A power system supply and demand imbalance risk measurement method

Abstract

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, comprising the following steps: based on wind and light output historical data, combining a Copula method to obtain typical scenes considering wind and light output correlation and their probabilities; based on wind and light output scenes, constructing a power system random optimization model considering wind and light output uncertainty; based on mathematical derivation of tail Gini measurement, obtaining a load supply-demand imbalance risk measurement model based on GWCVaR, and based on the GWCVaR model, constructing a power system random optimization objective function considering risk measurement. The application fuses tail Gini measurement and WCVaR, integrates CVaR values under multiple confidence degrees by introducing a weighting mechanism, and combines Gini difference measurement, so that tail risks are more comprehensively described, the one-sidedness of traditional CVaR methods under a single risk assumption is effectively overcome, and the application has a good market application prospect.

Description

Technical Field

[0001] This invention belongs to the field of power system operation optimization technology, specifically relating to a method for measuring the risk of power system supply and demand imbalance. Background Technology

[0002] In recent years, with the integration of a high proportion of renewable energy into the power system, the high uncertainty of power output has significantly increased the complexity of system dispatch and risk control. To ensure the economic efficiency and security of system operation, how to effectively characterize and address the cost and supply-demand imbalance risks caused by new energy sources such as wind and solar power has become an important issue in power dispatch research.

[0003] In traditional risk control methods, deterministic modeling mostly addresses risk by reserving backup capacity. While these methods are simple and computationally inexpensive, they struggle to accurately match actual risk levels, often resulting in redundant backup capacity in low-risk scenarios and insufficient protection in high-risk scenarios. To address this, in recent years, scholars have widely adopted stochastic optimization methods, using scenario construction and chance constraints to model uncertainty. Among these, the confidence-based CVaR model has gained widespread application due to its strong tail risk characterization and high numerical efficiency. However, CVaR also faces certain limitations in its application. Firstly, CVaR focuses only on the tail expectation under a single confidence level, potentially neglecting other risk scenarios and failing to comprehensively reflect the multiple risks faced by the system. Secondly, CVaR lacks a unified standard for confidence level selection, often relying on empirical settings and exhibiting strong subjectivity.

[0004] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method for measuring the supply and demand imbalance risk in power systems, which integrates the tail Gini metric and WCVaR. By introducing a weighting mechanism to integrate CVaR values ​​under multiple confidence levels, and combining it with the Gini variance metric, a more comprehensive characterization of tail risk can be achieved, overcoming the one-sidedness of traditional CVaR methods under a single risk assumption.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for measuring the risk of power system supply-demand imbalance includes the following steps:

[0008] S1. Based on historical power output data of wind power and photovoltaic power, the edge probability density functions of wind power and photovoltaic power are constructed by kernel density estimation method, and the Copula joint distribution model is established by combining the fitted Copula parameters. A large number of wind and solar power joint output scenarios are generated by Monte Carlo sampling and edge inverse transformation.

[0009] S2. The K-medoids clustering algorithm is used to cluster the wind and solar power combined output scenarios to obtain representative typical power output scenarios and their occurrence probabilities, and based on this, a stochastic optimization model of the power system considering the uncertainty of wind and solar power is constructed.

[0010] S3. In the optimization model constructed in S2, the tail Gini metric method is introduced to measure the risk difference of the tail of the gain or loss distribution under different confidence levels.

[0011] S4. Construct a weighted conditional value at risk (GWCVaR) function based on multiple CVaR confidence levels, and organically combine the tail Gini measure with CVaR at multiple confidence levels to form a comprehensive risk assessment indicator at multiple confidence levels.

[0012] S5. Introduce the GWCVaR function as a risk penalty term into the optimization objective function. Together with the expected operating cost of the system, it constitutes the optimization objective of the scheduling model, so as to simultaneously achieve cost minimization and risk control.

