, the actual output of the wind turbine exceeded the predicted value, and the output deviation reached the maximum uncertainty value. This is a negative, uncertain binary variable for the wind turbine, taking values ​​of [0,1]. This indicates that at time t, the actual output of the wind turbine did not fall below the predicted value and did not reach the maximum uncertainty value. express tThe actual output of the wind turbine was lower than the predicted value and the output deviation reached the maximum uncertainty value. For the uncertainty adjustment parameter of wind turbine output power, it means the maximum number of hours in a 24-hour period in which the actual output of the wind turbine reaches the maximum positive uncertainty deviation or the maximum negative uncertainty deviation is not allowed to be exceeded.

[0019] The load uncertainty model is shown in the following equation:

[0020] ;

[0021] In the formula, For load t Power at any given moment; For load t Predicted value at any time; For load t The maximum uncertainty in power change at any given time; Let be a positive, uncertain binary variable representing the load, with a value of [0,1]. This indicates that the actual load at time t did not exceed the predicted value and did not reach the maximum uncertainty value. express t The actual load value at any given time was higher than the predicted value, and the output deviation reached the maximum uncertainty value. This is a negative, uncertain binary variable representing the load, with a value of [0,1]. express t The actual load at any given time did not fall below the predicted value and reach the maximum uncertainty value. express t The actual load value at any given time was lower than the predicted value, and the output deviation reached the maximum uncertainty value. This is a load power uncertainty adjustment parameter, representing the maximum number of hours within a 24-hour period where the actual load value reaches the maximum positive or negative uncertainty deviation.

[0022] In step two, the objective function of the robust programming model in the first stage is:

[0023] ;

[0024] In the formula, This is the objective function for the first stage; and These are the investment cost and maintenance cost of the generating unit, respectively. A collection with installation units; For the unit Construction cost conversion factor; The discount rate; For the unit Service life; For the unit The unit capacity construction cost; For the unit Installation capacity; For the unit The unit capacity maintenance cost;

[0025] The objective function of the second-stage robust programming model is:

[0026] ;

[0027] In the formula, This is the objective function for the second stage; The coal consumption cost of thermal power units; The costs of curtailing wind and solar power; For carbon trading costs; Insufficient flexibility incurs penalties; This is a transaction cost item in the electricity market;

[0028] in,

[0029] ;

[0030] In the formula, All are coal combustion coefficients for thermal power units; For thermal power units t Efforts made at all times;

[0031] ;

[0032] In the formula, As a penalty factor for wind curtailment; This is a penalty factor for discarding light. for t Wind power curtailment at any time; for t Constantly abandoned photovoltaic power;

[0033] ;

[0034] In the formula, for t The cost of carbon trading at any given time is shown in the following formula:

[0035] ;

[0036] In the formula, The carbon trading price under the coupling of electricity and carbon; The incentive coefficient for selling carbon allowances after electro-carbon coupling; The cost growth factor for purchasing carbon allowances after electro-carbon coupling; for t The price of carbon trading at any time; These represent the step sizes for the negative and positive carbon emission intervals, respectively. for t The formula for calculating the carbon emission trading volume at any given time is as follows:

[0037] ;

[0038] In the formula, This is the baseline value for carbon emissions from thermal power plants; This is the base value for carbon emission quotas for thermal power plants; For time intervals, This indicates that each time period lasts for 1 hour;

[0039] ;

[0040] In the formula, A penalty factor for insufficient flexibility; They are respectively t The system lacks flexibility in both upward and downward operation.

[0041] ;

[0042] In the formula, for t Current market electricity price for t The market trading volume of electricity before the specified time; for t Real-time market electricity prices for t Real-time market-balanced power supply; for t Market prices for 24 / 7 assisted services for t Real-time auxiliary service procurement volume.

[0043] The two-stage robust programming model has the following constraints:

[0044] (1) The installed capacity constraint is:

[0045] ;

[0046] In the formula, These are the installed capacities of thermal power units, wind power units, photovoltaic units, and energy storage, respectively. These are the upper limits for the installed capacity of thermal power units, wind power units, photovoltaic units, and energy storage, respectively.

[0047] (2) Constraints of thermal power units:

[0048] a. The output constraint of thermal power units is:

[0049] ;

[0050] In the formula, These are the upper and lower limits of the output of thermal power units, respectively.

[0051] b. The ramping constraint for thermal power units is:

[0052] ;

[0053] In the formula, These represent the upward and downward ramp rates of thermal power plants, respectively. For thermal power units Efforts made at all times;

[0054] (3) Energy storage constraints:

[0055] a. The charging and discharging power constraint is:

[0056] ;

[0057] In the formula, They are respectively t The discharge and charging power that stores energy at all times; The coefficients are known. This represents the maximum limit of charging and discharging. This represents the maximum energy storage capacity. for t Constant charging and discharging status parameters;

[0058] b. The operating conditions for energy storage are as follows:

[0059] ;

[0060] c. The energy storage state of charge constraint is:

[0061] ;

[0062] In the formula, for t Constant energy storage state of charge; To improve the charging and discharging efficiency of energy storage; The starting power for energy storage;

[0063] These are the upper and lower limits of the energy storage state of charge.

[0064] d. The charge / discharge balance constraint is:

[0065] ;

[0066] (4) The power balance constraint is:

[0067] ;

[0068] In the formula, They are respectively t At any given moment, the output power of the wind turbine, the output power of the photovoltaic unit, and the load power are all uncertain variables.

