SYMMETRIC METHOD FOR OBTAINING BRANCH-MEAN-SQUARE-CURRENT COMPONENTS INDUCED BY SOURCES AND LOADS AT INDIVIDUAL BUSES IN AC POWER NETWORKS

Abstract

A symmetric method for obtaining branch-mean-square-current components induced by sources and loads at individual buses in AC power networks is invented. Two linear expressions of bus injection active and reactive powers in terms of translation voltages and voltage angles of all buses are established at first. Then a linear symmetric matrix-equation model for the steady state of the network is built. Manipulating this model by Moore-Penrose pseudoinverse produces a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection powers. Expressing the branch mean-square current in terms of source's and load's powers by this matrix expression, a symmetric algebraic calculation formula for obtaining the branch-mean-square-current components is produced after manipulating by Shapley value theorem, by which the obtaining of branch-mean-square-current components are achieved. The set of branch-mean-square-current components provides a new efficient tool for security correction of AC power networks.

Claims

1. A symmetric method for obtaining branch-mean-square-current components induced by sources and loads at individual buses in an AC power network, comprising the following steps: establishing two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses according to bus injection powers of sources and loads and branch admittances in the AC power network; establishing a linear symmetric matrix-equation model for the steady state of the AC power network according to the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses; establishing a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads according to the linear symmetric matrix-equation model for the steady state of the AC power network by using the Moore-Penrose pseudoinverse of a matrix; establishing a symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads according to the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads; and establishing a symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses according to the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads by using the Shapley value theorem.

2. The symmetric method according to claim 1, wherein the step of establishing the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses according to bus injection powers of sources and loads and branch admittances in the AC power network comprises: establishing the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses by the following equations: $P_i=\underset{k=1,k\ne i}{\overset{n}{.Math.}}\left(-{\theta }_i{b}_{\mathrm{ik}}+{\upsilon }_i{g}_{\mathrm{ik}}+{\theta }_k{b}_{\mathrm{ik}}-{\upsilon }_k{g}_{\mathrm{ik}}\right)$ $Q_i=\underset{k=1,k\ne i}{\overset{n}{.Math.}}\left(-{\theta }_i{g}_{\mathrm{ik}}-{\upsilon }_i{b}_{\mathrm{ik}}+{\theta }_k{g}_{\mathrm{ik}}+{\upsilon }_k{b}_{\mathrm{ik}}\right)$ wherein, both i and k denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belongs to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; P.sub.i and Q.sub.i denote the active and reactive powers of the source and load at bus i, respectively, and referred to collectively as the powers of the source and load at bus i; g.sub.ik and b.sub.ik denote the conductance and susceptance of branch ik connected between bus i and bus k, respectively, and referred to collectively as the admittance of branch ik; θ.sub.1 and θ.sub.k denote the voltage angles at bus i and bus k, respectively; and ν.sub.i and ν.sub.k denote the translation voltages at bus i and bus k, respectively, and both ν.sub.i and ν.sub.k are per-unit voltages translated by −1.0.

