Solving method for stability domain of water turbine adjusting system

Abstract

The invention relates to the technical field of nonlinear system stability judgment, and discloses a solving method for a stability domain of a water turbine adjusting system, which comprises the following steps: acquiring control parameters of the water turbine adjusting system, and establishing a two-dimensional rectangular coordinate system based on the control parameters; setting any point R greater than zero on the negative half axis of the X axis, clockwise rotating the OR ray, and when the included angle between the ray and the Y axis is the set rotation angle, searching a candidate point, closest to the boundary of the control parameter stability domain, of the Y axis by adopting a dichotomy method, and taking the candidate point as a first intersection point; based on the first intersection point, rotating the Y axis at a set rotation angle in the first quadrant by adopting a bipartite iteration method to perform iterative search, obtaining a plurality of intersection points of the Y axis and the boundary of the control parameter stability domain, and performing smooth connection to obtain the control parameter stability domain of the system; according to the method, the calculation amount of stability domain acquisition is reduced, whether the system is stable or not is effectively judged, safe and stable operation of the power system is guaranteed, and the flexibility and economical efficiency of power system dispatching are improved.

Description

Technical Field

[0001] The invention relates to the technical field of nonlinear system stability judgment, and in particular to a method for solving a stability domain of a water turbine regulating system. Background Art

[0002] my country is a major country in the development and utilization of water resources. It has built many giant hydropower stations on rivers such as the Jinsha River and the Yalong River in the southwest. With the formation of a pattern of parallel operation of multiple units in the power grid and the complementary and coordinated operation of multiple energy sources, the stability characteristics of intermittent energy have brought new challenges to the dispatching and safety of the power grid. The Routh criterion is an important method for judging the stability of linear systems and has been widely used in system design and analysis. The Routh criterion can be used to judge the distribution of the characteristic roots of the linear mathematical model of the hydropower unit in the S domain, and then the stability and dynamic characteristics of the system can be reasonably analyzed and explained. However, many actual systems, such as hydropower units, are strongly nonlinear systems. The Routh criterion cannot accurately judge their stability. Instead, it is necessary to establish their nonlinear models through a series of algebraic-differential equations and a variety of different technologies for judgment. In the nonlinear model, there are not only linear parts represented by transfer functions, but also nonlinear parts represented by neural networks, fuzzy systems or complex functions such as saturation and delay. At the same time, it is sometimes very difficult to linearize these nonlinear parts at a certain operating point, and the calculation is large, and careful processing is required to ensure the accuracy of linearization. Once an error occurs in the intermediate calculation, the inspection process is quite cumbersome. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for solving the stability domain of a turbine regulating system, which is used to solve the problems of linearization difficulty and large amount of calculation in the stability calculation process of a strongly nonlinear system in the prior art.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A method for solving the stability domain of a hydraulic turbine regulating system comprises the following steps:

[0006] S1. Obtain control parameters of a turbine regulating system and establish a two-dimensional rectangular coordinate system based on the control parameters;

[0007] S2. Taking the Y axis of the two-dimensional rectangular coordinate system based on the control parameters as the first ray, during the initial search, randomly select a point R on the negative semi-axis of the X axis of the two-dimensional rectangular coordinate system based on the control parameters, connect point R and the origin O, rotate the OR ray clockwise, and when the angle between the OR ray and the Y axis is the set rotation angle, draw a perpendicular line from point R to the Y axis to obtain a reference point, and iteratively search for a candidate point on the Y axis closest to the boundary of the stable domain of the control parameters using a binary search method based on the reference point, and use the candidate point as the first intersection point of the first ray and the boundary of the stable domain of the control parameters;

[0008] S3, during the second search, based on the first intersection point of the first ray with the boundary of the stable domain of the control parameter, a bisection method is used to rotate the first ray at a set rotation angle in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameter to perform an iterative search to obtain a second intersection point of the first ray with the boundary of the stable domain of the control parameter;

[0009] S4, after the second search, determine whether the first ray coincides with the X-axis of the two-dimensional rectangular coordinate system based on the control parameter, if so, obtain a number of intersections of the first ray and the boundary of the stable domain of the control parameter, otherwise, continue to iterate the search until the first ray coincides with the X-axis of the two-dimensional rectangular coordinate system based on the control parameter during the Nth search, stop the search, and obtain a number of intersections of the first ray and the boundary of the stable domain of the control parameter;

[0010] S5. Smoothly connect the first ray with several intersection points of the boundary of the control parameter stable domain to obtain the control parameter stable domain of the turbine regulation system.

