A transient voltage stability prevention control method based on transient voltage stability index polynomial approximation

Abstract

The present application relates to a kind of transient voltage stability prevention control method based on transient voltage stability index polynomial approximation. Including: firstly, a certain implicit function that control variable is mapped to certain TVSI (Transient Voltage Stability Index, TVSI) is introduced. Secondly, the polynomial approximation method based on collocation method is introduced to approximate implicit function, compared with the traditional prevention control method based on analysis, the approximate polynomial only includes control variable. Then, based on the approximate polynomial, the transient voltage stability constraint is constructed, and the prevention control model is converted into a non-linear programming (Non-Linear Programming NLP) problem, which is easy to solve by interior point method. Through the example analysis of actual system, the feasibility and accuracy of the proposed prevention control method are verified.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of power system automation, and particularly relates to a transient voltage stability prevention control method based on polynomial approximation of transient voltage stability index. BACKGROUND

[0002] The normal operation of society and the development of economy are deeply dependent on the safe and stable operation of power systems. With the increasing dependence of people on electricity, ensuring reliable power supply has become a crucial task for power systems. Today, in the face of great challenges, large-scale disturbances can threaten the stability of power systems, causing a series of serious consequences such as cascading failures, DC blocking failures, and blackouts. Looking back at history, the 2003 California blackout in the United States was caused by a three-phase short-circuit accident due to tree branches, while the 2012 India 7.30 blackout was caused by insufficient power supply and lagging power grid management system. In addition, in countries such as the Netherlands and Italy, there have also been blackouts caused by system instability. These disastrous events highlight the urgency and importance of strengthening practical control measures such as transient voltage stability prevention control. If the system is threatened by transient instability, effective control measures must be taken to improve the stability level of the system. The method of controlling the power system before a large disturbance occurs is called prevention control, while the control method taken after the disturbance occurs to prevent the system from falling into an unstable state is called emergency control.

[0003] Transient voltage stability prevention control, as an important aspect of power system transient stability, has long been the focus of attention of scholars. With the continuous expansion and completion of long-distance capacity transmission systems, transient voltage stability problems have become increasingly prominent. The receiving end of a high-voltage direct current transmission system relies on power transmission from the external system, but there is insufficient reactive power reserve within the system. Therefore, it is particularly important to pay attention to the transient voltage stability problem of the system. For the evaluation of transient voltage stability, there are various methods to choose from, including analytical methods based on physical and mathematical principles, emerging data-driven methods, and transient voltage index methods. Analytical methods can give a mechanism analysis of transient voltage stability, data-driven methods are suitable for transient voltage stability evaluation of large-scale systems, and index methods can give the degree of transient voltage stability of the system.

[0004] The approximation polynomial of transient voltage stability constraints in the prevention control method based on analysis is usually complex, resulting in a large model size and a long time for solving the model. In contrast, the nonlinear relationship between control variables and a certain TVSI cannot be represented by an approximation polynomial in the data-driven prevention control method, and the interpretability is not strong. SUMMARY

[0005] The present application aims at solving the above technical problems, and provides a transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index, which maps control variables to an implicit function of a specific TVSI, uses a polynomial approximation method of the collocation method to approximate the implicit function, has higher precision, and constructs transient voltage stability constraints based on the approximate polynomial, so that the preventive control model in the form of an initial NLP problem can be solved by using an interior point method, and corresponding preventive control measures can be obtained quickly, thereby achieving the purpose of maintaining safe and stable operation of a power system.

[0006] To achieve the above object, the technical scheme of the present application is as follows: a transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index, comprising the following steps:

[0007] A. Based on the power system differential algebraic equation with preventive control variables, the inclination of the transient voltage trajectory is divided into multiple regions by establishing a multi-binary table, different weights are given to different regions, the inclination characteristics of the transient voltage trajectory are described, and the TVSI implicit function of all nodes is defined;

[0008] B. The collocation method is introduced, and a polynomial approximation method is used to approximate the TVSI implicit function, the corresponding approximate polynomial of the TVSI implicit function is obtained by obtaining the base function and the corresponding coefficient of the base function;

[0009] C. The preselected critical fault method is used to construct the transient voltage stability constraint, and the preventive control model is converted into a nonlinear programming problem, so that the transient voltage stability preventive control problem can be easily solved by using an interior point method.

