CN115051418B - Load frequency control system stability analysis method considering AGC sampling hold - Google Patents
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Abstract
The invention provides a load frequency control system stability analysis method considering AGC sampling hold, comprising the following steps: parameters and control command periods of a load frequency control system of the power system are obtained, and a continuous sampling and mixing time-lag load frequency control system model is established; discretizing the time-lag variable to obtain a corresponding time-lag-free load frequency control system model; taking the control command period as a sampling period, performing discretization sampling on the non-time-lag load frequency control system model to obtain a discretization load frequency control system model, and solving key characteristic values of the discretization load frequency control system model; and establishing a stability criterion of the time-lag load frequency control system, and carrying out stability analysis on the time-lag load frequency control system according to the key characteristic value and the stability criterion. The invention can conveniently and effectively calculate the state matrix eigenvalue of the discretized load frequency control system model, and can rapidly and accurately judge the stability of the load frequency control system based on the stability criterion of eigenvalue analysis.
Description
Technical Field
The invention relates to the technical field of time-lapse power systems, in particular to a load frequency control system stability analysis method considering AGC sampling and holding.
Background
Load frequency control (Load Frequency Control, LFC) is one of the main functions of automatic power generation control (Automatic Generation Control, AGC) of a power system, and is currently widely used in frequency adjustment and power generation scheduling of the power system, and aims to reduce frequency deviation of the system and maintain the exchange power of a link between control areas at a planned value. With the rise of the large-area frequency modulation auxiliary service market, the load frequency control of the power system becomes more complex, and the stability of the LFC system becomes more important for the safe and economic operation of the power system under the participation of multi-area multi-market main bodies.
The inventor researches and discovers that the actual LFC system is a continuous sampling mixed time lag system with time lag characteristics and sampling characteristics, and when the stability of the LFC system is analyzed, the consideration of the time lag and the sampling characteristics of AGC is of great significance for guaranteeing the frequency safety and stability of the power system. The current stability judging method taking time lag and sampling characteristics into consideration is mainly based on an input delay method, a sampling item is processed into piecewise time-varying input delay, a time domain method is utilized to obtain a linear matrix inequality LMI as a stability criterion of a system, but a stability domain obtained by the time domain method is always conservative and cannot be directly used for characteristic analysis of the system.
Disclosure of Invention
The invention aims to provide a load frequency control system stability analysis method considering AGC sampling and holding, so as to solve the technical problem that the stability judgment of a sampling mixed time-lag load frequency control system in the prior art is unreliable.
The aim of the invention can be achieved by the following technical scheme:
a load frequency control system stability analysis method considering AGC sample hold includes:
Acquiring dynamic element model parameters, model parameters of automatic power generation control and control command periods of a load frequency control system of the power system, and establishing a continuous sampling mixed time-lag load frequency control system model of the power system, wherein the dynamic element model parameters at least comprise time-lag variables;
discretizing the time-lag variable to obtain a time-lag-free load frequency control system model corresponding to the time-lag load frequency control system model;
Taking the control command period as a sampling period, performing discretization sampling on the time-lag-free load frequency control system model to obtain a discretization load frequency control system model, and solving to obtain a key characteristic value of the discretization load frequency control system model, wherein the key characteristic value is the characteristic value with the maximum module value;
And establishing a stability criterion of the continuous sampling and mixing time-lag load frequency control system, and carrying out stability analysis on the time-lag load frequency control system according to the key characteristic value and the stability criterion.
Optionally, the time-lag load frequency control system model includes a continuous subsystem model and a sampling subsystem model;
The continuous subsystem model is a subsystem model in which both state variables and output variables are continuous signals, and the sampling subsystem model is a subsystem model in which the state variables and the output variables exist in a step-shaped sampling signal.
