CN108493931B - Electric power system static voltage stable domain boundary approximation method based on space tangent vector - Google Patents

Electric power system static voltage stable domain boundary approximation method based on space tangent vector Download PDF

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CN108493931B
CN108493931B CN201810321173.1A CN201810321173A CN108493931B CN 108493931 B CN108493931 B CN 108493931B CN 201810321173 A CN201810321173 A CN 201810321173A CN 108493931 B CN108493931 B CN 108493931B
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active power
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CN108493931A (en
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姜涛
李雪
陈厚合
李晓辉
王长江
李国庆
张儒峰
张嵩
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Northeast Electric Power University
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Northeast Dianli University
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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
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Abstract

The invention discloses a method for approximating a static voltage stability domain boundary of a power system based on a space tangent vector, which comprises the following steps of: taking ground state power flow as a starting point, searching a series of saddle node bifurcation points and tangent vectors thereof of the power system by adopting a continuous power flow method, and obtaining boundary points, namely saddle node bifurcation points, in a static voltage stability domain two-dimensional active power injection space; preliminarily dividing a static voltage stability domain formed by the obtained boundary points into a plurality of regions based on the space tangent vector, calculating the distance from the boundary points to the corresponding line segments by a bisection method, and obtaining a two-dimensional approximate boundary meeting the requirement of a certain distance error threshold; on the basis of the two-dimensional approximate boundary, a three-dimensional approximate boundary is established according to a triangle construction principle, a triangle approximate plane equation is further obtained, the maximum distance error from all SNB points to the plane in an approximate area corresponding to the S-th triangle approximate plane is calculated, and when the maximum distance error meets an error threshold value, approximation is finished, so that the three-dimensional SVSR triangle approximate boundary is obtained.

Description

Electric power system static voltage stable domain boundary approximation method based on space tangent vector
Technical Field
The invention relates to the field of static voltage stability domains, in particular to a power system static voltage stability domain boundary approximation method based on a space tangent vector.
Background
Since the 70's of the 20 th century, large-scale voltage collapse accidents have occurred successively in many countries around the world, causing enormous economic losses. Since then, the grid voltage stability problem has attracted great attention from the power industry and academia, and a lot of research has been carried out, while the research on the Static Voltage Stability Region (SVSR) has been a significant position in the field of safety and stability analysis of power systems.
The static voltage stabilization domain is a region that is composed of, and only of, all system operating points that satisfy static voltage stabilization. The key of obtaining the SVSR is the construction of the SVSR boundary, and the construction of the SVSR boundary is particularly difficult due to the high-dimensional nonlinearity of the SVSR boundary in the injection space, so an approximation method is proposed to construct the SVSR boundary.
The approximation method of the SVSR boundary mainly comprises a fitting method and a hyperplane approximation method:
1) the fitting method is developed from a traditional voltage stability analysis method, and according to the characteristic that a static voltage stability domain boundary is formed by saddle-node bifurcation points, the saddle-node bifurcation points of a Continuous Power Flow (CPF) method computing system are repeatedly used according to a possible power increasing direction from a ground state power flow, and finally the saddle-node bifurcation points form the voltage stability domain boundary. Although the method improves the calculation accuracy, a uniform hyperplane analytical formula is difficult to form, and the evaluation efficiency of the static voltage stability of the system is seriously influenced.
2) The hyperplane approximation method is not used for constructing the SVSR by searching saddle node bifurcation points point by point, but is used for constructing the SVSR by approximating a local boundary of a static voltage stability domain, and compared with the fitting method, the method has the advantage that the construction efficiency of the SVSR approximate boundary is remarkably improved, but the method has higher conservative property.
Due to the extremely complex boundary topological characteristics, the voltage stability domain boundary is difficult to be described by a uniform hyperplane analytic expression. Therefore, the construction of SVSR still lacks a general method that is efficient and ensures good accuracy.
Disclosure of Invention
The invention provides a method for approximating a boundary of a static voltage stability domain of a power system based on a space tangent vector, which constructs an SVSR approximate boundary on the basis of a Saddle Node Bifurcation (SNB) searched by a continuous power flow model at high precision, improves the precision of the SVSR approximate boundary of the power system, and can form a uniform hyperplane analytic expression with practical significance, which is described in detail as follows:
a method for approximating a static voltage stability domain boundary of a power system based on a space tangent vector comprises the following steps:
taking ground state power flow as a starting point, searching a series of saddle node bifurcation points and tangent vectors thereof of the power system by adopting a continuous power flow method, and obtaining boundary points, namely saddle node bifurcation points, in a static voltage stability domain two-dimensional active power injection space;
preliminarily dividing a static voltage stability domain formed by the obtained boundary points into a plurality of regions based on the space tangent vector, calculating the distance from the boundary points to the corresponding line segments by a bisection method, and obtaining a two-dimensional approximate boundary meeting the requirement of a certain distance error threshold;
on the basis of the two-dimensional approximate boundary, a three-dimensional approximate boundary is established according to a triangle construction principle, a triangle approximate plane equation is further obtained, the maximum distance error from all SNB points to the plane in an approximate area corresponding to the S-th triangle approximate plane is calculated, and when the maximum distance error meets an error threshold value, approximation is finished, so that the three-dimensional SVSR triangle approximate boundary is obtained.
