A harmonic tracing method based on fundamental harmonic impedance contrast under a multi-harmonic source power grid

Abstract

The application discloses a harmonic tracing method based on fundamental harmonic impedance contrast under a multi-harmonic source power grid. The method is applied to the technical field of harmonic tracing of a complex multi-harmonic source power grid. In view of the problem that a theoretical method cannot completely meet the actual harmonic tracing requirement in specific harmonic treatment, at least one potential harmonic source can be determined through a group of power grid flow data, all the potential harmonic sources can be Norton equivalent based on two groups of flow data, and the main harmonic source can be determined by comparing the effective values of harmonic currents of the potential harmonic sources.

Description

Technical Field

[0001] This invention belongs to the field of harmonic source tracing technology, specifically relating to a harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid. Background Technology

[0002] Because power systems contain a variety of harmonic sources, such as distributed generation, nonlinear loads, and electrified railways, these sources not only affect the power quality of the system but also endanger other users. Furthermore, due to the intertwining and mutual influence of these harmonic sources, they are often difficult to identify and assign blame to. Therefore, harmonic issues are among the most complex, prominent, and concerning problems in power system power quality.

[0003] To effectively manage harmonics, it is essential to understand the distribution and state of harmonic sources in the power grid. Accurately locating harmonic sources is crucial for harmonic analysis and mitigation, and is of great significance. The problem of harmonic source tracing was initially proposed as the inverse problem of harmonic power flow. Harmonic power discrimination methods measure the harmonic voltage and current at some nodes in the system and use state estimation methods to obtain the harmonic power injected into the system by the load. When the injected harmonic power is positive, the load is identified as a harmonic source. Another type of harmonic source tracing method based on load parameter identification studies the intrinsic relationship between distorted voltage and current waveforms, using corresponding harmonic load parameters as indicators for identifying harmonic sources.

[0004] However, in specific harmonic mitigation applications, these theoretical methods cannot fully meet practical requirements. The harmonic power discrimination method only yields accurate identification results under single harmonic source conditions. In complex low-voltage distribution network systems, multiple harmonic sources often interact, making this criterion prone to omissions and errors in harmonic source tracing. Furthermore, the harmonic load parameter identification method, which uses nonlinear calculations of resistance R, inductance L, and capacitance C based on measurements of voltage and current at the common coupling point, does not fully represent the actual load parameters; it only reflects the mathematical relationship between load voltage and current. Summary of the Invention

[0005] To address the shortcomings of the aforementioned background technology, this invention proposes a harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid.

[0006] A harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid includes the following steps:

[0007] (1) Calculate the fundamental impedance of each node in the observed power grid based on the fundamental power flow;

[0008] (2) Calculate the harmonic voltage vector of each node and the harmonic current vector flowing out to the next level grid based on the harmonic power flow.

[0009] (3) Based on the harmonic voltage vector and harmonic current vector of each node obtained in step (2), calculate the equivalent harmonic impedance of each node.

[0010] (4) Compare the fundamental impedance and equivalent harmonic impedance of each node calculated in steps (1) and (3) to verify their reliability and identify at least one potential harmonic source.

[0011] (5) Select the single node with the lowest confidence among all potential harmonic sources obtained in step (4), inject harmonic current of the same frequency into the node, and obtain a new set of harmonic power flow data.

[0012] (6) Based on the new harmonic power flow obtained in step (5), recalculate the harmonic voltage vector of each potential harmonic source node and the harmonic current vector flowing out to the next level grid.

[0013] (7) Combine the original harmonic power flow conditions to calculate the Norton equivalent model of each potential harmonic source node.

[0014] In the above technical solution, further, in step (1), the fundamental impedance of each node of the observed power grid is calculated based on the fundamental power flow and denoted as: R if +jX if Its calculation formula is as shown in equation (15):

[0015]

[0016] Among them, R if It is the fundamental frequency resistance, X if It is the fundamental reactance, where j is the imaginary unit. These are the fundamental phase voltages and phase currents of node i, obtained from the original fundamental power flow. The subscript i indicates the node number, and the subscript f indicates the fundamental wave.