[0069] Based on the objective function and constraints, the two-stage robust optimization model is transformed into:

[0070] ;

[0071] In the formula, The first stage target to be optimized is represented by equation (4); These are the variables to be optimized in the first stage. , These are the configuration capacities of thermal power units, wind power units, photovoltaic units, and energy storage; It is an uncertain set of wind and solar load; It is the range of the uncertain set; represent The constraint condition is equation (13). This represents the total system operating cost based on the unit configuration capacity obtained in the first stage, and is also the optimization target for the second stage, namely Equation (5). These are the variables to be optimized in the second stage. , , , , , , , These are the operating power of thermal power units, the operating power of wind power units, the operating power of photovoltaic units, the charging power of energy storage, the discharging power of energy storage, and the curtailed wind and solar power, which are determined by the capacity determined in the first phase and the uncertain variables. and They represent the second-stage inequality constraints and equality constraints, respectively, where the inequality constraints include equations (13)-(17), and the equality constraints include equations (18) and (19).

[0072] The algorithm for solving the two-stage robust programming model in step three is based on the dual theory and decomposition idea of ​​two-stage robust optimization. The model is decomposed into a main problem and sub-problems. The main problem is the first-stage capacity configuration optimization problem, which belongs to mixed integer linear programming problem. The decision variables are the installed capacity of thermal power units, wind power units, photovoltaic units and energy storage. The objective function is to minimize investment and maintenance costs.

[0073] The subproblem is the minimization of the second-stage operating cost problem, which is a continuous optimization problem with uncertain parameters. It uses the capacity output by the main problem as a constraint to find the minimum operating cost under a given uncertain scenario, including the costs of coal consumption, wind and solar curtailment penalties, carbon trading, and insufficient flexibility penalties.

[0074] Based on strong duality theory, the maximum value of the subproblem, i.e., the operating cost under the worst scenario, is transformed into the minimum value of the dual problem. The dual variables of the subproblem are the dual factors of the thermal power unit output and the dual factors of the energy storage charging and discharging power. The optimal objective value of the subproblem is embedded into the main problem in the form of linear constraints through the dual variables, forming the cutting plane of the main problem. The improved column generation mechanism avoids the computational explosion caused by exhaustive scenarios by screening columns of uncertain scenarios that have a significant impact on the objective function of the main problem. The interior point method uses the obstacle function to transform the inequality constraints of the subproblem into an unconstrained optimization problem. The Karush-Kuhn-Tucker (KKt) conditions are solved iteratively by Newton's method to quickly obtain the optimal solution of the subproblem and the dual information.

[0075] The operating status parameters in step three include thermal power output, energy storage charging and discharging power, and wind and solar curtailment.

[0076] Through the above design scheme, the present invention can bring the following beneficial effects:

[0077] This invention introduces an uncertainty adjustment parameter to construct a box-type uncertainty set with flexibly adjustable conservatism, effectively mitigating the inherent drawback of overly conservative traditional robust optimization methods. The introduction of this parameter allows the model to dynamically adjust the boundaries of the uncertainty set based on the different risk tolerance levels of the actual system, thus achieving a refined trade-off between economy and reliability during the planning stage. The existence of this core component ensures that the final power capacity configuration scheme avoids both operational risks caused by overly optimistic approaches and investment waste due to excessive conservatism.

[0078] Furthermore, the two-stage robust optimization model constructed in this invention, which considers the electricity-carbon coupling mechanism, incorporates carbon trading costs as an important component of operating costs into the objective function. This design directly produces a positive effect of reducing the overall carbon emissions of the system, causing planning schemes to automatically favor low-carbon and efficient resource allocation combinations, promoting the consumption of renewable energy, and effectively responding to the needs of the national green and low-carbon energy strategy.

[0079] Furthermore, the improved column generation and interior point hybrid algorithm designed in this invention proposes an adaptive scenario selection mechanism and a gradient-guided initialization strategy to address the double-layer nested structure and mixed-integer nonlinear characteristics of the model. This algorithm component directly solves the problem of low computational efficiency under large-scale uncertain scenarios, significantly shortens the solution time, and ensures the global optimality of the solution. This makes the method proposed in this invention applicable to the planning and calculation of practical large-scale power systems, and has good engineering application prospects.

[0080] Ultimately, the planning method provided by this invention can output a power capacity configuration scheme that combines economy, reliability and low carbon emissions, including the optimal installed capacity of thermal power, wind power, photovoltaic power and energy storage, as well as key operating status parameters. This provides decision-makers with clear and quantitative important basis and has important practical application value for promoting the construction of new power systems. Detailed Implementation

[0081] A two-stage robust planning method for demand-side capacity that considers both cost and flexibility resources includes the following steps, performed sequentially:

[0082] I. Constructing a Multiple Uncertainty Model

[0083] The large-scale integration of flexible loads and wind and solar power is a major factor leading to a sharp increase in power system uncertainty. This directly impacts the selection of planning schemes and the reliability of system operation during power system planning. Therefore, addressing these uncertainties during planning is essential. Since obtaining the probability distribution of the sources of uncertainty in wind and solar loads is very difficult, a set-based approach is used to represent uncertainty. Furthermore, the construction of the uncertainty set plays a decisive role in the accuracy of robust optimization model solutions. Below, we will construct a box-type uncertainty set using the critical values ​​of decision variables as constraints.

[0084] 1. The photovoltaic uncertainty model is shown in equation (1):

[0085] ;

[0086] In the formula: For photovoltaic units t Constant output power; t Take 24 moments at equal time intervals within a 24-hour period; For photovoltaic units t Predicted power values ​​at any given time; For photovoltaic units t The maximum uncertainty of the output power at any given moment; For the photovoltaic unit, there is a positive uncertain binary variable, taking the value [0,1]. express tAt any given time, the actual output of the photovoltaic units did not exceed the predicted value and did not reach the maximum uncertainty value. express t The actual output of the photovoltaic unit at that time was higher than the predicted value and the output deviation reached the maximum uncertainty value; This is a negative, uncertain binary variable for the photovoltaic unit, taking values ​​[0,1]. This indicates that at time t, the actual output of the photovoltaic unit did not fall below the predicted value and did not reach the maximum uncertainty value. express t The actual output of the photovoltaic unit was lower than the predicted value and the output deviation reached the maximum uncertainty value. This is a parameter for adjusting the uncertainty of photovoltaic (PV) unit output power. It represents the maximum number of hours within a 24-hour period during which the total number of hours in which the actual output of the PV unit reaches the maximum positive or negative uncertainty deviation is not allowed to exceed.

