Method for quantifying participation degree of source load based on alternating current and direct current power grid

Abstract

The invention discloses an AC / DC power grid source load participation degree quantification method, which relates to the field of AC / DC power grids, and comprises the following steps: constructing a probability distribution function of uncertain source load output based on historical data, and taking the uncertain source load output as an input and an AC / DC power grid probability static voltage stability margin as an output; establishing an AC / DC power grid probability static voltage stability margin calculation model; a Sobol'method based on an SPCE agent model is adopted to calculate global sensitivity indexes of the uncertainty source loads of the alternating current and direct current power grid to the probability static voltage stability margin, the importance sequence of the uncertainty source loads is obtained by comparing the global sensitivity indexes, and therefore the participation degree quantization of the source loads of the alternating current and direct current power grid is achieved. According to the method, the influence of the AC / DC power grid source load uncertainty on the power grid operation risk can be quickly and quantitatively evaluated, the participation degree of the uncertainty source load in the AC / DC power grid operation can be intuitively reflected, and response measures can be taken in time for the operation risk caused by the source load uncertainty.

Description

Technical Field

[0001] The present invention relates to the technical field of AC / DC power grid operation analysis, and in particular to a method for quantifying source-load participation degree of AC / DC power grids. Background Art

[0002] With the deterioration of the global climate and ecological environment, it has become a consensus among countries around the world to vigorously develop clean energy, actively promote the transformation of energy structure, and take the path of green and sustainable energy development. The power generation of renewable energy and its proportion continue to increase. Many new energy bases with a capacity of tens of millions of kilowatts have been built in North China, Northeast China, and Northwest China, with a cumulative installed capacity of more than 235 million kilowatts. Due to the volatility and randomness of renewable energy power generation, and the gradual increase in the scale of flexible loads in the power grid, the uncertainty of source and load in the power grid is becoming increasingly significant, which poses a challenge to the safe operation of the power grid. At the same time, with the development of large power grid operation technology, the cross-regional power transmission capacity of the power grid is gradually enhanced. Considering the coupling characteristics of AC and DC power grids, it is also of great significance to study the operation risks of AC and DC power grids. The uncertainty of source and load will increase the probability of failure of AC and DC power grids and increase the operation risks of AC and DC power grids.

[0003] At present, the impact of source-load uncertainty of AC and DC power grids on the operation risk of power grids is usually quantitatively evaluated based on various data analysis methods, including neural networks, principal component analysis, support vector machines, etc. Through the above methods, the measured information provided by the power grid measurement device can be analyzed from the perspective of data. However, the physical meaning of the analysis results obtained by the above methods is not clear enough and the interpretability is poor.

[0004] Therefore, there is a need for a method that can intuitively reflect the degree of participation of uncertain sources and loads in the operation of AC and DC power grids, and quickly quantify and evaluate the impact of source and load uncertainty of AC and DC power grids on the risk of power grid operation. For this reason, the inventor of this case has designed a method for quantifying the degree of participation of sources and loads in AC and DC power grids based on his own experience, which can efficiently calculate the global sensitivity index of uncertain sources and loads in AC and DC power grids to the probabilistic static voltage stability margin, and sort the importance of uncertain sources and loads by the index calculation results, so as to realize the quantification of the degree of participation of sources and loads in AC and DC power grids. Compared with the prior art, the beneficial effects of the present invention are: the global sensitivity index of uncertain sources and loads in AC and DC power grids to the probabilistic static voltage stability margin is calculated by using the Sobol' global sensitivity analysis method, which can intuitively reflect the degree of participation of uncertain sources and loads in the operation of AC and DC power grids, and quantitatively evaluate the impact of source and load uncertainty in AC and DC power grids on the risk of power grid operation; by introducing the SPCE proxy model and the minimum angle regression method, the calculation speed of the global sensitivity index is greatly improved, so that the quantification of the degree of participation of sources and loads in AC and DC power grids is more efficient, thereby helping to take timely countermeasures to the operational risks caused by source and load uncertainty. Summary of the invention

[0005] The purpose of the present invention is to provide a method for quantifying the degree of participation of sources and loads in AC and DC power grids, which can efficiently calculate the global sensitivity index of uncertain sources and loads in AC and DC power grids to the probabilistic static voltage stability margin, and sort the importance of uncertain sources and loads according to the index calculation results to achieve the quantification of the degree of participation of sources and loads in AC and DC power grids. This method can intuitively reflect the degree of participation of uncertain sources and loads in the operation of AC and DC power grids, and quickly quantify and evaluate the impact of source and load uncertainty in AC and DC power grids on the risk of power grid operation.

[0006] In order to achieve the above object, the present invention proposes a method for quantifying the participation degree of source and load in AC and DC power grids, comprising the following steps:

[0007] Step S1: Acquire basic data such as grid structure and line parameters of AC and DC power grids and historical data of uncertain source and load outputs such as renewable energy units and loads;

[0008] Step S2: constructing a probability distribution function of uncertain source load output based on historical data;

[0009] Step S3: establishing a calculation model for the probabilistic static voltage stability margin of an AC / DC power grid, the model taking the uncertain source and load output as input and the probabilistic static voltage stability margin of an AC / DC power grid as output;

[0010] Step S4: using the Sobol' method based on the SPCE proxy model to calculate the global sensitivity index of the probabilistic static voltage stability margin of the AC and DC power grids;

[0011] Step S5: The importance ranking of the uncertain sources and loads is obtained by comparing the sizes of the global sensitivity indicators, thereby quantifying the participation degree of the sources and loads in the AC and DC power grids.