Wherein the corresponding line segment specifically is:
in a two-dimensional active power injection space, the slope of a connecting line between a certain boundary point z and an origin O is recorded as kzLine segment l1The slope of the connection line between the two end points 1 and 2 and the origin O is kl1、kl2If k iszSize between kl1And k isl2In between is considered as l1Are the corresponding line segments of z.
Further, the obtaining of the two-dimensional proximity boundary meeting the requirement of the certain distance error threshold specifically includes:
searching critical points meeting the angle threshold requirement, connecting adjacent critical points meeting the angle threshold requirement, preliminarily establishing an SVSR two-dimensional approximate boundary, and calling the critical points meeting the angle threshold requirement as end points of the connection;
taking all SNB points in the boundary region approximated by the connection line of the (f-1) th to f (f) th end points, calculating the distance error from the SNB points to the connection line, and further obtaining the maximum distance error;
if the maximum distance error is less than or equal to the error threshold, f is f +1, and when f is less than or equal to the error threshold, f is equal to f +1>Number of endpoints nqIf so, the two-dimensional SVSR boundary approximation is finished; otherwise, segmenting the obtained static voltage stable domain approximate boundary, and approximating again.
Further, the searching for the critical point meeting the angle threshold requirement specifically includes:
setting a threshold value thetamaxFrom the first SNB point z0Starting from the direction of increasing active power injection of the i node, searching for a direction meeting a threshold value thetamaxA required critical point;
(r +1) SNB points can be searched by repeatedly calling the CPF method, and a connecting line between the SNB points is marked as zl-zmObtaining z0Tangent line l0And z0-z1The included angle of (A);
comparison of θ1And thetamaxIf theta is large or small1Less than thetamaxThen set z0Tangent line and z0-z2Is theta2Comparison of θ2And thetamaxUntil the angle is greater than the threshold value thetamaxStopping the search if z is the same0Tangent line and z0-ztIs thetatAnd thetatGreater than or equal to thetamaxTaking zt-1As a coincidence threshold thetamaxA required critical point;
to meet the threshold value thetamaxCritical point z of requirementt-1As a new starting point, in zt-1Making tangent line and continuing the above steps until all critical points meeting the requirement are searched, and taking the SNB point under the condition that only the i node has active power injection as the last conforming threshold thetamaxThe critical point is required so as to preliminarily establish an approximate boundary in the global range of the two-dimensional active power injection space of the static voltage stability region in the subsequent process.
In a specific implementation, the SVSR two-dimensional approximate boundary specifically includes:
ΔPj＝KΔPi+B
in the formula, K and B are respectively the expression parameters of the adjacent critical point connection equation meeting the threshold requirement: delta Pi、ΔPjRespectively representing active power injection variation of nodes i and j
Figure BDA0001625316680000031
B＝λfPfi-KλfPfj
In the formula, Pfi、PfjRespectively representing active power components corresponding to the nodes i and j in the power increasing direction of the f-th endpoint; p(f-1)i、P(f-1)jRespectively representing active power components corresponding to the nodes i and j in the (f-1) th endpoint power increasing direction; delta Pi、ΔPjRespectively representing the active power injection variable quantities of the nodes i and j; lambda [ alpha ]f、λf-1Respectively representing the load margins in the power increasing direction corresponding to the f-th endpoint and the (f-1) -th endpoint.
In the concrete implementation, the step of segmenting the obtained static voltage stable domain approximate boundary is specifically as follows:
ΔPj＝K1ΔPi+B1,(min{ΔP(f-1)i,ΔPwi}≤ΔPi≤max{ΔP(f-1)i,ΔPwi})
ΔPj＝K2ΔPi+B2,(min{ΔPwi,ΔPfi}≤ΔPi≤max{ΔPwi,ΔPfi})
in the formula, K1、B1Parameters respectively representing the first segment approximate boundary; k2、B2Parameters respectively representing the approximate boundaries of the second segment;
Figure BDA0001625316680000032
B1＝λwPwj-K1λwPwi
Figure BDA0001625316680000033
B2＝λwPwj-K2λwPwi
in the formula, λwRepresents the load margin in the power increasing direction corresponding to the w-th SNB point, Pwi、PwjRespectively represent the active power components corresponding to the nodes i and j in the w-th SNB point power increasing direction.
