CN111864741B - Quantitative analysis method and system for influence of line parameter errors on power distribution - Google Patents

Quantitative analysis method and system for influence of line parameter errors on power distribution Download PDF

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CN111864741B
CN111864741B CN202010731673.XA CN202010731673A CN111864741B CN 111864741 B CN111864741 B CN 111864741B CN 202010731673 A CN202010731673 A CN 202010731673A CN 111864741 B CN111864741 B CN 111864741B
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power
node
sensitivity
parameters
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CN111864741A (en
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吴正阳
傅中
程登峰
朱太云
朱胜龙
刘宇舜
李森林
夏令志
程洋
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Anhui Electric Power Co Ltd
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Electric Power Research Institute of State Grid Anhui Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

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Abstract

A quantitative analysis method and system of influence of line parameter error on power distribution solve the problem that research on influence of power grid parameter error on state estimation result focuses on a single line, influence of line parameter change on node voltage and adjacent line power is not considered, and overall precision is low, and the method comprises the steps of obtaining original parameters of a power system, calculating system load flow, solving phase angle and amplitude of voltage of each node and flowing power of each line; calculating partial derivatives of each element of the admittance matrix of the system to the line parameters; solving a sensitivity coefficient matrix according to a node constraint equation and a load flow calculation result; calculating the sensitivity of the node voltage phase angle and the amplitude to each line parameter; calculating the sensitivity of the active power and the reactive power flowing through the line to line parameter according to the relation between the line flowing power and the node voltage; meanwhile, the influences of the voltage phase angle and amplitude of the parameter error node and other line power are considered, and the accuracy of the obtained result is higher.

Description

Quantitative analysis method and system for influence of line parameter errors on power distribution
Technical Field
The invention belongs to the technical field of power system control, and particularly relates to a method and a system for quantitatively analyzing the influence of line parameter errors on power distribution.
Background
And the state estimation of the power system solves the state quantities such as voltage phase angle, amplitude value and line flowing power of each node when the power grid is stably operated according to each parameter in the power grid, the telemetering measurement value and the telemetering measurement value. The estimated value obtained by calculation is the basis of various advanced applications of the power grid, including static safety calculation of the system, available transmission capacity calculation and the like. Meanwhile, the difference between the state estimation result and the accurate value reflects the quality of the basic data of the power grid dispatching automation.
Factors influencing the state estimation result include the accuracy of the grid parameters and the accuracy of the measured data. With the development of the power grid communication technology, the accuracy of remote measurement and remote signaling of the dispatching automation is greatly improved, and the influence of the error on the accuracy of the state estimation result is gradually reduced. The main reasons for the errors of the parameters of the power grid include data errors provided by manufacturers of production and manufacturing equipment, line reconstruction, incomplete information control in environmental change and the like. The power grid parameter errors directly affect the load flow calculation result of the whole power grid, and further affect the accuracy of the state estimation result. Therefore, it is necessary to study the influence degree of the grid parameter error on each state quantity.
In the prior art, researches on the influence of power grid parameter errors on a state estimation result are few, and a document 'analysis on influence of power transmission line resistance parameter errors on a reactive state estimation result' published on 12/1/2015, which aims at the problem of reactive voltage state estimation result deviation frequently occurring in state estimation daily operation maintenance of a scheduling operation unit, analyzes the influence of line resistance parameters on the reactive state estimation result in detail, provides a solving direction when power grid reactive measurement data and the state estimation result are contradictory, and verifies the accuracy of the analysis result by combining with an example in production practice.
The invention discloses a high-voltage ring-shaped power grid state estimation method and device in Chinese patent with publication number CN106451433A and publication number 2017, 2, month 22 and provides a high-voltage ring-shaped power grid state estimation method and device, which can avoid errors of high-voltage ring-shaped power grid parameters and improve the accuracy of high-voltage ring-shaped power grid state estimation.
Although the prior art mentioned above all involve the sensitivity of the line flowing power to the line parameter, the model is based on a single line only, and the influence of the change of a certain line parameter on the power of the rest lines cannot be calculated. And node voltages on two sides of the line are set to be constant values in the model, and the influence of line parameter change on the node voltages is not considered, so that the sensitivity result error is large. During actual grid operation, errors in any line parameter can cause changes in the overall grid power flow, including the voltages at all nodes and the power flowing through the line. If the related sensitivity is calculated from the perspective of the power grid, the influence of the change of any line parameter on the voltage phase angle of the unbalanced node and the voltage amplitude of the PQ node needs to be considered at the same time, so that all load flow constraint equations need to be established simultaneously, and the sensitivity of the voltage of each node and the line power to each line parameter is calculated through an equivalent coefficient matrix.
Chinese patent application No. CN101635457A, published as 1/27/2010, discloses a power grid parameter estimation method based on state estimation residual parameter sensitivity, which derives the sensitivity of state estimation residual to each line parameter of a power grid according to an actual power grid model and real-time measurement data, and modifies the line parameters on an existing suspicious branch set by using a linear optimization method, thereby improving the reliability and accuracy of application software. In this patent document, the sensitivity of the residual error to the line parameter is calculated by comparing the residual error between the measured value and the actual value in the power grid, and the line parameter is identified by the sensitivity. In the document, only the relation between the power grid admittance matrix and the line parameters is considered in the sensitivity calculation, and a clear calculation formula of a residual error formula on the sensitivity of each element in the admittance matrix is not given.
Therefore, most of researches on the influence of power grid parameter errors on state estimation results in the prior art are only concentrated on a single line, the influence on line power when the parameters are changed is obtained through the relation between active power and reactive power flowing through the line in the pi-type equivalent circuit and the line parameters, the influence on node voltage and adjacent line power caused by the change of the line parameters is not considered, the problem of low overall precision is solved, and the method for quantitatively analyzing the influence of the more accurate line parameter errors on system power distribution is significant.
Disclosure of Invention
The invention aims to solve the problems that in the prior art, the research on the influence of power grid parameter errors on state estimation results is only concentrated on a single line, the influence of line parameter changes on node voltage and adjacent line power is not considered, and the overall accuracy is low.