[0012] In step S2, the probability distribution function construction method of the uncertain source and load output of the AC and DC power grid includes a parametric model method and a non-parametric model method. The parametric model method presupposes that the random variable obeys a specific probability distribution function through empirical rules, and uses the historical data of the random variable to derive the parameters of the probability distribution function. The non-parametric model method is based on the kernel density estimation method, and obtains the probability distribution function of the random variable through the linear superposition of multiple kernel functions. In the process of constructing the probability distribution function of the uncertain source and load output of the actual AC and DC power grid, it is necessary to take into account the actual experience and the distribution characteristics of the random variables, appropriately select the probability distribution function construction method, and improve the modeling accuracy as much as possible.

[0013] In step S3, the essence of the AC / DC grid probabilistic static voltage stability margin calculation model is to calculate the maximum value λ of the load growth factor λ when considering the uncertainty of the source load max The model is as follows:

[0014] min-λ

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] U dRi =U dIi +I di R dc

[0022]

[0023]

[0024] Q Gimin ≤Q Gi ≤Q Gimax

[0025] (Q Gi -Q Gimin )V ai =0

[0026] (Q Gi -Q Gimax )V bi =0

[0027] V Gi -(V Giref +V ai -V bi )=0

[0028] V ai ≥0,V bi ≥0

[0029] Where: P Li0 and Q Li0 is the initial active and reactive loads of node i; and is a constant, which is related to the growth mode of active and reactive power of node i load. and K pi is the number of pole pairs of the DC line connected to node i; U di ,I di and K is the DC side voltage, DC current and power factor angle of the DC converter station connected to node i; di and i X is the converter transformer ratio and converter control angle of the DC converter station connected to node i; ci is the commutation reactance of the DC converter station connected to node i; R dc is the DC line resistance; U dRi and U dIi is the DC voltage on the rectifier and inverter sides; Q Gi is the reactive power output of the i-th generator, Q Gimax and Q Gimin Q Gi The upper and lower bounds of V Gi and V Giref are the terminal voltage of the i-th generator and its given reference value respectively; V ai With V bi It is an auxiliary variable used to reflect the offset of the terminal voltage when the reactive output of the generator reaches the lower or upper limit.

[0030] In the above optimization model, the first four constraints are the power balance equations of the pure AC node and the AC node connected to the LCC DC converter station. The sign of the first constraint is negative for the rectifier station and positive for the inverter station. If node i is connected to a renewable energy generator, then P Gi =P REi , Q Gi =Q REi , P REi and Q REi is the uncertain active and reactive output of the renewable energy generator at node i. The 5th to 7th constraints are the operating characteristics of the LCC DC line. The 8th constraint is the equation describing the growth mode of the generator active output, is a constant, which is related to the growth mode of the output of the generator at node i. The ninth constraint indicates that the total increase of the load active power is distributed according to the proportion of the active power margin of the generators other than the balancing node generators to the total active power margin. The last five constraints are the complementary constraints of the generator terminal voltage and reactive power output.

[0031] In actual operation, the control mode of LCC DC transmission line is generally fixed DC current and fixed rectifier side DC voltage control mode. As the load increases, the AC node voltage on the inverter side of LCC DC decreases. In order to maintain the DC voltage unchanged, it is necessary to reduce the inverter control angle ξ Ii . Because Ii There is a minimum limit, and the control mode of the LCC DC transmission line needs to be changed to fixed inverter side minimum control angle control. Therefore, the constraints need to be added in the optimization model as follows:

[0032] (cosξ Iimin -cosξ Ii )V di =0

[0033] U dRi =U dRiref -V di

[0034] U dIi =U dIiref -V di

[0035] V di ≥0

[0036] Where: Iimin For Ii The minimum value of U dRiref and U dIiref For U dRi and U dIi The given reference value of V di is an auxiliary variable that reflects the offset of the DC voltage.

[0037] In step S4, the Sobol' method is a global sensitivity analysis method based on the analysis of variance (ANOVA) theory, which uses variance to characterize the uncertainty of system input and output variables, and attributes the variance of system output variables to each input variable and the interaction between input variables. Based on the Sobol decomposition theory, the AC and DC power grid probabilistic static voltage stability margin calculation model λ max =f(X) (X is the model input, i.e. the output of the uncertain source load) is decomposed as follows:

[0038]

[0039] If f(X) is square-integrable and the mean of each sub-term in the expansion is 0, then the sub-terms are mutually orthogonal and each sub-term can be uniquely determined:

[0040]

[0041] Where: X ～i Input random variables for the system except the i-th dimension; X ～(i,j) Input random variables for the system except for the i-th and j-th dimensions. Taking the variance on both sides of the equation, we get:

[0042]

[0043] in,

[0044]

[0045] Where: D i is the first-order partial variance, indicating a single input variable X i The contribution to the variance of the output variable; D i,j is the second-order partial variance, indicating that the input variable X i With X j The contribution of the interaction between the two factors to the variance of the output variable. By analogy, other orders of partial variance have similar meanings.

[0046] Input variable X i The total partial variance DT i represents the variable X i Single action and X i The degree of common contribution of interaction with other input variables to the variance of the system output variable:

[0047]

[0048] Where:

[0049] The standardized global sensitivity index calculation formula is as follows:

[0050]

[0051] Where: S i (1≤i≤M) represents the input variable X i The first-order sensitivity index (FSI) reflects the single input random variable X i Impact on the uncertainty (variance) of the output variable; ST i (1≤i≤M) is the input variable X i Total sensitivity index (TSI), which reflects the input variable X i Single action and X i The joint impact of interaction with other input variables on the uncertainty (variance) of the system output variable.