Further, the triangle construction principle specifically includes:
(1) the constructed triangle vertex is composed of the calculated endpoints, and the number of the calculated endpoints is d when u is setuThe number of endpoints for u +1 is du+1；
(2) The three vertexes of the same constructed triangle must simultaneously contain the end points required by u and u + 1;
(3) the triangles to be constructed need to be staggered and not overlapped, two adjacent staggered triangles are taken as a group of staggered triangles, and the number of the groups to be constructed should be (min { d) }u，du+1} -1) group.
Further, the establishing of the three-dimensional similarity boundary and the obtaining of the triangular approximation plane equation specifically include:
the triangle approximation boundary expression is:
aΔPi+bΔPj+cΔPk+d＝0
in the formula, a, b, c and d respectively represent the parameters of a triangular approximate plane equation:
Figure BDA0001625316680000041
Figure BDA0001625316680000042
Figure BDA0001625316680000043
Figure BDA0001625316680000044
wherein the maximum distance error specifically is:
Figure BDA0001625316680000045
in the formula, Psi、Psj、PskRespectively represents zsInjection power, λ, of corresponding i, j, k nodessRepresenting the load margin at the respective injection power.
The technical scheme provided by the invention has the beneficial effects that:
1. the method searches the SNB points in different power increasing directions on the basis of the SNB points obtained after the CPF is operated, and effectively improves the construction precision of the SVSR boundary in the two-dimensional active power injection space;
2. compared with the static voltage stability domain boundary constructed by the existing CPF-based fitting method, the approximation method not only greatly improves the construction efficiency, but also obviously improves the accuracy of the system voltage stability evaluation;
3. the approximation method can be applied to voltage stability domain construction of an actual power system, and conservatism can be further reduced compared with the existing hyperplane approximation method.
Drawings
FIG. 1 is a flow chart of a method for approximating a boundary of a stable region of a static voltage based on a space tangent vector;
FIG. 2 is a schematic diagram illustrating a region division of a stable region of a static voltage;
FIG. 3 is a schematic diagram of a continuous power flow method for searching saddle node bifurcation points of an electric power system;
FIG. 4 is a graph of a search satisfying a threshold θmaxA schematic diagram of the required critical points;
FIG. 5 is a schematic illustration of a piecewise approximation of a two-dimensional approximation method;
FIG. 6 is a schematic diagram of a triangular approximation of a three-dimensional approximation method;
FIG. 7 is a diagram of a test system of WECC-9(Western electric coding Council);
FIG. 8 is a diagram of the SNB point search result with WECC-9 system coordinate axis as the load node;
FIG. 9 is a schematic diagram of a two-dimensional SVSR segment approximation with WECC-9 system coordinate axis as load node;
FIG. 10 is a schematic diagram of the three-dimensional SVSR approximate boundary with WECC-9 system coordinate axis as load node.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
In order to realize the high-precision construction of the SVSR boundary of the power system, the embodiment of the invention provides a power system static voltage stability domain boundary approximation method based on a space tangent vector according to the good linear characteristic of the SVSR local boundary.
Firstly, the embodiment of the invention calculates the saddle node bifurcation point of the electric power system in the new power increasing direction by continuously calling the CPF method, and simultaneously searches for the tangent point meeting the requirement, thereby effectively reducing the calculation amount; and a piecewise approximation method is adopted to realize the construction of the SVSR approximate boundary on the premise of ensuring enough precision.
Example 1
The embodiment of the invention provides a method for approximating a static voltage stability domain boundary of a power system based on a space tangent vector, which comprises the following steps of:
101: taking ground state power flow as a starting point, searching a series of saddle node bifurcation points and tangent vectors thereof of the power system by adopting a continuous power flow method, and obtaining boundary points, namely SNB points, in a static voltage stability domain two-dimensional active power injection space;
102: acquiring a two-dimensional approximate boundary meeting the requirement of a certain distance error threshold;
the static voltage stability region formed by the obtained boundary points is preliminarily divided into several regions based on the space tangent vector, as shown in FIG. 2The static voltage stable region can be formed by R1And R2Two regions, formed by line segments l1Approximately representing the region R1By line segment l2Approximately representing the region R2And then calculating the distance from the boundary point to the corresponding line segment by a bisection method to obtain a two-dimensional approximate boundary meeting the requirement of a certain distance error threshold.
As shown in fig. 2, the corresponding line segment refers to a slope k of a connection line between a boundary point z and an origin O in a two-dimensional active power injection spacezLine segment l1The slope of the connection line between the two end points 1 and 2 and the origin O is kl1、kl2If k iszSize between kl1And k isl2Can be regarded as l1Are the corresponding line segments of z.
103: on the basis of the two-dimensional approximate boundary, a three-dimensional SVSR approximate boundary is constructed by a series of triangular planes.
