Power system supply and demand imbalance risk measurement method

Abstract

The invention belongs to the technical field of power system operation optimization, and particularly relates to a power system supply and demand imbalance risk measurement method, which comprises the following steps of: obtaining a typical scene considering wind and light output correlation and a probability thereof by combining a Copula method based on wind and light output historical data; constructing a power system stochastic optimization model considering the wind and light output uncertainty based on the wind and light output scene; mathematical derivation is performed based on tail Gini measurement to obtain a GWCVaR-based load supply and demand imbalance risk measurement model, and a power system stochastic optimization objective function considering risk measurement is constructed based on the GWCVaR model. According to the method, the tail Gini measurement and the WCVaR are fused, the CVaR values under multiple confidence coefficients are integrated by introducing a weighting mechanism, meanwhile, the Gini difference measurement is combined, more comprehensive description of the tail risk is achieved, the one-sidedness of a traditional CVaR method under a single risk hypothesis is effectively overcome, and the method has good market application prospects.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system operation optimization, and particularly relates to a power system supply-demand imbalance risk measurement method. BACKGROUND

[0002] In recent years, with high proportion of renewable energy connected to the power system, the high uncertainty of output significantly aggravates the complexity of system dispatching and risk control. In order to guarantee the economy and safety of system operation, how to effectively characterize and cope with the cost and supply-demand imbalance risk caused by wind and light and other new energy has become an important problem in power dispatching research.

[0003] In the traditional risk control method, the deterministic modeling mostly copes with the risk by reserving standby capacity, and such method has simple model and small calculation burden, but it is difficult to accurately match the actual risk level and is prone to the situation of standby capacity redundancy in low risk scenario and insufficient guarantee in high risk scenario. Therefore, in recent years, scholars widely adopt the stochastic optimization method to model the uncertainty through scene construction and opportunity constraints, and the CVaR model based on confidence degree is widely applied due to its strong tail risk characterization ability and high numerical calculation efficiency. However, CVaR also faces certain limitations in application. On the one hand, CVaR only focuses on the tail expectation under a single confidence degree, which may ignore other risk situations and is difficult to comprehensively reflect the multiple risks faced by the system. On the other hand, the selection of confidence degree by CVaR lacks a unified standard and is often dependent on experience, which is highly subjective.

[0004] The information disclosed in this BACKGROUND section is only for the purpose of increasing the understanding of the background of the application and should not be taken as an acknowledgment or any form of suggestion that this information forms prior art that is already known in this field. SUMMARY

[0005] The purpose of the present application is to provide a power system supply-demand imbalance risk measurement method, which integrates tail Gini index and WCVaR, integrates the CVaR values under multiple confidence degrees by introducing a weighting mechanism, and realizes more comprehensive characterization of tail risk by combining Gini difference index, thereby overcoming the one-sidedness of the traditional CVaR method under a single risk assumption.

[0006] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme: A power system supply-demand imbalance risk measurement method, comprising the following steps: S1, based on the historical output data of wind power and photovoltaic, respectively adopting kernel density estimation method to construct the marginal probability density function thereof, and combining the fitted Copula parameter to establish a Copula joint distribution model, generating a large number of wind and light joint output scenes through Monte Carlo sampling and marginal inverse transformation; S2, the K-medoids clustering algorithm is used to cluster the wind and light combined output scenarios, and representative typical output scenarios and their occurrence probabilities are obtained, and a power system random optimization model considering wind and light uncertainty is constructed accordingly; S3, in the optimization model constructed in S2, the tail Gini measurement method is introduced to measure the risk difference of the tail of the profit or loss distribution under different confidence levels; S4, based on multiple CVaR confidence levels, a weighted conditional value at risk function GWCVaR is constructed, which organically combines the tail Gini measurement with the CVaR under multiple confidence levels to form a comprehensive risk assessment index under multiple confidence levels; S5, the GWCVaR function is introduced as a risk penalty term into the optimization objective function, and the system expected operation cost is used to form the optimization objective of the scheduling model, so as to realize cost minimization and risk control at the same time.

