CN107133406B - Rapid search method for static voltage stability domain boundary of power system - Google Patents

Rapid search method for static voltage stability domain boundary of power system Download PDF

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CN107133406B
CN107133406B CN201710327744.8A CN201710327744A CN107133406B CN 107133406 B CN107133406 B CN 107133406B CN 201710327744 A CN201710327744 A CN 201710327744A CN 107133406 B CN107133406 B CN 107133406B
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姜涛
李雪
张明宇
陈厚合
李国庆
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Northeast Electric Power University
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Northeast Dianli University
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Abstract

A method for quickly searching the boundary of a static voltage stability domain of a power system comprises the following steps: determining a static voltage stability domain boundary general mathematical model; determining an initial static voltage stable domain boundary point; initializing quiescent voltage stability domain boundariesThe general mathematical model of (2); predicting boundary points of adjacent static voltage stability domains
Figure DDA0001290962460000011
Correcting the predicted point
Figure DDA0001290962460000012
Obtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction point
Figure DDA0001290962460000013
Correction point
Figure DDA0001290962460000014
The above process is adopted for initial value circulation, the next adjacent static voltage stable domain boundary point is searched, and in the circulation process, the simultaneous gradient matrix and the additionally added equation are replaced by s
Figure DDA0001290962460000015
The method is completed until the power increase direction angle β is smaller than 0 and the power increase direction angle β is larger than 90 degrees, and the SVSR boundary constructed by the method has higher precision and can realize the quick search of the boundary of the static voltage stability domain of the power system in a two-dimensional and high-dimensional active injection space.

Description

Rapid search method for static voltage stability domain boundary of power system
Technical Field
The invention relates to a static voltage stability domain boundary search problem. In particular to a method for rapidly searching the boundary of a static voltage stability domain of a power system.
Background
The interconnection scale of the regional power grid is continuously enlarged, the renewable energy with high permeability is connected to the grid in a large scale, the power electronic equipment is widely applied, the problems of power injection volatility, tide distribution randomness and the like are brought while the transmission capacity of the power system is enhanced and the operation flexibility and economy of the power system are improved, the operation risk of the power system is increased, and the problem of power grid interconnection scale and high permeability renewable energy is solvedThe system voltage stability brings hidden trouble difficult to predict[1]-[5]. Therefore, the research on the voltage stability under the background of high-permeability renewable energy grid connection and power electronics of the power system is of great significance[6]-[7]。
Currently, the Continuous Power Flow (CPF) method[8]The method is still a basic method for researching the static voltage stability of the power system, and the core idea of the method is to carry out point-by-point iteration according to the determined power increasing direction, calculate the maximum load margin of the system on the premise of meeting the voltage stability, and evaluate the voltage stability of the system through the load margin. The algorithm is easy to realize and has higher calculation precision, so the algorithm is widely applied to actual power systems[9]-[11]. However, with the large-scale application of the large-scale grid connection and demand side response technology of the renewable energy, the uncertainty of the power increase direction of the system is increased by the specific intermittency and randomness of the renewable energy and the demand side response, and the load margin obtained by calculation of the power increase direction determined by the load prediction and the unit combination cannot truly reflect the voltage stability of the system. If the real voltage stability of the system needs to be evaluated, the load margin of the CPF computing system needs to be repeatedly called according to the possible power increasing direction, which inevitably brings heavy computing burden and is not favorable for the efficiency of evaluating the static voltage stability of the system. Static voltage stability region of power system[12]The (static voltage stability region, SVSR) describes an operation region where the system has static voltage stability under the condition of determining the network topology and parameters. By the aid of the constructed SVSR, voltage stability of the system in the uncertain power increasing direction can be accurately evaluated, the defects of uncertainty of system load and power output of a traditional voltage stability analysis method are overcome, and the method is a reliable method for analyzing and evaluating voltage stability of a power system[13]。
