Power distribution network high-reliability load flow calculation method and system based on all-pure function

Abstract

The invention discloses a power distribution network high-reliability load flow calculation method and system based on a full-pure function, and relates to the technical field of power system power distribution network load flow calculation. The method comprises the following steps: acquiring a grid structure, line parameters and node operation data of a power distribution network; constructing a power flow equation containing all-pure embedded parameters, and converting the power flow equation into a linear recursion equation set in a power series form by introducing an auxiliary variable representing a node voltage reciprocal; decomposing the coefficient matrix based on a sparse matrix technology, and solving a voltage power series coefficient through recursive operation; utilizing a numerical approximation algorithm to calculate a voltage approximate solution when the physical significance value of the full-pure embedding parameter is taken, and taking the voltage approximate solution as a voltage initial value; and taking the initial voltage value as a starting condition, and carrying out iterative solution by adopting a Newton-Raphson method to obtain final power flow distribution. The method is used for solving the problems that a traditional Newton-Raphson method is highly sensitive to an initial value and is easy to diverge and low in convergence reliability under the condition of a heavy-load power distribution network.

Description

Technical Field

[0001] This invention relates to the field of power flow calculation technology for power distribution networks, and more specifically, to a method and system for calculating high-reliability power flow in distribution networks based on holomorphic functions. Background Technology

[0002] Distribution network power flow calculation is fundamental to power system planning, operation, and reliability assessment. With the high proportion of distributed generation, the structure and operation of distribution networks are becoming increasingly complex. Especially during distribution network reliability assessments, Monte Carlo simulations are typically used to perform thousands of random state simulations of the system. In this process, each simulation requires a power flow calculation based on randomly generated network topology and load levels, placing extremely high demands on the robustness and computational speed of the power flow calculation method.

[0003] In existing technologies, methods for solving power flow problems in distribution networks mainly include iterative algorithms and analytical algorithms. Among them, the Newton-Raphson method is the most widely used iterative algorithm, exhibiting quadratic convergence and extremely fast computation speed when the initial values ​​are chosen appropriately. Another type is the Holomorphic Embedding Method (HEM), which has emerged in recent years. This method uses complex analysis theory to transform the nonlinear power flow equations into power series forms of holomorphic functions. By recursively solving for the coefficients and combining this with Padé approximation, the power flow solution is obtained. Theoretically, it can guarantee convergence when a solution exists.

[0004] However, the aforementioned existing technologies still have significant shortcomings in practical applications, especially in large-scale Monte Carlo simulations. First, the Newton-Raphson method is highly sensitive to initial conditions. In heavily loaded, ill-conditioned, or randomly generated special topologies of distribution networks, the conventional "flat start" approach easily leads to iterative divergence or oscillation, resulting in no satisfactory results. Second, while the fully embedded method exhibits good convergence, achieving the extremely high accuracy required for engineering often necessitates the computation of numerous power series terms. Furthermore, the Padé approximation involves extensive matrix operations, typically resulting in higher computational time than the well-converged Newton method. In addition, during stochastic simulations, when the network structure changes due to faults or maintenance, existing algorithms lack an adaptive power adjustment mechanism, often leading to unsolvable power flow equations or failure to meet actual operational constraints, severely impacting simulation efficiency and confidence. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a high-reliability power flow calculation method for distribution networks based on holomorphic functions. This method utilizes a linear recursive equation system with introduced auxiliary variables and a voltage approximation solution obtained through numerical approximation as the initial value for the Newton-Raphson method. This addresses the problem that the traditional Newton-Raphson method is sensitive to initial values ​​and thus has difficulty converging in complex distribution networks.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A high-reliability power flow calculation method for distribution networks based on holomorphic functions includes the following steps: acquiring the distribution network structure, line parameters, and node operation data; constructing power flow equations containing holomorphic embedded parameters based on the data, and transforming the power flow equations into a linear recursive equation system in power series form using auxiliary variables representing the reciprocals of node voltages; decomposing the coefficient matrix of the linear recursive equation system based on a sparse matrix, and solving for the voltage power series coefficients through recursive operations; approximating the voltage power series coefficients using a numerical approximation algorithm, calculating the approximate voltage solution when the holomorphic embedded parameters take their physical values, and using this as the initial voltage value. During the approximation process of the voltage power series coefficients, an allowable error is set, and the maximum magnitude deviation of adjacent even-numbered columns in the Padé approximation table is compared in real time, which serves as a condition to control the termination and continuation of the recursive operation; using the initial voltage value as the starting condition, the Newton-Raphson method is used to iteratively solve the distribution network power flow equations until the convergence condition is met and the power flow distribution is obtained.