The invention solves the technical problems through the following technical scheme:
a quantitative analysis method for influence of line parameter errors on system power distribution is used for calculating sensitivity of power system line passing power to line parameters and quantifying influence of the line parameter errors on the power system power distribution, and is characterized by comprising the following steps:
step 1): acquiring original parameters of an electric power system, calculating the power flow of the system, and solving the voltage phase angle and amplitude of each node and the power flowing through each line;
step 2): calculating partial derivatives of each element of the admittance matrix of the system to the line parameters;
step 3): solving a sensitivity coefficient matrix according to a node constraint equation and a load flow calculation result;
step 4): calculating the sensitivity of the node voltage phase angle and amplitude to each line parameter, obtaining the voltage amplitude and phase angle of each node meeting a power flow constraint equation through preposed power flow calculation, simultaneously establishing the partial derivatives of all power flow equation constraint equations to the line parameters, and calculating the sensitivity of the voltage amplitude of the unbalanced node voltage phase angle and PQ node to the parameters through a matrix form;
and step 5): and calculating the sensitivity of the active power and the reactive power of the line current to the line parameters according to the relation between the line current power and the node voltage.
The method comprises the steps of obtaining voltage amplitude values and phase angles of all nodes meeting a power flow constraint equation through pre-power flow calculation, simultaneously establishing partial derivatives of all power flow equation constraint equations to line parameters, and calculating the sensitivity of voltage phase angles of unbalanced nodes and voltage amplitude values of PQ nodes to the parameters through a matrix form; and then, the sensitivity of the line power flow to parameters is calculated through the relation between the line power flow and the node voltage, the influence of line parameter errors on the system power distribution is quantitatively analyzed based on a power flow model, the influence of the node voltage phase angle and amplitude of the parameter errors and the influence of other line powers are considered, and the accuracy of the obtained result is higher.
As a further improvement of the technical scheme of the invention, the original parameters of the power system in the step 1) comprise active power and reactive power input by a generator, load of nodes and line parameters, a Newton-Raphson method is adopted for calculating the power flow of the system, and a voltage phase angle theta and an amplitude V of each node and power S flowing through each line are obtained L 。
As a further improvement of the technical scheme of the invention, the step 2): calculating partial derivatives of each element of an admittance matrix of the system to the line parameters, specifically: the real part and the imaginary part of each element in the node admittance matrix Y are respectively G ij And B ij For off-diagonal elements, G ij And B ij Is calculated as shown in equations (1) and (2):
Figure GDA0003782875780000041
Figure GDA0003782875780000042
wherein r is ij And x ij The resistance and reactance parameters of the line between node i and node j, G, respectively ij And B ij The real and imaginary parameters of the element between node i and node j in the admittance matrix Y, respectively.
For diagonal element G ii And B ii The calculation of (a) is shown in formulas (3) and (4), wherein b is a line capacitance parameter, and omega is all nodes directly connected with the i line;
Figure GDA0003782875780000051
Figure GDA0003782875780000052
wherein r is ia 、x ia And b ia Parameters for resistance, reactance and susceptance of the line between node i and node a, G ii And B ii The real and imaginary parameters of the diagonal elements in the admittance matrix Y, and Ω is the set of all nodes directly connected to the i-node by wire.
According to the formulas (1) and (2), the partial derivatives of the non-diagonal elements of the admittance matrix to the resistance and reactance of the line can be deduced as shown in the formulas (5) and (6):
Figure GDA0003782875780000053
Figure GDA0003782875780000054
according to the equations (3) and (4), the partial derivatives of the diagonal elements of the admittance matrix to the resistance and reactance of a certain line can be derived as shown in equations (7) and (8):
Figure GDA0003782875780000055
Figure GDA0003782875780000056
in addition, B ii The bias on line capacitance is as shown in equation (9):
Figure GDA0003782875780000061
as a further improvement of the technical scheme of the invention, the step 3): according to the node constraint equation and the load flow calculation result, solving a sensitivity coefficient matrix and a step 4): calculating the sensitivity of the node voltage phase angle and the amplitude to each line parameter, specifically as follows:
1) a node constraint equation of the power flow calculation of the power system is shown as a formula (10), wherein the superscript spec is a set value of the node power, and n is the number of nodes in the system; after the load flow calculation reaches the convergence standard, the values of the node voltage amplitude and the phase angle meet the establishment of an equation (10);
Figure GDA0003782875780000062
wherein, Δ P i And Δ Q i An unbalance of active and reactive power is injected for node i, respectively.
2) And (3) deriving the line parameter z on two sides of the active power constraint equation of the ith node to obtain:
Figure GDA0003782875780000063
in the formula:
Figure GDA0003782875780000064
H ij ＝-V i V j (B ij cosθ ij -G ij sinθ ij ) (13)
Figure GDA0003782875780000065
K ij ＝V i (G ij cosθ ij +B ij sinθ ij ) (15)
Figure GDA0003782875780000071
wherein, theta i And theta j The phase angle of the voltage at node i and node j, θ ij Is the voltage phase angle difference between node i and node j, i.e. θ ij ＝θ i –θ j ，V i And V j The voltage amplitudes of node i and node j, respectively. H ii And H ij Diagonal elements and off-diagonal elements, K, of the matrix of node voltage phase angles versus line parameter sensitivity coefficients in the equation of active power imbalance, respectively ii And K ij Diagonal elements and off-diagonal elements, C, of the node voltage amplitude pair versus line parameter sensitivity coefficient matrix in the active power imbalance equation 1i Constant matrix elements of the active power imbalance equation to the line parameter partial derivatives.