[0010] In an embodiment of the present application, in step A, the power system differential algebraic equation with preventive control variables is expressed as follows:

[0011]

[0012] In the formula, f is a differential equation, g is an algebraic equation, x is a system state variable vector, y is a system algebraic variable vector, and p is a control variable vector; each p defines a group of x and y trajectories through formula (1), and is expressed as an implicit function x(t;P) and y(t;P), and the transient voltage stability index I is defined as x(t;P) and y(t;P), I is an implicit function of p, and is denoted as I(p).

[0013] If an analytical expression of I(p) is obtained, I can be directly calculated from the value of p without calculating formula (1); on the other hand, the transient voltage stability constraint expressed by I(p) can be used as a substitute model of equation (1) composed of only p, thereby reducing the difficulty of solving the preventive control model.

[0014] However, the exact analytical expression of the implicit function I(p) is difficult or even impossible to obtain.

[0015] In an embodiment of the present application, I(p) is approximated by an explicit polynomial, denoted as ~I(p); according to the polynomial approximation theory, it is expressed as:

[0016]

[0017] where Φ k (p) is the kth basis function, c k is the coefficient of Φ k (p), and N b is the number of basis functions.

[0018] In an embodiment of the present application, in step A, the inclination of the transient voltage trajectory is divided into multiple regions by establishing a multi-binary table, different weights are assigned to different regions, the inclination characteristics of the transient voltage trajectory are described, and the TVSI implicit functions of all nodes are defined, as follows:

[0019] The voltage binary value table (V cr , T cr ) is used to describe the decline of the transient voltage trajectory when the maximum time T cr is lower than the threshold V cr ; however, the TVSI based on the single binary table cannot distinguish between the case of long time small voltage decline and the case of short time large voltage decline, and cannot well describe the characteristics of the transient voltage trajectory decline. Therefore, the multi-binary table as shown in FIG. 1 is used to divide the inclination of the transient voltage trajectory into multiple regions. Different weights are assigned to different regions, and the inclination characteristics of the transient voltage trajectory can be well described. Figure 1

[0020] Figure 1 is the multi-binary table corresponding to the voltage threshold V cr,i (1≤i≤n), where n is the number of binary tables; V N is the reference voltage; W i is the weight assigned to the region between V cr,i and V cr,i+1 ; t i is the time when the voltage trajectory enters the region during the voltage decline process, and t i ' is the time when the voltage trajectory leaves the corresponding region during the voltage recovery process; the inclination cumulative limit of the voltage trajectory described based on the multi-binary table is defined as the TVSI implicit function as follows:

[0021]

[0022] where I i is the TVSI implicit function of node i; V i ​(t) is the voltage of node i at time t; t j , t j+1 and t' j+1 , t' j are the time when the voltage trajectory enters and leaves the region between V cr,j and V cr,j+1 during the voltage drop process and recovery process respectively; Wj is the weight assigned to the region between V cr,j and V cr,j+1 , and its value is solved by the following formula, so that I i =0 corresponds to the critical stability of transient voltage;

[0023]

[0024] First, the I i of all critical nodes can be calculated, and the minimum value thereof is defined as the I of the system; second, a suitable multi-binary table needs to be designed according to actual operation requirements. In the present application, two binary tables are designed according to (0.75p.u, 1s) and (0.80p.u, 10s).

[0025] In an embodiment of the present application, in step B, the collocation method is introduced, and then the polynomial approximation method is used to approximate the implicit function of TVSI to be solved, and the corresponding approximation polynomial of the implicit function of TVSI is obtained by obtaining the base function and the corresponding coefficient of the base function, and the specific process is as follows:

[0026] In the present application, the polynomial approximation method based on the collocation method is introduced to approximate the implicit function, and two basic problems of the polynomial approximation of I(p) corresponding to formula (2) are how to form the base function Φ k (p) and how to calculate the base function coefficient c k .

