Probabilistic power flow calculation method and system considering the electrothermodynamic dynamics of overhead conductors

Abstract

The present invention belongs to the technical field of electric power engineering, and provides a probabilistic flow calculation method and system considering the electrothermodynamic dynamics of overhead conductors. The method includes: constructing a thermal model of the overhead conductor according to the change of conductor current and the meteorological conditions around the conductor; constructing a mechanical model of the overhead conductor according to the initial horizontal stress, cross-sectional area and conductor temperature of the line; constructing the mutual conductance function and mutual susceptance function of the conductor according to the conductor temperature and conductor length; constructing an electrothermal-mechanical coupling flow model based on the thermal model, mechanical model, mutual conductance function and mutual susceptance function; after considering uncertain factors, converting the electrothermal-mechanical coupling flow model into an electrothermal-mechanical coupling probabilistic flow model; solving the line current and conductor temperature in each set of uncertain factor scenarios; correcting the conductor temperature according to the calculated current to obtain the corrected conductor temperature; and obtaining the stress and sag of the corresponding line based on the corrected conductor temperature.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric power engineering, and in particular relates to a probabilistic power flow calculation method and system considering the electrothermodynamic dynamics of overhead conductors. Background Art

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

[0003] The concept of probabilistic power flow was proposed in 1974. It is a model that calculates the probability distribution of system states while considering the uncertainties of the power system. Since the proposal of probabilistic power flow, research related to its modeling and algorithms has always been the focus of researchers. Many uncertainties in the system, such as the uncertainty of faults, load power, wind power, photovoltaic power generation, etc., have been considered in the existing probabilistic power flow models, and some representative algorithms have been proposed, such as simulation method, approximate method and analytical method.

[0004] Traditional probabilistic power flow is committed to calculating the distribution of state variables (such as node voltage magnitude, angle, line power flow, etc.) while considering the uncertainty of power system operating conditions. One of its application scenarios is to analyze the safety risks of power generation plans and provide operators with information on the probability and severity of over-limit. Operators can decide whether to take preventive control to reduce the probability of over-limit based on their risk preferences. In addition, the probabilistic power flow model can also be used to check whether the preventive control decision meets the risk preferences of operators. However, for overhead lines in operation, their safety essentially depends on their thermal and mechanical states. For example, the increase in conductor temperature will accelerate the thermal aging of the conductor and cause the conductor sag to increase, while excessive tension will aggravate the fatigue and even fracture of the conductor. Therefore, it is necessary to introduce the thermal and mechanical states of overhead lines as state variables in the existing probabilistic power flow calculation to further provide operators with the distribution of the thermal and mechanical states of the lines, thereby revealing the safety risks of the power system from the thermodynamic nature of overhead conductor safety.

[0005] At the same time, people also began to pay attention to the mechanical nature that affects the safe operation of the line. In the last century, people established a mechanical model of overhead conductors and summarized the mechanical equations of the actual operating state of the conductors to calculate the mechanical state of overhead conductors under any weather and temperature. Based on the thermal and force relationship of the conductors, the calculation method and real-time monitoring technology of the conductor mechanical state were studied. Some scholars developed a tracking system by monitoring meteorological conditions and conductor tension to calculate the temperature and sag of the conductors, and then reflect the operating state of the line and track it with fixed values. The conductor tension monitoring device was introduced into the DTR system, the sag monitoring device was introduced into the DTR technology, and a risk warning model was established with the conductor current margin, operating temperature and ground clearance as indicators to conduct a safety assessment of the transmission line. However, all of them were analyzed based on the overhead line model in an offline state. The reason is that the mechanical calculation method of the overhead conductor needs to be solved iteratively, and its calculation speed cannot meet the needs of online calculation, which greatly limits its application in the online assessment of the mechanical state of overhead lines. Therefore, in order to monitor the safety of overhead lines from the thermodynamic nature, a dynamic thermal rating (DTR) system was developed to monitor the conductor temperature, tension, sag and surrounding meteorological conditions of overhead conductors. On this basis, the conductor temperature of overhead lines was introduced into the power flow calculation to improve the calculation accuracy and reveal the potential transmission capacity of overhead lines.

[0006] Although existing research has introduced conductor temperature as a state variable into power flow and probabilistic power flow calculations, there are still the following problems that need to be solved: (1) The mechanical state of overhead conductors, as an important physical state in probabilistic power flow calculations, has not been taken into account; (2) In the case of accidental events, since the thermodynamic state has inertia, the dynamic information of the thermodynamic state of overhead conductors should not be ignored when analyzing the transmission capacity and safety risks of overhead conductors. Therefore, the electrothermodynamic state of overhead conductors should be comprehensively considered in probabilistic power flow calculations; (3) The existing probabilistic power flow calculations do not consider the uncertainty of meteorological conditions around overhead conductors that affect the thermodynamic state of overhead conductors; (4) Considering the thermodynamic state and environmental uncertainty leads to an increase in the amount of probabilistic power flow calculation, and further research is needed to develop an efficient solution method that is suitable for this. Summary of the invention

[0007] In order to solve the technical problem of the dynamic distribution of electricity and heat in key lines under the uncertain operating environment of the power system in the above-mentioned background technology, the present invention provides a probabilistic power flow calculation method and system considering the electrothermodynamic dynamics of overhead conductors, which can enable operators to obtain the distribution of electricity and heat states of key lines under uncertain environments and detect potential system safety risks based on the thermal and mechanical nature of overhead line safety.