[0007] As preferred, in S1, based on the historical output data of wind power and photovoltaic, the kernel density estimation method is used to construct the marginal probability density function, which includes the following steps: The sample standard deviation of the historical wind power output sample set and the photovoltaic output sample set is calculated respectively ; The bandwidth of kernel density estimation is determined by using an empirical formula: ; In the formula, The bandwidth of kernel density estimation is denoted as The sample size is denoted as The sample standard deviation is denoted as The Gaussian kernel function is used to calculate the marginal probability density: ; In the formula, The estimated probability density function is denoted as The sample size is denoted as The kernel function is denoted as The random variable is denoted as The i-th sample output value is denoted as n, and the sample size is denoted as n. According to the above formula, the random sampling data is substituted to obtain the final and , which are used as the marginal probability density functions of wind power and photovoltaic output, respectively, to input the Copula joint distribution model.

[0008] As preferred, the construction and sampling process of the Copula joint distribution model in S1 includes: The Frank-Copula is selected, and its joint distribution function form is: ; In the formula, The joint distribution function; The edge distribution function value of wind power output , Edge distribution function value of photovoltaic power output These are the marginal probability density functions of wind power and solar power, respectively. and The cumulative distribution function value obtained by integration; The Copula parameters are obtained by fitting using the maximum likelihood method. In [0,1] 2 Within the probability space, N pairs of joint uniform samples are generated using the Monte Carlo method or Latin hypercube sampling. For each joint sample pair, perform the inverse transform of the marginal cumulative distribution function: ; In the formula, and They represent the results after sampling of the joint distribution function. and The sampled values, The wind power output value is obtained from the inverse transformation. The photovoltaic output value obtained by inverse transformation; By mapping these values ​​to actual wind and solar power output scenarios, a set of correlated wind and solar power output samples is obtained, which can be used for subsequent clustering and optimized scheduling analysis.

[0009] As a preferred method, S2 employs the K-medoids clustering algorithm to cluster the combined wind and solar power output scenarios, obtaining representative typical power output scenarios. Specifically, this includes the following steps: Initial center selection: Randomly select several points from the sample set as initial cluster centers; Sample assignment: For each scene, calculate its Euclidean distance to each cluster center, and assign each scene to the cluster represented by the nearest cluster center. The calculation formula is as follows: ; In the formula, Represents the i-th scene With the kth cluster center The Euclidean distance between them Indicates the first One scenario; Indicates the first Cluster centers; This refers to the dimension of a single moment within a day; and are the output values of the scene and the cluster center at time ; Update the center point: for each cluster, reselect a sample from the cluster that minimizes the total distance from all samples in the cluster to it as the new cluster center. The distance calculation is as follows: ; wherein denotes the total distance from all points in the cluster to the current center ; is an arbitrary point in the cluster ; For each point in the cluster , calculate the total distance corresponding to each point becoming the cluster center, and select the minimum as the updated cluster center. The calculation formula is as follows: ; wherein denotes the new center point of the cluster , and are the scene points in the cluster , wherein is the candidate center point in the cluster , is an arbitrary scene point in the cluster ; Iterative optimization: repeat the sample attribution division and cluster center point update operation until the cluster center no longer changes significantly, and the clustering process converges. The optimization goal of the K-medoids algorithm is to minimize the total distance sum in all cluster clusters: ; wherein J denotes the total distance sum of all cluster clusters, denotes the number of clusters.

[0010] As a preference, the calculation of the GWCVaR function comprises: Expression of the continuous tail Gini metric: ; wherein is the confidence level, denotes the tail Gini metric under the confidence level , is the decision variable, denotes the expected value of the loss distribution, denotes the second order quantile function of the loss distribution, is the integral variable; The confidence interval [0, Divide into v sub-intervals Then, a median approximation is used and correlated with CVaR, utilizing: ; In the formula, Indicates the j-th confidence level; The expression for the tail Gini metric is rewritten as: ; Therefore, GWCVaR can be expressed as: ; ; In the formula, This indicates that the weighted average value of the risk is determined by the Gini coefficient. The weight for the j-th confidence level, For the j-th confidence level, The number of confidence levels defined above; Risk penalty item construction: As a risk penalty term in the optimization objective, it is used through weight variables. By flexibly adjusting risk preferences at different confidence levels, multi-level quantitative control of system load shedding or power curtailment risks can be achieved.

[0011] Compared with the prior art, the present invention has the following beneficial effects: (1) In view of the problem that traditional CVaR risk measurement relies on a single confidence level, which is subjective and cannot fully reflect the tail risk, the power system supply and demand imbalance risk measurement method of the present invention introduces GWCVaR to weight CVaR at multiple confidence levels, which can reflect the tail loss of the system in a balanced way under different risk levels, reduce subjectivity, and improve the scientificity and rationality of risk measurement.