[0027] For a single parameter p i , if p i is considered to be in an interval, the base function φ ki (p i )(k i =0, 1, 2, …) thereof is as follows, wherein k i is the degree of φ ki (p i ), and the recursive expression of the polynomial is as follows:

[0028]

[0029] For a d-dimensional parameter vector p=(p1, p2, …, p d ), each of which is in an interval, the base function Φ k (p), wherein k is the order number of Φ k (p), and the base function Φk (p) is composed of the product of φ ki (p i )(1≤i≤d), that is It is defined that is equal to or less than the approximation order l, therefore, Φ k (p) is composed of the product of φ

[0030]

[0031] where denotes the tensor product, N b = (l+d)! / (l!d!) denotes the number of basis functions;

[0032] According to the theory of polynomial approximation, the coefficients c k of the basis functions Φ k (p) that minimize the 2-norm error should be:

[0033]

[0034] where <·,·> denotes the inner product; although the numerator of formula (7) is the integral of the implicit function I(p), it is difficult to obtain its value analytically, but it can be calculated by numerical method, and the specific formula is as follows:

[0035]

[0036] where M is the number of collocation points; P m and b m denote the mth collocation point and its corresponding integral coefficient, respectively;

[0037] The calculation of the collocation points P m (1≤m≤M) and the integral coefficients b m depends on the specific algorithm. Substituting Φ k (p) formed by formula (6) and c k calculated by formula (8) into formula (2) gives the approximation polynomial

[0038] In an embodiment of the present application, in step C, the preselected critical fault method is used to construct the transient voltage stability constraint, and the specific process is as follows:

[0039]

[0040] where d is the number of control variables, that is, the dimension of p; p s,0 and Δp s (1≤s≤d) are the initial value and control amount of the control variable p s , respectively; the transient voltage stability constraint formula (9) is composed of a simple approximation polynomial It is indicated that the approximate polynomial only consists of the control variable p; therefore, the preventive control model containing the transient voltage stability constraint can be expressed as an NLP problem.

[0041] In an embodiment of the present application, the preventive control model is converted into an NLP problem in step C, and the conversion is as follows:

[0042] The objective of the preventive control model is to minimize the change of the control variable, and the objective function is:

[0043]

[0044] In the formula, and w s is the weight coefficient of p s , reflecting the priority of control;

[0045] The operating constraints to be met are:

[0046]

[0047] In the formula, p smin and p smax respectively represent the minimum value and the maximum value of p s ; N represents the total number of system buses; P G,i and P in,i are respectively the output of the generator or the energy storage of node i; P L,i is the load of node i; V i and V j are respectively the voltage of nodes i and j; G ij and B ij are the conductance and the susceptance of line ij; θ ij is the voltage phase angle difference of nodes i and j; I ij is the current flowing through line ij; and the subscripts min and max respectively represent the minimum value and the maximum value of the corresponding parameters.

[0048] The present application also provides a transient voltage stability preventive control system based on polynomial approximation of a transient voltage stability index, characterized by comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor, when the processor executes the computer program instructions, the method steps as described above can be realized.

[0049] The present application also provides a computer readable storage medium, which stores computer program instructions capable of being executed by a processor, when the processor executes the computer program instructions, the method steps as described above can be realized.

[0050] Compared with the prior art, the method has the following beneficial effects: firstly, an implicit function of mapping the control variable to a certain TVSI (Transient Voltage Stability Index) is introduced; secondly, a polynomial approximation method based on the collocation method is introduced to approximate the implicit function; compared with the traditional analytical-based preventive control method, the approximate polynomial only contains the control variable; then, the transient voltage stability constraint is constructed based on the approximate polynomial, and the preventive control model is converted into a non-linear programming (NLP) problem, which is easy to solve by using the interior point method. Through the example analysis of an actual system, the feasibility and accuracy of the proposed preventive control method are verified; the corresponding preventive control measures can be quickly obtained by the method, so that the purpose of maintaining the safe and stable operation of the power system is achieved. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a transient voltage trajectory inclination angle division schematic diagram based on a multi-binary table.

[0052] Figure 2 is a partial structure schematic diagram of an actual simulation system.

[0053] Figure 3 is an approximate three-dimensional projection diagram of when l=3 .

[0054] Figure 4 is the change of the number of collocation points and epsilon 2 when l changes between 2 and 6.

[0055] Figure 5 is a PZ transient voltage trajectory diagram before and after preventive control. DETAILED DESCRIPTION

[0056] The following is to make the purpose, technical scheme and advantages of the present application clearer and more apparent, and the present application is further described in detail below in combination with embodiments and drawings, the illustrative embodiments of the present application and the description thereof are only used to explain the present application, and do not limit the present application.

