Kriging-based new energy AC / DC system uncertainty quantitative analysis method and system

Abstract

The invention discloses a Kriging-based new energy AC / DC system uncertainty quantitative analysis method and system, and the method comprises the steps: constructing an uncertainty model according to the probability distribution obeyed by a source load connected to an AC / DC coupling system and the characteristic parameters of the source load, describing the correlation between different types of source loads through Gaussian Copula, and carrying out the calculation of the uncertainty of the source load; the method comprises the following steps: sampling after forming a correlation matrix, performing load flow calculation on each group of samples by adopting an improved sequential AC / DC load flow algorithm considering the loss of a dynamic converter, training a Kriging agent model by taking the samples as input and a load flow calculation result as output, and finally performing prediction by using the trained model. Compared with a traditional method, the method is higher in calculation efficiency, and the accurate quantitative analysis result is obtained. The rapid and accurate analysis method provided by the invention is used for improving the uncertainty quantification precision and efficiency of the AC / DC hybrid system containing the high-proportion new energy, and provides theoretical support for uncertainty analysis of the AC / DC coupling power system containing the high-proportion new energy.

Description

Technical Field

[0001] The present invention belongs to the technical field of uncertainty analysis of new energy systems and AC-DC coupling systems, and mainly relates to a method and system for uncertainty quantification analysis of new energy AC-DC systems based on Kriging. Background Technique

[0002] As an important form of modern power grids, the AC-DC hybrid system realizes the wide-area consumption of renewable energy and cross-regional power transmission through the coordination of multi-voltage-level networks, significantly improving the energy transmission efficiency and the penetration rate of clean energy. Related technical research has become a core topic in energy transformation.

[0003] However, the AC-DC hybrid system faces the technical challenge of multi-dimensional uncertainty coupling of sources, grids, and loads. The randomness of new energy unit output and the dynamic characteristics of power electronic devices are intertwined, resulting in continuous fluctuations in the system operation boundary, directly affecting the power distribution and voltage stability of the power grid. To address this problem, probabilistic power flow calculation has become an important tool for evaluating system risks. However, the multi-physical field loss mechanism brought about by the deep coupling of AC-DC networks and the complex correlation between a large number of random variables make it difficult for traditional analysis methods to balance modeling accuracy and calculation efficiency. Therefore, how to construct an uncertainty quantification framework with dynamic learning ability while ensuring the completeness of the mechanism has become a key direction to break through the technical bottleneck. Summary of the Invention

[0004] In view of the synergistic problem of multi-source uncertainty coupling and dynamic loss modeling in the existing AC-DC hybrid system, the present invention proposes a method and system for uncertainty quantification analysis of new energy AC-DC systems based on Kriging. First, an uncertainty model is constructed according to the probability distribution and characteristic parameters that the sources and loads to be connected to the AC-DC coupling system follow. The correlation between different types of sources and loads is described by Gaussian Copula, and after forming a correlation matrix, sampling is performed. An improved sequential AC-DC power flow algorithm considering dynamic converter loss is used to perform power flow calculations for each group of samples. Using the samples as inputs and the results of the power flow calculations as outputs, a Kriging surrogate model is trained. Finally, predictions are performed on the trained model to obtain... The present invention uses a fast and accurate uncertainty quantification analysis method to perform uncertainty quantification analysis on the AC-DC hybrid system with a high proportion of new energy, effectively improving the accuracy and calculation efficiency of system uncertainty quantification, and providing theoretical support for the uncertainty analysis of AC-DC coupled power systems with a high proportion of new energy.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method and system for uncertainty quantification analysis of new energy AC-DC systems based on Kriging, including the following steps:

[0006] S1. Build an uncertainty model: Build an uncertainty model according to the probability distribution and its characteristic parameters that the source loads to be connected to the AC-DC coupling system follow. The uncertain source loads include at least wind power, photovoltaic power, and traditional loads. The ways of probability distribution include but are not limited to Weibull distribution, Beta distribution, and Gaussian distribution;

[0007] S2. Build a Gaussian Copula correlation matrix: Use Gaussian Copula to describe the correlation between different types of source loads, form a correlation matrix, combine the marginal distribution function with the Gaussian Copula structure to build a joint distribution function, and then perform sampling to generate an input sample set;

[0008] S3. AC-DC power flow calculation: Based on an improved AC-DC power flow algorithm that takes into account the dynamic converter loss, perform power flow calculation on each group of samples generated in step S2. During the calculation process, use the observed data of a specific node or branch as the model output and transfer it to the next step;

[0009] S4. Build a Kriging surrogate model and perform model training: Use the samples as input and the results of the power flow calculation as output to train the Kriging surrogate model to obtain the optimal model parameters;

[0010] S5. Execute prediction: Use the model trained in step S4 to execute prediction and efficiently obtain a relatively accurate uncertainty quantification analysis result.

[0011] As an improvement of the present invention, the wind speed in the wind power system in step S1 follows the Weibull distribution, and its probability density function is:

[0012]

[0013] where v represents the wind speed, k represents the shape parameter in the skewness characteristic of the wind speed distribution, λ represents the scale parameter of the regional average wind speed level, and f is the probability density function;

[0014] The photovoltaic probability distribution adopts the Beta distribution, and its probability density function is specifically:

[0015]

[0016] where the random variable x solar ∈(0,1) is the ratio of the actual light intensity to the local theoretical maximum light intensity, α and β are the shape parameters in the Beta distribution, which are used here to adjust the skewness of the light intensity distribution, and B is the Beta function, whose function is to normalize the probability density function of the Beta distribution to ensure that its integral is equal to 1 in the interval [0,1];

[0017] For the traditional loads in the system, they are usually set to follow the Gaussian distribution, and its probability density function is specifically:

[0018]

[0019] Among them, x corresponds to the actual power output value of the traditional load that follows a Gaussian random distribution. μ represents the mean of the data, and σ 2 represents the variance of the data.