[0052] When calculating the Sobol' global sensitivity index in practice, the Monte Carlo simulation (MCS) method is usually used. It is only necessary to calculate the output variable results of the AC / DC power grid probabilistic static voltage stability margin corresponding to the input random variable samples, and the calculation process is simpler. The specific calculation formulas for the mean and variance of the output variables and the partial variance of the input variables based on MCS are as follows:

[0053]

[0054] Where: W is the input-output sample size used by the MCS method; X (s) Input random variable sample for the s-th sampling system; They are samples X (s) Samples of variables in the i-th dimension and other than the i-th dimension; Input random variable samples for another set of independent sampling systems The variable samples of the i-th dimension and other than the i-th dimension in the s-th sampling. Based on the above calculation results, the calculation formula of the Sobol' global sensitivity index of the probabilistic static voltage stability margin of the AC and DC power grid is as follows:

[0055]

[0056] In step S4, the SPCE proxy model is a polynomial chaos expansion proxy model that uses a minimum angle regression strategy to sparse key basis functions, and the system model λ max =f(X) is expressed as the sparse chaotic expansion of orthogonal polynomials as follows:

[0057]

[0058] Where: i=[i1,i2,…,i M ](i j ≥0,j=1,2,…,M) is the index vector; is a multivariate orthogonal polynomial basis function, represented by the tensor product of a family of univariate orthogonal polynomials; a i is the coefficient corresponding to the orthogonal polynomial basis function; A S is the set of index vectors corresponding to the key orthogonal polynomial basis functions.

[0059] The key orthogonal polynomial basis functions are selected based on the minimum angle regression strategy. The specific steps are as follows:

[0060] (1) Initialize the coefficients of all candidate basis functions: a0 = a1 ... = a P-1 =0 (P is the number of candidate basis functions), and set the initial fitting result μ0=0, the initial residual r0=λ max -μ0=λ max , the key basis function set A of the SPCE surrogate model S is an empty set;

[0061] (2) Select from the candidate basis function set the function that matches the current residual r = λ max -μ The basis function with the largest correlation j (·) as the key basis function, specifically: calculate the correlation function C(Ψ) = Ψ T r, we get a vector of length P, whose component C i Represents the correlation coefficient between the i-th basis function and the current residual r. Select the key basis function Ψ according to the calculation result of the correlation function j (·), where, for any i≠j, C j ≥C i . The basis function Ψ j(·) Included in the key basis function set A S In the process, based on the current key basis function and the input-output samples of the model, the SPCE proxy model is fitted and the current key basis function set A is calculated. S The corresponding LOO error;

[0062] (3) Calculate the direction of the angle bisector of the current key basis function and the forward step length of the minimum angle regression method in this direction. Update the coefficients of the key basis function according to the calculation results and obtain a new fitting result μ.

[0063] (4) Repeat steps 2 to 3 until the residual is small enough or all candidate basis functions are included in the key basis function set. Select the key basis function set A corresponding to the minimum LOO error of the SPCE proxy model. S , and use it as the basis function set used in the actual proxy model construction to ensure the optimal generalization ability and fitting accuracy of the constructed SPCE proxy model. By sparsely expanding the chaotic expansion of the polynomial, the number of basis function coefficients required for calculation can be reduced, overcoming the overfitting and "curse of dimensionality" problems that may occur in the construction of the proxy model.

[0064] The polynomial chaos expansion can be rewritten as follows:

[0065]

[0066] Where:

[0067] Compared with the Sobol decomposition, since the Sobol decomposition is unique, we can get:

[0068]

[0069] According to the definition of the global sensitivity index, combined with the above formula, a single or a group of input random variables X can be obtained: u The calculation formulas for FSI and TSI are as follows:

[0070]

[0071]

[0072] Where:

[0073] Once the SPCE proxy model is determined, the global sensitivity index of the system input random variables can be calculated by simply using the coefficients of the expansion. Since the construction of the SPCE proxy model only requires a small number of input-output variable samples of the AC / DC power grid probabilistic static voltage stability margin calculation model, its calculation time is significantly reduced compared to the MCS method, which can overcome the problem of low efficiency in calculating the global sensitivity index.

[0074] In step S4, the steps for calculating the global sensitivity index of the AC / DC power grid probabilistic static voltage stability margin are as follows:

[0075] Step S41: Based on the MCS method, a small amount of (set the sample size to J S ) Input-output samples of the probabilistic static voltage stability margin calculation model for AC and DC power grids are used to build the SPCE proxy model.

[0076] Step S42: Establish input variable samples (X j ,λ max,j )(j=1,2,…,J S ) and the standard normal distribution variable sample z j (j=1,2,…,J S ), the transformation relationship between the standard normal distribution variable z and the original input random variable (X,λ max )’s global sensitivity indexes correspond respectively;

[0077] Step S43: Select the basis function type of the SPCE proxy model as the Hermite orthogonal polynomial, and transform the standard normal distribution variable sample z j (j=1,2,…,J S ) is used as the input variable sample of the proxy model, and the output variable sample is λ max,j (j=1,2,…,J S ), construct the SPCE proxy model;

[0078] Step S44: Calculate the FSI and TSI of the system input random variables using the SPCE proxy model expression.

[0079] In step S5, the participation degree of the source and load of the AC and DC power grids is quantified according to the global sensitivity index, specifically:

[0080] Based on the calculation results of the global sensitivity index of each uncertainty source load output obtained in step S4, the uncertainty source loads are ranked in importance. The larger the value of the global sensitivity index, the more important the corresponding uncertainty source load is and the higher the degree of participation is.