[0012] (2) In view of the problem that CVaR only focuses on a single tail interval and easily ignores non-extreme but still significant losses, the power system supply and demand imbalance risk measurement method of the present invention introduces the overall volatility of the distributed tail by combining GWCVaR with Tail Gini metric (TGM), so as to achieve a unified characterization of mild, moderate and extreme tail risks and make the risk characterization more comprehensive.

[0013] (3) In view of the problem that traditional methods over- or under-configure reserve capacity, resulting in an imbalance between economy and reliability, the power system supply and demand imbalance risk measurement method of the present invention, based on the risk optimization model of GWCVaR, can avoid redundant reserves while ensuring power supply reliability, improve the utilization rate of reserve resources, and thus reduce system operating costs. Attached Figure Description

[0014] Figure 1 is a schematic diagram of the method flow of the present application; Figure 2 is a wind power output curve adopted in the embodiment of the present application, wherein the numerical values are shown in the form of a unit, the vertical coordinate is the unit, and the horizontal coordinate is time (day) ; Figure 3 is a photovoltaic output curve adopted in the embodiment of the present application, wherein the numerical values are shown in the form of a unit, the vertical coordinate is the unit, and the horizontal coordinate is time (day) ; Figure 4 is a load curve adopted in the embodiment of the present application, wherein the numerical values are shown in the form of a unit, the vertical coordinate is the unit, and the horizontal coordinate is time (day) ; Figure 5 is the micro-grid dispatching result of case C1 in the embodiment of the present application, which shows the operation of gas turbine units, biogas units, renewable energy units and electric energy storage units, the vertical coordinate is power, the unit is kilowatt, and the horizontal coordinate is time (day) ; Figure 6 is the average operation cost and load shedding risk diagram of case C2 in the embodiment of the present application under different risk aversion coefficients, the left vertical coordinate axis corresponds to the column chart, which represents the average value of the total cost of the micro-grid in the entire operation period under different scenarios, the unit is 10 3 dollars, the right vertical coordinate axis corresponds to the line chart, which represents the load shedding risk value of the micro-grid in the entire operation period (the risk value under the selected confidence , the horizontal coordinate is the risk aversion coefficient, which corresponds to in formula (38), and the value is a dimensionless parameter. DETAILED DESCRIPTION

[0015] The technical solutions of the present application will be described below in a clear and complete manner. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0016] In the description of the present application, it should be noted that the orientation or position relationship indicated by terms such as "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like is based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the application.

[0017] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, terms such as "mounting", "connection", "connection" should be understood in a broad sense, for example, it can be fixed connection, or detachable connection, or integral connection; it can be mechanical connection, or electrical connection; it can be direct connection, or indirect connection through intermediate medium, or connection inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0018] Referring to the drawings Figure 1 The present application provides a power system supply and demand imbalance risk measurement method, which integrates the CVaR values under multiple confidence levels by introducing a weighting mechanism, and combines with Gini difference measurement to achieve a more comprehensive description of tail risk, effectively overcoming the one-sidedness of traditional CVaR method under single risk assumption. Specifically, the following steps are included: S1, based on wind and light output historical data, combining with Copula method to obtain typical scenes considering wind and light output correlation and their probabilities; S2, based on wind and light output scene, constructing a power system stochastic optimization model considering wind and light output uncertainty; S3, based on tail Gini measurement, mathematical derivation is carried out to obtain a load supply and demand imbalance risk measurement model based on GWCVaR, and a power system stochastic optimization objective function considering risk measurement is constructed based on the GWCVaR model.