[0007] In a preferred embodiment, the step of solving for the voltage power series coefficients through recursive operations includes: using the auxiliary variables to transform the constant power load terms in the power flow equations into a convolutional form of two polynomials; calculating the constant vector of the current order linear equation system based on the obtained preceding voltage power series coefficients and auxiliary variable coefficients; separating the linear equation system into real and imaginary parts according to the characteristics of PQ and PV nodes to handle the conjugate terms in the equations; and performing forward and backward substitution operations using the coefficient matrix after sparse decomposition and the constant vector to obtain the voltage power series coefficients and auxiliary variable coefficients of the current order.

[0008] In a preferred embodiment, the numerical approximation algorithm is the Padé approximation method; the calculation of the initial voltage value using the numerical approximation algorithm includes: constructing an auxiliary two-dimensional array table for Padé approximation based on the voltage power series coefficients; recursively calculating the element values ​​of subsequent columns in the table using the elements of the first two columns through nonlinear sequence transformation rules; and selecting the elements of even-numbered columns in the auxiliary two-dimensional array table as the voltage approximate solution when the holomorphic embedding parameter is 1.

[0009] In a preferred embodiment, the decomposition of the coefficient matrix of the linear recursive equation system based on the sparse matrix includes: storing the sparse coefficient matrix of the linear recursive equation system using a compressed row storage format, wherein the format includes three one-dimensional arrays, which respectively store the values ​​of the non-zero elements of the matrix, the column indices of the non-zero elements, and the position index of the first non-zero element in each row in the value array; and performing arithmetic operations on the non-zero elements using the position indexes during matrix decomposition and previous and back substitution operations.

[0010] In a preferred embodiment, in the step of acquiring the node operation data, the active power value of the power supply node is determined in the Monte Carlo simulation scenario of the distribution network in the following way: before the simulation starts, the power allocation weight coefficient of each power supply node is calculated according to the specified power, outgoing line capacity, and total system load and total outgoing line capacity of the power supply node; during the simulation, when the distribution network structure or load level changes, the weight coefficient remains unchanged, and the active power of each power supply node is calculated according to the current total system load demand based on the weight coefficient, which is used as node operation data to construct the power flow equation.

[0011] In a preferred embodiment, the iterative solution of the power flow equations of the distribution network using the Newton-Raphson method includes: constructing a linear correction equation containing a Jacobian matrix, wherein the Jacobian matrix is ​​composed of node voltage magnitude, phase angle, and admittance parameters; calculating the initial power imbalance using the initial voltage value; solving the linear correction equation to obtain the voltage correction amount; updating the node voltage until the maximum value of the node power imbalance is less than a preset convergence threshold.

[0012] In a preferred embodiment, the process of approximating the voltage power series coefficients using a numerical approximation algorithm employs an adaptive truncation strategy, including: setting an initial voltage value tolerance for initiating the Newton-Raphson method; during the construction of the auxiliary two-dimensional array table, for each new even-numbered column element obtained, calculating the maximum magnitude deviation between it and the previous even-numbered column element; if the maximum magnitude deviation is less than the tolerance, stopping the recursive calculation of the voltage power series coefficients and selecting the current even-numbered column element as the initial voltage value; otherwise, increasing the order and continuing the recursive calculation.

[0013] This invention provides a high-reliability power flow calculation system for distribution networks based on holomorphic functions, comprising: a data acquisition module for acquiring the network structure, line parameters, and node operation data of the distribution network; a holomorphic embedding operation module for constructing power flow equations containing holomorphic embedding parameters based on the data, and transforming the power flow equations into a linear recursive equation system in power series form using auxiliary variables representing the reciprocals of node voltages; decomposing the coefficient matrix of the linear recursive equation system based on a sparse matrix, and solving for the voltage power series coefficients through recursive operations; a voltage initial value calculation module for approximating the voltage power series coefficients using a numerical approximation algorithm, calculating the approximate voltage solution when the holomorphic embedding parameters take their physical values, as the initial voltage value; and a power flow solution module for iteratively solving the power flow equations of the distribution network using the initial voltage value as the starting condition, employing the Newton-Raphson method until the convergence condition is met to obtain the power flow distribution.