3. The symmetric method according to claim 1, wherein the step of establishing the linear symmetric matrix-equation model for the steady state of the AC power network according to the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses comprises: establishing the linear symmetric matrix-equation model for the steady state of the AC power network by the following equation:
[P.sub.1Q.sub.1 . . . P.sub.iQ.sub.i . . . P.sub.nQ.sub.n].sup.T=(G*,*)[θ.sub.1ν.sub.i . . . θ.sub.iν.sub.i . . . θ.sub.nν.sub.n].sup.T wherein (G*,*) is set to zero at first, and then the branches are scanned and accumulated as follows: G.sub.2i-1,2i-1=G.sub.2i-1,2i-1−b.sub.ij, G.sub.2i-1,2i=G.sub.2i-1,2i+g.sub.ij, G.sub.2i-1,2j-1=G.sub.2i-1,2j-1+b.sub.ij, G.sub.2i-1,2j=G.sub.2i-1,2j−g.sub.ij, G.sub.2i,2i-1=G.sub.2i,2i-1−g.sub.ij, G.sub.2i,2i=G.sub.2i,2i−b.sub.ij, G.sub.2i,2j-1=G.sub.2i,2j-1+g.sub.ij, G.sub.2i,2j=G.sub.2i,2j+b.sub.ij; and wherein, both i and j denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; P.sub.1 and Q.sub.1 denote the active and reactive powers of the source and load at bus 1, respectively, and referred to collectively as the powers of the source and load at bus 1; P.sub.i and Q.sub.i denote the active and reactive powers of the source and load at bus i, respectively, and referred to collectively as the powers of the source and load at bus i; P.sub.n and Q.sub.n denote the active and reactive powers of the source and load at bus n, respectively, and referred to collectively as the powers of the source and load at bus n; g.sub.ij and b.sub.ij denote the conductance and susceptance of branch ij connected between bus i and bus j, and referred to collectively as the admittance of branch ij; θ.sub.1, θ.sub.i and θ.sub.n denote the voltage angles at bus 1, bus i and bus n, respectively; ν.sub.1, ν.sub.i and ν.sub.n denote the translation voltages at bus 1, bus i and bus n, respectively, and the ν.sub.1, ν.sub.i and ν.sub.n are all per-unit voltages translated by −1.0; (G*,*) is the full bus admittance matrix with a dimension of 2n×2n; and G.sub.2i-1,2i-1, G.sub.2i-1,2i, G.sub.2i-1,2j-1, G.sub.2i-1,2j, G.sub.2i,2i-1, G.sub.2i,2i, G.sub.2i,2j-1 and G.sub.2i,2j are elements of the full bus admittance matrix (G*,*).

4. The symmetric method according to claim 1, wherein the step of establishing the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads according to the linear symmetric matrix-equation model for the steady state of the AC power network by using the Moore-Penrose pseudoinverse of a matrix comprises: establishing the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads by the following equations:
[θ.sub.1ν.sub.1 . . . θ.sub.iν.sub.i . . . θ.sub.nν.sub.n].sup.T=(α*,*)[P.sub.1Q.sub.i . . . P.sub.iQ.sub.i . . . P.sub.nQ.sub.n].sup.T
(α*,*)=(G*,*).sup.+ wherein, i denotes the serial number of a bus in the AC power network and belongs to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; θ.sub.1, θ.sub.i and θ.sub.n denote the voltage angles at bus 1, bus i and bus n, respectively; ν.sub.1, ν.sub.i and ν.sub.n denote the translation voltages at bus 1, bus i and bus n, respectively, and the ν.sub.1, ν.sub.i and ν.sub.n are all per-unit voltages translated by −1.0; P.sub.1 and Q.sub.1 denote the active and reactive powers of the source and load at bus 1, respectively, and referred to collectively as the powers of the source and load at bus 1; P.sub.i and Q.sub.i denote the active and reactive powers of the source and load at bus i, respectively, and referred to collectively as the powers of the source and load at bus i; P.sub.n and Q.sub.n denote the active and reactive powers of the source and load at bus n, respectively, and referred to collectively as the powers of the source and load at bus n; (G*,*) is the full bus admittance matrix with a dimension of 2n×2n; the superscript symbol + is an operator to find the Moore-Penrose pseudoinverse of a matrix; and (α*,*) denotes the Moore-Penrose pseudoinverse of the full bus admittance matrix (G*,*).

5. The symmetric method according to claim 1, wherein the step of establishing the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads according to the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads comprises: based on the general knowledge of the branch mean-square current: I.sub.ik.sup.2=(g.sub.ik.sup.2+b.sub.ik.sup.2)[(θ.sub.i−θ.sub.k).sup.2+(ν.sub.i—ν.sub.k).sup.2], establishing the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads by the following equation: $I_{\mathrm{ik}}^2=\left(g_{\mathrm{ik}}^2+b_{\mathrm{ik}}^2\right)\left\{\begin{array}{c}{\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i-1,2h-1}-a_{2k-1,2h-1}\right)P_h+\left(a_{2i-1,2h}-a_{2k-1,2h}\right)Q_h\right)\right]}^2\\ +{\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i,2h-1}-a_{2k,2h-1}\right)P_h+\left(a_{2i,2h}-a_{2k,2h}\right)Q_h\right)\right]}^2\end{array}\right\}$ wherein, i, k and h denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; g.sub.ik and b.sub.ik denote the conductance and susceptance of branch ik connected between bus i and bus k, and referred to collectively as the admittance of branch ik; I.sub.ik.sup.2 is the branch mean-square current through branch ik connected between bus i and bus k; α.sub.2i-1,2h-1, α.sub.2k-1,2h-1, α.sub.2i-1,2h, α.sub.2k-1,2h, α.sub.2i,2h-1, α.sub.2k,2h-1, α.sub.2i,2h and α.sub.2k,2h are elements of the Moore-Penrose pseudoinverse of the full bus admittance matrix with a dimension of 2n×2n; P.sub.h and Q.sub.h denote the active and reactive powers of the source and load at bus h, respectively, and referred to collectively as the powers of the source and load at bus h.