[0081] The beneficial effects of the present invention are as follows: the global sensitivity index of uncertain sources and loads of AC and DC power grids to the probabilistic static voltage stability margin is calculated by using the Sobol' global sensitivity analysis method, which can intuitively reflect the degree of participation of uncertain sources and loads in the operation of AC and DC power grids, and quantitatively evaluate the impact of source and load uncertainty of AC and DC power grids on power grid operation risks; by introducing the SPCE proxy model and the minimum angle regression method, the calculation speed of the global sensitivity index is greatly improved, and the quantification of the degree of participation of sources and loads in AC and DC power grids is made more efficient, thereby facilitating timely taking countermeasures to the operation risks caused by source and load uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 The present invention is a flow chart of a method for quantifying the degree of participation of sources and loads in AC and DC power grids.

[0083] Figure 2 The present invention is: an AC / DC power grid topology diagram containing a renewable energy unit.

[0084] Figure 3 This is the cumulative probability function diagram of the probabilistic static voltage stability margin of AC and DC power grids under different scenarios of the present invention. DETAILED DESCRIPTION

[0085] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0086] Reference Figure 1 The flowchart of the method for quantifying the participation degree of source and load in AC and DC power grids is shown. The specific process of the method includes:

[0087] Step S1: Acquire basic data such as grid structure and line parameters of AC and DC power grids and historical data of uncertain source and load outputs such as renewable energy units and loads;

[0088] Step S2: constructing a probability distribution function of uncertain source load output based on historical data;

[0089] Preferably, in step S2, the method for constructing the probability distribution function of the uncertain source and load output of the AC / DC power grid includes a parametric model method and a non-parametric model method. The parametric model method presupposes that the random variable obeys a specific probability distribution function through empirical rules, and uses the historical data of the random variable to derive the parameters of the probability distribution function. The non-parametric model method is based on the kernel density estimation method, and obtains the probability distribution function of the random variable through the linear superposition of multiple kernel functions. In the process of constructing the probability distribution function of the uncertain source and load output of the actual AC / DC power grid, it is necessary to take into account both the actual experience and the distribution characteristics of the random variables, appropriately select the probability distribution function construction method, and improve the modeling accuracy as much as possible.

[0090] Step S3: establishing a calculation model for the probabilistic static voltage stability margin of an AC / DC power grid, the model taking the uncertain source and load output as input and the probabilistic static voltage stability margin of an AC / DC power grid as output;

[0091] Preferably, in step S3, the essence of the AC / DC power grid probabilistic static voltage stability margin calculation model is to calculate the maximum value λ of the load growth factor λ when the uncertainty of the source load is considered. max The model is as follows:

[0092] min-λ

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] U dRi =U dIi +I di R dc

[0100]

[0101]

[0102] Q Gimin ≤Q Gi ≤Q Gimax

[0103] (Q Gi -Q Gimin )V ai =0

[0104] (Q Gi -Q Gimax )V bi =0

[0105] V Gi -(V Giref +V ai -V bi )=0

[0106] V ai ≥0,V bi ≥0

[0107] Where: P Li0 and Q Li0 is the initial active and reactive loads of node i; and is a constant, which is related to the growth mode of active and reactive power of node i load. and K pi is the number of pole pairs of the DC line connected to node i; U di ,I di and K is the DC side voltage, DC current and power factor angle of the DC converter station connected to node i; di and i X is the converter transformer ratio and converter control angle of the DC converter station connected to node i; ci is the commutation reactance of the DC converter station connected to node i; R dc is the DC line resistance; U dRi and U dIi is the DC voltage on the rectifier and inverter sides; Q Gi is the reactive power output of the i-th generator, Q Gimax and Q Gimin Q Gi The upper and lower bounds of V Gi and V Giref are the terminal voltage of the i-th generator and its given reference value respectively; V ai With V bi It is an auxiliary variable used to reflect the offset of the terminal voltage when the reactive output of the generator reaches the lower or upper limit.

[0108] In the above optimization model, the first four constraints are the power balance equations of the pure AC node and the AC node connected to the LCC DC converter station. The sign of the first constraint is negative for the rectifier station and positive for the inverter station. If node i is connected to a renewable energy generator, then P Gi =P REi , Q Gi =Q REi , PREi and Q REi is the uncertain active and reactive output of the renewable energy generator at node i. The 5th to 7th constraints are the operating characteristics of the LCC DC line. The 8th constraint is the equation describing the growth mode of the generator active output, is a constant, which is related to the growth mode of the output of the generator at node i. The ninth constraint indicates that the total increase of the load active power is distributed according to the proportion of the active power margin of the generators other than the balancing node generators to the total active power margin. The last five constraints are the complementary constraints of the generator terminal voltage and reactive power output.

[0109] In actual operation, the control mode of LCC DC transmission line is generally fixed DC current and fixed rectifier side DC voltage control mode. As the load increases, the AC node voltage on the inverter side of LCC DC decreases. In order to maintain the DC voltage unchanged, it is necessary to reduce the inverter control angle ξ Ii . Because Ii There is a minimum limit, and the control mode of the LCC DC transmission line needs to be changed to fixed inverter side minimum control angle control. Therefore, the constraints need to be added in the optimization model as follows:

[0110] (cosξ Iimin -cosξ Ii )V di =0

[0111] U dRi =U dRiref -V di

[0112] U dIi =U dIiref -V di

[0113] V di ≥0

[0114] Where: Iimin For Ii The minimum value of U dRiref and U dIiref For U dRi and U dIi The given reference value of V di is an auxiliary variable that reflects the offset of the DC voltage.