[0014] A high-reliability power flow calculation device for distribution networks based on holomorphic functions includes a memory and a processor: the memory is used to store a program; the processor is used to execute the program to implement the various steps of the high-reliability power flow calculation method for distribution networks based on holomorphic functions.

[0015] A readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the various steps of a high-reliability power flow calculation method for distribution networks based on holomorphic functions.

[0016] The technical effects and advantages of this invention, based on a holomorphic function-based high-reliability power flow calculation method for distribution networks, are as follows: This invention transforms complex nonlinear power flow equations into a system of linear recursive equations with a constant coefficient matrix by introducing an auxiliary variable representing the reciprocal of node voltages. It also combines sparse matrix techniques to efficiently calculate voltage power series coefficients. The physical voltage approximation solution obtained by numerical approximation algorithm is used as the initial value for the Newton-Raphson method, effectively overcoming the shortcomings of the traditional Newton-Raphson method, such as high sensitivity to initial values ​​and easy divergence under heavy-load networks. It organically combines the strong robustness of the fully embedded method with the efficient convergence characteristics of the Newton-Raphson method, significantly improving the convergence reliability and calculation speed of power flow calculation in distribution networks. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the high-reliability power flow calculation method for distribution networks based on holomorphic functions provided in an embodiment of the present invention; Figure 2 This is a block diagram of a high-reliability power flow calculation system for distribution networks based on holomorphic functions, provided in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1, Figure 1 This invention presents a method for calculating high-reliability power flow in distribution networks based on holomorphic functions, comprising the following steps: S1, obtains the grid structure, line parameters and node operation data of the distribution network.

[0020] It should be noted that this step involves reading the topological connection relationship of the distribution network structure and the line impedance parameters to construct a node admittance matrix to describe the electrical characteristics of the power grid. At the same time, it collects the operating status data of each node, specifically identifying the number and location of slack nodes, PQ nodes, and PV nodes in the system. For PQ nodes, it obtains the injected active power and reactive power; for PV nodes, it obtains the injected active power and voltage amplitude; and for slack nodes, it sets the voltage amplitude and phase angle reference value.

[0021] In the step of acquiring the node operation data, the active power value of the power supply node is determined in the Monte Carlo simulation scenario of the distribution network in the following way: Before the simulation begins, the power allocation weight coefficient for each power node is calculated based on its specified power, outgoing line capacity, total system load, and total outgoing line capacity. Specifically, under fault-free system operation, the weight is determined by combining the ratio of the specified power of the power supply to its outgoing line interval capacity with the ratio of the total system load to the total outgoing line capacity. Power allocation weighting coefficient The calculation formula is as follows: (1) In the formula, For power nodes The specified power; For power nodes Outgoing capacity, i.e., power node The sum of the capacities of all operating outgoing bays; The total system load, This represents the total outgoing line capacity of the system. When the power is not specified, the weighting coefficient is set to 1.

[0022] During the simulation, when the distribution network structure or load level changes, the weighting coefficients remain unchanged. Based on the current total system load demand, the active power of each power source node is calculated according to the weighting coefficients, and this active power is used as node operating data to construct the power flow equations. Specifically, in the stochastic scenario of the Monte Carlo simulation, all power source nodes except the slack node are considered PV nodes. The pre-calculated weighting coefficients reflect the importance of the power source in the power supply area, thereby automatically adjusting the power output to adapt to network changes. active power The calculation formula is as follows: (2) The active power determined by the above method It will be used as a known quantity in the construction and solution of subsequent power flow equations.

[0023] S2, Based on the data, construct power flow equations containing fully embedded parameters, and transform the power flow equations into a linear recursive equation system in power series form by using auxiliary variables representing the reciprocals of node voltages.

[0024] In practice, the node voltage equations of the power grid are first established based on Kirchhoff's current law. For a given grid containing... In a network with independent nodes, the relationship between node voltage and injected current is expressed by the node voltage equation, which is as follows: (3) In the formula, The vector formed by the injected current at each node. ; It is a vector composed of the voltages of each node. ; Let be the node admittance matrix of the network.

[0025] The expression for a matrix is: (4) in, ( ) is a node The self-admittance is the sum of the path admittances connected to node i; ( ; ; ) represents the mutual admittance between node i and node j, and its value is equal to the negative of the branch admittance between the two nodes.