6. The symmetric method according to claim 1, wherein the step of establishing the symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses according to the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads by using the Shapley value theorem comprises: establishing the symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses by the following equation: $I_{\mathrm{ik},j}^2=\left(g_{\mathrm{ik}}^2+b_{\mathrm{ik}}^2\right)\left\{\begin{array}{c}\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i-1,2h-1}-a_{2k-1,2h-1}\right)P_h+\left(a_{2i-1,2h}-a_{2k-1,2h}\right)Q_h\right)\right]\\ \times \left(\left(a_{2i-1,2j-1}-a_{2k-1,2j-1}\right)P_j+\left(a_{2i-1,2j}-a_{2k-1,2j}\right)Q_j\right)\\ +\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i,2h-1}-a_{2k,2h-1}\right)P_h+\left(a_{2i,2h}-a_{2k,2h}\right)Q_h\right)\right]\\ \times \left(\left(a_{2i,2j-1}-a_{2k,2j-1}\right)P_j+\left(a_{2i,2j}-a_{2k,2j}\right)Q_j\right)\end{array}\right\}$ wherein i, j, k and h denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; g.sub.ik and b.sub.ik denote the conductance and susceptance of branch ik connected between bus i and bus k, and referred to collectively as the admittance of branch ik; I.sub.ik.sup.2 is the branch mean-square current through branch ik connected between bus i and bus k; α.sub.2i-1,2h-1, α.sub.2k-1,2h-1, α.sub.2i-1,2h, α.sub.2k-1,2h, α.sub.2i,2h-1, α.sub.2k,2h-1, α.sub.2i,2h, α.sub.2k,2h, α.sub.2i-1,2j-1, α.sub.2k-1,2j-1, α.sub.2i-1,2j, α.sub.2k-1,2j, α.sub.2i,2j-1, α.sub.2k,2j-1, α.sub.2i,2j and α.sub.2k,2j are elements of the Moore-Penrose pseudoinverse of the full bus admittance matrix with a dimension of 2n×2n; P.sub.h and Q.sub.h denote the active and reactive powers of the source and load at bus h, respectively, and referred to collectively as the powers of the source and load at bus h; P.sub.j and Q.sub.j denote the active and reactive powers of the source and load at bus j, respectively, and referred to collectively as the powers of the source and load at bus j.

7. A computer-readable storage medium, on which a computer program is stored, wherein the computer program can carry out the steps of the symmetric method for obtaining the branch-mean-square-current components induced by sources and loads at individual buses in the AC power network according to claim 1 when implemented by a processor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to explain the technical solution of embodiments of the present application more clearly, the drawings used in the description of the embodiments will be briefly described hereinbelow. Obviously, the drawings in the following description are some embodiments of the present application, and for persons skilled in the art, other drawings may also be obtained on the basis of these drawings without any creative work.

[0015] FIG. 1 is an implementation flow chart of a symmetric method for obtaining branch-mean-square-current components induced by sources and loads at individual buses in an AC power network in accordance with an embodiment of the present application; and

[0016] FIG. 2 is a structural schematic diagram of a universal mode of an AC power network in accordance with an embodiment of the present application.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] In the description hereinbelow, for purposes of explanation rather than limitation, specific details such as specific systematic architectures and techniques are set forth in order to provide a thorough understanding of the embodiments of the present application. However, it will be apparent to persons skilled in the art that the present application may also be implemented in absence of such specific details in other embodiments. In other instances, detailed descriptions of well-known systems, devices, circuits and methods are omitted so as not to obscure the description of the present application with unnecessary detail.