[0017] Furthermore, the harmonic voltage vectors of each node calculated based on harmonic power flow in step (2) are denoted as: The harmonic current vector flowing out of each node is denoted as: In the formula, the subscript i represents the node number, the subscript h represents the harmonic order, and the subscript 1 represents the original data.

[0018] Further, in step (3), based on the harmonic voltage vector and harmonic current vector of each node obtained from the harmonic power flow data, the equivalent harmonic impedance of each node is calculated and denoted as: R ih +jX ih Its calculation formula is as shown in equation (16):

[0019]

[0020] in, It is the h-th harmonic voltage vector and current vector of node i calculated by harmonic power flow. The subscript i indicates the node number, the subscript h indicates the harmonic order, and the subscript 1 indicates the original data.

[0021] Furthermore, in step (4), the comparison calculation of the fundamental impedance and equivalent harmonic impedance of each node is as follows: if a node does not clearly satisfy the condition that the harmonic resistance is equal to the fundamental resistance and the harmonic reactance is equal to h times the fundamental reactance within a certain deviation range ξ, that is, the fundamental harmonic resistance and reactance of the node do not satisfy equation (17) and equation (18), then it can be determined as a potential harmonic source.

[0022] |R ih -R if |<ξR if (17)

[0023] |X ih -hX if |<ξhX if (18)

[0024] Furthermore, in step (5), the single node with the lowest confidence level among all potential harmonic sources, i.e., the node with the largest comprehensive deviation value δ, is injected with a harmonic current of the same frequency. The subscript p is the node number, and the subscript h represents the harmonic order. The formula for calculating the comprehensive deviation value δ is shown in equation (19).

[0025]

[0026] Further, in step (6), after injecting current, a new set of harmonic power flow data is obtained. The harmonic voltage vectors of the nodes identified as potential harmonic source nodes are calculated from the new harmonic power flow data, denoted as: The harmonic current vector flowing out of each node is denoted as: In the formula, the subscript i represents the node number, the subscript h represents the harmonic order, and the subscript 2 represents the new data.

[0027] Furthermore, in step (7), Norton equivalent model calculations are performed on each potential harmonic source node. The specific calculation method is as follows:

[0028] For nodes without secondary harmonic current injection, i.e., potential harmonic source nodes other than node p, the Norton equivalent model calculation method is as follows:

[0029]

[0030]

[0031]

[0032] in, Z is the effective value of the h-th equivalent harmonic current source at node i. ih It is the h-th equivalent harmonic of node i;

[0033] The Norton equivalent model calculation method for the potential harmonic source node p of the secondary injected harmonic current is as follows:

[0034]

[0035]

[0036]

[0037] in, Z is the effective value of the h-th equivalent harmonic current source at node p. ph It is the h-th equivalent harmonic of node p.

[0038] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0039] This invention fully considers the limited number of power quality monitoring devices in actual power grids, which is insufficient for large-scale harmonic source tracing. To ensure power quality, harmonic source tracing needs to be carried out across multiple substations and loads. Based on this, a harmonic source tracing method based on the Norton equivalent model is proposed for multi-harmonic source power grids. This method overcomes the limitation of the harmonic power discrimination method, which only yields accurate identification results under single-harmonic source conditions, and avoids the inaccuracies of harmonic load parameters calculated nonlinearly using the parameter identification method. The harmonic source tracing method based on the Norton equivalent model in multi-harmonic source power grids can identify at least one potential harmonic source using a set of power flow data. Based on two sets of power flow data, Norton equivalence can be performed on all potential harmonic sources. By comparing the effective values ​​of the harmonic currents of each potential harmonic source, the main harmonic source can be determined. Attached Figure Description

[0040] Figure 1 It is a topology structure for a 220kV high-voltage ring network.