[0019] Wherein, the method of step S1 based on Copula model to obtain typical scenes considering wind and light output correlation and their probabilities is as follows: S11, Copula-based wind and light output correlation scene generation, specifically including: 1) Edge distribution modeling: edge density function modeling is carried out based on kernel density estimation, and the density functions of wind and light output are obtained respectively, and the wind and light distribution functions are obtained based on the wind and light edge probability density functions; 2) Based on the wind and light distribution functions, Frank-Copula function is constructed to simulate the correlation structure between wind power and photovoltaic to obtain the wind and light joint distribution function: (1) In the formula, is the joint distribution function, , are the distribution functions of two variables respectively; here is the edge distribution function value of wind power output , is the edge distribution function value of photovoltaic output , are the edge probability density functions of wind power and photovoltaic respectively and the cumulative distribution function value obtained by integration; a Copula parameter, the value of which can be obtained by using a maximum likelihood method; 3) performing a Monte Carlo method to sample from the Copula joint distribution and obtaining a large number of wind-solar output scenarios through inverse transformation of respective marginal distribution functions; S12, adopting a K-mediods clustering algorithm to cluster the large number of wind-solar output scenarios to obtain typical scenarios and their probabilities, specifically including: 1) initial center selection: randomly selecting several points from the sample set as initial clustering centers; 2) sample attribution division: for each scenario, calculating the Euclidean distance between it and each clustering center, and attributing each scenario to the cluster represented by the nearest center; 3) updating the center point: for each clustering cluster, reselecting one from the samples in the cluster as a new center. The new center point should make the total distance of all samples in the cluster to it minimum; 4) iterative optimization: repeatedly performing sample attribution division and center point updating operations until the clustering centers no longer change significantly and the clustering process converges; the optimization objective of the K-medoids algorithm is to minimize the total distance sum in all clustering clusters.

[0020] Considering that different scenarios present different characteristics in terms of wind power, photovoltaic power and load, etc., the K-medoids clustering algorithm can be used to divide them into several categories to obtain representative typical scenarios and determine the probability of occurrence of each category of scenarios.

[0021] The specific content of step S2 of constructing a power system stochastic optimization model considering wind-solar output uncertainty based on wind-solar output scenarios is as follows: constructing a power system stochastic optimization model: the variables are the output of conventional thermal power units and the operation strategy of energy storage, the objective function is the sum of the minimum total operation cost and load shedding risk, the constraint conditions include thermal power unit constraints, renewable energy unit constraints, energy storage constraints, transmission constraints and power balance constraints; specifically as follows: 1) objective function: The objective function is composed of the average operation cost of the system under different scenarios and the load shedding risk function, expressed as follows: (2) (3) (4) (5) (6) wherein, represents the average cost of all typical scenarios, represents the risk-aversion coefficient of cutting load, represents the unit cutting load cost, represents the cutting load risk function under the confidence level, which will be described in the third step, represents the total cost of typical scenario The cutting load amount at time ; represents the probability of scenario occurrence, represents the total cost of typical scenario ; represents the fuel cost of typical scenario , represents the unit cost of typical scenario ; , , is the fuel cost function coefficient, is the power generation amount of generator in typical scenario at time ; represents the operation state of unit at time , represents that the unit is in the starting state, and vice versa.

[0022] and are the starting and stopping costs of unit , respectively; for unit , the starting and stopping costs are and , respectively. At time , if the unit performs a starting operation, the corresponding binary variable ; if a stopping operation is performed, . When and , it means that the operation state of the unit at that time remains unchanged, i.e., no start-stop operation occurs.

[0023] 2) Thermal unit constraints: Thermal unit constraints mainly include unit output constraints, unit ramping constraints, and unit start-stop constraints; (7) (8) (9) (10) (11) (12) where, and denote the upper and lower bounds of the thermal power unit output, denote the unit At time, 0 / 1 variable representing the operating state, denote the unit is in the start state, otherwise it is in the shutdown state; and denote the upward and downward climbing ability of the generator, and denote the minimum start-up and minimum shutdown time of the generator unit, denote the time index of the unit operating state within the minimum start-up / shutdown time, which is different from .

[0024] 3) Renewable energy unit constraints: (13) where, denotes the output of the renewable energy unit, denotes the typical scenario At time, the capacity factor of the renewable energy unit , and denote the upper and lower bounds of the output of the renewable energy unit.

[0025] 4) Energy storage constraints: (14) (15) (16) (17) where, denotes the SOC state of the energy storage at time t, denotes the SOC state of the energy storage at time t-1, and denote the charging / discharging power of the energy storage, and denote the charging / discharging efficiency of the energy storage; and denote the upper and lower bounds of the SOC of the energy storage; denote the installed capacity of the charging and discharging power; The number of time periods representing the storage period.

[0026] In formula (17), The initial SOC state of the energy storage, The final state of the energy storage at the end, so as to ensure that the initial and final states of the energy storage are consistent, and the sustainable cyclic operation of the system is ensured.

[0027] 5) Transmission constraints: (19) In the formula, The node The load demand at the time .

