Reactive voltage support measure calculation method and system considering line resistance variation

Abstract

This invention provides a method and system for calculating reactive power voltage support measurement considering changes in line resistance. Based on the thermal relationships of power transmission lines during operation, an electrothermal coupling model of the transmission line is established. The transmission line resistance is considered as a state variable of power flow. The electrothermal coupling equations and power flow equations are combined to construct a power flow calculation model considering electrothermal coupling, which is then iteratively solved. Based on the obtained Jacobian matrix, the reactive power voltage support measurement of the corresponding node is determined. This invention can quantify the impact of changes in line resistance with external conditions on reactive power voltage support measurement, providing a theoretical basis for accurately assessing voltage stability.

Description

Technical Field

[0001] This invention belongs to the field of power system analysis technology, specifically relating to a method and system for calculating reactive voltage support measurement considering changes in line resistance. Background Technology

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

[0003] With changes in external conditions and increasing load intensity in regional power grids, transmission lines frequently operate under heavy or overload conditions. IEEE standards clearly state that overhead transmission line currents and external conditions can cause significant changes in line resistance, placing higher demands on the accuracy of calculations for power grid safety and stability assessment indicators. Therefore, research considering the impact of external conditions on overhead transmission line resistance and more accurately grasping the magnitude of reactive power voltage support is crucial for the safe and stable operation of the power grid.

[0004] Voltage stability refers to the ability of a power system to maintain all bus voltages at an acceptable steady-state value under normal operating conditions or after disturbances; this patent refers to it as the reactive power voltage support measure. The main cause of voltage instability is insufficient reactive power capacity in the power system. The standard for judging whether a system voltage is stable is that, under normal operating conditions, when the injected reactive power to a bus is increased, the voltage of that bus should increase accordingly. If the bus voltage decreases, it indicates that the system is unstable. Currently, domestic and international scholars have conducted extensive research on voltage stability. Voltage stability evaluation indicators mainly include: the minimum singular value index of the Jacobian matrix, the collapse point index, etc. These methods can assess the stability of node voltages, but they do not consider the changes in line resistance caused by external factors of overhead transmission lines, which can easily lead to a large deviation between the calculated reactive power voltage support measure and the actual value. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a method and system for calculating reactive voltage support measurement that takes into account changes in line resistance. This invention can quantify the impact of changes in line resistance with external conditions on reactive voltage support measurement, providing a theoretical basis for accurately assessing voltage stability.

[0006] According to some embodiments, the present invention adopts the following technical solution:

[0007] A method for calculating reactive voltage support taking into account line resistance includes the following steps:

[0008] Based on the heat relationship of power transmission lines during operation, an electrothermal coupling model of transmission lines is established.

[0009] By treating the transmission line resistance as a state variable of power flow, the power flow calculation model considering the electrothermal coupling of the transmission line and the power flow equation are combined and constructed. The model is then iteratively solved, and the reactive voltage support measure of each node is calculated based on the obtained Jacobian matrix.

[0010] As an alternative implementation, the thermal relationship of the line is a thermal balance between the heat generated by the line resistance and the external conditions of the overhead transmission line, as well as a functional relationship between the conductor resistance and temperature.

[0011] As a further defined implementation, the heat balance relationship is as follows:

[0012]

[0013] Among them, I a r represents the line's current carrying capacity. a The actual series resistance of the circuit is T; L is the length of the circuit; assuming uniform temperature distribution in the conductor, T c For the conductor temperature, T a H represents the ambient temperature surrounding the conductor. e V represents altitude. l q represents the wind speed around the line. s The heat absorbed by the line due to solar radiation is expressed in T. c T a and H e q is a function of the independent variable; r The heat dissipated by the circuit due to surface radiation is expressed in T. c T a q is a function of the independent variable; c The heat dissipated by the line due to air convection is expressed in T. c T a H e and V l A function with respect to the independent variable.

[0014] As a further defined implementation, the functional relationship between the resistance of the metallic conductor and temperature Tc is as follows:

[0015] r a (T c )=R(1+σ(T c -T))

[0016] Where σ is the temperature coefficient of resistance, and R is the resistance per unit length of conductor at the rated ambient temperature T.

[0017] As an alternative implementation method, Newton's method is used for iterative solution.

[0018] As an alternative implementation method, the line electrothermal coupling equation and the node power balance equation are combined to obtain the power flow calculation model. After Taylor series expansion and omitting higher-order terms, the modified equation is obtained.

[0019] As a further defined implementation, the extended Jacobian matrix in the modified equation is used to express the linear relationship between power and current and voltage and resistance when the rate of change of the dynamic element is zero. At each operating point, power and current are kept constant, and a contracted system Jacobian matrix is ​​constructed to directly express the slope between node voltage and node injected reactive power.

