High-order analysis power flow and carbon flow tracking method based on full-pure embedding

Abstract

The invention relates to a high-order analysis power flow and carbon flow tracking method based on full-pure embedding, and the method comprises the specific steps: introducing a complex embedding parameter s, constructing a node voltage vector, an injection power vector and a tracking matrix in a power grid power flow equation into an analysis power series and an analysis power series of the complex embedding parameter s based on the analysis continuation characteristic of full-pure embedding, solving a node voltage initial value when the power grid is in a basic operation state by adopting a Newton-Raphson method; calculating a zero-order line active power vector based on the node voltage initial value, and constructing a zero-order distribution matrix representing a power distribution relation in a basic operation state of the power grid; solving a zero-order power flow tracking matrix based on the zero-order line active power vector and the zero-order power distribution matrix; calculating node indirect total carbon emission based on the zero-order power flow tracking matrix; and replacing the power distribution matrix, the node outflow power and the power flow direction matrix in the zero-order power distribution matrix with power series expansion of corresponding variables.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system analysis and carbon management, in particular to a high-order analytical power flow and carbon flow tracking method based on holomorphic embedding. BACKGROUND

[0002] The power system is rapidly transforming towards a high proportion of new energy, the grid topology structure is becoming increasingly complex, and the operation characteristics are showing strong nonlinearity, which puts higher requirements on the accuracy and convergence of power flow tracking. As the core technology for quantifying the proportion of power supply to load, the result of power flow tracking directly determines the accuracy of carbon flow distribution identification. Carbon flow tracking needs to allocate carbon emission contributions of different power sources based on this power supply ratio, providing a key basis for carbon emission right allocation and carbon cost accounting.

[0003] The current power flow tracking technology has significant bottlenecks: 1. Iterative power flow tracking method (such as Newton-Raphson method): only provides the result of a single power flow operating point, in the scenario of frequent changes in power flow direction caused by high proportion of new energy grid connection and strong nonlinearity, the power flow needs to be solved repeatedly, which is computationally intensive and cannot depict the influence of power flow operating point changes on power distribution; 2. Linearized power flow tracking method (such as DC power flow method): ignores the coupling effect of voltage amplitude and reactive power, and does not consider the nonlinearity of network loss caused by line resistance, resulting in large power flow tracking error and difficulty in meeting the accuracy requirements of carbon flow tracking in high proportion of new energy grid; 3. Existing technology gap: there is currently no analytical power flow tracking method based on holomorphic embedding (HELM). Although HELM has shown strong analyticality and guaranteed convergence in power flow calculation, it has not been applied to the power flow tracking scenario. Traditional power flow tracking methods cannot capture high-order nonlinear coupling effects, making it difficult to achieve analytical power flow-carbon flow tracking in high proportion of new energy grid. SUMMARY

[0004] In order to solve the problems existing in the prior art, the present application proposes a high-order analytical power flow and carbon flow tracking method based on holomorphic embedding.

[0005] The technical solution of the present application is as follows: On the one hand, the present application proposes a high-order analytical power flow and carbon flow tracking method based on holomorphic embedding, the specific steps of which include: Introducing a complex embedding parameter s, based on the analytical continuation characteristics of holomorphic embedding, constructing the node voltage vector, injected power vector and tracking matrix in the power flow equation of the power grid as an analytical power series of the complex embedding parameter s, solving the initial value of the node voltage when the power grid is in the basic operating state using the Newton-Raphson method; The zero-order line active power vector is calculated based on the initial value of the node voltage, and a zero-order distribution matrix representing the power distribution relationship in the basic operation state of the power grid is constructed; the zero-order power flow tracking matrix is solved based on the zero-order line active power vector and the zero-order power distribution matrix; and the indirect total carbon emission between nodes is calculated based on the zero-order power flow tracking matrix. The power distribution matrix, node outflow power and power flow direction matrix in the zero-order power distribution matrix are replaced by the power series expansion of the corresponding variables, and the k-order power distribution matrix and the recursive formula of the power flow tracking matrix are obtained by equating the k-order coefficients after expansion, that is, the high-order power distribution matrix and the power flow tracking matrix, and the high-order power distribution matrix coefficient is solved according to the power series expansion formula. The power series function of the active power injection of the generator is brought into the zero-order indirect total carbon emission between nodes, and the k-order indirect carbon emission increment between nodes is obtained after expansion and equating the power series coefficients, and the k-order indirect carbon emission increment between nodes is substituted into the power series of the indirect carbon emission between nodes, so that the indirect total carbon emission between nodes can be solved.