[0115] Step S4: using the Sobol' method based on the SPCE proxy model to calculate the global sensitivity index of the probabilistic static voltage stability margin of the AC and DC power grids;

[0116] Preferably, in step S4, the Sobol' method is a global sensitivity analysis method based on the analysis of variance (ANOVA) theory, which uses variance to characterize the uncertainty of system input and output variables, and attributes the variance of system output variables to each input variable and the interaction between input variables. Based on the Sobol decomposition theory, the AC / DC power grid probabilistic static voltage stability margin calculation model λ max =f(X) (X is the model input, i.e. the output of the uncertain source load) is decomposed as follows:

[0117]

[0118] If f(X) is square-integrable and the mean of each sub-term in the expansion is 0, then the sub-terms are mutually orthogonal and each sub-term can be uniquely determined:

[0119]

[0120] Where: X ～i Input random variables for the system except the i-th dimension; X ～(i,j) Input random variables for the system except for the i-th and j-th dimensions. Taking the variance on both sides of the equation, we get:

[0121]

[0122] in,

[0123]

[0124] Where: D i is the first-order partial variance, indicating a single input variable X i The contribution to the variance of the output variable; D i,j is the second-order partial variance, indicating that the input variable X i With X j The contribution of the interaction between the two factors to the variance of the output variable. By analogy, other orders of partial variance have similar meanings.

[0125] Input variable X i The total partial variance DT i represents the variable X i Single action and X i The degree of common contribution of interaction with other input variables to the variance of the system output variable:

[0126]

[0127] Where:

[0128] The standardized global sensitivity index calculation formula is as follows:

[0129]

[0130] Where: S i (1≤i≤M) represents the input variable X i The first-order sensitivity index (FSI) reflects the single input random variable X i Impact on the uncertainty (variance) of the output variable; ST i (1≤i≤M) is the input variable X i Total sensitivity index (TSI), which reflects the input variable X i Single action and X i The joint impact of interaction with other input variables on the uncertainty (variance) of the system output variable.

[0131] When calculating the Sobol' global sensitivity index in practice, the Monte Carlo simulation (MCS) method is usually used. It is only necessary to calculate the output variable results of the AC / DC power grid probabilistic static voltage stability margin corresponding to the input random variable samples, and the calculation process is simpler. The specific calculation formulas for the mean and variance of the output variables and the partial variance of the input variables based on MCS are as follows:

[0132]

[0133] Where: W is the input-output sample size used by the MCS method; X (s) Input random variable sample for the s-th sampling system; They are samples X (s) Samples of variables in the i-th dimension and other than the i-th dimension; Input random variable samples for another set of independent sampling systems The variable samples of the i-th dimension and other than the i-th dimension in the s-th sampling. Based on the above calculation results, the calculation formula of the Sobol' global sensitivity index of the probabilistic static voltage stability margin of the AC and DC power grid is as follows:

[0134]

[0135] Preferably, in step S4, the SPCE proxy model is a polynomial chaos expansion proxy model that uses a minimum angle regression strategy to sparse key basis functions, and the system model λ max =f(X) is expressed as the sparse chaotic expansion of orthogonal polynomials as follows:

[0136]

[0137] Where: i=[i1,i2,…,i M ](i j ≥0,j=1,2,…,M) is the index vector; is a multivariate orthogonal polynomial basis function, represented by the tensor product of a family of univariate orthogonal polynomials; a i is the coefficient corresponding to the orthogonal polynomial basis function; A S is the set of index vectors corresponding to the key orthogonal polynomial basis functions.

[0138] The key orthogonal polynomial basis functions are selected based on the minimum angle regression strategy. The specific steps are as follows:

[0139] (1) Initialize the coefficients of all candidate basis functions: a0 = a1 ... = a P-1 =0 (P is the number of candidate basis functions), and set the initial fitting result μ0=0, the initial residual r0=λ max -μ0=λ max , the key basis function set A of the SPCE surrogate model S is an empty set;

[0140] (2) Select from the candidate basis function set the function that matches the current residual r = λ max -μ The basis function with the largest correlation j (·) as the key basis function, specifically: calculate the correlation function C(Ψ) = Ψ T r, we get a vector of length P, whose component C i Represents the correlation coefficient between the i-th basis function and the current residual r. Select the key basis function Ψ according to the calculation result of the correlation function j (·), where, for any i≠j, C j ≥C i . The basis function Ψ j (·) Included in the key basis function set A S In the process, based on the current key basis function and the input-output samples of the model, the SPCE proxy model is fitted and the current key basis function set A is calculated. S The corresponding LOO error;

[0141] (3) Calculate the direction of the angle bisector of the current key basis function and the forward step length of the minimum angle regression method in this direction. Update the coefficients of the key basis function according to the calculation results and obtain a new fitting result μ.

[0142] (4) Repeat steps 2 to 3 until the residual is small enough or all candidate basis functions are included in the key basis function set. Select the key basis function set A corresponding to the minimum LOO error of the SPCE proxy model. S , and use it as the basis function set used in the actual proxy model construction to ensure the optimal generalization ability and fitting accuracy of the constructed SPCE proxy model. By sparsely expanding the chaotic expansion of the polynomial, the number of basis function coefficients required for calculation can be reduced, overcoming the overfitting and "curse of dimensionality" problems that may occur in the construction of the proxy model.

[0143] The polynomial chaos expansion can be rewritten as follows:

[0144]

[0145] Where:

[0146] Compared with the Sobol decomposition, since the Sobol decomposition is unique, we can get:

[0147]

[0148] According to the definition of the global sensitivity index, combined with the above formula, a single or a group of input random variables X can be obtained: u The calculation formulas for FSI and TSI are as follows:

[0149]

[0150]

[0151] Where:

[0152] Once the SPCE proxy model is determined, the global sensitivity index of the system input random variables can be calculated by simply using the coefficients of the expansion. Since the construction of the SPCE proxy model only requires a small number of input-output variable samples of the AC / DC power grid probabilistic static voltage stability margin calculation model, its calculation time is significantly reduced compared to the MCS method, which can overcome the problem of low efficiency in calculating the global sensitivity index.

