Calculation method and system for carbon flow uncertainty of alternating-current and direct-current hybrid power system

Abstract

The invention discloses a method and a system for calculating the carbon flow uncertainty of an AC / DC hybrid power system, and the method comprises the steps: building a corresponding probability distribution model for the new energy output and load uncertainty in the AC / DC hybrid power system, describing the correlation dependence relation between different uncertainty sources through employing Gaussian Copula, and calculating the carbon flow uncertainty of the AC / DC hybrid power system. Generating an uncertainty input sample set through correlation sampling; introducing the uncertainty sample into an AC-DC hybrid load flow calculation model, completing carbon flow calculation on the basis of load flow calculation convergence, and obtaining a carbon flow calculation result of each node; taking the uncertainty input sample and the corresponding carbon flow calculation result as training samples, and constructing a polynomial chaos expansion agent model for approximately representing a mapping relation between the uncertainty input and the carbon flow output; and based on a polynomial chaos expansion agent model, executing Sobol global sensitivity analysis by adopting an analytical calculation mode, and quantitatively evaluating the influence degree of each uncertainty source and interaction thereof on the carbon flow result uncertainty.

Description

Calculation Methods and Systems for Carbon Flow Uncertainty in AC / DC Hybrid Power Systems Technical Field

[0001] This invention belongs to the technical field of carbon flow analysis and uncertainty analysis in power systems, and mainly relates to a calculation method and system for carbon flow uncertainty in AC / DC hybrid power systems. Background Technology

[0002] Driven by the ongoing global energy transition and the "dual-carbon" strategic goals, building a new power system with new energy sources as the mainstay has become an important way to achieve a low-carbon energy structure and sustainable development of the power system. With the large-scale integration of renewable energy sources such as wind power and photovoltaics, AC / DC hybrid power systems, with their multi-voltage level coordinated operation and long-distance, large-capacity transmission capabilities, are playing an increasingly important role in improving the absorption of new energy sources, enhancing grid flexibility, and optimizing energy allocation, and have become an important development form of modern power systems.

[0003] Meanwhile, the increasing demand for low-carbon operation of power systems has led to a shift in carbon emission assessment from macro-statistics to more refined and node-based approaches. Carbon flow analysis methods, by characterizing the transmission paths and distribution characteristics of carbon emissions from the generation side within the power system, provide crucial technical support for load-side carbon responsibility allocation, low-carbon dispatching, and carbon market operation. However, in AC / DC hybrid power systems, complex power coupling relationships exist between AC networks, DC networks, and converter equipment. Factors such as converter losses and DC line losses further exacerbate the complexity of carbon flow distribution mechanisms, making traditional carbon flow analysis methods, which are primarily designed for AC systems, difficult to apply directly.

[0004] Furthermore, the random fluctuations in renewable energy output and the uncertainty of load changes result in significant stochastic characteristics in the power distribution and carbon flow of AC / DC hybrid power systems. Existing research typically employs methods such as Monte Carlo simulations to analyze system uncertainties. However, given the deep coupling and high correlation of multiple uncertainty sources in AC / DC systems, these methods often require large sample calculations, leading to low computational efficiency and failing to meet the demands for rapid assessment and online analysis in engineering applications. Simultaneously, traditional uncertainty analysis methods tend to focus on the statistical characteristics of results, making it difficult to further quantify the impact of different uncertainty sources and their interactions on carbon flow results, thus limiting their guiding value in system planning and operational decision-making.

[0005] Therefore, how to construct an analytical method that can efficiently characterize carbon flow uncertainty and quantitatively assess the impact of each uncertainty source on carbon flow results, based on a full consideration of the structural characteristics of AC / DC hybrid power systems and the carbon flow transfer mechanism, has become an urgent technical problem to be solved in the field of low-carbon operation and uncertainty analysis of AC / DC hybrid power systems. Summary of the Invention

[0006] This invention addresses the significant uncertainties in renewable energy output and load in existing AC / DC hybrid power systems, the complex carbon flow transfer mechanism, and the difficulty in quantifying the impact of different uncertainty sources on carbon flow results. It provides a method and system for calculating carbon flow uncertainty in AC / DC hybrid power systems. For the uncertainties in renewable energy output and load in AC / DC hybrid systems, probability distribution models for wind power, photovoltaic power, and load are established separately. Based on Gaussian Copula, the correlation between different uncertainty sources is described, a correlation matrix is ​​constructed, and correlation sampling is performed. A probabilistic carbon flow model for AC / DC hybrid power systems considering converter power loss is established. For each sample, joint calculations of AC / DC power flow and carbon flow are performed to obtain the probability distribution characteristics of node carbon intensity. Using uncertain input samples as input and carbon flow calculation results as output, a surrogate model based on multinomial chaotic expansion is trained. Based on this, a rapid analytical calculation of the global sensitivity index is achieved, thereby significantly reducing the computational complexity compared to traditional Monte Carlo methods while ensuring statistical accuracy. This invention proposes an efficient and accurate carbon flow analysis method for AC / DC hybrid power systems, which can quantitatively characterize the impact of new energy sources and load uncertainties on carbon flow distribution, providing a theoretical basis and technical support for low-carbon operation and carbon responsibility allocation of AC / DC coupled power systems with a high proportion of new energy sources.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a calculation method for the uncertainty of carbon flow in AC / DC hybrid power systems, comprising the following steps:

[0008] S1. Construct an uncertainty input model: For uncertain source loads in AC / DC hybrid power systems, establish corresponding probability distribution models; the uncertainty model includes a probability distribution model and a power conversion model. Uncertain source loads include at least wind power, photovoltaic, or traditional loads. Based on the probability distribution function of the uncertain source loads, the power corresponding to each uncertain source load is obtained through the power conversion model; the form of the probability distribution includes, but is not limited to, Weibull distribution, beta distribution, and normal distribution, etc.

[0009] S2. Constructing the Gaussian Copula correlation matrix: The Gaussian Copula is used to describe the dependencies between different uncertainty sources. The correlation matrix of the uncertainty sources is constructed. The marginal distribution functions of each uncertainty source are combined with the Gaussian Copula structure to form a joint probability distribution function. Based on the joint distribution, sampling is performed to generate an uncertainty input sample set.