Optionally, the continuous subsystem model is:
Wherein, Is a matrix of coefficients for the successive sub-systems,Is a state vector of n state variables of the continuous subsystem,As a derivative of x c,For the time-lag variable, k is the coefficient vector of the time-lag variable, τ is the delay time of the time-lag variable, d is the position of the delay variable in the state vector x c, s is the position of the output sampling variable of the AGC sampling system in the state variable x c,Is the unit column vector with the s < th > and d < th > elements being 1,The transpose of e d,n is given,For the transpose of e s,n, b c is the input matrix of the continuous subsystem, and u d and y c are the input stepped sample signal and the output continuous control signal, respectively, of the continuous subsystem.
Optionally, the sampling subsystem model is:
Wherein, T is a control command period of automatic power generation control, x c,k is a discrete sampling point of the state vector x c, y c is an input continuous control signal of the sampling subsystem, and u d is an output stepped sampling signal of the sampling subsystem.
Optionally, the time-lag load frequency control system model is:
Wherein, Is the derivative of x c (t),Is a matrix of coefficients for the successive sub-systems,Is a state vector composed of n state variables of a continuous subsystem at the moment T, tau is the delay time of a time-lag variable, k is a coefficient vector of the time-lag variable, b c is an input matrix of the continuous subsystem, x c (T-tau) is a time-lag term, T represents the sampling period of the sampling subsystem, d is the position of the time-lag variable in the state vector x c, s is the position of an output sampling variable of an automatic power generation control sampling system in the state variable x c, e s,n,The s < th >, d < th > element is a unit column vector of 1,The transpose of e d,n is given,Transposed to e s,n, x c,k is the discrete sample point of the state vector x c; the continuous subsystem is a subsystem of which the state variable and the output variable in the load frequency control system are continuous signals.
Optionally, discretizing the time-lag variable includes:
And discretizing the time-lag variable of the time-lag load frequency control system model by using a chebyshev discretization method.
Optionally, the corresponding time-lag-free load frequency control system model is obtained as follows:
Wherein, Is the state vector of the model of the time-lag-free load frequency control system, x k is the kth discrete sampling point of the state vector, A N,And the coefficient matrixes of the continuous subsystem and the sampling subsystem of the time-lag-free load frequency control system model are respectively adopted.
Optionally, the discretized load frequency control system model is:
where x k+1 is the (k+1) th discrete sample point of the state vector.
Optionally, solving to obtain the key feature value of the discretized load frequency control system model includes:
and performing similarity transformation on the state matrix of the discretization load frequency control system model to obtain a similarity matrix with the same eigenvalue, and solving the similarity matrix to obtain the key eigenvalue of the discretization load frequency control system model.
Optionally, the stability criterion of the time-lag load frequency control system is:
The characteristic values of the state matrix of the discretized load frequency control system model are all positioned in a complex plane unit circle; and the coefficient matrix of the continuous subsystem of the time-lag-free load frequency control system model has no non-negative real part characteristic value, so that the imaginary part is n pi/T, and n is a non-zero integer.
The invention provides a load frequency control system stability analysis method considering AGC sampling hold, comprising the following steps: acquiring dynamic element model parameters, model parameters of automatic power generation control and control command periods of a load frequency control system of the power system, and establishing a continuous sampling and mixing time-lag load frequency control system model of the power system; discretizing the time-lag variable to obtain a time-lag-free load frequency control system model corresponding to the time-lag load frequency control system model; taking the control command period as a sampling period, performing discretization sampling on the time-lag-free load frequency control system model to obtain a discretization load frequency control system model, and solving to obtain a key characteristic value of the discretization load frequency control system model, wherein the key characteristic value is the characteristic value with the maximum module value; and establishing a stability criterion of the continuous sampling and mixing time-lag load frequency control system, and carrying out stability analysis on the time-lag load frequency control system according to the key characteristic value and the stability criterion.