[0057] The present application provides a transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index, and the corresponding preventive control measures can be quickly obtained by applying the method, so that the purpose of maintaining the safe and stable operation of the power system is achieved. The method comprises the following steps:

[0058] A, starting from the given power system differential algebraic equation with preventive control variables, the inclination angle of the transient voltage trajectory is divided into multiple regions by using a multi-binary table, different weights are assigned to different regions, the inclination angle characteristics of the transient voltage trajectory are further described, and the TVSI of all nodes can be defined;

[0059] B, introduce the polynomial approximation method based on the matching method, constantly approaching the implicit function to be analyzed, and then solve to obtain the base function and the corresponding coefficient of the base function, and finally obtain the corresponding approximation polynomial of the implicit function;

[0060] C, construct the transient voltage stability constraint by preselecting the critical failure method; convert the preventive control model into a nonlinear programming problem, so that the interior point method can be used to solve the transient voltage stability preventive control problem.

[0061] The differential algebraic equation of the power system with preventive control variables introduced can be expressed as follows:

[0062]

[0063] In the formula, f is the differential equation, g is the algebraic equation, x is the system state variable vector, y is the system algebraic variable vector, and p is the control variable vector. Each p defines a set of x and y trajectories through formula (1), which is expressed as an implicit function x(t;P) and y(t;P). The transient voltage stability index I defined later is x(t;P) and y(t;P), so it is also an implicit function of p, denoted as I(p).

[0064] If the analytical expression of I(p) is obtained, I can be calculated directly from the value of p without calculating formula (1); on the other hand, the transient voltage stability constraint expressed by I(p) can be used as a substitute model of equation (1) composed only of p, thereby reducing the difficulty of solving the preventive control model.

[0065] However, the exact analytical expression of the implicit function I(p) is difficult or even impossible to obtain, but it can be approximated by a polynomial, which is an explicit polynomial denoted as ~I(p). According to the polynomial approximation theory, ~I(p) can be expressed as:

[0066]

[0067] In the formula, Φ k (p) is the kth base function; c k is the coefficient of Φ k (p); N b is the number of base functions.

[0068] The voltage binary value table (V cr ,T cr ) is used to describe the decline of the transient voltage trajectory when the maximum time T cr is lower than the threshold value V cr . However, the TVSI based on the single binary table cannot distinguish between long-time small voltage decline and short-time large voltage decline, and cannot well describe the characteristics of the transient voltage trajectory decline. Therefore, the method shown inFigure 1 The multi-binary table divides the inclination of the transient voltage trajectory into multiple regions. Different weights are assigned to different regions, which can well describe the inclination characteristics of the transient voltage trajectory.

[0069] Figure 1 Vth is the voltage threshold value cr,i (1≤i≤n) multi-binary tables, where n is the number of binary tables; V N is the reference voltage; W i is the weight assigned to the region between V cr,i and V cr,i+1 ; t i is the time when the voltage trajectory enters the region during the voltage drop process, t i ' is the time when the voltage trajectory leaves the corresponding region during the voltage recovery process. Based on the cumulative limit of the inclination of the voltage trajectory described by the multi-binary table, the present application defines TVSI as follows:

[0070]

[0071] In the formula, I i is the TVSI of node i; V i (t) is the voltage of node i at time t; t j , t j+1 and t′ j+1 , t′ j are the times when the voltage trajectory enters and leaves the region between V cr,j and V cr,j+1 during the voltage drop and recovery processes, respectively, and Wj is the weight assigned to the region between V cr,j and V cr,j+1 , which is solved by the following formula, so that I i =0 corresponds to the critical stability of the transient voltage.

[0072]

[0073] Firstly, I i of all critical nodes can be calculated, and the minimum value thereof is defined as the I of the system; secondly, appropriate multi-binary tables need to be designed according to actual operation requirements, and two binary tables are designed in this paper according to the national standards (0.75 p.u, 1s) and (0.80 p.u, 10s).

[0074] The introduced polynomial approximation method based on the collocation method is used to approximate the implicit function, and two basic problems of the polynomial approximation of I(p) corresponding to formula (2) are how to form the basis function Φ k (p) and how to calculate the basis function coefficient c k .

[0075] For a single parameter pi If we consider p i Within an interval, its basis function φ ki (p i (k) i =0,1,2,...), where k i For φ ki (p i The degree of the polynomial is given by the following recursive expression:

[0076]

[0077] For a d-dimensional parameter vector p = (p1, p2, ..., p...), d Each of these is located within an interval, and its basis functions Φ k (p), where k is Φ k The index of (p) can be determined by φ ki (p i The product of (1≤I≤d) is formed, that is Specifically, it is stipulated that Equal to or less than the approximate order l, therefore, Φ k The set of (p) is as follows:

[0078]

[0079] In the formula N represents the tensor product. b =(l+d)! / (l!d!) represents the number of basis functions.