[0020] As another improvement of the present invention, the correlation matrix R in the step S2 is an n×n matrix, specifically:

[0021]

[0022] Among them, when i≠j, the off-diagonal element R set is the pre-set correlation between different source loads, set as a number between 0 and 1 for testing; when i = j, it is the diagonal element of the correlation matrix, which is the autocorrelation between source loads and is always 1;

[0023] The joint distribution function is specifically:

[0024] H(x1,...,x n ) = C(F1(x1), F2(x2),..., F n (x n ))

[0025] Among them, F i is the marginal cumulative distribution function of the i-th variable, C is the Copula function, and X = [x1, x2......, x n is the input random variable of n uncertain models.

[0026] As another improvement of the present invention, the step S3 specifically includes the following steps:

[0027] S31. Construct a converter model and a dynamic loss model based on this model: The algebraic equation of the converter model is as follows:

[0028]

[0029] Among them, P s and Q s respectively represent the active power and reactive power on the AC side, P c and Q c represent the active and reactive power on the converter side, G c and B c are the real part and imaginary part of the converter admittance, δ s and δ c are the phase angles of the voltages on the AC side and the converter side respectively, U s is the voltage source on the AC side, Uc is the converter voltage, Z c is the impedance of the phase reactor;

[0030] The mathematical expression of the loss model of the converter is:

[0031]

[0032] where I c is the magnitude of the current, a is the no-load loss, and b and c are the loss coefficients linearly and quadratically related to the magnitude of the current respectively;

[0033] By constructing the power algebraic equations of the AC side and the converter and the dynamic loss model of the converter, on the one hand, a preliminary connection between the two is constructed for subsequent construction of the coupled power balance equation between the two; on the other hand, with the dynamic loss model, the algorithm can be closer to reality, and the iterative solution is more flexible, facilitating the convergence of subsequent iterative calculations;

[0034] S32. Define the AC side model of the system and combine it with the converter model to construct the power balance equation for the coupling of the converter and the AC side. The specific power balance equation is:

[0035]

[0036] where P i , Q i are the active and reactive powers of the i-th bus, U i , δ i are the voltage magnitude and phase angle of the i-th bus, G ij and B ij are the conductance and susceptance between each bus in the system, and m is the total number of buses in the system. After the power balance equation for the coupling of the converter and the AC side is fully constructed, the algorithm can calculate the power of the converter by inferring from the active power of the AC side through the traditional voltage-power relationship, or infer the power injection of the AC side from the power of the converter. After obtaining the power of the converter, it can be passed to the next stage for DC side calculation;

[0037] S33. In the DC network, construct the DC side model through the relationship between the admittance matrix and power. The specific DC side model is:

[0038] First, the DC side model mainly focuses on the admittance matrix Y dc of the DC system and expands as follows:

[0039]

[0040] The element Y dc of the admittance matrix Y ijDenotes the conductance between node i and node j. These admittance elements are related to the resistance or impedance of the transmission lines in the system, and the admittance Y of the line ij is composed of the series impedance Z of the line ij and its shunt capacitance;

[0041] Next, in a DC power grid, there is a clear equation relationship between current injection and voltage. Generally, an admittance matrix is used to describe the electrical characteristics of the DC power grid; if a DC power grid contains n buses, where the voltage U of each bus dc,i and current I dc,i are known, and since the current in the 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:

[0042]

[0043] where P dc,i is the power injection of node i, Y dc,ij is the admittance between node i and node j, U dc,i and U dc,j are the DC voltages of node i and node j respectively. This equation shows the relationship between the power of node i and the voltage difference of its adjacent nodes. The power injection of node i is calculated from the voltage differences between it and all other nodes through the network admittance;

[0044] Through this model, the current injection of each DC bus can be calculated; combined together, the current injections of all buses can also be expressed in vector form as:

[0045] I dc = Y dc U dc

[0046] So far, by separately constructing three subsystems: the AC network, the DC network, and the converter, and establishing the connections between them, through the slack bus, the loop of the next part of the slack iteration solution can be started;

[0047] S34. Using the slack iteration calculation method, in the AC-DC power flow calculation, decouple the AC and DC networks alternately, solve the subsystem equations respectively, and iteratively correct the converter station power and voltage:

[0048] First, initialize the AC network voltage and the DC network voltage and set the reference voltage of the DC slack node Subsequently, perform the AC network power flow calculation to solve the node power balance equation:

[0049] ΔS ac = Sinj -V ac ·(Y ac V ac ) * =0

[0050] Among them, Y ac is the admittance matrix of the AC network, and S inj is the nodal injection power vector; after solving the AC side, calculate the converter loss, and at the same time calculate the converter power. Take the converter power P c as the injection power and input it into the DC network to solve the DC network equation:

[0051]

[0052] If the power of the DC slack node does not converge, update its power value according to the relaxation factor:

[0053]

[0054] S35. Select the node data with large fluctuations as the observation data, set it as the output, and as a part of the training set, transfer it to the model training step for the training of the kriging surrogate model.

[0055] As another improvement of the present invention, step S4 specifically includes the following steps:

[0056] S41. Input the data set including uncertain source loads, use the observation data point data as the output, collect the input-output sample data, and determine the training data set:

[0057]

[0058] S42. According to the data characteristics obtained in step S41, select a suitable basic trend function as the basic reference for the global pattern between an input variable and a response variable, describe the overall trend of the data, and help extract the global behavior from the data more efficiently

[0059] μ(x) = β T f(x)

[0060] Among them, β represents the weighting parameter for the deterministic trend function;

[0061] S43. Select the type of kernel function that describes the spatial correlation. The kernel function includes but is not limited to linear kernel, exponential kernel, Gaussian kernel, and Matérn kernel;

[0062] S44. Select the hyperparameter estimation method and solve the optimal parameters by maximizing the joint probability density function of the observation data;

[0063] S45. Solve for the optimal relevant parameters based on the optimization algorithm according to the parameters selected in steps S42, S43, and S44;

[0064] S46. Determine the model settings according to the optimal parameters in step S45. After training the model, evaluate the model accuracy to obtain the optimal model parameters.

