Middle and low voltage distribution network three-phase load flow calculation method considering line reactance change

Abstract

The invention discloses a medium and low voltage distribution network three-phase load flow calculation method considering line reactance change. The method comprises the following steps: step 1, acquiring topological information of a medium voltage distribution network; 2, performing three-phase unbalanced load flow calculation on each low-voltage power distribution network to obtain three-phase power and three-phase current on the low-voltage side of a boundary node, and transmitting the three-phase power and the three-phase current to the medium-voltage power distribution network; step 3, carrying out reactance adjustment calculation on a three-phase line of the medium-voltage power distribution network; 4, performing single-phase load flow calculation on three phases of the medium-voltage power distribution network to obtain three-phase voltage of a medium-voltage side of each boundary node, and transmitting the three-phase voltage to each low-voltage power distribution network; and 5, three-phase unbalanced load flow calculation is carried out again until the voltages and the powers of all boundary nodes are converged to be smaller than a given precision threshold value. According to the method, the influence of three-phase unbalanced operation of the low-voltage power distribution network on the medium-voltage power distribution network can be fully reflected, high-dimensional three-phase modeling calculation of the medium-voltage power distribution network is reduced into split-phase single-phase modeling calculation, and the calculation precision and efficiency are improved.

Description

Technical Field

[0001] This invention relates to the field of power technology, specifically to a method for calculating three-phase power flow in medium- and low-voltage distribution networks that considers changes in line reactance. Background Technology

[0002] Power flow calculation is a fundamental function of distribution network energy management systems for advanced applications such as analysis, prediction, simulation, and control, and its role is extremely important. In my country's power network hierarchy, medium-voltage distribution networks typically refer to distribution networks with rated voltage levels of 10kV to 35kV, which usually serve as an important intermediate link connecting high-voltage grids and low-voltage user sides; low-voltage distribution networks typically refer to distribution networks with rated voltage levels of 1kV and below (commonly 380 / 220V), which are mainly used to provide power to end-user urban users.

[0003] Currently, for the problem of power flow calculation in medium and low voltage distribution networks, there are two main methods for modeling low voltage distribution networks:

[0004] (1) The three-phase unbalanced operation caused by load imbalance in the low-voltage distribution network is not considered, and the single-phase modeling method is directly adopted. In this method, both the medium-voltage distribution network and the low-voltage distribution network adopt single-phase modeling and assume three-phase balanced operation. The solution is obtained by alternating iterative solution between the medium-voltage and low-voltage distribution networks.

[0005] (2) Considering the three-phase unbalanced operation caused by load imbalance in low-voltage distribution networks, both medium-voltage and low-voltage distribution networks adopt a three-phase modeling approach, establishing power balance equations for each node according to phase. This approach is more accurate and the results are more consistent with the actual operation of distribution networks. However, because it requires simultaneous modeling of the three phases, the scale of the power flow equations for large-scale medium- and low-voltage distribution networks is very large, making the solution complex.

[0006] While the aforementioned existing technical methods can all be applied to power flow calculations in medium and low voltage distribution networks, they still have the following shortcomings:

[0007] (1) If the three-phase unbalanced operation is not considered, and only a simple single-phase model is performed on the low-voltage distribution network, when faced with the current situation that there are a large number of unbalanced loads such as single-phase photovoltaic and single-phase electric vehicle charging piles in the urban low-voltage distribution network, the power flow calculation results of the medium and low voltage distribution network cannot accurately reflect the actual voltage and power distribution.

[0008] (2) If the three-phase unbalanced operation is considered, three-phase modeling is used for both medium-voltage and low-voltage distribution networks. Although the three-phase power flow distribution can be accurately calculated, the scale of variables and the number of equations to be solved are about three times that of the single-phase modeling method because the three-phase power flow models of medium-voltage and low-voltage distribution networks need to be constructed and solved separately. Each iteration of the solution requires processing a large-scale sparse matrix, which consumes a lot of computational resources. When applied to actual large-scale medium- and low-voltage distribution networks, the computational efficiency is very low and the power flow calculation may even fail to converge. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the three-phase power flow of medium and low voltage distribution networks that takes into account changes in line reactance, so as to improve calculation efficiency while ensuring accuracy.