In summary, in the embodiment of the present invention, a series of SNB points and tangent vectors thereof are obtained by the continuous power flow method through the steps 101 to 103, and the critical points meeting the threshold requirement are quickly searched, so as to achieve the approximation of the boundary of the static voltage stability region.
Example 2
The scheme of embodiment 1 is further described below with reference to specific calculation formulas and accompanying fig. 3, fig. 4, fig. 5, and fig. 6, and is described in detail as follows:
201: repeatedly calling continuous power flow by taking the ground state power flow as a starting point to obtain a series of SNB points in different power increasing directions, tangent vectors corresponding to the SNB points and a load margin lambda;
wherein, the SNB point under the condition that only the j node has active power injection is recorded as z0Along the direction that the active power injection of the i node gradually increases, the obtained SNB points are respectively marked as z1、z2…zr(r is divide by z0Number of SNB points obtained outside). And mapping the SNB point and the tangent vector thereof to a two-dimensional active power injection space with the active power injection of the i and j nodes as coordinate axes.
202: performing segment approximation on the boundary of a static voltage stability domain formed by all SNB points by adopting a segment approximation method to obtain an approximation boundary of a two-dimensional SVSR;
wherein the step 202 comprises:
1) search for compliance with threshold θmaxThe required critical points are searched in the following specific process:
(1) setting a threshold value thetamaxFrom the first SNB point z0Starting from the direction of increasing active power injection of the i node, searching for a direction meeting a threshold value thetamaxA required critical point;
(2) (r +1) SNB points can be searched by repeatedly calling the CPF method, and a connecting line between the SNB points is marked as zl-zm(subscripts l and m denote the l-th and m-th SNB points, respectively);
Figure BDA0001625316680000061
in the formula, theta1Denotes z0Tangent line l0And z0-z1The included angle of (A); k is a radical of0Denotes a tangent line l0The slope of (a) of (b) is,
Figure BDA0001625316680000062
represents a connecting line z0-z1The slope of (a).
(3) Comparison of θ1And thetamaxIf theta is large or small1Less than thetamaxThen set z0Tangent line and z0-z2Is theta2Comparison of θ2And thetamaxUntil the angle is greater than the threshold value thetamaxStopping the search if z is the same0Tangent line and z0-ztIs thetat(where t is less than r), and θtGreater than or equal to thetamaxTaking zt-1As a coincidence threshold thetamaxThe critical point required.
(4) To meet the threshold value thetamaxCritical point z of requirementt-1As a new starting point, in zt-1Making tangent line and continuing the above steps until all the satisfied ones are searchedCalculating a critical point, and taking the SNB point under the condition that only the i node has active power injection as the last coincidence threshold value thetamaxThe critical point required.
2) As shown in FIG. 5, in z0As a first coincidence threshold thetamaxThe critical point of the requirement is set to a searchable coincidence threshold thetamaxThe critical point required is z0、z(t-1)、zrLet the number of endpoints n q3, let z0、z(t-1)、zrRespectively setting counting symbols f for endpoints 1, 2 and 3, and setting f to be 2;
3) will be adjacent to satisfy the threshold value thetamaxThe required critical points are connected, as shown by z in FIG. 50And ztZ for connecting lines0-zt；z(t-1)And zrZ for connecting lines(t-1)-zrPreliminarily establishing an SVSR two-dimensional approximate boundary;
ΔPj＝KΔPi+B(2)
wherein K and B are adjacent coincidence threshold values thetamaxThe expression parameters of the required critical point connection equation:
Figure BDA0001625316680000071
B＝λfPfi-KλfPfj(4)
in the formula, Pfi、PfjRespectively representing active power components corresponding to the nodes i and j in the power increasing direction of the f-th endpoint; p(f-1)i、P(f-1)jRespectively representing active power components corresponding to the nodes i and j in the (f-1) th endpoint power increasing direction; delta Pi、ΔPjRespectively representing the active power injection variable quantities of the nodes i and j; lambda [ alpha ]f、λf-1Respectively representing the load margins in the power increasing direction corresponding to the f-th endpoint and the (f-1) -th endpoint.
4) Taking all SNB points in the boundary region approximated by the connection line between the (f-1) th and the f-th end points, calculating the distance error between the SNB points and the connection line, and setting the w-th SNB point between the (f-1) th and the f-thf boundary regions approximated by end-point connections and having a maximum distance error εwmaxThe following formula:
Figure BDA0001625316680000072
in the formula,. DELTA.Pwi、ΔPwjRespectively representing the active power injection variation of the w-th SNB point corresponding to the nodes i and j.