3) And (3) differentiating the line parameter z on two sides of the reactive power constraint equation of the ith node to obtain:
Figure GDA0003782875780000072
in the formula:
Figure GDA0003782875780000073
L ij ＝-V i V j (G ij cosθ ij +B ij sinθ ij ) (19)
Figure GDA0003782875780000074
K ij ＝V i (G ij sinθ ij -B ij cosθ ij ) (21)
Figure GDA0003782875780000075
wherein L is ii And L ij Respectively, node voltage phase angle in reactive power imbalance equation versus line parametersDiagonal and off-diagonal elements of the sensitivity coefficient matrix, M ii And M ij Diagonal elements and off-diagonal elements, C, of the node voltage amplitude versus line parameter sensitivity coefficient matrix in the reactive power imbalance equation 2i Constant matrix elements that are the partial derivatives of the reactive power imbalance equation to the line parameters.
4) Constructing a coefficient matrix of node voltage phase angle and amplitude to line parameter sensitivity; according to equations (11) - (22), the power imbalance of all nodes are simultaneously derived from the line parameters, as shown in equation (23), where A eq A coefficient matrix which is a sensitivity model;
Figure GDA0003782875780000081
wherein, Δ P is a matrix formed by active power imbalance equations of all non-equilibrium nodes, Δ Q is a matrix formed by reactive power imbalance equations of all PQ nodes, H is a matrix of sensitivity coefficients of node voltage phase angles to line parameters in the active power imbalance equations, K is a matrix of sensitivity coefficients of node voltage amplitude values to line parameters in the active power imbalance equations, L is a matrix of sensitivity coefficients of node voltage phase angles to line parameters in the reactive power imbalance equations, M is a matrix of sensitivity coefficients of node voltage amplitude values to line parameters in the reactive power imbalance equations, V and theta are a matrix of node voltage amplitude values and phase angles, C is a matrix of node voltage amplitude values and phase angles 1 Constant matrix, C, being the partial derivative of the line parameters by the equation of the active power imbalance 2 And the constant matrix is a constant matrix of the reactive power imbalance equation to the line parameter partial derivatives.
The nodes in the power flow calculation of the power system can be divided into a PQ node, a PV node and a balance node, wherein the voltage phase angle and the amplitude of the PQ node are required to be solved, the node reactive power input and the node voltage phase angle of the PV node are required to be solved, the balance node is used as a reference node, the node voltage phase angle and the amplitude are given, and other parameters are required to be solved; suppose the number of PQ nodes in the system is n PQ The system has n-1 active power imbalance equations in total, n PQ A reactive power imbalance equation; the coefficient matrix A is thus eq Is (n-1 + n) PQ )×(n–1+n PQ ) Wherein the H matrix is a (n-1) x (n-1) square matrix and the K matrix is a (n-1) x n square matrix PQ L matrix is n PQ X (n-1), M is n PQ ×n PQ A square matrix of (a);
5) and (3) solving the sensitivity of the node voltage phase angle and the amplitude to the line parameters, and obtaining a corresponding solving formula according to the formula (23) as follows:
Figure GDA0003782875780000091
as a further improvement of the technical solution of the present invention, the line parameter z includes a line resistance, a reactance, or a capacitance.
As a further improvement of the technical scheme of the invention, the step 5): the specific method for calculating the sensitivity of the active power and the reactive power flowing through the line to the parameters of the line and the like according to the relationship between the flowing power of the line and the node voltage comprises the following steps: power S of line flow Lia The relationship between the node voltage and the line parameters is shown in formula (25), wherein the subscript represents the conjugate value of the corresponding value.
Figure GDA0003782875780000092
Wherein S is Lia For the power flowing through the line between node i and node a, P Lia And Q Lia Active and reactive power, Y, respectively, flowing through the line between node i and node a ia Is the admittance matrix, θ, of the line between node i and node a a Is the voltage phase angle of node a, V a Is the voltage amplitude of node a, G ia And B ia Are the real and imaginary parameters of the element between node i and node a in the admittance matrix Y.
So that the active power P flowing through the line Lij And reactive power Q Lij Respectively as follows:
P Lij ＝-(V i 2 -V i V j cosθ ij )G ij +V i V j sinθ ij B ij (26)
Figure GDA0003782875780000101
wherein G is ij And B ij The real and imaginary parts of the elements between node i and node j in the admittance matrix Y, respectively.
By taking the derivative of the line parameter z by equation (26), we can obtain:
Figure GDA0003782875780000102
for line reactive power Q Lij Due to the line capacitance parameter b ij The presence of (a) requires distinguishing the sensitivity to capacitance and other parameters when calculating the corresponding sensitivity; the sensitivity of the line flowing through reactive power to the capacitance b is:
Figure GDA0003782875780000103
wherein, B ij Is the imaginary parameter of the element between node i and node j in the admittance matrix Y.
For the line resistance parameters, the sensitivity of the obtained line reactive power to the resistance parameters is shown as a formula (30);
Figure GDA0003782875780000111
a quantitative analysis system for influence of line parameter errors on system power distribution is used for calculating sensitivity of power flowing through a line of an electric power system to line parameters and quantifying influence of the line parameter errors on the power distribution of the electric power system, and comprises the following steps:
the data acquisition and calculation module: the system is used for obtaining original parameters of the power system, calculating the power flow of the system, and solving the voltage phase angle and amplitude of each node and the power flowing through each line;
a line parameter partial derivative calculation module: the system is used for calculating the partial derivatives of the elements of the admittance matrix of the system to the line parameters;
and a sensitivity coefficient matrix solving module: the method comprises the steps of solving a sensitivity coefficient matrix according to a node constraint equation and a load flow calculation result;
the node voltage sensitivity calculation module for the line parameters comprises: the device is used for calculating the sensitivity of the node voltage phase angle and amplitude to each line parameter;
a power-to-line parameter sensitivity calculation module: and the method is used for calculating the sensitivity of the active power and the reactive power flowing through the line to the line parameters according to the relation between the power flowing through the line and the node voltage.