The key point of constructing the SVSR lies in accurately and quickly searching the stable domain boundary thereof, and the method for calculating the SVSR boundary mainly comprises a fitting method[14]-[15]And approximation method[16]-[18]Two kinds. The fitting method is developed by the traditional voltage stability analysis method,according to the characteristic that the SVSR boundary is mainly composed of saddle node bifurcation points, starting from the ground state power flow, CPF is repeatedly called to calculate saddle node bifurcation points in different power increasing directions, and finally the searched saddle node bifurcation points form the SVSR boundary[14]-[15]. The method focuses on constructing the SVSR boundary by using the saddle node bifurcation point and has higher precision. However, the core calculation algorithm for searching saddle node bifurcation points is still CPF, so that a large amount of iterative operations are brought when the whole SVSR boundary is searched, and the offline calculation amount is huge. The approximation method does not perform point-by-point search on saddle node bifurcation points on the SVSR boundary points, but improves the SVSR construction speed by locally approximating the SVSR boundary. Document [16]]-[18]Through the research on the topological characteristics of the SVSR boundary, the SVSR local boundary is found to present good linear characteristics, a hyperplane can be adopted for approximation, and a local analytic expression capable of approximately expressing the SVSR boundary is deduced on the basis. The method can quickly generate a certain hyperplane according to actual needs on the premise of meeting the calculation precision so as to approximately replace the local boundary of the SVSR. The hyperplane can describe local topological characteristics of the SVSR boundary, but has larger conservative property, the global precision of the SVSR boundary cannot be ensured, and different key parameter selections have larger influence on the SVSR boundary topological structure, so that the SVSR boundary topological structure is difficult to describe and obtain a general conclusion by using a unified analytic expression. At present, the SVSR boundary topological characteristic is explored, and the SVSR construction is still a difficulty of SVSR research on the basis of considering both the calculation precision and the calculation efficiency.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for quickly searching the boundary of a static voltage stability domain of a power system.
The technical scheme adopted by the invention is as follows: a quick search method for a static voltage stability domain boundary of a power system fully utilizes the incidence relation between adjacent saddle node bifurcation points on the static voltage stability domain boundary to improve the search efficiency, and specifically comprises the following steps:
1) determining a static voltage stability domain boundary general mathematical model;
2) determining an initial static voltage stable domain boundary point;
3) initializing a general mathematical model of the static voltage stability domain boundary;
4) predicting boundary points of adjacent static voltage stability domains
Figure BDA0001290962440000021
5) Correcting the predicted point
Figure BDA0001290962440000022
Obtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction point
Figure BDA0001290962440000023
6) Correction point
Figure BDA0001290962440000024
Performing initial value circulation, adopting the steps 4) to 5) to search the next adjacent static voltage stable domain boundary point, and replacing s in the simultaneous gradient matrix and the additionally added equation in the step (3) in the step 4) into s in the circulation process
Figure BDA0001290962440000025
And ending until the power increase direction angle β is less than 0 and the power increase direction angle β is greater than 90 degrees.
The step 1) comprises the following steps:
(1) the continuous power flow equation is combined with the boundary criterion of the static voltage stable domain to construct and describe the given power increasing direction d0The mathematical model of the corresponding static voltage stability domain boundary point is as follows:
Figure BDA0001290962440000026
wherein, x is a vector of a static state variable of the system, and g (x) is 0, which is a conventional power flow equation of the power system; λ is the system load margin, d0L is a left eigenvector corresponding to a zero eigenvalue of the tidal current Jacobian matrix, J is a power increase directionT(x) Is a tideA transposed matrix of the stream jacobian matrix;
(2) the general mathematical model for determining the boundary of the stable region of the static voltage is as follows:
Figure BDA0001290962440000027
wherein η and gamma are new power parameters, respectively describing the power increasing direction d0When the two-dimensional active power injection space of the nodes i and j changes, the active power variation quantity e of the corresponding static voltage stability domain boundary point on the nodes i and jiAnd ejVectors representing unit changes of active injection power of nodes i and j, respectively, eiAnd ejLength of (d)0The same vector, and only the ith and jth elements are 1, and the rest elements are 0; lambda [ alpha ]0d0For the operating point in the direction of power increase d0And (4) a lower load margin.