[0006] As a preferred embodiment, based on the analytic continuation characteristics of the holomorphic embedding, the analytic power series of the complex embedding parameter s is specifically constructed as follows: based on the inverse matrix of the node admittance matrix, the analytic power series of the complex embedding parameter s is expanded.

[0007] As a preferred embodiment, the zero-order tracking matrix includes the outflow association matrix , the inflow association matrix and the voltage difference matrix A, and the following are predefined: The outflow association matrix is 1 if the line flows out of node i, otherwise 0; The inflow association matrix is 1 if the line flows into node i, otherwise 0; As a preferred embodiment, when the topology of the power grid changes, the outflow association matrix A + and the inflow association matrix A - are automatically updated, and all steps are re-executed.

[0008] As a preferred embodiment, the calculation formula of the high-order power distribution matrix is specifically:

[0009] In the formula, k is the order, m is the intermediate variable of the order; is the m-order active power increment vector; the superscript inv represents the associated variable after taking the inverse of the original variable; is the node outflow power between the m-order and the k-order.

[0010] As a preferred embodiment, the convergence of the high-order power flow tracking matrix is guaranteed by a spectral radius condition, specifically:

[0011] wherein, is the spectral radius of the high-order power distribution matrix , that is, the maximum modulus of the eigenvalues of the matrix.

[0012] As a preferred embodiment, the convergence threshold of the convergence of the high-order power flow tracking matrix is preset as:

[0013] wherein, is the high-order power flow tracking matrix, is the zero-order power flow tracking matrix.

[0014] As a preferred embodiment, the carbon emission intensity includes the carbon emission intensity of new energy power sources and the carbon emission intensity of traditional fossil energy power sources, wherein the carbon emission intensity of new energy power sources is 0, and the carbon emission intensity of traditional fossil energy power sources is determined according to the fuel type and power generation efficiency thereof.

[0015] On the other hand, the present application proposes an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, said processor implementing a high-order analytical power flow and carbon flow tracking method based on holomorphic embedding according to any one of the embodiments of the present application when executing said program.

[0016] On the other hand, the present application proposes a computer readable storage medium having a computer program stored thereon, which program, when executed by a processor, implements a high-order analytical power flow and carbon flow tracking method based on holomorphic embedding according to any one of the embodiments of the present application.

[0017] The present application has the following beneficial effects: 1. The present application greatly improves the tracking accuracy by performing analytical power series expansion of the complex embedding parameter s based on the inverse matrix of the node admittance matrix and multiplying the high-order distribution matrix with the active power tracking matrix accumulated by all previous orders.

[0018] 2. Based on the analytical continuation characteristics of holomorphic embedding, the convergence radius is determined by the system stability boundary, and the recursive convergence is ensured by the spectral radius condition. According to the linear algebra convergence criterion, the matrix power series converges when the spectral radius is less than 1, completely avoiding the convergence risk of traditional iterative methods, especially suitable for strong nonlinear scenarios with high proportion of new energy grid-connected.

[0019] 3、The application supports the bidirectional flow scenario of the high-proportion new energy power grid. The sign tracking matrix is used to reserve the power flow direction, and can cover multiple core scenarios: power grid planning: combined with the piecewise continuous tracking method, the result is clear and convenient for scheme comparison; real-time scheduling: combined with the adaptive topology updating method, the tracking logic can be adjusted in real time according to the change of the flow direction; suitable for carbon market settlement and meeting the demand of carbon transaction accounting. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 The step flowchart of the application is shown. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0022] It should be understood that the step numbers used herein are only for the convenience of description, and are not limited to the execution sequence of the steps.