As a further improvement of the technical scheme of the invention, the original parameters of the power system in the data acquisition and calculation module comprise active power and reactive power input by a generator, load of nodes and line parameters, the load flow of the calculation system adopts a Newton-Raphson method to calculate the load flow of the system, and a voltage phase angle theta and an amplitude value V of each node and power S flowing through each line are obtained L 。
As a further improvement of the technical solution of the present invention, the partial derivatives of the line parameters by each element of the admittance matrix of the computing system in the line parameter partial derivative computing module specifically include: the real part and the imaginary part of each element in the node admittance matrix Y are respectively G ij And B ij For off-diagonal elements, G ij And B ij Is calculated as shown in equations (1) and (2):
Figure GDA0003782875780000121
Figure GDA0003782875780000122
wherein r is ij And x ij The resistance and reactance parameters of the line between node i and node j, G ij And B ij Respectively, the real of the elements between node i and node j in the admittance matrix YPartial and imaginary parameters.
For diagonal element G ii And B ii The calculation of (a) is shown in formulas (3) and (4), wherein b is a line capacitance parameter, and omega is all nodes directly connected with the i line;
Figure GDA0003782875780000123
Figure GDA0003782875780000124
wherein r is ia 、x ia And b ia Parameters for resistance, reactance and susceptance of the line between node i and node a, G ii And B ii For the real and imaginary parameters of the diagonal elements in the admittance matrix Y, Ω is the set of all nodes directly connected to the i-node by wire.
According to the formulas (1) and (2), the partial derivatives of the non-diagonal elements of the admittance matrix to the resistance and reactance of the line can be deduced as shown in the formulas (5) and (6):
Figure GDA0003782875780000125
Figure GDA0003782875780000126
according to the equations (3) and (4), the partial derivatives of the diagonal elements of the admittance matrix to the resistance and reactance of a certain line can be derived as shown in equations (7) and (8):
Figure GDA0003782875780000131
Figure GDA0003782875780000132
in addition, the inventive method is characterized in that，B ii The bias on line capacitance is as shown in equation (9):
Figure GDA0003782875780000133
as a further improvement of the technical scheme of the present invention, the sensitivity of the calculated node voltage phase angle and amplitude to each line parameter in the sensitivity calculation module for solving the sensitivity coefficient matrix and the line parameter sensitivity of the node voltage according to the node constraint equation and the load flow calculation result in the sensitivity coefficient matrix module is specifically:
1) a node constraint equation of the power flow calculation of the power system is shown as a formula (10), wherein the superscript spec is a set value of the node power, and n is the number of nodes in the system; after the load flow calculation reaches the convergence standard, the values of the node voltage amplitude and the phase angle meet the establishment of an equation (10);
Figure GDA0003782875780000134
wherein, Δ P i And Δ Q i An unbalance of active and reactive power is injected for node i, respectively.
2) And (3) deriving the line parameter z on two sides of the active power constraint equation of the ith node to obtain:
Figure GDA0003782875780000135
in the formula:
Figure GDA0003782875780000141
H ij ＝-V i V j (B ij cosθ ij -G ij sinθ ij ) (13)
Figure GDA0003782875780000142
K ij ＝V i (G ij cosθ ij +B ij sinθ ij ) (15)
Figure GDA0003782875780000143
wherein, theta i And theta j The phase angles of the voltages, θ, at nodes i and j, respectively ij Is the voltage phase angle difference between node i and node j, i.e. θ ij ＝θ i –θ j ，V i And V j The voltage amplitudes of node i and node j, respectively. H ii And H ij Diagonal elements and off-diagonal elements, K, of the matrix of node voltage phase angles versus line parameter sensitivity coefficients in the equation of active power imbalance, respectively ii And K ij Diagonal elements and off-diagonal elements, C, of the node voltage amplitude pair versus line parameter sensitivity coefficient matrix in the active power imbalance equation 1i Constant matrix elements of the active power imbalance equation to the line parameter partial derivatives.
3) And (3) deriving the line parameter z on two sides of the reactive power constraint equation of the ith node to obtain:
Figure GDA0003782875780000144
in the formula:
Figure GDA0003782875780000145
L ij ＝-V i V j (G ij cosθ ij +B ij sinθ ij ) (19)
Figure GDA0003782875780000151
K ij ＝V i (G ij sinθ ij -B ij cosθ ij ) (21)
Figure GDA0003782875780000152
wherein L is ii And L ij Diagonal elements and off-diagonal elements, M, of the matrix of node voltage phase angles versus line parameter sensitivity coefficients in the reactive power imbalance equation ii And M ij Diagonal elements and off-diagonal elements, C, of the node voltage amplitude versus line parameter sensitivity coefficient matrix in the reactive power imbalance equation 2i Constant matrix elements that are the partial derivatives of the reactive power imbalance equation to the line parameters.
4) Constructing a coefficient matrix of node voltage phase angle and amplitude to line parameter sensitivity; according to equations (11) - (22), the power imbalance of all nodes are simultaneously derived from the line parameters, as shown in equation (23), where A eq A coefficient matrix which is a sensitivity model;
Figure GDA0003782875780000153
wherein, Δ P is a matrix formed by active power imbalance equations of all non-equilibrium nodes, Δ Q is a matrix formed by reactive power imbalance equations of all PQ nodes, H is a matrix of sensitivity coefficients of node voltage phase angles to line parameters in the active power imbalance equations, K is a matrix of sensitivity coefficients of node voltage amplitude values to line parameters in the active power imbalance equations, L is a matrix of sensitivity coefficients of node voltage phase angles to line parameters in the reactive power imbalance equations, M is a matrix of sensitivity coefficients of node voltage amplitude values to line parameters in the reactive power imbalance equations, V and theta are a matrix of node voltage amplitude values and phase angles, C is a matrix of node voltage amplitude values and phase angles 1 Constant matrix, C, being the partial derivative of the line parameters by the equation of the active power imbalance 2 And the constant matrix is a constant matrix of the reactive power imbalance equation to the line parameter partial derivatives.
