HELM power flow calculation method considering static load characteristics

Abstract

This invention discloses a HELM (Heteromorphic Power Flow) method for calculating power flow in a distribution network considering the static characteristics of loads. The method first establishes a mathematical model of the distribution network including PQ nodes, then constructs holomorphic functions considering the static characteristics of loads using the HELM method, and finally derives the recursive formula for the holomorphic functions considering the static characteristics of loads to calculate the power flow considering these characteristics. This invention utilizes the HELM method to consider the static characteristics of nodal loads, derives the recursive formula for the holomorphic functions considering these characteristics, and can calculate power flow considering these characteristics. It can be used for power flow calculation and voltage analysis and control considering static load characteristics, offering simpler and faster calculation speeds and avoiding the convergence problem of ill-conditioned power flow.

Description

Technical Field

[0001] This invention belongs to the field of power information technology, and specifically relates to a HELM power flow calculation method that considers the static characteristics of loads. Background Technology

[0002] Currently, traditional power flow algorithms mainly include iterative methods such as Newton's iteration method, forward-backward substitution, PQ decomposition, and Gauss-Seidel iteration. Newton's iteration method transforms the problem into a corresponding system of linear equations and then solves it iteratively. This method is widely used in power system power flow calculations, and its convergence speed is not highly dependent on the structural scale of the power system and has a relatively fast convergence rate. However, Newton's iteration method is highly dependent on the initial values, and its convergence speed is closely related to the selection of the initial values. It is also relatively complex to program, and may fail to converge when encountering ill-conditioned networks. Forward-backward substitution is widely used in distribution networks. Although it does not require solving the Jacobian matrix during the calculation process, it requires hierarchical numbering of nodes and branches, resulting in complex calculation processes and low program efficiency. It is also difficult to handle ring networks. PQ decomposition significantly improves the solution speed by decomposing the coefficient matrix into two sub-matrices and replacing the coefficient matrix that changes during iteration with constants. This avoids recalculating the coefficient matrix after each iteration, thus greatly improving efficiency. [4] Therefore, the PQ decomposition method is highly efficient and relatively simple to program, making it widely used in power systems. However, it can also fail to converge when encountering ill-conditioned networks. The Gauss-Seidel iterative method has a simple and easy-to-understand computational principle, but it is not easy to converge during the computation process, especially in complex large-scale power grids. The increased number of nodes leads to a higher number of iterations, resulting in a significant increase in computational load and a decrease in efficiency. Furthermore, it is even more difficult to converge in ill-conditioned networks.

[0003] The active and reactive power absorbed by a power system load generally changes with variations in its terminal voltage; this is known as the load's static characteristic. To ensure that power flow calculations accurately reflect the actual system conditions, the static characteristics of nodal loads should generally be considered. Traditional power flow calculation methods require corrections to the Jacobian matrix when considering load static characteristics.

[0004] In the past two years, a power flow calculation method based on Holomorphic embedding load flow method (HELM) has been proposed. This method completely overturns the traditional Newton-Lambert method, is non-iterative, and does not rely on node initial values ​​to determine whether a power flow solution exists. This method can completely change traditional problems in power system power flow calculation, reactive power optimization, and voltage stability analysis. Currently, HELM can solve power flow including PQ and PV nodes, but how to use HELM to calculate power flow considering static load characteristics is still lacking in the literature. Summary of the Invention

[0005] To address the shortcomings of existing HELM power flow calculation techniques, this invention proposes a HELM power flow calculation method that considers the static characteristics of loads. This method can be used for power flow calculations that take into account the static characteristics of loads. It is fast, simple to calculate, and does not have iterative convergence problems, thus having high theoretical significance and application value.

[0006] The specific technical solution of this invention is as follows:

[0007] A method for calculating the HELM power flow of a power grid considering the static characteristics of the load includes the following steps:

[0008] Step 1: Establish a mathematical model of the power grid, including the static characteristics of the load.

[0009] The static characteristics of nodal loads can be expressed using a polynomial:

[0010]

[0011] In the formula These represent the voltages at node i as V. i0 The set of active and reactive power values ​​at the nodes at that time; the set of points Let a1, b1, and c1 represent the injected active power and injected reactive power of node i, respectively; a1, b1, and c1 are the constant power load factor, constant current load factor, and constant impedance load factor of the active power of node i, respectively; and a2, b2, and c2 are the constant power load factor, constant current load factor, and constant impedance load factor of the reactive power of node i, respectively, where a1+b1+c1=1 and a2+b2+c2=1.

[0012] Converted to per-unit form, it can be simplified to:

[0013]

[0014] Step 2: Construct the embedded pure virtual function model of the PQ node using the HELM method:

[0015]

[0016] In the formula, m is the set of PQ nodes, and i and k are node numbers; V i V k The voltages at nodes i and k are respectively; Y ik S is the admittance between node i and node k; i Let N be the injected power at node i; N is the total number of nodes; the superscript * indicates a conjugate relationship.