[0041] Figure 2 This is a flowchart of the harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to the present invention. Detailed Implementation

[0042] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] A harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid includes the following steps:

[0044] (1) Calculate the fundamental impedance of each node in the observed power grid based on the fundamental power flow;

[0045] (2) Calculate the harmonic voltage vector of each node and the harmonic current vector flowing out to the next level grid based on the harmonic power flow.

[0046] (3) Based on the harmonic voltage vector and harmonic current vector of each node obtained in step (2), calculate the equivalent harmonic impedance of each node.

[0047] (4) Compare the fundamental impedance and equivalent harmonic impedance of each node calculated in steps (1) and (3) to verify their reliability and identify at least one potential harmonic source.

[0048] (5) Select the single node with the lowest confidence among all potential harmonic sources obtained in step (4), inject harmonic current of the same frequency into the node, and obtain a new set of harmonic power flow data.

[0049] (6) Based on the new harmonic power flow obtained in step (5), recalculate the harmonic voltage vector of each potential harmonic source node and the harmonic current vector flowing out to the next level grid.

[0050] (7) Combine the original harmonic power flow conditions to calculate the Norton equivalent model of each potential harmonic source node.

[0051] In step (1), the fundamental impedance of each node in the observed power grid is calculated based on the fundamental power flow and denoted as: R if +jX if Its calculation formula is as shown in equation (26):

[0052]

[0053] In equation (26), R if It is the fundamental frequency resistance, X if It is the fundamental reactance, where j is the imaginary unit. These are the fundamental phase voltages and phase currents of node i, obtained from the original fundamental power flow. The subscript i indicates the node number, and the subscript f indicates the fundamental wave. The calculation formula is as shown in equation (27):

[0054]

[0055] in, It is the conjugate complex number of the fundamental single-phase apparent power at node i. It is the conjugate complex number of the fundamental phase voltage at node i.

[0056] In step (2), the harmonic voltage vectors of each node calculated based on the harmonic power flow are denoted as: The harmonic current vector flowing out of each node is denoted as: Its calculation formula is as shown in equation (28):

[0057]

[0058] in, It is the single-phase apparent power conjugate complex number of the h-th harmonic at node i. It is the conjugate complex number of the h-th harmonic voltage at node i, where the subscript i represents the node number, the subscript h represents the harmonic order, and the subscript 1 represents the original data.

[0059] In step (3), based on the harmonic voltage vector and harmonic current vector of each node obtained from the harmonic power flow data, the equivalent harmonic impedance of each node is calculated and denoted as: R ih +jX ih Its calculation formula is as shown in equation (29):

[0060]

[0061] in, These are the h-th harmonic voltage vector and harmonic current vector of node i, calculated from the harmonic power flow.

[0062] In step (4), the comparison calculation of the fundamental impedance and equivalent harmonic impedance of each node is as follows: if a node does not clearly satisfy the condition that the harmonic resistance is equal to the fundamental resistance and the harmonic reactance is equal to h times the fundamental reactance within a certain deviation range, that is, the fundamental harmonic resistance and reactance of the node do not satisfy equation (30) and equation (31), then it can be determined as a potential harmonic source.

[0063] |R ih -R if |<ξR if (30)

[0064] |X ih -hX if |<ξhX if (31)

[0065] In step (5), the single node with the lowest confidence level among all potential harmonic sources, i.e., the node with the largest comprehensive deviation value δ, is injected with a harmonic current of the same frequency. The subscript p represents the node number, and the subscript h represents the harmonic order. The formula for calculating the comprehensive deviation δ is shown in equation (32):

[0066]

[0067] In step (6), after injecting current, a new set of harmonic power flow data is obtained. From the new harmonic power flow data, several harmonic voltage vectors that are identified as potential harmonic source nodes are calculated, denoted as: The harmonic current vector flowing out of each node is denoted as: Its calculation formula is as shown in equation (33):

[0068]

[0069] in, It is the single-phase apparent power conjugate complex number of the h-th harmonic at node i. It is the conjugate complex number of the h-th harmonic voltage at node i. In each formula, the subscript i represents the node number, the subscript h represents the harmonic order, and the subscript 2 represents new data.

