Flexible demand modeling method based on probability box

Abstract

The invention relates to a flexibility demand modeling method based on a probability box, and belongs to the field of flexibility demands of power systems. According to the method, a probability box theory P-Box is introduced to describe random uncertainty and cognitive uncertainty of wind power output, photovoltaic output and load demand prediction errors; introducing a conditional value-at-risk theory CVaR to a confidence interval boundary of the probability box, and intercepting an uncertainty factor boundary; and establishing a source-load double-side flexibility quantification model based on a prediction error of intercepting an uncertain factor boundary.

Description

Technical Field

[0001] The present invention belongs to the field of flexibility demand of power system, and in particular relates to a flexibility demand modeling method based on probability box. Background Art

[0002] In recent years, in order to overcome the problems of traditional fossil energy shortage, ecological pollution and climate change, the grid connection of renewable energy such as solar energy and wind energy has become an inevitable trend. Building a new power system with new energy as the main body is an important measure to achieve the "dual carbon" goal. However, in the process of gradually increasing the proportion of new energy, large-scale centralized new energy access at the source end, and the increase in distributed and interactive loads at the load end, the uncertainty at multiple levels of source, grid and load has put forward higher requirements for the balance of supply and demand of the system. Therefore, it is necessary to study the uncertainty of the new power system, and introduce the concept of flexibility to characterize and reflect the resilience of the power grid in dealing with multiple uncertainties, and to construct a planning model that considers the balance of supply and demand of flexibility by establishing a quantitative model of flexibility on both sides of the source and load.

[0003] The new power system with renewable energy as the main body needs to have a certain degree of flexibility by optimizing the allocation of various available resources. Previous methods usually used specific prediction error coefficients to take into account the uncertainty of renewable energy output and load demand in the process of quantifying flexibility needs. However, the prediction error of wind, solar and load is not a constant and will change with time and space. At the same time, the change rules of the prediction errors of wind, solar and load are not consistent. Therefore, the use of specific prediction error coefficients will affect the accuracy of the model.

[0004] In addition, most of the previous methods used to predict errors believe that the prediction errors conform to a certain probability function distribution, such as normal distribution, Beta distribution, mixed Gaussian distribution, etc., but ignore the possibility of fluctuations in the probability function parameters. That is, the prediction errors basically conform to a certain probability function distribution type, but its parameters may vary within a certain range, and cannot accurately describe the impact of uncertainty.

[0005] In summary, the existing flexibility demand quantification methods cannot guarantee accuracy and cannot adapt well to changes in source and grid loads. Summary of the invention

[0006] Based on the uncertainty of power prediction errors and distribution parameters on both sides of supply and demand, the present invention provides a flexibility demand modeling method based on probability box, and establishes a source-load bilateral flexibility quantification model based on the prediction error.

[0007] To achieve the above object, the technical solution of the present invention is: a flexibility demand modeling method based on probability box, comprising:

[0008] The probability box theory P-Box is introduced to describe the random uncertainty and epistemic uncertainty of wind power output, photovoltaic output and load demand forecast errors;

[0009] The conditional value at risk theory CVaR is introduced at the confidence interval boundary of the probability box to intercept the boundary of the uncertainty factor.

[0010] In one embodiment of the present invention, a source-load dual-side flexibility quantification model is established based on the prediction error of the intercepted uncertainty factor boundary.

[0011] In one embodiment of the present invention, the method specifically comprises the following steps:

[0012] S1. Obtain system flexibility supply data and system flexibility demand data;

[0013] S2. Introduce the probability box theory P-Box to determine the probability box distribution of wind power output, photovoltaic output and load demand forecast errors;

[0014] S3. Introduce the conditional value at risk theory CVaR, consider the tail risk to set the confidence variable interval boundary, and calculate the CVaR value under the confidence variable interval boundary;

[0015] S4. Establish a flexibility quantification model with the minimum flexibility risk penalty cost as the objective function;

[0016] S5. Solve the flexibility quantitative model.