[0011] Furthermore, step S1 specifically includes:

[0012] The control parameters of the turbine regulating system including the proportional coefficient and the integral coefficient are obtained, and a two-dimensional rectangular coordinate system based on the control parameters is established with the proportional coefficient as the X-axis horizontal coordinate and the integral coefficient as the Y-axis vertical coordinate.

[0013] Furthermore, the rotation angle is set to:

[0014]

[0015] Among them, θ represents the set rotation angle, θ1 represents the total rotation angle, that is, the total angle of the first quadrant of the two-dimensional rectangular coordinate system based on the control parameters, and n represents the number of rotations of the Y axis in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameters.

[0016] Furthermore, step S2 specifically includes:

[0017] S201, take the Y axis of the two-dimensional rectangular coordinate system based on the control parameters as the first ray, and select any point R on the negative semi-axis of the X axis of the two-dimensional rectangular coordinate system based on the control parameters, and make the distance from the origin O to the point R greater than zero, rotate the OR ray clockwise and when the angle between the OR ray and the Y axis is the set rotation angle, draw a perpendicular line from point R to the Y axis to obtain the reference point R t , and take the origin O of the Y axis as the maximum candidate point, and the infinity of the Y axis as the second candidate point;

[0018] S202, compare each candidate point with the reference point R t The formed angle is used as the dynamic angle, and the positions of the first candidate point and the second candidate point are converted into polar coordinates to generate the upper and lower bounds of the dynamic angle, namely:

[0019]

[0020] Among them, α represents the dynamic angle, dθ represents the size of the set rotation angle, The polar coordinates of the lower bound or first candidate point of the dynamic angle, The polar coordinates representing the upper bound of the dynamic angle or the second candidate point;

[0021] S203, setting the current number of iterations to 1;

[0022] S204, judging whether the current number of iterations reaches the maximum number of iterations, if so, there is no control parameter that stabilizes the turbine dispatching system, and the iterative search is terminated, otherwise, setting the initial inertia weight;

[0023] S205, updating the dynamic angle according to the inertia weight to generate an updated dynamic angle, that is:

[0024] α′=ωα l +(1-ω)α u

[0025] Among them, α′ represents the updated dynamic angle, ω represents the inertia weight, and α l represents the lower bound of the dynamic angle, α u Indicates the upper bound of the dynamic angle;

[0026] S206, calculating the updated candidate points according to the updated dynamic angle, that is:

[0027]

[0028] Among them, P i represents the updated candidate point, Represents the origin O to the updated candidate point P i The distance Indicates the origin O to the reference point R tdL represents the length of the perpendicular line from point R to the Y axis, and tan represents the tangent function;

[0029] S207, obtaining the proportional coefficient and integral coefficient of the updated candidate point in the two-dimensional rectangular coordinate system, that is:

[0030]

[0031] Among them, K P Represents the proportionality coefficient, K I represents the integral coefficient, cos represents the cosine function, sin represents the sine function, and β represents the angle between the OR ray and the positive half axis of the X axis;

[0032] S208, judging whether the turbine regulating system is stable under the control of the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system, if so, executing step S209, otherwise executing step S212;

[0033] S209, taking the polar coordinates of the updated candidate point as the lower bound of the dynamic angle, keeping the upper bound of the updated dynamic angle unchanged, generating the upper and lower bounds of the dynamic angle updated again, and re-determining the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle updated again, and adding 1 to the current number of iterations, and executing steps S205-S207, judging whether the difference between the proportional coefficient and the integral coefficient in two adjacent iterations is less than the first set value, if so, executing step S210, otherwise, executing step S211;

[0034] S210, outputting the proportional coefficient and the integral coefficient in the current iteration, obtaining the stable control parameters of the turbine regulating system, and taking the polar coordinates of the candidate point updated in the current iteration as the position of the first intersection of the first ray and the boundary of the stable domain of the control parameter;

[0035] S211, continue to execute steps S205-S207;

[0036] S212, taking the polar coordinates of the updated candidate point as the upper bound of the dynamic angle, keeping the lower bound of the updated dynamic angle unchanged, generating the upper and lower bounds of the dynamic angle updated again, and re-determining the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle updated again, and adding 1 to the current number of iterations, and executing steps S205-S207, judging whether the difference between the proportional coefficient and the integral coefficient in two adjacent iterations is less than the first set value, if so, executing step S213, otherwise, executing step S214;

[0037] S213, outputting the proportional coefficient and the integral coefficient in the current iteration, obtaining the stable control parameters of the turbine regulating system, and taking the polar coordinates of the candidate point updated in the current iteration as the position of the first intersection of the first ray and the boundary of the stable domain of the control parameter;

[0038] S214. Continue to execute steps S205-S207.