5) Let the error threshold be epsilonmaxChecking for epsilonwmaxIf epsilonwmaxLess than or equal to a threshold value epsilon set according to actual needsmaxExecuting step 7); otherwise, executing step 6);
6) segmenting the obtained static voltage stable domain approximate boundary, and approximating again;
wherein the step 6) comprises:
(1) the approximate boundary of the static voltage stable region obtained in the last step is in epsilonwmaxThe corresponding power system saddle node bifurcation point is approximately segmented as follows:
Figure BDA0001625316680000073
in the formula, K1、B1Parameters respectively representing the first segment approximate boundary; k2、B2Parameters respectively representing the approximate boundaries of the second segment are as follows:
Figure BDA0001625316680000074
B1＝λwPwj-K1λwPwi(8)
Figure BDA0001625316680000075
B2＝λwPwj-K2λwPwi(10)
in the formula, λwRepresents the load margin in the power increasing direction corresponding to the w-th SNB point, Pwi、PwjRespectively represent the active power components corresponding to the nodes i and j in the w-th SNB point power increasing direction.
(2) Let the w-th SNB point be the new end point, nq＝nq+1, numbering all endpoints 1, 2.. n along the direction of increasing i-node active power injectionqAnd f is set to be 2, and the step 3) is executed again.
7) f is f +1, if f>nqIf yes, the two-dimensional SVSR boundary is approximately ended, go to step 203; otherwise, continuing to execute the step 3).
203: and performing three-dimensional approximation of the boundary on the basis of the two-dimensional approximation of the SVSR boundary.
Wherein step 203 comprises:
1) active power injection of i, j and k nodes is selected as an X axis, a Y axis and a Z axis of a three-dimensional coordinate axis;
2) under the condition that only node k has active power injection, the variation P of the injection power of the node k is obtainedkWhen the corresponding load margin is λkSetting the total construction times of the two-dimensional approximation as v times;
3) let u equal to 0;
4) under the condition that the power increase of the k node is not changed, the power increase of the i node and the j node is changed to ensure that
Figure BDA0001625316680000081
Calculating active power injection of i, j and k nodes corresponding to the approximate boundary end points of each section by using a sectional approximation method in a two-dimensional active power injection space of the nodes i and j;
5) if u is equal to u +1, if u is equal to or less than v, returning to the step 4), otherwise, ending the search of the end point, and entering the step 6);
6) let u equal to 0;
7) constructing a plurality of triangles by using all endpoints corresponding to u and u +1, wherein the triangle construction principle is as follows:
(1) the constructed triangle vertex is composed of the calculated endpoints, and the number of the calculated endpoints is d when u is setuThe number of endpoints for u +1 is du+1；
Wherein, taking the shaded part in FIG. 6 as an example, the three vertexes of the triangles 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 are all composed of the calculated endpoints, and in this case du＝7，du+1＝5。
(2) The three vertexes of the same constructed triangle must simultaneously contain the end points required by u and u + 1;
as shown by the shaded triangles in fig. 6.
(3) The constructed triangles need to be staggered and not overlapped to the maximum extent, two adjacent staggered triangles are recorded as a group of staggered arrangement, the maximum staggered arrangement is to make the number of staggered arrangement groups to be the maximum, and the maximum constructed staggered arrangement group number needs to be (min { d) }u，du+1} -1) group; let u be u +1, if u<v, returning to the step 7), otherwise, entering the step 8);
wherein, taking the shaded portion in FIG. 6 as an example, triangles 1 and 7, 2 and 8, 3 and 9, 4 and 10 have been formed (min { d }u，du+1}-1)＝du+1And 4 groups are staggered, so that the requirement that the number of the groups is 4 is met, and therefore the triangles 5 and 6 do not form staggered arrangement, so that the triangle is constructed according to the principle that three sides of the triangle are not overlapped, namely, the triangle is not intersected.
8) And (3) completing the primary construction of the three-dimensional approximation boundary: assuming that the number of the three-dimensional SVSR triangle approximation boundaries which can be preliminarily constructed is N, entering the step 9);
9) let S be 1;
10) let S (S ≦ N) triangle approximation boundary expression as:
aΔPi+bΔPj+cΔPk+d＝0 (11)
in the formula, a, b, c and d respectively represent the parameters of a triangular approximate plane equation:
Figure BDA0001625316680000091
Figure BDA0001625316680000092
Figure BDA0001625316680000093
Figure BDA0001625316680000094
in the formula (I), the compound is shown in the specification,
Figure BDA0001625316680000095
respectively representing active power injection of i, j and k nodes corresponding to the 1 st vertex of the triangular approximate plane;
Figure BDA0001625316680000096
respectively representing active power injection of i, j and k nodes corresponding to the 2 nd vertex of the triangular approximate plane;
Figure BDA0001625316680000097
respectively representing active power injection of i, j and k nodes corresponding to the 3 rd vertex of the triangular approximate plane;
Figure BDA0001625316680000098
respectively represent the active power injection of the i, j and k nodes as
Figure BDA0001625316680000099
Figure BDA00016253166800000910
Load margin in the case.