[0018] Technical solution of the present application is explained hereinbelow by particular embodiments.

[0019] Please refer to FIG. 1 and FIG. 2, the symmetric method for obtaining the branch-mean-square-current components induced by sources and loads at individual buses in the AC power network may be conducted according to the following steps: [0020] in step S101, two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses are established according to bus injection powers of sources and loads and branch admittances in the AC power network; [0021] in step S102, a linear symmetric matrix-equation model for the steady state of the AC power network is established according to the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses; [0022] in step S103, a linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads is established according to the linear symmetric matrix-equation model for the steady state of the AC power network by using the Moore-Penrose pseudoinverse of a matrix; [0023] in step S104, a symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads is established according to the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads; and [0024] in step S105, a symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses is established according to the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads by using the Shapley value theorem.

[0025] Calculating using the above symmetric algebraic calculation formula for all branch mean-square currents and all bus injection powers of sources and loads at individual buses in the AC power network will produce a set of branch-mean-square-current components induced by sources and loads at individual buses, thereby the branch-mean-square-current components induced by sources and loads at individual buses in the AC power network are obtained. This symmetric and accurate relation between the branch-mean-square-current components and the bus injection powers of sources and loads at individual buses solves the problems of the time-consuming, unreliability, inaccuracy and inefficiency inherent in the existing methods for security correction control of AC power networks.

[0026] The step S101 of establishing the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses according to bus injection powers of sources and loads and branch admittances in the AC power network is specifically as follows: [0027] the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses is established by the following equations:

[00001]$P_i=\underset{k=1,k\ne i}{\overset{n}{.Math.}}\left(-{\theta }_i{b}_{\mathrm{ik}}+{\upsilon }_i{g}_{\mathrm{ik}}+{\theta }_k{b}_{\mathrm{ik}}-{\upsilon }_k{g}_{\mathrm{ik}}\right)$$Q_i=\underset{k=1,k\ne i}{\overset{n}{.Math.}}\left(-{\theta }_i{g}_{\mathrm{ik}}-{\upsilon }_i{b}_{\mathrm{ik}}+{\theta }_k{g}_{\mathrm{ik}}+{\upsilon }_k{b}_{\mathrm{ik}}\right)$ [0028] in which, both i and k denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; P.sub.i and Q.sub.i denote the active and reactive powers of the source and load at bus i, respectively, and referred to collectively as the powers of the source and load at bus i; the P.sub.i equals to the active power of the power source minus the active power of the load at bus i; the Q.sub.i equals to the reactive power of the power source minus the reactive power of the load at bus i; g.sub.ik and b.sub.ik denote the conductance and susceptance of branch ik connected between bus i and bus k, respectively, and referred to collectively as the admittance of branch ik; θ.sub.i and θ.sub.k denote the voltage angles at bus i and bus k, respectively; ν.sub.i and ν.sub.k denote the translation voltages at bus i and bus k, respectively, and both ν.sub.i and ν.sub.k are per-unit voltages translated by −1.0.

[0029] The step S102 of establishing the linear symmetric matrix-equation model for the steady state of the AC power network according to the two linear expressions of bus injection active and reactive powers of sources and loads in terms of translation voltages and voltage angles of all buses is specifically as follows: [0030] the linear symmetric matrix-equation model for the steady state of the AC power network is established by the following equation:

[P.sub.1Q.sub.1 . . . P.sub.iQ.sub.i . . . P.sub.nQ.sub.n].sup.T=(G*,*)[θ.sub.1ν.sub.i . . . θ.sub.iν.sub.i . . . θ.sub.nν.sub.n].sup.T [0031] where (G*,*) is set to zero at first, and then the branches are scanned and the accumulations are done as follows: G.sub.2i-1,2i-1=G.sub.2i-1,2i-1−b.sub.ij, G.sub.2i-1,2i=G.sub.2i-1,2i+g.sub.ij, G.sub.2i-1,2j-1=G.sub.2i-1,2j-1+b.sub.ij, G.sub.2i-1,2j=G.sub.2i-1,2j−g.sub.ij, G.sub.2i,2i-1=G.sub.2i,2i-1−g.sub.ij, G.sub.2i,2i=G.sub.2i,2i−b.sub.ij, G.sub.2i,2j-1=G.sub.2i,2j-1+g.sub.ij, G.sub.2i,2j=G.sub.2i,2j+b.sub.ij.