[0010] S3. Perform AC / DC hybrid probabilistic carbon flow calculation: Input each set of uncertainty samples generated in step S2 into the AC / DC hybrid power flow calculation model, complete the carbon flow calculation based on the power flow calculation results, obtain the carbon flow results of each node, and output the corresponding carbon flow calculation samples.

[0011] S4. Construct a polynomial chaotic expansion surrogate model and train the model: Using the uncertainty source load as input and the carbon flow calculation result obtained in step S3 as output, construct a polynomial chaotic expansion surrogate model, establish the mapping relationship between the uncertainty input and the carbon flow output, train the model, obtain the optimal model, and obtain the carbon flow calculation result.

[0012] As an improvement of the present invention, it further includes step S5: performing global sensitivity analysis on the carbon flow calculation results; based on the polynomial chaotic expansion surrogate model constructed in step S4, analytically calculating the Sobol global sensitivity index to quantify the influence of each uncertainty source and its interaction on the uncertainty of the carbon flow results; the global sensitivity index includes at least a first-order sensitivity index and a total effect sensitivity index.

[0013] As an improvement of the present invention, the AC / DC hybrid power flow calculation model in step S3 includes at least an AC grid model, a DC grid model, and a converter model. The coupling relationship between the three is established. By selecting a relaxed bus as the initial condition, a solution strategy based on relaxation iteration is adopted, and a joint AC / DC solution based on sequential iteration is executed. During the AC / DC power flow calculation, the AC network model, DC network model, and converter model are alternately decoupled for calculation. Overall convergence is achieved by iteratively updating the DC-side power of the converter station.

[0014] After the AC / DC power flow calculations converge, a carbon flow model for the AC / DC hybrid power system is constructed based on the calculation results. The mathematical expression for the nodal carbon intensity is as follows:

[0015]

[0016] in, Indicates the carbon intensity of node i; This represents the total power output of node i. and These represent the carbon emission coefficient and active power output of a conventional generator g, respectively. This represents the set of upstream nodes that provide power to node i; This represents the power flow from node j to node i; This represents the active power loss of converter c associated with node i; The equivalent carbon intensity of the converter;

[0017] Based on the carbon flow model, and by introducing uncertainties in renewable energy output and load, the deterministic carbon flow model of the AC / DC hybrid power system is extended to a probabilistic carbon flow model, thus obtaining the probabilistic distribution characteristics of nodal carbon intensity; its mathematical expression is as follows:

[0018]

[0019] in, Represents a random vector consisting of the carbon intensity of each node in the system; This represents the active power output vector of a conventional power generation unit; and Represent the vectors of random variables corresponding to new energy output and load power, respectively; functions This represents the mapping relationship between power distribution and carbon flow allocation in a hybrid AC / DC power system.

[0020] As another improvement of the present invention, the algebraic equations of the converter model in step S3 are as follows:

[0021]

[0022]

[0023]

[0024]

[0025] in, and These represent the active power and reactive power on the AC side, respectively. and This indicates the active and reactive power of the converter. and These are the real and imaginary parts of the converter admittance. and These are the phase angles of the AC side and the converter voltage, respectively. It is the voltage source on the AC side. It is the converter voltage;

[0026] In the AC power grid model, the power balance equation for the converter coupled to the AC side is specifically as follows:

[0027]

[0028]

[0029] in, and is Active and reactive power of the i-th bus and These are the voltage magnitude and phase angle of the i-th bus. and It represents the conductance and susceptance between the buses in the system, and l is the total number of buses in the system;

[0030] The DC grid model uses the admittance matrix Y of the DC system. dc Expand:

[0031]

[0032] Wherein, the admittance matrix Y dc element Y ij This represents the electrical conductance between node i and node j.

[0033] As another improvement of the present invention, in the polynomial chaotic expansion surrogate model in step S4, the functional relationship between the uncertain input variable and the nodal carbon intensity output is represented in the form of a polynomial chaotic expansion, and its mathematical expression is:

[0034]

[0035] in, Let be the probabilistic carbon intensity of node i. For the polynomial chaotic expansion coefficients, These are basis functions for multivariate orthogonal polynomials. Multiple indices are used to characterize the order of basis functions;

[0036] Polynomial chaotic expansion at the largest polynomial order Truncate at this point to obtain the contents A finite set of basis functions for each term, wherein Through a model training process based on sample data, the expansion coefficients are determined, and the optimal polynomial chaotic expansion surrogate model is obtained, which replaces the original AC / DC probabilistic carbon flow model.

[0037] To achieve the above objectives, the present invention also adopts the following technical solution: a calculation system for carbon flow uncertainty in AC / DC hybrid power systems, comprising a computer program, wherein the computer program, when executed by a processor, implements the steps of any of the methods described above.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] (1) In the power flow carbon flow algorithm for AC / DC systems, this invention solves the problem that traditional methods cannot effectively describe the coupling relationship of AC / DC systems by proposing a carbon flow calculation model for AC / DC hybrid power systems. This model improves the accuracy and reliability of carbon flow calculation by accurately characterizing the power transfer relationship between AC networks, DC networks, and converters. Compared with traditional carbon flow analysis models, the probabilistic carbon flow modeling method of this invention can quantify the uncertainty of new energy access and load fluctuations, accurately assess the impact of various uncertainty sources on carbon flow results, and effectively simulate multi-source uncertainty in power systems by incorporating the probability distribution and correlation of uncertainty inputs into the model, providing an accurate and comprehensive analysis tool for low-carbon dispatch and optimization decision-making.

[0040] (2) This invention innovatively employs the Gaussian Copula method to handle multi-source uncertainties in AC / DC hybrid power systems. Traditional methods typically assume that the uncertain sources are independent or describe their dependencies using linear correlations. However, such assumptions often fail to accurately reflect the complex dependencies between different source loads in real power systems. This invention describes the nonlinear correlations between uncertain sources using Gaussian Copula, which can effectively capture and model the interactions between source loads, improving the accuracy of uncertainty modeling and enhancing the reliability of system carbon flow analysis.