[0028] The GWCVaR-based load supply and demand imbalance risk measurement method in step S3 is as follows: S31, GWCVaR risk measurement model based on tail Gini measurement: In power systems, different degrees of load shedding risk are caused by uncertainty. In existing methods, CVaR is a commonly used risk measurement method for quantifying the expected value of potential losses exceeding the VaR value. Using CVaR, decision makers can intuitively understand the potential risks they face through the size of default losses. However, CVaR only focuses on the risk at a single confidence level, which may ignore losses in other parts. Therefore, a weighted CVaR method (GWCVaR) based on Gini mean difference is proposed, which enables participants to manage power system load shedding risks at multiple confidence levels.

[0029] 1) Traditional CVaR model: Assuming that there is a decision variable , its VaR value represents the maximum loss value that the scheduling strategy may cause at a given confidence level . CVaR is the weighted average of expected losses exceeding VaR. The discretization calculation method of CVaR is as follows: (20) In the formula, The probability of scenario i, The decision variable of scenario i, The loss function of scenario i, The , max represents the larger of the two.

[0030] The calculation of CVaR can be realized by solving the problem of minimizing CVaR, which is equivalent to the following linear programming problem: (21) wherein, is an auxiliary variable whose value represents the fraction of the loss that is greater than the VaR value, denotes the probability of scenario i, N denotes the number of scenarios, min denotes the minimization function, subject to denotes the constraint condition.

[0031] 2) GWCVaR model based on tail Gini measure: The Gini mean difference directly reflects the overall volatility using the absolute difference, converts its discrete model into continuous integral, and converts it into a single variable integral using the symmetry of the absolute value: (22) wherein, denotes the Gini mean difference of ; denotes the expected value of variable ; is the second order quantile function, which is the integral of the first order quantile function; the first order quantile function is the inverse function of the cumulative distribution function (CDF) of variable ; is the integral variable; The definition of the tail Gini measure is to reduce the interval of the above formula to (0, ) and normalize it through , to obtain: (23) (24) wherein, is the confidence level, denotes the tail Gini measure under the confidence level ; is the decision variable, denotes the expected value of the loss distribution, denotes the second order quantile function of the loss distribution, is the integral variable, is the integral variable; Using numerical integral to approximate the integral expression of the tail Gini measure, the integral interval (0, ) of the tail Gini measure is discretized and divided into , to obtain: (25) wherein, denotes the jth confidence level; The above formula can be converted to: (26) The expression of CVaR for left tail risk problem is: (27) Combining (27), (26) can be expanded to: (28) Using midpoint value approximation, assume that in each sub-interval , is approximately constant, then: (29) After substituting (29) into (28) and rearranging, we get: (30) Using the idea of approximate difference, assume , the above formula can be further simplified as: (31) Finally, GWCVaR can be approximately expressed as: (32) where, (33) In the formula, represents the Gini-weighted conditional value at risk, is the weight of the jth confidence level, is the number of confidence levels divided above; Similarly, for the right tail risk problem with cost as an example, the tail risk region becomes , and the interval is discretely divided into , the expression of GWCVaR can be derived as: (34) (35) S32, based on the GWCVaR model, a risk-considered power system stochastic optimization objective function is constructed: The GWCVaR is introduced to measure the load shedding risk of microgrid, and the load shedding risk calculated based on GWCVaR is expressed as follows: (36) (37) In the formula, and are the confidence level symbols and are the equivalent substitutes in the right tail risk, represents the confidence level The VaR value of the risk of load shedding.

[0032] The objective function (2) of the optimization problem is finally obtained as follows: (38) To show the advantages of the method of the present application, this embodiment carries out simulation test under an electricity-methane coupled microgrid, which is scaled in proportion to the reference IEEE24 system, wherein a farm methane power generation system, two wind power plants and two solar power plants are accessed, and the simulation parameters of the farm methane power generation system come from a certain state-owned farm biomass energy power generation system in Jiangsu, China. The parameters of various types of equipment are configured as follows: the installed capacity of the gas generator is 13460kW, the total installed capacity of the photovoltaic is 2240kW, the installed capacity of the wind power plant is 2240kW, the capacity of the battery energy storage system is 500kW / 1000kWh, and the charging and discharging efficiency is 95%; the installed capacity of the methane generator is 1500kW, the capacity of the electric heating boiler is 600kW, the volume of the anaerobic fermentation tank is 20000m 3 , the initial total solid concentration is 25kgVS / m 3 , the initial temperature is 25℃, the methane yield potential is 0.42m 3 / kg, the microbial fermentation parameters are 0.015 / –0.129 / 0.802, the material heat exchange efficiency is 50%; the capacity of the biogas storage tank is 1000m 3 / 60000m 3 , the charging and discharging efficiency is 92%, the low heat value of the biogas is 6.6278kWh / m 3 , and the biogas power generation efficiency is 35%. Figure 2 is the wind power output unit curve adopted by the microgrid, Figure 3 is the photovoltaic output unit curve adopted by the microgrid, Figure 4 is the power load demand unit curve adopted in the embodiment of the present application.