[0017] In one embodiment of the present invention, step S1 is specifically implemented as follows:

[0018] The flexibility supply of thermal power units is composed of the maximum output of thermal power units, the maximum output of oil injection combustion depth peak regulation and the climbing ability. The calculation formula is as follows:

[0019]

[0020] Where: They represent the upward and downward flexibility of thermal power units that have undergone deep peak load regulation transformation; Respectively represent the up and down climbing rates of thermal power units; is the maximum output of the thermal power unit; P g,t Provide power for thermal power units; It is the deep peak-shaving extreme output of the deep peak-shaving thermal power units with oil injection and combustion assistance;

[0021] The flexibility of a hydropower unit is composed of its maximum output, minimum output and its climbing ability, which can be calculated as follows:

[0022]

[0023] Where: They represent the upward and downward adjustment flexibility of the hydropower units respectively; Respectively represent the up and down climbing ability of the hydropower unit; P s,t Real-time output of hydropower units; and Respectively represent the maximum output and minimum output of the hydropower unit;

[0024] The flexibility of energy storage is related to its own factors including state of charge and charging and discharging power, and its calculation formula is as follows:

[0025]

[0026] Where: They represent the upward and downward flexibility of energy storage respectively; Respectively represent the rated charging and discharging power of energy storage; P c,t , P f,t Respectively represent the real-time charging and discharging power of energy storage; E max 、E min Respectively represent the rated capacity and minimum power storage value of energy storage; E t is the energy storage value at time t; η e The charging and discharging efficiency of energy storage;

[0027] In summary, the total flexibility supply in the system is the sum of the flexibility of each flexibility resource on the supply side of the system, and its calculation formula is:

[0028]

[0029] Where: They represent the total upward and downward flexibility supply of the system respectively;

[0030] The demand-side flexibility of the power system comes from two aspects: on the one hand, the volatility of the net load of the system, which reflects the uncertainty of load demand over time; on the other hand, the error of load forecasting, which reflects the possible deviation between the forecasting model and the actual load demand; it is measured by the change of net load at adjacent moments on a time scale, and its expression is:

[0031]

[0032] Where: They represent the upward and downward flexibility requirements of the system respectively; is the net load at the current moment; is the net load forecast value at the next moment; They respectively represent the upper and lower limits of the net load prediction error at the next moment; wherein, the upper and lower limits of the net load prediction error at the next moment are derived from the uncertainty of wind power output, photovoltaic output and load prediction error at the next moment.

[0033] In one embodiment of the present invention, in step S2, the probability box distribution of the wind power output prediction error is solved as follows:

[0034] Assume that the wind power output prediction error It is believed that the wind power output prediction error follows a normal distribution with parameters varying in a certain interval, where the parameter of the normal distribution is μ∈(μ d ,μ u ),σ∈(σ d ,σ u ), μ d , μ u They represent the lower and upper limits of the mean of the normal distribution, σ d , σ u They represent the lower limit and upper limit of the standard deviation of the normal distribution respectively. The upper and lower limits of the parameters respectively form four probability cumulative functions. The interval formed by the four probability cumulative functions is the probability box distribution of the prediction error, thus obtaining the probability box distribution of the wind power output prediction error;

[0035] Since historical data is discrete, the probability box boundary function should have intersection points where the cumulative probability is 0 and 1, so ΔP t W The range is expressed as:

[0036]

[0037] Where: and are the errors of the probability box boundary when the cumulative probability value is 0 and 1, respectively, which represent the maximum and minimum values ​​of the wind power output prediction error;

[0038] The confidence interval β is set to select the interval boundary, and the range of wind power output prediction error is expressed as:

[0039]

[0040] Where: and are the upper and lower limits of wind power output prediction error under the confidence interval β; F1 and F2 represent the cumulative probability; β u , β d are the cumulative probabilities corresponding to the upper and lower limits of wind power output prediction error under the confidence interval;

[0041] Similarly, the range of the photovoltaic output and load demand prediction errors is obtained.