[0041] (3) This invention also employs a global sensitivity analysis method based on polynomial chaotic expansion, which solves the computational complexity problem of traditional sampling methods when dealing with large-scale uncertainties. By constructing a polynomial chaotic expansion surrogate model, sensitivity analysis can be performed efficiently, quantifying the impact of each uncertainty source on the carbon flow results, avoiding the problem of high computational load in traditional Monte Carlo simulation methods, while maintaining high computational accuracy. This method not only improves the efficiency of sensitivity analysis but also enhances the interpretability of the analysis results, providing strong support for low-carbon dispatch and optimization decision-making in power systems. Attached Figure Description

[0042] Figure 1 is a flowchart of the calculation method for carbon flow uncertainty in AC / DC hybrid power systems according to the present invention. Detailed Implementation

[0043] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0044] Example 1

[0045] The calculation method for carbon flow uncertainty in AC / DC hybrid power systems, as shown in Figure 1, includes the following steps:

[0046] Step S1: Construct an uncertainty input model: For the uncertain sources of load in the AC / DC hybrid power system, establish a corresponding probability distribution model to characterize the uncertainty characteristics of new energy output fluctuations and load changes. The uncertain sources include at least wind power output, photovoltaic power output and load power.

[0047] Define the distribution and characteristic parameters of the source loads that need to be connected to the AC / DC coupled system, such as wind power and photovoltaics.

[0048] S11. Establish an uncertainty model for the wind power system:

[0049] The stochastic power output characteristics of a wind farm are modeled using a dual approach, considering both the probability distribution of wind speed and the power conversion function. Wind speed is assumed to follow a Weibull distribution, with its probability density function expressed as:

[0050]

[0051] Where v represents wind speed, shape parameter k reflects the skewness of wind speed distribution, scale parameter λ characterizes the regional average wind speed level, and f is the probability density function.

[0052] S12. Establish an uncertainty model for the photovoltaic power plant system:

[0053] For the light intensity of a photovoltaic power station, the probability distribution is represented by a beta function:

[0054]

[0055] in, Rated light intensity, Representing the actual light intensity, α and β are the shape parameters in the beta distribution, respectively. It is a gamma function;

[0056] For traditional loads in a system, they are usually assumed to follow a Gaussian distribution, and their probability density function is as follows:

[0057] in, The actual power output value corresponding to a conventional load that follows a Gaussian random distribution, μ represents the mean of the data, and σ 2 Indicates the variance of the data;

[0058] S13. Establish a correct power conversion model;

[0059]

[0060] in, This indicates that the uncertainty in the system is composed of multiple uncertainty sources. For example, wind power, photovoltaics, and traditional loads all have uncertainties, which can be defined by different probability distributions such as the Weib distribution, beta distribution, and Gaussian distribution.

[0061] From wind speed to active power The transformation model is described using piecewise functions:

[0062]

[0063] in, This is the rated power. The model also considers the cut-in wind speed. with extreme wind speeds The cutoff effect.

[0064] The conversion of solar irradiance into power in photovoltaic power plants can traditionally be defined by a simple linear model, such as:

[0065]

[0066] in, This refers to the rated power of the photovoltaic power plant. This represents the actual incident light intensity. This is the rated light intensity; the conversion efficiency of the photovoltaic system is... It means, and It is the temperature coefficient, used to describe the effect of temperature on the performance of photovoltaic systems; This refers to the actual operating temperature of the photovoltaic cell. This is the battery temperature under standard test conditions.

[0067] The above formula shows that the output power of a photovoltaic system is affected not only by solar irradiance but also by the correction for temperature changes on the output power of the photovoltaic cells. Through this dual modeling, the formula can more accurately reflect the power output of a photovoltaic system under actual operating conditions.

[0068] Step S2: Construct a Gaussian Copula correlation matrix and generate a sample set: Use Gaussian Copula to describe the correlation and dependence between different uncertainty sources, construct the correlation matrix of uncertainty sources, combine the marginal distribution function of each uncertainty source with the Gaussian Copula structure to form a joint probability distribution function, and perform correlation sampling based on the joint distribution to generate an uncertainty input sample set.

[0069] The correlation between different types of source loads is described by Gaussian Copula, forming a correlation matrix, and then sampling is performed.

[0070] S21. Model the multi-source uncertainties such as wind power, photovoltaic and traditional load fluctuations as input random variables, and specify their marginal distribution functions respectively. Among them, wind speed input adopts Weibu distribution, photovoltaic input adopts beta distribution, and traditional load adopts Gaussian distribution, forming n input random variables;

[0071]

[0072] S22. According to step S21, the correlation structure between the above marginal distributions is described using Gaussian Copula. Let the correlation matrix R be an n x n matrix, then:

[0073]

[0074] Where, when i≠j, the off-diagonal elements in the correlation matrix Used to characterize the correlation between different source loads, the value range is set between 0 and 1 for numerical testing; when i=j, the diagonal elements of the corresponding matrix reflect the correlation characteristics of each source load itself, and their value is fixed at 1.

[0075] The final correlation matrix is ​​shown in the following form:

[0076]

[0077] S23. Based on steps S21 and S22, combine the marginal distribution function with the Gaussian Copula structure to construct the joint distribution function:

[0078]

[0079] in, Let represent the s-th uncertain input variable, s=1,...,M, where M represents the total number of uncertain input variables; each uncertain input variable Each corresponds to a marginal cumulative distribution function, i.e. , representing uncertain input variables The cumulative probability under its corresponding marginal distribution.

[0080] The core of the Gaussian copula function lies in decoupling the marginal distribution from the correlation structure, allowing for unified modeling of heterogeneous random variables such as wind power (Weib distribution), photovoltaics (Beta distribution), and traditional loads (Gaussian distribution).

[0081] The multidimensional dependency relationship is constructed using Gaussian Copula, and its mathematical form is defined as follows:

[0082]

[0083] in, It is the inverse function of the standard normal distribution. Let R represent the multivariate normal distribution function defined by the covariance matrix R.

[0084] S24. Based on the joint distribution function constructed in step S23, generate the input sample set from the joint distribution using the Latin hypercube sampling (LHS) method or other sampling methods.

[0085]

[0086] Where t represents the total number of samples.

[0087] Step S3: Perform AC / DC hybrid probabilistic carbon flow calculation: Take each set of uncertain input samples generated in step S2 as input, run the AC / DC hybrid power flow calculation model, complete the carbon flow calculation based on the convergence of the power flow calculation, obtain the carbon flow results of each node, and output the corresponding carbon flow calculation samples to the next step.

[0088] An improved sequential AC / DC power flow algorithm that takes into account dynamic converter losses is adopted to perform power flow calculations for each group of samples, and then the carbon intensity of each node is calculated based on the results of the power flow calculations.