[0017] Construct an inline pure virtual function:

[0018]

[0019] In the formula, s is the embedded parameter factor; V i (s) represents the s-series expansion of node i; n is the order of the s-series; V i [n] represents the coefficients of the nth-order term of the s-series voltage at node i. n Let n represent the nth term of the frequency domain operator s;

[0020] If the node is a PQ node, substituting into equation (5) yields:

[0021]

[0022] In the formula: S i Injected active power for node i. Y ii Y represents the self-admittance of node i in the node admittance matrix; ik Y represents the mutual admittance between nodes i and k in the nodal admittance matrix; i，shunt Let i be the ground admittance of node i.

[0023] Substituting equation (1) into equation (5), we can obtain the following: assuming Y in the distribution network i，shunt =0:

[0024]

[0025] In the formula: A1 = a1 - ja2; B1 = b1 - jb2; C1 = c1 - jc2

[0026] Assumption:

[0027]

[0028]

[0029] Based on the fact that the coefficients of the S-series are equal, we can obtain:

[0030] d k [0] = 1 / V k [0] (9)

[0031]

[0032]

[0033] If the node is a PQ node, substituting equation (9) into equation (6) yields:

[0034]

[0035] When s = 0, we can obtain from equation (12):

[0036]

[0037] When s = 1, we can obtain from equation (12):

[0038]

[0039] When s = n, we can obtain from equation (12):

[0040]

[0041] Step 3: Recursively calculate the power flow based on the constructed holomorphic function power flow calculation model;

[0042] 1) First, calculate V according to equation (13). k [0], d is obtained according to equation (9). k [0];

[0043] 2) When s = 1, calculate V according to (14). k [1] d is obtained according to equation (10). k [1];

[0044] 3) When s = n, calculate V according to equation (15). k [n], d is obtained according to equation (11) k [n];

[0045] 4) As n gradually increases, repeat step 2) to successively calculate all V. k [n]、d k [n].

[0046] Therefore, we can obtain:

[0047]

[0048] When s = 1, the solution for the power flow can be obtained.

[0049] The present invention has the following advantages: it can be used for power flow calculation, voltage sensitivity calculation, voltage stability analysis and voltage control of power grids that consider the static characteristics of loads, and the calculation speed is simpler and faster, avoiding the problem of ill-conditioned power flow convergence. Attached Figure Description

[0050] Figure 1 A mathematical model of a 33-node power grid is established for the original data in a specific application example.

[0051] Figure 2 A schematic diagram of the Newton-Raphson power flow results considering the static characteristics of the load.

[0052] Figure 3 A schematic diagram of power flow results using the HELM method, taking into account the static characteristics of the load.

[0053] Figure 4 A schematic diagram showing the error values ​​of power flow results from the HELM method and the Newton method, taking into account the static characteristics of the load. Detailed Implementation

[0054] This invention provides a HELM power flow calculation method considering the static characteristics of nodal loads, comprising the following steps:

[0055] Step 1, according to Figure 1 The original data is used to establish a mathematical model of the power grid, as shown in Equation (1). The original data is shown in Table 1. In this power grid, one node is the slack node, and the other nodes are PQ nodes.

[0056]

[0057] In the formula, m is the set of PQ nodes, and i and k are node numbers; V i V k The voltages at nodes i and k are respectively; Y ik S is the admittance between node i and node k; i Let N be the injected power at node i; N is the total number of nodes; the superscript * indicates a conjugate relationship.

[0058] The static characteristics of nodal loads can be expressed using a polynomial:

[0059]

[0060] In the formula These represent the voltages at node i as V. i0 The set of active and reactive power values ​​at the nodes at that time; the set of points Let a1, b1, and c1 represent the injected active power and injected reactive power of node i, respectively; a1, b1, and c1 are the constant power load factor, constant current load factor, and constant impedance load factor of the active power of node i, respectively; and a2, b2, and c2 are the constant power load factor, constant current load factor, and constant impedance load factor of the reactive power of node i, respectively, where a1+b1+c1=1 and a2+b2+c2=1.

[0061] Converted to per-unit form, it can be simplified to:

[0062]

[0063] Step 2: Construct a holomorphic function mathematical model using the HELM method.

[0064]

[0065] In the formula, m is the set of PQ nodes, and i and k are node numbers; V i V k The voltages at nodes i and k are respectively; Y ik S is the admittance between node i and node k; i Let N be the injected power at node i; N is the total number of nodes; the superscript * indicates a conjugate relationship.

[0066] Construct an inline pure virtual function:

[0067]

[0068] In the formula, s is the embedded parameter factor; V i (s) represents the s-series expansion of node i; n is the order of the s-series; V i [n] represents the coefficients of the nth-order term of the s-series voltage at node i. n Let n represent the nth term of the frequency domain operator s;

[0069] If the node is a PQ node, substituting into equation (5) yields:

[0070]

[0071] In the formula: S i Injected active power for node i. Y ii Y represents the self-admittance of node i in the node admittance matrix; ik Y represents the mutual admittance between nodes i and k in the nodal admittance matrix; i，shunt Let i be the ground admittance of node i.