[0020] A reactive voltage support measurement and calculation system that takes into account changes in line resistance includes:

[0021] The electrothermal coupling model construction module is configured to establish an electrothermal coupling model of the power transmission line based on the heat relationship of the line during the operation of the power system transmission line;

[0022] The iterative solution module is configured to treat the transmission line resistance as a state variable of power flow, combine the transmission line electrothermal coupling equation with the power flow equation, construct a power flow calculation model considering electrothermal coupling, and perform iterative solution. Based on the obtained Jacobian matrix, the reactive voltage support measure of the corresponding node is determined.

[0023] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.

[0024] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps in the above method.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0026] This invention considers the influence of external conditions on the resistance of transmission lines, avoiding the deviations in reactive power voltage support measurement results caused by traditional models neglecting the influence of the surrounding environment of transmission lines. Furthermore, it can accurately identify weak points and relative stability of the power system. The proposed method is intuitive and convenient to calculate, requiring only a small amount of data to reflect a wealth of information.

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0028] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0029] Figure 1 This is a flowchart of this embodiment. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0032] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0033] A method and system for calculating reactive voltage support measurement that takes into account changes in line resistance, such as... Figure 1 As shown, it includes the following steps:

[0034] Step 1: Input the original power flow calculation data and transmission line external factor data, set the convergence conditions of the Newton-Raphson method, and initialize the number of iterations, node voltages, and line resistances.

[0035] Step 2: Establish an electrothermal coupling model of the transmission line;

[0036] During the stable operation of overhead transmission lines, the heat generated by the line resistance exists in a heat balance relationship with the heat radiated from the transmission line surface, the heat dissipated by air convection, and the heat absorbed by solar radiation. The heat balance equation can be described as follows:

[0037]

[0038] In the formula: I a r represents the line's current carrying capacity. a The actual series resistance of the circuit is T; L is the length of the circuit; assuming uniform temperature distribution in the conductor, T c For the conductor temperature, T a H represents the ambient temperature surrounding the conductor. e V represents altitude. l q represents the wind speed around the line.s The heat absorbed by the line due to solar radiation is expressed in T. c T a and H e q is a function of the independent variable; r The heat dissipated by the circuit due to surface radiation is expressed in T. c T a q is a function of the independent variable; c The heat dissipated by the line due to air convection is expressed in T. c T a H e and V l A function with respect to the independent variable.

[0039] Formula (2) can be derived from formula (1):

[0040]

[0041] In the formula: r (l) I (l) r a I a Unit value; S b This is the power reference value.

[0042] The functional relationship between the resistance of a general metallic conductor and temperature can be described as follows:

[0043] r a (T c )=R(1+σ(T c -T)) (3)

[0044] In the formula: σ is the temperature coefficient of resistance, and R is the resistance per unit length of conductor at the rated ambient temperature T.

[0045] Step 3: Establish a method for calculating reactive voltage support measurement that takes into account changes in line resistance;

[0046] The Jacobian matrix for power flow calculation is a prerequisite for reactive voltage support measurement. To this end, a unified power flow model considering electrothermal coupling was first established, and Newton's method was used for iterative solution. The Jacobian matrix of the last iteration was selected for reactive voltage support measurement.

[0047] Assuming all overhead power lines are connected in a star configuration, and the phase current equals the line current, the formula is as follows:

[0048]

[0049] In the formula, V i and V j These represent the voltage magnitudes at nodes i and j, respectively; θ i and θj The voltage phase angles at nodes i and j are respectively; X ij Let be the reactance from node i to node j.

[0050] Subtracting formula (2) from formula (4) yields formula (5).

[0051] h (l) (v,θ,r)=h1(r (l) )-h2(V i V j ,θ i ,θ j ,r (l) )=0 (5)

[0052] By combining the line electrothermal coupling equation and the node power balance equation, the electrothermal coupling power flow model is obtained as shown in equation (6):

[0053]

[0054] In the formula, n is the number of nodes in the network; l is the number of overhead transmission lines; vector r represents the series resistance; vector v represents the node voltage phase angle; and vector θ represents the node voltage phase angle. F(v,θ,r) is the power balance equation; H(v,θ,r) represents the electrothermal coupling equations for each transmission line, all of which are functions of v, θ, and r as independent variables.

[0055] Expanding formula (6) using Taylor series and omitting higher-order terms yields the corrected equation.

[0056]

[0057] In the formula, ΔP is the increment of node active power; ΔQ is the increment of node reactive power; ΔI 2 The increment of the square of the line current; Δθ is the increment of the node voltage phase angle; ΔV is the increment of the node voltage amplitude; Δr is the increment of the line resistance.