[0065] As another improvement of the present invention, in step S5, sampling is performed by the Monte Carlo method, the trained Kriging surrogate model is called, and based on the conditional Gaussian distribution and the sample set for prediction to obtain the predicted estimated value as the output.

[0066] To achieve the above object, the technical solution adopted by the present invention is also: an uncertainty quantification analysis system for a new energy AC-DC system based on Kriging, including a computer program, and when the computer program is executed by a processor, it implements the steps of any one of the above methods.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] (1) In the power flow algorithm part of the AC-DC system, the present invention constructs models for the AC network, DC network, and converter through multiple equations, enabling the algorithm to achieve fast iterative convergence in a shorter time; and the model considering the dynamic converter loss is different from the common static assumptions or assumptions of ignoring losses in traditional methods. This innovation makes the system modeling closer to the actual working conditions and improves the authenticity and accuracy of the calculation results.

[0069] (2) The Gaussian Copula function method used in the present invention has significant innovation and advantages in dealing with multi-source uncertainty quantification analysis. Traditional power system analysis methods usually assume that each uncertainty source load is independent, or simply describe their relationship through linear correlation. However, this assumption often cannot accurately reflect the complex dependence relationship between different loads or sources in the actual system. Gaussian Copula can effectively capture the dependence between different types of source loads through its flexible non-linear correlation description ability. This method can more accurately simulate the interaction of multi-source uncertainties in the system, further improving the accuracy and reliability of power system analysis.

[0070] (3) The present invention provides an effective quantification analysis method, which overcomes the need for a new quantification method in traditional power systems to analyze the volatility and uncertainty of new energy, and while ensuring the calculation efficiency, maintains a high analysis accuracy.

[0071] (4) The Kriging surrogate model used in the present invention is widely applied in the training and prediction of systems in reality. Its essence is a data-driven method. The Kriging model infers the potential behavior and response of the system by making full use of known sample data, making Kriging an ideal tool for solving uncertainty problems in complex power systems. The Kriging surrogate model may be deeply integrated with artificial intelligence technology in the future to further improve its prediction accuracy and generalization ability through machine learning algorithms. Description of the Drawings

[0072] Figure 1 is the flowchart of the steps of the method for quantifying the uncertainty of the new energy AC-DC system based on Kriging of the present invention;

[0073] Figure 2 is the comparison of the calculation result accuracy in Embodiment 1 of the present invention. Detailed Embodiments

[0074] The present invention will be further clarified below in conjunction with the drawings and detailed embodiments. It should be understood that the following detailed embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0075] Embodiment 1

[0076] A method for quantifying the uncertainty of a new energy AC-DC system based on Kriging, as Figure 1 shown, includes the following steps:

[0077] Step S1, construct an uncertainty model, and define the distributions and their characteristic parameters that the source loads such as wind power and photovoltaic need to be connected to the AC-DC coupling system.

[0078] S11, establish an uncertainty model for the wind power system:

[0079] The random output characteristics of the wind farm are modeled by double modeling of the wind speed probability distribution and the power conversion function. The wind speed follows the Weibull distribution, and its probability density function is:

[0080]

[0081] where v represents the wind speed, the shape parameter k reflects the skewness characteristics of the wind speed distribution, the scale parameter λ characterizes the regional average wind speed level, and f is the probability density function.

[0082] S12, establish an uncertainty model for the photovoltaic power plant system:

[0083] For the light intensity of the photovoltaic power station, the probability distribution is characterized by the beta function:

[0084]

[0085] Among them, the random variable x is defined solar ∈(0,1) is the ratio of the actual light intensity to the local theoretical maximum light intensity. α and β are the shape parameters in the beta distribution, which are used here to adjust the skewness of the light intensity distribution. B is the beta function, and its role is to normalize the probability density function of the beta distribution to ensure that its integral is equal to 1 over the interval [0,1].

[0086] For the traditional loads in the system, they are usually assumed to follow a Gaussian distribution, and its probability density function is specifically:

[0087]

[0088] Among them, x corresponds to the actual power output value of the traditional load following a Gaussian random distribution, μ represents the mean of the data, and σ 2 represents the variance of the data.

[0089] S13. Establish a correct power conversion model;

[0090] X = [x1, x2......, x n

[0091] Among them, X = [x1, x2......, x n indicates that the uncertainties in the system are composed of multiple uncertainty sources. For example, wind power, photovoltaic power, and traditional loads all have uncertainties and can be defined using different probability distributions such as the Weibull distribution, beta distribution, and Gaussian distribution.

[0092] The conversion model from wind speed to active power P Wind is described by a piecewise function:

[0093]

[0094] Among them, P r is the rated power. This model simultaneously considers the truncation effects of the cut-in wind speed v cut-in and the extreme wind speed v cut-off .

[0095] For the conversion of light intensity to power in a photovoltaic power plant, traditionally, it can be defined as a simple linear model such as:

[0096] P solar = P r-solar x

[0097] Among them, P r-solar is the rated power of the photovoltaic power plant.

[0098] ​Step S2: Describe the correlation between different types of source loads through Gaussian Copula, form a correlation matrix, and then perform sampling.