[0008] In order to achieve the above object, the present invention adopts the following technical solution:

[0009] A first aspect of the present invention provides a probabilistic power flow calculation method taking into account the electrothermodynamic dynamics of overhead conductors.

[0010] The probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors includes:

[0011] Construct a thermal model of overhead conductors based on the changes in conductor current and the meteorological conditions around the conductors;

[0012] According to the initial horizontal stress, cross-sectional area and conductor temperature of the line, the mechanical model of the overhead conductor is constructed;

[0013] According to the conductor temperature and the conductor length, the mutual conductance function and the mutual susceptance function of the conductor are constructed;

[0014] Based on the thermal model, mechanical model, mutual conductance function and mutual susceptance function, an electro-thermal-mechanical coupled power flow model is constructed;

[0015] After considering the uncertain factors, the electro-thermal-mechanical coupled power flow model is converted into an electro-thermal-mechanical coupled probabilistic power flow model.

[0016] Under each set of uncertain factors, solve the line current and conductor temperature;

[0017] By using the positive correlation between the current carried by the conductor and the temperature, the calculated result of the conductor temperature is corrected according to the calculated current to obtain the corrected conductor temperature;

[0018] Based on the corrected conductor temperature, the stress and sag calculation results of the corresponding wire section are obtained;

[0019] All scenarios are calculated one by one to obtain the power grid flow and the probability distribution of line conductor temperature, stress and sag.

[0020] Furthermore, the thermal model is:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] Among them, I l (t) is the line current, is the convection coefficient, v l,k,s is the wind speed around the conductor, δ l,k,s is the angle between the wind and the conductor axis, l is the conductor, k is the tension section, and s is the line section; Tl,k,s is the conductor temperature of the middle line section s of the kth tension section of line l; m l C l It is the product of the mass per unit length of the overhead line l and the specific heat capacity; is the convective heat dissipation of the conductor per unit length in the center line section s of the kth tension section along the line l at time t; is the radiation heat dissipation of the conductor per unit length in the center line section s of the kth tension section along the line l at time t; is the current heating of the conductor per unit length in the middle section s of the kth tension section along the line l at time t; is the solar heating of the conductor per unit length in the center line section s of the kth tension section along the line l at time t; is the reference temperature T per unit length of line l ref Reference resistance at (20°C); S B is the basic capacity of the power system; β is the sunshine absorption rate; is the solar radiation heat intensity around the conductor of the kth tension section along the line l at time t; D l is the wire diameter; is the ambient temperature around the conductor of the kth tension section along line l at time t; is the radiation heat transfer coefficient per unit length of conductor l; α is the resistance temperature coefficient.

[0027] Furthermore, the mechanical model includes: the relationship between conductor stress and line length, and the relationship between conductor stress and line sag.

[0028] Furthermore, the relationship between the conductor stress and the line length is:

[0029]

[0030] The relationship between the conductor stress and the line sag is:

[0031]

[0032] Among them, a l,k,s is the length of the center line section s of the kth tension section of conductor l; X l,k,s is the stress coefficient of the middle line segment s of the kth tension section of conductor l; is the initial horizontal stress in the kth tension section of conductor l; h is the conductor length of the middle line section s of the kth tension section of conductor l; l,k,s is the height difference along the line between the two suspension points of the centerline section s of the line l tension section k; l,k,s It is the conductor load ratio on the middle line section s of the line l tension section k, which is related to meteorological conditions; is the sag of the middle line section s of the line l tension section k; O l is the cross-sectional area of ​​the conductor l.

[0033] Furthermore, the mutual conductance function is:

[0034]

[0035] The mutual susceptance function is:

[0036]

[0037]

[0038] Among them, T l is a vector consisting of the conductor temperatures of all wire sections of wire l, T l ∈{T l,k,s |k=1,…,n l,ts ,s=1,…,n l,k,span};L l It is a vector composed of the lengths of all the wires in the conductor l. l ∈{L l,k,s |k=1,…,n l,ts ,s=1,…,n l,k,span};[t0,t f ] is the research time range; n l,k,span is the number of wires in the kth tension section of conductor l; n l,ts is the number of tension sections of conductor l; is the reference temperature T per unit length of the conductor l ref The reference resistance under the condition of α is the temperature coefficient of resistance; x l is the reactance per unit length of conductor.

[0039] Furthermore, the electrothermal-mechanical coupled power flow model

[0040]

[0041] Where i∈SN,i≠slack,l∈(i,j),t∈[t0,t f ]

[0042]

[0043] where i∈SPQ,l∈(i,j),t∈[t0,t f ]

[0044] Where P i (t) and Q i (t) is the net injected active power and reactive power at node i at time t; V i (t) and Vj (t) are the voltage amplitudes of nodes i and j at time t; n node is the total number of nodes; θ ij (t) is the phase angle difference between nodes i and j at time t; SN is the set of all nodes; SN is the set of PQ nodes; slack is the equilibrium node.