[0010] To achieve the above objectives, the technical solution of the present invention is as follows:

[0011] A method for calculating three-phase power flow in medium- and low-voltage distribution networks considering changes in line reactance includes:

[0012] Step 1: Perform path identification on the low-voltage connection nodes in the medium-voltage distribution network to obtain the topology information of the medium-voltage distribution network;

[0013] Step 2: Perform three-phase unbalanced power flow calculations on each low-voltage distribution network based on the boundary node voltage to obtain the three-phase power and three-phase current on the low-voltage side of the boundary node, and then transfer them to the medium-voltage distribution network.

[0014] Step 3: Based on the medium-voltage distribution network topology information and the three-phase current on the low-voltage side of the boundary node, perform reactance adjustment calculations on the three-phase lines of the medium-voltage distribution network to obtain the adjusted three-phase impedance;

[0015] Step 4: Based on the adjusted three-phase impedance and the three-phase power on the low-voltage side of the boundary node, perform single-phase power flow calculations on the three phases of the medium-voltage distribution network to obtain the three-phase voltage on the medium-voltage side of each boundary node, and transmit it to each low-voltage distribution network.

[0016] Step 5: Recalculate the three-phase unbalanced power flow, iterating alternately until the voltage and power of all boundary nodes converge to less than the given accuracy threshold.

[0017] Optionally, the reactance adjustment calculation for the three-phase lines of the medium-voltage distribution network includes:

[0018] Calculation of line reactance adjustment based on the degree of imbalance in three-phase circuits and calculation of reactance adjustment for medium-voltage distribution lines with multi-node unbalanced current access.

[0019] Optionally, the line reactance adjustment calculation based on the degree of three-phase circuit imbalance includes:

[0020] Assume a three-phase power distribution line of length l is arranged symmetrically in an equilateral triangle, with each phase conductor having a radius of r and a distance D between conductor axes; under the action of a three-phase symmetrical sinusoidal alternating current in the line, the magnetic flux linkage intersecting with phase a conductor is:

[0021] (1)

[0022] In the formula, L and M are the self-inductance and mutual inductance per unit length of the line, respectively; i a i b and i c These are the three-phase currents, a, b, and c, respectively. Permeability of free space; denoted as the geometric mean distance between cylindrical conductors; D is the phase-to-phase distance between conductors.

[0023] When three-phase balanced current flows through the line Equation (1) simplifies to:

[0024] (2)

[0025] The equivalent inductance of phase a is:

[0026] (3)

[0027] Since the three-phase conductors are arranged symmetrically, the inductance calculation process for phases b and c is the same as that for phase a;

[0028] When a three-phase unbalanced current flows through the line, let Then equation (1) becomes:

[0029] (4)

[0030] Simplifying this expression, we get:

[0031] (5)

[0032] In the case of three-phase imbalance, the expression for the equivalent inductance of phase a is modified as follows:

[0033] (6)

[0034] Equal inductance for phases b and c and The calculation is similar; we only need to introduce s respectively. b and s c This can be used to represent the imbalance effect produced by the corresponding phase, that is:

[0035] (7)

[0036] (8).

[0037] Optionally, the calculation of reactance adjustment for the multi-node unbalanced current access medium-voltage distribution line includes:

[0038] (9)

[0039] (10)

[0040] (11)

[0041] in, Let be the current at node l of phase a. Let m be the current at node m of phase a. Let be the current at the l-phase node. Let m be the current at node m of phase b. Let L be the current at node l of phase c. Let be the current at node m of phase c.

[0042] Optionally, step 5 includes:

[0043] Calculate the three-phase voltage and power deviations at the boundary nodes after the k-th iteration. If the absolute value of each deviation is not greater than the given convergence deviation threshold, the convergence condition is met and the calculation ends, outputting the power flow calculation results for the entire medium- and low-voltage distribution network. Otherwise, let the iteration number k ← k+1, and repeat steps 2 to 4 until the convergence condition is met or the maximum iteration number k is reached. max .

[0044] Optionally, for the k-th iteration, the maximum voltage deviation and maximum power deviation of the boundary nodes are calculated as shown in equations (12) and (13), respectively.