[0087] 2. The uncertain model for wind power is shown in equation (2):

[0088] ;

[0089] In the formula: For wind turbines t Constant output power; For wind turbines t Predicted power values ​​at any given time; For wind turbines t The maximum uncertainty of the output power at any given moment; This is a positively indeterminate binary variable for the wind turbine, taking values ​​[0,1]. express t At any given time, the actual output of the wind turbines did not exceed the predicted value and did not reach the maximum uncertainty value. express t At any given moment, the actual output of the wind turbine exceeded the predicted value, and the output deviation reached the maximum uncertainty value. This is a negative, uncertain binary variable for the wind turbine, taking values ​​of [0,1]. This indicates that at time t, the actual output of the wind turbine did not fall below the predicted value and did not reach the maximum uncertainty value. express t The actual output of the wind turbine was lower than the predicted value and the output deviation reached the maximum uncertainty value. This is a parameter for adjusting the uncertainty of wind turbine output power. It represents the maximum number of hours within a 24-hour day during which the actual output of the wind turbine reaches the maximum positive or negative uncertainty deviation.

[0090] 3. The load uncertainty model is shown in equation (3):

[0091] ;

[0092] In the formula, For load t Power at any given moment; For load t Predicted value at any time; For load t The maximum uncertainty in power change at any given time; Let be a positive, uncertain binary variable representing the load, with a value of [0,1]. This indicates that the actual load at time t did not exceed the predicted value and did not reach the maximum uncertainty value. express t The actual load value at any given time was higher than the predicted value, and the output deviation reached the maximum uncertainty value. This is a negative, uncertain binary variable representing the load, with a value of [0,1]. express t The actual load at any given time did not fall below the predicted value and reach the maximum uncertainty value. express t The actual load value at any given time was lower than the predicted value, and the output deviation reached the maximum uncertainty value. This is a load power uncertainty adjustment parameter, representing the maximum number of hours within a 24-hour period where the actual load value reaches the maximum positive or negative uncertainty deviation.

[0093] II. Construction of a Two-Stage Robust Programming Model for Power Supply Capacity Considering Multiple Uncertainties

[0094] With the continuous increase in the installed capacity of wind and solar power in the power system, their output power is constrained by natural conditions, and load changes depend on user electricity consumption behavior. This results in significant uncertainties on both the power generation and load sides of the power system, making the planning of power systems with a high proportion of renewable energy sources far more difficult than that of power systems without renewable energy. Therefore, to address the uncertainties in renewable energy output and load changes, this paper adopts a two-stage robust optimization model. The first stage focuses on the capacity of the units to be installed, namely the configuration capacity of wind power, solar power, thermal power, and energy storage, given without knowing the uncertainty set. In the second stage, once the uncertainty set is obtained, the decisions of the first stage are adjusted based on the actual operating results of the system to minimize the additional costs or losses caused by uncertainties, i.e., to minimize the system operating cost.

[0095] 1. Objective function

[0096] (1) The objective function for the first stage is shown in equation (4):

[0097] ;

[0098] In the formula, This is the objective function for the first stage; and These are the investment cost and maintenance cost of the generating unit, respectively. A collection with installation units; For the unit Construction cost conversion factor; The discount rate; For the unit Service life; For the unit The unit capacity construction cost; For the unit Installation capacity; For the unit The unit capacity maintenance cost.

[0099] (2) The objective function for the second stage is shown in equation (5):

[0100] ;

[0101] In the formula, This is the objective function for the second stage; The coal consumption cost of thermal power units; The costs of curtailing wind and solar power; For carbon trading costs; Insufficient flexibility incurs penalties; This is a transaction cost item in the electricity market;

[0102] The specific calculation formula is as follows:

[0103] a. Coal consumption cost of thermal power units As shown in equation (6):

[0104] ;

[0105] In the formula, All are coal combustion coefficients for thermal power units; For thermal power units t Efforts are made at all times.

[0106] b. Penalties for wind and solar power curtailment As shown in equation (7):

[0107] ;

[0108] In the formula, As a penalty factor for wind curtailment; This is a penalty factor for discarding light. for t Wind power curtailment at any time; for t Constantly abandoned photovoltaic power.

[0109] c. Carbon trading costs As shown in equation (8):

[0110] ;

[0111] In the formula, for t The carbon trading cost at any given time is shown in equation (9):

[0112] ;

[0113] In the formula, The carbon trading price under the coupling of electricity and carbon; The incentive coefficient for selling carbon allowances after electro-carbon coupling; The cost growth factor for purchasing carbon allowances after electro-carbon coupling; for t The price of carbon trading at any time; These represent the step sizes for the negative and positive carbon emission intervals, respectively. for t The carbon emission trading amount at any given time is calculated as shown in equation (10):

[0114] ;

[0115] In the formula, This is the baseline value for carbon emissions from thermal power plants; This is the base value for carbon emission quotas for thermal power plants; For time intervals, This indicates that each time period lasts for 1 hour.

[0116] d. Insufficient flexibility and penalty costs As shown in equation (11):

[0117] ;

[0118] In the formula, A penalty factor for insufficient flexibility; They are respectively t The system lacks flexibility in both upward and downward directions.

[0119] e. Electricity market transaction costs As shown in equation (12):

[0120] ;

[0121] In the formula, for t Current market electricity price for t The market trading volume of electricity before the specified time; for t Real-time market electricity prices for t Real-time market-balanced power supply; for t Market prices for 24 / 7 assisted services for t Real-time auxiliary service procurement volume.

[0122] 2. Constraints

[0123] (1) The installed capacity constraint is shown in equation (13):

[0124] ;

[0125] In the formula, These are the installed capacities of thermal power units, wind power units, photovoltaic units, and energy storage, respectively. These are the upper limits for the installed capacity of thermal power units, wind power units, photovoltaic units, and energy storage, respectively.