[0032] In which, both i and j denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; P.sub.1 and Q.sub.1 denote the active and reactive powers of the source and load at bus 1, respectively, and referred to collectively as the powers of the source and load at bus 1; the P.sub.1 equals to the active power of the power source minus the active power of the load at bus 1; the Q.sub.1 equals to the reactive power of the power source minus the reactive power of the load at bus 1; P.sub.i and Q.sub.i denote the active and reactive powers of the source and load at bus i, respectively, and referred to collectively as the powers of the source and load at bus i; the P.sub.i equals to the active power of the power source minus the active power of the load at bus i; the Q.sub.i equals to the reactive power of the power source minus the reactive power of the load at bus i; P.sub.n and Q.sub.n denote the active and reactive powers of the source and load at bus n, respectively, and referred to collectively as the powers of the source and load at bus n; the P.sub.n equals to the active power of the power source minus the active power of the load at bus n; the Q.sub.n equals to the reactive power of the power source minus the reactive power of the load at bus n; g.sub.ij and b.sub.ij denote the conductance and susceptance of branch ij connected between bus i and bus j, and referred to collectively as the admittance of branch ij; θ.sub.1, θ.sub.i and θ.sub.n denote the voltage angles at bus 1, bus i and bus n, respectively; ν.sub.1, ν.sub.i and ν.sub.n denote the translation voltages at bus 1, bus i and bus n, respectively, and the ν.sub.1, ν.sub.i and ν.sub.n are all per-unit voltages translated by −1.0. (G*,*) is the full bus admittance matrix with a dimension of 2n×2n; G.sub.2i-1,2i-1, G.sub.2i-1,2i, G.sub.2i-1,2j-1, G.sub.2i-1,2j, G.sub.2i,2i-1, G.sub.2i,2i, G.sub.2i,2j-1 and G.sub.2i,2j are the row-2i−1 and column-2i−1, the row-2i−1 and column-2i, the row-2i−1 and column-2j−1, the row-2i−1 and column-2j, the row-2i and column-2i−1, the row-2i and column-2i, the row-2i and column-2j−1 and the row-2i and column-2j elements of the full bus admittance matrix (G*,*), respectively.

[0033] In the above linear matrix-equation model for the steady state of the AC power network, all bus injection powers of sources and loads at individual buses are introduced and identically treated without any bias, namely, symmetrically treated. This is the reason why the above model is called the linear symmetric matrix-equation model.

[0034] The step S103 of establishing the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads according to the linear symmetric matrix-equation model for the steady state of the AC power network by using the Moore-Penrose pseudoinverse of a matrix is specifically as follows: [0035] the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads is established by the following equation:

[θ.sub.1ν.sub.1 . . . θ.sub.iν.sub.i . . . θ.sub.nν.sub.n].sup.T=(α*,*)[P.sub.1Q.sub.i . . . P.sub.iQ.sub.i . . . P.sub.nQ.sub.n].sup.T