[0080] According to the polynomial approximation theory, the 2-norm error is... Minimal basis function Φ k The coefficient c of (p) k It should be:

[0081]

[0082] In the formula, <·, ·> represent the inner product. Although the numerator of formula (7) is an integral of the implicit function I(p), it is difficult to obtain its value analytically, but it can be calculated numerically. The specific formula is as follows:

[0083]

[0084] In the formula, M is the number of collocation points; P m and b m This represents the m-th configuration point and its corresponding integral coefficient.

[0085] Match point P m (1≤m≤M) and integral coefficient b m The calculation depends on the specific algorithm. The Φ formed by formula (6)k (p) and c calculated by equation (8) k Substitute equation (2) to get the approximate polynomial

[0086] The pre-selected critical failure method introduced is constructed as follows:

[0087]

[0088] where d is the number of control variables, i.e., the dimension of p; p s,0 and Δp s (1≤s≤d) are the initial value and control variable of control variable p s , respectively. It can be seen that the transient voltage stability constraint equation (9) is represented by a simple approximate polynomial , which is composed of only control variable p. Therefore, the preventive control model containing the transient voltage stability constraint can be represented as an NLP problem as shown in the following subsection.

[0089] The objective of the preventive control proposed in the present application is to minimize the change of control variables, and the objective function is:

[0090]

[0091] where, and w s is the weight coefficient of p s , reflecting the priority of control.

[0092] The operating constraints to be satisfied are:

[0093]

[0094] where p smin and p smax represent the minimum and maximum values of p s , respectively; N represents the total number of system buses; P G,i , P in,i are the output of the generator or energy storage of node i; P L,i is the load of node i; V i , V j are the voltages of nodes i, j; G ij , B ij are the conductance and susceptance of line ij; θ ij is the voltage phase angle difference of nodes i, j; I ij is the current flowing through line ij; and subscripts min and max represent the minimum and maximum values of the corresponding parameters, respectively.

[0095] To verify the correctness and effectiveness of the proposed transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index, a simulation program is written, and an example of a practical system with 7638 nodes and 10465 branches is studied on the software. Figure 3 The computer used has a main frequency of 2.4G and a memory of 16G.

[0096] The fault set is a three-phase short-circuit fault near PZ, which is restored at 0.2s. Because the steady-state voltage of PZ is very low, and the fault occurs near PZ, the I PZ as the research object.

[0097] The generator output of WZ_2, the generator output of YQ_1 and the load power of ST are denoted as p G1 , p G2 and p L respectively. Since in the actual system, the control of generator output power is usually preferred to the control of load power, the initial values and variation ranges of the weighting coefficients w s and the corresponding control variables p s and p s are set as Table 1.

[0098] Table 1 Parameter setting

[0099] Controlling variable p s ]]> w s ]]> Initial value Variation range p G1 ]]> 0.2 1.6 p.u. p G1 ∈ [0.6, 1.8] p.u. p G2 ]]> 0.2 1.8 p.u. p G2 ∈ [1.0, 2.0] p.u. p L ]]> 0.6 1.6 p.u. p L ∈ [0.6, 1.8] p.u.

[0100] The present application uses the polynomial approximation method to approximate the implicit function I(p) of the mapping p G1 , p G2 and p L to I. The approximation order l is set to 3. The base function Φ k (p) (1≤k≤(N b =20)) is formed according to formula (6), and then the base function coefficients c k of Φ k (p) are calculated according to formula (8). Φ k (p) and c k are substituted into formula (2) to obtain the approximation polynomial as follows:

[0101]

[0102] To verify the accuracy of formula (12), the error indicators ε 1 and ε 2 are defined as follows:

[0103]

[0104] ε of formula (12) 1 and ε 2 corresponding to l = 3, ε 1 and ε 2 are only 0.00551 and 0.00246 respectively; on the other hand, the number of collocation points, i.e. the number of simulations, is only 64, and the computation time of each simulation is 63 seconds, which means that the total computation time is only 1h7min12s. In summary, formula (12) has less computation time and higher accuracy.

[0105] The three-dimensional projection of formula (12), i.e. as shown in Figure 3 , and It can be seen that for this system, the relationship between p G1 , p G2 or p L and is nonlinear. However, formula (12) is only a polynomial approximation of the nonlinear relationship when l = 3.