[0126] (2) Constraints of thermal power units

[0127] a. The output constraint of thermal power is shown in equation (14):

[0128] ;

[0129] In the formula, These represent the upper and lower limits of the output of thermal power units, respectively.

[0130] b. The ramping constraint for thermal power units is shown in equation (15):

[0131] ;

[0132] In the formula, These represent the upward and downward ramp rates of thermal power plants, respectively. For thermal power units Efforts are made at all times.

[0133] (3) Energy storage constraints

[0134] a. The charging and discharging power constraint is shown in equation (16):

[0135] ;

[0136] In the formula, They are respectivelyt The discharge and charging power that stores energy at all times; The coefficients are known. This represents the maximum limit of charging and discharging. This represents the maximum energy storage capacity. for t Constant charging and discharging status parameters.

[0137] b. The operating conditions constraints for energy storage are shown in equation (17):

[0138] .

[0139] c. The energy storage state of charge constraint is shown in equation (18):

[0140] ;

[0141] In the formula, for t Constant energy storage state of charge; To improve the charging and discharging efficiency of energy storage; The starting power for energy storage;

[0142] These are the upper and lower limits of the energy storage state of charge.

[0143] d. The charge-discharge balance constraint is shown in equation (19):

[0144] .

[0145] (4) The power balance constraint is shown in equation (20):

[0146] ;

[0147] In the formula, They are respectively t At any given moment, the output power of the wind turbine, the output power of the photovoltaic unit, and the load power are all uncertain variables.

[0148] 3. Model Building

[0149] Based on the above objective function and its constraints, a two-stage robust optimization model is transformed into equation (21):

[0150] ;

[0151] In the formula, The first stage target to be optimized is represented by equation (4); These are the variables to be optimized in the first stage. , These are the configuration capacities of thermal power units, wind power units, photovoltaic units, and energy storage; It is an uncertain set of wind and solar load; It is the range of the uncertain set; represent The constraint condition is equation (13). This represents the total system operating cost based on the unit configuration capacity obtained in the first stage, and is also the optimization target for the second stage, namely Equation (5). These are the variables to be optimized in the second stage. , , , , , , , These are the operating power of thermal power units, the operating power of wind power units, the operating power of photovoltaic units, the charging power of energy storage, the discharging power of energy storage, and the curtailed wind and solar power, which are determined by the capacity determined in the first phase and the uncertain variables. and They represent the second-stage inequality constraints and equality constraints, respectively, where the inequality constraints include equations (13)-(17), and the equality constraints include equations (18) and (19).

[0152] III. Solution Algorithm

[0153] 1. Algorithm Design Background and Innovation Positioning

[0154] To address the solution requirements of a two-stage robust planning model for power capacity considering source-load uncertainty and electro-carbon coupling, an improved column generation-interior point hybrid algorithm is designed, taking into account the model's double-layer nested structure of "main problem-subproblem," multi-type constraint coupling, and the discretization characteristics of uncertainty sets. The algorithm's innovation lies in three aspects: First, it constructs an adaptive column generation framework, replacing the traditional fixed scenario set with a dynamic uncertainty scenario selection mechanism, thus solving the problem of low solution efficiency caused by scenario redundancy in column generation algorithms. Second, it proposes a gradient-guided interior point initialization strategy, utilizing the dual information of the main problem to optimize the initial iteration points of subproblems, overcoming the limitations of single algorithms in handling mixed integer programming and continuous optimization subproblems. Third, it introduces an electro-carbon coupling cost correction factor to realize gradient transfer between the subproblem objective function and the main problem decision variables, improving the algorithm's convergence accuracy for multi-objective optimization scenarios. The algorithm can effectively handle complex optimization problems with binary variables, nonlinear cost functions, and multi-dimensional constraints, balancing solution efficiency and optimality.

[0155] 2. Core Principles and Mathematical Foundations of the Algorithm

[0156] The algorithm is based on the duality theory and decomposition idea of ​​two-stage robust optimization, decomposing the original model into a "main problem (first-stage capacity configuration optimization)" and a "sub-problem (second-stage operating cost minimization)". The global optimal solution is obtained through iterative interaction. The main problem is a mixed-integer linear programming problem, with decision variables being the installed capacity of thermal power units, wind power units, photovoltaic units, and energy storage. The objective function is to minimize investment and maintenance costs. The sub-problem is a continuous optimization problem with uncertain parameters, using the capacity output of the main problem as a constraint to solve for the minimum operating cost (including coal consumption, wind and solar curtailment penalties, carbon trading, and insufficient flexibility penalties) under a given uncertainty scenario.

[0157] According to strong duality theory, the maximum value of a subproblem (the operating cost in the worst-case scenario) can be transformed into the minimum value of the dual problem. Let the dual variables of the subproblem be the dual factor of thermal power output, the dual factor of energy storage charging and discharging power, etc. The optimal objective value of the subproblem is embedded into the main problem in the form of linear constraints through the dual variables, forming the cutting plane of the main problem. The improved column generation mechanism avoids computational explosion caused by exhaustive scenario enumeration by filtering uncertain scenarios (columns) that significantly affect the objective function of the main problem. The interior-point method uses barrier functions to transform the inequality constraints of the subproblem into an unconstrained optimization problem. The optimal solution and dual information of the subproblem are quickly obtained by iteratively solving the KKT (Karush-Kuhn-Tucker) conditions using Newton's method.

[0158] 3. Algorithm Solution Process

[0159] (1) Initialization phase

[0160] a. Set the basic parameters of the algorithm: maximum number of iterations Convergence accuracy Initial uncertainty adjustment parameter , Column generation scenario filtering threshold .