11) Calculating the distance error between all SNB points in the approximate area corresponding to the S-th triangular approximate plane and the S-th triangular approximate plane, and assuming that an SNB point z exists on the three-dimensional boundary of the SVSRsIt belongs to the approximate area corresponding to the S-th triangle approximate plane, and the maximum distance error between the existing point and the plane is hsmax：
Figure BDA00016253166800000911
In the formula, Psi、Psj、PskRespectively represents zsInjection power, λ, of corresponding i, j, k nodessRepresenting the load margin at the respective injection power.
12) Let the point-to-plane error threshold be hmaxChecking hsmaxIf h issmaxLess than or equal to the threshold h set according to actual needsmaxExecuting step 14); otherwise, executing step 13);
13) let v ═ v +1, go to step 3);
14) s +1, if S > N, go to step 15), otherwise go to step 10);
15) and after the approximation is finished, obtaining a three-dimensional SVSR triangle approximation boundary.
In summary, in the embodiment of the present invention, the SNB point obtained by repeatedly calling the CPF method is used as the basis in the above steps 201 to 204, so as to approximate the SVSR boundary; the method obviously improves the precision and the construction speed of the approximate boundary of the voltage stability region, and has practical application value for voltage stability evaluation.
Example 3
The feasibility verification of the solutions of examples 1 and 2 is carried out below with reference to the specific examples, fig. 7, fig. 8, fig. 9 and table 1, as described in detail below:
in this example, the two-dimensional SVSR approximate boundary of the WECC3 machine 9 node system is searched for example, to verify the validity of the method, and the WECC3 machine 9 node test system is shown in fig. 7.
The load nodes 5 and 9 are used as voltage stabilization key nodes, active power injection of the nodes 5 and 9 is selected as a coordinate axis, and the SVSR is constructed in a two-dimensional active power injection space by adopting the method.
Setting different power increasing directions, and repeatedly calling the continuous power flow method to search to obtain a series of SNB points and tangent vectors thereof, such as points 1 and 2 … 13 shown in FIG. 8. The coordinates of the SNB point and its tangent vector in the two-dimensional active power injection space are shown in table 1.
TABLE 1 search SNB Point results based on repeatedly invoking CPF method
Figure BDA0001625316680000101
On the basis of SVSR boundary point search, the method is adopted to search a critical point meeting the condition, the direction from the point 1 to the i-node active power injection growth is searched, and the tangent line at the point 1 can be calculated according to the tangent vector at the point 1 and the coordinate of the point 1. Let θmaxThe included angles between the tangent line of the point 1 and the connecting lines 1-2, 1-3, 1-4, 1-5 and 1-6 are respectively 0.8446, 3.0588, 5.2562, 7.7154 and 10.5435; due to 10.5435>10, then making tangent line from point 5, continuously searching tangent points meeting requirements in the direction of active power injection increase of i node, and searching all obtained tangent points meeting the threshold value thetamaxThe critical points required are point 1, point 5, point 7, and point 9.
After the critical point meeting the condition is obtained through searching, the SVSR approximate boundary is further constructed. Based on SNB points 1 and 5, points 5 and 7, points 7 and 9, points 9 and 13, establishing an SVSR preliminary approximate boundary expression, and obtaining:
-0.4121ΔP9-ΔP5+3.5018＝0(0≤ΔP9≤1.7441)
-0.8452ΔP9-ΔP5+4.2572＝0(1.7441≤ΔP9≤2.4814)
-1.4411ΔP9-ΔP5+5.7357＝0(2.4814≤ΔP9≤3.0255)
-2.6640ΔP9-ΔP5+9.4357＝0(3.0255≤ΔP9≤3.5419)
the line segments corresponding to the above expressions are respectively denoted as line1, line2, line3, and line 4.
Set epsilonmax0.05, calculating the distance error from the SNB points 1, 2, 3, 4, 5 to line1, which are respectively 0, 0.0566, 0.0767, 0.0607, 0; distance errors of points 5, 6, 7 to line2, which are 0, 0.0324, 0, respectively; distance errors from points 7, 8, 9 to line3, which are 0, 0.0289, 0, respectively; the distance errors from the points 9, 10, 11, 12, 13 to the line4 are 0, 0.0396, 0.0403, 0.0084, respectively,0。
It can be seen that there is ε to line2wmax0.0342, sowmax≤εmax(ii) a Has ε for line3wmax0.0289, sowmax≤εmax(ii) a Has ε for line4wmax0.0403, sowmax≤εmax(ii) a For line1 to ε at SNB Point 3wmax0.0767 has ∈wmax≥εmaxFurther utilizing SNB points 1 and 3, 3 and 5 to establish an SVSR boundary expression; obtaining:
Figure BDA0001625316680000111
corresponding to line5, line6, line2, line3, and line4, respectively, in fig. 9. The two-dimensional SVSR boundary approximately ends.
