Electric grid state estimation system and method based on boundary fusion

Abstract

The invention provides an electric grid state estimation system and method based on a boundary fusion. The system includes an electric grid data acquisition module, a communication module including a local data unit and a state estimation unit, and a data fusion module, wherein the state estimation unit includes a memory storing a state estimation program and a display displaying a program running and outputting a state variable; the state estimation program is performed to realize an electric grid state estimation; the estimation method includes the following steps of dividing a regional electric grid, then establishing a measurement equation for each region, solving an internal quantity and a boundary quantity, fusing the boundary quantities of two regions, correcting the boundary quantity, performing a non-linear transformation on the intermediate variable, solving the estimated values of the state variable by the least square method, and performing outputting.

Claims

1. An electric grid state estimation method based on a boundary fusion, realized by adopting an electric grid state estimation system based on the boundary fusion, the electric grid state estimation system based on the boundary fusion, comprising an electric grid data acquisition module, a communication module and a data fusion module, wherein: the electric grid data acquisition module comprises a plurality of data acquisition units, the number of which is the same as that of divided regions, and the data acquisition units are used for acquiring a measurement value of each node, including active power and reactive power of each node, and power of each branch; the communication module comprises a plurality of data transmission units, the number of which is the same as that of the divided regions, and data collected by the data acquisition units is transmitted to the data fusion module by the data transmission units through a data transmitter; and the data fusion module comprises a local data unit and a state estimation unit, wherein the local data unit is used for storing electric grid network line parameters and a branch-node correlation matrix; the state estimation unit comprises a memory and a display, wherein the memory stores a computer-executable state estimation program based on the boundary fusion, wherein the program is executed to realize an electric grid state estimation based on the boundary fusion; and the display is used for displaying a state estimated value run and output by the state estimation program based on the boundary fusion, the method comprising the following steps of: step 1: through division of a regional electric grid, dividing nodes in each region into boundary nodes and internal nodes; step 2: acquiring measurement data of all nodes in each region through the data acquisition unit of each region, including the active power and reactive power of each node, and the power of each branch, and transmitting data collected by the data acquisition units to the data fusion module by the data transmission units through the data transmitter; step 3: for each regional electric grid, establishing a measurement equation for the divided region according to the relationship between the branch power and the node voltage amplitude, introducing an intermediate variable, and calculating an internal quantity and a boundary quantity respectively according to the divided node types; step 4: constructing a fusion matrix for adjacent regions, applying an intelligent algorithm to fuse the boundary quantities of two regions, and replacing the original boundary value with the fused value; step 5: performing a non-linear transformation on the corrected intermediate variable for each region, and then obtaining a state variable estimated value by a least square method; and step 6: outputting all state variable estimated values.

2. The electric grid state estimation method based on the boundary fusion according to claim 1, wherein the step of dividing the regional electric grid in the step 1 comprises: preliminarily dividing the electric grid into N regions by node tearing, and obtaining a region set K={1, 2, . . . , N}, wherein N is an integer greater than or equal to 2; adding one or more nodes in each region so that a common branch is formed between adjacent regions, and then completing the division of the regions; and according to the division of the regions, dividing the nodes into internal nodes and boundary nodes of the region, wherein the boundary nodes are nodes on the common branch.

3. The electric grid state estimation method based on the boundary fusion according to claim 2, wherein the step 3 comprises: for subregions m, n.Math.K, establishing a measurement equation for the divided region m according to the relationship between the branch power and the node voltage amplitude, introducing an intermediate variable, as shown in the following formula:
Z.sub.m=Ay.sub.m+e=A[y.sub.m_inBond.sub.m_ab].sup.T+e, wherein Z.sub.m is the measurement value of the region m; A is a constant matrix; e is a measurement error vector; y.sub.m is an intermediate variable; y.sub.m_in is an internal quantity of the region m; a and b are nodes on the common branch of the regions m and n; Bond.sub.m_ab is a boundary quantity of the region m, which has the following expression form: ${\mathrm{Bond}}_{\mathrm{m\_ab}}=\left[\begin{array}{c}{W}_{\mathrm{ab}}\\ S_{\mathrm{ab}}\\ F_a\end{array}\right]=\left[\begin{array}{c}{V}_a{V}_b\cos {}_{\mathrm{ab}}\\ V_a{V}_b\sin {}_{\mathrm{ab}}\\ V_a^2\end{array}\right];$ wherein V.sub.a and V.sub.b are respectively the node voltages of a and b; .sub.ab=.sub.a.sub.b is the phase angle difference of the two nodes a and b; for the region n, the boundary quantity is Bond.sub.n_ba, which has the following expression form: ${\mathrm{Bond}}_{\mathrm{n\_ba}}=\left[\begin{array}{c}{W}_{\mathrm{ba}}\\ S_{\mathrm{ba}}\\ F_b\end{array}\right]=\left[\begin{array}{c}{V}_b{V}_a\cos {}_{\mathrm{ba}}\\ V_b{V}_a\sin {}_{\mathrm{ba}}\\ V_b^2\end{array}\right];$ wherein .sub.ba=.sub.b.sub.a is the phase angle difference of the two nodes b and a.