[0042] In one embodiment of the present invention, in step S2, the system flexibility requirement and The expression is as follows:

[0043]

[0044] Where: and are the upper and lower limits of the load demand forecast error under the confidence interval β, respectively; and are the upper and lower limits of the photovoltaic output prediction error under the confidence interval β; P L,t+1 , P w,t+1 , P P,t+1 They are load demand, wind power output, and photovoltaic power output forecast power respectively.

[0045] In one embodiment of the present invention, step S3 is specifically implemented as follows:

[0046] For the decision variable x, let the probability density function of the random variable ξ be p(ξ), then the probability that the loss function f(x,ξ) caused by ξ does not exceed the threshold α is:

[0047]

[0048] The VaR value under the confidence interval β is expressed as:

[0049]

[0050] The corresponding CVaR value is expressed as:

[0051]

[0052] In one embodiment of the present invention, step S4 is specifically implemented as follows:

[0053] Taking into account the flexibility supply and demand risk of the system to ensure the stable operation of the system, the flexibility risk penalty objective function is established as follows:

[0054]

[0055]

[0056] Where: C F Penalize costs for system flexibility risk; Penalize for insufficient flexibility within the confidence interval; is the conditional value at risk of flexibility risk outside the confidence interval; Penalize unit costs for insufficient flexibility, upward or downward respectively; To adjust the flexibility requirements upward and downward respectively. They are to adjust flexibility supply upward and downward respectively; They are the unit costs of upward and downward flexibility risk penalty outside the confidence interval, respectively; is an auxiliary variable, and its value is 1 / (1-β); is a 0-1 variable, representing whether it is within the confidence interval, 1 means outside the confidence interval, and 0 means within the confidence interval; α ξ is the flexibility risk function; They are the probabilities of upward and downward adjustments to flexibility risk.

[0057] The present invention also provides a flexibility demand modeling system based on probability boxes, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0058] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0059] Compared with the prior art, the present invention has the following beneficial effects: the method of the present invention can comprehensively consider all aspects of uncertainty, so that the optimization scheme can effectively cope with uncertainty fluctuations and ensure economy. The method extracts the interval boundary of uncertainty factors based on P-Box theory and CVaR theory. The advantage of this method is that it can ensure the integrity of uncertain information, fully consider all uncertainties, avoid the scheme being too conservative or too aggressive, and make it the best balance between safety and economy. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Schematic diagram of wind power prediction error boundary.

[0061] Figure 2 Schematic diagram of the probability box boundary under the confidence interval.

[0062] Figure 3 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0063] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0064] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0065] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0066] The present invention provides a flexibility demand modeling method based on probability box, comprising:

[0067] The probability box theory P-Box is introduced to describe the random uncertainty and epistemic uncertainty of wind power output, photovoltaic output and load demand forecast errors;

[0068] The conditional value at risk theory CVaR is introduced at the confidence interval boundary of the probability box to intercept the boundary of the uncertainty factor.

[0069] A source-load bilateral flexibility quantitative model is established based on the prediction error of intercepting the boundary of uncertainty factors.

[0070] The method of the present invention is described in detail as follows:

[0071] 1. Supply-side flexibility quantitative model

[0072] Considering the deep peak-shaving transformation of thermal power units, the flexibility supply is the maximum output of the thermal power units, the deep peak-shaving limit output of oil injection and combustion assistance, and the climbing ability. The calculation formula is as follows:

[0073]

[0074] Where: They represent the upward and downward flexibility of thermal power units that have undergone deep peak load regulation transformation; Respectively represent the up and down climbing rates of thermal power units; is the maximum output of the thermal power unit; P g,t Provide power for thermal power units; It is the deep peak-shaving extreme output of the deep peak-shaving thermal power units with oil injection and combustion assistance;

[0075] The flexibility of a hydropower unit is composed of its maximum output, minimum output and its climbing ability, which can be calculated as follows:

[0076]

[0077] Where: They represent the upward and downward adjustment flexibility of the hydropower units respectively; Respectively represent the up and down climbing ability of the hydropower unit; P s,t Real-time output of hydropower units; and Respectively represent the maximum output and minimum output of the hydropower unit;

[0078] The flexibility of energy storage is related to its own state of charge, charging and discharging power and other factors. The calculation formula is as follows:

[0079]

[0080] Where: They represent the upward and downward flexibility of energy storage respectively; Respectively represent the rated charging and discharging power of energy storage; P c,t , P f,t Respectively represent the real-time charging and discharging power of energy storage; E max 、E min Respectively represent the rated capacity and minimum power storage value of energy storage; E t is the energy storage value at time t; η e The charging and discharging efficiency of energy storage;

[0081] In summary, the total flexibility supply in the system is the sum of the flexibility of each flexibility resource on the supply side of the system, and its calculation formula is:

[0082]

[0083] Where: Represent the total upward and downward flexibility supply of the system respectively.

[0084] 2. Demand-side flexibility quantitative model

[0085] The demand-side flexibility of the power system mainly comes from two aspects: on the one hand, the volatility of the net load of the system, which reflects the uncertainty of load demand over time; on the other hand, the error of load forecasting, which reflects the possible deviation between the forecasting model and the actual load demand; it is measured by the change of net load at adjacent moments on a time scale, and its expression is:

[0086]

[0087] Where: They represent the upward and downward flexibility requirements of the system respectively; is the net load at the current moment; is the net load forecast value at the next moment; They represent the upper and lower limits of the net load forecast error at the next moment, respectively; the upper and lower limits of the net load forecast error at the next moment are derived from the uncertainty of the wind power output, photovoltaic output and load forecast error at the next moment. In order to accurately quantify the flexibility requirements of the system, the forecast errors of the wind power, photovoltaic output and load demand of the system are described based on P-box, and the flexibility requirements of the system are obtained. For example, it is assumed that the wind power output prediction error obeys the normal distribution with parameters varying in a certain interval, where the parameter of the normal distribution is μ∈(μ d ,μ u ),σ∈(σ d ,σ u ), μ d , μ u They represent the lower and upper limits of the mean of the normal distribution, σ d , σ u They represent the lower and upper limits of the normal distribution standard deviation respectively. The upper and lower limits of the parameters form four probability cumulative functions respectively. The interval formed by the four probability cumulative functions is the probability box distribution of the prediction error. From this, the probability box distribution diagram of the wind power output prediction error is obtained, as shown in Figure 1 shown.

[0088] Depend on Figure 1 It can be seen that since the historical data is discrete, the probability box boundary function should have intersection points where the cumulative probability is 0 and 1, then The range is expressed as:

[0089]

[0090] Where: and are the errors of the probability box boundary when the cumulative probability value is 0 and 1, respectively, which represent the maximum and minimum values ​​of the wind power output prediction error;

[0091] However, the cumulative probability distribution function of the standard normal distribution has asymptotic properties at the tail, which can easily lead to the conservatism of the scheme. Therefore, the confidence interval β is set to select the appropriate interval boundary. Figure 2 The figure shows the boundary diagram under the confidence interval β. At this time, the range of wind power output prediction error can be expressed as:

[0092]

[0093] Where: and are the upper and lower limits of wind power output prediction error under the confidence interval β; F1 and F2 represent the cumulative probability; β u , β d are the cumulative probabilities corresponding to the upper and lower limits of the wind power output prediction error under the confidence interval;

[0094] Similarly, the range of the photovoltaic output and load demand forecast error can be obtained. Then the system flexibility demand can be obtained. and The expression is as follows:

[0095]

[0096] Where: and are the upper and lower limits of the load demand forecast error under the confidence interval β, respectively; and are the upper and lower limits of the photovoltaic output prediction error under the confidence interval β; P L,t+1 , P w,t+1 , P P,t+1 They are load demand, wind power output, and photovoltaic power output forecast power respectively.

[0097] Directly using the probability box boundary can easily lead to the conservatism of the solution. However, setting the confidence interval ignores the flexibility risk outside the interval, which can easily lead to the confidence interval of the optimization solution being too small, resulting in insufficient robustness of the solution. Therefore, the conditional risk value of the flexibility risk of the tail can be calculated to take the tail risk into consideration and increase the applicability of the solution.