[0013] As a preferred embodiment, in S1, based on the historical output data of wind power and photovoltaic power, the marginal probability density functions are constructed using the kernel density estimation method, specifically including the following steps:

[0014] Using historical wind power output sample sets and photovoltaic power output sample sets as inputs, calculate their sample standard deviations respectively. ;

[0015] The bandwidth for kernel density estimation is determined using an empirical formula:

[0016] ;

[0017] In the formula, This represents the bandwidth for kernel density estimation. For the sample size, The standard deviation is the sample standard deviation.

[0018] Using Gaussian kernel function Calculate the marginal probability density:

[0019] ;

[0020] In the formula, To estimate the probability density function, The number of samples; For kernel function, Let be a random variable, representing the output value. This represents the output value of the i-th sample.

[0021] Based on the above formula, substituting the random sampled data, we finally obtain... and The marginal probability density functions of wind power and photovoltaic power output are respectively input into the Copula joint distribution model.

[0022] As a preferred embodiment, the construction and sampling process of the Copula joint distribution model in S1 includes:

[0023] Using the Frank-Copula model, its joint distribution function is as follows:

[0024] ;

[0025] 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.

[0026] 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.

[0027] For each joint sample pair, perform the inverse transform of the marginal cumulative distribution function:

[0028] ;

[0029] In the formula, and They represent the joint distribution function after sampling. and The sampled values, The wind power output value is obtained from the inverse transformation. The photovoltaic output value obtained by inverse transformation;

[0030] 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.

[0031] 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:

[0032] Initial center selection: Randomly select several points from the sample set as initial cluster centers;

[0033] 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:

[0034] ;

[0035] 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;

[0036] Update centroids: For each cluster, select a new cluster center from the samples within the cluster that minimizes the total distance from all samples in that cluster to the new centroid; the intra-cluster distance is calculated as follows:

[0037] ;

[0038] In the formula, Cluster All points within the current center The total distance; For clusters Any point in;

[0039] For clusters Each point in Calculate the total distance for each point to become a cluster center, and select the smallest distance as the updated cluster center. The calculation formula is as follows:

[0040] ;

[0041] In the formula, Cluster The new center point and For clusters The scene points in the middle, among which It is a cluster Candidate center points in It is a cluster Any scene point in the;

[0042] Iterative optimization: Repeat the sample assignment and cluster center update operations until the cluster centers no longer change significantly and the clustering process converges; the optimization objective of the K-medoids algorithm is to minimize the sum of distances within all clusters.

[0043] ;

[0044] In the formula, J represents the total distance sum of all clusters. Indicates the number of clusters.

[0045] Preferably, the calculation of the GWCVaR function includes:

[0046] The expression for the continuous tail Gini metric:

[0047] ;

[0048] In the formula, For confidence level, Indicates at confidence level The tail section of the ginni measurement, As decision variables, This represents the expected value of the loss distribution. The second-order quantile function representing the loss distribution. For integration variables;

[0049] The confidence interval is [0, Divided into Sub-intervals Then, a median approximation is used and correlated with CVaR, utilizing:

[0050] ;

[0051] In the formula, Indicates the j-th confidence level; The first-order quantile function is a decision variable. The inverse function of the cumulative distribution function (CDF);

[0052] The expression for the tail Gini metric is rewritten as:

[0053] ;

[0054] Therefore, GWCVaR can be expressed as:

[0055] ;

[0056] ;

[0057] 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 for the division;

[0058] 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.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] (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.

[0061] (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.

[0062] (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

[0063] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0064] Figure 2This is the wind power output curve used in the embodiment of the present invention, wherein the values ​​are displayed in per-unit value form, the vertical axis is the per-unit value, and the horizontal axis is time (day).

[0065] Figure 3 This is the photovoltaic power output curve used in the embodiments of the present invention, where the values ​​are displayed in per-unit form, with the vertical axis representing the per-unit value and the horizontal axis representing time (days).