The step 2) comprises the following steps:
(1) acquiring basic data including a system ground state tide state variable and a system topological structure;
(2) according to a given power increase direction d0Determining the state variable x corresponding to the boundary point of the initial static voltage stability domain through the continuous power flow equation0And a load margin lambda0And thus obtaining an initial static voltage stable domain boundary point.
The step 3) comprises the following steps:
(1) determining a power flow Jacobian matrix J (x) at the boundary point of the initial static voltage stability domain0) Left eigenvector L corresponding to zero eigenvalue0Setting the initial value of newly added power parameter gamma0＝η0＝0；
(2) Universal mathematical model initial value z for determining initialization static voltage stable domain boundary0＝[x0,L0,γ0，η0]T，
In the formula, x0And the state variables corresponding to the boundary points of the initial static voltage stable domain.
The step 4) comprises the following steps:
(1) solving the gradient matrix of the general mathematical model of the static voltage stability domain boundary to the partial derivatives of each variable as follows:
Figure BDA0001290962440000031
(2) the following equations are additionally added on the basis of the gradient matrix to specify the magnitude and direction of a certain component in the tangent vector,
Figure BDA0001290962440000032
the power growth direction angle is defined as follows:
Figure BDA0001290962440000033
in the formula (I), the compound is shown in the specification,
Figure BDA0001290962440000034
is composed of
Figure BDA0001290962440000035
Corresponding to the new power parameter η, e is taken to be + -1, when e is taken to be +1,
Figure BDA0001290962440000036
pointing to the side where the power increase direction angle β increases, pointing to the side where the power increase direction angle β decreases when e takes-1, J (x)0) Is a tidal current Jacobian matrix at the boundary point of an initial static voltage stable domain, JT(x) As a transposed matrix of the tidal current Jacobian, L0Is J (x)0) A left eigenvector corresponding to the zero eigenvalue;
(3) the simultaneous gradient matrix and the additional added equation are as follows, and the tangent vector of the boundary point of the initial static voltage stable domain is determined
Figure BDA0001290962440000037
The following formula:
Figure BDA0001290962440000038
Figure BDA0001290962440000039
wherein s is [0 … 01 ]]，E＝[0 … 0 e]TBoth lengths of
Figure BDA00012909624400000310
Equal;
(4) setting step size sigma, predicting boundary point z of stable region of initial static voltage0Adjacent static voltage stable region boundary point
Figure BDA0001290962440000041
The following formula:
Figure BDA0001290962440000042
in the formula (I), the compound is shown in the specification,
Figure BDA0001290962440000043
is a normalized tangent vector.
Step 5) comprises the following steps:
(1) determining a passing predicted point
Figure BDA0001290962440000044
And is tangent to
Figure BDA0001290962440000045
Perpendicular hyperplane, as follows:
Figure BDA0001290962440000046
wherein z is a free variable;
(2) giving a correction equation to predict the point
Figure BDA0001290962440000047
As an initial value, the correction point is solved by Newton method
Figure BDA0001290962440000048
The following were used:
Figure BDA0001290962440000049
the method for quickly searching the boundary of the static voltage stability domain of the power system can realize quick search of the boundary of the static voltage stability domain of the power system in two-dimensional and high-dimensional active power injection space, overcomes the defect of conservatism in the construction of the SVSR boundary by an approximation method, and simultaneously avoids the calculation burden of iteratively calculating saddle node bifurcation points one by adopting a CPF method when the SVSR boundary is searched globally and accurately. The SVSR boundary constructed by the method has higher precision, and compared with the calculation efficiency of the CPF-based static voltage stability domain construction method, the calculation time for constructing the static voltage stability domain of the power system is greatly reduced, and the construction efficiency of the voltage stability domain of the power system is obviously improved.