[0045] (12)

[0046] (13)

[0047] Among them, the number of iterations ; For the set of boundary nodes; for the set of three phases ;

[0048] During the iterative solution process, the iterative process is considered to have converged and the calculation is terminated if and only if equations (14) and (15) are satisfied simultaneously, where the required deviation threshold is... and Configure according to actual calculation needs;

[0049] (14)

[0050] (15)

[0051] Compared with the prior art, the advantages of this invention are as follows:

[0052] 1) A method for adjusting the equivalent reactance of lines based on the degree of three-phase current imbalance in low-voltage distribution networks is designed. This method adjusts the reactance of each phase of each line by considering the three-phase currents at each low-voltage distribution network boundary node and the network topology of the medium-voltage distribution network. This aims to comprehensively characterize the impact of three-phase imbalance operation of the low-voltage distribution network on its voltage and power distribution within the framework of single-phase power flow modeling for medium-voltage distribution networks. Furthermore, this method can accurately analyze the impact of connecting a large number of single-phase photovoltaic systems and single-phase electric vehicle charging piles to the low-voltage distribution network.

[0053] (2) Three-phase decoupled single-phase power flow modeling of medium-voltage distribution network is performed, which reduces the scale of variables and equations in each calculation to only 1 / 3 of that of traditional three-phase power flow modeling method, significantly reducing the complexity of solving power flow equations and greatly improving computational efficiency.

[0054] (3) An alternating iterative update mechanism for boundary node variables between medium-voltage and low-voltage distribution networks was designed. By iteratively calculating and updating the three-phase voltage and power of the boundary nodes and converging to a value less than the given voltage and power deviation threshold of the boundary nodes, the power flow calculation results of medium-voltage and low-voltage distribution networks were fully matched, and the consistency of the power flow calculation results of the entire medium- and low-voltage distribution network was achieved. Attached Figure Description

[0055] Figure 1 The main flowchart of the three-phase power flow calculation method for medium and low voltage distribution networks considering changes in line reactance provided in the embodiments of this application;

[0056] Figure 2 This diagram illustrates the impact of unbalanced current at each node when multiple nodes are connected.

[0057] Figure 3 A schematic diagram illustrating the transfer of boundary variables between medium-voltage and low-voltage distribution networks;

[0058] Figure 4 Wiring diagram for a 10kV medium-voltage distribution network;

[0059] Figure 5 Wiring diagram for a 380V low-voltage distribution network;

[0060] Figure 6 This refers to the iterative process of a medium- and low-voltage combined power distribution network system. Detailed Implementation

[0061] Example:

[0062] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0063] See Figure 1 As shown in the figure, the three-phase power flow calculation method for medium and low voltage distribution networks considering line reactance variations provided in this embodiment mainly includes the following steps:

[0064] Step 1: Perform path identification on the low-voltage connection nodes in the medium-voltage distribution network, find their upstream lines, and obtain the topology information of the medium-voltage distribution network to prepare for the subsequent reactance adjustment calculation of the three-phase lines of the medium-voltage distribution network.

[0065] In practice, this step also includes inputting known quantities, including the three-phase voltage and phase angle at the equilibrium node, the convergence deviation threshold, and the maximum number of convergence attempts k. max Initialize all unknowns, including the three-phase voltage magnitude and phase angle at each node, and set the initial voltage at the boundary nodes. and initial power , Let the number of iterations be k=1.

[0066] Step 2: Based on the boundary node voltage Three-phase unbalanced power flow calculations were performed on each low-voltage distribution network to obtain the three-phase power on the low-voltage side of the boundary nodes. , and three-phase current And transmit it to the medium-voltage distribution network;

[0067] Step 3: Based on the medium-voltage distribution network topology information and the three-phase current on the low-voltage side of the boundary nodes... The reactance adjustment calculation of the three-phase lines of the medium-voltage distribution network is performed to obtain the adjusted three-phase impedance;

[0068] Step 4: Based on the adjusted three-phase impedance and the three-phase power on the low-voltage side of the boundary node... , Single-phase power flow calculations were performed on each of the three phases of the medium-voltage distribution network to obtain the three-phase voltages on the medium-voltage side of each boundary node. And transmit it to each low-voltage distribution network;

[0069] Step 5: Recalculate the three-phase unbalanced power flow, iterating alternately until the voltage and power of all boundary nodes converge to less than the given accuracy threshold.

[0070] Therefore, this method adjusts the phase reactance of each line based on the three-phase currents at each low-voltage distribution network boundary node and the network topology of the medium-voltage distribution network. This allows for a complete characterization of the impact of three-phase unbalanced operation of the low-voltage distribution network on its voltage and power distribution within the framework of single-phase power flow modeling for the medium-voltage distribution network. Furthermore, this method can accurately analyze the impact of numerous single-phase photovoltaic systems and single-phase electric vehicle charging piles connected to the low-voltage distribution network. This method effectively reflects the impact of three-phase unbalanced operation of the low-voltage distribution network on the medium-voltage distribution network, while reducing the high-dimensional three-phase modeling calculation of the medium-voltage distribution network to phase-by-phase single-phase modeling calculation, thus improving computational accuracy and efficiency.