[0098] In the field of economics, Value at Risk (VaR) is an indicator that measures the maximum potential loss that an investment portfolio may suffer under a specific confidence level, and is also applied to the power sector. However, the risk value theory cannot accurately quantify extreme risks. In recent years, the CVaR model has been widely used to solve power system risk problems. Based on the probability box, this method sets a variable interval and calculates the flexible tail risk through conditional risk value, making the optimization scheme more adaptable.

[0099] For the decision variable x, let the probability density function of the random variable ξ be p(ξ), then the probability that the loss function f(x,ξ) caused by ξ does not exceed the threshold α is:

[0100]

[0101] The VaR value under the confidence interval β is expressed as:

[0102]

[0103] The corresponding CVaR value is expressed as:

[0104]

[0105] 3. Risk penalty cost of flexibility supply and demand imbalance

[0106] As mentioned above, if the system's flexibility resource regulation capacity is limited, when the prediction error of wind and solar load power exceeds its regulation capacity, wind and solar power abandonment or load abandonment losses will occur. Therefore, it is necessary to consider the system's flexibility supply and demand risks to ensure the stable operation of the system. The flexibility risk penalty objective function can be established as follows:

[0107]

[0108] Where: C F Penalize costs for system flexibility risk; Penalize for insufficient flexibility within the confidence interval; is the conditional value at risk of flexibility risk outside the confidence interval; Penalize unit costs for insufficient flexibility, upward or downward respectively; To adjust the flexibility requirements upward and downward respectively. They are to adjust flexibility supply upward and downward respectively; They are the unit costs of upward and downward flexibility risk penalty outside the confidence interval, respectively; is an auxiliary variable, and its value is 1 / (1-β); is a 0-1 variable, representing whether it is within the confidence interval, 1 means outside the confidence interval, and 0 means within the confidence interval; α ξ is the flexibility risk function; They are the probabilities of upward and downward adjustments to flexibility risk.

[0109] like Figure 3 As shown in the figure, the overall process of the method of the present invention is proposed. Aiming at the defects of previous methods in predicting renewable energy output and load demand with insufficient accuracy and ignoring the problem of flexibility supply and demand, a new method for establishing a source-load dual-side flexibility quantification model is proposed. The method adopts an interval boundary extraction method based on P-Box and CVaR theory, which can properly handle the prediction errors of wind power, photovoltaic output and load power.

[0110] The method of this embodiment can comprehensively consider uncertainties in all aspects, so that the optimization scheme can effectively cope with uncertainty fluctuations and ensure economy. This method extracts the interval boundaries of uncertainty factors based on P-Box theory and CVaR theory. The advantage of this method is that it can ensure the integrity of uncertain information, fully consider all uncertainties, avoid the scheme being too conservative or too aggressive, and put it in the best balance between safety and economy. In order to verify the effectiveness and superiority of the method, the upper and lower limits of the prediction errors of wind power, photovoltaic output and load power are first obtained according to the probability box method, and different confidence intervals are set. The optimal confidence interval obtained by the interval boundary extraction method based on P-Box and CVaR theory is 95.5%, and the upper and lower limits of the prediction errors under different confidence intervals are specifically shown in Table 1.

[0111] Table 1 Upper and lower limits of prediction errors under different confidence intervals

[0112]

[0113] According to Table 1, if the probability box method is used directly to calculate the upper and lower bounds of the prediction error, that is, when the confidence interval is 100%, the upper and lower bounds of the error will be too conservative. Among them, the negative prediction error of photovoltaics is as high as 0.78. If such low-probability risks are taken into consideration in the global planning, it may have a negative impact on the economic efficiency of the scheme. Therefore, the interval boundary extraction method based on the P-Box theory and the CVaR theory introduces a confidence interval to the probability box boundary to truncate the tail of the probability box. When the confidence interval is 90%, the wind and solar load prediction error interval is almost halved. This method not only retains the advantage of the P-Box method for the integrity of error information, but also avoids the disadvantage of over-conservatism that may be caused by directly using the probability box boundary by flexibly setting the confidence interval.