[0153] Preferably, in step S4, the steps of calculating the global sensitivity index of the probabilistic static voltage stability margin of the AC / DC power grid are as follows:

[0154] Step S41: Based on the MCS method, a small amount of (set the sample size to J S ) Input-output samples of the probabilistic static voltage stability margin calculation model for AC and DC power grids are used to build the SPCE proxy model.

[0155] Step S42: Establish input variable samples (X j ,λ max,j )(j=1,2,…,J S ) and the standard normal distribution variable sample z j (j=1,2,…,J S ), the transformation relationship between the standard normal distribution variable z and the original input random variable (X,λ max )’s global sensitivity indexes correspond respectively;

[0156] Step S43: Select the basis function type of the SPCE proxy model as the Hermite orthogonal polynomial, and transform the standard normal distribution variable sample z j (j=1,2,…,J S ) is used as the input variable sample of the proxy model, and the output variable sample is λ max,j (j=1,2,…,J S ), construct the SPCE proxy model;

[0157] Step S44: Calculate the FSI and TSI of the system input random variables using the SPCE proxy model expression.

[0158] Step S5: The importance ranking of the uncertain sources and loads is obtained by comparing the sizes of the global sensitivity indicators, thereby quantifying the participation degree of the sources and loads in the AC and DC power grids.

[0159] Preferably, in step S5, the quantification of the participation degree of the source and load in the AC and DC power grids is achieved according to the global sensitivity index, specifically:

[0160] Based on the calculation results of the global sensitivity index of each uncertainty source load output obtained in step S4, the uncertainty source loads are ranked in importance. The larger the value of the global sensitivity index, the more important the corresponding uncertainty source load is and the higher the degree of participation is.

[0161] In order to demonstrate the applicability of the present invention in practical applications, it is applied to the problem of quantifying the degree of source-load participation in an AC / DC power grid containing actual renewable energy sources:

[0162] The AC / DC grid in the example model consists of an IEEE 118-node AC grid (sending grid, including multiple wind farms) and an IEEE 39-node AC grid (receiving grid). The two AC grids are connected by a DC line (sending grid node 88-receiving grid node 9). The DC line connection method is a conventional LCC DC transmission line. The AC / DC grid topology is shown in Figure 1. Figure 2 As shown, the sending-end power grid has wind turbines at nodes 23, 33, 75, 84, and 88; the receiving-end power grid load is divided into four areas, covering nodes 1-9, nodes 10-18, nodes 19-24, and nodes 25-29, respectively, and it is assumed that the random fluctuations of the loads in the same area are the same.

[0163] The sampling scale of the MCS method is J = 10000. The system input random variables set are: the output power P of the five wind turbines in the sending grid R,i (i=23、33、75、84、88); random load fluctuations in the four areas of the receiving power gridξ D,i (i=1,2,3,4). The highest polynomial order of the SPCE proxy model is p=5, and the sample size J used in model constructionS =600. The probabilistic static voltage stability margin of the AC / DC power grid is selected as the output response, and the Sobol' global sensitivity index of each input random variable to the output response is calculated based on the formula. The specific values ​​of the calculated global sensitivity index are shown in Table 1.

[0164] Table 1 Calculation results of global sensitivity index of uncertain sources and loads to probabilistic static voltage stability margin

[0165]

[0166] As can be seen from Table 1, only a small number of system input random variables have large FSI numerical results, indicating that not all uncertain sources and loads have a significant impact on the probabilistic static voltage stability margin of the AC and DC power grids. At the same time, under the design parameter conditions of this example, the impact of the uncertain wind power generation in the sending-end power grid on the probabilistic static voltage stability margin can be ignored, and the impact of the load fluctuation uncertainty factors in the receiving-end power grid on the probabilistic static voltage stability margin is more significant than the impact of the wind power uncertainty factors in the sending-end power grid.

[0167] Taking the system input random variables with larger FSI numerical results as the uncertainty source load with a higher degree of participation, the key input variables with the highest degree of participation and the most significant impact on the probabilistic static voltage stability margin of the AC and DC power grids are the uncertainty loads in the receiving power grid areas 1, 3, and 4.

[0168] Furthermore, in order to verify the effectiveness of the proposed DC grid source-load participation quantification method in identifying key uncertain sources with a high degree of participation, the following three scenarios are set: case 1: considering the randomness of all nine input variables; case 2: considering only the randomness of three key input variables, and the remaining non-key input variables with a low degree of participation take fixed values; case 3: considering only the randomness of the remaining non-key input variables, and the three key input variables with a high degree of participation take fixed values. Based on the calculation of the probabilistic static voltage stability margin of AC and DC power grids, the cumulative probability distribution functions of the probabilistic static voltage stability margin under the three scenarios can be obtained respectively as follows: Figure 3 shown.

[0169] Depend on Figure 3It can be seen that when only the randomness of three key input variables with high participation is considered (case 2), the cumulative probability distribution function of the probabilistic static voltage stability margin is basically consistent with that when the randomness of all nine input variables is considered (case 1); on the contrary, when the three key input variables with high participation take fixed values ​​and only the randomness of the remaining input variables is considered (case 3), the cumulative probability distribution function of the probabilistic static voltage stability margin is very different from that of case 1. The example results show that the key input variables with high participation identified by the proposed DC grid source and load participation quantification method have a significant impact on the probabilistic static voltage stability margin, and their randomness is the main source of the randomness of the probabilistic static voltage stability margin. Furthermore, the proposed method is verified to be effective in quantifying the source and load participation and identifying key uncertain sources and loads with high participation.