[0039] Furthermore, in step S208, according to the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system, the specific process of judging whether the turbine regulating system is stable under the control of the proportional coefficient and integral coefficient is as follows:

[0040] Step 1: Input the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system to obtain the step response waveform of the turbine regulation system;

[0041] Step 2: Perform zero-mean processing on the step response waveform of the turbine regulating system to obtain a zero-mean processed step response waveform;

[0042] Step 3: Obtain the zero-crossing position and number of zero-crossing points of the step response waveform processed by zero mean value;

[0043] Step 4: Determine whether the number of zero-crossing points of the step response waveform processed by zero mean value is less than the second set value. If so, the turbine regulating system is stable. Otherwise, execute Step 5.

[0044] Step 5: Sort the zero-crossing points in descending order according to the time sequence, taking two adjacent zero-crossing points as a pair, and obtain a number of zero-crossing point pairs sorted from large to small, and obtain the maximum value of the absolute value of the waveform between the two zero-crossing points in each zero-crossing point pair and form a vector to obtain the maximum value vector waveform;

[0045] Step 6: Calculate the difference between the last element and the first element in the maximum value vector waveform, that is, the oscillation trend, and determine whether the difference is less than zero. If so, the turbine regulation system is stable, otherwise the turbine regulation system is unstable.

[0046] Furthermore, step Step 3 specifically includes:

[0047] The first point to the second to last point on the step response waveform processed by the zero mean is used as the first vector waveform, and the second point to the last point on the step response waveform processed by the zero mean is used as the second vector waveform;

[0048] Multiplying the first vector waveform by the second vector waveform to obtain a new vector waveform;

[0049] The positions where the elements in the new vector waveform are less than 0 are used as the positions of the zero-crossing points of the step response waveform processed with zero mean, so as to obtain the positions of the zero-crossing points and the number of the zero-crossing points of the step response waveform processed with zero mean.

[0050] Furthermore, in step S209 or step S212, the specific process of re-determining the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle updated again is:

[0051] If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is less than the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z1;

[0052] If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is greater than the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z2;

[0053] If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is the same as the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z3.

[0054] Furthermore, in step S3, when the first ray is rotated at a set rotation angle in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameter for iterative search using the bisection method, a reference point is obtained by making a perpendicular line to the position of the first ray during the second search using the position of the first intersection point, and an iterative search is performed using the bisection method to obtain the position of the second intersection point of the first ray with the boundary of the stable domain of the control parameter.

[0055] The present invention has the following beneficial effects:

[0056] The present invention proposes a solution method for the stability domain of a turbine regulation system, which adopts a dichotomy method to obtain control parameters that reflect the stability of the turbine regulation system, and obtains the stability domain of the turbine regulation system under the control parameters, thereby reducing the amount of calculation and being able to effectively determine whether the turbine regulation system is stable, thereby better ensuring the safe and stable operation of the power system and improving the dispatching flexibility and economy of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic flow chart of a method for solving the stability domain of a hydraulic turbine regulating system proposed by the present invention;

[0058] Figure 2 Schematic diagram of simulation calculation of control parameter stability domain boundary in the embodiment. DETAILED DESCRIPTION

[0059] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0060] like Figure 1 As shown, a method for solving the stability domain of a turbine regulating system includes the following steps:

[0061] S1. Obtain control parameters of the turbine regulating system and establish a two-dimensional rectangular coordinate system based on the control parameters.

[0062] Specifically, step S1 includes:

[0063] The control parameters of the turbine regulating system including the proportional coefficient and the integral coefficient are obtained, and a two-dimensional rectangular coordinate system based on the control parameters is established with the proportional coefficient as the X-axis horizontal coordinate and the integral coefficient as the Y-axis vertical coordinate.