(α*,*)=(G*,*).sup.+ [0036] in which, i denotes the serial number of a bus in the AC power network and belongs to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; θ.sub.1, θ.sub.i and θ.sub.n denote the voltage angles at bus 1, bus i and bus n, respectively; ν.sub.1, ν.sub.i and ν.sub.n denote the translation voltages at bus 1, bus i and bus n, respectively, and the ν.sub.1, ν.sub.i and ν.sub.n are all per-unit voltages translated by −1.0; P.sub.1 and Q.sub.1 denote the active and reactive powers of the source and load at bus 1, respectively, and referred to collectively as the powers of the source and load at bus 1; the P.sub.1 equals to the active power of the power source minus the active power of the load at bus 1; the Q.sub.1 equals to the reactive power of the power source minus the reactive power of the load at bus 1; P.sub.i and Q.sub.i denote the active and reactive powers of the source and load at bus i, respectively, and referred to collectively as the powers of the source and load at bus i; the P.sub.i equals to the active power of the power source minus the active power of the load at bus i; the Q.sub.i equals to the reactive power of the power source minus the reactive power of the load at bus i; P.sub.n and Q.sub.n denote the active and reactive powers of the source and load at bus n, respectively, and referred to collectively as the powers of the source and load at bus n; the P.sub.n equals to the active power of the power source minus the active power of the load at bus n; the Q.sub.n equals to the reactive power of the power source minus the reactive power of the load at bus n; (G*,*) is the full bus admittance matrix with a dimension of 2n×2n; the superscript symbol + is an operator to find the Moore-Penrose pseudoinverse of a matrix; and (α*,*) denotes the Moore-Penrose pseudoinverse of the full bus admittance matrix (G*,*).

[0037] The step S104 of establishing the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads according to the linear symmetric matrix expression of translation voltages and voltage angles of all buses in terms of bus injection active and reactive powers of all sources and loads is specifically as follows: [0038] based on the general knowledge of branch mean-square current: I.sub.ik.sup.2=(g.sub.ik.sup.2+b.sub.ik.sup.2)[(θ.sub.i−θ.sub.k).sup.2+(ν.sub.i−ν.sub.k).sup.2], the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads is established by the following equation:

[00002]$I_{\mathrm{ik}}^2=\left(g_{\mathrm{ik}}^2+b_{\mathrm{ik}}^2\right)\left\{\begin{array}{c}{\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i-1,2h-1}-a_{2k-1,2h-1}\right)P_h+\left(a_{2i-1,2h}-a_{2k-1,2h}\right)Q_h\right)\right]}^2\\ +{\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i,2h-1}-a_{2k,2h-1}\right)P_h+\left(a_{2i,2h}-a_{2k,2h}\right)Q_h\right)\right]}^2\end{array}\right\}$ [0039] in which, i, k and h denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; g.sub.ik and b.sub.ik denote the conductance and susceptance of branch ik connected between bus i and bus k, and referred to collectively as the admittance of branch ik; I.sub.ik.sup.2 is the branch mean-square current through branch ik connected between bus i and bus k; α.sub.2i-1,2h-1, α.sub.2k-1,2h-1, α.sub.2i-1,2h, α.sub.2k-1,2h, α.sub.2i,2h-1, α.sub.2k,2h-1, α.sub.2i,2h, α.sub.2k,2h are the row-2i−1 and column-2h−1, the row-2k−1 and column-2h−1, the row-2i−1 and column-2h, the row-2k−1 and column-2h, the row-2i and column-2h−1, the row-2k and column-2h−1, the row-2i and column-2h and the row-2k and column-2h elements of the Moore-Penrose pseudoinverse of the full bus admittance matrix with a dimension of 2n×2n, respectively; P.sub.h and Q.sub.h denote the active and reactive powers of the source and load at bus h, respectively, and referred to collectively as the powers of the source and load at bus h; the P.sub.h equals to the active power of the power source minus the active power of the load at bus h; the Q.sub.h equals to the reactive power of the power source minus the reactive power of the load at bus h.

[0040] The step S105 of establishing the symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses according to the symmetric algebraic expression of the branch mean-square current in terms of bus injection active and reactive powers of all sources and loads by using the Shapley value theorem is specifically as follows: [0041] the symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses is established by the following equation:

[00003]$I_{\mathrm{ik},j}^2=\left(g_{\mathrm{ik}}^2+b_{\mathrm{ik}}^2\right)\left\{\begin{array}{c}\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i-1,2h-1}-a_{2k-1,2h-1}\right)P_h+\left(a_{2i-1,2h}-a_{2k-1,2h}\right)Q_h\right)\right]\\ \times \left(\left(a_{2i-1,2j-1}-a_{2k-1,2j-1}\right)P_j+\left(a_{2i-1,2j}-a_{2k-1,2j}\right)Q_j\right)\\ +\left[\underset{h=1}{\overset{n}{.Math.}}\left(\left(a_{2i,2h-1}-a_{2k,2h-1}\right)P_h+\left(a_{2i,2h}-a_{2k,2h}\right)Q_h\right)\right]\\ \times \left(\left(a_{2i,2j-1}-a_{2k,2j-1}\right)P_j+\left(a_{2i,2j}-a_{2k,2j}\right)Q_j\right)\end{array}\right\}$ [0042] in which, i, j, k and h denote serial numbers of buses in the AC power network and belong to the set of continuous natural numbers, namely belong to {1, 2, . . . , n}; n denotes the total number of buses in the AC power network; g.sub.ik and bk denote the conductance and susceptance of branch ik connected between bus i and bus k, and referred to collectively as the admittance of branch ik; I.sub.ik.sup.2 is the branch mean-square current through branch ik connected between bus i and bus k; α.sub.2i-1,2h-1, α.sub.2k-1,2h-1, α.sub.2i-1,2h, α.sub.2k-1,2h, α.sub.2i,2h-1, α.sub.2k,2h-1, α.sub.2i,2h, α.sub.2k,2h, α.sub.2i-1,2j-1, α.sub.2k-1,2j-1, α.sub.2i-1,2j, α.sub.2k-1,2j, α.sub.2i,2j-1, α.sub.2k,2j-1, α.sub.2i,2j and α.sub.2k,2j are the row-2i−1 and column-2h−1, the row-2k−1 and column-2h−1, the row-2i−1 and column-2h, the row-2k−1 and column-2h, the row-2i and column-2h−1, the row-2k and column-2h−1, the row-2i and column-2h, the row-2k and column-2h, the row-2i−1 and column-2j−1, the row-2k−1 and column-2j−1, the row-2i−1 and column-2j, the row-2k−1 and column-2j, the row-2i and column-2j−1, the row-2k and column-2j−1, the row-2i and column-2j and the row-2k and column-2j elements of the Moore-Penrose pseudoinverse of the full bus admittance matrix with a dimension of 2n×2n, respectively; P.sub.h and Q.sub.h denote the active and reactive powers of the source and load at bus h, respectively, and referred to collectively as the powers of the source and load at bus h; the P.sub.h equals to the active power of the power source minus the active power of the load at bus h; the Q.sub.h equals to the reactive power of the power source minus the reactive power of the load at bus h; P.sub.j and Q.sub.j denote the active and reactive powers of the source and load at bus j, respectively, and referred to collectively as the powers of the source and load at bus j; the P.sub.j equals to the active power of the power source minus the active power of the load at bus j; the Q.sub.j equals to the reactive power of the power source minus the reactive power of the load at bus j.

[0043] The above symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses is applicable to all buses in the AC power network, and all bus injection powers of sources and loads are identically treated in it. This is the reason why the present application is called a symmetric method for obtaining the branch-mean-square-current components induced by sources and loads at individual buses in the AC power network. Moreover, as this symmetric algebraic calculation formula for obtaining the branch-mean-square-current components induced by sources and loads at individual buses is in terms of the global (not incremental) variables representing the bus injection powers of sources and loads, it is accurate for wide range change of the bus injection powers of sources and loads. This symmetric and accurate relation between the branch-mean-square-current components and the bus injection powers of the sources and loads solves the problems of the time-consuming, unreliability, inaccuracy and inefficiency inherent in the existing methods for security correction control of the AC power network.

[0044] An embodiment of the present application provides a computer-readable storage medium on which a computer program is stored. The computer program may be a source code program, an object code program, an executable file or some intermediate form. The computer program can carry out the steps of the symmetric method for obtaining the branch-mean-square-current components induced by sources and loads at individual buses in the AC power network as described in the above embodiments when implemented by a processor. The computer-readable storage medium may include any entity or device capable of carrying computer programs, such as a U disk, a mobile hard disk, an optical disk, a computer memory, a random-access memory and the like.

[0045] The embodiments disclosed herein are merely used to illustrate the technical solutions of the present application, but not aimed to limit the present application. Although the present application is described in detail with reference to the foregoing embodiments, it should be understood for persons skilled in the art that modifications, or equivalent replacements of some of the technical features can be implemented under the spirit of the present application, and these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included by the protection scope of the present application.