[0026] Since most loads in a distribution network exhibit constant power characteristics, linear equations cannot be directly solved; therefore, complex power equations must be introduced. These equations are based on the net injected complex power at each node. The relationship between voltage and current allows for the derivation of a nonlinear equation relating node voltage and injected power. To transform this nonlinear problem into a series of linear problems, this step introduces holomorphic embedded parameters. A fully embedded power flow equation is constructed. For the slack bus, its voltage is set to be about... holomorphic functions, in When the voltage is unit, When the given value is reached Its expression is as follows: (5) In the formula, Let be the voltage phasor function of the relaxed node. The given voltage setting value for the relaxation node.

[0027] For the PQ node, the admittance matrix elements are decomposed into mutual admittances. and parallel admittance ,in , And move the nonlinear term to the right side of the equation, embedding the variable. The resulting power flow equations are as follows: (6) In the formula, For the current computing node Voltage phasor function; For nodes Connected nodes Voltage phasor function; Represents a node The conjugate function of voltage, It is a node The conjugate of the injected complex power.

[0028] For PV nodes, due to reactive power Unknown, set it as about holomorphic functions Furthermore, voltage amplitude constraint equations need to be added. The embedded PV node power flow equations are as follows: (7) (8) In the formula, The active power given for the PV node. The voltage amplitude given for the PV node. Injecting reactive power into PV nodes is related to holomorphic functions.

[0029] In order to eliminate the voltage reciprocal terms in equations (6) and (7) above The resulting nonlinearity necessitates the introduction of an auxiliary variable representing the reciprocal of the node voltage. Its definition is as follows: (9) Based on this definition, Substituting into the power flow equations transforms both sides of the equations into a product of polynomials. Then, the voltage... Auxiliary variables and reactive power All expanded to include information about The power series form, for example ,in For nodes The first power series of voltage The coefficients of the terms. Using the property of power series convolution, both sides of the equation... The coefficients of the same power are equal, thus deriving a linear recurrence relation. For the th power series... Term coefficients (corresponding to the solution) (For problems of order), move the unknown quantity to be solved to the left side of the equation, including the known quantity. The convolution terms of the term coefficients are moved to the right, and the real and imaginary parts are separated, ultimately yielding the result used to solve the _th ... The system of linear recurrence equations with coefficients of the terms has the following matrix form: (10) In the formula, Given the order of the power series already determined, the equation is used to solve for the th power series. The term coefficients; the large matrix on the left is the system's coefficient matrix, whose elements are derived from the real parts of the nodal admittance matrix. and the virtual part Composition, in which and Representing nodes respectively and nodes The conductance and susceptance of the admittance remain unchanged for all series terms in the calculation.

[0030] In the vector to be solved, and They are nodes Voltage power series The real and imaginary parts of the term coefficient, The power series of reactive power at PV nodes Term coefficient.

[0031] Right-hand vector For a constant vector, from the previous The result of a convolution operation with known coefficients is used. For a PQ node, its corresponding elements involve... Items, among which For auxiliary variables The conjugate of the term coefficients; for PV nodes, their corresponding elements involve Equal convolution terms reflect the influence of historical calculations on the current term.

[0032] This step successfully transformed the complex nonlinear power flow equations into a system of linear recursive equations with a constant coefficient matrix by introducing fully embedded parameters and auxiliary variables, laying the foundation for efficient subsequent solutions.

[0033] S3. The coefficient matrix of the linear recursive equation system is decomposed based on the sparse matrix, and the voltage power series coefficients are solved by recursive operation.

[0034] The process of solving for the voltage power series coefficients through recursive calculation includes: The constant power load term in the power flow equation is transformed into a convolution of two polynomials using the aforementioned auxiliary variable; specifically, based on the properties of holomorphic functions, the voltage reciprocal auxiliary variable is transformed... With voltage Product relationship Expanding into a power series product, i.e., a discrete convolution form, thus establishing... and The recursive relationship between them, when the first part of the voltage power series is known. When the coefficient of the term is , the first Auxiliary variable coefficients It can be calculated using the following formula: (11) In the formula, For nodes The initial voltage is usually the equilibrium node voltage; and These are the corresponding order coefficients for voltage and auxiliary variables, respectively.

