Power system weak link assessment method based on electrothermal coupling modal analysis

Abstract

The present disclosure belongs to the technical field of power systems and provides a method for evaluating weak links in a power system based on electrothermal coupling modal analysis, comprising the following steps: obtaining component states of the power system; performing electrothermal coupling power flow calculations on the obtained component states to obtain a sample set of non-convergent power flow in the power system; constructing an electrothermal coupling modal analysis model of a transmission line; and calculating evaluation indicators of weak links in the power system based on the electrothermal coupling modal analysis model and the sample set of non-convergent power flow in the power system.

Description

Technical Field

[0001] The present disclosure belongs to the technical field of power systems, and particularly relates to a method for evaluating weak links in power systems based on electrothermal coupling modal analysis. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] In recent years, climate warming has continued, further increasing the risk of extreme weather events. Furthermore, climate varies significantly across regions, increasing the impact of severe meteorological conditions and phenomena on the safe operation of power grids. Frequent severe weather events lead to power grid accidents, adding pressure on the safe and stable operation of the grid. Therefore, it is important to study the impact of environmental factors on the evaluation of grid voltage stability. The Jacobian matrix is ​​not only an essential quantity for finding power flow solutions using the Newton-Raphson iteration method, but also the computational basis for voltage stability analysis methods such as VQ sensitivity analysis and QV modal analysis. However, changes in transmission line resistance inevitably lead to changes in the elements of the Jacobian matrix, further affecting the calculation results of power system analysis models. The temperature of overhead transmission lines is affected by current and environmental factors, and the conductor resistance parameters are related to the conductor temperature. Therefore, the conductor resistance parameters vary during actual power system operation.

[0004] According to the inventors, relevant scholars have verified that meteorological conditions such as conductor current, ambient temperature, wind speed, and light intensity significantly influence conductor resistance. Furthermore, conductor resistance and temperature vary with load and ambient parameters. Existing power system analysis methods focus primarily on model development and algorithm research, with less consideration of variations in transmission line resistance parameters. Therefore, the introduction of electrothermal coupling theory provides new insights into system stability assessment. Summary of the Invention

[0005] In order to solve the above problems, the present disclosure proposes a method for evaluating weak links in power systems based on electrothermal coupling modal analysis. The Latin hypercube sampling method is combined to randomly sample the system status, and the electrothermal coupling power flow calculation method is used to calculate the power flow, and samples with non-convergent power flow are screened out. The electrothermal coupling equation of the transmission line is combined with the conventional power flow equation to derive a modal analysis calculation method taking electrothermal coupling into account, calculate the minimum eigenvalue and corresponding participation factor of the screened samples, and identify the weak links of the system, providing an effective and accurate method for accurately identifying the weak links in the power system.

[0006] According to some embodiments, the technical solution of the present disclosure provides a method for evaluating weak links in a power system based on electrothermal coupling modal analysis, which adopts the following technical solutions:

[0007] A method for evaluating weak links in a power system based on electrothermal coupling modal analysis includes the following steps:

[0008] Obtain the status of power system components;

[0009] Perform electrothermal coupled power flow calculation on the obtained component states to obtain a sample set of non-convergent power flow of the power system;

[0010] Construct an electrothermal coupled modal analysis model for transmission lines;

[0011] Based on the electrothermal coupling modal analysis model and the power system power flow non-convergence sample set, an evaluation index of a weak link in the power system is calculated.

[0012] As a further technical limitation, the component status of the power system is obtained based on the Latin hypercube sampling method, and the component status at least includes a working state and a failure state.

[0013] Furthermore, the judgment condition of the component state is: when the random number generated by the Latin hypercube sampling method is greater than the failure probability of the component, the component state is a working state; otherwise, the component state is a failure state.

[0014] As a further technical limitation, before constructing the electrothermal coupling modal analysis model of the transmission line, a transmission line model taking electrothermal coupling into account is established.

[0015] Furthermore, the influencing factors of the transmission line model taking into account electrothermal coupling include at least the current carrying capacity of the transmission line, the length of the transmission line, the ambient temperature, wind speed, light intensity, the resistance temperature coefficient of the transmission line and the conductor resistance per unit length.