4. The electric grid state estimation method based on the boundary fusion according to claim 3, wherein the step 4 comprises: defining a fusion vector fuse as below: $\mathrm{fuse}=\left[\begin{array}{c}{A}_{\mathrm{ab}}\\ B_{\mathrm{ab}}\\ C_a\\ D_b\end{array}\right];$ wherein A.sub.ab, B.sub.ab, C.sub.a and D.sub.b are respectively four variables to be solved; defining an objective function as below:
min f=(|W.sub.ab||A.sub.ab|).sup.2+(|W.sub.ba||A.sub.ab|).sup.2+(|S.sub.ab||B.sub.ab|).sup.2+(|S.sub.ba||B.sub.ab|).sup.2+(C.sub.aF.sub.a).sup.2+(D.sub.bF.sub.b).sup.2
s.t. A.sub.ab.sup.2+B.sub.ab.sup.2=C.sub.aD.sub.b
sgn(A.sub.ab)=sgn(W.sub.ab)
sgn(B.sub.ab)=sgn(S.sub.ab) wherein sgn is a sign function; solving the objective function by using the intelligent algorithm to obtain the fusion vector fuse; premultiplying the fusion vector fuse by matrices T.sub.mn and T.sub.nm to obtain fusion boundary values Bond*.sub.m_ab=T.sub.mnfuse and Bond*.sub.n_ab=T.sub.nmfuse, wherein $T_{\mathrm{mn}}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\end{array}\right];$ $T_{\mathrm{nm}}=\left[\begin{array}{cccc}-1& 0& 0& 0\\ 0& -1& 0& 0\\ 0& 0& -1& 0\end{array}\right];$ returning the updated boundary values to each region so that an updated intermediate variable y.sub.opt is obtained, wherein the corresponding intermediate variables for the regions m, n are respectively y.sub.mopt and y.sub.nopt, and the specific expression forms are respectively as below:
y.sub.mopt=[y.sub.m_inBond*.sub.m_ab].sup.T; and
y.sub.nopt=[y.sub.n_inBond*.sub.n_ab].sup.T.

5. The electric grid state estimation method based on the boundary fusion according to claim 4, wherein the step 5 comprises: performing the non-linear transformation on the updated intermediate variable y.sub.opt, wherein the transformation form is as below: $y_{\mathrm{opt}}->L=\left[\begin{array}{c}\ln \left(W_{\mathrm{ij}}^2+S_{\mathrm{ij}}^2\right)\\ {\tan }^{-1}\frac{S_{\mathrm{ij}}}{W_{\mathrm{ij}}}\\ \ln F_i\end{array}\right]=\left[\begin{array}{c}2\ln V_i+2\ln V_j\\ {}_i-{}_j\\ 2\ln V_i\end{array}\right];$ wherein i, j are the numbers of nodes at two ends of any branch in the region; enabling .sub.i=ln F.sub.i=2 ln V.sub.i, .sub.ij=.sub.i.sub.j and .sub.ij=.sub.i+.sub.j, then L=[.sub.ij,.sub.ij,.sub.i].sup.T; enabling the form of a state variable x to be $x=\left[\begin{array}{c}\\ \end{array}\right],\mathrm{then}\left[\begin{array}{c}{}_{\mathrm{ij}}\\ {}_{\mathrm{ij}}\\ {}_i\end{array}\right]=\left[\begin{array}{cc}.Math.G^T.Math.& 0\\ 0& G_r^T\\ I& 0\end{array}\right]\left[\begin{array}{c}\\ \end{array}\right]+e_L$ wherein e.sub.L is an error vector of the intermediate variable L; G is a branch-node correlation matrix; G.sub.r is a simplified matrix of G, which can be obtained by modifying each row of |G.sup.T| according to .sub.ij=.sub.i.sub.j and .sub.ij=.sub.i+.sub.j; solving the equation by a weighted least square method, wherein the solution is:
x=(J.sup.TQ.sub.mJ).sup.1J.sup.TQ.sub.mm wherein $J=\left[\begin{array}{cc}.Math.G^T.Math.& 0\\ 0& G_r^T\\ I& 0\end{array}\right],$ Q.sub.m=(E.sup.T).sup.1cov.sup.1(y)E.sup.1, and E is a jacobian matrix obtained by deriving L to y; and transforming the obtained x so that the state variable estimated value of each node, namely the voltage V and the phase angle , can be obtained.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a structural block diagram of an electric grid state estimation system based on a boundary fusion provided by one embodiment of the invention;