Drawings
FIG. 1 is a diagram of a fast search of SVSR boundaries;
FIG. 2 is a flow chart of a fast search method for the boundary of the static voltage stability domain of the power system according to the present invention;
FIG. 3 is a diagram of a WECC-9 test system;
FIG. 4 is a SVSR with WECC-9 system coordinate axis as the active power consumption of the load node;
FIG. 5 is a comparison graph of the computed error of the SVSR boundary.
Detailed Description
The following describes a method for fast searching for the boundary of the static voltage stability domain of the power system in detail with reference to the embodiments and the accompanying drawings.
The following description and the drawings sufficiently illustrate specific embodiments of the invention to enable those skilled in the art to practice them. Other embodiments may incorporate structural, logical, electrical, process, and other changes. The examples merely typify possible variations. Individual components and functions are optional unless explicitly required, and the sequence of operations may vary. Portions and features of some embodiments may be included in or substituted for those of others. The scope of embodiments of the invention encompasses the full ambit of the claims, as well as all available equivalents of the claims. Embodiments of the invention may be referred to herein, individually or collectively, by the term "invention" merely for convenience and without intending to voluntarily limit the scope of this application to any single invention or inventive concept if more than one is in fact disclosed.
The static voltage stability domain of the power system is a multidimensional space surrounded by all saddle node bifurcation points in the system, and the system operates in the static voltage stability domain which is constructed by taking the saddle node bifurcation points as boundaries and is a necessary condition for maintaining voltage stability, so that the search of the SVSR boundary can be equivalent to the search of the saddle node bifurcation points.
As shown in fig. 1 and fig. 2, the method for rapidly searching the boundary of the static voltage stability domain of the power system according to the present invention is characterized in that the association relationship between adjacent saddle node bifurcation points on the boundary of the static voltage stability domain is fully utilized to improve the search efficiency, and specifically includes the following steps:
1) determining a static voltage stability domain boundary general mathematical model; the method comprises the following steps:
(1) the continuous power flow equation is combined with the boundary criterion of the static voltage stable domain to construct and describe the given power increasing direction d0The mathematical model of the corresponding static voltage stability domain boundary point is as follows:
Figure BDA0001290962440000051
wherein, x is a vector of a static state variable of the system, and g (x) is 0, which is a conventional power flow equation of the power system; λ is the system load margin, d0L is a left eigenvector corresponding to a zero eigenvalue of the tidal current Jacobian matrix, J is a power increase directionT(x) A transposed matrix of the tidal current Jacobian matrix;
(2) the general mathematical model for determining the boundary of the stable region of the static voltage is as follows:
Figure BDA0001290962440000052
wherein η and gamma are new power parameters, respectively describing the power increasing direction d0When the two-dimensional active power injection space of the nodes i and j changes, the active power variation quantity e of the corresponding static voltage stability domain boundary point on the nodes i and jiAnd ejVectors representing unit changes of active injection power of nodes i and j, respectively, eiAnd ejLength of (d)0The same vector, and only the ith and jth elements are 1, and the rest elements are 0; lambda [ alpha ]0d0For the operating point in the direction of power increase d0And (4) a lower load margin.
2) Determining an initial static voltage stable domain boundary point; the method comprises the following steps:
(1) acquiring basic data including a system ground state tide state variable and a system topological structure;
(2) according to a given power increase direction d0Determining the state variable x corresponding to the boundary point of the initial static voltage stability domain through the continuous power flow equation0And a load margin lambda0And thus obtaining an initial static voltage stable domain boundary point.