[0064] In this embodiment, in the stability analysis, if the stability domain boundary of the system control parameter is obtained, the stability of the system under the given control parameter can be quickly determined. Therefore, when the control parameters of the turbine regulation system, i.e., the proportional coefficient and the integral coefficient, are known, a two-dimensional rectangular coordinate system with the proportional coefficient as the abscissa and the integral coefficient as the ordinate can be established, and the control parameter stability domain boundary of the turbine regulation system can be generated, wherein the control parameter stability domain boundary is as follows: Figure 2 The solid blue line shown in Figure 2 The horizontal axis is the proportional coefficient K P , the vertical axis is the integration coefficient K I , the blue solid line is the actual control parameter stability domain boundary; at the same time, considering that the value of the control parameter is generally a positive real number, and from Figure 2 It can be seen that when a ray starting from the origin is made at a fixed angle in the first quadrant of the two-dimensional rectangular coordinate system XOY, it must intersect with the boundary of the stable domain of the control parameter. Therefore, based on this principle, as long as these intersection points can be accurately found and smoothly connected, the stable domain of the control parameter can be determined. Therefore, the purpose of establishing a two-dimensional rectangular coordinate system based on the control parameters in this embodiment is to facilitate the subsequent steps of making rays in the two-dimensional rectangular coordinate system to find the intersection points with the boundary of the stable domain of the control parameter, so as to calculate the stable domain of the control parameters of the turbine regulation system.

[0065] S2. Take the Y-axis of the two-dimensional rectangular coordinate system based on the control parameters as the first ray. During the initial search, select any point R on the negative half axis of the X-axis of the two-dimensional rectangular coordinate system based on the control parameters, connect point R and the origin O, rotate the OR ray clockwise and when the angle between the OR ray and the Y-axis is the set rotation angle, draw a perpendicular line from point R to the Y-axis to obtain the reference point, and based on the reference point, use the binary search method to iteratively search for the candidate point on the Y-axis that is closest to the boundary of the stable domain of the control parameters, and use the candidate point as the first intersection point of the first ray and the boundary of the stable domain of the control parameters.

[0066] In this embodiment, according to the stability criterion, a ray starting from the origin is made at every fixed angle in the first quadrant of the two-dimensional rectangular coordinate system XOY, and it must intersect with the boundary of the stable domain of the control parameter; therefore, the Y axis is taken as the first ray, and the binary search is performed iteratively, so that several intersection points of the first ray and the boundary of the stable domain of the control parameter can be obtained, so as to facilitate subsequent smooth connection and obtain the stable domain of the control parameters of the turbine regulation system. In addition, since there is no intersection point obtained from the previous search during the first search, in order to ensure the calculation, the first point on the Y axis is determined by defining point R as any point greater than zero on the negative half axis of the X axis, and by rotating the OR ray. When the angle between the OR ray and the Y axis reaches the set rotation angle, the first intersection point on the Y axis is obtained by using the binary search method. Then, based on the position of the first intersection point, the position of the second intersection point can be calculated by using the binary search method. By analogy, in the next search, the intersection point of the next search is calculated using the position of the previous search, and all intersection points and positions can be obtained. And when the first ray is rotated to coincide with the X axis and the last intersection point is determined, the entire search process for the boundary of the stable domain ends. For example: Figure 2 As shown in the figure, it is assumed that after a search, the intersection point of the first ray and the boundary of the stable domain of the control parameter is R0, and the intersection point of the first ray and the boundary of the stable domain of the control parameter in the next search is R1. Therefore, in order to accurately find the position of R1, several candidate points can be calculated in sequence on the ray OR1 through an iterative algorithm based on the dichotomy method, such as the candidate point P i , P j , until a point R is obtained that is sufficiently close to R1 t , that is, to get the exact position of R1, so each search is based on Figure 2 The principle shown uses a binary search to find the intersection point under the current search. In addition, for the convenience of calculation, a fixed rotation angle (set rotation angle) is used, that is, the rotation angle each time is equal to the total rotation angle (ie 90°) divided by the number of rotations of the first ray in the first quadrant.

[0067] Specifically, the rotation angle is set as:

[0068]

[0069] Among them, θ represents the set rotation angle, θ1 represents the total rotation angle, that is, the total angle of the first quadrant of the two-dimensional rectangular coordinate system based on the control parameters, and n represents the number of rotations of the Y axis in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameters.

[0070] Specifically, step S2 specifically includes S201-S214:

[0071] S201, take the Y axis of the two-dimensional rectangular coordinate system based on the control parameters as the first ray, and select any point R on the negative semi-axis of the X axis of the two-dimensional rectangular coordinate system based on the control parameters, and make the distance from the origin O to the point R greater than zero, rotate the OR ray clockwise and when the angle between the OR ray and the Y axis is the set rotation angle, draw a perpendicular line from point R to the Y axis to obtain the reference point R t , and take the origin O of the Y axis as the maximum candidate point and the infinity of the Y axis as the second candidate point.