[0045] Furthermore, the specific process of correcting the wire temperature calculation result according to the calculated current includes:

[0046] According to the temperature distribution of the conductor, the temperature distribution curve is fitted to obtain a quadratic curve; according to a certain temperature step, the quadratic curve is linearized into several intervals;

[0047] Using the positive correlation between conductor current and temperature, when the conductor temperature first falls into a certain temperature range, the electric, thermal and mechanical coupling power flow model is first used to obtain the conductor current, and then the conductor temperature is calculated based on the conductor current; the temperature correction value ΔT of the temperature range is calculated. cor =T ac -T linear And it is used as the temperature correction value within the temperature range;

[0048] Use ΔT cor For other T falling within this temperature range linear Make corrections and output T l,k,s,z =T linear +ΔT cor As the corrected final temperature calculation result;

[0049] Among them, T ac is the wire current value, T l,k,s,z is the corrected conductor temperature value, T linear The conductor temperature value is obtained by substituting the current obtained by solving the linear power flow model (18) into (19). Here, only the correction process of the temperature correction method is introduced, so the subscripts l, k, and s are not indicated. When this method is actually used for calculation, it is only necessary to substitute the line segment s data of the kth tension section of conductor s into the calculation.

[0050] A second aspect of the present invention provides a probabilistic power flow calculation system taking into account the electrothermodynamic dynamics of overhead conductors.

[0051] The probabilistic power flow calculation system considering the electrothermodynamic dynamics of overhead conductors includes:

[0052] A thermal model building module is configured to: build a thermal model of the overhead conductor according to changes in conductor current and meteorological conditions around the conductor;

[0053] A mechanical model building module is configured to: build a mechanical model of the overhead conductor according to the initial horizontal stress, cross-sectional area and conductor temperature of the line;

[0054] A function building module, which is configured to: build a mutual conductance function and a mutual susceptance function of the wires according to the wire temperature and the wire length;

[0055] An electro-thermal-mechanical coupled power flow model building module is configured to: build an electro-thermal-mechanical coupled power flow model based on a thermal model, a mechanical model, a mutual conductance function and a mutual susceptance function;

[0056] An electro-thermal-mechanical coupling probabilistic power flow model conversion module is configured to: after considering uncertain factors, convert the electro-thermal-mechanical coupling power flow model into an electro-thermal-mechanical coupling probabilistic power flow model;

[0057] A solution module, which is configured to: solve the line current and the conductor temperature in each set of uncertain factor scenarios;

[0058] A correction module is configured to: utilize the positive correlation between the current carried by the wire and the temperature, and correct the calculated result of the wire temperature according to the calculated current to obtain a corrected wire temperature;

[0059] A stress and sag calculation module, which is configured to: obtain stress and sag calculation results of the corresponding wire section based on the corrected conductor temperature;

[0060] The power flow calculation module is configured to calculate all scenarios one by one to obtain the power grid power flow and the probability distribution of line conductor temperature, stress and sag.

[0061] A third aspect of the present invention provides a computer-readable storage medium.

[0062] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors as described in the first aspect above.

[0063] A fourth aspect of the present invention provides a computer device.

[0064] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors as described in the first aspect above are implemented.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] 1. The present invention establishes an electrothermal-mechanical coupled power flow model, couples the thermodynamic state of the overhead line with the power flow, and takes the thermodynamic state of the overhead line into consideration in the power flow calculation.

[0067] 2. The present invention proposes a calculation framework for an electro-thermal-mechanical coupling probabilistic power flow model, and takes into account the uncertainty of meteorological conditions around overhead wires in the electro-thermal-mechanical coupling probabilistic power flow model, thereby improving the influencing factors of the probabilistic power flow.

[0068] Advantages of additional aspects of the present invention will be given in part in the description that follows, and in part will be obvious from the description that follows, or will be learned through practice of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0070] Figure 1 This is a schematic diagram of the electrical, thermal and mechanical coupling relationship of the power system shown in the first embodiment of the present invention;

[0071] Figure 2 The present invention is a framework for implementing the electro-thermal-mechanical coupling probabilistic power flow calculation method based on Monte Carlo simulation shown in the first embodiment of the present invention;

[0072] Figure 3 This is a flow chart of an approximate calculation method according to the first embodiment of the present invention;

[0073] Figure 4 The conductor temperature diagram under different currents shown in the first embodiment of the present invention;

[0074] Figure 5 A diagram showing the relationship between overhead conductor current and temperature using a quadratic function to fit the relationship between overhead conductor current and temperature shown in the first embodiment of the present invention;

[0075] Figure 6 A structural diagram of a regional power system shown in Embodiment 1 of the present invention;

[0076] Figure 7 This is a comparison chart of the over-limit probability results of calculating the conductor temperature using different methods in the first engineering example shown in the first embodiment of the present invention;

[0077] Figure 8 This is a comparison diagram of the probability of exceeding the limit of the ground clearance calculated by different methods in the engineering example 1 shown in the embodiment 1 of the present invention;

[0078] Fig. 9 This is a comparison chart of the over-limit probability results of calculating the conductor temperature using different methods in the second engineering example shown in the first embodiment of the present invention;

[0079] Fig.10This is a comparison chart of the probability of exceeding the limit of the clearance distance to the ground calculated by different methods in the second engineering example shown in the first embodiment of the present invention. DETAILED DESCRIPTION

[0080] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0081] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0082] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0083] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the methods and systems according to various embodiments of the present disclosure. It should be noted that each box in the flowchart or block diagram can represent a module, a program segment, or a part of a code, and the module, program segment, or a part of a code may include one or more executable instructions for implementing the logical functions specified in each embodiment. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, or they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the flowchart and / or block diagram, and the combination of boxes in the flowchart and / or block diagram can be implemented using a dedicated hardware-based system that performs a specified function or operation, or can be implemented using a combination of dedicated hardware and computer instructions.