[0089] S31. Construct a converter model and a dynamic loss model based on this model:

[0090] In AC networks, voltage source converters are typically connected to the AC bus via phase reactors and transformers, thus they can be equivalently represented as a controlled voltage source connected in series with a complex impedance. In converter modeling, the converter is often abstracted as an adjustable voltage source, forming a composite impedance network with phase reactors, transformers, and filters. Its basic operating mechanism involves controlling the voltage waveform output by this voltage source to regulate the power injected into the AC grid. For high-voltage direct current (HVDC) transmission systems, establishing an accurate converter model is crucial, as it not only performs energy conversion but also directly affects the power balance between the AC and DC sides. The algebraic equations of the converter model are shown below.

[0091]

[0092]

[0093]

[0094]

[0095] in, and These represent the active power and reactive power on the AC side, respectively. and This indicates the active and reactive power of the converter. and These are the real and imaginary parts of the converter admittance. and These are the phase angles of the AC side and the converter voltage, respectively. It is the voltage source on the AC side. It is the converter voltage;

[0096] The mathematical expression for the loss model of the converter is:

[0097]

[0098] in, The current is the converter current. Coefficient a represents the fixed loss generated by the converter under no-load conditions. Coefficients b and c are used to describe the characteristics of linear and quadratic changes in loss with current, respectively.

[0099] By establishing the power algebraic relationship between the AC side and the converter, as well as the converter dynamic loss model, the initial connection between the AC side and the converter is clarified, laying the foundation for the subsequent construction of their coupled power balance relationship. On the other hand, the introduction of the dynamic loss model can more realistically reflect the converter's operating characteristics, giving the algorithm better flexibility and convergence performance during the iterative solution process.

[0100] The converter current can be calculated as follows:

[0101]

[0102] S32. Define the AC side model of the system, and combine it with the converter model to construct the power balance equations for the coupling between the converter and the AC side:

[0103] On the AC system side, at each bus i, the power balance equations can be represented by the following two equations:

[0104]

[0105]

[0106] in, and is Active and reactive power of the i-th bus and These are the voltage magnitude and phase angle of the i-th bus. and It represents the conductance and susceptance between the buses in the system, and l is the total number of buses in the system;

[0107] During the coupling process between the AC side and the converter, the power injection from the converter station will affect the power flow of the AC network. To address this impact, the power calculation of the converter station is divided into active and reactive power components. Then, based on prior information and the calculation results, different converter control modes need to be selected. Common control modes include PQ control mode and PV control mode.

[0108] In PQ control mode, the active and reactive power of the converter station are treated as a fixed load injection; therefore, their impact on the power flow equations can be adjusted through the power imbalance term. The specific equations are:

[0109]

[0110]

[0111] in, This represents the active power error of the i-th bus in the k-th iteration. This represents the active power output of the i-th bus. This represents the load power of the i-th bus. This represents the active power injected into the i-th bus by the converter station. This indicates that the active power is calculated based on the voltage and phase angle of the AC network in the k-th iteration, and the reactive power equation is calculated similarly. However, for converter stations that select PV control mode, their reactive power is unknown. In this case, the node where the converter station is located will be regarded as a fixed voltage node and participate in the AC power flow calculation.

[0112] S33. Construct a DC-side model by using the relationship between the admittance matrix and the power;

[0113] In DC networks, the admittance matrix is ​​the core component describing the current-voltage relationships between nodes. It is commonly used to represent the electrical coupling relationships between nodes in a DC system, thereby aiding in the analysis of power flow between nodes. In multi-terminal DC systems, the admittance matrix not only plays a crucial role in the calculation process but also forms the basis for power flow analysis, optimization, and other evaluations.

[0114] Admittance matrix elements The admittance elements represent the conductance between node i and node j. These admittance elements are related to the resistance and impedance of the transmission lines in the system. That is, the admittance matrix is ​​related to the resistance of each transmission line, while the admittance of a typical line is... It is due to the series impedance of the line. It consists of the admittance matrix and its parallel capacitors. For example, for a DC network with n nodes, the basic structure of the admittance matrix is:

[0115]

[0116] In a DC power grid, there is a clear equation relating current injection and voltage, and the electrical characteristics of the DC power grid are typically described using the admittance matrix. If a DC power grid contains n buses, where the voltage of each bus... and current It is known that, and since the current in a DC power grid is driven by the voltage difference between the buses, the current injection relationship between the buses can be described by the following equation:

[0117]

[0118] The power balance equations at DC nodes are the core equations for calculating power flow in a DC power grid. In multi-terminal DC systems, there is a close relationship between power injection and voltage difference at each node. Based on the characteristics of power transmission in DC systems, the power balance equations for each node can be derived. For node i, its power balance can be expressed by the voltage difference between the node voltage and the voltages of other nodes:

[0119]

[0120] in, It is the power injection of node i. It is the admittance between node i and node j. and Let be the DC voltages of nodes i and j, respectively. This equation illustrates the relationship between the power of node i and the voltage difference between it and its neighboring nodes. The power injection of node i is calculated from the network admittance using the voltage difference between it and all other nodes.

[0121] This model calculates the current injection into each DC bus and represents the current injection amount of each DC bus in vector form.

[0122]

[0123] Under certain specific operating conditions, such as bipolar DC networks, the relationship between power injection and voltage at the DC bus can also be described by the following equation:

[0124]

[0125] Finally, the DC slack bus is the bus that controls the DC voltage, and its power injection is a variable to be solved. To ensure the power balance of the DC grid, an iterative method is needed to calculate the power injection of the DC slack bus. The power injection P of the DC slack bus... slack It is determined by the sum of power injections from other buses, and the calculation formula is as follows:

[0126]

[0127] By combining the equations for the DC side with those for the converter, this set of nonlinear equations can also be solved iteratively using methods such as the Newton-Laurel method.

[0128] S34. Using the relaxation iterative calculation method, in the AC / DC power flow calculation, the AC and DC networks are decoupled alternately, the subsystem equations are solved separately, and the power and voltage of the converter station are iteratively corrected to gradually approach global convergence.