[0035] Based on the obtained coefficients of the preceding voltage power series and the coefficients of the auxiliary variables, the constant vector of the current order linear equation system is calculated; specifically: using the preceding... Known voltage coefficient and auxiliary variable coefficients Calculate the convolution term on the right-hand side of the power flow equation. For PQ nodes, the conjugate of their injected complex power... Conjugate with auxiliary variables The product is expanded into a convolution term. In solving the first... When considering the coefficients of terms, the known terms contained in the constant vector on the right-hand side of the equation are mainly... This is combined with the shunt admittance term. For PV nodes, active power needs to be addressed. and Convolution and reactive power and The convolution, the known terms contained in the constant vector on the right-hand side of the equation are mainly... Subtract the convolution sum of historical reactive power coefficient and auxiliary variable coefficient .

[0036] Based on the characteristics of PQ and PV nodes, the linear equations are separated into real and imaginary parts to handle conjugate terms in the equations; specifically, because the power flow equations contain conjugate terms of the reciprocal of voltage and power, the equations are not in terms of complex variables. The simple analytical function cannot be directly solved in the complex domain by simple coefficient comparison. Furthermore, the reactive power of the PV node... Since the integer part is a real number, it increases the constraint complexity in complex equations. Therefore, this embodiment adopts a strategy of separating the real and imaginary parts to solve the first integer part. Term voltage coefficient Split into real part and the virtual part Construct a system of linear equations in the real field as shown in equation (10) in the preceding steps.

[0037] By performing forward and backward substitution operations on the coefficient matrix obtained after sparse decomposition and the constant vector, the voltage power series coefficients and auxiliary variable coefficients of the current order are obtained. Specifically, since the coefficient matrix remains unchanged in each order of recursion, only one LU decomposition is needed to decompose the coefficient matrix into a lower triangular matrix. and upper triangular matrix In solving the... When calculating the term coefficients, the calculated right-hand constant vector is denoted as... First, solve the previous equations. Obtain the intermediate vector ,Right now: (12) Then solve the back-substitution equation. Obtain the solution vector of the current order. (Including voltage coefficient and reactive power coefficient), that is: (13) In the formula, That is, the vector to be determined on the left side of equation (10); This is the intermediate variable vector. We obtain... Then, use equation (11) to update the auxiliary variable. This process is repeated until the preset calculation order is reached.

[0038] The decomposition of the coefficient matrix of the linear recursive equation system based on sparse matrices includes: The sparse coefficient matrix of the linear recurrence equation system is stored using a compressed row storage format. This format includes three one-dimensional arrays, which store the values ​​of the non-zero elements, the column indices of the non-zero elements, and the position index of the first non-zero element in each row within the value array, respectively. Specifically, the arrays are defined as follows: Store all non-zero elements in the matrix sequentially; define an integer array. Storage array The column number corresponding to each non-zero element; define an integer array. The first non-zero element in each row of the storage matrix is ​​in the array. The position index in the table, i.e., the row pointer.

[0039] During matrix decomposition and forward and backward substitution operations, the position indices are used to perform arithmetic operations on non-zero elements. Specifically, during the LU decomposition and the solution of equations (12) and (13), the array is read... Fast localization matrix non-zero elements in the array and The starting and ending positions are used to read and operate only on these non-zero elements, skipping zero elements.

[0040] This step utilizes the recursive nature of analytical extension to ensure that the coefficient matrix of the linear equation system remains unchanged throughout the calculation process, thus requiring only one time-consuming LU decomposition. Combined with sparse matrix compression storage technology, it greatly reduces computer memory usage and avoids invalid operations on zero elements, significantly improving the speed and efficiency of fully embedded initial value calculation.

[0041] S4 uses a numerical approximation algorithm to approximate the voltage power series coefficients and calculates the approximate voltage solution when the fully embedded parameters take their physical values, which is used as the initial voltage value. In the process of approximating the voltage power series coefficients, the maximum amplitude deviation of adjacent even-numbered columns in the Padé approximation table is compared in real time by setting an allowable error, which is used as a condition to control the termination and continuation of the recursive operation.

[0042] The numerical approximation algorithm is the Padé approximation method; the calculation of the initial voltage value using the numerical approximation algorithm includes: Based on voltage power series coefficients, an auxiliary two-dimensional array table (i.e., the Padé approximation table) is constructed for Padé approximation; specifically, a numerical algorithm for Padé approximation is called... Algorithm for constructing a two-dimensional array , is called Table, where subscripts Indicates column indicators, superscript The numbers represent the rows from top to bottom, as shown in Table 1.