[0099] S21: Model multi-source uncertainty factors such as wind power, photovoltaic, and traditional load fluctuations as input random variables, and respectively specify their marginal distribution functions. Among them, the wind speed input adopts the Weibull distribution, the photovoltaic input adopts the beta distribution, and the traditional load adopts the Gaussian distribution, forming n input random variables;

[0100] X = [x1, x2......, x n

[0101] S22: According to Step S21, use Gaussian Copula to describe the correlation structure between the above-mentioned marginal distributions. Assume that the correlation matrix R is an n×n matrix, then:

[0102]

[0103] Among them, when i≠j, the off-diagonal element R set is the correlation between different source loads. We can set it as a number between 0 and 1 for testing. When i = j, that is, the diagonal element of the correlation matrix, it is the autocorrelation between source loads and is always 1;

[0104] The finally obtained correlation matrix is in the following form:

[0105]

[0106] S23: Combine the marginal distribution function and the Gaussian Copula structure according to Steps S21 and S22 to construct a joint distribution function:

[0107] H(x1,..., x n ) = C(F1(x1), F2(x2),..., F n (x n ))

[0108] Among them, where F i is the marginal cumulative distribution function of the i-th variable, and C is the Copula function.

[0109] The core of the Gaussian copula function lies in decoupling the marginal distribution and the correlation structure, allowing unified modeling of heterogeneous random variables such as wind power (Weibull distribution), photovoltaic (beta distribution), and traditional load (Gaussian distribution).

[0110] Use Gaussian Copula to construct a multi-dimensional dependence relationship, and its mathematical form is defined as:

[0111] C(u; R) = Φ​R (Φ -1 (u1), Φ -1 (u2),..., Φ -1 (u n ))

[0112] where Φ -1 (u) is the inverse function of the standard normal distribution, and Φ R represents the multivariate normal distribution function defined by the covariance matrix R.

[0113] S24. Based on the joint distribution function constructed in step S23, use the Latin hypercube sampling (LHS) method or other sampling methods to generate an input sample set from the joint distribution

[0114]

[0115] where N represents the total number of samples.

[0116] Step S3. Use an improved sequential AC-DC power flow algorithm considering dynamic converter losses to perform power flow calculations for each group of samples, and use the observed data of a certain node or branch as the model output and transfer it to the next step.

[0117] S31. Construct a converter model and a dynamic loss model based on this model:

[0118] The voltage source converter in the AC network is connected to the AC bus through a phase reactor and a transformer, and its equivalent model is a controlled voltage source in series with a complex impedance. In the modeling of the voltage source converter, the converter can be regarded as a composite impedance network composed of a controllable voltage source, a phase reactor, a transformer, and filters. The working principle of the converter depends on the control voltage source generating a specific voltage waveform to adjust the power injection into the AC grid. In a high-voltage DC transmission system, the modeling of the converter is very important because it not only involves power conversion but also is closely related to the power balance relationship between the AC side and the DC side. The power balance equation of the voltage source converter usually consists of the voltage source U s on the AC side, the converter voltage U c , the phase reactor impedance Z c , and the transformer, etc. The converter power flow model is described by the power exchange between the AC side voltage U s and the converter voltage U c , and the detailed algebraic equations are as follows:

[0119]

[0120] In the above equations, P s and Q s respectively represent the active power and reactive power on the AC side, P c and Qc represent the active and reactive power on the converter side. G c and B c are the real and imaginary parts of the converter admittance, and δ s and δ c are the phase angles of the voltages on the AC side and the converter side respectively.

[0121] The loss model of the converter is modeled based on its current magnitude I c The total losses of the converter can be decomposed into three parts: no-load losses, losses linearly related to the current magnitude, and losses proportional to the square of the current. The mathematical expression is:

[0122]

[0123] where a is the no-load loss, and b and c are the loss coefficients linearly and quadratically related to the current magnitude respectively. The calculation method of the converter current is as follows:

[0124]

[0125] S32. Define the AC side model of the system and combine it with the converter model to construct the power balance equation for the coupling of the converter and the AC side:

[0126] On the AC system side, at each bus i, the power balance equation can be shown as the following two equations:

[0127]

[0128] where P i , Q i are the active and reactive powers of the i-th bus, U i , δ i are the voltage magnitude and phase angle of the i-th bus, G ij and B ij are the conductance and susceptance between each bus in the system, and m is the total number of buses in the system.

[0129] During the coupling process between the AC side and the converter, the power injection of the converter station will affect the power flow of the AC network. To deal with this influence, the power calculation of the converter station is divided into active and reactive parts, and then different converter control modes need to be selected based on the previously known information and the calculation results. The common control modes include the PQ control mode and the PV control mode.

[0130] In the PQ control mode, the active and reactive powers of the converter station are regarded as fixed load injections. Therefore, their influence on the power flow equation can be adjusted through the power imbalance term. The specific equations are:

[0131] ΔP i (k) = P gen,i - (P load,i - P s,i ) - P i (U (k) , δ (k) )

[0132]

[0133] where ΔP i (k) represents the active power error of the i-th bus at the k-th iteration, P gen,i represents the active power output of the i-th bus, P load,i represents the load power of the i-th bus, P s,i represents the active power injected by the converter station into the i-th bus, P i (U (k) , δ (k) ) represents the calculation of active power based on the voltage and phase angle of the AC network at the k-th iteration. The reactive power equation is the same. For the converter station selected in the PV control mode, its reactive power is unknown. At this time, the node where the converter station is located will be regarded as a fixed voltage node and participate in the AC power flow calculation.

[0134] S33. Construct the model of the DC side through the relationship between the admittance matrix and power;

[0135] In the DC network, the admittance matrix is the core to describe the relationship between current and voltage of each node, and is often used to represent the electrical coupling relationship between each node in the DC system, so as to help analyze the power flow between nodes. In the multi-terminal DC system, the admittance matrix not only plays an important role in the calculation process, but also is the basis for power flow analysis, optimization and other evaluations.

