Transient voltage stability domain boundary determination method based on stability index polynomial approximation

Abstract

The invention relates to a transient voltage stability domain boundary determination method based on stability index polynomial approximation. The method comprises the following steps: firstly, adopting a transient voltage stability index defined based on a multi-binary table criterion so as to quantitatively evaluate the transient voltage stability degree of a system; secondly, proposing a polynomial approximation method based on a collocation method to approximate a polynomial function of a transient voltage stability index and a system operation condition, and proposing a parameter space transient voltage stability domain boundary determination method based on the polynomial function according to a transient voltage stability critical index value; the invention also discusses a method for judging the existence of the boundary of the transient voltage stability domain and realizing the visualization of the boundary of the transient voltage stability domain. The method disclosed by the invention has relatively high practicability, and relatively well meets actual requirements.

Description

Technical Field

[0001] The invention belongs to the technical field of power systems, and in particular relates to a method for determining a transient voltage stability domain boundary in a parameter space based on stability index polynomial approximation. Background Art

[0002] The increasing proportion of renewable energy in the power system and the continuous growth of long-distance cross-regional DC transmission have reduced the voltage support capacity of the power system, aggravated the hollowing out of urban loads, and highlighted the problem of transient voltage stability. How to quantitatively evaluate the transient voltage stability of the system and determine the stability domain to ensure the stable operation of the transient voltage of the system has become one of the core challenges facing the operation of large power grids.

[0003] Existing methods for determining the boundary of transient voltage stability domain in parameter space, such as the bisection method and the piecewise approximation method, rely on a large number of simulations to obtain critical stability points in the parameter space and approximate the boundary of transient voltage stability domain by fitting these points, resulting in a large amount of calculation. Summary of the invention

[0004] In view of the shortcomings of the above methods, the present invention, on the basis of adopting a transient voltage stability index based on a multi-binary table, proposes a polynomial approximation method based on a collocation method to establish a polynomial function of a transient voltage stability index and a variable parameter, and uses the polynomial function to approximate the boundary of the transient voltage stability domain in the parameter space, thereby eliminating a large number of simulation processes.

[0005] The present invention includes the following:

[0006] Step (1): using a transient voltage stability index based on a multi-binary table to quantitatively evaluate the transient voltage stability margin of the system;

[0007] Step (2): using the collocation method, determine the collocation point set in the parameter space spanned by the variable parameters corresponding to the variable operating conditions, and simulate at each collocation point in the collocation point set to obtain the transient voltage stability index corresponding to each collocation point;

[0008] Step (3): according to the transient voltage stability index corresponding to each distribution point obtained in step (2), determine the existence of the transient voltage stability domain boundary in the parameter space, and if it exists, go to step (4);

[0009] Step (4): According to the transient voltage stability index corresponding to each matching point obtained in step (2), a polynomial approximation method based on the matching point method is used to approximate the polynomial function of the transient voltage stability index and the variable parameter, and then the transient voltage stability domain boundary determined based on the index polynomial function and the index critical value is converted into a visual form.

[0010] Compared with the prior art, the present invention has the following beneficial effects:

[0011] (1) In order to solve the problem that repeated simulation is required to determine the transient voltage stability index corresponding to different operating conditions, the present invention proposes to use a polynomial approximation method based on the collocation method to approximate the polynomial function of the transient voltage stability index and the variable parameters, thereby saving a lot of simulation processes.

[0012] (2) In order to solve the problem that the existing method for determining the boundary of transient voltage stability region in parameter space has a large amount of calculation, the present invention proposes a method for determining the boundary of transient voltage stability region based on index polynomial function approximation.