[0084] Embodiment 1

[0085] like Figure 1As shown, this embodiment provides a probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors. This embodiment uses the method applied to a server as an example for illustration. It is understandable that the method can also be applied to a terminal, and can also be applied to a system including a terminal and a server, and is implemented through the interaction between the terminal and the server. The server can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network servers, cloud communications, middleware services, domain name services, security services CDN, and big data and artificial intelligence platforms. The terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited to this. The terminal and the server can be directly or indirectly connected via wired or wireless communication, which is not limited in this application. In this embodiment, the method includes the following steps:

[0086] Construct a thermal model of overhead conductors based on the changes in conductor current and the meteorological conditions around the conductors;

[0087] According to the initial horizontal stress, cross-sectional area and conductor temperature of the line, the mechanical model of the overhead conductor is constructed;

[0088] According to the conductor temperature and the conductor length, the mutual conductance function and the mutual susceptance function of the conductor are constructed;

[0089] Based on the thermal model, mechanical model, mutual conductance function and mutual susceptance function, an electro-thermal-mechanical coupled power flow model is constructed;

[0090] After considering uncertain factors (including node injection power and meteorological environment around key lines), the electro-thermal-mechanical coupled power flow model is converted into an electro-thermal-mechanical coupled probabilistic power flow model.

[0091] Decouple the electric, thermal and mechanical coupled probabilistic power flow model;

[0092] Based on the probability distribution curve of uncertain factors, Latin square sampling is performed on the uncertain factors to obtain the corresponding scenarios;

[0093] In each scenario of uncertain factors, the linear power flow calculation method and the linearized solution method of the heat balance equation are used to calculate the line current and conductor temperature respectively for the model after the decoupling of electricity, heat and force;

[0094] By using the positive correlation between the current carried by the conductor and the temperature, the calculated result of the conductor temperature is corrected according to the calculated current to obtain the corrected conductor temperature;

[0095] Based on the corrected conductor temperature calculation results, the overhead line mechanical equations (6), (12) and (13) are solved to obtain the stress and sag calculation results of the corresponding line section;

[0096] All scenarios are calculated one by one to obtain the power grid flow and the probability distribution of line conductor temperature, stress and sag.

[0097] The solution of this embodiment can be implemented according to the following contents:

[0098] 1 Basic Model

[0099] Due to the thermal and mechanical characteristics of overhead conductors, there is an electrical, thermal and mechanical coupling relationship in the operating power system. Figure 1 As shown, in the power system, the fluctuations of the current of the overhead line and the surrounding meteorological conditions will cause changes in the conductor temperature, stress and sag. On the one hand, due to the resistance-temperature effect of the conductor, the change of the conductor temperature will directly cause the change of the line resistance, thereby affecting the system power flow. On the other hand, the changes in the conductor temperature (thermal state) and stress and sag (mechanical state) will cause the conductor deformation (such as changes in the conductor length and cross-sectional area) due to the thermal elongation effect and stress-strain effect of the conductor, thereby indirectly affecting the line electrical parameters and system power. Therefore, a running power system can be regarded as an electrothermal-mechanical coupled dynamic system. The present invention establishes a power flow model that takes into account the electrothermal-mechanical state to describe the system. As the basis of the model, the thermal model and mechanical model of the overhead conductor will be introduced in the following sections 1.1 and 1.2.

[0100] 1.1 Thermal model of overhead conductors

[0101] For overhead conductors in operation, their thermal dynamics depend on the changes in line current and the meteorological conditions around the conductors. According to the CIGRE standard, the thermal balance equation in the sth line section of the kth tension section of conductor l can be expressed as:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] In (1)-(5), it is assumed that the line current I l (t) is consistent along the line. Convection coefficient Mainly determined by the wind speed v around the conductor l,k,s The angle δ between the wind and the conductor axis l,k,s The parameter calculation formulas in (2)-(5) can refer to the CIGRE standard, and the present invention will not repeat them in detail.

[0108] 1.2 Mechanical model of overhead conductors

[0109] For the kth tension section of the conductor along conductor l, its horizontal stress H l,k,s It can be expressed as the initial horizontal stress of the tension section k The stress coefficient X of the line segment s l,k,s The product of X l,k,s It can be obtained by solving equation (6):

[0110]

[0111] In (6), K s,1 ,…,K s,4 It can be expressed as follows:

[0112]

[0113]

[0114]

[0115]

[0116] in, is the slant span of line gear s, It can be expressed in the following form:

[0117]

[0118] In (6)–(11), a l,k,s is the length of the centerline section s of the kth tension section of line l; X l,k,s is the stress coefficient of the middle line section s of the kth tension section of line l; E l is the elastic coefficient of line l; O l is the cross-sectional area of ​​line l; is the initial horizontal stress in the kth tension section of line l; ε l is the thermal expansion coefficient of line l; T l,k,s is the conductor temperature of the middle section s of the kth tension section of line l; is the conductor temperature in the initial state; m l is the conductor mass per unit length; F s is the conductor stress factor for three consecutive spans.