[0033] This embodiment sets three schemes for comparison: C1: the microgrid is not subjected to load shedding risk control, and only economic efficiency is considered; C2: the GWCVaR model proposed in this paper is introduced to measure and control the load shedding risk of the microgrid; C3: the traditional CVaR model is introduced to measure and control the load shedding risk of the microgrid (95% confidence level).

[0034] After optimization calculation, the operation cost, the load shedding risk value under different confidence levels and the value of tail Gini measurement of each scheme can be obtained, as shown in the following table:

[0035] Figure 5The microgrid scheduling results for C1, Figure 6 The average operating cost and load shedding risk chart for C2 under different risk aversion coefficients. The comparison results of C1 and C2 show that although the introduction of GWCVaR will increase the average operating cost by 3.3%, it significantly reduces the load shedding risk. Under different confidence levels, GWCVaR can achieve an average of 85.3% reduction in load shedding risk, while CVaR can only achieve an average of 81.8% risk reduction under the same conditions. Therefore, although the cost increases slightly, GWCVaR can better control the load shedding risk of different degrees.

[0036] In order to compare the performance of CVaR and GWCVaR in risk measurement, C2 and C3 are evaluated under the premise of close average cost by adjusting the risk aversion coefficient. As shown in the table, although the average cost of C3 is 0.029% higher than that of C2, its risk control effect is not as good as that of C2.

[0037] Specifically, at a confidence level of 95%, C3 reduces the load shedding risk by only 3.6% compared to C2; while at other confidence levels, the risk of C4 increases by an average of 44.9%, and the value of the tail Gini metric also increases by 28.6%. This is because GWCVaR can achieve more comprehensive coverage of tail risk, optimize risk performance at multiple confidence levels, and effectively reduce the GMD of the tail. While CVaR only focuses on the risk at a certain confidence level, its singularity and subjectivity to some extent limit the effectiveness of risk control. Therefore, in a microgrid, compared to CVaR, GWCVaR can provide a more scientific and comprehensive tail risk control method.

[0038] The foregoing description of specific exemplary embodiments of the application is intended to be illustrative only and is not intended to limit the application to the precise forms described. Many modifications and variations are possible in light of the above teachings without departing from the spirit or essential characteristics of the application. The exemplary embodiments were chosen and described in order to explain the principles of the application and its practical application and to allow others skilled in the art to understand the application for various exemplary embodiments with various modifications being suited to the particular use contemplated. The scope of the application is intended to be defined by the claims and their equivalents.

Claims

1. A method for measuring the risk of power system supply and demand imbalance, characterized in that, The method comprises the following steps: S1, based on the historical output data of wind power and photovoltaic, respectively, the edge probability density function is constructed by using kernel density estimation method, and the Copula joint distribution model is established by combining the fitted Copula parameter, a large number of wind and light joint output scenes are generated by Monte Carlo sampling and edge inverse transformation; S2, the K-medoids clustering algorithm is used to cluster the wind and light joint output scenes, the representative typical output scenes and their occurrence probabilities are obtained, and a power system random optimization model considering wind and light uncertainty is constructed; S3, in the optimization model constructed in S2, the tail Gini measurement method is introduced to measure the risk difference of the tail of the profit or loss distribution under different confidence levels; S4, based on multiple CVaR confidence levels, a weighted conditional value at risk function GWCVaR is constructed, the tail Gini measurement and CVaR under multiple confidence levels are organically combined to form a comprehensive risk evaluation index under multiple confidence levels; S5, the GWCVaR function is introduced into the optimization objective function as a risk penalty term, and the system expected operation cost is used to form the optimization objective of the scheduling model, so as to realize cost minimization and risk control at the same time.