[0066] Figure 4 This is the load curve used in the embodiment of the present invention, where the values ​​are displayed in per-unit value form, with the vertical axis representing the per-unit value and the horizontal axis representing time (days).

[0067] Figure 5 The microgrid dispatching results of Case C1 in this embodiment of the invention show the operation status of equipment such as gas turbine units, biogas units, renewable energy units, and electric energy storage. The vertical axis represents power in kilowatts, and the horizontal axis represents time (days).

[0068] Figure 6 This is a graph showing the average operating cost and load shedding risk under different risk aversion coefficients for Case C2 in this embodiment of the invention. The left vertical axis corresponds to a bar chart, which represents the average total cost of the microgrid during its entire operation under different scenarios, in units of 10. 3 The figure in US dollars, with the right vertical axis corresponding to the line graph, represents the load shedding risk value of the microgrid during the entire operation period (at a selected confidence level). The risk value below), the horizontal axis is the risk aversion coefficient, corresponding to the risk value in equation (38). This value is a dimensionless parameter. Detailed Implementation

[0069] The technical solution of this invention patent will be clearly and completely described below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention.

[0070] In the description of this invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention.

[0071] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0072] See attached document Figure 1 This invention provides a method for measuring the supply-demand imbalance risk in power systems. By introducing a weighted mechanism to integrate CVaR values ​​under multiple confidence levels, and combining this with a Gini variance measure, it achieves a more comprehensive characterization of tail risk, effectively overcoming the limitations of traditional CVaR methods under a single risk assumption. Specifically, it includes the following steps:

[0073] S1. Based on historical data of wind and solar power output, and combined with the Copula method, typical scenarios and their probabilities considering the correlation between wind and solar power output are obtained.

[0074] S2. Construct a stochastic optimization model for the power system that considers the uncertainty of wind and solar power output based on wind and solar power output scenarios;

[0075] S3. Based on the tail Gini metric, a load supply and demand imbalance risk measurement model based on GWCVaR is derived mathematically, and a stochastic optimization objective function for the power system considering risk measurement is constructed based on the GWCVaR model.

[0076] In step S1, the typical scenario considering the correlation between wind and solar power output and its probabilistic method are obtained based on the Copula model as follows:

[0077] S11. Generation of wind-solar output correlation scenarios based on Copula, specifically including:

[0078] 1) Edge distribution modeling: Edge density function modeling is performed based on kernel density estimation to obtain the density function of wind and solar power output, and the wind and solar distribution function is obtained based on the wind and solar edge probability density function.

[0079] 2) Based on the wind-solar distribution function, a Frank-Copula function is constructed to simulate the correlation structure between wind power and photovoltaics, thus obtaining the joint wind-solar distribution function:

[0080] (1)

[0081] In the formula, For the joint distribution function, , These are the distribution functions of the two variables; here... 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 parameter can be obtained using the maximum likelihood method;

[0082] 3) The Monte Carlo method is used to sample from the Copula joint distribution, and a large number of wind and solar power output scenes are obtained by inverse transformation of their respective marginal distribution functions;

[0083] S12. Using the K-mediods clustering algorithm, the large number of wind and solar power output scenes are clustered to obtain typical scenes and their probabilities, specifically including:

[0084] 1) Initial center selection: Randomly select several points from the sample set as initial cluster centers;

[0085] 2) Sample assignment: For each scene, calculate its Euclidean distance to each cluster center, and assign each scene to the cluster represented by the nearest center.

[0086] 3) Update centroids: For each cluster, select a new centroid from the samples within the cluster. The new centroid should minimize the total distance from all samples within the cluster to it.

[0087] 4) Iterative optimization: Repeat the sample assignment and centroid update operations until the cluster centers no longer change significantly and the clustering process converges; the optimization goal of the K-medoids algorithm is to minimize the sum of distances within all clusters.

[0088] Considering that different scenarios exhibit different characteristics in terms of wind power, photovoltaics, and load, the K-medoids clustering algorithm can be used to divide them into several categories to obtain representative typical scenarios and determine the probability of each scenario occurring.