Based on the technical scheme, the invention has the beneficial effects that:
According to the invention, by establishing a continuous sampling mixed time-lag load frequency control system model, discretizing time-lag variables of the time-lag load frequency control system model, and discretizing a single time-lag variable, the order of a discretization system matrix is increased by N orders; when discretizing and sampling the model of the time-lag-free load frequency control system, the dynamic characteristics of the system are effectively reserved; meanwhile, the characteristic value calculation speed of the discretized load frequency control system model is not affected excessively by the processing of the time-lag variable, and the state matrix characteristic value of the discretized load frequency control system model can be calculated conveniently and effectively; the stability criterion based on eigenvalue analysis can rapidly and accurately judge the stability of the continuous sampling and mixing time-lag load frequency control system.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a schematic flow chart of an embodiment of the method of the present invention;
FIG. 3 is a simplified schematic diagram of a load frequency control system of the power system of the present invention;
FIG. 4 is a diagram illustrating a first characteristic trace according to an embodiment of the present invention;
FIG. 5 is a second exemplary feature value trace diagram according to an embodiment of the present invention;
fig. 6 is a frequency response graph of an embodiment of the present invention.
Detailed Description
Term interpretation:
QR algorithm: the QR algorithm can obtain an upper triangular matrix when the number of the recursion wheels is proper, so as to obtain the characteristic value.
The embodiment of the invention provides a load frequency control system stability analysis method considering AGC sampling and holding, which aims to solve the technical problem that the stability judgment of a sampling mixed time-lag load frequency control system is unreliable in the prior art.
In order that the invention may be readily understood, a more complete description of the invention will be rendered by reference to the appended drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
Because LFC systems employ centralized control, their control signals are mainly frequency and actual switching power. The control signal measured by the remote measuring device is required to be transmitted through an open communication network, the delay of the data acquisition and monitoring control System (SCADA) of the large-area power system for acquiring frequency data can be up to 5s, the delay of the data acquisition connecting line can be up to 8s, the signal transmission has obvious delay, and the time lag of the signal transmission can cause the deterioration of the running condition of the AGC system, and the global frequency oscillation phenomenon of the power system can be caused. On the other hand, the AGC is mainly based on the LFC system to participate in the frequency adjustment process of the power system from 10s to several minutes, in order to avoid mechanical abrasion caused by the change of the running state of the generator set due to the frequent change of the power generation control command, the AGC adopts a successive approximation control method, the control period is longer, and the sampling interval can reach 4-8 s. Therefore, the actual LFC system is a continuous sampling mixed time lag system with time lag characteristics and sampling characteristics, and when the stability of the LFC system is analyzed, the consideration of the time lag and the sampling characteristics of AGC has important significance for guaranteeing the frequency safety and stability of the power system.
In the aspect of researching the stability of a time-lapse power system, the current time domain method is mainly based on Lyapunov stability theory, a Linear Matrix Inequality (LMI) is constructed as a stability criterion of the system, but a stability domain obtained based on the method is always conservative. In the frequency domain method, stability judgment of the system is carried out by calculating a time lag stability margin based on Rekasius replacement, schure-Cohn and other methods, and the method based on eigenvalue analysis such as Pade approximation, spectrum discretization and the like can be used for judging the stability of the system and can also be used for system characteristic analysis. When the stability study of the LFC system is performed in consideration of the sampling characteristic of the AGC, the conventional method discretizes the whole system with the sampling period of the AGC and then performs stability analysis based on the z-domain eigenvalue, but it cannot be directly used for the time-lapse system. The current stability judging method taking time lag and sampling characteristics into consideration is mainly based on an input delay method, a sampling item is processed into a piecewise time-varying input delay, and then LMI is obtained by using a time domain method as a system stability criterion, but the conservation of the time domain method still exists, and the time domain method cannot be directly used for characteristic analysis of a system.
Referring to fig. 1, a first embodiment of the present invention provides a method for analyzing stability of a load frequency control system considering AGC sample-and-hold, including:
S100: acquiring dynamic element model parameters, model parameters of automatic power generation control and control command periods of a load frequency control system of the power system, and establishing a continuous sampling mixed time-lag load frequency control system model of the power system, wherein the dynamic element model parameters at least comprise time-lag variables;
S200: discretizing the time-lag variable to obtain a time-lag-free load frequency control system model corresponding to the time-lag load frequency control system model;
S300: taking the control command period as a sampling period, performing discretization sampling on the time-lag-free load frequency control system model to obtain a discretization load frequency control system model, and solving to obtain a key characteristic value of the discretization load frequency control system model, wherein the key characteristic value is the characteristic value with the maximum module value;
S400: and establishing a stability criterion of the continuous sampling and mixing time-lag load frequency control system, and carrying out stability analysis on the time-lag load frequency control system according to the key characteristic value and the stability criterion.