[0072] S202, compare each candidate point with the reference point R t The formed angle is used as the dynamic angle, and the positions of the first candidate point and the second candidate point are converted into polar coordinates to generate the upper and lower bounds of the dynamic angle, namely:

[0073]

[0074] Among them, α represents the dynamic angle, dθ represents the size of the set rotation angle, The polar coordinates of the lower bound or first candidate point of the dynamic angle, Indicates the upper bound of the dynamic angle or the polar coordinates of the second candidate point.

[0075] In this embodiment, the purpose of determining the first candidate point and the second candidate point is to determine the upper and lower bounds of the dynamic angle, so as to subsequently obtain the candidate point closest to the boundary of the control parameter stability domain by updating the upper and lower bounds of the dynamic angle, thereby determining the position of the first intersection.

[0076] S203, set the current number of iterations to 1.

[0077] S204, judging whether the current number of iterations reaches the maximum number of iterations, if so, there is no control parameter that stabilizes the turbine dispatching system, and the iterative search is terminated, otherwise, setting the initial inertia weight.

[0078] In this embodiment, the initial inertia weight is set to 0.5, and the maximum number of iterations is 30.

[0079] S205, updating the dynamic angle according to the inertia weight to generate an updated dynamic angle, that is:

[0080] α′=ωα l +(1-ω)α u

[0081] Among them, α′ represents the updated dynamic angle, ω represents the inertia weight, and α l represents the lower bound of the dynamic angle, α u Represents the upper bound of the dynamic angle.

[0082] S206, calculating the updated candidate points according to the updated dynamic angle, that is:

[0083]

[0084] Among them, P i represents the updated candidate point, Represents the origin O to the updated candidate point P i The distance Indicates the origin O to the reference point R t , dL represents the length of the perpendicular line from point R to the Y axis, and tan represents the tangent function.

[0085] In this embodiment, the origin O to the reference point R t The distance is calculated as: Represents the distance from the origin O to the first intersection point R0.

[0086] S207, obtaining the proportional coefficient and integral coefficient of the updated candidate point in the two-dimensional rectangular coordinate system, that is:

[0087]

[0088] Among them, K P Represents the proportionality coefficient, K I represents the integral coefficient, cos represents the cosine function, sin represents the sine function, and β represents the angle between the OR ray and the positive half axis of the X-axis.

[0089] S208. According to the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system, determine whether the turbine regulating system is stable under the control of the proportional coefficient and integral coefficient. If so, execute step S209; otherwise, execute step S212.

[0090] Specifically, in step S208, according to the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system, the specific process of judging whether the turbine regulating system is stable under the control of the proportional coefficient and integral coefficient is as follows:

[0091] Step 1: Input the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system to obtain the step response waveform of the turbine regulation system.

[0092] Step 2: Perform zero-mean processing on the step response waveform of the turbine regulating system to obtain the zero-mean processed step response waveform.

[0093] Step 3: Get the zero-crossing position and number of zero-crossing points of the step response waveform processed by zero mean, specifically:

[0094] The first point to the second to last point on the step response waveform processed with zero mean is taken as the first vector waveform, and the second point to the last point on the step response waveform processed with zero mean is taken as the second vector waveform; the first vector waveform is multiplied by the second vector waveform to obtain a new vector waveform; the position where the element in the new vector waveform is less than 0 is taken as the position of the zero-crossing point of the step response waveform processed with zero mean, and the zero-crossing point position and the number of zero-crossing points of the step response waveform processed with zero mean are obtained.

[0095] Step 4: Determine whether the number of zero-crossing points of the step response waveform processed by zero mean value is less than the second set value. If so, the turbine regulating system is stable. Otherwise, execute step 5.

[0096] Step 5: Sort the zero-crossing points in chronological order from large to small, taking two adjacent zero-crossing points as a pair, and obtain several zero-crossing point pairs sorted from large to small, and obtain the maximum absolute value of the waveform between the two zero-crossing points in each zero-crossing point pair and form a vector to obtain the maximum value vector waveform.

[0097] Step 6: Calculate the difference between the last element and the first element in the maximum value vector waveform, that is, the oscillation trend, and determine whether the difference is less than zero. If so, the turbine regulation system is stable, otherwise the turbine regulation system is unstable.

[0098] S209. Use the polar coordinates of the updated candidate point as the lower bound of the dynamic angle, keep the upper bound of the updated dynamic angle unchanged, generate the upper and lower bounds of the dynamic angle that are updated again, and redetermine the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle that are updated again. At the same time, add 1 to the current number of iterations, and execute steps S205-S207 to determine whether the difference between the proportional coefficient and the integral coefficient in two adjacent iterations is less than the first set value. If so, execute step S210; otherwise, execute step S211.