[0170] The beneficial effects of the present invention are as follows: the global sensitivity index of uncertain sources and loads of AC and DC power grids to the probabilistic static voltage stability margin is calculated by using the Sobol' global sensitivity analysis method, which can intuitively reflect the degree of participation of uncertain sources and loads in the operation of AC and DC power grids, and quantitatively evaluate the impact of source and load uncertainty of AC and DC power grids on power grid operation risks; by introducing the SPCE proxy model and the minimum angle regression method, the calculation speed of the global sensitivity index is greatly improved, and the quantification of the degree of participation of sources and loads in AC and DC power grids is made more efficient, thereby facilitating timely taking countermeasures to the operation risks caused by source and load uncertainty.

[0171] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be considered exemplary and non-restrictive in all respects, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present invention.

[0172] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for quantifying the degree of participation of sources and loads in AC and DC power grids, characterized in that: The following steps are involved: Step S1: Acquire basic data of AC and DC power grids and historical data of uncertain source and load output; the basic data include grid structure and line parameters, and the historical data of uncertain source and load output include renewable energy units and loads; Step S2: constructing a probability distribution function of uncertain source load output based on historical data; Step S3: establishing a calculation model for the probabilistic static voltage stability margin of an AC / DC power grid, the model taking the uncertain source and load output as input and the probabilistic static voltage stability margin of an AC / DC power grid as output; Step S4: using the Sobol' method based on the SPCE proxy model to calculate the global sensitivity index of the probabilistic static voltage stability margin of the AC and DC power grids; Step S5: By comparing the size of the global sensitivity index, the importance ranking of the uncertain sources and loads is obtained, and the participation degree of the sources and loads in the AC and DC power grids is quantified.

2. The method for quantifying the participation degree of source and load in AC and DC power grids according to claim 1, characterized in that: In step S2, the method for constructing the probability distribution function of the uncertain source and load output of the AC / DC power grid includes a parametric model method and a non-parametric model method. The parametric model method pre-assumes that the random variable obeys a specific probability distribution function through empirical rules, and uses the historical data of the random variable to derive the parameters of the probability distribution function. The non-parametric model method is based on the kernel density estimation method and obtains the probability distribution function of the random variable through the linear superposition of multiple kernel functions.

3. The method for quantifying the participation degree of source and load in AC and DC power grids according to claim 1, characterized in that: In step S3, the essence of the AC / DC grid probabilistic static voltage stability margin calculation model is to calculate the maximum value λ of the load growth factor λ when the source load uncertainty is considered. max , the model is as follows: min-λ U dRi =U dIi +I di R dc Q Gimin ≤Q Gi ≤Q Gimax (Q Gi -Q Gimin )V ai =0 (Q Gi -Q Gimax )V bi =0 V Gi -(V Giref +V ai -V bi )=0 V ai ≥0,V bi ≥0 Where: P Li0 and Q Li0 is the initial active and reactive loads of node i; and As a constant, take and K pi is the number of pole pairs of the DC line connected to node i; U di ,I di and K is the DC side voltage, DC current and power factor angle of the DC converter station connected to node i; di and i X is the converter transformer ratio and converter control angle of the DC converter station connected to node i; ci is the commutation reactance of the DC converter station connected to node i; R dc is the DC line resistance; U dRi and U dIi is the DC voltage on the rectifier and inverter sides; Q Gi is the reactive power output of the i-th generator, Q Gimax and Q Gimin Q Gi The upper and lower bounds of V Gi and V Giref are the terminal voltage of the i-th generator and its given reference value respectively; V ai With V bi It is an auxiliary variable, used to reflect the offset of the terminal voltage when the reactive output of the generator reaches the lower or upper limit; In the above optimization model, the first four constraints are the power balance equations of the pure AC node and the AC node connected to the LCC DC converter station. The sign of the first constraint is negative for the rectifier station and positive for the inverter station. If node i is connected to a renewable energy generator, then P Gi =P REi , Q Gi =Q REi , P REi and Q REi is the uncertain active and reactive output of the renewable energy generator set at node i, the 5th to 7th constraints are the operating characteristics of the LCC DC line, and the 8th constraint is the equation describing the growth mode of the active output of the generator. is a constant. The ninth constraint indicates that the total increase in load active power is distributed according to the proportion of the active power margin of other generators except the balancing node generators to the total active power margin. The last five constraints are the complementary constraints of the generator terminal voltage and reactive power output. The constraints added to the optimization model are as follows: (cosξ Iimin -cosξ Ii )V di =0 U dRi =U dRiref -V di U dIi =U dIiref -V di V di ≥0 Where: Iimin For Ii The minimum value of U dRiref and U dIiref For U dRi and U dIi The given reference value of V di It is an auxiliary variable, reflecting the offset of DC voltage.