[0119] For overhead wires in operation, due to the stress-strain effect of the wires, the wire stress H l,k,sThe change of will affect the length, sag and cross-sectional area of ​​the conductor. The cross-sectional area can be calculated by assuming that the overhead conductor is a uniform cylinder and the volume of the cylinder remains unchanged before and after the conductor is stressed. Conductor stress H l,k,s And line length And the conductor stress H l,k,s And line sag The relationship between can be expressed as (12) and (13) respectively:

[0120]

[0121]

[0122] in, h l,k,s is the height difference along the line between the two suspension points of the centerline section s of the line l tension section k; l,k,s It is the specific load of the conductor on the center line section s of the line l tension section k, which is related to meteorological conditions.

[0123] 1.3 Electric, thermal and mechanical coupled power flow model

[0124] From the above, we can see that the elements in the real and imaginary parts of the system node admittance matrix (G and B) are functions of the wire temperature and line length. The mutual conductance and mutual susceptance (g ij and b ij ) can be written as (14) and (15):

[0125]

[0126]

[0127] Among them, T l is a vector consisting of the conductor temperatures of all line segments of line l, T l ∈{T l,k,s |k=1,…,n l,ts ,s=1,…,n l,k,span};L l is a vector consisting of the lengths of all wires in line l, L l ∈{L l,k,s |k=1,…,n l,ts ,s=1,…,n l,k,span};[t0,t f ] is the research time range. Among them, n l,k,span is the number of wires in the kth tension section of line l; n l ,ts is the number of tension sections of line l; is the reference temperature T per unit length of line l refThe reference resistance at 20°C; α is the temperature coefficient of resistance; x l is the reactance per unit length of line l. Based on the above analysis, the electro-thermal-mechanical coupled power flow model can be expressed by (1), (6), (12), (14) and (15), and (16) and (17) are obtained.

[0128]

[0129]

[0130] Where P i (t) and Q i (t) is the net injected active power and reactive power at node i at time t; V i (t) and V j (t) are the voltage amplitudes of nodes i and j at time t; n node is the total number of nodes; θ ij (t) is the phase angle difference between nodes i and j at time t; SN is the set of all nodes; SN is the set of PQ nodes; slack is the equilibrium node.

[0131] 1.4 Electrothermal-mechanical coupled probabilistic power flow model

[0132] After considering various uncertain factors, an electro-thermal-mechanical coupled power flow model was formed, in which conductor temperature, stress and conductor length were introduced as new state variables to obtain an electro-thermal-mechanical coupled probabilistic power flow model; this model can describe the electro-thermal-mechanical coupled state of the power system.

[0133] The Monte Carlo simulation method is used to solve the electro-thermal-mechanical coupling probabilistic power flow, and the Latin hypercube sampling method is used to sample the scenarios. The implementation framework of the electro-thermal-mechanical coupling probabilistic power flow calculation method based on Monte Carlo simulation is as follows: Figure 2 The fast calculation method mentioned in step ⑤ is introduced in Section 2.

[0134] 2 Rapid calculation method of electrothermodynamic state of overhead wire

[0135] The present invention first decouples the electrothermodynamic state of the power system, and then replaces the traditional AC power flow solution with linear power flow and uses the fast solution method of the heat balance equation to improve the calculation efficiency of the electrothermodynamic coupling probabilistic power flow proposed in Section 1 of the present invention. However, the accuracy of the linear power flow solution of the line current is limited, so it needs to be corrected.

[0136] 2.1 Decoupling of electrothermodynamic states

[0137] Compared with traditional power flow calculation, the computational complexity of probabilistic power flow taking into account electrothermodynamics is greatly increased, and the meteorological factors around the overhead line are required, which brings greater difficulties to engineering application. In engineering practice, only a few key line sections that determine the safety of the line are paid attention to and monitored by DTR technology. In addition, due to the resistance-temperature coefficient of the conductor (about 0.004 for aluminum conductor) and the thermal elongation coefficient (about 23.1×10 -6 K -1 ) is small, and the elastic modulus of the conductor is large, the influence of conductor temperature and stress on power is limited. Therefore, it is reasonable to solve the power flow model, thermal model and mechanical model within the critical span of the overhead conductor in sequence and independently without sacrificing the accuracy of the electrothermodynamic calculation of the overhead conductor. In this section, the linear power flow calculation method and the linearization technology of the heat balance equation are used to approximate the electrothermodynamic state of the overhead conductor under each system scenario, thereby further reducing the calculation time of the electrothermomechanical coupled probabilistic power flow.

[0138] 2.1 Rapid solution of linear power flow and heat balance equations

[0139] In order to improve the calculation efficiency of the electro-thermal-mechanical coupled probabilistic power flow model, this embodiment proposes a fast calculation method to simplify the analysis of the electro-thermal-mechanical coupled probabilistic power flow model from the perspective of decoupling.

[0140] The linearized power flow model is used to speed up the calculation of AC power flow. The linearized power flow model at time interval z can be expressed as:

[0141]

[0142] After solving the linearized power flow model (18), the current of the key line can be obtained. The temperature of the conductor can be obtained by solving the linearized heat balance equation of the conductor as follows:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] Where Δt is the difference step size; subscripts z and z-1 represent the current time interval and the previous time interval, respectively; m l C l It is the product of the mass per unit length of the overhead line and the specific heat capacity; and is the ambient temperature around the line l tension section k; l,z is the current flowing through line l; S B is the basic capacity of the power system; the remaining parameters are differential representations of the parameters in (1)-(5) and will not be repeated here.