[0013] (3) The present invention discusses the existence judgment method and visualization method of the transient voltage stability domain boundary in the parameter space, which is highly practical and better meets the actual needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flow chart of the method of the present invention;

[0015] Figure 2 is the approaching TVSRB;

[0016] Figure 3 is the relative error of TVSRB represented by the induction motor load ratio. DETAILED DESCRIPTION

[0017] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent modifications of the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0018] like Figure 1 As shown, the present application provides a method for determining the boundary of transient voltage stability domain in parameter space based on stability index polynomial approximation, which comprises the following steps:

[0019] Step (1): using a transient voltage stability index based on a multi-binary table to quantitatively evaluate the transient voltage stability margin of the system;

[0020] Step (2): using the collocation method, determine the collocation point set in the parameter space spanned by the variable parameters corresponding to the variable operating conditions, and simulate at each collocation point in the collocation point set to obtain the transient voltage stability index corresponding to each collocation point;

[0021] Step (3): according to the transient voltage stability index corresponding to each distribution point obtained in step (2), determine the existence of the transient voltage stability domain boundary in the parameter space, and if it exists, go to step (4);

[0022] Step (4): According to the transient voltage stability index corresponding to each matching point obtained in step (2), a polynomial approximation method based on the matching point method is used to approximate the polynomial function of the transient voltage stability index and the variable parameter, and then the transient voltage stability domain boundary determined based on the index polynomial function and the index critical value is converted into a visual form.

[0023] According to the solution of the present invention, the step (1) is specifically:

[0024] In actual engineering applications, the bus voltage after a fault is often required to be within the time limit T cr Recovers to the voltage limit V cr The requirement is expressed as a binary table [V cr ,T cr ]. This application is based on a multi-binary table [V cr.i ,T cr.i ]| 1￡i￡n , n is the number of binary tables, the transient voltage sag process is divided into multiple regions, and different weights are assigned to the voltage sag degrees in different regions, thereby refining the impact of the severity of voltage sag on transient voltage stability.

[0025] The transient voltage stability index defined based on the multi-binary table criterion adopted in this embodiment is as follows:

[0026]

[0027] Among them, V N is the rated value of the system voltage; V(t) is the value of the bus voltage at time t; t k and t k+1 and t' k+1 and t' k They are the transient response curve of the bus voltage entering and leaving V during the drop and recovery process. cr.k and V cr.k+1 The time in the area between k | k＝1,2,...,n It is a different weight coefficient assigned to different voltage drop degrees. Its value can be solved step by step according to the system satisfying I=0 under the transient voltage critical stability during the transient response process. The specific formula is as follows:

[0028]

[0029] According to the solution of the present invention, the step (2) is specifically divided into two steps:

[0030] First, the orthogonal polynomial system corresponding to the variable parameters is determined. Then, the point set in the parameter space is determined based on the orthogonal polynomial system. Then, the transient voltage stability index corresponding to each point in the point set is determined through system simulation:

[0031] For a single parameter pi , p i The orthogonal polynomial system y(p i ) and p i The probability density function ω(p i ) corresponds to, defined as y(p i ) is 0. Based on practical application, this application assumes a single parameter p i The single parameter p is uniformly distributed within the parameter variation range. i The orthogonal polynomial system y(p i ) is the Legendre polynomial, and its recursive expression is as follows:

[0032]

[0033] where y m (p i ) represents a single parameter p i The mth order polynomial of , m=0,1,2,…

[0034] For an n-dimensional parameter vector p, let a parameter p in p i The orthogonal polynomial system is y(p i ), where r i The polynomial is denoted by Right now Then the calculation formula of the orthogonal polynomial system Y(p) of the parameter vector p is as follows, where N represents the approximation order, Represents the tensor product operation.

[0035]

[0036] The parameter p i The N+1 order polynomial F N+1 (p i ) is denoted as Where i = 1, 2, ..., n, n is the dimension of the parameter vector p, and N is the approximation order. The collocation point set of the parameter vector p is obtained by using the following tensor product operation: The number of points in S is M = (N+1) n . Let the collocation point in S be p m | m＝1,2,...,M , determine p through system simulation m The corresponding voltage trajectory, and then based on the voltage trajectory, p is obtained m The corresponding I(p m ).

[0037] According to the solution of the present invention, the step (3) is specifically to determine the existence of the transient voltage stability domain boundary in the parameter space according to the transient voltage stability index corresponding to each distribution point obtained in step (2):

[0038] Based on the fact that the I values ​​corresponding to the parameter points on both sides of the transient voltage stability region boundary are around 0, the n-dimensional parameters p1, p2, ..., p n The collocation point method is used to select the collocation point set S in the parameter space, and the existence of the transient voltage stability region boundary is judged according to the I value of the collocation point in S.