3) Initializing a general mathematical model of the static voltage stability domain boundary; the method comprises the following steps:
(1) determining a power flow Jacobian matrix J (x) at the boundary point of the initial static voltage stability domain0) Left eigenvector L corresponding to zero eigenvalue0Setting the initial value of newly added power parameter gamma0＝η0＝0；
(2) Universal mathematical model initial value z for determining initialization static voltage stable domain boundary0＝[x0,L0,γ0，η0]T，
In the formula, x0And the state variables corresponding to the boundary points of the initial static voltage stable domain.
4) Predicting boundary points of adjacent static voltage stability domains
Figure BDA0001290962440000053
The method comprises the following steps:
(1) solving the gradient matrix of the general mathematical model of the static voltage stability domain boundary to the partial derivatives of each variable as follows:
Figure BDA0001290962440000061
(2) the following equations are additionally added on the basis of the gradient matrix to specify the magnitude and direction of a certain component in the tangent vector,
Figure BDA0001290962440000062
the power growth direction angle is defined as follows:
Figure BDA0001290962440000063
in the formula, Δ η -zIs composed of
Figure BDA0001290962440000064
Corresponding to the newly added power parameter η, e is + -1, and Δ z is zero when e is +1zPointing to the side where the power increase direction angle β increases, pointing to the side where the power increase direction angle β decreases when e takes-1, J (x)0) Is a tidal current Jacobian matrix at the boundary point of an initial static voltage stable domain, JT(x) As a transposed matrix of the tidal current Jacobian, L0Is J (x)0) A left eigenvector corresponding to the zero eigenvalue;
(3) the simultaneous gradient matrix and the additional added equation are as follows, and the tangent vector of the boundary point of the initial static voltage stable domain is determined
Figure BDA0001290962440000065
The following formula:
Figure BDA0001290962440000066
Figure BDA0001290962440000067
wherein s is [0 … 01 ]]，E＝[0 … 0 e]TBoth lengths of
Figure BDA0001290962440000068
Equal;
(4) setting step size sigma, predicting boundary point z of stable region of initial static voltage0Adjacent static voltage stable region boundary point
Figure BDA0001290962440000069
The following formula:
Figure BDA00012909624400000610
in the formula (I), the compound is shown in the specification,
Figure BDA00012909624400000611
is a normalized tangent vector.
5) Correcting the predicted point
Figure BDA00012909624400000612
Obtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction point
Figure BDA00012909624400000613
The method comprises the following steps:
(1) determining a passing predicted point
Figure BDA00012909624400000614
And is tangent to
Figure BDA00012909624400000615
Perpendicular hyperplane, as follows:
Figure BDA00012909624400000616
wherein z is a free variable;
(2) giving a correction equation to predict the point
Figure BDA00012909624400000617
As an initial value, the correction point is solved by Newton method
Figure BDA00012909624400000618
The following were used:
Figure BDA0001290962440000071
6) correction point
Figure BDA0001290962440000072
Performing initial value circulation, adopting the steps 4) to 5) to search the next adjacent static voltage stable domain boundary point, and replacing s in the simultaneous gradient matrix and the additionally added equation in the step (3) in the step 4) into s in the circulation process
Figure BDA0001290962440000073
And ending until the power increase direction angle β is less than 0 and the power increase direction angle β is greater than 90 degrees.
At the adoption of correction points
Figure BDA0001290962440000074
Searching the next adjacent static voltage stable region boundary point to obtain the correction point
Figure BDA0001290962440000075
When vector is cut, the simultaneous gradient matrix in the step 4) and the step (3) and the additionally added equation are replaced by s
Figure BDA0001290962440000076
Namely, the augmentation gradient matrix of the formula (6) in the next adjacent static voltage stable domain boundary point prediction link can be directly replaced by the Jacobian matrix of the formula (10) in the previous static voltage stable domain boundary point correction link, and so on until the power increase direction angle β is less than 0, ending from the initial static voltage stable domain boundary pointAnd further returning to the initial saddle node bifurcation point, taking the parameter E as-1, and then searching the static voltage stability domain boundary point in the direction of increasing to β according to the steps until β is more than 90 degrees.