[0016] Furthermore, through the constructed transmission line model taking into account electrothermal coupling, the line current, voltage and impedance are calculated to obtain the line electrothermal coupling equation, which is then combined with the power flow equation of the transmission line to obtain the power flow equation taking into account electrothermal coupling.

[0017] Furthermore, the obtained power flow equation taking into account the electrothermal coupling is linearized, and the electrothermal coupling modal analysis model of the transmission line is obtained by combining the eigenvalues ​​and eigenvectors of the Jacobian matrix.

[0018] As a further technical limitation, the minimum eigenvalue and the corresponding participation factor of the non-convergent sample set of the power system flow are calculated based on the electrothermal coupling modal analysis model of the transmission line, the influence of the electrothermal coupling parameters on the power system is taken into account, the evaluation indicators of the weak links of the power system are calculated, and the weak links of the system are identified.

[0019] Furthermore, the non-convergent sample set of the power system power flow is used as input data, combined with the electrothermal coupling modal analysis model, to output an assessment of the weak links of the power system.

[0020] Furthermore, the evaluation indicators of the weak links in the power system include the minimum eigenvalue and the corresponding participation factor.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] This paper not only quantifies the impact of electrothermal coupling parameters on the system's minimum eigenvalue and participation factor, but also analyzes the impact of different component failures on voltage stability. By calculating the system's minimum eigenvalue and participation factor, which incorporates electrothermal coupling, the participation factors of different nodes can be more accurately calculated, providing data support for developing more accurate remedial measures. The proposed solution algorithm is easy to implement and requires minimal computation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings, which constitute a part of the present disclosure, are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation to the present disclosure.

[0024] Figure 1 It is a flow chart of a method for evaluating weak links in a power system based on electrothermal coupling modal analysis in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0025] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0026] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present disclosure belongs.

[0027] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0028] In the absence of conflict, the embodiments of the present disclosure and the features thereof may be combined with each other.

[0029] Example 1

[0030] The disclosed embodiments introduce a method for evaluating weak links in a power system based on electrothermal coupling modal analysis.

[0031] like Figure 1 A power system weak link assessment method based on electrothermal coupling modal analysis is shown, comprising the following steps:

[0032] Step S01: Selecting the state of system components based on the Latin hypercube sampling method;

[0033] Step S02: Based on the generated system state S, the electric-thermal coupled power flow calculation method is used to calculate the power flow and filter out the samples S where the system power flow does not converge. ncon ;

[0034] Step S03: establishing a transmission line model taking into account electrothermal coupling;

[0035] Step S04: establishing an electrothermal coupling modal analysis model of the transmission line;

[0036] Step S05: Calculate weak link evaluation indicators of the power system.

[0037] As one or more implementation methods, in step S01, for a system consisting of n components (including generator sets, overhead transmission lines, and transformers), its state variable S can be expressed as:

[0038] S=[S1,S2,…,S i ,…S n ] (1)

[0039] Where S i Indicates the status of component i.

[0040] Accordingly, the state of element i after N samplings can be expressed as:

[0041]

[0042] Where, Indicates the state of the kth sampling of element i.

[0043] For the kth sampling of component i, there are two states: working and failed. The failures of different components are independent of each other. The judgment condition of the component state is shown in formula (3).

[0044]

[0045] Where: Q i represents the failure probability of component i; = denotes the Latin hypercube sampling method used to simulate the generation of random numbers in the interval [0,1]. Each component in the system is sampled and its state is determined according to formula (3). The states of n components together form the state S of the system.