[0039] The specific method in this embodiment is as follows: 1) If the I value of the distribution point in S is always greater than 0, then the parameter space is considered to be a transient voltage stable space, that is, the transient voltage stable domain boundary does not exist; 2) If the I value of the distribution point in S is always less than 0, then the parameter space is considered to be a transient voltage unstable space, that is, the transient voltage stable domain boundary does not exist; 3) If there are distribution points in S whose I values ​​are above and below 0 and are adjacent, then it is considered that there is a transient voltage stable domain boundary in the parameter space.

[0040] According to the solution of the present invention, the step (4) is specifically to approximate the index polynomial based on the polynomial approximation method based on the collocation method based on the simulation results of each collocation point set obtained in step (2), and convert the index polynomial into a visual form:

[0041] In this embodiment, the I(p m ) is substituted into the following formula to calculate the coefficient c of each order basis function k , where c k is a constant, and its calculation formula is The operator E[·] represents the expectation, M specifies the total number of points, p m represents the mth matching point, q m is the integral coefficient corresponding to the mth collocation point, and combined with the orthogonal polynomial system given in step (2), the approximation result of the index polynomial is obtained. Where N b is the number of basis functions and N b =(N+n)! (N!n!), where N and n are the approximation order and the number of parameters respectively.

[0042]

[0043] Secondly, from About a single parameter p j Starting from the perspective of rate of change, define the measure p j Critical size indicator L j As shown in the following formula, where p m is the mth collocation point, M is the total number of collocation points, p jrepresents the jth parameter. Select L from the parameter vector p j The largest parameter is used as the key parameter affecting the transient voltage stability of the system. k , the remaining parameters are treated as independent parameters

[0044]

[0045] Finally, p k As the approximated variable, As an approximation variable, the polynomial approximation method based on the collocation method is used again to The corresponding transient voltage stability region boundary is expressed as A visual form of Representative is a polynomial function of the independent variable.

[0046] In summary, the present invention firstly proposes to use a polynomial approximation method based on the collocation method to approximate the polynomial function of transient voltage stability index and system variable parameters based on multi-binary table criteria; secondly, a method for determining the boundary of transient voltage stability domain based on polynomial function approximation in parameter space is proposed, and the existence judgment method and visualization method of transient voltage stability domain boundary in parameter space are discussed. This method has strong practicality and better meets the actual needs.

[0047] Verification example:

[0048] A simulation platform was built based on BPA software. Taking the actual system as an example, the accuracy and practicality of the proposed method (TVSRB determination method) were verified. The example analysis was carried out on a computer with a processor frequency of 3.40 GHz and a memory of 16 GB.

[0049] 1. System description and fault settings

[0050] In order to verify whether the method proposed in this application is practical in an actual system, some actual power grid data is taken. The fault of the power grid in this area is set to a three-phase short circuit fault in the double-circuit line of bus GLD and bus ZOH at 0.2s, and the three-phase short circuit fault of the two lines is cleared at 0.3s. Since bus ZPZ is close to the fault location, it is greatly affected by the fault, and the voltage is low in steady state, so the I determined according to the voltage trajectory of bus ZPZ is used. ZPZ I as a system.

[0051] 2. Approaching TVSRB

[0052] The polynomial approximation order of the index is set to 3. The polynomial approximation method based on the collocation method is also used to obtain the polynomial function of the transient voltage stability index I and the induction motor load proportion p1, load multiple p2 and new energy proportion p3. The polynomial function is used to determine TVSRB as shown in the following formula.

[0053]

[0054] Figure 2 The approximate TVSRB is shown. As can be seen from the figure, when the proportion of renewable energy remains unchanged, as the proportion of induction motor load increases, the load multiple on TVSRB decreases, indicating that the greater the proportion of induction motor load in the system, the worse the transient voltage stability of the system after the fault; when the load multiple remains unchanged, as the proportion of renewable energy increases, the proportion of induction motor load on TVSRB decreases, indicating that the access of a high proportion of renewable energy in the system leads to a deterioration in transient voltage stability.