In step S100, the dynamic element model mainly includes a governor, a prime mover, and a generator, and an automatic power generation control system (AGC) includes a controller and a sampling system (zero-order holder). In this embodiment, a mathematical model of a load frequency control system of a power system is divided into two parts: a continuous subsystem model and a sampling subsystem model; the continuous subsystem refers to a subsystem in which state variables and output variables in the load frequency control system are continuous signals, namely an open loop system consisting of a generator, a prime motor, a speed regulator, an AGC controller and the like. While the system in which the state variable and the output variable are present as stepped sampling signals is called the sampling subsystem, i.e. the zero-order keeper.
Specifically, the continuous subsystem model is:
Wherein, Is a matrix of coefficients for the successive sub-systems,Is a state vector of n state variables of the continuous subsystem,As a derivative of x c,For the time-lag variable, k is the coefficient vector of the time-lag variable, τ is the delay time of the time-lag variable, d is the position of the delay variable in the state vector x c, s is the position of the output sample variable of the AGC sample system in the state variable x c, e s,n,Is the unit column vector with the s < th > and d < th > elements being 1,The transpose of e d,n is given,For the transpose of e s,n, b c is the input matrix of the continuous subsystem, and u d and y c are the input stepped sample signal and the output continuous control signal, respectively, of the continuous subsystem.
It should be noted that, in the continuous subsystem, the't' of the state variable x c (t) can be omitted, but the't' of the time-lag term x c (t- τ) cannot be omitted; the superscript T denotes a transpose.
Specifically, the sampling subsystem model is:
Wherein, T is a control command period of automatic power generation control, x c,k is a discrete sampling point of the state vector x c, y c is an input continuous control signal of the sampling subsystem, and u d is an output stepped sampling signal of the sampling subsystem.
The time-lag load frequency control system model of continuous sampling mixing corresponding to the formula (1) and the formula (2) is as follows:
wherein x c (t- τ) is the time-lag term.
The time-lag load frequency control system is a continuous sampling mixed time-lag system with time-lag characteristics and sampling characteristics, and therefore the time-lag load frequency control system model is a continuous sampling mixed time-lag system model.
In step S200, a chebyshev discretization method is adopted to perform discretization processing on the time-lag variable, and a corresponding time-lag-free load frequency control system model is obtained as follows:
Wherein, Is the state vector of the model of the time-lag-free load frequency control system, x k is the kth discrete sampling point of the state vector, A N,And the coefficient matrixes of the continuous subsystem and the sampling subsystem of the time-lag-free load frequency control system model are respectively adopted.
Note that n+1 is the number of chebyshev discrete points selected, i.e., N is an integer greater than 0. The method can be freely selected, and the larger N is, the more accurate the key characteristic value of the obtained time-lag-free system is.
For the convenience of understanding, a discretization model of a single-time-lag load frequency control system is provided, and the method is further popularized to a multi-time-lag system; for time-lag variablesDefining a set of variables at the chebyshev discrete point [ - τ,0] τ=τ N＜τN-1＜…＜τ1＜τ0 =0I=0, 1, …, N, chebyshev discrete points are:
Defining vectors at discrete points Formula (6) can be obtained on both sides [ - τ,0 ]:
Combining properties of chebyshev spectral differential matrices A time-lag-free load frequency control system model represented by the formula (4) can be obtained, and the time-lag-free discretization model of the load frequency control system is as follows:
Wherein: matrix array Sum vectorThe method comprises the following steps of:
Wherein D N is an (N+1) -order Chebyshev spectrum differential matrix.