[0129] The basic logic of iterative calculation is as follows: first, initialize the AC network voltage. With DC network voltage And set the reference voltage for the DC relaxation node. Then, power flow calculations were performed on the AC network to solve the node power balance equations:

[0130]

[0131] in, Let be the admittance matrix of the communication network. Inject power vectors into the nodes. After completing the AC side solution, calculate the converter losses and power simultaneously. Then, input the converter power... As an input DC network for injected power, solve the DC network equations:

[0132]

[0133] If the power at the DC relaxation node does not converge, update its power value according to the relaxation factor:

[0134]

[0135] Where α∈(0,1] is the relaxation factor, and the iteration is repeated alternately until both the AC residual and the DC residual satisfy the convergence condition ϵ<10. −6 The algorithm ultimately outputs the power flow solution for the entire network. The core logic of the iterative calculation of the relaxed nodes in the DC network lies in alternately solving the AC and DC networks and dynamically updating the power of the relaxed nodes to achieve global convergence.

[0136] S35. After the AC / DC power flow calculation converges, based on the power flow calculation results of the AC / DC system, a carbon flow model of the AC / DC hybrid power system is constructed to characterize the transmission and distribution relationship of carbon emissions from the generation side in each node, branch, and converter of the system. The mathematical expression for the nodal carbon intensity is as follows:

[0137]

[0138] in, Indicates the carbon intensity of node i; This represents the total power output of access node i, which includes the power output of traditional generators and the power output of new energy sources; and These represent the carbon emission coefficient and active power output of a conventional generator g, respectively. This represents the set of upstream nodes that provide power to node i; This represents the power flow from node j to node i, where the active power flow includes both AC branch power and DC power branch power. This represents the active power loss of converter c associated with node i; The equivalent carbon intensity of the converter is the carbon intensity of the AC side connection node of the converter.

[0139] S36. Based on the carbon flow model described in step S35, a carbon flow conservation equation for the AC / DC hybrid power system is further established to constrain the balance of carbon emissions in the system among the generation side, load side, line losses, and converter losses. Its mathematical expression is:

[0140]

[0141] in, D represents the carbon emissions of generator g; D represents the set of system load nodes. This represents the active load of load node i; and These represent the AC branch set and the DC branch set, respectively. and These represent the active power losses of the AC lines; C represents the set of converters in the system. Indicates the carbon strength of the circuit;

[0142] Based on this, by introducing uncertainties in new energy output and load, the deterministic carbon flow model of the AC / DC hybrid power system is extended to a probabilistic carbon flow model, the mathematical expression of which is as follows:

[0143]

[0144] in, Represents a random vector consisting of the carbon intensity of each node in the system; This represents the active power output vector of a conventional power generation unit; and Represent the vectors of random variables corresponding to new energy output and load power, respectively; functions This represents the mapping relationship between power distribution and carbon flow allocation in an AC / DC hybrid power system. Based on the probabilistic carbon flow model described in the previous steps, the carbon intensity of each node in the system is calculated to obtain the probabilistic distribution characteristics of node carbon intensity, providing basic data support for subsequent analysis.

[0145] Step S4: Based on the uncertain input samples generated in step S2 and the corresponding carbon flow calculation results obtained in step S3, a polynomial chaotic expansion surrogate model is constructed. By learning the mapping relationship between the uncertain input samples and the carbon flow output samples, the functional relationship between the uncertain input variables and the node carbon intensity output is approximately represented in polynomial chaotic expansion form. Its mathematical expression is:

[0146]

[0147] in, Let be the probabilistic carbon intensity of node i. For the polynomial chaotic expansion coefficients, These are basis functions for multivariate orthogonal polynomials. This is a multiple index used to characterize the order of basis functions. In practical applications, polynomial chaotic expansions are found at the maximal polynomial order. Truncate at that point to obtain the result containing A finite set of basis functions for each term, wherein ;

[0148] The expansion coefficients are determined through a training process based on sample data, enabling the polynomial chaotic expansion surrogate model to replace the original AC / DC probabilistic carbon flow model while maintaining the accuracy of carbon flow calculation, and to be used for subsequent uncertainty analysis calculations.

[0149] Step S5: Based on the polynomial chaotic expansion surrogate model constructed in step S4, the Sobol global sensitivity index is directly calculated by performing analytical operations on the polynomial chaotic expansion coefficients, so as to realize the quantitative analysis of the contribution of uncertain input variables to the uncertainty of carbon flow results.

[0150] S51. Based on the polynomial chaotic expansion proxy model constructed in step S4, obtain its polynomial chaotic expansion coefficients, and perform analytical calculations on the polynomial chaotic expansion coefficients to establish the analytical calculation basis for the Sobol global sensitivity index.

[0151] S52. Based on the analytical calculation results, directly calculate the Sobol global sensitivity index, wherein the Sobol global sensitivity index includes a first-order sensitivity index. and overall effect sensitivity index .

[0152] Among them, for the nodal carbon intensity random variable Its variance can be directly calculated from the polynomial chaotic expansion coefficients and further used to construct the Sobol sensitivity index. First, the influence of each uncertain input variable on the carbon flow result is calculated using the Sobol index, where the first-order Sobol index is expressed as:

[0153]

[0154] in, The total variance of the carbon flow results represents the uncertainty of the carbon flow results; Given uncertain input variables The conditional expected value reflects the expected value of the carbon flow outcome with respect to that variable, while keeping other input variables fixed. This formula characterizes the independent contribution of the s-th uncertain input variable to the uncertainty of the carbon flow outcome.

[0155] The total effect Sobol index is calculated using the following formula:

[0156]

[0157] in, This indicates the removal of the s-th uncertain input variable. Then, the variance contribution of other uncertain input variables to the carbon flow results.

[0158] The overall effect sensitivity index comprehensively considers the impact of the interaction between a single uncertain input variable and other uncertain input variables on the uncertainty of carbon flow results.

[0159] If we substitute the polynomial chaotic expansion (PCE) proxy model, the Sobol index calculation can be equivalent to:

[0160]

[0161] in, The coefficients of the polynomial chaotic expansion Let be the set of coefficients corresponding to the uncertainty source s.

[0162] S53. Based on the calculated Sobol global sensitivity index, quantitatively analyze the contribution of each uncertain input variable to the uncertainty of the carbon flow result; among them, the first-order sensitivity index is used to characterize the independent contribution of the s-th uncertain input variable to carbon intensity, and the total effect sensitivity index is used to characterize the comprehensive contribution of the s-th uncertain input variable and its interaction with other uncertain input variables to the variance of nodal carbon intensity.