In conclusion, compared with the static voltage stability domain boundary constructed by the existing CPF-based fitting method, the approximation method not only greatly improves the construction efficiency, but also obviously improves the accuracy of the system voltage stability evaluation.
Example 4
The feasibility verification of the solutions of examples 1 and 2 is described below in connection with the specific examples, fig. 7, fig. 10, and table 2, and is described in detail below:
in this embodiment, the effectiveness of the method is verified by taking searching for the three-dimensional SVSR approximate boundary of the WECC3 machine 9 node system as an example, and the WECC3 machine 9 node testing system is shown in fig. 7. The load nodes 5, 7 and 9 are used as voltage stabilization key nodes, active power injection of the nodes 5, 7 and 9 is selected as a coordinate axis, and the SVSR is constructed in a three-dimensional active power injection space by adopting the method.
Setting an initial power increase direction d0＝[ΔSd2,ΔSd3,ΔSd4,ΔSd5,ΔSd6,ΔSd7,ΔSd8,ΔSd9]T＝[0,0,0,0,0,9,0,0]TAt this time λk＝0.4309，λkPk3.8781, setting the two-dimensional SVSR approximate boundary construction times v to 5, and it can be concluded from step 204 that the end point sits every time the two-dimensional approximate boundary is constructedMarking, and further preliminarily constructing a triangular approximate plane; from step 205, a threshold h is setmaxThe three-dimensional SVSR triangle approximation boundary that can be finally constructed is shown in fig. 10, which is 0.5. The partial expression of the constructed triangle approximating hyperplane is shown in table 2.
TABLE 2 partial three-dimensional SVSR boundary triangle hyperplane approximation results
Figure BDA0001625316680000121
In conclusion, compared with the static voltage stability domain boundary constructed by the existing CPF-based fitting method, the approximation method not only greatly improves the construction efficiency, but also obviously improves the accuracy of the system voltage stability evaluation.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (9)

1. A method for approximating a static voltage stability domain boundary of a power system based on a space tangent vector is characterized by comprising the following steps of:
taking ground state power flow as a starting point, searching a series of saddle node bifurcation points and tangent vectors thereof of the power system by adopting a continuous power flow method, and obtaining boundary points, namely saddle node bifurcation points, in a static voltage stability domain two-dimensional active power injection space;
preliminarily dividing a static voltage stability domain formed by the obtained boundary points into a plurality of regions based on the space tangent vector, calculating the distance from the boundary points to the corresponding line segments by a bisection method, and obtaining a two-dimensional approximate boundary meeting the requirement of a certain distance error threshold;
on the basis of the two-dimensional approximate boundary, a three-dimensional approximate boundary is established according to a triangle construction principle, a triangle approximate plane equation is further obtained, the maximum distance error from all SNB points to the plane in an approximate area corresponding to the S-th triangle approximate plane is calculated, and when the maximum distance error meets an error threshold value, approximation is finished, so that the three-dimensional SVSR triangle approximate boundary is obtained.
2. The method according to claim 1, wherein the corresponding line segments specifically include:
in a two-dimensional active power injection space, the slope of a connecting line between a certain boundary point z and an origin O is recorded as kzLine segment l1The slope of the connection line between the two end points 1 and 2 and the origin O is kl1、kl2If k iszSize between kl1And k isl2In between is considered as l1Are the corresponding line segments of z.
3. The method according to claim 1, wherein the obtaining of the two-dimensional approximation boundary that meets the requirement of a certain distance error threshold specifically comprises:
searching critical points meeting the angle threshold requirement, connecting adjacent critical points meeting the angle threshold requirement, preliminarily establishing an SVSR two-dimensional approximate boundary, and calling the critical points meeting the angle threshold requirement as end points of the connection;
taking all SNB points in the boundary region approximated by the connection line of the (f-1) th to f (f) th end points, calculating the distance error from the SNB points to the connection line, and further obtaining the maximum distance error;
if the maximum distance error is less than or equal to the error threshold, f is f +1, and when f is less than or equal to the error threshold, f is equal to f +1>Number of endpoints nqIf so, the two-dimensional SVSR boundary approximation is finished; otherwise, segmenting the obtained static voltage stable domain approximate boundary, and approximating again.