[0043] Table 1

[0044] By using nonlinear sequence transformation rules, the element values ​​of subsequent columns in the table are recursively calculated using the elements of the first two columns; specifically, firstly... The first two columns of the table are initialized, with all elements in column -1 being 0, and the elements in column 0 being the coefficients of the power series as described above. (i.e., the voltage coefficient obtained in the aforementioned steps) In fully embedded parameters The elements at the truncated portion are then used, and subsequently, the elements of the subsequent columns are calculated using a non-linear recursive formula based on the elements of the first two columns. The initialization and recursive calculation formulas are as follows: (14) In the formula, for The table of numbers Liede Row elements; The first power series of voltage Term coefficient; A value of 1 represents the physical meaning of the fully embedded parameter.

[0045] The even-numbered columns of the auxiliary two-dimensional array table are selected as the voltage approximation solution when the holomorphic embedding parameter is 1. Specifically: The even-numbered sequence of values ​​in the algorithm corresponds to the diagonal Padé approximation of the power series function, which can effectively overcome the convergence problem that may exist in the direct summation of the power series. The analytic extension value of the holomorphic function is calculated to the physical point. The voltage approximation solution when the holomorphic embedding parameter is 1 is given by the following formula: (15) In the formula, Representation function The order is The Padé approximation value is the voltage approximation solution used as the initial value for the Newton-Raphson method.

[0046] Furthermore, to maximize computational efficiency while ensuring the quality of the initial value, this embodiment employs an adaptive truncation strategy to determine the initial voltage value. Specifically: Set a more lenient startup threshold. (For example, take) ); In use During the algorithm's calculation process, whenever a new diagonal Padé approximation value is calculated... At that time, calculate its approximation value with the previous order. The deviation norm: ; like This indicates that the current approximate voltage solution has stabilized and is sufficient to fall within the convergence region of the Newton-Raphson method. At this point, the recursive process of the power series coefficients in S2 and S3 should be terminated immediately, and the solution should be directly applied. If the output is the initial voltage value, proceed to step S5; otherwise, let... Then return to S3 to continue calculating the next coefficient. This strategy allows the algorithm to switch when dealing with simple networks by calculating only a few terms, while automatically increasing the number of calculated terms to ensure convergence in complex networks.

[0047] This step is passed. The Padé approximation algorithm analytically extends the voltage function calculated using a finite number of power series coefficients to... This allows us to obtain a voltage value with a clear physical meaning that is very close to the true solution, with only a few series terms to be calculated (i.e., a low-order approximation). This value can then be used as the initial value for the subsequent Newton-Raphson method, thus solving the technical problem that the Newton-Raphson method is sensitive to initial values ​​and prone to divergence under heavy-load networks.

[0048] S5. Using the initial voltage value as the starting condition, the Newton-Raphson method is used to iteratively solve the power flow equation of the distribution network until the convergence condition is met and the power flow distribution is obtained.

[0049] The iterative solution of the power flow equations of the distribution network using the Newton-Raphson method includes: A linear correction equation is constructed, comprising a Jacobian matrix consisting of node voltage magnitudes, phase angles, and admittance parameters; specifically: for A power system with 1 node has one slack node. One PQ node, PV nodes, the voltage phase angle to be determined and the effective value of voltage Write in vector form , No. The linear correction equation for the next iteration is as follows: (16) In the formula, and For the first The vector of active and reactive power imbalance in the next iteration; This is the voltage phase angle correction vector; This is the voltage amplitude relative correction vector; the matrix on the right is the Jacobian matrix, and its sub-blocks... The elements are calculated based on the node voltage magnitude, phase angle, and admittance matrix elements, where the off-diagonal elements ( The calculation formula for ) is as follows: (17) In the formula, and These are the real and imaginary parts of the nodal admittance matrix elements, respectively; For the first Node at the next iteration With nodes The voltage phase angle difference.

[0050] The initial power imbalance is calculated using the initial voltage value; specifically, the approximate voltage solution obtained in step S4 through pure embedding and Padé approximation is used as the initial value. Substitute into the power equation to calculate the active power injected at the nodes. and reactive power The deviation between the calculated value and the given value, i.e.: (18) In the formula, They are nodes The active power injected by the generator and the active power consumed by the load; They are nodes The generator injects reactive power and the load consumes reactive power.