[0163] In summary, the method of this invention constructs an uncertainty input model and a correlation description mechanism, combines an AC / DC hybrid power flow and carbon flow calculation model, and utilizes surrogate model technology to efficiently approximate the complex carbon flow calculation process. Furthermore, it achieves quantitative analysis of the impact of uncertainty sources on carbon flow results, thereby significantly improving computational efficiency while ensuring analytical accuracy. By introducing surrogate models and global sensitivity analysis methods, this invention effectively avoids the problem of high computational complexity in traditional Monte Carlo simulations for carbon flow analysis in AC / DC hybrid systems, achieving rapid and accurate analysis of carbon flow uncertainty. This provides reliable technical support for low-carbon operation analysis, carbon responsibility allocation, and planning decisions in AC / DC hybrid power systems.

[0164] Example 2

[0165] A method for calculating the uncertainty of carbon flow in AC / DC hybrid power systems includes the following steps:

[0166] Step S1: Construct an uncertainty input model: For uncertain sources of load in AC / DC hybrid power systems, establish a corresponding probability distribution model to characterize the characteristics of new energy access and load fluctuation.

[0167] In this embodiment, the AC-side network uses the case5_stagg system as the basic model, and the DC-side network is extended using the case5_stagg_HVDC model, forming an AC / DC hybrid power system structure with a single DC connection. In this system, a wind farm and a photovoltaic power station are connected to the two AC buses respectively to simulate the typical access method of new energy in AC / DC systems.

[0168] In terms of uncertainty modeling for new energy sources, wind power output is described by wind speed randomness, assuming that wind speed follows a Weibull distribution with parameters k=1.5 and λ=12, and the random output characteristics of the wind farm are characterized by the wind speed-power conversion relationship. The uncertainty of photovoltaic output is modeled by solar irradiance, assuming it follows a Beta distribution with parameters α=3.7 and β=1.8 to reflect the impact of changes in irradiance conditions on photovoltaic power output. Regarding load modeling, all conventional loads in the system are assumed to follow a Gaussian distribution to characterize the random fluctuations of conventional loads during operation.

[0169] In the small-system example, all the aforementioned uncertain inputs were set up according to the assumption of mutual independence and identical distribution, thus providing unified and standardized random input conditions for subsequent probabilistic carbon flow calculations and sensitivity analysis. Except for the renewable energy access nodes, all other bus loads in the system were treated as conventional loads, and their power fluctuations were uniformly assumed to follow a Gaussian distribution to characterize the random variation characteristics of conventional loads during operation.

[0170] Meanwhile, in order to complete the carbon flow calculation, different types of power generation units in the system are assigned corresponding carbon emission coefficients to characterize the carbon emission intensity generated per unit of power generation. The carbon emission coefficient of new energy units is taken as zero or approximately zero, while the carbon emission coefficient of conventional generator units is set according to their power generation type.

[0171] After establishing the power conversion model, define the uncertainty input sources:

[0172]

[0173] in, This indicates that the uncertainty in the system consists of multiple sources of uncertainty.

[0174] Step S2: Describe the correlation between different types of source loads using Gaussian Copula, form a correlation matrix, and then perform sampling.

[0175] Multi-source uncertainties, including wind power, solar power, and traditional load fluctuations, are modeled as input random variables, and their marginal distribution functions are specified. Wind speed input uses a Weibull distribution, solar power input uses a Beta distribution, and traditional load input uses a Gaussian distribution, forming n input random variables. ;

[0176] The correlation structure between the above edge distributions is described using Gaussian Copula. In this embodiment 1, the correlation between different source loads is set to 0, that is, different types of source loads are independent of each other.

[0177] Next, the marginal distribution function is combined with the Gaussian Copula structure to construct the joint distribution function:

[0178]

[0179] Finally, based on the constructed joint distribution function, this embodiment uses the Latin hypercube sampling (LHS) method to extract a total of 50 samples, generating the input sample set from the joint distribution.

[0180]

[0181] Step S3: Using an improved sequential AC / DC power flow algorithm that takes into account dynamic converter losses, power flow calculation is performed on each sample group, and the carbon flow of each branch node is calculated and passed to the next step.

[0182] S31. Construct a converter model and a dynamic loss model based on this model.

[0183]

[0184] In this embodiment, a is set to 11.033 x 10. -3 b and c are 3.464 x 10 -3 and 4.4x10 -3 .

[0185] S32. Define the AC side model of the system and, in conjunction with the converter model, construct the power balance equations for the coupling between the converter and the AC side. The coupling part between the AC side and the converter mainly revolves around four balance equations:

[0186]

[0187]

[0188]

[0189]

[0190] S33. Construct a DC-side model by using the relationship between the admittance matrix and the power;

[0191] The DC-side network does not need to consider reactive power; the conversion relationships between power, voltage amplitude, and current are all developed around the admittance matrix Y.

[0192]

[0193] S34. Using the relaxation iterative calculation method, in the AC / DC power flow calculation, the AC and DC networks are decoupled alternately, the subsystem equations are solved separately, and the power and voltage of the converter station are iteratively corrected to gradually approach global convergence.

[0194] The main iterative strategy revolves around this equation:

[0195]

[0196] If problems such as slow convergence are encountered, it is necessary to adjust the iteration factor α and the convergence tolerance appropriately. In this embodiment, the convergence tolerance is set to the default value of 10. −5 .

[0197] S35. After the AC / DC power flow calculation converges, based on the power flow calculation results of the AC / DC system, a carbon flow model of the AC / DC hybrid power system is constructed to characterize the transmission and distribution relationship of carbon emissions from the generation side in various nodes, branches, and converters of the system:

[0198]

[0199] Based on the carbon flow model described in step S35, a carbon flow conservation equation for the AC / DC hybrid power system is further established to constrain the balance of carbon emissions in the system among the generation side, load side, line losses, and converter losses. Its mathematical expression is:

[0200]

[0201] Based on this, by introducing uncertainties in new energy output and load, the deterministic carbon flow model of the AC / DC hybrid power system is extended to a probabilistic carbon flow model, the mathematical expression of which is as follows:

[0202]

[0203] Based on the probabilistic carbon flow model described in the above steps, the carbon intensity of each node in the system is calculated to obtain the probability distribution characteristics of the node carbon intensity, providing basic data support for subsequent analysis.