(2) FIG. 2 is an IEEE14 node system after the division of regions provided by one embodiment of the invention; and

(3) FIG. 3 is a flow chart of a state estimation process in the electric grid state estimation method based on the boundary fusion provided by one embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(4) The embodiments of the invention are described in details below with reference to the accompanying drawings and embodiments. The following embodiments are used to describe the invention but are not used to limit the scope of the invention.

(5) An electric grid state estimation system based on a boundary fusion as shown in FIG. 1 comprises an electric grid data acquisition module, a communication module and a data fusion module, wherein:

(6) The electric grid data acquisition module comprises a plurality of data acquisition units, the number of which is the same as that of divided regions, and the data acquisition units are used for acquiring the measurement value of each node, including active power and reactive power of each node, and power of each branch;

(7) The communication module comprises a plurality of data transmission units, the number of which is the same as that of the divided regions, and data collected by the data acquisition units is transmitted to the data fusion module by the data transmission units through a data transmitter.

(8) The data fusion module comprises a local data unit and a state estimation unit, wherein the local data unit is used for storing electric grid network line parameters and a branch-node correlation matrix; the state estimation unit comprises a memory and a display, wherein the memory stores a computer-executable state estimation program based on the boundary fusion, wherein the program is executed to realize an electric grid state estimation based on the boundary fusion; and the display is used for displaying a state estimated value run and output by the state estimation program based on the boundary fusion.

(9) An electric grid state estimation method based on the boundary fusion, which is realized by adopting the electric grid state estimation system based on the boundary fusion, and specially comprises the following steps of:

(10) Step 1: through division of a regional electric grid, dividing nodes in each region into boundary nodes and internal nodes.

(11) Preliminarily dividing the electric grid into N regions by node tearing, and obtaining a region set K={1, 2, . . . , N}, wherein N is greater than or equal to 2; adding one or more nodes in each region so that a common branch is formed between adjacent regions, and then completing the division of the regions; according to the division of the regions, dividing the nodes into internal nodes and boundary nodes of the region, wherein the boundary nodes are nodes on the common branch.

(12) In the embodiment, the electric grid is divided into two sub-regions, namely regions 1 and 2, and nodes 6, 7, 9, and 12 are boundary nodes, and FIG. 2 shows the IEEE14 node system after division of the regions.

(13) Step 2: acquiring the measurement data Z.sub.i of all nodes in each region through the data acquisition unit of each region, including the active power and reactive power of each node, and the power of each branch, and transmitting data collected by the data acquisition units to the data fusion module by the data transmission units through a data transmitter.

(14) According to the measurement data Z.sub.i of the nodes in each region, a state estimation process of each region is performed in the state estimation unit of the data fusion module, and the flow chart of the estimation process is shown in FIG. 3, and the specific steps are described as below.

(15) Step 3: for each regional electric grid, establishing a measurement equation for the divided region according to the relationship between the branch power and the node voltage amplitude, introducing an intermediate variable, and calculating an internal quantity and a boundary quantity respectively according to the divided node types.