[0106] In order to explore the l that is suitable for the polynomial approximation of this nonlinear relationship, Figure 4 shows the change of the number of collocation points and ε 2 when l changes between 2 and 6. It can be seen from Figure 5 that as l increases, the decreasing rate of ε 2 slows down, while the increasing rate of the number of collocation points speeds up. Therefore, l = 2 is not suitable because its ε 2 = 0.00365 is too large; l = 4, 5, 6 are also not suitable because their number of collocation points, i.e. the number of simulations, is too large, resulting in too heavy computation burden, but their ε 2 does not improve significantly compared with that when l = 3. In summary, l = 3 is more suitable for this system.

[0107] Based on the corresponding approximate polynomial of formula (12), the preventive control model composed of formulas (9-11) is established. The optimal preventive control strategy obtained by solving the NLP problem is shown in Table 2.

[0108] Table 2 Optimal preventive control strategy

[0109]

[0110]

[0111] With the preventive control strategy shown in Table 2, the PZ transient voltage trajectory before and after preventive control is as shown in Figure 5The I is -0.1744 before the preventive control and is 0.0002 after the preventive control, which is very close to 0. Therefore, the preventive control effectively and accurately improves the stability of the transient voltage.

[0112] To verify the optimality of the obtained preventive control strategy, the optimal values of the control variables given in Table 2 are fluctuated by 1%, and 8 control strategies are obtained. The F and I of them are calculated respectively, and details are shown in Table 3. As shown in Table 3, the optimal preventive control strategy corresponds to F=0.0975, I=0.0002. In comparison, the I of cases 1-4 corresponds to I<0<0.0002, which indicates that cases 1-4 cannot guarantee the transient voltage stability; the F of cases 5-8 corresponds to F>0.0975, which indicates that cases 5-8 are not optimal solutions. Therefore, the preventive control strategy obtained in Table 2 is optimal.

[0113] Verification of optimality of the method in Table 3

[0114]

[0115] It can be seen that the transient voltage stability preventive control method based on transient voltage stability index polynomial approximation can effectively give transient voltage stability preventive control measures, and has good practical use value.

[0116] Those skilled in the art will understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code.

[0117] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems), and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The means for performing the functions specified in one or more flows and / or blocks.

[0118] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flow Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0119] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0120] The specific implementation described above is further explained in detail for the purpose of the present application, technical solutions and beneficial effects, it should be understood that the above is only a specific embodiment of the present application, and is not used to limit the protection scope of the present application, any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index, characterized by, The method comprises the following steps: A. Based on the power system differential algebraic equation with preventive control variables, the angle of the transient voltage trajectory is divided into multiple regions by establishing multiple binary tables, different weights are given to different regions, the angle characteristics of the transient voltage trajectory are described, and the TVSI implicit functions of all nodes are defined; B. The collocation method is introduced, and the polynomial approximation method is used to approximate the TVSI implicit function, the corresponding approximation polynomial of the TVSI implicit function is obtained by obtaining the basis function and the corresponding coefficient of the basis function; C. The preselected critical fault method is used to construct the transient voltage stability constraint, and the preventive control model is converted into a nonlinear programming problem, so that the transient voltage stability preventive control problem is easy to solve by using the interior point method; In step A, the power system differential algebraic equation with preventive control variables is expressed as follows: In the formula, f is a differential equation, g is an algebraic equation, x is a system state variable vector, y is a system algebraic variable vector, and p is a control variable vector; each p defines a group of x and y trajectories through formula (1), which is expressed as an implicit function x(t;P) and y(t;P), and a transient voltage stability index I is defined as x(t;P) and y(t;P), I is an implicit function of p, and is denoted as I(p); In step B, the collocation method is introduced, and the polynomial approximation method is used to approximate the TVSI implicit function, the corresponding approximation polynomial of the TVSI implicit function is obtained by obtaining the basis function and the corresponding coefficient of the basis function, and the specific process is as follows: For a single parameter p i , if p i is considered to be in an interval, then its basis function φ ki (p i )(k i = 0, 1, 2,...), where k i is the degree of φ ki (p i ), has the recursive representation as follows: For a d-dimensional parameter vector p = (p1, p2, ..., p...), d Each of these is located within an interval, and its basis functions Φ k (p), where k is Φ k The index of (p), the basis function Φ k (p) by φ ki (p i The product of (1≤i≤d) is formed, that is Regulation Equal to or less than the approximate order l, therefore, Φ k The set of (p) is as follows: wherein denotes the tensor product, N b = (l+d)! / (l!d!) denotes the number of basis functions; According to the polynomial approximation theory, the 2-norm error The basis function Φ k The coefficient c k Should be: In the formula, <·, ·> represents the inner product; although the numerator of formula (7) is the integral of the implicit function I(p), it is difficult to obtain its value analytically, but it can be calculated by using a numerical method, and the specific formula is as follows: where M is the number of points; P m and b m denotes the mth point and its corresponding integral coefficient; Φ k c k Substituting equation (2) gives the approximate polynomial In step C, the preselected critical fault method is used to construct the transient voltage stability constraint, and the specific process is as follows: where d is the number of control variables, i.e., the dimension of p; p s,0 and Δp s (1≤s≤d) are the initial value and control variable of the control variable p s respectively; the transient voltage stability constraint equation (9) is represented by a simple approximate polynomial which consists of only the control variable p; therefore, the preventive control model including the transient voltage stability constraint can be represented as an NLP problem.