[0071] In one specific embodiment, the reactance adjustment calculation of the three-phase lines of the medium-voltage distribution network includes the line reactance adjustment calculation based on the degree of three-phase current imbalance and the reactance adjustment calculation of medium-voltage distribution lines under the condition of multi-node unbalanced current access.

[0072] The line reactance adjustment calculation based on the degree of three-phase current imbalance includes:

[0073] Assume a three-phase power distribution line of length l is arranged symmetrically in an equilateral triangle, and the radius of each phase conductor is r. The distance between the conductor axes is D. Under the action of a three-phase symmetrical sinusoidal alternating current in the line, the magnetic flux linkage intersecting with the a-phase conductor is:

[0074] (1)

[0075] In the formula, L and M represent the self-inductance and mutual inductance per unit length of the line, respectively; the derivation of the formula is omitted here. a i b and i c Let a, b, and c be the three-phase currents, respectively. The currents here can be instantaneous values ​​or phasors. The following derivations will all use instantaneous values. The permeability of free space is usually taken as . H / m; denoted as the geometric mean distance between cylindrical conductors; D is the phase distance between conductors.

[0076] When three-phase balanced current flows through the line Equation (1) can be simplified to:

[0077] (2)

[0078] Therefore, the equivalent inductance of phase a is:

[0079] (3)

[0080] Since the three-phase conductors are arranged symmetrically, the inductance calculation process for phases b and c is the same as that for phase a.

[0081] However, when a three-phase unbalanced current flows through the line, it is advisable to assume... Then equation (1) becomes:

[0082] (4)

[0083] Further simplification of the expression yields:

[0084] (5)

[0085] Therefore, in the case of three-phase imbalance, the expression for the equivalent inductance of phase a is modified as follows:

[0086] (6)

[0087] The calculation of the equivalent inductances of phases b and c is similar; it only requires introducing s respectively. b and s c This can be used to represent the imbalance effect produced by the corresponding phase, that is:

[0088] (7)

[0089] (8)

[0090] After this operation, the degree of influence of three-phase unbalanced operation on the inductance of each phase can be separately determined by s. a s b and s c This is reflected in and affects the network node admittance matrix of the system; it can be seen that s a s b and s c All are dimensionless values, and their magnitude depends on the ratio of the three-phase unbalanced current to the current of each phase. In actual power flow calculations, variables are all represented by phasors. The phase of the three-phase unbalanced current phasor and the phase of the current phasor of each phase is not necessarily the same. In this case, it can be approximated by using the ratio of the magnitude of the three-phase unbalanced current to the magnitude of the current of each phase. In addition, another advantage of this approach is that the inductance calculated by equation (6) is the equivalent inductance of a certain phase under the condition of three-phase unbalanced operation. In the corresponding medium-voltage distribution network power flow calculation, only the single-phase power flow calculation of that phase is needed to reflect the power flow distribution of that phase under the condition of three-phase unbalanced operation, without the need for complex three-phase modeling.

[0091] The calculation for reactance adjustment of multi-node unbalanced current connected to medium-voltage distribution lines includes:

[0092] In practical low-voltage distribution networks, each 10kV medium-voltage distribution feeder often has multiple nodes connected to a three-phase unbalanced low-voltage distribution network. In this case, the reactance adjustment method proposed in the previous section needs to be further extended and applied to this situation. For example... Figure 2 The diagram shows a typical trunk-type medium-voltage distribution feeder, where node p is the balancing node (i.e., the low-voltage side node of a 110kV substation). A feeder (including nodes i~m) originates from p, and low-voltage distribution networks (with three-phase unbalanced operation) are connected at nodes k, l, and m. It can be seen that the current i flowing into the low-voltage distribution network at node k... k The path is its upstream path from p to k, and the current i flowing into the low-voltage distribution network at node l is... l The path is its upstream path p to l, and the current i flowing into the low-voltage distribution network at node m. m The path is its upstream path p to m. Therefore, lines ij and jk are simultaneously affected by the imbalance of the low-voltage distribution networks at nodes k, l, and m, while line kl is affected by the low-voltage distribution networks at nodes l and m, and line lm is only affected by the low-voltage distribution network at node m. Therefore, for line jk, if the reactance adjustment method from the previous section is used, the current flowing through its a-phase should be... This refers to the sum of the a-phase currents flowing into the low-voltage distribution network at nodes k, l, and m. The same applies to phases b and c. Similarly, for line kl, its a-phase current is... This refers to the sum of the phase a currents flowing into the low-voltage distribution networks at nodes l and m. In this case, the impact of unbalanced operation of the low-voltage distribution network connected to upstream node k is no longer necessary. Therefore, in general, under a trunk-type distribution feeder topology, if the reactance adjustment method described in the previous section is used, the unbalanced current at any connection point will affect the reactance of all lines in its upstream path; and any branch will be affected by the unbalanced currents at all its downstream connection points.