(16) The relations between the branch power and the node voltage and between the branch power and the phase angle are as below:
P.sub.ij=V.sub.i.sup.2g.sub.ijV.sub.iV.sub.j cos .sub.ijg.sub.ij+V.sub.iV.sub.j sin .sub.ijb.sub.ij
Q.sub.ij=V.sub.i.sup.2(b.sub.ij+y.sub.c)+V.sub.iV.sub.j cos .sub.ijb.sub.ijV.sub.iV.sub.j sin .sub.ijb.sub.ij

(17) wherein i and j are the number of nodes on any branch in the region; g.sub.ij, b.sub.ij and y.sub.c are respectively the pi-mode equivalent circuit series conductance, series susceptance and ground susceptance of the branch ij, and .sub.ij=.sub.i.sub.j is a phase angle difference between two nodes; and P.sub.ij and Q.sub.ij are the active power and the reactive power on the branch ij;

(18) enabling y to be

(19) $y=\left[\begin{array}{c}{W}_{\mathrm{ij}}\\ S_{\mathrm{ij}}\\ F_i\end{array}\right]=\left[\begin{array}{c}{V}_i{V}_j\cos {}_{\mathrm{ij}}\\ V_i{V}_j\sin {}_{\mathrm{ij}}\\ V_i^2\end{array}\right]\mathrm{then}$$P_{\mathrm{ij}}=F_i{g}_{\mathrm{ij}}-W_{\mathrm{ij}}{g}_{\mathrm{ij}}+S_{\mathrm{ij}}{b}_{\mathrm{ij}}$$Q_{\mathrm{ij}}=-F_i\left(b_{\mathrm{ij}}+y_c\right)+W_{\mathrm{ij}}{b}_{\mathrm{ij}}-S_{\mathrm{ij}}{g}_{\mathrm{ij}}$$V_i^2=F_i$

(20) from above, obtaining the measurement equation
z=Ay+e

(21) wherein z is a measurement vector, y is an intermediate variable, e is an error vector, and A is a constant coefficient matrix.

(22) In the embodiment, for the region 1, a measurement equation is established for the divided region according to the relationship between the node voltage amplitude and the branch power:
Z.sub.1=Ay.sub.1+e=A[y.sub.1_inBond.sub.1_79Bond.sub.1_612].sup.T+e

(23) wherein Z.sub.1 is measurement values in region 1, y.sub.1_in is an internal quality, and of which the form is similar as that of Bond.sub.1_79, only numbers of nodes of subscript number are converted into numbers of nodes of internal nodes in the region 1; and Bond.sub.1_79 and Bond.sub.1_612 are boundary quantities, and Bond.sub.1_79 is as below:

(24) ${\mathrm{Bond}}_{1\_79}=\left[\begin{array}{c}{W}_{79}\\ S_{79}\\ F_7\end{array}\right]=\left[\begin{array}{c}{V}_7{V}_9\cos {}_{79}\\ V_7{V}_9\sin {}_{79}\\ V_7^2\end{array}\right]$

(25) wherein nodes 7 and 9 are boundary nodes.

(26) Similarly, in the region 2, Bond.sub.2_97 is as below:

(27) 0${\mathrm{Bond}}_{2\_97}=\left[\begin{array}{c}{W}_{97}\\ S_{97}\\ F_9\end{array}\right]=\left[\begin{array}{c}{V}_9{V}_7\cos {}_{97}\\ V_9{V}_7\sin {}_{97}\\ V_9^2\end{array}\right].$

(28) In the region 1, the least square solution of equation Z.sub.1=Ay.sub.i+e is
y.sub.1=(A.sup.TWA).sup.1A.sup.TWZ.sub.1

(29) wherein W is a weighting matrix.

(30) Step 4: constructing a fusion matrix for adjacent regions, applying a gravitation algorithm to fuse the boundary quantities of two regions, and replacing the original boundary value with the fusion value.

(31) For the regions 1 and 2, defining a fusion vector fuse, establishing an objective function, and performing solving by the gravitation algorithm;

(32) defining the fuse vector as:

(33) $\mathrm{fuse}=\left[\begin{array}{c}{A}_{79}\\ B_{79}\\ C_7\\ D_9\end{array}\right]$

(34) defining the objective function as:
min f=(|W.sub.79||A.sub.79|).sup.2+(|W.sub.97||A.sub.79|).sup.2+(|S.sub.79||B.sub.79|).sup.2+(|S.sub.97||B.sub.79|).sup.2+(C.sub.7F.sub.7).sup.2+(D.sub.9F.sub.9).sup.2
s.t. A.sub.79.sup.2+b.sub.79.sup.2=C.sub.7D.sub.9
sgn(A.sub.79)=sgn(W.sub.79)
sgn(B.sub.79)=sgn(S.sub.79)