Specific examples are given below:
in this example, we take an example of searching the SVSR boundary of the WECC3 machine 9 node system to verify the validity of the fast search method for the boundary of the static voltage stability domain (SVSR), and the WECC3 machine 9 node test system is shown in fig. 3.
Load nodes 5 and 7 are selected as voltage stabilization key nodes, and SVSR boundaries are searched by the method in a two-dimensional active load space with active injection of the nodes 5 and 7 as coordinate axes. As shown in FIG. 4, the initial power increasing direction d is set with the ground state as the starting point0＝[ΔS2,ΔS3,ΔS4,ΔS5,ΔS6,ΔS7,ΔS8,ΔS9]T＝[0,0,0,0.9,0,1,0,0]TThe amount of power imbalance caused by the power increase is compensated by the generator in which the balancing node is located, where Δ SiFor the complex power of node i, CPF edge d is used0The initial SNB point 9 in fig. 4 is tracked with coordinates (2.323, 2.091). Dependent on the initial SNB-related state variable x0Calculated L0Initialization z0＝[x0,L0,γ0，η0]T，z0The detailed values are shown in Table 1, and θ in Table 1iAnd ViRespectively, the phase angle and magnitude of the voltage at node i.
TABLE 1 search for the results of the calculation of the relevant parameters in the next SNB procedure using prediction-correction based on the initial SNB
Figure BDA0001290962440000077
Figure BDA0001290962440000081
Setting the corresponding unit vector e according to the selected key node 5, 75、e7Selecting prediction step length sigma 0.3 and E parameter E1, and calculating tangent vector delta z of SNB point 90＝[Δx0,ΔL0,Δγ0，Δη0]TWherein Δ γ0＝-0.920 0、Δη01.0000 for Δ z0Normalized by Delta gamma0＝-0.663 5、Δη00.7203. Get the first predicted point
Figure BDA0001290962440000082
The detailed values of the state variables are shown in table 1.
Will be provided with
Figure BDA0001290962440000083
Carrying out solving by adopting an equation (10) to obtain a state variable at the SNB point 8
Figure BDA0001290962440000084
The detailed results are shown in Table 1. To be provided with
Figure BDA0001290962440000085
As an initial value, the method proposed by the present invention is used to continue the next SNB point, so that SNB points 7, 6, 5, 4, 3,2, 1, and 0 can be obtained, and the coordinates and the specific values of γ and η in each prediction-correction process are shown in table 2.
Table 2 β SNB search results in the decreasing direction
Numbering ηpre γpre ηcor γcor Coordinates of the object
7 0.4423 -0.4130 0.4188 -0.4182 (2.7421,1.6728)
6 0.6206 -0.6370 0.6167 0.6421 (2.9401,1.4489)
5 0.8103 -0.8705 0.8062 -0.8756 (3.1295,1.2154)
4 0.9907 -1.1133 0.9861 -1.1182 (3.3095,0.9728)
3 1.1609 -1.3649 1.1559 -1.3696 (3.4792,0.7214)
2 1.3198 -1.6248 1.3144 -1.6292 (3.6377,0.4618)
1 1.4667 -1.8922 1.4608 -18963 (3.7841,0.1947)
0 1.6006 -2.1663 1.5942 -2.1698 (3.9176,-0.0788)
Wherein point 0 is located outside the first quadrant in fig. 4, and β is not more than 0, which marks the end of searching the SVSR critical point from the initial SNB point to the decreasing direction β in the first quadrant of the active injection space, at this time, it is required to return to the initial SNB point again, and search the SVSR critical point to the increasing direction β in the first quadrant of the active injection space, so as to read in the initial SNB point information again, and set the parameter e in the set type (10) as-1, and the first prediction and correction point is obtained by the prediction-correction method
Figure RE-GDA0001339419260000091
And
Figure RE-GDA0001339419260000092
(corresponding to the point 10 in FIG. 4), the state variables obtained by calculation are shown in Table 1, the subsequent calculation process is the same as the above, when the point 19 of SNB is calculated, β is larger than or equal to 90 degrees, the calculation is finished, the coordinates of the points 10 to 19 of SNB and the specific values of gamma and η in each prediction-correction process are shown in Table 3, all the SNB points are connected one by one, and the SVSR boundary in the two-dimensional active power injection power space can be obtained.