In step S300, the control command period is taken as a sampling period, the time-lag-free load frequency control system model is subjected to discretization sampling to obtain a discretization load frequency control system model, and a key characteristic value of the discretization load frequency control system model is obtained by solving, wherein the key characteristic value is a characteristic value with the maximum module value.
Specifically, the obtained discretized load frequency control system model is as follows:
where x k+1 is the (k+1) th discrete sample point of the state vector.
The state matrix A of the discretized load frequency control system model is as follows:
Wherein, Is an identity matrix, and the state matrix A can be used for calculating the eigenvalue of the discrete model of the continuous sampling mixed load frequency control system.
In a preferred embodiment, the solving to obtain the key eigenvalue of the discretized load frequency control system model includes:
and performing similarity transformation on the state matrix of the discretization load frequency control system model to obtain a similarity matrix with the same eigenvalue, and solving the similarity matrix to obtain the key eigenvalue of the discretization load frequency control system model.
In step S300, the similarity transformation method adopted is:
The matrix Λ is a diagonal matrix composed of eigenvalues of matrix a N, and λ 1、…λn represents n eigenvalues of a N, that is, diagonal elements of matrix Λ. Thus, the first and second substrates are bonded together,
Firstly, calculating a modal matrix Λ and a modal matrix V consisting of the eigenvalue and the right eigenvector of A N through a QR algorithm; then, a similarity matrix of the state matrix A is formedAnd solving the corresponding key characteristic values of the discretization system by using a QR algorithm. At this time, the key feature value of the discretization system is the feature value with the maximum modulus value.
In step S400, a stability criterion of the continuous sampling and mixing time-lag load frequency control system is established, and stability analysis is performed on the time-lag load frequency control system according to the key characteristic value and the stability criterion.
Specifically, the stability criterion of the continuous sampling and mixing time-lag load frequency control system model is specifically as follows: the eigenvalues of the discretization system state matrix A are all positioned in the complex plane unit circle; coefficient matrix A N of the time-lag-free load frequency control system model (time-lag-free mixed system) obtained by discretization of time lag variable does not have a non-negative real part characteristic value to satisfy that the imaginary part is n pi/T, wherein n is a non-zero integer.
According to the invention, by establishing a continuous sampling mixed time-lag load frequency control system model, discretizing time-lag variables of the time-lag load frequency control system model, and discretizing a single time-lag variable, the order of a discretization system matrix is increased by N orders; when discretizing and sampling the model of the time-lag-free load frequency control system, the dynamic characteristics of the system are effectively reserved; meanwhile, the characteristic value calculation speed of the discretized load frequency control system model is not affected excessively by the processing of the time-lag variable, and the state matrix characteristic value of the discretized load frequency control system model can be calculated conveniently and effectively; the stability criterion based on eigenvalue analysis can rapidly and accurately judge the stability of the continuous sampling and mixing time-lag load frequency control system.
Referring to fig. 2, a load frequency control system stability analysis method considering AGC sample and hold provided by a second embodiment of the present invention includes the following steps:
1) And acquiring a dynamic element model and model parameters, an AGC model and model parameters and an AGC control command period of the load frequency control system of the power system, and establishing a continuous sampling mixed load frequency control system mathematical model of the power system.
2) Performing discretization on the time-lag variable by using a chebyshev discretization method to obtain a time-lag-free mixed system model of the continuous sampling mixed system;
3) Taking the system state trajectory as a piecewise function sequence, representing the time-lag-free hybrid system by a function space method, and performing discretization sampling on the time-lag-free hybrid system by taking the AGC control command period as a sampling period to obtain a new state matrix A of the discretization system;
4) Establishing a similar matrix with the same characteristic value as the new state matrix A through similar transformation Then accurately solving key characteristic values of the discretization system by using a QR method;
5) And establishing a stability criterion of the continuous sampling mixing system, and analyzing the stability of the mixing system according to the obtained key characteristic values.