[0161] b. Construct the initial master problem (MP0): Based on the known baseline scenario, i.e., a scenario where the wind and solar load forecasts are unbiased, initialize the capacity variable of the units to be installed: the installed capacity of thermal power units. Wind turbine installation capacity Photovoltaic unit installed capacity Energy storage installation capacity The value is 80% to 120% of the historical optimal configuration capacity of the planning area. The objective function is the sum of investment and maintenance costs shown in equation (4). The constraints include the upper limit constraint of the installed capacity in equation (12), and the uncertainty-related constraints are ignored.

[0162] c. Solving the initial master problem: The branch and bound method is used to solve MP0 to obtain the initial capacity allocation solution. and the corresponding objective function value .

[0163] (2) Subproblem solving and dual information extraction

[0164] a. Constructing Subproblems (SPk): Configuring the capacity based on the output of the main problem in the k-th iteration. For constraints, Let represent the installed capacity of thermal power units, wind power units, photovoltaic units, and energy storage units, respectively, as output by the main problem in the k-th iteration. The objective function is the total operating cost shown in equation (5). The constraints include thermal power output, energy storage operation, and power balance constraints in equations (13)-(19). The uncertainty parameters include the uncertainty parameters representing the wind power output, photovoltaic output, and load demand at time t, respectively. These are used to describe the possible values ​​of wind power, photovoltaic power output, and load demand within the uncertainty set, respectively, and are generated based on the box set of equations (1) to (3). The number of initial generated scenarios is 3 times the number of time nodes.

[0165] b. Solving subproblems using the interior-point method: Introducing a barrier function. ,in Let the inequality constraint function be the subproblem. The index represents the subproblem inequality constraint, used to sequentially refer to the... Inequality constraints This represents the total number of inequality constraints in the subproblems, transforming constrained optimization into an unconstrained optimization problem. ,in, Let represent the objective function of the subproblem, corresponding to equation (5). The obstacle parameter is initialized to 1, and each iteration is performed according to... attenuation.

[0166] c. Iteratively solve the KKT conditions: Calculate the gradient of the objective function. Constructing the Hessian matrix via Newton's direction Update variables .when When the optimal solution to the subproblem is obtained. and optimal target value .in, This represents the gradient of the objective function of the subproblem, i.e., the objective function. The vector of first-order partial derivatives with respect to the optimization variable x; The gradient of the barrier function is represented by the barrier function itself. For optimization variables x The vector of first-order partial derivatives; The Hessian matrix is ​​represented by the second derivatives of the objective function and the barrier function, reflecting the curvature characteristics of the function. The Hessian matrix represents the objective function of the subproblem, i.e., the objective function. The matrix of second-order partial derivatives with respect to the optimization variable x; The Hessian matrix representing the barrier function, i.e., the barrier function itself. The matrix of second-order partial derivatives with respect to the optimization variable x; This indicates the Newton direction, which is the search direction calculated using the inverse of the Hessian matrix, and guides variable updates; Describes the inverse of the Hessian matrix. This represents the value of the variable at the (k+1)th iteration, i.e., the updated value of the variable; This represents the value of the variable at the k-th iteration, i.e., the value of the variable before the update; Indicates the step size, i.e., the control along the Newtonian direction. The magnitude of the update variable; This represents the convergence accuracy threshold, which indicates that the subproblem is considered optimal when the norm of the gradient is less than this value. Represent the optimal solution to the subproblem; This represents the optimal objective value of the subproblem.

[0167] d. Extract dual information: Based on the KKT conditions, extract the dual variables corresponding to the subproblem constraints. satisfy ,in Including thermal power output constraint dual factor Energy storage state of charge constraint dual factor and power balance constraint dual factor ,Will and This feedback information is passed to the main question. Let represent the optimal dual variable corresponding to the subproblem constraint, satisfying the KKT conditions to characterize the marginal effect of the constraint on the objective function. Indicates the first The constraint functions are in the optimal solution of the subproblem. The gradient at a given point, i.e., the vector of first-order partial derivatives of the constraint function with respect to the optimization variables, is the dual factor of the thermal power output constraint. This reflects the marginal impact of the tightness of thermal power output constraints on the objective function, and is the dual factor of the energy storage state of charge constraint. This reflects the marginal impact of the tightness of the energy storage state of charge constraint on the objective function, and is the dual factor of the power balance constraint. This reflects the marginal impact of the tightness or looseness of the power balance constraint on the objective function.

[0168] (3) Adaptive column generation and master problem update

[0169] a. Scenario Selection and Column Generation: Calculate the deviation rate between the optimal objective value of the subproblem corresponding to each uncertainty scenario and the objective value of the benchmark scenario. ,reserve For high-impact scenes, construct cutting plane constraints for the preserved scenes: ;

[0170] in, The deviation rate is the ratio of the deviation between the optimal objective value of a sub-problem in a certain scenario and the objective value of the benchmark scenario, and is used to screen high-impact scenarios. This represents the target value of the sub-problem in the baseline scenario, i.e., the benchmark reference value for calculating the deviation rate; This represents the deviation rate threshold, a critical value used to filter "high-impact scenarios" and retain them. The scene; This represents the objective function of the subproblem, which takes the capacity variable of the main problem as input and calculates the system operating cost under the scenario. This represents the vector of capacity variables for the main problem, which includes decision variables for the main problem such as thermal power units, wind power units, photovoltaic units, and energy storage capacity. This represents the capacity solution of the main problem in the k-th iteration, that is, the capacity configuration result obtained after the k-th iteration.

[0171] b. Update the main question ( ): The selected cutting plane constraints are added to the original master problem to form a new set of constraints; the objective function is still the investment and maintenance cost minimization of equation (4), the decision variables remain unchanged, and the new constraints ensure that the operating cost of the master problem solution is controllable in the worst scenario.