[0089] Step S2 involves constructing a stochastic optimization model for the power system that considers the uncertainties in wind and solar power output. The specific details are as follows:

[0090] A stochastic optimization model for the power system is constructed, with variables including conventional thermal power unit output and energy storage operation strategies. The objective function is to minimize the sum of total operating costs and load shedding risks. Constraints include thermal power unit constraints, renewable energy unit constraints, energy storage constraints, transmission constraints, and power balance constraints; details are as follows:

[0091] 1) Objective function:

[0092] The objective function consists of the average operating cost of the system under different scenarios and the load shedding risk function, expressed as follows:

[0093] (2)

[0094] (3)

[0095] (4)

[0096] (5)

[0097] (6)

[0098] In the formula, This represents the average cost across all typical scenarios. This represents the load shedding risk aversion coefficient. This represents the unit load shedding cost. Indicates confidence level The load shedding risk function will be described in detail in step three. Representing typical scenarios At any moment The amount of load shedding; Representing a scene The probability of occurrence Representing typical scenarios Total cost; Representing typical scenarios fuel costs, Representing typical scenarios The unit start-up and shutdown costs; , , These are the coefficients of the fuel cost function. For generator In typical scenarios time The amount of electricity generated; Representative unit exist A 0 / 1 variable representing the running state at any given moment. This indicates that the unit is in the startup state, and the opposite indicates that it is in the shutdown state.

[0099] and The units Start-up and shutdown costs; for the unit Its start-up and shutdown costs are denoted as follows: and At that moment If the unit performs a startup operation, the corresponding binary variable If a shutdown operation is performed, then .when and When the time is specified, it indicates that the unit's operating status remains unchanged at that moment, meaning that no start-up or shutdown operation has occurred.

[0100] 2) Constraints of thermal power units:

[0101] The constraints on thermal power units mainly include unit output constraints, unit ramping constraints, and unit start-up and shutdown constraints;

[0102] (7)

[0103] (8)

[0104] (9)

[0105] (10)

[0106] (11)

[0107] (12)

[0108] In the formula, and These represent the upper and lower limits of the output of thermal power units, respectively. Representative unit exist A 0 / 1 variable representing the running state at any given moment. This indicates that the unit is in the startup state, and the opposite indicates that it is in the shutdown state; and These represent the generator's upward and downward climbing capabilities, respectively. and These represent the minimum start-up and minimum shutdown times of the generator set, respectively. The time index represents the unit's operating status within the minimum start / stop time, distinct from the one in the same formula. .

[0109] 3) Constraints on renewable energy units:

[0110] (13)

[0111] In the formula, Indicates the output of renewable energy units. Representing typical scenarios exist Renewable Energy Units capacity factor, and These represent the upper and lower limits of the output of renewable energy units, respectively.

[0112] 4) Energy storage constraints:

[0113] (14)

[0114] (15)

[0115] (16)

[0116] (17)

[0117] In the formula, This represents the SOC state of the energy storage at time t. This indicates the SOC state of the energy storage at time t-1. and These represent the charging / discharging power of the energy storage, and These represent the charging / discharging efficiency of energy storage, respectively. and Indicates the upper and lower bounds of the SOC of energy storage; The installed capacity indicates the charge / discharge power. Indicates the number of periods in a savings cycle.

[0118] In equation (17), This indicates the initial SOC state of the energy storage. This indicates the final state of energy storage, thus ensuring consistency between the initial and final states of energy storage and guaranteeing the sustainable cyclical operation of the system.

[0119] 5) Transmission constraints:

[0120] (18)

[0121] In the formula, Represents a node exist The load demand at any given time.