[0093] Taking line kl as an example, the equivalent inductance of phase a after modification is calculated as shown in equation (9), where s a The ratio of current modulus is used for approximate calculation. The values ​​of l and D can be obtained by querying actual power distribution feeder data. Similarly, equations (10)-(11) can also be used to obtain the equivalent inductance of phase b and phase c after modification, and then convert it into the reactance required for subsequent power flow calculation.

[0094] (9)

[0095] (10)

[0096] (11)

[0097] In one specific embodiment, the three-phase power flow calculation method for medium- and low-voltage distribution networks considering line reactance variations provided in this embodiment employs an alternating iterative approach between medium- and low-voltage distribution networks for solution, such as... Figure 3 As shown, by continuously transmitting boundary node variable information (voltage and power) between the medium-voltage and low-voltage distribution networks and performing local power flow calculations and correcting boundary node variables, a complete match is achieved between the power flow calculation results of the medium-voltage and low-voltage distribution networks, realizing consistency in the power flow calculation results of the entire medium- and low-voltage distribution network. Therefore, the iterative cycle described in step 5, until all boundary node voltages and powers converge to less than a given accuracy threshold, includes:

[0098] Calculate the three-phase voltage and power deviations at the boundary nodes after the k-th iteration. If the absolute value of each deviation is not greater than the given convergence deviation threshold, the convergence condition is met and the calculation ends, outputting the power flow calculation results for the entire medium- and low-voltage distribution network. Otherwise, let the iteration number k ← k+1, and repeat steps 2 to 4 until the convergence condition is met or the maximum iteration number k is reached. max .

[0099] For the k-th iteration, the maximum voltage deviation and maximum power deviation of the boundary nodes are calculated as shown in equations (12) and (13), respectively.

[0100] (12)

[0101] (13)

[0102] Among them, the number of iterations ; For the set of boundary nodes; for the set of three phases .

[0103] During the iterative solution process, the iterative process is considered to have converged and the calculation is terminated if and only if equations (14) and (15) are satisfied simultaneously, where the required deviation threshold is... and It can be set according to actual calculation needs.

[0104] (14)

[0105] (15)

[0106] The following example application scenario will be used to further verify and illustrate the three-phase power flow calculation method for medium and low voltage distribution networks that considers changes in line reactance provided in this embodiment:

[0107] The medium- and low-voltage distribution network example used consists of one 10kV medium-voltage distribution network and three 380V low-voltage distribution networks. Specific line and load parameters are derived from an actual urban distribution network and are not detailed here. The hardware environment of the test system for the example is an Intel(R) Core(TM) Ultra 7 265K CPU @3.90 GHz, 32GB of RAM, and a Win11 64-bit operating system. All relevant calculation programs are programmed in Python 3.12.

[0108] The 10kV medium-voltage distribution network comprises 256 nodes and 255 branches. The balancing node of this network is set as the 10kV side bus of the upstream 110kV substation, i.e., node 1. The three 380V low-voltage distribution networks are all 19-node systems with the same network structure, but the impedance of each branch and the load of each node are different. They are connected to the medium-voltage distribution network through nodes 35, 56 and 103, respectively. In the low-voltage distribution network, node 9 is connected to a single-phase electric vehicle charging pile and node 12 is connected to a single-phase photovoltaic power generation system to simulate the three-phase unbalanced operation. Figure 4 The diagram shows the wiring of the 10kV medium-voltage distribution network and the access nodes of the low-voltage distribution network. Figure 5 The diagram shows the wiring diagram for a 380V low-voltage distribution network.