Flow of electric power systemThe nodes in calculation can be divided into a PQ node, a PV node and a balance node, wherein the voltage phase angle and the amplitude of the PQ node are required to be solved, the node reactive power input and the node voltage phase angle of the PV node are required to be solved, the balance node is used as a reference node, the node voltage phase angle and the amplitude are given, and other parameters are required to be solved; suppose the number of PQ nodes in the system is n PQ The system has n-1 active power imbalance equations in total, n PQ A reactive power imbalance equation; the coefficient matrix A is thus eq Is (n-1 + n) PQ )×(n–1+n PQ ) Wherein the H matrix is a (n-1) x (n-1) square matrix and the K matrix is a (n-1) x n square matrix PQ L matrix is n PQ X (n-1), M is n PQ ×n PQ A square matrix of (a);
5) and (3) solving the sensitivity of the node voltage phase angle and the amplitude to the line parameters, and obtaining a corresponding solving formula according to a formula (23) as follows:
Figure GDA0003782875780000161
as a further improvement of the technical solution of the present invention, a specific method for calculating sensitivities of line parameters to active and reactive power flowing through the line according to a relationship between line flowing power and node voltage in the power-to-line parameter sensitivity calculation module is as follows: power S of line flow Lia The relationship between the node voltage and the line parameters is shown in equation (25), where the superscript represents the conjugate of the corresponding value.
Figure GDA0003782875780000171
Wherein S is Lia For the power flowing through the line between node i and node a, P Lia And Q Lia Active and reactive power, Y, respectively, flowing through the line between node i and node a ia Is an admittance matrix, θ, of the line between node i and node a a Is the voltage phase angle of node a, V a Is the voltage amplitude of node a, G ia And B ia Are the real and imaginary parameters of the element between node i and node a in the admittance matrix Y.
So that the active power P flowing through the line Lij And reactive power Q Lij Respectively as follows:
P Lij ＝-(V i 2 -V i V j cosθ ij )G ij +V i V j sinθ ij B ij (26)
Figure GDA0003782875780000172
wherein G is ij And B ij The real and imaginary parts of the elements between node i and node j in the admittance matrix Y, respectively.
By deriving the line parameter z from equation (26), we can obtain:
Figure GDA0003782875780000173
for line reactive power Q Lij Due to the line capacitance parameter b ij The presence of (a) the need to distinguish between sensitivity to capacitance and other parameters when calculating the corresponding sensitivity; the sensitivity of the line flowing through reactive power to the capacitance b is:
Figure GDA0003782875780000181
wherein, B ij Is the imaginary parameter of the element between node i and node j in the admittance matrix Y.
For the line resistance parameters, the sensitivity of the obtained line reactive power to the resistance parameters is shown as a formula (30);
Figure GDA0003782875780000182
the invention has the advantages that:
(1) according to the method, the voltage amplitude and the phase angle of each node meeting a power flow constraint equation are obtained through pre-power flow calculation, the partial derivatives of all power flow equation constraint equations to line parameters are combined, and the sensitivity of the voltage phase angle of an unbalanced node and the voltage amplitude of a PQ node to the parameters is calculated through a matrix form; and then, the sensitivity of the line power flow to parameters is calculated through the relation between the line power flow and the node voltage, the influence of line parameter errors on the system power distribution is quantitatively analyzed based on a power flow model, the influence of the node voltage phase angle and amplitude of the parameter errors and the influence of other line powers are considered, and the accuracy of the obtained result is higher.
(2) The invention can simultaneously calculate the sensitivity of the power distribution of the system to all the line parameters, has higher calculation efficiency, and can verify the correctness of the sensitivity by adopting a continuous parameter modification method through repeated load flow calculation.
Drawings
FIG. 1 is a schematic flow chart of a method for quantitatively analyzing influence of line parameter errors on system power distribution based on load flow calculation according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an IEEE RTS-79 test system for a method for quantitatively analyzing the influence of line parameter errors on system power distribution based on load flow calculation according to an embodiment of the present invention;
FIG. 3 is a verification curve diagram of the sensitivity of active power flowing through the lines 20-23 of the test system to the reactance parameters of the lines 15-21 according to the quantitative analysis method for the influence of the line parameter errors on the system power distribution based on load flow calculation in the embodiment of the invention;
fig. 4 is a graph showing verification of sensitivity of reactive power flowing through the lines 20-23 of the test system to reactance parameters of the lines 15-21 in the method for quantitatively analyzing the influence of line parameter errors on system power distribution based on load flow calculation according to the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme of the invention is further described by combining the drawings and the specific embodiments in the specification:
example one
As shown in fig. 1, a method for quantitatively analyzing the influence of line parameter errors on system power distribution includes the following steps:
1. and acquiring original parameters of the power system, including active power and reactive power input by the generator, load of the node, line parameters and the like. Calculating the power flow of the system by adopting a Newton-Raphson method to obtain the voltage phase angle theta and the amplitude V of each node and the power S flowing through each line L 。
2. And calculating partial derivatives of each element in the admittance matrix of the system to parameters such as line resistance, reactance, susceptance and the like. The real part and the imaginary part of each element in the node admittance matrix Y are respectively G ij And B ij . For off-diagonal elements, G ij And B ij Is shown in equations (1) and (2), where r and x are the line resistance and reactance parameters, respectively.
Figure GDA0003782875780000201
Figure GDA0003782875780000202
For diagonal element G ii And B ii The calculation of (a) is shown in equations (3) and (4), where b is the line capacitance parameter and Ω is all the nodes directly connected to i line.
Figure GDA0003782875780000203
Figure GDA0003782875780000204
According to the formulas (1) and (2), the partial derivatives of the non-diagonal elements of the admittance matrix to the resistance and reactance of the line can be deduced as shown in the formulas (5) and (6).
Figure GDA0003782875780000205
Figure GDA0003782875780000206
According to the formulas (3) and (4), the partial derivatives of diagonal elements of the admittance matrix to the resistance and reactance of a certain line can be deduced as shown in the formulas (7) and (8). In addition, B ii The bias on the line capacitance is shown in equation (9).
Figure GDA0003782875780000211
Figure GDA0003782875780000212
Figure GDA0003782875780000213
3. And solving a sensitivity coefficient matrix according to the node constraint equation and the load flow calculation result, and calculating the sensitivity of the node voltage phase angle and the amplitude to each line parameter.