[0099] Specifically, according to the oscillation trend of the upper and lower bounds of the dynamic angle that are updated again, the specific process of re-determining the inertia weight is as follows:

[0100] If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is smaller than the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z1.

[0101] In this embodiment, the value of z1 is 0.6.

[0102] If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is greater than the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z2.

[0103] In this embodiment, the value of z2 is 0.4.

[0104] If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is the same as the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z3.

[0105] In this embodiment, the value of z3 is 0.5.

[0106] S210, outputting the proportional coefficient and the integral coefficient in the current iteration, obtaining stable control parameters of the turbine regulating system, and taking the polar coordinates of the candidate point updated in the current iteration as the position of the first intersection of the first ray and the boundary of the control parameter stable domain.

[0107] S211. Continue to execute steps S205-S207.

[0108] S212. Use the polar coordinates of the updated candidate point as the upper bound of the dynamic angle, keep the updated lower bound of the dynamic angle unchanged, generate the updated upper and lower bounds of the dynamic angle again, and redetermine the inertia weight according to the oscillation trend of the updated upper and lower bounds of the dynamic angle. At the same time, add 1 to the current number of iterations, and execute steps S205-S207 to determine whether the difference between the proportional coefficient and the integral coefficient in two adjacent iterations is less than the first set value. If so, execute step S213; otherwise, execute step S214.

[0109] S213, outputting the proportional coefficient and the integral coefficient in the current iteration, obtaining the stable control parameters of the turbine regulating system, and taking the polar coordinates of the candidate point updated in the current iteration as the position of the first intersection of the first ray and the boundary of the stable domain of the control parameter.

[0110] S214. Continue to execute steps S205-S207.

[0111] S3. During the second search, based on the first intersection of the first ray and the boundary of the stable domain of the control parameter, a bisection method is used to rotate the first ray at a set rotation angle in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameter to perform an iterative search to obtain the second intersection of the first ray and the boundary of the stable domain of the control parameter.

[0112] Specifically, in step S3, when the first ray is rotated at a set rotation angle in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameter for iterative search using the bisection method, a perpendicular line is drawn from the position of the first intersection point to the position of the first ray during the second search to obtain a reference point, and an iterative search is performed using the bisection method to obtain the position of the second intersection point of the first ray with the boundary of the stable domain of the control parameter.

[0113] In this embodiment, since the stable domain is uncertain, and according to the above stability criterion, as long as the points intersecting with the stable boundary of the control parameters are found and these points are smoothly connected, the stable domain of the control parameters of the system can be obtained to judge the stability of the system. Therefore, the present invention adopts the binary search method to find these points, thereby reducing the amount of calculation and improving the calculation efficiency.

[0114] S4. After the second search, determine whether the first ray coincides with the X-axis of the two-dimensional rectangular coordinate system based on the control parameters. If so, obtain several intersection points of the first ray and the boundary of the stable domain of the control parameters. Otherwise, continue the iterative search until the first ray coincides with the X-axis of the two-dimensional rectangular coordinate system based on the control parameters during the Nth search, stop the search, and obtain several intersection points of the first ray and the boundary of the stable domain of the control parameters.

[0115] S5. Smoothly connect the first ray with several intersection points of the boundary of the control parameter stable domain to obtain the control parameter stable domain of the turbine regulation system.

[0116] In this embodiment, the first ray obtained after several searches is smoothly connected with several intersection points of the control parameter stable domain boundary to obtain the actual control parameter stable domain boundary curve, and the partial area formed by the curve and the horizontal and vertical coordinates is used as the stable area, and the partial area outside the curve is used as the unstable area to determine the stability of the system.

[0117] In summary, the present invention proposes a method for solving the stability domain of a turbine regulation system, which adopts a dichotomy method to obtain control parameters that reflect the stability of the turbine regulation system, and obtains the stability domain of the turbine regulation system under the control parameters, thereby reducing the amount of calculation and being able to effectively determine whether the turbine regulation system is stable, thereby better ensuring the safe and stable operation of the power system and improving the flexibility and economy of the power system dispatch.

