CN107133406B - Rapid search method for static voltage stability domain boundary of power system - Google Patents
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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 domainsCorrecting the predicted pointObtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction pointCorrection pointThe 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 sThe 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
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;
5) Correcting the predicted pointObtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction point
6) Correction pointPerforming 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 processAnd 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:
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:
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:
(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,
the power growth direction angle is defined as follows:
in the formula (I), the compound is shown in the specification,is composed ofCorresponding to the new power parameter η, e is taken to be + -1, when e is taken to be +1,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 determinedThe following formula:
(4) setting step size sigma, predicting boundary point z of stable region of initial static voltage0Adjacent static voltage stable region boundary pointThe following formula:
Step 5) comprises the following steps:
wherein z is a free variable;
(2) giving a correction equation to predict the pointAs an initial value, the correction point is solved by Newton methodThe following were used:
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:
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:
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 domainsThe 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:
(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,
the power growth direction angle is defined as follows:
in the formula, Δ η -zIs composed ofCorresponding 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 determinedThe following formula:
(4) setting step size sigma, predicting boundary point z of stable region of initial static voltage0Adjacent static voltage stable region boundary pointThe following formula:
5) Correcting the predicted pointObtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction pointThe method comprises the following steps:
wherein z is a free variable;
(2) giving a correction equation to predict the pointAs an initial value, the correction point is solved by Newton methodThe following were used:
6) correction pointPerforming 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 processAnd 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 pointsSearching the next adjacent static voltage stable region boundary point to obtain the correction pointWhen vector is cut, the simultaneous gradient matrix in the step 4) and the step (3) and the additionally added equation are replaced by sNamely, 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.
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
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 pointThe detailed values of the state variables are shown in table 1.
Will be provided withCarrying out solving by adopting an equation (10) to obtain a state variable at the SNB point 8The detailed results are shown in Table 1. To be provided withAs 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 |
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 methodAnd(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
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.
[ reference documents ]
[1] Jing Zi, Lizhou Jing, Lizhongqing, etc., a new method for calculating load margin sensitivity based on wide-area measurement information [ J ]. report of electrotechnology, 2016,31(21): 102-.
[2] Boundary approximation method for thermal stability safety domain of cross-regional interconnected power grid [ J ] electric and technical science, 2016,31 (8): 134-146.
[3] Xue Yu Sheng, Rexing, Xue Feng, etc. comments on the impact of wind uncertainty on the power system [ J ]. Chinese Motor engineering reports, 2014, 34 (29): 5029-5040.
[4] Zhanwei, early morning, zhangyulong, et al. grid load security domain based on voltage level constraints [ J ]. china electro-mechanical engineering report, 2016, 36 (23): 6389-6400.
[5] Available transmission capacity [ J ] of an ac/dc system taking into account static voltage stability constraints, chen hei, li national qing, billows 2012, 36 (2): 76-81.
[6]Yuan Haoyu,Jiang Tao,Jia Hongjie,et al.Real-time wide-area loadingmargin sensitivity(WALMS)in power systems[C].IEEE PES General Meeting,2015.
[7]Jiang Tao,Bai Lingquan,Jia Hongjie,et al.Identification of voltagestability critical injection region in bulk power systems based on therelative gain of voltage coupling[J].IET Generation Transmission&Distribution,2016,10(7):1495-1503.
[8]Chiang H D,Flueck AJ,Shah K S,et al.CPFLOW:a practical tool fortracing power system steady-state stationary behavior due to load andgeneration variations[J].IEEE Transactions on Power Systems,1995,10(2):623-634.
[9]Iba K,Suzuki H,Egawa M,et al.Calculation of critical loadingcondition with nose curve using homotopy continuation method[J].IEEETransactions on Power Systems,1991, 6(2):584-593.
[10] Grandbin, lith, bright and bright, et al. 77-82.
[11] Strategy study to improve robustness of continuous tidal current computing [ J ] proceedings of china electro-mechanical engineering, 2005, 25 (22): 7-11.
[12]Liu C C,Wu F F.Steady-state voltage stability regions of powersystems[C].IEEE Conference on Decision and Control,1984,6(1):23-31.
[13] Power system flow feasible domain boundary topological properties and boundary algorithm [ J ] power system automation, 2006, 30 (10): 6-11.
[14] Mytilus, sovereign peak, jiahongjie, large electric power system voltage stabilization feasible domain visualization initial exploration [ J ] electric power system automation, 2001, 25 (22): 1-5.
[15] Miao Weiwei, Jia hongjie, board tiger.minimum load shedding algorithm [ J ] based on active load injection space static voltage stable region, China Motor engineering report, 2012, 32 (16): 44-41.
[16] Wang chengshan, xu xiao fei, yu xin, etc. local visual description of voltage stability domain of power system and its application [ J ]. proceedings of electrical engineering of china, 2004, 24 (3): 1-5.
[17] Korean, mytilus, li hui ling, etc. the practical expression of the power system injected into the space static voltage stability domain boundary [ J ] the chinese electro-mechanical engineering report, 2005, 25 (5): 8-14.
[18] Korean qi, mytilus, giantager, etc. nonlinear approximate analytic expression of static voltage stability domain boundaries [ J ] power system automation, 2005, 29 (11): 10-14.
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:
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:
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 domainsThe 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:
(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,
the power growth direction angle is defined as follows:
in the formula (I), the compound is shown in the specification,is composed ofCorresponding to the new power parameter η, e is taken to be + -1, when e is taken to be +1,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 determinedThe following formula:
(4) setting step size sigma, predicting boundary point z of stable region of initial static voltage0Adjacent static voltage stable region sideBoundary pointThe following formula:
5) Correcting the predicted pointObtaining a boundary point z between the initial static voltage and the stable region0Adjacent static voltage stable region boundary correction pointThe method comprises the following steps:
wherein z is a free variable;
(2) giving a correction equation to predict the pointAs an initial value, the correction point is solved by Newton methodThe following were used:
6) correction pointPerforming 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 processAnd 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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