The stability analysis method of the load frequency control system considering AGC sampling and holding provided by the embodiment of the invention is a stability analysis method of a continuous sampling mixed LFC time-lag system, and is based on eigenvalue analysis of a mixed system discretization model, and has the advantages that: the processing of the time-lag variable does not affect the characteristic value calculation speed of the discretization system excessively, and the discretization processing of the single time-lag variable enables the order of the discretization system matrix to be increased by N orders; the function space method is adopted to represent the discretized time-lag-free mixed system, and when the discretized sampling is carried out on the time-lag-free mixed system, the dynamic characteristics of the system are effectively reserved; on the basis, a similar transformation technology is provided, so that the characteristic value of the discretization system state matrix can be conveniently and effectively calculated; the stability criterion based on eigenvalue analysis can rapidly and accurately judge the stability of the mixing system.
The following is one embodiment of the present invention:
In order to verify the accuracy of the stability analysis method of the load frequency control system provided by the invention, the embodiment verifies the accuracy of the method on the single-area load frequency control system. A simplified model diagram of a single-area load frequency control system is shown in fig. 3, an integral controller is adopted by a controller of Automatic Generation Control (AGC) of the power system, the sampling characteristic of the AGC is represented by a zero-order retainer with a sampling period equal to the AGC control command period, the sampling period is 6s, and a simplified first-order system model is used by a speed regulator and a prime motor.
The number of state variables of the continuous subsystem is 4, N=20 is taken to carry out chebyshev discretization on the time lag variable, and then the characteristic value of the discretization system is calculated by the method. Fig. 4 and 5 are graphs of discretized system eigenvalue traces in which the delay time increases from 0s to 5s in steps of 0.1s, and for convenience of analysis, the eigenvalue traces of the discretized system mapped to the s domain are obtained by using the mapping relationship between the z domain eigenvalue and the s domain eigenvalue. As can be seen from fig. 4 and fig. 5, the modulus of the key feature value of the discretization system increases with the increase of the delay time, and crosses the complex plane unit circle within the time interval of τ e (4.4 s,4.5 s), and the time lag stability margin of the system is located in the time interval according to the stability criterion established by the present invention; for a eigenvalue trace mapped to the s-domain, which crosses the complex plane imaginary axis in a time interval of τ e (4.4 s,4.5 s), the time-lag stability margin of the system is located in this time interval. The stability analysis result based on the z-domain eigenvalue analysis is consistent with the stability analysis result based on the s-domain eigenvalue.
And (3) iteratively solving the accurate time-lag stability margin by adopting a dichotomy in the time interval of tau epsilon (4.4 s,4.5 s), wherein the result is 4.436s. Table 1 is a numerical calculation result of the characteristic value of the discretization system, and table 1 gives a numerical calculation result of the characteristic value of the discretization system under a partial delay time and a corresponding stability analysis result, wherein the dominant mode oscillation period corresponding to the key characteristic value is solved by the characteristic value mapped to the s domain.
TABLE 1
In order to verify the stability analysis results shown in table 1, a simplified model of the single-area load frequency control system shown in fig. 3 is used to perform load step disturbance time domain simulation verification, the load disturbance is set to be 0.1p.u., the disturbance occurrence time is 10s, and the frequency response of the continuous sampling hybrid system under different delay times is shown in fig. 6. As can be seen from fig. 6, when τ=4.436 s, the frequency waveform of the system is in a constant amplitude oscillation state, and the oscillation period is about 32s, at this time, the system is in a critical steady state. At τ of 0s, 4s, and 4.4s, the system is in a damped oscillation state, and as τ increases, the damping characteristics of the system are continuously deteriorated. At τ=4.5 s, the system exhibits amplified oscillations, the dominant mode being negative damped, when the system is in an unstable state.
Based on the simulation result analysis, the stability analysis result of the frequency domain shown in table 1 matches the time domain simulation result. Therefore, the stability analysis method of the load frequency control system provided by the invention is an effective method for analyzing the stability of a continuous sampling mixed system based on the stability analysis method of the characteristic value analysis of a discretization system.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, which are not repeated herein.