[0152] 2.2 Revision process

[0153] Although the effectiveness and high calculation accuracy of the linearized power flow model have been verified, the thermodynamic state of the conductor is very sensitive to the change of current, so the calculation error of the line current cannot be ignored. The calculated conductor temperature needs to be corrected according to the line current calculated by the linearized power flow.

[0154] During the thermal inertia time of overhead conductors (usually less than 30 minutes), the changes in meteorological conditions around the conductors are limited. In this case, the line current plays a dominant role in the change of conductor temperature. Figure 3 As shown, although the distribution range of the conductor temperature (the upper and lower limits of the interval are respectively Figure 3 The red and green lines in the figure increase with the increase of current, but there is a strong positive correlation between current and conductor temperature. Using this characteristic, the conductor temperature based on linearized power flow calculation is corrected as follows:

[0155] a. Based on the attachment Figure 3 The temperature distribution of the conductor shown in the figure is obtained by curve fitting. Figure 4 Then, according to a certain temperature step length (the step length selected in the present invention is 5°C), the quadratic curve is segmented and linearized into several intervals, as shown in the attached figure. Figure 4 shown.

[0156] b. When the line current calculated based on the linear power flow model using (19) falls into the adjacent Figure 4 When the temperature is within a certain range, the traditional AC power flow calculation is performed first, and the accurate line current (denoted as I AC ). Then, by putting I AC Substituting into (19), the exact conductor temperature (expressed as T AC ). Calculate the temperature correction value ΔT for the temperature range cor =T ac -T linear And it is used as the temperature correction value within this temperature range.

[0157] c. Use ΔT cor For other linear Make corrections and output T l,k,s,z =T linear +ΔT cor As the corrected final temperature calculation result.

[0158] As mentioned above, in the above steps, the traditional AC power flow calculation is only performed once in each conductor temperature range, so compared with solving the AC power flow in each system scenario, the calculation time can be greatly reduced. The fast calculation process is shown in the attached figure. Figure 5 shown.

[0159] Engineering Example 1

[0160] In order to better verify the technical concept of the present invention, a specific example analysis is given below: The structure of the 25-node regional power grid in Shandong Province is selected as shown in the attached figure. Figure 6 As shown. The rated voltage of the system is 220KV, and the basic capacity of the system is set to 100MVA. The type of overhead line conductor is ACSR 300 / 40 (the cross-sectional area of ​​the aluminum part is 300mm2, and the cross-sectional area of ​​the steel core is 40mm2). In this example, the maximum allowable temperature of the overhead conductor is set to 70℃, the research time range is 30 minutes, and the discretization time interval Δt is set to 5 minutes.

[0161] In order to detect potential emergencies in the regional system, probabilistic power flow is used to analyze possible emergencies. Taking the outage of Line 9-23 as an example, Line 12-23 is considered to be a critical line. The length of the suspended insulator string along Line 12-23 is 1.6m, the weight is 130kg, and the length of the tension tower insulator string is 1.95m, the weight is 150kg. Along Line 12-23, the 6th line section of the 9th tension section was determined as the critical line section, and DTR facilities were installed. In the probabilistic power flow calculation, the 4 meteorological elements and active power injection near the overhead wire of node 14 and the critical line section are regarded as random parameters. The injected power (generation and load) of other nodes in the system is regarded as a deterministic parameter, and its value has an increasing trend within the study time range.

[0162] Attached Figure 7 and attached Figure 8 The conductor temperature and the probability of exceeding the limit of the key line clearance to the ground calculated by three methods are shown. Table 2 shows the calculation time of these three methods.

[0163] Table 1. Description of the three methods

[0164]

[0165] Table 2. Computation time of different methods

[0166]

[0167] From the attached Figure 7 , Attachment Figure 8 The following conclusions can be drawn from Table 1: (1) The calculation error between Method II and Method III is very small. Since the resistance temperature coefficient of the 220KV overhead line is small and the reactance of the transmission line is much larger than the resistance, the reactance is the main parameter that determines the power flow distribution. Therefore, the influence of the conductor temperature on the power flow by affecting the resistance is limited. However, Method III does not completely ignore the influence of the conductor temperature on the resistance. The resistance will be updated according to the calculation results of the conductor temperature in the previous time period, which will further narrow the difference between the calculation results of the two methods. The calculation time of Method II is only 27.26% less than that of Method I. (2) The calculation error of Method III is very small (based on the calculation results of Method I, in all sampling scenarios, the average absolute percentage errors of Method III for conductor temperature, stress and gap distance are 1.78%, 1.54% and 1.58% respectively). In addition, the calculation time of Method III is significantly less than that of Method I (the calculation time is reduced by 71.29%). This shows that Method III can greatly improve the calculation speed of electrothermal coupled probabilistic power flow at the cost of smaller calculation accuracy.

[0168] Engineering Example 2

[0169] In order to verify the performance of the proposed fast calculation method in large-scale power systems, the IEEE 300-node system is taken as an example, assuming that the conductor type is ACSR300 / 40, and the electrical parameters of all lines are recalculated (the line length is determined by matching the line reactance parameters of the standard system). The base capacity of the test system is 100MVA and the rated voltage is 345KV. In the revised system, taking the outage event of line 186-188 as an example, assuming that the outage event occurs at 0min, the outage will aggravate the power flow of line 181-188, so line 181-188 is regarded as a critical line in this case study. It is assumed that the power generation and load demand are increasing after the power outage, and there is a tension section on line 181-188 that is the same as in engineering example 1, and the 6th line section of the tension section is determined to be the critical line section. The other calculation conditions are the same as those given in engineering example 1. For this test system, the calculation time of different methods is shown in Table 3, and the calculation results are shown in Appendix. Fig. 9 , Attachment Fig.10 .