[0122] Step S3, the method for measuring the load supply and demand imbalance risk based on GWCVaR, is as follows:

[0123] S31. Derivation of the GWCVaR risk measurement model based on tail Gini metric:

[0124] Uncertainty in power systems leads to varying degrees of load shedding risk. Among existing methods, CVaR (Variable Rate of Loss) is a commonly used risk metric to quantify the expected value of potential losses exceeding the VaR value. Using CVaR, decision-makers can intuitively understand the potential risks their decisions face by observing the magnitude of default losses. However, CVaR only focuses on risk at a single confidence level, potentially neglecting losses in other areas. Therefore, this paper proposes a weighted CVaR method based on Gini mean difference (GWCVaR), enabling participants to manage power system load shedding risk at multiple confidence levels.

[0125] 1) Traditional CVaR model:

[0126] Assume there are decision variables Then its VaR value represents the value at a given confidence level. The maximum potential loss value that the scheduling strategy may cause. CVaR is the weighted average of the expected loss exceeding VaR. The discretization calculation method for CVaR is as follows:

[0127] (19)

[0128] In the formula, Let i represent the probability of scenario i. Let i represent the decision variables for scenario i. Let i represent the loss function for scenario i. express , max means taking the larger of the two.

[0129] The calculation of CVaR can be achieved by solving the problem of minimizing CVaR, which is equivalent to the following linear programming problem:

[0130] (20)

[0131] In the formula, As an auxiliary variable, its value represents the portion of the loss that exceeds the VaR value. Let N represent the probability of scenario i, N represent the number of scenarios, min represent the minimization function, and subject to represent the constraints.

[0132] 2) GWCVaR model based on tail gini metric:

[0133] The Gini mean difference directly reflects the overall volatility using the absolute difference. Its discrete model can be transformed into a continuous integral, and by utilizing the symmetry of the absolute value, it can be converted into a univariate integral, yielding:

[0134] (twenty one)

[0135] in, express The difference in Gini mean, Representing decision variables Expected value; The second-order quantile function is the integral of the first-order quantile function; the first-order quantile function... Decision variables The inverse function of the cumulative distribution function (CDF); For integration variables;

[0136] The tail ginni metric is defined as the interval of the above formula reduced to (0, ...). ) and through Standardization yields:

[0137] (twenty two)

[0138] (twenty three)

[0139] In the formula, For confidence level, Indicates at confidence level The tail section of the ginni measurement, For integration variables;

[0140] By approximating the integral expression of the tail Gini metric using numerical integration, the integration interval of the tail Gini metric (0, ...) is given. Discretization partitioning We can obtain:

[0141] (twenty four)

[0142] In the formula, Indicates the j-th confidence level;

[0143] The above formula can be transformed into:

[0144] (25)

[0145] The expression for CVaR for the left-tailed risk problem is:

[0146] (26)

[0147] Combining (27), we can expand (26) to obtain:

[0148] (27)

[0149] Using the midpoint value approximation, assume that in each subinterval... Inside, If we approximate it to be a constant, then:

[0150] (28)

[0151] Substituting (28) into (27) and rearranging, we get:

[0152] (29)

[0153] Using the approximate difference concept, assume Then the above equation can be further approximated and simplified as follows:

[0154] (30)

[0155] Finally, GWCVaR can be approximated as:

[0156] (31)

[0157] in,

[0158] (32)

[0159] 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, The number of confidence levels defined above;

[0160] Similarly, for the right-tail risk problem using cost as an example, the tail risk area becomes... For interval Discretization The GWCVaR expression can be derived as follows:

[0161] (33)

[0162] (34)

[0163] S32. Constructing a risk-considered stochastic optimization objective function for power systems based on the GWCVaR model:

[0164] GWCVaR is introduced to measure the load shedding risk of microgrids. The load shedding risk calculated based on GWCVaR is expressed as follows:

[0165] (35)

[0166] (36)

[0167] In the formula, and The confidence level symbol above and Equivalent substitution in right-tail risk Indicates confidence level VaR value of the risk of shearing load.