[0023] It should be understood that the terms used in the specification of the application are only for the purpose of describing specific embodiments and are not intended to limit the application. As used in the specification and the appended claims of the application, the singular forms "a", "an" and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0024] The terms "comprise" and "include" indicate the presence of the described features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0025] The term "and / or" refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0026] Embodiment one: Reference Figure 1 A high-order analytic power flow and carbon flow tracking method based on holomorphic embedding, the specific steps include: A complex embedding parameter s is introduced, based on the analytic continuation characteristics of holomorphic embedding, the node voltage vector, injected power vector and tracking matrix in the power flow equation are constructed into an analytic power series of the complex embedding parameter s, the analytic power series is solved, and the Newton-Raphson method is used to solve the initial value of the node voltage when the power grid is in the basic operating state; In this embodiment, this step is specifically: introducing complex embedding parameters for the base power flow solution, for the target operating point), according to the core definition of the analytic continuation method. The power flow physical quantities (voltage , power , and tracking matrix ) are expanded into an analytic power series of parameters, and the specific expansion form is as follows: Node voltage: , and ; wherein n is the number of nodes, k is the order, Re is the real part of the voltage vector, and Im is the imaginary part of the voltage vector.

[0027] The complex power flow is decomposed according to the line admittance , and the node voltage . The real part of the line power and the imaginary part of the power are decomposed according to the real and imaginary parts of the apparent power . Among them, G is the conductance vector, and B is the susceptance vector.

[0028] Injection power: generation power , and load power , wherein P is the base power vector, and ΔP is the tracking power increment vector. The inverse matrix of the node admittance matrix Zbus matrix is specifically as follows: The actual base power flow solution (P , V ) solved by the Newton-Raphson method is used as the initial value when t , which ensures consistency with the definition of the base operating point of the analytic continuation.

[0029] Based on the initial value of the node voltage, the zero-order line active power vector is calculated, and the zero-order distribution matrix representing the power distribution relationship under the base operating state of the power grid is constructed. The zero-order power flow tracking matrix is solved based on the zero-order line active power vector and the zero-order power distribution matrix. The inter-node indirect total carbon emission is calculated based on the zero-order power flow tracking matrix. In this embodiment, this step is specifically as follows: The matrix representing the power distribution relationship under the base operating state of the power grid is specifically as follows: Outflow association matrix (original A+): if the line flows out of node i, , otherwise 0. ​​​​​​​​​inflow incidence matrix (A-): if line inflow node i, , otherwise 0; voltage difference matrix : describes the voltage difference relationship between the two ends of the line.

[0030] where A is the line incidence matrix, where N represents the number of nodes, and L represents the number of loops; First, calculate the zero-order line active power vector:

[0031]

[0032] where real(•) represents the real part, represents the element-by-element multiplication of a matrix, represents the voltage at the beginning of the line, represents the voltage at the end of the line, and k represents the order, represents the voltage at the beginning of the zero-order line, and YL represents the loop admittance matrix, represents the transpose of the outflow incidence matrix, represents the transpose of the inflow incidence matrix.

[0033] Next, calculate the zero-order active power flow matrix and the total outflow power of the node: Calculate the active power flow matrix: where, represents the total active power flowing from node j to node i; Calculate the total outflow power of the node: where, is the zero-order total outflow power of the node, i.e., for each node, accumulate the active power of all its sending end lines; Based on the zero-order active power flow matrix and the total outflow power of the node, calculate the zero-order power distribution matrix :

[0034]

[0035]

[0036] where, represents the zero-order power distribution matrix, is the zero-order power flow matrix, represents the vector variable diagonal matrix, i.e., generates a matrix with vectors as diagonal elements; the superscript inv represents the incidence variable after taking the inverse of the original variable, and when the outflow power of node i is less than the numerical zero threshold value (10^ 8p.u., the accuracy of power flow calculation is generally controlled within 10 6p.u., taking high 2 orders of magnitude to ensure that it does not affect the accuracy of power flow), considering that the node has no power outflow, in the power distribution matrix , the corresponding row is set to zero vector, and does not participate in downstream power distribution.

[0037] Finally, the zero-order power flow tracking matrix is calculated:

[0038] wherein, is an N-dimensional unit diagonal matrix, is a generator association matrix.

[0039] Then, the zero-order indirect total carbon emission between nodes is calculated:

[0040] wherein, represents the zero-order indirect total carbon emission between nodes, is the carbon emission intensity of the generator, representing the carbon emission per unit active power of each generator; is the injected power of the generator.