[0170] Table 3. Computation time of different methods

[0171]

[0172] For larger systems, the computational time savings of Method III are still significant (compared to Method I, the computational time of Method II and Method III is reduced by 29.07% and 79.51%, respectively). Using the calculation results of Method I as a benchmark, the average absolute percentage deviation of Method III for wire temperature, stress, and gap distance in all sampled scenarios is 2.12%, 86%, and 1.96%, respectively.

[0173] Embodiment 2

[0174] This embodiment provides a probabilistic power flow calculation system that takes into account the electrothermodynamic dynamics of overhead conductors.

[0175] The probabilistic power flow calculation system considering the electrothermodynamic dynamics of overhead conductors includes:

[0176] A thermal model building module is configured to: build a thermal model of the overhead conductor according to changes in conductor current and meteorological conditions around the conductor;

[0177] A mechanical model building module is configured to: build a mechanical model of the overhead conductor according to the initial horizontal stress, cross-sectional area and conductor temperature of the line;

[0178] A function building module, which is configured to: build a mutual conductance function and a mutual susceptance function of the wires according to the wire temperature and the wire length;

[0179] An electro-thermal-mechanical coupled power flow model building module is configured to: build an electro-thermal-mechanical coupled power flow model based on a thermal model, a mechanical model, a mutual conductance function and a mutual susceptance function;

[0180] An electro-thermal-mechanical coupling probabilistic power flow model conversion module is configured to: after considering uncertain factors, convert the electro-thermal-mechanical coupling power flow model into an electro-thermal-mechanical coupling probabilistic power flow model;

[0181] A solution module, which is configured to: solve the line current and the conductor temperature in each set of uncertain factor scenarios;

[0182] A correction module is configured to: utilize the positive correlation between the current carried by the wire and the temperature, and correct the calculated result of the wire temperature according to the calculated current to obtain a corrected wire temperature;

[0183] A stress and sag calculation module, which is configured to: obtain stress and sag calculation results of the corresponding wire section based on the corrected conductor temperature;

[0184] The power flow calculation module is configured to calculate all scenarios one by one to obtain the power grid power flow and the probability distribution of line conductor temperature, stress and sag.

[0185] It should be noted here that the above-mentioned thermal model construction module, mechanical model construction module, function construction module, electrothermal-mechanical coupling power flow model construction module, electrothermal-mechanical coupling probability power flow model conversion module, solution module, correction module, stress and sag calculation module and power flow calculation module are the same as the examples and application scenarios implemented by the steps in the first embodiment, but are not limited to the contents disclosed in the first embodiment. It should be noted that the above-mentioned modules as part of the system can be executed in a computer system such as a set of computer executable instructions.

[0186] Embodiment 3

[0187] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps in the probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors as described in the first embodiment above are implemented.

[0188] Embodiment 4

[0189] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead wires as described in the first embodiment above are implemented.

[0190] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.

[0191] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0192] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0193] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0194] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0195] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors, characterized in that: include: Construct a thermal model of overhead conductors based on the changes in conductor current and the meteorological conditions around the conductors; According to the initial horizontal stress, cross-sectional area and conductor temperature of the line, the mechanical model of the overhead conductor is constructed; According to the conductor temperature and the conductor length, the mutual conductance function and the mutual susceptance function of the conductor are constructed; Based on the thermal model, mechanical model, mutual conductance function and mutual susceptance function, an electro-thermal-mechanical coupled power flow model is constructed; After considering the uncertain factors, the electro-thermal-mechanical coupled power flow model is converted into an electro-thermal-mechanical coupled probabilistic power flow model. Under each set of uncertain factors, solve the line current and conductor temperature; By using the positive correlation between the current carried by the conductor and the temperature, the calculated result of the conductor temperature is corrected according to the calculated current to obtain the corrected conductor temperature; Based on the corrected conductor temperature, the stress and sag calculation results of the corresponding wire section are obtained; Calculate all scenarios one by one to obtain the power grid flow, as well as the probability distribution of line conductor temperature, stress and sag; The electrothermal-mechanical coupled power flow model Where i∈SN,i≠slack,l∈(i,j),t∈[t0,t f ] where i∈SPQ,l∈(i,j),t∈[t0,t f ] Where P i (t) and Q i (t) is the net injected active power and reactive power at node i at time t; V i (t) and V j (t) are the voltage amplitudes of nodes i and j at time t; n node is the total number of nodes; θ ij (t) is the phase difference between nodes i and j at time t; SN is the set of all nodes; SN is the set of PQ nodes; slack is the equilibrium node, G ij (T l (t),L l (t)) represents the mutual conductance function, B ij (T l (t),L l (t)) represents the mutual susceptance function.