[0114] Randomly simulate 10,000 sets of forecast errors and obtain the probability of exceeding the limit under different confidence intervals; then, bring the forecast error boundaries under each confidence interval into the scheduling model to obtain the total cost and the risk penalty cost of flexibility supply and demand imbalance. Table 2 compares the simulation results under different confidence intervals.

[0115] Table 2 Comparison of results under different confidence intervals

[0116]

[0117] It can be seen from Table 1 and Table 2 that as the confidence interval increases, the wind and solar load prediction error interval increases. When the confidence interval is 95.5%, the probability of exceeding the limit is only 0.76%. When the confidence interval changes from 95.5% to 100%, the cost increases by 12%, and the flexibility demand of the system nearly doubles. That is, the selection of the confidence interval affects the wind and solar load prediction error interval, and then affects the flexibility demand and risk of the system. The interval boundary extraction method based on P-Box and CVaR theory can achieve optimal safety while ensuring economy.

[0118] The present invention also provides a flexibility demand modeling system based on probability boxes, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0119] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0120] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0121] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0122] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0123] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0124] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for modeling flexibility requirements based on probability boxes, characterized in that: include: The probability box theory P-Box is introduced to describe the random uncertainty and epistemic uncertainty of wind power output, photovoltaic output and load demand forecast errors; The conditional value at risk theory CVaR is introduced at the confidence interval boundary of the probability box to intercept the boundary of the uncertainty factor.

2. The method for modeling flexibility requirements based on probability boxes according to claim 1, characterized in that: A source-load bilateral flexibility quantitative model is established based on the prediction error of intercepting the boundary of uncertainty factors.

3. The method for modeling flexibility requirements based on probability boxes according to claim 2, characterized in that: The method specifically comprises the following steps: S1. Obtain system flexibility supply data and system flexibility demand data; S2. Introduce the probability box theory P-Box to determine the probability box distribution of wind power output, photovoltaic output and load demand forecast errors; S3. Introduce the conditional value at risk theory CVaR, consider the tail risk to set the confidence variable interval boundary, and calculate the CVaR value under the confidence variable interval boundary; S4. Establish a flexibility quantification model with the minimum flexibility risk penalty cost as the objective function; S5. Solve the flexibility quantitative model.

4. The method for modeling flexibility requirements based on probability boxes according to claim 3 is characterized in that: Step S1 is specifically implemented as follows: The flexibility supply of thermal power units is composed of the maximum output of thermal power units, the maximum output of oil injection combustion depth peak regulation and the climbing ability. The calculation formula is as follows: Where: They represent the upward and downward flexibility of thermal power units that have undergone deep peak load regulation transformation; Respectively represent the up and down climbing rates of thermal power units; is the maximum output of the thermal power unit; P g,t Provide power for thermal power units; It is the deep peak-shaving extreme output of the deep peak-shaving thermal power units with oil injection and combustion assistance; The flexibility of a hydropower unit is composed of its maximum output, minimum output and its climbing ability, which can be calculated as follows: Where: They represent the upward and downward adjustment flexibility of the hydropower units respectively; Respectively represent the up and down climbing ability of the hydropower unit; P s,t Real-time output of hydropower units; and Respectively represent the maximum output and minimum output of the hydropower unit; The flexibility of energy storage is related to its own factors including state of charge and charging and discharging power, and its calculation formula is as follows: Where: They represent the upward and downward flexibility of energy storage respectively; Respectively represent the rated charging and discharging power of energy storage; P c,t , P f,t Respectively represent the real-time charging and discharging power of energy storage; E max 、E min Respectively represent the rated capacity and minimum power storage value of energy storage; E t is the energy storage value at time t; η e The charging and discharging efficiency of energy storage; In summary, the total flexibility supply in the system is the sum of the flexibility of each flexibility resource on the supply side of the system, and its calculation formula is: Where: They represent the total upward and downward flexibility supply of the system respectively; The demand-side flexibility of the power system comes from two aspects: on the one hand, the volatility of the net load of the system, which reflects the uncertainty of load demand over time; on the other hand, the error of load forecasting, which reflects the possible deviation between the forecasting model and the actual load demand; it is measured by the change of net load at adjacent moments on a time scale, and its expression is: Where: They represent the upward and downward flexibility requirements of the system respectively; is the net load at the current moment; is the net load forecast value at the next moment; They respectively represent the upper and lower limits of the net load prediction error at the next moment; wherein, the upper and lower limits of the net load prediction error at the next moment are derived from the uncertainty of wind power output, photovoltaic output and load prediction error at the next moment.