[0070] In step (7), Norton equivalent model calculations are performed on each potential harmonic source node. The specific calculation method is as follows:

[0071] For nodes without secondary harmonic current injection, i.e., potential harmonic source nodes other than node p, the Norton equivalent model calculation method is as follows:

[0072]

[0073]

[0074]

[0075] in, Z is the effective value of the h-th equivalent harmonic current source at node i. ih It is the h-th equivalent harmonic of node i.

[0076] The Norton equivalent model calculation method for the potential harmonic source node p of the secondary injected harmonic current is as follows:

[0077]

[0078]

[0079]

[0080] in, Z is the effective value of the h-th equivalent harmonic current source at node p. jh It is the h-th equivalent harmonic of node p.

[0081] To verify the feasibility and accuracy of the proposed harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid, a simulation model of a 220kV high-voltage ring network was built on the MATLAB / Simulink platform. The simulation model consists of six nodes, including one 220kV fundamental source node and five 220 / 110kV substations. Impedance equivalence was performed on all five substation nodes using RLC-load modules, and the lines all adopted π-type equivalent circuits. This simulation model uses the common fifth harmonic in the power grid as an example for verification. Three of the five substation nodes are potential fifth harmonic sources. The simulation model is shown below. Figure 1 As shown.

[0082] Table 1 shows the fundamental power data of each node under the initial state. Combined with the three-phase fundamental phase voltage vector data of each node under the initial state in Table 2, the three-phase fundamental phase current vector data of each node under the initial state are calculated as shown in Table 2.

[0083] Table 1

[0084] Node number Fundamental active power (W) Fundamental reactive power (var) 1 246532584.9 36053106.68 2 220805032.3 55585314.38 3 129328228.4 19305157.65 4 124389672.4 47798546.48 5 854196379.5 -80294100.81 6 131406667.1 27404415.02

[0085] Table 2

[0086]

[0087] Table 3 shows the fifth harmonic power data of each node under the initial state. Combined with the fifth harmonic phase voltage vector data of the three phases A, B, and C of each node under the initial state in Table 4, the fifth harmonic current vector data of the three phases A, B, and C of each node under the initial state are calculated as shown in Table 4.

[0088] Table 3

[0089] Node number Harmonic active power (W) Harmonic reactive power (var) 1 399726.8359 -1830243.131 2 378362.2335 476519.4871 3 -33484.87399 -674989.5998 4 406164.3095 -887139.7943 5 118432.5061 1488222.523 6 273599.6977 285307.1267

[0090] Table 4

[0091]

[0092] Table 5 shows the three-phase fundamental and harmonic impedance data of each node calculated based on the fundamental and harmonic power flow under the initial state. Comparison of the data reveals that nodes 1, 3, and 4, other than the fundamental source node 4, are potential harmonic source nodes.

[0093] Table 5

[0094]

[0095] Table 6 shows the harmonic power data of each node after injecting a fifth harmonic current with an amplitude of 20A into node 3, the potential harmonic source node with the lowest confidence level in the fundamental harmonic impedance comparison. Combined with the three-phase fifth harmonic phase voltage vector data of each node in the new harmonic power flow, the three-phase fifth harmonic current vector data of each node under the new harmonic power flow are calculated and shown in Table 7.

[0096] Table 6

[0097] Node number Harmonic active power (W) Harmonic reactive power (var) 1 358272.235 -2102607.156 2 466798.338 587687.6234 3 158644.831 -1079555.304 4 435629.5439 -1019346.633 5 146702.4372 1843462.393 6 337180.5336 351485.7894

[0098] Table 7

[0099]

[0100] Table 8 shows the Norton equivalent results for potential harmonic source nodes.