[0172] c. Solving the updated main problem: using the improved branch and bound method. By introducing dual information from subproblems to guide the branching order, priority is given to branching on the thermal power and energy storage capacity variables (because they have a higher weight in terms of their impact on operating costs); thus, a new capacity configuration solution is obtained. and objective function value .in, This represents the objective function value of the main problem in the (k+1)th iteration, which is the calculation result of the main problem "minimizing investment and maintenance costs". This represents the installed capacity of thermal power units output by the main problem in the (k+1)th iteration. This represents the installed capacity of wind turbine units output by the main problem in the (k+1)th iteration. This represents the installed capacity of photovoltaic units output by the main problem in the (k+1)th iteration. This represents the energy storage installation capacity output by the main problem in the (k+1)th iteration.

[0173] 4. Iterative convergence judgment and parameter adjustment

[0174] a. Convergence test: Calculate the relative deviation of the objective function values ​​of the main problem between the two iterations. and Euclidean distance of capacity variables ;

[0175] in, ; .

[0176] like and or the number of iterations reaches If the iteration stops, the optimal capacity configuration solution is output. and the optimal operating cost of the corresponding subproblems .in, This represents the relative deviation of the objective function values ​​in two iterations, thus measuring the degree of convergence of the objective function. This represents the objective function value of the main problem in the (k+1)th iteration, i.e., the numerator of the relative deviation calculation. This represents the objective function value of the main problem in the k-th iteration, i.e., the denominator term in the relative deviation calculation. The Euclidean distance represents the capacity variable and measures the degree of difference between the capacity configuration solutions in two iterations. This represents the convergence accuracy threshold; the final capacity configuration result output after iterative convergence. The optimal capacity including thermal, wind, solar, and energy storage.

[0177] b. Uncertainty adjustment parameter correction: If convergence is not achieved, adjust according to the duality factor of the subproblem. (i.e., power balance constraint dual factor) Adjustment parameter for uncertainty correction: , , Similarly, among them To correct the step size, The partial derivatives of the wind power uncertainty parameters with respect to operating costs are obtained from the sensitivity analysis of the subproblem. The corrected parameters are used to generate the uncertainty scenario set for the next iteration, returning to step (2) for subproblem solving and dual information extraction, and resolving the subproblem. This represents the wind power uncertainty adjustment parameter, which controls the generation range of wind power uncertainty scenarios and reflects the impact of wind power uncertainty on planning; This represents the correction step size, controlling the correction magnitude of the uncertainty adjustment parameter; in this paper, it is taken as 0.1. The partial derivative of the wind power uncertainty parameter with respect to operating costs is obtained through sub-problem sensitivity analysis, reflecting the rate at which changes in wind power uncertainty affect operating costs. This represents the photovoltaic uncertainty adjustment parameter for the (k+1)th iteration. This represents the load uncertainty adjustment parameter for the (k+1)th iteration.

[0178] 5. Optimal Solution Verification and Output

[0179] Optimal solution feasibility verification: The final capacity configuration solution... Substitute the original two-stage robust programming model, traverse all uncertain scenarios (twice the number of initial scenarios), and verify whether all constraints are met, especially key constraints such as the upper limit of installed capacity, the ramp-up rate of thermal power, and the state of charge of energy storage.

[0180] Objective function decomposition calculation: based on Calculate the investment cost of the first phase (including the converted construction and maintenance costs) and the operating costs of each item in the second phase (coal consumption, wind and solar curtailment penalties, carbon trading, and insufficient flexibility penalties), and output a detailed breakdown of the total cost.

[0181] Output results include the optimal power capacity configuration scheme (specific installed capacity of thermal power, wind power, photovoltaic, and energy storage), objective function values ​​at each stage, operating status parameters under key uncertainty scenarios (thermal power output, energy storage charging and discharging power, and wind and solar curtailment), and algorithm convergence curves. Example

[0182] Taking a power system as an example, this analysis uses measured data from wind farms and photovoltaic power plants under typical daily scenarios as predicted output values ​​for wind and photovoltaic power. The uncertain ranges for wind power output, photovoltaic output, and load changes are set at 20%, 15%, and 10% of the predicted values, respectively. Based on the characteristics of wind and photovoltaic output, it can be concluded that the time periods for wind power output and photovoltaic output have a good complementary effect. Therefore, the combined grid connection of wind and photovoltaic power can effectively alleviate the volatility of new energy output.

[0183] 1. The impact of uncertainty adjustment parameters on planning schemes

[0184] The table below shows the installed capacity and total planned construction cost of each unit under different uncertainty adjustment parameters.

[0185]

[0186] As can be seen from the table, when the parameter is uncertain... and When all power supplies in the system have the same capacity, the total planning and construction cost is also the lowest compared to other scenarios. At this point, the two-stage robust programming model is equivalent to a deterministic optimization model, meaning it does not consider the uncertainties of wind and solar power output and load changes; the values ​​of wind power output, solar power output, and load power are all predicted values. At this time, only two periods of wind and solar power output and load power reach the boundary values. In this case, the impact of uncertainties on the system's installed capacity is relatively small. The total cost of planning and construction at that time was lower than Because of the situation Characterizing the uncertainties of wind and solar power is beneficial for the system's ability to absorb wind and solar power output, thereby reducing the penalty costs for wind and solar curtailment and thus lowering the overall planning and construction costs. The time is slightly lower.

[0187] With uncertainty parameters As the power output, the probability of wind power, solar power, and load power reaching the predicted boundary increases, leading to a gradual increase in the configured capacity of wind and solar power, and consequently, an increase in the configured capacity of energy storage. At this point, the planning model for power capacity configuration is significantly affected by the uncertainties in the system's wind and solar load, resulting in a corresponding increase in the total cost of system planning and construction. In this scenario, the energy storage capacity is slightly smaller compared to other situations, and the total planned cost is also reduced. Under these conditions, the system operation and the absorption rate of wind and solar power are at their optimal levels, requiring less power from the energy storage system, thus leading to a reduction in the configured energy storage capacity. Furthermore... The power supply reliability requirements of the system can be fully met, so the solution obtained under this condition is the optimal one.