TABLE 3 SNB search results in increasing directions of 3 β
Figure BDA0001290962440000093
Further fig. 5 compares the calculation accuracy of SVSR constructed by using the method of the present invention and CPF. Theoretically, the SVSR boundary is formed by a series of SNB points, for any SVSR boundary point, the system power flow Jacobian matrix is singular, the minimum eigenvalue is 0, and therefore the precision of the SVSR construction method and the precision of the SVSR construction method by the CPF can be judged by judging the distance between the minimum eigenvalue obtained by actual calculation and 0. Obviously, the accuracy of the SNB points searched by the method provided by the invention is far higher than that of the SNB points tracked by the CPF except for the SNB point 9. The minimum eigenvalues of SNB points 3, 5, 6, 7, 10, 11, 12, 13, 14 and 17 obtained by tracing by using CPF in the graph are all larger than 10-3Minimum value of 0.110X 10-3At SNB point 16, maximum 6.81X 10-3At point SNB point 18, the resulting average minimum feature value is 2.63 × 10-3(ii) a The average value of the minimum characteristic value calculated by the method provided by the invention is 7.25 multiplied by 10-4And all the minimum feature values obtained by calculation are less than 1.00 multiplied by 10-3And compared with the CPF, the calculation result has higher precision.
The computing time (CPU IntelCore i5-4210H, dominant frequency 2.9GHz and memory 8GB) of the SVSR boundary obtained by the method and the CPF search is 13.9263s and 1.6402s respectively. The results show that: the time consumption of the method of the invention is about one tenth of that of the CPF when the same number of SNB points on the SVSR boundary are searched.
The method provided by the invention considers the accuracy and the calculation burden of the SVSR boundary at the same time, and the high-accuracy static voltage stability domain boundary of the power system is obtained at high efficiency.
Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can make modifications and equivalents to the embodiments of the present invention without departing from the spirit and scope of the present invention, which is set forth in the claims of the present application.
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Claims (1)

1. A quick search method for a static voltage stability domain boundary of an electric power system is characterized in that incidence relations between adjacent saddle node bifurcation points on the static voltage stability domain boundary are fully utilized, and search efficiency is improved, and the method specifically comprises the following steps:
1) determining a static voltage stability domain boundary general mathematical model; the method comprises the following steps:
(1) the continuous power flow equation is combined with the boundary criterion of the static voltage stable domain to construct and describe the given power increasing direction d0The mathematical model of the corresponding static voltage stability domain boundary point is as follows:
Figure FDA0002323942690000011
wherein, x is a vector of a static state variable of the system, and g (x) is 0, which is a conventional power flow equation of the power system; λ is the system load margin, d0L is a left eigenvector corresponding to a zero eigenvalue of the tidal current Jacobian matrix, J is a power increase directionT(x) A transposed matrix of the tidal current Jacobian matrix;
(2) the general mathematical model for determining the boundary of the stable region of the static voltage is as follows:
Figure FDA0002323942690000012
wherein η and gamma are new power parameters, respectively describing the power increasing direction d0When the two-dimensional active power injection space of the nodes i and j changes, the active power variation quantity e of the corresponding static voltage stability domain boundary point on the nodes i and jiAnd ejVectors representing unit changes of active injection power of nodes i and j, respectively, eiAnd ejLength of (d)0The same vector, and only the ith and jth elements are 1, and the rest elements are 0; lambda [ alpha ]0d0For the operating point in the direction of power increase d0A lower load margin;
2) determining an initial static voltage stable domain boundary point; the method comprises the following steps:
(1) acquiring basic data including a system ground state tide state variable and a system topological structure;
(2) according to a given power increase direction d0Determining the state variable x corresponding to the boundary point of the initial static voltage stability domain through the continuous power flow equation0And a load margin lambda0So as to obtain an initial static voltage stable domain boundary point;
3) initializing a general mathematical model of the static voltage stability domain boundary; the method comprises the following steps:
(1) determining a power flow Jacobian matrix J (x) at the boundary point of the initial static voltage stability domain0) Left eigenvector L corresponding to zero eigenvalue0Setting the initial value of newly added power parameter gamma0＝η0＝0；
(2) Universal mathematical model initial value z for determining initialization static voltage stable domain boundary0＝[x0,L0,γ0，η0]T，
In the formula, x0The state variables corresponding to the boundary points of the initial static voltage stability domain are obtained;
4) predicting boundary points of adjacent static voltage stability domains
Figure FDA0002323942690000013
The method comprises the following steps:
(1) solving the gradient matrix of the general mathematical model of the static voltage stability domain boundary to the partial derivatives of each variable as follows:
Figure FDA0002323942690000021
(2) the following equations are additionally added on the basis of the gradient matrix to specify the magnitude and direction of a certain component in the tangent vector,
Figure FDA0002323942690000022
the power growth direction angle is defined as follows:
Figure FDA0002323942690000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002323942690000024
is composed of
Figure FDA0002323942690000025
Corresponding to the new power parameter η, e is taken to be + -1, when e is taken to be +1,
Figure FDA0002323942690000026
pointing to the side where the power increase direction angle β increases, pointing to the side where the power increase direction angle β decreases when e takes-1, J (x)0) Is a tidal current Jacobian matrix at the boundary point of an initial static voltage stable domain, JT(x) As a transposed matrix of the tidal current Jacobian, L0Is J (x)0) A left eigenvector corresponding to the zero eigenvalue;
(3) the simultaneous gradient matrix and the additional added equation are as follows, and the tangent vector of the boundary point of the initial static voltage stable domain is determined
Figure FDA0002323942690000027
The following formula:
Figure FDA0002323942690000028
Figure FDA0002323942690000029
wherein s is [0 … 01 ]]，E＝[0…0 e]TBoth lengths of
Figure FDA00023239426900000210
Equal;
(4) setting step size sigma, predicting boundary point z of stable region of initial static voltage0Adjacent static voltage stable region sideBoundary point
Figure FDA00023239426900000211
The following formula:
Figure FDA00023239426900000212
in the formula (I), the compound is shown in the specification,
Figure FDA00023239426900000213
as normalized tangent vector
5) Correcting the predicted point
Figure FDA00023239426900000214
Obtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction point
Figure FDA00023239426900000215
The method comprises the following steps:
(1) determining a passing predicted point
Figure FDA00023239426900000216
And is tangent to
Figure FDA00023239426900000217
Perpendicular hyperplane, as follows:
Figure FDA00023239426900000218
wherein z is a free variable;
(2) giving a correction equation to predict the point
Figure FDA0002323942690000031
As an initial value, the correction point is solved by Newton method
Figure FDA0002323942690000032
The following were used:
Figure FDA0002323942690000033
6) correction point
Figure FDA0002323942690000034
Performing initial value circulation, adopting the steps 4) to 5) to search the next adjacent static voltage stable domain boundary point, and replacing s in the simultaneous gradient matrix and the additionally added equation in the step (3) in the step 4) into s in the circulation process
Figure FDA0002323942690000035
And ending until the power increase direction angle β is less than 0 and the power increase direction angle β is greater than 90 degrees.
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