A node constraint equation of the power flow calculation of the power system is shown in a formula (10), wherein the superscript spec is a set value of the node power, and n is the number of nodes in the system. After the load flow calculation reaches the convergence standard, the values of the node voltage amplitude and the phase angle satisfy the equation (10).
Figure GDA0003782875780000214
And (3) deriving a line parameter z (parameters such as line resistance, reactance or capacitance) on two sides of an active power constraint equation of the ith node to obtain:
Figure GDA0003782875780000215
in the formula:
Figure GDA0003782875780000216
H ij ＝-V i V j (B ij cosθ ij -G ij sinθ ij ) (13)
Figure GDA0003782875780000221
K ij ＝V i (G ij cosθ ij +B ij sinθ ij ) (15)
Figure GDA0003782875780000222
and (3) differentiating the line parameter z on two sides of the reactive power constraint equation of the ith node to obtain:
Figure GDA0003782875780000223
in the formula:
Figure GDA0003782875780000224
L ij ＝-V i V j (G ij cosθ ij +B ij sinθ ij ) (19)
Figure GDA0003782875780000225
K ij ＝V i (G ij sinθ ij -B ij cosθ ij ) (21)
Figure GDA0003782875780000226
and constructing a coefficient matrix of the node voltage phase angle and amplitude to the sensitivity of the line parameters. According to equations (11) - (22), the partial derivatives of the power unbalance of all nodes to the line parameters are simultaneously represented by equation (23), wherein A eq Is a coefficient matrix of the sensitivity model.
Figure GDA0003782875780000231
The nodes in the power flow calculation of the power system can be divided into a PQ node, a PV node and a balance node, wherein the voltage phase angle and the amplitude of the PQ node are required to be solved, the node reactive power input and the node voltage phase angle of the PV node are required to be solved, the balance node is used as a reference node, the node voltage phase angle and the amplitude are given, and other parameters are required to be solved. Suppose the number of PQ nodes in the system is n PQ The system has n-1 active power imbalance equations in total, n PQ And a reactive power imbalance equation. The coefficient matrix A is thus eq Is (n-1 + n) PQ )×(n–1+n PQ ) Wherein the H matrix is a (n-1) x (n-1) square matrix and the K matrix is a (n-1) x n square matrix PQ L matrix is n PQ X (n-1), M is n PQ ×n PQ A square matrix of (a).
And (3) solving the sensitivity of the node voltage phase angle and the amplitude to the line parameters, and obtaining a corresponding solving formula according to a formula (23) as follows:
Figure GDA0003782875780000232
4. and calculating the sensitivity of the active power and the reactive power flowing through the line to parameters such as line resistance, reactance, susceptance and the like according to the relation between the power flowing through the line and the node voltage.
Power S of line flow Lia The relationship with the node voltage and the line parameters is shown in equation (25).
Figure GDA0003782875780000241
So that the line current flows through the active power P Lij And reactive power Q Lij Respectively as follows:
P Lij ＝-(V i 2 -V i V j cosθ ij )G ij +V i V j sinθ ij B ij (26)
Figure GDA0003782875780000242
by deriving the line parameter z from equation (26), we can obtain:
Figure GDA0003782875780000243
for line reactive power Q Lij Due to the line capacitance parameter b ij The sensitivity to capacitance and other parameters need to be distinguished when calculating the respective sensitivities. The sensitivity of the line flowing through reactive power to the capacitance b is:
Figure GDA0003782875780000244
for other line parameters, taking resistance as an example, the sensitivity of the obtained line reactive power to the resistance parameter is shown as the formula (30).
Figure GDA0003782875780000251
Application example and result analysis of the embodiment: taking the IEEE RTS-79 test system shown in fig. 2 as an example, the system has 24 nodes, 13 PQ nodes; the system has 34 lines in total, wherein the lines 3-24, 9-11, 9-12, 10-11 and 10-12 are transformer lines; the reference power is 100MVA, and the reference voltage is the average rated voltage.
The reactive parameters of the lines 15-21 were used as the study targets, the original reactive parameters were 0.0245pu, and the sensitivities of the active and reactive power flowing through each line to the reactive parameters of the line were calculated according to the above method and are shown in table 1.
TABLE 1 sensitivity of active and reactive power of each line to reactance parameters of the lines 15-21
Figure GDA0003782875780000252
The sensitivity of the power flowing through lines 20-23 to the reactance parameters of lines 15-21 is selected to verify the accuracy of the proposed model. The power flowing through the lines 20-23 is-0.6341-j0.5298pu under the original parameters. The reactance parameters of the lines 15-21 were varied between 0.9 and 1.1 times their original parameters, and the power of the lines 20-23 flowing through it, calculated using the continuous modified parameters method and the proposed sensitivity model, was shown in fig. 3 and 4. It can be seen that the result obtained by the calculation of the model and the result obtained by the calculation of the continuous parameter modification method are tangent at the initial value, the result obtained by the calculation of the continuous parameter modification method and the result obtained by the calculation of the sensitivity have only one intersection point, and the intersection point is the initial value of the line parameter, so the correctness of the sensitivity value can be verified. In addition, the maximum error of comparing the two results is 1.1987 × 10 –6 pu (active power) and 4.7219 x 10 –7 pu (reactive power), which is almost negligible compared to the line flowing power, also verifies the correctness of the sensitivity results.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (9)