[0109] The method proposed in this embodiment is used to perform three-phase unbalanced power flow calculations on the aforementioned medium- and low-voltage distribution network. The convergence deviation threshold for the boundary nodes of the medium- and low-voltage distribution network is set as follows: =10 -4 pu and =10 -3 kW / kVar, maximum number of iterations k max =20. The maximum deviation of the boundary nodes in the iterative process of power flow calculation for medium-voltage and low-voltage distribution networks varies with the number of iterations, as shown below. Figure 6 As shown, the vertical axis uses a logarithmic coordinate system. It can be seen that the system reached convergence after 4 iterations, with a total solution time of 7.22 seconds. This result demonstrates that the method proposed in this invention exhibits good convergence characteristics and high overall computational efficiency when applied to the calculation of three-phase unbalanced power flow in practical large-scale medium- and low-voltage distribution networks.

[0110] To compare the accuracy of the calculation results of the method proposed in this invention, the calculation results of the traditional simplified power flow calculation method are selected for comparison for the same example system. The traditional simplified power flow calculation method is as follows: first, a three-phase power flow calculation is performed on the low-voltage distribution network given the boundary node voltages; then, the boundary node power is directly transferred to the medium-voltage distribution network as a node load for single-phase power flow calculation of phases a, b, and c, thus obtaining the three-phase unbalanced power flow calculation results of the medium and low-voltage distribution networks. The traditional simplified power flow calculation method does not adjust the reactance of the medium-voltage distribution lines, nor does it iterate the boundary node voltages and power of the medium-voltage and low-voltage distribution networks until they converge. The following is a comparative analysis of the results of the two methods from the perspectives of boundary node power / voltage consistency, partial node voltages, and branch power.

[0111] (1) Power / voltage consistency at boundary nodes

[0112] Three boundary nodes (35 / 56 / 103) connected to a low-voltage distribution network in a medium-voltage distribution network were selected. Three-phase unbalanced power flow calculations were performed using both methods. Table 1 shows a comparison of the active power at the boundary nodes in the medium-voltage and low-voltage distribution networks obtained using the method proposed in this invention (since the traditional simplified power flow calculation method only involves one power transfer without an alternating iteration process, the power on both the medium-voltage and low-voltage sides is consistent, so it is not listed here). Table 2 shows a comparison of the voltage at the boundary nodes in the medium-voltage and low-voltage distribution networks obtained using the two methods. In Table 2, the left side of the " / " sign represents the calculation result of the method proposed in this invention, and the right side represents the calculation result of the traditional simplified power flow calculation method. It can be seen that the method proposed in this invention, through alternating iteration between the medium-voltage and low-voltage distribution networks, achieves consistency in the three-phase active power and voltage at the boundary nodes on both the medium-voltage and low-voltage sides, thus achieving consistency in the power flow calculation results across the entire network. In contrast, the traditional simplified power flow calculation method, due to the lack of alternating iteration and updating of boundary node information, results in significant voltage deviations on both the medium-voltage and low-voltage sides at the same boundary nodes, which is clearly inconsistent with actual power grid operation. In each iteration, the method of this invention transfers the three-phase power flow results of the low-voltage distribution network to the medium-voltage distribution network. Based on the three-phase current imbalance at the boundary nodes, the reactance of the medium-voltage distribution lines is adjusted phase-by-phase. Then, the boundary three-phase voltages from the phase-by-phase power flow calculations of the medium-voltage distribution network are transferred to the low-voltage distribution network. This process is repeated iteratively until the power and voltage deviations at the boundary nodes of the medium-voltage and low-voltage distribution networks meet the given convergence accuracy. The resulting final result not only achieves numerical consistency in power and voltage on both sides of the boundary nodes but also more realistically reflects the impact of the three-phase imbalance operation of the low-voltage distribution network on the power flow distribution of the medium-voltage distribution network.

[0113] Table 1. Results of active power at boundary nodes obtained using the method of this invention.

[0114] Table 2 Comparison of boundary node voltage magnitude results obtained by the two methods