(35) wherein sgn is a sign function, and nodes 7 and 9 are nodes in a common branch;

(36) after solving by the gravitation algorithm, premultiplying the matrices T.sub.12 and T.sub.21 to enable Bond*.sub.1_79=T.sub.12fuse and Bond*.sub.2_97=T.sub.21fuse, wherein matrices T.sub.12 and T.sub.21 are specially as below:

(37) $T_{12}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\end{array}\right]$$T_{21}=\left[\begin{array}{cccc}-1& 0& 0& 0\\ 0& -1& 0& 0\\ 0& 0& 1& 0\end{array}\right]$

(38) Similarly, a consistent treatment is also made for nodes 6 and 12, so that Bond*.sub.1_612 and Bond*.sub.2-126 can be obtained.

(39) The updated boundary values are returned to each region to obtain an updated intermediate variable;

(40) In the region 1, the form of the intermediate variable y.sub.1opt is as below:
y.sub.1opt=[y.sub.1_inBond*.sub.1_79Bond*.sub.1_612].sup.T

(41) Similarly, in the region 2, the form of the intermediate variable can be obtained as below:
y.sub.2opt=[y.sub.2_inBond*.sub.2_79Bond*.sub.2_126].sup.T.

(42) Step 5: performing a non-linear transformation on the corrected intermediate variable for each region, and then obtaining a state variable estimated value by a least square method.

(43) More specifically, performing the non-linear transformation on y.sub.1opt and y.sub.2opt, enabling

(44) $y_{\mathrm{opt}}->L=\left[\begin{array}{c}\ln \left(W_{\mathrm{ij}}^2+S_{\mathrm{ij}}^2\right)\\ {\tan }^{-1}\frac{S_{\mathrm{ij}}}{W_{\mathrm{ij}}}\\ \ln F_i\end{array}\right]=\left[\begin{array}{c}2\ln V_i+2\ln V_j\\ {}_i-{}_j\\ 2\ln V_i\end{array}\right]$

(45) wherein i and j are the numbers of nodes at any branch in the region;

(46) enabling .sub.i=ln F.sub.i=2 ln V.sub.i, .sub.ij=.sub.i.sub.j and .sub.ij=.sub.i+.sub.j, then L=[.sub.ij,.sub.ij,.sub.i].sup.T;

(47) enabling the form of a state variable x to be:

(48) $x=\left[\begin{array}{c}\\ \end{array}\right],$
enabling

(49) $\left[\begin{array}{c}{}_{\mathrm{ij}}\\ {}_{\mathrm{ij}}\\ {}_i\end{array}\right]=\left[\begin{array}{cc}.Math.G^T.Math.& 0\\ 0& G_r^T\\ I& 0\end{array}\right]\left[\begin{array}{c}\\ \end{array}\right]+e_L$

(50) wherein e.sub.L is an error vector of the intermediate variable L; G is a branch-node correlation matrix; G.sub.r is a simplified matrix of G, which can be obtained by modifying each row of |G.sup.T| according to .sub.ij=.sub.i.sub.j and .sub.ij=.sub.i+.sub.j;

(51) solving the equation by a weighted least square method, wherein the solution is:
x=(J.sup.TQ.sub.mJ).sup.1J.sup.TQ.sub.mm

(52) wherein

(53) $J=\left[\begin{array}{cc}.Math.G^T.Math.& 0\\ 0& G_r^T\\ I& 0\end{array}\right],$
Q.sub.m=(E.sup.T).sup.1cov.sup.1(y)E.sup.1, and E is a jacobian matrix obtained by deriving L to y; and

(54) transforming the obtained x so that the state variable estimated value of each node, namely the voltage V and the phase angle can be obtained.

(55) Step 6: outputting all state variable estimated values.

(56) Finally, it should be noted that the above embodiments are only used to describe the technical scheme of the invention without limitation to the invention. Although the invention has been described in details with reference to the aforesaid embodiments, those skilled in the art should understand that modifications may be made to the technical schemes recorded in the aforesaid embodiments, or some or all of the technical characteristics therein may be equivalently substituted. Such modifications or substitutions should not deviate the nature of the corresponding technical scheme from the scope as defined by the attached claims.