2. The transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index according to claim 1, characterized in that, I(p) is approximated by an explicit polynomial, denoted as ~I(p); according to the polynomial approximation theory, it is expressed as: where Φ k (p) is the kth basis function, c k is the coefficient of Φ k (p), N b is the number of basis functions. 3.The transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index according to claim 1, characterized in that, In step A, the angle of the transient voltage trajectory is divided into multiple regions by establishing multiple binary tables, different weights are given to different regions, the angle characteristics of the transient voltage trajectory are described, and the TVSI implicit functions of all nodes are defined, and the specific process is as follows: Voltage binary value table (V cr , T cr ) to describe the transient voltage trajectory in the maximum time T cr below the threshold V cr ; with a voltage threshold V cr,i corresponding multi-binary table, where n is the number of binary tables; V N is a reference voltage; W i is the weight assigned to the region between V cr,i and V cr,i+1 . t i t is the time instant when the voltage trajectory enters the region during the voltage drop process i t is the time instant when the voltage trajectory leaves the corresponding region during the voltage recovery process; Based on the voltage trajectory inclination cumulative limit described by the multi-binary table, the TVSI implicit function is defined as follows: where I i is the TVSI implicit function for node i; V i (t) is the voltage of node i at time t; t j , t j+1 and t' j+1 , t' j are the instants when the voltage trajectory enters and leaves the region between V cr,j and V cr,j+1 during the voltage drop and recovery processes, respectively; Wj is the weight assigned to the region between V cr,j and V cr,j+1 , whose value is solved by the equation I i = 0 corresponding to the critical stability of the transient voltage. I of all the key nodes are calculated i and the minimum value among them is defined as the I of the system; then, the corresponding multi-binary table is designed.

4. The transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index according to claim 3, characterized in that, Two binary tables are designed according to (0.75p.u, 1s) and (0.80p.u, 10s).

5. The transient voltage stability preventive control method based on polynomial approximation of transient voltage stability index according to claim 1, characterized in that, In step C, the preventive control model is converted into a nonlinear programming problem, that is, an NLP problem, and the specific process is as follows: The objective of the preventive control model is to minimize the change of the control variable, and the objective function is: In the formula, and w s is a weight coefficient of p s reflecting the priority of control; The operating constraints to be met are: where p smin and p smax represent the minimum and maximum values of p s , respectively; N represents the total number of buses; P G,i and P in,i are the power outputs of the generators or energy storages of node i, respectively; P L,i is the load of node i; V i and V j are the voltages of nodes i and j, respectively; G ij and B ij are the conductance and susceptance of line ij, respectively. θ ij is the voltage phase angle difference for node i,j; I ij Iij is the current flowing through the line ij, and the subscripts min and max denote the minimum and maximum values of the corresponding parameter, respectively.

6. A transient voltage stability preventive control system based on polynomial approximation of transient voltage stability indicators, characterized by, The computer program instructions stored in the memory and capable of being executed by the processor can realize the steps of the method according to any one of claims 1-5 when the processor executes the computer program instructions.

7. A computer readable storage medium, having stored thereon computer program instructions capable of being executed by a processor, which can realize the steps of the method according to any one of claims 1-5 when the processor executes the computer program instructions.

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