[0115] (2) Partially representing node voltages

[0116] Three boundary nodes (35 / 56 / 103) and some upstream nodes of a medium-voltage distribution network connected to a low-voltage distribution network were selected as representative nodes. Three-phase unbalanced power flow calculations were performed using two different methods. The magnitude and average value of the three-phase voltages at the nodes obtained by the two methods were statistically analyzed, and the difference between the average values ​​obtained by the two methods was also compared. The calculation results are shown in Table 3, where V... av1 and V av2 ΔV represents the average value of the nodal three-phase voltage amplitude obtained by the method proposed in this invention and the traditional simplified power flow calculation method, respectively. av The difference in average values ​​obtained by the two methods is shown. It can be seen that, compared to the traditional simplified power flow calculation method, the proposed method, after considering phase reactance adjustment and performing boundary node information interaction iteration, results in an overall decrease in the average three-phase voltage of representative nodes of approximately 0.1% to 0.3% (≈0.001 pu~0.003 pu). This change roughly matches the voltage drop caused by the reactance adjustment increment. Simultaneously, due to the alternating iterative solution, the boundary node voltages are consistent between medium-voltage and low-voltage distribution networks. Therefore, it avoids the overestimation of node voltages caused by the traditional simplified power flow calculation method, which does not consider the impact of three-phase imbalance operation of the low-voltage distribution network on the line reactance of the medium-voltage distribution network, and is more consistent with the actual operation of the distribution network.

[0117] Table 3 Comparison of representative node voltage magnitudes obtained by the two methods

[0118] (3) Transmission power of some branches

[0119] Three upstream branches from three boundary nodes 35 / 56 / 103 connected to the low-voltage distribution network in a medium-voltage distribution network to the slack node 1 were selected as representative branches. Three-phase unbalanced power flow calculations were performed using two different methods. The comparison of the a-phase transmission power of the representative branches calculated by the two methods is shown in Table 4. It can be seen that the traditional simplified power flow calculation method results in zero-power branches downstream of the boundary nodes, and multiple adjacent branches in the upstream channel leading to the slack node exhibit almost identical active power (e.g., 0.0078 in the table). The method proposed in this invention, however, essentially eliminates these two phenomena. The power of each branch changes continuously with the extension of the branch, more closely resembling the actual operating state of the distribution network. Since most non-boundary nodes have virtually no load, the traditional simplified power flow calculation method results in no power outflow when passing through these nodes. The active power of multiple consecutive branches in the upstream channel from the boundary nodes to the slack node exhibits a nearly constant value, roughly the same as the equivalent load of the boundary nodes. The method proposed in this invention considers the three-phase unbalanced operation of the low-voltage distribution network. By acquiring the three-phase unbalanced current on the low-voltage side and identifying the upstream branches of the boundary nodes through path identification, the reactance of the entire upstream branch is adjusted and varied. This incorporates the additional power loss caused by the unbalanced current into the model, resulting in a continuously decreasing power distribution across the upstream segments, rather than the constant value found in traditional simplified power flow calculation methods. This result demonstrates that the method proposed in this invention can more realistically and accurately reflect the impact of three-phase unbalanced operation of the low-voltage distribution network on the power flow distribution of medium and low-voltage distribution networks.

[0120] Table 4 Comparison of Phase a Power of Representative Branches Calculated by the Two Methods

[0121] In summary, the three-phase power flow calculation method for medium and low voltage distribution networks that considers line reactance variations provided in this embodiment has the following advantages compared with existing technologies:

[0122] (1) A method for adjusting line reactance based on the degree of three-phase current imbalance is proposed and extended to the case where multiple nodes have unbalanced currents connected simultaneously, to reflect the impact of three-phase unbalanced operation on the line reactance of the medium-voltage distribution network. In the actual power flow calculation of medium and low-voltage distribution networks, based on the three-phase unbalanced currents of the boundary nodes obtained from the low-voltage distribution network solution and the connection method from the boundary nodes to the balance nodes in the medium-voltage distribution network, the equivalent reactance of the upstream branches is adjusted in three phases, and then single-phase power flow calculation is performed in three phases. This method can ensure that the impact of unbalanced operation of the low-voltage distribution network is considered while performing single-phase modeling and power flow calculation of the medium-voltage distribution network. It has both simplicity and accuracy and has high engineering applicability.

[0123] (2) Based on the line reactance adjustment method, a hierarchical collaborative power flow solution framework of "low-voltage three-phase unbalanced power flow modeling + medium-voltage three-phase single-phase power flow modeling" is further proposed. In the process of power flow calculation, the three-phase unbalanced modeling of the low-voltage distribution network is maintained, while the three-phase decoupling of the medium-voltage distribution network is performed. Based on the impedance and load data after phase adjustment, three single-phase power flow calculations are performed respectively. Finally, the calculations are performed by alternating between the medium-voltage and low-voltage distribution networks.