1. A quantitative analysis method for influence of line parameter errors on power distribution is characterized by comprising the following steps:
step 1): acquiring original parameters of a power system, calculating the load flow of the system, and solving the phase angle and amplitude of the voltage of each node and the power of each line flowing through;
step 2): calculating partial derivatives of each element of the admittance matrix of the system to the line parameters;
step 3): solving a sensitivity coefficient matrix according to a node constraint equation and a load flow calculation result;
step 4): calculating the sensitivity of the node voltage phase angle and amplitude to each line parameter, obtaining the voltage amplitude and phase angle of each node meeting a power flow constraint equation through preposed power flow calculation, simultaneously establishing the partial derivatives of all power flow equation constraint equations to the line parameters, and calculating the sensitivity of the voltage amplitude of the unbalanced node voltage phase angle and PQ node to the parameters through a matrix form;
step 5): calculating the sensitivity of the active power and the reactive power of the line current to line parameters according to the relation between the line current power and the node voltage;
the method for solving the sensitivity coefficient matrix according to the node constraint equation and the load flow calculation result in the step 3) and calculating the sensitivity of the node voltage phase angle and the amplitude to each line parameter in the step 4) specifically comprises the following steps:
1) a node constraint equation of the power flow calculation of the power system is shown as a formula (10), wherein the superscript spec is a set value of the node power, and n is the number of nodes in the system; after the load flow calculation reaches the convergence standard, the values of the node voltage amplitude and the phase angle meet the establishment of an equation (10);
Figure FDA0003789775370000011
2) and (3) deriving the line parameter z on two sides of the active power constraint equation of the ith node to obtain:
Figure FDA0003789775370000021
in the formula:
Figure FDA0003789775370000022
H ij ＝-V i V j (B ij cosθ ij -G ij sinθ ij ) (13)
Figure FDA0003789775370000023
K ij ＝V i (G ij cosθ ij +B ij sinθ ij ) (15)
Figure FDA0003789775370000024
3) and (3) deriving the line parameter z on two sides of the reactive power constraint equation of the ith node to obtain:
Figure FDA0003789775370000025
in the formula:
Figure FDA0003789775370000026
L ij ＝-V i V j (G ij cosθ ij +B ij sinθ ij ) (19)
Figure FDA0003789775370000027
K ij ＝V i (G ij sinθ ij -B ij cosθ ij ) (21)
Figure FDA0003789775370000028
4) constructing a coefficient matrix of node voltage phase angle and amplitude to line parameter sensitivity; according to equations (11) - (22), the power imbalance of all nodes are simultaneously derived from the line parameters, as shown in equation (23), where A eq A coefficient matrix which is a sensitivity model;
Figure FDA0003789775370000031
nodes in the power flow calculation of the power system can be divided into PQ nodes, PV nodes and balance nodes, wherein voltage phase angles and amplitudes of the PQ nodes are required to be solved, node reactive power input and node voltage phase angles of the PV nodes are required to be solved, the balance nodes serve as reference nodes, the node voltage phase angles and amplitudes are given, and other parameters are required to be solved; suppose the number of PQ nodes in the system is n PQ The system has n-1 active power imbalance equations in total, n PQ A reactive power imbalance equation; the coefficient matrix A is thus eq Is (n-1 + n) PQ )×(n–1+n PQ ) Wherein the H matrix is a (n-1) x (n-1) square matrix and the K matrix is a (n-1) x n square matrix PQ L matrix is n PQ X (n-1), M is n PQ ×n PQ A square matrix of (a);
5) and (3) solving the sensitivity of the node voltage phase angle and the amplitude to the line parameters, and obtaining a corresponding solving formula according to a formula (23) as follows:
Figure FDA0003789775370000032
2. the method as claimed in claim 1, wherein the original parameters of the power system in step 1) include active and reactive powers input by the generator, loads of nodes and line parameters, the power flow of the system is calculated by newton-raphson method to obtain phase angle θ and amplitude V of voltage at each node, and power S flowing through each line L 。
3. The method for quantitatively analyzing the influence of the line parameter error on the power distribution according to claim 1, wherein the calculating of the partial derivatives of the line parameters by the elements of the admittance matrix of the system in step 2) specifically comprises: the real part and imaginary part of each element in the node admittance matrix Y are respectively G ij And B ij For off-diagonal elements, G ij And B ij Is calculated as shown in equations (1) and (2):
Figure FDA0003789775370000041
Figure FDA0003789775370000042
for diagonal element G ii And B ii The calculation of (a) is shown in formulas (3) and (4), wherein b is a line capacitance parameter, and omega is all nodes directly connected with the i line;
Figure FDA0003789775370000043
Figure FDA0003789775370000044
according to the formulas (1) and (2), the partial derivatives of the non-diagonal elements of the admittance matrix to the resistance and reactance of the line can be deduced as shown in the formulas (5) and (6):
Figure FDA0003789775370000045
Figure FDA0003789775370000046
according to the equations (3) and (4), the partial derivatives of the diagonal elements of the admittance matrix to the resistance and reactance of a certain line can be derived as shown in equations (7) and (8):
Figure FDA0003789775370000051
Figure FDA0003789775370000052
in addition, B ii The bias on line capacitance is as shown in equation (9):
Figure FDA0003789775370000053
4. the method of claim 1, wherein the line parameter z comprises a line resistance, a reactance, or a capacitance.