[0118] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0119] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for solving the stability domain of a turbine regulating system, characterized in that: The following steps are involved: S1. Obtain control parameters of a turbine regulating system and establish a two-dimensional rectangular coordinate system based on the control parameters; S2. Taking the Y axis of the two-dimensional rectangular coordinate system based on the control parameters as the first ray, during the initial search, randomly select a point R on the negative semi-axis of the X axis of the two-dimensional rectangular coordinate system based on the control parameters, connect point R and the origin O, rotate the OR ray clockwise, and when the angle between the OR ray and the Y axis is the set rotation angle, draw a perpendicular line from point R to the Y axis to obtain a reference point, and iteratively search for a candidate point on the Y axis closest to the boundary of the stable domain of the control parameters using a binary search method based on the reference point, and use the candidate point as the first intersection point of the first ray and the boundary of the stable domain of the control parameters; S3, during the second search, based on the first intersection point of the first ray with the boundary of the stable domain of the control parameter, a bisection method is used to rotate the first ray at a set rotation angle in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameter to perform an iterative search to obtain a second intersection point of the first ray with the boundary of the stable domain of the control parameter; S4, after the second search, determine whether the first ray coincides with the X-axis of the two-dimensional rectangular coordinate system based on the control parameter, if so, obtain a number of intersections of the first ray and the boundary of the stable domain of the control parameter, otherwise, continue to iterate the search until the first ray coincides with the X-axis of the two-dimensional rectangular coordinate system based on the control parameter during the Nth search, stop the search, and obtain a number of intersections of the first ray and the boundary of the stable domain of the control parameter; S5. Smoothly connect the first ray with several intersection points of the boundary of the control parameter stable domain to obtain the control parameter stable domain of the turbine regulation system.

2. The method for solving the stability region of a hydraulic turbine regulating system according to claim 1, characterized in that: Step S1 specifically includes: The control parameters of the turbine regulating system including the proportional coefficient and the integral coefficient are obtained, and a two-dimensional rectangular coordinate system based on the control parameters is established with the proportional coefficient as the X-axis horizontal coordinate and the integral coefficient as the Y-axis vertical coordinate.

3. The method for solving the stability region of a hydraulic turbine regulating system according to claim 2, characterized in that: The rotation angle is set to: Among them, θ represents the set rotation angle, θ1 represents the total rotation angle, that is, the total angle of the first quadrant of the two-dimensional rectangular coordinate system based on the control parameters, and n represents the number of rotations of the Y axis in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameters.

4. The method for solving the stability region of a hydraulic turbine regulating system according to claim 3, characterized in that: Step S2 specifically includes: S201, take the Y axis of the two-dimensional rectangular coordinate system based on the control parameters as the first ray, and select any point R on the negative semi-axis of the X axis of the two-dimensional rectangular coordinate system based on the control parameters, and make the distance from the origin O to the point R greater than zero, rotate the OR ray clockwise and when the angle between the OR ray and the Y axis is the set rotation angle, draw a perpendicular line from point R to the Y axis to obtain the reference point R t , and take the origin O of the Y axis as the maximum candidate point, and the infinity of the Y axis as the second candidate point; S202, compare each candidate point with the reference point R t The formed angle is used as the dynamic angle, and the positions of the first candidate point and the second candidate point are converted into polar coordinates to generate the upper and lower bounds of the dynamic angle, namely: Among them, α represents the dynamic angle, dθ represents the size of the set rotation angle, The polar coordinates representing the lower bound or first candidate point of the dynamic angle, The polar coordinates representing the upper bound of the dynamic angle or the second candidate point; S203, setting the current number of iterations to 1; S204, judging whether the current number of iterations reaches the maximum number of iterations, if so, there is no control parameter that stabilizes the turbine dispatching system, and the iterative search is terminated, otherwise, setting the initial inertia weight; S205, updating the dynamic angle according to the inertia weight to generate an updated dynamic angle, that is: a′=ωα l +(1-ω)a u Among them, α′ represents the updated dynamic angle, ω represents the inertia weight, and α l represents the lower bound of the dynamic angle, α u Indicates the upper bound of the dynamic angle; S206, calculating the updated candidate points according to the updated dynamic angle, that is: Among them, P i represents the updated candidate point, Represents the origin O to the updated candidate point P i The distance Indicates the origin O to the reference point R t dL represents the length of the perpendicular line from point R to the Y axis, and tan represents the tangent function; S207, obtaining the proportional coefficient and integral coefficient of the updated candidate point in the two-dimensional rectangular coordinate system, that is: Among them, K P Represents the proportionality coefficient, K I represents the integral coefficient, cos represents the cosine function, sin represents the sine function, and β represents the angle between the OR ray and the positive half axis of the X axis; S208, judging whether the turbine regulating system is stable under the control of the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system, if so, executing step S209, otherwise executing step S212; S209, taking the polar coordinates of the updated candidate point as the lower bound of the dynamic angle, keeping the upper bound of the updated dynamic angle unchanged, generating the upper and lower bounds of the dynamic angle updated again, and re-determining the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle updated again, and adding 1 to the current number of iterations, and executing steps S205-S207, judging whether the difference between the proportional coefficient and the integral coefficient in two adjacent iterations is less than the first set value, if so, executing step S210, otherwise, executing step S211; S210, outputting the proportional coefficient and the integral coefficient in the current iteration, obtaining the stable control parameters of the turbine regulating system, and taking the polar coordinates of the candidate point updated in the current iteration as the position of the first intersection of the first ray and the boundary of the stable domain of the control parameter; S211, continue to execute steps S205-S207; S212, taking the polar coordinates of the updated candidate point as the upper bound of the dynamic angle, keeping the lower bound of the updated dynamic angle unchanged, generating the upper and lower bounds of the dynamic angle updated again, and re-determining the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle updated again, and adding 1 to the current number of iterations, and executing steps S205-S207, judging whether the difference between the proportional coefficient and the integral coefficient in two adjacent iterations is less than the first set value, if so, executing step S213, otherwise, executing step S214; S213, outputting the proportional coefficient and the integral coefficient in the current iteration, obtaining the stable control parameters of the turbine regulating system, and taking the polar coordinates of the candidate point updated in the current iteration as the position of the first intersection of the first ray and the boundary of the stable domain of the control parameter; S214. Continue to execute steps S205-S207.