[0188] when At this point, the wind power output probability reaches the prediction boundary for 12 time periods, and the photovoltaic output probability reaches the prediction boundary for almost all time periods. This also results in the highest required configuration capacity and total system planning and construction cost for both wind and photovoltaic power. While the planning scheme obtained under these circumstances is more capable of handling uncertainty, it is overly conservative and economically inefficient. Therefore, considering uncertainty is to improve system reliability. If the planning scheme is too conservative, although it improves system reliability, it will worsen the economic efficiency of the plan.

[0189] The above analysis shows that when using a two-stage robust optimization method with uncertainty adjustment parameters for power capacity configuration, the planning scheme can simultaneously consider both economy and reliability by reasonably selecting the uncertainty adjustment parameters. Furthermore, the uncertainty adjustment parameters can accurately characterize the uncertainty of wind and solar power output, playing a crucial role in improving the system's ability to absorb wind and solar power.

Claims

1. A two-stage robust planning method for demand-side capacity that accounts for both cost and flexibility resources, characterized by: The method comprises the following steps of: And the following steps are sequentially performed: Step 1, constructing a multi-uncertainty model Including a photovoltaic uncertainty model, a wind power uncertainty model and a load uncertainty model; Step 2, constructing a two-stage robust planning model of power supply capacity considering multi-uncertainty Wherein, the first-stage robust planning model is based on the capacity of the to-be-installed unit, that is, the configuration capacity of the wind power, the photovoltaic power, the thermal power and the energy storage, is given without the uncertainty set, and the sum of the investment cost and the maintenance cost of the unit is taken as the objective function; Wherein, the second-stage robust planning model adjusts the decision of the first stage according to the actual system operation result after the uncertainty set is obtained, so as to minimize the additional cost or loss caused by the uncertainty factor, that is, to minimize the system operation cost; Step 3, solving the two-stage robust planning model, and outputting the results including an optimal power supply capacity configuration scheme, that is, the specific installed capacity of the thermal power, the wind power, the photovoltaic power and the energy storage, the objective function value of each stage, the operation state parameter under the key uncertainty scenario and the algorithm convergence curve; The photovoltaic uncertainty model is as follows: ； In the formula: For photovoltaic units t Constant output power; t Take 24 moments at equal time intervals within a 24-hour period; For photovoltaic units t Predicted power values ​​at any given time; For photovoltaic units t The maximum uncertainty of the output power at any given moment; For the photovoltaic unit, there is a positive uncertain binary variable, taking the value [0,1]. express t At any given time, the actual output of the photovoltaic units did not exceed the predicted value and did not reach the maximum uncertainty value. express t The actual output of the photovoltaic unit at that time was higher than the predicted value and the output deviation reached the maximum uncertainty value; This is a negative, uncertain binary variable for the photovoltaic unit, taking values ​​[0,1]. This indicates that at time t, the actual output of the photovoltaic unit did not fall below the predicted value and did not reach the maximum uncertainty value. express t The actual output of the photovoltaic unit was lower than the predicted value and the output deviation reached the maximum uncertainty value. For photovoltaic power output power uncertainty adjustment parameters, it means the maximum number of hours in a 24-hour period where the actual output of the photovoltaic unit reaches the maximum positive or negative uncertainty deviation is not allowed to exceed. The wind power uncertainty model is as follows: ； In the formula: is the wind turbine t instantaneous output power; is the wind turbine t instantaneous power prediction value; is the wind turbine t maximum uncertainty value of the instantaneous output power; is a positive uncertainty binary variable of the wind turbine, taking values in [0, 1], represents t the situation that the actual output of the wind turbine at time t does not exceed the prediction value and reaches the maximum uncertainty value, represents t the situation that the actual output of the wind turbine at time t exceeds the prediction value and the output deviation reaches the maximum uncertainty value; is a negative uncertainty binary variable of the wind turbine, taking values in [0, 1], represents the situation that the actual output of the wind turbine at time t does not fall below the prediction value and reaches the maximum uncertainty value, represents t the situation that the actual output of the wind turbine at time t falls below the prediction value and the output deviation reaches the maximum uncertainty value; is an uncertainty adjustment parameter of the output power of the wind turbine, representing the maximum number of hours that the total number of hours in which the actual output of the wind turbine reaches the positive maximum uncertainty deviation or the negative maximum uncertainty deviation is not allowed to exceed in 24 hours of a day; The load uncertainty model is as follows: ； wherein, is the load t power at time t; is the load t predicted value at time t; is the load t maximum uncertainty of power variation at time t; is a positive uncertainty binary variable of the load, taking values in [0, 1], indicates that the load actual value at time t has not appeared higher than the predicted value and reached the maximum uncertainty value, indicates t that the load actual value at time t has appeared higher than the predicted value and the output deviation has reached the maximum uncertainty value; is a negative uncertainty binary variable of the load, taking values in [0, 1], indicates t that the load actual value at time t has not appeared lower than the predicted value and reached the maximum uncertainty value, indicates t that the load actual value at time t has appeared lower than the predicted value and the output deviation has reached the maximum uncertainty value; is a load power uncertainty adjustment parameter, indicating the maximum hour number that the total number of hours in which the load actual value reaches the positive maximum uncertainty deviation or the negative maximum uncertainty deviation within 24 hours of a day is not allowed to exceed. 2.The method of claim 1, wherein: In step 2, the objective function of the first-stage robust planning model is: ； In the formula, is the first stage objective function; and are the investment cost and maintenance cost of the unit, respectively; is the set of units with installed units; is the unit construction cost conversion factor; is the discount rate; is the unit service life; is the unit unit capacity construction cost; is the unit installed capacity; is the unit unit capacity maintenance cost; The objective function of the second-stage robust planning model is: ； In the formula, is a second stage objective function; is a coal consumption cost of the thermal power unit; is a wind and light curtailment penalty cost; is a carbon trading cost; is an insufficient flexibility penalty cost; is an electricity market trading cost term; Wherein, ； In the formula, are the coal consumption factors of the thermal power generating units; are the coal consumption factors of the thermal power generating units t are the coal consumption factors of the thermal power generating units ； In the formula, is a wind curtailment penalty factor; is a light curtailment penalty factor; is t is the wind curtailment power at the moment; is t is the photovoltaic curtailment power at the moment; ； wherein is t The instantaneous carbon trading cost is given by the following equation: ； In the formula, is the carbon trading price under the electricity-carbon coupling; is the reward coefficient of the sold carbon quota after the electricity-carbon coupling; is the cost increase coefficient of the purchased carbon quota after the electricity-carbon coupling; is the carbon emission amount of the power grid in the current period; t is the price of the carbon trading at the moment; are the step lengths of the negative and positive intervals of the carbon emission amount, respectively; is the carbon emission amount of the power grid in the current period; t is the carbon emission right trading amount at the moment, and the calculation formula is as shown in the following formula: ； In the formula, is the base value of carbon emissions of thermal power; is the base value of carbon emissions quota of thermal power; is the time interval, , indicates that each time period lasts for 1 hour; ； wherein is a lack of flexibility penalty factor; respectively t the lack of flexibility of the system at the moment of time ； wherein, is t the day-ahead market price at time instant, is t the day-ahead market traded energy at time instant ; is t the real-time market price at time instant, is t the real-time market balanced energy at time instant ; is t the ancillary service market price at time instant, is t the ancillary service procurement at time instant.