5. The method as claimed in claim 1, wherein the step 5) of calculating the influence of the line current on the power distribution according to the relationship between the power of the line current and the node voltageThe specific method of the sensitivity of the power and reactive power to the line parameters is as follows: power S of line flow Lia The relationship with node voltage and line parameters is shown in equation (25),
Figure FDA0003789775370000054
so that the active power P flowing through the line Lij And reactive power Q Lij Respectively as follows:
P Lij ＝-(V i 2 -V i V j cosθ ij )G ij +V i V j sinθ ij B ij (26)
Figure FDA0003789775370000055
by taking the derivative of the line parameter z by equation (26), we can obtain:
Figure FDA0003789775370000061
for line reactive power Q Lij Due to the line capacitance parameter b ij The presence of (a) the need to distinguish between sensitivity to capacitance and other parameters when calculating the corresponding sensitivity; the sensitivity of the line flowing through reactive power to the capacitance b is:
Figure FDA0003789775370000062
for the line resistance parameters, the sensitivity of the obtained line reactive power to the resistance parameters is shown as a formula (30);
Figure FDA0003789775370000063
6. a system for quantitatively analyzing an influence of a line parameter error on a power distribution, comprising:
the data acquisition and calculation module: the system is used for obtaining original parameters of the power system, calculating the power flow of the system, and solving the voltage phase angle and amplitude of each node and the power flowing through each line;
a line parameter partial derivative calculation module: the system is used for calculating the partial derivatives of the elements of the admittance matrix of the system to the line parameters;
and a sensitivity coefficient matrix solving module: the method comprises the steps of solving a sensitivity coefficient matrix according to a node constraint equation and a load flow calculation result;
the node voltage sensitivity calculation module for the line parameters comprises: the sensitivity of the node voltage phase angle and amplitude to each line parameter is calculated;
a power-to-line parameter sensitivity calculation module: the device is used for calculating the sensitivity of the active power and the reactive power of the line current to line parameters according to the relation between the line current power and the node voltage;
the method for solving the sensitivity of the sensitivity coefficient matrix according to the node constraint equation and the load flow calculation result in the sensitivity coefficient matrix solving module and calculating the sensitivity of the node voltage phase angle and the amplitude to each line parameter in the node voltage to line parameter sensitivity calculating module comprises the following specific steps:
1) a node constraint equation of the power flow calculation of the power system is shown as a formula (10), wherein the superscript spec is a set value of the node power, and n is the number of nodes in the system; after the load flow calculation reaches the convergence standard, the values of the node voltage amplitude and the phase angle meet the establishment of an equation (10);
Figure FDA0003789775370000071
2) and (3) deriving the line parameter z on two sides of the active power constraint equation of the ith node to obtain:
Figure FDA0003789775370000072
in the formula:
Figure FDA0003789775370000073
H ij ＝-V i V j (B ij cosθ ij -G ij sinθ ij ) (13)
Figure FDA0003789775370000081
K ij ＝V i (G ij cosθ ij +B ij sinθ ij ) (15)
Figure FDA0003789775370000082
3) and (3) deriving the line parameter z on two sides of the reactive power constraint equation of the ith node to obtain:
Figure FDA0003789775370000083
in the formula:
Figure FDA0003789775370000084
L ij ＝-V i V j (G ij cosθ ij +B ij sinθ ij ) (19)
Figure FDA0003789775370000085
K ij ＝V i (G ij sinθ ij -B ij cosθ ij ) (21)
Figure FDA0003789775370000086
4) constructing a coefficient matrix of node voltage phase angle and amplitude to line parameter sensitivity; according to equations (11) - (22), the power imbalance of all nodes are simultaneously derived from the line parameters, as shown in equation (23), where A eq A coefficient matrix which is a sensitivity model;
Figure FDA0003789775370000091
the nodes in the power flow calculation of the power system can be divided into a PQ node, a PV node and a balance node, wherein the voltage phase angle and the amplitude of the PQ node are required to be solved, the node reactive power input and the node voltage phase angle of the PV node are required to be solved, the balance node is used as a reference node, the node voltage phase angle and the amplitude are given, and other parameters are required to be solved; suppose the number of PQ nodes in the system is n PQ The system has n-1 active power imbalance equations in total, n PQ A reactive power imbalance equation; the coefficient matrix A is thus eq Is (n-1 + n) PQ )×(n–1+n PQ ) Wherein the H matrix is a (n-1) x (n-1) square matrix and the K matrix is a (n-1) x n square matrix PQ L matrix is n PQ X (n-1), M is n PQ ×n PQ A square matrix of (a);
5) and (3) solving the sensitivity of the node voltage phase angle and the amplitude to the line parameters, and obtaining a corresponding solving formula according to a formula (23) as follows:
Figure FDA0003789775370000092
7. a line parameter error versus work as in claim 6The system for quantitatively analyzing the influence of the rate distribution is characterized in that the original parameters of the power system in the data acquisition and calculation module comprise active power and reactive power input by a generator, load of nodes and line parameters, the load flow of the calculation system adopts a Newton-Raphson method to calculate the load flow of the system, and a voltage phase angle theta and an amplitude value V of each node and power S flowing through each line are obtained L 。
8. The system according to claim 6, wherein the partial derivatives of the line parameters by the elements of the admittance matrix of the computing system in the line parameter partial derivative computing module are specifically: the real part and imaginary part of each element in the node admittance matrix Y are respectively G ij And B ij For off-diagonal elements, G ij And B ij Is calculated as shown in equations (1) and (2):
Figure FDA0003789775370000101
Figure FDA0003789775370000102
for diagonal element G ii And B ii The calculation of (a) is shown in formulas (3) and (4), wherein b is a line capacitance parameter, and omega is all nodes directly connected with the i line;
Figure FDA0003789775370000103
Figure FDA0003789775370000104
according to the formulas (1) and (2), the partial derivatives of the non-diagonal elements of the admittance matrix to the resistance and reactance of the line can be deduced as shown in the formulas (5) and (6):
Figure FDA0003789775370000105
Figure FDA0003789775370000106
according to the equations (3) and (4), the partial derivatives of the diagonal elements of the admittance matrix to the resistance and reactance of a certain line can be derived as shown in equations (7) and (8):
Figure FDA0003789775370000107
Figure FDA0003789775370000111
in addition, B ii The bias on line capacitance is as shown in equation (9):
Figure FDA0003789775370000112
9. the system of claim 6, wherein the power-to-line parameter sensitivity calculation module calculates the sensitivity of the line current active and reactive power to the line parameter based on the relationship between the line current power and the node voltage by: power S of line flow Lia The relationship with the node voltage and the line parameters is shown in formula (25);
Figure FDA0003789775370000113
so that the active power P flowing through the line Lij And reactive power Q Lij Respectively as follows:
P Lij ＝-(V i 2 -V i V j cosθ ij )G ij +V i V j sinθ ij B ij (26)
Figure FDA0003789775370000114
by deriving the line parameter z from equation (26), we can obtain:
Figure FDA0003789775370000121
for line reactive power Q Lij Due to the line capacitance parameter b ij The presence of (a) requires distinguishing the sensitivity to capacitance and other parameters when calculating the corresponding sensitivity; the sensitivity of the line flowing through reactive power to the capacitance b is:
Figure FDA0003789775370000122
for the line resistance parameters, the sensitivity of the line reactive power to the resistance parameters is obtained as shown in a formula (30);
Figure FDA0003789775370000123
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