[0136] The element Y dc of the admittance matrix Y ij represents 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. Usually, the admittance Y ij of the line is composed of the series impedance Z ij of the line and its shunt capacitance. For example, for a DC network with n nodes, the basic structure of the admittance matrix is:

[0137]

[0138] In the DC power grid, there is a clear equation relationship between current injection and voltage. Generally, the admittance matrix is used to describe the electrical characteristics of the DC power grid. If a DC power grid contains n buses, and the voltage U of each busdc,i and the current I dc,i is known. Since the current in a DC power grid is driven by the voltage difference between buses, the current injection relationship between buses can be described by the following equation:

[0139]

[0140] The DC nodal power balance equation is the core equation for calculating the power flow in a DC power grid. In a multi-terminal DC system, there is a close relationship between the power injection and voltage difference at each node. According to the characteristics of power transmission in a DC system, the power balance equation 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:

[0141]

[0142] where, P dc,i is the power injection of node i, Y dc,ij is the admittance between node i and node j, U dc,i and U dc,j are the DC voltages of node i and node j respectively. This equation shows the relationship between the power of node i and the voltage differences of its adjacent nodes. The power injection of node i is calculated from the voltage differences between it and all other nodes through the network admittance.

[0143] Through this model, the current injection of each DC bus can be calculated. Combining them together, the current injections of all buses can also be expressed in vector form as

[0144] I dc = Y dc U dc

[0145] In some special cases such as a bipolar DC network, the relationship between the power injection and voltage of a DC bus can also be expressed by the following equation:

[0146] P dc,i = 2U dc,i I dc,i

[0147] 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 power grid, an iterative method is needed to calculate the power injection of the DC slack bus. The power injection P slack of the DC slack bus is determined by the sum of the power injections of other buses, and the calculation formula is as follows:

[0148]

[0149] By combining the above DC side equations with the converter equations, the nonlinear equations can also be processed by, for example, the Newton method and solved iteratively.

[0150] S34. Using the relaxation iterative calculation method, in the AC and DC power flow calculation, by alternately decoupling the AC and DC networks, solving the subsystem equations separately and iteratively correcting the converter station power and voltage, gradually approaching global convergence;

[0151] The basic logic of iterative calculation is as follows: First, initialize the AC network voltage and DC network voltage And set the reference voltage of the DC relaxation node Then perform AC network power flow calculation to solve the node power balance equation:

[0152] ΔS ac =S inj -V ac ·(Y ac V ac ) * =0

[0153] Among them, Y ac is the admittance matrix of the AC network, S inj Inject power vector into the node. After completing the AC side solution, calculate the converter power by calculating the converter loss. c Input the DC network as the injected power and solve the DC network equation:

[0154]

[0155] If the DC relaxation node power has not converged, update its power value according to the relaxation factor:

[0156]

[0157] Among them, α∈(0,1] is the relaxation factor, and the alternating iteration is carried out until the AC residual and the DC residual both meet the convergence condition ∈<10 -6 , ultimately outputting the full network power flow solution. During the algorithmic process, the core logic of the iterative calculation of the relaxed nodes of the DC network lies in alternately solving the AC and DC networks and dynamically updating the relaxed node power to ultimately achieve global convergence.

[0158] S35. Select node data with large fluctuations or obvious changes as observation data, set it as output, and pass it to the next step to train part of the agent model, such as:

[0159] Y=[y1,y2......,y n ]

[0160] Among them, y is the observed data we selected.

[0161] Step S4: Using the samples as the input and the results of power flow calculation as the output, start training the Kriging surrogate model, and the performance of the trained model can be initially verified by methods such as cross-validation.

[0162] S41: Using the data set containing the uncertainty sources as the input and the set observed data point data as the output, collect the input-output sample data to determine the training data set:

[0163]

[0164] S42: According to the data characteristics obtained in step S41, initially select the form of the basic trend function (constant / linear / polynomial / custom)

[0165] μ(x) = β T f(x)

[0166] Among them, the trend term is used as the mean function of the Gaussian process and has a fundamental impact on the prediction ability of the model. β represents the weighting parameter for the deterministic trend function;

[0167] The mathematical form of the trend term needs to be selected according to prior knowledge or data characteristics. Its essence is to capture the global change law of the response function by introducing a deterministic component. The most basic trend form is the constant trend. Simple Kriging assumes that the trend is a known fixed constant, and its expression can be written as:

[0168] β T f(x) = c

[0169] Here, c is a pre-specified constant value, and the model does not estimate the trend coefficient. When prior information is lacking, it is more common to use Ordinary Kriging, which regards the trend as an unknown constant term:

[0170] β T f(x) = β0

[0171] This form estimates the value of β0 in a data-driven manner, which not only maintains the simplicity of the model but also can adapt to most scenarios without significant trend characteristics. For systems with obvious nonlinear characteristics, Universal Kriging needs to be used to construct a more complex trend term. This method uses a linear combination of polynomial basis functions:

[0172]

[0173] Among them, the basis function f(x) can be flexibly selected according to the characteristics of the problem. A typical configuration is to use a multivariate polynomial basis function. For example, for an M-dimensional input space, a P-degree polynomial trend can be expanded as:

[0174]

[0175] S43. Select the type of kernel function that describes spatial correlation:

[0176] The correlation function is a core component of the Kriging method, which quantifies the correlation between the response values of sample points at different positions in the input space. The construction of the correlation function needs to meet two necessary conditions: positive definiteness and symmetry. Commonly used kernel functions are linear kernel, exponential kernel, Gaussian kernel, and Matérn kernel.