[0124] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating three-phase power flow in medium- and low-voltage distribution networks considering changes in line reactance, characterized in that, include: Step 1: Perform path identification on the low-voltage connection nodes in the medium-voltage distribution network to obtain the topology information of the medium-voltage distribution network; Step 2: Perform three-phase unbalanced power flow calculations on each low-voltage distribution network based on the boundary node voltage to obtain the three-phase power and three-phase current on the low-voltage side of the boundary node, and then transfer them to the medium-voltage distribution network. Step 3: Based on the medium-voltage distribution network topology information and the three-phase current on the low-voltage side of the boundary node, perform reactance adjustment calculations on the three-phase lines of the medium-voltage distribution network to obtain the adjusted three-phase impedance; Step 4: Based on the adjusted three-phase impedance and the three-phase power on the low-voltage side of the boundary node, perform single-phase power flow calculations on the three phases of the medium-voltage distribution network to obtain the three-phase voltage on the medium-voltage side of each boundary node, and transmit it to each low-voltage distribution network. Step 5: Recalculate the three-phase unbalanced power flow, iterating alternately until the voltage and power of all boundary nodes converge to less than the given accuracy threshold.

2. The method for calculating three-phase power flow in medium and low voltage distribution networks considering changes in line reactance as described in claim 1, characterized in that, The reactance adjustment calculation for the three-phase lines of the medium-voltage distribution network includes: Calculation of line reactance adjustment based on the degree of imbalance in three-phase circuits and calculation of reactance adjustment for medium-voltage distribution lines with multi-node unbalanced current access.

3. The method for calculating three-phase power flow in medium and low voltage distribution networks considering changes in line reactance as described in claim 2, characterized in that, The line reactance adjustment calculation based on the degree of three-phase circuit imbalance includes: Assume a three-phase power distribution line of length l is arranged symmetrically in an equilateral triangle, with each phase conductor having a radius of r and a distance D between conductor axes; under the action of a three-phase symmetrical sinusoidal alternating current in the line, the magnetic flux linkage intersecting with phase a conductor is: (1) In the formula, L and M are the self-inductance and mutual inductance per unit length of the line, respectively; i a i b and i c These are the three-phase currents, a, b, and c, respectively. Permeability of free space; is the geometric mean distance between cylindrical conductors; D is the phase distance between conductors; When three-phase balanced current flows through the line Equation (1) simplifies to: (2) The equivalent inductance of phase a is: (3) Since the three-phase conductors are arranged symmetrically, the inductance calculation process for phases b and c is the same as that for phase a; When a three-phase unbalanced current flows through the line, assume Then equation (1) becomes: (4) Simplifying this expression, we get: (5) In the case of three-phase imbalance, the expression for the equivalent inductance of phase a is modified as follows: (6) Equal inductance for phases b and c and The calculation is similar; we only need to introduce s respectively. b and s c This can be used to represent the imbalance effect produced by the corresponding phase, that is: (7) (8)。 4. The method for calculating three-phase power flow in medium and low voltage distribution networks considering changes in line reactance as described in claim 3, characterized in that, The calculation of reactance adjustment for multi-node unbalanced current access in medium-voltage distribution lines includes: (9) (10) (11) in, Let be the current at node l of phase a. Let m be the current at node m of phase a. Let be the current at the l-phase node. Let m be the current at node m of phase b. Let L be the current at node l of phase c. Let be the current at node m of phase c.

5. The method for calculating three-phase power flow in medium and low voltage distribution networks considering changes in line reactance as described in claim 1, characterized in that, Step 5 includes: Calculate the three-phase voltage and power deviations at the boundary nodes after the k-th iteration. If the absolute value of each deviation is not greater than the given convergence deviation threshold, the convergence condition is met and the calculation ends, outputting the power flow calculation results for the entire medium- and low-voltage distribution network. Otherwise, let the iteration number k ← k+1, and repeat steps 2 to 4 until the convergence condition is met or the maximum iteration number k is reached. max .

6. The method for calculating three-phase power flow in medium and low voltage distribution networks considering changes in line reactance as described in claim 5, characterized in that, For the k-th iteration, the maximum voltage deviation and maximum power deviation of the boundary nodes are calculated as shown in equations (12) and (13), respectively: (12) (13) Among them, the number of iterations ; For the set of boundary nodes; for the set of three phases ; During the iterative solution process, the iterative process is considered to have converged and the calculation is terminated if and only if equations (14) and (15) are satisfied simultaneously, where the required deviation threshold is... and Configure according to actual calculation needs; (14) (15)。

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