2. The probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors according to claim 1 is characterized in that: The thermal model is: Among them, I l (t) is the line current, is the convection coefficient, v l,k,s is the wind speed around the conductor, δ l,k,s is the angle between the wind and the conductor axis, l is the conductor, k is the tension section, s is the line section; T l,k,s is the conductor temperature of the middle section s of the kth tension section of line l; m l C l It is the product of the mass per unit length of the overhead line l and the specific heat capacity; is the convective heat dissipation of the conductor per unit length in the center line section s of the kth tension section along the line l at time t; is the radiation heat dissipation of the conductor per unit length in the kth tension section along the line l at time t; is the current heating of the conductor per unit length in the middle section s of the kth tension section along the line l at time t; is the solar heating of the conductor per unit length in the center line section s of the kth tension section along the line l at time t; is the reference temperature T per unit length of line l ref Reference resistance at (20°C); S B is the basic capacity of the power system; β is the sunshine absorption rate; is the solar radiation heat intensity around the conductor of the kth tension section along the line l at time t; D l is the wire diameter; is the ambient temperature around the conductor of the kth tension section along line l at time t; is the radiation heat transfer coefficient per unit length of conductor l; α is the resistance temperature coefficient.

3. The probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors according to claim 1 is characterized in that: The mechanical model includes: the relationship between conductor stress and line length, and the relationship between conductor stress and line sag.

4. The probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors according to claim 3 is characterized in that: The relationship between the conductor stress and the line length is: The relationship between the conductor stress and the line sag is: Among them, a l,k,s is the length of the center line section s of the kth tension section of conductor l; X l,k,s is the stress coefficient of the middle line segment s of the kth tension section of conductor l; is the initial horizontal stress in the kth tension section of conductor l; L l，k，s h is the conductor length of the middle line section s of the kth tension section of conductor l; l,k,s is the height difference along the line between the two suspension points of the centerline section s of the line l tension section k; l,k,s It is the conductor load ratio on the middle line section s of the line l tension section k, which is related to meteorological conditions; is the sag of the middle line section s of the line l tension section k; O l is the cross-sectional area of ​​the conductor l.

5. The probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors according to claim 1 is characterized in that: The mutual conductance function is: The mutual susceptance function is: Among them, T l is a vector consisting of the conductor temperatures of all the wire sections of wire l, T l ∈{T l,k,s |k=1,…,n l,ts ,s=1,…,n l,k,span };L l It is a vector composed of the lengths of all the wires in the conductor l. l ∈{L l,k,s |k=1,…,n l,ts ,s=1,…,n l,k,span };[t0,t f ] is the research time range; n l,k,span is the number of wires in the kth tension section of conductor l; n l,ts is the number of tension sections of conductor l; is the reference temperature T per unit length of the conductor l ref The reference resistance under the condition of α is the temperature coefficient of resistance; x l is the reactance per unit length of conductor.

6. The probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors according to claim 1 is characterized in that: The specific process of correcting the wire temperature calculation result according to the calculated current includes: According to the temperature distribution of the conductor, the temperature distribution curve is fitted to obtain a quadratic curve; according to a certain temperature step, the quadratic curve is linearized into several intervals; Using the positive correlation between conductor current and temperature, when the conductor temperature first falls into a certain temperature range, the electric, thermal and mechanical coupling power flow model is first used to obtain the conductor current, and then the conductor temperature is calculated based on the conductor current; the temperature correction value ΔT of the temperature range is calculated. cor =T ac -T linear And it is used as the temperature correction value within the temperature range; Use ΔT cor For other linear Make corrections and output T l,k,s,z =T linear +ΔT cor As the corrected final temperature calculation result; Among them, T ac is the wire current value, T l,k,s,z is the corrected conductor temperature value, T linear is the conductor temperature value.

7. A probabilistic power flow calculation system considering the electrothermodynamic dynamics of overhead conductors, characterized in that: The method for calculating a probabilistic power flow considering the electrothermodynamic dynamics of overhead conductors according to any one of claims 1 to 6 comprises: A thermal model building module is configured to: build a thermal model of the overhead conductor according to changes in conductor current and meteorological conditions around the conductor; A mechanical model building module is configured to: build a mechanical model of the overhead conductor according to the initial horizontal stress, cross-sectional area and conductor temperature of the line; A function building module, which is configured to: build a mutual conductance function and a mutual susceptance function of the wires according to the wire temperature and the wire length; An electro-thermal-mechanical coupled power flow model building module is configured to: build an electro-thermal-mechanical coupled power flow model based on a thermal model, a mechanical model, a mutual conductance function and a mutual susceptance function; An electro-thermal-mechanical coupling probabilistic power flow model conversion module is configured to: after considering uncertain factors, convert the electro-thermal-mechanical coupling power flow model into an electro-thermal-mechanical coupling probabilistic power flow model; A solution module, which is configured to: solve the line current and the conductor temperature in each set of uncertain factor scenarios; A correction module is configured to: utilize the positive correlation between the current carried by the wire and the temperature, and correct the calculated result of the wire temperature according to the calculated current to obtain a corrected wire temperature; A stress and sag calculation module, which is configured to: obtain stress and sag calculation results of the corresponding wire section based on the corrected conductor temperature; The power flow calculation module is configured to calculate all scenarios one by one to obtain the power grid power flow and the probability distribution of line conductor temperature, stress and sag.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors as described in any one of claims 1 to 6 are implemented.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the probabilistic power flow calculation method considering the electrothermodynamic dynamics of overhead conductors as described in any one of claims 1 to 6 are implemented.

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