[0072] Substituting equation (2) into equation (5), we can obtain the following: assuming Y in the distribution network i，shunt =0:

[0073]

[0074] In the formula: A1 = a1 - ja2; B1 = b1 - jb2; C1 = c1 - jc2

[0075] Assumption:

[0076]

[0077]

[0078] Based on the fact that the coefficients of the S-series are equal, we can obtain:

[0079] d k [0] = 1 / V k [0] (9)

[0080]

[0081]

[0082] If the node is a PQ node, substituting equation (9) into equation (6) yields:

[0083]

[0084] When s = 0, we can obtain from equation (12):

[0085]

[0086] When s = 1, we can obtain from equation (12):

[0087]

[0088] When s = n, we can obtain from equation (12):

[0089]

[0090] Step 3: Calculate the power flow recursively based on the constructed holomorphic function power flow calculation model.

[0091] 1) First, calculate V according to equation (13). k [0], d is obtained according to equation (9). k [0];

[0092] 2) When s = 1, calculate V according to (14). k [1] d is obtained according to equation (10). k [1];

[0093] 3) When s=n, calculate V according to equation (15). k [n], d is obtained according to equation (11) k[n];

[0094] 4) As n gradually increases, repeat step 2) to successively calculate all V. k [n]、d k [n].

[0095] Therefore, we can obtain:

[0096]

[0097] When s = 1, the solution for the power flow can be obtained.

[0098] The power flow is recursively calculated based on the constructed holomorphic function power flow calculation model. The Newton-Layer method power flow results considering the static characteristics of the load are as follows: Figure 2 As shown, the power flow results of the HELM method considering the static characteristics of the load are as follows: Figure 3 As shown. The scaling factors of the ZIP load model used in this invention are as follows: constant power load (Z∶I∶P=0∶0∶1); constant current load (Z∶I∶P=0∶1∶0); constant impedance load (Z∶I∶P=1∶0∶0); combination one (Z∶I∶P=0.1∶0.2∶0.7); combination two (Z∶I∶P=0.2∶0.7∶0.1); combination three (Z∶I∶P=0.7∶0.1∶0.2).

[0099] Figure 4 The error values ​​of the HELM power flow calculation and the Newton-Lager method power flow calculation, which take into account the static characteristics of the load, show that the error values ​​of the two methods are very small, indicating that the method of calculating the power flow of the power grid considering the static characteristics of the load using the HELM method in the embodiment of the present invention is correct and feasible.

[0100] Table 1 Standard Data for 33-Node Power Grid Systems

[0101]

[0102]

Claims

1. A method for calculating the HELM power flow of a power grid considering the static characteristics of the load, characterized in that, Includes the following steps: Step 1: Establish a mathematical model of the power grid, including the static characteristics of the load. The static characteristics of nodal loads are expressed using a polynomial: In the formula These represent the voltages at node i as V. i0 The set of active and reactive power values ​​at the nodes at that time; the set of points Let a1, b1, and c1 represent the injected active power and injected reactive power of node i, respectively; a1, b1, and c1 are the constant power load factor, constant current load factor, and constant impedance load factor of the active power of node i, respectively; and a2, b2, and c2 are the constant power load factor, constant current load factor, and constant impedance load factor of the reactive power of node i, respectively, where a1+b1+c1=1 and a2+b2+c2=1. Converted to per-unit form, it can be simplified to: Step 2: Construct the embedded pure virtual function model of the PQ node using the HELM method: In the formula, m is the set of PQ nodes, and i and k are node numbers; V i V k The voltages at nodes i and k are respectively; Y ik S is the admittance between node i and node k; i Let N be the injected power at node i; N is the total number of nodes; the superscript * indicates a conjugate relationship. Construct an inline pure virtual function: In the formula, s is the embedded parameter factor; V i (s) represents the s-series expansion of node i; n is the order of the s-series; V i [n] represents the coefficients of the nth-order term of the s-series voltage at node i; s n Let n represent the nth term of the frequency domain operator s; If the node is a PQ node, substituting into equation (3) yields: In the formula: S i Injected active power for node i. Y ii Y represents the self-admittance of node i in the node admittance matrix; ik Y represents the mutual admittance between nodes i and k in the nodal admittance matrix; i,shunt Let i be the ground admittance of node i; Substituting equation (2) into equation (5), we can obtain the following: assuming Y in the distribution network i,shunt =0: In the formula: A1 = a1 - ja2; B1 = b1 - jb2; C1 = c1 - jc2 Assumption: Based on the fact that the coefficients of the S-series are equal, we get: d k [0]=1 / V k [0] (9) If the node is a PQ node, substituting equations (4) and (7) into equation (6) yields: When s = 0, we get from equation (12): When s = 1, we can obtain from equation (12): When s = n, we can obtain from equation (12): Step 3: Recursively calculate the power flow based on the constructed holomorphic function power flow calculation model; 1) First, calculate V according to equation (13). k [0], d is obtained according to equation (9). k [0]; 2) When s = 1, calculate V according to (14). k [1] d is obtained according to equation (10). k [1]; 3) When s = n, calculate V according to equation (15). k [n], d is obtained according to equation (11) k [n]; 4) As n gradually increases, repeat step 2) to successively calculate all V. k [n]、d k [n]; Therefore, we can obtain: When s = 1, the solution for the power flow can be obtained.

Images