In the embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other manners. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of the units is merely a logical function division, and there may be additional divisions when actually implemented, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be an indirect coupling or communication connection via some interfaces, devices or units, which may be in electrical, mechanical or other form.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied essentially or in part or all of the technical solution or in part in the form of a software product stored in a storage medium, including instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A load frequency control system stability analysis method taking into account AGC sample hold, comprising:
Acquiring dynamic element model parameters, model parameters of automatic power generation control and control command periods of a load frequency control system of the power system, and establishing a continuous sampling mixed time-lag load frequency control system model of the power system, wherein the dynamic element model parameters at least comprise time-lag variables;
discretizing the time-lag variable to obtain a time-lag-free load frequency control system model corresponding to the time-lag load frequency control system model;
Taking the control command period as a sampling period, performing discretization sampling on the time-lag-free load frequency control system model to obtain a discretization load frequency control system model, and solving to obtain a key characteristic value of the discretization load frequency control system model, wherein the key characteristic value is the characteristic value with the maximum module value;
Establishing a stability criterion of a continuous sampling mixed time-lag load frequency control system, and carrying out stability analysis on the time-lag load frequency control system according to the key characteristic value and the stability criterion;
the time-lag load frequency control system model comprises a continuous subsystem model and a sampling subsystem model;
The continuous subsystem model is a subsystem model of which the state variable and the output variable are continuous signals, and the sampling subsystem model is a subsystem model of which the state variable and the output variable exist in a step-shaped sampling signal;
The continuous subsystem model is:
；
Wherein, Is a matrix of coefficients for the successive sub-systems,Is a state vector of n state variables of the continuous subsystem,Is thatIs used for the purpose of determining the derivative of (c),For a time-lag variable, k is a coefficient vector of the time-lag variable,Is the delay time of the time lag variable, d is the delay variable in the state vectorS is the output sampling variable of the AGC sampling system in the state variableIs provided with a plurality of positions,Is the unit column vector with the s < th > and d < th > elements being 1,Is thatIs to be used in the present invention,Is thatIs to be used in the present invention,Is an input matrix for the continuous subsystem,AndRespectively inputting a stepped sampling signal and outputting a continuous control signal of the continuous subsystem;
The sampling subsystem model is as follows:
；
Wherein, For the control command period of the automatic power generation control,Is a discrete sample of state vector x c,Is an input continuous control signal to the sampling subsystem,Is the output stepped sample signal of the sampling subsystem.
2. The method for analyzing stability of a load frequency control system taking into account AGC sample and hold as defined in claim 1, wherein discretizing the time-lag variable comprises:
And discretizing the time-lag variable of the time-lag load frequency control system model by using a chebyshev discretization method.
3. The method for analyzing the stability of the load frequency control system taking AGC sample and hold into consideration according to claim 2, wherein the corresponding time-lapse-free load frequency control system model is obtained as follows:
；
Wherein, For a state vector of a dead load frequency control system model,Is the kth discrete sample point of the state vector,、And the coefficient matrixes of the continuous subsystem and the sampling subsystem of the time-lag-free load frequency control system model are respectively adopted.
4. The method for analyzing stability of load frequency control system considering AGC sample and hold according to claim 3, wherein the discretized load frequency control system model is:
；
where x k+1 is the (k+1) th discrete sample point of the state vector.
5. The method for analyzing stability of a load frequency control system taking AGC sample and hold into consideration according to claim 1, wherein solving for key eigenvalues of the discretized load frequency control system model comprises:
and performing similarity transformation on the state matrix of the discretization load frequency control system model to obtain a similarity matrix with the same eigenvalue, and solving the similarity matrix to obtain the key eigenvalue of the discretization load frequency control system model.
6. The method for analyzing stability of load frequency control system considering AGC sample and hold according to claim 1, wherein the stability criterion of the time-lapse load frequency control system is:
the characteristic values of the state matrix of the discretized load frequency control system model are all positioned in a complex plane unit circle; and the coefficient matrix of the continuous subsystem of the time-lag-free load frequency control system model does not have non-negative real part characteristic value to satisfy the imaginary part as N is a non-zero integer.
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