[0041] Replace the power distribution matrix, node outflow power and power flow direction matrix in the zero-order power distribution matrix with the power series expansion of the corresponding variables, and equalize the k-order coefficients after expansion to obtain the recursive formula of the k-order power distribution matrix and the power flow tracking matrix, that is, the high-order power distribution matrix and the power flow tracking matrix, and solve the high-order power distribution matrix coefficient according to the power series expansion formula; In this embodiment, this step is specifically: Calculate the high-order line active power increment: solve the k-order distribution coefficient matrix coefficient D[0], according to the physical meaning, first solve the k-order power flow direction matrix , the line power increment and the node outflow power , replace , , in the zero-order power distribution matrix formula with the power series expansion of the corresponding variables , , , equalize the k-order coefficients after expansion to obtain the recursive formula of the k-order incremental power distribution matrix, and the specific expansion formula is as follows:

[0042]

[0043]

[0044] wherein, represents the k-th order active power increment vector; represents the k-th order line head voltage.

[0045] Calculate the high-order power distribution matrix coefficient : According to the physical meaning, it is necessary to solve first-order power flow direction matrix , line power and node outflow power . It should be noted that when the k-th order recursion is solved, the increment influence is calculated, and the above matrices need to be adjusted to the increment form. At the same time, due to the limitation of , the meaning of and the inverse of the simple k-th order are not consistent. The specific calculation formula is as follows:

[0046]

[0047]

[0048]

[0049] Calculate the high-order active tracking matrix :

[0050] In the formula, k is the order, and m is the intermediate variable of the order.

[0051] High-order power flow tracking matrix , corresponding to the embedded factor k order power increment influence, the core method is to use low-order coefficients to derive through recursive formula.

[0052] The power series function of the active power injection of the generator is brought into the zero-order indirect total carbon emission between nodes, and after expansion, the same power series coefficients are taken to obtain the k-order indirect carbon emission increment between nodes. Then, the k-order indirect carbon emission increment between nodes is substituted into the power series of the indirect carbon emission between nodes, and the indirect total carbon emission between nodes can be obtained.

[0053] In this embodiment, this step is specifically: Based on the total active tracking matrix and the carbon emission intensity of the power supply, the node-level carbon flow density quantification is realized, the core logic is "coupling the power distribution ratio with the carbon emission intensity of the power supply, quantifying the carbon emission contribution of each power supply to the node", the power injection power series function of the generator is brought into the zero-order node indirect total carbon emission formula, and after the same power series coefficient is obtained, the k-order node indirect carbon emission increment recursive formula can be obtained, and then the k-order node indirect carbon emission increment is substituted into the node indirect carbon emission power series, the value of s is between [0, 1], that is, the node indirect total carbon emission under the corresponding embedding factor condition can be obtained, and the specific calculation formula is as follows:

[0054] In the formula, is the active power injected by the zero-order generator, is the active power injected by the first-order generator.

[0055] As a preferred embodiment of the present embodiment, based on the analytic continuation characteristics of the full pure embedding, the analytic power series step of the complex embedding parameter s is specifically: based on the inverse matrix of the node admittance matrix, the analytic power series expansion of the complex embedding parameter s is carried out.

[0056] As a preferred embodiment of the present embodiment, the zero-order tracking matrix includes the outflow association matrix , the inflow association matrix and the voltage difference matrix A, and the following is predefined: The outflow association matrix : if the line flows out of the node i, , otherwise 0; The inflow association matrix : if the line flows into the node i, , otherwise 0; As a preferred embodiment of the present embodiment, when the power grid topology changes, the outflow association matrix A + and the inflow association matrix A - are automatically updated, and all steps are re-executed.

[0057] As a preferred embodiment of the present embodiment, the calculation formula of the high-order power distribution matrix is specifically:

[0058] In the formula, k is the order, and m is the intermediate variable of the order; is the m-order active power increment vector; the superscript inv represents the associated variable after taking the inverse of the original variable; is the node outflow power between the m-order and the k-order.

[0059] As a preferred embodiment of the present embodiment, the convergence of the high-order power flow tracking matrix is guaranteed by a spectral radius condition, specifically:

[0060] wherein, is the spectral radius of the high-order power distribution matrix , that is, the maximum modulus of the eigenvalues of the matrix.

[0061] As a preferred embodiment of the present embodiment, the convergence threshold of the convergence of the high-order power flow tracking matrix is preset as:

[0062] wherein, is the high-order power flow tracking matrix, is the zero-order power flow tracking matrix.