[0046] As one or more implementation modes, in step S02,

[0047] According to the generated system state S, the Newton-Raphson method is used to iteratively solve the power flow equation established by formula (9) taking into account the electrothermal coupling characteristics of the overhead line to obtain the power flow calculation results, and to screen out the samples S where the system power flow does not converge. ncon ;

[0048] As one or more implementation methods, in step S03, the electrothermal coupling static heat balance equation of the overhead transmission line is as shown in formulas (4)-(5):

[0049]

[0050] r a (T c )=R+σ(T c (t)-T) (5)

[0051] Where, I a is the line current carrying capacity; r a is the actual series resistance of the line; L is the length of the line; assuming that the conductor temperature is uniformly distributed, T c is the conductor temperature, T a is the ambient temperature of the conductor, H e is the altitude, V l is the wind speed around the line, D is the conductor diameter, ε is the emissivity, is the wind direction angle, α is the absorptivity of the conductor to light, Q s is the solar intensity, δ is the solar declination angle, ω is the hour angle, L a is the geographical latitude, Z c and Z l are the azimuths of the sun and the conductor respectively; σ is the temperature coefficient of resistance, and R is the resistance per unit length of conductor at the rated ambient temperature T.

[0052] Formula (6) can be derived from formula (4) and formula (5).

[0053]

[0054] in:

[0055]

[0056]

[0057] Where r (l) , I (l) r a , I a Unit value; S b, Z b , I b 、U b They are the power, impedance, current and voltage reference values ​​respectively.

[0058] In one or more embodiments, in step S04, since the current calculated by equation (6) is consistent with the line current calculated by voltage and impedance, the two are subtracted to obtain the line electrothermal coupling equation, and the resistance is introduced as a variable into the conventional power flow equation. The power flow equation is a prerequisite for modal analysis. To this end, this paper combines the line electrothermal coupling equation with the conventional power flow equation to obtain a power flow equation that takes into account the electrothermal coupling characteristics of the overhead line, as shown in equation (9).

[0059]

[0060] Linearizing formula (9) yields:

[0061]

[0062] Where, ΔP, ΔQ, ΔV, Δθ, and Δr are the node active power increment, reactive power increment, line current increment, voltage amplitude increment, voltage angle increment, and resistance increment, respectively. In order to analyze the voltage stability relationship of the Q and V increment relationship, we take ΔP = 0 and Then formula (10) is simplified to:

[0063] ΔQ=(J R1 +J R2 +J R3 )ΔV=J R ΔV (11)

[0064] in:

[0065]

[0066] The voltage stability of the system can be calculated by calculating the contracted system Jacobian matrix J R The eigenvalues ​​and eigenvectors are determined by the matrix J R It can be expressed as:

[0067] J R =X R ΛX L (13)

[0068] Where Λ is the matrix J R The diagonal mode matrix composed of all eigenvalues ​​of R is the matrix J R The modal matrix composed of all right eigenvectors of L is the matrix J RThe modal matrix composed of all left eigenvectors in rows; According to formula (13), we can get:

[0069]

[0070] Substituting formula (14) into formula (11) yields:

[0071] ΔV=X R Λ -1 X L ΔQ (15)

[0072] Or expanded to:

[0073]

[0074] Where, v i 、 The matrix J R The eigenvalue λ i The corresponding right and left eigenvectors define the i-th mode of the QV response.

[0075] because Therefore, formula (15) can be written as:

[0076] V m =Λ -1 Q m (17)

[0077] Where V m =X L ΔV is called the modal voltage change vector; Q m =X L ΔQ is called the modal reactive power change vector.

[0078] Formula (17) represents n uncoupled first-order equations, so for the i-th mode, we have

[0079]

[0080] To explore the relationship between node VQ sensitivity and J R The relationship between the eigenvalues. In formula (16), let ΔQ = e k , e k represents a vector whose elements are all zero except k ones.

[0081]

[0082] Where u ki for u i The kth element of .

[0083] The partial derivative of V with respect to Q at node k can be expressed as:

[0084]

[0085] The relative participation of busbar k in mode i can be measured by the busbar participation factor:

[0086] p ki =u ki v ki (twenty one)

[0087] From formula (21), we can see that p ki Determines λ i The contribution to the bus kV-Q sensitivity is the characteristic value λ i And the participation factor of the corresponding node k. The larger the value, the more significant the effect of node k on the eigenvalue λ. i For the participation factors of different nodes corresponding to the minimum eigenvalue, the larger the participation factor of the node, the greater the impact of its reactive power change on the system voltage stability, and the weaker the node.