[0177] Taking the Gaussian kernel as an example:

[0178]

[0179] S44. Select a hyperparameter estimation method, such as maximum likelihood estimation:

[0180] Maximum likelihood estimation is based on the probability characteristics of the Gaussian process and solves for the optimal parameters by maximizing the joint probability density function of the observed data. For an experimental design X with N design points, its likelihood function can be expressed as:

[0181]

[0182] Among them, σ 2 is the process variance, the system response Y is the output of a deterministic physical model such as a power flow equation, β represents the weighting parameter for the deterministic trend function, R is the correlation matrix between data points, and F is the function value of the trend part in the Kriging model, that is, the matrix composed of the values of the trend function f(x) at each experimental design point x. The cross-validation method uses a data resampling strategy to estimate the parameters by minimizing the prediction error.

[0183] S45. According to the parameters selected in steps S42, S43, and S44, select different optimization algorithms (such as genetic algorithm / L-BFGS) to combine and solve for the optimal correlation parameters:

[0184] The reason for choosing a mixed optimization strategy is that usually, challenges such as multi-dimensionality, non-convexity, and multi-extrema are faced. Using a global optimization algorithm for search, such as a genetic algorithm or a particle swarm optimization algorithm, can conduct extensive exploration in the parameter space. This mixed strategy not only avoids local extreme value traps but also ensures the convergence speed.

[0185] S46. Based on the determined model settings, train the model and evaluate the model accuracy through methods such as cross-validation.

[0186] Step S5: Conduct multiple samplings using traditional methods such as Monte Carlo, then use the trained model to perform predictions, and compare the predicted values with the actual values fitted by the traditional method to verify the accuracy of the model.

[0187] S51: Set the number of Monte Carlo samples, perform the Monte Carlo experiment, and approach to fit the characteristics of the real data.

[0188] The reason for choosing the Monte Carlo method is that the Monte Carlo simulation is a classic method for quantitative analysis of the uncertainty of power systems. Its core lies in mapping the probability space to the system response space through random sampling, so as to quantify the global impact of input uncertainty on the grid operation state, directly quantify the central tendency and fluctuation intensity of the system output, and the accuracy of the simulation results is relatively high.

[0189] S52: Call the trained kriging model, and perform predictions based on the conditional Gaussian distribution and the sample set to obtain the predicted estimated values as the output.

[0190] S53: Based on the predicted values and the data of the Monte Carlo experiment, plot the probability density function images and compare them to verify whether the prediction accuracy of the model is accurate and effective. At the same time, record the calculation time of both to compare the calculation efficiency.

[0191] Embodiment 2

[0192] A method for quantitative analysis of multi-source uncertainty of AC-DC systems with a high proportion of new energy based on the Kriging surrogate model, including the following steps:

[0193] S1: Construct an uncertainty model, and define the distributions and their characteristic parameters that the source loads such as wind power and photovoltaic power need to be connected to the AC-DC coupling system.

[0194] In this embodiment, the IEEE RTS1996 system is selected for the AC side network, and a total of 8 wind power access points are set. While correctly defining the wind power settings according to the model, the wind speed is set as a wind power cluster with a heterogeneous Weibull distribution to simulate the wind power characteristics in different geographical locations.

[0195] Similarly, in the part of the photovoltaic power plant settings, 8 photovoltaic power plant access points are also set and set as an asymmetric beta distribution to reflect the difference in the output curves of the light intensity in different regions. At the same time, 4 traditional loads are selected, which follow a Gaussian distribution, to simulate the randomness of the loads in the traditional system.

[0196] After establishing the power conversion model, define the uncertainty input source:

[0197] X = [x1, x2......, x n

[0198] where X = [x1, x2......, x n indicates that the uncertainty in the system consists of multiple uncertainty sources.

[0199] Step S2: Describe the correlation between different types of source loads through Gaussian Copula, form a correlation matrix, and then perform sampling.

[0200] S21: Model multi-source uncertainty factors such as wind power, photovoltaic, and traditional load fluctuations as input random variables, and respectively specify their marginal distribution functions. Among them, the wind speed input adopts the Weibull distribution, the photovoltaic input adopts the beta distribution, and the traditional load adopts the Gaussian distribution, forming n input random variables X = [x1, x2......, x n ;

[0201] S22: According to Step S21, use Gaussian Copula to describe the correlation structure between the above marginal distributions. 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;

[0202] S23: Combine the marginal distribution function and the Gaussian Copula structure according to Steps S21 and S22 to construct a joint distribution function:

[0203] H(x1,..., x 20 ) = C(F1(x1), F2(x2),..., F 20 (x 20 ))

[0204] S24: Based on the joint distribution function constructed in Step S23, this embodiment adopts the Latin Hypercube Sampling (LHS) method to extract a total of 200 groups of samples and generate an input sample set from the joint distribution

[0205]

[0206] Step S3: Use an improved sequential AC-DC power flow algorithm considering dynamic converter losses to perform power flow calculations for each group of samples, and use the observed data of a certain node as the model output and transfer it to the next step;

[0207] S31: Construct a converter model and a dynamic loss model based on this model

[0208]

[0209] In this embodiment, let a be 11.033x10 -3 ​, b and c are 3.464x10 -3 and 4.4x10 -3 .

[0210] S32. Define the AC-side model of the system, and combine it with the converter model to construct the power balance equation for the coupling of the converter and the AC side. In the coupling part of the AC side and the converter, it mainly focuses on four balance equations:

[0211]

[0212] S32. Construct the DC-side model through the relationship between the admittance matrix and power;

[0213] For the DC-side network, reactive power does not need to be considered. The conversion relationships among power, voltage amplitude, and current are all centered around the admittance matrix Y:

[0214]

[0215] S33. Use the relaxation iteration calculation method. In the AC-DC power flow calculation, decouple the AC and DC networks alternately, solve the subsystem equations respectively, and iteratively correct the converter power and voltage to gradually approach global convergence;

[0216] The main iteration strategy is centered around this equation:

[0217]

[0218] If problems such as slow convergence speed are encountered, the iteration factor α and the convergence tolerance ∈ need to be reasonably adjusted. In this embodiment, the convergence tolerance is set to the default value of 10 -6 .