[0051] Solving the linear correction equation yields the voltage correction amount, which is then used to update the node voltage until the maximum value of the node power imbalance is less than the preset convergence threshold. Specifically, the correction amount is obtained by solving the correction equation (16). and The current voltage vector is updated using this correction, and the update formula is as follows: (19) The convergence condition is then checked, specifically whether the maximum norm of the power imbalance at all nodes is less than a given allowable error. The formula for judgment is as follows: (20) If this condition is met, stop the iteration and output the current node voltage and phase angle as the final power flow distribution result; otherwise, let Repeat the Jacobian matrix calculation and correction steps described above.

[0052] This step utilizes the initial voltage value provided by the Padé approximation, enabling the Newton-Raphson method to avoid the iterative divergence problem caused by improper initial values. It fully leverages the quadratic convergence characteristic of the Newton method near the solution, achieving high-precision convergence in a very small number of iterations. This significantly improves computational efficiency while ensuring high reliability of power flow calculations in distribution networks.

[0053] Example 2, Figure 2 A high-reliability power flow calculation system for distribution networks based on holomorphic functions is presented, including: The data acquisition module is used to acquire the grid structure, line parameters, and node operation data of the power distribution network. The fully embedded computation module is used to construct power flow equations containing fully embedded parameters based on the data, and to transform the power flow equations into a linear recursive equation system in power series form by using auxiliary variables representing the reciprocals of node voltages; to decompose the coefficient matrix of the linear recursive equation system based on a sparse matrix, and to solve for the voltage power series coefficients through recursive operations. The voltage initial value calculation module is used to approximate the voltage power series coefficients using a numerical approximation algorithm, and calculate the approximate voltage solution when the fully pure embedded parameters take their physical values, which is then used as the voltage initial value. The power flow solution module uses the initial voltage value as the starting condition and employs the Newton-Raphson method to iteratively solve the power flow equations of the distribution network until the convergence condition is met to obtain the power flow distribution.

[0054] Example 3: A high-reliability power flow calculation device for distribution networks based on holomorphic functions, comprising a memory and a processor: the memory is used to store a program; the processor is used to execute the program to implement any of the embodiments in Example 1.

[0055] Since the high-reliability power flow calculation device for distribution networks based on holomorphic functions described in this embodiment is the same device used to implement the method in Embodiment 1 of this invention, those skilled in the art can understand the specific implementation methods and various variations of the electronic device in this embodiment based on the method described in Embodiment 1 of this application. Therefore, how the electronic device implements the method in this application embodiment will not be described in detail here. Any device used by those skilled in the art to implement the method in this application embodiment falls within the scope of protection of this application.

[0056] Example 4: A readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the embodiments in Example 1.

[0057] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0058] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0059] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0060] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0061] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0062] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A power distribution network high reliable power flow calculation method based on holomorphic functions, characterized in that, The method comprises the following steps: obtaining the network structure, line parameters and node operation data of a power distribution network; constructing a power flow equation containing holomorphic embedding parameters based on the data, and converting the power flow equation into a linear recursive equation group in the form of a power series by means of an auxiliary variable representing the reciprocal of the node voltage; decomposing the coefficient matrix of the linear recursive equation group based on a sparse matrix, and solving the voltage power series coefficient by means of recursive operation; approximating the voltage power series coefficient by means of a numerical approximation algorithm, and calculating the voltage approximate solution when the holomorphic embedding parameter takes a physically meaningful value as the voltage initial value, wherein in the process of approximating the voltage power series coefficient, the maximum amplitude deviation of the adjacent even column elements in the Padé approximation table is compared in real time by setting the allowable error, and the termination and continuation of the recursive operation are controlled as the condition; taking the voltage initial value as the starting condition, and iteratively solving the power flow equation of the power distribution network by means of the Newton-Raphson method until the convergence condition is met to obtain the power flow distribution.

2. The holomorphic function based power grid high reliable power flow calculation method according to claim 1, characterized in that, The method for solving the voltage power series coefficient by means of recursive operation comprises the following steps: converting the constant power load term in the power flow equation into the convolution operation form of two polynomials by means of the auxiliary variable; calculating the constant vector of the linear equation group of the current order based on the previously obtained voltage power series coefficient and auxiliary variable coefficient; separating the linear equation group into real and imaginary parts to process the conjugate term in the equation according to the PQ node and PV node characteristics; performing the forward substitution and back substitution operation by means of the coefficient matrix decomposed based on the sparse matrix and the constant vector to obtain the voltage power series coefficient and auxiliary variable coefficient of the current order.