[0168] The objective function (2) of the optimization problem is finally obtained as follows:

[0169] (37)

[0170] To demonstrate the advantages of the method of this invention, this embodiment conducts simulation tests under an electric-biogas coupled microgrid. The microgrid is scaled proportionally to the IEEE 24 system and includes one farm biogas power generation system, two wind farms, and two solar farms. The simulation parameters of the farm biogas power generation system are derived from the biomass power generation system of a state-owned farm in Jiangsu, China. The parameters of various equipment are configured as follows: gas generator installed capacity 13460kW, total photovoltaic installed capacity 2240kW, wind farm installed capacity 2240kW, battery energy storage system capacity 500kW / 1000kWh, charge / discharge efficiency 95%; biogas generator installed capacity 1500kW, electric heating boiler capacity 600kW, anaerobic digester volume 20000m³. 3 Initial total solids concentration: 25 kgVS / m³ 3 With an initial temperature of 25°C, the methane production potential is 0.42m. 3 / kg, microbial fermentation parameters are 0.015 / –0.129 / 0.802, material heat exchange efficiency is 50%; biogas storage tank capacity is 1000m³. 3 / 60000m 3 The gas filling and releasing efficiency is 92%, and the lower heating value of biogas is 6.6278 kWh / m³. 3 The biogas power generation efficiency is 35%. Figure 2 This is the per-unit wind power output curve used in microgrids. Figure 3 This is the per-unit value curve of photovoltaic output used in microgrids. Figure 4 This is the per-unit curve of power load demand used in the embodiments of the present invention.

[0171] This embodiment sets up three schemes for comparison:

[0172] C1: No load shedding risk control is implemented for microgrids; only economic efficiency is considered.

[0173] C2: The GWCVaR model proposed in this paper is introduced to measure and control the load shedding risk of microgrids;

[0174] C3: Introduce the traditional CVaR model to measure and control the load shedding risk of microgrids (at 95% confidence level).

[0175] After optimization calculations, the operating costs of each scheme, the load shedding risk values ​​at different confidence levels, and the tail Gini metric values ​​are obtained, as shown in the table below:

[0176]

[0177] Figure 5 The microgrid dispatch results for C1, Figure 6 The graph shows the average operating cost versus load shedding risk for C2 under different risk aversion coefficients. The comparison between C1 and C2 shows that although introducing GWCVaR increases the average operating cost by 3.3%, it significantly reduces load shedding risk. At different confidence levels, GWCVaR achieves an average reduction of 85.3% in load shedding risk, while CVaR only achieves an average reduction of 81.8% under the same conditions. Therefore, despite a slight increase in cost, GWCVaR can better control different levels of load shedding risk.

[0178] To fairly compare the performance of CVaR and GWCVaR in risk measurement, the risk aversion coefficient was adjusted so that C2 and C3 were evaluated under the premise that their average costs were similar. 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.

[0179] Specifically, at a 95% confidence level, C3 reduced load shedding risk by only 3.6% compared to C2; while at other confidence levels, C4's risk increased by an average of 44.9%, and the tail Gini metric also increased by 28.6%. This is because GWCVaR can achieve more comprehensive coverage of distributed tail risks, optimize risk performance at multiple confidence levels, and effectively reduce tail GMD. CVaR, on the other hand, only focuses on risk at a specific confidence level, and its singularity and subjectivity limit the effectiveness of risk control to some extent. Therefore, in microgrids, compared to CVaR, GWCVaR provides a more scientific and comprehensive tail risk control method.