[0219] S34. Select the node data with large fluctuations or obvious changes as the observed data, set it as the output, and transfer it to the next step for use in training a part of the surrogate model.

[0220] In this embodiment, the monitoring indicators are the power injections of branch numbers 220 and 223 of the IEEE RTS1996 system to evaluate the impact of multi-scale uncertainty propagation on the grid collaborative control, and the power injection of branch number 220 is used as a reference for comparison in subsequent comparative experiments.

[0221] Step S4. Use the samples as the input and the results of the power flow calculation as the output to start training the Kriging surrogate model, and the performance of the trained model can be preliminarily verified through methods such as cross-validation.

[0222] S41. Use the dataset containing uncertainty sources as the input and the set observed data point data as the output to collect the input-output sample data and determine the training dataset:

[0223]

[0224] S42. According to the data characteristics obtained in step S41, in this embodiment, an exponential function is selected as the trend function.

[0225] μ(x) = β T f(x)

[0226] S43. Select the kernel function type for describing spatial correlation. In this embodiment, the Matérn correlation kernel function is selected.

[0227] S44. The maximum likelihood estimation is selected as the hyperparameter estimation method.

[0228] S45. According to the parameters selected in steps S42, S43, and S44, a hybrid genetic algorithm is selected as the optimization algorithm to solve for the optimal parameters.

[0229] S46. Based on the determined model settings, train the model, and through cross-validation, the model accuracy is initially verified.

[0230] Step S5. Use the Monte Carlo method to sample multiple times, then use the trained model to perform predictions, and compare the predicted values with the actual values fitted by the Monte Carlo method to verify the accuracy of the model.

[0231] S51. In this embodiment, the number of Monte Carlo samples is set to 20,000, and the Monte Carlo experiment is performed to approximate and fit the real data characteristics.

[0232] S52. Call the trained kriging model, and based on the conditional Gaussian distribution and the sample set perform predictions to obtain the predicted estimated values as the output.

[0233] S53. Based on the predicted values and the data of the Monte Carlo experiment, plot the probability density function images of the injection into the 220th branch road and compare them to verify whether the prediction accuracy of the model is accurate and effective. At the same time, record the calculation times of both for comparing the calculation efficiency.

[0234] The AC-DC system with a high proportion of new energy used in this embodiment includes a total of 50 nodes, among which 7 nodes are coupled with DC lines, there are 20 new energy accesses in total, and the access ratio is 40%. According to the steps of the present invention, a multi-source uncertainty quantification analysis of the AC-DC system with a high proportion of new energy based on the Kriging surrogate model is carried out, and the accuracy comparison of the prediction calculation results is as Figure 2As shown. Usually, when the complete true situation of an unknown system is not known, the data characteristics fitted by the Monte Carlo method are assumed to be the true data characteristics based on its random process and the characteristics of a large number of samples. Starting from Figure 2 It can be seen from Figure 2 that the accuracy of the prediction calculation of the uncertainty quantification analysis method of the new energy AC-DC system based on Kriging proposed by the present invention is basically the same as the result of the Monte Carlo method, that is, the calculation accuracy is relatively accurate.

[0235] The comparison of the calculation time required for this analysis method and 20,000 Monte Carlo samplings is shown in Table 1.

[0236] Table 1 Calculation time under different models

[0237]

[0238]

[0239] It can be seen from the above table that when using the uncertainty quantification analysis method based on the Kriging surrogate model, if the model training time is not considered, the prediction calculation time is only 0.0046 seconds. Compared with Monte Carlo sampling, while maintaining the calculation accuracy, the calculation efficiency is higher.

[0240] Therefore, this method conducts efficient and accurate uncertainty quantification analysis on the AC-DC coupling system with a high proportion of new energy by extracting key samples, which is of great significance for improving the uncertainty analysis efficiency of large-scale systems. The method of the present invention breaks through the limitations of traditional quasi-static modeling by establishing a dynamic converter loss model; combines Gaussian Copula multivariate correlation modeling with Kriging surrogate technology, adopts an adaptive sampling strategy, reduces the computational complexity while ensuring the accuracy of power flow calculation, and improves the computational efficiency.

[0241] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can still be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A method for uncertainty quantification analysis of new energy AC-DC systems based on Kriging, characterized in that, It includes the following steps: S1. Construct an uncertainty model: Construct an uncertainty model according to the probability distribution and its characteristic parameters of the source loads to be connected to the AC-DC coupling system. The uncertainty source loads include at least wind power, photovoltaic power, and traditional loads. The ways of probability distribution include but are not limited to Weibull distribution, beta distribution, and Gaussian distribution; S2. Construct a Gaussian Copula correlation matrix: Use Gaussian Copula to describe the correlation between different types of source loads, form a correlation matrix, combine the marginal distribution function with the Gaussian Copula structure to construct a joint distribution function, and then perform sampling to generate an input sample set; S3. AC-DC power flow calculation: Based on an improved AC-DC power flow algorithm considering dynamic converter losses, perform power flow calculation on each group of samples generated in step S2. During the calculation process, use the observed data of a specific node or branch as the model output, transfer it to the model training stage, and use it as part of the training set; S4. Construct a Kriging surrogate model and perform model training: Use the samples as input and the results of power flow calculation as output to train the Kriging surrogate model to obtain the optimal model parameters; S5. Execute prediction: Use the model trained in step S4 to execute prediction to obtain the quantitative analysis results for the multi-source uncertainty system.