[0204] Step S4: Based on the uncertain input samples generated in step S2 and the corresponding carbon flow calculation results obtained in step S3, a polynomial chaotic expansion surrogate model is constructed. By learning the mapping relationship between the uncertain input samples and the carbon flow output samples, the functional relationship between the uncertain input variables and the node carbon intensity output is approximately represented in the form of a polynomial chaotic expansion.

[0205]

[0206] The polynomial chaos expansion method can be constructed using an orthogonal polynomial system that matches the distribution of the random variable. For example, Hermite polynomials can be used for uncertain inputs that follow a Gaussian distribution. The one-dimensional Hermite polynomial can be expressed as:

[0207]

[0208] Where z is a standard Gaussian random variable and n is the order of the polynomial. Hermite polynomials are orthogonal in Gaussian probability space and are suitable for describing uncertain inputs that follow a Gaussian distribution, such as traditional load fluctuations.

[0209] For uncertain input variables that follow a uniform distribution, the Legendre orthogonal polynomial can be used as the expansion basis function, which is defined as follows:

[0210]

[0211] Where z∈[-1,1], Legendre polynomials are often used for modeling standardized random variables in polynomial chaotic expansions, and can also be used as expansion basis functions after variable mapping in other distribution cases.

[0212] In this embodiment, to uniformly describe the mapping relationship between multi-source uncertain inputs and carbon flow outputs, a surrogate model is constructed using a polynomial chaotic expansion method based on orthogonal polynomials. By selecting orthogonal polynomial basis functions that match the statistical characteristics of the uncertain inputs and training the expansion coefficients with sample data, the variation characteristics of the carbon flow response in random space of the AC / DC hybrid power system can be effectively approximated, providing an analytical and efficient model foundation for subsequent global sensitivity analysis.

[0213] The expansion coefficients are determined through a training process based on sample data, enabling the polynomial chaotic expansion surrogate model to replace the original AC / DC probabilistic carbon flow model while maintaining the accuracy of carbon flow calculation, and to be used for subsequent uncertainty analysis calculations.

[0214] Step S5: Based on the polynomial chaotic expansion proxy model constructed in step S4, the Sobol global sensitivity index is directly calculated by performing analytical operations on the polynomial chaotic expansion coefficients, so as to realize the quantitative analysis of the contribution of uncertain input variables to the uncertainty of carbon flow results.

[0215] Meanwhile, the analysis results are compared with those obtained by Monte Carlo simulation and their computation time to verify the advantages of the proposed method in terms of analytical accuracy and computational efficiency.

[0216] In this embodiment, a Monte Carlo sample size of 5000 was set to perform a Monte Carlo experiment to approximate the characteristics of the real data. Simultaneously, the analysis results of the proposed method were compared with the sensitivity results and computation time obtained by the Monte Carlo simulation method to verify the advantages of the proposed method in terms of analytical accuracy and computational efficiency.

[0217] Table 1 compares the computation time required for this analytical method with that required for 5000 Monte Carlo samplings.

[0218] Table 1 Computation time under different models

[0219]

[0220] As shown in the table above, the computation time using the method proposed in this invention is only 9.85 seconds, which is more efficient than Monte Carlo sampling. A comparison of computational accuracy is shown in Table 2.

[0221] Table 2. Computational accuracy under different models

[0222]

[0223] As shown in Table 2 above, the Sobol sensitivity results obtained by the proposed method are very close to those obtained by the Monte Carlo method. Looking at the error data, the root mean square error (RMSE) between the two methods is 0.0121, and the mean absolute percentage error (MAPE) is 5.38%. This indicates that the proposed method achieves higher computational efficiency while maintaining high computational accuracy.

[0224] In summary, this invention constructs a probabilistic carbon flow analysis framework for AC / DC hybrid power systems, systematically modeling and quantitatively evaluating the carbon flow uncertainty caused by renewable energy output and load fluctuations. This enables efficient analysis of the influencing factors of system carbon flow uncertainty, which is of great significance for improving the scientific rigor of carbon emission analysis and low-carbon operation decisions in AC / DC hybrid power systems. Based on AC / DC power flow calculation results, this invention introduces probabilistic carbon flow modeling, overcoming the limitations of traditional carbon flow analysis methods in handling multi-source uncertainties. Simultaneously, by combining a polynomial chaotic expansion surrogate model and a global sensitivity analysis method, it avoids the computational burden of extensive random sampling while ensuring the accuracy of carbon flow analysis, effectively reducing computational complexity and significantly improving analysis efficiency. Therefore, this invention provides an efficient and feasible technical path for assessing carbon flow uncertainty and identifying key influencing factors in large-scale AC / DC hybrid power systems.

[0225] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A calculation method for the uncertainty of carbon flow in AC / DC hybrid power systems, characterized in that... The process includes the following steps: S1. Constructing an uncertainty input model: Based on the probability distribution characteristics of the source loads in the AC / DC coupled system, an uncertainty model is established. The uncertainty model includes a probability distribution model and a power conversion model. The uncertainty source loads include at least wind power, photovoltaic, or traditional loads. Based on the probability distribution function of the uncertainty source loads, the power corresponding to each uncertainty source load is obtained through the power conversion model. S2. Constructing a Gaussian Copula correlation matrix: The Gaussian Copula is used to describe the dependency relationship between different uncertainty sources. A correlation matrix of uncertainty sources is constructed. The marginal distribution functions of each uncertainty source are combined with the Gaussian Copula structure to form a joint probability distribution function. Based on the joint distribution, sampling is performed to generate an uncertainty input sample set. S3. Performing AC / DC hybrid probabilistic carbon flow calculation: Each set of uncertainty samples generated in step S2 is input into the AC / DC hybrid power flow calculation model. Based on the power flow calculation results, the carbon flow calculation is completed to obtain the carbon flow results of each node and output the corresponding carbon flow calculation samples. S4. Construct a polynomial chaotic expansion surrogate model and train the model: Using the uncertainty source load as input and the carbon flow calculation result obtained in step S3 as output, construct a polynomial chaotic expansion surrogate model, establish the mapping relationship between the uncertainty input and the carbon flow output, train the model, obtain the optimal model, and obtain the carbon flow calculation result.

2. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 1, characterized in that: It also includes step S5: performing a global sensitivity analysis on the carbon flow calculation results; based on the polynomial chaotic expansion surrogate model constructed in step S4, analytically calculating the Sobol global sensitivity index, and quantifying the degree of influence of each uncertainty source and its interaction on the uncertainty of the carbon flow results; The global sensitivity index includes at least a first-order sensitivity index and a total effect sensitivity index.

3. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 1, characterized in that: In step S1, the wind speed follows a Weibull distribution, and its probability density function is: Where v represents wind speed, k represents the shape parameter in the skewness characteristic of wind speed distribution, λ represents the scale parameter of the regional average wind speed level, and f is the probability density function; the photovoltaic probability distribution adopts a beta distribution, and its probability density function is as follows: ;in, Rated light intensity, α and β represent the actual illumination intensity, respectively, and are the shape parameters in the beta distribution. It is a gamma function; the traditional load follows a Gaussian distribution, and its probability density function is as follows: ;in, The actual power output value corresponding to a conventional load that follows a Gaussian random distribution, μ represents the mean of the data, and σ 2 Represents the variance of the data; wind speed to active power The transformation model is described using piecewise functions: ;in, Rated power, To cut into wind speed, For extreme wind speeds; the conversion of light intensity to power is a linear model, specifically: ;in, This refers to the rated power of the photovoltaic power plant. This represents the actual incident light intensity. This is the rated light intensity; For the conversion efficiency of photovoltaic systems, It is the temperature coefficient; This is the actual operating temperature of the photovoltaic cell. This is the battery temperature under standard test conditions.

4. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 1, characterized in that: The correlation matrix of the uncertainty sources in step S2 It is an n * n matrix, specifically: Where, when i≠j, the off-diagonal elements in the correlation matrix Used to characterize the correlation between different source loads, the value range is set between 0 and 1 for numerical testing; when i=j, the diagonal elements of the corresponding matrix reflect the correlation characteristics of each source load itself, and their value is fixed at 1; the joint probability distribution function is specifically: ;in, Let represent the s-th uncertain input variable, s=1,...,M, where M represents the total number of uncertain input variables; each uncertain input variable Each corresponds to a marginal cumulative distribution function, i.e. , representing uncertain input variables The cumulative probability under its corresponding marginal distribution.

5. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 1, characterized in that: The AC / DC hybrid power flow calculation model in step S3 includes at least an AC grid model, a DC grid model, and a converter model. The coupling relationship between these three is established. A relaxed bus is selected as the initial condition, and a solution strategy based on relaxation iteration is adopted. A joint AC / DC solution based on sequential iteration is executed. During the AC / DC power flow calculation, the AC network model, DC network model, and converter model are alternately decoupled for calculation. Overall convergence is achieved by iteratively updating the DC-side power of the converter station. After the AC / DC power flow calculation converges, a carbon flow model of the AC / DC hybrid power system is constructed based on the power flow calculation results of the AC / DC system. The mathematical expression for the nodal carbon intensity is: ;in, Indicates the carbon intensity of node i; This represents the total power output of node i. and These represent the carbon emission coefficient and active power output of a conventional generator g, respectively. This represents the set of upstream nodes that provide power to node i; This represents the power flow from node j to node i; This represents the active power loss of converter c associated with node i; The equivalent carbon intensity of the converter is given. Based on the carbon flow model, uncertainties in new energy output and load are introduced to extend the deterministic carbon flow model of the AC / DC hybrid power system into a probabilistic carbon flow model, obtaining the probabilistic distribution characteristics of the node carbon intensity. Its mathematical expression is as follows: ;in, Represents a random vector consisting of the carbon intensity of each node in the system; This represents the active power output vector of a conventional power generation unit; and Represent the vectors of random variables corresponding to new energy output and load power, respectively; functions This represents the mapping relationship between power distribution and carbon flow allocation in a hybrid AC / DC power system.

6. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 5, characterized in that: The algebraic equations of the converter model in step S3 are as follows: ; ; ; ;in, and These represent the active power and reactive power on the AC side, respectively. and This indicates the active and reactive power of the converter. and These are the real and imaginary parts of the converter admittance. and These are the phase angles of the AC side and the converter voltage, respectively. It is the voltage source on the AC side. This refers to the converter voltage; in the AC grid model, the power balance equation for the converter coupled to the AC side is specifically as follows: ; ;in, and is Active and reactive power of the i-th bus and These are the voltage magnitude and phase angle of the i-th bus. and These are the conductance and susceptance between the buses in the system, where l is the total number of buses in the system; the DC grid model uses the admittance matrix Y of the DC system. dc Expand: Wherein, the admittance matrix Y dc element Y ij This represents the electrical conductance between node i and node j.

7. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 1, characterized in that: In step S4, the polynomial chaotic expansion surrogate model represents the functional relationship between the uncertain input variables and the nodal carbon intensity output in the form of a polynomial chaotic expansion. Its mathematical expression is: ;in, Let be the probabilistic carbon intensity of node i. Here are the coefficients of the polynomial chaotic expansion. These are basis functions for multivariate orthogonal polynomials. Multiple indices characterizing the order of basis functions; polynomial chaotic expansion at the maximal polynomial order Truncate at this point to obtain the contents A finite set of basis functions for each term, wherein ； By training the model based on sample data, the expansion coefficients are determined, and the optimal polynomial chaotic expansion surrogate model is obtained, which replaces the original AC / DC probabilistic carbon flow model.

8. The calculation method for carbon flow uncertainty in AC / DC hybrid power systems as described in claim 2, characterized in that: The first-order sensitivity index in the global sensitivity index of step S5 is used to characterize the independent contribution of the s-th uncertain input variable to carbon intensity, specifically: ;in, This represents the total variance of the carbon flow results; Given uncertain input variables The conditional expected value; Let be the nodal carbon intensity random variable; the total effect sensitivity index is used to characterize the comprehensive contribution of the s-th uncertain input variable and its interaction with other uncertain input variables to the variance of nodal carbon intensity, specifically: ;in, This indicates the removal of the s-th uncertain input variable. Then, the variance contribution of other uncertain input variables to the carbon flow results.

9. A calculation system for the uncertainty of carbon flow in AC / DC hybrid power systems, including a computer program, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-8 above.

Images