[0101] Table 8

[0102]

Claims

1. A harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid, characterized in that, Includes the following steps: (1) Calculate the fundamental impedance of each node of the observed power grid based on the fundamental power flow; (2) Calculate the harmonic voltage vector of each node and the harmonic current vector flowing out to the next level power grid based on the harmonic power flow. (3) Based on the harmonic voltage vector and harmonic current vector of each node obtained in step (2), calculate the equivalent harmonic impedance of each node; (4) Compare the fundamental impedance and equivalent harmonic impedance of each node calculated in steps (1) and (3) to verify their reliability and identify at least one potential harmonic source. (5) Select the single node with the lowest confidence among all potential harmonic sources obtained in step (4), inject harmonic current of the same frequency into the node, and obtain a new set of harmonic power flow data. (6) Based on the new harmonic power flow obtained in step (5), recalculate the harmonic voltage vector of each potential harmonic source node and the harmonic current vector flowing out to the next level power grid. (7) Combine the original harmonic power flow conditions to calculate the Norton equivalent model of each potential harmonic source node.

2. The harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 1, characterized in that, In step (1), the fundamental impedance of each node of the observed power grid calculated based on the fundamental power flow is denoted as: Its calculation formula is as shown in equation (1): （1） in, It is the fundamental frequency resistance. It is the fundamental frequency reactance. The imaginary unit, , These are the fundamental phase voltage and phase current of node i obtained from the original fundamental power flow. The subscript i indicates the node number, and the subscript f indicates the fundamental wave. In formula (1) The calculation formula is as shown in equation (2): （2） in, It is the conjugate complex number of the fundamental single-phase apparent power at node i. It is the conjugate complex number of the fundamental phase voltage at node i.

3. The harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 2, characterized in that, In step (2), the harmonic voltage vector of each node is denoted as: The harmonic current vector flowing out of each node is denoted as: The calculation formula is as follows: （3） in, It is the single-phase apparent power conjugate complex number of the h-th harmonic at node i. It is the conjugate complex number of the h-th harmonic voltage at node i, where the subscript i represents the node number, the subscript h represents the harmonic order, and the subscript 1 represents the original data.

4. The harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 3, characterized in that, In step (3), the equivalent harmonic impedance of each node is denoted as: The calculation formula is as follows: （4） in, , These are the h-th harmonic voltage vector and harmonic current vector of node i, calculated from the harmonic power flow.

5. A harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 4, characterized in that, The specific steps (4) are as follows: If the fundamental harmonic resistance and reactance of a certain node do not satisfy equations (5) and (6), then it is determined to be a potential harmonic source. （5） （6） in, This represents the percentage of the maximum credible deviation range.

6. The harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 5, characterized in that, Step (5) specifically involves selecting the single node p with the lowest confidence level among all potential harmonic sources, i.e., the comprehensive deviation value. The largest node-injected harmonic current Overall deviation value The calculation formula is as follows: （7） in, The value represents the overall deviation. The subscript p is the node number, and the subscript h represents the harmonic order.

7. A harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 6, characterized in that, In step (6), the harmonic voltage vector of each potential harmonic source node is denoted as: The harmonic current vector flowing out of each node is denoted as: The calculation formula is as follows: （8） in, It is the single-phase apparent power conjugate complex number of the h-th harmonic at node i. It is the conjugate complex number of the h-th harmonic voltage at node i, where the subscript i indicates the node number, the subscript h indicates the harmonic order, and the subscript 2 indicates new data.

8. The harmonic source tracing method based on fundamental harmonic impedance comparison in a multi-harmonic source power grid according to claim 7, characterized in that, The specific step (7) is as follows: The Norton equivalent model calculation method for each potential harmonic source node is as follows: For nodes without secondary harmonic current injection, i.e., potential harmonic source nodes other than node p, the Norton equivalent model calculation method is as follows: （9） （10） （11） in, It is the vector of the h-th equivalent harmonic current source at node i. It is the h-th equivalent harmonic impedance of node i; The Norton equivalent model calculation method for the potential harmonic source node p of the secondary injected harmonic current is as follows: （12） （13） （14） in, It is the vector of the h-th equivalent harmonic current source at node p. It is the h-th equivalent harmonic impedance of node p; , Let be the harmonic voltage and harmonic current at node p under the initial power flow. , Let be the harmonic voltage and harmonic current at node p under the new power flow after the injected current.

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