4. The method for quantifying the participation degree of source and load in AC and DC power grids according to claim 1, characterized in that: In step S4, based on the Sobol decomposition theory, the AC / DC power grid probabilistic static voltage stability margin calculation model λ max =f(X) (X is the model input, i.e. the output of the uncertain source load) is decomposed as follows: If f(X) is square-integrable and the mean of each sub-term in the expansion is 0, then the sub-terms are mutually orthogonal and each sub-term can be uniquely determined: Where: X ～i Input random variables for the system except the i-th dimension; X ～(i,j) For the random variables of the system input except the i-th and j-th dimensions, taking the variance on both sides of the equation, we can get: in, Where: D i is the first-order partial variance, indicating a single input variable X i The contribution to the variance of the output variable; D i,j is the second-order partial variance, indicating that the input variable X i With X j The contribution of the interaction between them to the variance of the output variable, and so on; Input variable X i The total partial variance DTi represents the variable X i Single action and X i The degree of common contribution of interaction with other input variables to the variance of the system output variable: Where: The standardized global sensitivity index calculation formula is as follows: Where: S i (1≤i≤M) represents the input variable X i The first-order sensitivity index (FSI) reflects the single input random variable X i Impact on the uncertainty (variance) of the output variable; STi (1≤i≤M) is the input variable X i Total sensitivity index (TSI), which reflects the input variable X i Single action and X i The joint impact of interaction with other input variables on the uncertainty (variance) of the system output variable; When calculating the Sobol' global sensitivity index, the Monte Carlo simulation (MCS) method is used. It is only necessary to calculate the output variable results of the AC / DC power grid probabilistic static voltage stability margin corresponding to the input random variable samples. The specific calculation formulas for the mean and variance of the output variables and the partial variance of the input variables based on MCS are as follows: Where: W is the input-output sample size used by the MCS method; X (s) Input random variable sample for the s-th sampling system; They are samples X (s) Samples of variables in the i-th dimension and other than the i-th dimension; Input random variable samples for another set of independent sampling systems Based on the above calculation results, the calculation formula of the Sobol' global sensitivity index of the probabilistic static voltage stability margin of the AC and DC power grid is obtained for the variable samples of the i-th dimension and other than the i-th dimension in the s-th sampling as follows:

5. The method for quantifying the participation degree of source and load in AC and DC power grids according to claim 1, characterized in that: In step S4, the SPCE proxy model is a polynomial chaos expansion proxy model that uses a minimum angle regression strategy to sparse key basis functions, and the system model λ max =f(X) is expressed as the sparse chaotic expansion of orthogonal polynomials as follows: Where: i=[i1,i2,…,i M ](i j ≥0,j=1,2,…,M) is the index vector; is a multivariate orthogonal polynomial basis function, represented by the tensor product of a family of univariate orthogonal polynomials; a i is the coefficient corresponding to the orthogonal polynomial basis function; A S is the set of index vectors corresponding to the key orthogonal polynomial basis functions; The key orthogonal polynomial basis functions are selected based on the minimum angle regression strategy. The specific steps are as follows: (1) Initialize the coefficients of all candidate basis functions: a0 = a1 ... = a P-1 =0 (P is the number of candidate basis functions), and set the initial fitting result μ0=0, the initial residual r0=λ max -μ0=λ max , the key basis function set A of the SPCE surrogate model S is an empty set; (2) Select from the candidate basis function set the function that matches the current residual r = λ max -μ The basis function with the largest correlation j (·) as the key basis function, specifically: calculate the correlation function C(Ψ) = Ψ T r, we get a vector of length P, whose component C i Represents the correlation coefficient between the i-th basis function and the current residual r; Select the key basis function Ψ according to the calculation result of the correlation function j (·), where, for any i≠j, C j ≥C i ; The basis function Ψ j (·) Included in the key basis function set A S In the process, based on the current key basis function and the input-output samples of the model, the SPCE proxy model is fitted and the current key basis function set A is calculated. S The corresponding LOO error; (3) Calculate the direction of the angle bisector of the current key basis function and the forward step length of the minimum angle regression method in this direction; update the coefficients of the key basis function according to the calculation results, and obtain a new fitting result μ; (4) Repeat steps 2 to 3 until the residual is small enough or all candidate basis functions are included in the key basis function set; select the key basis function set A corresponding to the minimum LOO error of the SPCE proxy model S , which is used as the basis function set when constructing the actual proxy model, can ensure the optimal generalization ability and fitting accuracy of the constructed SPCE proxy model; The polynomial chaos expansion can be rewritten as follows: Where: Compared with the Sobol decomposition, since the Sobol decomposition is unique, we get: According to the definition of the global sensitivity index, combined with the above formula, we can get a single or a group of input random variables X u The calculation formulas for FSI and TSI are as follows: Where: Once the SPCE proxy model is determined, the global sensitivity index of the system input random variables can be calculated using the coefficients of the expansion.

6. The method for quantifying the participation degree of source and load in AC and DC power grids according to claim 1, characterized in that: In step S4, the steps for calculating the global sensitivity index of the AC / DC power grid probabilistic static voltage stability margin are as follows: Step S41: Obtaining a sample size of J based on the MCS method S Input-output samples of the probabilistic static voltage stability margin calculation model for AC and DC power grids are used to build the SPCE proxy model; Step S42: Establish input variable samples (X j ,λ max,j )(j=1,2,…,J S ) and the standard normal distribution variable sample z j (j=1,2,…,J S ), the transformation relationship between the standard normal distribution variable z and the original input random variable (X,λ max )’s global sensitivity indexes correspond respectively; Step S43: Select the basis function type of the SPCE proxy model as the Hermite orthogonal polynomial, and transform the standard normal distribution variable sample z j (j=1,2,…,J S ) is used as the input variable sample of the proxy model, and the output variable sample is λ max,j (j=1,2,…,J S ), construct the SPCE proxy model; Step S44: Calculate the FSI and TSI of the system input random variables using the SPCE proxy model expression.

7. The method for quantifying the participation degree of source and load in AC and DC power grids according to claim 1, characterized in that: In step S5, the participation degree of the source and load of the AC and DC power grids is quantified according to the global sensitivity index, specifically: Based on the calculation results of the global sensitivity index of each uncertainty source load output obtained in step S4, the uncertainty source loads are ranked in importance. The larger the value of the global sensitivity index, the more important the corresponding uncertainty source load is and the higher the degree of participation is.

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