[0058] In formula (7), J New To extend the Jacobian matrix, the specific description is shown in Equation (8).

[0059]

[0060] The elements of the Jacobian matrix give the slope between power and node voltage.

[0061] For all dynamic components, when dΔx / dt = 0, the linear relationships between their power and current and voltage and resistance are as follows:

[0062]

[0063] At each running point, keeping P and I constant, let ΔP = 0 and ΔI = 0 in formula (9). 2 =0, therefore:

[0064] ΔQ=J N ΔV=(J1+J2+J3)ΔV (10)

[0065] in:

[0066]

[0067] In the formula, J N The contracted system Jacobian matrix directly reflects the slope between node voltage and node injected reactive power, as shown in Equation (12).

[0068]

[0069] In the formula, It is a contracted Jacobian matrix, whose i-th diagonal element is the reactive voltage support measure of node i.

[0070] The content not described in detail above is existing technology known to those skilled in the art.

[0071] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating reactive voltage support measurement considering changes in line resistance, characterized in that, Includes the following steps: Based on the heat relationship of power transmission lines during operation, an electrothermal coupling model of transmission lines is established. By treating the transmission line resistance as a state variable of power flow, the electrothermal coupling equation of the transmission line and the power flow equation are combined to construct a power flow calculation model considering electrothermal coupling, and iteratively solve the model. Based on the obtained Jacobian matrix, the reactive voltage support measure of the corresponding node is determined. Among them, the line electrothermal coupling equation and the node power balance equation are combined to obtain the power flow calculation model. After Taylor series expansion and omitting higher-order terms, the modified equation is obtained. Using the extended Jacobian matrix in the modified equation, the linear relationship between power and current and voltage and resistance is expressed when the rate of change of dynamic elements is zero. At each operating point, power and current are kept constant, and a contracted system Jacobian matrix is ​​constructed to directly express the slope between node voltage and node injected reactive power. The diagonal elements of this contracted system Jacobian matrix are taken as the reactive voltage support measure of the corresponding node.

2. The method for calculating reactive voltage support measurement considering line resistance variation as described in claim 1, characterized in that, The thermal relationship of the line is a thermal balance between the heat generated by the line resistance, the heat radiated from the surface of the transmission line, the heat radiated by air convection, and the heat absorbed by solar radiation, as well as the functional relationship between the resistance of the conductor and the temperature.

3. The method for calculating reactive voltage support measurement considering line resistance variation as described in claim 2, characterized in that, The heat balance relationship is as follows: in, I a Line carrying capacity; r a This is the actual series resistance of the circuit; L Let the length of the line be denoted by '(');'; and assume that the conductor temperature is uniformly distributed. T c For conductor temperature, T a The ambient temperature surrounding the conductor. H e Altitude V l Wind speed around the line; q s The heat absorbed by the line due to solar radiation, which is... T c , T a and H e A function of the independent variable; q r The heat dissipated by the circuit due to surface radiation is expressed as... T c , T a A function of the independent variable; q c The heat dissipated by the line due to air convection is... T c , T a , H e and V l A function with respect to the independent variable.

4. The method for calculating reactive voltage support measurement considering line resistance variation as described in claim 2, characterized in that, Resistance and temperature of metallic conductors Tc The functional relationship between them is: in, σ Temperature coefficient of resistance R Rated ambient temperature T The resistance per unit length of conductor.

5. The method for calculating reactive voltage support measurement considering line resistance variation as described in claim 1, characterized in that, When performing iterative solutions, Newton's method is used.

6. A reactive power voltage support measurement and calculation system that takes into account changes in line resistance, characterized in that, include: The electrothermal coupling model construction module is configured to establish an electrothermal coupling model of the power transmission line based on the heat relationship of the line during the operation of the power system transmission line; The iterative solution module is configured to treat the transmission line resistance as a state variable of power flow, combine the transmission line electrothermal coupling equation with the power flow equation, construct a power flow calculation model considering electrothermal coupling, and perform iterative solution. Based on the obtained Jacobian matrix, the reactive voltage support measure of the corresponding node is determined. Among them, the line electrothermal coupling equation and the node power balance equation are combined to obtain the power flow calculation model. After Taylor series expansion and omitting higher-order terms, the modified equation is obtained. Using the extended Jacobian matrix in the modified equation, the linear relationship between power and current and voltage and resistance is expressed when the rate of change of dynamic elements is zero. At each operating point, power and current are kept constant, and a contracted system Jacobian matrix is ​​constructed to directly express the slope between node voltage and node injected reactive power. The diagonal elements of this contracted system Jacobian matrix are taken as the reactive voltage support measure of the corresponding node.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps of the method according to any one of claims 1-5.

Images