[0180] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. A method for measuring the risk of power system supply-demand imbalance, characterized in that, Includes the following steps: S1. Based on historical power output data of wind power and photovoltaic power, the edge probability density functions of wind power and photovoltaic power are constructed by kernel density estimation method, and the Copula joint distribution model is established by combining the fitted Copula parameters. A large number of wind and solar power joint output scenarios are generated by Monte Carlo sampling and edge inverse transformation. S2. The K-medoids clustering algorithm is used to cluster the wind and solar power combined output scenarios to obtain representative typical power output scenarios and their occurrence probabilities, and based on this, a stochastic optimization model of the power system considering the uncertainty of wind and solar power is constructed. S3. In the optimization model constructed in S2, the tail Gini metric method is introduced to measure the risk difference of the tail of the gain or loss distribution under different confidence levels. S4. Construct a weighted conditional value at risk (GWCVaR) function based on multiple CVaR confidence levels, organically combining the tail Gini metric with CVaR at multiple confidence levels to form a comprehensive risk assessment indicator under multiple confidence levels; the construction of the GWCVaR function specifically includes the following steps: For continuous tail Gini measurement, there exists the following expression: ； ； In the formula, For confidence level, Indicates at confidence level The tail section of the ginni measurement, As decision variables, This represents the expected value of the loss distribution. The second-order quantile function representing the loss distribution; The first-order quantile function representing the loss distribution is the decision variable. The inverse function of the cumulative distribution function; For integration variables, It is also an integral variable; The confidence interval [0, α] of CVaR is divided into... Sub-intervals For each sub-interval, calculate its corresponding conditional value-at-risk (CVaR) value: ； In the formula, Indicates at confidence level Conditional Value at Risk (VaR); Indicates the j-th confidence level; The expression for the tail Gini metric is rewritten as: ； Accordingly, the CVaR values ​​are weighted and combined to form the GWCVaR function, the expression of which is: ； ； 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 for the division; S5. Introduce the GWCVaR function as a risk penalty term into the optimization objective function. Together with the expected operating cost of the system, it constitutes the optimization objective of the scheduling model, so as to simultaneously achieve cost minimization and risk control.

2. The method for measuring the risk of power system supply and demand imbalance according to claim 1, characterized in that, Based on historical power output data for wind and solar power, S1 constructs marginal probability density functions using kernel density estimation methods, specifically including the following steps: Using historical wind power output sample sets and photovoltaic power output sample sets as inputs, calculate their sample standard deviations respectively. ; The bandwidth for kernel density estimation is determined using an empirical formula: ； In the formula, This represents the bandwidth for kernel density estimation. For the sample size, The standard deviation is the sample standard deviation. Using Gaussian kernel function Calculate the marginal probability density: ； In the formula, To estimate the probability density function, The number of samples; For kernel function, Let be a random variable, representing the output value. This represents the output value of the i-th sample. Based on the above formula, substituting the random sampled data, we finally obtain... and The marginal probability density functions of wind power and photovoltaic power output are respectively input into the Copula joint distribution model.

3. The method for measuring the risk of power system supply-demand imbalance according to claim 2, characterized in that, The construction and sampling process of the Copula joint distribution model in S1 includes: Using the Frank-Copula model, its joint distribution function is as follows: ； 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 joint distribution function after sampling. 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.

4. The method for measuring the risk of power system supply-demand imbalance according to claim 1, characterized in that, In S2, the K-medoids clustering algorithm is used to cluster the combined wind and solar power output scenarios to obtain representative typical power output scenarios. The specific steps include: 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 The scene and cluster center at time respectively The output value; Update centroids: For each cluster, select a new cluster center from the samples within the cluster that minimizes the total distance from all samples in that cluster to the new centroid; the intra-cluster distance is calculated as follows: ； In the formula, Cluster All points within the current center The total distance; For clusters Any point in; For clusters Each point in Calculate the total distance for each point to become a cluster center, and select the smallest distance as the updated cluster center. The calculation formula is as follows: ； In the formula, Cluster The new center point and For clusters The scene points in the middle, among which It is a cluster Candidate center points in It is a cluster Any scene point in the; Iterative optimization: Repeat the sample assignment and cluster center update operations until the cluster centers no longer change significantly and the clustering process converges; the optimization objective of the K-medoids algorithm is to minimize the sum of distances within all clusters. ； In the formula, J represents the total distance sum of all clusters. Indicates the number of clusters.

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