3. The holomorphic function based power grid high reliable power flow calculation method according to claim 1, characterized in that, The numerical approximation algorithm is the Padé approximation method; The method for calculating the voltage initial value by means of the numerical approximation algorithm comprises the following steps: constructing an auxiliary two-dimensional array table for Padé approximation based on the voltage power series coefficient; recursively calculating the element values of the subsequent columns in the table by means of the first two columns of elements by means of a nonlinear sequence transformation rule; selecting the elements of the even columns in the auxiliary two-dimensional array table as the voltage approximate solution when the holomorphic embedding parameter is 1.

4. The holomorphic function based power grid high reliable power flow calculation method of claim 1, wherein, The method for decomposing the coefficient matrix of the linear recursive equation group based on the sparse matrix comprises the following steps: storing the sparse coefficient matrix of the linear recursive equation group in a compressed row storage format, and the format comprises three one-dimensional arrays for storing the values of the non-zero elements of the matrix, the column indexes of the non-zero elements and the position indexes of the first non-zero elements of each row in the value array; performing arithmetic operation on the non-zero elements by means of the position indexes when performing matrix decomposition and forward substitution and back substitution operation.

5. The holomorphic function based power grid high reliable power flow calculation method according to claim 1, characterized in that, In the step of obtaining the node operation data, the active power value of the power supply node is determined in the following manner in the Monte Carlo simulation scenario of the power distribution network: Before the simulation starts, the power distribution weight coefficient of each power supply node is calculated according to the specified power of the power supply node, the outgoing line capacity and the total load and total outgoing line capacity of the system; During the simulation process, when the power distribution network structure or load level changes, the weight coefficient remains unchanged, and the active power of each power supply node is calculated according to the current total load demand of the system according to the weight coefficient, which is used as the node operation data for constructing the power flow equation.

6. The holomorphic function based power grid high reliable power flow calculation method according to claim 1, characterized in that, The method for iteratively solving the power flow equation of the power distribution network by means of the Newton-Raphson method comprises the following steps: A linear correction equation including a Jacobian matrix composed of node voltage amplitude, phase angle and admittance parameter is constructed; An initial power imbalance is calculated by using the voltage initial value; A voltage correction is obtained by solving the linear correction equation, and the node voltage is updated until the maximum value of the node power imbalance is less than a preset convergence threshold.

7. The holomorphic function based power grid high reliable power flow calculation method according to claim 3, characterized in that, An adaptive truncation strategy is adopted in the process of approximating the voltage power series coefficient by using the numerical approximation algorithm, including: Setting a voltage initial value tolerance error for starting the Newton-Raphson method; In the process of constructing the auxiliary two-dimensional array table, the maximum amplitude deviation between the newly calculated even column element and the previous even column element is calculated; If the maximum amplitude deviation is less than the tolerance error, the recursive operation of the voltage power series coefficient is stopped, and the current even column element is selected as the voltage initial value; otherwise, the order is increased to continue the recursive operation.

8. A system using the holomorphic function based power grid high reliable power flow calculation method according to any one of claims 1 to 7, characterized in that, It includes: A data acquisition module is configured to acquire the network structure, line parameters and node operation data of a power distribution network; A holomorphic embedding operation module is configured to construct a power flow equation including a holomorphic embedding parameter based on the data, and convert the power flow equation into a linear recursive equation set in a power series form by using an auxiliary variable representing the reciprocal of the node voltage; decompose the coefficient matrix of the linear recursive equation set based on a sparse matrix, and solve the voltage power series coefficient by using a recursive operation; A voltage initial value calculation module is configured to approximate the voltage power series coefficient by using a numerical approximation algorithm, and calculate the voltage approximate solution when the holomorphic embedding parameter takes a physical significance value as the voltage initial value; A power flow solving module is configured to use the voltage initial value as a starting condition, and solve the power flow equation of the power distribution network by using the Newton-Raphson method until a convergence condition is met to obtain the power flow distribution.

9. A computer device, comprising: The device includes a processor and a memory: The memory is configured to store a computer program, and send instructions of the computer program to the processor; The processor executes the computer program according to the instructions to implement the power distribution network high reliability power flow calculation method based on the holomorphic function according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is executed by the processor to implement the power distribution network high reliability power flow calculation method based on the holomorphic function according to any one of claims 1 to 7.

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