[0055] Figure 3 The relative error ε between the actual TVSRB and the approximate TVSRB represented by the induction motor load proportion p1 is shown. RE1 , the error points are 400 parameter points sampled evenly within the range of load multiple p2 and new energy proportion p3. As can be seen from the figure, the relative error of all sampling points ε RE1 They are all within 3%, and considering that the polynomial approximation order of the indicator is 3, the process of determining TVSRB only requires 64 time domain simulations, which verifies the accuracy and practicality of the TVSRB determination method proposed in this paper.

[0056] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made according to the scope of the patent application of the present invention should fall within the scope of the present invention.

Claims

1. A method for determining the boundary of transient voltage stability region based on stability index polynomial approximation, characterized in that The method includes the following: Step (1): using a transient voltage stability index based on a multi-binary table to quantitatively evaluate the transient voltage stability margin of the system; Step (2): using the collocation method, determine the collocation point set in the parameter space spanned by the variable parameters corresponding to the variable operating conditions, and simulate at each collocation point in the collocation point set to obtain the transient voltage stability index corresponding to each collocation point; Step (3): according to the transient voltage stability index corresponding to each distribution point obtained in step (2), determine the existence of the transient voltage stability domain boundary in the parameter space, and if it exists, go to step (4); Step (4): Based on the transient voltage stability index corresponding to each matching point obtained in step (2), a polynomial approximation method based on the matching point method is used to approximate the transient voltage stability index and the index polynomial function of the variable parameter, and then the transient voltage stability domain boundary determined based on the index polynomial function and the index critical value is converted into a visual form.

2. The method for determining the transient voltage stability region boundary based on stability index polynomial approximation according to claim 1, characterized in that: In step (1), the transient voltage drop process is divided into multiple regions based on a multi-binary table, and different weights are assigned to the voltage drop degrees in different regions, thereby refining the impact of the severity of the voltage drop on the transient voltage stability.

3. The method for determining the transient voltage stability region boundary based on stability index polynomial approximation according to claim 2 is characterized in that: The transient voltage stability index I is expressed as follows: Among them, V N is the rated value of the system voltage; V(t) is the value of the bus voltage at time t; t k and t k+1 They are the transient response curve of the bus voltage entering and leaving the voltage limit V during the drop process. cr.k and V cr.k+1 The time in the area between k+1 and t′ k They are the transient response curve of the bus voltage entering and leaving the voltage limit V during the recovery process. cr.k and V cr.k+1 The time in the area between k | k＝1,2,...,n It is the different weight coefficients assigned to different voltage drop levels.

4. The method for determining the transient voltage stability region boundary based on stability index polynomial approximation according to claim 1, characterized in that: The step (2) is specifically as follows: firstly, determining the orthogonal polynomial system corresponding to the variable parameters; secondly, determining the point set in the parameter space based on the orthogonal polynomial system; and determining the transient voltage stability index corresponding to each point in the point set through system simulation.

5. The method for determining the transient voltage stability region boundary based on stability index polynomial approximation according to claim 1, characterized in that: The step (3) is specifically: 1) If the transient voltage stability index I of the points in the point set S is always greater than 0, the parameter space is considered to be a transient voltage stability space, that is, the boundary of the transient voltage stability domain does not exist; 2) If the transient voltage stability index I of the points in the point set S is always less than 0, the parameter space is considered to be a transient voltage unstable space, that is, the boundary of the transient voltage stability domain does not exist; 3) If there are adjacent matching points whose transient voltage stability index I is around 0 in the matching point set, it is considered that there is a transient voltage stability domain boundary in the parameter space.

6. The method for determining the transient voltage stability region boundary based on stability index polynomial approximation according to claim 1, characterized in that: The step (4) is specifically: Calculate the coefficients of basis functions of each order based on the transient voltage stability index corresponding to each distribution point in the distribution point set; The approximation result of the index polynomial is obtained by combining the coefficients of the basis functions of each order with the orthogonal polynomial system; The approximated variable and the approximating variable are obtained from the approximation result, and the polynomial approximation method based on the collocation method is used again to represent the transient voltage stability domain boundary corresponding to the index polynomial function being equal to the index critical value in a visual form.

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