[0088] As one or more implementation methods, in step S05, samples of the system power flow that do not converge are screened out based on the electrothermal coupling modal analysis model, and the minimum eigenvalue and the corresponding participation factor are calculated using equations (16) and (21). The minimum eigenvalue is the minimum value of the eigenvector λ, which takes into account the influence of the electrothermal coupling parameters on the system.

[0089] This embodiment quantifies the impact of electrothermal coupling parameters on the system's minimum eigenvalue and participation factor, and can also analyze the impact of different component failures on voltage stability. By calculating the system's minimum eigenvalue and participation factor, which takes into account electrothermal coupling, the participation factors of different nodes can be more accurately calculated, providing data support for developing more accurate remedial measures. The proposed solution algorithm is easy to implement and has a short computation time.

[0090] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Those skilled in the art should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A method for evaluating weak links in power systems based on electrothermal coupling modal analysis, characterized in that: The following steps are involved: Obtain the status of power system components; Perform electrothermal coupled power flow calculation on the obtained component states to obtain a sample set of non-convergent power flow of the power system; Construct an electrothermal coupled modal analysis model for transmission lines; Calculating evaluation indicators of weak links in the power system based on the electrothermal coupling modal analysis model and the power system power flow non-convergence sample set; Acquiring component states of the power system based on a Latin hypercube sampling method, wherein the component states include at least a working state and a failure state; Before constructing the electrothermal coupling modal analysis model of the transmission line, a transmission line model taking electrothermal coupling into account is established; The influencing factors of the transmission line model taking into account electrothermal coupling include at least the current carrying capacity of the transmission line, the length of the transmission line, the ambient temperature, the wind speed, the light intensity, the resistance temperature coefficient of the transmission line and the conductor resistance per unit length; The static heat balance equation of the electrothermal coupling of overhead transmission lines is: Where, I a is the line current carrying capacity; r a is the actual series resistance of the circuit; L is the length of the line; assuming the conductor temperature is uniformly distributed, T c is the conductor temperature, T a is the ambient temperature of the conductor, H e is the altitude, V l is the wind speed around the line, D is the conductor diameter, is the emissivity, is the wind direction angle, is the absorptivity of the conductor to light, Q s is the solar radiation intensity, is the solar declination angle, is the hour angle, is the geographical latitude, Z c and Z l are the azimuths of the sun and the conductor respectively; is the temperature coefficient of resistance, R Rated ambient temperature T The resistance of a conductor per unit length under ; By using the constructed transmission line model that takes into account electrothermal coupling, the line current, voltage and impedance are calculated to obtain the line electrothermal coupling equation. Then, combined with the power flow equation of the transmission line, the power flow equation that takes into account electrothermal coupling is obtained. The obtained power flow equation taking into account electrothermal coupling is linearized and combined with the eigenvalues ​​and eigenvectors of the Jacobian matrix to obtain the electrothermal coupling modal analysis model of the transmission line. Based on the electrothermal coupling modal analysis model of the transmission line, the minimum eigenvalue and the corresponding participation factor of the non-convergent sample set of the power system flow are calculated. The influence of the electrothermal coupling parameters on the power system is taken into account, the evaluation index of the weak link of the power system is calculated, and the weak link of the system is identified.

2. The method for evaluating weak links in a power system based on electrothermal coupling modal analysis as claimed in claim 1, characterized in that: The judgment condition of the component state is: when the random number generated by the Latin hypercube sampling method is greater than the failure probability of the component, the component state is a working state; otherwise, the component state is a failure state.

3. The method for evaluating weak links in a power system based on electrothermal coupling modal analysis as claimed in claim 1, characterized in that: The non-convergent sample set of the power system power flow is used as input data, combined with the electrothermal coupling modal analysis model, and output is an assessment of the weak links of the power system.

4. The method for evaluating weak links in a power system based on electrothermal coupling modal analysis as claimed in claim 3, characterized in that: The evaluation indicators of the weak links of the power system include the minimum eigenvalue and the corresponding participation factor.

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