5. The method for modeling flexibility requirements based on probability boxes according to claim 4 is characterized in that: In step S2, the probability box distribution of wind power output prediction error is solved as follows: Assume that the wind power output prediction error It is believed that the wind power output prediction error follows a normal distribution with parameters varying in a certain interval, where the parameter of the normal distribution is μ∈(μ d ,μ u ),σ∈(σ d ,σ u ), μ d , μ u They represent the lower and upper limits of the mean of the normal distribution, σ d , σ u They represent the lower limit and upper limit of the standard deviation of the normal distribution respectively. The upper and lower limits of the parameters respectively form four probability cumulative functions. The interval formed by the four probability cumulative functions is the probability box distribution of the prediction error, thus obtaining the probability box distribution of the wind power output prediction error; Since historical data is discrete, the probability box boundary function should have intersection points where the cumulative probability is 0 and 1, so ΔP t W The range is expressed as: Where: and are the errors of the probability box boundary when the cumulative probability value is 0 and 1, respectively, which represent the maximum and minimum values ​​of the wind power output prediction error; The confidence interval β is set to select the interval boundary, and the range of wind power output prediction error is expressed as: Where: and are the upper and lower limits of wind power output prediction error under the confidence interval β; F1 and F2 represent the cumulative probability; β u , β d are the cumulative probabilities corresponding to the upper and lower limits of wind power output prediction error under the confidence interval; Similarly, the range of the photovoltaic output and load demand prediction errors is obtained.

6. The method for modeling flexibility requirements based on probability boxes according to claim 5, characterized in that: In step S2, the system flexibility requirement and The expression is as follows: Where: and are the upper and lower limits of the load demand forecast error under the confidence interval β, respectively; and are the upper and lower limits of the photovoltaic output prediction error under the confidence interval β; P L,t+1 , P w,t+1 , P P,t+1 They are load demand, wind power output, and photovoltaic power output forecast power respectively.

7. The method for modeling flexibility requirements based on probability boxes according to claim 5, characterized in that: Step S3 is specifically implemented as follows: For the decision variable x, let the probability density function of the random variable ξ be p(ξ), then the probability that the loss function f(x,ξ) caused by ξ does not exceed the threshold α is: The VaR value under the confidence interval β is expressed as: The corresponding CVaR value is expressed as:

8. The method for modeling flexibility requirements based on probability boxes according to claim 7, characterized in that: Step S4 is specifically implemented as follows: Taking into account the flexibility supply and demand risk of the system to ensure the stable operation of the system, the flexibility risk penalty objective function is established as follows: Where: C F Penalize costs for system flexibility risk; Penalize for insufficient flexibility within confidence intervals; is the conditional value at risk of flexibility risk outside the confidence interval; Penalize unit costs for insufficient flexibility, upward or downward respectively; To adjust the flexibility requirements upward and downward respectively. They are to adjust flexibility supply upward and downward respectively; They are the unit costs of upward and downward flexibility risk penalty outside the confidence interval, respectively; is an auxiliary variable, and its value is 1 / (1-β); is a 0-1 variable, representing whether it is within the confidence interval, 1 means outside the confidence interval, and 0 means within the confidence interval; α ξ is the flexibility risk function; They are the probabilities of upward and downward adjustments to flexibility risk.

9. A flexibility requirement modeling system based on probability box, characterized in that: The method comprises a memory, a processor and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps as claimed in any one of claims 1 to 8 can be implemented.

10. A computer-readable storage medium having stored thereon computer program instructions that can be executed by a processor, and when the processor executes the computer program instructions, the method steps according to any one of claims 1 to 8 can be implemented.

Images