2. The power system supply and demand imbalance risk measurement method according to claim 1, characterized in that, In S1, based on the historical output data of wind power and photovoltaic, respectively, the edge probability density function is constructed by using kernel density estimation method, which comprises the following steps: With the historical wind power output sample set and the photovoltaic output sample set as inputs, the sample standard deviations thereof are calculated ; The bandwidth of kernel density estimation is determined by using empirical formula: ； wherein denotes the bandwidth of the kernel density estimate, is the number of samples, is the sample standard deviation; Gaussian kernel function , computes the edge probability density: ； wherein is the probability density function, is the number of samples; is the kernel function, is the random variable, representing the output value, is the i-th sample output value, n is the number of samples; According to the above formula, substitute the randomly sampled data, and finally get With As the marginal probability density function of wind power and photovoltaic power output, respectively, input the Copula joint distribution model.

3. The power system supply and demand imbalance risk measurement method according to claim 2, characterized in that, The construction and sampling process of the Copula joint distribution model in S1 includes: The Frank-Copula is selected, and the joint distribution function form is: ； wherein, is the joint distribution function; is the marginal distribution function value of the wind power output , is the marginal distribution function value of the photovoltaic power output are the cumulative distribution function values obtained by integrating the marginal probability density functions of the wind power and photovoltaic power, respectively; and ; is the Copula parameter, which is obtained by fitting through the maximum likelihood method; Within the probability space [0,1] 2 , N pairs of jointly uniform samples are generated using the Monte Carlo method or Latin hypercube sampling; For each joint sample pair, the inverse transformation of the edge cumulative distribution function is performed: ； In the formula, and respectively represent the sampling values of the joint distribution function and is the wind power output value obtained by inverse transformation, is the photovoltaic output value obtained by inverse transformation;​ Map it to the actual wind power and photovoltaic output scene to get a set of wind and light output samples with correlation, which is used for subsequent clustering and optimization scheduling analysis.

4. The method of claim 1, wherein, In S2, the K-medoids clustering algorithm is used to cluster the wind and light joint output scenes, and the representative typical output scenes are obtained, which comprises the following steps: Initial center selection: randomly select several points from the sample set as the initial clustering center; Sample attribution division: for each scene, calculate the Euclidean distance between it and each clustering center, and attribute each scene to the cluster represented by the nearest clustering center, and the calculation formula is as follows: ； In the formula, Represents the i-th scene With the kth cluster center The Euclidean distance between them Indicates the first One scenario; Indicates the first Cluster centers; This refers to the dimension of a single moment within a day; and The scene and cluster center at time respectively The output value; Update center point: for each cluster, reselect a point from the samples in the cluster as the new clustering center, so that the total distance of all samples in the cluster to it is minimized; the cluster distance calculation method is: ； wherein represents a cluster of all points to the current center of the cluster ; For each cluster For each point , the total distance when each point becomes the cluster center is calculated, the minimum one is selected as the updated cluster center, and the calculation formula is as follows: ； wherein denotes a cluster of new center points, and are scene points in the cluster wherein is a candidate center point in the cluster and is an arbitrary scene point in the cluster . Iterative optimization: repeat the sample attribution division and clustering center point update operation until the clustering center no longer changes significantly, and the clustering process converges; the optimization objective of the K-medoids algorithm is to minimize the total distance sum of all clustering clusters: ； where J represents the total distance sum of all cluster clusters, represents the number of clusters.

5. The method of claim 1, wherein, The calculation of the GWCVaR function includes: The expression of the continuous tail Gini measurement: ； wherein is the confidence level, denotes the tail Gini metric at the confidence level is the decision variable, denotes the expected value of the loss distribution, denotes the second order quantile function of the loss distribution, is the integration variable;​ The confidence interval [0, ] is divided into v sub-intervals and then approximated by the median point and associated with CVaR using: ； In the formula, denotes the jth confidence level; Rewrite the expression of the tail Gini measurement as: ； Therefore, GWCVaR can be represented as: ； ； wherein denotes the Gini-weighted conditional value at risk, is the weight of the jth confidence level, is the jth confidence level, is the number of confidence levels partitioned above. Risk penalty term construction: the risk penalty term is constructed as As the risk penalty term in the optimization objective, the risk penalty term is constructed as Flexibly adjust the risk preference under different confidence levels to achieve multi-level quantitative control of system load shedding or curtailment risk.

Images