[0063] As a preferred embodiment of the present embodiment, the carbon emission intensity includes the carbon emission intensity of new energy power sources and the carbon emission intensity of traditional fossil energy power sources, wherein the carbon emission intensity of new energy power sources is 0, and the carbon emission intensity of traditional fossil energy power sources is determined according to the fuel type and the power generation efficiency thereof.

[0064] In the present embodiment, for example, the carbon emission intensity of a coal-fired unit is about 800 , and the carbon emission intensity of a wind power or photovoltaic power unit is 0.

[0065] The above only describes the embodiments of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation using the content of the present application specification and drawings, or direct or indirect application in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A high-order analytical power flow and carbon flow tracing method based on fully embedded systems, characterized in that, The specific steps include: introducing complex embedding parameters s; based on the analytical extension characteristics of fully embedded parameters, constructing the node voltage vector, injected power vector, and tracking matrix in the power flow equations as analytical power series of complex embedding parameters s; using the Newton-Raphson method to solve for the initial node voltage values ​​when the power grid is in basic operating condition; calculating the zero-order line active power vector based on the initial node voltage values ​​and constructing a zero-order allocation matrix characterizing the power distribution relationship under basic operating condition; solving for the zero-order power flow tracking matrix based on the zero-order line active power vector and the zero-order power allocation matrix; and calculating the total indirect carbon emissions between nodes based on the zero-order power flow tracking matrix. The power allocation matrix, node outflow power, and power flow direction matrix in the zero-order power allocation matrix are replaced with power series expansions of the corresponding variables. After expansion, the k-th order coefficients are equal to obtain the recursive expressions for the k-th order power allocation matrix and power flow tracking matrix, which are the higher-order power allocation matrix and power flow tracking matrix. The coefficients of the higher-order power allocation matrix are then solved according to the power series expansion. The power series function of generator active power injection is substituted into the zero-order node indirect total carbon emissions. After expansion, the k-th order node indirect carbon emission increment is obtained by taking the same power series coefficients. The node indirect total carbon emissions are then substituted into the node indirect carbon emission power series to obtain the node indirect total carbon emissions.

2. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 1, characterized in that, The specific steps for constructing the analytical power series of complex embedding parameters s based on the analytical extension property of fully pure embedding are as follows: performing an analytical power series expansion of complex embedding parameters s based on the inverse matrix of the node admittance matrix.

3. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 1, characterized in that, The zero-order tracking matrix includes the outflow correlation matrix. Inflow correlation matrix And the voltage difference matrix A, and predefined: Outflow correlation matrix If the line flows out from node i, Otherwise, it is 0; Inflow correlation matrix If the line flows into node i, Otherwise, it is 0.

4. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 3, characterized in that, When the power grid topology changes, the outflow correlation matrix A is automatically updated. + Inflow correlation matrix A - Then repeat all the steps.

5. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 1, characterized in that, The specific formula for calculating the higher-order power allocation matrix is ​​as follows: In the formula, k is the order, and m is an intermediate variable representing the order; This is the m-th order active power increment vector; the superscript inv indicates the related variable after inverting the original variable. This represents the outflow power of nodes between order m and order k.

6. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 5, characterized in that, The convergence of the high-order power flow tracking matrix is ​​guaranteed by the spectral radius condition, specifically: in, For higher-order power allocation matrix The spectral radius is the maximum modulus of the matrix eigenvalues.

7. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 6, characterized in that, The convergence threshold for the high-order power flow tracking matrix is ​​preset as follows: In the formula, For advanced trend tracking matrix, This is a zero-order power flow tracking matrix.

8. The high-order analytical power flow and carbon flow tracing method based on fully embedded systems according to claim 1, characterized in that, The carbon emission intensity includes the carbon emission intensity of new energy power sources and the carbon emission intensity of traditional fossil energy power sources. The carbon emission intensity of new energy power sources is 0, while the carbon emission intensity of traditional fossil energy power sources is determined based on their fuel type and power generation efficiency.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a high-order analytical power flow and carbon flow tracing method based on fully embedded systems as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements a high-order analytical power flow and carbon flow tracing method based on fully embedded systems as described in any one of claims 1 to 8.

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