2. The uncertainty quantification analysis method for new energy AC-DC systems based on Kriging according to claim 1, characterized in that: In step S1, the wind speed in the wind power system follows a Weibull distribution, and its probability density function is: where, v represents the wind speed, k represents the shape parameter in the skewness characteristic of the 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 specifically: where x solar ∈(0, 1) is the ratio of the actual light intensity to the local theoretical maximum light intensity, α and β are shape parameters in the beta distribution, and B is the beta function; The traditional load follows a Gaussian distribution, and its probability density function is specifically: Among them, x corresponds to the actual power output value of the traditional load subject to Gaussian random distribution, μ represents the mean of the data, and σ 2 represents the variance of the data.

3. The uncertainty quantification analysis method for new energy AC / DC systems based on Kriging according to claim 2, characterized in that: The correlation matrix R in step S2 is an n×n matrix, specifically: Among them, when i≠j, the non-diagonal element R set is the correlation between different source loads, which is set as a number between 0 and 1 for testing; when i = j, it is the diagonal element of the correlation matrix, which is the autocorrelation between source loads and is always 1; The joint distribution function is specifically: H(x1,...,x n ) = C(F1(x1), F2(x2),..., F n (x n )) Among them, F i is the marginal cumulative distribution function of the i-th variable, C is the Copula function, and X = [x1, x2......, x n is the input random variable of n uncertain models.

4. The uncertainty quantification analysis method for the new energy AC-DC system based on Kriging according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31. Construct a converter model and a dynamic loss model based on this model: The algebraic equation of the converter model is as follows: Among them, P s and Q s respectively represent the active power and reactive power on the AC side. P c and Q c represent the active and reactive powers on the converter side. G c and B c are the real part and the imaginary part of the converter admittance. δ s and δ c are the phase angles of the voltages on the AC side and the converter side respectively. U s is the voltage source on the AC side. U c is the converter voltage. Z c is the impedance of the phase reactor; The mathematical expression of the loss model of the converter is: where I c is the magnitude of the current, a is the no-load loss, and b and c are the loss coefficients linearly and quadratically related to the magnitude of the current, respectively; S32. Define the AC side model of the system, and combine it with the converter model to construct a power balance equation for the coupling of the converter and the AC side. The power balance equation is specifically: Among them, P i , Q i are the active and reactive powers of the i-th bus, U i , δ i are the voltage magnitude and phase angle of the i-th bus, G ij and B ij are the conductance and susceptance between the buses in the system, and m is the total number of buses in the system; S33. In the DC network, construct the DC side model through the relationship between the admittance matrix and power; the DC side model is specifically: The model on the DC side mainly focuses on the admittance matrix Y of the DC system dc and expands as follows: Among them, the admittance matrix Y dc whose element Y ij represents the conductance between node i and node j; The voltage U of each busbar dc,i and the current I dc,i Specifically: Among them, Y dc,ij is the admittance between node i and node j, and U dc,i and U dc,j are the DC voltages of node i and node j respectively; Calculate the current injection of each DC bus. The vector representation of the current injection of the bus is specifically: I dc = Y dc U dc By separately constructing three subsystems of the AC network, DC network, and converter, and establishing the connection between them, start the loop of the next part of the relaxation iteration solution through the slack bus; S34. Use the relaxation iteration calculation method to alternately decouple the AC and DC networks in the AC-DC power flow calculation, solve the equations of the AC network, DC network, and converter respectively, and iteratively correct the DC side power of the converter station; Initialize the AC network voltage and the DC network voltage and set the reference voltage of the DC slack node Perform an AC network power flow calculation to solve the nodal power balance equation: ΔS ac = S inj - V ac ·(Y ac V ac ) * = 0 where Y ac is the admittance matrix of the AC network, and S inj is the nodal injection power vector; After completing the solution on the AC side, calculate the converter losses and at the same time calculate the converter power; use the converter power P c as the injection power to input into the DC network and solve the DC network equations: If the solution converges, output the calculation result; if the DC slack node power does not converge, update its power value according to the relaxation factor: S35. Select the node data with large fluctuations as the observed data, set it as the output, and pass it to step S4 as part of the training set for continued model training to train the kriging surrogate model.

5. The uncertainty quantification analysis method for the new energy AC-DC system based on Kriging according to claim 2, wherein: The specific steps of step S4 are as follows: S41. Input the data set including uncertain source loads, with the observed data point data as the output, collect the input-output sample data, and determine the training data set: S42. According to the data characteristics obtained in step S41, select the basic trend function as the basic reference for the global pattern between an input variable and the response variable to describe the overall trend of the data, so as to extract the global behavior from the data: μ(x) = β T f(x) Among them, β represents the weighting parameter for the deterministic trend function; S43. Select the kernel function type describing spatial correlation, and the kernel function includes but is not limited to linear kernel, exponential kernel, Gaussian kernel, Matérn kernel; S44. Select the hyperparameter estimation method, and solve the optimal parameters by maximizing the joint probability density function of the observed data; S45. According to the parameters selected in steps S42, S43, and S44, based on the optimization algorithm, solve the optimal correlation parameters; S46. According to the optimal parameters in step S45, determine the model settings. After training the model, evaluate the model accuracy to obtain the optimal model parameters.

6. The uncertainty quantification analysis method for the new energy AC / DC system based on Kriging according to claim 1, characterized in that: In the step S5, sampling is performed by the Monte Carlo method, the trained Kriging surrogate model is called, and based on the conditional Gaussian distribution and the sample set predictions are made to obtain the predicted estimated values as the output.

7. A Kriging-based uncertainty quantification analysis system for new energy AC-DC systems, including a computer program, characterized in that: When the computer program is executed by the processor, it implements the steps of any one of the above methods.

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