4. The method according to claim 3, wherein the searching for the critical point meeting the angle threshold requirement specifically comprises:
setting a threshold value thetamaxFrom the first SNB point z0Starting from the direction of increasing active power injection of the i node, searching for a direction meeting a threshold value thetamaxA required critical point;
(r +1) SNB points can be searched by repeatedly calling the CPF method, and a connecting line between the SNB points is marked as zl-zmObtaining z0Tangent line l0And z0-z1The included angle of (A);
comparison of θ1And thetamaxIf theta is large or small1Less than thetamaxThen set z0Tangent line and z0-z2Is theta2Comparison of θ2And thetamaxUntil the angle is greater than the threshold value thetamaxStopping the search if z is the same0Tangent line and z0-ztIs thetatAnd thetatGreater than or equal to thetamaxTaking zt-1As a coincidence threshold thetamaxA required critical point;
to meet the threshold value thetamaxCritical point z of requirementt-1As a new starting point, in zt-1Making tangent line and continuing the above steps until all critical points meeting the requirement are searched, and taking the SNB point under the condition that only the i node has active power injection as the last conforming threshold thetamaxThe critical point is required so as to preliminarily establish an approximate boundary in the global range of the two-dimensional active power injection space of the static voltage stability region in the subsequent process.
5. The method according to claim 3, wherein the SVSR two-dimensional approximation boundary specifically comprises:
ΔPj＝KΔPi+B
in the formula, K and B are respectively the expression parameters of the adjacent critical point connection equation meeting the threshold requirement: delta Pi、ΔPjRespectively representing active power injection variation of nodes i and j
Figure FDA0002782500340000021
B＝λfPfi-KλfPfj
In the formula, Pfi、PfjRespectively representing active power components corresponding to the nodes i and j in the power increasing direction of the f-th endpoint; p(f-1)i、P(f-1)jRespectively representing active power components corresponding to the nodes i and j in the (f-1) th endpoint power increasing direction; delta Pi、ΔPjRespectively representing the active power injection variable quantities of the nodes i and j; lambda [ alpha ]f、λf-1Respectively representing the load margins in the power increasing direction corresponding to the f-th endpoint and the (f-1) -th endpoint.
6. The method according to claim 5, wherein the step of segmenting the obtained static voltage stability domain approximate boundary is to perform the approximation again specifically as follows:
ΔPj＝K1ΔPi+B1,(min{ΔP(f-1)i,ΔPwi}≤ΔPi≤max{ΔP(f-1)i,ΔPwi})
ΔPj＝K2ΔPi+B2,(min{ΔPwi,ΔPfi}≤ΔPi≤max{ΔPwi,ΔPfi})
in the formula, K1、B1Parameters respectively representing the first segment approximate boundary; k2、B2Parameters respectively representing the approximate boundaries of the second segment;
Figure FDA0002782500340000022
B1＝λwPwj-K1λwPwi
Figure FDA0002782500340000031
B2＝λwPwj-K2λwPwi
in the formula, λwRepresents the load margin in the power increasing direction corresponding to the w-th SNB point, Pwi、PwjRespectively representing active power components corresponding to nodes i and j in the power increasing direction of the w-th SNB point; delta PwiIndicating that the w-th SNB point corresponds to the active power injection variation of the node i.
7. The method according to claim 1, wherein the triangle construction principle is specifically as follows:
(1) the constructed triangle vertex is composed of the calculated endpoints, and the number of the calculated endpoints is d when u is setuThe number of endpoints for u +1 is du+1；
(2) The three vertexes of the same constructed triangle must simultaneously contain the end points required by u and u + 1;
(3) the triangles to be constructed need to be staggered and not overlapped, two adjacent staggered triangles are taken as a group of staggered triangles, and the number of the groups to be constructed should be (min { d) }u，du+1} -1) group.
8. The method according to claim 6, wherein the establishing of the three-dimensional approximation boundary and the obtaining of the triangular approximation plane equation specifically include:
the triangle approximation boundary expression is:
aΔPi+bΔPj+cΔPk+d＝0
Figure FDA0002782500340000032
Figure FDA0002782500340000033
Figure FDA0002782500340000034
Figure FDA0002782500340000035
in the formula, a, b, c and d respectively represent the parameters of a triangular approximate plane equation;
Figure FDA0002782500340000036
respectively representing active power injection of i, j and k nodes corresponding to the 1 st vertex of the triangular approximate plane;
Figure FDA0002782500340000037
respectively representing active power injection of i, j and k nodes corresponding to the 2 nd vertex of the triangular approximate plane;
Figure FDA0002782500340000038
respectively representing active power injection of i, j and k nodes corresponding to the 3 rd vertex of the triangular approximate plane;
Figure FDA0002782500340000039
respectively represent the active power injection of the i, j and k nodes as
Figure FDA00027825003400000310
Load margin in the case.
9. The method according to claim 8, wherein the maximum distance error is specifically:
Figure FDA0002782500340000041
in the formula, Psi、Psj、PskRespectively represents zsInjection power, λ, of corresponding i, j, k nodessRepresenting the load margin at the respective injection power.
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