3. The method of two-stage robust planning for demand-side capacity considering cost and flexibility resources according to claim 2, characterized in that: The two-stage robust planning model has the following constraint conditions: (1) the installed capacity constraint is: ； In the formula, respectively are the installed capacities of thermal power units, wind power units, photovoltaic units, and energy storage; respectively are the upper limits of the installed capacities of thermal power units, wind power units, photovoltaic units, and energy storage; (2) the thermal power unit constraint is: a. the thermal power unit output constraint is: ； In the formula, respectively, the upper limit and the lower limit of the thermal power generating unit output b. the thermal power unit climbing constraint is: ； In the formula, respectively, the up and down ramping rates of thermal power; thermal power unit output at the moment (3) the energy storage constraint is: a. the charge and discharge power constraint is: ； In the formula, respectively t Discharge and charge power at the moment; is a known coefficient; is the maximum limit of charge and discharge; is the maximum capacity of the energy storage; is t State quantity of charge and discharge at the moment; b. the energy storage operation condition constraint is: ； c. the energy storage state of charge constraint is: ； In the formula, is t Instantaneous energy storage state of charge; is the energy storage charge and discharge efficiency; is the energy storage starting electric quantity; SoCmin, SoCmaxare the upper and lower limits of the state of charge; d. the charge and discharge balance constraint is: ； (4) the power balance constraint is: ； In the formula, respectively t The wind turbine output power, photovoltaic output power and load power at the moment are all uncertain variables.

4. The method of two-stage robust planning for demand-side capacity considering cost and flexibility resources according to claim 3, characterized in that: According to the objective function and the constraint condition, the two-stage robust optimization model is converted into: ； In the formula, represents the first stage to be optimized target, that is, formula (4); is the first stage to be optimized variable, , are the configuration capacities of thermal power units, wind power units, photovoltaic units and energy storage, respectively; is the uncertain set of wind and light loads; is the range of the uncertain set; represents the constraint condition of formula (13); represents the total system operation cost under the unit configuration capacity obtained according to the first stage, which is also the second stage to be optimized target, that is, formula (5); is the second stage to be optimized variable, , , , , , , , are the running power of thermal power units, the running power of wind power units, the running power of photovoltaic units, the charging power of energy storage, the discharging power of energy storage and the abandoned wind and light power, respectively, which are determined by the capacity and uncertain variable determined in the first stage; and represent the second stage inequality constraint and equality constraint, respectively, wherein the inequality constraint includes formulas (13)-(17), and the equality constraint includes (18) and (19).

5. The method of two-stage robust planning for demand-side capacity considering cost and flexibility resources according to claim 4, characterized in that: The algorithm for solving the two-stage robust planning model in step 3 is based on the duality theory and the decomposition idea of the two-stage robust optimization, and the model is decomposed into a master problem and a subproblem. The master problem is a first-stage capacity configuration optimization problem, which belongs to a mixed integer linear programming problem, the decision variable is the installed capacity of the thermal power unit, the wind power unit, the photovoltaic unit and the energy storage, and the objective function is to minimize the investment and maintenance cost. 6.The method of two-stage robust optimization considering cost and flexibility resource of demand side capacity according to claim 5, characterized in that: The subproblem is a second-stage operation cost minimization problem, which belongs to a continuous optimization problem containing uncertainty parameters, takes the capacity output by the master problem as the constraint, and solves the minimum operation cost containing the coal consumption, the wind and light curtailment penalty, the carbon trading and the flexibility deficiency penalty cost under a given uncertainty scenario. According to the strong duality theory, the maximum value of the subproblem, that is, the operation cost under the worst scenario, is converted into the minimum value of the dual problem, the dual variable of the subproblem is the thermal power unit output dual factor and the energy storage charge and discharge power dual factor, the optimal objective value of the subproblem is embedded into the master problem in the form of linear constraint through the dual variable, and the cutting plane of the master problem is formed. The improved column generation mechanism avoids the calculation explosion caused by the exhaustive scenarios by screening the columns of the uncertainty scenarios which have significant influence on the main problem objective function; the interior point method converts the inequality constraints of the sub-problems into unconstrained optimization problems by using the barrier function, and iteratively solves the Karush-Kuhn-tucker (KKt) conditions by using the Newton method to quickly obtain the optimal solution of the sub-problems and the dual information.

7. The method of claim 1, wherein: The running state parameters in the step three include the thermal power output, the energy storage charging and discharging power, and the abandoned wind and light amount.

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