5. The method for solving the stability region of a hydraulic turbine regulating system according to claim 4, characterized in that: In step S208, the specific process of judging whether the turbine regulating system is stable under the control of the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system is as follows: Step 1: Input the updated proportional coefficient and integral coefficient of the candidate point in the two-dimensional rectangular coordinate system to obtain the step response waveform of the turbine regulation system; Step 2: Perform zero-mean processing on the step response waveform of the turbine regulating system to obtain a zero-mean processed step response waveform; Step 3: Obtain the zero-crossing position and number of zero-crossing points of the step response waveform processed by zero mean value; Step 4: Determine whether the number of zero-crossing points of the step response waveform processed by zero mean value is less than the second set value. If so, the turbine regulating system is stable. Otherwise, execute Step 5. Step 5: Sort the zero-crossing points in descending order according to the time sequence, taking two adjacent zero-crossing points as a pair, and obtain a number of zero-crossing point pairs sorted from large to small, and obtain the maximum value of the absolute value of the waveform between the two zero-crossing points in each zero-crossing point pair and form a vector to obtain the maximum value vector waveform; Step 6: Calculate the difference between the last element and the first element in the maximum value vector waveform, that is, the oscillation trend, and determine whether the difference is less than zero. If so, the turbine regulation system is stable, otherwise the turbine regulation system is unstable.

6. The method for solving the stability region of a hydraulic turbine regulating system according to claim 5, characterized in that: Step 3 specifically includes: The first point to the second to last point on the step response waveform processed by the zero mean is used as the first vector waveform, and the second point to the last point on the step response waveform processed by the zero mean is used as the second vector waveform; Multiplying the first vector waveform by the second vector waveform to obtain a new vector waveform; The positions where the elements in the new vector waveform are less than 0 are used as the positions of the zero-crossing points of the step response waveform processed with zero mean, so as to obtain the positions of the zero-crossing points and the number of the zero-crossing points of the step response waveform processed with zero mean.

7. The method for solving the stability region of a hydraulic turbine regulating system according to claim 6, characterized in that: The specific process of re-determining the inertia weight according to the oscillation trend of the upper and lower bounds of the dynamic angle updated again in step S209 or step S212 is as follows: If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is less than the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z1; If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is greater than the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z2; If the absolute value of the oscillation trend corresponding to the lower limit of the dynamic angle updated again is the same as the absolute value of the oscillation trend corresponding to the upper limit of the dynamic angle updated again, the weight value of the inertia weight is z3.

8. The method for solving the stability region of a water turbine regulating system according to claim 7, characterized in that: In step S3, when the first ray is rotated at a set rotation angle in the first quadrant of the two-dimensional rectangular coordinate system based on the control parameter for iterative search using the bisection method, a perpendicular line to the position of the first ray during the second search is used as the position of the first intersection point to obtain a reference point, and an iterative search is performed using the bisection method to obtain the position of the second intersection point of the first ray and the boundary of the stable domain of the control parameter.

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